Global mean temperature (GMT) has recently surpassed 1 ∘C warming above pre-industrial levels (IPCC, 2018). The impact of the realized change in climate has also started to become detectable in natural, human or managed systems such as freshwater resources, terrestrial water systems, coastal systems, oceans, food production systems, the economy, human health, security and livelihoods (IPCC, 2014). The causal chain from climate change to climate impacts is often complex and intertwined with additional drivers, such as changes in management that alter climate-induced changes in crop yields (Butler et al., 2018; Iizumi et al., 2018; Zhu et al., 2019) and land use changes adding to climate-driven changes in biodiversity (Hof et al., 2018).

Attribution in its most general definition aims to quantify the drivers of change in a system. The systems and drivers considered in attribution studies vary between disciplines. In climate science, the “classical” attribution framework refers to the attribution of changes in the climate system to anthropogenic forcing (Hegerl et al., 2010; WGI contribution to IPCC, 2013) (“climate attribution”; see first arrow in Fig. 1). It addresses the following question: what is the contribution of anthropogenic emissions of greenhouse gases and aerosols or land use changes to observed changes in climatic variables, most prominently temperature and precipitation? As the response of the climate system to these forcings is often veiled by the chaotic nature of the climate system, climate attribution usually builds on probabilistic approaches comparing an entire ensemble of climate model simulations including anthropogenic forcings against a counterfactual ensemble excluding these forcings as, e.g., generated within DAMIP (Gillett et al., 2016) to separate forced changes from internal variability. Climate attribution can refer to observed long-term trends (WGI contribution to IPCC, 2013, chap. 10) or individual events (Trenberth et al., 2015; NAS, 2016; Stott et al., 2016). Given the probabilistic setting, results are often formulated as statements such as “anthropogenic climate forcing has increased the probability of occurrence of the observed trend or the intensity or duration of a specific extreme event”. In a non-probabilistic framework the intensity of an observed event can be attributed to the observed realization of climate change by comparing the event magnitude in the observed time series to the magnitude of the same event in a detrended version of the observed time series (quantification of the “contribution of the observed trend to event magnitude”, Diffenbaugh et al., 2017). This type of attribution to climate change does not address the reasons of the observed climate trend.

In addition to climate attribution, research on impact attribution addresses the following question: to what degree are observed changes in natural, human and managed systems induced by observed changes in climate (Fig. 1, second arrow)? In the Working Group II (WGII) contribution to the IPCC AR5, an entire chapter was dedicated to the topic including the following definition: an impact of climate change is “detected” if the observed state of the system differs from a counterfactual baseline that characterizes the system's behavior in the absence of changes in climate (IPCC, 2014, chap. 18.2.1), and “attribution” is the quantification of the contribution of climate change to the observed change in the natural, human or managed system. In both cases “climate change refers to any long-term trend in climate, irrespective of its cause” (IPCC, 2014, chap. 18.2.1).

While in principle changes in natural, human and managed systems could also be attributed to anthropogenic climate forcing (“impact attribution to anthropogenic climate forcing”, first and second arrow in Fig. 1, Pall et al., 2011; Schaller et al., 2016; Mitchell et al., 2016), we focus on “impact attribution to climate change” as described in the WGII definition and introduce a climate dataset that can be used as input to climate impact models to characterize the system's behavior in the absence of climate change (second arrow in Fig. 1). The dataset is derived from the observed realization of climate, excluding the analysis how climate variability could produce alternative realizations of factual or counterfactual climate. The attribution approach is thus deterministic and not probabilistic, focusing on the separation of climate change from direct human influences as potential drivers of changes in the impacted systems. Concerning the internal variability within impacted systems, impact models to date largely do not resolve such variability and model a deterministic response to external drivers. Our approach would however allow for probabilistic attribution to climate change once impact models resolve internal variability.

The method proposed here is designed to generate a stationary climate without long-term changes. The statistical model used to produce this counterfactual climate removes the long-term change correlated with (but not necessarily caused by) large-scale climate change, represented by GMT change instead of a simple temporal trend (see Methods). The method preserves the internal variability of the observed time series by additively (e.g., for temperature) or multiplicatively (e.g., for precipitation) removing a long-term trend, such that a particularly warm or dry day compared to the long-term trend remains a particularly warm or dry day in the counterfactual climate. In this regard, the approach is similar to the subtraction of a climate trend done by Diffenbaugh and Burke (2019) to attribute historical changes in economic growth or to attribute changes in land area burned by wildfires (Abatzoglou and Williams, 2016). However, while both studies subtract the anthropogenic warming derived from climate model simulations, we subtract the realized long-term trend of the data irrespective of its cause (see WGII definition).

