Satellite Solar-Induced Chlorophyll Fluorescence Reveals Heat Stress Impacts on Wheat Yield in India

With continued global warming, the frequency and severity of heat wave events increased over the past decades, threatening both regional and global food security in the future. There are growing interests to study the impacts of drought on crop. However, studies on the impacts of heat stress on crop photosynthesis and yield are still lacking. To fill this knowledge gap, we used both statistical models and satellite solar-induced chlorophyll fluorescence (SIF) data to assess the impacts of heat stress on wheat yield in a major wheat growing region, the Indo-Gangetic Plains (IGP), India. The statistical model showed that the relationships between different accumulated degree days (ADD) and reported wheat yield were significantly negative. The results confirmed that heat stress affected wheat yield across this region. Building on such information, satellite SIF observations were used to further explore the physiological basis of heat stress impacts on wheat yield. Our results showed that SIF had strong negative correlations with ADDs and was capable of monitoring heat stress. The SIF results also indicated that heat stress caused yield loss by directly impacting the photosynthetic capacity in wheat. Overall, our findings demonstrated that SIF as an effective proxy for photosynthetic activity would improve our understanding of the impacts of heat stress on wheat yield.


Introduction
Wheat is one of the most widely grown crops in the world and plays a vital role in global food security. As a crop that is planted in autumn and harvested before the following summer, winter wheat (Triticum aestivum L.) prefers cooler temperatures. High temperatures can cause heat stress in wheat, especially during the grain-filling stage [1]. Excessive heat can accelerate leaf senescence and shorten grain-filling duration, resulting in yield loss [2][3][4]. With increasing risks of high temperatures under global warming, yield loss due to heat stress could be the main issue to the major wheat-producing regions [5]. For example, in the Indo-Gangetic Plains (IGP) of India, heat stress has already caused great yield loss in wheat over the past few decades [6][7][8]. In 2010, extreme heat stress affected this region and caused a significant reduction of wheat yields [9].
High temperature during the grain-filling period might slightly increase the grain-filling rates of wheat, but cannot completely compensate the disadvantage of shortened duration [4]. However, further damage would occur to the leaf photosynthetic apparatus when temperature exceeds a critical

Study Area
The study area was located in the Indo-Gangetic Plains (IGP), a major wheat-producing region in Northwest India, with abundant irrigation and fertilizer ( Figure 1). In the IGP, winter wheat is usually planted from November to December and harvested during May of the following year. The variations in planting and harvest dates across this region are around 20 days, and heat stress mainly occurs during the grain-filling stage of wheat [4]. We conducted this study focusing on March and April, to ensure all districts were at the grain-filling stage and all data we used in this study could be well-matched in temporal resolution (i.e., monthly). The wheat harvested area with 0.083° spatial resolution was identified via http://www.sage.wisc.edu [30,31]. Green pixels indicate grid cells with more than 40% wheat. The base map at the top-right corner is that of commonly recognized world regions.

Meteorological and Yield Data
Previous studies used daily mean temperature to compute the relationship between heat stress and crop yield [9,13]. However, daily mean temperature might underestimate the impacts of heat stress, because canopy temperature could be often higher than air temperature, especially when heat stress occurs [32]. Field observations indicated that the use of maximum temperature could improve the relationship significantly [14]. Therefore, the daily maximum temperature with 0.5° spatial resolution was used in this study, which was obtained from Climate Prediction Center (CPC) Global Temperature data products (https://www.esrl.noaa.gov/psd/). The gridded rainfall data were the monthly average rain precipitation rate (mm s -1 ) obtained from the Global Land Data Assimilation System (GLDAS), with the Noah land surface model (https://ldas.gsfc.nasa.gov/) [33]. The annual district-level statistical reports of wheat yield were collected from Datanet India (https://www.indiastat.com/). Considering the yield loss caused by unseasonal rains and hailstorm in 2015, we did not use the data from 2015 in this study [34]. Green pixels indicate grid cells with more than 40% wheat. The base map at the top-right corner is that of commonly recognized world regions.

