Do Derived Drought Indices Better Characterize Future Drought Change?

Current methods for climate change assessment ignore the significant differences in uncertainty in model projections of the two key constituents of drought, precipitation, and evapotranspiration. We present here a new basis for assessing future drought using climate model simulations that addresses this limitation. The new method estimates the Standardized Precipitation Evapotranspiration Index (SPEI) in a two‐stage process. The first stage of our proposed approach is to derive the Standardized Precipitation Index (SPI) using reliable atmospheric variables, which are filtered with a wavelet‐based spectral transformation. This derived SPI is then converted to an equivalent SPEI by combining it with climate model evapotranspiration simulations. We assess the performance of our proposed approach across Australia. The consistency of general circulation model (GCM) drought projections, in terms of both frequency and severity, is improved using the derived SPI. Incorporating evapotranspiration further improves the consistency of the multiple GCMs and drought time scales. The proposed framework can also be generalized to other water resources applications, where the differences in GCM uncertainty for precipitation and evapotranspiration affect climate change impact assessments.


10.1029/2022EF003350
2 of 17 low humidity, and low-frequency climate fluctuations (e.g., El Niño-Southern Oscillation (ENSO), including both warm (El Niño) and cold (La Niña) phases of ENSO) (Okumura et al., 2017;Rashid et al., 2020;Risbey et al., 2009). Because of this, it is vital to understand how the GCM biases and uncertainty in each of these variables interact. While GCMs provide reasonable simulations of large-scale atmospheric variables (e.g., temperature, sea level pressure, etc.), their skill in representing local scale sustained hydrological anomalies is limited due to their coarse scale, incomplete model structures, feedback loops including the albedo and land-atmosphere interactions and in the case of precipitation, the parameterization of clouds and convection (Haerter et al., 2011;Masson & Knutti, 2011;Maurer et al., 2013;Meehl, 2007;Randall et al., 2007;Sun et al., 2006).
Downscaling is often used to address the issues discussed above in GCM simulations (Fowler et al., 2007). Often precipitation is downscaled and then used to calculate the drought statistics of interest. As downscaling requires the use of selected atmospheric predictors (lateral and lower boundary conditions of temperature, humidity, and wind fields in the case of dynamical downscaling, and equivalent co-located variables in the case of statistical alternatives), the resulting precipitation product can be thought of as a "derived" estimate. An alternative to downscaling precipitation is downscaling the drought indices directly (Jiang et al., 2020). This has the advantage that drought indices such as the Standardized Precipitation Index (SPI) are, by definition, normally distributed which means that simpler downscaling model structures can be used compared to the models required for downscaling highly skewed precipitation distributions. For example, the presence of dry spells or dry days generally requires a two-part model or a mixture distribution further complicating precipitation downscaling (Mehrotra et al., 2004). Future drought projections are also affected by changes in evapotranspiration (ET) (Asadi Zarch et al., 2015). Drought indices such as the Standardized Precipitation Evapotranspiration Index (SPEI) (Vicente-Serrano et al., 2010) and Reconnaissance Drought Index (RDI) (Tsakiris & Vangelis, 2005) are therefore vital when evaluating future water stress. A number of studies have thus considered future drought using GCM simulations of precipitation and evapotranspiration (Aadhar & Mishra, 2020;Dewe et al., 2017;Gupta et al., 2020;Shi et al., 2020;Yao et al., 2020).
The uncertainty in future drought projection under climate change is large. This uncertainty comes from the climate model structure and parameterization, drought indices type and time scale, as well as emission scenarios (Burke & Brown, 2008;Saharwardi & Kumar, 2021;Ukkola et al., 2020). Importantly there are considerably different uncertainties inherent in future precipitation simulations compared to the climatic variables that affect ET (Eghdamirad et al., 2017;Johnson & Sharma, 2009;Kim et al., 2020). In fact, we could question whether it is even necessary to downscale more reliably simulated variables such as ET; instead, the direct use of model-simulated ET may be acceptable. The predictors that would be chosen in a downscaling model for precipitation will also be different from those useful for ET. Therefore, a combined downscaling approach for SPEI or RDI will require a large number of predictors and the uncertainty of the two components of the drought index (i.e., precipitation and evapotranspiration) will be very different.
