An overview of approaches for reducing uncertainties in hydrological forecasting: progress, and challenges

doi:10.21203/rs.3.rs-2802423/v1

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Systematic Review

An overview of approaches for reducing uncertainties in hydrological forecasting: progress, and challenges

https://doi.org/10.21203/rs.3.rs-2802423/v1

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published 19 Oct, 2024

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In the present study, we review the methods and approaches used for uncertainty handling in hydrological forecasting of streamflow, floods, and snow. This review has six thematic sections: (1) general trends in accounting uncertainties in hydrological forecasting, (2) sources of uncertainties in hydrological forecasting, (3) methods used in the studies to address uncertainty, (4) multi-criteria approach for reducing uncertainty in hydrological forecasting and its applications (5) role of remote sensing data sources for hydrological forecasting and uncertainty handling, (6) selection of hydrological models for hydrological forecasting. Especially, a synthesis of the literature showed that approaches such as multi-data usage, multi-model development, multi-objective functions, and pre-/post-processing are widely used in recent studies to improve forecasting capabilities. This study reviews the current state-of-the-art and explores the constraints and advantages of using these approaches to reduce uncertainty. The comparative summary provided in this study offers insights into various methods of uncertainty reduction, highlighting the associated advantages and challenges for readers, scientists, hydrological modelers, and practitioners in improving the forecast task. A set of freely accessible remotely sensed data and tools useful for uncertainty handling and hydrological forecasting are reviewed and pointed out.

Hydrology

uncertainty analysis

uncertainty reduction

hydrological forecasting

multi-criteria approach

multi-data

multi-model

remote sensing data

Climate change and anthropogenic activities are influencing the rise in global temperature and altering precipitation occurrences. Consequently, the intensity and frequency of floods and droughts are increasing (IPCC, 2021). Besides, the global water demand is also increasing due to rapid population growth, urbanization, and industrialization. Supplying water and diminishing the consequences of hydrological extremes are major tasks for decision-makers in this modern era. This requires a clear assessment of current and future water resources availability and an understanding of the impacts of environmental changes such as climate (Krysanova et al., 2018), land use and land cover (Chawla and Mujumdar, 2018) on hydrological systems. In this regard, hydrological modeling and forecasting are widely used to investigate, understand, and predict various natural processes of hydrology (Papacharalampous et al., 2020; Lakshmi and Sudheer, 2021; Moges et al., 2021; Horton et al., 2022).

Hydrological modeling techniques (HMTs) are found useful in various hydrological forecasting applications such as streamflow (e.g., Abbasi et al., 2021; Althoff et al., 2021; De Santis et al., 2021; Hassan and Hassan, 2021; Lee et al., 2021; Liang et al., 2021), floods (e.g., Adams and Dymond, 2019; Bhola et al., 2019; Rajib et al., 2020; Tran et al., 2020; Silvestro et al., 2021; Xu et al., 2021). Similarly, HMTs are applied to watershed assessment applications such as water balance, rainfall-runoff process, water availability, streamflow (e.g., Ashraf Vaghef et al., 2019; Huang et al., 2020; Hui et al., 2020; Lilhare et al., 2020; Papacharalampous et al., 2020; Papacharalampous et al., 2020b), snow melt modelling (e.g., Di Marco et al.,2021, Dion et al., 2021; Thornton et al., 2021; Zaremehrjardy et al., 2021). Other applications of HMTs include reservoir inflow, soil moisture, and groundwater applications (e.g., Wu and Zeng, 2013; Fraga et al., 2019; Chen et al., 2020; Kasiviswanathan et al., 2020; Fathololoumi et al., 2021; Klotz et al., 2021; Valdez et al., 2021). In overall, HMTs are used in various application of water resources management such as irrigation and drainage management, flood management and adaptation, reservoir inflow predictions and operations, framing short-term and long-term water supply strategies, and mitigating floods and droughts’ negative impacts.

The hydrological models that are in use can be classified into two major types (i) data-driven and (ii) process-driven (conceptual models and physically based models) (Papacharalampous et al., 2020; Lakshmi and Sudheer, 2021). These models vary in providing solutions at different levels of complexity (Hortan et al.,2022, Moges et al.,2021, Papacharalampous et al.,2020), e.g., data-type (Hassan and Hassan, 2021), conceptual-level (Thiboult et al., 2015; Humphrey et al., 2016), physically-based (e.g., Fraga et al., 2019; Her et al., 2019), semi-distributed level (Huang et al., 2020), fully distributed-level (Abbot et al., 1986), and process integration-level (Van Steenbergen et al., 2012; Habert et al., 2016). Although advancements have been seen in hydrological modeling for the past four decades, handling uncertainty in hydrological models is still pertinent to address new developments (Blöschl et al., 2019).

These developments require at least three-prerequisites: (1) objective definition and input preparation, (2) parameters definition and model conceptualization (3) model calibration and validation. All these stages of development contain uncertainty in connection with measurement (e.g., Das Bhowmik et al., 2020; Piazzi et al., 2020; Yang et al., 2020), scope of inputs (e.g., Althoff et al.,2021; De Santis et al., 2021; Hassan and Hassan, 2021), model parameters (e.g., Liu et al., 2020; Tran et al., 2020; Liang et al., 2021), conceptualization (e.g., Bhola et al., 2019; Lee et al., 2021; McInerney et al., 2021), and simulation/forecasting platform employed (e.g., Siqueira et al., 2021; Mazrooei et al., 2021; Xu et al., 2021). Therefore, efforts must be undertaken to address these uncertainties and produce reliable hydrological forecasting that can be communicated to decision-makers and the public (Blöschl et al., 2019). Since the early work in hydrological forecasting, several researchers have tried to account for various facets of uncertainty using various techniques and tools (Pappenberger and Beven, 2006; Montanari, 2007; Blöschl et al., 2019). However, the site-specific nature and complexities involved in developing such models have kept studies on uncertainty handling as one of the unsolved problems in hydrology (Moges et al.,2021, Papacharalampous et al.,2020, Blöschl et al.,2019). Strictly speaking, there are inherent challenges in handling uncertainty linked to the nature, scope and perception of this uncertainty when associated with the model under consideration and its expected outcome. It is for instance open to debate whether this uncertainty is static or dynamic.

In this respect, uncertainty in hydrological forecasting may evolve due to one or some of the following reasons: (1) measurement error (Tauro et al., 2018; Vema et al., 2020), (2) input error (Hrachowitz et al., 2013; Tauro et al., 2018; Blöschl et al., 2019), (3) errors in model conceptualization (McInerney et al., 2021), (4) initial setting of the parameters (Vema et al., 2020), (5) simulation error (Tran et al., 2020; Wang et al., 2017, Vema et al., 2020), (6) techniques and assumptions used in calibration procedures (Sivapalan et al., 2003), (7) assumptions used in the hydrological projections (Brigode et al., 2013), and (8) modeler’s experience (Moges et al., 2021). Evaluation of recent studies suggests that much progress has been made in addressing the measurements, input, and conceptual uncertainties. This has been achieved with the awareness of increased data availability, the arrival of remote sensing and digital recording, the development of non-invasive measurement systems, and new tracer-based methods (Tauro et al., 2018). Advancements in hydrological modeling, such as physically based and fully integrated models, require many parameters depending on the assessed hydrological process. These parameters must be adjusted compared to the measured data, e.g., for calibration purposes (Shafii et al., 2015). However, parameter uncertainty also occurs because of the initial setting and approximations that are part of the modelling approach employed (Khoi and Thom, 2015). For this purpose, many studies have attempted to reduce the parameter uncertainties in hydrological forecasting while addressing the measurement, input, and conceptual uncertainties (Chawla and Mujumdar, 2018; Lafaysse et al., 2017; Meng et al., 2017; Mustafa et al., 2020; McInerney et al., 2021).

Although considerable progress has been accomplished in addressing various uncertainties of hydrological modeling, model uncertainty (or structural uncertainty) is still a major challenge in hydrology (Pappenberger and Beven 2006; Montanari 2007; Mustafa et al., 2020) and is more elusive than other uncertainties (Kirchner 2006). Hence, a more consistent framework for addressing the different types of uncertainty is required while considering the context-dependence and uniqueness of the study context (Beven, 2000) in hydrological forecasting despite developing a range of alternative models (e.g., Clark et al., 2015; Blöschl et al., 2019).

In the past four decades, studies related to uncertainties in hydrological forecasting have evolved in terms of methods of uncertainty quantification, impacts of these uncertainties in hydrological forecasting, and sources involved in the hydrological forecasting. Because of the importance of hydrological forecasting which supports irrigation and drainage management, flood early warning, drought monitoring, snow accumulation, and melting, recently, studies related to uncertainty handling have shifted towards improving hydrological forecasting by devising methods for reducing uncertainty level and improving the model structure for reliable forecasts.

Our initial literature search in terms of existing review papers in this field identified eleven survey papers investigating the aspect of uncertainty in hydrological modelling and forecasting. These reviews can be classified into three major classes (1) data and input (Dong, 2018; Maggioni and Massari, 2018; McMillan et al., 2018; Jose and Dwarkish, 2020), (2) developments on models and methodology for hydrological forecasting (Rossa et al., 2011; Wu and Zeng, 2013; Li et al., 2017; Guo et al., 2021; Moges et al., 2021; Troin et al., 2021), and (3) methodological developments in quantification and reduction of these uncertainties in hydrological forecasting (Wu et al., 2020). However, our scrutinizing of these reviews also revealed the lack of global scope and comprehensive analysis of alternative methods in dealing with uncertainty, which calls for further research and updated reviews in this field.

To our knowledge, no review has focused on reducing uncertainty for improving hydrological forecasting, which motivates our current work in this paper. The main objective of this study is to compile the current progress and challenges, while categorizing existing solutions for reducing uncertainty involved in hydrological forecasting by replying to the following research questions:

Q1. What are the latest developments in reducing uncertainty in hydrological forecasting?

Q2. How do various methods of hydrological forecasting address the various uncertainties, and what are their advantages and disadvantages?

Q3. How does remotely sensed data impact uncertainty in hydrological forecasting?

Q4. What are the criteria for selecting a model to reduce the uncertainties in hydrological forecasting?

The significant contributions from this review are threefold. First, it synthesizes the methods and tools for reducing uncertainties in hydrological forecasting. Second, it provides insights into the advantages and limitations of the current developments / solutions for reducing uncertainty in hydrological forecasting. Third, the role of remote sensing in reducing uncertainties of hydrological forecasting is elucidated. Finally, an extensive review of existing hydrological models with respect to uncertainty has been carried out with an emphasize on multi-criteria approaches, and open-source data sources in a way to simulate further studies in this field. The paper is organized as follows. Section 2 of this paper presents the methodology employed in this review. Section 3 provides an general trends in the analysis. In Section 4, an overview of uncertainty handling in hydrological forecasting is discussed, Section 5 focuses on different methods used for uncertainty reduction, Section 6 focuses on multi-criteria approaches for uncertainty handling and comment on current practices and future directions. Section 7 discuss the remote sensing applications in reducing the uncertainties, Section 8 provides summary of criteria to choose hydrological models, Finally, conclusion and recommendations are given in Section 6.

We have utilized PRISMA protocol for systematic literature search for our review as shown in Fig. 1. The proposed research theme was to collect, organize, and categorize the latest developments of uncertainty handling in hydrological forecasting and comprehend how different approaches were used. The keywords used as search terms are given in Table 1.

The search starts by crawling the results from three academic research databases: Scopus, Web of Science, and Google Scholar whenever the keywords appear in title, abstract, or keyword list of the papers. The choice of these database is justified by our desire to restrict the search to peer-reviewed papers. Besides, we restricted our search to papers published in the last decade (from 2010 till 2023). Research works contributing to reducing uncertainty are then taken further for a full screening and review. The scope of this review is narrowed down to forecasting streamflow, flooding, snow, and other applications such as rainfall-runoff process and soil moisture. The groundwater aspects of the modeling and forecasting were not taken into account due to their high volume, which would require a separate review by itself. Based on the selected criteria, 96 pieces of literature were chosen for conducting this review research. See Fig. 1 and Table 1 for a high level description of the review method carried out in this study.

Table 1

Characteristics list of review method employed in this study
Features	Uncertainty handling in hydrological forecasting
Question	To classify the uncertainties and reduce uncertainties using multi-source data
Source	Google Scholar, web of science, Scopus
Keywords &/ search terms	“Uncertainties in hydrological modeling”, “hydrological forecasting”, “uncertainty quantification in hydrological modeling”, “multi-source data in hydrological modeling”, “conceptual uncertainty in hydrological forecasting”, “reducing uncertainties”, “improving hydrological forecasting”
Evaluation method	Comparative, critical evaluation
Synthesis	Qualitative & Quantitative in certain aspects
Inferences	Evidence-based

The reviewed literature was classified based on the type of modeling, forecasting, and type of uncertainty addressed by the articles. Classification of uncertainties involved in hydrological forecasting was assessed according to methods and data used for reducing this uncertainty. The outcome of this categorization is elucidated later on in this paper. Besides, attempts were made to synthesize the possible questions that need to be addressed in the field of uncertainty handling in hydrological forecasting. Finally, using the outcome of this review, a large number of resources and freely accessible remotely sensed data are prepared to facilitate subsequent hydrological studies and guide future research.

3.1 General trends in the analysis

With a focus on data-related uncertainty, model / methodological developments for uncertainty analysis, model conceptualization, use of remotely sensed data and open-source data, research on ungauged basins, and uncertainty propagation in forecasting systems, interesting reviews have been identified and listed in Table 2.

Table 2

List of review papers and its advantages and limitations.
Sl. No	Review paper	Advantages	Limitations
1	McMillan et al. 2018	Uncertainties related to the hydrological data are discussed in detail. Data uncertainties are summarized into five categories.	Other sources of uncertainties in the hydrological modeling have not been discussed. The methods to overcome the other sources of uncertainties are not discussed.
2	Jose and Dwarakish, 2015	Uncertainties associated with GCMs are discussed in detail.	This study is limited to GCMs and its uncertainties in the hydrological modelling.
3	Maggioni and Massari, 2018	They have summarized common satellite products, associated errors and uncertainties.	This review restricted to the remotely sensed precipitation products in the flood forecasting applications.
4	Dong 2018	Uncertainties related to the application of remote sensing, hydrological modelling, and in situ measurements in snow cover research. They have listed merits and demerits of the application of remote sensing.	This review restricted to the snow cover research. Uncertainties are discussed related to the remote sensing products.
5	Troin et al. 2021	40 years of ensemble streamflow forecast research studies are summarized in this review.	Uncertainties discussed in this review is restricted to the ensemble streamflow forecast.
6	Moges et al. 2021	Reviewed hydrological model uncertainties. This review summarized the different methods of uncertainty analysis.	Computational efficiency of the uncertainty analysis not discussed. It is not elaborate on how to overcome the uncertainties in the hydrological forecasting.
7	Guo et al. 2021	This review discussed the improvement in the regionalization of the parameters and application of the remote sensing in this field.	It has not brough the broad spectrum of uncertainties involved in the hydrological modeling.
8	Li et al. 2017	Comprehensive review on post processing techniques for the reduction of uncertainties.	Not discussed other methods for reducing the uncertainties in the hydrological forecasting.
9	Rossa et al. 2011	Uncertainties pertaining to the groundwater systems are summarized	This review is not including the recent studies. Limited to groundwater system.
10	Wu and Zeng, 2013	Uncertainties pertaining to the groundwater systems are summarized	This review is not including the recent studies. Limited to groundwater system.
11	Wu et al. 2020	Comprehensive review on the ensemble flood forecasting.	Restricted to ensemble flood forecasting. Not discussed any methods to overcome the uncertainties related to hydrological forecasting.

McMillan et al., 2018 focused on the different sources of uncertainties associated with data used in hydrological modeling and forecast. They summarized uncertainties in data into five categories: measurement, derived data, interpolation, scaling, and data management. The article discussed the implications of data uncertainty on the hydrological process representation and consequent improvements in the simulations.

Jose and Dwarkish, 2020 addressed the uncertainties related to applying Global Climate Models (GCMs) and summarized these uncertainties into three categories: scenario uncertainty, climate scenario selection, and model uncertainty. This review recommended applying a multi-model ensemble approach to minimize error occurrence in climate change projections. Also, it advocated applying a range of climate models to understand the effects of climate change on hydrological systems. Maggioni and Massari, 2018 summarized the remotely sensed precipitation products on the application of riverine flood modeling. They focused on the common satellite precipitation products (SPPs) and associated errors and uncertainties of two products: Tropical Rainfall Measuring Mission (TRMM) and Global Precipitation Mission (GPM). They discussed the various uncertainties related to flood modeling by using satellite products, topography, precipitation type, and seasonality. Dong 2018 reviewed the application of remote sensing, hydrological modeling, and in-situ measurements in snow cover research. They focused on the possibilities of improving the remote sensing data through ground observations. Their paper summarized the advantages, limitations, and current progress in snow cover research in hydrological modeling.