Meteorological and Yield Data
Previous studies used daily mean temperature to compute the relationship between heat stress and crop yield [9,13]. However, daily mean temperature might underestimate the impacts of heat stress, because canopy temperature could be often higher than air temperature, especially when heat stress occurs [32]. Field observations indicated that the use of maximum temperature could improve the relationship significantly [14]. Therefore, the daily maximum temperature with 0.5 • spatial resolution was used in this study, which was obtained from Climate Prediction Center (CPC) Global Temperature data products (https://www.esrl.noaa.gov/psd/). The gridded rainfall data were the monthly average rain precipitation rate (mm s −1 ) obtained from the Global Land Data Assimilation System (GLDAS), with the Noah land surface model (https://ldas.gsfc.nasa.gov/) [33]. The annual district-level statistical reports of wheat yield were collected from Datanet India (https://www.indiastat.com/). Considering the yield loss caused by unseasonal rains and hailstorm in 2015, we did not use the data from 2015 in this study [34].

Satellite-Based Solar-Induced Chlorophyll Fluorescence Data and Vegetation Indices
Long-term satellite SIF observations could be derived from the Global Ozone Monitoring Instrument 2 (GOME-2) on board EUMETSAT's MetOp-A platform. These SIF observations contain information about canopy photosynthesis with 0.5 • spatial resolution at the global scale, from 2007 to present [35]. In this study, we used the monthly gridded GOME-2 SIF dataset from GOME_F SIF product to conduct our analysis instead of the raw data [36]. The product (level 3, version 2.8.0) was performed in the 734-758 nm spectral window (peak of the far-red chlorophyll fluorescence at 740 nm) and had various filtering applied for better quality [37,38]. The dataset was composited by daily-averaged SIF estimates, based on a single observation. The daily-averaged SIF estimates were normalized by the cosine of the solar zenith angle to eliminate the effect of variation in photosynthetically active radiation (PAR), with hours. The dataset and detailed information are available via https://avdc.gsfc.nasa.gov/pub/data/satellite/MetOp/GOME_F/. Moreover, the OCO-2 SIF product with 0.05 • spatial resolution (https://doi.org/10.3334/ORNLDAAC/1696/) was used to compare with the coarse-resolution GOME-2 SIF product. The OCO-2 SIF data had high temporal-spatial resolution, but could be limited by its short time-series (from 2014 to present). In addition, we also used the VI product (MOD13C2) to conduct this study (https://lpdaac.usgs.gov/products/mod13c2v006/). Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI) from this product were used to compare with the SIF results, for understanding the advantages and disadvantages of SIF and VIs in assessing heat stress impact on wheat and in estimating the yield loss.

Analysis
This study focused on impacts of heat stress on wheat yield in the IGP during 2008-2018, except for the year 2015. The data of 2015 was not used in our analysis if not specifically mentioned. To match the temporal resolution of GOME-2-based SIF observations and the spatial resolution of wheat planting area, all datasets were resampled and aggregated into monthly composites, at approximately 0.083 • spatial resolution. The critical temperatures during the grain-filling stage of wheat are difficult to identify. For the present analysis, we chose the threshold values from some previous studies, based on field experiment and crop model [4,14]. Meanwhile, we also considered the uncertainty caused by different wheat cultivars. Then, the gradient threshold values were defined as 27 • C, 30 • C, and 34 • C, to calculate the accumulated degree days (ADD), respectively. The ADD above different daily maximum temperatures were calculated to represent different levels of heat stress. The ADD is defined as follows: where t represents the daily time step, N is the total number of days in the month, DD represents degree days, T lower and T upper are the different lower and upper limit temperatures, respectively, in different accumulated temperature ranges. In this study, T lower was set to 0 • C, 27 • C, 30 • C, and 34 • C, T upper was set to 27 • C, 30 • C, 34 • C, and ∞. We computed the ADD over 0 • C, 27 • C, 30 • C, and 34 • C (T lower = 0 • C, 27 • C, 30 • C, and 34 • C), and termed them ADD >0 • C , ADD >27 • C , ADD >30 • C , and ADD >34 • C , respectively. It was noted that all daily maximum temperatures in March-April were not below 0 • C, across our study area, and therefore, ADD >0 • C was also defined as the total ADD. The different ADDs (i.e., ADD >0 • C , ADD >27 • C , ADD >30 • C , and ADD >34 • C ) represent different levels of heat stress. To quantify the impacts of different heat stresses on wheat yield, a multivariable linear regression was applied to each ADD: where Yield d,y is wheat yield in district d and year y, ADD lower represents the accumulated degree days of March-April in the corresponding district and year, over different lower limit temperatures (i.e., ADD >27 • C , ADD >30 • C , and ADD >34 • C ), Rainfall represents the average rain precipitation rate in March-April, β 0 is the intercept, β 1 and β R are the regression coefficients, ε is the residual. Wheat in the IGP is well-irrigated, so water stress was not considered in this study. Rainfall was included in the model because it could alleviate heat stress and offset some negative effects on wheat yield [4]. We also calculated the variance inflation factor (VIF) to test co-linearity in our multiple regressions. SIF was regarded as a proxy for photosynthetic activity. In this study, a simple linear regression based on satellite SIF observations was used to estimate wheat yield: where Yield d,y is wheat yield in district d and year y, SIF represents the mean satellite SIF observations of March-April in corresponding district and year, β 0 is the intercept, β 1 is the regression coefficient, and ε is the residual. Moreover, we also conducted another multivariable linear regression for assessing the contributions of climatic factors on improving the performance and accuracy of yield estimations: where β 0 is the intercept, β 1 , β 2 , and β R is the regression coefficients, and ε is the residual. The normalized anomalies of variables were calculated on a pixel-by-pixel basis to compare the spatial-temporal variations in ADDs, rainfall, and SIF: var =(var t − var)/σ var (6) where var represents the normalized anomalies of variables, var t represents the original value of variables at time t, var and σ var represent the mean and standard deviation of variables during 2008-2018 (except the year 2015), respectively.

