Increasing Sensitivity of Winter Wheat Yield to Snow Drought

doi:10.21203/rs.3.rs-4937390/v1

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Increasing Sensitivity of Winter Wheat Yield to Snow Drought

https://doi.org/10.21203/rs.3.rs-4937390/v1

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The global crop ecosystem is critically dependent on snow availability, which has diminished in numerous snow-dependent regions due to increasing snow droughts associated with warmer winters. However, our understanding of crop yield sensitivity to snow droughts and how this sensitivity evolves remains limited. In this study, we find that from 1960 to 2020, approximately 51% of winter wheat croplands have experienced a significant increase (5.3−6.7% per year) in the frequency of snow droughts. To assess the sensitivity of winter wheat yield to snow droughts, we utilized explainable machine learning, gridded yield datasets, and the standardized snow water equivalent index (SWEI) from 1982 to 2016. Our findings reveal a positive association between yield anomalies and SWEI under snow drought conditions and a significant increase in the sensitivity of yield to SWEI over 24% of Northern Hemisphere winter wheat croplands. Additionally, enhanced accumulation of growing degree days, increased vapor pressure deficit (VPD), a slight decrease in total precipitation, and increased heavy rainfall are identified as dominant factors amplifying yield sensitivity to snow droughts. These findings highlight an increasing vulnerability of crop systems to snow droughts over the past three decades, which is crucial for informing risk management and adaptation of agriculture to a warming future with less snow.

Earth and environmental sciences/Climate sciences/Climate change/Climate-change impacts

Earth and environmental sciences/Hydrology

Snowpack provides critical water resources to human societies and ecosystems^1,2, playing a key role in sustaining overwintering crop production^3–6. Recent observations have highlighted an increasing shift in cold-season precipitation from snow to rain², resulting in a decrease in snowpack⁷. This shift has garnered significant attention from researchers, practitioners, and policymakers, particularly in regions experiencing extremely low snowpack^7–10. A notable instance was the winter of 2014/15 when the western United States experienced widespread record-low snowpack, a phenomenon referred to as a snow drought^7,10. The economic impact of this drought in California alone was estimated at $2.7 billion¹¹. Moreover, the subsequent winter of 2020/21 further underscored the region’s vulnerability to snow drought, exacerbating the existing 2020 warm-season drought¹². Similar events have been observed in many countries around the world. Afghanistan faced a snow drought in the winter of 2017/18, contributing to crop failures and food insecurity for over 10.6 million people¹³. European countries have also experienced snow droughts^14,15. These cases highlight the global threat posed by snow droughts to food security¹⁶.

Snow droughts pose a triple threat to overwintering crop production, including a reduction in the insulation of soil and early vegetation^5,17, a reduction in the amount of snowmelt runoff^9,18 for irrigation^3,19, and an increase in the risk of agricultural droughts in the following warm-seasons⁸. Field studies and model simulations have shown that decreased snow cover might compromise the insulation of crops like winter wheat against frost and freeze^5,7,20, particularly during ear emergence and early crop growth²¹. Moreover, lower snowmelt rate may reduce meltwater to croplands, leading to insufficient agricultural water for later crop growth^4,18,22, especially in regions like the western United States where agricultural water availability relies heavily on snowmelt^7,8. Furthermore, earlier snowmelt during the winter and early spring may exacerbate the challenges of hotter and drier summers due to the absence of snowmelt runoff^18,19,22. There is strong theoretical, model-based, and empirical evidence that snow droughts will increase in a warming climate^9,23,24. However, no global studies have comprehensively analyzed the risk to overwintering crop yield from snow droughts, even though the dependence of crop production on snowmelt has long been recognized as a key climate change risk^16,25,26.

Winter wheat, a particularly snow-dependent crop³, is the major cereal crop grown globally. In this study, we first investigate the hotspots and trends of snow drought across winter wheat croplands during the period of 1960–2020, based on the standardized snow water equivalent index (SWEI) obtained from the ERA5-Land and GLDAS datasets. Additionally, we examine the sensitivity of winter wheat yield to SWEI and changes in yield sensitivity to SWEI for the period of 1982–2016. We also explore the underlying mechanisms behind the increasing sensitivity of yield to SWEI. Our findings highlight an increasing risk of snow drought across winter wheat croplands and significantly increasing the sensitivity of winter wheat yield to snow drought during the last three decades, a fact not underscored by existing research works.

Hotspots and trends of snow drought across winter wheat croplands

Before assessing the impact of snow droughts on crop yields, we examined changes in the frequency of snow droughts across winter wheat croplands. The standardized snow water equivalent index (SWEI) was estimated using a 3-month sum of daily snow water equivalent (SWE) for the months of January, February, and March, providing a reliable approximation of annual snowpack dynamics⁷. Snow drought was defined as the SWEI values below − 0.8⁷ (or below − 1). The frequency was calculated based on the 10-year blocks (or 15-year blocks) (See Section Methods: Identification of snow drought).

