Adverse Weather Impacts on Winter Wheat, Maize and Potato Yield Gaps in northern Belgium

: Adverse weather conditions greatly reduce crop yields, leading to economic losses and lower food availability. The characterization of adverse weather and the quantiﬁcation of their potential impact on arable farming is necessary to advise farmers on feasible and effective adaptation strategies and to support decision making in the agriculture sector. This research aims to analyze the impact of adverse weather on the yield of winter wheat, grain maize and late potato using a yield gap approach. A time-series analysis was performed to identify the relationship between (agro-)meteorological indicators and crop yields and yield gaps in Flanders (northern Belgium) based on 10 years of ﬁeld trial and weather data. Indicators were calculated for different crop growth stages and multiple soils. Indicators related to high temperature, water deﬁcit and water excess were analyzed, as the occurrence frequency and intensity of these weather events will most likely increase by 2030–2050. The concept of “yield gap” was used to analyze the effects of adverse weather in relation to other yield-reducing factors such as suboptimal management practices. Winter wheat preferred higher temperatures during grain ﬁlling and was negatively affected by wet conditions throughout the growing season. Maize was especially vulnerable to drought throughout the growing season. Potato was more affected by heat and drought stress during tuber bulking and by waterlogging during the early growth stages. The impact of adverse weather on crop yield was inﬂuenced by soil type, and optimal management practices mitigated the impact of adverse weather.


Introduction
The influence of climate change on crop production is manifested in several ways.Changes in seasonal temperature, water availability and radiation incidence can have direct effects on crop growth and biomass production through their influence on crop physiological processes [1].The indirect effects of climate change encompass changes in nutrient availability (higher temperatures increase soil organic matter degradation), the emergence of new pests and diseases, or alterations in the phenological calendar [2].In addition to changes in the mean value of meteorological variables, an increased variability includes a more frequent occurrence of adverse and extreme weather conditions [3].Adverse weather conditions are meteorological conditions that may cause damage to crops, such as temperatures higher than optimal for plant growth.The definition of extreme weather relates to extremes in the historical distribution, for example, heat waves, droughts or floods [4].Adverse and extreme weather might greatly reduce crop yields, leading to economic losses and lower food availability.One third of the global yield variability is attributed to climatic variability and the incidence of weather extremes [5], highlighting the importance of measures such as agricultural insurance schemes, emergency food supply strategies and adaptations at the farm level to reduce yield losses.The characterization of adverse and extreme weather and the quantification of their potential impacts on arable farming is necessary to develop feasible and effective adaptation strategies and to support decision making in the agriculture sector.
Approaches to studying the impact of weather extremes are based on empirical models or process-based models, which directly or indirectly relate weather conditions to final crop yield.Empirical models aim to relate crop yields to a set of explanatory variables, which are (agro-)meteorological indices in this context [2,6].Meteorological indicators are directly calculated from weather variables, such as air temperature or rainfall.Agrometeorological indicators are indirectly related to the prevailing weather conditions, as they are influenced by crop type, crop growth and soil properties.Process-based or dynamic crop growth models comprise multiple mathematical equations which relate crop development, biomass production and final yield to several location-and time-specific environmental characteristics [7,8].Empirical models are typically based on the analysis of yield and weather time series, while dynamic crop growth models are most often constructed from greenhouse or field experiments.
The impact of adverse and extreme weather on crop production can be studied in terms of absolute yield or in terms of yield penalty (yield reduction or loss).Typically, yield loss is defined as a reduction from the long-term detrended average yield [2,[9][10][11][12][13][14]. Another way of expressing yield reduction is via the concept of the yield gap [15], but it is less frequently used for adverse and extreme weather impact studies.The yield gap theory indicates that agricultural production is to a large extent determined by climate and weather [16].Potential yield is location-specific, meaning that for a given crop genotype, it is determined by the prevailing climate, soil type and topography.Therefore, a shifted mean in the distribution of a climatic variable might affect the potential yield.The actual yield depends on several yield-reducing factors, including weather, whereby extreme weather events might significantly reduce the actual yield.Multiple methods exist to determine potential yields, ranging from simple proxies, such as the upper 5th or 1st percentile of the yield distribution, to more complex (crop) models [17].
Many studies using empirical or process-based crop models tend to overestimate yields in extreme years [18].In addition to the simplicity of the data or the models used, climate impact studies often focus on large areas with coarse resolution weather data and make use of meteorological variables averaged over the whole growing season.Extreme weather events occur at a small spatial scale due to substantial regional differences in weather.In addition, such events may take place within short timeframes, ranging from a couple of hours to a few days.As a result of studying larger areas and longer timeframes, average yields are obtained, while interannual yield variability is underestimated.Weather extremes may be "hidden" and thus not accounted for.Moreover, the impact of an extreme weather event on crop production is crop-specific and highly depends on its timing within the crop growth cycle [2].
This research aims to analyze the impact of adverse weather on the crop yield of winter wheat (Triticum aestivum), maize (Zea mays) and potato (Solanum tuberosum) using a yield gap approach while taking into account critical crop stages, soil and management practices.The following research questions were addressed: (1) Which (agro-)meteorological indicators best explain yield and yield gap variability?(2) To what extent do soil and management practices play a role in mitigating the impact of adverse weather conditions?
A time-series analysis was performed to identify the relationship between (agro-)meteorological indicators and crop yields and yield gaps in Flanders (northern Belgium) based on 10 years of weather and yield data for 4 soil types and 2 different crop management systems.A literature review was carried out to gain insights on climate impact analysis methods and to decide on which (agro-)meteorological indices to use in this study.

