The Reference evapotranspiration (ET0) also referred to as Potential Evapotranspiration (PET) or Atmospheric Evaporative Demand (AED) is a measure for the amount of water that the atmosphere can take up from a saturated reference surface with unlimited water supply. Following we use watered crop land with an albedo of 0.23 as reference surface.

Over the last century a variety of methods have been developed to approximate the PET, including the methods introduced by and . Although used often, both approximations are not reliable under changing climate conditions . In contrast, Eq. () provides a more complex combination of parameters to approximate ET0 with a closer link to the underlying physical processes. This approximation is more adequate and recommended by FAO and ASCE . It is derived from and and includes several variables like the soil heat flux density G, mean daily air temperature at 2 m Td, wind speed at 2 m u2, the psychometric constant γ, saturation and actual vapor pressure es and ea, such as net radiation at plants surface Rn and heat flux density G. Δ is the slope of the vapor pressure curve . Instead of 0.12 m short grassland we assume a crop height of 0.5 m following . With adjusted crop coefficients (1600 and 0.38) for monthly time steps this leads to the ASCE equation for standardized reference crop evapotranspiration for tall surfaces ETRS : 1ET0=ETRS=0.408Δ(Rn-G)+γ1600T+273u2(es-ea)Δ+γ(1+0.38u2) and provide detailed instructions on the calculation of the psychometric constant and how to approximate variables that may not be available in observational or model data (i.e. u2 from wind speed at 10 m, Rn from downwards short wave radiation and Td from monthly mean daily minimum and maximum temperature).

In contrast to its predecessor SPI, which is solely based on precipitation, the SPEI includes additional atmospheric variables through potential or reference evapotranspiration ET0. While the SPEI, as originally proposed by , uses only temperature data to approximate ET0 , we make use of a more complex approximation described above. The SPEI is calculated from ET0 and P by fitting a probability distributions of water budget (ET0-P) over a chosen reference period and transfer it to a standard distribution. In contrast to precipitation in the SPI the water budget can be negative, therefore a three parameter distribution like the generalized log-logistic is used : 2F(D)=1+αD-γβ-1 In Eq. () F is the probability distribution of a variable D with α, β and γ being scale, shape and location parameters. The fit is performed for each grid cell and each month of the year individually. It is further possible to apply the index on different time scales by defining the number of accumulated months. Similar to we choose 6 months, which is within the range of 3–6 months of accumulation for agricultural droughts recommended by the . To quantify the strength of a drought (or wet spell) the probabilities are mapped to SPEI values and can be assigned to categories shown in Table  . A more detailed guide on the described calculations can be found in and .

Due to changes in precipitation and potential evapotranspiration in many regions over the last decades, the definition of the reference period is important for the resulting SPEI values. It is recommended to use a reference period of 30 years or more, aligning well with 30 year climate normals which are standard for benchmarking in climate change assessments . However, we found that calibrating the SPEI on short reference periods (30 values per month of the year) can lead to an artificial increase in the occurrence of extreme events. Prolonging the period into the past on the other hand decreases the accuracy and availability of global observations of atmospheric variables. As a compromise we choose a reference period of 65 years (1950–2014) and show the evaluation for its last 35 years (1980–2014).

For this study we used the open source SPEI R-package to calculate ET0 and the SPEI .

The metrics used to evaluate the models used in this study are listed below with their corresponding equations. Spatial statistics are generally area weighted, but for temporal statistics the variable months lengths is neglected and monthly accumulated units are avoided when possible (i.e. precipitation in mm d⁻¹ rather than mm per month). All metrics and the SPEI calculation is applied for each model individually and multi-model means are calculated afterwards.

To analyze the drought characteristics, we calculate ET0 and SPEI as described on the same regular 1° × 1° for 18 CMIP6 models, described in Sect. . We calculate multi-model means of the following metrics to compare them across different scenarios.

We make use of the IPCC AR6 WG1 Land reference regions to apply regionally integrated statistics. Our main focus are regions with a significant amount of crop production and agricultural land use. We identified these regions by their relative amount of harvest area in 2010 according to the GFSAD1KCM dataset . Figure  shows a regridded combination of major and minor rain-fed and irrigated harvest area masks. The reference regions are shown as overlay in panel (a). Panel (b) shows the relative amount of harvest area for each region. Regions above 33.3 % harvest area are considered as highly relevant for agriculture throughout this study. The agricultural most relevant regions are namely Western&Central-Europe (WCE), C. North-America (CNA), S. Asia (SAS), E. Asia (EAS), E. Europe (EEU), Western-Africa (WAF), S. E. South-America (SES), W. Siberia (WSB), Mediterranean (MED), N. E. South-America (NES), S. Australia (SAU). They are highlighted in Fig. b.

