US crop yield losses from hydroclimatic hazards

Hydroclimatic stresses can negatively impact crop production via water deficits (low soil water supply and high atmospheric demand) or surpluses (high soil water supply and low atmospheric demand). However, the impact of both stresses on crop yields at regional scales is not well understood. Here we quantified yield sensitivities and corresponding spatio-temporal yield losses of US rainfed maize, soybeans, sorghum, and spring wheat to hydroclimatic stresses by considering the joint impacts of root-zone soil moisture and atmospheric evaporative demand from 1981 to 2020. We show that crop yields can be reduced similarly by two major hydroclimatic hazards, which are defined as the most yield damaging conditions over time: ‘Low Supply + High Demand’ and ‘High Supply + Low Demand’. However, more exposure to ‘Low Supply + High Demand’ hazard led to the largest annual yield losses (7%–17%) across all four crops over time. Modeled yield losses due to these hazards were significantly associated with crop insurance lost costs. The extent of yield losses varies considerably by crop and location, highlighting the need for crop-specific and regionally tailored adaptation strategies.

Much is known about the physiological impact of hydroclimatic stresses related to SM and VPD in determining plant productivity.Yet, these supplydemand mechanisms are not often factored into hydroclimatic impact assessments for crop yields.Most studies evaluating the effects of drought or excessive water on crops have focused solely on water supply, as indicated by SM or rainfall [16][17][18][19].However, the impact of low SM can be exacerbated or reduced depending on whether VPD conditions are high or low (supplementary figure S1) [1,7].The Standardized Precipitation Evapotranspiration Index is also often used to characterize drought stress by incorporating potential evapotranspiration and rainfall as indicators of water demand and supply [20][21][22].However, relying solely on rainfall as a measure of water supply for predicting crop yields may be unreliable due to the influence of other factors such as runoff and soil types [7,16].Therefore, understanding crop yield responses to hydroclimatic stresses by considering the joint impacts of SM and VPD is crucial for improving the accuracy of current and future hydroclimatic impact assessments for agriculture.
Furthermore, less is known about the joint impacts of SM and VPD on yield losses across different crops and locations [4,7].Most recent studies considering combined SM and VPD conditions have focused solely on maize or/and soybeans in the Midwest [4,7], which hinders our understanding of regional differences in hydroclimatic stresses across crops.For example, although sorghum is known as a heat and drought tolerant crop, a recent study emphasized that its yield losses are largely driven by high heat and rainfall stress throughout its growing season in the US [23].It is therefore of great importance to systematically quantify the yield sensitivities and losses of different crops to hydroclimatic stresses across locations and time.
In this study, we estimated the impact of hydroclimatic stresses on major US rainfed crops and corresponding spatio-temporal yield losses from 1981 to 2020 by considering the joint impacts of land water supply (i.e.SM) and atmospheric evaporative demand (i.e.VPD).We focused on maize, soybeans, spring wheat, and sorghum because they account for a major portion of the global production (32%, 31%, 15%, and 6%, respectively) [24] and their rainfed areas cover the contiguous US with varying climates (supplementary figure S2).By combining the most up-to-date SM reanalysis data and highresolution, observational VPD data, along with a statistical regression model for crop yields, we identified the most yield damaging conditions, defined as hydroclimatic hazards, and evaluated the corresponding spatio-temporal patterns of yield losses.Furthermore, we compared our estimated yield losses to crop insurance loss costs to ensure the robustness of our metrics across sectors, and to identify possible co-occurring hazards from crop insurance.

