Evaluating temperature bias corrections in regional climate models: Insights from Rajkot's historical and future data

Introduction

Global and regional climate models (GCMs and RCMs) frequently exhibit biases, which necessitate correction against observational or reanalysis datasets to ensure their outputs are suitable for impact studies and practical applications, such as evaluating the effects of climate change on climate extremes (Eccles et al., 2021; Trancoso et al., 2020) [3,9] . GCMs simulate atmospheric circulation patterns but with a coarse spatial resolution of 100-200 km. Compared to GCMs, RCMs are more adept at capturing mesoscale precipitation patterns, including topographic effects and sea-land contrasts (Frei et al., 2006; Grose et al., 2019) [5,6] . However, RCMs still exhibit significant biases due to factors such as imperfect boundary conditions derived from reanalysis or GCM data and systematic errors inherent in the model itself (Ehret et al., 2012; Teutschbein & Seibert, 2012) [4,8] . Bias correction is a crucial preliminary step in most climate change impact studies and involves adjusting model outputs to reduce systematic errors, thereby improving their fit to observed data (Maraun, 2016) [7] . There are various methods of bias correction, ranging from simple linear scaling to more sophisticated techniques like quantile mapping (Casanueva et al., 2020; Chen et al., 2013) [1,2] . Linear scaling adjusts projections by accounting for monthly errors but only corrects the mean, which can be inadequate for extreme events and other statistical characteristics, such as variability (Teutschbein and Seibert, 2012) [8] .

In contrast, distribution mapping methods, including quantilequantile mapping, can correct for both variability and extremes, offering a more comprehensive approach to bias correction (Teutschbein and Seibert, 2012) [8] . The Coordinated Regional Downscaling Experiment (CORDEX) provides enhanced regional climate change projections on a global scale, offering detailed predictions that can be easily applied to any region. These datasets are valuable for vulnerability and adaptation studies as well as climate research. In the past, climate change impact assessments primarily relied on General Circulation Models (GCMs) or Regional Climate Models (RCMs), but CORDEX has expanded the ability to produce more refined and region-specific climate projections. CORDEX data, like other climate model outputs, often exhibit biases that necessitate careful analysis when studying future climate projections. To address these biases, it is essential to compare future simulations (post-2006) with historical simulations (1961-2005) produced by the same CORDEX models. This comparison helps in understanding the deviations and provides a more accurate representation of future climate conditions. The CORDEX initiative offers data for three key Representative Concentration Pathways (RCPs) -RCP 2.6, RCP 4.5 and RCP 8.5 -which represent different possible scenarios for greenhouse gas emissions and land-use changes. By examining these scenarios, researchers can better understand the potential range of future climate outcomes and their implications. RCP 8.5 represents the most pessimistic scenario, where no significant climate policy is implemented, leading to high population growth and elevated levels of greenhouse gas emissions by 2100. This scenario assumes a future where the global community fails to take substantial action to mitigate climate change, resulting in severe environmental consequences. On the other hand, RCP 4.5 depicts a more moderate scenario, where efforts are made to stabilize greenhouse gas emissions by the end of the century. This pathway suggests that, while some measures are taken to address climate change, they are not aggressive enough to reverse the trends entirely, leading to a stabilized but warmer climate. RCP 2.6 is the most optimistic scenario, assuming a significant reduction in greenhouse gas emissions, resulting in a projected global temperature rise of only 1.6°C by 2100 relative to pre-industrial levels. This scenario envisions a future where strong international cooperation and stringent climate policies lead to substantial mitigation efforts, keeping global warming to a minimum. Comparing climate projections across these three scenarios is crucial for understanding the potential impacts of varying levels of anthropogenic activity, particularly in terms of greenhouse gas emissions. The differences between these pathways highlight the importance of policy decisions and their long-term effects on the global climate. In recent years, the increasing frequency of extreme climate events has underscored the need to analyze future climate projections using Regional Climate Models (RCMs) under different RCP scenarios. These extreme events, ranging from heatwaves to intense storms, are becoming more common as the climate continues to change, posing significant challenges for communities and ecosystems worldwide. However, the outputs of RCMs, like all climate models, are not free from biases. These biases must be corrected to ensure that the projections are accurate and reliable, especially when used for decision-making in climate adaptation and mitigation efforts. This study aims to assess the effectiveness of distribution mapping techniques for bias correction in temperature data simulated by the RCA4 RCM for a specific study area under different RCP scenarios. By focusing on bias correction, the study seeks to improve the reliability of climate projections, providing more accurate data for researchers and policymakers. This approach is critical for developing effective strategies to address the impacts of climate change, particularly in regions that are highly vulnerable to shifts in temperature and precipitation patterns.