To load and pre-process the CMIP6 model simulation output and reanalysis data, described in the next section, ESMValTool is used. ESMValTool is an open source software for community-developed diagnostic and performance metrics to evaluate ESM simulations including CMIP contributions . Since its first release in 2016 , the software has been developed continuously and experienced technical improvements in terms of performance and usability . The new benchmarking and model evaluation capabilities of ESMValTool are shown by . Existing diagnostics for extreme event analysis are described by .

The ESMValTool framework contains a dedicated python module, called ESMValCore, for data handling and general processing, and a collection of scientific diagnostics. Recipes can be used to setup experiments as a specification of input data, pre-processing methods and a list of diagnostics to be applied to the data. We used the ESMValCore v2.11 to load the described data, converted them to comparable physical units, masked and regridded them to the same 1° × 1°regular grid .

The methods described in this section and multiple plotting routines are added to the ESMValTool framework as a set of diagnostics in the scope of this study. This allows to reproduce the results and re-use the methods for further studies i.e. analysis for upcoming CMIP7 simulations.

We are interested in the capabilities of models to project long-term characteristics like mean and change rates of drought relevant variables. Therefore we compare these variables with observations and reanalysis with time integrated metrics for the period 1980–2014 to estimate the reliability of these simulated variables. The pattern correlations of all 18 analyzed models, CRU TS v. 4.07 and CDS-SM data with ERA5 are shown in Fig. .

The temporal averaged pattern of CMIP6 models over the period 1980–2014 show high similarity (P>0.8 for most models) with the ERA5 reference data for surface downwelling shortwave radiation (RSdown), reference evapotranspiration (ET0), surface pressure (psurf) and daily minimum and maximum temperature (Tmin, Tmax). Lower pattern correlation (0.6<P<0.8) is found for precipitation (P). The agreement of wind speed at 10 m (V10m) and soil moisture (SMsurf) patterns is the lowest with correlation coefficients P<0.6 for most models, also with a higher spread between the models. The averaged soil moisture pattern of the CDS-SM dataset based on satellite observation does not show higher correlation to ERA5 than the models, which makes it difficult to judge model performance based solely on ERA5. However, we see high agreements in the most important input variables for ET0 (RSdown, psurf, Tmin and Tmax). This propagates to a ET0 pattern correlation above 0.8 for 12 out of 18 analyzed models.

Figure b shows the centered median between each models root mean squared distance σ^ (Eq. ) when compared with ERA5 (upper left rectangles). For the models providing soil moisture the CDS-SM dataset is used as an alternative reference REF2 (bottom right). For the other variables CRU is used as alternative, where available. Due to the normalization, this plot lacks information about the actual distance to the reference, but instead highlights the relative performance between the models for multiple variables. A blue color indicates smaller errors to the reference and therefore better performance compared to the other models. Errors larger than multi-model median are shown in red. Biases in model simulations directly contribute to RMSD, while the normalized SPEI is able to ignore them. Therefore, it is possible that models with high RMSD are still able to project drought conditions reliably. The AWI-CM-1-1-MR and MIROC6 models for example show the highest RMSD to ERA5 for ET0 and Tmin. BCC-CSM2-MR, CanESM5 and FGOALS-g3 simulate ET0 more similar to ERA5 but with large differences to the alternative reference dataset CRU. Throughout all models ACCESS-CM2, CMCC-ESM2, CNRM-CM6-1, EC-Earth3-Veg-LR, FIO-ESM-2-0, GFDL-ESM4, and MPI-ESM1-2-LR perform better in simulating ET0 than the ensemble median in respect to both reference datasets. For soil moisture we find low agreement in RMSDs between reference datasets ERA5 and the CDS-SM satellite observations. We are not able to comment on model performance in these cases.

In the IPCC AR6 a similar method has been used to evaluate CMIP5 and CMIP6 model performance for the period 1980–1999 Fig. 3.42. Comparing precipitation, where ERA5 has been used for reference, we find that our centralized RMSD values are generally higher, because the median model in our subset is performing better for precipitation than the median of the 58 model ensemble analyzed in . Despite a few exceptions, this is in agreement with the relative ranking between the subset of 18 models for the period 1980–2014 used in this study.

Due to the importance of precipitation and reference evapotranspiration for drought formation, they are evaluated further in the following. Similar figures for other variables can be found in Appendix A (Figs. , , ).

