Weather typing.

Weather typing, also referred to as weather pattern-based, is a multivariate statistical downscaling method that relies on conditional resampling. It involves grouping local meteorological variables in relation to different classes of atmospheric circulation [22]. The main advantage of this method is that local variables are closely linked to global circulation [23]. However, reliability depends on having a static relationship between large scale circulation patterns and local climate [23]. For watershed modeling, where hourly or daily precipitation is an important variable, this method may not always be useful because typically the correlation between local precipitation and large-scale circulation patterns is not strong [23]. Approaches that have been used to improve weather typing include Constructed Analogs and variations such as Bias Corrected Constructed Analogs, Localized Constructed Analogs and Multivariate Adaptive Constructed Analogs.

Constructed analogs.

Constructed Analog (CA) relies on matching large-scale variables from observations with GCM model output and using the analog relationship as a scaling factor for future climate [24–26]. CA assumes that if an exact analog (in the historical record) to current weather can be found, future weather should follow the same analog [24]. The method is similar to principal component analysis (PCA) where multiple dependent variables represent similar relations. CA uses linear regression to develop a best-fit analog of GCM output from historical data [24]. A key limitation of the original CA is that it neglects model bias and is unable to project climates if no analog could be identified [25].

Bias Corrected Constructed Analog (BCCA) use bias correction to improve the CA method [25]. Biases between the models are removed, typically using a quantile mapping technique, which adjusts simulated values by quantile to better match observations. Another modification to the CA method, called Localized Constructed Analogs (LOCA), has the added benefit of being less sensitive to spatial scale and is better able to estimate extreme values [27]. LOCA produces downscaled estimates suitable for hydrologic modeling by using a multi-scale spatial matching scheme to pick appropriate analogs from observed data. Multivariate Adaptive Constructed Analogs (MACA) is another statistical downscaling method that utilizes meteorological training data (observations) to remove historical biases and match spatial patterns in climate model output [28].

Flint and Flint (2012) used statistically downscaled future climate projects from CA, then further downscaled them spatially using a gradient-inverse-distance-squared approach for hydrologic modeling at a 270-m spatial resolution [24]. They used continental-scale historical (observed) patterns of daily precipitation and air temperature at coarse resolution and their fine-resolution (approximately 12 km) equivalents with a statistical approach to climate and bias correction [24, 29]. Results indicate successful downscaling as the 270-m resolution was closer to the measured monthly station data for the 18-year record than the 4-km PRISM model [24].

Teutschbein et al. (2011) investigated the variability of seasonal streamflow and flood-peak projections using three statistical methods to downscale precipitation (analog, SDSM, and a multi-objective fuzzy-rule-based classification (MOFRBC) [17]. The analog method used historical observed data to identify a set of previous analog events that most resembled the target time period [17]. MOFRBC is a circulation-pattern classification method combined with a conditional precipitation model (a stochastic weather generator) [17, 30]. MOFRBC employs the circulation patterns in order to classify weather situations of different types [17, 30].

Statistical down scaling model.

The Statistical Down Scaling Model (SDSM) is a conditional weather generator that uses atmospheric circulation indices and regional moisture variables to estimate time-varying parameters (e.g., precipitation and temperature) that describe the daily weather at individual sites/stations [35]. SDSM is a useful method because multiple, low-cost, single site scenarios for daily climate parameters can be generated easily and rapidly for different climate forcing conditions [36].

A test of SDSM for streamflow modeling in Quebec showed that SDSM provides reasonable downscaling data (local scale temperature and precipitation) when using predictors that represent observed current climate [37]. However, the performance was less reliable when using GCM predictors [37]. The choice of downscaling methods has a significant impact on streamflow simulations: while SDSM was found to suitable for downscaling precipitation for a river basin in Sweden, Teutschbein et al. (2011) concluded that an ensemble approach was preferable [17].

Canonical correlation analysis.

Canonical Correlation Analysis (CCA) is used to identify and measure the relationship among sets of variables. It is sometimes used in place of multiple regression when there are multiple intercorrelated variables. CCA seeks an optimal linear combination between predictors and predictands and selects pairs of patterns so that a maximum correlation is produced [39, 40]. Before CCA, predictors and predictands are projected onto their empirical orthogonal functions (EOFs) to eliminate unwanted noise (small-scale features) and to reduce data space dimensionsionality [40]. Given the approach used to develop the correlations, CCA allows a physical interpretation of the mechanism controlling regional climate variability [40].

