Crop yield data for the period 1965–2020 over the 21 Swedish counties (län in Swedish) was obtained from Statistics Sweden (Statistikdatabasen, 2023), for the most commonly grown cereals in the country, i.e. winter wheat, spring wheat, spring barley and oats (Fig. 1). The percentage of unavailable data was 18 %, 33 %, 1 % and 13 %, respectively, and can be ascribed to either uncertainty in yearly yield cultivation (i.e., yield not meeting reporting criteria) or confidentiality reasons (i.e., crop sown only in few fields, Statistikdatabasen). The fraction of cultivated area per county was higher in the south where conditions are more favorable, permitting cultivation of all four crops, whereas only oats and spring barley were reported for the north (Fig. 1).

For meteorological data, we used gridded observed daily precipitation as well as average, minimum and maximum daily temperature values from E-Obs gridded data (Cornes et al., 2018) version 26.0e at 0.1 resolution. Counties extend over 2.9–98.2 km² and include large areas that are not cropped due to unsuitable climatic and soil conditions. Hence, we considered as representative of each county the gridded meteorological data averaged over cropped areas of the county. The cropped area was assumed to match the Non-irrigated arable fields in the CORINE land cover map (European Environment Agency, 2020). The 2006 map (CLC2006) was used as representative of the entire period.

We used linear mixed effect models (Bürger et al., 2012; Smith et al., 2005) to explore crop yield responses to climatic indicators during the identified periods. We fitted separate models for each crop, with yield Y as the dependent variable, and a set of explanatory climatic indicators as fixed effects. Neither yields nor climatic indicators were de-trended, and log-transformation of yields was unnecessary because the yields were not skewed. This also had the advantage that fitted parameters could be directly interpreted as changes in yield per unit change in the climatic conditions. We included time elapsed from year 1965 (t) as a continuous variable in all models, thus accounting for the combined impacts of climate change and increasing CO₂ emissions, as well as technological improvements, including variety and management changes. Furthermore, year and county were included as categorical random effects in all models to consider spatiotemporal heterogeneity and variations over the study area.

We considered three types of models for each crop. The first type had the composite precipitation-temperature indicator, dryness index, as explanatory variable to capture the role of precipitation and temperatures at the same time. Dryness index can summarize key aspects of soil water availability essential for crop growth through interplay between precipitation and temperature, thus being used as an indicator to capture balance between water supply and energy-driven demand. As such, dryness index provides a more process-oriented view at the relationship between precipitation, temperature, and their interactions. We included also quadratic dependence of yield on dryness index to account for excessive dryness (Luan et al., 2022). The fixed part of the model was 1Y=β0+βtt+βDIDI+βDI2DI2 where Y is the yield of the crop of interest, β0 is the global intercept, βt, βDI and βDI2 represent dependences of yield on t, DI and DI², respectively.

The second type of model aimed at quantifying the role of conditions that either extend over the whole period considered (e.g., averages), or for a potentially substantial part of that (e.g., dry spells). We focused on pairs of interacting indicators representing precipitation (x_P) and temperature (x_T) characteristics, separately. We considered three pairs of x_P and x_T indicators, each reflecting different aspects: (i) Precipitation sums (Psum) and temperature averages (Tmean), characterizing average conditions, (ii) precipitation and temperature variance (Pvar and Tvar), characterizing the variability of the conditions, or (iii) maximum length of the dry spells (CDD) and temperature averages (Tmean), characterizing the occurrence of dry spells, the effect of which is expected to be more marked at higher temperature. As fixed effects, in its most complex form, the model included a quadratic dependence on x_P and x_T as well as all the possible two-way interactions, because the damaging effects of low precipitations are stronger with high temperatures and vice versa. The fixed part of the model was 2Y=β0+βtt+βP(x_P)+βT(x_T)+βP2(x_P)2+βT2(x_T)2+βPT(x_P)(x_T)+βP2T(x_P)2(x_T)+βPT2(x_P)(x_T)2+βP2T2(x_P)2(x_T)2 where β0 is the global intercept, βtβP and βT are the slopes of the linear dependencies of crop yield on time, precipitation and temperature indicators, respectively, and βP2 and βT2 are quadratic dependencies of crops to the same indicators. Including a quadratic dependence on x_P and X_T allows for intermediate yield-maximizing conditions. The interactions between precipitation and temperature indicators are represented by βPT, βP2T and βPT2. We compared the performance of the most complex model (Eq. 2) with nine model variants of decreasing complexity, for a total of 10 model variants for each of pair of x_P and X_T indicator, period of the year, and crop. For each period of the year, crop and pair of climatic indicators, among the variants of Eq. (2), we first selected the model with lowest Akaike Information criterion (AIC). AIC is a statistical performance measure that accounts for the model complexity, thus allowing a fair comparison of models differing in number of coefficients. For each crop and for each set of explanatory indicators, among the models with lowest AIC relative to the different periods, we picked the one with highest complexity as the final model. With this strategy, we had models of comparable complexity for separate crops and separate indicators.

