Introduction

Extreme weather events such as high-intensity rainfall, heat waves and drought can cause damage to crops, jeopardizing the food security at global, regional and local level1,2,3. Extreme weather events are expected to occur more frequently in the future4,5, so it is important to quantify the impact of these events on yield. This knowledge is a prerequisite to be able to take adequate measures in terms of risk management and adaptation strategies such as improving soil resilience.

Most studies assessing climate change impacts on crop yields use crop modeling6. Crop models however simulate potential yields, not actual yields, and they have limited ability to assess the effects of extreme events7,8,9. Hence, this calls for empirical methods to assess impacts in farmers’ fields10. In the past, multiple studies have been performed to empirically evaluate the effect of extreme weather on crop yield3,11,12,13. While substantial differences in yield are found from year-to-year, it is nevertheless unclear how much of these differences can actually be accounted to the differences in weather (extremes) on farmers’ fields. The reason is that year-to-year changes are not only caused by weather changes but also by changes in soil and crop management and at larger spatial and temporal scales also by technology, markets, and policy14,15. Decoupling these effects is important, as it is the only way to fully understand the impact of extreme weather on yield, and consequently reason about the impact of soil and crop management given the weather circumstances during the growing season.

In order to decouple these effects, detailed information is required about weather extremes, soil quality and management decisions that could possibly influence yield16. Even though such data are necessary to estimate the (causal) effect of weather on yield, the availability of these data are scarce, especially at regional or global level. At local level, a farmer in the south of the Netherlands collected data that allow such an analysis. He mainly cultivates potato (Solanum tuberosum L.) for the French Fries industry on over 160 fields spanning over 600 ha per year (Fig. 1a), partly rented from other farmers. He has collected extensive data about the soils, the farm’s management and yield from 2015 up to 2020 (see Fig. 1 and Supplementary Materials Table SM.1 for more details)17. Moreover, detailed data of the weather during the season are available through a weather station nearby the farm (about 20 km away)18. These six years of data included an extremely wet year (2016), dry and hot years (2018 and 2020) and years with favorable growing conditions (2015 and 2017) (Fig. 1c). These data provide the opportunity to empirically analyze the causal effect of extreme weather on yield on farmer’s fields, which is important, because these extremes have occurred in the past 30 years relatively often (drought in about 20% of the years and extreme rainfall in 17% of the years (Fig. 2)). The mean yields at the farm are similar to mean yields on other farms and at national level (see Fig. 6a19) and when analyzing data from fields from a farm, the temporal yield variability is larger than when analyzing data at provincial or farm level (Fig. 6b19). This implies that an analysis at regional level, like13, cannot represent the variability experienced at farmers’ fields. Our analysis complements such analyses.

Fig. 1: Overview of farm characteristics and weather extremes.
figure 1

a The locations of all fields in the year 2020 of the farm. The area in which the fields lie is similar each year. The red dot indicates the location of the farm, of which the coordinates are given. b The average yield per year and its standard deviation. c The number of extreme weather events per year using definitions of the Agro Climate Calender on farmer’s fields in the south of the Netherlands21,22. For more details, see Supplementary Material Table SM.2.

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Fig. 2: Frequency of drought, high-intensity rainfall and sustained wet weather in the current period and in a period around 2100 under four different climatic scenarios.
figure 2

KNMI'23 scenarios are downscaled from the CMIP6 at high temporal and spatial resolution at national level. L (H) refers to the scenario with low (high) greenhouse submissions. d (n) refers to the scenario where the climate becomes drier (wetter).

