This study utilizes both observed and modeled temperature datasets over the continental United States to bias-correct regional-scale Earth system model projections. The datasets are described as follows:

WRF-CCSM : building off of previous studies , this study uses modeled 3-hourly temperature data at a 12 km spatial resolution for three time periods–historical (1995–2004), mid-century (2045–2054), and late-century (2085–2094). These projections, called WRF-CCSM, are generated by dynamically downscaling the Community Climate System Model version 4 (CCSM4) using the Weather Research and Forecasting (WRF) model version 3.3.1 . For future periods (mid- and late-century), we use the Representative Concentration Pathway 8.5 (RCP8.5) scenario, which corresponds to a high greenhouse gas concentration trajectory, reaching approximately 8.5 W m⁻² of radiative forcing by 2100 . The model uses the Grell–Devenyi convective parametrization , the Yonsei University planetary boundary layer scheme , the Noah land surface model , the longwave and shortwave radiative schemes of the Rapid Radiation Transfer Model for GCM , and the Morrison microphysics scheme . Spectral nudging is applied at 6-hour intervals to large-scale features, including air temperature, geopotential height, and wind, for levels above 850 hPa and wavelengths around 1200 km, using a nudging coefficient of 3×10-5 s⁻¹. Additionally, a 1-year spin-up period is implemented to allow the model to reach equilibrium before each of the three simulations. Details on the model design and configurations are provided in and .

We therefore apply bias correction after the 12 km dynamical-downscaling step, allowing the adjustment to address both the large-scale biases inherited from the driving GCM and the additional systematic errors introduced by the regional model itself. To bias-correct future regional model projections, we used the historical observational data (Livneh) over the period (1995–2004). The WRF-CCSM simulation spanning the same time period (historical; 1995–2004) is used to learn the bias correction model (explained in Sect.  and ). Daily mean temperature data are calculated from the 3 h outputs of WRF-CCSM to match the temporal resolution of the observed Livneh data. Similarly, the 1/16° Linveh data is remapped onto the 12 km simulation mesh used by WRF-CCSM using the bilinear interpolation operator provided in the Climate Data Operator software version 2.5.2 to match the spatial scales.

We estimate a transfer function that aligns the empirical distribution of the WRF–CCSM daily series with the corresponding Livneh observations for 1995–2004, and then apply this function to correct the future WRF–CCSM projections. By correcting the learned biases, the model generates bias-corrected future predictions that scale more closely with observational data, thereby reducing systematic and known biases in the model output.

To assess the performance and generalizability of the proposed EMDBC method, we conducted a validation study using historical data from 1995 to 2004. This period was split into two parts: the first half (1995–1999) was used to develop and train our bias correction models, while the second half (2000–2004) was reserved for validation. The Livneh daily observed temperature series served as the reference dataset, and the EMDBC approach was applied to correct the daily temperature projections from CCSM. For a comprehensive spatial evaluation, we randomly selected seven areas, each measuring 25×25 grid cells (300 km × 300 km), from major subregions defined in the Fifth National Climate Assessment across the continental United States, shown in Fig. , ensuring a diverse set of conditions. The seven areas are geographically defined in Appendix .

Quantile mapping (QM) is one of the most widely adopted bias correction (BC) techniques, designed to align the statistical distribution of model outputs with observations (see for a comprehensive review). By adjusting model outputs to match observed quantiles, QM can effectively reduce systematic biases related to both the central tendency and variability. Two prominent variants of this framework are briefly described below: Basic Quantile Mapping (QM) and Quantile Delta Mapping (QDM).

Basic Quantile Mapping (QM): this approach directly corrects model outputs by aligning their quantile functions to that of the observed data . Let To the observed data, and Tphist the historical model simulation. For a future model output Tpfut, the bias-corrected value Tpfut,BC is given by:1Tpfut,BC=Fo-1FmhistTpfut,where Fmhist is the empirical CDF of the model outputs in the historical period Tphist, and Fo is the empirical CDF of the observed data To. To bias-correct the future WRF–CCSM projections, we use the 1995–2004 Livneh observations as the calibration reference. Although QM ensures perfect distributional alignment for the historical period, it implicitly assumes that the observed CDF remains valid under future conditions – an assumption that can distort projected trends when the future outputs differs significantly from the historical weather regime.