To address this issue, a new approach for projecting drought is proposed here. The approach has two steps: the first derives SPI and then the second step post-processes the SPI using future potential evapotranspiration (PET) estimates to calculate the SPEI. The advantages of this approach are that the downscaling method can be designed to focus on the variability and uncertainty in precipitation that is the primary driver of multi-year variability in drought projections, but it does not neglect the important contribution of PET to future drought projections. As such, our major contribution is to combine precipitation and evapotranspiration in understanding future drought impacts accounting for their relative uncertainty difference from GCM simulations. Previous studies have investigated the uncertainty of PET from different estimation methods (Aadhar & Mishra, 2020;Dewes et al., 2017;Kingston et al., 2009;Yuan & Quiring, 2014), For instance, Aadhar and Mishra (2020) suggested that when projecting drought under climate change the increase in PET by the Thornthwaite equation is substantially higher than Penman-Monteith based estimate. However, there is limited work addressing the differences in the relative uncertainty of the two key components of drought. This gap is addressed here through the new two-step approach to projecting drought.
In this paper, the effectiveness of this new drought projection framework is assessed by considering historical and future drought anomalies across a range of time scales in Australia. The remainder of the paper is organized as follows. Section 2 summarizes the data and methods with details of how the SPEI is ascertained using the derived SPI projections as well as a summary of the historical data and climate models used for the assessments. In Section 3, the results of derived drought indices and assessments for both historical and projected future droughts are presented. Concluding remarks are given in Section 4.

Methods and Data
This section develops the new post-processing method for calculating SPEI and summarizes all the data and evaluation methods used in this study. There are four parts: (a) the basis of post-processed drought indices accounting for the influence of evapotranspiration, (b) SPI downscaling with the spectral transformation, and (c) the climate variables used for downscaling and computing drought indices from GCMs across Australia.

Using SPI as the Basis for Estimating SPEI
SPI is commonly used to assess drought because of its simplicity and adaptability in representing a range of time scales (Guttman, 1998;Hayes et al., 1999;Mishra & Desai, 2005). This allows different types of droughts to be quantified such as flash droughts as well as multi-year droughts which are important for agricultural and water resources management (Jiang et al., 2019;Yao et al., 2020). The standardization in SPI also allows it to be compared across time scales and regions. However, as discussed above, just considering precipitation in assessing future drought will lead to biased estimates of water security. To date, there have been two broad approaches for defining a drought index to account for the effects of evapotranspiration in the context of climate change. Considering the relationship between SPI and SPEI for example, it is possible to: (a) Derive SPEI by calculating the difference between GCM simulated precipitation and PET, which is calculated using the GCM simulated temperature. (b) Downscale SPEI directly using atmospheric predictors simulated by GCMs.