Study Area

Rajkot is a prominent city located in the Saurashtra region of Gujarat, India, and serves as the administrative headquarters of the Rajkot district. It is situated at 22.

Data Collection

The research utilized gridded rainfall and temperature data prepared by the Indian Meteorological Department (IMD) for various regions in India. The datasets included daily gridded rainfall at a 0.25 x 0.25-degree resolution and daily maximum and minimum temperatures at a 0.5 x 0.5-degree resolution. These datasets were provided in the Network Common Data Format (NetCDF). To access and process this data, the NetCDF4Excel add-in can be downloaded and installed, enabling the conversion of NetCDF files to Excel format using ArcGIS software. This climatic data was crucial for studying future climate change projections. Regional Climate Models (RCMs) are effective tools for understanding and predicting climate changes. In this research, climate change data was sourced from the CORDEX-South Asia Multi-Model Output, accessible through the Centre for Climate Change Research at the Indian Institute of Tropical Meteorology, Pune. The CORDEX data includes simulations using the RCA4 (Rossby Centre regional atmospheric model version 4) model for various regions, available at two resolutions: the standard 0.44 degrees (~50 km, EUR-44) and a finer 0.11 degrees (~12.5 km, EUR-11). These datasets provide projections for daily rainfall (in mm) and temperature (in °C) under different Representative Concentration Pathway (RCP) scenarios-2.6, 4.5, and 8.5-covering both historical and future periods. Similar to the IMD data, these climate data file, also in NetCDF format, were converted to Excel format using ArcGIS for further analysis.

Methodology

The historical daily maximum and minimum temperature records for Junagadh, covering 55 years (1951-2005), were obtained from the Indian Meteorological Department (IMD). Simulated maximum and minimum temperatures for the same location were also acquired from the CORDEX database for various Representative Concentration Pathways (RCPs). The baseline period (1951-2005) was used as a reference for comparison with future projections (2006-2100) under different RCP scenarios, including RCP 2.6, RCP 4.5, and RCP 8.5. Simulations from Regional Climate Models (RCMs) often exhibit biases due to inherent model errors, such as inaccuracies in model formulation, spatial discretization, and grid cell averaging. These biases make direct application of RCM outputs in hydrological impact studies challenging. To address this, it is recommended to use an ensemble of RCM simulations and apply bias correction techniques. These methods adjust the simulated climate data to better match observed values. In this study, the period from 1951 to 1995 was used for model calibration, while 1996 to 2005 served as the validation period. A probability distribution-based scaling method was applied to correct the RCM-simulated temperatures. This method uses cumulative distribution functions to align the simulated data with observed temperature distributions. The annual temperature cycle, being symmetric, was modeled using a normal distribution with monthly-specific means and standard deviations, allowing for a more accurate representation of temperature variability.

Distribution Mapping Method

The Distribution Mapping (DM) method was used to align the distribution of modeled data with that of observed data. This method adjusts key statistical parameters, such as the mean, standard deviation, and quantiles, while aiming to maintain the integrity of extreme values. However, a limitation of this approach in the assumption that both observed and simulated meteorological variables share the same underlying distribution, which may not always be the case and can introduce additional biases. For temperature time series, the Gaussian distribution method was often assumed to be the most suitable. This distribution defined by two parameters: the mean (μ), which determines the centre of the distribution, and the standard deviation (σ), which influences its spread. A smaller standard deviation (σ) results in a narrower distribution with fewer extreme values, while a larger standard deviation leads to a wider distribution, increasing the probability of extremes. To adjust the temperature data using this method, the Gaussian cumulative distribution function (CDF) and its inverse are applied, allowing for the transformation of simulated data to more closely resemble observed data. For temperature adjustments, the process involves using the Gaussian (normal) CDF (FN) cumulative distribution function (CDF) and its inverse (F N -1 ).