As highlighted in the introduction, QDM improves upon QM by allowing for distributional shifts from historical and future time periods. Nonetheless, most quantile-based methods effectively treat the entire time series on a single timescale, leaving biases at monthly, seasonal, or longer frequencies insufficiently addressed. This omission can result in residual errors that accumulate over extended periods, undermining confidence in long-term projections – a critical factor for both robust resilience assessments and strategic decision-making. These issues underscore the need for an approach that not only preserves the distributional changes in future projections but also captures timescale-dependent biases. In the next sections, we introduce the proposed EMDBC framework, which disentangles time-series of atmospheric variables produced by Earth system models into their intrinsic oscillatory modes. By applying tailored bias corrections to each timescale-specific component and subsequently recombining them, EMDBC aims to overcome the core limitations of QM and QDM, thereby offering a more robust and detailed method for bias correction in future projections.

Empirical Mode Decomposition (EMD) is a data-driven method to adaptively decompose a time series x(t) into a finite set of oscillatory components, called intrinsic mode functions (IMFs), plus a residual monotonic trend. Formally, EMD expresses a time series as: 3x(t)=∑i=1nci(t)+r(t), where ci(t) are the IMFs – each capturing variations over distinct timescales – and r(t) is the residual. Although EMD has found utility in diverse application domains, it can suffer from mode mixing, where oscillations of different frequencies end up blended in a single IMF.

To address this issue, Ensemble Empirical Mode Decomposition (EEMD) was introduced. EEMD has been successfully incorporated in several recent studies, for example, , , and . It adds multiple realizations of low-amplitude random noise, ϵj(t), to the original signal x(t) to form an ensemble of signals: xj(t)=x(t)+ϵj(t). EMD is then applied to each noise-added realization, and the resulting IMFs are averaged: 4ciEEMD(t)=1N∑j=1Nci,j(t), where ci,j(t) denotes the ith IMF from the jth noise realization, and N is the ensemble size. By smoothing over numerous noise realizations, EEMD mitigates mode mixing, yielding a more robust and interpretable decomposition. This reliability is especially valuable for timescale-specific bias correction. We use the EEMD function available in the Python package PyEMD to decompose temperature signals into IMFs.

Building on EEMD, we introduce an Empirical Mode Decomposition-based Bias Correction (EMDBC) framework for rectifying model biases across multiple timescales. As sketched in Fig. , EMDBC proceeds in three steps: i.

timescale decomposition – the daily Livneh and CCSM series (Row 1) are split via EEMD into four bands (Rows 2–4);

Here, we include a comprehensive evaluation of traditional bias correction methods alongside our proposed approach. By applying the bias correction models to both the historical training scenario and the historical validation scenario, we can effectively assess each models ability to address biases and generalize across temporal scales where observed data does not exist (i.e., the future mid- and late century scenarios).

We implement QDM and the proposed EMDBC to bias-correct the validation dataset introduced in Sect. . Figure  top panel shows the spatial distribution of the average absolute bias across these subregions and highlights the consistent performance gains achieved by EMDBC on held-out validation data. In addition, we examined the distributional similarity of the observed series and the model-projected series (both before and after bias correction) using the Wasserstein distance (WD). WD is defined as a distance between two probability measures P and Q on a metric space (X,‖⋅‖) by 12Wp(P,Q)=inf⁡γ∈Γ(P,Q)∫X×X‖x-y‖pdγ(x,y)1/p, where Γ(P,Q) denotes the set of all couplings with marginals P and Q; throughout this study we use the common choice p=1 . Figure  down panel illustrates the WD across all subregions, demonstrating that the EMDBC correction preserves a distributional similarity to the observed series comparable to the QDM approach.