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Hence, as a first contribution of this study, we quantified the causal effect of extreme weather on yield, by estimating between-year differences in potato yield solely caused by differences in weather circumstances. This was ensured by using a matching strategy with propensity scores, such that the fields under comparison were similar in terms of management and soil variables, basically mimicking a randomized trial20. These between-year differences were then analyzed using the definitions of extreme weather events in the Agro Climate Calendar for potato21, which we extended with drought based on22, resulting in estimates of the impact of extreme weather. As a second main contribution, because within each year, yields highly varied (Fig. 1b), we investigated how the impact of extreme weather differed between different kinds of fields. Third, using the KNMI’23 scenarios recently downscaled from CMIP623,24 at high temporal and spatial resolution, we showed how the frequency of extreme weather changes due to climate change.

Results

Estimated impact of extreme weather

Average yield levels ranged from 35 ± 14 ton ha−1 (2016) to 55 ± 10 ton ha−1 (2017) (Fig. 1b). In order to analyze the impact of extreme weather on yield, a prerequisite was to estimate the mean differences in yield between years caused by the weather. Separately for each pair of years, we created pairs of fields with similar propensity scores. For all pairs, we obtained good quality matches (see Table SM.4 of the Supplementary Material). Consequently, we were able to estimate fifteen pairwise differences in yield caused by weather (Fig. 3 and Table SM.3 of the Supplementary Material). There are small differences between 2015 and 2017 (the two favorable years), and there are also small differences between 2016 and 2018 (the years with high-intensity rainfall and drought, respectively). Large differences are observed when yields of 2015 or 2017 are compared to 2016 or 2018.

Fig. 3
figure 3

Yield differences between each pair of years.

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Using Spearman’s Rank Correlation, the between-year differences in yield were correlated with the between-year differences in weather extremes as defined in the Agro Climate Calender21. Definitions of drought were included based on refs. 22,25 to get a first indication of the impact of drought during summer and spring on potato yield. As the correlation between yield differences and differences in drought during summer was high, we evaluated how applicable this definition of drought was. In order to do so, we performed a sensitivity analysis varying the threshold for drought (length of period and amount of rainfall) (see Supplementary Material Table SM.5). The appropriate definition was identified as a period of 30 days with a total of less than 10 mm of rain, because it had the highest correlation with yield, and resulted in periods of drought in 2018 and 2020.

The results indicated that the main causes of yield loss were drought, high-intensity rainfall and sustained wet weather (Fig. 1a), while all other extreme events had a lower impact on yield loss. In 2016, high-intensity rainfall occurred in the same period as the period of sustained wet weather (in a period of three weeks, the total precipitation was 190 mm). The damage of the potato plants was mainly caused by the large amounts of water: ditches and streams flooded, and farmers were not able to drain the water from their parcels26. This indicated that the low yields of 2016 were caused by a combination of circumstances: wet circumstances before the high-intensity rainfall event caused the soil to already be saturated before the high-intensity rainfall event, resulting in large damage on the potato plants. Based on these observations, and given that there was no significant difference in yield between 2016 and 2018, we concluded that the impact of a period of 60 days of drought (as also observed in 2018) and high-intensity rainfall combined with sustained wet weather is similar, and that these two types of extreme weather events have the most impact on yield differences between years.

We used these two extreme events into a linear regression equation as independent variables. We found that a period of high-intensity rainfall combined with sustained wet weather resulted in 19 ± 0.8 ton ha−1 yield loss, and a period of drought 7 ± 0.4 ton ha−1 yield loss, which doubled if the period of drought is twice as long. Only 2 ± 0.5 ton ha−1 in yield differences came from other (extreme) weather events, such as heat waves. As years without any extreme weather events obtained about 54 ton ha−1 on average, high-intensity rainfall causes a yield loss of 35%, and drought a yield loss of around 13% (Fig. 4).

Fig. 4: The effect of extreme weather on potato yield differences on sandy soils in the south of the Netherlands.
figure 4

a The results of Spearman’s Rank Correlation between the extreme weather events and potato yield. `*' indicates that p-value  < 0.05, `ns' indicates a non-significant result. b The estimated effect of high-intensity rainfall and drought on potato yield. 98% of the variability can be explained with these extremes.