Data
Annual county-level rainfed yields for maize, soybeans, sorghum, and spring wheat for the years 1981-2020 were obtained from the USDA National Agricultural Statistics Service (USDA-NASS, https:// quickstats.nass.usda.gov/).We converted the yield unit from bushel per acre into kilograms per hectare (kg/ha) using crop conversion factors [25].We limited our analysis to rainfed counties, in which at least 10% of their harvested areas were not irrigated (supplementary figures S9 and S10).The threshold of 10% was based on previous studies [26,27].
We obtained daily maximum and minimum vapor pressure deficit (VPD) from the PRISM Climate Group (http://prism.oregonstate.edu)[28] and daily root-zone volumetric soil moisture (SM) from the National Climate Assessment-Land Data Assimilation System (NCA-LDAS) Version 3 [29].Their specifications are detailed in supplementary materials.We averaged SM (m 3 /m 3 ) over the 0-100 cm soil layer.The gridded SM and VPD datasets were spatially averaged for each county over grid cells containing cropland in the Global Food Security-Support Analysis Cropland Extent 2010 North America 30 m data [30].County definitions are based on the county boundary map from the 2017 US Census Bureau.
Insurance loss cost is the dollar ($) value of insurance payouts (indemnities), normalized by the maximum insured risk value (liabilities) underwritten by the yield-and revenue-based policies of the USDA Risk Management Agency (RMA) (equation ( 1)).We obtained the annually aggregated crop-countyhazard-specific indemnities from the RMA Cause of Loss dataset and the yearly aggregated crop-countyspecific liabilities from the Summary of Business dataset.We chose insurance hazards related to water deficit and surplus stress, which include drought and excessive rain and flood (rain/flood).We additionally included heat and disease insurance hazards, as they are often concurrent with drought or rain/flood hazards [31][32][33] and not easily reported by farmers separately.Therefore, four insurance hazards were included: drought, heat, rain/flood, and disease.Loss cost C i,j,t is an unitless index expressed in dollars ($) [34] and specified as: where I i,j,t is insurance payouts caused by crop insurance hazard j, relative to total liabilities L i,t in county i in year t.Further details of crop insurance data are provided in supplementary materials.

Statistical model
We utilized a statistical regression framework that examines the relationship between crop yield and a matrix of daily SM and VPD exposure [7].We used this framework to assess 40 years of hydroclimatic stresses for yields for four crops.State-specific full growing seasons (before harvest) of each crop were included, as they had the best explanatory predictive power (supplementary materials, table S1 and figure S15).We normalized the length of the growing seasons to 100% for each crop for comparisons of the four crops across the US.Daily SM and VPD values were binned into their 0-10th, 10-30th, 30-50th, 50th-70th, 70-90th, and 90-100th percentiles [4,6,9].For each crop, we analyzed the response of rainfed yields Y in county i and year t: (2) X d,s,i,t is the exposure time (% of growing season) to each VPD d and SM s bins.We excluded one of the 36 SM-VPD bins as the 'optimal bin' to avoid perfect multicollinearity of the explanatory variables.β d,s , which are the estimated coefficients, are interpreted as the change in yield sensitivities (kg/ha/%) relative to the optimal bin that maximizes yields.Z i,t is the exposure time (%) to low temperature with γ as its coefficient.A covariance analysis of SM and VPD is detailed in supplementary methods.f i are the year-level fixed effects that capture year-specific common shocks (e.g.technological and policy changes) while δ t are the county-level fixed effects that capture county-specific factors that influence spatial yield heterogeneity (e.g.soil type).ϵ i,t is the error.Coefficient uncertainties were estimated by two-way clustering of standard errors by county and year to account for spatial-temporal autocorrelation in our model residuals (supplementary figure S11).Note that our results remained qualitatively consistent with the changes in the minimum number of observations for a county to be included in the analysis, which we set to 20 years (supplementary figure S9), as well as the different numbers of bins.We also found similar patterns of yield sensitivities in the same model with crop-specific evapotranspiration (ET c ) as our variable of atmospheric evaporative demand (supplementary results, figures S7 and S8).However, it provided lower explanatory power relative to models with VPD across all four crops (supplementary table S1).