Precipitation is the main source of fresh water for most agricultural regions and therefore a crucial variable in drought analysis. In the multi-model mean of CMIP6 models and both reanalysis datasets we find mean patterns that qualitatively agree over the period 1980–2014 in Fig. . Average daily precipitation close to 0 mm can be found for dry regions in northern Africa and South-west Asia. Regions of high precipitation caused by topological boundaries like mountain ranges can be seen clearly for the Andes in South America and for the Himalayas, which forms the northern boundary of the Indian monsoon climate in the CMIP6 multi-model mean and both reference datasets. The CMIP6 simulations also agree with ERA5 and CRU reanalysis precipitation over rain forest regions of South America (8–10 mm d⁻¹) and Central Africa (3–6 mm d⁻¹).

For the eleven crop producing regions, selected in Sect. , seasonal cycles of 18 simulations and two reanalysis are shown in Fig. . The regional average for each month of the year is calculated according to Eq. () over the period 1980–2014. For each region at least 15 of the 18 models are able to reproduce the main features of the seasonal cycles derived from ERA5 and CRU.

All simulations for regions of Northern Hemisphere summer monsoon – Western-Africa (WAF), Eastern-Asia (EAS) and Southern-Asia (SAS) – agree in less than 1 mm d⁻¹ precipitation in the winter months (DJF) and maximum precipitation during the summer (JJA). For WAF the average August precipitation spreads throughout 3 mm d⁻¹ (FGOALS-g3) and 11.5 mm d⁻¹ (GFDL-ESM4), with most simulations being closer to the reanalysis around 7.5 mm d⁻¹. For SAS the precipitation during JJA is slightly underestimated by many models. The highest discrepancy to ERA5 and CRU is found in CanESM5 with 4 mm d⁻¹ less precipitation in July. EAS seasonal cycle is captured by all simulations within a maximum distance of 2 mm d⁻¹ to ERA5 or CRU.

The seasonal precipitation in Southern Hemisphere summer monsoon regions N. E. South-America (NES) and S. E. South-America is also qualitatively captured by all simulations. Mentionable is that both reanalysis show significant lower precipitation (6–7 mm d⁻¹) for NES over the first three months of the year. presents seasonal cycles of Northeast Brazil over the period 1971–2000 for different reanalysis and observations including the NCEP/NCAR dataset, with 8 mm d⁻¹ average precipitation in February.

For the other regions North-American, European and Australian regions the seasonal signal of precipitation is much lower and captured by most simulations. Exceptions are the historical simulations of the FGOALS-g3 and KACE-1-0-G models. Both underestimate summer precipitation in higher latitudes and do not represent the seasonal cycle of Western & Central-Europe (WCE), E. Europe (EEU) and W. Siberia (WSB) as described by ERA5 or CRU. However, overall the regional features of the annual precipitation cycle are captured by most of the models in most of the regions, that are relevant to this study. The seasonal temperature cycles are recreated much closer by all models, with only one exception (MIROC6) overestimating temperatures in a few regions. A figure similar to Fig. , but for temperature, is appended as Fig. .

ET0 is calculated for ERA5 and the CMIP6 model output using Eq. () based on the same set of variables. The ET0 provided by the CRU dataset is derived using a similar method, but with a crop height of 0.12 m and included relative humidity to calculate the vapor pressure deficit . The differences in the methods might cause some systematical differences, but we can still see a general agreement in the ET0 pattern over the period 1980–2014 between all datasets in Fig. . Further, we can find that models reproduce expected temporal mean features like decreasing ET0 towards high latitudes due to decreasing temperatures, low ET0 at the high altitude Tibetan Plateau and highest ET0 values at the Sahara due to high temperature and low cloud coverage in an arid region.

For this study only non glaciated land area is considered and referred to as global in the following. The global mean of P and ET0 for the base period and different future scenarios are shown in Fig. . For both variables a higher positive trend can be noticed with higher emission scenarios from SSP1-2.6 to SSP5-8.5. The increase of ET0 is significantly higher compared to precipitation. This results in a decreasing water budget for future projections and a general shift of SPEI towards drier conditions, which we can see in the corresponding annual SPEI time series, the third plot in Fig. . All 18 analyzed models agree in a projected decrease in global mean water budget over the period 2015–2100 in SSP2-4.5 and SSP5-8.5 scenarios. The general downward trend of water budget and a shift towards drier climate in higher emission scenarios agrees with several other studies .