Case Study Area
The timeseries of crop yields and meteorological data were investigated for three main crop types in Flanders (northern Belgium): winter wheat, grain maize and late potato.In this way, winter and summer crops; grain and root crops; and C3 and C4 crops were included.In addition, the analysis was carried out for multiple soil types.
Belgium is located in the Northern hemisphere, at the western border of the European continent, and the climate is determined by (1) the interplay between cold air masses coming from the North Pole and warm air masses coming from the subtropics, which drives the alternation of seasons, and by (2) the presence of the North Sea and the Atlantic Ocean, which levels off temperature fluctuations and brings year-round precipitation [22].According to the Köppen-Geiger climate classification, the climate in Belgium is Cfb: a warm temperate climate (C), fully humid (f) and with warm summers (b) [23].During the 1991-2020 period, the mean annual temperature was 11 • C, ranging from 3.7 • C in January to 18.7 • C in July; the mean annual precipitation was 837.1 mm/year, ranging from 46.7 mm in April to 87.4 mm in December; and the mean daily solar radiation was 1037.6 kWh/m 2 , ranging from 16.8 kWh/m 2 in December to 155.5 kWh/m 2 in June [22].
Flanders is divided into 7 agricultural zones depending on the major soil type and agricultural activities (Figure 1) [24].Crop information was obtained from field trials located across Flanders.Determination of the soil textural class on the field trial locations was based on soil profiles, with soil information according to the Belgian soil classification system [25].The soil textural classes were converted to the USDA textural classes using the conversion matrix given in Appendix A (Table A1).The soil textural classes are clay loam in Koksijde; silt loam in Poperinge and Huldenberg; silt in Sint-Denijs, Nieuwenhove and Tongeren; and sandy loam in Tongerlo.cated across Flanders.Determination of the soil textural class on the field trial locations was based on soil profiles, with soil information according to the Belgian soil classification system [25].The soil textural classes were converted to the USDA textural classes using the conversion matrix given in Appendix A (Table A1).The soil textural classes are clay loam in Koksijde; silt loam in Poperinge and Huldenberg; silt in Sint-Denijs, Nieuwenhove and Tongeren; and sandy loam in Tongerlo.

Yield Gap Analysis
The concept "yield gap" was used to analyze the effects of extreme weather in relation to other yield-reducing factors.The theory and possible approaches to yield gap analysis are explained profoundly by [17].Yield gaps can be calculated by subtracting two yield levels (Equation ( 1)) and may also be expressed as a percentage of the highest yield level (Equation ( 2)).This is illustrated for the yield gap (YG) between water-limited (YW) and actual yield (YA):

Yield Gap Analysis
The concept "yield gap" was used to analyze the effects of extreme weather in relation to other yield-reducing factors.The theory and possible approaches to yield gap analysis are explained profoundly by [17].Yield gaps can be calculated by subtracting two yield levels (Equation ( 1)) and may also be expressed as a percentage of the highest yield level (Equation ( 2)).This is illustrated for the yield gap (YG) between water-limited (Y W ) and actual yield (Y A ): Each yield gap is explained by one or more yield-reducing factors, such as weather conditions, nutrient availability, the prevalence of weeds, pests, diseases and pollutants, farmer's skills or applied farming practices, such as irrigation and technology (Figure 2) [17].Through the identification of these factors for a given situation, case-specific gap-closing measures can be formulated.
Each yield gap is explained by one or more yield-reducing factors, such as weather conditions, nutrient availability, the prevalence of weeds, pests, diseases and pollutants, farmer's skills or applied farming practices, such as irrigation and technology (Figure 2) [17].Through the identification of these factors for a given situation, case-specific gapclosing measures can be formulated.
In this research, three yield levels were considered (Figure 2): (1) actual yield as observed on farms (YA), (2) yield as observed in experimental fields where optimal management practices are maintained (YM) and (3) simulated potential yield (YP).The actual yields (YA) were obtained from Statbel, the Belgian statistical office, [26] and are averaged per agricultural zone.
The optimal management yields (YM) were obtained from variety trials performed across Flanders throughout the past 10 years (Figure 1).Data on variety trials were obtained from In this research, three yield levels were considered (Figure 2): (1) actual yield as observed on farms (Y A ), (2) yield as observed in experimental fields where optimal management practices are maintained (Y M ) and (3) simulated potential yield (Y P ).
The actual yields (Y A ) were obtained from Statbel, the Belgian statistical office, [26] and are averaged per agricultural zone.
The optimal management yields (Y M ) were obtained from variety trials performed across Flanders throughout the past 10 years (Figure 1).Data on variety trials were obtained from agricultural experimental stations for winter wheat, maize and potato [27][28][29].The trials were held under optimal management practices.For example, pest and disease pressure was kept to a minimum.For winter wheat and maize, yields were averaged over all cultivars tested in the respective trials.For potato, only yields for the variety Fontane were used, since this is the most common late potato variety.
The potential yields (Y P ) were simulated using the crop growth model AquaCrop.One of the advantages of the AquaCrop model is its balance between simplicity, accuracy and robustness [30].The model makes use of a small number of explicit and widely available input variables at daily time steps which are necessary to account for extreme weather impacts.AquaCrop considers water and temperature as the major drivers for crop growth, which suits the focus on water and temperature related extreme weather events.For each growing season, the model was calibrated using weather, soil and crop growth data: (1) Daily weather data (minimum temperature, maximum temperature, average temperature, precipitation, wind speed, solar radiation, sun duration and relative humidity) for each trial location were obtained from the 5 km interpolated weather grid for Belgium [31].Daily reference evapotranspiration (ET0) was calculated by AquaCrop based on the latitude and altitude of the location, in addition to the available weather data.(2) Depending on the trial location, a soil file was created with either clay loam, silt, silt loam or sandy loam soil.Hydraulic characteristics were based on [32].(3) The default crop files of wheat, maize and potato were adjusted with information obtained from the field trials (Table 4): sow density, sowing, flowering and harvesting dates for winter wheat and maize and plant density, planting, haulm killing and harvesting dates for potato.The reference harvest index (HI0) was assimilated such that the simulated dry yield corresponded with the actual dry yield observed in the field trials.After calibration, the model was run in calendar mode, and the potential yield was calculated by multiplying the potential biomass with the HI0.By running the model in calendar mode instead of growing degree day (GDD) mode, the model did not consider the effect of temperature on crop phenology (and thus on final yield) [30].The potential biomass is the biomass obtained under water and optimal temperature conditions.The yield was calculated for each growing season, and the highest value was taken as the potential yield for the respective crop type on the corresponding soil.The most important AquaCrop parameters are listed in Appendix B (Tables A2-A4).

