4.1 Soil water content and ETc simulation
Figure 1 shows the observed and simulated soil water content plots at different depths (0.2 m, 0.4 m, 0.6 m, 0.8 m, and 1m). The optimized parameters used to match observed and simulated SWC is shown in Table 2, and the model performance indicated by the statistical indices is presented in Table 3. Across the depths, the averaged simulated SWC was higher than the observed. At the start of the simulation, both observed and simulated SWC gradually decreased in response to evaporation and, to a lesser extent, transpiration since the crop is at its developmental stage. Changes in soil water content were also a result of response to rainfall. A 50 mm rain on the June 15 caused soil water content to increase both in the observed and simulated content.
A higher and almost constant soil water content was observed at deeper depths (> 60 cm). This can be explained by management practice and groundwater contribution. In 2011, subsoiling was done prior to the start of the growing season to loosen the soil compaction in the field (Mante et al. 2018). This may have also aided capillary action. Satchithanantham et al. (2014) reported that during a 4-day dry period, groundwater supplied and replenished 96% of the crop ET. As the season progressed, there was a closer match between simulated and observed soil water content at the upper depth (0–40 cm). This corresponds to the depth of the soil layer with the largest root density, given that potato is a shallow root crop with a maximum root depth of about 30–60 cm (Iwama 2008, Allen et al. 1998).
Overall, temporal plots of observed and simulated soil water content and statistical indices (Table 3) during calibration (R2 = 0.85, RMSE = 0.0158 m3/m3, MBE = -0.003, and MAE = 0.0133) and validation (R2 = 0.741, RMSE = 0.0243 m3/m3, MBE = 0.0102, and MAE = 0.0199) were acceptable, although the model performed better during calibration.
Table 2
Optimized soil hydraulic parameters
Depth (m)
|
θr (m3 m− 3)
|
θs (m3 m− 3)
|
α
|
n
|
Ks (m/day)
|
l
|
0–0.4
0.4–0.6
0.6–1.0
1.0–2.5
|
0.069
0.042
0.042
0.040
|
0.40284
0.42075
0.42026
0.42881
|
0.07655
0.02825
0.01670
0.03596
|
1.293
1.576
1.442
1.173
|
1.4627
1.1626
3.0676
3.50
|
0.5
0.5
0.5
0.5
|
Although Hydrus model performance was satisfactory (Table 3), discrepancies between observed and simulated SWC could be due to heterogeneities within the soil profile. In the Hydrus model, Richard’s equation expresses temporal changes in SWC to ET and unsaturated soil hydraulic properties. In the field, soil properties are highly variable in vertical and horizontal directions (Hou et al. 2018, Maheu et al. 2018). Soil hydraulic properties controlling soil water dynamics and redistribution vary from point to point. In this study, the van Genuchten model was selected to determine the soil hydraulic properties and water retention variables (θr, θs, α, n, Ks). Through inverse modelling, observed and simulated soil water content was fitted. Model parameterization is subject to uncertainty which can significantly affect simulation results. Baroni et al. (2011) reported that pedotransfer functions (PTFs) are the most significant source of uncertainty affecting soil water simulations. They found the saturated conductivity (Ks) and alpha (α) parameters caused the highest variability. Similarly, Holländer et al. (2016) reported that n is the most sensitive parameter affecting soil water content simulation results.
Numerous studies have also reported the performance of the HYDRUS model in simulating SWC. For example, Mante and Sri Ranjan (2017) simulated SWC in the same study area for plots under the FDIR treatment. They reported R2 ranging from 0.68–0.89, NSE ranging from 0.75–0.99, PBIAS ranging from − 1.99 to 1.16% and RSR values ranging from 0.33–0.61. Slama et al. (2019) simulated water content over the 0.90 m depth using the HYDRUS-1D model in Tunisia and reported R2 ranging from 0.75–0.93, RMSE ranging from 0.003–0.01 m3/m3. Gabiri et al. (2018) reported R2 ranging from 0.36–0.92, RMSE ranging from 0.02–0.13. Gonzalez et al. 2015 applied the HYDRUS-1D model to simulate soil water content under full and deficit irrigation in Brazil. They reported R2 > 0.92, RMSE < 0.025 and model efficiency of > 89%. These studies confirmed the versatility of the HYDRUS-1D model.
