Bias Correction Technique Research Articles

Skill of Subseasonal Forecasts in Europe: Effect of Bias Correction and Downscaling Using Surface Observations

AbstractSubseasonal predictions bridge the gap between medium‐range weather forecasts and seasonal climate predictions. This time horizon is of crucial importance for many planning purposes, including energy production and agriculture. The verification of such predictions is normally done for areal averages of upper‐air parameters. Only few studies exist that verify the forecasts for surface parameters with observational stations, although this is crucial for real‐world applications, which often require such predictions at specific surface locations. With this study we provide an extensive station‐based verification of subseasonal forecasts against 1,637 ground based observational time series across Europe. Twenty years of temperature and precipitation reforecasts of the European Centre for Medium‐Range Weather Forecasts Integrated Forecasting System are used to analyze the period of April 1995 to March 2014. A lead time and seasonally dependent bias correction is performed to correct the daily temperature and precipitation forecasts at all stations individually. Two bias correction techniques are compared, a mean debiasing method and a quantile mapping approach. Commonly used skill scores characterizing different aspects of forecast quality are computed for weekly aggregated forecasts with lead times of 5–32 days. Overall, promising skill is found for temperature in all seasons except spring. Temperature forecasts tend to show higher skill in Northern Europe and in particular around the Baltic Sea, and in winter. Bias correction is shown to be essential in enhancing the forecast skill in all four weeks for most of the stations and for both variables with QM generally performing better.

Multivariate bias corrections of mechanistic water quality model predictions

Water quality networks usually do not include observations on a continuous timescale over a long period. Statistical models that use streamflow and mechanistic models that use meteorological information and land-use are commonly employed to develop continuous streamflow and nutrient records. Given the availability of long meteorological records, mechanistic models have the potential to develop continuous water quality records, but such predictions suffer from systematic biases on both streamflow and water quality constituents. This study proposes a multivariate bias correction technique based on canonical correlation analysis (CCA) – a dimension reduction technique based on multivariate multiple regression – that reduces the bias in both streamflow and loadings simultaneously by preserving the cross-correlation. We compare the performance of CCA with linear regression (LR) in removing the systematic bias from the SWAT model forced with precipitation and temperature for three selected watersheds from the Southeastern US. First, we compare the performance of CCA with LR in removing the bias in SWAT model outputs in predicting the observed streamflow and total nitrogen (TN) loadings from the Water Quality Network (WQN) dataset. We also evaluate the potential of CCA in removing the bias in SWAT model predictions at daily and monthly time scales by considering the LOADEST model predicted loadings as the predictand for CCA and LR. Evaluation of CCA with the observed dataset and at daily and streamflow time scales shows that the proposed multivariate technique not only reduces the bias in the cross-correlation between streamflow and loadings, but also improves the joint probability of estimating observed streamflow and loadings. Potential implications of the proposed bias-correction technique, CCA, in water quality forecasting and management are also discussed.

A new region-aware bias-correction method for simulated precipitation in areas of complex orography

Abstract. Regional climate modelling is used to simulate the hydrological cycle, which is fundamental for climate impact investigations. However, the output of these models is affected by biases that hamper its direct use in impact modelling. Here, we present two high-resolution (2 km) climate simulations of precipitation in the Alpine region, evaluate their performance over Switzerland and develop a new bias-correction technique for precipitation suitable for complex topography. The latter is based on quantile mapping, which is applied separately across a number of non-overlapping regions defined through cluster analysis. This technique allows removing prominent biases while it aims at minimising the disturbances to the physical consistency inherent in all statistical corrections of simulated data. The simulations span the period 1979–2005 and are carried out with the Weather Research and Forecasting model (WRF), driven by the ERA-Interim reanalysis (hereafter WRF-ERA), and the Community Earth System Model (hereafter WRF-CESM). The simulated precipitation is in both cases validated against observations in Switzerland. In a first step, the area is classified into regions of similar temporal variability of precipitation. Similar spatial patterns emerge in all datasets, with a clear northwest–southeast separation following the main orographic features of this region. The daily evolution and the annual cycle of precipitation in WRF-ERA closely reproduces the observations. Conversely, WRF-CESM shows a different seasonality with peak precipitation in winter and not in summer as in the observations or in WRF-ERA. The application of the new bias-correction technique minimises systematic biases in the WRF-CESM simulation and substantially improves the seasonality, while the temporal and physical consistency of simulated precipitation is greatly preserved.