The Heat Stress across the IGP during the Wheat Grain-Filling Stage
This study analyzed the relationships between ADDs and wheat yield using statistical models, to assess the impacts of heat stress on wheat yield across the IGP. The total ADD (i.e., ADD >0 • C ) across this region during the wheat grain-filling stage was high ( Figure 2a). Wheat in this region suffered from high temperature over the past 10 years. Our results showed that the total ADD had a negative correlation with yield ( Figure 2b). On the contrary, rainfall was conducive to wheat growth and had a positive effect on yield ( Figure 2c). In general, excessive temperature and heat would stunt wheat growth and result in yield loss. Although rainfall could alleviate heat stress by decreasing leaf and land surface temperatures (Figure 2d), it would still fail to prevent yield loss from increasing ADD. Each regression was carried out to assess the impacts of rainfall and different ADD on wheat yield. Our results showed that yield was negatively correlated with ADD>27°C, ADD>30°C, and ADD>34°C, while it had a positive correlation with rainfall ( Figure 3). Different heat stresses (i.e., ADDs) can impact wheat growth to varying extent. All regressions and their variables were statistically significant (p < 0.05). In each regression, the Pearson correlation coefficients between rainfall and ADD (i.e., ADD>27°C, ADD>30°C, and ADD>34°C) were -0.67, -0.63, and -0.52, respectively. The values of VIF showed that there was almost no co-linearity (0 < VIF < 2) in our regression equations. Our findings demonstrated that heat stress seriously affected wheat growth during the grain-filling stage and could be one of the main factors of yield loss across the IGP. The climate variables could explain the phenomenon of yield loss, but it would be difficult to evaluate the underlying physiological basis (e.g., photosynthesis) of heat stress impacts on wheat yield, at large scales. Each regression was carried out to assess the impacts of rainfall and different ADD on wheat yield. Our results showed that yield was negatively correlated with ADD >27 • C , ADD >30 • C , and ADD >34 • C , while it had a positive correlation with rainfall ( Figure 3). Different heat stresses (i.e., ADDs) can impact wheat growth to varying extent. All regressions and their variables were statistically significant (p < 0.05). In each regression, the Pearson correlation coefficients between rainfall and ADD (i.e., ADD >27 • C , ADD >30 • C , and ADD >34 • C ) were −0.67, −0.63, and −0.52, respectively. The values of VIF showed that there was almost no co-linearity (0 < VIF < 2) in our regression equations. Our findings demonstrated that heat stress seriously affected wheat growth during the grain-filling stage and could be one of the main factors of yield loss across the IGP. The climate variables could explain the phenomenon of yield loss, but it would be difficult to evaluate the underlying physiological basis (e.g., photosynthesis) of heat stress impacts on wheat yield, at large scales.

