The Earth's hydrological cycle is a key element of the climate system with important impacts on society. For example, the intensity and distribution of precipitation determine the abundance or scarcity of fresh water in a certain region. They are also related to the severity of hazardous events such as flooding or droughts. Several studies have shown an acceleration of the hydrological cycle and an intensification of both dry and wet extremes in a warming climate (IPCC, 2013). A simple investigation of total precipitation-related quantities can hide some of the most relevant aspects of the hydrological cycle and its extremes, which can be highlighted through the joint use of the concept of hydroclimatic intensity and related indices (e.g. Giorgi et al., 2014). The hydroclimatic intensity (Giorgi et al., 2011), derived as the product of mean daily precipitation and dry spell length normalized over a reference period, offers a joint view of both dry and wet conditions, allowing for the unique quantification of the response in the intensity of the hydrological cycle in a changing climate. The hyint (hydroclimatic intensity) diagnostic was developed to calculate several indices for hydroclimatic and climate extremes and allow a multi-index evaluation of climate models.

The recipe_hyint.yml calculates six indices for evaluating the global warming response of the hydrological cycle including both wet and dry extremes. The indices are selected according to Giorgi et al. (2014), including the simple precipitation intensity index (SDII), the maximum dry spell length (DSL) and wet spell length (WSL), the hydroclimatic intensity index (HY-INT, calculated as normalized DSL times normalized SDII), which is a measure of the intensity of the hydroclimatic cycle compared to a reference period (Giorgi et al., 2011), and the precipitation area (PA), i.e. the area over which precipitation occurs on any given day (Giorgi et al., 2014). The recipe_hyint_extreme_events.yml can also ingest the 27 temperature- and precipitation-based Expert Team on Climate Change Detection and Indices (ETCCDI) (Zhang et al., 2011) calculated by the recipe_extreme_events.yml to produce a multi-index analysis (see Sect. 3.2 for further details). The diagnostics perform a subsequent analysis calculating time series and trends of the selected indices for predefined continental areas, normalized to a reference period. The linear model (lm) function of R is used to calculate trends. Statistical significance is tested based on a Student's t test under a non-null coefficients hypothesis. Trend coefficients and their statistics, including standard error, p value, and precipitation above the 95th percentile of the reference distribution, are stored. The recipe created several plots, including global and regional maps, time series with spread, trend lines, and summary plots of trend coefficients. Results are stored in NetCDF files, including relevant information such as normalization functions and thresholds, and as figures. Figures 1 and 2 show examples of an analysis performed with the hyint diagnostic. A map of the HY-INT index (Fig. 1) calculated from EC-EARTH model data shows the projected average HY-INT compared to the reference period (1976–2005): hydroclimatic intensity is projected to greatly increase in some regions (e.g. eastern South America, northern Africa, and the Arabian peninsula) and to decrease over other regions (e.g. Antarctica, Greenland, central and north-eastern Asia, central Africa, and western and northern South America), with large areas showing only moderate changes. Trends shown in Fig. 2 exhibit a relatively low inter-model spread for HY-INT. The projected increase in HY-INT seen for all models with values ranging around 10 % per century (also reflected as large geographical patterns) can also be seen in the precipitation intensity (SDI) and heavy precipitation indices (R95), the latter with an increased spread between 10 % and 30 % per century. Precipitation area (PA) is projected to increase by most models, whereas for projected changes in the dry spell length (DSL) and especially in the wet spell length (WSL), models do not agree on the sign of the projected changes, which is also reflected in high geographical variability (not shown).

Three main types of droughts can be separated: (i) meteorological, (ii) hydrological, and (iii) agricultural droughts. Any type of drought needs to be defined in the context of local and seasonal characteristics, implying that a drought should be identified as an anomalous condition rather than being based on an absolute threshold.

Meteorological droughts are negative anomalies in precipitation. Depending on the local characteristics, a drought can be defined as an extended period of daily precipitation amounts below a given threshold. The threshold value is defined as the minimum amount of precipitation that is needed to recharge the soil moisture content. This approach requires good knowledge of the local and seasonal characteristics of the soil moisture content. However, it is a useful analysis to investigate climate models' distributions of wet and dry periods, which are indicative of how well suited the model is to couple to hydrological impact models. For example, CMIP5 models have been shown to generally underestimate the number of consecutive dry days (Sillmann et al., 2013b; Cheng et al., 2016). The standardized precipitation index (SPI; McKee et al., 1993) describes local precipitation anomalies and is often used to identify meteorological droughts. The SPI was developed as a replacement for the commonly used Palmer drought indices (Palmer, 1965) to better capture dry and wet anomalies. The SPI is calculated using monthly mean precipitation. Therefore, it does not account for the intensity of single precipitation events and the runoff process. Furthermore, SPI does not account for evaporation from the surface. This implies that one component of the water fluxes at the surface is lacking, which makes SPI incompatible with the concept of hydrological droughts. Evaluation of SPI from CMIP5 models shows large model biases (Ukkola et al., 2018).

