Editorial Type:
Article
Article Type:
Research Article

Select Representative General Circulation Model Runs Using Envelope-Based Technique

Seyed Kourosh Mahjour Geo-Intelligence Laboratory, Ingram School of Engineering, Texas State University, San Marcos, Texas

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John P. Tiefenbacher Department of Geography and Environmental Studies, Texas State University, San Marcos, Texas

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Salah A. Faroughi Department of Chemical Engineering, University of Utah, Salt Lake City, Utah

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Online Publication:
18 Mar 2025
Print Publication:
01 Apr 2025
DOI:
https://doi.org/10.1175/JCLI-D-24-0219.1
Page(s):
1627–1650
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Abstract

A subset of ensemble general circulation models (GCMs), known as representative GCMs (RGCMs), is typically used in climate change analysis to reduce computational cost. This study presents a new envelope-based workflow for RGCM selection beginning with history matching to better preserve the full ensemble uncertainty range and replicate past climate characteristics, in contrast to an envelope-based standard workflow that begins with capturing climatic means. Our workflow contains a three-stage selection process that leverages monthly ground-truth data from the reference period 1981–2005, along with monthly simulation outputs for the periods 1981–2010 and 2071–2100 from GCM runs in phase 5 of the Coupled Model Intercomparison Project (CMIP5), starting with an initial pool of 105 and 77 runs under representative concentration pathways 4.5 and 8.5, respectively. The performance of the proposed workflow is compared with the standard workflow using the Kolmogorov–Smirnov test measuring D max, the largest absolute difference between two cumulative distributions of changes in mean air temperature ΔT and precipitation ΔP from the full set of GCM runs and RGCM runs, and the mean-square error (MSE) evaluating reproduction of past climate data. The comparisons for Texas show that the new workflow reduces mean D max for ΔT by 23% and ΔP by 20%, while improving the mean MSE by 105% and 6% for monthly average of mean air temperature and precipitation, respectively. Further evaluation in Bihar, India, and New York State, United States, regions with distinct climatic conditions from those of Texas consistently shows lower D max and MSE for our workflow, indicating that it selects RGCM runs that better represent the full set of GCM runs.

© 2025 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Salah A. Faroughi, salah.faroughi@utah.edu

Abstract

A subset of ensemble general circulation models (GCMs), known as representative GCMs (RGCMs), is typically used in climate change analysis to reduce computational cost. This study presents a new envelope-based workflow for RGCM selection beginning with history matching to better preserve the full ensemble uncertainty range and replicate past climate characteristics, in contrast to an envelope-based standard workflow that begins with capturing climatic means. Our workflow contains a three-stage selection process that leverages monthly ground-truth data from the reference period 1981–2005, along with monthly simulation outputs for the periods 1981–2010 and 2071–2100 from GCM runs in phase 5 of the Coupled Model Intercomparison Project (CMIP5), starting with an initial pool of 105 and 77 runs under representative concentration pathways 4.5 and 8.5, respectively. The performance of the proposed workflow is compared with the standard workflow using the Kolmogorov–Smirnov test measuring D max, the largest absolute difference between two cumulative distributions of changes in mean air temperature ΔT and precipitation ΔP from the full set of GCM runs and RGCM runs, and the mean-square error (MSE) evaluating reproduction of past climate data. The comparisons for Texas show that the new workflow reduces mean D max for ΔT by 23% and ΔP by 20%, while improving the mean MSE by 105% and 6% for monthly average of mean air temperature and precipitation, respectively. Further evaluation in Bihar, India, and New York State, United States, regions with distinct climatic conditions from those of Texas consistently shows lower D max and MSE for our workflow, indicating that it selects RGCM runs that better represent the full set of GCM runs.

© 2025 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Salah A. Faroughi, salah.faroughi@utah.edu
Keywords: Climate change; Uncertainty; Climate models

1. Introduction

The impact analysis of climate change is heavily based on future climate projections provided by general circulation models (GCMs) (Lutz et al. 2016b; Pawar et al. 2024). The availability of GCMs for climate change projections is increasing rapidly. For example, phase 3 of the Coupled Model Intercomparison Project (CMIP3) archive, used for the Intergovernmental Panel on Climate Change’s (IPCC) fourth assessment report (Meehl et al. 2007), includes outputs from 25 distinct GCMs. In comparison, the CMIP5 archive, used for the fifth IPCC assessment report, includes outputs from 61 different GCMs (Emori et al. 2016). Furthermore, these GCMs often consist of multiple ensemble members, significantly augmenting the number of available model runs. Despite advances in CMIP5 models in terms of process representation compared to CMIP3, significant uncertainties persist regarding future climate projections (Kaini et al. 2020). Given the wide range of climate models and the limitations imposed by computational and human resources, comprehensive climate change impact studies cannot incorporate all projections. Instead, researchers typically select one climate model or a small ensemble of models for their assessments. However, determining which models should be included in the ensemble, while being representative of the region of interest and capturing the full range of uncertainties, is not a straightforward process and often relies on multiple criteria.

To address the challenges associated with model interdependence and improve the efficiency and usability of GCM run selection, researchers have developed several model number reduction approaches that aim to quantify uncertainty while retaining key features of the full set. These approaches include Bayesian inference (Gouveia et al. 2022; Jackson 2009), reduced-order modeling (Jacquier et al. 2021; Kashinath et al. 2021), and selecting representative GCM runs from multimodel ensemble (Kaini et al. 2020; Shrestha and Pradhanang 2022). The last approach, selecting representative GCM runs (RGCM runs), involves choosing a subset of GCM runs based on their performance in representing reference climate patterns, sensitivity to changes in greenhouse gas concentrations, and ability to reproduce the major climate variables (i.e., temperature and precipitation) (Parding et al. 2020). RGCM run selection methods can be broadly classified into two main groups: the past-performance approach (Pierce et al. 2009; Biemans et al. 2013) and the envelope-based approach (Seager et al. 2007).

The past-performance approach selects GCM runs based on their ability to simulate past and present climate conditions, assuming that models with good performance in the past are more likely to provide reliable projections of future climate change (Parding et al. 2020; Biemans et al. 2013). However, this approach may result in a limited range of future projections, as models that are less skilled at simulating present and past climate conditions might be excluded, potentially missing plausible future scenarios (Pierce et al. 2009). The envelope-based approach, on the other hand, aims to select models that cover a wide range of projections for one or more climate variables of interest. This approach seeks to include all potential futures projected by the full set of GCMs (Immerzeel et al. 2013). However, one drawback of this approach is that it does not consider the skill of models to accurately predict present and past climates (Lutz et al. 2016b). Therefore, less reliable models in simulating present and past climate conditions may be included in the selection, potentially leading to less accurate projections of future climate changes. To address these limitations, Lutz et al. (2016b) developed a modified approach that integrates both past performance and envelope-based approaches to select RGCM runs. This approach aims to reproduce simulations of past climates while considering projected changes in key climate variables. It focuses on simulating a manageable number of climate model runs that represent the most probable future mean air temperature, precipitation, and expected changes in extreme climate variables. However, it is important to note that while the modified approach developed by Lutz et al. (2016b) provides a balance between past performance and envelope-based considerations, it is still challenging to fully cover the full range of uncertainty associated with climatic variables.

Therefore, it is necessary to develop a workflow that goes beyond the modified approach to improve the representativeness of the selected RGCM runs and provide a more robust understanding of the uncertainty associated with climate projections. In this study, we propose a new workflow by reordering the standard envelope-based model to select RGCM runs that better preserve the uncertainty domain of the full set and yield a more precise representation of past climates. We consider different regions, Texas and New York in the United States and Bihar in India, each possessing different climatic conditions to check the effectiveness of our workflow. We evaluate a large set of 105 and 77 GCM runs for the two representative concentration pathways (RCPs) of RCP4.5 and RCP8.5, respectively. Our selection process is based on three criteria in the following order: i) matching historical and reference datasets, ii) capturing the range of changes in climate means, and iii) capturing the range of changes in extreme indices. Capturing the range of changes involves the process of maintaining main variations in the mean climatic parameters. By employing this framework, our main aim is to identify a subset of four RGCM runs for each RCP that can best represent the full ensemble’s uncertainty range. RGCM runs are useful for downscaling climate parameters (Kaini et al. 2020; Ruane and McDermid 2017) and, in turn, these climate parameters can be used effectively both in hydrological (Kaini et al. 2021; Parding et al. 2020) and in crop modeling (Kaini et al. 2021; Qian et al. 2021).

The structure of this paper is organized as follows: section 2 provides background information on the study area and discusses the data sources used in this study. In section 3, we outline our proposed workflow that incorporates various criteria and scoring methods to select the RGCM runs. Section 4 presents the results obtained showcasing the selected RGCM runs. Finally, in section 5, we present the main conclusions derived from this research endeavor.

2. Focus area and datasets

a. Focus area

To develop and validate the effectiveness of our proposed workflow for the selection of RGCM runs, we first focus our attention on Texas located in the south-central region of the United States. Two other regions, i) Bihar located in the eastern region of India and ii) New York State located in the northeastern United States, with totally different climatic conditions than those of Texas, are later used to further test the capability of our proposed workflow to preserve uncertainty. As shown in Fig. 1, Texas is geographically diverse, with certain areas classified as part of the South United States, while others are designated as part of the Southwest United States. The vast expanse of the state includes a wide range of climate and geographical features, including coastal areas, plains, deserts, and mountainous regions. These elements are important to develop and validate our RGCM run selection workflow, ensuring its robustness and adaptability in various areas.

Fig. 1.
Fig. 1.

Topography map of the (a) United States and (b) zoomed-in section highlighting the study area in Texas. Texas is geographically located in both the south-central region of the United States.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

b. Datasets

In this study, three data sources are used, including i) the output fields of the GCMs in CMIP5, ii) the extreme indices derived from CMIP5, and iii) the reference (ground-truth) datasets. From these datasets, a set of comparison variables is derived to develop and evaluate our workflow. The following sections explain the data sources and the derived variables.

c. CMIP5 output fields

In both long-term and short-term experiments as part of CMIP5, four RCPs are commonly used. RCPs are created based on various greenhouse gas concentration trajectories (e.g., CO2, CH4, N2O) to model and analyze future potential climate changes (Mahjour et al. 2024). These pathways include RCP8.5 with very high CO2 emissions, RCP4.5 and RCP6.0 with moderate CO2 emissions, and RCP2.6 with low CO2 emissions and significant mitigation efforts. It is assumed that RCPs, as defined by the IPCC (Emori et al. 2016), characterize future emission scenarios and associated radiative forcing. Given that the four RCPs represent anticipated radiative forcing levels by 2100 based on the existing literature, ideally each should receive equal consideration for inclusion in climate change impact studies. However, in practice, there is often a trade-off in these studies with respect to the number of RCPs and climate models that can be feasibly included within given time and resource constraints, while ensuring the production of robust and reliable results (Lutz et al. 2016a). In this study, we select emission scenarios that cover a wider range of radiative forcing and future temperature anomalies. Accordingly, we choose RCPs that have the least deviation from the actual observed CO2 emission trend and increase rates. RCP2.6 is excluded from our selection due to its lower likelihood among the four alternatives (van Vuuren et al. 2011; Kaini et al. 2020). Furthermore, the implementation of RCP2.6, which requires significant mitigation efforts, is currently impractical (Mora et al. 2013; Sanford et al. 2014). It calls for a sustained global reduction in CO2 emissions of approximately 3% annually, a target that is currently unattainable (Khan and Koch 2018). Considering the remaining three RCPs, we have selected two: RCP8.5, characterized by high baseline emissions, and RCP4.5, which represents medium stabilization. This decision aligns with the observed trend of an average annual increase of approximately 3% in CO2 emissions between 2005 and 2012 (Peters et al. 2013; Mora et al. 2013). For scenarios involving medium stability, both RCP4.5 and RCP6.0 are suitable, but RCP4.5 is chosen for the GCM runs collection process because it closely matches the average annual CO2 emission growth rate of approximately (≈1.5%) the average annual CO2 between 2005 and 2012, compared to RCP6.0’s rate of approximately (≈1%) (Sanford et al. 2014). Although we plan to focus on RCP4.5 and RCP8.5, our approach can be extended to model ensembles for the remaining RCPs. In our analysis, we leverage the CMIP5 GCMs simulation data conducted based on RCP4.5 and RCP8.5 for the two 30-yr periods of 1981–2010 and 2071–2100.