However, these changes are not distributed uniformly over the globe. We found significant regional differences in quantity of water budget and therefore SPEI changes in future scenarios as shown in Fig. . It shows maps of the multi-model mean decadal change of SPEI over the period 2015–2100 for three different future scenarios. The SPEI is calculated and calibrated for each model individually using 1950–2014 as common baseline for all three scenarios. While the change rates are different between the scenarios, the general pattern and signs of the trends are the same for most regions. Beside the decrease in most parts of North and South America, Africa and Southwest Asia small regions with increasing water budget can be identified, mainly in the Arctic and Subarctic as well as some mountain regions with relatively low crop production. Positive and negative changes are intensified for the SSP5-8.5 scenario compared to SSP1-2.6.

Change rates on their own are not sufficient to describe the development of projected drought characteristics. Due to regional differences we analyze the statistical distribution of the drought index for individual IPCC AR6 WG1 reference regions of similar climatic conditions . We further select eleven harvest regions based on their relative land use for crop production. The selection method and regions are described in Sect. . An overview of the distribution for combined and individual harvest regions is given in Fig. . The same figure for global distribution and all non glaciated land regions is appended as Fig.  and for semi arid regions of Europe and Asia as Fig. .

In Fig. a we can see the distribution of index values for the reference period 1950–2014 and the last 30 years of the projected century 2070–2100 for three future scenarios, collected over the most relevant agricultural regions. While the values in the reference period follow a Gaussian distribution, which is centered at zero by definition, the distributions of the future scenarios are shifted towards negative indices (drier climate), which agrees with the observed global downward trend in Fig. . We also expect more extremes for higher emission scenarios, according to widening distributions.

The hexagons in panel (b) are shown to provide a spatial overview of the regions and their projected SPEI decadal change in the SSP5-8.5 scenario. Due to the symmetric Gaussian distribution of the SPEI the decadal change of the mean is roughly proportional to the shift of the distribution. Similar to Fig.  the lower emission scenarios SSP1-2.6 and SSP2-4.5 show smaller change rates (Fig. ) but qualitatively agree with Fig. b for most regions.

The regional statistics in Fig. c show the distributions as box plots for the IPCC AR6 WG1 land reference regions, ordered by median in the SSP5-8.5 scenario. For nine of the 11 regions a clear shift towards lower median SPEI values enhancing with higher emission scenarios can be found. This implies a general shift towards drier conditions and we find more severe and extreme droughts towards the end of the century in all three future scenarios based on SPEI projections of 18 ESMs. For the MED region we see the median of the drought index for 2070–2100 being below -2 following the SSP5-8.5. Which means the 2.3 % driest conditions during the simulated period 1950–2014 can be considered as normal in the Mediterranean during the projected period 2070–2100. The Mediterranean is mentioned as a hotspot for increase of extreme events including heat waves and droughts in other studies . For East and South Asia no general shift can be found, but the number of months classified as extreme droughts is also higher compared to historical reference.

The first five of all global non-glaciated land regions (Fig. ) SAH, ARP, MED, WCA and ECA are neighbors and part of northern Africa, southern Europe and western Asia. A general shift towards drier conditions with increasing forcing scenarios can be seen for 32 of the 42 regions. Seven regions (GIC, RAR, RFE, NEN, NWN, NEU, CAF) show an opposite shift towards wetter conditions. Six of them are located at high latitudes. While the widening of the index distribution for future scenarios can be found for all of the analyzed regions, it is most prominent in Western Africa (WAF) region.

Using the ability of the SPEI to assign a category for the severity of drought based on climatic conditions we calculated the area that is covered by drought conditions of a certain category at any time. This allows us to quantify the relative area that might be affected by droughts under changing atmospheric conditions in future projections as given in Eq. ().

In contrast to spatial mean time series the area fraction plots show the increase in wet and dry conditions at the same time without compensating positive and negative index values.

Furthermore, area fraction plots are not influenced by localized extreme SPEI values, as they focus on the proportion of cells exceeding a certain threshold rather than the magnitude of the values themselves, unlike mean time series which can be skewed by a few cells with exceptionally high trends.

Figure  compares the event area fraction for an intervals during the historical period 1970–1990 with the end of century 2070–2100 over the selected harvest area. The complete series 1950–2100 is appended as Fig. .

The first interval in Fig.  presents the relative surface area for each index category during the calibration period. As each individual grid cell and month of the year is calibrated to match a normal distribution with certain shape, it is expected that we see 2.3 % of the area under extreme drought conditions without seasonal cycle on average. The interval 1970–1990 roughly represents this. However, the 2080–2100 interval selected from the end of the projected future shows significantly more area under moderate to extreme droughts for all three scenarios especially in autumn. Further the temporal resolution reveals an increasing seasonal dependency of the spatial extent of droughts.