The stationary climate dataset can then be used as input to climate impact models for impact attribution to climate change, as illustrated in Fig. 2. In a first step the climate impact model forced by observed climate and socio-economic drivers has to demonstrate being able to reproduce the observed changes in natural, human and managed systems as measured by an impact indicator (comparison of black and blue solid lines in Fig. 2). The attribution of the observed changes in natural, human and managed systems is built on a high explanatory power of the factual simulations. Then, in a second step, that factual simulation can be compared to a counterfactual simulation, forced by counterfactual climate but otherwise the same input as in the factual simulation. Such a comparison allows for a quantification of the contribution of climate change to both the observed trend in the impact indicator (CT in Fig. 2) and the observed magnitude of an individual impact event (CE in Fig. 2). This assumes that the climate impact model calibrated to perform well in the factual simulation performs robustly also with counterfactual climate input data.

Process-based impact models such as those taking part in the ISIMIP project (http://www.isimip.org, last access: 4 August 2021) are ideal tools to address impact attribution as they generally describe the response of natural, human or managed systems not only to climate but also direct (human) drivers. For example, crop models can simulate the response of crop yields to changes in land use, irrigation patterns, fertilizer input and crop varieties (Lobell et al., 2011; Challinor et al., 2014; Minoli et al., 2019). Similarly, hydrological models can be used to simulate how dam construction and water withdrawal affect river discharge (Veldkamp et al., 2017, 2018). In addition, those models allow for a process-based representation of the extent of, e.g., river floods and droughts that can be combined with maps of asset distribution and empirical damage functions to estimate the direct economic damages induced by weather extremes. The impact attribution framework could then be used to approximate the contribution of climate change to observed trends in reported damages. Using process-based climate impact models, this contribution can be explicitly separated from changes in damages driven by changes in exposure or vulnerability. In this regard it goes beyond available approaches of damage attribution that simply estimate the contribution of anthropogenic climate forcing to observed damages by multiplying the fraction of attributable risk associated with weather extremes by the observed damage (Frame et al., 2020). In the same way, it could improve the attribution of health impacts (Mitchell et al., 2016).

In this paper we introduce a detrending method tailored to support impact attribution and illustrate its application to one of the observational climate datasets provided within ISIMIP3a (https://protocol.isimip.org/protocol/ISIMIP3a, last access: 4 August 2021; see Sect. 2 below). The quality of the associated impact attribution studies will critically depend on the quality of that observational dataset. Deficits in the observational data may lead to artifacts in the derived historical trends. For the dataset used here, we identify some of those artifacts. Since it is expected that other artifacts will be found for other observational datasets, impact attribution studies should ideally be based on a range of different observational datasets to facilitate a quantification of the contribution of observational climate data uncertainty to the uncertainty of the attribution results. This is also planned within ISIMIP3a. For the dataset considered here and potential additional ones we propose a collection of control plots that should be used to scan the observational climate data for artifacts in preparation of each individual impact attribution study. While we provide the control plots for a set of large-scale world regions and all climate variables covered by our observational climate dataset, they should be adjusted to the regions and variables of interest in an impact attribution study as part of the analysis of the factual impact simulation (Fig. 2). Low-quality factual climate forcing data are expected to result in a low-quality reproduction of observed variations in the impact indicators of interest. If that is the case, the simulation setup outlined here does not allow for an attribution of the observed changes in impacts to climate change.

For ISIMIP3a, we construct counterfactual climate data for the global observational dataset GSWP3-W5E5. This dataset has daily temporal and 0.5∘ spatial resolution and consists of two parts: W5E5 v2.0 for the period 1979–2019 and GSWP3 v1.09 homogenized with W5E5 for the period 1901–1978. In the following, we describe these two parts as well as why and how they were combined for ISIMIP3a.

The GSWP3 v1.09 dataset is from the third phase of the Global Soil Wetness Project (GSWP3), an ongoing land model intercomparison project, which shares its experiment protocol with “land-hist” of the Land Surface, Snow and Soil moisture Model Intercomparison Project (LS3MIP; van den Hurk et al., 2016) and covers the years 1901–2014 (Kim, 2017). It is a dynamically downscaled and bias-adjusted version of the 20th Century Reanalysis (20CR; Compo et al., 2011) and has been used as a meteorological forcing dataset in several climate impact assessments such as those carried out in ISIMIP2a (e.g., Müller Schmied et al., 2016; Chang et al., 2017; Schewe et al., 2019; Padrón et al., 2020) as well as in broader modeling studies (e.g., Krinner et al., 2018; Tangdamrongsub et al., 2018; Tokuda et al., 2019). GSWP3 is also provided for the impact model evaluation task within ISIMIP3a.