(Agro-)Meteorological Indicators
Only indicators related to high temperature, water deficit and excess were analyzed, as the occurrence frequency and intensity of these weather events will most likely increase by 2030-2050 [6,33].In line with previous research (Tables 1-3), four different indicators were defined.The indices were calculated for the main crop growth stages, since the impact of adverse weather depends on its timing within the crop growth cycle.Figure 3 shows the critical stages and the cropping calendar for winter wheat, maize and potato in Belgium.
Agronomy 2023, 13, x FOR PEER REVIEW 11 of 27 by 2030-2050 [6,33].In line with previous research (Tables 1-3), four different indicators were defined.The indices were calculated for the main crop growth stages, since the impact of adverse weather depends on its timing within the crop growth cycle.Figure 3 shows the critical stages and the cropping calendar for winter wheat, maize and potato in Belgium.The first meteorological indicator studied is the heat stress index (HSI) (Equation ( 3)): where t is the time in days and T is the temperature.Topt is the optimum temperature at which crop physiological processes run optimally, and Tmax is the maximum temperature at which physiological processes are greatly reduced.Table 5 shows the BBCH code [34], Topt and Tmax [35][36][37] for the main phenological stages of winter wheat, maize and potato.The first meteorological indicator studied is the heat stress index (HSI) (Equation ( 3)): where t is the time in days and T is the temperature.Topt is the optimum temperature at which crop physiological processes run optimally, and Tmax is the maximum temperature at which physiological processes are greatly reduced.Table 5 shows the BBCH code [34], Topt and Tmax [35][36][37] for the main phenological stages of winter wheat, maize and potato.Secondly, the precipitation deficit index (PDI) is calculated as the difference between precipitation (P) and the Penman-Monteith reference evapotranspiration (ET0) (Equation ( 4)).The indicator provides information about the excess or shortage of rainfall as compared with the requirements for overall plant growth.The water deficit index (WDI) and the waterlogging index (WLI) are indirectly related to the prevailing weather conditions, as they are based on the soil water balance.The soil water balance is influenced by crop type, crop growth and soil properties.The WDI (Equation ( 5)) and WLI (Equation ( 6)) indices are calculated as follows: Wr, FC(t) − Wr(t) Wr, FC(t) − Wr, PWP(t) , f or Wr(t) < Wr, FC(t) W LI(t) = Wr(t) − Wr, FC(t) Wr, SAT(t) − Wr, FC(t) , f or Wr(t) > Wr, FC where Wr(t) is the water content in the root zone at time t (days) and Wr,FC(t), Wr,PWP(t) and Wr,SAT(t) are the water content in the root zone at field capacity, permanent wilting point and saturation point, respectively.The crop growth stages emergence (S1) and flowering and tuber setting (S3) have an average duration of 14 days.For these stages, the daily (agro-)meteorological indicators were averaged.For the stages of vegetative growth (S2), grain filling/ripening and tuber bulking (S4), the daily indicators were integrated over the whole duration of the growth stage.
For the calculation of stage-bound HSI, the daily temperature data were used together with the phenological information from the field trials.PDI is based on daily rainfall and ET0.The daily root zone water content was modeled using the calibrated AquaCrop crop files for each growing season, which was subsequently used to calculate WDI and WLI.The relationship between (agro-)meteorological variables was investigated using descriptive statistics and linear regression in Rstudio [38].Correlation matrices were visualized using the package "corrplot", and significance tests were performed using the "cor_test" function in the package "rstatix".All variables significantly correlated, and a significance level of 10% (alpha = 0.1) was extracted.Subsequently, the goodness-of-fit indicators were calculated for multiple linear regression models, including all (agro-)meteorological indicators, with or without soil type as an additional explanatory variable.The package "modelsummary" was used to extract the goodness-of-fit indicators: Akaike's Information Criterion (AIC), coefficient of determination (R 2 ) and root mean square error (RMSE), as well as the package "hydroGOF" for mean absolute error (MAE) and index of agreement (d).Potential dry yields for potato were higher on silt loam (22.6 t.ha −1 ) compared with silt (16.0 t.ha −1 ) (Figure 6).Averaged over the growing seasons, the optimal management yield was higher for silt loam (12.4 t.ha −1 ) as compared with silt (9.5 t.ha −1 ).The average actual yield was slightly higher on silt loam (9.1 t.ha −1 ) as compared with silt (8.7 t.ha −1 ).The yield gap, however, was higher for silt loam.Under optimal management conditions, 55% of the potential yield was obtained on silt loam as compared with 59% on silt.Potential dry yields for potato were higher on silt loam (22.6 t.ha −1 ) compared with silt (16.0 t.ha −1 ) (Figure 6).Averaged over the growing seasons, the optimal management yield was higher for silt loam (12.4 t.ha −1 ) as compared with silt (9.5 t.ha −1 ).The average actual yield was slightly higher on silt loam (9.1 t.ha −1 ) as compared with silt (8.7 t.ha −1 ).The yield gap, however, was higher for silt loam.Under optimal management conditions, 55% of the potential yield was obtained on silt loam as compared with 59% on silt.