We identified spatial patterns of snow drought frequency across the Northern Hemisphere's winter wheat croplands (Fig. 1a), highlighting frequent occurrences in the United States, Europe, Central Asia, and Eastern Asia, with peaks at 3–4 events per decade. Between 1960 and 2020, snow drought frequency shows a significant increase (5.3–6.7% events per year, P < 0.05) across the United States, Europe, Central Asia, and Eastern Asia (Fig. 1b-1e). Therefore, our study focused on these four crucial wheat-producing and snow-dependent regions, collectively accounting for 77% of the total winter wheat yield globally from 1982 to 2016. Any major winter wheat yield loss in these regions could significantly affect global food trade and food security²⁷. Additionally, proportions of croplands exposed to snow drought show a significant increasing trend (P < 0.001) across the Northern Hemisphere, the United States, Europe, Central Asia, and Eastern Asia (Fig. 1f). This proportion rose from approximately 46–54% during the period of 1960–1970 to about 70–99% during the period of 2010–2020 (Fig. 1f). Overall, approximately 51% of winter wheat croplands show a significant upward trend in snow drought frequency (Fig. 1g). The results show a consistent trend for the alternative GLDAS dataset (Fig. 1g and Supplementary Fig. S1). We also conducted analyses using different thresholds of SWEI (Supplementary Fig. S2) and different sizes of moving blocks (Supplementary Fig. S3) to verify the robustness of the observed increases in snow drought frequency.

The western United States, identified as particularly susceptible to snow droughts, experienced remarkable snow drought events from the winter of 2014/15 (Supplementary Fig. S4). Consequently, winter wheat yields were severely impacted by snow drought in the summer of 2015 (Supplementary Fig. S4d), resulting in a loss of $810 million in crop revenue and over 17,100 jobs in California¹¹. The analysis of snow drought frequency over winter wheat croplands provides crucial insights into the impacts of a warming climate on food stability. This observed increase in snow drought frequency aligns with previous findings^7,15,23 and presents an additional layer of complexity that must be considered in the influences of snow droughts on agriculture systems.

Sensitivity of winter wheat yield to standardized snow water equivalent index (SWEI)

To evaluate impacts of snow anomalies on winter wheat yield variability, convergent cross mapping (CCM)²⁸ was constructed to study climate-crop causal mechanisms. CCM is a powerful tool for conducting the causal inference between winter wheat yield and SWEI, as it accounts for the influences of other factors in complex ecosystems²⁹. Our results (Supplementary Fig. S5) reveal that the skill level in cross mapping from winter wheat yield to SWEI (with a Pearson correlation coefficient (ρ) of 0.31– statistically insignificant) is much lower than that from SWEI to winter wheat yield (ρ = 0.51, statistically significant with P < 0.001). This finding suggests that snow anomalies contribute to yield anomalies in winter wheat production.

To better understand the impact of snow drought on crop yield, we developed an explainable machine learning model (SHapley Additive exPlanations; SHAP)³⁰ using random forests (Supplementary Fig. S6). This approach enabled us to separate the contribution of SWEI to winter wheat yield anomalies from the influence of other climate extremes (Supplementary Table S3). Specifically, we excluded (1) non-snow croplands and grid cells where (2) the random forest model did not perform well (cross-validation out-of-bag score, OOB R² < 0) due to limited crop activities or substantial human management. The partial dependence plots (Fig. 2a) highlight the positive sensitivity of winter wheat yields to SWEI, corresponding to snow drought occurrences (SWEI ≤ ‒0.8). In other words, when SWEI values fall below ‒0.8, the results suggest that lower SWEI (severe snow drought) might lead to higher yield losses, such as in the United States, Europe, and Central Asia (Fig. 2c-2e). This implies that decreasing snowpack plays a critical role in inhibiting wheat growth by increasing the risk of spring frost³¹, drying agricultural soil water²³, and reducing irrigation^3,4,19.

We conducted a comprehensive analysis of the overall sensitivity of winter wheat yield to SWEI from 1982 to 2016 (Methods: Overall sensitivity of winter wheat yield to SWEI). The significantly (P < 0.05) positive sensitivity indicates that decreases in SWEI suppress winter wheat yield. Figure 2b shows that the area fraction of croplands with positive overall sensitivity is higher than those with negative overall sensitivity over United States. Overall, approximately 37% of the Northern Hemisphere croplands experienced a significantly (P < 0.05) adverse impact from snow droughts, primarily concentrated in the western United States (46%), western and northern Europe (36%), Central Asia (21%), and the Huai-Hai River Basin in China (18%). The yield effects of lower SWEI highlight the significant impact of snow drought stress, with extreme heat and declining precipitation being particularly influential^22,32. However, in some croplands, the observed negative sensitivity indicates that decreased SWEI tends to benefit winter wheat yield, potentially due to the decreased risk of damage from snow molds³³. In addition, other factors (i.e., temperature and radiation) likely contribute to the negative yield sensitivity to SWEI. Energy-related variables have been identified as main controls on winter wheat croplands³⁴, and agricultural water supply relies heavily on alternative water resources^3,19.