The drawback of the first option is the lack of reliability of GCM precipitation simulations (Eghdamirad et al., 2017;Kim et al., 2020), and this option is named as one-step SPEI estimate approach hereafter. The second alternative is complicated by the need to identify the atmospheric predictors because the response (SPEI) depends on two causative variables (precipitation and PET). Because PET, and especially its estimation based on the Thornthwaite equation, is strongly dependent on temperature, its uncertainty will be markedly different from the precipitation uncertainty which is largely dependent on locally varying atmospheric predictor variables, such as geopotential height, humidity, and wind (Diez-Sierra & del Jesus, 2020; Eghdamirad et al., 2017;Rashid et al., 2018). For instance, projections of precipitation and temperature from the latest Coupled Model Intercomparison Project phase 6 (CMIP6) models suggested that precipitation is likely to have larger uncertainty than temperature, especially when considering its large spatial variability in the projected climates (Almazroui et al., 2020). In terms of the uncertainty in the trends of these two variables, Konapala et al. (2020) also showed that evaporation trends are more consistent than precipitation trends. Here, we propose a third method for calculating SPEI by post-processing the downscaled SPI to derive SPEI using projections of PET to address the issues discussed above. This new method has been named the two-step SPEI downscaling approach. The basis of this new method is to derive SPEI by first downscaling SPI using its relevant atmospheric predictors and then calculating the SPEI by correcting the SPI to account for PET calculated from the GCM temperature simulations. Given a time series of x i , a simple k-moving summation can be defined as = ∑ + −1 = and the associated standard deviation as , where the subscript (X) denotes the variable (precipitation, P, PET, or the difference between P and PET, P-PET) of interest, and i refers to the index of time series. Here, we formulate SPI and SPEI as the standardized quantities as follows: We can then express SPEI as: where and −PET are the standard deviation, and and PET are aggregated values at different time scales (k) as per the standard approach for calculating SPI or SPEI. The above equations form the basis of the derived SPEI results presented in later sections. The logic adopted here is motivated by needing to project the precipitation component of the SPEI using downscaling, while using direct estimations of PET to derive the SPEI. The basis for this is the difference in uncertainty between GCM projections of precipitation and PET, and that downscaling can reduce the uncertainty in precipitation projections. PET can be estimated indirectly from meteorological parameters using physically based (e.g., Penman-Monteith method) and empirical relationship models, depending on data availability (Gu et al., 2019;Guo et al., 2016). Since PET is included in the drought index calculation to obtain a relative temporal estimation, a reasonable estimation method needs to be adopted (Vicente-Serrano et al., 2010). Previous studies have shown that using alternate methods to calculate PET provides similar results when estimating drought indices such as PDSI (Mavromatis, 2007;van der Schrier et al., 2011), RDI (Zarei & Mahmoudi, 2017), and SPEI (Um et al., 2020). Consequently, the simplest approach for estimating PET has been used in the results presented later (Thornthwaite, 1948), requiring monthly temperature information which is routinely available in data repositories storing GCM simulations. We now present details of the method used to downscale SPI as the input to Equation 2.

Derived SPI Using Spectrally Transformed GCM Atmospheric Predictors
The first step in calculating the new SPEI is to calculate future SPI. Jiang et al. (2020) showed good skill in downscaling SPI for a small study region using spectral transformation of the predictors. However, this earlier work had a limited spatial scope and did not consider if downscaling SPI added value compared to directly estimating SPI from the GCM precipitation simulations. Here, the effectiveness of the spectral transformations in characterizing sustained drought anomalies is investigated for all of Australia by comparing downscaled SPI and GCM simulations of precipitation. For the historical period, SPI is downscaled using reanalysis data to calibrate the downscaling model and then applied using GCM simulations. The downscaling is carried out in two ways-the first using the wavelet-based transformation of Jiang et al. (2020) on the atmospheric predictors and also using the predictors directly (i.e., no transformation). Essentially, the wavelet-based variance transformation (VT) method refines the spectral representation of the predictor variables by redistributing the variance in the frequency domain using wavelet transform to create greater similarity in the spectral attributes of the transformed predictor and the response it is used to predict. In other words, the use of VT-based downscaling helps to strengthen the relationship between predictor and response. By separating the long-term trend and short-term fluctuations, VT amplifies the information that is more relevant for deriving the response while filtering out the irrelevant information present in the predictor, thereby defining a less uncertain relationship. In the framework of the VT approach, a distribution-independent measure (Sharma et al., 2016), namely partial informational correlation (PIC), is used to identify significant predictors when formulating the downscaling model. The details of wavelet-based VT, as well as PIC, are given in Text S1 and S2 of the Supporting Information S1, respectively. Readers are referred to  and  for additional details as well as the software to apply this step in practice. A flowchart of the proposed wavelet-based drought downscaling framework is presented in Figure 1, where VT represents the models using the wavelet-based transformation for the GCM predictors compared to using the GCM atmospheric predictors using a standard bias correction (Std). The SPI calculated by NCEP reanalysis data, NCEP(VT), is used as the benchmark model. GCM simulated atmospheric variables and precipitation were bias-corrected using quantile delta mapping (Cannon, 2018;Cannon et al., 2015). Following the first stage, the risk of future droughts across a range of time scales is investigated by using both projected SPI and the two-step method to calculate SPEI where evapotranspiration is included. In summary, five models are compared for the historical climate-models one and two are based on directly estimating the two-step SPEI directly using precipitation and PET (either from observations or GCM simulations), whilst models 3 to 5 are based on downscaling SPI from atmospheric predictors and then calculating SPEI ( Figure 1). For future drought projection, in addition to models using two-step approaches, the one-step approach model, which obtains estimates of SPEI from bias-corrected GCM without going through the SPI route, is included to further assess the merits of the proposed two-step downscaling approach.