The GCM output resolution is 2.5° × 2.5° (i.e., approximately 250 × 250 km2) that has been regridded using the Royal Netherlands Meteorological Institute (Koninklijk Nederlands Meteorologisch Instituut) (KNMI) Climate Explorer (KNMI 2023). The GCMs and GCM runs (i.e., different runs from a certain GCM) employed in this study are listed on the KNMI website. There are 105 runs for RCP4.5 and 77 runs for RCP8.5, which are assumed to cover the range of future climate projections from the selected GCMs sufficiently. The ensembles consist of multiple runs from certain GCMs, identified by their “rip,” representing the initial state realizations r, initialization techniques i, and physics versions p. In this study, we recognize the unique attributes of each GCM and its corresponding realizations. From the simulation outputs, we use two main fields, namely, mean air temperature (T measured in °C) and precipitation (P measured in mm day−1).

d. CMIP5-derived extreme indices

We use the extreme climate indices extracted from the archive generated by the Expert Team on Climate Change Detection and Indices (ETCCDI) (Levesque 2021; Pielke and Wilby 2012; Lutz et al. 2016b). The ETCCDI indices are a set of standardized climate indices developed to monitor changes in climate extremes. They primarily focus on temperature and precipitation and are widely used to assess the impacts of climate change on extreme weather events. These indices are made accessible through the Canadian Centre for Climate Modeling and Analysis. The data obtained from this archive are collected and downloaded using the KNMI Climate Explorer. Table 1 reports a list of indices selected for analysis in our study.

Table 1.

ETCCDI indices focusing on extreme climate conditions.
Table 1.

e. Reference datasets

Reference (ground-truth) climatic datasets are used to evaluate the ability of GCMs to accurately simulate observed climate conditions. The reference mean air temperature data are taken from the fifth major global reanalysis produced by the European Centre for Medium-Range Weather Forecasts, ERA5, (Parding et al. 2020). ERA5 data cover land and water with a grid resolution of approximately 31 km. In addition, reference precipitation data are taken from the Global Precipitation Climatology Project (GPCP), version 2.3 (Adler et al. 2003). GPCP data provide monthly precipitation estimates on a 2.5° × 2.5° grid, incorporating data from various sources, such as stations, satellites, and soundings. The ERA5 and GPCP datasets are collected for a 25-yr reference period, from 1981 to 2005, following Lutz et al. (2016b). This period is assumed to represent the ground-truth climatic conditions and serves as a basis for comparing the outputs of the chosen GCMs.

f. Derived variables

In our three-stage workflow for selecting RGCMs, several variables derived from mean air temperature T (measured in °C) and precipitation P (measured in mm day−1) are required. Table 2 lists the variables used in our analysis. These variables are calculated as follows.

Table 2.

Derived variables from mean air temperature (T measured in °C) and precipitation (P measured in mm day−1) to be used in our analysis.
Table 2.

First, since evaluating changes in climate variables over time is one of the goals, we need to determine changes in mean air temperature ΔT (measured in °C) and precipitation ΔP (measured in %) between the two simulation periods. The process of computing ΔT and ΔP for each GCM run begins by collecting the monthly variables for each grid point (i.e., T and P at a grid point for each month from January to December for all the 30 years in each simulation period). This yields two matrices of 12 months × 30 years for each grid point: one for the first 30-yr simulation period (1981–2010) and another for the second 30-yr simulation period (2071–2100). The next step involves calculating the difference between these matrices at each grid point, yielding a difference matrix (12 × 30) for each variable. Further, the data points in the difference matrices are aggregated through several averaging steps: i) a monthly average is obtained by calculating the mean for each month across 30 years, reducing the matrix to a single column of 12 values; ii) the annual average is calculated by averaging these 12 values to obtain a single value for the changes in mean air temperature and precipitation at each grid point. Figure 2 shows this value across Texas for each RCP, averaged over the CMIP5 GCM ensemble; and iii) in the final averaging step, the values of the changes in mean air temperature and precipitation are averaged across the grid points covering the area of interest (e.g., Texas as shown in Fig. 2) to generate a pair of (ΔT, ΔP) for each GCM run; see Table 2. These pairs will be used as the basis for our envelope-based workflow to assess broader climate trends.

Fig. 2.
Fig. 2.

Changes in mean air temperature and precipitation in Texas between the period 2071–2100 and 1981–2010, based on the CMIP5 ensemble: (a) mean air temperature change for RCP4.5, (b) mean precipitation change for RCP4.5, (c) mean air temperature change for RCP8.5, and (d) mean precipitation change for RCP8.5.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Second, in our analysis, we also compare the simulation results obtained from a GCM run with reference datasets over a certain period (in this study, a 25-yr period from 1981 to 2005). To facilitate this comparison, we use the monthly averages of mean air temperature (measured in °C) and precipitation (measured in mm day−1), denoted as T¯ and P¯, respectively; see Table 2. To calculate these variables, we again construct matrices for the simulation and reference monthly data at each grid point (e.g., 12 × 25) and then compute an average over the period for each month (e.g., average T or P for all Augusts within the 25 years of consideration). This is followed by averaging across grid points, yielding 12 values of T¯ and P¯ for each GCM run or reference dataset, which can be compared head-to-head to assess the capability of the GCM to reproduce the reference data.

Last, we calculate a pair of (T distance, P distance) values for each GCM run compared to the reference datasets over a certain period. In this process, we use the matrices constructed for both the GCM run and the reference datasets over the 25 years of consideration (similar to those used in the calculation of T¯ and P¯). However, in this case, we first compute a grid-point average, resulting in a single matrix for both the GCM runs and the reference data. Then, a yearly average is obtained by calculating the mean for each year across the 12 months, reducing the matrix to a single column of 25 values (years), representing the yearly average for T and P. The same procedure is applied to the reference data matrix. Finally, the yearly values from both matrices are subtracted and summed over all the years, yielding a single pair of (T distance, P distance) for each GCM run compared to the reference data.

3. Methodology

In this study, we introduce a three-stage envelope-based procedure for selecting RGCM runs that better preserves the uncertainty domain of the full set of GCM runs, while still providing a more accurate estimate of the past climate characteristics. This workflow considers various climate scenarios, including historical references and projected future conditions. Our proposed approach involves three steps for reducing the number of GCM runs: i) matching historical and reference datasets (i.e., history matching), ii) capturing the range of changes in mean air temperature and precipitation, and iii) capturing the range of changes in mean extreme indices.

To assess the effectiveness of the proposed envelope-based workflow in preserving the uncertainty domain, a thorough comparison is made with the commonly used envelope-based workflow as a standard workflow found in the literature (Kaini et al. 2020; Khan et al. 2006; Lutz et al. 2016b; Tenfie et al. 2022; Shrestha and Pradhanang 2022). For simplification, our proposed workflow is referred to as workflow A, while the standard workflow is designated as workflow B. Figure 3 compares the steps in workflow A and workflow B. Workflow B starts by capturing the range of changes in climatic means, followed by analyzing extreme indices and history matching steps. However, in workflow A, the initial selection step involves history matching, followed by capturing the range of changes in the climatic means, and the analysis of mean extreme indices. The objective here is to show that workflow A, which is just a reordering of the standard workflow, excels in preserving the uncertainty domain of the full set by the representative GCM runs.

Fig. 3.
Fig. 3.

Methodology flowchart. The proposed workflow A begins with history matching, followed by an analysis of changes in mean air temperature and precipitation climatology, and then examines changes in mean extreme indices. Workflow B (standard envelope based) starts with capturing the range of changes in mean air temperature and precipitation climatology, then continues with analyzing extreme indices, and concludes with history matching.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

a. Initial selection of GCM runs

The initial step in selecting GCM runs involves a process known as history matching, where we evaluate how effectively GCM runs replicate reference climate characteristics during a specific historical period.

To implement history matching, we first use the pair of (ΔT, ΔP) calculated for each GCM run for the two distinct periods of 1981–2010 and 2071–2100; see section 2. Subsequently, we calculate the 50th percentile values for ΔT and ΔP across all GCM runs. These two percentiles act as representations of the median changes in mean air temperature and precipitation among various GCM runs. Using these two percentile values, we partition the data on a scatterplot, where the x axis represents ΔT and the y axis represents ΔP, into four distinct quadrants. These quadrants serve the purpose of categorizing GCM runs based on their performance. In this categorization scheme, GCM runs located in the top left quadrant are denoted as “warm-dry” GCM runs, while those in the top right quadrant are classified as “warm-wet” GCM runs. GCM runs situated in the bottom left quadrant receive the label of “cold-dry” GCM runs, and those positioned in the bottom right quadrant are identified as “cold-wet” GCM runs. It is essential to understand that the terms “cold” and “dry” used here do not necessarily imply lower temperatures or reduced precipitation when compared to the reference period. Instead, they signify the relative position of these scenarios among the ensemble of climatic models. Following this categorization, we proceed to assess the performance of the GCM runs in each quadrant to replicate reference mean air temperature and precipitation data during 25 years, from 1981 to 2005, In this step, following the work by Lutz et al. (2016b), five GCM runs are selected for each quadrant, resulting in 20 RGCM runs for each RCP. This number has been determined to effectively capture the full range of uncertainty associated with climate projections, while also ensuring that computational requirements remain manageable.

To carry out this evaluation, we calculate the T distance and P distance, as described in section 2, to implement a multiobjective distance-based scoring approach. This approach first normalizes the two distances for T and P across the GCMs in each quadrant to bring them into the same range [0–1] using the min–max scaling, followed by calculating the arithmetic average of the distances as a closeness score to the reference data. Ultimately, we select five GCM runs in each quadrant with the highest closeness score (i.e., with the smallest distance from the reference).

