Multivariate Bias Correction of Climate Model Output: Matching Marginal Distributions and Intervariable Dependence Structure

2016 ◽  
Vol 29 (19) ◽  
pp. 7045-7064 ◽  
Author(s):  
Alex J. Cannon
Keyword(s):  
Bias Correction ◽  
Climate Model ◽  
Pearson Correlation ◽  
Water Vapor Transport ◽  
Dependence Structure ◽  
Model Output ◽  
Quantile Mapping ◽  
Marginal Distributions ◽  
Temperature And Precipitation ◽  
Climate Model Output

Abstract Univariate bias correction algorithms, such as quantile mapping, are used to address systematic biases in climate model output. Intervariable dependence structure (e.g., between different quantities like temperature and precipitation or between sites) is typically ignored, which can have an impact on subsequent calculations that depend on multiple climate variables. A novel multivariate bias correction (MBC) algorithm is introduced as a multidimensional analog of univariate quantile mapping. Two variants are presented. MBCp and MBCr respectively correct Pearson correlation and Spearman rank correlation dependence structure, with marginal distributions in both constrained to match observed distributions via quantile mapping. MBC is demonstrated on two case studies: 1) bivariate bias correction of monthly temperature and precipitation output from a large ensemble of climate models and 2) multivariate correction of vertical humidity and wind profiles, including subsequent calculation of vertically integrated water vapor transport and detection of atmospheric rivers. The energy distance is recommended as an omnibus measure of performance for model selection. As expected, substantial improvements in performance relative to quantile mapping are found in each case. For reference, characteristics of the MBC algorithm are compared against existing bivariate and multivariate bias correction techniques. MBC performs competitively and fills a role as a flexible, general purpose multivariate bias correction algorithm.

scholarly journals Constructing High-Resolution, Bias-Corrected Climate Products: A Comparison of Methods

2021 ◽  
Vol 60 (4) ◽  
pp. 455-475
Author(s):  
Maike F. Holthuijzen ◽  
Brian Beckage ◽  
Patrick J. Clemins ◽  
Dave Higdon ◽  
Jonathan M. Winter
Keyword(s):  
High Resolution ◽  
Bias Correction ◽  
Climate Model ◽  
Maximum Temperature ◽  
Daily Maximum Temperature ◽  
Model Output ◽  
Quantile Mapping ◽  
Station Data ◽  
Climate Model Output ◽  
Mapping Techniques

AbstractHigh-resolution, bias-corrected climate data are necessary for climate impact studies at local scales. Gridded historical data are convenient for bias correction but may contain biases resulting from interpolation. Long-term, quality-controlled station data are generally superior climatological measurements, but because the distribution of climate stations is irregular, station data are challenging to incorporate into downscaling and bias-correction approaches. Here, we compared six novel methods for constructing full-coverage, high-resolution, bias-corrected climate products using daily maximum temperature simulations from a regional climate model (RCM). Only station data were used for bias correction. We quantified performance of the six methods with the root-mean-square-error (RMSE) and Perkins skill score (PSS) and used two ANOVA models to analyze how performance varied among methods. We validated the six methods using two calibration periods of observed data (1980–89 and 1980–2014) and two testing sets of RCM data (1990–2014 and 1980–2014). RMSE for all methods varied throughout the year and was larger in cold months, whereas PSS was more consistent. Quantile-mapping bias-correction techniques substantially improved PSS, while simple linear transfer functions performed best in improving RMSE. For the 1980–89 calibration period, simple quantile-mapping techniques outperformed empirical quantile mapping (EQM) in improving PSS. When calibration and testing time periods were equivalent, EQM resulted in the largest improvements in PSS. No one method performed best in both RMSE and PSS. Our results indicate that simple quantile-mapping techniques are less prone to overfitting than EQM and are suitable for processing future climate model output, whereas EQM is ideal for bias correcting historical climate model output.

scholarly journals Technical Note: The impact of spatial scale in bias correction of climate model output for hydrologic impact studies

2016 ◽  
Vol 20 (2) ◽  
pp. 685-696 ◽  
Author(s):  
E. P. Maurer ◽  
D. L. Ficklin ◽  
W. Wang
Keyword(s):  
Spatial Scale ◽  
Statistical Downscaling ◽  
Bias Correction ◽  
Large Scale ◽  
Climate Model ◽  
Model Output ◽  
Quantile Mapping ◽  
Impact Studies ◽  
Mapping Bias ◽  
Climate Model Output

