A combined wavelet analysis–quantile mapping (WA-QM) method for bias correction: capturing the intra-annual temporal patterns in climate model precipitation simulations and projections

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Abstract Despite recent improvements, global climate models (GCMs) still have biases that prevent their direct application. Quantile mapping (QM) has been widely used in bias correction due to its effectiveness in aligning the cumulative density function of climate model data with observations. However, QM has a significant limitation: it fails to consider the temporal correspondence between the model data and observations, which restricts its ability to represent intra-annual temporal patterns. To address this issue, this study integrated wavelet analysis (WA) into QM to develop a combined method termed WA-QM, which aimed to preserve QM's efficacy in overall bias correction and preservation of climate change signals, while capturing the intra-annual temporal patterns. The effectiveness of WA-QM was investigated using monthly precipitation data from five CMIP6 models in the Pan Third Pole region, which includes central Asia (CA), southeast Asia (SEA), and the Tibetan Plateau (TP). Quantile delta mapping (QDM) and scaled distribution mapping (SDM) served as the benchmark methods for assessment. The results indicated that integrating WA into QDM or SDM did not compromise the ability of QDM or SDM to correct overall biases and preserve the model’s climate change signal. Furthermore, WA could be an effective tool to overcome QM’s limitation in capturing intra-annual temporal patterns. The WA approach employed discrete wavelet transformation to decompose GCM data into various frequency bands and then adjusted their standard deviations and signs to ensure that their relative relationships were consistent with those in observations. Compared to the standalone QM approach, WA-QM showed greater accuracy in monthly statistical metrics. In the CA region, WA-SDM reduced the monthly root mean square error of the mean by 25.2%, the standard deviation by 17.6%, and the 90th percentile by 26.7% compared to SDM. The effectiveness of WA-QM was demonstrated across different data periods, spatial areas, and GCMs.