The model’s performance was estimated by cross-validation out-of-bag score (OOB R²), indicating that 52%‒71% of the variation in winter wheat yields can be explained by climate extremes variations in United States, Europe, and Eastern Asia. In Central Asia, 22% of the yield variation can be explained by these climate factors (Supplementary Fig. S7). The overall sensitivity analysis was also tested with untransformed climate extreme indices in their original units (Supplementary Table S3) to directly interpret impacts. Widespread croplands exhibit higher R² values (Supplementary Fig. S7) and stronger sensitivity values (Supplementary Fig. S8) based on de-trended climate extreme indices compared to the original climate extreme indices, excluding Central Asia. Additionally, the results of March-April-May (MAM) SWEI and January-February-March (JFM) SWEI show agreements in their spatial patterns (Supplementary Fig. S9). These proportions differ slightly for MAM SWEI with absence of values over the southern United States due to earlier snowmelt in lower latitudes.

Increasing sensitivity of winter wheat yield to SWEI

To conduct an assessment of the temporal variation in snow drought effects, we performed an analysis of the sensitivity of yield to SWEI by 10-year blocks, spanning from 1982 to 2016. In this analysis, we focused solely on snow-affected croplands exhibiting a significant (P < 0.1) overall sensitivity of yield to SWEI, aiming to minimize the influence of other factors. Consequently, these sensitivity values fluctuated across the moving blocks time series, with slopes estimated via the Theil-sen regression. These changing sensitivities over time were represented as the trend in sensitivity ($\:{T}_{sen}$; Methods: trends of sensitivity of winter wheat yield to SWEI; Supplementary Fig. S6). We categorized an increasing trend in the sensitivity of yield to SWEI ($\:{T}_{sen+}$) as those sensitivity values that exhibit a significant (P < 0.05) increase from the initial moving window (e.g., 1982–1992) to the final one (e.g., 2006–2016), representing more pronounced impacts of snow droughts on yields. Similarly, a decreasing trend in the sensitivity of yield to SWEI ($\:{T}_{sen-}$) was defined by sensitivity values showing a significant decrease, suggesting reduced impacts from snow droughts.

During the period of from 1982 to 2016 in the Northern Hemisphere croplands, we observed a significant increase in $\:{T}_{sen}$ (slope = 0.019 t ha^‒1 mm^‒1 year^‒1, P < 0.001; Fig. 3a). The sensitivity increased from ‒0.45 ± 1.11 to 0.1 ± 1.24 t ha^‒1 mm^‒1 from the initial to the final moving window. We also observed escalating $\:{T}_{sen}$ over four key winter wheat-producing regions (Fig. 3c-3f), with a slope of 0.022 (P < 0.001) for United States’ croplands, a slope of 0.009 (P > 0.1) for Europe’s croplands, a slope of 0.029 (P < 0.001) for Central Asia’s croplands, and a slope of 0.044 (P < 0.001) for Eastern Asia’s croplands. Across the Northern Hemisphere croplands, the proportions for $\:{T}_{sen+}$ and $\:{T}_{sen-}$ were 24% and 11%, respectively. This indicates a prevalence of croplands with increasing sensitivity over those with decreasing sensitivity. Specifically, the proportions for $\:{T}_{sen+}$ and $\:{T}_{sen-}$ were 29% and 11% across the United States. Overall, a significant increase in yield sensitivity to SWEI was found in approximately 24% of winter wheat croplands, primarily concentrated across western and southern United States, western and southeastern Europe, Central Asia, and northern China (Fig. 3g-3j).

We validated the robustness of our results through (1) testing different thresholds of OOB R², which represent the performance of random forest models (Supplementary Fig. S10), (2) repeating the analysis with 15-year blocks (Supplementary Fig. S11), (3) testing different grid sizes (3×3 and 5×5) (Supplementary Fig. S12), and (4) repeating the analysis with an alternative GLDAS dataset (Supplementary Fig. S13). In all these cases, we found similar results. Moreover, the analysis also conducted on the county-level over United States winter wheat croplands based on observational county-level crop yield dataset (USDA NASS database)³⁵. The results with county-level winter wheat yield data were consistent (Supplementary Fig. S14 and Supplementary Fig. S15). Overall, our findings from two independent snow datasets and two winter wheat yield datasets suggest an increased impact of snow droughts on wheat yields over the past three decades in the key winter wheat-producing regions.