Abstract. Statistical downscaling is a commonly used technique for translating large-scale climate model output to a scale appropriate for assessing impacts. To ensure downscaled meteorology can be used in climate impact studies, downscaling must correct biases in the large-scale signal. A simple and generally effective method for accommodating systematic biases in large-scale model output is quantile mapping, which has been applied to many variables and shown to reduce biases on average, even in the presence of non-stationarity. Quantile-mapping bias correction has been applied at spatial scales ranging from hundreds of kilometers to individual points, such as weather station locations. Since water resources and other models used to simulate climate impacts are sensitive to biases in input meteorology, there is a motivation to apply bias correction at a scale fine enough that the downscaled data closely resemble historically observed data, though past work has identified undesirable consequences to applying quantile mapping at too fine a scale. This study explores the role of the spatial scale at which the quantile-mapping bias correction is applied, in the context of estimating high and low daily streamflows across the western United States. We vary the spatial scale at which quantile-mapping bias correction is performed from 2° ( ∼  200 km) to 1∕8° ( ∼  12 km) within a statistical downscaling procedure, and use the downscaled daily precipitation and temperature to drive a hydrology model. We find that little additional benefit is obtained, and some skill is degraded, when using quantile mapping at scales finer than approximately 0.5° ( ∼  50 km). This can provide guidance to those applying the quantile-mapping bias correction method for hydrologic impacts analysis.

scholarly journals Technical Note: The impact of spatial scale in bias correction of climate model output for hydrologic impact studies

2015 ◽  
Vol 12 (10) ◽  
pp. 10893-10920 ◽  
Author(s):  
E. P. Maurer ◽  
D. L. Ficklin ◽  
W. Wang
Keyword(s):  
Spatial Scale ◽  
Statistical Downscaling ◽  
Bias Correction ◽  
Large Scale ◽  
Climate Model ◽  
Model Output ◽  
Quantile Mapping ◽  
Impact Studies ◽  
Mapping Bias ◽  
Climate Model Output

Abstract. Statistical downscaling is a commonly used technique for translating large-scale climate model output to a scale appropriate for assessing impacts. To ensure downscaled meteorology can be used in climate impact studies, downscaling must correct biases in the large-scale signal. A simple and generally effective method for accommodating systematic biases in large-scale model output is quantile mapping, which has been applied to many variables and shown to reduce biases on average, even in the presence of non-stationarity. Quantile mapping bias correction has been applied at spatial scales ranging from areas of hundreds of kilometers to individual points, such as weather station locations. Since water resources and other models used to simulate climate impacts are sensitive to biases in input meteorology, there is a motivation to apply bias correction at a scale fine enough that the downscaled data closely resembles historically observed data, though past work has identified undesirable consequences to applying quantile mapping at too fine a scale. This study explores the role of the spatial scale at which the quantile-mapping bias correction is applied, in the context of estimating high and low daily streamflows across the Western United States. We vary the spatial scale at which quantile mapping bias correction is performed from 2° (∼ 200 km) to 1/8° (∼ 12 km) within a statistical downscaling procedure, and use the downscaled daily precipitation and temperature to drive a hydrology model. We find that little additional benefit is obtained, and some skill is degraded, when using quantile mapping at scales finer than approximately 0.5° (∼ 50 km). This can provide guidance to those applying the quantile mapping bias correction method for hydrologic impacts analysis.

scholarly journals Multivariate bias adjustment of high-dimensional climate simulations: the Rank Resampling for Distributions and Dependences (R<sup>2</sup>D<sup>2</sup>) bias correction

2018 ◽  
Vol 22 (6) ◽  
pp. 3175-3196 ◽  
Author(s):  
Mathieu Vrac
Keyword(s):  
Bias Correction ◽  
Climate Model ◽  
Regional Climate ◽  
Grid Cell ◽  
Dependence Structure ◽  
Historical Period ◽  
Temporal Properties ◽  
Temperature And Precipitation ◽  
Climate Simulations ◽  
Site Dependence