Temporal and spatial analysis of crop-specific hydroclimatic hazards
Based on the estimated yield sensitivities of each crop and the associated exposure times, we defined hydroclimatic hazards as the set of SM-VPD conditions constituting the most damaging 15% of exposure throughout the growing seasons of 1981-2020.The exposure threshold of 15% was selected because we found that this roughly corresponded with a breakpoint towards much more negative yield sensitivities (supplementary figure S4).We categorized the hydroclimatic hazards into four groups using 'High/Low Supply + High/Low Demand' names, e.g. one group of hydroclimatic hazards is referred to as, 'Low Supply + High Demand' .
We calculated nationally averaged annual yields (tonnes/ha) with and without crop-specific hydroclimatic hazards using our crop-specific models.The yields with hydroclimatic hazards are the predictions of our models with historical weather conditions.In contrast, the yields without hydroclimatic hazards were calculated by redistributing the exposure in the bins associated with hydroclimatic hazards to the bin that represents the optimal condition.Therefore, yield losses (tonnes/ha) refer to the differences between the yields with and without the hazards averaged over all counties, weighted by the annually averaged harvested area of each county (supplementary figure S2).
For each crop, we analyzed the magnitude of the yield losses relative to yields without the hazards.We also reported the national yield losses of each hydroclimatic hazard averaged over time (%/year) and the two worst yield loss years with the corresponding spatial maps (supplementary figure S5).We used the coefficient of variation to measure the inter-annual variability of the annual yield losses due to hydroclimatic hazards; this is defined as the standard deviation of annual yield loss normalized by the yield loss averaged over 1981-2020.The version of figure 2 with observed historical annual yields is shown in supplementary figure S12.
We identified spatial hot spots of average yield losses (%/year) of the four crops from two major hydroclimatic hazards: 'Low Supply + High Demand' and 'High Supply + Low Demand' (figure 3).These two hazards were selected because they were responsible for more than 80% of the total yield losses from 1981 to 2020 across all four crops (figure 2).Average yield losses (%/year) are the differences between the yields with and without the hazards averaged over time and across all crops, weighted by the annually averaged harvested area of each crop (supplementary figure S2).Additionally, we identified the crop associated with the greatest average yield loss in each county.The spatial map of crop-specific average yield loss (%/year) is shown in supplementary figure S6.

Analysis with crop insurance loss costs
Crop insurance data were utilized to validate our model-estimated annual yield losses due to hydroclimatic hazards (figure 4).We linked our estimated annual yield losses (tonnes/ha) of each hydroclimatic hazard to the loss cost ($) of the four crop insurance hazards for each crop.To quantify their correlations, we used a non-parametric Mann-Kendall tau correlation coefficient (τ ), which shows the strength and direction of the monotonic trend (−1 for most decreasing trends, 1 for most increasing trends) [35].Note that our correlation results remained qualitatively consistent across Spearman and Pearson coefficient of correlations (supplementary figure S13) and yield-and revenue-based policies (supplementary figure S14).