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Within-farm variability in impact of extreme weather

The impact of drought and high-intensity rainfall varied per field category (drought sensitivity, possibility of irrigation, nutrient richness; Fig. 5, Supplementary Material Tables SM.6 and SM.7). Interestingly, drought had the highest impact on wet fields, and the smallest on dry fields. Two explanations are likely: dry fields were planted first, and therefore potato plants were larger and thus stronger during the period of drought, making them more resistant against extreme events. In addition, irrigation was not possible on all fields. Dry fields were more often irrigated than average and wet fields, which explains why the impact of high-intensity rainfall was smaller on fields that are irrigated. Finally, the nutrient content level of the soil had a positive effect in tempering the impact of drought, given that the estimated effect monotonically decreased if the nutrient content increased. The impact of high-intensity rainfall was the smallest on poor fields, most likely because over 50% of all poor fields were also dry.

Fig. 5: Estimated effect of high-intensity rainfall combined with sustained wet weather and drought on each of the classes within each field category.
figure 5

Drought sensitivity level relates to the electrical conductivity of a field, where fields with a high electrical conductivity were wet, with a medium electrical conductivity were average, and with a low electrical conductivity were dry. Irrigation indicated whether this was possible on a field. Richness relates to nutrient content level: poor fields were expected to have no N and K supply, average fields were expected to have 50 N kg ha−1 and 50 K kg ha−1 supply, and rich fields were expected to have 100 N kg ha−1 and 100 K kg ha−1 supply. It should be noted that there is an interaction between drought sensitivity and irrigation, where dry fields are more often irrigated than average and wet fields.

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Frequency and impact of extreme weather events in the past and in the future

In the last decade (between 1991 and 2020), there was an episode of drought or high-intensity rainfall in 37% of the years. In those years, even though high-intensity rainfall occurred in 17% of the years, only in 7% of the years (i.e., 1998 and 201626,27) this event caused water damage on crops. As in 2016, the water damage in 1998 co-occurred with sustained wet weather, indicating that non-beneficial weather circumstances need to be surrounding the high-intensity rainfall event in order to cause damage to crops.

The frequency of drought, high-intensity rainfall and sustained wet weather increases in all four climate scenarios of KNMI’23 compared to the current period (Hd,Hn,Ld and Ln), consisting of high and low greenhouse emissions (H and L, respectively), both simulated in the case that the climate becomes drier (d) or wetter (n) (Fig. 2 and Supplementary Material SM.8). In 2100, under the L scenarios, the frequency of events of high-intensity rainfall and drought is expected to stay similar to the current period, but there is an increase in sustained wet weather (from 27% up to 33–40%). This increases the chance that high-intensity rainfall occurs simultaneously with sustained wet weather, and thus increases the risk of large yield losses, even though the total affected years with drought or high-intensity rainfall does not increase. In both H scenarios, the total number of affected years will increase to 47%-50%. If the climate becomes drier (Hd), the frequency of drought will substantially increase from 20% up to 33%, the frequency of high-intensity rainfall will increase as well (from 17% up to 23%), but the frequency of sustained wet weather will substantially decrease (from 27% to only 10%). This indicates that the chance that high-intensity rainfall will occur with a period of sustained wet weather will be significantly smaller, and thus the risk of large yield losses due to this combination as well. At the same time, the chance that both drought and high-intensity rainfall occur in the same year will increase, which may also cause flooding problems because of the reduced infiltration capacity. If the climate becomes wetter (Hn), the increase in periods of drought will be small (from 20% up to 23%), whereas the frequency of high-intensity rainfall is expected to increase substantially (from 17% up to 27%) and the frequency of periods with sustained wet weather is expected to stay the same. This implies an increased frequency of high-intensity rainfall in combination with drought or sustained wet weather, and hence increased yield losses. Overall, in the current period, the average yearly yield loss is about 4% and is expected to increase up to 6.3% due to an increase in frequency of high-intensity rainfall and drought.