The third type of model focused on short-duration, but potentially damaging, conditions. We considered four short-term indicators as explanatory variables. These indicators were selected from the pool of reviewed indicators (Sect. 2.2.1), due to their damaging nature and reflected complementary behaviors, two reflecting precipitation characteristics (NDP1, NDP20), and two temperature characteristics (NDT25 and Frost). The fixed part of the model was 3Yield=β0+βtt+βNDP1NDP1+βNDT25NDT25+βNDP20NDP20+βFrostFrost+βNDP1-2NDP12+βNDT25-2NDT252+βNDP20-2NDP202+βFrost-2(Frost)2 where βNDP1 and βNDP20 represent the linear dependencies of yield to two precipitation indicators NDP1 and NDP20 and βNDT25 and βFrost to two temperature indicators NDT25 and Frost, respectively. βNDP1-2, βNDP20-2, βNDT25 and βFrost represent the quadratic dependencies of the crops to the same indicators. We introduced quadratic dependences to allow for yield-maximizing intermediate conditions and high levels of damaging conditions. We did not include any interaction terms, because these conditions do not likely compound. We did not perform any model selection and simplification for this model.

We applied the first type of model, that based on DI, to all four periods, including pre- growing season, while the second and third types of models were applied on three periods, i.e., the entire growing season, pre-flowering and after flowering.

We selected indicator combinations and models to balance data availability, simplicity, and interpretability, guided by our ecophysiological understanding (Luan et al., 2022; Ortiz-Bobea et al., 2021; Ray et al., 2015). This approach allowed us to avoid physiologically unsupported or overly complex combinations. We fitted each model via the restricted maximum likelihood method using fitlme function in MatLab R2023a. Based on AIC, we determined which climatic indicators, model structures and periods had the highest performance (Fig. 3). The same approach was used to compare the different lengths of the pre- (main) growing periods (30, 60, 90 d). Beyond AIC, we considered the fraction of explained variance by fixed effects only (r2marg) or by both fixed effects and random effects (r2cond) as additional metric of model performance (Nakagawa and Schielzeth, 2013). We considered effects significant when p<0.05. We then plotted crop yield as a function of best performing set of climatic indicators and pre- (main) growing dryness index, relative to the intermediate year 1992 (Figs. 4–5). The MatLab statement for each of the three types of models can be found in the Supplement, showing yield dependence to both random and fixed effects.

Our models explained up to 85 % of yield variability, in line with results of previous analyses relative to other climates (e.g., Luan et al., 2021; Ray et al., 2015; Zampieri et al., 2017). The models including average conditions performed better than those based on short-term potentially damaging conditions (Fig. 3). Although negative effects of heatwaves (i.e., temperatures exceeding 28 or 30 °C) at flowering have been observed in spring barley in Finland and winter barley in Minnesota (Hakala et al., 2020; Sadok et al., 2022), models based on such short-term damaging conditions performed less well in our analysis. We surmise that the lower performance of models based on short-term damaging conditions is in part due to their infrequent occurrence in our records. Moreover, the effects of these short-term conditions might be averaged out across the cropped land in each county, either because crops in different fields are not simultaneously at the most sensitive stage or because of extreme-cancelling averaging of climatic conditions.