Modeling yield sensitivities to joint impacts of SM and VPD
Our statistical regression model uncovered that imbalances between SM and VPD provide significantly negative effects (p < 0.05) on rainfed maize, soybeans, sorghum, and spring wheat yields (figure 1).Both low SM-high VPD (water deficits) and high SM-low VPD (water surpluses) conditions were most detrimental to all four crops, consistent with the expected yield responses of crops (supplementary figure S1).Just 1% exposure to the lowest SMhighest VPD condition (upper left bin) during their respective growing seasons induced an average yield loss of 105 kg/ha for maize, 25 kg/ha for soybeans, 64 kg/ha for sorghum, and 56 kg/ha for spring wheat.In contrast, 1% exposure to the highest SM-lowest VPD conditions (bottom right bin) led to yield losses of 92 kg/ha for maize, 22 kg/ha for soybeans, 52 kg/ha for sorghum, and 20 kg/ha for spring wheat.Overall, our model explained a large proportion of the county-year level yield variations for maize (83%), soybeans (83%), sorghum (72%), and spring wheat (75%) (supplementary table S1).
The extent to which joint SM-VPD conditions affected the yields varied by crop.Maize, soybeans, and spring wheat (figures 1(a), (b) and (d)) exhibited relatively less sensitivity to midrange VPD conditions (approximately 0.7-1.2kPa).Sorghum (figure 1(c)) was unique in that it was sensitive to most of the joint SM-VPD conditions outside its optimal condition, but sorghum was also exposed to higher VPD conditions, on average, than the other crops.For spring wheat (figure 1(d)), detrimental yield sensitivities in the highest VPD conditions stood out in contrast with a relatively insensitive yield response to the lowest VPD conditions.
The identification of hydroclimatic hazards also differed by crop (supplementary figures S3 and S4).With hydroclimatic hazards defined as the most yield damaging SM-VPD conditions (methods), we found maize and soybeans to be sensitive to three hazards: Low Supply + High Demand, High Supply + Low Demand, and High Supply + High Demand hazards (figures 1(a) and (b)).Sorghum was sensitive to all four hazards (figure 1(c)), while spring wheat was sensitive to Low Supply + High Demand, High Supply + High Demand, and Low Supply + Low Demand hazards (figure 1(d)).We also found that High Supply + High Demand and Low Supply + Low Demand hazards were classified as hydroclimatic hazards, despite indicating a balance between SM and VPD conditions (supplementary figure S1).

Temporal variations in yield losses due to hydroclimatic hazards
We found that hydroclimatic hazards led to an average loss of 11-19%/year in nationally average yields for all four crops, compared to their expected yields without the hydroclimatic hazards from 1981 to 2020 (figure 2).Individually, Low Supply + High Demand hazard reduced the yields of maize by 7%/year, soybean by 7%/year, sorghum by 11%/year, and spring wheat by 17%/year compared to their expected yields in absence of the hazards.Similarly, High Supply + Low Demand hazard resulted in yield reductions of 5%/year for maize, 2%/year for soybeans, and 3%/year for sorghum.High Supply + High Demand hazard decreased the yields of all four crops by approximately 2%/year, while Low Supply + Low Demand hazard reduced the yields of sorghum by 1%/year and spring wheat by 0.4%/year.
Although the yield losses of the four crops appeared to decline over time, the magnitude and inter-annual variability of the losses varied by crop.Crucially, of all the hydroclimatic hazards, Low Supply + High Demand hazard was responsible for the largest proportional yield losses for all four crops (figure 2).This was particularly evident with sorghum (average yield loss: 11%/year) (figure 2(c)) and spring wheat (average yield loss: 17%/year) (figure 2(d)).Both crops consistently experienced yield losses due to Low Supply + High Demand hazard throughout the years, with low inter-annual variability (coefficient of variation, CV) of 0.6 for sorghum and 0.7 for spring wheat.Maize and soybeans (figures 2(a) and (b)) had relatively lower yield loss rates (7%/year, respectively), but their inter-annual variabilities (CV: 1.2 for maize and 1.0 for soybeans) were higher compared to sorghum and spring wheat.Maize and soybeans suffered their biggest yield losses due to Low Supply + High Demand hazard in 1988 and 2012, with losses of 44% and 30% for maize, and 39% and 25% for soybeans, respectively (supplementary figure S5).For sorghum, 1983 and 2012 were recorded as the two worst years with hazardinduced yield losses of 25% and 31%, respectively (supplementary figure S5).Spring wheat experienced its worst years in 1987 and 2005, leading to yield losses of 70% and 37%, respectively (supplementary figure S5).
High Supply + Low Demand hazard induced the second-largest yield losses across years for maize, soybeans, and sorghum (2-5%/year), with relatively consistent losses (CV < 1) across years (figures 2(a)-(c)).1993 and 1996 were the most severe years for maize and soybeans, with hazard-induced yield losses of 10% and 8% for maize, and 5.8% and 4.6% for soybeans, respectively (supplementary figure S5).Similarly, the worst years for sorghum were Yield sensitivity (kg/ha/%) indicates the yield change (kg/ha) for 1% exposure to each SM-VPD condition during the crop growing seasons, relative to its optimal condition (denoted by a dashed line).Four hydroclimatic hazards were defined across the crops (Methods), and the corresponding SM-VPD conditions of these hazards were outlined in color for each crop.A ' * ' represents statistically significant yield sensitivities (p < 0.05), estimated by two-way clustering of standard errors at the county and year level.