Evaluation Metrics of Drought to Assess Model Performance
There are different ways of defining and characterizing a drought event. Van Loon (2015) used the threshold level method to define a drought event, and either a fixed or a variable threshold can be used. As standard in many drought impact assessments ( Once a drought event is defined, it can be characterized by its duration, deficit, and intensity. The duration of a drought event is simply the amount of time when the drought index is continuously below the adopted threshold. Measures of severity often include two different types, deficit volume and maximum deviation from the threshold level. Drought duration and severity are positively related, and the deficit is often used for flux variables while intensity is commonly used as a measure of state variables (e.g., soil moisture and groundwater storage).
Here, the deficit was defined as the cumulative deficiency of the index below the threshold over the drought, while the intensity of a drought event was calculated as the maximum deviation from the threshold, as shown in Equation 3, where SDI refers to the standardized drought index in question (whether SPI or SPEI), D is the drought duration and θ is the adopted threshold. Figure 2 illustrates how the drought events and their statistics were defined, and shows the total number of drought events that occurred at a selected grid in Southeast Australia (location of the grid is presented in Figure  S1 of the Supporting Information S1). The red line is the adopted threshold, and each drought event can be identified. The length of the blue lines indicates the drought duration, the area below the red line represents the drought deficit, and the distance between the blue line and the red line is the drought intensity. The red numbers designate the reference number of each drought event. An example of the statistics from observed SPI at the grid is shown in Table 1, where 14 drought events (TDE, the total sum of drought events) occurred in the study period. The 9th drought event has the largest deficit and the highest intensity, and the longest duration. According to the drought classification by (McKee et al., 1993;Paulo et al., 2012), this event (SPEI less than −2) belongs to the extreme drought class. , while SPI_P ̂ represents the downscaled SPI using either NCEP or GCM simulated atmospheric variables. In addition, "direct estimate" here refers to the derivation of Standardized Precipitation Evapotranspiration Index (SPEI) using SPI using either observed or GCM simulated precipitation, while "downscaling" refers to the scenario where SPEI is derived using SPI estimated via atmospheric predictor variables. PET SOURCE refers to potential evapotranspiration (PET) estimated using the Thornthwaite method and temperature data, where SOURCE denotes either observations (obs), GCM, or NCEP data.
To assess the skill of the simulated drought characteristics over the historical period, we have derived two measures of similarity between modeled and observed drought across space and time scales. The two metrics include the most important aspects of drought characterization at a location, including an event related metric and a frequency metric (Equation 4). The event metric is calculated by the Euclidean distance between observations and simulations in the (Duration, Deficit, Intensity) space. The frequency metric is defined as the absolute value of the bias in TDE: where (x, y, z) represents the drought statistics (Duration, Deficit, Intensity), and subscripts m and o refer to the modeled and observed statistics, respectively. It should be noted that the paired values of (x, y, z) were rescaled to account for the large spatial discrepancy. The rescaling was done by dividing each value by the standard deviation of observed statistics individually (i.e., = Duration∕ Duration,obs , = Def icit∕ Def icit,obs , and = Intensity∕ Intensity,obs ), and the distance was calculated with reference to the mean value of rescaled observations ( , , ) .