Using SIF to Assess Heat Stress and Its Impacts on Wheat
It could be insufficient to only use climate-related variables to monitor crop growth and predict yield. We need more physiological measurements to assess them. Our results showed that the relationships between SIF and ADDs were significantly negative (p < 0.05) ( Figure 4). Heat stress could cause a decline in SIF by weakening photosynthetic activity in wheat. The variations in actual photosynthetic capacity could be one main physiological mechanism of crops in response to heat stress. Therefore, our findings indicated that SIF could be used to reveal the physiological processes under heat stress and assess the impacts on wheat growth. Additionally, using NDVI and EVI, we could also monitor heat stress and assess the impacts on wheat. The results of NDVI and EVI were similar, but had a few differences with those of SIF in spatial distribution (Supplementary Material, Figure S1).

Using SIF to Assess Heat Stress and Its Impacts on Wheat
It could be insufficient to only use climate-related variables to monitor crop growth and predict yield. We need more physiological measurements to assess them. Our results showed that the relationships between SIF and ADDs were significantly negative (p < 0.05) (Figure 4). Heat stress could cause a decline in SIF by weakening photosynthetic activity in wheat. The variations in actual photosynthetic capacity could be one main physiological mechanism of crops in response to heat stress. Therefore, our findings indicated that SIF could be used to reveal the physiological processes under heat stress and assess the impacts on wheat growth. Additionally, using NDVI and EVI, we could also monitor heat stress and assess the impacts on wheat. The results of NDVI and EVI were similar, but had a few differences with those of SIF in spatial distribution (Supplementary Material, Figure S1). photosynthetic capacity could be one main physiological mechanism of crops in response to heat stress. Therefore, our findings indicated that SIF could be used to reveal the physiological processes under heat stress and assess the impacts on wheat growth. Additionally, using NDVI and EVI, we could also monitor heat stress and assess the impacts on wheat. The results of NDVI and EVI were similar, but had a few differences with those of SIF in spatial distribution (Supplementary Material, Figure S1).  The spatial distribution of multiyear mean yield based on SIF (Figure 5a) was consistent with the district-level statistical reports (Figure 5b). The simple linear regression using SIF data performed better result (R 2 = 0.56, p < 0.05) than only the statistical model, when using climatic factors. SIF had a negative response to ADDs, but had a positive relationship with yield. In other words, SIF as an intermediary factor was related to both heat stress and yield. The variations in yield caused by heat stress could accurately be estimated by SIF. Therefore, our findings demonstrated that heat stress could impact wheat yield by directly declining photosynthetic capacity. In the SIF model, the added climate variables could only slightly improve the accuracy of yield estimation (R 2 = 0.59, p < 0.05). The spatial distribution of multiyear mean yield based on SIF (Figure 5a) was consistent with the district-level statistical reports (Figure 5b). The simple linear regression using SIF data performed better result (R 2 = 0.56, p < 0.05) than only the statistical model, when using climatic factors. SIF had a negative response to ADDs, but had a positive relationship with yield. In other words, SIF as an intermediary factor was related to both heat stress and yield. The variations in yield caused by heat stress could accurately be estimated by SIF. Therefore, our findings demonstrated that heat stress could impact wheat yield by directly declining photosynthetic capacity. In the SIF model, the added climate variables could only slightly improve the accuracy of yield estimation (R 2 = 0.59, p < 0.05).

The Capability of SIF to Monitor the Extreme Heat Event
In 2010, heat waves spread over the whole region with strong impacts on wheat. In particular, ADD>34°C was almost doubled in March-April, compared to other years (Figure 6a). The 2010 extreme heat event gradually evolved in February and quickly expanded until the wheat was harvested. Extreme heat occurred severely and was more widespread across the IGP, especially in March and April. The total ADD was extremely high (> 2σ) when the heat stress peaked in April (Figure 6b). Meanwhile, the monthly average rainfall had a significant decrease both in March and April ( Figure  6c). The negative rainfall anomalies could further aggravate heat stress in wheat. However, higher rainfall in May could offset some negative impacts of extreme heat and compensate some yield loss. In general, extreme heat would cause more yield loss in 2010 than usual. Our results showed that the interaction of heat stress and rainfall would lead to the spatial-temporal variations in SIF and yield. For example, the spatial-temporal variations in SIF showed discontinuous and heterogeneous anomalies (Figure 6d). Varying degrees of decrease in SIF were detected over the IGP, with the largest negative anomalies less than -2σ. However, there were also some positive anomalies of SIF in each