Assessment and Adaptive Correction of Observations in Atmospheric Sounding Channels of the Satellite Microwave Radiometer MTVZA-GY

The microwave radiometer MTVZA-GY on board the Russian polar orbiting meteorological satellite Meteor-M N2 is briefly described. Errors and biases in antenna brightness temperatures are documented. Observation errors are found to be dependent on the solar angles. An adaptive bias correction technique for MTVZA-GY antenna temperatures is motivated and developed. The technique accounts for the solar angles and sequentially assimilates observed minus simulated radiances in a perpetual 24 h cycle in order to estimate up-to-date correction coefficients defined to be functions of the zenith and azimuth solar angles. The simulated radiances are computed by the RTTOV radiative transfer model from three-dimensional numerical weather prediction fields. The correction technique is implemented for atmospheric temperature and humidity sounding channels of MTVZA-GY. The corrected observations are shown to be significantly more accurate as compared with raw antenna temperatures and with observations that undergo simpler and more traditional corrections. The accuracy of corrected MTVZA-GY observations is compared with the accuracy of AMSU-A and MHS data.

Inter-Comparison of Gauge-Corrected Global Satellite Rainfall Estimates and Their Applicability for Effective Water Resource Management in a Transboundary River Basin: The Case of the Meghna River Basin

The Meghna River basin is a transboundary basin that lies in Bangladesh (~40%) and India (~60%). Due to its terrain structure, the Bangladesh portion of the basin experiences frequent floods that cause severe human and economic losses. Bangladesh, as the downstream nation in the basin, faces challenges in receiving hydro-meteorological and water use data from India for effective water resource management. To address such issue, satellite rainfall products are recognized as an alternative. However, they are affected by biases and, thus, must be calibrated and verified using ground observations. This research compares the performance of four widely available gauge-adjusted satellite rainfall products (GSRPs) against ground rainfall observations in the Meghna basin within Bangladesh. Further biases in the GSRPs are then identified. The GSRPs have both similarities and differences in terms of producing biases. To maximize the usage of the GSRPs and to further improve their accuracy, several bias correction and merging techniques are applied to correct them. Correction factors and merging weights are calculated at the local gauge stations and are spatially distributed by adopting an interpolation method to improve the GSRPs, both inside and outside Bangladesh. Of the four bias correction methods, modified linear correction (MLC) has performed better, and partially removed the GSRPs’ systematic biases. In addition, of the three merging techniques, inverse error-variance weighting (IEVW) has provided better results than the individual GSRPs and removed significantly more biases than the MLC correction method for three of the five validation stations, whereas the two other stations that experienced heavy rainfall events, showed better results for the MLC method. Hence, the combined use of IEVW merging and MLC correction is explored. The combined method has provided the best results, thus creating an improved dataset. The applicability of this dataset is then investigated using a hydrological model to simulated streamflows at two critical locations. The results show that the dataset reproduces the hydrological responses of the basin well, as compared with the observed streamflows. Together, these results indicate that the improved dataset can overcome the limitations of poor data availability in the basin and can serve as a reference rainfall dataset for wide range of applications (e.g., flood modelling and forecasting, irrigation planning, damage and risk assessment, and climate change adaptation planning). In addition, the proposed methodology of creating a reference rainfall dataset based on the GSRPs could also be applicable to other poorly-gauged and inaccessible transboundary river basins, thus providing reliable rainfall information and effective water resource management for sustainable development.

Climate change impact projections at the catchment scale in Tunisia using the multi-model ensemble mean approach

In this work, we developed a mean projection for climate change and assessed its impact on some hydro-meteorological indicators relevant to climatic condition, precipitation extremes magnitude and frequency for the Siliana catchment in Tunisia based on an ensemble of seven combinations of global circulation models (GCMs) and regional climate models (RCMs) derived from the EU-FP6 ENSEMBLES project. We performed quantile-based mapping (QM) bias correction technique of climate model projection using local observations. Because there is no warranty that the best climate model based on its performances in reproducing historic climate will be superior to other models in simulating future climate, we used the multi-model ensemble (MME) mean approach to derive a mean projection as the best guess for climate change projection for the Siliana catchment. We also quantified the uncertainty of the MME in the projected change in the selected indicators by comparing their values in the reference period (1981–2010) to these in the future period (2041–2070). Results reveal that the Siliana catchment will be prone to drier and warmer climate in the future with less rainy days for each month. The uncertainty associated with the MME projection suggests that no clear general tendency for extreme rainy days in the future is expected. These findings highlight the need to consider an ensemble of multi-climate models with an uncertainty framework if reliable climate change impact study is sought at the catchment scale.