In the future period, TDE, the total sum of drought duration (TDD), and the total sum of drought severities (TDS) as measured by deficit (Van Loon, 2015), are computed for each grid between 2021 and 2070. They are then compared to the historical period  to understand changes in drought variability across a range of time scales. The cumulative distribution function (CDF) is used to investigate future droughts from the perspective of  7 of 17 drought duration between current and future periods. In the absence of observations to verify the future drought projections, the degree of certainty for climate projections can be generally assessed in both qualitative and quantitative ways (Mastrandrea et al., 2010). In this study, we adopt a quantitative approach to describe the level of agreement among various GCMs regarding changes in future droughts (Johnson & Sharma, 2009). The term consistency is defined as the proportion of GCMs simulating the same direction of change across the study region. This is detailed in Equations 5 and 6: where N represents the total number of grids or sub-domains in the study area (N = 115), and n is the total number of GCMs assessed in the study (n = 7). θ is the threshold level for defining the extreme event of variable X i,j (θ = 20th percentile) for GCM i and at a grid j. The variable F i,j (θ) is simply represented by the sign of change of variable (here X is the drought indices, e.g., TDS) for each individual GCM and at the given location.

Data
As shown in Figure 1, the data used in the study include precipitation and temperature (used to calculate PET) time series and the atmospheric variables that were used in the downscaling models. The observed SPI was computed from monthly global gridded high-resolution station (land) data for precipitation, originally derived by the Center for Climatic Research Department of Geography University of Delaware Newark (Willmott, 2000) for the period 1951-2000, and it was spatially averaged from 0.5° × 0.5° to 2.5° × 2.5° resolution. The observed PET was estimated using observed temperature data from the University of Delaware.
The monthly time series of six atmospheric variables were pre-selected as potential predictor variables for downscaling (Table 2) and these climate variables have often been used as predictor variables for Australian rainfall (Mehrotra & Sharma, 2006;Rashid et al., 2018). Three pressure levels were included for the five atmospheric variables with the last variable being sea level pressure. Therefore, in total, we have 16 potential climate variables for model specification, and at each grid there could be more than one climate variable relevant to the target response, which are referred to as the 1st, 2nd, and 3rd order predictor, etc. A maximum of four predictors is selected at any one location to avoid overfitting. The atmospheric variables for formulating the downscaling model of SPI were obtained from the NCEP/NCAR Reanalysis data (Kalnay et al., 1996) and are available on a grid resolution of 2.5° × 2.5°. Surface air temperature at 2 m height was used to calculate PET and hence post-process SPI to form SPEI and was obtained from the reanalysis data for the historical period simulations.
The study domain was all over Australia.  To demonstrate the impact of the new post-processing and spectral transformation methods on how climate models represent historical drought, simulations from two GCMs were used, namely ACCESS1.0 and CanESM2. ACCESS1.0 has been adopted since it is an Australian model and can be expected to perform well in modeling the Australian climate system. CanESM2 has been widely used in model comparisons in Australia and shown to perform well (Asadi Zarch et al., 2017;Eghdamirad et al., 2017). All GCMs used in this study are the commonly used GCMs in Phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP) for assessing future drought frequency and severity (e.g., Song et al., 2022). Future drought projections were then calculated from a larger subset of seven GCMs for Representative Concentration Pathway (RCP) 8.5. Detailed information on the GCMs used in the study can be found in Table S1 of the Supporting Information S1. For each GCM, only the first ensemble (r1i1p1) was used to maintain the consistency between the models and between historical and RCP8.5 simulations (Saharwardi & Kumar, 2021). GCM simulated precipitation was also used to calculate SPI in both historical and future periods. Historical and future drought indices were assessed for two periods, 1951-2000 and 2021-2070, respectively. The GCMs simulations were interpolated to a resolution of 2.5° × 2.5° using bilinear interpolation to match the resolution of NCEP Reanalysis data. The coarse resolution adopted here is considered sufficient to investigate how the transformed climate variables characterize the variability of drought across a range of time scales at the continental scale.