On the other hand, ensemble forecasts have been used widely in recent decades as a key methodological framework for reducing uncertainty. For instance, Troin et al., 2021 reviewed the methods and approaches of the past four decades in the ensemble streamflow forecast. They have summarized the strengths and weaknesses of the three streamflow forecasts systems (statistics-based systems, climatology-based ensemble systems, and numerical weather prediction-based systems) which are widely used in literature. Uncertainties associated with ensemble streamflow forecasts are discussed in detail and future challenges and prospects have been given in their study. Moges et al., 2021 reviewed uncertainty involved in hydrological models from the perspectives of input, model structure, calibration, and parameters.

Hydrological data scarcity is one of the major global issues, and hydrological forecasting in an ungagged catchment is acknowledged to be very challenging. In this sense, Guo et al., 2021 have reviewed various improvements in the regionalization of the hydrological parameters. Their review work also supports the application of remote sensing data in improving hydrological forecasting. Li et al., 2017 conducted a comprehensive review of the statistical post-processing techniques used to reduce the uncertainties in hydrological forecasting, and three aspects of hydrometeorological forecasts are of special interest: (i) postprocessing of hydrological and meteorological forecasts (ii) postprocessing of forecasts from multiple models and (iii) ensemble members that save the intervariable dependecy are discussed. Rossa et al., 2011, Wu and Zeng, 2013 reviewed the origination of uncertainties in the numerical simulation of the groundwater system. Their review mainly discussed the different sources of groundwater modeling uncertainty and predictive uncertainty of model outputs. Wu et al., 2020 carried out an overview analysis of literature published on ensemble flood forecasting in the past decade after the international Hydrologic Ensemble Prediction Experiment.

4.1 Definition of uncertainties in hydrological forecasting

In hydrological modeling and forecasting, the term ‘uncertainty’ deals with the reliability of the data utilized, accuracy of the conceptualized model employed, the quality of the calibration and the validation, and the accuracy of the predicted results. In other words, the uncertainty term is mainly used to quantify the extent to which a particular input, model or result match or genuinely represent the reality (McMillan et al., 2018; Moges et al., 2021; Troin et al., 2021). Indeed, a key difference between real-world data and measured data manifests in the corresponding input uncertainty; a faithful representation of a given hydrological system depends on the quality of the various natural processes involved in the description of the hydrological system, known as conceptual model uncertainty; parameter related uncertainty arises from inherent conceptual simplification of the model (Moges et al., 2021); finally, the differences between the simulated hydrological model and the reality corresponds to predictive uncertainties. The types of uncertainties, their sources, and examples are given in Table 3.

Table 3

Types and definitions of uncertainties in the hydrological forecasting
Sl. No	Types	Source	Definition	Examples
1	Measurement uncertainty	Errors in the manual or instruments during the measurements	Uncertainty in the value of the measured hydro-climatological data, compared to the true quantity at the same scale of measurement (McMillan et al. 2018).	Uncertainties in the precipitation, temperature, discharge, soil moisture at a given location
2	Input uncertainty	Data that interpolated, data which are scaled up/down, derived data	Inaccuracies in the model inputs are develop input uncertainties (Moges et al. 2021). Often inputs in the measurement leads to greater input uncertainties.	Uncertainties due to the application of derived data such as interpolated rainfall data.
3	Parameter uncertainty	Model calibration, parameterizations, conceptual simplifications, observation errors	Uncertainties due to the failure or inability of the model to capture the hydrological process using a set of parameters.	Equifinality is an example of parameter uncertainty
4	Conceptual model uncertainty	Numerical simplification, process simplifications, limitations of theories, model structure	Uncertainties that are cascade into the results of the hydrological forecasting due to the deficient representation of the hydrological process in the model.	Inaccurate representation of the hydrological system or processes.
5	GCMs uncertainty	Application of different GCMs, RCMs and downscaling methods	Uncertainty in the usage of climate models for the scenario development of future climate impacts (Jose and Dwarakish, 2020).	Uncertainties in the future climate impact scenarios of hydrological variables such as discharge.
6	Forecast uncertainty	All other sources of uncertainties of the hydrological forecasting	Forecast uncertainties are the results from the combinations of the above said uncertainties reflected in the hydrological forecasts (Moges et al. 2021).	Uncertainties in the different forecasts such as streamflow, flood depth, and snow cover.
7	Unknown uncertainty	Uncertainties remain inherent even after the quantification of all uncertainties.	Unknown uncertainties are the results from the lack of ‘true’ model due to natural complexities and limitations of data (Moges et al. 2021)	Uncertainties remained in the forecasts

Table 3 revealed seven types of uncertainty: measurement uncertainty, input uncertainty, parameter uncertainty, conceptual uncertainty, GCMs uncertainty, Forecast uncertainty, Unknown uncertainty.

We would like to address the uncertainty issues involved in hydrological forecasting through the lens of the literature and HMT’s perspective. Few literature reviews (mentioned in the previous section) have already defined uncertainties in hydrological forecasting. We want to further investigate the issue taking into account the historical development in the field. The uncertainties and their impacts on the hydrological forecasting are illustrated in Fig. 2.

4.2 Impacts of uncertainties on hydrological forecasting

Hydrological forecasting is the process of translating hydro-meteorological inputs into useful hydrological parameters such as discharge, runoff, and flood depth. This translating process involves the application of different hydrological models at various temporal scales from a few hours (i.e., flood forecasting) to daily forecasts (i.e., streamflow predictions), or seasonal forecasting (e.g., snow and streamflow seasonal forecasting). Depending upon the hydrological forecasting used, uncertainty in the forecast does impact the decision-making process and can yield catastrophic consequences. For example, a flood forecasting model with high uncertainty may have severe social, economic, and human losses. Similarly, unreliable streamflow predictions to the reservoir operations may have different impacts on operational decisions (Di Marco et al., 2021). Hence, the uncertainties involved in hydrological forecasting systems should be taken into account to avoid severe negative consequences. Recently, different approaches are used and highlighted to address these issues and communicate the uncertainties to decision-makers and stakeholders.

The conventional flow of a hydrological forecasting system is being improved with numerous advancements to address these uncertainties and enhance the reliability of forecasting. These improvements contribute to enhancing the accuracy of input data as well as devising new methodological developments for the uncertainty quantification and integration of various workflows associated with model calibration, and remote sensing data, among others. These improvements provide effective decision-making tools that can assist in real-time applications. Improved hydrological forecasting systems can provide fundamental supports to deal with climate change, especially for managing frequent hydrological extremes. Apart from these improvements in hydrological forecasting, other factors such as forecasting skill, assessment of water system services, risks involved in finance, stakeholder’s level of risk aversion, availability of tools and data to test the forecast-informed operations, legacy guidance of local issues may influence the decision-making results as well.

However, the hydrological community is continuously working towards improving the hydrological forecasting systems at different stages of the forecasting processes. Figure 3 outlines these potential improvements in the hydrological forecasting systems to address uncertainty issues.

4.3 Uncertainties in hydrological forecasting

Since the early development of hydrological modeling, the reliability of the resulting simulated results is open to debate. Conventionally, the streamflow at the basin outlet was used as a reliable method for determining the performances of hydrologic models. Meanwhile, the fine-tuning development of the various forecasting stages not only increases the model reliability but also the process complexity. Nevertheless, increasing the complexity or using a multi-criteria-like approach is not always in favor of uncertainty reduction. Therefore, there is a need to select suitable combinations of modeling tools and approaches for a specific case that will likely yield uncertainty reduction. Ultimately, this section should account for the various types of uncertainty pointed out previously involved in hydrological forecasting tasks. Figure 4 shows the number of hydrological forecasting and uncertainties reviewed in these studies.

4.3.1 Measurements and inputs

Hydrological modeling and forecasting mainly depend on the measurements of various catchment inputs such as hydrology, meteorology, and topography. A developmental time frame for the measurements of hydrological data is shown in Fig. 5. These inputs are used for model conceptualization, calibration of the model parameters, and validation of the results. The development of the basic datasets for hydrological modelling is encouraged through different research agendas and outreach activities of hydrological communities. Meanwhile, the global hydrological system changes must be accounted for in the modeling, as highlighted in the water cycle diagram by USGS 2022 (USGS 2022). Hydrological community researchers are working towards developing process-based approaches to accommodate the changes, and relevant processes and address the data scarcity issues. The success of this task depends on the improvements and integration of field measurements (Penny et al., 2020). Continuous monitoring of the fields is made possible through advancements in remotely sensed applications, developments of automatic sensors, modern equipment, and multiple field investigations. Through this continuous acquisition of data, it becomes possible to improve the forecast (Brigode et al., 2013), and to explain the changes in the catchment system.

The second important aspect of measurement acquisition is data accuracy and availability. A degradation in accuracy and availability can occur in modern sensory systems such as remote observation or complex IoT sensor networks and the usage of sensors. In such cases, any prior knowledge about measurement accuracy can be integrated into a qualitative /quantitative estimation of errors (Das Bhowmik et al., 2020). This knowledge of measurement error can help reduce measurement uncertainty, thereby, increasing the forecasts' reliability.

Reducing measurement uncertainty plays a significant role in improving the forecasting task, especially in streamflow where it directly impacts the model conceptualization, calibration, and validation processes. The impact of initial conditions has been acknowledged in several hydrological systems, e.g., flood forecasting (Meng et al., 2017), snow-dominated hydrological processes (DeChant and Moradkhani, 2011; Singh and Sankarasubramanian, 2014), and soil moisture studies. In this case, uncertainty on initial conditions in input variables plays a major role in the quality of the forecasts, which stresses the importance of appropriate handling of initial condition-related uncertainty to improve the overall system accuracy.

The classification of types of data that are being used in hydrological forecasting in recent times ranging from conventional data sources to modern-day data sources (e.g., remote sensory systems, crowdsourcing) is outlined in Fig. 6.

Uncertainty in hydro-meteorological data input can cause a higher error in the forecast estimate than uncertainties in model structure or parameters (Singh and Sankarasubramanian, 2014; Xue et al., 2018; Thornton et al., 2021; Zaremehrjardy et al., 2021). In this context, uncertainties are mainly due to the lack of spatial coverage (DeChant and Moradkhani, 2011; Zappa et al., 2011) and higher data gap frequency in the temporal scale (Thornton et al., 2021). In addition, the uncertainty in climate change projection is found to be more significant than the parameter uncertainty (Her et al., 2019). Topographical data sources such as land use and land cover, soil information, slope, and elevation information must be cautiously chosen based on the forecasting application. The non-stationarity nature of topographical data is an important factor in reducing forecasting uncertainty. Similarly, remotely sensed products are beneficial in data-scarce regions (Panchanathan et al., 2023); nonetheless, accounting for such sources in hydrological applications requires ground verification for the reliabilities and application to real-time forecasting. As listed in Fig. 6, the application of local knowledge is new to the hydrological community. It has been successfully applied in recent studies due to the growing field of data acquisition.

Nevertheless, it is essential to mention that comprehensively accounting for all physical processes is almost impossible, and measurement uncertainty is likely to prevail in all three types of sources (Gan et al., 2018). This can be attributed to the complexity of the hydrological processes and the inherent challenges in representing the various facets of these processes (Helfricht et al., 2014). However, the hydrologic community is working towards synthesizing multiple data sources to address measurement uncertainty. Recent studies built on the foundation of multiple evidence to bring reliable forecasts demonstrate such improvements (Helfricht et al., 2014; Hassan & Hassan, 2020; Penny et al., 2020). Therefore, there is potential to further reduce such uncertainty by enhancing our understanding of related challenges and applying the right combination of datasets and models. For example, hydro-meteorological data and its influence on uncertainty can be tackled by considering meteorological bias and dispersion threshold (Klotz et al., 2021)

4.3.2 Parameter uncertainty

Parameter uncertainties are considered important due to their nature in the hydrological modeling setup and their influence on the forecasts (Vema et al., 2020). For instance, although the inputs are likely to change according to spatial-temporal coverage, the model parameters are often applied uniformly over the simulation period (Thornton et al., 2021). So, the choice of model parameters is critical, as any misrepresentation of these parameters may lead to a misrepresentation of the hydrological system (Piazzi et al., 2020). Trivially, this depends on the type of datasets used, the model employed (conceptual or physical model), and the forecast task (Short term or long-term forecast) being applied in the study (Sun et al., 2018). Especially for short-term forecasting, model parameters play a more vital role (Tran et al., 2020). The parameters' uncertainty has two main implications: parameter equifinality (Xue et al., 2018; Ashraf Vaghef et al., 2019), and dimensionality of the optimization process (Lilhare et al., 2020). In some cases, increasing the number of calibration parameters reduces the performance of the forecasts (Poulin et al., 2011) and reduces the forecast quality due to equifinality (Demirel et al., 2013). To overcome the parameter uncertainties and equifinality, recent studies suggest limiting the number of parameters that control the major processes in the catchment (Lilhare et al., 2020). This process requires experience, consideration of the hydrological model structure, and understanding of the hydrological processes within the basin (Zappa et al., 2011; Xue et al., 2018). However, sufficient observations can regulate major parameters in the calibration process, but special attention needs to be given to larger catchments with varying landscape properties. It is also important to understand the sensitivity of these parameters concerning each catchment scenario (He et al., 2011).

4.3.3 Conceptualization of models

The conceptualization of complex models plays an important role, and the associated uncertainties depend on the type of chosen models for the specific problem at hand and the prior knowledge in the specific field of hydrological forecasting. Typically, hydrological models have to be assessed for their suitability by selecting the best-suited model that represents the specific site or catchment. So, a comprehensive assessment of the models is needed prior to the model selection (Paul et al., 2021). The uncertainty of hydrological projections from hydrological modelling generally originates from the model structure and its inherent parameters (Yuan et al., 2017). However, hydrological model structure uncertainty is more significant than parameter uncertainty (Poulin et al., 2011). Forecast skill is also closely linked to the hydrological model performance (Siqueira et al., 2021). Errors in model structure can be compensated by calibration, thus, parameter uncertainty and structural uncertainty can be linked to concept model uncertainty as well (Essery et al., 2013).

In general, the conceptual model uncertainty arises due to the conflicts in the representation of the hydrological processes. This uncertainty is more significant than other types of uncertainties because misrepresentation may lead to completely different forecasting. Most studies on forecasting uncertainties highlight the fact that the conceptualization of hydrological models is closely associated with forecasting skills (Siqueira et al., 2021). Specifically, the hydrological modeling uncertainties occur due to the following reasons: (a) propagation of input uncertainties; (b) less suitable chosen model and its limitations on the requirements (Patil and Ramsankaran, 2017); (c) parameterization of the models; (d) the representation of stationarity or non-stationarity (Chawla and Mujumdar, 2018); (e) complexities and catchment characteristics; (f) initial conditions, model parameterizations, and numerical limitations (Zarzar et al., 2018); (g) spatial and temporal evaluation of the modeling parameters; (h) modeler’s experience; (i) usage of “one model fits all”.

To overcome the model structural uncertainties, recent studies have shown the inherent link between model complexity and uncertainty. However, this idea of increasing complexity led to both positive and negative feedback (Ashraf Vaghef et al., 2019). Indeed, increasing model complexity increases the number of parameters as well, which, in turn, calls for support from ground truth for the validation of the process. Contrastingly, the usage of different hydrological models for the same catchment would bring different results which may influence the forecasts (Her et al., 2019), but in a few other studies, this has helped to reduce the model errors effectively (DeChant et al., 2014). This approach of multimodal approach can be useful as it captures the impact of models on reliability (Singh and Sankarasubramanian, 2014). However, choosing the right processing flow and supporting techniques such as data assimilation, calibration method, ensemble methods, and post-processing methods would influence the model performance in addition to the model structure (Krysanova et al., 2018; Her et al., 2019; De Santis et al., 2021).