Spatial variations in yield losses due to major hydroclimatic hazards
We detected substantial regional variations in average yield losses of the four crops due to two major hydroclimatic hazards which represent water deficit and surplus stresses over time (Methods): Low Supply + High Demand and High Supply + Low Demand hazards (figure 3).The Great Plains and Carolinas were the regions most affected by Low Supply + High Demand hazard, with an average loss of 24%/year across all four crops (figures 3(a) and (c)).Within the Great Plains, where maize and sorghum are heavily cultivated, the yield loss hot spot for maize was central Texas, while the yield loss hot spot for sorghum was western Texas (supplementary figure S6).In the Carolinas where maize and soybeans are widely cultivated, soybeans were the crop with the most dominant yield loss (supplementary figure S6).Meanwhile, there were relatively lower impacts across the Midwest, with average yield losses of 9.4%/year ± 3.3.
Conversely, yield loss hot spots under High Supply + Low Demand hazard were found in portions of the Midwest, the Southern Plains, and Pennsylvania, with average losses of 4.7%/year, 5%/year, and 7.8%/year, respectively (figures 3(b) and (d)).In the Midwest where maize and soybeans are widely grown, maize was the dominant crop experiencing hazard-induced losses, particularly in Iowa and Wisconsin (supplementary figure S6).In the Southern Plains, sorghum was the crop with the most dominant yield losses across eastern Kansas and central Texas (supplementary figure S6).

Connecting yield losses to crop insurance loss costs
Our model-estimated annual yield losses (tonnes/ha) of two major hydroclimatic hazards were significantly correlated (τ with p < 0.001) with crop insurance payouts categorized for hydrologic hazards such as drought and rain/flood (figure 4).For all four crops, the yield losses due to Low Supply + High Demand hazard were highly (τ ∼ = 0.4 on average, p < 0.001) associated with drought and heat stress-induced lost costs ($), as measured by insurance payouts normalized by maximum insured risk values.Additionally, maize losses due to Low Supply + High Demand hazard had a significant correlation (τ ∼ = 0.24, p < 0.001) with disease-induced insurance loss costs.For High Supply + Low Demand hazard, maize, soybeans, and sorghum yield losses were significantly correlated (τ ∼ = 0.17 on average, p < 0.001) with rain/floodinduced loss costs.
In contrast, the other two hydroclimatic hazards, High Supply + High Demand and Low Supply + Low Demand, showed relatively weak correlations with the insurance loss costs for hydrologic hazards.For example, although the yield losses due to High Supply + High Demand hazard were associated with both drought and heat-induced loss costs, the magnitude of the correlation was less than 0.07 on average.Low Supply + Low Demand hazard showed nearly zero correlations with any of the crop insurance loss costs, though these conditions occurred the least over time.