Investigation of the Behavior of an Agricultural-Operated Dam Reservoir Under RCP Scenarios of AR5-IPCC

In regions where the Mediterranean climate prevails, the agricultural sector and agricultural-operated dam reservoirs are threatened by climate change. In this respect, the prediction of hydro-meteorological changes that may occur in surface water resources under climate change scenarios is essential to examine the sustainability of reservoirs. In this paper, Demirkopru reservoir in the Gediz Basin/Turkey, a reservoir operated for irrigation purposes, was analyzed against the RCP4.5 and RCP 8.5 scenarios specified in the AR5 report of the IPCC. Projection period was evaluated as 2016-2050 water year period. First, statistical downscaling, Bayesian model averaging and quantile delta mapping bias correction techniques were respectively applied to monthly total precipitation and monthly average temperatures of meteorological stations in the region using 12 GCMs. According to RCP4.5 and RCP8.5, negligible reductions in precipitation are foreseen, while significant increases of 1.3 and 1.8 °C, respectively, are projected for temperatures under the same scenarios. Following the calibration of rainfall-runoff models for the sub-basins feeding the reservoir, streamflow simulations were also performed with projected precipitation and temperatures. In particular, according to the RCP 8.5 scenario, reservoir inflows during the period 2016-2050 could be reduced by 21% compared to the reference scenario results. Finally, the projected crop water demands and hydro-meteorological changes are evaluated together and the reservoir performances are examined using various indices. Assuming that the performance of the past irrigation yields will not change in the future, it is foreseen that reservoir’s sustainability will decrease by 16% under the RCP8.5 scenario. Even if the irrigation efficiency is increased by 40%, the reservoir cannot reach past sustainability characteristics.

Climate downscaling over South America for 1971–2000: application in SMAP rainfall-runoff model for Grande River Basin

This paper aims to validate inflow simulations concerning the present-day climate at Agua Vermelha Hydroelectric Plant (AVHP—located on the Grande River Basin) based on the Soil Moisture Accounting Procedure (SMAP) hydrological model. In order to provide rainfall data to the SMAP model, the RegCM regional climate model was also used working with boundary conditions from the MIROC model. Initially, present-day climate simulation performed by RegCM model was analyzed. It was found that, in terms of rainfall, the model was able to simulate the main patterns observed over South America. A bias correction technique was also used and it was essential to reduce mistakes related to rainfall simulation. Comparison between rainfall simulations from RegCM and MIROC showed improvements when the dynamical downscaling was performed. Then, SMAP, a rainfall-runoff hydrological model, was used to simulate inflows at Agua Vermelha Hydroelectric Plant. After calibration with observed rainfall, SMAP simulations were evaluated in two different periods from the one used in calibration. During calibration, SMAP captures the inflow variability observed at AVHP. During validation periods, the hydrological model obtained better results and statistics with observed rainfall. However, in spite of some discrepancies, the use of simulated rainfall without bias correction captured the interannual flow variability. However, the use of bias removal in the simulated rainfall performed by RegCM brought significant improvements to the simulation of natural inflows performed by SMAP. Not only the curve of simulated inflow became more similar to the observed inflow, but also the statistics improved their values. Improvements were also noticed in the inflow simulation when the rainfall was provided by the regional climate model compared to the global model. In general, results obtained so far prove that there was an added value in rainfall when regional climate model was compared to global climate model and that data from regional models must be bias-corrected so as to improve their results.