To test the selection process of the GCM runs based on their past performance, we compare the monthly average of mean air temperature T¯ and precipitation P¯ data obtained for each GCM runs with reference datasets (see section 2). For this comparison, we use the mean-square error (MSE) (Mahjour et al. 2024) defined as
MSE=1n∑i=1n(yS,i−yG,i)2,
where n is the number of samples, ys,i is the projected value of the ith sample from simulation, and yG,i is the ground-true value of the ith observation. The variable y in Eq. (1) can be T¯ or P¯. By calculating the MSE, we can evaluate the effectiveness of the selected RGCMs based on our distance-based approach with the smallest deviation from the reference values. If the MSE for the GCM runs is small, it indicates that the behavior of the RGCM runs is close to the reference values. This suggests that the selected GCM runs exhibit a good representation of the reference climate characteristics.

b. Refined selection of GCM runs

The refined selection step of GCM runs is based on determining the 10th and 90th percentile values of ΔT and ΔP for RCP4.5 and RCP8.5 GCM runs (Tenfie et al. 2022). These values represent the four quadrants of the scatterplot based on ΔT versus ΔP. The 10th percentile values for ΔT and ΔP indicate the cold-dry region. The 10th percentile value for ΔT and the 90th percentile value for ΔP represent the cold-wet region. The 90th percentile value for ΔT and the 10th percentile value for ΔP represent the warm-dry region. The 90th percentile values for ΔT and ΔP indicate the warm-wet region. In the selection process, we start with the initial subset of five GCM runs, selected in the initial step, in each quadrant. From this subset, we select two GCM runs based on how close their percentile rank scores are to the 10th and 90th percentiles of the entire projection space for ΔT and ΔP. The 10th and 90th percentiles are chosen to avoid selecting the outliers of the GCM runs. This selection is made using the Euclidean distance metric d defined as
d=(x2−x1)2+(y2−y1)2,
where the point (x1, y1) represents the pair of (ΔT, ΔP) for the respective 10th and 90th percentiles of the quadrants and the point (x2, y2) represents the pair of (ΔT, ΔP) for the five RGCMs selected in the initial selection step. Following this procedure, the two RGCM runs with the smallest d values are selected from each quadrant, resulting in a total of eight RGCM runs for each RCP.

c. Final selection of GCM runs

The final step in selecting GCM runs involves focusing on projected changes in extreme climate indices. Extreme climate events and their potential impact on humanity and ecosystems are emphasized in the Special Report on Extreme Events (SREX) by the Intergovernmental Panel on Climate Change (Murray and Ebi 2012). As described in section 2, we focus on ETCCDI indices for extreme mean air temperature and precipitation events listed in Table 1. For air temperature extremes, the warm spell duration index (WSDI) and the cold spell duration index (CSDI) are calculated. Similarly, for precipitation extremes, consecutive dry days (CDDs) and total precipitation from very wet days (R95pTOT) are evaluated. These indices provide information on the occurrence and intensity of extreme temperature and precipitation events. This information guides our decision-making process in selecting RGCM runs that effectively capture the extreme climate conditions of interest. It ensures that RGCM runs provide a better representation of the extreme climate scenarios under consideration.

To initiate the analysis, we calculate the four extreme indices in both simulation periods of 2071–2100 and 1981–2010 within the study area. To this end, the database compiled by Sillmann et al. (2013) is used. However, for GCM runs not included in this database, we obtain the respective data from the climate4impact portal (Climate4Impact 2023) and employ the Max-Planck Institute for Meteorology’s Climate Data Operator (CDO-version 1.6.4) (Kaini et al. 2020) to calculate the respective ETCCDI extreme indices. To evaluate the variability in climate extremes, the indices need to be averaged over the two 30-yr periods, and the difference in their averages is determined. Subsequently, the selection of GCM runs is based on the highest averaged normalized index changes for the respective ensemble quadrant, as outlined in Table 3. For example, projections of warm and dry conditions prioritize ETCCDI indices for extreme heat (WSDI) and extreme drought (CDD).

Table 3.

ETCCDI indices selected to rank the GCM runs for each quadrant of the two-dimensional scatterplot of ΔT vs ΔP for each GCM runs.
Table 3.

Accordingly, we first normalize all changes in the indices from each GCM run to a common range [0, 1] using min–max scaling. This normalization step involves adjusting each index change relative to the minimum and maximum changes observed across all runs for that index. After this initial normalization, we refine our selection by identifying two preferred GCM runs per quadrant based on the previous selection criteria. For each of these selected runs, we then compute a secondary average of the normalized values for the two indices specific to each quadrant (i.e., WSDI and CDD for the warm-dry quadrant). The GCM run that exhibits the highest secondary average in each quadrant is selected as the representative run. This secondary averaging specifically refers to the averaging of normalized index changes for the selected indices within each quadrant, thereby ensuring we prioritize runs that consistently exhibit higher magnitudes of extreme conditions across the indices relevant to that quadrant (Lutz et al. 2016b; Ruane and McDermid 2017; Qian et al. 2021).

d. Uncertainty evaluation

After selecting the subset of GCM runs in each step of selection, the uncertainty domains of the selected GCM runs are compared to the full ensemble. The method of uncertainty measurement is crucial to evaluating the GCM run subsets using a selection framework. Traditionally, the measurement of the uncertainty space in GCM runs has relied on statistical parameters such as means, medians, variances, and the range (maximum and minimum) of the climatic parameters of the GCM runs and the complete set (Mahjour et al. 2021). However, as the distribution of the simulation output expands beyond statistical parameters, it becomes necessary to compare the uncertainty domain of the GCM run subsets with the full ensemble using alternative approaches (Khan et al. 2006).

In this study, we assess the closeness of the uncertainty ranges in the projected changes of temperature (ΔT) and precipitation (ΔP). We accomplish this by comparing the cumulative distribution function (CDF) curves derived from ΔT and ΔP for the selected GCM runs with those of the full ensemble (Mahjour and Faroughi 2023). We then perform the Kolmogorov–Smirnov (KS) test (Mahjour et al. 2020) to measure the maximum vertical difference Dmax between the CDFs of two sets, F(x)subset,m and G(x)fullset,n. The Dmax value is defined as
Dmax⁡=max⁡∀x|F(x)subset,m−G(x)fullset,n|,
where m is the number of GCM runs in the subsets and n is the number of GCM runs in the full set. In Eq. (3), x can be ΔT or ΔP. By comparing the CDF curves and calculating the maximum vertical difference using the KS test, we can assess the closeness of the uncertainty domain between the GCM run subsets and the full ensemble. This can help to understand the performance and reliability of RGCMs within the uncertainty modeling framework.

4. Results and discussion

a. Initial GCM selection for Texas

In workflow A, the initial step of GCM run selection involves grouping the full set GCM runs based on their prediction of ΔT and ΔP between the periods of 1981–2010 and 2071–2100 across the grid cells measuring 2.5° × 2.5° in the Texas region. Subsequently, the 50th percentile values for ΔT and ΔP are considered to divide a two-dimensional scatterplot, created by plotting ΔT versus ΔP, into four quadrants: warm-dry, warm-wet, cold-dry, and cold-wet. Figure 4 represents the scatterplot, highlighting the four quadrants of the full climatic spectrum with different colors for Texas. The analysis reveals that the projection range for ΔT and ΔP is significantly broader in the RCP8.5 model pool compared to the RCP4.5 model pool. For RCP4.5, ΔT ranges from 0.7° to 3.5°C, while ΔP ranges from −21.3% to 17.1%. In contrast, for RCP8.5, the corresponding ranges are from 2.8° to 6.1°C for ΔT and from −35.7% to 19.6% for ΔP.

Fig. 4.
Fig. 4.

Initial selection of GCM runs in workflow A for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between the periods of 2071–2100 and 1981–2010. The variation in projected ΔT and ΔP is significantly greater for the RCP8.5 model pool than for the RCP4.5 model pool. The 50th percentile value for ΔT and ΔP is highlighted by the pink square symbol. The 50th percentile value for ΔT and ΔP is used to divide the scatterplot into four quadrants: warm-dry, warm-wet, cold-dry, and cold-wet, which are highlighted with distinct colors.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

After dividing the scatterplot into the four projection quadrants, the selection of GCM runs within each quadrant is performed through an evaluation of their historical performance. In this process, we use the multiobjective distance-based approach to compare the GCM runs output data within each quadrant against the reference datasets. This comparative analysis is conducted within the framework of the 25-yr reference period, which includes the years from 1981 to 2005. The selection process for each quadrant is based on the averaged normalized T distance and P distance, as described in section 3. Five GCM runs are selected from each quadrant, exhibiting the lowest averaged distance. This method of selection may result in GCM runs with the lowest P distance not being chosen due to a high T distance or vice versa. Consequently, we choose the GCM runs that provide the best match to the reference data for both temperature and precipitation based on the lowest MSE. Figure 5 highlights the five GCM runs that are selected in each quadrant from the initial selection of GCM runs, resulting in a total of 20 GCM runs for each RCP. The gray circles in Fig. 5 represent the GCM runs that are not selected for the subsequent step of GCM run selection, while the highlighted color-coded GCM runs are chosen for the refined selection of GCM runs.

Fig. 5.
Fig. 5.

Initial selection of GCM runs in workflow A for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between periods of 2071–2100 and 1981–2010. The selection process for each climatic quadrant is based on the average of normalized T distance and P distance to the reference datasets. Five GCM runs from each quadrant are selected based on the lowest averaged normalized T distance and P distance. Gray circles represent the GCM runs that are not chosen. From the 105 GCM runs of RCP4.5 and 77 GCM runs of RCP8.5, a total of 20 GCM runs are selected for each RCP.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

The initial selection process in workflow B is based on the projected ΔT and ΔP between the periods 1981–2010 and 2071–2100. For each GCM run in each quadrant, the Euclidean distance to the 10th and 90th percentile values in that quadrant is calculated. Subsequently, the five GCM runs with the shortest Euclidean distance to each quadrant are chosen. To ensure a fair comparison regarding the number of selected GCM runs, we also choose five GCM runs using workflow B, leading to a total of 20 GCM runs for each RCP. This allows an equitable evaluation between workflow A and workflow B. Figure 6 illustrates the results of the initial selection of GCM runs using workflow B for each RCP, which focuses primarily on capturing the range of changes in climate means. The gray circles represent the GCM runs that are not selected for the subsequent step of GCM run selection, while the GCM runs that are highlighted with colors are selected for the next step of GCM run selection.

Fig. 6.
Fig. 6.

Initial selection of GCM runs in workflow B for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between 2071–2100 and 1981–2010. The 10th and 90th percentile values for ΔT and ΔP are highlighted by red square symbols. Gray circles represent the model runs that are not chosen. In each quadrant, five GCM runs with the shortest Euclidean distance to their respective 10th or 90th percentile values are selected for the refined selection of GCM runs. From the 105 GCM runs of RCP4.5 and 77 GCM runs of RCP8.5, a total of 20 GCM runs for each RCP are selected.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Figure 7 illustrates the comparison of CDF curves for ΔT and ΔP under different RCP scenarios (RCP4.5 and RCP8.5) and workflows (workflow A and workflow B), considering the following GCM run sets: 20 GCM runs selected by workflow A, 20 GCM runs selected by workflow B, and the full set of GCM runs. The corresponding Dmax values are reported in Table 4, indicating that workflow A performs better in preserving uncertainty compared to workflow B in the initial selection step. For ΔT, workflow A has an average Dmax value of 0.10 considering both RCPs, while workflow B has a higher average value of 0.17, representing an improvement of 70%. Similarly, for ΔP, the average Dmax values derived for workflow A and workflow B are 0.10 and 0.23, respectively. This suggests that workflow A has an average Dmax value 130% lower than workflow B. These findings indicate that the selected GCM runs from workflow A demonstrate better representativeness compared to workflow B.

Fig. 7.
Fig. 7.

CDF curves of (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full set of GCM runs, 20 GCM runs selected by workflow A, and 20 GCM runs selected by workflow B. For ΔT, workflow A has an average Dmax value of 0.10 considering both RCPs, while workflow B has a higher average value of 0.17. Similarly, for ΔP, the average Dmax values derived for workflow A and workflow B are 0.10 and 0.23, respectively. The results show that the selected GCM runs from workflow A demonstrate better representativeness compared to workflow B.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Table 4.