4.3.4 Uncertainties in GCMs

Recent developments in climate change impact studies and the applications of various GCMs, RCMs, and climate change projections call for efficient quantification of associated uncertainties (Xue et al., 2018). This is indeed a requirement in the development of reliable climate change adaptation and mitigation plans. The uncertainties in the GCMs may influence the different hydrological parameters at different scales. For instance, in the study investigated by Her et al., 2019, the influence of GCMs was found higher on the direct runoff, whereas they were lower than the parameter uncertainties for the slower components of hydrology such as soil moisture and groundwater flow. This may be because uncertainties are more associated with the predictions of rainfall and temperature, highlighting the need for a closer look at the improvements in precipitation and temperature data. The uncertainties in the GCMs may be due to the selection of appropriate GCMs, downscaling methods, and model structure (Brigode et al., 2013; Singh and Sankarasubramanian, 2014; Yuan et al., 2017). In other cases, it may be due to the interaction between the GCMs and the model structure or the assumption of stationarity (Chawla and Mujumdar, 2018). In addition to the inherent uncertainties in GCMs, the application of GCMs to different regions needs to be assessed as it has different impacts (Zaremehrjardy et al., 2021). In essence, the forecast uncertainty can be reduced if the above-discussed uncertainties are addressed using supporting techniques (Xu et al., 2021).

The uncertainties in hydrological forecasting are handled at three stages as shown in Fig. 7. Initially, the measurement and input uncertainties can be addressed at stage-I with the help of preprocessing and improving the data quality. Stage-II is a model conceptualization and set up. At this level, the uncertainties generated due to the model conceptualization, model selection, and model setup will be dealt with using multi-model approaches. Stage III is Calibration and Validation strategies. At this level, the parameter uncertainties are mainly handled by incorporating different strategies like applying multi-objective calibration, multi-site calibration, data assimilation techniques, and applications of remote sensing techniques.

Table 4

List of reviewed studies with various models, methods and techniques used in hydrological forecasting to reduce uncertainties at different stages of modeling
Sl. No	Models used	Hydrological forecasting	Multi-criteria approach used for reducing uncertainties	Studies	Uncertainties addressed	Country	Number of case studies	Approach/data used	Observations	Journal
1	MGB (acronym of Modelo de Grandes Bacias)	Streamflow forecasting	Post processing	Siqueira et al. 2021	Forecasting	South America, Continental scale	Continental scale	Statistical postprocessing, The Ensemble Model Output Statistics (EMOS) technique, ECC multivariate postprocessing	Streamflow, meteorological inputs	Journal of hydrology
2	SWAT	Streamflow forecasting	Multi-objective function	Liang et al. 2021	Parameter, forecasting	China	1	Sequential Uncertainty Fitting version 2 (SUFI-2), Generalized Likelihood Uncertainty Estimation (GLUE) and Particle Swarm Optimization (PSO), weighted correlation network analysis (WGCNA)	Streamflow	Journal of hydrology
3	MISDc-2L (Brocca et al., 2012; Massari et al., 2018)	Streamflow forecasting	Multi-data	De Santis et al. 2021	Forecasting	Europe	700	Data assimilation of soil moisture products, Ensemble Kalman Filter (EnKF)	Soil moisture	Water Resources Research
4	Data-Driven Models (DDMs): Support Vector Regression (SVR) and Multiple Linear Regression (MLR)	Streamflow forecasting	Multi-model, Preprocessing	Abbasi et al. 2021	Forecasting	Iran	1	Combinations of the SVR and MLR models with the RF, DAE, and PCA methods to improve the accuracy of monthly streamflow prediction	Streamflow	Journal of hydrology
5	ANN based	Streamflow forecasting	Pre processing	Hassan and Hassan, 2021	Input	Pakistan, India, Tibet	1	the Box-cox transformation after finding a suitable power factor through histogram statistics and probability plots	Streamflow	KSCE Journal of Civil Engineering
6	Variable Infiltration Capacity (VIC) (Wood et al., 1992; Liang et al., 1994; Liang et al., 1996) model	Streamflow forecasting	Multi-data	Mazrooei and Sankarasubramanian, 2021	Forecasting	USA	1	Variational data assimilation technique for assimilation of observed streamflow data	streamflow data	Journal of Hydrology
7	SWAT, RSWAT	Streamflow forecasting	Multi-data	Lee et al. 2021	Conceptual model	USA	1	improved representation of soil moisture dynamics	hourly precipitation, temperature, solar radiation, relative humidity, and wind speed; RS- ET data	Sustainability (Switzerland)
8	Multi model approach: dynamic Budyko (DB), G´enie Rural `a 4 param`etres Journalier (GR4J), and Probability Distributed Model (PDM) model	Streamflow forecasting	Multi-data	Nayak et al. 2021	Conceptual model	USA	43	Streamflow prediction improvement based on the soil moisture data, application of Genetic algorithm	Soil moisture, discharge	Journal of Hydrology
9	GR4J rainfall-runoff model	Streamflow forecasting	Multi-data	McInerney et al. 2021	Conceptual model, forecasting	Australia	11	flow dependance, non parametric sampling, Multi-Temporal Hydrological Residual Error (MuTHRE) model for uncertainty quantification	RAINFALL, PET, streamflow	Water resources research
10	long short-term memory (LSTM)	Streamflow forecasting	Multi-data	Althoff et al. 2021	Input, Conceptual model	Brazil	1	multiparameter ensemble to a dropout ensemble, dropout regularization technique	rainfall, evapotranspiration	Stochastic Environmental Research and Risk Assessment
11	Error Reduction and Representation In Stages (ERRIS) model into Infiltration Capacity Model, Variable Infiltration Capacity (VIC) macroscale	Streamflow forecasting	Post processing	Liu et al. 2020	Parameter	China	1	Error Reduction and Representation In Stages (ERRIS) model	Streamflow, snow depth data	Journal of hydrology
12	MESH, Hydrological and land surface model	Streamflow forecasting	Multi-data, multi-objective function	Budhathoki et al. 2020	Input, forecasting	Canada	1	data assimilation of soil moisture, evapotranspiration	Soil moisture and Evapotranspiration	Hydrological sciences
13	Bayesian dynamic hierarchical model (BDHM) West and Harrison (2006)	Streamflow forecasting	Multi-data	Das Bhowmik et al. 2020	Observation, Input, Forecasting	USA	4	The inclusion of true error improves the BDHM's performance by lowering the CRPS (continuous rank probability score) values.	streamflow	Water Resources Research
14	GR5J	Streamflow forecasting	Multi-data	Piazzi et al. 2021	Observation, Input, Forecasting	France	232	Ensemble Kalman Filtter (Sequential DA)	streamflow, precipitation, temperature	Water Resources Research
15	rainfall-runoff model GR4J (Perrin	Streamflow forecasting	Multi-model, multi objective function	Lerat et al. 2020	Input	Australia	508	multiple obejective functions, multi model approach	rainfall, runoff	Journal of Hydrology
16	ANN	Streamflow forecasting	Multi-data	Yang et al. 2020	Observation and forecast	China	1	Bayesian ensemble forecast method, comprising of a Gaussian mixture model (GMM), a hydrological uncertainty processer (HUP), and an Autoregressive (AR) model	rainfall, streamflow	Water
17	simulation–optimization framework	Streamflow forecasting	Multi-model	Vema et al. 2020	Parameter, simulation	India	1	Monte Carlo simulations, simulation-optimization framework	streamflow	Stochastic Environmental Research and Risk Assessment
18	A feed forward neural network trained via two layer Broyden Fletcher Goldfarb Shanno algorithm is used for model development.	Streamflow forecasting	Multi-data	Hassan & Hassan 2020	Input, forecasting	Pakistan, India, Tibet	1	data assimilation of snow cover area	rainfall, Data assimilation fo Snow Cover Area, GROUND OBSERVATIONS	Acta Geophysica
19	mesoscale Hydrologic Model (mHM)	Streamflow forecasting	Multi-data, multi-variate calibration strategies	Dembélé et al. 2020	Input, Parameter	West Africa (Six countries)	1	A bias-insensitive and multicomponent spatial pattern matching metric for multiobjective function.	stremflow, Rainfall, temperature, Leaf Area Index, Terrestrial water storage anomaly, surface soil moisture, actual evaporation, Land suraface temperature	Water resources research
20	‘abcd’ model	Streamflow forecasting	Multi-data	Mazrooei and Sankarasubramanian, 2019	Input, forecasting	USA	340	Data assimilationof soil moisture and groundwater recharge using Ensemble Kalman Filter	Streamflow, groundwater recharge, soil moisture	Journal of hydrology
21	Canonical run-off generating mechanisms, field measurements	Streamflow forecasting	Multi-data	Penny et al. 2020	Input	India	1	process-based approach to calibrate the lack of measured data situations	streamflow	Hydrological Processes
22	CREST	Streamflow forecasting	Multi-model, multi objective function	Gan et al. 2018	Parameter, forecasting	China	10	Multi-objective optimization, step wise sensitive analysis	PET, Streamflow, precipitation	Journal of Hydrology
23	WATFLOOD, SWAT	Streamflow forecasting	Multi-model, post processing	Muhammad et al. 2018	Parameter, forecasting	Canada	1	Post processing of LR, Quantile mapping, quantile model averaging, Bayesien model averaging	Streamflow	Water
24	Variable Infiltration Capacity (VIC-3)	Streamflow forecasting	Multi-data	Das et al. 2018	Input, forecasting	India	1	Reliability Ensemble Averaging (REA) and possibility theory in projecting streamflows	rainfall and temperature	Water resources management
25	hydrological uncertainty processor (HUP)	Streamflow forecasting	Multi-data	Liu et al. 2018	Forecasting	China	1	hydrological uncertainty processor (HUP)	streamflow	Hydrological sciences
26	SWAT	Streamflow forecasting	Multi-data	Patil and Ramsankaran, 2017	Observation, parameter, conceptual model, forecasting	India	1	SUFI-2, assimilation of soil moisture data using Ensemble Kalman Filter	Assimilation remotely sensed soil moisture	Journal of Hydrology
27	VIC	Streamflow forecasting	Multi-data	Chawla and Mujumdar, 2018	Conceptual model, forecasting	India	1	ensemble pro-processor (EPP) to post-process the Global Ensemble Forecast System (GEFS) and Climate Forecast System version 2 (CFSv2) with four designed schemes, regression based methodology, ANOVA	RAINFALL, TEMPERATURE, STREAMFLOW	Advances in water resources
28	GR4J conceptual rainfall-runoff model + Bayesian artificial neural network (ANN) statistical forecasting model.	Streamflow forecasting	Multi-data, multi-model	Humphrey et al. 2016	Parameter, conceptual model, forecasting	Australia	3	Hybrid approach hydrological model with ANN	PET, Streamflow	Journal of Hydrology
29	CUE model	Streamflow forecasting	Multi-data	Chen et al. 2016	Forecasting	China	1	Application of historical inflow series, copula function,	Streamflow	Journal of Hydrology
30	HSAMI, HMETS, MOHYSE and GR4J-6	Streamflow forecasting	Multi-model, multi objective function	Arsenault et al. 2015	Conceptual model, forecasting	USA	429	Weighted hydrograph methods	Streamflow	Journal of Hydrology
31	MISDc	Streamflow forecasting	Multi-data	Massari et al. 2015	Input, forecasting	Italy	5			Remote sensing
32	HBV: Five variant models	Streamflow forecasting	Multi-model	Li et al. 2015	Parameter, forecasting	Norway	1		Discharge, snow pillow, groundwater	Journal of Hydrology
33	SWAT	Streamflow forecasting	Multi-data	Uniyal et al. 2015	Parameter, forecasting	India	1	SUFI-2	rainfall, streamflow	Hydrological Processes
34	multimodel climate forecasts with multiple watershed models (MM-P), linear model 'abcd'	Streamflow forecasting	Multi-data, multi-model	Singh and Sankarasubramanian, 2014	Input, forecasting	USA	2	single model and multi model precipitation forecast, streamflow forecast, climate ensemble models	streamflow	Water Resources Research
35	Hydrotel (Fortin et al., 1995, 2001) is a semi-physical distrib- uted hydrological model that	Streamflow forecasting	Multi-data	Abaza et al. 2014	Conceptual model, forecasting	Canada	1	Sequential streamflow assimilation techniques	streamflow	Journal of hydrology
36	GR4J and HBV	Streamflow forecasting	Multi-model	Demirel et al. 2013	Input, parameter, forecasting	Germany	1			Water Resources Research
37	SAC-SMA model, SNOW-17	Streamflow forecasting	Multi-data	Dechant and Mordkhani. 2011	Forecasting	USA	1	Observed forcing, resampled historical forcing, data siimilation	Streamflow	Hydrology and Earth System Sciences
38	Copula function, MCMC simulation,	Flood forecasting	Multi-data	Xu et al. 2021	Input, forecasting	China	1	temporal and spatial dependencies of precipitation data, copula function, MCMC, simulations of flooding		Journal of hydrology
39	Continuum	Flood forecasting	Multi-data	Silvestro et al. 2021	Observation, Input	Italy	1	Data assimilation	Streamflow, soil moisture, water level	Hydrology Research
40	SWAT and LISFLOOD-FP	Flood forecasting	Multi-data, multi-site calibration	Rajib et al. 2020	Forecasting	USA	1	Spatial resolution of stream network, accounting local relevance (stream network)	streamflow, flood inundation	Journal of hydrology
41	NAM, Polynomial Chaos Expansion	Flood forecasting	Multi-data, Posterior function	Tran et al. 2020	Parameter, forecasting	Vietnam	1	posterier distributioins, Single and dual EnKF		Water Resources Research
42	Markov-chain extreme online Markov chains,	Flood forecasting	Multi-data, multi-model	Bonakdari et al. 2019	Parameter, forecasting	USA	6	online updating of the optimum state number as well as updating Markov Matrix, Satellite signals werte used instead of real time discharge monitoring		Journal of hydrology
43	Tank model, Bayes theorem based forecasting, B-Ensemble forecast model	Flood forecasting	Multi-data	Seo et al. 2019	Forecasting	South Korea	35	Posterior information for the streamflow forecast, a deterministic tank model	historical information of prior information, observed streamflow, posterior information to ensemble forescast of streamflow	Hydrology research
44	sac MODEL. Conditional bias-penalized ensemble Kalman filter (CBEnKF)	Flood forecasting	Multi-data	Lee et al. 2019	Conceptual model, forecasting	USA	10	Data assimilation of hourly streamflow data into soil moisture accounting	RAINFALL, STREAMFLOW	Journal of hydrology
45	Monte carlo experiment	Flood forecasting	Multi-data	Adams et al. 2019	Input, forecasting	USA	796	Quantitative Precipitation Estimate (QPE) and Quantitative Precipitation Forecast (QPF) errors	improvements of rainfall data	Journal of hydrology
46	HEC-RAS 2-D	Flood forecasting	Multi-data	Bhola et al. 2019	Observation, parameter, conceptual model, forecasting	Germany	1	Constraining parameters to roughness. Reduced flood inundation uncertainty bounds.	Measured water level	Natural Hazards and Earth System Sciences
47	integrated long short-term memory (LSTM) and reduced order model (ROM) framework has	Flood forecasting	Multi-data	Hu et al. 2019	Forecasting	Japan	1	LSTM-ROM through RMSE		Journal of Hydrology
48	HEC-RAS 2D	Flood forecasting	Multi-data, Post processing	Zarzar et al. 2018	Observation, parameter, forecasting	USA	1	Ensemble streamflow prediction, WATER EXTENT, WATER DEPTH AND FLOW VELOCITY	streamflow, water depth, water extent	Journal of the American Water Resources Association
49	Six Early Warning Systems (EWS) based on contrasted forecasting systems: 20 models were investigated	Flood forecasting	Multi-data, multi-model	Thiboult et al. 2017	Parameter, conceptual model, forecasting	Canada	20	Relative Economic Value (REV), which is a flexible measure to quantify the potential economic benefits of an EWS.		Journal of Hydrology
50	Xin’anjiang (XAJ)	Flood forecasting	Multi-data	Meng et al. 2017	Observation, input, conceptual model, forecasting	Synthetic case studies	2	synthetic datasets identical to the real world flooding data	soil moisture, streamflow	Journal of Hydrology
51	MISDc and STAFOM-RCM	Flood forecasting	Multi-model	Barbetta et al. 2017	Forecasting	Italy	1	Multi temporal muilti model approach		Journal of Hydrology
52	data-driven hydrodynamic simulator based on the 1-D hydraulic solver dedicated, MASCARET	Flood forecasting	Multi-data, Post processing	Habert et al. 2016	Observation, parameter	France	1	Improving the topography and bathymetry information, locally correct friction coefficiets in the river bed and flood plain, data assimilation using extended Kalman Filter	topography, bathymetry, friction coefficient, in situ water level, discharge measurements	Journal of Hydrology
53	a combination of catchment hydrological and river hydrodynamic models and a data-assimilation (DA) method for real-time model updating: NAM, MIKE 11	Flood forecasting	Post processing, wisdom of crowd	Van Steenbergen et al. 2012	Forecasting	Belgium	3	Statistical analysis of historical flood forecasting results. 3D interpolation in the error matrix		Environmental Modelling and Software
54	ensemble numerical weather prediction (NWP) model (COSMO-LEPS, 16 members), the uncertainty in real-time assimilation of weather radar precipitation fields expressed using an ensemble approach (REAL, 25 members), and the equifinal parameter realizations of the hydrological model adopted (PREVAH, 26 members).	Flood forecasting	Multi-data, multi-model	Zappa et al. 2011	Input, parameter, forecasting	Switzerland	1	Super imposition of three sources of uncertainties		Journal of hydrology
55	Probabilistic hydrological modelling, MK blueprint methodology, GR2M model	Streamflow forecasting	Post processing, wisdom of crowd	Papacharalampous et al. 2020	Parameter, forecasting	USA	270	ensemble post-processing methodology, probabilistic prediction combination, two-stage post processing technique		Advances in water resources
56	SWAT, SWIM, VIC	Streamflow forecasting	Multi-model	Huang et al. 2020	Parameter, conceptual model, forecasting	USA, Germany, China	3		streamflow, evapotranspiration	Climate change
57	SWAT	Streamflow forecasting	Multi-data, multi-optimization	Hui et al. 2020	Parameter	China	1		Streamflow, ET	Remote sensing
58	variable infiltration capacity (VIC) model.	Water budget	Multi-objective function	Lilhare et al. 2020	Input, parameter	USA	1	Multi-Objective COMplex Evolution Algorithm (MOCOM-UA) minimizes, variogram analysis of response surfaces (VARS) technique	streamflow	Hydrological Processes
59	GR2M hydrological model, probabilistic hydrological modelling	Streamflow forecasting	Multi-data, Post processing	Papacharalampous et al. 2020b	Forecasting	USA	270	ensemble learning post-processing methodology	rainfall, runoff	Advances in water resources
60	ABCD is a spatially lumped, continuous monthly hydrological model	Streamflow forecasting	Multi-parameter, multi-GCM ensemble	Her et al. 2019	Parameter, forecasting	USA	156	GLUE method	runoff, soil moisture, groundwater	Scientific Reports
61	SWAT	Streamflow forecasting, Water budgets	Multi-data	Ashraf Vaghef et al. 2019	Input, forecasting	Canada	17	Analysis of Variance (ANOVA)- Sequential Uncertainty Fitting Program approach, SWAT-CUP		Climate dynamics
62	TOPMODEL with snow melt and tographic index algorithm	Runoff, snow	Multi-data	Xue et al. 2018	Parameter, conceptual model	China	1	GLUE, improved temperature indicator, Conceptual model has been improved using snowmelt and topographic index		Scientific reports
63	Global and regional hydrological models	Streamflow, water balance parameters	Multi-model	Krysanova et al. 2018	Forecasting	Methodology paper		comparison of ensemble model and conventionala modeling approach		Hydrological Sciences Journal
64	Variable Infiltration Capacity (VIC)	Streamflow forecasting	Multi-data	Sun et al. 2018	Paramter, forecasting	China	1	Application of multiple satellite gauge merged precipitation, Monte carlo MC method	Prcipitation	Journal of Hydrology
65	SWAT	Streamflow forecasting	Multi-model	Rajib et al 2018	Input, parameter, forecasting	USA	1			Journal of Hydrology
66	SWAT	Streamflow forecasting	Multi-data	Herman et al. 2018	Forecasting	USA	1		Streamflow and ET	Journal of Hydrology
67	HYMOD model over, Integration of particle Markov chain Monte Carlo and factorial polynomial chaos expansion	Streamflow forecasting	Post processing, Posterior function	Wang et al. 2017	Parameter, forecasting	China	1	probabilistic framework that merges the strengths of particle Markov chain Monte Carlo (PMCMC) and factorial polynomial chaos expansion (FPCE) algorithms to robustly quantify and reduce uncertainties in hydrologic predictions	Streamflow, soil moisture	Journal of Hydrology
68	VIC, XAJ	Streamflow forecasting	Multi-model	Yuan et al. 2017	Parameter, forecasting	China	1	Uncertainties emission scenarios, climate models, statistical modeling and hydsrological modeling	streamflow, ET, daily runoff	Journal of Hydrology
69	20 conceptual lumped models	Streamflow forecasting	Multi-data, Multi-model	Thiboult et al. 2015	Conceptual model, forecasting	Canada	20	meteorological forcing		Hydrology and Earth System Sciences Discussions
70	The SNOW-17 and Sacramento Soil Moisture Accounting (SAC-SMA) models, VIC	Streamflow forecasting	Multi-data	DeChant et al. 2014	Conceptual model, forecasting	USA	3	ensemble data assimilation and Sequential Bayesian Combination	passive microwave radiance, LST, aturalized flow data	Journal of HYdrology
71	Xinanjiang model	Streamflow forecasting	Multi-site evaluation, posterior functions	Lin et al. 2014	Parameter, forecasting	China	1	GLUE, Shuffled Complex Evolution Metropolis (SCEM-UA) sampling (i) the dependence of the optimal parameter set on the climate characteristics of the calibration period and (ii) the use of several posterior parameter sets over a given calibration period.	Addition discharge data in the downstream and multi location measurements	Journal of Hydroinformatics
72	GR4J rainfall-runoff model, TOPMo (six free parameters), inspired by TOPMODEL (Beven and Kirkby, 1979; Michel et al., 2003),	Streamflow forecasting	Multi-model	Brigode et al. 2013	Parameter, conceptual model, forecasting	France	89	Resampling of parameters by calibrating different sets of observational years representing dry periods, wet periods, Markov Chain Monte Carlo (MCMC) sampling method for parametersampling. the DREAM algorithm (Vrugt et al., 2009) and the GL objective function (Scho- ups and Vrugt, 2010))		Journal of hydrology
73	SWAT	streamflow forecasting	Multi-data	Anandharuban et al. 2023	Parameter, conceptual model, forecasting	India	1	Application of remote sensing data	streamflow data	International Journal of River Basin Management
74	The HydrOlOgical Prediction LAboratory (HOOPLA) toolbox (Thiboult et al., 2019) CEQUEAU GR4J HBV HYMOD IHACRES MOHYSE SIMHYD TOPMODEL	Snow forecasting	Multi-model	Dion et al. 2021	Forecasting	Canada	5	Ensemble forecasting systems (EFSs), Ensemble Kalman Filter (EnKF), data assimilation, hydro- logical modeling, data post-processing and multi-model clustering, Data assimilation and post processing	Streamflow, runoff, snowfall, PET	Journal of hydrology
75	TOPMELT and PDM models	Snow forecasting	Multi-data, Multi-objective function	Di Marco et al. 2021	Parameter, conceptual model, forecasting	Italy	1	MODIS snow cover data, GLUE	Streamflow, remotely sensed snow cover	Journal of hydrology
76	SWAT, Energy-Balance Modules (EBMs) and Temperature-Index Modules (TIMs)	Snow forecasting	Multi-data, Multi-model	Zaremehrjardy et al. 2021	Parameter, forecasting	Canada	1	the contribution of uncertainty due to the use of Temperature Index Modules (TIMs) and Energy Balance Modules (EBMs) in projection of snowmelt and snow depth in regional studies is poorly understood. We implemented the ANOVA uncertainty decomposition approaches, where a process-based TIM and EBM snowmelt routines, as well as two different snow density modules were coupled within the Soil and Water Assessment Tool (SWAT) source code	Observed snow depth, discharge,	Journal of Hydrology
77	a model-independent framework for integrating high-resolution snow observations in distributed snow- pack simulations, WaSiM	Snow forecasting	Multi-data, Multi-objective function	Thornton et al. 2021	Parameter, forecasting	Switzerland	1	calibration of an energy balance-based snow model that additionally accounts for gravitational redistribution is presented.	remote sensing data, in situ snow obeservations	Journal of Hydrology
78	SURFEX/ISBA/Crocus unidimensional multilayer physical snowpack model	Snow forecasting	Multi-data	Lafaysse et al. 2017	Observation, input, conceptual model	France	1	deterministic coupled multilayer ground/snowpack model SUR- FEX/ISBA/Crocus.		Cryosphere
79	Remotely sensed data	Snow forecasting	Multi-data	Thackeray et al. 2016	Conceptual model, forecasting	Northern hemisphere region		The strong temperature–SCE linkage suggests thatmodel uncertainty in projections of SCE could be potentially reduced through improved simulation of spring season warming over land		Journal of Climate
80	Combination of remotely sensed data, LIDAR, GPR	Snow forecasting	Multi-data	Helfricht et al. 2014	Conceptual model	Austria	1	ground pene- trating radar (GPR) profiles on four glaciers	Ground truth measurements are compared with the model simulated snow cover, LIDAR data, remotely sensed data, snow accumulation data	Cryosphere
81	Common Land Model coupled with a snow grain size growth algorithm	Snow forecasting	Multi-data	Che et al. 2014	Forecasting	Siberia	9	Japan Meteorological Administration—Global Spectral Model (JMA-GSM) operational global data assimilation system. The Microwave Emission Model of Layered Snowpacks (MEMLS), Assimilating passive microwave remote sensing data	snow water estimation	Remote Sensing of Environment journal
82	Snow and ice melt model (SES)	Snow forecasting	Multi-data, Multi-objective function	Schober et al. 2014	Observation, parameter, conceptual model	Austria	1	Application of ALS TECHNIQUE, FIELD MEASUREMENTS, Ground penetrating radar techniques. Calibrated datasets are used to simulate the snow melt	Observed accumulation patterns are related to the topography (elevation, slope and curvature), Snow cover data	Journal of Hydrology
83	Application of remote sensing data: snow-cover retrieval models	Snow forecasting	Multi-data	Rittger et al. 2013	Forecasting	USA	1	Application of remote sensing data	Landsat ETM+, MODIS snow cover produscts	Advances in water resources
84	SnowMIP	Snow forecasting	Multi-model	Essery et al. 2013	Parameter, conceptual model	France	1	combined with single model with combining existing parameterizations of different complexities in many configurations to generate large ensembles of simulations	Snow ,ass, snow depth, albedo and surface temperature	Advances in Water Resources
85	snow water equivalent (SWE)	Snow forecasting	Multi-data	Slater et al. 2013	Parameter, conceptual model	USA (snotel NETWORKS)	Multi basin	Model structural and parameter uncertainty are eliminated by using a perfect model scenario i.e. comparing results to modelled control runs.	Snow water extent	Advances in Water Resources
86	Different sources of snow cover data from remote sensing	Snow forecasting	Multi-data	Brown and Robinson 2011	Input	Northern hemisphere		regression based estimate and multi-dataset estimates of confidence intervals	Application of multiple remote sensing datasets	Cryosphere
87	Snow 17 model, SNOw TELmetry (SNOTEL) sites	Snow forecasting	Multi-data, posterior function	He et al. 2011	Parameter, forecasting	USA	8	the Latin Hypercube Sampling (LHS), utilized within the Generalized Sensitivity Analysis (GSA), The Generalized Sensitivity Analysis (GSA) method, The Differential Evolution Adaptive Metropolis (DREAM) algorithm	Precipitation, air temperature, areal extent of snow cover, snowpack	Advances in Water Resources
88	SNOW-17	Snow forecasting	Multi-data	Leisenring et al. 2011	Observation, parameter	USA	1	EnKF, EnSRF, four variants of particle filter		Stochastic Environmental Research and Risk Assessment
89	HYDROTEL, HSAMI	Snow forecasting	Multi-data, Multi-model	Poulin et al. 2011	Parameter, conceptual model	Canada	1	Bayesian Model Averaging (BMA)	observed snow water equivalent (SWE)	Journal of Hydrology
90	SNOW-17	Snow forecasting	Multi-model	Franz et al. 2011	Parameter, conceptual model	USA	6	Bayesian Model Averaging (BMA)		Advances in Water Resources
91	SM was estimated using a Triangular method (Tr) and Landsat derived indices, DEM, and in-situ SM data	Soil moisture	Multi-data	Fathololoumi et al. 2021	Input	Iran	1	Greenness, brightness, wetness, and land surface temperature are the surface biophysical characteristics and the topographical characteristics including elevation, slope, aspect, Topographic Wetness Index (TWI) and solar local incident angle calculated using Tas- seled Cap Transformation, Single Channel algorithm used in this study.	Soil moisture data	Journal of Hydrology
92	ANN, ORYZA2000–Rice crop simulation model	reservoir inflow	Multi-data	Kasiviswanathan et al. 2020	Input, parameter	India	1	ANN, optimization method	rainfall, streamflow	Paddy and Water Environment
93	LSTM model, Probability based models	Rainfall-runoff process	Multi-data	Klotz et al. 2021	Parameter	USA	531	aleatoric uncertainty,epistemic uncertainty, public data-driven benchmarking scheme for uncertainties;	precipitation, streamflow	HESS Discussions
94	overland flow model Iber, HEC-HMS	Rainfall-runoff process	Multi-data	Fraga et al. 2019	Input	Spain	1	generalized likelihood uncertainty estimation (GLUE)	rainfall, streamflow	Hydrological Processes
95	HOOPLA (HydrOlOgical Prediction LAboratory) modular framework	Precipitation forecast	Multi-model	Valdez et al. 2021	Observation, conceptual model	Canada	30	Ensemble Kalman Filter	preceipitation	HESS Discussions
96	Neural network based	Precipitation forecast	Pre and post processing	Chen et al. 2020	Input, forecasting	China	1	combination of the precipitation post-processor and the quantification of uncertainty from initial condition	rainfall	Water