According to the SPEI for future projections following a worst case scenario SSP5-8.5 between 20 % and 40 % of the land area in agricultural active regions would experience extreme drought conditions at the end of century. In contrast, for the SSP1-2.6 the extreme drought area does not exceed 10 %. For the drought categories we find peaks in Northern Hemisphere autumn (September–November), resulting from high evapotranspiration and low precipitation accumulated over the previous six months in spring and summer. In the extreme drought category we identify the largest differences between the scenarios. However, the peak area under at least severe (moderate) conditions also ranges from 20 % (35 %) to 50 % (60 %) throughout the scenarios.

For wet spells we find a similar increasing seasonality with opposite phase peaking in early spring. The area of wet spells with SPEI >1.5 does not clearly expand from the expected occurrence rate of 16.9 % (Table ). It stays below 20 % on yearly multi-model average in all scenarios. Nevertheless we see a significant growth in area of extreme wet spells, which is consistent with the broadening and shifting of the global SPEI distribution for different scenarios (Fig. a), which overlap at SPEI between -1 and -2.

The historical evaluation in Sect.  is meant to be a sanity check for the ET0 calculation methods and a validation for the model projections in the first place. Considering the spread of ET0 and P between CMIP6 model projections some sort of performance based weighting in the multi model ensemble could improve the results based on a more sophisticated evaluation taking seasonal distributions and biases into account. The differences in reanalysis and lack of reliable global observations especially for wind and precipitation is an additional challenge .

We decided to use the SPEI for our analysis of the development of agricultural drought characteristics, due to its ability to be applied globally while being spatially comparable over different regions. However, the statistical approach of standardized indices implies that the intensity or severity of a drought is calculated based on its rarity and not based on the actual physical soil parameters or how it impacts crop growths. Analyzing the actual water balance levels and how they impact yield for different crop types on a regional level would be a valuable addition to this study.

Beside the relative nature of the index we also have to consider that most of the area with highest increase in droughts in high emission scenarios are already arid regions i.e. the Sahara desert. Nevertheless, found a tenfold higher agricultural exposure to severe compound droughts towards the end of century using model projections from RCP8.5 in CMIP5.

While root zone soil moisture is a good indicator for agricultural droughts, the availability of reliable global soil moisture data is limited and simulations show high inter model variability (Fig. ). Further, available water is not the only parameter responsible for crop failure. A high atmospheric evaporative demand can also cause increasing plant water stress. Figure  illustrates the difference between a purely hydrological approach to quantify droughts like soil moisture and approaches like SPEI, that consider the influence of ET0. In the upper panels (a, b), we can see a that regions with an average water budget below -5 mm d⁻¹ correspond to arid regions with low soil moisture. Especially Northern Africa, South West Asia and Australia. However, under the SSP2-4.5 future scenario, soil moisture is expected to decrease over Europe and South America, but shows no or even positive changes in arid regions (Fig. d), because there is not much water available to evaporate or runoff (other scenarios can be found in Fig. ). The atmospheric demand of water, shown in Fig. c, can further increase even if the soil does not contain water at all. However, the influence of ET0 on crop failure and agricultural drought severity might need further research to be quantified exactly.

Due to the above mentioned reasons the SPEI might be suited to investigate the impact of changes in climate to the characteristics of droughts, but this is not directly transferable to any ecological impact regardless of the focuses on regions with lot of harvest area. With this study we hope to provide further motivation for research on regional impact. analyzed SPEI characteristics projected by CMIP6 models for the same three future scenarios, with a different set of models and focus on the Northern Hemisphere in summer (JJA). We do not show occurrence rates in this work, but based on regional distribution shifts and the increase of extreme dry area we can confirm the highest increase in projected droughts for the MED region, less but still increased drying in WCE EEU and WSB. By investigating the change of extreme drought (SPEI <-2) in addition to severe droughts, we find higher difference between the future scenarios for regions where the SPEI stays below -1.5 for many months. We also complement their study by providing SPEI analysis for additional regions and over all seasons, even though it is most important for agriculture during growing season.

Although, the SPEI is symmetric, which makes it possible to apply it to wet spells in a similar way, it is not well suited to identify extreme events such as floods. Therefore, we focus the analysis on droughts, while still discussing the whole distribution of the index over all categories.