Attribution of $\:{\varvec{T}}_{\varvec{s}\varvec{e}\varvec{n}}$

We conducted an attribution analysis (Methods: Attribution analysis) to understand the changes in $\:{T}_{sen}$, which can be explained by trends of relevant hydro-climatic variables across the winter wheat growing season (Supplementary Table S1), including air temperature, rainfall, vapor pressure deficit (VPD), soil moisture, climate extreme indices (Supplementary Table S3), and snow droughts. Our findings suggest that these factors in the attribution analysis collectively explain over 71% of the spatial variability in $\:{T}_{sen}$ (Supplementary Fig. S16). Specifically, we identified strong relationships between observed spatial patterns of $\:{T}_{sen}$ and trends in (1) accumulation of growing degree days (GDD), (2) average growing-season VPD, (3) total growing-season precipitation, and (4) heavy rainfall (Max. 5D Rain).

We categorized the regions with significantly (P < 0.05) enhanced and weakened yield sensitivity, denoted as $\:{T}_{sen+}$ and $\:{T}_{sen-}$, respectively (Fig. 4). Both groups experienced comparable warming of 0.17 ± 0.08°C per decade and benefited from increased GDD over the recent three decades (Supplementary Fig. S17). However, areas with $\:{T}_{sen+}$ exhibited significantly greater VPD trends compared to $\:{T}_{sen-}$ regions (Fig. 4b), suggesting that intensified VPD trends contribute to increasing snow drought effects. These results align with previous studies indicating a significant relationship between VPD and vegetation drought^35,36, as well as the non-linear response of VPD to higher heat stress³⁶ due to the increases in plant water demand³⁷. Furthermore, small decreases in total precipitation (Fig. 4c) and enhanced heavy rainfall (Max. 5D Rain; Fig. 4d) may trigger drastic changes in $\:{T}_{sen}$, reflecting a non-linear crop water response³². Our results also suggest that deeper soil moisture generally cannot compensate for precipitation decreases to affect $\:{T}_{sen}$. Although the root-zone soil moisture trends also play a role in $\:{T}_{sen}$ (Supplementary Fig. S16), they are less prominent than rainfall trends³⁸.

Additionally, we identified the key drivers of the increasing $\:{T}_{sen}$ detected across the United States and Europe. Despite the increased GDD (Supplementary Fig. S17c), winter and spring freezing (FDD) stress and heat stress (EDD) emerged as the most relevant controls of spatial variations in $\:{T}_{sen}$ across the United States’ croplands (Supplementary Fig. S18). Conversely, enhanced spring heat stress (EDD) effects on $\:{T}_{sen}$ were stronger in Europe’s croplands (Supplementary Fig. S19).

To evaluate the implications of snow droughts for crop yields under warming conditions, we utilized explainable machine learning, which can effectively isolate the impact of snow drought on winter wheat yield from other relevant drivers, transcending purely correlation-based analyses. Our findings reveal a significant increase in the sensitivity of yield to SWEI during 1982‒2016, primarily attributable to intensified heat stress (i.e., VPD) and dramatic fluctuations in water supply (i.e., slight decrease in total precipitation and enhanced heavy rainfall). This underscores the importance of jointly considering snow variation and across-season cropping systems to comprehend changes in the crop-snow interplay. Generally, the observed increase in wheat yield sensitivity to snow drought highlights heightened ecosystem vulnerability to a low-to-no snow future³⁹. By pinpointing regions of pronounced and escalating yield sensitivity, our study identifies the hotspot areas where rising snow drought trends could lead to more severe impacts on overwintering crop yields.

Snow droughts may interact with crop systems, potentially yielding both positive and adverse effects. On one hand, snow drought occurrences may benefit crop yield by hastening growth stages and extending the growing season, thereby enhancing productivity⁴⁰. Moreover, the impacts of snow droughts might be tempered by the migration of croplands over time and space, as warming conditions could open up new agriculturally suitable areas⁴¹. Additionally, expansion of irrigation may alleviate crop yield sensitivity⁴². On the other hand, snow droughts can detrimentally affect crop yield by altering soil microenvironments³³ and increasing the risk of freezing damage to early crops^5,31,40. Furthermore, snow droughts are expected to intensify in a warming future, exacerbating the risk of water scarcity in many snow-dependent croplands³, necessitating alternative sources of agricultural water¹⁹.