Crop yields were better explained by growing season conditions compared with those during a specific developmental stage, in line with results from analyses of data from long-term experiments in Sweden and Poland (Marini et al., 2020). This could be due to crops compensating any unfavorable conditions during one period with growth during other periods (Foulkes et al., 2011). In contrast to our results, conditions around and after flowering explained yields better than those of the entire growing season over larger climatic gradients (Hamed et al., 2023; Hoffman et al., 2020; Suliman et al., 2024). However, these large scale analyses extended over warmer conditions compared to our study area, with temperatures at flowering likely exceeding the crop optimum. We also acknowledge the uncertainties inherent in estimating the developmental stages through models, as done here, instead of observations, and in assuming that the model-estimated maturity date coincides with the harvest date. Despite performing worse according to the AIC, conditions relative to sub-periods of the (main) growing season, as well as pre- (main) growing dryness index explained a fraction of yield variance comparable to that of the conditions during the entire (main) growing season for all crops. As such, conditions during sub-periods add complementary information to what can be deduced from the entire (main) growing season.

The explanatory power of climatic conditions were lower for oats and spring barley yields compared with spring and winter wheat (Fig. 4). A possible explanation is that wheat yield data refer to southern Sweden only, whereas spring barley and oats are grown under a wider range of latitudes and hence conditions, including soil characteristics and day length. Moreover, the need to adapt to such a wide variety of conditions likely resulted in cultivation of different varieties, e.g. six- vs. two-row barley (Skoglund, 2022), which was not explicitly considered in our analyses.

The temperature at which yields approached their maxima increased with precipitation sums and decreased with dry spell length (Fig. 4), highlighting the strong interacting effects of temperature and precipitation. These patterns are consistent with survey analyses across a wider climatic gradients (e.g., Carter et al., 2018; Luan et al., 2021; Matiu et al., 2017) and ecophysiological evidence that crop response to temperature depends on water availability (e.g., Suzuki et al., 2014). High temperatures combined with prolonged dry periods reduce yields through water and heat stress, lowering net photosynthesis and shortening the grain filling period (Fischer, 1985; Porter and Semenov, 2005; Slafer et al., 2023), ultimately producing smaller kernels and lower yields (Hatfield and Prueger, 2015). Yield losses from high temperatures can be partly offset by higher precipitation, which enhances evaporative cooling via transpiration, particularly in oats and wheat (Martin et al., 2012; Peltonen-Sainio et al., 2018; Schauberger et al., 2017; Tack et al., 2015). At the opposite extreme, wet and cool conditions could reduce yields (Sjulgård et al., 2023), via waterlogging, which limits root functioning and growth (Tian et al., 2021) and/or reduced solar radiation (Díaz-Torres et al., 2017; Ewel, 1999).

The dryness index (DI) explained a fraction of yield variability that was lower than that of the best-performing model including precipitation and temperature indicators, but of comparable magnitude, consistent with findings from studies conducted across broader climatic gradients and under warmer conditions (Luan et al., 2022). Its relatively high performance is the result of DI inherently capturing the interactive effects of temperature and precipitation, by combining precipitation with the potential evapotranspiration, which increases with temperature.

Dryness index prior to the (main) growing season explained yields of all crops except oats, showing the importance of legacy effect and supporting its use as an early indicator of the final yield (Anand et al., 2024), possibly to guide management decision and planning, for example by informing the timing and location of sowing or the choice of crops. The period with the highest performance was 60 d period before the growing season for spring wheat yields, and 90 d for the other crops. The shorter period emerging for spring wheat might be due to this crop being grown exclusively in southern Sweden (Fig. 1), where snowpack is shallower than in the north, and hence the memory in the form of accumulated snow more limited. An increase in DI, i.e. an increase in temperature or a decrease in precipitation, was beneficial for winter wheat up to DI =1.2 mm mm⁻¹ and over most of the observed range for spring crops, although absolute changes in yields were small. High DI generally reduces soil saturation, which can advance sowing and benefit yields by improving field access (Trnka et al., 2011). Excessive soil moisture can increase nitrogen losses through denitrification and leaching (Guo et al., 2014). Further, a higher temperature can contribute to earlier snowmelt (Pan et al., 2022), reduced soil water and quicker warming in spring, that can hamper crop establishment due to rapid drying of superficial soil layers.

During pre-flowering, the range of required precipitation for winter wheat was lower than for spring wheat (Supplement Figs. S1–S2). This is likely a consequence of winter wheat being already established prior to the start of the main growing season, i.e. with deeper roots that can access larger water stores (He et al., 2020; Thorup-Kristensen et al., 2020; Wang et al., 2017).