(Agro-)Meteorological Indicators
Figures 7-9 show the correlation matrices for all variables: stage-bound (agro-)meteorological indicators, soil type, optimal management yield and yield gap and actual yield and yield gap. Table 6 shows the variables that have a significant correlation (alpha = 0.1) with the absolute yields and the yield gaps.
For winter wheat (Figure 7; Table 6), both optimal management and actual yields were highly correlated to water deficit and waterlogging during the grain filling and ripening stage.However, waterlogging during the grain filling and ripening stage only occurred in one season.Higher yields were observed at higher water deficit levels during vegetative growth, flowering, grain filling and ripening.This trend corresponded to the evolution in the precipitation deficit index, where higher yields were obtained at more negative values of the precipitation deficit index.Heat stress in winter wheat mainly occurred during flowering, grain filling and ripening, and the effect on yield was more pronounced during grain filling and ripening.Higher yields were obtained at temperatures higher than the optimum temperature.Both the optimal management and actual yield gaps were highly correlated with heat stress during flowering, grain filling and ripening and with waterlogging during the vegetative growth stage.Higher heat stress resulted in lower yield gaps and higher absolute yields, while higher waterlogging resulted in higher yield gaps and lower absolute yields.Potential yields of winter wheat on clay loam (21.3 t.ha −1 ) were higher as compared with silt (17.3 t.ha −1 ) or silt loam (15 t.ha −1 ) (Figure 4).Averaged over the growing seasons, the optimal management yield was higher for clay loam (12.7 t.ha −1 ) as compared with silt (12.4 t.ha −1 ) and silt loam (10.6 t.ha −1 ).The difference was less pronounced for actual yield: 9 t.ha −1 for clay loam and silt compared with 8.6 t.ha −1 for silt loam.The highest yield gap for winter wheat was on clay loam.Under optimal management conditions, only 59% of the potential yield was obtained during the growing seasons of the 2011-2021 period, while on silt and silt loam it was 71%.
Potential yields for maize were the highest for silt (16.2 t.ha −1 ), followed by silt loam (14.9 t.ha −1 ) and sandy loam (14.7 t.ha −1 ) (Figure 5).Averaged over the growing seasons, the optimal management yield was higher for silt (13.6 t.ha −1 ) as compared with silt loam (11.8 t.ha −1 ) and sandy loam (11.3 t.ha −1 ).In contrast, the average actual yield on silt and silt loam were similar (11.6 resp.11.8 t.ha −1 ), while on sandy loam the yield was significantly lower (9.1 t.ha −1 ).The lowest yield gap was obtained for maize on silt.Under optimal management conditions, 84% of the potential yield was obtained on silt, while this was only 79% and 77% for silt loam and sandy loam, respectively.
Potential dry yields for potato were higher on silt loam (22.6 t.ha −1 ) compared with silt (16.0 t.ha −1 ) (Figure 6).Averaged over the growing seasons, the optimal management yield was higher for silt loam (12.4 t.ha −1 ) as compared with silt (9.5 t.ha −1 ).The average actual yield was slightly higher on silt loam (9.1 t.ha −1 ) as compared with silt (8.7 t.ha −1 ).The yield gap, however, was higher for silt loam.Under optimal management conditions, 55% of the potential yield was obtained on silt loam as compared with 59% on silt.