Several limitations of our study should be acknowledged. First, while we focus on winter wheat across the Northern Hemisphere as a snow-dominated cultivated crop, insights from other crops and regions could provide valuable ecological perspectives and enhance the generalizability of our findings. Second, although our analysis spans the full growing season and winter months (January-February-March), future work could explore the importance of early snowmelt triggered by snow droughts, particularly concerning crop growth phases and springtime variations in root-zone soil moisture. Third, interactive effects of extreme heat⁶, heavy rainfall⁴³, spring frosts³¹, and soil droughts³² warrant further investigation. Finally, other factors such as hail and wind, pests and disease³³, groundwater, and irrigation systems⁴², even though not included in our analysis due to spatial resolution constraints, likely contribute to or mediate yield responses, potentially explaining regional variations.

Linking snow drought information to agriculture systems holds particular significance in crop-producing countries, where the impacts of snow drought can propagate globally through trade networks and exacerbate food insecurity¹⁶. Snow exhibits significant sensitivity to different levels of future warming^44–46. For this reason, snow droughts are projected to become increasingly frequent⁸ due to warming winters, with escalating impacts on crop growth (Fig .3). However, these impacts may not be uniform across all regions, with some croplands experiencing significant water availability implications while others remain relatively unaffected. Understanding differential vulnerabilities and managing them is crucial for comprehending the implications of snow droughts on crop production. Such insights, informed by comprehensive analyses that consider all sources of uncertainty, including datasets and definition choices, are essential for developing efficient and effective adaptations to a less snowy future. Assessing the influences of snow droughts on crop systems represents a critical step toward informed decision-making and resource management in agriculture.

Data

Yield data

To estimate the crop exposure to snow droughts, we used the Global Dataset of Historical Yield (GDHY)⁴⁷ for winter wheat yields, assessing its sensitivity to snow drought. The GDHY dataset provides gridded winter wheat yields for the period of 1982–2016, with a spatial resolution of 0.5°. It is grounded in the crop calendar⁴⁸, which provides relatively accurate planting and harvesting dates for each winter wheat cultivation globally, at a 0.5° spatial resolution. Comprising agricultural census statistics and satellite remote sensing, the GDHY dataset has been widely used as a primary source in recent global crop-climate studies^49–52. In addition, to enhance the robustness of the sensitivity of winter wheat yield to snow droughts, we also used an alternative winter wheat yield dataset at county-level obtained from the USDA NASS QuickStats³⁵ for the period of 1980–2018 (Supplementary Fig. S14 and Supplementary Fig. S15).

Climate data

Climate data, including hourly 2-m air temperatures (°C), daily precipitation (mm), and monthly vapor pressure deficit (VPD; hPa) computed from dew point temperature (°C), were obtained from the ERA5-Land dataset from 1960 to 2020. ERA5-Land is a global atmospheric reanalysis product produced by the European Centre for Medium-Range Weather Forecasts (ECMWF)⁵³. The center has recently made substantial improvements in data accuracy, enhancing its applicability to various land surface applications. Daily root-zone soil moisture was obtained from the Global Land Evaporation Amsterdam Model (GLEAM) dataset⁵⁴. The GLEAM datasets are observationally constrained and have been widely used to analyze global and regional soil moisture changes⁵⁵.

To assess the impacts of extreme heat stress, extreme freezing stress, dry stress, and heavy rainfall on wheat yields during snow drought conditions, we analyzed climate extreme events across growing seasons (fall, winter, and spring) due to their adverse impacts on winter wheat growth⁵⁶. We calculated the cumulative exposures to growing degree days between the base and optimum growth temperature thresholds (GDD, ℃d, Eq. (1)), extreme growing degree days (EDD, ℃d, Eq. (2)) above the optimum growing temperature thresholds, and freezing growing degree days (FDD, ℃d, Eq. (3)) below the freezing growing temperature thresholds over the winter wheat growing season. GDDs, EDDs and FDDs are calculated using the following formulas⁵⁷:

$$\:\text{G}\text{D}\text{D}=\sum\:_{h=1}^{N}{DD}_{h};\:{DD}_{h}=\:\left\{\begin{array}{c}\frac{{T}_{opt}-{T}_{base}}{24},\:\:{T}_{h\:}>\:{T}_{opt}\:\:\\\:\frac{{T}_{h}-{T}_{base}}{24},{\:{T}_{base}\le\:T}_{h\:}\le\:\:{T}_{opt}\\\:0,{T}_{h\:}<\:{T}_{base}\end{array}\right.$$

$$\:\text{E}\text{D}\text{D}=\sum\:_{h=1}^{N}{DD}_{h};\:{DD}_{h}=\:\left\{\begin{array}{c}0,{\:\:\:\:\:\:\:\:\:T}_{h\:}\le\:\:{T}_{opt}\:\\\:\frac{{T}_{h}-{T}_{opt}}{24},\:{T}_{h\:}>\:{T}_{opt}\end{array}\right.$$

$$\:\text{F}\text{D}\text{D}=\sum\:_{h=1}^{N}{DD}_{h};\:{DD}_{h}=\:\left\{\begin{array}{c}0,{\:\:\:\:\:\:\:\:\:\:\:\:\:\:T}_{h\:}>\:{T}_{frez}\:\\\:\frac{{T}_{frez}-{T}_{h}}{24},\:{T}_{h\:}\le\:\:{T}_{frez}\end{array}\right.$$