Abstract. Climate simulations often suffer from statistical biases with respect to observations or reanalyses. It is therefore common to correct (or adjust) those simulations before using them as inputs into impact models. However, most bias correction (BC) methods are univariate and so do not account for the statistical dependences linking the different locations and/or physical variables of interest. In addition, they are often deterministic, and stochasticity is frequently needed to investigate climate uncertainty and to add constrained randomness to climate simulations that do not possess a realistic variability. This study presents a multivariate method of rank resampling for distributions and dependences (R2D2) bias correction allowing one to adjust not only the univariate distributions but also their inter-variable and inter-site dependence structures. Moreover, the proposed R2D2 method provides some stochasticity since it can generate as many multivariate corrected outputs as the number of statistical dimensions (i.e., number of grid cell  ×  number of climate variables) of the simulations to be corrected. It is based on an assumption of stability in time of the dependence structure – making it possible to deal with a high number of statistical dimensions – that lets the climate model drive the temporal properties and their changes in time. R2D2 is applied on temperature and precipitation reanalysis time series with respect to high-resolution reference data over the southeast of France (1506 grid cell). Bivariate, 1506-dimensional and 3012-dimensional versions of R2D2 are tested over a historical period and compared to a univariate BC. How the different BC methods behave in a climate change context is also illustrated with an application to regional climate simulations over the 2071–2100 period. The results indicate that the 1d-BC basically reproduces the climate model multivariate properties, 2d-R2D2 is only satisfying in the inter-variable context, 1506d-R2D2 strongly improves inter-site properties and 3012d-R2D2 is able to account for both. Applications of the proposed R2D2 method to various climate datasets are relevant for many impact studies. The perspectives of improvements are numerous, such as introducing stochasticity in the dependence itself, questioning its stability assumption, and accounting for temporal properties adjustment while including more physics in the adjustment procedures.

scholarly journals Does Quantile Mapping of Simulated Precipitation Correct for Biases in Transition Probabilities and Spell Lengths?

2016 ◽  
Vol 29 (5) ◽  
pp. 1605-1615 ◽  
Author(s):  
Jan Rajczak ◽  
Sven Kotlarski ◽  
Christoph Schär
Keyword(s):  
Climate Models ◽  
Climate Model ◽  
Transition Probabilities ◽  
Weather Generator ◽  
Mapping Technique ◽  
Model Output ◽  
Quantile Mapping ◽  
Stochastic Weather Generator ◽  
Simulated Precipitation ◽  
Climate Model Output

Abstract Climate impact studies constitute the basis for the formulation of adaptation strategies. Usually such assessments apply statistically postprocessed output of climate model projections to force impact models. Increasingly, time series with daily resolution are used, which require high consistency, for instance with respect to transition probabilities (TPs) between wet and dry days and spell durations. However, both climate models and commonly applied statistical tools have considerable uncertainties and drawbacks. This paper compares the ability of 1) raw regional climate model (RCM) output, 2) bias-corrected RCM output, and 3) a conventional weather generator (WG) that has been calibrated to match observed TPs to simulate the sequence of dry, wet, and very wet days at a set of long-term weather stations across Switzerland. The study finds systematic biases in TPs and spell lengths for raw RCM output, but a substantial improvement after bias correction using the deterministic quantile mapping technique. For the region considered, bias-corrected climate model output agrees well with observations in terms of TPs as well as dry and wet spell durations. For the majority of cases (models and stations) bias-corrected climate model output is similar in skill to a simple Markov chain stochastic weather generator. There is strong evidence that bias-corrected climate model simulations capture the atmospheric event sequence more realistically than a simple WG.

scholarly journals Scaled distribution mapping: a bias correction method that preserves raw climate model projected changes

2017 ◽  
Vol 21 (6) ◽  
pp. 2649-2666 ◽  
Author(s):  
Matthew B. Switanek ◽  
Peter A. Troch ◽  
Christopher L. Castro ◽  
Armin Leuprecht ◽  
Hsin-I Chang ◽  
...  
Keyword(s):  
Error Correction ◽  
Bias Correction ◽  
Climate Model ◽  
Correction Method ◽  
Climate Change Signal ◽  
Quantile Mapping ◽  
Temperature And Precipitation ◽  
Distribution Mapping ◽  
Projected Changes ◽  
Time Invariant

Abstract. Commonly used bias correction methods such as quantile mapping (QM) assume the function of error correction values between modeled and observed distributions are stationary or time invariant. This article finds that this function of the error correction values cannot be assumed to be stationary. As a result, QM lacks justification to inflate/deflate various moments of the climate change signal. Previous adaptations of QM, most notably quantile delta mapping (QDM), have been developed that do not rely on this assumption of stationarity. Here, we outline a methodology called scaled distribution mapping (SDM), which is conceptually similar to QDM, but more explicitly accounts for the frequency of rain days and the likelihood of individual events. The SDM method is found to outperform QM, QDM, and detrended QM in its ability to better preserve raw climate model projected changes to meteorological variables such as temperature and precipitation.