Next, we assessed the performance of EMDBC at four distinct timescales – biweekly, monthly, seasonal, and half-annual – by comparing it to both QDM and the original CCSM output. To focus on each timescale, we used a Fast Fourier Transformation (FFT) based bandpass filtering method. First, the daily temperature series was transformed into the frequency domain. Then, all frequencies outside the target range were set to zero before an inverse transform was applied to reconstruct the filtered signal. This approach allowed us to isolate and compare how effectively each bias correction method captures variability at different temporal scales. Figure  shows the spatial distribution of the absolute bias across subregions for each filtered timescale. While EMDBC and QDM perform comparably at shorter timescales (biweekly), EMDBC demonstrates a progressively closer alignment with the observed series at longer timescales (monthly, seasonal, half-annual). Accurate bias correction at coarser temporal resolutions is especially important for large-scale resilience assessments and long-term planning, where cumulative effects and extended trends play a crucial role. This includes common uses cases of RCM and GCM, such as global, national, or regional impact studies ; policy planning for risk assessment ; energy infrastructure trends for long-term heating or cooling demands ; drought security ; agriculture planning ; and understanding ecosystem biodiversity shifts . In other words, EMDBC shows promising ability to reduce temperature trend distortion caused by systematic biases due to model uncertainties and better capture temperature trend dynamics. This improved ability to preserve these longer-term patterns makes it a more reliable choice than QDM for applications that depend on consistent performance across multiple timescales.These results demonstrate that EMDBC successfully preserves bias-corrected signals over a broad range of temporal frequencies. By confirming EMDBC's effectiveness in an out-of-sample setting in this validation experiment, we gain confidence that it retains crucial physical relationships within the model more effectively than the traditional QDM, particularly at longer timescales. In the next section, we will evaluate its performance on the full GCM domain.

We apply EMDBC and QDM to the expanded model domain – covering all relevant time periods – to illustrate each method’s impact on temperature bias correction. As an initial illustration, Fig.  presents a single sampled location, decomposed in multiple timescales via the EMD-based approach described in Sect. . While QDM and EMDBC both perform well at the daily (training) scale, EMDBC more accurately preserves the longer-term fluctuations (e.g., seasonal and annual) seen in the observed Livneh data.

Turning next to broader spatial analyses, Fig.  focuses on various sub-regions across continental United States (CONUS). In each sub-region, the top panel compares the absolute temperature bias between the model projected and the observed series before and after correction with EMDBC and QDM, whereas the bottom panel shows the distribution of the average temperature. This figure demonstrates that EMDBC consistently reduces biases while maintaining an overall temperature distribution comparable to QDM.

To verify whether these distributional consistencies hold across individual seasons, we next analyze Fig. , which illustrates the spatial distribution of seasonal-average temperature for the Livneh observations, the raw WRF-CCSM outputs, and their bias-corrected counterparts. At this aggregated seasonal level, both EMDBC and QDM move the model's temperature distribution closer to the observed data while retaining the overall projected warming trends through the mid- and late-century timeframes. This consistency further suggests that EMDBC not only reduces bias magnitude but also closely matches observed seasonal temperature patterns.

Finally, Figs.  and  show the average predicted daily bias (d–f) and the corresponding spatial maps ((g–i); e.g., annual or multi-year averages) for the raw and bias-corrected WRF-CCSM outputs. For reference, average Livneh observation data is also plotted, along with the average WRF-CCSM historical bias before and after correction (a–c). Here, “predicted bias” refers to the difference between the modeled temperature and its bias-corrected counterpart. EMDBC generally applies a stronger correction than QDM, resulting in slightly cooler daily temperature fields and a more uniform reduction of bias across the domain. Although we cannot fully validate future-period corrections in the absence of observations, EMDBC’s stronger alignment with historical data and its lower bias in validation sub-regions suggest it is well-equipped to handle changing conditions while preserving both short- and long-term temperature variability.