Where hourly temperature ($\:{T}_{h\:}$) was obtained from the ERA5-Land and GLDAS datasets, respectively. $\:{T}_{base}$ and $\:{T}_{opt}$ are the base and optimum growing temperature thresholds specific to each growing phase of wheat (Supplementary Table S2). $\:{T}_{frez}$ is the temperature causes freeze injury (Supplementary Table S2).

In addition to snow effect, rainfall act as an important water supply to affect winter wheat growth. In this study, precipitation was partitioned into rainfall and snow to represent water supply in different forms on the basis of daily temperature using the following empirical model:

$$\:\text{R}\text{a}\text{i}\text{n}\text{f}\text{a}\text{l}\text{l}\:=\left\{\begin{array}{c}Pre,\:\:{T}_{d}\:>\:{T}_{rain}\\\:Pre\left(\frac{{T}_{a}-{T}_{snow}}{{T}_{rain}-{T}_{snow}}\right),\:\:{{T}_{rain}\ge\:T}_{d}\ge\:{T}_{snow}\\\:0,\:\:{T}_{d}\le\:{T}_{snow}\:\:\:\:\:\end{array}\right.$$

Where Pre is daily precipitation (mm) and $\:{T}_{d}$ is average daily air temperature (℃). Partitioning thresholds $\:{T}_{rain}$ and $\:{T}_{snow}$ are 3.0 and $\:-$1.0 ℃, respectively^5,58. To estimate the effects on winter wheat yields due to specific rainfall extremes, we used two extreme rainfall indices (DrySpell and Max.5D Rain)⁵⁹ to represent the effect of rainfall deficit and excess on crop yields. The DrySpell (days) is defined as the maximum number of consecutive days with no rainfall in each season. The Max.5D Rain (mm) is defined as the maximum accumulative rainfall in a five-day period in each season.

Snow data

We identified snow droughts using two datasets: ERA5-Land⁵³ and GLDAS⁶⁰. The choice to use these reanalysis datasets is due to their inclusion of essential snow variables (snow depth and snow depth water equivalent) with global winter wheat croplands at the daily timescale, enabling a comprehensive and uniform analysis across different regions and across-season periods². More importantly, the daily snow water equivalent of ERA5-Land agrees better with station observations compared with other datasets, making it an ideal dataset to characterize snow droughts^23,61. We used the ERA5-Land dataset for our main analysis, and assessed the sensitivity of our results with the alternative GLDAS dataset.

Identification of snow drought

We calculated daily snow water equivalent (SWE; mm) from 1 October to 31 May for the entire water year 1948–2022, using a 7-day moving window⁹. We then restricted the analysis to winter wheat croplands in the Northern Hemisphere during the winter season, particularly for January-February-March (JFM) accumulations of daily SWE, to compute the standardized SWE index (SWEI). This is because the date of 1 April is commonly used in water supply management to distinguish winter snow accumulations and spring snowmelt, representing as a proxy for the date of maximum annual SWE^8,22,62.

We calculated the SWEI at the yearly scale, choosing the 1961‒1990 as a reference baseline, by fitting a Gamma distribution for each year of snow dynamics, at each grid cell. The SWEI thus provides a comprehensive measure of snow balance over consecutive years, facilitating active monitoring of snow droughts (e.g., SWE on April 1; Supplementary Fig. S4). The SWEI is also useful for finer-scale analyses of crop-snow response corresponding to the occurrence of snow droughts⁸. Here, snow drought is defined as the SWEI values below − 0.8^7,63.

Trends of snow drought frequency

Grid cells with SWEI ≤ − 0.8 (or SWEI ≤ − 1 in Supplementary Fig. S2) are defined as snow drought-affected croplands, indicating potential impacts on crop growth due to snow deficits. To address temporal variations of snow drought frequency across winter wheat croplands, we split the data from the entire 1960‒2020 period into 50 10-year blocks (1960‒1970, 1961‒1971 … 2010‒2020). We identified the frequency of snow droughts independently by 3 × 3 data points if more than 50 data points were included. We defined the slope of trends in snow drought frequency estimated from the Theil-sen regression. We then used the Mann-Kendall’s test⁶⁴ to detect the statistical significance of the trend in snow drought frequency (Fig. 1), which did not require data with a normal distribution. To ensure the robustness of the 10-year blocks, we also assessed trends of snow drought frequency in 15-year blocks and found no significant differences (Supplementary Fig. S3).