Direct estimates of SPI were calculated using long-term precipitation time series according to Equation 1, and SPI was calculated across multiple time scales including 12, 36, 60, 84, and 108 months, namely SPI12, SPI36, SPI60, SPI84, and SPI108. The fitted gamma distribution at each location was used to derive the SPI from GCM simulated precipitation in both historical and future periods. In the context of Australia, droughts with large time scales (more than 12 months) are of great interest (Kiem et al., 2016) and thus were the focus of this study.

Application to Drought Assessment Across Australia
In this section, we first evaluate the performance of the downscaled SPI. Following this, we assess the derived SPEI results for the current and future climates obtained based on the downscaled SPI. Results from the four models for SPEI (the drought indices from the model using observations are used to calculate the evaluation metrics) are first compared for the current climate across multiple time scales. The two CMIP5 models are first used to illustrate the complete process of the proposed method, while the consistency of simulated future SPEI is assessed using seven GCMs (two CMIP5 and additional five CMIP6 GCMs) across time scales. In addition, CDFs of SPI and SPEI projections for the historical and future climates are presented to give an overall picture of what the future holds.

Downscaled Drought Indices of SPI
The downscaling of SPI using large-scale atmospheric variables includes two main steps, predictor selection and response prediction. Results of the predictor selection using both original (Std) and variance-transformed (VT) climate variables are shown in Figure 3. The first-order predictor of SPI12 at each grid across Australia is presented, while the frequency of the first-order predictors identified for SPI12, SPI36, SPI60, SPI84, and SPI108 are summarized in Figure 4. The Std model identifies hgt as the main driver while the model using transformed climate variables identifies both shum and hgt as significant drivers. When considering untransformed climate variables, significant predictors are identified in Southeast Australia but there are no significant predictors in central or southwest Australia. This is because of the large number of dry months which are difficult to link with potential predictors at the monthly time scales (i.e., a large difference in their frequency domain). The model using transformed predictors is able to identify significant predictors at all grids (a total of 115) in Australia. The Std model also selected fewer predictors than the VT model, especially for SPI with longer time scales (as shown in Figure 4). This is because of the larger difference in the spectral domains of multi-year SPI; the non-transformed predictors are informative on shorter time scales but do not fully capture long-term variability and underlying trend induced by global warming (Maraun et al., 2010). For the locations where no significant predictor was identified in the Std model, hgt was adopted as the predictor since it was the most frequently selected predictor across all locations.
The frequency of selecting each atmospheric predictor variable across the different drought time scales is shown in Figure 5. More atmospheric variables known to be relevant to Australian rainfall and droughts are identified by the VT approach. As the drought time scale increases, fewer predictors are able to be identified for the Std model. More details on the number of predictors are provided in Tables S2 and S3 of the Supporting Information S1.
SPI12 in the historical period is shown in Figure 6 for each of the four different models at the same location used in Figure 2. It is clear that SPI12 estimated using the NCEP predictors with VT represents the observations very well. For the three GCM SPI12 models, exact matches between the observed and modeled time series are not expected due to the lack of time correspondence in the GCM simulations. The GCM(VT) and the direct GCM  . Frequency (i.e., how many locations) of each atmospheric variable is selected as the first-order predictor in Australia for the models with (VT, yellow) and without (Std, black) variance transformation. The first-order predictor refers to the most influential predictor. Each subplot represents drought indices with different durations ranging from 12 to 108 months (SPI12, SPI36, SPI60, SPI84, and SPI108).  simulations capture the multi-year drought variability well. The downscaled SPI12 from GCM(Std) performs poorly which is likely due to the difference in the time scale of the predictor (i.e., monthly atmospheric variables) to the response (i.e., SPI at time scales longer than 12 months). Non-transformed monthly predictors can represent shorter time scales (e.g., seasonal) drought, but it is difficult to capture the variability of drought over longer time scales. First, precipitation (and temperature in the case of SPEI) variability at longer time scales, such as annual or multi-year, is influenced by a different set of factors compared to shorter time scales. In addition, the relationship between precipitation, temperature, and drought can be complex and nonlinear, which may require the additional transformation of the predictor variables to accurately capture the relationship with the drought index.