Busuioc et al. (2007) used CCA to downscale precipitation in Italy [40]. Three indices were used that focused on extreme rainfall events: the number of events exceeding the long-term 90^th percentile of rainy days, simple daily intensity, and the maximum number of consecutive dry days [40]. Busuioc et al. found that, generally, the combination of the first five to six EOFs and first two EOFs for all regional indices provided the best results [40].

Bias correction and spatial disaggregation.

Bias Correction and Spatial Disaggregation (BCSD) relies on a historic dataset at the same grid scale as the spatially downscaled variables, corrects biases using quantile mapping of modeled against observed climate, and then applies anomalies in the observed variables to the spatially interpolated model [24, 25, 41]. Quantile mapping has the advantage of not having a specific requirement for the length of time or the number of observed stations and it has been found to have the best performance in reducing biases. BCSD has been used in several hydrologic impact analyses and has demonstrated downscaling capabilities comparable to other statistical and dynamic methods [13, 41]. A major limitation, however, is that often monthly data is used and while the output can be converted to daily, unrealistic meteorology may result which is problematic for watershed modeling [41].

Maurer and Hidalgo (2008) compared CA with BCSD across the western US [13]. Coarse scale precipitation and temperature were employed in both downscaling approaches as predictors [13]. CA downscaled daily large-scale data directly but at a coarse spatial resolution whereas BCSD downscaled monthly data, with a random resampling technique to generate daily values [13]. Both methods struggled to reproduce wet and dry extremes for precipitation and were better at reproducing temperature, though the CA method exhibited slightly more accuracy with the extremes [13].

Maurer et al. (2010) later compared CA, BCSD, and a hybrid BCCA (using quantile-mapping bias correction prior to the CA method) downscaling for use with the VIC hydrologic model [42]. The bias correction considered in BCCA was essentially identical to that of BCSD, however, quantile mapping was used for all daily values (precipitation, maximum and minimum temperature) within each month [42]. While the bias correction included with BCCA forced the cumulative distribution function to match observations for the historical (observed) period, some biases due to the downscaling methods remained [42]. The three downscaling methods produced reasonable streamflow statistics at most locations, but the BCCA method consistently performed better than the other methods in simulating streamflow [42]. All methods performed well for generating extreme peak flows, but the hybrid BCCA method generated a better match of annual flow volume, showing that BCCA is also better at longer temporal scales [42].

Mizukami et al. (2015) examined the effects of four statistical downscaling methods (BCCA, BCSD daily and BCSD monthly, and asynchronous regression (AR)) on retrospective hydrologic simulations using three hydrologic models (CLM, VIC, and PRMS) [43]. Each SD method produced a different meteorological dataset including differences in precipitation, wet-day frequency, an energy input [43]. BCCA was found to consistently underestimate precipitation across the US leading to unrealistic hydrologic portrayals, whereas the other three methods overestimated precipitation, though BCSD-daily overestimated the wet-day frequency the most [43]. Despite this, the choice of downscaling method was found to impact runoff estimates less (excluding BCCA) than the choice of hydrologic model (with default parameters) [43].

Change factor.

The Change Factor (CF) method, sometimes called the Delta Change method, calculates differences between simulated current and future climate and adds these differences to observed time series [18]. The CF method is based on the assumption that GCMs are more reliable simulating relative rather than absolute values, thus the observed time series is adjusted by either adding the difference or multiplying the ratio of parameters between future and present climate as simulated by the GCM [18, 23]. An additive CF is the arithmetic difference between future and baseline projections, whereas a multiplicative CF is the ratio between future and baseline projections [44]. Additive and multiplicative CFs can be combined depending on the empirical distribution functions and any data limitations [44]. The selection of time periods, temporal domains, temporal scales, number of change factors, and type of change factors varies depending on the meteorological parameters and needs of the study [44]. Applying the CF method to hydrologic modeling, especially for urban watersheds, can present challenges because precipitation data need to be at fine time increments and change factors can produce negative precipitation values, can overestimate precipitation, or can increase the number of precipitation events [44, 45].

A combined change factor method (CCFM) can be applied as a secondary bias-correction technique to reduce a number of the issues associated with the traditional CF method [44]. This is typically done by computing empirical cumulative distribution functions (ECDF) for both baseline and future time periods, sorting them to create ratio and difference plots, which facilitating the selection of additive or multiplicative CFs, with differences and ratios calculated for each percentile of the cumulative distribution function (CDF) [44]. Adjustments are typically then made to address negative values, overestimations, and to eliminate artificially high numbers of precipitation events [38]. The combined method eliminated or reduced these issues, and the predicted precipitation time series closely matched observed precipitation patterns [44].