A hydrological drought occurs when low water supply effects streams, reservoirs, and groundwater levels and is usually caused by extended periods of meteorological droughts. These hydrological processes are usually not simulated with sufficient detail in climate models. As a consequence, agricultural droughts (i.e. when crops become affected by the hydrological drought) also cannot be simulated properly by the models. Hydrological droughts can, however, be estimated in climate models by accounting for evapotranspiration. This allows for the estimation of surface water retention. The standardized precipitation–evapotranspiration index (SPEI; Vicente-Serrano et al., 2010) has been developed to take into account the effect of evapotranspiration on surface water fluxes. Evapotranspiration is typically not provided by CMIP models, so SPEI often takes other inputs to estimate it, e.g. with the Thornthwaite method based on temperature (Thornthwaite, 1948), the Hargreaves method using the monthly mean of daily minimum and maximum near-surface temperature (tasmin and tasmax) (Hargreaves, 1994), or the Penman–Monteith method using minimum and maximum temperature together with 2 m wind speed (Allen et al., 1994), which is estimated from the surface wind (at 10 m). However, it has been shown that the method used to derive the potential evapotranspiration has little impact on the drought statistics (Burke et al., 2006). In contrast to this finding, Shaw and Riha (2011) conclude that, especially for future scenarios with rising temperatures, potential evapotranspiration based on estimates considering temperature only can lead to an overestimation of SPEI.

In order to assess the performance of drought characteristics in climate models, three diagnostics have been implemented into the ESMValTool (v2.0): consecutive dry days, SPI, and SPEI. The consecutive dry days diagnostic (recipe_consecdrydays.yml) has been implemented consistently with the CDO method “eca_cdd” (Climate Data Operators, Schulzweida, 2018), and the SPI and SPEI diagnostics (recipe_spei.yml) are based on the R package SPEI (https://cran.r-project.org/web/packages/SPEI/SPEI.pdf, last access: 1 June 2021; Vicente-Serrano et al., 2010). The recipe recipe_spei.yml computes the SPI and SPEI quantities for each model and summarizes the statistics of both indices as global averages in categories from “extremely dry” to “extremely wet”; see Figs. 3 and 4. By including an estimate for evapotranspiration, the model biases are reduced, particularly for the overly frequent “moderately wet” category. For SPI (Fig. 3), the bias plot shows a clear underestimation of dry and wet conditions, which are mainly compensated for by overly frequent moderately and extremely wet conditions. For the neutral condition category, the results differ depending on the models, with a tendency towards overly frequent occurrence in most models. For SPEI (Fig. 4) the bias plot indicates overly frequent neutral conditions at the expense of mainly dry and wet conditions. Moderate and extreme wet conditions are overestimated in practically all models, whereas moderately and extremely dry conditions show the opposite behaviour.

Using the SPI calculation described above, a recipe analysing drought events (recipe_martin18.yml) has been developed. Following Martin (2018), a drought event is defined as any consecutive number of months with extremely dry conditions (SPI <-2). The characteristics of these events from historical and future scenario model runs (see Fig. 5) as well as from observational data are then compared. The characteristics investigated are frequency, length, average SPI, and the severity index following Peters (2014), which is a measure combining the length and the SPI value of a drought. Figure 5 shows an increase in the number of drought events, the severity index, and to a lesser extent the duration of drought events in the RCP8.5 scenario compared to the historical model runs, especially in subtropical areas. The results support the finding that regions with already dry conditions are much more likely to show a higher number of drought events for the RCP8.5 scenario, known as the “dry gets drier and the wet gets wetter” (DDWW) paradigm (Greve et al., 2014).

Heat waves are expected to become one of the greatest threats to human health in the 21st century due to projected increases in both frequency and severity (IPCC, 2013; Ouzeau et al., 2016), while the duration, intensity, and frequency of cold waves are expected to decrease. It is not clear yet, however, what the impact of changes in heat waves and cold waves on related mortality will be, since mortality due to heat waves and cold waves inferred from historical simulations is typically overestimated. This is partly due to challenges in the correct simulation of extremes (Wang et al., 2016). In the case of heat waves in particular, models have been shown to contain biases in the 90th and 10th percentiles over the historical period (Pereira et al., 2017). However, by using a bias adjustment method based on percentiles, climate models are able to produce output which is consistent with events observed during the historical period (Ouzeau et al., 2016).