5.1. Stage I: Input preparation and pre-processing

As discussed in the previous section, uncertainties involved in the measurements and inputs can be reduced at this stage. This can be possible with the help of an understanding of measurement errors and pre-processing techniques employed. The estimation of measurement errors within the modeling framework will help to reduce these uncertainties (Das Bhowmik et al., 2020). The accuracy level of the measurement error does matter in influencing the outcomes according to the employed modeling framework and type of measurement inputs. For example, gauge-specific measurements can be accurate for the estimation of measurement errors. However, the forecast variance may increase due to the consideration of measurement errors. This can be tackled by a suitable model structure to assess the tradeoff between measurement errors and forecast performance. High frequent data collection can also support the measurement and input uncertainties, as exemplified in the measurement of the rating curve (Das et al., 2018).

Few studies found that soil moisture, streamflow, and flood forecasting are sensitive to the initial conditions, which calls for a model adjustment strategy prior to the forecasting task to reduce such uncertainties (Meng et al., 2017). In this case, ensemble techniques can be used to correct the model’s initial states through the assimilation of additional data. For instance, applying ensemble streamflow prediction would help enhance operational capacity (Muhammad et al., 2018). Similarly, hydrometeorological ensembles can help to reduce the uncertainties in modeler subjectivity and improve flood inundation maps (Zarzar et al., 2018). Also, this depends on the type of hydrologic model and the required hydrologic forecasting (Mazrooei et al., 2019). However, the assimilation of additional data and its positive influence may change with respect to the model structure and type of forecasts (e.g., seasonal forecast of streamflow has shown a trade-off with model errors than the initial state) (DeChant et al., 2014).

Providing additional data and improving measurements' temporal and spatial resolution would help reduce these uncertainties. For example, improvements in the additional bathymetry have improved the performance of water level simulation (Habert et al., 2016), and systematic errors in the spatial resolution of the Digital Elevation Model were assessed for Ground Penetrating Radar techniques that assisted in improving the measurement errors (Helfricht et al., 2014), snow data assimilation have shown improvements in snow modelling, such as assimilation of Snow Cover Area (Che et al., 2014)

The application of suitable input data has a greater impact on precipitation products. For example, the application of global precipitation products and remotely sensed precipitation products needs prior assessment and preprocessing of the data (Sun et al., 2018). Similarly, the application of various GCMs, RCMs, and climate change projections needs proper downscaling and prior estimation of errors concerning ground observation for the suitability of the catchments.

Preprocessing techniques can be chosen based on the linear and nonlinear characteristics of the hydrologic variables (Abbasi et al., 2021). The catchment-specific requirements also need to be considered to reduce the measurements and input errors in hydrological forecasting (Zaremehrjardy et al., 2021). For example, mountainous regions require higher spatial resolution information for modelling, application of gridded data needs more ground observation for the validation of the model for the now simulation, and the inclusion of snow water equivalent has improved the snow simulation in alpine areas (Schober et al., 2014). Hence, improvements in historical data can enhance the reliability of the model by reducing uncertainties.