Our models, explaining a large fraction of yield variability, can provide insights into the effects of specific climatic conditions on cereals in Northern Europe, including future climates.

Under conditions like those of the Northern Europe, warming is often presumed to be beneficial for crops thanks to lengthened growing season (Slafer et al., 2023; Wiréhn, 2018). Rising CO₂ concentrations could further support crop production by increasing photosynthesis and improving water-use efficiency (Rezaei et al., 2023). In Sweden, the average annual temperature is expected to increase by 2–6 °C by the end of the century, depending on greenhouse gas emission scenarios (IPCC, 2021). At the same time, annual precipitation is projected to increase (Grusson et al., 2021; Teutschbein et al., 2023b), but with increases concentrated in the winter and no change or even a slight decrease during summer (Breinl et al., 2020). Furthermore, climate change is expected to intensify hot and dry damaging periods, making the prolonged 2018 warm drought common (Toreti et al., 2019) and shift precipitation toward more frequent short, intense events while reducing growing-season water availability (Westra et al., 2014).

Our models clearly show that warming benefited yields only when precipitation increased or dry spells shortened, otherwise warming reduced yields (Fig. 4). As such, the combined effects of projected changes in temperature and precipitation in Sweden is negative (Grusson et al., 2021), particularly in southern Sweden where precipitation is already limited and crops correlated negatively with temperature (Sjulgård et al., 2023; Skoglund, 2022; Wallén, 1917). In line with our results, yields were reduced by 50 % on average in 2018 in Sweden (Beillouin et al., 2020; Statistiska-Meddelanden, 2018), when summer temperature was on average 2.8 °C warmer than the 1981–2010 average temperatures and the maximum dry spell length was on average 37 d – more than three times the long-term mean of 11.5 d in May August 1950–2020 (Teutschbein et al., 2023a; Wilcke et al., 2020). Our results also point to abundant precipitation being associated with reduced yields, although they had low explanatory power (Fig. 3, Tables S1–S4). As their frequency increases, the mechanical damage or increased frequency of excessive soil water (Iizumi et al., 2024) might become more common.

Crops had their highest yields at (main) growing season temperature averages of 12–14 °C. Cultivars bred and sown in Sweden have so far been selected to perform best under these cool temperatures, with short growing seasons compensated by long days (Hakala et al., 2012). If warmer conditions locally result in exceeding this range, warm-adapted varieties will be necessary. At the same time, increasing temperatures might push northward the optimal ranges of climatic conditions for crop growth beyond central Sweden, opening new possibilities for wheat where it has been historically difficult to cultivate it (Elsgaard et al., 2012). The timing of sowing of spring crops is and will remain critical under climate change, offering an important adaptation measure. High soil moisture in spring can delay sowing of spring crops, while warmer temperatures might allow an earlier start, enabling better use of winter-stored soil water. However, higher summer temperatures counteract this positive effect by e.g. shortening the grain filling period (Sofield et al., 1977; Zhou et al., 2024). There is therefore a relatively small time-window that allows for sowing of spring crops between these two contrasting contributions of water. Climate change could further reduce this window, as higher temperatures increase soil water evaporation, While early-season precipitation, already limited in Sweden, is expected to decline further, potentially compromising crop establishment without irrigation (Peltonen-Sainio et al., 2021).

Another promising adaptation to warmer and drier growing seasons is to replace spring cereals with winter wheat and other winter cereals. Winter cereals are already well established at the onset of the main growing season. They can thus handle precipitation deficits better than spring cereals, thanks to their more extensive root system that allow access to water deeper in the soil (Thorup-Kristensen et al., 2020). However, high precipitation in winter through climate change, combined with high temperatures will result in lower snow accumulation (Tootoonchi et al., 2023) that can negatively impact winter crops, due to the damaging effects of cold spells without the mitigating effects of snow (Vico et al., 2014). Milder winters can also facilitate damage from repeated freezing and thawing cycles or snow mold development (Andrews, 1996). As such, the net effects of altered winter and spring conditions on winter crops need further examination. An alternative adaptation measure to reduce failure risk from both insufficient and excessive water is mixing crops or varieties with different rooting depths and architectures allowing for the use of water at different depths (Manevska-Tasevska et al., 2024).