Comparison of Dmax values calculated using Eq. (3) for the full set of GCM runs and 20 GCM runs selected by workflow A and workflow B for Texas.
Table 4.

b. Refined GCM selection for Texas

In this stage of GCM run selection in workflow A, a more refined selection is achieved by considering the projected ΔT and ΔP between the periods 1981–2010 and 2071–2100. Between GCM runs and the 10th and 90th percentile (as representative values of each quadrant), the Euclidean distance is calculated as described in section 3. Subsequently, two GCM runs out of five GCM runs that have the shortest Euclidean distance are selected. The results of this refined selection of GCM runs for each RCP are shown in Fig. 8. In this step, a total of eight (8) GCM runs are selected out of 20 GCM runs from each RCP.

Fig. 8.
Fig. 8.

Refined step for selecting GCM runs in workflow A for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between 2071–2100 and 1981–2010. The 10th and 90th percentile values (representing the quadrants of the full climatic spectrum) for ΔT and ΔP are highlighted by red square symbols. Two GCM runs with the shortest Euclidean distance to each quadrant are selected out of five for the final selection of GCM runs step. From the 20 GCM runs of each RCP4.5 and RCP8.5, a total of eight (8) GCM runs for each RCP are selected at this stage.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Figure 9 shows the refined selection of GCM runs in workflow B for Texas under the RCP4.5 scenario. The normalized changes in ETCCDI indices, including R95pTOT, CDD, WSDI, and CSDI, are used to evaluate each GCM run’s performance within four projection quadrants: warm-wet, warm-dry, cold-wet, and cold-dry. The indices highlighted in yellow represent the two indices used for model selection in each quadrant. From this evaluation, the GCM runs with the highest and second-highest averaged normalized index changes are highlighted in green. Ultimately, eight GCM runs are selected from an initial set of 20 for RCP4.5, ensuring that the final subset best represents the full ensemble’s uncertainty and captures both mean and extreme climate behaviors. It is important to note that this approach to calculating an averaged normalized index may exclude GCM runs with the greatest change in one ETCCDI index due to the lowest change in another. For example, in the cold and wet corner under the RCP4.5 scenario, the model GFDL-ESM2M r1i1p1 predicts the most substantial decreases in R95pTOT. Nevertheless, it was selected due to a higher averaged normalized index compared to GFDL-ESM2G r1i1p1, MPI-ESM-MR r1i1p1, and bcc-csm1-1 r1i1p1. Figure 10 provides a similar analysis, but for the RCP8.5 scenario. As in the RCP4.5 case, normalized ETCCDI index changes (R95pTOT, CDD, WSDI, and CSDI) are used to evaluate and select the GCM runs. The yellow-highlighted cells show the two indices considered for each quadrant, while the green-highlighted rows indicate the GCM runs with the highest and second-highest averaged normalized index changes. From the initial pool of 20 GCM runs, eight are selected for RCP8.5, ensuring a robust representation of the uncertainty space in both mean climate and extreme conditions across all quadrants.

Fig. 9.
Fig. 9.

Refined selection of GCM runs in workflow B for Texas from RCP4.5. The normalized change in the ETCCDI indices (R95pTOT, CDD, WSDI, and CSDI) for all quadrants (wrm-wet, warm-dry, cold-wet, and cold-dry) is considered. The yellow-highlighted cells indicate the two normalized index changes considered in each quadrant for selecting the GCM runs. From each quadrant, the GCM runs with the highest and second-highest averaged normalized index changes are selected (highlighted in green). Out of the 20 GCM runs for RCP4.5, a total of eight (8) GCM runs are chosen.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Fig. 10.
Fig. 10.

Refined selection of GCM runs in workflow B for Texas from RCP8.5. The normalized change in the ETCCDI indices (R95pTOT, CDD, WSDI, and CSDI) for all quadrants (warm-wet, warm-dry, cold-wet, and cold-dry) is considered. The yellow-highlighted cells indicate the two normalized index changes considered in each quadrant for selecting the GCM runs. From each quadrant, the GCM runs with the highest and second-highest averaged normalized index changes are selected (highlighted in green). Out of the 20 GCM runs for RCP4.5, a total of eight (8) GCM runs are chosen.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

For refined selection steps of both workflows, we can also assess the selected GCM runs in terms of preserving uncertainty. Figure 11 illustrates the comparison of CDF curves for ΔT and ΔP for RCP4.5 and RCP8.5 in workflow A and workflow B. This analysis considers three GCM run sets: eight (8) GCM runs selected by workflow A for each RCP, eight (8) GCM runs selected by workflow B for each RCP, and the full set of GCM runs for each RCP. The corresponding Dmax values are provided in Table 5. Although the average Dmax values for ΔT determined from both RCPs are comparable in workflows A and B, the average Dmax for ΔP determined for both RCPs using workflows A and B is 0.23 and 0.28, respectively, which shows that workflow A exhibits a mean Dmax value that is 22% lower than that of workflow B. The results demonstrate that workflow A consistently outperforms workflow B with respect to uncertainty preservation during the refined selection phase, replicating its performance observed in the initial selection phase.

Fig. 11.
Fig. 11.

CDF curves of (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full set of GCM runs, eight GCM runs selected by workflow A, and eight GCM runs selected by workflow B. While workflow A exhibits an average Dmax value of 0.24 for ΔT determined from both RCPs, workflow B shows a slightly lower value of 0.23. However, for ΔP, the average Dmax values considering both RCPs for workflow A and workflow B are 0.23 and 0.28, respectively. These findings indicate that the selected GCM runs from workflow A, up until this step, demonstrate better representativeness compared to workflow B.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Table 5.

Comparison of Dmax values calculated using Eq. (3) between the full set of GCM runs and eight GCM runs considering ΔT and ΔP in workflow A and workflow B for Texas.
Table 5.

To further illustrate the uncertainty domain preservation, a visual analysis of the uncertainty domain is conducted including the full set and the GCM runs selected in the refined selection step of both workflows. Figures 12 and 13 present the monthly averages of mean air temperature T¯ and precipitation P¯ for the selected GCM runs, considering a reference period spanning 25 years from 1981 to 2005. The GCM runs selected by workflow A exhibit a better representation of the overall uncertainty domain of the full set compared to workflow B, for both RCPs. The data points from GCM runs in workflow A span a broader range than those in workflow B, covering a greater variety of potential future scenarios predicted by the ensemble of GCMs. There is also considerable variability in precipitation across all models, as opposed to temperature, indicating a wider range of uncertainty associated with precipitation. This variability can be attributed to various factors specific to Texas, including atmospheric circulation Hassanzadeh et al. (2020), moisture transport Roy et al. (2019), and terrain Zheng et al. (2018), all of which contribute to increased uncertainty in precipitation compared to temperature.

Fig. 12.
Fig. 12.

Comparing monthly averages of mean air temperature T¯ data for Texas until refined selection step. The data include a reference dataset from ERA5, full set of GCM runs (gray color), and the GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP8.5, and (d) workflow B/RCP8.5. The results show that the GCM runs selected in workflow A exhibit a better representation of the overall uncertainty domain of the full ensemble compared to workflow B in both RCPs.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Fig. 13.
Fig. 13.

Comparing monthly averages of mean precipitation P¯ data for Texas until refined selection step. The data include reference dataset from GPCP, version 2.3, full set of GCM runs, and GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP8.5, and (d) workflow B/RCP8.5. The results show that the GCM runs selected in workflow A exhibit a better representation of the overall uncertainty domain of the full ensemble compared to workflow B for both RCPs. Precipitation also exhibits significant variability across all models, in contrast to temperature, implying a wider range of uncertainty associated with precipitation.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

c. Final GCM selection for Texas

In workflow A, following the selection of GCM runs based on reference data and projected changes in climate means, the final selection step involves assessing the changes in extreme indices. We calculate the differences in the four defined ETCCDI indices (see Table 1) between the periods of 1981–2010 and 2071–2100 for the remaining GCM runs after the refined GCM run selection (a total of eight for each RCP). One RGCM run is selected for each quadrant of RCP4.5 and RCP8.5 based on the highest averaged normalized index changes associated with each quadrant. Therefore, four RGCM runs are ultimately selected for each RCP, taking into account the four quadrants. The results are presented in Fig. 14. The yellow-highlighted cells indicate the two normalized indices changes corresponding to each quadrant for selecting the RGCM runs. Four final RGCM runs are chosen for each RCP, which are highlighted in green.

Fig. 14.
Fig. 14.

Final selection of GCM runs in workflow A for Texas. The normalized change in the ETCCDI indices (R95pTOT, CDD, WSDI, and CSDI) for all quadrants (warm-wet, warm-dry, cold-wet, and cold-dry) is considered for both RCPs. The yellow-highlighted cells indicate the two normalized index changes considered in each quadrant for selecting the GCM runs. From each quadrant, the GCM runs with the highest averaged normalized index changes are selected (highlighted in green). Out of the eight (8) GCM runs for each RCP, a total of four (4) GCM runs are chosen.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

In contrast, in the final step of workflow B, the selection of four RGCM runs is performed with the multiobjective distance-based approach for history matching. The calculation of distances between the GCM runs and the reference datasets for the 25-yr period, 1981–2005, is explained in section 2. By evaluating the average of normalized T distance and P distance, the GCM run that exhibits the lowest values is chosen from each quadrant of the RCPs. The resulting distance measurements are presented in Fig. 15, where the four selected RGCM runs for each RCP are highlighted in green.

Fig. 15.
Fig. 15.

Final selection of GCM runs in workflow B for Texas. The selection process for each climatic quadrant is based on the average of normalized T distance and P distance to the reference datasets. One GCM run from each quadrant is selected based on the lowest averaged distance. Out of the eight (8) GCM runs for each RCP, a total of four (4) RGCM runs are chosen.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

The RGCM runs selected in the final step are then tested in terms of their ability to preserve uncertainty. Figure 16 shows the CDF curves for ΔT and ΔP from RCP4.5 and RCP8.5 obtained for workflow A and workflow B. This analysis includes three sets of GCM runs: four RGCM runs selected by workflow A for each RCP, four RGCM runs selected by workflow B for each RCP, and the full set of GCM runs for each RCP. The corresponding Dmax values are also reported in Table 6. The findings again reveal that workflow A outperforms workflow B in terms of preserving uncertainty during the final selection step. Regarding ΔT, workflow A demonstrates an average Dmax value of 0.31, derived from both RCPs, while workflow B shows a higher value of 0.38, indicating 23% improvement by using workflow A. Similarly, for ΔP, the average Dmax values for workflow A and workflow B are 0.30 and 0.36, respectively. Based on the findings, it can be inferred that workflow A exhibits an average Dmax value that is 20% lower than workflow B. Therefore, the results suggest that the RGCM runs chosen from workflow A demonstrate better representativeness compared to those selected from workflow B. Figure 17 lists the final RGCM runs selected from workflow A and workflow B across a range of climate projections and RCPs. Note that workflows A and B are entirely data driven, adhering to specific criteria at each stage of the process. As a result, the selection of the same GCM run at various stages may or may not occur. For example, in both RCP4.5 and RCP8.5, the RGCM runs from workflow A and workflow B are the same in the warm-dry projection.

Fig. 16.
Fig. 16.