We now proceed to the second stage of our drought projection framework, which is estimating SPEI based on derived SPI and converting it into drought metrics, frequency and event metrics, as given in Section 2.3.

Comparison of Drought Metrics Over Current Period Simulations
As described previously, two metrics (i.e., event and frequency) have been derived from drought statistics to quantify the skill of each model in characterizing drought across space and time scales. Figure 7 shows the scatter plots of averaged Euclidean distance across Australia between modeled and observed SPEI by event and frequency metrics. The calibrated model of NCEP(VT) is the benchmark model, and it is the same for both ACCESS1.0 and CanESM2 (as shown in Figure 7). Note that the GCM results use GCM precipitation, while the other three downscale SPI using the identified predictor variables.
GCM(VT) is the closest to the calibrated NCEP(VT) and it is consistently close to the observations across all time scales as well as between two climate models. This suggests a strong capability of the VT approach in characterizing droughts, especially at longer time scales. The VT improves the ability of the models to correctly represent the frequency of drought as seen in Figure 7a. Even with bias correction, there are substantial differences between different GCM simulations of drought, and the ability to simulate droughts directly from the GCMs generally deteriorates with longer time scales in terms of both frequency and event metrics. In addition, Figure 7b shows that direct estimates of drought from CanESM2 precipitation are worse than ACCESS1.0, especially with the event metric. Two-step SPEI based on the downscaled SPI using untransformed climate variables has a significant bias in both event and frequency metrics, as was also evident in the downscaled time series (Figure 6). These estimates of SPEI using untransformed climate variables are the poorest, and thus not used for comparison in future drought assessments. More details can be found in Table S4 of the Supporting Information S1, which shows the associated numbers of averaged distance by event and frequency metrics in detail.
Corresponding results in this section for SPI are included in the Supporting Information S1 ( Figure S2 and Table S5). There is a reasonable similarity between the SPI and SPEI results presented in this section, which is to be expected given the main difference between the two is the contribution of evapotranspiration, a variable that is simulated with reasonable consistency across most time scales and between two GCMs. However, when evapotranspiration is incorporated, there is less uncertainty and thus a smaller increase in the event metric with models using transformed atmospheric predictors than the results of GCM(Std) and the direct GCM simulations. This is because droughts are well characterized especially over longer time scales by using the proposed drought projection framework.
Corresponding results for the first stage (focusing on SPI alone) are included in the Supporting Information S1. In the sections that follow, the consistency of future drought changes using both SPI and SPEI is assessed using the two-stage framework proposed in this study.

Consistency of Projected Changes in Drought Characteristics
In the absence of observations to verify the future drought projections, the consistency of the projections from different GCMs is often considered as a pseudo-validation of model performance (Maraun et al., 2010;Nguyen et al., 2017). Figure 8 presents the consistency of TDE and TDS changes among seven GCMs for all the modeled time scales, and its associated values of consistency are given in Table S6 of the Supporting Information S1. The consistency of the two-step downscaling approach model is higher than the direct approach drought projections for both TDE and TDS across all time scales, with the exception of TDE at time scales of 12 months. The one-step approach has relatively high consistency at the time scale of 12 months, which is probably due to the fact that GCMs have better skill in simulating the annual cycle of the earth system than longer time scale persistence. To sum up, the improved consistency across multiple time scales is the result of the post-processed SPI from the two-step model since the projected SPI is less uncertain than using the GCM simulated precipitation. In addition, two-step approaches (where precipitation is translated to SPI) have higher consistency than the one-step approach, demonstrating that non-standardized precipitation has higher uncertainty. The majority of grids in Australia show decreases in TDE and increases in TDS are projected across all time scales, suggesting in the future more sustained long droughts are likely (less frequent but more severe). ," compared to using GCM atmospheric predictors from a standard bias correction, "GCM(Std)." The derived Standardized Precipitation Index from NCEP atmospheric predictors, NCEP(VT), is used as the benchmark model for the two-step downscaling approach while the model of "GCM" stands for the model using the two-step direct estimate approach.