Hay et al. (2007) tested the delta change method for precipitation, temperature, and runoff across three mountainous regions in the US. For the basins tested, realistic runoff scenarios were simulated successfully using statistically downscaled NCEP (National Center for Environmental Prediction) output, but not using statistically downscaled HadCM2 (Hadley Centre for Climate Prediction and Research) GCM [18].

Camici et al. (2014) compared the downscaling ability of delta change and bias correction through quantile mapping for two GCMs for hourly rainfall, discharge and flood modeling [46]. The delta change method projected a decrease in the flood frequency curve, but with quantile mapping, one GCM predicted a decrease in the frequency of annual maximum discharge and the other predicted an increase [46]. As with other similar studies, a key conclusion was that an ensemble GCM with multiple downscaling methods is preferable for flood mapping [46].

Machine learning and artificial neural networks.

Artificial neural networks, sometimes called adaptable random forests, are still a relatively new and uncommon methods for SD that rely on machine learning. Though there are still only a few examples of random forest (RF) methods, they typically rely on the nonlinear relationship between predictors and predictands, making them particularly useful for downscaling precipitation, since this relationship is often nonlinear [47]. RF is an adaptable method that can be applied to downscale data from models, remote sensing retrievals, or gridded observations at a range of different resolutions [47].

An early example of machine learning for downscaling compared SDSM with Smooth Support Vector Machine (SSVM) for hydrologic modeling [48]. SSVM is a supervised machine learning method that uses limited sample information on an unconstrained convex quadratic optimization problem using smoothing [48]. Rainfall varied greatly between the two downscaling methods, though SDSM was found to have better performance than SSVM [48].

Later, He et al. (2016) developed Prec-DWARF (Precipitation Downscaling with Adaptable Random Forests), a machine-learning based method for statistical downscaling of precipitation across the continental US [47]. Different RF methods were tested and shown to reasonably reproduce the spatial and temporal patterns of precipitation [47]. A single RF tended to underestimate precipitation extremes, but predictions were improved by adding a second RF that was specifically designed to capture the relationship between covariates and target rainfall field for heavy and extreme precipitation. He et al. (2016) were able to successfully reproduce the geometrical and statistical characteristics of precipitation using RF [47]. It is still a somewhat limited method in that it consistently underestimates spatial variability, temporal dependence, and frequency of very high rainfall rates, and overestimates the amount and spatial extent of low intensity rainfall [47].

Nested models.

Nested RCMs are built using two or more RCM over a selected spatial domain at different grid scales, constrained by initial and time-dependent meteorological lateral boundary conditions from a GCM [50, 52]. Nested RCMs are intended to add more realistic sub-GCM grid-scale detail [52]. One way nesting is subject to mismatches between simulated parameters and those of the GCM, whereas two-way nesting partially addresses this by having the RCM feed information back into the GCM model [60, 61]. Multiple nesting, where consecutive nested models are used at increasing resolutions, can be used to reach highly localized areas [61, 62]. However, adding nesting becomes increasingly computationally expensive.

For example, Prein et al. (2013) used the Weather Research and Forecasting (WRF) model on three single-domain simulations with horizontal grid spacing of 4 km, 12 km, and 36 km over the Colorado headwaters [63]. Only the 4-km simulation correctly simulated precipitation totals, though in winter the 4- and 12-km simulations had similar performance [63]. The main advantage of the 4-km simulation was the improved mesoscale patterns of heavy precipitation and the larger-scale patterns of heavy precipitation [63].

Nudging.

Nudging is a method that adds a correction to the predictive equations of variables to prevent the RCM drift from GCM results [64, 65]. Spectral Nudging can be used to constrain RCM biases and improve results by forcing the RCM to follow the large-scale (GCM) driving boundary conditions [49]. What this does is relax the simulation by adding a nudging term to selected parameters that is proportional to the difference between the simulated and prescribed states (similar to the delta change method) [49]. This results in greater consistency between RCM and GCM. Nudging can, however, force the RCM to retain and potentially exacerbate biases from the GCM [49].