Empirical correction factors can be applied to correct the biases in the solid precipitation and other measurement deficiencies (Thornton et al., 2021). The model performance can be evaluated with the provision of well-measured catchments. However, the model structure plays a vital role in deciding its performance (Essery et al., 2013). Therefore, reducing the input uncertainty first is critical before reducing hydrologic model uncertainty (Singh and Sankarasubramanian, 2014). The meteorological forecast and its deficiencies can be solved by applying appropriate pre-processing techniques (Thiboult et al., 2015).

5.2. Stage II: Model conceptualization uncertainty

The model structural uncertainties are compensated or solved at this stage. The selection of appropriate model structure and model flow provides insights to solve the parameter uncertainty to a greater extent. Applying multi-model approaches may help reduce the model structural uncertainties depending upon the chosen models. It must be chosen in a way that should comprehend the overall modeling uncertainties. In this case, the extent of structural uncertainty captured is more important than the number of models chosen for the study (Dion et al., 2021). The importance of the model selection task is because distributed or semi-distributed models can provide more insights into the system's functioning details than a lumped model. Data assimilation in a multi-model approach helps to reduce uncertainties by reducing the errors in the initial states (DeChant et al., 2014).

Hydrological model structure influences the forecasting skill to a large extent, however, the forecast skill is also influenced by various other factors such as process spatial representation, model calibration, and the application of inputs especially the precipitation forecast used for the initial conditions, which can potentially yield complex model (Siqueira et al., 2021).

One of the arguments that were extensively discussed in the hydrology community to produce reliable forecasts is model complexity. Nevertheless, it is open to debate whether increased model complexity always leads to an increase in forecast performance. For instance, Tran et al., 2020 advocated the use of model complexity to deal with real-time and ensemble flood forecasts, Essery et al., 2013 claimed there is a limit beyond which we cannot expect higher model complexity would help to increase the model performance. Appropriate representations of the error components in the modelling flow can help in improving the reliability of the hydrological forecasts (McInerney et al., 2021). For instance, Liu et al.,2021 showed that temporally varied error statistics with finer error models helped to improve forecasting accuracy. Similarly, any additional information about the hydrological processes within the catchment would reduce the model structural uncertainties in the hydrological forecasts, e.g., the application of multi-source data (Hassan and Hassan, 2020). Therefore, it is important to prioritize model structure to fine-tune input measurement in the study area (De Santis et al., 2021).

Another exemplification is inspired by streamflow measurement. Model structures for snow modelling need a detailed energy balance method for snow representation (Mazrooei et al., 2019). Forecast reliability depends on spatial resolution (DeChant et al., 2014), while ensemble streamflow prediction with data assimilation is found to help improve the forecasts (DeChant and Moradkhani, 2011). Energy balance modules and temperature index modules share a large portion of uncertainties in the snow modelling of the Hilly region (Zaremehrjardy et al., 2021). The initial state of the model structure plays a vital role and implementing an appropriate error reduction scheme of this initial state is found to help reduce the uncertainties and improve the forecasts (Mazrooei et al., 2019).

5.3. Stage III: Calibration and validation strategies

At this stage of the hydrological modelling, calibration and validation strategies are used to adjust the model parameters according to the measured data. Eventually, this helps improve the model's performance. Especially, this procedure helps to resolve structural uncertainties to a reasonable extent, so that the parameters and model structural uncertainties are connected (Essery et al., 2013). However, care should be given to the potential problem of overfitting the parameters through calibration procedures.

The conventional calibration procedure of streamflow calibration at the outlet of the basin can provide significant information on the streamflow pattern but there are chances to misrepresent another important hydrological phenomenon which may lead to parameter and prediction uncertainties. Eventually, this causes a bias toward estimating hydrological components in the simulation. For example, a biased estimation of evapotranspiration is reported by Rajib et al., 2018. The equifinality can be reduced by reducing the number of parameters or increasing the number of observed variables in the calibration procedure (Rajib et al., 2018). Calibration of additional parameters helps to improve the forecast. For example, calibrating soil moisture sensors and the corresponding spatial measurement sensors are found to improve streamflow forecasts (Wang et al., 2017).

Calibrating hydrological parameters in multi-sites and constraining the related parameters with different climatic conditions are found to improve the model performance (Huang et al., 2020). However, studies need further assessment to evaluate the extent of the uncertainty reduction due to the improvements in the calibration procedures.

On the other hand, the spatial dependency of the hydrological parameters can be resolved using spatial validation of multi-objective parameters and uncertainty assessments. For example, constraining snow parameters with snow ground measurements improves the parameters in snow modelling (De Marco et al., 2021). Historical evaluation of model performance is necessary; however, it is not sufficient when looking into future aspects of hydrological changes such as the prediction of climate change, land use, and land cover changes (Krysanova et al., 2018).

Another aspect that impacts the calibration method is the period during which this calibration is carried out. For instance, the selection of calibration and validation time-period in a catchment case-study should represent both the dry and wet climatic conditions for better model performances (Brigode et al., 2013). The calibration performance also depends on the method used, the objective function employed, and the inherent constraints in the catchment area. Baseline information may be used for the verification of model results in the case of no ground truth information, as used by Zarzar et al., 2018 for the flood inundation maps. However, this is subject to uncertainty in the forecast. Besides, parameter sensitivity is highly variable from site to site, and uncertainties due to parameters are higher than that of the inputs (He et al., 2011; Demirel et al., 2013). Therefore, the choice of calibration methods straightforwardly influences the prediction uncertainty bounds (Brigode et al., 2013)

In this respect, combinations of multimodal approaches with data assimilation and post-processing techniques are found to reduce uncertainties and improve forecasts (Dion et al., 2021; Siquira et al., 2021). For post-processing or updating the forecasts, finer temporal granularity is recommended for better quantification of uncertainties. Coarser temporal granularities are recommended in the case of a lower computational cost (Liu et al., 2020). Bayes theorem-based ensemble streamflow prediction models are used to produce a posterior mean which helps to update the forecast (Seo et al., 2019).

Statistical post-processing can improve the forecasting accuracy in some studies, although this should be subject to testing the post-processing techniques across multiple catchments, lead times, multiple hydrological models, and various sample sizes. The accuracy of post-processing techniques depends on the models used, ensemble size, the complexity of the basin, and the time used for analysis. Regarding the time-period of the post-processing task, in contrast to calibration, the post-processing task can generate relatively good quality results with a relatively stationary hydrologic time-period for model training (Muhammad et al., 2018).

The usage of post-processing techniques should be investigated thoroughly before the application of multi-model approaches for better forecast results. Among post-processing techniques, probabilistic approaches and ensemble predictions are increasingly popular in practice. An important aspect of post-processing includes communication of uncertainties that may occur at different stages of the hydrological forecasting pipeline. Indeed, communication uncertainty in hydrological forecasting is equally important as the quantification of these uncertainties, as it directly affects the lives of individuals, e.g., flood forecasting. Uncertainty communication in different ways such as linguistic, graphical, numeric, or combinations of these (Van Steenbergen et al., 2012).

In this section, the multi-criteria approach or supporting techniques used for reducing the uncertainties in the reviewed literature are summarized. Figure 5 shows the list of approaches found in the literature as a measure of reducing uncertainties in hydrological forecasting. Multi-site calibration and multi-objective calibration for the streamflow are increasingly in use since the last decade (Table 4). Knowing the type of forecasts and the interconnections between the process representation and the uncertainties will help to alleviate the uncertainties. The process representation improvements through random error components will help reduce the total hydrological uncertainties in short forecast leads (McInerney et al., 2021). As discussed in the earlier sections, the criteria followed in the reviewed studies are inter-related, for example when we apply multi-source data for improving model conceptualization, the model parameters must be calibrated for better performances of the hydrological model. Likewise, this section will summarize the requirements for the multi-criteria used to reduce the uncertainties and their applications and limitations. A systematic uncertainty analysis is required to find the sources of uncertainties and their reduction in the forecasting processes (Demirel et al., 2013)

Data assimilation can be used to assimilate additional data sources before the model conceptualization and update the output variables using the real-time measured data during the forecast period.

Model performance and the forecast horizon are ultimately connected as the model performance may degrade beyond the forecast horizon. For such cases, assimilation of real-time measurement would help main the standard of the model performance. Nonetheless, additional information on the hydrological process through supporting techniques is recommended to reduce such uncertainties. For example, in contrast to the conventional outlet calibration, multi-site evaluation of parameters is one of the ways employed to reduce the uncertainties (Lin et al., 2014), while accounting for spatial variation in the hydrological processes. Krysanova et al., 2018 showed that conventional modeling and validation of the hydrological modeling using historical data perform better than the multi-model ensemble approach for the projections of the climate change data. Wang et al., 2017 demonstrated that data assimilation along with the uncertainty quantification method can provide a robust hydroclimatic forecasting framework. Thiboult et al., 2017 showed that different qualities of the forecast system are intrinsically connected, and one should first attempts to improve forecast accuracy to yield improvement in forecast reliability.