Difference Between SPI and SPEI Projections for the Future Climate
This section investigates the difference between the SPI and SPEI projected changes in drought. There is a large improvement in the consistency of TDS when using two-step downscaled projections instead of the direct approach across various time scales (Table 3), with an average improvement of approximately 55% and 11% for SPI and SPEI, respectively. On the other hand, the estimated SPI and SPEI through the spectral transformation lead to better TDE consistency, with the improvement for SPEI being about 27% while the improvement from SPI is 64%. Given that PET derived from temperature projections is more consistent among various climate models, the improved consistency from SPEI is mainly attributed to the fact that the SPI has been estimated from spectrally transformed predictors. Figure 9 examines future droughts from the perspective of drought duration between current and future periods, and the difference in CDFs of TDD between SPI and SPEI is shown. It is apparent that future droughts are more common using SPEI12 than SPI12 when the influence of evapotranspiration is taken into consideration, regardless of the difference among different GCMs. When SPEI is used, in the future, most regions in Australia are under drought for more than half of the time investigated, while it is the opposite for drought conditions derived by SPI. This also suggests that in the future under the worst climate change scenario, there will be more extreme drought events with long durations and large severity. Similar results from multiple models showed significant increases in various drought metrics, except frequency, with larger changes in the standardized soil moisture index compared to SPI (Kirono et al., 2020). Figure 8. Consistency of total sum of drought events and total sum of drought severities changes across multiple general circulation models and time scales. "One-step" refers to the method of estimating Standardized Precipitation Evapotranspiration Index from bias-corrected general circulation model without going through the Standardized Precipitation Index. Two-step approaches include "direct estimate" and "downscaling" approaches, and "Two-step (direct)" refers to the consistency using "direct estimate" approach while "Two-step (downscaled)" indicates the result from the "downscaling" approach.
SPI-derived projections suggest that droughts in the future are uncertain, even though the two-step downscaling approach improved the consensus between the GCMs (Table 3). One of the major shortcomings of these drought projections is that evapotranspiration is not considered in the SPI (Afroz et al., 2021), despite the influence of evapotranspiration on the water balance becoming increasingly important in the future. As discussed earlier, the use of indices such as SPEI or RDI estimated directly from precipitation and evapotranspiration is problematic because the uncertainty associated with precipitation in GCM future simulations is markedly different from that associated with evapotranspiration (Asadi Zarch et al., 2015). As a result, we combine downscaled SPI with evapotranspiration so that the sources of uncertainty can be separately considered, and substantial improvements in the consistency of future drought characteristics across time scales have been observed.

Conclusions
In this work, we have presented an approach for characterizing future droughts using a new SPEI calculation method. The approach first derives SPI and then post-processes the SPI using future PET estimates to calculate the SPEI. When used with spectral transformations of the predictors, the downscaling method can account for the low-frequency variability and uncertainty in precipitation that is the primary driver of multi-year variability in drought projections, as well as the important contribution of PET to future drought projections. Our results demonstrate that the two-step approach provides better skill in projecting future climate change, especially for longer droughts, compared to directly calculated SPEI from GCMs or downscaled SPI projections.
We also investigated the effectiveness of spectral transformation in characterizing sustained precipitation anomalies, with the aim of addressing the significantly different uncertainties between GCM-simulated precipitation and climate variables that affect precipitation. Droughts were assessed based on changes in frequency and severity, and using the model consensus as the primary evidence of robust skill in projecting future climate change. It suggests that our approach improves the consistency of future GCM projections of drought and offers significant advantages in dealing with varying contributions of uncertainty from the representation of climate variables.
Varying contributions to the overall uncertainty in natural systems is a common issue and approaches for parsimoniously addressing this under climate change have until now been neglected. The new approach proposed here provides a path forward for focusing modeling studies on the major sources of uncertainty in terms of both differences in spectral response and varying contributions of uncertainty from the representation of climate variables. Post-processing to incorporate a common, more certain trend such as evapotranspiration, provides a simple method to undertake future drought assessments.   Table S1 of the Supporting Information S1 contains information needed to download the corresponding climate models.