The Capability of SIF to Monitor the Extreme Heat Event
In 2010, heat waves spread over the whole region with strong impacts on wheat. In particular, ADD >34 • C was almost doubled in March-April, compared to other years (Figure 6a). The 2010 extreme heat event gradually evolved in February and quickly expanded until the wheat was harvested. Extreme heat occurred severely and was more widespread across the IGP, especially in March and April. The total ADD was extremely high (>2σ) when the heat stress peaked in April (Figure 6b). Meanwhile, the monthly average rainfall had a significant decrease both in March and April (Figure 6c). The negative rainfall anomalies could further aggravate heat stress in wheat. However, higher rainfall in May could offset some negative impacts of extreme heat and compensate some yield loss. In general, extreme heat would cause more yield loss in 2010 than usual. Our results showed that the interaction of heat stress and rainfall would lead to the spatial-temporal variations in SIF and yield. For example, the spatial-temporal variations in SIF showed discontinuous and heterogeneous anomalies (Figure 6d). Varying degrees of decrease in SIF were detected over the IGP, with the largest negative anomalies less than −2σ. However, there were also some positive anomalies of SIF in each month. The positive and negative anomalies could be converted to each other with time. Our findings showed that satellite SIF observations could inform more details about photosynthetic activity at large scales. The dynamic changes in SIF could reveal the responses of photosynthetic processes in wheat to extreme heat stress. The relationship between yield and SIF was significant under extreme heat stress (R 2 = 0.68, p < 0.05). The spatial distribution of yield loss based on SIF showed great spatial heterogeneity in 2010 (Figure 7a). Even within one district, different cultivars or agronomic management measures could lead to different wheat yields, especially under extreme heat stress. Although the relationship between SIF and yield was good, the coarse-resolution of the GOME-2 SIF product would limit the performance. Compared to the district-level statistical reports (Figure 7b), the SIF results showed mosaic-like and irregular yield estimates. The relationship between yield and SIF was significant under extreme heat stress (R 2 = 0.68, p < 0.05). The spatial distribution of yield loss based on SIF showed great spatial heterogeneity in 2010 (Figure 7a). Even within one district, different cultivars or agronomic management measures could lead to different wheat yields, especially under extreme heat stress. Although the relationship between SIF and yield was good, the coarse-resolution of the GOME-2 SIF product would limit the performance. Compared to the district-level statistical reports (Figure 7b), the SIF results showed mosaic-like and irregular yield estimates. Overall, satellite-based SIF had the capability to monitor the response of wheat to heat stress. The variation in SIF could reveal spatial-temporal dynamic of photosynthetic activity in wheat and the impacts of heat stress on yield. The process of how heat stress impacts wheat yield by directly declining photosynthetic capacity is becoming clearer in an extreme heat event. With long time-series, the GOME-2 SIF product has the potential to solve more climate change issues, but its low spatial resolution would limit the applications at the regional scale. Our findings suggest that satellite SIF observations could diagnose the impact of heat wave on wheat yield, and the performance would be improved by more fine-resolution SIF products in the future.