Discussion

Crop models often have trouble explaining yield anomalies in farmers’ fields, because the impact of extremes is not modeled adequately, in that crops continue to grow as if no damage occurred after the extreme weather event15,28,29. In addition, calibrating a crop model requires to make model choices according to the soil and management, and it is hard to do this correctly, especially given the fact that hundreds of fields need to be calibrated. Alternatives to the use of crop models can be found in qualitative or statistical approaches, but many of the existing studies on the impact of extremes are not causal and imprecise (i.e., a reported range of the impact of high-intensity rainfall between 25% and 75%)21,22,30, or use regional data, averaging out the often local impact of extreme weather13,25. Our empirical approach, in contrast, corrects for all management and soil differences between years due to the matching procedure used, which allows us to adequately estimate the between-year differences in yield solely caused by the weather, and to quantify the impact of extreme weather precisely.

High-intensity rainfall combined with sustained wet weather and drought were the main causes of yield loss of potato on sandy soils in the Netherlands, causing respectively a yield loss of 36% and 13%, of which the latter is doubled if the period of drought is twice as long. Other weather extremes such as wet fields during winter, and heat waves explain only a very small part of the between-year variability in yield differences. The new climate scenarios indicate that their impact will increase in the future, and about 50% of the years will be affected by an extreme weather event with impact under the high emission scenarios.

Crop models in the current form estimate that, because of the elevated CO2 levels, potato yields will increase up to 27%15,31. This beneficial effect on potato growth cannot be captured with the used empirical approach. To capture both the effect of gradual changes and extreme events, data-driven and process-based models should be combined9,15,32.

While previous studies on the effect of extreme weather identified high-intensity rainfall as one of the main causes of yield loss in potato production in the Netherlands before21,22,25,30,33, the effect of drought was less apparent. In contrast to the results of our study, these papers identified heat waves causing second-growth as one of the major climatic risks for potato production. In the Netherlands, a period of drought during summer is often accompanied with one or more heat waves, but the occurrence of a heat wave does not necessarily have to be accompanied with a period of drought (period between 1991–202034). Therefore, the impact of heat waves and drought becomes intertwined and the effect of drought on yield could also be accounted to heat waves. Our analysis included two years in which heat waves occurred without a period of drought (2015 and 2019). In fact, 2015 was the year in which yields were the highest (after matching), and 2019 included the hottest day ever recorded since the start of the temperature measurements35, and the difference between 2015 and 2019 was only small. Therefore, it seems that potatoes - or at least Fontane, the most used variety at the farm - is relatively robust to a short period of heat, and yield losses only occur when heat waves are combined with a period of drought. Experiments in 2019 and 2020 that aimed to improve the simulation of potential potato yields also support this statement36.

The south of the Netherlands has a moderate maritime climate, and the area in which the farmer operates mainly consists of sandy soils. These soils are heterogeneous, because the farmer cultivates many small parcels rented from other farmers (and thus all have a different past) that are spread out over a large area surrounding the farm (60 km2). Due to the heterogeneity of soils, other potato farms that operate on sandy soils in a moderate maritime climate are expected to experience a similar impact of extreme weather on yield17. This area is important for potato production, because potato is one of the major crops throughout the world37 and the Netherlands has the second highest export value globally of agricultural commodities38.

In order to adapt against drought, irrigation shows to have the highest potential, given the large reduction in yield loss. Interestingly, when irrigation is possible on a field, the impact is not reduced to zero. At the farm, the irrigation machinery capacity is limited and irrigation is not possible on all fields, and timing of irrigation is not always optimal19. Therefore, improvement of the irrigation management is helpful to adapt against drought, where opportunities could lie in studies such as39 that aim to improve allocation of irrigation. Other opportunities to adapt against drought lie in the improvement of the water holding capacity of the soil. This has as an advantage that it is possible on all fields, and it could even further increase the impact of irrigation. Soils can be improved by applying soil organic matter to improve water holding capacity40.