Table 3
Statistical Indices during calibration and validation across the soil profile (0-1m)
Calibration
|
|
|
|
|
Validation
|
|
|
Depth (m)
|
R2
|
RMSE
|
MBE
|
MAE
|
R2
|
RMSE
|
MBE
|
MAE
|
Overall
|
0.8559
|
0.0158
|
-0.0030
|
0.0133
|
0.7413
|
0.0243
|
0.0102
|
0.0199
|
4.2 ETc simulation
Figure 3 shows the plot of simulated cumulative evaporation (108.26 mm), transpiration (242.16 mm), and actual crop evapotranspiration (350.42 mm). Evaporation and transpiration represented 30.9 and 69.1% of the total ETc. Overall, the simulated ETc for potatoes compares well with related studies in the Canadian Prairies and other regions. Mante and Sri Ranjan (2017) reported a crop ET of 356.05 mm in the same study area. Recently, Kumar et al. (2020) reported a cumulative potato ETc of about 400 mm in the humid subtropical climate. Similarly, Ghazouani et al. (2109) applied the HYDRUS-1D to simulate the crop ET for potato under deficit irrigation as 135–175 mm. In the semiarid climate of Tunisia, Mguidiche et al. (2015) reported the total measured crop water use for potato was 277.4 mm while Hou et al. (2018) reported 183 mm in China.
4.3 ETo model impact on SWC simulation
The impact of ETo models on SWC was analysed for the upper layer (20 cm) since it is the depth where observable changes in SWC due to root water extraction, rainfall, and ET is the highest. Figure 4 shows the comparison between observed and simulated water content from the selected ETo models. Figure 4 also showed that all the ETo models followed a similar pattern in simulating SWC, with that all the models overestimating SWC at the start of the growing season. After the June 22 rainfall of 50 mm, a closer match between the observed and simulated SWC from Irmak, Priestly-Taylor, and the FAO PM models while large deviations were observed for the Hargreaves Samani, Romanenko, Penman, and FAO-PM (missing) models. This could be because these models underestimated evaporation and transpiration (ET), leading to less soil water depletion and increased SWC in the profile. T-test results also showed that there was no significant difference between the observed and simulated SWC using Irmak, Priestly-Taylor, and the FAO PM models, while a significant difference (p < 0.05) was recorded for Hargreaves-Samani, Romanenko, Penman, and FAO PM (limiting) models.
Statistical analysis (Table 4) showed that all the models performed relatively well based on the R2 values. However, RMSE and NSE values indicate that only Irmak, Priestly-Taylor, and the FAO PM models are acceptable.
Table 4
Model performance of selected ETo models in comparison to measured soil water content at the 20 cm depth
ETo models
|
R2
|
RMSE
|
MBE
|
MAE
|
NSE
|
Hargreaves- Samani
|
0.88
|
0.049
|
4.53
|
0.0453
|
-0.71
|
Irmak
|
0.92
|
0.0129
|
0.4
|
0.0105
|
0.882
|
Penman
|
0.88
|
0.043
|
4.00
|
0.04
|
-0.327
|
Priestly-Taylor
|
0.92
|
0.0127
|
-0.113
|
0.0106
|
0.89
|
Romanenko
|
0.86
|
0.0552
|
5.11
|
0.0511
|
-1.159
|
FAO PM (missing)
|
0.85
|
0.0577
|
5.33
|
0.0533
|
-1.358
|
FAO PM
|
0.92
|
0.0129
|
0.1
|
0.0107
|
0.883
|
Overall, the results showed that the ETo model could affect soil water dynamics using the HYDRUS model.