Discussion and conclusions
Our study enhances the understanding of the yield sensitivities of US rainfed maize, soybeans, sorghum, and spring wheat to hydroclimatic stresses from SM and VPD (figure 1), and the resulting yield losses across time and locations (figures 2 and 3).We found that our two major hydroclimatic hazards, defined as the most yield damaging SM-VPD conditions, were highly correlated with crop insurance loss costs categorized for drought and rain/flood.Furthermore, our comparison of the hazard-induced yield losses with the insurance loss costs identified cooccurring insurance hazards, such as heat and disease (figure 4).
The distinct yield sensitivity patterns of the four crops in figure 1 are likely associated with the physiological responses of each crop across SM-VPD conditions.The differing optimal SM-VPD conditions across the four crops are likely due to their varying tolerance and resistance to hydroclimatic stresses during their respective growing seasons.The similar patterns of maize and soybean sensitivities may be because they are grown in comparable areas (supplementary figure S2) and have been developed as the best-suited cultivars for their current agro-climate conditions [26].However, it is noteworthy that changes in SM conditions had a less significant impact on maize and soybean yields for mid-range VPD conditions (approximately 0.7-1.2kPa).This result contrasts with other studies that have shown a decrease in gross primary productivity and surface conductance over reduced surface SM in grassland [1] and maize [4] for a given VPD.By incorporating ET c into our models as the atmospheric evaporative demand, which for variations in VPD, available energy, and wind speed, found changes in the gradients yield sensitivities to different SM at moderate VPD (supplementary figures S7 and S8).However, our findings suggest that models with VPD generally provide better explanatory power than those using ET c (supplementary results and table S1).Further research is needed to investigate how different atmospheric evaporative demands with diverse datasets can change yield sensitivities.The differing hydroclimatic hazards for each crop emphasize the distinct interactions of the soil-plantatmosphere continuum in controlling crop yields across different locations (figure 1).While three hydroclimatic hazards were similarly defined for maize and soybeans, sorghum and spring wheat showed greater yield sensitivities to an additional hydroclimatic hazard: Low Supply + Low Demand.The highly detrimental impact of Low Supply + Low Demand hazard on sorghum may be related to that crop's lower tolerance to cold temperatures [26,36], even though our model attempted to control for cold temperature exposure (Supplementary methods).Though the sensitivity of sorghum to Low Supply + Low Demand hazard was high, the exposure was only 1.46% of its growing season (supplementary figure S3).In the case of spring wheat, it was the only crop that was not severely impaired by High Supply + Low Demand hazard.This may be partly because, despite a recent increase in growing season precipitation over the eastern parts of North and South Dakota as well as Minnesota from 2010 to 2015 [37], this change was not significant enough to be linked to the hazard.Additionally, a recent study indicated that spring wheat yield was negatively impacted by high SM conditions only towards the harvest phase, as slightly dry conditions are favorable for harvest [26].However, our analysis excluded such grain dry-down phase (i.e.harvest) to focus on yield effects during the growing season, thereby supporting the definitions of hydroclimatic hazards for the growth of spring wheat.
The largest yield losses of all four crops were driven by Low Supply + High Demand hazard throughout the years (figure 2), though the magnitude of these losses extensively varied across the US (figure 3).Although both Low Supply + High Demand and High Supply + Low Demand hazards were similarly detrimental to all four crops (figure 1), more exposure to Low Supply + High Demand hazard over the years induced the largest yield losses (figure 2).On average, sorghum had 4% more yield losses per year than maize (11%/year for sorghum and 7%/year for maize) (figures 2(a) and (c)).This difference may be partly due to the differences in land-atmosphere interactions in the regions these crops are cultivated.For example, the intensification of maize and soybeans in the upper Midwest has benefited regional yields via increased atmospheric moisture and cooling [38][39][40][41][42]. On the other hand, the Southern Plains, which are heavily cultivated with sorghum, have experienced more increasing VPD conditions, possibly associated with changes in the Pacific Decadal Oscillation and the Southern Oscillation [42].We note that additional drivers can affect yields beyond hydroclimatic hazards, and provide discussion of variability about modeled yields without hazards (figure 2) in the supplementary results.In the regional yield hot spots of High Supply + Low Demand hazard (figure 3(b)), the largest yield losses correspond closely to poorly drained soil regions [18,43], where the water-logged root zone challenges the uptake of oxygen and nutrients and further restricts plant growth [1,7].This highlights the critical role of soil types in determining stress from water surplus.
The significant, positive correlation between our hazard-induced yield losses and crop insurance loss costs corroborates the robustness of our cropspecific hydroclimatic hazard definitions and further provides insights into compound extremes (figure 4).Specifically, the positive correlation between maize yield losses due to Low Supply + High Demand hazard and disease-induced insurance loss costs supports studies showing that increasing aflatoxin contamination is associated with frequent drought and heat stress during the reproductive phase of maize in the southern US [44][45][46][47][48][49].This highlights the potential for combined impacts of disease and drought/heat stress on maize yield losses.We note that the weak correlations for High Supply + High Demand and Low Supply + Low Demand hazards were likely due to their infrequent occurrence, which did not require insurance payouts.
Taken together, our study highlights the importance of quantifying yield responses of crops to hydroclimatic stresses using both SM and VPD, enhancing the accuracy of present and future hydroclimatic hazard assessment and adaptation strategies for agriculture.The extensive spatio-temporal variations in average yield losses highlight the need for regionally tailored crop-specific adaptations, such as crop choice [50], irrigation adoption [51], and artificial drainage [52], carefully weighing the benefits of these practices against potential environmental impacts.Finally, continued efforts to improve observationbased hydroclimatic variables (VPD, SM, and ET c ) would be crucial for advancing science and supporting informed decision-making.