The potential to adapt against high-intensity rainfall is less obvious: dry fields cope better with high-intensity rainfall, probably also because they are planted earlier. Planting earlier on wetter fields is not always feasible, because the seed potatoes would rot due to the soil’s condition. Therefore, other adaptation measures are necessary as well, such as developing varieties that can better cope with high-intensity rainfall (and preferably to drought as well)11,22. In addition, during the growing season, if an extreme weather event has occurred, management should be adjusted according to its impact. In that case, the farmer could lower the amount of fertilization in order to support the expected growth, preventing a surplus of provided nutrients25,41.

Currently, the highest potato yields of the Netherlands are obtained in the province of Flevoland and Noord-Brabant42. The latter is the province in which our farm is located, and based on Fig. 2, we can expect that due to climate change the frequency of drought and high-intensity rainfall will increase to at least 50% of all years in the near future. These extreme events both significantly reduce potato yields and consequently, lead to high between-year variability in yield. Therefore, the productivity and income of the farms will highly vary from year-to-year as well, in line with the results of ref. 30. Climate change is not the only issue that might affect the possibility for crop production in this area: the soils are burdened with excessive amounts of ammonia and nitrogen oxides43. This affects protected areas, where soils become acid and biodiversity decreases. The Netherlands has the obligation to protect nature by European law44, and therefore the government needs to reduce these emissions. Both the increase in extreme weathers due to climate change and the nitrogen crisis reduce the chance that this area can play a similar role in potato production in the future as it has played in the past. Opportunities for this region highly rely on the effectiveness of the adaptation strategies, and the costs to invest in those.

Methods

Data collection

The data were collected by Van den Borne Aardappelen, a farmer in the South of the Netherlands. Data from 2015 until 2020 were used (see Supplementary Material Table SM.1 for all variables). Within these six years, we have two years with favorable conditions for potato production (2015 and 2017). Between the years 2006 and 2020, the year 2017 was a great year for potato production, with the highest average yield in the Netherlands within these 15 years (see Fig. 1 in ref. 19). The data of the industry and FADN dataset indicates that in 2015 yields were also high. In addition, we see that very high yields were also obtained in 2015 on an other farm (i.e., Scholtenzate, Fig. 4 in ref. 19). Moreover, in ref. 13, Fig. 1 indicates that in 2015 and 2017 no weather extremes took place. This indicates that these two favorable years are representative for good circumstances for potato production in a longer time window.

The farmer mainly cultivates Fontane potatoes for the French fries industry. This variety stayed the same across the years and often cultivated by farmers on sandy soils, as the yields of Fontane are often high19,36. The fields were spread over the south of the Netherlands and the north of Belgium. This area contains sandy soils. As potatoes can only be cultivated on the same parcel once per four years, most fields vary from year-to-year, but in 2015 and 2019 as well in 2016 and 2020 there were fields cultivated in both years. Between the years in which the farmer of the case study cultivated the fields, other farmers manage the fields to cultivate them with different crops, and thus changing the nutrient content of the field. In addition, the farmer of the case study did not manage these fields exactly in the same manner in the years when he cultivated the fields: the seed potato size often changed, as well as the seed potato supplier. Because of these changes, we assumed that all fields were unique. Additionally, the farmer collected data of all kind of variables that could influence yield, including soil nutrient content and management variables.

Climatic conditions

The Netherlands has a temperate maritime climate. In Eindhoven, 22 kilometer away from the farm, a meteorological station captured temperature, radiation and rainfall. From 2000 until 2020, the average temperature was around 6.7 °C during winter (December until January). Temperature slowly increases during spring and reaches a maximum of 23.5 °C in the summer (June until August). During summer, the average solar radiation is 17.7 MJ m−2, decreasing to 3.1 MJ m−2 in the winter. The average yearly rainfall is 755.8 mm y−1.