CDF curves of (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full set of GCM runs, four GCM runs selected by workflow A, and four GCM runs selected by workflow B. Regarding ΔT, workflow A demonstrates an average Dmax value of 0.31, derived from both RCPs, while workflow B exhibits a higher value of 0.38. Similarly, for ΔP, the average Dmax values for workflow A and workflow B are 0.30 and 0.36, respectively. Based on the findings, it can be inferred that workflow A shows an average Dmax value that is 20% lower than workflow B suggesting that the RGCM runs chosen by workflow A demonstrate better representativeness compared to those selected by workflow B.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Table 6.

Comparison of Dmax values calculated using Eq. (3) between the full set of GCM runs and four GCM runs selected by workflow A and workflow B for Texas.
Table 6.
Fig. 17.
Fig. 17.

Comparison of final RGCM runs selected by workflow A and workflow B for Texas. In both RCP4.5 and RCP8.5, the RGCM runs from workflow A and workflow B are the same in the warm-dry projection. For RCP4.5, the selected RGCM run is CMCC-CMSr1i1p1, and for RCP8.5, it is CMCC-CMr1i1p1. In the cold-dry projection under RCP8.5, the RGCM run selected is also the same for both workflow A and workflow B, being EC-EARTHr8i1p1.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

The performance of the selected GCM runs by each workflow is further assessed for their effectiveness in simulating past climates during the 25-yr reference period. Figures 18 and 19 represent the averaged values of T¯ and P¯ across all models at different stages of selection, respectively. The corresponding MSE values between the four selected RGCM runs and the reference data for each RCP are provided in Table 7. For T¯, workflow A produces an average MSE value of 0.71, considering both RCPs, while workflow B produces a higher value of 1.46, indicating a 105% improvement by using workflow A. The average MSE values for P¯ derived from both RCPs from workflow A and workflow B are 0.33 and 0.35, respectively. This indicates that workflow A has an average MSE value 6% lower than workflow B.

Fig. 18.
Fig. 18.

Comparing averaged values of T¯ across all models at different stages of selection for Texas. The data include reference dataset from ERA5, the full GCM runs, and the GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP4.5, and (d) workflow B/RCP8.5. Workflow A exhibits an average MSE value of 0.71, considering both RCPs, while workflow B shows a higher value of 1.46, indicating a 105% improvement by using workflow A. These findings demonstrate that the RGCM runs selected by workflow A offer a better representation of the reference climate characteristics compared to those selected by workflow B.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Fig. 19.
Fig. 19.

Comparing averaged values of P¯ across all models at different stages of selection for Texas. The data include reference dataset from GPCP-version 2.3, full GCM runs, and the GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP4.5, and (d) workflow B/RCP8.5. The average MSE values for workflow A and workflow B, derived from both RCPs, are 0.33 and 0.35, respectively. This indicates that workflow A has an average MSE value 6% lower than workflow B. These findings demonstrate that the RGCM runs selected by workflow A offer a better representation of the reference climate characteristics compared to those selected by workflow B.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Table 7.

Comparison of MSE values between the full set of GCM runs and four GCM runs selected by workflow A and workflow B.
Table 7.

Our results show that the order of steps in an envelope-based workflow significantly impacts the outcomes. The findings in this work suggest that the specific order of steps in workflow A contributes to its favorable balance between preserving uncertainty and replicating past climate characteristics. In workflow A, the first step involves matching historical and reference datasets, which assesses how well GCM runs reproduce past climate characteristics. This step serves as the foundation for subsequent selections. By first ensuring that the selected GCM runs have strong historical performance, we set a high bar for their accuracy in reproducing past climate conditions. Workflow A gradually incorporates the complexity of uncertainty preservation. After ensuring historical performance, it moves on to capture changes in climatic means. This step introduces the ability to simulate changes in mean climate variables over time, which is a necessary progression after establishing past performance. Workflow A then proceeds to capture changes in the mean extreme indices. By addressing uncertainty and simulating extremes later in the process, workflow A prioritizes the preservation of uncertainty in the final selection. In contrast, workflow B starts with capturing the range of changes in climatic means precipitation and air temperature and then moves to capture changes in mean extreme indices before matching historical and reference datasets. This order introduces complexity before ensuring historical performance, potentially leading to a selection that may not adequately reproduce past climate characteristics. In workflow B, history matching is performed after selecting GCM runs based on changes, potentially leading to a suboptimal representation of past climate conditions and a reduced capacity for uncertainty preservation.

Accordingly, the sequence of steps in workflow A is more suitable for the selection of RGCM runs. This claim has been tested and validated for Texas, as detailed in the preceding sections. To further assess the relative applicability of workflow A compared to workflow B, we subject both workflows to testing in two additional regions, i.e., blind tests, as outlined in the following section.

d. Blind testing

In this section, we evaluate workflow A and workflow B in two additional regions, referred to as blind test areas. This main goal is to assess the performance of each workflow (i.e., preserving the uncertainty range of the full set) when applied to regions with climatic characteristics entirely different from those of Texas. These regions are i) Bihar, located in the eastern region of India, and ii) New York State, located in the northeastern region of the United States. In Bihar, the subtropical climate with sweltering summers and frigid winters can pose obstacles related to extreme weather events such as intense rainfall and heat stress during different seasons, affecting crop production and food security [Tesfaye et al. (2017)], while New York State has a humid continental climate with hot summers and cold winters (Kinney et al. 2015). We obtained the GCM simulation outputs for these new regions from the sources described in section 2 and followed the same procedures as described in detail in section 3.

Figures 20 and 21 compare the final four RGCM runs selected using workflow A and workflow B across a range of climate projections and RCPs in Bihar and New York, respectively. It can be seen that the workflows have one projection with identical RGCM runs in each RCP. The final four RGCM runs in the test areas are also evaluated in terms of their ability to preserve uncertainty. Figures 22 and 23 compare the CDF curves for ΔT and ΔP under RCP4.5 and RCP8.5 using workflow A and workflow B, representing Bihar and New York, respectively. This analysis includes four RGCM runs selected by workflow A for each RCP, four RGCM runs selected by workflow B for each RCP, and the full set of GCM run for both Bihar and New York. The corresponding Dmax values for these locations are presented in Table 8. The results again indicate that workflow A outperforms workflow B in preserving uncertainty throughout the selection steps for both Bihar and New York. Concerning ΔT, workflow A demonstrates an average Dmax value of 0.33 across both RCPs for Bihar, while workflow B shows a higher average of 0.47. Likewise, in the case of New York, workflow A produces an average Dmax value of 0.26, whereas workflow B yields 0.29, implying that workflow B shows an 11% lower value for average Dmax compared to workflow B for ΔT. Concerning ΔP, workflow A demonstrates an average Dmax value of 0.29 across both RCPs for Bihar, while workflow B shows an average of 0.32. Similarly, in the case of New York, workflow A produces an average Dmax value of 0.29, while workflow B yields 0.39, implying that workflow A shows a 34% lower value for average Dmax compared to workflow B for ΔP.

Fig. 20.
Fig. 20.

Comparison of final RGCM runs selected by workflow A and workflow B for Bihar, India. The RGCM runs exhibit no difference between the cold-wet projection under RCP4.5 and the cold-dry projection under RCP8.5 in both workflows.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Fig. 21.
Fig. 21.

Comparison of final RGCM runs from workflow A and workflow B for New York State, United States. The RGCM runs exhibit no difference between the cold-wet projection under RCP4.5 and the cold-wet projection under RCP8.5 in both workflows.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Fig. 22.
Fig. 22.

CDF curves for selected RGCM runs in Bihar, (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full GCM runs, four GCM runs from workflow A, and four GCM runs from workflow B. Regarding ΔT, workflow A demonstrates an average Dmax value of 0.33, derived from both RCPs, while workflow B exhibits a higher value of 0.47. Similarly, for ΔP, the average Dmax values for workflow A and workflow B are 0.29 and 0.32, respectively. Based on the findings, it can be inferred that the RGCM runs chosen by workflow A demonstrate better representativeness compared to those selected by workflow B.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Fig. 23.
Fig. 23.

CDF curves for selected RGCM runs in New York State, (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5, considering the full GCM runs, four GCM runs from workflow A, and four GCM runs from workflow B. Regarding ΔT, workflow A demonstrates an average Dmax value of 0.26, derived from both RCPs, while workflow B exhibits a higher value of 0.29. Similarly, for ΔP, the average Dmax values for workflow A and workflow B are 0.29 and 0.39, respectively. Based on the findings, it can be inferred that the RGCM runs chosen by workflow A demonstrate better representativeness compared to those selected by workflow B.

Citation: Journal of Climate 38, 7; 10.1175/JCLI-D-24-0219.1

Table 8.

Comparison of Dmax values calculated using Eq. (3) between the full set GCM runs and four RGCM runs selected by workflow A and workflow B for Bihar and New York State.
Table 8.

The performance of the final RGCM runs selected by each workflow is further tested for their ability to simulate past climates during the 25-yr reference period in Bihar and New York State. The corresponding MSE values between the four selected RGCM runs and the reference data for each RCP are provided in Table 9. For Bihar, workflow A shows an average MSE value of 0.34 for T¯, considering both RCPs, while workflow B shows a higher value of 0.47, representing a 38% increase. Similarly, for P¯, the average MSE values derived from both RCPs in workflow A and workflow B are 0.30 and 0.32, respectively. This suggests that workflow A has an average MSE value 7% lower than workflow B in Bihar. Similarly, for New York, workflow A demonstrates an average MSE value of 0.26 for T¯, considering both RCPs, while workflow B shows a higher value of 0.29, representing an 11% increase. For P¯, the average MSE values derived from both RCPs in workflow A and workflow B are 0.29 and 0.40, respectively. This suggests that workflow A has an average MSE value 37% lower than workflow B in New York.

Table 9.

Comparison of MSE values between the full-set of GCM runs and four RGCM runs selected by workflow A and workflow B for Bihar and New York.
Table 9.

Our results collectively demonstrate that workflow A not only successfully selects RGCM runs (a smaller set) that better preserves the uncertainty space of the full set of GCM runs in the test area but also ensures an accurate representation of historical climate data. Therefore, we recommend using the RGCM runs selected from workflow A for further in-depth investigations and analyses of climate change in regions studied here.

The choice of workflows is not arbitrary rather giving preference to the accuracy of models and uncertainty of future scenarios. The reordered steps in workflow A prioritize a balance while preserving uncertainty and reproducing past climates, placing a higher emphasis on history matching over changes in climatic means. In contrast, workflow B prioritizes changes in climatic means over history matching. This balance is a key strength making workflow A valuable for selecting representative GCM runs for climate change impact studies. Future work can test the performance of workflow A in more regions, using newer GCM ensembles (e.g., CMIP6), considering additional performance metrics, applying correlation analysis against observations, and incorporating GCM model interdependence weights. Addressing these points can further improve the robustness of envelope-based workflows used for GCM subset selection and facilitate accurate climate change impact assessments and adaptation planning.

e. Limitations

While the current process of selecting RGCM runs for impact assessments considers important aspects of future climate change and past performance, we must acknowledge and address potential sources of error. One such source of error lies in our assumption of independence among all GCM runs, disregarding the fact that certain models may share code or employ the same validation and forcing data, leading to model interdependence. This interdependence becomes particularly relevant in our study, considering the inclusion of multiple ensemble members from the same GCM’s initial condition ensemble. To mitigate this issue, future research can explore the incorporation of weighting measures that account for the degree of interdependence between CMIP5 GCM models. By doing so, a more comprehensive selection process can be achieved, improving the reliability and robustness of GCM run choices for impactful climate change assessments.