Table 5

Multi-criteria approaches used for reducing the uncertainties its advantages and limitations
	Model used	Hydrological forecasting	Multi-criteria approach used for reducing uncertainties	Study	Advantages of the study	Challenges/disadvantages/Limitations of the study	Journal
1	MISDc-2L (Brocca et al., 2012; Massari et al., 2018)	Streamflow forecasting	Multi-data	De Santis et al. 2021	Soil moisture data assimilations help to improve the streamflow prediction. SM information provide added values to the poor open loop simulation of streamflow.	Open loop simulation added with remotely sensed SM appears to be weak for majority of the catchments. This may be due to the vegetation, orographic characteristics, rescaling techniques, choices of model and assimilation filter.	Water Resources Research
2	Variable Infiltration Capacity (VIC) (Wood et al., 1992; Liang et al., 1994; Liang et al., 1996) model	Streamflow forecasting	Multi-data	Mazrooei and Sankarasubramanian, 2021	VAR DA address the bias correction issues in VIC model. Initial state correction improves the streamflow simulation 7–8 days forecast of lead time.	VAR DA for larger river basins should account streamflow with different lags. VAR DA uses numerical approximation algorithms or adjoint models for the optimization problems, developing such algorithms are challenging due to the nonlinear behavior of hydrologic system. Precise estimation of model error statistics is challenging, and it need ensemble approach.	Journal of Hydrology
3	SWAT, RSWAT	Streamflow forecasting	Multi-data	Lee et al. 2021	Application RS-ET data reduces the equifinality and predictive uncertainty in the streamflow prediction.	Application of this study cannot be taken as uniform framework. It needs to be studied with various catchments with different climatic conditions.	Sustainability (Switzerland)
4	Multi model approach: dynamic Budyko (DB), G´enie Rural `a 4 param`etres Journalier (GR4J), and Probability Distributed Model (PDM) model	Streamflow forecasting	Multi-data	Nayak et al. 2021	SM assimilation helps to improve the performance of DB.	Root zone depth definition in the hydrological models has the influence over the correlation between RS-SM with simulations. Simulation of Budyko function is poor in DB model than GR4J and PDM.	Journal of Hydrology
5	The MuTHRE-FD model	Streamflow forecasting	Multi-data	McInerney et al. 2021	The MuTHRE-FD model improves the reliability of high flow events. Sharpness is better for low flows, worse for high flow events. Short time streamflow forecast performs well, so the cumulative volume forecast is better at longer lead times. This model is persistence in residuals which reduce the uncertainty at short lead times.	Underestimate the uncertainties of high flow forecasts and risk of high flows. To improve the reliability this model, need to compensate on the sharpness. Nonparametric flow dependent models has to be verified with ephemeral catchments.	Water resources research
6	long short-term memory (LSTM) ANN based	Streamflow forecasting	Multi-data	Althoff et al. 2021	computationally cheap. Longer look back series used in this study has captured the seasonal pattern well. This helps to improve the performance of the models. ET helps to increase the performance. the dropout technique helps to avoid overfitting by the model.	This framework is does not consider the changes in land use and land cover, soil types, interface is for calibration of parameters only. This model is oversensitive to the rainfall especially with high flow.	Stochastic Environmental Research and Risk Assessment
7	Bayesian dynamic hierarchical model (BDHM) West and Harrison (2006)	Streamflow forecasting	Multi-data	Das Bhowmik et al. 2020	Since this model used various spatial and temporal level consideration of uncertainties, it performs better for the 1-day lead time streamflow forecasts. The addition of measurement error increases the forecasting skill.	Model performance decreases for the higher lead times. Inclusion of measurement error leads to higher CRPS (Continuous ranked probability score), however it increases the forecast uncertainty. Measurement across the basin is lacking in this study to represent the hierarchy in the BDHM.	Water Resources Research
8	GR5J	Streamflow forecasting	Multi-data	Piazzi et al. 2021	EnKF-based estimation of initial conditions has shown improvement in predictive accuracy for short lead time when accounting only for meteorological uncertainty. Since routing dynamic has greatest influence on the accuracy, updating initial level routing for the forecast leads to significant improvement in the forecast accuracy.	The DA-based estimation is less efficient for improving forecast with the production store level which accounts SM at each time step. The DA-based update of the unit hydrograph state is not an efficient approach to enhance the streamflow forecasting skill. Since their update can modify the system response to meteorological forcings. The parameter updated based on the assimilation of historical data is not the optimal representation of the forecast with different lead time i.e., 10-days. This may lead to parameter equifinality.	Water Resources Research
9	ANN	Streamflow forecasting	Multi-data	Yang et al. 2020	The AR model is effective in correcting GEFS precipitation thereby improve the simulation accuracy, it is simple and feasible. This method can contribute to reduce the rainfall input uncertainty and hydrological models.	The proposed techniques should evaluate with longer forecast horizon and its practical significance.	Water
10	A feed forward neural network trained via two-layer Broyden Fletcher Goldfarb Shanno algorithm is used for model development.	Streamflow forecasting	Multi-data	Hassan and Hassan, 2020	The proposed approach performed better for streamflow estimation with the multi-source information. Fusion of SCA and gauge observations helps to represents the watershed better.	Selection of neural network architect is challenging because increasing complexity may have over fitting, while lighter version leads to underfitting.	Acta Geophysica
11	‘abcd’ model	Streamflow forecasting	Multi-data	Mazrooei and Sankarasubramanian, 2019	Application of lumped model for seasonal streamflow forecast has shown improvement by avoiding the uncertainties in the temporal-disaggregation of climate forecasts	The proposed approach DA approach for the high monthly flows must be improved.	Journal of hydrology
12	Canonical run-off generating mechanisms, field measurements	Streamflow forecasting	Multi-data	Penny et al. 2019	Process based approach to account the hydrological changes for the data scare region has shown improvement in hydrological predictions through integration of data from field investigation, use of proxies and space time substitution. This technique offers a method to evaluate the catchment’s past function, even in the absence of data	With multiple working hypotheses approach it’s difficult to avoid underdetermination due to insufficient evidence to fully constrain past processes. This technique requires multiple field investigations.	Hydrological Processes
13	Variable Infiltration Capacity (VIC-3)	Streamflow forecasting	Multi-data	Das et al. 2018	This study able to identify the differences in uncertainties associated with GCMs and scenarios. Bias correction has helped slightly to improve the performance.	Uncertainty lies within the downscaling method has not been addressed	Water resources management
14	hydrological uncertainty processor (HUP)	Streamflow forecasting	Multi-data	Liu et al. 2018	The proposed framework provides combined characterization of uncertainty, quantiles with specified exceedance probabilities, prediction intervals with specified inclusion probabilities, and probabilities of exceedance for specified thresholds.	HUP framework proposed in this study does not consider and characterize the stochastic dependence among variables.	Hydrological sciences
15	The Xin’anjiang (XAJ) model	Flood forecasting	Multi-data	Meng et al. 2017	The proposed framework accounts real-time updating for the streamflow estimation. This techniques accounts uncertainties from input, model, and measurements. It compensates the time delay with EnKF for the runoff estimation, which is important in flood forecasting for a short term.	Application of EnKF is challenging because it may be affected by initial conditions, the time window, and assimilation interval.	Journal of Hydrology
16	SWAT	Streamflow forecasting	Multi-data	Patil and Ramsankaran, 2017	Soil profile is improved using soil water storage.	The proposed soil profile has not showed significant improvement due to the limitation in	Journal of Hydrology
17	VIC	Streamflow forecasting	Multi-data	Chawla and Mujumdar, 2018	Application of non-stationarity in applications of hydrological modeling helps to reduce the parameter uncertainties	(a) Results are limited to the datasets of present study. Uncertainties in the model structure has not been considered. (b) Multi-objective optimization function has not been considered.	Advances in water resources
18	CUE model	Streamflow forecasting	Multi-data	Chen et al. 2016	CUE method helps to surpass the limitations of conventional uncertainty evolution models.		Journal of Hydrology
19	MISDc	Streamflow forecasting	Multi-data	Massari et al. 2015	Soil moisture assimilation helps to improve the streamflow predictions	Application of SM assimilation need to consider the local conditions to find the optimal solutions.	Remote sensing
20	SWAT	Streamflow forecasting	Multi-data	Uniyal et al. 2015	Application of various calibration tools helps to identify suitable parameters for the streamflow predictions.	All uncertainties from input, model and output must be accounted and quantified for more robust modeling results	Hydrological Processes
21	Hydrotel (Fortin et al., 1995, 2001) is a semi-physical distrib-	Streamflow forecasting	Multi-data	Abaza et al. 2014	Uncertainties in the initial conditions and its inclusion helps to improve the assimilation technique performances.	Forecast uncertainty is not explored. To assess the streamflow and snow information in a single study it may require different version of ensemble Kalman filter.	Journal of hydrology
22	SAC-SMA model, SNOW-17	Streamflow forecasting	Multi-data	DeChant and Moradkhani. 2011	Snow data assimilation improves the seasonal streamflow prediction	Spatial representation of the catchment is lacks in this study, which makes SNOTEL to adjust elevation bands inaccurately. These can be rectified using accounting errors, or using more representative datasets	Hydrology and Earth System Sciences
23	Copula function, MCMC simulation,	Flood forecasting	Multi-data	Xu et al. 2021	Analysis of flood risk of multi-reservoir system helps to overcome Spatial and temporal dependencies of uncertainties in real time flood forecasting.	Lack of representation of spatial dependencies in a multi-reservoir system may lead to under estimation of flood risk for an individual reservoir within the system.	Journal of hydrology
24	Continuum	Flood forecasting	Multi-data	Silvestro et al. 2021	Assimilation of streamflow helps to improve the performance of the open loop configuration.	Spatial distribution of correction factors can be improved for the state variables. consequences of increasing the assimilation frequency could be investigated.	Hydrology Research
25	Tank model, Bayes theorem based forecasting, B-Ensemble forecast model	Flood forecasting	Multi-data	Seo et al. 2019	B-ESP model improves the forecast accuracy of the ESP model.	The proposed B-ESP model has limitation against probabilistic forecasts, as it reduces the performances in probabilistic forecasts.	Hydrology research
26	sac MODEL. Conditional bias-penalized ensemble Kalman filter (CBEnKF)	Flood forecasting	Multi-data	Lee et al. 2019	the CBEnKF improves the performance of the forecast with the lead times of up to the time-to-peak of the basin over EnKF. This improvement was seen proportional with the quantity of flow.	The proposed CBEnKF is computationally expensive	Journal of hydrology
27	Monte carlo experiment	Flood forecasting	Multi-data	Adams et al. 2019	Application of NEXARD derived Quantitative Precipitation Estimate has improved hydrologic simulations. This dataset helps to improve the model states and reduces the need for assimilation of data for model state update. This will increase the confidence in the probabilistic forecasts.	Application of QPF for the smaller basins has the problem of mis representation of the catchment characteristics, especially in the use of flash floods. Hence, it needs separate study to find the limitations of application in the flood forecasting of smaller basins.	Journal of hydrology
28	HEC-RAS 2-D	Flood forecasting	Multi-data	Bhola et al. 2019	Usage of measured water level data have helped to reduce the uncertainty	This study requires high computational cost if it involves full dynamic hydrodynamic model. Only one event was used to validate the parameters, Pluvial components are not considered in this study	Natural Hazards and Earth System Sciences
29	integrated long short-term memory (LSTM) and reduced order model (ROM) framework has	Flood forecasting	Multi-data	Hu et al. 2019	Computational cost is reduced three times, but the performance of LSTM-ROM is maintained at the same level of accuracy. This helps to predict floods rapidly and accurately.	The proposed approach should be verified for other lead times of the forecast as the performance reduces for the higher lead times.	Journal of Hydrology
30	SWAT	Streamflow forecasting, Water budgets	Multi-data	Ashraf Vaghefi et al. 2019	The proposed ANNOVA-SUFI-2 approach has helped to quantify the different sources of uncertainties such as parameterization, regionalization, climate models, downscaling methods, ET estimations and their interactions.	Different models have to be used and verified for the proposed approach.	Climate dynamics
31	TOPMODEL with snow melt and tographic index algorithm	Runoff, snow	Multi-data	Xue et al. 2018	Application of snow melt data and topographic index has helped to improve the TOPMODEL for snow modeling.	The optimal parameters set used out of Monte-Carlo simulations. To reduce the computational time requirements, rigorous sample selection has not been carried out.	Scientific reports
32	Variable Infiltration Capacity (VIC)	Streamflow forecasting	Multi-data	Sun et al. 2018	Application of multiple global satellite gauge merged precipitation products enhance the hydrologic simulations.	The Bayesian Model Average model can be improved with dynamic weights considering the nature of forecast and catchment states.	Journal of Hydrology
33	SWAT	Streamflow forecasting	Multi-data	Herman et al. 2018	Two techniques such as multi-variable calibration and Genetic Algorithms have helped to improve the actual evapotranspiration in the simulations. However, improvements in GA have been compromised with the streamflow simulations for evapotranspiration.	Selection of remotely sensed data products for a particular study needs detailed analysis prior to application. As different sources provide different values.	Journal of Hydrology
34	The SNOW-17 and Sacramento Soil Moisture Accounting	Streamflow forecasting	Multi-data	DeChant et al. 2014	Data assimilation improves the forecasting capabilities in VIC. Forecast reliability have been evaluated over spatial dependencies. In the probable event predictions initial conditions has stronger control over reliability of the predictions. Using different model structures has helped to reduce the model errors, which improves the forecasts.	DA has shown least improvement in the regions of thick forest covers. Highlighting the challenges in utilizing remotely sensed products for the data pertaining to land surface.	Journal of Hydrology
35	SURFEX/ISBA/Crocus unidimensional multilayer physical snowpack model	Snow forecasting	Multi-data	Lafaysse et al. 2017	The proposed methodology in this study helps to identify the modeling errors for the study region and improved the modeling capacities. It helps in hazard forecasting in the avalanche region.	Assumptions made for the input errors is one of the important limitations of this study. As it may affect the model output to a significant extent. Suitable type of error estimation of meteorological uncertainties for snow modeling has greater impacts.	Cryosphere
36	Remotely sensed data	Snow forecasting	Multi-data	Thackeray et al. 2016	Uncertainties in projections have been reduced by increasing the number of realizations from models.	Future projections of warming and snow cover in the northern hemisphere could perform model development to alleviate the process level biases to reduce the model uncertainty.	Journal of Climate
37	Combination of remotely sensed data, LIDAR, GPR	Snow forecasting	Multi-data	Helfricht et al. 2014	Combination of Airborne Laser Scanning derived elevation information and ground penetrating radar data for snow depth helps to estimate the difference in the estimation of the snow depths.	In snow accumulation areas, ALS data alone may lead to systematic under estimation of snow depth distribution	Cryosphere
38	Common Land Model coupled with a snow grain size growth algorithm	Snow forecasting	Multi-data	Che et al. 2014	Data assimilation of remote sensing data for the estimation of snow depth helps to improve the model performance during the accumulation period. The proposed method can be utilized for the operational frameworks.	During ablation period the uncertainties increased due to the influence of wet snow on the PM data. this system does not account the microwave radiation from the forest and atmosphere	Remote Sensing of Environment journal
39	Application of remote sensing data: snow-cover retrieval models	Snow forecasting	Multi-data	Rittger et al. 2013	Application of spectral mixing is more accurate for identifying snow covered area, snow free area. The performance is maintained for all land cover classes and large topography range.	Spatial effects cause implicit errors in the MODIS data. Thick clouds are flagged as a snow covers. Uncertainty in the snow cover measurement will influence the sensitivity of the input variables in the model. So, the uncertainties in the snow cover measurement should be quantified.	Advances in water resources
40	snow water equivalent (SWE)	Snow forecasting	Multi-data	Slater et al. 2013	Temperature index proposed in this study helps to reduce the input uncertainty. It is a simplified model.	The simplified model does not account for rain on snow events, cold content of the snowpack, melt flux from soil interface. The largest uncertainties will be arisen from the precipitation and its phase. It can be reduced by data assimilation of measured data or satellite data; however, it is not possible for the operational use.	Advances in Water Resources
41	Different sources of snow cover data from remote sensing	Snow forecasting	Multi-data	Brown and Robinson 2011	Northern hemisphere spring snow cover extent has been updated applying new climate data record. It helps to reduce the uncertainties.	The snow cover responses to the developed dataset are varying with respect to the continents and climate. This phenomenon needs more clarity.	Cryosphere
42	SNOW-17	Snow forecasting	Multi-data	Leisenring et al. 2011	Seasonal prediction of snow accumulation and ablation has been improved using data assimilation techniques. The accuracy was higher in the particle filter variants with similar bias of Kalman filter techniques.	This study does not account the non-linearity of the dynamical processes.	Stochastic Environmental Research and Risk Assessment
43	SM was estimated using a Triangular method (Tr) and Landsat derived indices, DEM, and in-situ SM data	Soil moisture	Multi-data	Fathololoumi et al. 2021	Remote sensing base soil moisture data helps to estimate the soil moisture for ungauged catchments. Inclusion of surface characteristics classes helps to reduce the uncertainties in the soil moisture prediction.	In situ soil moisture data have to be improved with more points dispersed geographically.	Journal of Hydrology
44	ANN, ORYZA2000–Rice crop simulation model	reservoir inflow	Multi-data	Kasiviswanathan et al. 2020	Two stage ensemble approach used in this study help to reduce the input and parameter uncertainties in the forecasted inflow.	This framework requires more field data to test this to an operational level. Also, uncertainty quantification information is also needed to decide based on the simulated information.	Paddy and Water Environment
45	LSTM model, Probability based models	Rainfall-runoff process	Multi-data	Klotz et al. 2021	Distributional prediction method proposed in this study produces reliable, precise, and strong single point estimates.	The limitation of the freely available data sources leads to over-fitting on the test data. Probabilistic approach lacks in consistency, precision, and specific events.	HESS Discussions
46	overland flow model Iber, HEC-HMS	Rainfall-runoff process	Multi-data	Fraga et al. 2019	Inclusion of input uncertainties from rainfall has helped to reduce the equifinality of the models. Thereby increase the streamflow predictions in the semi distributed model. This study emphasizes the importance of accounting input uncertainty rather than increasing the model complexity.	Uncertainty in the rainfall data has only limited effects on the improvement of the accuracy of the streamflow predictions.	Hydrological Processes
47	simulation–optimization framework	Streamflow forecasting	Multi-model	Vema et al. 2020	Uncertainties associated with the operation of a water conservation structure has been considered in this study.	Failures of the conservation structure needs to be included	Stochastic Environmental Research and Risk Assessment
48	HBV: Five variant models	Streamflow forecasting	Multi-model	Li et al. 2015	Increasing the complexities of the model has helped to improve the model predictions.	Applicability of the results in this study needs to be verified for other catchments. Non-stationarity of the processes is not considered.	Journal of Hydrology
49	GR4J and HBV	Streamflow forecasting	Multi-model	Demirel et al. 2013	Combinations of the input and parameter uncertainty quantification are considered in two different hydrological models to identify the right combination of the modeling for the catchment. The consideration of parameter uncertainty in the forecast has produced good improvements in the forecasts.	The analysis of right combinations of the uncertainties to be accounted in a forecast needs more clarity and studies. In some cases, consideration of total uncertainties has doubled the number of false alarms.	Water Resources Research
50	GR4J, TOPMO model	Streamflow forecasting	Multi-data, Multi-model, posterior function	Brigode et al. 2013	Two sources of parameter uncertainties were assessed using optimal parameter set on the climate change characteristics and the application of posterior parameter sets during calibration period. This study suggests that lack of robustness in the model has more impact on the uncertainties of the streamflow prediction for climate change studies.	Providing general applicability of this study is challenging. The robustness of the model must be verified thoroughly. The median for the mean annual flow was greater than 10% in this study. This is a notable limitation of application of hydrological models to simulate extreme high or low flows.	Journal of Hydrology
51	MISDc and STAFOM-RCM	Flood forecasting	Multi-model	Barbetta et al. 2017	Multi-model approach proposed in this study has improved the forecasts by reducing the uncertainties mainly during low, medium flow conditions.	The proposed method requires more data for verification. Predictive uncertainties are evaluated without weather forecasts.	Journal of Hydrology
52	SWAT, SWIM, VIC	Streamflow forecasting	Multi-model	Huang et al. 2020	Enhanced model parameterization proposed in this study has helped to reduce the total uncertainty.	The application of different models has brought differences in the results which needs further study for the clarification	Climate change
53	Global and regional hydrological models	Streamflow, water balance parameters	Multi-model	Krysanova et al. 2018	Detailed recommendations are given for the selection, evaluation of hydrological models at different scales.	Conditioning on uncertainty of historical data and evaluating the impacts of bias corrected climate change data needs further evaluation.	Hydrological Sciences Journal
54	SWAT	Streamflow forecasting	Multi-model	Rajib et al 2018	Including bio-physical parameters in the parameterization has helped the prediction accuracy for streamflow and ET. Further model accuracy can be enhanced with the calibration of the biophysical parameters mentioned in this study.	Choices of model, parameters and calibration strategies has implications in the results and its challenging. Spatial validation of ET would be challenging.	Journal of Hydrology
55	VIC, XAJ	Streamflow forecasting	Multi-model	Yuan et al. 2017	Climate models contributes higher uncertainties considering the low flow, ET, and streamflow. In case of extreme flood projections PD contributes more uncertainties in the estimation	Climate projection has the limitations of the models that are being used to rely upon for the making the decision.	Journal of Hydrology
56	The HydrOlOgical Prediction LAboratory (HOOPLA) toolbox (Thiboult et al., 2019)	Snow forecasting	Multi-model	Dion et al. 2021	This study has demonstrated that the application of combination of data assimilation and post processing can reduce the uncertainties and improve the forecasts. The proposed method was simple and can be used in the operational context.	The proposed methodology needs to be extended for more than several years for the better assessment. Findings in this study limited to the forecast lead-time used in this study. The selection of hydrological models can change the results produced in this study based on the structural uncertainties of the selected models. Similarly, the selection of the catchments also has the role in the production of the results as it may bring different results for the different climatic regions. The proposed methodology maybe limited to some users due to the limitation of the resources.	Journal of hydrology
57	SnowMIP	Snow forecasting	Multi-model	Essery et al. 2013	This study has produced more clarity than previous studies on the applications of intercomparison projects.	In the proposed methodology the prediction during warmer winters was challenging due to the failure of predictions of early and mid-winter melt events.	Advances in Water Resources
58	SNOW-17	Snow forecasting	Multi-model	Franz et al. 2010	The usage of individual best model and the ensemble mean matches the performance of the simulation.	Input uncertainties were not considered in this study which may improve the forecasts. Also, the relationship between model structure and catchments, climate characteristics, data bias and model weights need to be considered for the selection of subset of models.	Advances in Water Resources
59	HOOPLA (HydrOlOgical Prediction LAboratory) modular framework	Precipitation forecast	Multi-model	Valdez et al. 2021	The precipitation post processor used in this study has helped to improve the predictions to a large extent in reducing bias and improving the reliability. This study revealed that the combination of DA and post processor can be a good alternative for longer lead times.	The application of proposed post processor is subject to the forecast lead time and catchment size in the applications of hydrological forecasts. Including all sources of uncertainties in the post processor may reduce the hydrological forecast performance and its need careful evaluation.	HESS Discussions
60	SWAT	Streamflow forecasting	Multi-objective function	Liang et al. 2021	This study has revealed the importance of groundwater recharge to streamflow in YLRB catchment and efficacy of SUFI-2 in SWAT model calibration.	Usage of different methods to optimize the parameters may produce confusion as in this study. It may also be due to the complexities involved in the catchment characteristics.	Journal of hydrology
61	variable infiltration capacity (VIC) model.	Water budget	Multi-objective function	Lilhare et al. 2020	This study found precipitation is more important than temperature in water budget studies, intercomparison and partitioning of the precipitation were not consistent among the selected land surface models. SA results can be more useful if it can be aligned with the objectives of the forecasts.	Multi-criteria SA approach under various conditions may be useful in improving the forecasts. Initial conditions and boundary conditions of soil moisture and ET model sensitivity can be included in this kind of studies.	Hydrological Processes
62	ABCD is a spatially lumped, continuous monthly hydrological model	Streamflow forecasting	Multi-parameter, multi-GCM ensemble	Her et al. 2019	Analysis and application 22 GCMs and their variants suggest that the selection of GCM may influence the uncertainties in the modeling.	Lumped representation of the watershed processes reduce the parameterization accuracy during calibration.	Scientific Reports
63	Xinanjiang model	Hydrologic modeling	Multi-site evaluation, posterior functions	Lin et al. 2014	This study confirmed that accounting interior flow information can reduce the parameter uncertainty.	However, the proposed method is not able to cover the high and low flows at the same time.	Journal of Hydroinformatics
64	mesoscale Hydrologic Model (mHM)	Streamflow forecasting	Multi-data, multi-variate calibration strategies	Dembélé et al. 2020	Multi-variate calibration helps to produce the reliable spatial and temporal models.	Lack of in situ data collection. Structural uncertainties and shortcomings of modeling data sets.	Water resources research
65	GR4J conceptual rainfall-runoff model + Bayesian artificial neural network (ANN) statistical forecasting model.	Streamflow forecasting	Multi-data, multi-model	Humphrey et al. 2016	Hybrid modelling methodology proposed in this study has improved the better representation of initial conditions by accounting soil moisture data. It produces most accurate forecasts particularly higher flows.	It requires more time and expertise than conventional methods.	Journal of Hydrology
66	multimodel climate forecasts with multiple watershed models (MM-P), linear model 'abcd'	Streamflow forecasting	Multi-data, multi-model	Cha et al. 2014	Reducing the uncertainties in the inputs can improve the hydrological modeling predictions. This study suggests precipitation to be more accurate for the streamflow predictions accuracy.	This study suggests reducing the uncertainties in the climate model and hydrological model for improving the streamflow predictions.	Water Resources Research
67	Markov-chain extreme online Markov chains,	Flood forecasting	Multi-data, multi-model	Bonakdari et al. 2019	Proposed IVI index helps to reduce the defects in the regression models.	More powerful regression models can be used instead of MC based models.	Journal of hydrology
68	Six Early Warning Systems (EWS) based on contrasted forecasting systems: 20 models were investigated	Flood forecasting	Multi-data, multi-model	Thiboult et al. 2017	The economic value of a hydro-meteorological forecast can be increased by addressing uncertainties in initial condition, structure, and meteorological forcing.	Selecting a single best model for the forecast does not improve the economic value. In addition, the best performing model does not perform the best scenarios to all the lead times.	Journal of Hydrology
69	ensemble numerical weather prediction (NWP) model (COSMO-LEPS, 16 members), the uncertainty in real-time assimilation of weather radar precipitation fields expressed using an ensemble approach (REAL, 25 members), and the equifinal parameter realizations of the hydrological model adopted (PREVAH, 26 members).	Flood forecasting	Multi-data, multi-model	Zappa et al. 2011	The application of radar-based precipitation and parameter uncertainties helps to improve the streamflow prediction.	For larger river basin studies, it requires changes in number of simulations.	Journal of hydrology
70	20 conceptual lumped models	Streamflow forecasting	Multi-data, Multi-model	Thiboult et al. 2015	Combined application of multi-models, EnKF, and meteorological forcing can help to reduce the uncertainties in the structure, initial conditions, and inputs.	High computational cost.	Hydrology and Earth System Sciences Discussions
71	SWAT, Energy-Balance Modules (EBMs) and Temperature-Index Modules (TIMs)	Snow forecasting	Multi-data, multi-model	Zaremehrjardy et al. 2021	This study suggests that EBMs and TIMs cannot be generalized to a regional scale or longer period. Multi-scale and temporal analysis are needed for the assessment of cascading effects of uncertainties.	The proposed method for the streamflow was overestimated in the mountainous region.	Journal of Hydrology
72	HYDROTEL, HSAMI	Snow forecasting	Multi-data, Multi-model	Poulin et al. 2011	This study has analyzed hydrological model and parameter uncertainty. It revealed that structural uncertainties are important to improve the model predictions.	The applicability of the proposed methodology has to be verified with various physically based hydrological models and catchments.	Journal of Hydrology
73	MESH, Hydrological and land surface model	Streamflow forecasting	Multi-data, multi-objective function	Budhathoki et al. 2020	Accounting more data into the calibration methods improve the hydrological representation in the hydrological modeling. Multi-objective calibration helps to reduce the parameter uncertainty.	The application of the remote sensing data must be verified with the observed data. However, in the absence of field data remote sensing data can be helpful in improving the model.	Hydrological sciences
74	TOPMELT and PDM models	Snow forecasting	Multi-data, Multi-objective function	Di Marco et al. 2021	Application of MODIS snow products improve the SWE predictions.	Lack of field observations lead to reliability analysis was performed in this study.	Journal of hydrology
75	a model-independent framework for integrating high-resolution snow observations in distributed snow- pack simulations, WaSiM	Snow forecasting	Multi-data, Multi-objective function	Thornton et al. 2021	Accounting the spatial calibration helped to reduce the uncertainties in the prediction.	Very basic spatial interpolation scheme is used. A single layer snow model was employed, Wind distribution data was accounted for.	Journal of Hydrology
76	SWAT	Streamflow	Multi-data, multi-objective function	Panchanathan et al. 2023	Application of MODIS ET data, regionalization of parameters and multi data approacmeng h is discussed	Lack of field observations for the spatial validation of the ET data	International Journal of River Basin Management
77	Snow and ice melt model (SES)	Snow forecasting	Multi-data, Multi-objective function	Schober et al. 2014	Application of multi-temporal ALS data and field data helps to improve the hydrological simulations. This simple technique can be very much helpful in the operational models of snow cover estimations.	The uncertainties of the predictions are linear to the accuracy of the ALS data.	Journal of Hydrology
78	SWAT	Streamflow forecasting	Multi-data, multi-optimization	Hui et al. 2020	Combined algorithm proposed in this study has revealed that it improves the physical rationality of the parameter. Thereby it reduces the parameter uncertainty.	Combined approach proposed in this study must be verified for the other regions for the verification. Application of additional constraints has hep to improve the ET simulations, however the uncertainties are high during high value periods. Used data in this study might be the reasons for the over or under estimation of the simulations needs further studies.	Remote sensing
79	HEC-RAS 2D	Flood forecasting	Multi-data, Post processing	Zarzar et al. 2018	The approach proposed in this study that links the hydrodynamic predictions with ensemble approach helps to reduce the uncertainties.	The spatial applicability of the proposed work has the limitation of the hydraulic models.	Journal of the American Water Resources Association
80	data-driven hydrodynamic simulator based on the 1-D hydraulic solver dedicated, MASCARET	Flood forecasting	Multi-data, Post processing	Habert et al. 2016	Data driven enhanced bathymetry helps to improve the water level simulations. Consequently, it improves the flow rating curve in the operational context.	Equifinality has not been accounted. Friction coefficient must be extended to a long distance to improve the forecast lead times. Spatial and time varying correction of the hydraulic parameters can be included.	Journal of Hydrology
81	GR2M hydrological model, probabilistic hydrological modelling	Streamflow forecasting	Multi-data, Post processing	Papacharalampous et al. 2020	The proposed methodology is flexible and easy to apply for the hydrological prediction to improve the accuracy.	Computational cost is high and intensive procedures.	Advances in water resources
82	SWAT and LISFLOOD-FP	Flood forecasting	Multi-data, multi-site calibration	Rajib et al. 2020	This study validates the application of SWAT-LISFLOOD for the flood forecasting. Proposed methodology improves the predictability. Linking these two models helps to interpolate the parameters between the models.	Trying to improve the accuracy of the streamflow prediction by using the parameter calibration alone is challenging.	Journal of hydrology
83	NAM, Polynomial Chaos Expansion	Flood forecasting	Multi-data, Posterior function	Tran et al. 2020	Proposed method helped to improve the accuracy of the flood forecasting.	Less computationally efficient for the development of complex models.	Water Resources Research
84	Snow 17 model, SNOw TELmetry (SNOTEL) sites	Snow forecasting	Multi-data, posterior function	He et al. 2011	Accuracy of the precipitation data and the portioning of the snow-precipitation are important factors in improving the snow accumulation and melting processes in the snow modelling. In depth knowledge of snow accumulation phase helps to improve the snow cover and extent.	Low correlation between parameter sensitivity and the catchment investigated in the SNOW-17 model. this is because of the lack of regionalization information.	Advances in Water Resources
85	Data-Driven Models (DDMs): Support Vector Regression (SVR) and Multiple Linear Regression (MLR)	Streamflow forecasting	Multi-model, Preprocessing	Abbasi et al. 2021	The proposed framework helped to improve the prediction accuracy.	Nonlinear regression models performs better than linear models.	Journal of hydrology
86	rainfall-runoff model GR4J (Perrin	Streamflow forecasting	Multi-model, multi objective function	Lerat et al. 2020	In the absence of the daily flow data, monthly analysis is viable for understanding the streamflow pattern of the catchment.	Monthly simulations do not show the flood peaks and its timing, in addition the daily streamflow pattern will not be resembled in the monthly simulations.	Journal of Hydrology
87	CREST	Streamflow forecasting	Multi-model, multi objective function	Gan et al. 2018	The proposed sensitivity analysis reduced the number of parameters and improved the calibration procedures.	Lack of data leads to less accurate regionalization of the parameters. Thereby increase the uncertainties in the simulations.	Journal of Hydrology
88	HSAMI, HMETS, MOHYSE and GR4J-6	Streamflow forecasting	Multi-model, multi objective function	Arsenault et al. 2015	Multi-objective functions in the calibration procedure helps to improve the model performance.	Methods tested in this study does not perform to the level it was expected.	Journal of Hydrology
89	WATFLOOD, SWAT	Streamflow forecasting	Multi-model, post processing	Muhammad et al. 2018	Ensemble combined with deterministic model helps to improve the forecast and operational decision-making capacities.	The post-processing technique used in this study is subject to the limitations of the following: the number of models, the ensemble sample size, basin complexity, and the study period.	Water
90	ANN based	Streamflow forecasting	Preprocessing	Hasan and Hasan, 2021	Preprocessed data improves the model prediction efficiency and reduces the error.	The developed approach performed well in the training phase, however failed in the testing phase.	KSCE Journal of Civil Engineering
91	MGB (acronym of Modelo de Grandes Bacias)	Streamflow forecasting	Post processing	Siqueira et al. 2021	In the absence of in situ hydrometeorological data the continental scale model combined with EMOS and ECC-T can provide skillful predictions.	Raw ensemble streamflow forecast may lead to lower performance of the model. EMOS was not able to produce skillful forecasts in large rivers.	Journal of hydrology
92	Error Reduction and Representation In Stages (ERRIS) model into Infiltration Capacity Model, Variable Infiltration Capacity (VIC) macroscale	Streamflow forecasting	Post processing	Liu et al. 2020	The proposed methodology can utilize the information from the previous day.	ERRIS-A performance in post-processing high flows is low. conventional temporally unvaried error models are inefficient in reducing errors in mountain region.	Journal of hydrology
93	Neural network based	Precipitation forecast	Pre and post processing	Chen et al. 2020	the proposed EPP can improve the accuracy and reduce the uncertainty of ensemble forecasts. it can be helpful solution for long-term forecast of precipitation.	the progress by EPP highly depends on the design of canonical events, the performance may vary in different regions.	Water
94	a combination of catchment hydrological and river hydrodynamic models and a data-assimilation (DA) method for real-time model updating: NAM, MIKE 11	Flood forecasting	Post processing, wisdom of crowd	Van Steenbergen et al. 2012	This method provides solutions to the problem of heteroscedasticity of the forecast residuals. It does not apply any predefined probability distribution. very simple and easy to understand for communicating the uncertainties.	This type of communication cannot be supported in the decision-making system. it contains fewer details on the temporal changes of water levels and maximum water level. The method does not allow estimation of forecast uncertainties for values that are not in the range of the historical water level forecasts.	Environmental Modelling and Software
95	Probabilistic hydrological modelling, MK blueprint methodology, GR2M model	Streamflow forecasting	Post processing, wisdom of crowd	Papacharalampous et al. 2020	Computational requirements and limitations are mostly few.	○ Their performance depends to some extent on the sample size. ○ They lack interpretability	Advances in water resources
96	HYMOD model over, Integration of particle Markov chain Monte Carlo and factorial polynomial chaos expansion	Streamflow forecasting	Post processing, Posterior function	Wang et al. 2017	Proposed framework that merges the strengths of the PMCMC and the FPCE algorithms. It improves the efficiency of the prediction.	Minimization of the errors in simulating high-flow events would significantly improve the overall accuracy of hydrologic predictions.	Journal of Hydrology