4.4 ETc comparison
Figure 5 shows the cumulative daily observed and simulated ETc. Table 5 shows the statistical indices of observed and simulated ETc. Model performance results from ETc comparison followed the same trend as the SWC simulation, with the Irmak, Priestly-Taylor, and the FAO PM models performing satisfactorily (R2 > 0.5). Numerous studies have reported good agreement between observed and simulated results using the FAO PM model in hydrologic modelling studies (Mastrocico et al. 2010, Maranda and Anctil 2015, Tadesse et al. 2019). This justifies why FAO PM model is the globally accepted, recommended, and standard ETo model. This has been attributed to the FAO PM being a physically-based model comprising both energy and aerodynamic factors controlling the ET process (Allen et al. 1998).
The results also showed that despite requiring lesser data compared to the FAO PM, the Irmak and Priestly-Taylor models are viable alternative empirical ETo models for the area. This could be related to the fact that they are radiation-based and the influence of radiation on ET in the study area (Martel et al. 2018, Ndulue et al. 2020). On the other hand, poor performance was recorded for Hargreaves Samani, Romanenko, Penman, and FAO-PM (missing) models based on their statistics indices (Table 5).
In comparison with SWC model performance, we observed decreased model performance. This may be due to the approach used in computing the observed ETc. While observed ETc was calculated using the crop coefficient approach, the HYDRUS model determines the actual crop ETc by reducing the ETo according to the simulated root water uptake and evaporation rates, dependent on the simulated soil water content (Hou et al. 2018). Other studies have compared simulated ETc with ETc obtained from soil water balance or lysimeter (Allen et al. 1998, Utset et al. 2004, Lopez-Urrea et al. 2006, Gervais et al. 2010).
Table 5
Models
|
R2
|
RMSE (mm/day)
|
MBE (%)
|
MAE
|
NSE
|
p-value
|
Hargreaves Samani
|
0.55
|
2.37
|
-179.7
|
1.82
|
-0.75
|
< 0.0000*
|
Priestly-Taylor
|
0.59
|
1.15
|
0.38
|
0.94
|
0.58
|
0.9853NS
|
Irmak
|
0.61
|
1.18
|
-7.78
|
1.01
|
0.57
|
0.691 NS
|
Penman
|
0.29
|
2.10
|
-143.3
|
1.65
|
-038
|
< 0.0000*
|
Romanenko
|
0.22
|
2.27
|
-209.6
|
2.13
|
-1.22
|
< 0.0000*
|
FAO Limiting
|
0.38
|
2.84
|
-227.3
|
2.29
|
-1.51
|
< 0.0000*
|
FAO PM
|
0.57
|
1.18
|
4.46
|
0.98
|
0.57
|
0.8262NS
|
*significantly different, NS Non-significant |
The t-test results also showed that the Hargreaves Samani, Romanenko, Penman, and FAO-PM (missing data) are statistically different from the observed ETc while ETc derived from Irmak, Priestly-Taylor, and the FAO PM models are not significantly different from the observed ETc.
Our results agree with Utset et al. 2003, Xing et al. 2008, Tadesse et al. 2019, Akumaga and Alderman (2019). A simulation study using the SWAP model, Utset et al. (2003) found no significant difference between the Priestly – Taylor model and the FAO PM. Similarly, Xing et al. (2008) found out that there was an insignificant difference between the Priestly – Taylor model and the FAO PM despite requiring fewer inputs, while Martel et al. (2018) reported that the Turc and Priestly-Taylor models performed well in estimating ETc, ranking first and third, respectively, with an NSE > 0.7 for both models. On the other hand, our result disagrees with Oudin et al. (2005), Wang et al. (2006). They reported that simple temperature-based models such as Hargreaves Samani gave similar results as the complex FAO PM model. This has been attributed to model parameter calibration, which can fit observed and simulated (Paturel et al. 1995, Bia et al. 2016).