5. Conclusions

The study introduced a new three-stage envelope-based workflow (workflow A) for the selection of representative general circulation model (RGCM) from the CMIP5 ensemble under RCP4.5 and RCP8.5 scenarios. Workflow A begins with history matching, followed by capturing the range of changes in climatic means and extreme indices. This structure contrasts with the standard method (workflow B), which starts with capturing the range of changes in climatic means. Workflows A and B were compared to select four RGCM runs from an initial pool of 105 GCM runs for RCP4.5 and four RGCM runs from an initial pool of 77 GCM runs for RCP8.5. It is noted that workflows A and B are entirely data driven, adhering to specific criteria at each step, which may result in selecting the same GCM run at certain points, or they may differ. The comparison metrics assessed how closely the RGCM runs captured the uncertainty range of the full set of GCM runs, as well as their performance in accurately reproducing past climatic characteristics. In this context, the Kolmogorov–Smirnov test was employed to calculate the maximum difference Dmax between the cumulative distribution functions (CDFs) of the full set of GCM runs and the selected RGCM subsets, while the mean-square error (MSE) was used to assess the performance of the RGCM runs in reproducing past climate conditions. In all test regions, Texas (United States), Bihar (India), and New York (United States), each with distinct climatic conditions, workflow A achieved a significant reduction in Dmax and notably lower MSE values. For instance, in Texas, workflow A reduced Dmax by 23% and 20% for the CDFs of changes in mean air temperature and precipitation (ΔT and ΔP) between the full set and RGCM runs, demonstrating better uncertainty domain preservation. Furthermore, workflow A achieved a 105% lower MSE when reproducing monthly mean air temperature data, demonstrating its superior performance in replicating past climate conditions. For Bihar and New York, the same trend was observed.

This study, thus, highlights the robustness of workflow A for representative GCM selection, making it suitable for a wide range of climate impact assessments. Future research should further explore the integration of more advanced statistical measures and interdependence weights between GCMs to enhance the workflow’s efficiency in capturing climate extremes and ensuring broader applicability across regions and climate conditions.

Acknowledgments.

S. A. F. and J. P. T. would like to acknowledge support from the Department of Energy’s Biological and Environmental Research (BER) program (Award DE-SC0023044).

Data availability statement.

The data and materials used in this study are available upon request.

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  • Adler, R. F., and Coauthors, 2003: The Version-2 Global Precipitation Climatology Project (GPCP) monthly precipitation analysis (1979–present). J. Hydrometeor., 4, 1147–1167, https://doi.org/10.1175/1525-7541(2003)004<1147:TVGPCP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Biemans, H., L. H. Speelman, F. Ludwig, E. J. Moors, A. J. Wiltshire, P. Kumar, D. Gerten, and P. Kabat, 2013: Future water resources for food production in five South Asian river basins and potential for adaptation—A modeling study. Sci. Total Environ., 468–469, S117–S131, https://doi.org/10.1016/j.scitotenv.2013.05.092.

    • Search Google Scholar
    • Export Citation

  • Climate4Impact, 2023: Climate4Impact. Accessed 2 July 2023, https://www.climate4impact.eu/c4i-frontend/.

  • Emori, S., K. Taylor, B. Hewitson, F. Zermoglio, M. Juckes, M. Lautenschlager, and M. Stockhause, 2016: CMIP5 data provided at the IPCC Data Distribution Centre. Fact Sheet of the Task Group on Data and Scenario Support for Impact and Climate Analysis (TGICA) of the Intergovernmental Panel on Climate Change (IPCC), 8 pp., https://www.ipcc.ch/site/assets/uploads/2020/11/TGICA_Fact_Sheet_CMIP5_data_provided_at_the_IPCC_DDC_Ver_1_2016.pdf.

  • Gouveia, C. D., R. Rodrigues Torres, J. A. Marengo, and A. Avila-Diaz, 2022: Uncertainties in projections of climate extremes indices in South America via Bayesian inference. Int. J. Climatol., 42, 7362–7382, https://doi.org/10.1002/joc.7650.

    • Search Google Scholar
    • Export Citation

  • Hassanzadeh, P., C.-Y. Lee, E. Nabizadeh, S. J. Camargo, D. Ma, and L. Y. Yeung, 2020: Effects of climate change on the movement of future landfalling Texas tropical cyclones. Nat. Commun., 11, 3319, https://doi.org/10.1038/s41467-020-17130-7.

    • Search Google Scholar
    • Export Citation

  • Immerzeel, W. W., F. Pellicciotti, and M. F. P. Bierkens, 2013: Rising river flows throughout the twenty-first century in two Himalayan glacierized watersheds. Nat. Geosci., 6, 742–745, https://doi.org/10.1038/ngeo1896.

    • Search Google Scholar
    • Export Citation

  • Jackson, C. S., 2009: Use of Bayesian inference and data to improve simulations of multi-physics climate phenomena. J. Phys.: Conf. Ser., 180, 012029, https://doi.org/10.1088/1742-6596/180/1/012029.

    • Search Google Scholar
    • Export Citation

  • Jacquier, P., A. Abdedou, V. Delmas, and A. Soulaïmani, 2021: Non-intrusive reduced-order modeling using uncertainty-aware Deep Neural Networks and Proper Orthogonal Decomposition: Application to flood modeling. J. Comput. Phys., 424, 109854, https://doi.org/10.1016/j.jcp.2020.109854.

    • Search Google Scholar
    • Export Citation

  • Kaini, S., S. Nepal, S. Pradhananga, T. Gardner, and A. K. Sharma, 2020: Representative general circulation models selection and downscaling of climate data for the transboundary Koshi river basin in China and Nepal. Int. J. Climatol., 40, 4131–4149, https://doi.org/10.1002/joc.6447.

    • Search Google Scholar
    • Export Citation

  • Kaini, S., S. Nepal, S. Pradhananga, T. Gardner, and A. K. Sharma, 2021: Impacts of climate change on the flow of the transboundary Koshi River, with implications for local irrigation. Int. J. Water Resour. Dev., 37, 929–954, https://doi.org/10.1080/07900627.2020.1826292.

    • Search Google Scholar
    • Export Citation

  • Kashinath, K., and Coauthors, 2021: Physics-informed machine learning: Case studies for weather and climate modelling. Philos. Trans. Roy. Soc., 379, 20200093, https://doi.org/10.1098/rsta.2020.0093.

    • Search Google Scholar
    • Export Citation

  • Khan, A. J., and M. Koch, 2018: Selecting and downscaling a set of climate models for projecting climatic change for impact assessment in the Upper Indus Basin (UIB). Climate, 6, 89, https://doi.org/10.3390/cli6040089.

    • Search Google Scholar
    • Export Citation

  • Khan, M. S., P. Coulibaly, and Y. Dibike, 2006: Uncertainty analysis of statistical downscaling methods. J. Hydrol., 319, 357–382, https://doi.org/10.1016/j.jhydrol.2005.06.035.

    • Search Google Scholar
    • Export Citation

  • Kinney, P. L., and Coauthors, 2015: New York City panel on climate change 2015 report chapter 5: Public health impacts and resiliency. Ann. N. Y. Acad. Sci., 1336, 67–88, https://doi.org/10.1111/nyas.12588.

    • Search Google Scholar
    • Export Citation

  • KNMI, 2023: Climate explorer. Accessed 2 July 2023, https://climexp.knmi.nl/start.cgi.

  • Levesque, K., 2021: Identifying western North American tree populations vulnerable to drought under observed and projected climate change. M.S. thesis, Dept. of Forest Sciences, University of Freiburg, 57 pp.

  • Lutz, A., W. Immerzeel, H. Biemans, H. ter Maat, V. Veldore, and A. Shrestha, 2016a: Selection of climate models for developing representative climate projections for the Hindu Kush Himalayan region. HI-AWARE Working Paper 1, 46 pp., http://hdl.handle.net/10625/57516.

  • Lutz, A. F., H. W. ter Maat, H. Biemans, A. B. Shrestha, P. Wester, and W. W. Immerzeel, 2016b: Selecting representative climate models for climate change impact studies: An advanced envelope-based selection approach. Int. J. Climatol., 36, 3988–4005, https://doi.org/10.1002/joc.4608.

    • Search Google Scholar
    • Export Citation

  • Mahjour, S. K., and S. A. Faroughi, 2023: Selecting representative geological realizations to model subsurface CO2 storage under uncertainty. Int. J. Greenhouse Gas Control, 127, 103920, https://doi.org/10.1016/j.ijggc.2023.103920.

    • Search Google Scholar
    • Export Citation

  • Mahjour, S. K., A. A. S. Santos, M. G. Correia, and D. J. Schiozer, 2020: Developing a workflow to select representative reservoir models combining distance-based clustering and data assimilation for decision making process. J. Pet. Sci. Eng., 190, 107078, https://doi.org/10.1016/j.petrol.2020.107078.

    • Search Google Scholar
    • Export Citation

  • Mahjour, S. K., A. A. S. Santos, M. G. Correia, and D. J. Schiozer, 2021: Scenario reduction methodologies under uncertainties for reservoir development purposes: Distance-based clustering and metaheuristic algorithm. J. Pet. Explor. Prod. Technol., 11, 3079–3102, https://doi.org/10.1007/s13202-021-01210-5.

    • Search Google Scholar
    • Export Citation

  • Mahjour, S. K., G. Liguori, and S. A. Faroughi, 2024: Selection of representative general circulation models under climatic uncertainty for western North America. J. Water Climate Change, 15, 686–702, https://doi.org/10.2166/wcc.2024.541.

    • Search Google Scholar
    • Export Citation

  • Meehl, G. A., C. Covey, T. Delworth, M. Latif, B. McAvaney, J. F. B. Mitchell, R. J. Stouffer, and K. E. Taylor, 2007: The WCRP CMIP3 multimodel dataset: A new era in climate change research. Bull. Amer. Meteor. Soc., 88, 1383–1394, https://doi.org/10.1175/BAMS-88-9-1383.

    • Search Google Scholar
    • Export Citation

  • Mora, C., and Coauthors, 2013: The projected timing of climate departure from recent variability. Nature, 502, 183–187, https://doi.org/10.1038/nature12540.

    • Search Google Scholar
    • Export Citation

  • Murray, V., and K. L. Ebi, 2012: IPCC special report on managing the risks of extreme events and disasters to advance climate change adaptation (SREX). J. Epidemiol. Community Health, 66, 759–760, https://doi.org/10.1136/jech-2012-201045.

    • Search Google Scholar
    • Export Citation

  • Parding, K. M., and Coauthors, 2020: Gcmeval—An interactive tool for evaluation and selection of climate model ensembles. Climate Serv., 18, 100167, https://doi.org/10.1016/j.cliser.2020.100167.

    • Search Google Scholar
    • Export Citation

  • Pawar, N. M., R. Soltanmohammadi, S. K. Mahjour, and S. A. Faroughi, 2024: ESM data downscaling: A comparison of super-resolution deep learning models. Earth Sci. Inform., 17, 3511–3528, https://doi.org/10.1007/s12145-024-01357-9.

    • Search Google Scholar
    • Export Citation

  • Peters, G. P., and Coauthors, 2013: The challenge to keep global warming below 2°C. Nat. Climate Change, 3, 4–6, https://doi.org/10.1038/nclimate1783.