The data from 2015 up to 2020 were used to analyze the between-year differences. 2016 was a very wet year, with large yield losses due to high-intensity rainfall. The years 2018 and 2020 were extremely hot and dry years, with almost no rain for a period of 60 and 30 days, respectively. 2019 experienced multiple heat waves. In one of those heat waves the highest temperature until date was achieved, reaching over 40 C∘. The years 2015 and 2017 had very favorable growing conditions, resulting in high yields.

Estimating yield differences caused by the weather

We estimated pairwise yield differences caused by weather using the Potential Outcome Model45. Here, it is a requirement that the fields under comparison are only randomly different from one another on all background covariates (e.g., management and soil variables), both observed and unobserved. In this study, these differences are non-random, because the analysis of the on-farm collected data can be seen as an observational (non-randomized) study in which there are dependencies among management and soil variables, and among the year in which the field is cultivated (and thus the extreme weather events as well). In order to estimate the causal effect of weather on yield, our goal was thus to design our nonexperimental study as if it was a randomized experiment.

This goal was achieved by creating pairs of fields between each set of two years that have similar background variables, using a matching method16, for which we assumed that there were no unobserved confounders anymore. In order to match fields, it was first necessary to define the distance or closeness of the fields in terms of their background variables. This distance defined how similar a pair of fields was. It should be noted that fields could be similar for many reasons, e.g., some fields might be similar because they have a high N soil content, others might be similar because they have a low K soil content. Therefore, the distance measure ensures that the selected fields from each of the two years have a similar within-year variability with respect to the background variables when the exact same weather would occur.

To define the distance, two aspects were considered: which variables to include and how to combine these variables into one distance measure. For the first aspect, we only used variables that were fixed in the beginning of the season, such as soil samples, the possibility to irrigate and seed size. We excluded three different variable types. First, we excluded variables that were a response to the weather (e.g., the number of times a farmer irrigated, or which diseases occurred). Second, we excluded variables that were visible through other variables (e.g., manure application before planting is visible in the soil samples that are taken later on), and third, we excluded variables that were a reaction to other included variables (e.g., fertilizer amount is based on the soil samples or nutrient content level of the field). This ensured that only variables were included that could directly influence yield independent of weather circumstances, and were not related to the causal relation we were interested in. We included variables related to yield due to the sample size (about 50-70 fields per year). Which variables to include was determined by applying Spearman Rank correlation between the background variables and yield for each year separately.

For the second aspect, all used variables had a significant correlation with yield in each of the yearly analyses (which resulted in soil N, soil K, soil S, seed potato size and irrigation to be selected). These variables were included as independent variables into a logistic regression model that predicted in which year the field was cultivated. We used the linear predictors as the propensity score of field i, e.g.,

$${e}_{i}=\hat{\beta }{X}_{i}$$
(1)

with \(\hat{\beta }\) the estimated coefficients of the background variables in the logistic regression. The linear predictors tend to be closer to a normal distribution than the corresponding predicted probabilities46.

The propensity score was used to calculate the similarity between two fields; two fields with similar propensity scores were considered to have similar background variables. Two years had similar sets of fields if the propensity scores of all fields cultivated in one year were similar to the propensity scores of fields in the other year (e.g., those years had a similar distribution of propensity scores). The distance between each field i from the first year of the pairwise comparison and field j from the second year was calculated as follows:

$${D}_{ij}=\parallel {e}_{i}-{e}_{j}\parallel$$
(2)

We used 1: 1 nearest neighbor matching to create pairs of fields47 with a caliper of 0.25 standard deviations to avoid poor matches48. The MatchIt package of R was used to perform the matching procedure49.