(Agro-)Meteorological Indicators
Figures 7-9 show the correlation matrices for all variables: stage-bound (agro-)meteorological indicators, soil type, optimal management yield and yield gap and actual yield and yield gap. Table 6 shows the variables that have a significant correlation (alpha = 0.1) with the absolute yields and the yield gaps.
For winter wheat (Figure 7; Table 6), both optimal management and actual yields were highly correlated to water deficit and waterlogging during the grain filling and ripening stage.However, waterlogging during the grain filling and ripening stage only occurred in one season.Higher yields were observed at higher water deficit levels during vegetative growth, flowering, grain filling and ripening.This trend corresponded to the evolution in the precipitation deficit index, where higher yields were obtained at more negative values of the precipitation deficit index.Heat stress in winter wheat mainly occurred during flowering, grain filling and ripening, and the effect on yield was more pronounced during grain filling and ripening.Higher yields were obtained at temperatures higher than the optimum temperature.Both the optimal management and actual yield gaps were highly correlated with heat stress during flowering, grain filling and ripening and with waterlogging during the vegetative growth stage.Higher heat stress resulted in lower yield gaps and higher absolute yields, while higher waterlogging resulted in higher yield gaps and lower absolute yields.For maize (Figure 8; Table 6), both optimal management and actual yields were highly correlated with heat stress during the grain filling and ripening stage and water deficit index during flowering and grain filling and ripening.The opposite trend for winter wheat was observed for the water deficit index.Yields dropped as the water deficit index increased during vegetative growth, flowering, grain filling and ripening.The trend in water deficit index corresponded to the trend in precipitation deficit index: higher yields were observed at higher values for the precipitation deficit index, closer to zero.Heat stress mainly occurred during grain filling and ripening.Lower yields were observed at higher heat stress.Throughout the growing season, maize was only marginally affected by waterlogging.Similar trends were observed for the optimal management and For maize (Figure 8; Table 6), both optimal management and actual yields were highly correlated with heat stress during the grain filling and ripening stage and water deficit index during flowering and grain filling and ripening.The opposite trend for winter wheat was observed for the water deficit index.Yields dropped as the water deficit index increased during vegetative growth, flowering, grain filling and ripening.The trend in water deficit index corresponded to the trend in precipitation deficit index: higher yields were observed at higher values for the precipitation deficit index, closer to zero.Heat stress mainly occurred during grain filling and ripening.Lower yields were observed at higher heat stress.Throughout the growing season, maize was only marginally affected by waterlogging.Similar trends were observed for the optimal management and actual yield gaps, which were highly correlated with heat stress during grain filling and ripening, precipitation deficit during flowering and grain filling and ripening and water deficit during flowering and grain filling and ripening.Higher heat stress and higher water deficit resulted in higher yield gaps and lower yields, while higher precipitation deficit resulted in lower yield gaps and higher yields.Potato optimal management yields (Figure 9; Table 6) were highly correlated with heat stress during the tuber bulking stage, while actual yields also showed a high correlation with precipitation deficit and water deficit during tuber bulking and waterlogging after planting.Actual yields were lower when the water deficit index decreased during tuber bulking.This corresponded with the trend in the precipitation deficit index, where yields increased with precipitation deficit.In contrast with the tuber bulking stage, a positive trend was observed for the water deficit index for actual yields during emergence, vegetative growth and tuber set.Heat stress in potato occurred in all crop growth stages, and the effect on both yield levels was most pronounced when heat stress occurred during tuber bulking.Lower yields were obtained at higher heat stress levels.Waterlogging occurred in all stages, but a slightly negative correlation was observed for actual yields and almost no correlation for optimally managed yields.In contrast to absolute yields, the optimal management had no significant correlation with any of the (agro-)meteorological Potato optimal management yields (Figure 9; Table 6) were highly correlated with heat stress during the tuber bulking stage, while actual yields also showed a high correlation with precipitation deficit and water deficit during tuber bulking and waterlogging after planting.Actual yields were lower when the water deficit index decreased during tuber bulking.This corresponded with the trend in the precipitation deficit index, where yields increased with precipitation deficit.In contrast with the tuber bulking stage, a positive trend was observed for the water deficit index for actual yields during emergence, vegetative growth and tuber set.Heat stress in potato occurred in all crop growth stages, and the effect on both yield levels was most pronounced when heat stress occurred during tuber bulking.Lower yields were obtained at higher heat stress levels.Waterlogging occurred in all stages, but a slightly negative correlation was observed for actual yields and almost no correlation for optimally managed yields.In contrast to absolute yields, the optimal management had no significant correlation with any of the (agro-)meteorological variables, while the actual yield gap was only significantly correlated to heat stress during emergence.Table 6 shows the variables that were significantly correlated (alpha = 0.1) with the yields and yield gaps of winter wheat, maize and potato.A small number of weather var iables were significantly correlated with potato yield (gaps) as compared with winter wheat and maize yield (gaps).Table 6 shows the variables that were significantly correlated (alpha = 0.1) with the yields and yield gaps of winter wheat, maize and potato.A small number of weather variables were significantly correlated with potato yield (gaps) as compared with winter wheat and maize yield (gaps).
Significant correlations were observed between explanatory variables, resulting in the muti-collinearity of regression and less reliable statistical inferences.However, the focus was on analyzing the explanatory value of all weather variables on yield.Figures 7-9 show the goodness of fit of the multiple linear regression for winter wheat, maize and potato.Adding soil type as an explanatory variable improved the model goodness of fit, indicating that soil type is a key variable for explaining yield (gap) variability.For all three crops, the multiple linear regression models for actual yield (gap) had better goodness-of-fit indicators compared with the models for optimal management yield (gap).For actual yield (gap), a higher proportion of the variability (higher R 2 ) was explained by the (agro-)meteorological variables as compared with the optimal management yield (gap).