Discussion
The effect of climate change on crop yield is a rapidly growing research field. In this study, we focused on assessing the impacts of different heat stresses on wheat yield. The accumulation of daily maximum temperature, termed ADD, was used to represent the heat stress in wheat. Previous studies indicated that uses of daily maximum temperature instead of daily mean temperature could significantly improve the relationship between heat stress and relative yield loss [2,14,39]. Maximum air temperature could be closer to the actual canopy temperature under heat stress [32,40]. Additionally, since high temperature could be one of the main limiting factors for the wheat production of the IGP [4,9], we did not further analyze other climate variables (e.g., soil moisture, evapotranspiration, vapor pressure deficit, and so on). Upon further analysis, the extent to which heat stress affects wheat yield in the IGP was demonstrated through statistical models. Although our results showed that rainfall could offset some negative impacts of heat stress on wheat, high temperature would still cause yield loss. This study did not consider water stress, since wheat is well irrigated across this region [17]. Instead, we assessed the effects of rainfall on decreasing leaf and land surface temperatures in our regression model. Our findings suggest that continued warming affected the wheat production of the IGP, and adaptation strategies are necessary to be taken to prevent more loss in the future [3].
Satellite SIF observations were used to reveal the heat stress impacts on photosynthetic activity and estimate yield loss. The SIF results extended our statistical model findings to pixel scale, with strong physiological significance. Our study demonstrated that SIF could assess the impacts of heat stress on wheat yield, and the results were consistent with previous studies [9, 25,41]. Meanwhile, the spatial-temporal variation in SIF showed significant and quick responses to heat stress. Our results Overall, satellite-based SIF had the capability to monitor the response of wheat to heat stress. The variation in SIF could reveal spatial-temporal dynamic of photosynthetic activity in wheat and the impacts of heat stress on yield. The process of how heat stress impacts wheat yield by directly declining photosynthetic capacity is becoming clearer in an extreme heat event. With long time-series, the GOME-2 SIF product has the potential to solve more climate change issues, but its low spatial resolution would limit the applications at the regional scale. Our findings suggest that satellite SIF observations could diagnose the impact of heat wave on wheat yield, and the performance would be improved by more fine-resolution SIF products in the future.