    • Search Google Scholar
    • Export Citation

  • Pielke, R. A., Sr., and R. L. Wilby, 2012: Regional climate downscaling: What’s the point? Eos, Trans. Amer. Geophys. Union, 93, 52–53, https://doi.org/10.1029/2012EO050008.

    • Search Google Scholar
    • Export Citation

  • Pierce, D. W., T. P. Barnett, B. D. Santer, and P. J. Gleckler, 2009: Selecting global climate models for regional climate change studies. Proc. Natl. Acad. Sci. USA, 106, 8441–8446, https://doi.org/10.1073/pnas.0900094106.

    • Search Google Scholar
    • Export Citation

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  • Roy, T., J. A. Martinez, J. E. Herrera-Estrada, Y. Zhang, F. Dominguez, A. Berg, M. Ek, and E. F. Wood, 2019: Role of moisture transport and recycling in characterizing droughts: Perspectives from two recent U.S. droughts and the CFSv2 system. J. Hydrometeor., 20, 139–154, https://doi.org/10.1175/JHM-D-18-0159.1.

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  • Ruane, A. C., and S. P. McDermid, 2017: Selection of a representative subset of global climate models that captures the profile of regional changes for integrated climate impacts assessment. Earth Perspect., 4 (1), 1, https://doi.org/10.1186/s40322-017-0036-4.

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  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Topography map of the (a) United States and (b) zoomed-in section highlighting the study area in Texas. Texas is geographically located in both the south-central region of the United States.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Changes in mean air temperature and precipitation in Texas between the period 2071–2100 and 1981–2010, based on the CMIP5 ensemble: (a) mean air temperature change for RCP4.5, (b) mean precipitation change for RCP4.5, (c) mean air temperature change for RCP8.5, and (d) mean precipitation change for RCP8.5.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Methodology flowchart. The proposed workflow A begins with history matching, followed by an analysis of changes in mean air temperature and precipitation climatology, and then examines changes in mean extreme indices. Workflow B (standard envelope based) starts with capturing the range of changes in mean air temperature and precipitation climatology, then continues with analyzing extreme indices, and concludes with history matching.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Initial selection of GCM runs in workflow A for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between the periods of 2071–2100 and 1981–2010. The variation in projected ΔT and ΔP is significantly greater for the RCP8.5 model pool than for the RCP4.5 model pool. The 50th percentile value for ΔT and ΔP is highlighted by the pink square symbol. The 50th percentile value for ΔT and ΔP is used to divide the scatterplot into four quadrants: warm-dry, warm-wet, cold-dry, and cold-wet, which are highlighted with distinct colors.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Initial selection of GCM runs in workflow A for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between periods of 2071–2100 and 1981–2010. The selection process for each climatic quadrant is based on the average of normalized T distance and P distance to the reference datasets. Five GCM runs from each quadrant are selected based on the lowest averaged normalized T distance and P distance. Gray circles represent the GCM runs that are not chosen. From the 105 GCM runs of RCP4.5 and 77 GCM runs of RCP8.5, a total of 20 GCM runs are selected for each RCP.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    Initial selection of GCM runs in workflow B for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between 2071–2100 and 1981–2010. The 10th and 90th percentile values for ΔT and ΔP are highlighted by red square symbols. Gray circles represent the model runs that are not chosen. In each quadrant, five GCM runs with the shortest Euclidean distance to their respective 10th or 90th percentile values are selected for the refined selection of GCM runs. From the 105 GCM runs of RCP4.5 and 77 GCM runs of RCP8.5, a total of 20 GCM runs for each RCP are selected.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    CDF curves of (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full set of GCM runs, 20 GCM runs selected by workflow A, and 20 GCM runs selected by workflow B. For ΔT, workflow A has an average Dmax value of 0.10 considering both RCPs, while workflow B has a higher average value of 0.17. Similarly, for ΔP, the average Dmax values derived for workflow A and workflow B are 0.10 and 0.23, respectively. The results show that the selected GCM runs from workflow A demonstrate better representativeness compared to workflow B.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    Refined step for selecting GCM runs in workflow A for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between 2071–2100 and 1981–2010. The 10th and 90th percentile values (representing the quadrants of the full climatic spectrum) for ΔT and ΔP are highlighted by red square symbols. Two GCM runs with the shortest Euclidean distance to each quadrant are selected out of five for the final selection of GCM runs step. From the 20 GCM runs of each RCP4.5 and RCP8.5, a total of eight (8) GCM runs for each RCP are selected at this stage.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    Refined selection of GCM runs in workflow B for Texas from RCP4.5. The normalized change in the ETCCDI indices (R95pTOT, CDD, WSDI, and CSDI) for all quadrants (wrm-wet, warm-dry, cold-wet, and cold-dry) is considered. The yellow-highlighted cells indicate the two normalized index changes considered in each quadrant for selecting the GCM runs. From each quadrant, the GCM runs with the highest and second-highest averaged normalized index changes are selected (highlighted in green). Out of the 20 GCM runs for RCP4.5, a total of eight (8) GCM runs are chosen.

  • <sc>Fig</sc>. 10.
    View in gallery
    Fig. 10.

    Refined selection of GCM runs in workflow B for Texas from RCP8.5. The normalized change in the ETCCDI indices (R95pTOT, CDD, WSDI, and CSDI) for all quadrants (warm-wet, warm-dry, cold-wet, and cold-dry) is considered. The yellow-highlighted cells indicate the two normalized index changes considered in each quadrant for selecting the GCM runs. From each quadrant, the GCM runs with the highest and second-highest averaged normalized index changes are selected (highlighted in green). Out of the 20 GCM runs for RCP4.5, a total of eight (8) GCM runs are chosen.

  • <sc>Fig</sc>. 11.
    View in gallery
    Fig. 11.

    CDF curves of (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full set of GCM runs, eight GCM runs selected by workflow A, and eight GCM runs selected by workflow B. While workflow A exhibits an average Dmax value of 0.24 for ΔT determined from both RCPs, workflow B shows a slightly lower value of 0.23. However, for ΔP, the average Dmax values considering both RCPs for workflow A and workflow B are 0.23 and 0.28, respectively. These findings indicate that the selected GCM runs from workflow A, up until this step, demonstrate better representativeness compared to workflow B.

  • <sc>Fig</sc>. 12.
    View in gallery
    Fig. 12.

    Comparing monthly averages of mean air temperature T¯ data for Texas until refined selection step. The data include a reference dataset from ERA5, full set of GCM runs (gray color), and the GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP8.5, and (d) workflow B/RCP8.5. The results show that the GCM runs selected in workflow A exhibit a better representation of the overall uncertainty domain of the full ensemble compared to workflow B in both RCPs.

  • <sc>Fig</sc>. 13.
    View in gallery
    Fig. 13.

    Comparing monthly averages of mean precipitation P¯ data for Texas until refined selection step. The data include reference dataset from GPCP, version 2.3, full set of GCM runs, and GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP8.5, and (d) workflow B/RCP8.5. The results show that the GCM runs selected in workflow A exhibit a better representation of the overall uncertainty domain of the full ensemble compared to workflow B for both RCPs. Precipitation also exhibits significant variability across all models, in contrast to temperature, implying a wider range of uncertainty associated with precipitation.

  • <sc>Fig</sc>. 14.
    View in gallery
    Fig. 14.

    Final selection of GCM runs in workflow A for Texas. The normalized change in the ETCCDI indices (R95pTOT, CDD, WSDI, and CSDI) for all quadrants (warm-wet, warm-dry, cold-wet, and cold-dry) is considered for both RCPs. The yellow-highlighted cells indicate the two normalized index changes considered in each quadrant for selecting the GCM runs. From each quadrant, the GCM runs with the highest averaged normalized index changes are selected (highlighted in green). Out of the eight (8) GCM runs for each RCP, a total of four (4) GCM runs are chosen.

  • <sc>Fig</sc>. 15.
    View in gallery
    Fig. 15.

    Final selection of GCM runs in workflow B for Texas. The selection process for each climatic quadrant is based on the average of normalized T distance and P distance to the reference datasets. One GCM run from each quadrant is selected based on the lowest averaged distance. Out of the eight (8) GCM runs for each RCP, a total of four (4) RGCM runs are chosen.

  • <sc>Fig</sc>. 16.
    View in gallery
    Fig. 16.

    CDF curves of (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full set of GCM runs, four GCM runs selected by workflow A, and four GCM runs selected by workflow B. Regarding ΔT, workflow A demonstrates an average Dmax value of 0.31, derived from both RCPs, while workflow B exhibits a higher value of 0.38. Similarly, for ΔP, the average Dmax values for workflow A and workflow B are 0.30 and 0.36, respectively. Based on the findings, it can be inferred that workflow A shows an average Dmax value that is 20% lower than workflow B suggesting that the RGCM runs chosen by workflow A demonstrate better representativeness compared to those selected by workflow B.

  • <sc>Fig</sc>. 17.
    View in gallery
    Fig. 17.

    Comparison of final RGCM runs selected by workflow A and workflow B for Texas. In both RCP4.5 and RCP8.5, the RGCM runs from workflow A and workflow B are the same in the warm-dry projection. For RCP4.5, the selected RGCM run is CMCC-CMSr1i1p1, and for RCP8.5, it is CMCC-CMr1i1p1. In the cold-dry projection under RCP8.5, the RGCM run selected is also the same for both workflow A and workflow B, being EC-EARTHr8i1p1.

  • <sc>Fig</sc>. 18.
    View in gallery
    Fig. 18.

    Comparing averaged values of T¯ across all models at different stages of selection for Texas. The data include reference dataset from ERA5, the full GCM runs, and the GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP4.5, and (d) workflow B/RCP8.5. Workflow A exhibits an average MSE value of 0.71, considering both RCPs, while workflow B shows a higher value of 1.46, indicating a 105% improvement by using workflow A. These findings demonstrate that the RGCM runs selected by workflow A offer a better representation of the reference climate characteristics compared to those selected by workflow B.

  • <sc>Fig</sc>. 19.
    View in gallery
    Fig. 19.

    Comparing averaged values of P¯ across all models at different stages of selection for Texas. The data include reference dataset from GPCP-version 2.3, full GCM runs, and the GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP4.5, and (d) workflow B/RCP8.5. The average MSE values for workflow A and workflow B, derived from both RCPs, are 0.33 and 0.35, respectively. This indicates that workflow A has an average MSE value 6% lower than workflow B. These findings demonstrate that the RGCM runs selected by workflow A offer a better representation of the reference climate characteristics compared to those selected by workflow B.

  • <sc>Fig</sc>. 20.
    View in gallery
    Fig. 20.

    Comparison of final RGCM runs selected by workflow A and workflow B for Bihar, India. The RGCM runs exhibit no difference between the cold-wet projection under RCP4.5 and the cold-dry projection under RCP8.5 in both workflows.

  • <sc>Fig</sc>. 21.
    View in gallery
    Fig. 21.

    Comparison of final RGCM runs from workflow A and workflow B for New York State, United States. The RGCM runs exhibit no difference between the cold-wet projection under RCP4.5 and the cold-wet projection under RCP8.5 in both workflows.

  • <sc>Fig</sc>. 22.
    View in gallery
    Fig. 22.

    CDF curves for selected RGCM runs in Bihar, (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full GCM runs, four GCM runs from workflow A, and four GCM runs from workflow B. Regarding ΔT, workflow A demonstrates an average Dmax value of 0.33, derived from both RCPs, while workflow B exhibits a higher value of 0.47. Similarly, for ΔP, the average Dmax values for workflow A and workflow B are 0.29 and 0.32, respectively. Based on the findings, it can be inferred that the RGCM runs chosen by workflow A demonstrate better representativeness compared to those selected by workflow B.