(Agro-)Meteorological Indicators, Yield and Yield Gap Variability
The reference harvest index (HI) was crop-and cultivar-specific and generally ranged between 45-50%, 48-52% and 70-85% for wheat, maize and potato, respectively [30].The simulated harvest indices differed between the growing seasons of the 2011-2021 period.For winter wheat in 2016, HI was noticeably lower than its mean value.The 2016 spring was unusually wet [31] and disease pressure was high [39], resulting in large yield losses.AquaCrop, however, was not able to consider the disease pressure and simulated high yields due to ample water supply.This indicated that modeling of extreme weather is difficult, as multiple yield-reducing factors interact.
Simulated potential yields of winter wheat, maize and potato varied by region within Flanders due to differences in weather and soil type.Though the growing seasons varied largely in weather conditions and yields, the simulated potential yields were in line with previous research, thereby indicating a good performance of AquaCrop for crop yield simulation [30].For winter wheat, the simulated potential yields were 15, 17.3 and 21.3 t.ha −1 for silt loam, silt and clay loam, respectively.The simulated genetic yield potential for rainfed winter wheat across Europe was 11 t.ha −1 to 13 t.ha −1 , based on 13 sites [40].In the study presented here, potential yield was simulated under optimal water supply and was therefore higher than the potential yield estimated by [40].Simulated potential yields of maize were 14.7, 14.9 and 16.2 t.ha −1 on sandy loam, silt loam and silt, respectively.The simulated potential yields for rainfed maize ranged from 10.6 to 17.5 t.ha −1 across Europe and from 12-13 t.ha −1 for Belgium [41].The differences with our study are explained by the water-limited potential yield and the country-averaged actual yields, as simulated by the crop growth model WOFOST calibrated for larger agro-ecological zones.Simulated potential yields for potato ranged from 89 t.ha −1 on silt to 113 t.ha −1 on silt loam, whereby fresh yields were corrected for wheel traffic lanes and headlands.Potential potato yields can be up to 128 t.ha −1 , provided that irrigation is abundant, solar irradiation is high and the growing season is long [42].In Belgium, solar radiation levels are relatively low and potential yields may reach around 88 t.ha −1 [42], which is similar to the lowest simulated potential yield in this study.On average, 65%, 80% and 57% of the potential yield was achieved for winter wheat, maize and potato, respectively, under optimal management conditions.Achieving potential yields may not be economically and environmentally desirable.Yields on farmers' fields tend to reach a plateau at around 75-85% of the potential yield [16,17]. Achieving optimal crop and soil management is difficult, and the yield response to inputs follows the law of diminishing returns, so achieving potential yield may not be cost-effective for the farmer [16].In addition, natural resource efficiency may decline as farm yields approach potential yields.
Winter wheat preferred high temperatures to wet conditions (Figure 7; Table 6).Higher yields were obtained with a higher water deficit index (lower soil water content relative to field capacity) and a lower precipitation deficit index (less rainfall relative to evaporative demand).Higher yields were observed at temperatures higher than optimal, suggesting that the winter wheat varieties cultivated in Flanders can tolerate high temperatures.Heat tolerance in winter wheat has also been reported by other studies.Winter wheat in Germany [9] was less sensitive to heat during flowering, grain filling and ripening than to drought and waterlogging.A greater percentage of low winter wheat yields in Belgium was explained by excessive rainfall during flowering than by combined heat and drought during the growing season [2].A study of weather impacts on winter wheat cultivars in Europe indicated that several cultivars tolerated high temperatures, but it suggested that this may be partly explained by overall better weather conditions associated with higher temperatures [12].For winter wheat in Japan, a negative correlation was found between yield gap and both air temperature and vapor pressure deficit at grain filling, but no significant correlation was found for rainfall [15].Winter wheat yields and yield gaps were influenced by soil type, and (agro-)meteorological indicators better explained the variability in actual yield and yield gap as compared with optimal management yield and yield gap (Table 7).
Table 7. Goodness-of-fit indicators for a multiple linear model for winter wheat including all (agro-)meteorological variables, with and without soil type, for optimal management yield gap (Y P -Y M ), actual yield gap (Y P -Y A ), optimal management yield (Y M ) and actual yield (Y A ).

Model Type
Goodness-of-Fit Indicators Maize yields were the most vulnerable to heat stress during the grain filling and ripening stage and to water deficit index during flowering, grain filling and ripening (Figure 8; Table 6).For the studied growing seasons, heat stress mainly occurred during the grain filling and ripening stage, where lower yields were obtained at higher heat stress levels.Maize yields were negatively correlated with the water deficit index, while winter wheat yields were positively correlated.The opposite was true for the precipitation deficit index.Maize was more susceptible to drought in the 2011-2021 period compared with winter wheat.Although C4 crops have a higher water-use efficiency, the results of this study underline the importance of water availability and the absence of water deficit.Compared with winter wheat, the flowering date of maize occurs later in the year, when the frequency and intensity of (combined) heat and drought are higher [2].The occurrence of (combined) heat and drought stress has affected cereal crops across Flanders and is projected to increase in the near future [19,33].The sensitivity of maize to drought and heat stress was also reported in previous studies.In France, the predictive performance for extreme maize yield loss was high for both the temperature and precipitation indicators, but maize was found to be more vulnerable during the vegetative stage compared with the reproductive stage [10].For a similar study in Germany, drought had a higher impact on maize yield than heat and waterlogging, and the impact was higher when the drought event occurred during flowering and grain filling [9].Drought sensitivity in maize was also found in Belgium, where high rainfall was the indicator most associated with high yield [13].However, another study on weather impacts on winter wheat in Belgium showed that yield variation was mainly explained by low temperatures and excessive rainfall and to a lesser extent by combined heat and drought [2].Differences in results could be explained by a different analysis method, a different time window of the (agro-)meteorological variables studied or a difference in the frequency of occurrence of extreme weather conditions.Maize yields and yield gaps were influenced by soil type, and (agro-)meteorological indicators better explained the variability in actual yield (gap) as compared with optimal management yield (gap) (Table 8).Both optimal management and actual potato yields were correlated with heat stress during tuber bulking, with higher heat stress resulting in lower yields (Figure 9; Table 6).The emergence stage was most susceptible to waterlogging.Potato yields in farmers' fields were also highly correlated with the precipitation deficit index and the water deficit index during tuber bulking: yields increased when the ratio of rainfall to evaporative demand was more balanced and decreased when the soil water content dropped below field capacity.Optimal management and actual yield gaps showed overall less correlation with the (agro-)meteorological variables than absolute yields.In the Netherlands, drought during the growing season explained a large part of low potato yields, but most of the variability was explained by waterlogging at harvest [14].In Belgium, combined heat and drought around tuber set explained most of the low yields, while waterlogging around planting also explained a large proportion of the variability [2].Another study of weather impacts on potato in Belgium also indicated sensitivity to drought, and high rainfall was most associated with high yields [13].Potato yield (gap) was also influenced by soil type, and (agro-)meteorological indicators better explained the variability in actual yield and yield gap compared with optimal management yield and yield gap (Table 9).This study focuses on the effect of single adverse weather events.Compound events, such as the combined occurrence of heat and drought stress, can significantly affect yields [2].The effect of a single event may not be significant, while the combined occurrence with another event may greatly reduce yields.Significant (alpha = 0.1) interaction effects were observed, but no multiple linear model was constructed due to lack of observations.