Where, T * contr = corrected value of temperature of control period T contr = uncorrected value of temperature of control period T * scen = corrected value of temperature for scenario period T scen = uncorrected value of temperature of scenario period F N = Gaussian CDF F -1 N = Inverse Gaussian CDF µ contr = monthly mean of simulated time series of daily temperature during for control period σ 2 obs = monthly standard deviation of observed time series of temperature during control period µ obs = monthly mean of observed time series of daily temperature during control period σ 2 contr = monthly standard deviation of simulated time series of daily temperature during control period.

Results and Discussion

The study focused on bias corrections for daily maximum and minimum temperatures, covering both a baseline period (1951-2005) and future scenarios (2006-2100). It involved calibration (1951-1995) and validation (1996-2005) phases, comparing simulated data with actual observations. Specifically, the bias correction was applied to temperatures simulated by RCA4 for Rajkot, using observed data for comparison. The analysis provided temperature data for both the control period (1951-2005) and the projected future period (2006-2100).

A) Daily Maximum Temperature Control Period (1951-2005)

The computed monthly mean of daily observed, Raw RCM and Bias corrected RCM of maximum temperature of Rajkot for the calibration period (1951-1995) and validation period of (1996-2005) shown in 5 Showed that the raw RCM daily maximum temperature with higher coefficient of variation than the observed maximum temperature data for all months. After applying the bias correction, the coefficient of variation of BC RCM maximum temperature were matched with the observed coefficient of variation of maximum temperature. For validation period (1996-2005), the coefficient of variation of both observed and bias corrected data were found lower than the coefficient of variation of raw RCM maximum temperature for all months. However, after applying the bias correction, the coefficient of variation of BC RCM maximum temperature were matched with the observed coefficient of variation of maximum temperature. The relationship between the monthly coefficient of variation of observed, Raw and bias corrected daily maximum temperature for calibration period (1951-1995) showed the comparison of Kurtosis coefficient (Ck) of observed, raw and bias corrected daily maximum temperature for calibration and validation period respectively. For calibration period it was found positive for January, November and December and for rest of months it was found as negative and for validation period it was found positive for June and for rest of months it was found as negative. It can be seen that the bias correction by adopting Gaussian distribution cannot correct the third and fourth moments. 5 Showed that the raw RCM daily maximum temperature with higher coefficient of variation than the observed minimum temperature data for all months. After applying the bias correction, the coefficient of variation of BC RCM minimum temperature were matched with the observed coefficient of variation of minimum temperature. For validation period (1996-2005), the coefficient of variation of both observed and bias corrected data were found lower than the coefficient of variation of raw RCM minimum temperature for all months. However, after applying the bias correction, the coefficient of variation of BC RCM minimum temperature were matched with the observed coefficient of variation of minimum temperature. The relationship between the monthly coefficient of variation of observed, Raw and bias corrected daily minimum temperature for calibration period (1951-1995) The SD was highest in March (2.69 °C) and lowest in August (0.54 °C). High SD values in the cooler months (e.g., January to March and November to December) suggested higher temperature variability, possibly due to the transition between winter and summer or between summer and monsoon seasons. Lower SD in monsoon and post-monsoon months (e.g., August) indicated more stable temperatures with less fluctuation, possibly due to the moderating effects of monsoon rains. Fig 3b .2 showed the coefficients of variation (Cv). Cv values range from 0.02 (August) to 0.17 (February), indicating varying degrees of relative temperature variability across the months. Higher Cv in the cooler months (January, February, November, December) suggested relatively higher variability compared to their means, while lower Cv in the warmer months (June, July, August) indicated more consistent temperatures relative to their means. Fig 3b .3 showed the skewness coefficient (Cs). Positive skewness (e.g., January: 1.31, February: 0.55, December: 1.17) indicated that the temperature distributions were right-skewed with more instances of below-average temperatures and occasional higher extreme temperatures. Negative skewness (e.g., April: -0.22, July: -0.40, August: -1.16) suggested a leftskewed distribution with more occurrences of above-average temperatures and some lower extreme temperatures. Months with near-zero skewness (e.g., March: -0.02, October: -0.05) have temperature distributions that were approximately symmetric around the mean. 1 showed the mean daily minimum temperatures, the mean temperatures increase from January (13.35°C) to June (27.81°C), indicating a warming trend leading up to the pre-monsoon period. After June, temperature slightly decrease, reaching a minimum in December (16.24°C). This pattern reflected the typical seasonal cycle, with the warmest months occurring just before the monsoon and cooler temperature following the monsoon and continuing through winter. SD values range from a minimum of 0.44°C in August to a maximum of 2.56°C in December. Higher SD values in the cooler months (January, February, November, December) suggested more significant temperature variability, which could be due to greater fluctuation between daytime and nighttime temperatures or weather transitions in those months. Lower SD values in June (0.84°C) and August (0.44°C) indicated more stable temperatures, likely due to consistent monsoon conditions and cloud cover moderating temperatures. the mean daily minimum temperatures, the mean temperatures showed an increase from January (15.70°C) to July (29.85°C), indicating a warming trend towards the middle of the year, which was typical for this region as it moves towards the summer. The highest mean temperature was in July (29.85°C), after which there was a gradual decrease until December (15.70°C), reflecting the cooling trend into the winter season. SD values range from a minimum of 0.85°C in August to a maximum of 3.22°C in February. The higher SD values in January (2.99°C) and February (3.22°C) suggested greater temperature variability during these winter months, which could be due to more unpredictable weather patterns. Lower SD values in August (0.85°C) and July (0.92°C) suggested more stable temperatures during the peak summer and early monsoon period.