  • <sc>Fig</sc>. 23.
    View in gallery
    Fig. 23.

    CDF curves for selected RGCM runs in New York State, (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5, considering the full GCM runs, four GCM runs from workflow A, and four GCM runs from workflow B. Regarding ΔT, workflow A demonstrates an average Dmax value of 0.26, derived from both RCPs, while workflow B exhibits a higher value of 0.29. Similarly, for ΔP, the average Dmax values for workflow A and workflow B are 0.29 and 0.39, respectively. Based on the findings, it can be inferred that the RGCM runs chosen by workflow A demonstrate better representativeness compared to those selected by workflow B.

Fig. 1.

Topography map of the (a) United States and (b) zoomed-in section highlighting the study area in Texas. Texas is geographically located in both the south-central region of the United States.
Fig. 2.

Changes in mean air temperature and precipitation in Texas between the period 2071–2100 and 1981–2010, based on the CMIP5 ensemble: (a) mean air temperature change for RCP4.5, (b) mean precipitation change for RCP4.5, (c) mean air temperature change for RCP8.5, and (d) mean precipitation change for RCP8.5.
Fig. 3.

Methodology flowchart. The proposed workflow A begins with history matching, followed by an analysis of changes in mean air temperature and precipitation climatology, and then examines changes in mean extreme indices. Workflow B (standard envelope based) starts with capturing the range of changes in mean air temperature and precipitation climatology, then continues with analyzing extreme indices, and concludes with history matching.
Fig. 4.

Initial selection of GCM runs in workflow A for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between the periods of 2071–2100 and 1981–2010. The variation in projected ΔT and ΔP is significantly greater for the RCP8.5 model pool than for the RCP4.5 model pool. The 50th percentile value for ΔT and ΔP is highlighted by the pink square symbol. The 50th percentile value for ΔT and ΔP is used to divide the scatterplot into four quadrants: warm-dry, warm-wet, cold-dry, and cold-wet, which are highlighted with distinct colors.
Fig. 5.

Initial selection of GCM runs in workflow A for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between periods of 2071–2100 and 1981–2010. The selection process for each climatic quadrant is based on the average of normalized T distance and P distance to the reference datasets. Five GCM runs from each quadrant are selected based on the lowest averaged normalized T distance and P distance. Gray circles represent the GCM runs that are not chosen. From the 105 GCM runs of RCP4.5 and 77 GCM runs of RCP8.5, a total of 20 GCM runs are selected for each RCP.
Fig. 6.

Initial selection of GCM runs in workflow B for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between 2071–2100 and 1981–2010. The 10th and 90th percentile values for ΔT and ΔP are highlighted by red square symbols. Gray circles represent the model runs that are not chosen. In each quadrant, five GCM runs with the shortest Euclidean distance to their respective 10th or 90th percentile values are selected for the refined selection of GCM runs. From the 105 GCM runs of RCP4.5 and 77 GCM runs of RCP8.5, a total of 20 GCM runs for each RCP are selected.
Fig. 7.

CDF curves of (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full set of GCM runs, 20 GCM runs selected by workflow A, and 20 GCM runs selected by workflow B. For ΔT, workflow A has an average Dmax value of 0.10 considering both RCPs, while workflow B has a higher average value of 0.17. Similarly, for ΔP, the average Dmax values derived for workflow A and workflow B are 0.10 and 0.23, respectively. The results show that the selected GCM runs from workflow A demonstrate better representativeness compared to workflow B.
Fig. 8.

Refined step for selecting GCM runs in workflow A for Texas. Scatterplots show ΔT vs ΔP projected for all GCM runs in (a) RCP4.5 and (b) RCP8.5 between 2071–2100 and 1981–2010. The 10th and 90th percentile values (representing the quadrants of the full climatic spectrum) for ΔT and ΔP are highlighted by red square symbols. Two GCM runs with the shortest Euclidean distance to each quadrant are selected out of five for the final selection of GCM runs step. From the 20 GCM runs of each RCP4.5 and RCP8.5, a total of eight (8) GCM runs for each RCP are selected at this stage.
Fig. 9.

Refined selection of GCM runs in workflow B for Texas from RCP4.5. The normalized change in the ETCCDI indices (R95pTOT, CDD, WSDI, and CSDI) for all quadrants (wrm-wet, warm-dry, cold-wet, and cold-dry) is considered. The yellow-highlighted cells indicate the two normalized index changes considered in each quadrant for selecting the GCM runs. From each quadrant, the GCM runs with the highest and second-highest averaged normalized index changes are selected (highlighted in green). Out of the 20 GCM runs for RCP4.5, a total of eight (8) GCM runs are chosen.
Fig. 10.

Refined selection of GCM runs in workflow B for Texas from RCP8.5. The normalized change in the ETCCDI indices (R95pTOT, CDD, WSDI, and CSDI) for all quadrants (warm-wet, warm-dry, cold-wet, and cold-dry) is considered. The yellow-highlighted cells indicate the two normalized index changes considered in each quadrant for selecting the GCM runs. From each quadrant, the GCM runs with the highest and second-highest averaged normalized index changes are selected (highlighted in green). Out of the 20 GCM runs for RCP4.5, a total of eight (8) GCM runs are chosen.
Fig. 11.

CDF curves of (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full set of GCM runs, eight GCM runs selected by workflow A, and eight GCM runs selected by workflow B. While workflow A exhibits an average Dmax value of 0.24 for ΔT determined from both RCPs, workflow B shows a slightly lower value of 0.23. However, for ΔP, the average Dmax values considering both RCPs for workflow A and workflow B are 0.23 and 0.28, respectively. These findings indicate that the selected GCM runs from workflow A, up until this step, demonstrate better representativeness compared to workflow B.
Fig. 12.

Comparing monthly averages of mean air temperature T¯ data for Texas until refined selection step. The data include a reference dataset from ERA5, full set of GCM runs (gray color), and the GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP8.5, and (d) workflow B/RCP8.5. The results show that the GCM runs selected in workflow A exhibit a better representation of the overall uncertainty domain of the full ensemble compared to workflow B in both RCPs.
Fig. 13.

Comparing monthly averages of mean precipitation P¯ data for Texas until refined selection step. The data include reference dataset from GPCP, version 2.3, full set of GCM runs, and GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP8.5, and (d) workflow B/RCP8.5. The results show that the GCM runs selected in workflow A exhibit a better representation of the overall uncertainty domain of the full ensemble compared to workflow B for both RCPs. Precipitation also exhibits significant variability across all models, in contrast to temperature, implying a wider range of uncertainty associated with precipitation.
Fig. 14.

Final selection of GCM runs in workflow A for Texas. The normalized change in the ETCCDI indices (R95pTOT, CDD, WSDI, and CSDI) for all quadrants (warm-wet, warm-dry, cold-wet, and cold-dry) is considered for both RCPs. The yellow-highlighted cells indicate the two normalized index changes considered in each quadrant for selecting the GCM runs. From each quadrant, the GCM runs with the highest averaged normalized index changes are selected (highlighted in green). Out of the eight (8) GCM runs for each RCP, a total of four (4) GCM runs are chosen.
Fig. 15.

Final selection of GCM runs in workflow B for Texas. The selection process for each climatic quadrant is based on the average of normalized T distance and P distance to the reference datasets. One GCM run from each quadrant is selected based on the lowest averaged distance. Out of the eight (8) GCM runs for each RCP, a total of four (4) RGCM runs are chosen.
Fig. 16.

CDF curves of (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full set of GCM runs, four GCM runs selected by workflow A, and four GCM runs selected by workflow B. Regarding ΔT, workflow A demonstrates an average Dmax value of 0.31, derived from both RCPs, while workflow B exhibits a higher value of 0.38. Similarly, for ΔP, the average Dmax values for workflow A and workflow B are 0.30 and 0.36, respectively. Based on the findings, it can be inferred that workflow A shows an average Dmax value that is 20% lower than workflow B suggesting that the RGCM runs chosen by workflow A demonstrate better representativeness compared to those selected by workflow B.
Fig. 17.

Comparison of final RGCM runs selected by workflow A and workflow B for Texas. In both RCP4.5 and RCP8.5, the RGCM runs from workflow A and workflow B are the same in the warm-dry projection. For RCP4.5, the selected RGCM run is CMCC-CMSr1i1p1, and for RCP8.5, it is CMCC-CMr1i1p1. In the cold-dry projection under RCP8.5, the RGCM run selected is also the same for both workflow A and workflow B, being EC-EARTHr8i1p1.
Fig. 18.

Comparing averaged values of T¯ across all models at different stages of selection for Texas. The data include reference dataset from ERA5, the full GCM runs, and the GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP4.5, and (d) workflow B/RCP8.5. Workflow A exhibits an average MSE value of 0.71, considering both RCPs, while workflow B shows a higher value of 1.46, indicating a 105% improvement by using workflow A. These findings demonstrate that the RGCM runs selected by workflow A offer a better representation of the reference climate characteristics compared to those selected by workflow B.
Fig. 19.

Comparing averaged values of P¯ across all models at different stages of selection for Texas. The data include reference dataset from GPCP-version 2.3, full GCM runs, and the GCM runs selected by (a) workflow A/RCP4.5, (b) workflow B/RCP4.5, (c) workflow A/RCP4.5, and (d) workflow B/RCP8.5. The average MSE values for workflow A and workflow B, derived from both RCPs, are 0.33 and 0.35, respectively. This indicates that workflow A has an average MSE value 6% lower than workflow B. These findings demonstrate that the RGCM runs selected by workflow A offer a better representation of the reference climate characteristics compared to those selected by workflow B.
Fig. 20.

Comparison of final RGCM runs selected by workflow A and workflow B for Bihar, India. The RGCM runs exhibit no difference between the cold-wet projection under RCP4.5 and the cold-dry projection under RCP8.5 in both workflows.
Fig. 21.

Comparison of final RGCM runs from workflow A and workflow B for New York State, United States. The RGCM runs exhibit no difference between the cold-wet projection under RCP4.5 and the cold-wet projection under RCP8.5 in both workflows.
Fig. 22.

CDF curves for selected RGCM runs in Bihar, (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5 considering the full GCM runs, four GCM runs from workflow A, and four GCM runs from workflow B. Regarding ΔT, workflow A demonstrates an average Dmax value of 0.33, derived from both RCPs, while workflow B exhibits a higher value of 0.47. Similarly, for ΔP, the average Dmax values for workflow A and workflow B are 0.29 and 0.32, respectively. Based on the findings, it can be inferred that the RGCM runs chosen by workflow A demonstrate better representativeness compared to those selected by workflow B.
Fig. 23.

CDF curves for selected RGCM runs in New York State, (a) ΔT for RCP4.5, (b) ΔT for RCP8.5, (c) ΔP for RCP4.5, and (d) ΔP for RCP8.5, considering the full GCM runs, four GCM runs from workflow A, and four GCM runs from workflow B. Regarding ΔT, workflow A demonstrates an average Dmax value of 0.26, derived from both RCPs, while workflow B exhibits a higher value of 0.29. Similarly, for ΔP, the average Dmax values for workflow A and workflow B are 0.29 and 0.39, respectively. Based on the findings, it can be inferred that the RGCM runs chosen by workflow A demonstrate better representativeness compared to those selected by workflow B.
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