The diagnostics of the recipe_heatwaves_coldwaves.yml uses the daily maximum or minimum temperatures to estimate the relative change in heat wave and cold wave characteristics in future climates compared to a reference period. The user selects the model, emissions scenario, the region of interest, and the reference as well as the projection periods and the percentile which will be used to compute the threshold for exceedance or non-exceedance from the reference period (a separate threshold is computed for each day of the selected season and grid point using the quantile bootstrapping method described in Zhang et al., 2005b). Further options which can be selected include whether to compute the frequency of exceedances or non-exceedances of extremely high or extremely low temperature events, respectively. Additionally, the minimum duration of an event to be classified as a heat wave or cold wave and the season of interest can be set. The diagnostic calculates the number of consecutive days over which temperature exceeds or does not exceed the given threshold in future climate projections. The result is presented as annual time series of the total number of heat wave or cold wave days for the selected season at each grid point, and the average number of these days for the selected season in the future climate projections is calculated; see Fig. 8.

High mortality rates, increases in hospital admissions, and major economic losses are often associated with extreme events (Meehl et al., 2000; Zhang et al., 2011; Fouillet et al., 2006; Whitman et al., 1997). This emphasizes the need for monitoring and forecasting extreme events, in particular since some studies suggest that extremes are increasing in both frequency and severity with increasing anthropogenic greenhouse gases (Alexander et al., 2006; Donat et al., 2013).

The recipe recipe_extreme_index.yml allows a user to compute the combined climate extreme index, which is defined as a combination of different extreme values linked to precipitation, surface temperature, and surface wind speed. This index is similar to the climate extremes index (CEI; Karl et al., 1996), the modified CEI (mCEI; Gleason et al., 2008), and the actuaries climate index (ACI; American Academy of Actuaries, 2018). In recipe_extreme_index.yml, the user defines the area, the reference period, the period of interest, and the weights assigned for each individual component of the index. The weights allow the user to put emphasis on the extremes that are more relevant to them and/or completely exclude non-relevant ones. Temperature and precipitation extremes are defined in a similar fashion as in Donat et al. (2013) and are part of the larger set of extreme indices compiled by the ETCCDI (Zhang et al., 2011). The different components of the multi-metric index are the following:

weight_t90p representing the number of days when the maximum temperature exceeds the 90th percentile,

The daily temperature range (DTR) corresponds to the difference between the minimum and maximum temperature within a period of 24 h at a given location. The usefulness of the global average DTR has been demonstrated using both observations and climate model simulations (Braganza et al., 2004). Changes in the mean and variability of the DTR have been shown to have a wide range of impacts on society, for example on the transmission of diseases (Lambrechts et al., 2011; Paaijmans et al., 2010) and energy consumption (Déandreis et al., 2014).

In the energy sector, a vulnerability indicator based on the DTR has been defined to identify locations which may experience increased diurnal temperature variations in the future (Déandreis et al., 2014). Increased diurnal temperature variations put additional stress on the operational management of urban heating systems. A measure for increased diurnal temperature variations is defined as the DTR exceeding the value of the reference period by 5 K at a given location and for a given day of the year. Projections of this measure are currently subject to large uncertainties as projections of both daily maximum and minimum near-surface temperature (tasmax and tasmin) in future climate projections are highly uncertain.

The recipe recipe_diurnal_temperature_index.yml computes the mean DTR for a given reference period using historical simulations and then the number of days on which the DTR in future climate projections exceeds that of the reference period by 5 K or more. The user can define both the reference and projection periods, as well as the region to be analysed. The output produced by this recipe consists of a four-panel plot showing the maps of the projected mean DTR indicator for each season (see Fig. 10) and a NetCDF file containing the corresponding data.

The energy sector is the largest contributor to greenhouse gas (GHG) emissions (IPCC, 2014b). Therefore, many countries have adopted mitigation strategies to increase the fraction of energy generated from renewable sources in the forthcoming years. However, renewable energy sources like wind power and solar power rely heavily on atmospheric conditions to produce energy and are therefore exposed to risks from climate variability and long-term change in the case that they lead to detrimental atmospheric conditions. The relationship between wind speed and energy production by wind turbines is highly non-linear because turbines are designed to be efficient for a narrow band of wind speed conditions. Therefore, changes in the wind speed distribution can impact electricity generation and thus the revenues and economic viability of wind farms. The capacity factor is a normalized indicator of the suitability of wind speed conditions to produce electricity, irrespective of the size and number of installed turbines. The factor is provided for wind turbines designed for low, medium, and high wind speed conditions grouped into three different classes (IEC, 2005).