Conclusion

The study shows a comprehensive bias correction analysis on daily maximum and minimum temperatures for Rajkot, focusing on the baseline period (1951-2005) and future scenarios (2006-2100) under three Representative Concentration Pathways (RCP 2.6, RCP 4.5, and RCP 8.5). The bias correction process used the Gaussian distribution mapping method to adjust the simulated data from the RCA4 regional climate model (RCM) against observed data, ensuring a more accurate representation of temperature trends. For daily maximum temperatures during the control period (1951-2005), the raw RCM data consistently underestimated observed temperatures across all months during both the calibration (1951-1995) and validation (1996-2005) phases. The Gaussian distribution mapping method significantly corrected these biases, bringing the bias-corrected RCM data in close agreement with observed data for all months. This was confirmed by high R² values, indicating a strong goodness of fit between the bias-corrected and observed data. The coefficient of variation (CV) for the bias-corrected data also closely matched the observed data, demonstrating that the method effectively adjusted for variability. However, the bias correction method was less effective in fully correcting the skewness (third moment) and kurtosis (fourth moment), suggesting limitations in adjusting the tails and peaks of the temperature distribution. For daily minimum temperatures during the same period, a similar pattern was observed. The raw RCM data underestimated observed minimum temperatures, but after applying the Gaussian distribution mapping method, the bias-corrected data closely aligned with the observed data in terms of mean temperatures and CVs. Yet, like with maximum temperatures, there were notable discrepancies in skewness and kurtosis between the bias-corrected and observed data, indicating that while the correction method effectively adjusted for mean temperature biases, it did not fully account for the distribution's shape. In future scenarios (2006-2100), the analysis under RCP 2.6, RCP 4.5, and RCP 8.5 highlighted distinct temperature trends. Under RCP 2.6 and RCP 4.5, there was a noticeable warming trend before the monsoon season and cooling post-monsoon. The bias correction process-maintained consistency in these projections, ensuring that mean temperatures were aligned with expected trends. However, under the more extreme RCP 8.5 scenario, the warming trends were more pronounced across all months, reflecting a significant increase in maximum and minimum temperatures due to higher greenhouse gas concentrations. Despite the effectiveness of the bias correction in aligning simulated data with observed mean temperatures across all RCP scenarios, variations in standard deviation, skewness, and kurtosis across different months indicated persistent challenges in accurately modeling temperature extremes and variability. These variations suggest that while the Gaussian distribution mapping method is robust for correcting mean biases, it has limitations in adjusting higher-order statistical moments, which are crucial for understanding the full range of temperature variability and extreme events in the future.

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