6.1. Multi-objective function and multi-parameter calibration

The multi-objective approach helps to enhance the identification of the hydrological model. It also helps identify the best choice in a multi-model approach to streamflow forecast (Arsenault et al., 2015). It essentially helps to reduce the biases in the simulation of streamflow. For example, in snow-dominated catchments, streamflow measurements can be simultaneously used with the measurements of snow or remotely sensed data (Di Marco et al., 2021). Multi-variate calibration can reveal the interconnection between the variables, possibly providing insights regarding whether the uncertainty originated from input, model structure, or lack of knowledge about the hydrological system.

The objective functions or the model performance indicators are subject to the modeler’s choice. However, numerous available indices /tools can assist in this task. This includes Nash-Sutcliffe efficiency, Root Mean Square Error (RMSE), and Klinge-Gupta efficiency index. These indices can be chosen based on the literature and the subject of interest (streamflow, snow, flood forecast), the types of models used, and the application constraints for the selected process of hydrological modelling (Zaramella et al., 2019; Di Marco et al., 2021). Applying a combination of these indicators helps alleviate the deficiencies in other indices and enhances the parameter selection and predictive performance (Wang et al., 2017). In a multi-model framework, the identified best models can benefit from applying the multi-objective function. Sometimes for a high value of Nash-Sutcliffe efficiency, the representation of high and low flows may not be captured, and the biases maybe higher than 10%. This is due to the limitations of a single index score. The application of a multi-objective function can overcome this (Brigode et al., 2013).

6.2. Data assimilation contribution

Data assimilation of additional data can be used to enhance the performance of low (resp. high) flow simulations using the assimilation of streamflow (resp. soil moisture) (Mazrooei and Sankarasubramanian, 2019). This is found to be helpful in ungauged catchments (Meng et al., 2017). The authors also showed that any minor improvement in deep soil layer representation improves the streamflow prediction after applying vertical error correlation for soil moisture. Patil and Ramsankaran, 2017 found that the ensemble propagation method, along with ensemble generation methods, can handle some types of uncertainty due to weak model structure.

Multi-site observation and calibration of streamflow have revealed unique responses to climate change (Chien et al 2013). Accounting, other variables, such as ET, soil moisture, and groundwater, can be added to model calibration would improve the representation of the system and model performance. Rajib et al., 2018 found that the application of Moderate-resolution Imaging Spectroradiometer (MODIS) ET data in the calibration have improved the simulation performance. Similarly, introducing groundwater storage in the calibration has helped to improve the model performance (Qiao et al., 2013). Researchers also showed that the predictability of hydrological models can be significantly improved when jointly calibrating with streamflow and satellite-based ET data (Rajib et al., 2018; Panchanathan et al., 2023).

Data assimilation-based forecast estimations provide a comprehensive representation of system uncertainties, although the predictive accuracy is influenced by the choice of the DA method and modeling scheme (Piazzi et al., 2020). Often extra information is required to successfully perform the data assimilation task depending on dominant hydrological processes in the catchment. For example, a snow-dominated catchment needs different Ensemble Kalman Filter implementations to combine the streamflow and snow information (Abaza et al., 2014), while for flood forecasting, the performance depends on the initial soil moisture (Meng et al., 2017).

The effect of DA of SM on hydrological models depends on the model structure, and calibration practices (De Santis et al., 2021). Also, the effect of data assimilation may have different impacts on different seasons. So, special care should be given to aspects of the ‘one model fits all’ paradigm.

The application of specific remotely sensed products and their accuracy trivially have effects on data assimilation techniques and outcomes. The accuracy of the products is influenced by factors such as the local efficiency of satellite observations due to climatic factors such as snow, and humid conditions (De Santis et al., 2021).

The integration of this additional information of the catchment in the modelling scheme yields better outcomes than enforcing high NSE values or low statistical errors. The satellite-derived snow cover area can serve as one of the predictors for streamflow estimation in the snow-dominated region (Hassan and Hassan, 2020).