scholarly journals Impact of a Statistical Bias Correction on the Projected Hydrological Changes Obtained from Three GCMs and Two Hydrology Models

2011 ◽  
Vol 12 (4) ◽  
pp. 556-578 ◽  
Author(s):  
Stefan Hagemann ◽  
Cui Chen ◽  
Jan O. Haerter ◽  
Jens Heinke ◽  
Dieter Gerten ◽  
...  
Keyword(s):  
Bias Correction ◽  
Climate Model ◽  
Hydrological Cycle ◽  
Coupled Model ◽  
Model Output ◽  
Hydrological Models ◽  
Statistical Bias ◽  
Max Planck ◽  
Climate Model Output ◽  
Statistical Bias Correction

Abstract Future climate model scenarios depend crucially on the models’ adequate representation of the hydrological cycle. Within the EU integrated project Water and Global Change (WATCH), special care is taken to use state-of-the-art climate model output for impacts assessments with a suite of hydrological models. This coupling is expected to lead to a better assessment of changes in the hydrological cycle. However, given the systematic errors of climate models, their output is often not directly applicable as input for hydrological models. Thus, the methodology of a statistical bias correction has been developed for correcting climate model output to produce long-term time series with a statistical intensity distribution close to that of the observations. As observations, global reanalyzed daily data of precipitation and temperature were used that were obtained in the WATCH project. Daily time series from three GCMs (GCMs) ECHAM5/Max Planck Institute Ocean Model (MPI-OM), Centre National de Recherches Météorologiques Coupled GCM, version 3 (CNRM-CM3), and the atmospheric component of the L’Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL CM4) coupled model (called LMDZ-4)—were bias corrected. After the validation of the bias-corrected data, the original and the bias-corrected GCM data were used to force two global hydrology models (GHMs): 1) the hydrological model of the Max Planck Institute for Meteorology (MPI-HM) consisting of the simplified land surface (SL) scheme and the hydrological discharge (HD) model, and 2) the dynamic global vegetation model called LPJmL. The impact of the bias correction on the projected simulated hydrological changes is analyzed, and the simulation results of the two GHMs are compared. Here, the projected changes in 2071–2100 are considered relative to 1961–90. It is shown for both GHMs that the usage of bias-corrected GCM data leads to an improved simulation of river runoff for most catchments. But it is also found that the bias correction has an impact on the climate change signal for specific locations and months, thereby identifying another level of uncertainty in the modeling chain from the GCM to the simulated changes calculated by the GHMs. This uncertainty may be of the same order of magnitude as uncertainty related to the choice of the GCM or GHM. Note that this uncertainty is primarily attached to the GCM and only becomes obvious by applying the statistical bias correction methodology.

scholarly journals Bias correction of temperature and precipitation over China for RCM simulations using the QM and QDM methods

2020 ◽  
Author(s):  
Yao Tong ◽  
Xuejie Gao ◽  
Zhenyu Han ◽  
Yaqi Xu ◽  
Ying Xu ◽  
...  
Keyword(s):  
Bias Correction ◽  
General Circulation ◽  
Climate Model ◽  
Regional Climate ◽  
General Circulation Models ◽  
Grid Spacing ◽  
Quantile Mapping ◽  
Temperature And Precipitation ◽  
June July August ◽  
June July

Abstract Two different bias correction methods, the quantile mapping (QM) and quantile delta mapping (QDM), are applied to simulated daily temperature and precipitation over China from a set of 21st century regional climate model (the ICTP RegCM4) projections. The RegCM4 is driven by five different general circulation models (GCMs) under the representative concentration pathway RCP4.5 at a grid spacing of 25 km using the CORDEX East Asia domain. The focus is on mean temperature and precipitation in December–January–February (DJF) and June–July–August (JJA). The impacts of the two methods on the present day biases and future change signals are investigated. Results show that both the QM and QDM methods are effective in removing the systematic model biases during the validation period. For the future changes, the QDM preserves the temperature change signals well, in both magnitude and spatial distribution, while the QM artificially modifies the change signal by decreasing the warming and modifying the patterns of change. For precipitation, both methods preserve the change signals well but they produce greater magnitude of the projected increase, especially the QDM. We also show that the effects of bias correction are variable- and season-dependent. Our results show that different bias correction methods can affect in different way the simulated change signals, and therefore care has to be taken in carrying out the bias correction process.