Data pre-processing

The SWE, snow depth, soil moisture, VPD, precipitation, and temperature data, obtained from ERA5-Land, GLDAS, and GLEAM datasets, were re-gridded to the same resolution of 0.5° × 0.5° using the bilinear interpolation. In all experiments and for all hydro-climatic variables, we selected growing-season data based on the crop calendar dataset⁴⁸ for temporal consistency. The winter wheat growing season, defined as the number of days between the planting date and harvesting date, remains consistent within each growth cycle from 1982 to 2016. We aggregated the daily energy-related (i.e., VPD and temperature) values to growing-season averages and the daily water-related (i.e., soil moisture and rainfall) values to growing-season sums. Daily SWE data were aggregated using 3-month (JFM) sum to calculate yearly SWEI to match yearly yield data. Climate extreme indices of GDD, EDD, FDD, DrySpell, and Max.5D Rain were calculated in fall, winter, and spring, respectively (Supplementary Table S3). We restricted the analysis to winter wheat croplands in the Northern Hemisphere.

Seasonality and long-term trends were removed to obtain the anomaly of every single yield and climate extremes indices by subtracting the long-term mean monthly signals and by subtracting a locally weighted scatterplot smoothing regression (LOESS) with a smoothing span of 0.3, respectively. LOESS is one of well-known de-trending methods for studying crop-climate interactions to remove the long-term effect of technological improvements^27,49,51. In this way, we excluded long-term trends derived by changes in the equilibrium state, such as long-term successional cycles and human frequent management. We also excluded regions without snow-affected winter wheat croplands and focus specifically on the short-term crop yield responses to snow anomalies.

Detection of causal relationships between winter wheat yields and snow droughts

Convergent cross mapping (CCM) is a powerful method that can help distinguish causality from spurious correlation in time series of non-linear dynamical systems^28,55. In CCM, causality is detected by measuring the extent to which the sign of the affected variable Y (e.g., yield anomalies) reliably estimates the states of a causal variable X (e.g., SWEI). That is, if variable SWEI is influencing winter wheat yield, then, based on the generalized Takens’ theorem^28,65, the causal variable SWEI can be recovered from the historical record of the affected variable yields. The skill of cross mapping is defined as the coefficient (ρ) of the Pearson correlation between predictions and observations of SWEI. If the ρ increases with the length of time series and convergence is present, then the causal effect of SWEI on yields can be inferred²⁹.

Overall sensitivity of winter wheat yield to SWEI

Wheat yields are affected not only by snow droughts, but also by the occurrence of soil droughts, freezing stress, spring frosts, and severe heats^6,31,66. To examine the sensitivity of winter wheat yield to snow anomalies, we first trained random forest models and then employed explainable machine learning (SHapley Additive exPlanations; SHAP) to isolate the contribution of SWEI to yield anomalies from the influence of other climate extremes stress (Supplementary Fig. S6). Random forest⁶⁷ is one of the data-driven models based on a bootstrap aggregating strategy for improving the stability of model results, and it requires no statistical assumptions on predictors and target variables, given sufficient data. SHAP ³⁰ is a game theoretic approach to explain the outputs of the random forest model by accounting for contributions of individual variables to the overall prediction. We treated the yield anomaly as the target variable and corresponding season climate extreme indices, including season anomalies of GDD, EDD, FDD, DrySpell, and Max.5D Rain, as well as SWEI are the predictors.

We collected all predictors and target data during 1982‒2016 from one grid cell and the surrounding grid cells (3×3 shape) to train a model if more than 50 data points were included. We removed grid cells that model performance worse than the mean of training data itself using OOB R² < 0⁶⁸. Generally, 22%‒71% of the yield variability can be explained by relevant climate extremes variability (Supplementary Fig. S7).

For each trained model, we employed the SHAP dependence method to isolate the marginal contributions of SWEI on the yield anomaly. We defined the overall sensitivity as the slope estimated from the Theil-sen regression between SHAP dependence for yield and SWEI, by assuming that the grid cell-level interaction between yield anomaly and SWEI is nearly linear. It is important to note that because sensitivity is inferred through linear regression, it may not capture the entirety of the interactions between yield and SWEI for each grid cell. This method combines the benefits of bootstrap aggregating and non-distribution assumption through random forest modeling, as well as the advantages of global interpretations being consistent with the local explanations in the SHAP algorithm, hence strengthening the robustness of the results than using traditional statistical methods⁶⁸.