For example, Xu and Yang (2015) compared three sets of RCMs with identical model configurations [except for the initial and lateral boundary conditions] with and without spectral nudging, and with bias corrections and nudging where the nudging strength was progressively reduced [49]. Bias correction was done by interpolating the NNRP (National Centers for Environmental Prediction/National Center for Atmospheric Research Reanalysis Project) data to Community Atmosphere Model (CAM) grids, then computing the CAM biases in mean and variance and removing the biases by subtracting the mean bias and scaling variance from the original CAM simulation. Spectral nudging was applied to air temperature, horizontal winds, and geopotential height [49]. Both bias correction and spectral nudging improved results, though not consistently across all parameters [49]. Precipitation responded inconsistently to spectral nudging, with some regions and some seasons overestimating and some underestimating [49].

Grid nudging.

Grid nudging, sometimes referred to as analysis nudging, is a variant of spectral nudging where nudging is performed for every grid cell and for all spatial scales [49]. It is used to ensure that the simulated large-scale fields are consistent with the driving fields [64, 65]. Grid nudging is sometimes superior to spectral nudging if appropriate nudging coefficients are chosen to adjust the strength of the nudging force [64, 65]. This method, is however, extremely computationally expensive.

Liu et al. (2012) compared grid and spectral nudging in the downscaling of National Centers for Environmental Prediction (NCEP) and National Center for Atmospheric Research (NCAR) data with the Weather Research and Forecasting (WRF) model [66]. Compared with grid nudging, spectral nudging provides a better balance between the need to keep RCM results consistent with the large scale driving forces that would be provided by GCMs, and at the same time, allowed more variance to be added at smaller scales [66]. Additionally, the improvement at the small scale allowed by spectral nudging is not only reflected in spatial variability, but temporal variability as well [66].

Bowden et al. (2012) evaluated interior nudging techniques using the WRF model in a two-way nested configuration for downscaling with both the spectral and gridded approach [67]. Temperature behaved similarly regardless of which method was used, though for precipitation, gridded nudging generates monthly precipitation totals, intensity, and frequency more accurately than spectral nudging [67]. Gridded nudging appears to suppress the variability in predictions more strongly than spectral nudging [67].

Wooten et al. (2016) used the grid nudging approach using the WRF model to simulate precipitation over Puerto Rico [68]. Grid nudging generally resulted in lower precipitation than are observed but use of convective-permitting simulations improved the annual cycle, intensity, and location of rainfall [68].

Variable resolution grid models.

Variable resolution grid models (also known as stretched grid models) rely on a higher resolution over the region of interest. These are not as widely used but the advantage of a variable resolution stretched-grid is that it does not require any lateral boundary conditions for forcing, which reduces the computational challenges [69]. The result is that it provides self-consistent interactions between global and regional scales while maintaining global circulation with a uniform grid [69]. It is also portable, so the area of interest can be located anywhere [69].

McGregor (2015) provided a summary of five variable resolution downscaled climate models. Some of the benefits include the absence of any lateral boundaries and the related problems with spurious reflections [70]. Useful interactions may also occur between the fine-resolution and coarser regions [70]. Two variable grid models employ the Schmidt transformation (ARPEGE and CCAM), the other three employ spherical coordinates that independently stretch the longitudes and latitudes (GEOS-SG, GEM, and LMDZ) [70]. However, lower-boundary forcing is still needed for sea-ice and sea surface temperatures [70]. Variable grid GCMs can downscale to a finer resolution, correcting some GCM biases [70]. Variable grid GCMs are increasingly being used to downscale ensemble GCMs [70].

Corney et al. (2013) implemented a variable resolution method for dynamically downscaling six GCMs for two emissions scenarios [71]. They found that application of bias adjustment and multi-staged increased resolution, the simulation can better reproduce observations, explaining more than 95% of the temperature spatial variance for ~ 90% for precipitation [71]. Variable grid downscaling significantly improve the temporal distribution of variables and improved the seasonal variability predictions compared to the GCM [71].

Reinitialization.

Reinitialization is a method consisting of running short simulations that are frequently reinitialized. This allows the RCM to take advantage of the assimilated observations, both at the lateral boundaries and over the entire 3D atmosphere, while preserving the time sequence of the weather events from the driving field [51]. The benefit of reinitialization is that it is likely to prevent drift in climate from the GCM that wouldn’t be predicted at a localized scale.

For example, Lucas-Picher et al. (2013) tested RCMs with the inclusion of reinitialization to evaluate the downscaling performance of HIRHAM5 [57]. Surface conditions were kept continuous while the atmosphere was reinitialized every 24-hours from ERA-I using a 6-hr spin up. The individual 24-hour simulations were concatenated into a single massive time series. The reinitialization successfully prevented seasonal drift towards wetter climate conditions and improved predictions near the boundary [57]. The annual mean and the deviation were also improved by reinitialization [57]. However, the approach is time-consuming and adds substantial computational requirements [57].