20CR assimilates subdaily surface pressure and sea-level pressure observations and uses monthly sea-surface temperature (SST) and sea-ice distributions from the Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST; Rayner et al., 2003) as lower boundary conditions. To produce GSWP3, the first of the 56 members of the 20CR ensemble was dynamically downscaled to T238 (about 0.5∘) spatial resolution using the incremental correction of a single member (ICS) method of Yoshimura and Kanamitsu (2013) and the Scripps Institution of Oceanography (SIO)/Experimental Climate Prediction Center (ECPC) Global Spectral Model (GSM) with spectral nudging (Yoshimura and Kanamitsu, 2008) and vertically weighted damping coefficients (Hong and Chang, 2012). The ICS method additively adjusts the prognostic fields of a single ensemble member such that at the monthly timescale each adjusted field is identical to the corresponding ensemble mean field while all higher-frequency parts of the fields are retained. Hence, the adjusted fields represent the 20CR best estimates at the monthly timescale while they do not suffer from the increase in synoptic variability over time found in the 20CR ensemble mean (Compo et al., 2011) that is due to a decrease in the ensemble spread over time, which in turn reflects the increase in available observational constraints (Yoshimura and Kanamitsu, 2013).

The downscaled 3-hourly data were then bilinearly interpolated from T238 to a regular 0.5∘ latitude–longitude grid. In addition, selected variables (precipitation, surface downwelling shortwave and longwave radiation, near-surface wind speed, near-surface air temperature, surface air pressure, and near-surface specific humidity) were bias-adjusted with different methods and observational reference datasets. Precipitation was bias-adjusted at the monthly timescale using an undercatch-corrected version of the Global Precipitation Climatology Centre (GPCC) Full Data Monthly Product Version 7 (Schneider et al., 2014). The bias adjustment was done by rescaling all monthly mean values to the GPCC estimates. Radiation was bias-adjusted at the daily timescale using Surface Radiation Budget (SRB; Stackhouse et al., 2011) primary-algorithm estimates of daily mean values from SRB release 3.1 for longwave radiation and SRB release 3.0 for shortwave radiation. Since those estimates are only available for 1983–2007, bias-adjusted daily values were computed as the sum of a rescaled monthly mean value and a rescaled daily anomaly from the monthly mean, with the rescaling done such that, for the 1983–2007 time period, both the monthly mean climatology and the anomaly standard-deviation climatology matched the respective SRB estimates. Wind speed was bias-adjusted at the monthly timescale over land using mean monthly climatologies from the Climatic Research Unit (CRU) CL2.0 dataset (New et al., 2002). The bias adjustment was done by monthly rescaling such that the 1961–1990 mean monthly climatology matched that of CRU CL2.0. Temperature, pressure and humidity were bias-adjusted at the 3-hourly timescale using the WATCH forcing data methodology (Weedon et al., 2014) and monthly mean temperatures plus monthly mean diurnal temperature ranges from the CRU TS3.23 dataset (Harris et al., 2014), which covers the full 1901–2014 time period.

As a consequence of its derivation, the quality of the GSWP3 data varies over time. It varies in line with variations in the availability of the pressure, SST and sea-ice observations used to produce 20CR (Compo et al., 2011; Rayner et al., 2003) as well as with variations in the availability of the precipitation and temperature observations used to bias-adjust GSWP3 (Schneider et al., 2014; Weedon et al., 2014). Examples of temporal inhomogeneities in GSWP3 that are relevant for this study include artificial drying trends over northwest China and the Tibetan Plateau over the first half of the 20th century (Fig. 10) that are inherited from GPCC (Chen and Frauenfeld, 2014) and spurious trends in shortwave radiation and wind speed over Alaska, Northern Canada and Greenland over the first half of the 20th century (Figs. 9 and S12 in the Supplement), which are related to artificial extratropical cyclone trends in 20CR over that time period (Wang et al., 2013). Generally, the quality of 20CR, and hence GSWP3, becomes relatively stable around mid-century over the Northern Hemisphere, earlier over Europe and later over the Southern Hemisphere, in line with variations in the availability of pressure observations for data assimilation in the reanalysis (Compo et al., 2011).