Trends of sensitivity of winter wheat yield to SWEI

Grid cells with non-significant (P ≥ 0.1) overall sensitivities are defined as non-snow controlled regions, meaning that energy-related variables such as temperature, radiation, and VPD could dominantly control crop growth, and the detected dependence on water is likely due to other alternative agriculture water. Therefore, we excluded non-significant grid cells (P ≥ 0.1) for studying changes in crop-snow relationships. To address temporal variations in winter wheat yield sensitivity to SWEI, we split the data from the entire 1982‒2016 period into 25 10-year blocks (1982‒1992, 1983‒1993…2006‒2016). We independently trained random forests models again for each 3 × 3 data point if more than 25 data points were included, inferring temporal sensitivity through the SHAP and Theil-sen regression, assuming that the grid cell-level interaction between yield and SWEI within 10-year blocks was nearly linear (Supplementary Fig. S6).

We excluded grid cells with OOB R² < 0 and increasing thresholds of OOB R² did not affect our main conclusions (Supplementary Fig. S10). We also used the Mann-Kendall’s test to detect the statistical significance of the trend in yield sensitivity to SWEI ($\:{T}_{sen}$). To confirm the 10-year split would not bias results, we examined the $\:{T}_{sen}$ using 15-year blocks and found no significant differences (Supplementary Fig. S11). To confirm the 3×3 split does not bias results, we tested the $\:{T}_{sen}$ based on 5×5 data point and found similar results (Supplementary Fig. S12).

Attribution analysis

To understand changes in $\:{T}_{sen}$, we used random forests and the SHAP attribution method to predict the $\:{T}_{sen}$. We treated the $\:{T}_{sen}$ as the target variable, and multiple relevant hydro-climatic trends (i.e., GDD, EDD, FDD, DrySpell, and Max.5D Rain, total precipitation, VPD, and soil moisture) and snow drought frequency as predictors to train a random forest model^68,69.

Then we employed SHAP values to quantify marginal contributions of each single factor trends on $\:{T}_{sen}$ and then rank the variable importance by the sum of absolute contributions across all grid cells. We ensured that the model performed effectively by maintaining a cross-validation out-of-bag R² higher than 0.5^67,69. After identifying the dominant factors for $\:{T}_{sen}$ (Supplementary Fig. S16), we presented the combined impact from the top four important factors which were GDD trends, VPD trends, total precipitation trends, and Max.5D Rain trends to elucidate potential mechanisms across winter wheat croplands (Fig. 4).

Data availability

All data used in this study are publicly available. The Crop Calendarand the Global Dataset of Historical Yield of winter wheat yields are accessible through https://sage.nelson.wisc.edu/data-and-models/datasets/crop-calendar-dataset/ and https://doi.org/10.1594/PANGAEA.909132. Yearly county-level winter wheat yields are obtained from USDA NASS QuickStats (https://quickstats.nass.usda.gov/). Hourly 2-m air temperatures, daily precipitation, and dew point temperature were obtained from ERA5-Land reanalysis datasets https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-land?tab=overview. The daily snow depth water equivalent and snow depth were obtained from the ERA5-Land reanalysis datasets https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-land?tab=overview and the GLDAS Catchment Land Surface Model L4.0 https://disc.gsfc.nasa.gov/datasets/GLDAS_CLSM025_D_2.0/summary?keywords=GLDAS . Daily root-zone soil moisture was obtained from the Global Land Evaporation Amsterdam Model (GLEAM) dataset https://www.gleam.eu/. The datasets used to reproduce the methods and findings of this study are available at https://zenodo.org/records/10781059.

Code availability

The code used for this study is available at https://zenodo.org/records/10781059.

Acknowledgements

The work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU/RGC 15232023) and the Hong Kong Polytechnic University (Project No. P0052737).

Author contributions

H.C. and S.W. designed the study. H.C. carried out the analysis and drafted the manuscript. S.W. supervised the analysis and contributed to the interpretation and discussion of the results. Z.P. and A.A. provided comments and suggestions for improving the quality of this manuscript. All authors edited the manuscript.

Competing interests

The authors declare no competing interest.

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Increasing Sensitivity of Winter Wheat Yield to Snow Drought

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Abstract

Figures

Introduction

Results

Hotspots and trends of snow drought across winter wheat croplands

Sensitivity of winter wheat yield to standardized snow water equivalent index (SWEI)

Increasing sensitivity of winter wheat yield to SWEI

Attribution of \(\:{\varvec{T}}_{\varvec{s}\varvec{e}\varvec{n}}\)

Discussion and conclusions

Data and methods

Data

Yield data

Climate data

Snow data

Identification of snow drought

Trends of snow drought frequency

Data pre-processing

Detection of causal relationships between winter wheat yields and snow droughts

Overall sensitivity of winter wheat yield to SWEI

Trends of sensitivity of winter wheat yield to SWEI

Attribution analysis

Declarations

References

Additional Declarations

Supplementary Files

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