After matching, we evaluated the quality of the matches using three balance measures50:

  • Standardized difference of means of the propensity score (should be less than 0.5),

  • Ratio of variance of the propensity scores (should be between \(\frac{1}{2}\) and 2),

  • For each background variable, the ratio of the variance of the residuals orthogonal to the propensity score (good if the value is between \(\frac{4}{5}\) and \(\frac{5}{4}\), of concern if it is between \(\frac{1}{2}\) and \(\frac{4}{5}\) or \(\frac{5}{4}\) and 2, and bad otherwise).

If the quality of the matches was good and thus balance was achieved, we pooled the matched fields into two datasets and applied a t-test to calculate the mean difference.

Analyzing the impact of extreme weather

In 2005, policy makers and other local stakeholders initiated a study to assess the impact of climate change on the major crops in the north of the Netherlands21. The goal of this study was to identify the most important risks and to determine which adaptation measures would be the most cost-efficient under different scenarios of climate change. The final result was the Agro Climate Calender: of multiple extreme weather events the impact on crop production was assessed based on expert judgment, literature and crop models for different agro-ecological regions, including clay, peat and sandy soils21. As the Agro Climate Calender was specifically designed for the Netherlands, including regions with sandy soils such as the region in which the farm lies, we used its definitions (see Supplementary Material SM.2 for a list of all events). For potato, we extended the set of events by with a definition of drought, and calculated which and how many extreme weather events occurred per year. As we use meteorological definitions, the intensity of an extreme weather event is captured by a combination of rainfall amount, temperature and number of days. For example, a period of drought becomes more intense when it spans a larger number of days. The main purpose of these meteorological definitions is that they capture the extreme conditions within each year properly, such that we could calculate the difference in frequency of the extreme weather event for each pair of years. These were then combined with the pairwise differences in yield. For each extreme weather event, we calculated the correlation between the differences in frequency and the differences in yield using Spearman Rank Correlation. Based on the results, we used linear regression to predict yield differences with the most severe extreme weather events, of which the estimated coefficients indicate the quantitative impact the weather extremes on yield. The quality of this model was verified using the R2 (linear regression on the observed and predicted observations). Because there is a dependency between the observations, the estimation could possibly result in a lower estimate for the standard error of the linear regression coefficients, but it is likely that it does not influence the estimated sizes51.

As there was no adequate definition of drought for potato yet, we analyzed different definitions of drought for potato varying from a period of drought of three weeks up to a period of drought of 60 days with steps of five days each (with an exception of the first increase, where we added just four days), based on the definition of drought for sugar beet given in ref. 22. In addition, we changed the amount for rain with steps of 5 mm from 5 mm up to 15 mm to investigate how strict the definition of drought should be. For each definition of drought, we calculated the difference in drought between each pair of years, calculated the correlation with mean differences in yield using Spearman Rank Correlation to determine the events with the highest relation to yield and then choosing the longest period of drought with the highest correlation to yield. In order to further justify this choice, we also checked in which years periods of drought were found: in both 2018 and 2020 the potato plants were damaged due to drought, which was not the case in the other years. Therefore, besides a high correlation, we ensured that the definition also matched with the observations in practice.

Analyzing within-farm variability in impact of extreme weather

The within-year yield variability at the farm was high (about 10 ton ha−1 on average each year) (Fig. 1b) due to variability in management and soils17. This soil and management variability could influence the impact of extreme weather events on yield, and therefore also indicate how effective climate adaption actually is. Therefore, in order to get a first impression of how effective adaptation measures are, we analyzed the impact of extreme weather on different field categories within each matched pair of years. The used categories were the drought sensitivity, the possibility to irrigate, and the nutrient content level of a field. The drought sensitivity level (wet, average or dry) related to the electrical conductivity and the judgement of the farmer himself: in practice, fields with a higher electrical conductivity were likely to be wet, while fields with a lower electrical conductivity were more likely to be dry. The nutrient content level of a field (rich, average or poor) related to the expected nutrient supply throughout the season, which was mainly driven by the manure application at the beginning of the season. On rich fields, it was expected that 100 N kg ha−1 and 100 K kg ha−1 was supplied, on average fields, 50 N kg ha−1 and 50 K kg ha−1 was supplied, and on poor fields, there was no N or K supply possible. Both the drought sensitivity and the richness level were used by the farmer: based on the drought sensitivity level, the planting order was adjusted (with drier fields planted sooner), and based on the nutrient level, the farmer adjusted the fertilization throughout the season. Finally, irrigation was not possible on all fields, and dry fields were more often irrigated than wet fields.