Effect of Soil and Management Practices
Especially for winter wheat and maize, soil type added to the explained variability.For optimal potato management and actual yields, the added value of soil type was not clear.Soil type is indirectly related to the agro-meteorological variables' water deficit index and waterlogging index, as soil texture influences soil hydraulic characteristics.To further investigate the effect of soil type, separate correlation matrices per soil type were constructed (supplementary materials).Optimally managed maize yield on silt was significantly higher and had a lower yield variability compared with sandy loam and silt loam, indicating that crop yields on silt were less influenced by suboptimal weather conditions.Maize yields and yield gaps appear to be less correlated with weather variables on silt compared with silt loam and sandy loam (Figures S3-S6).For grain crops, the soil water holding capacity affected crop response to weather extremes due to its intrinsic relationship with soil texture [43].
The results of the multiple linear regression show that the prediction performance for actual yields and yield gaps is higher than for the optimal management yields and yield gaps for all three crops.The variation in actual yield and yield gap is better explained by weather variables, suggesting that optimal management practices mitigate the impact of adverse and extreme weather.Similarly, [44] advocated a decoupling of weather extremes and crop yield extremes due to irrigation, and [14] speculated a decoupling due to fungicide use.

Limitations and Future Perspectives
For the identification of weather-yield relationships using time-series analysis, long yield time series (≥10 y) are examined, as greater interannual weather and yield variability improve the validity of the results [12].For Flanders, considerable weather and yield variability was observed during the 2011-2021 growing seasons.Weather conditions ranged from "normal" to "unusually" wet, dry or warm compared with the 30-year average [31], and both "extremely" high (90th percentile) and low (10th percentile) yields compared with the 30-year average were obtained [26].The impact of certain weather extremes may be over-or underestimated if the frequency of occurrence during the period studied differs from that of other weather extremes [14], and therefore, not all adverse weather conditions were equally considered in this study.For instance, the occurrence of heat stress around early growth stages and waterlogging around late growth stages did not occur frequently during the 2011-2021 growing seasons.
The use of long yield time series most often requires detrending, as overall yields may increase due to technological improvements and climate change [7].By detrending yield time series, the interannual yied variability is better captured, and as interannual yield variability is associated with weather variability, the impact of weather extremes can be more accurately analyzed.No detrending was performed, as a maximum of 10 consecutive growing seasons was examined.In addition, yield stagnation has been observed for several crop types in Europe [7,45].
Other improvements include the use of longer (detrended) time series.Variety trials are organized each growing season to test the performance of several cultivars.Information from future field trials could be added to the current database.Future investigations could also look at nonlinear yield responses to weather extremes and the impact of compound events.

Conclusions
A yield gap analysis was carried out on 10 years of field trial data, and (agro-)meteorological indicators were related to the size of the yield gap between potential and management yield and between potential and actual yield.Temperature-and water-related indices were calculated for the main crop growth stages of winter wheat, maize and potato: emergence, vegetative growth, flowering/tuber set and grain filling and ripening/tuber bulking.
The yield gap approach allowed weather-related risk assessment, which in turn enables the formulation of adaptation or mitigation strategies at the field to farm scale.Winter wheat preferred higher temperatures at grain filling and was negatively affected by wet conditions throughout the growing season.Additional efforts are needed to reduce drought stress, such as improved varieties or mulching, and to improve field drainage.Maize was particularly vulnerable to drought throughout the growing season.Although C4 crops have a higher water-use efficiency, the results underline the importance of water availability and the absence of water deficit.Adaptation and mitigation strategies for maize should focus on reducing drought stress through improved varieties, irrigation or mulching.Potato was especially susceptible to heat and drought stress during tuber bulking and to waterlogging during the early growth stages, hence the importance of heat-tolerant varieties, proper soil management and good drainage practices to close the potato yield gap.
The (agro-)meteorological indicators better explained the variability in the actual yield gap compared with the optimal management yield gap for all three crops.Optimal management practices could therefore mitigate the impact of adverse and extreme weather and should be considered in future climate impact studies.

Conflicts of Interest:
The authors declare no conflict of interest.

Figure 1 .
Figure 1.Locations of field trials within the agricultural zones of Flanders.Labels w, m and p stand for winter wheat, maize and potato.The major soil textural classes (USDA) are sandy loam in the Campines, silt in the Loam Region, clay loam in the Polder Region and silt loam in the Sandy-Loam Region.

Figure 1 .
Figure 1.Locations of field trials within the agricultural zones of Flanders.Labels w, m and p stand for winter wheat, maize and potato.The major soil textural classes (USDA) are sandy loam in the Campines, silt in the Loam Region, clay loam in the Polder Region and silt loam in the Sandy-Loam Region.

Figure 2 .
Figure 2. Definitions of yield levels and yield gap approach used in this study, with potential yield (YP), optimal management yield (YM) and actual yield (YA).