scholarly journals Adjusting spatial dependence of climate model outputs with cycle-consistent adversarial networks

2021 ◽  
Author(s):  
Bastien François ◽  
Soulivanh Thao ◽  
Mathieu Vrac
Keyword(s):  
Bias Correction ◽  
Spatial Dependence ◽  
Climate Model ◽  
Correction Method ◽  
Mapping Method ◽  
Dependence Structure ◽  
Spatial Correlations ◽  
Temperature And Precipitation ◽  
Climate Simulations ◽  
Spatial Correlation Structure

AbstractClimate model outputs are commonly corrected using statistical univariate bias correction methods. Most of the time, those 1d-corrections do not modify the ranks of the time series to be corrected. This implies that biases in the spatial or inter-variable dependences of the simulated variables are not adjusted. Hence, over the last few years, some multivariate bias correction (MBC) methods have been developed to account for inter-variable structures, inter-site ones, or both. As proof-of-concept, we propose to adapt a computer vision technique used for Image-to-Image translation tasks (CycleGAN) for the adjustment of spatial dependence structures of climate model projections. The proposed algorithm, named MBC-CycleGAN, aims to transfer simulated maps (seen as images) with inappropriate spatial dependence structure from climate model outputs to more realistic images with spatial properties similar to the observed ones. For evaluation purposes, the method is applied to adjust maps of temperature and precipitation from climate simulations through two cross-validation approaches. The first one is designed to assess two different post-processing schemes (Perfect Prognosis and Model Output Statistics). The second one assesses the influence of nonstationary properties of climate simulations on the performance of MBC-CycleGAN to adjust spatial dependences. Results are compared against a popular univariate bias correction method, a “quantile-mapping” method, which ignores inter-site dependencies in the correction procedure, and two state-of-the-art multivariate bias correction algorithms aiming to adjust spatial correlation structure. In comparison with these alternatives, the MBC-CycleGAN algorithm reasonably corrects spatial correlations of climate simulations for both temperature and precipitation, encouraging further research on the improvement of this approach for multivariate bias correction of climate model projections.

scholarly journals Multivariate bias adjustment of high-dimensional climate simulations: The Rank Resampling for Distributions and Dependences (R<sup>2</sup>D<sup>2</sup>) Bias Correction

2018 ◽  
Author(s):  
Mathieu Vrac
Keyword(s):  
Bias Correction ◽  
Climate Model ◽  
Regional Climate ◽  
Dependence Structure ◽  
Historical Period ◽  
Grid Cells ◽  
Temporal Properties ◽  
Temperature And Precipitation ◽  
Climate Simulations ◽  
Site Dependence

Abstract. Climate simulations often suffer from statistical biases with respect to observations or reanalyses. It is therefore common to correct (or adjust) those simulations before using them as inputs into impact models. However, most bias correction (BC) methods are univariate and so do not account for the statistical dependences linking the different locations and/or physical variables of interest. In addition, they are often deterministic, while stochasticity is frequently needed to investigate climate uncertainty and to add constrained randomness to climate simulations that do not possess a realistic variability. This study presents a multivariate method of rank resampling for distributions and dependences (R2D2) bias correction allowing to adjust not only the univariate distributions, but also their inter-variable and inter-site dependence structures. Moreover, the proposed R2D2 method provides some stochasticity since it can generate as many multivariate corrected outputs as the number of statistical dimensions (i.e., number of grid-cells × number of climate variables) of the simulations to be corrected. It is based on an assumption of stability in time of the dependence structure – allowing to deal with a high number of statistical dimensions –, that lets the climate model drive the temporal properties and their changes in time. R2D2 is applied on temperature and precipitation reanalyses time series with respect to high-resolution reference data over South-East of France (1506 grid-cells). Bivariate, 1506-dimensional and 3012-dimensional versions of R2D2 are tested over a historical period and compared to a univariate BC. How the different BC methods behave in a climate change context is also illustrated with an application to regional climate simulations over the 2071–2100 period. The results indicate that the 1d-BC basically reproduces the climate model multivariate properties, 2d-R2D2 is only satisfying in the inter-variable context, 1506d-R2D2 strongly improves inter-site properties and 3012d-R2D2 is able to account for both. Applications of the proposed R2D2 method to various climate datasets are relevant for many impact studies. The perspectives of improvements are numerous, such as introducing stochasticity in the dependence itself, questioning its stability assumption, and accounting for temporal properties adjustment while including more physics in the adjustment procedures.

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