Ensemble Kalman Filter at the data assimilation stage can reduce the difference between the measurement and the ensemble streamflow predictions by accounting for uncertainties in hydrometeorological measurements (Dion et al., 2021). Data assimilation may not be able to reduce the model structural deficiencies, and it may even in certain cases reduce the model performances. So, care should be given to the selection of DA methods (De Santis et al., 2021).

Di Marco et al., 2021 found that remotely sensed MODIS products for snow cover areas improve the identifiability of combined melt factor parameters. Mazrooei and Sankarasubramanian, 2019 claimed that streamflow accuracy can be enhanced by using data assimilation of groundwater storage and soil moisture storage of streamflow observations prior to the model iterations using EnKF.

Application of Global satellite-gauge merged precipitation products and their ensembles have also been found to improve the decision making through the reduction of the parameter and model structural uncertainties (Sun et al., 2018).

Model structural uncertainty has been reduced by updating the soil water routing through perturbed soil water storages (Patil and Ramsankaran, 2017). Additional bathymetry data has helped to improve the floodplain friction coefficient. This procedure improves the relationship between water level-discharge and reduces the uncertainties concerning the time-dependent friction coefficient (Habert et al., 2016).

Additional field data and multi-temporal airborne laser scanning data have improved hydrologic simulations of snow-dominated catchments (Schober et al., 2014). Especially, it enhanced the estimation of snow density, which depends on various factors such as elevation, terrain features, parameterization, precipitation gradients, and accumulation pattern.

Overall, it is stressed that in most data assimilation techniques, it is essential to know the uncertainty contribution before applying any measurement data. If the uncertainties are larger in quantity, they must be reconstructed with the following information (1) the final date of seasonal snow cover, (2) the potential snowmelt model, (3) appropriate parameterization, (4) the selection of relevant data (Slater et al., 2013). Especially, data assimilation methods showed significant improvements in seasonal accumulation and ablation of SWE predictions in the SNOW-17 model (Leisenring et al., 2011).

6.3. Multi-conceptual model:

To deal with the conceptual deficiencies in a single model, it has recently been proposed to have a multi-model approach. This can be carried out using different complexities of the same model and the application of different hydrologic models for the same studies using, for instance, ensemble techniques. This helps to enhance the performance of the forecasts by reducing model error.

Multi-model ensembles are useful for large basins for the applications of climate change on streamflow. For communication, the ensemble results must be verified and compared with the individual performance of the models (Krysanova et al., 2018).

In the forecasting context, the economic values of using multi-model approaches instead of a single model should be transparent. The choice of models and selection of the best model to deliver the forecast not only depends on model performance criteria but also on the reliability and accuracy of the forecast (Thiboult et al., 2017). For this purpose, Thiboult et al., 2015 advocate the use of ensemble methods for a probabilistic meteorological forecast. This can reduce the accumulation of past errors in the initial conditions.

6.4. Pre and post-processing

Pre-processing helps to reduce the uncertainties accumulated in the datasets prior to the conceptualizations (Abbasi et al., 2021). Depending upon the type of forecast, models used, and variable of interest, the input uncertainties shall be addressed using pre-processing techniques, utilizing, e.g., precipitation data for streamflow prediction (Abbasi et al., 2021), bathymetry for flood studies, snow density for the snow modeling.

A combination of pre-processing methods and non-linear model has improved the prediction accuracy to a significant extent (Abbasi et al., 2021). Typically, pre-processing helps to reduce the number of predictor variables. For instance, dimensionality reduction and variable selections contribute to improving the accuracy of prediction (Her et al., 2019).

The development of remote sensing data such as Landsat products, soil moisture data, evapotranspiration data, and various products of the snow data such as snow cover data, snow water extent, and snow water estimation are used widely to improve hydrological forecasting. Table 6 shows the list of studies reviewed that apply remotely sensed data products to reduce uncertainties in hydrological forecasting. The application of remotely sensed data is reported to help address input uncertainty (Dembélé et al., 2020; Hassan and Hassan, 2020), parameter uncertainty (Gan et al., 2018; Dembélé et al., 2020; Liu et al., 2020; Papacharalampous et al., 2020), forecast uncertainty (Gan et al., 2018; Hassan and Hassan, 2020; Papacharalampous et al., 2020; Abbasi et al., 2021; De Santis et al., 2021; Mazrooei et al., 2021), conceptual model uncertainty (Lee et al., 2021; Nayak et al., 2021). The availability of remotely sensed data makes this application feasible even in data scare conditions for improving hydrological modelling. For detailed information on the applications, and limitations of remotely sensed data products, we illustrated in Table 6 the detailed review of the studies. Table 7 shows the list of open-source data available in vegetation, soil, evapotranspiration, and climate that can contribute to this task. The web addresses provide more information on the availability, usage, and limitations of the data products.

Table 6 List of remotely sensed data used and their applications

Table 7 List of open source remotely sensed products that can be utilized for reducing the uncertainties in hydrological forecasting

Selecting a suitable hydrological model and understanding the catchment plays a vital role in reducing uncertainties. These two factors are interconnected and influence each other in forecasting results. This section will discuss the key aspects of hydrological models and catchment characteristics that have been highlighted in the reviewed studies.

8.1 Choice of models

Recent studies suggest that devising different combinations of model structures can effectively reduce model errors and forecast uncertainty (DeChant et al., 2014)
Knowing the watershed characteristics is important to select a hydrological model, for example, to choose a simple ABCD model, the watershed’s hydrological response could be reproduced concerning a given rainfall and temperature (Her et al.,2019)
The performance can degrade when we have not chosen an appropriate hydrological model or model structure. This situation cannot be considered uncertain, rather it can be the result of model selection in some cases (Lin et al., 2014). Low flows were not able to simulate well in this study due to the selection of the model or model structure (Lin et al., 2014).
Care should be given when we use any model for extreme rainfall events. Few models cannot capture those events, e.g., VIC (Chawla and Mujumdar, 2018)
Similarly, for low flows, the GR4J model overestimates, whereas HBV is prone to underestimate low flows (Demirel et al., 2013)

8.2 Model Complexity

6. The application of multi-level complex model implementation can be considered for a given study to identify the suitable model structure and improve forecasting (He et al., 2011; Huang et al., 2020). However, we cannot assume that model performance will improve if we only increase the model complexity. For example, well-known empirical parameterizations can perform as well as physically based models (Essery et al., 2013)

7. So, the selection of model structure in terms of complexity, model structure, and parameters may influence the results of the supporting applications such as data assimilation, and remote sensing (De Santis et al., 2021)

8. The explicit assessment of the influence of data errors (Franz et al., 2011), modelling structures, and parameters (He et al., 2011), are required for a more comprehensive understanding of the total uncertainty

9. The field data should support increasing the model complexity to reduce these uncertainties.

10. It is crucial to meet the balancing hydrological model structure that can represent the near real-time complexity as well as to meet the computational requirements (Di Marco et al., 2021).

11. Hydrological modeling and its reliability in snow-dominated catchments depend on the capability of simulating snow accumulation and melting as it affects the runoff and streamflow.

8.3 Allied techniques

12. Hydrological models tend to have lower efficiency in representing both low and high flows due to the effects of climate change (Brigode et al., 2013). This is also rooted back to various ill-known parameters resulting from the calibration processes (Lin et al., 2014). The alternative option to avoid parameter equifinality can be the application of multi-criteria approaches.

13. Selection of appropriate processing flow such as pre-processing, model structure, parameter selections, calibration techniques, and post-processing enhances hydrological forecasting performance (Abbasi et al., 2021; Patil et al., 2017).

14. In some cases, an individual model can produce better performance than ensemble models of streamflow. In this case, it is important to select an appropriate forecasting model.

15. In addition, reducing various uncertainties requires the application of allied techniques such as sampling distributions, the ensemble means, and probabilistic approaches in the prediction task together with multi-criteria-based approaches as discussed in (Klotz et al., 2021). Regardless of this processing flow, uncertainty quantification is vital for hydrological forecasting

16. The accuracy of remotely sensed products in data assimilation plays a vital role in the uncertainty quantification of the forecasted results. Depending on the model structure used, this can have a different outcome (Loizu et al., 2018).

8.4 Model calibration

17. Meanwhile, any developed technique or methodology to reduce the uncertainties in one study cannot be directly assumed to provide similar results. In some cases, it may downgrade the accuracy of the models (Seo et al., 2019).

18. For any modelling structure, flow, techniques, tools, and established methodology, the application of the same technique to a new study or region requires detailed investigations and understanding before the selection of processes (Klotz et al., 2021).

19. Previously published works are always cautious about the final recommendation of their work, highlighting the factors involved in the study and the replication of the same method can produce different results for different requirements. For example, high-performing lower lead-time forecasts may not be suitable for the higher lead-time forecast requirements. However, the developed approaches can be considered as the base of the specific problem we are trying to address (Habert et al., 2016; Seo et al., 2019; Tran et al., 2020; Dion et al., 2021).

20. Care should be undertaken for using the specific published techniques: ensemble methods, and data assimilation techniques (Seo et al., 2019). All individual techniques contain different challenges, which should be considered before the selection.

21. Spatial analysis of uncertainties is a more sophisticated process to consider. However, recent studies suggest promising results for the enhancement of hydrological mode performances when using the appropriate spatial dataset (Zaremehrjardy et al., 2021).

8.5 Characteristics of the Basins in the uncertainty studies

Hydrological forecast skill depends on the catchment characteristics such as the area of the basin, geography, topography, hydro-climatic features, and flow regimes. With larger catchments, the complexity of the catchment increases. Thereby, the forecast skill is expected to be lower (Krysanova et al., 2018; Siqueira et al., 2021).
The role of the catchment characteristics has to be well evaluated for hydrological forecasting. Depending upon the applications of the forecast, influencing factors should be emphasized as follows:

Streamflow forecasting should include the size of the catchments and dominant catchment processes.
Snow-based catchments should be given importance in the aspects of snow accumulation and melt, liquid water storage, and refreezing (Essery et al., 2013) (Di Marco et al., 2021). Additionally, snow accumulation and melting abilities of a hydrological model contributes largely to model the snow-dominated catchments.
For flood forecasting, sensitive parameters should be adjusted prior to forecasting such as initial soil moisture to reduce the uncertainty in the forecast.
Forest thickness may affect the land surface state information derived from remotely sensed data for the data assimilation techniques, in which case ground observation data are important to improve the modelling (DeChant et al., 2014).
Non-stationarity should be considered in hydrological modelling such as land use and land cover.

3. Catchment’s dominant process identification is a key factor in conceptualizing the right combination of the model (Paiva et al., 2012). This helps to identify the uncertainties potentially involved in the process (Chawla and Mujumdar, 2018). This process requires various analyses at different stages of the hydrological modelling.

4. For rainfall-runoff-dominated basins, the accuracy of the high flow events influences the performances of the streamflow predictions (Wang et al., 2017). For such basins, reducing the uncertainties in seasonal climate forecasts requires more care for the higher rainfall seasons (Singh and Sankarasubramanian, 2014).

5. The catchments responding to floods quickly need to be studied in finer spatial and temporal scales for reducing the uncertainty of flood forecasting (Thiboult et al., 2017).

6. The applications of GCMs, RCMs, downscaling methods, and their interactions influence the uncertainty of hydrological modelling. Since meteorological factors influence these, the regions with less temperature variability e.g., colder seasons in mountainous regions have less impact on snow formation (Zaremehrjardy et al., 2021), whereas the impact of wind is higher (Thornton et al., 2021). Estimation of air temperature at higher elevations may produce biases if it contains any incorrect assumptions with lapse rate

7. The uncertainty evaluation also should be categorized in terms of the hydroclimatic conditions (Brigode et al., 2013) as it influences a specific hydrological process according to the seasons of the considered catchment. For example, monsoon-based catchments have higher rainfall in a shorter duration, while snow-based catchments (Brigode et al., 2013) should be considered more carefully in winter months (Essery et al., 2013).

8. In special cases like high-elevation areas, climate data inputs are likely to be more important than the model selection and process representation (Zaremehrjardy et al., 2021).

9. It is suggested that for regions with an intensive distribution of topographical index, high runoff accumulations and improved temperature indicators would help to improve the snow melt process (Xue et al., 2018).

10. The number of catchments studied in a particular study and the region of those catchments influences the results of any developed methodology. Different regions and even the area of the catchments in some cases can influence hydrological forecasting (Dion et al., 2021). The parameter uncertainties in hydrological forecasting cannot be justified or generalized in the case of larger catchments with a variety of landscape properties.

11. Various studies suggest that techniques should be tested, validated and standardized against multiple catchments (e.g., see (Liu et al., 2020) for statistical post-processing techniques; (Essery et al.,2013; Meng et al.,2017; Huang et al., 2020; De Santis et al., 2021) for now-based studies; (Patil and Ramsankaran, 2017) for soil water routing; (Humphrey et al., 2016) for soil moisture driven).

12. Seasonal flow predictions should consider the region of highly changing weather patterns in the catchment from summer to snowfall in the winter (Abbasi et al., 2021).

To our best understanding from this review work, we would like to suggest that the application and the usage of more than one hydrological model structure or models with different levels of complexities in combination with the application of different catchments are needed to develop a unified methodology for reducing uncertainties. This approach requires widespread cooperation among the hydrologic communities.

This study reviewed 96 representative studies for exploring the latest developments in reducing uncertainty in hydrological forecasting. Applications of multi-criteria-based approaches in hydrological forecasting studies have seen a wide share of the collected studies as evidenced by the fact that 73 studies advocate a combination of multiple data with multi-parameter calibration and objective functions. On the other hand, 27 studies utilized more than one model, and 35 studies utilized more than one catchment to test their hypotheses for the improvement in hydrological forecasting. These applications helped to reduce uncertainties at different levels to enhance the reliability of the forecast. We have listed the advantages and disadvantages of each reviewed study. We have summarized the application of remotely sensed data in reducing these uncertainties. Based on the reviewed literature, we have summarized the criteria for selecting a hydrological model to reduce uncertainty in hydrological forecasting. Thus, our review work provides a comprehensive understanding of the current state-of-the-art techniques for handling uncertainty in hydrological forecasting together with their associated advantages and limitations in a way to guides both researcher and practitioner.

Finally, it is also worth asking, "Is it essential to address all the uncertainties in hydrological forecasting? Without claiming a full answer to this question, it is worth pointing out that this depends on the context and study requirement. This review highlights various classes of uncertainty associated with hydrological forecasting, including input, model parameter, structural, model conceptual, calibration, and validation uncertainty. Besides, the interlink between these uncertainties cannot be neglected. Therefore, estimating a single type of uncertainty may not be suitable in many real case studies. On the other hand, the link between the system's complexity and uncertainty has also been highlighted. This complexity explains the challenge of replication in the hydrological forecast due to large-scale horizon time and emerging and study area constraints and specificities. Because “unknown factors” are the key elements to explore in a way that improves our understanding regarding hydrological process forecast. In this regard, we support Blöschl et al.,2019’s note regarding “the importance of local or regional works to be done effectively for reducing uncertainties in hydrological predictions or forecasting”.

Acknowledgment

This work is partly supported Waterline project which is an EU CHIST-ERA-2019-funded research project under the Grant reference number 344750. The authors would like to acknowledge the funding.

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Tables 6 and 7 are available in the Supplementary Files section

Competing interests:

The authors declare no competing interests.

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An overview of approaches for reducing uncertainties in hydrological forecasting: progress, and challenges

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Abstract

Figures

1. Introduction

2. Method Of Review

3. Relevant Review Papers

3.1 General trends in the analysis

4. Uncertainties In Hydrological Forecasting: An Overview

4.1 Definition of uncertainties in hydrological forecasting

4.2 Impacts of uncertainties on hydrological forecasting

4.3 Uncertainties in hydrological forecasting

4.3.1 Measurements and inputs

4.3.2 Parameter uncertainty

4.3.3 Conceptualization of models

4.3.4 Uncertainties in GCMs

5. How Are Uncertainties Handled In Hydrological Forecasting?

5.1. Stage I: Input preparation and pre-processing

5.2. Stage II: Model conceptualization uncertainty

5.3. Stage III: Calibration and validation strategies

6. Multi-criteria Approach For Reducing The Uncertainties In Hydrological Forecasting

6.1. Multi-objective function and multi-parameter calibration

6.2. Data assimilation contribution

6.3. Multi-conceptual model:

6.4. Pre and post-processing

7. Role Of Remote Sensing Applications In Reducing Uncertainties Of Hydrological Forecasting

8. Criteria For The Model Selections And Reducing Uncertainties In Hydrological Forecasting

9. Conclusions

Declarations

Acknowledgment

References

Tables 6 And 7

Additional Declarations

Supplementary Files

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