The W5E5 v2.0 dataset (Lange et al., 2021) was compiled to support the bias adjustment of climate input data carried out within ISIMIP3b and covers the years 1979–2019. It combines the WFDE5 v2.0 dataset (WATCH Forcing Data methodology applied to ERA5 reanalysis data; Cucchi et al., 2020) over land with data from the latest version of the European Reanalysis (ERA5; Hersbach et al., 2020) over the ocean. WFDE5 is a meteorological forcing dataset based on ERA5. For the variables included, it is a spatially aggregated (to 0.5∘) and bias-adjusted version of ERA5. Compared to 20CR used for GSWP3, many more observations were used for data assimilation in ERA5, including precipitation observations (Hersbach et al., 2020). That is why we consider ERA5 to better represent reality than 20CR for 1979 onwards. Similarly, WFDE5 is considered to better represent reality than GSWP3, in particular with respect to day-to-day variability for variables that were bias-adjusted using only monthly mean values in both datasets, such as temperature and precipitation.

Since W5E5 is considered the more realistic dataset but only covers 1979–2019, it was extended backward in time to generate GSWP3-W5E5 for ISIMIP3a. In this extended dataset, GSWP3 data for 1901–1978 were homogenized with W5E5 data using the ISIMIP2BASD v2.5 quantile mapping method (Lange, 2019, 2021). The resulting GSWP3-W5E5 data are identical to the original W5E5 data from 1979 onwards but different from the original GSWP3 data before 1979. The goal of the homogenization was to smooth the transition from one dataset to the other in 1978/1979. To that end, for every climate variable and grid cell individually, the original GSWP3 time series for 1901–2004 were quantile-mapped to time series which have the same trends but whose distributions match those of the corresponding W5E5 data over the 1979–2004 reference period. The resulting, homogenized GSWP3 data for 1901–1978 were then used to extend W5E5 backward in time. The preservation of trends implies that differences between trends in GSWP3 and W5E5 data were not homogenized. Consequently, some inhomogeneities at the 1978/1979 transition remain. This problem particularly affects surface downwelling shortwave radiation over northern Europe and the Mediterranean Basin (Fig. 8) as discussed further in the results section.

Assuming that “climate change refers to any long-term trend in climate, irrespective of its cause” (IPCC, 2014, chap. 18), we here present a method to generate time series of stationary climate data from observational daily data by removing the long-term trend while preserving the internal day-to-day variability. In the following, we first describe the general characteristics of our approach followed by a more detailed formal description of the method. Then we introduce the set of global and regional evaluation plots we recommend to regionally adjust and consider within each attribution study using the counterfactual data generated here or when applying the detrending approach to other observational climate data.

The counterfactual dataset evaluated in the following is free to download through the ISIMIP data portal (https://data.isimip.org/search/climate_scenario/counterclim/, last access: 4 August 2021) along with the underlying original data. Our method strongly reduces the observed difference between multi-year averages over the beginning of the century (1901–1930) and the end of the observational period (1990–2019) for most locations and variables (Figs. 5 and 6). The remaining differences are largest for precipitation over the Tibet region and for wind speed over Greenland. In the following we exemplarily zoom into these regions to resolve the temporal evolution of the regionally averaged factual and counterfactual data (Figs. 7–10, left panels) and evaluate the detrending for each day of the year (Figs. 7–10, right panels). We start with temperature and precipitation in northern Europe where the detrending works well and then focus on regions where the factual data show artifacts that may make them inadequate for impact attribution within the proposed setup.

The attribution of changes in the climate system to anthropogenic interference with the climate system is a mature research field (IPCC, 2013; Gillett et al., 2016; NAS, 2016; Stott et al., 2016). Less work has been done on the attribution of changes in natural, human and managed systems affected by climate change in combination with other time-evolving drivers. Impact attribution as defined in the introduction aims to quantify the role of climate change versus the other drivers of change. Impact attribution needs a comparison of the observed state of the considered system to its hypothetical, counterfactual state without climate change. The reason for the change in climate trends and a separation of anthropogenically forced changes from climate variability are not necessarily required. Thus, a simplified methodology that detrends observational data is sufficient without the need for probabilistic climate model simulations. The proposed design of the counterfactual climate forcing data and the associated impact simulation framework mean a restriction to “impact attribution to climate change” instead of “impact attribution to anthropogenic climate forcing”. The latter is necessary to, for example, attribute a fraction of an impact to a greenhouse gas emitter and support climate litigation (Marjanac et al., 2017; Burger et al., 2020). Thus the counterfactual climate data generated here are not intended to replace climate simulations with counterfactual greenhouse gas forcings such as the histNAT CMIP6 experiments' (Gillett et al., 2016) large climate model ensembles that are required to attribute changes in climate or impacts to anthropogenic emissions.