Bias correction.

All GCMs have from some bias in their output, which when applied as boundary condition for an RCM may impact the results, sometimes substantially [72]. GCM biases can be passed through to the RCM via lateral and lower boundary conditions. There are two general approaches for bias correction: determining the differences (deltas) between predicted and observed/historic values for reference period that are then applied to observed historical data to construct future time series, or calculating scaling parameters to apply to future predictions to more closely fit observed climate [73]. One common technique is quantile-quantile mapping (QM) [74, 75]. For a given meteorological variable, the simulated cumulative density function (CDF) is compared to the observed CDF to calculate a correction function for each quantile [74, 75]. Then the corrected function is used to remove bias from the variables in each quantile [74, 75].

For example, Chen et al. (2019) used bias-correction with QM to downscale CMIP5 in Nevada at a station scale [76]. This involved: (1) validating PRISM data as the historic observed data, (2) bias correcting the CMIP5 dataset, and (3) validating the QM bias-correction process [76]. Hydrology was then simulated using Precipitation Runoff Modeling System (PRMS). Results fit well with observations of both temperature and precipitation as well as density distribution [76]. Piani et al. (2010) also used statistical bias correction to correct GCM output to produce internally consistent values that had a similar statistical distribution to the observations [77]. The approach performed unexpectedly well; in addition to improving the mean and other moments of the precipitation intensity CDF, drought predictions and heavy precipitation indeces also improved [77].

Themeßl et al. (2012) investigated the effect of quantile mapping on RCMs for its success in reducing systematic RCM errors and the ability to predict “new extremes” (values outside the calibration range) [78]. QM reduced the bias of daily mean, minimum, and maximum temperature, precipitation amount, derived indices of extremes by about one order of magnitude, and improved the frequency distributions [78]. In this case, QM was based on the CDF rather than on paired data and using empirical CDFs rather than theoretical CDFs [78]. QM was applied on a daily basis for each grid cell separately. In a 40-years RCM validation, QM was applicable to longer climate simulations and multiple parameters, irrespective of spatial and temporal error characteristics, which suggests transferability of QM to other RCMs [78].

Muerth et al. (2012) studied the importance of bias correction on daily runoff simulated with four different hydrologic models driven by different ensemble RCMs (CRCM4, RACMO2, and RCA3) [73]. Precipitation was bias corrected using the Local Intensity (LOCI) scaling method while air temperature was modified using a monthly additive correction [73]. Both methods were chosen for their simplicity, though they both have inherent flaws [73]. The monthly correction may create jumps in the corrected dataset between months and the LOCI performance has been shown to be slightly inferior to QM, especially at higher precipitation intensities [73]. As expected, bias correction of the RCMs systematically provides a more accurate representation of the actual hydrology, including mean and low flows [73]. High flow indicators are less affected, likely because the simulation of high flows is more dependent on the hydrological model’s structure [73].

Pierce et al. (2015) tested three bias correction techniques (QM, CDF-transform (CDF-t), and equidistant quantile matching (EDCDFm)) on temperature and precipitation for 21 GCMs [79]. CDF-t bias correction determines a transformation to map the predicted CDF of a variable in the historical period to the observed CDF, then uses the map to adjust the future CDF [79]. EDCDFm corrects a future predicted value within a quantile in the future CDF by adding the historical value of the future CDF to the predicted change in value [79]. QM and CDF-t significantly altered the GCM downscaling by up to 30% for precipitation. EDCDFm better preserved the temperature values but not precipitation [79].

Teutschbein and Seibert (2012) compared the effectiveness of a range of bias correction methods on an ensemble of 11 RCMs across five watersheds in Sweden [80]. The comparison consisted of no correction, linear scaling, LOCI, power transformation, variance scaling, distribution transfer, and delta-change with observed data from 1961–1990 [74]. Biases were found to vary substantially. All temperature-bias corrections improved the raw RCM simulations, though the linear scaling method was least effective [80]. All precipitation bias corrections also improved the RCM simulation, though linear scaling and LOCI still had larger variability ranges and similar biases in terms of magnitude to uncorrected precipitation [80]. The largest differences between approaches were observed for the probability of dry days and intensity of wet days; LOCI and distribution mapping performed better for these two statistics of daily precipitation [80]. The other approaches partly decreased variability, but were unable to generate RCM predictions closer to observed values [80].