For each class within each category (eight classes in total), we calculated the mean difference in yield between a pair of years using a t-test, which resulted in fifteen pairwise mean differences for all eight classes. We then applied the same strategy as when analyzing the aggregated effect of extreme weather on yield: we applied Spearman Rank Correlation to determine which extreme weather events had the most severe effect on yield, and used these in a linear regression equation as independent variables to estimate their quantitative impact on yield. The quality of the model was assessed using R2 (linear regression on the observed and predicted observations).

Future frequencies of extreme weather events

As a result of climate change it is expected that the number of extreme weather events increases and, therefore, it will become more frequent that potato yield is affected by extreme weather. To quantitatively estimate the increased occurrence of extreme weather, we compared the past thirty years (1991-2020) with the future expected climate of the Netherlands under four scenarios (Ln, Ld, Hn and Hd) as described in the KNMI’23 scenarios23. These scenarios are downscaled from the CMIP624 at high temporal and spatial resolution to make them specific for the Netherlands. In contrast to the CMIP6, the KNMI does not differentiate between different models and outputs, but groups all solutions with respect to the four scenarios. In the L (Low) scenarios, the greenhouse emissions are limited, and therefore the temperature rise is limited as well, in line with the Paris Agreement52. Under the L scenarios, the temperature rise is expected to be about  + 0. 9 ∘C in 2050, and will not rise any further. On the other hand, under the H scenarios, the highest emission scenario is assumed, and therefore the temperature rise will be high (about  + 1. 5 ∘C, in 2050, and  +4 ∘C in 2100). n and d refer to the yearly precipitation: under the n scenarios, the amount of yearly precipitation will increase, while under the d scenario, the yearly precipitation will decrease.

The KNMI’23 scenarios consist of two different projected time series; bias corrected series (BC) and time transformed series (TT). The main difference is that the TT transforms the observed time series using the output of the climate models preserving the statistics of the future climate, and that the BC uses the time series from the future climate runs directly, and corrects them for biases in the runs (with the same model) for the current climate. In addition, the BC was based on a grid (12 by 12 km), and every grid was potentially based on multiple observation stations, while the TT was based on an individual time series of one observational station. The BC consisted of many runs, which needed to be aggregated, while the TT resulted in one transformed final time series per scenario. As a result, the weather extremes were slightly flattened in the BC in comparison to the TT. Using the TT scenarios53, we obtained four climate projections for the region in which the farm lies for a period around 2100 (2086–2115) (as it is expected that under the L scenarios the climate does not change any further). These projections were then used to calculate the frequency of extreme weather events: throughout this projected period, for each scenario, we calculated how many times the weather extremes occurred as defined by the Agro Climate Calender and the additional definition of drought (Section 3). These were then compared with the current frequency of extreme weather. The estimated frequencies allowed us to analyze the impact of climate change on potato yield. In order to calculate the yearly average effect, we calculated the probability of each weather extreme based on the historic data between 1991–2020.

In addition, we assumed that if two weather extremes that did not happen in the same year resulted in large yield losses, were mutually exclusive, e.g., a year is either wet or dry (and never both). Based on these assumptions, we calculated the probability that an weather extreme or a combined effect of two weather extremes occurred within one year, which we then multiplied with the estimated impact on yield, resulting in the average yearly yield loss.