The recipe recipe_capacity_factor.yml computes the wind capacity factor for these three wind turbine classes (see Fig. 11) by taking as input the daily instantaneous surface wind speed and extrapolating to the wind speed at 100 m of height as described in (Lledo et al., 2019). The user can select the region, period, and season of interest. The result of the recipe is the capacity factor for each of the three turbine classes saved as a NetCDF file.

The output of solar photovoltaic (PV) systems depends on the time of the day, season, and weather conditions. The PV capacity factor is a measure of which fraction of the maximum possible energy is produced per grid cell. The solar power generation of a PV system mainly depends on the amount of incoming surface solar radiation but is also influenced by other atmospheric variables that affect the efficiency of PV cells, which decreases as their temperature increases. The recipe_pv_capacity_factor.yml computes the PV capacity factor using the daily incoming surface solar radiation and the surface temperature with a method described in Bett and Thornton (2016). The user can select temporal range, season, and region of interest. An example is shown in Fig. 12 for ERA-Interim and five CMIP5 models.

Climate or Earth system models with a fully coupled ocean are important tools to project the future evolution of the climate system in response to anthropogenic forcings, such as the increase in GHG concentrations. Despite their coarse horizontal resolutions (typically of the order of 100 km or less) these models can provide climate information at the regional scale to allow for assessing the impacts of climate change. The ability of these models to simulate regional climate is an important aspect of model evaluation.

The recipe recipe_flato13ipcc.yml includes a subset of diagnostics and figures from the model evaluation chapter of the IPCC AR5 (chapter 9, Flato et al., 2013), which compares surface parameters (such as temperature and precipitation) from models and observations at regional scales.

The mean seasonal cycle of precipitation and temperature is calculated over land areas within selected regions for individual models, the multi-model mean, and observation and/or reanalysis data (see Fig. 13). Regional biases, including 5th, 25th, 50th, 75th, and 95th percentiles of the biases, in seasonal and annual mean temperature and precipitation are evaluated for several land, polar, and oceanic regions (see Figs. 14 and 15). Diagnostics allow the comparison of the multi-model mean for different projects (i.e. CMIP3, CMIP5) including information on the amplitude of the root mean square error. The regions used in this recipe can be irregular polygons and are defined following the IPCC Special Report on Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation (SREX) land regions (Seneviratne et al., 2012). In addition to the regions described here, the ESMValTool preprocessor can be used to run many diagnostics on distinct regions defined by latitude and longitude limits. We plan to also include regions with more complex boundaries like the CORDEX (Coordinated Regional Downscaling Experiment) regions (Gutowski et al., 2016).

Systematic biases in modelled projections (Boberg and Christensen, 2012) can be investigated by ranking models against observed monthly mean temperature (see Fig. 16).

The stochastic downscaling recipe is an example of how the ESMValTool (including its pre-processing functionalities) can be used to create a post-processing chain for further downscaling applications, but it is strictly speaking not a diagnostic.

The application of climate model projections and forecasts to impact studies at small scales, such as hydrological modelling or ecological modelling, requires bridging the large gap between the spatial resolution of current global and regional climate models and the scales required for a correct representation of the spatial and temporal structure of precipitation at fine scales as well as of the probability of extreme precipitation events. In the absence of a dynamical, physically based representation, a possible approach is the use of stochastic rainfall downscaling techniques. In particular, the Rainfall Filtered AutoRegressive Model (RainFARM; Rebora et al., 2006; D'Onofrio et al., 2014; Terzago et al., 2018) method is a weather generator which has only one free parameter (which can be derived from large scales) and which requires no further calibration. RainFARM can create ensembles of high-resolution precipitation fields from coarse-scale climate model data. This method also allows quantification of uncertainties and a realistic representation of subgrid-scale variability of precipitation and of precipitation extremes, which is a crucial prerequisite for impact studies in the water sector.

The recipe recipe_rainfarm.yml allows running RainFARM within the ESMValTool. Downscaled output can be produced directly from the climate model results read by the ESMValTool and exploiting its input checking, validation, and pre-processing features. The recipe produces ensembles of downscaled fields (see Fig. 17) over selected regions in NetCDF format, which can then be used by users for further analysis. Notice how the downscaled fields introduce fine-scale precipitation structures while still maintaining on average the original coarse-resolution precipitation. Different stochastic realizations are shown to demonstrate how an ensemble of realizations can be used to reproduce unresolved subgrid variability.