Climate impact models can be considered as ideal tools to address impact attribution as they are usually designed to represent the response of impact indicators to climate disturbances but also account for direct human interventions such as agricultural management changes, water abstraction or flood protection measures. Within the model, individual drivers can be controlled, and a factual run (observed climate change + observed direct human interventions, Fig. 2 blue line) can be compared to a counterfactual run (counterfactual climate + observed direct human interventions, Fig. 2 orange line).

By providing climate forcing data for counterfactual climate impact runs, we facilitate impact attribution following the basic IPCC AR5 WGII definition utilizing the strength of impact models to address the important question of to what degree climate change is already affecting natural, human and managed systems. So far the contribution of climate change to long-term historical changes in human, natural or managed systems is often addressed by model simulation where direct human interventions are fixed while only climate is allowed to change according to historical observations (e.g., Sauer et al., 2021). However, this alternative definition may also lead to different results and does not allow for the attribution of the magnitude of individual impact events to climate change as described in Fig. 2.

Attribution draws a causal connection and quantifies the change due to the cause. An important part of the attribution work is thus to ensure that the cause–effect relationship is correctly captured in the model. This requires careful analysis and model evaluation to show that the change estimated by an impact model is a reliable estimate of the real-world change. Simulated changes need to agree with observed changes, and it needs to be ruled out whether this agreement is due to confounding factors that drive observed changes but are not part of the model simulations. The ISIMIP3a historical simulations serve to address these points and demonstrate the explanatory power of impact models as an integral part of the attribution work.

Our method ultimately builds on the correlation between a regional climate variable and decadal GMT change to remove long-term trends in the regional climate variables without implying causality. It is well possible that changes in regional climate variables have other reasons than global warming such as local effects of land use changes and aerosol emissions as well as regional characteristics of large-scale decadal climate oscillations. However, our study shows that GMT change is generally a powerful predictor allowing for generating stationary counterfactual climate data. Major detrending failures seem to be related to artifacts in the factual observational climate data that particularly affect the first half of the century and prevent impact attribution in the proposed framework.

Our detrending approach does not guarantee the maintenance of physical consistency of different climate variables in the counterfactual datasets in terms of, e.g., energy closure or water budgets. However, the applied quantile mapping preserves ranks, which means that relatively high values before the mapping are also relatively high after the mapping and similarly for relatively low values. Statistically speaking, univariate quantile mapping independently applied to all climate variables preserves the multivariate rank distribution (the copula) over all variables. In that sense the statistical dependence between variables is preserved by our detrending method, and the risk of producing physically inconsistent counterfactual climate data is at least limited. This is critical for the attribution of the extreme event magnitude to observed climate trends (see introduction) because several climate variables can contribute to impact extremes.

Here, we deliberately excluded the question of what drives climate change, i.e., the attribution of changes in the climate system to greenhouse gas emissions, as it often implies a focus on this aspect and less attention is paid to the separation of climate change from direct human interventions as drivers of observed changes in natural, human and managed systems. The restriction of the research question to “impact attribution to climate change in general” makes the assessments independent of climate simulations and their potential limitation in reproducing processes relevant for historical climate change. Instead, the restricted framework is directly linked to impact model evaluation and the question of how well we understand the observed changes in human, natural and managed systems. This question can most directly be addressed by the factual impact simulations proposed here rather than with impact simulations based on simulated historical climate. In addition, as opposed to large ensembles of climate model simulations, such a dataset is easily integrated into an impact model intercomparison project such as ISIMIP, which includes models of very different computational costs. In this way the approach allows for an exploration of structural uncertainty in climate impact attribution, based on a multi-impact-model ensemble, combined with a variety of damage functions where appropriate.

With the methods and data presented here, we aim to advance the field of impact attribution and reveal past and present societal and environmental sensitivities to climate change. Getting a better understanding of the drivers of observed changes in natural, human and managed systems will help us to better estimate future risks related to ongoing global warming and develop adequate adaptation measures.