Discussion
The effect of climate change on crop yield is a rapidly growing research field. In this study, we focused on assessing the impacts of different heat stresses on wheat yield. The accumulation of daily maximum temperature, termed ADD, was used to represent the heat stress in wheat. Previous studies indicated that uses of daily maximum temperature instead of daily mean temperature could significantly improve the relationship between heat stress and relative yield loss [2,14,39]. Maximum air temperature could be closer to the actual canopy temperature under heat stress [32,40]. Additionally, since high temperature could be one of the main limiting factors for the wheat production of the IGP [4,9], we did not further analyze other climate variables (e.g., soil moisture, evapotranspiration, vapor pressure deficit, and so on). Upon further analysis, the extent to which heat stress affects wheat yield in the IGP was demonstrated through statistical models. Although our results showed that rainfall could offset some negative impacts of heat stress on wheat, high temperature would still cause yield loss. This study did not consider water stress, since wheat is well irrigated across this region [17]. Instead, we assessed the effects of rainfall on decreasing leaf and land surface temperatures in our regression model. Our findings suggest that continued warming affected the wheat production of the IGP, and adaptation strategies are necessary to be taken to prevent more loss in the future [3].
Satellite SIF observations were used to reveal the heat stress impacts on photosynthetic activity and estimate yield loss. The SIF results extended our statistical model findings to pixel scale, with strong physiological significance. Our study demonstrated that SIF could assess the impacts of heat stress on wheat yield, and the results were consistent with previous studies [9, 25,41]. Meanwhile, the spatial-temporal variation in SIF showed significant and quick responses to heat stress. Our results indicated that SIF could capture the spatial-temporal dynamics of heat stress. Previous studies proved that SIF could be a direct and functional proxy for photosynthetic activity [42][43][44][45]. Therefore, it could be a good choice to use SIF to quantify the impacts of heat stress on wheat yield. In our study, SIF was regarded as an intermediary factor to represent actual photosynthesis under heat stress. Our results showed that satellite SIF observations could be used to assess the capability of monitoring heat stress, especially in extreme heat events. In general, our findings suggest that SIF could be a bridge to explore the relationship between heat stress and crop yield.
The monthly gridded SIF dataset we used in this study was the GOME-2 product composited by the estimated daily-averaged SIF values. This dataset was also normalized by PAR, which could be used to indicate the effective fluorescence yield and eliminate the effect of variation in PAR [28,41]. Some previous studies also used the absorbed photosynthetically active radiation (APAR) to further eliminate the effect of APAR on SIF [9,22]. The SIF normalized by APAR (referred to as SIF yield ) could be identified to indicate photosynthetic efficiency of plants. Actually, heat stress could remarkably reduce both photosynthetic capacity and efficiency, and even change the canopy structure. Although our results showed the negative response of SIF to heat stress at large scales, more studies are needed to explore the impact and process at the canopy scale. Additionally, the sensor degeneration of GOME-2 could create some potential uncertainties [45,46], which also needs more attention in future studies.
Although Song et al. [9] showed that GOME-2 SIF has a better performance of monitoring heat stress in wheat, high spatial and temporal resolution of VIs could provide similar and even better results. In this study, the spatial distribution and spatial-temporal dynamic of VIs ( Figure S1, S2) showed some differences with those of SIF. The responses of VIs to heat stress could have a potential hysteresis effect. However, the SIF data we used was retrieved from a far-red band, which could represent the instantaneous state of photosynthetic capacity in wheat. The performances of VIs and SIF should be assessed by considering specific objective and study area. It should be careful to directly compare them, since their retrieval and production methods are different. Moreover, we also used VIs to estimate wheat yield to compare the differences with those results of SIF ( Figure S3). We conducted the yield estimations with longer time-series (2008-2014, 2016-2018) than the previous study (2008)(2009)(2010)(2011)(2012)(2013) [9]. The results showed that NDVI and EVI could capture the interannual variation in wheat yield better than GOME-2 SIF, which was opposite to their results [9]. Considering the differences of data source and processing algorithm between ours and theirs, the performance of yield estimation using VIs or SIF should be further verified and discussed.
For exploring the performance of yield estimation using high-resolution SIF data and informing the potential limitation of using the coarse-resolution GOME-2 SIF product, we conducted a comparison with the recent OCO-2 SIF product [47]. The results showed that the yield estimations based on four satellite data were as good as each other ( Figure S4). Although we tried to match the data of the wheat harvested area with high resolution SIF data for improving yield estimation, the high-resolution OCO-2 SIF data could not perform better than coarse-resolution GOME-2 SIF product. The effect of mixed pixel could still cause error and uncertainty of relationship between satellite-based SIF and statistical yield. Moreover, the selected study period could also affect the results. In this comparison, the OCO-2 SIF with short time-series could not show the complete performance of yield estimation. During 2016-2018, the interannual variations in yield for each district were obvious (Table S1), but those in SIF were not (Table S2). We assessed the relationships between ADDs and yield using a simple linear regression. The results showed that the negative impacts of ADDs on yield could be weaker during 2016-2018 than those during 2008-2018 (Table S3). The variations in yield could be caused by some other factors, and might not be a result of the decline of photosynthetic capacity. Our findings suggest that the yield loss, which was not caused by the limitation of photosynthesis, would not be detected or estimated by SIF data. Overall, higher resolution SIF product with long time-series would be needed for further assessing and improving the performance of yield estimation.
For application of SIF in agriculture, previous studies demonstrated that SIF could capture spatial-temporal variation in environmental stress and was able to estimate crop yield [9, 25,26]. Our results also confirmed that satellite SIF observations had a high sensitivity to heat stress and a good correlation with wheat yield. On the one hand, heat stress could decline photosynthetic capacity and weaken vegetation fluorescence [48]. On the other hand, heat stress could also speed up wheat senescence and shorten the growing period [4]. Both reasons could lead to the reduction of SIF in March-April and result in yield loss. Overall, our findings showed that satellite SIF observations have its unique sensitivity to the impacts of environmental stress on crop. In future, more studies and satellite-based SIF products are needed for further extending its application and improving its results [49,50].

Conclusions
Using statistical model and satellite SIF observations, this study assessed the impacts of heat stress on wheat yield in the IGP, India. The results, based on statistical models, showed that ADDs have negative correlations with wheat yield, and then demonstrated that heat stress could be one of the main factors of yield loss. On this basis, further analysis indicated that SIF has physiological meaning and is useful to reveal the relationship between heat stress and yield. SIF as an effective proxy for photosynthetic activity could be used to detect the variations in wheat growth and the responses to different heat stresses. Our results demonstrated that heat stress could impact wheat yield by directly declining photosynthetic capacity. SIF could be used to improve both the results of monitoring heat stress and estimating crop yield. Overall, our study quantified the impacts of heat stress on wheat yield and revealed its physiological pathway. As novel spaceborne data, satellite SIF observations showed its great potential of monitoring crop growth and assessing the impacts of heat stress on yield.