Figure 1 .
Figure 1.Negative yield sensitivities of (a) maize, (b) soybeans, (c) sorghum, and (d) spring wheat to joint impacts of SM-VPD conditions and associated hydroclimatic hazard categories.High and low conditions of SM and VPD are separated from their 50th percentiles (denoted by dashed arrows).Yield sensitivity (kg/ha/%) indicates the yield change (kg/ha) for 1% exposure to each SM-VPD condition during the crop growing seasons, relative to its optimal condition (denoted by a dashed line).Four hydroclimatic hazards were defined across the crops (Methods), and the corresponding SM-VPD conditions of these hazards were outlined in color for each crop.A ' * ' represents statistically significant yield sensitivities (p < 0.05), estimated by two-way clustering of standard errors at the county and year level.

Figure 2 .
Figure 2. Annual variations in nationally average yield losses due to hydroclimatic hazards for (a) maize, (b) soybeans, (c) sorghum, and (d) spring wheat, 1981-2020.Yields with hydroclimatic hazards (denoted by solid lines) refer to the nationally averaged annual yields calculated with crop-specific yield sensitivities and exposure time to the hazards.Yields without hydroclimatic hazards (denoted by dashed lines) indicate the expected annual yields when the exposure to the hazards was removed.The colors depict the amount of yield loss (tonnes/ha) due to hydroclimatic hazards.The loss (%) at the bottom of each panel presents the aggregated yield losses across all hazards (Methods).A similar version with annual observed yields added can be found in supplementary figure S12.

Figure 3 .
Figure 3. Spatial hot spots of average yield losses due to two major hydroclimatic hazards (a) Low Supply + High Demand and (b) High Supply + Low Demand, with the indicator of the county's most dominant yield loss crop in color (c and d).Average yield losses (%/year) are the differences between the yields with and without hydroclimatic hazards averaged over 1981-2020 and across all crops, weighted by the annually averaged harvested area of each crop.The most dominant yield loss crop depicts the crop with the largest average yield loss (%/year) for a given county across the crops.The spatial map of crop-specific average yield loss (%/year) is shown in supplementary figure S6.

Figure 4 .
Figure 4. Correlations between our model-estimated annual yield losses of hydroclimatic hazards and crop insurance loss cost due to drought, heat, rain/flood, and disease, 1989-2020.Estimated yield losses (tonnes/ha) indicate the difference in our crop-specific model-estimated annual yields with and without hydroclimatic hazards (Methods).Crop insurance loss cost ($) is a normalized value of insurance payouts for insurance hazard category by total liability (Methods).The correlation was analyzed at the county-year level using the non-parametric Mann-Kendall tau correlation coefficient (τ ).Positive correlations are represented in red while negative correlations are represented in blue.Black outlines of bubbles indicate the statistical significance of these correlations (p < 0.05).Increasing bubble size represents higher exposure (%) of each crop to its respective hazard.