Figure 2 .
Figure 2. Definitions of yield levels and yield gap approach used in this study, with potential yield (Y P ), optimal management yield (Y M ) and actual yield (Y A ).

Figure 3 .
Figure 3. Cropping calendar for winter wheat, maize and late potato in Belgium.

Figure 3 .
Figure 3. Cropping calendar for winter wheat, maize and late potato in Belgium.

1 . 27 Figure 4 .
Figures 4-6 show the yield gaps of winter wheat, maize and potato for the growing seasons of the 2011-2021 period.Agronomy 2023, 13, x FOR PEER REVIEW 13 of 27

Figure 5 .
Figure 5. Maize yield gaps during the 2011-2021 period: potential yield (YP), optimal management yield (YM) and actual yield (YA). Significant differences (Wilcoxon test; p < 0.05 or p < 0.001) YM on the three soils (yellow), for YA on the three soils (gray) and for the difference between YM and YA for each soil type separately (green, orange and purple) are indicated by a different letter.

Figure 4 . 27 Figure 4 .
Figure 4. Winter wheat yield gaps during the 2011-2021 period: potential yield (Y P ), optimal management yield (Y M ) and actual yield (Y A ). Significant differences (Wilcoxon test; p < 0.05 or p < 0.001) Y M on the three soils (yellow), for Y A on the three soils (gray) and for the difference between Y M and Y A for each soil type separately (green, orange and purple) are indicated by a different letter.

Figure 5 .
Figure 5. Maize yield gaps during the 2011-2021 period: potential yield (YP), optimal management yield (YM) and actual yield (YA). Significant differences (Wilcoxon test; p < 0.05 or p < 0.001) YM on the three soils (yellow), for YA on the three soils (gray) and for the difference between YM and YA for each soil type separately (green, orange and purple) are indicated by a different letter.

Figure 5 .
Figure 5. Maize yield gaps during the 2011-2021 period: potential yield (Y P ), optimal management yield (Y M ) and actual yield (Y A ). Significant differences (Wilcoxon test; p < 0.05 or p < 0.001) Y M on the three soils (yellow), for Y A on the three soils (gray) and for the difference between Y M and Y A for each soil type separately (green, orange and purple) are indicated by a different letter.

Figure 6 .
Figure 6.Potato yield gaps during the 2011-2021 period: potential yield (YP), optimal management yield (YM) and actual yield (YA). Significant differences (Wilcoxon test; p < 0.05 or p < 0.001) YM on the two soils (yellow), for YA on the two soils (gray) and for the difference between YM and YA for each soil type separately (green and orange) are indicated by a different letter.

Figure 6 .
Figure 6.Potato yield gaps during the 2011-2021 period: potential yield (Y P ), optimal management yield (Y M ) and actual yield (Y A ). Significant differences (Wilcoxon test; p < 0.05 or p < 0.001) Y M on the two soils (yellow), for Y A on the two soils (gray) and for the difference between Y M and Y A for each soil type separately (green and orange) are indicated by a different letter.

Figure 7 .
Figure 7. Correlation matrix (Pearson's) for winter wheat with potential yield (Y M ), optimal management yield (Y M and actual yield (Y A ). Heat stress index (HSI), precipitation deficit index (PDI), water deficit index (WDI) and waterlogging index (WLI) for emergence (S1), vegetative growth (S2), flowering (S3) and grain filling and ripening (S4).Darker blue colors indicate more positive correlation and darker red colors indicate more negative correlation.

Figure 8 .
Figure 8. Correlation matrix (Pearson's) for maize with potential yield (Y P ) optimal management yield (Y M ) and actual yield (Y A ). Heat stress index (HSI), precipitation deficit index (PDI), water deficit index (WDI) and waterlogging index (WLI) for emergence (S1), vegetative growth (S2), flowering (S3) and grain filling and ripening (S4).Darker blue colors indicate more positive correlation and darker red colors indicate more negative correlation.

Table 1 .
Effects of (agro-)meteorological indicators during crop growth stages on winter wheat yield.An overview of studies using yield-weather time series.

Table 2 .
Effects of (agro-)meteorological indicators during crop growth stages on maize yield.An overview of studies using yield-weather time series.

Table 3 .
Effects of (agro-)meteorological indicators during crop growth stages on potato yield.An overview of studies using yield-weather time-series.

Table 4 .
Overview of crop information obtained from field trials across Flanders used for calibration of AquaCrop and the assimilated reference harvest index (HI0) during calibration.
[2]o data were provided in the field trials.A norm value for potato in Flanders was adapted from[2].

Table 5 .
Optimal and maximal temperatures for main growth stages of winter wheat, maize and late potato.

Table 5 .
Optimal and maximal temperatures for main growth stages of winter wheat, maize and late potato.

Table 8 .
Goodness-of-fit indicators for a multiple linear model for maize including all (agro-)meteorological variables, with and without soil type, for optimal management yield gap (Y P -Y M ), actual yield gap (Y P -Y A ), optimal management yield (Y M ) and actual yield (Y A ).

Table 9 .
Goodness-of-fit indicators for a multiple linear model for potato including all (agro-)meteorological variables, with and without soil type, for optimal management yield gap (Y P -Y M ), actual yield gap (Y P -Y A ), optimal management yield (Y M ) and actual yield (Y A ).

Table A3 .
Relevant conservative and nonconservative crop parameters in AquaCrop for maize.

Table A4 .
Relevant conservative and nonconservative crop parameters in AquaCrop for potato.