Bias correction for time series factor models

ABSTRACTIn this paper we work with multivariate time series that follow a Factor Model. In particular, we consider the setting where factors are dominated by highly persistent AutoRegressive (AR) processes and samples that are rather small. Therefore, the factors' AR models are estimated using small sample bias correction techniques. A Monte Carlo study reveals that bias-correcting the AR coefficients of the factors allows to obtain better results in terms of prediction interval coverage. As expected, the simulation shows that bias-correction is more successful for smaller samples. We present the results assuming the AR order and number of factors are known as well as unknown. We also study the advantages of this technique for a set of Industrial Production Indexes of several European countries.

Evaluation of TIGGE Ensemble Forecasts of Precipitation in Distinct Climate Regions in Iran

The application of numerical weather prediction (NWP) products is increasing dramatically. Existing reports indicate that ensemble predictions have better skill than deterministic forecasts. In this study, numerical ensemble precipitation forecasts in the TIGGE database were evaluated using deterministic, dichotomous (yes/no), and probabilistic techniques over Iran for the period 2008–16. Thirteen rain gauges spread over eight homogeneous precipitation regimes were selected for evaluation. The Inverse Distance Weighting and Kriging methods were adopted for interpolation of the prediction values, downscaled to the stations at lead times of one to three days. To enhance the forecast quality, NWP values were post-processed via Bayesian Model Averaging. The results showed that ECMWF had better scores than other products. However, products of all centers underestimated precipitation in high precipitation regions while overestimating precipitation in other regions. This points to a systematic bias in forecasts and demands application of bias correction techniques. Based on dichotomous evaluation, NCEP did better at most stations, although all centers overpredicted the number of precipitation events. Compared to those of ECMWF and NCEP, UKMO yielded higher scores in mountainous regions, but performed poorly at other selected stations. Furthermore, the evaluations showed that all centers had better skill in wet than in dry seasons. The quality of post-processed predictions was better than those of the raw predictions. In conclusion, the accuracy of the NWP predictions made by the selected centers could be classified as medium over Iran, while post-processing of predictions is recommended to improve the quality.

Consistent estimation of polychotomous treatment effects with selection-bias and unobserved heterogeneity using panel data correlated random coefficients model

We estimate multiple treatment effects in presence of selection-bias and response heterogeneity, using panel data. A control function was added to a fixed-effects based correlated random coefficients model. Selection model to create the control function was contrasted between multinomial logit and multinomial probit. For the multinomial logit model, parametric and semi-parametric bias correction techniques, as proposed in Lee (Econometrica 51(2):507–512, 1983), Dubin and McFadden (Econometrica 52(2):345–362, 1984) and Dahl (Econometrica 70(6):2367–2420, 2002) respectively, were implemented. We find that controlling time-varying endogeneity, allowing response heterogeneity, the type of bias correction method and the choice of the selection model, each had significant impact on the estimated treatment effects. Using the case of biologic DMARDs, we show that in the presence of heterogeneity and multiple treatments, the specification of the latent index model should be carefully chosen along with selection bias correction techniques appropriate to the choice of the latent index model. These issues have an important impact on policy. Under one set of assumptions, we may accept a formulary expansion policy on biologic DMARDs to be cost-neutral, while rejecting the same policy as not cost-saving under another set of assumptions.

Can Bias Correction of Regional Climate Model Lateral Boundary Conditions Improve Low-Frequency Rainfall Variability?

Global climate model simulations inherently contain multiple biases that, when used as boundary conditions for regional climate models, have the potential to produce poor downscaled simulations. Removing these biases before downscaling can potentially improve regional climate change impact assessment. In particular, reducing the low-frequency variability biases in atmospheric variables as well as modeled rainfall is important for hydrological impact assessment, predominantly for the improved simulation of floods and droughts. The impact of this bias in the lateral boundary conditions driving the dynamical downscaling has not been explored before. Here the use of three approaches for correcting the lateral boundary biases including mean, variance, and modification of sample moments through the use of a nested bias correction (NBC) method that corrects for low-frequency variability bias is investigated. These corrections are implemented at the 6-hourly time scale on the global climate model simulations to drive a regional climate model over the Australian Coordinated Regional Climate Downscaling Experiment (CORDEX) domain. The results show that the most substantial improvement in low-frequency variability after bias correction is obtained from modifying the mean field, with smaller changes attributed to the variance. Explicitly modifying monthly and annual lag-1 autocorrelations through NBC does not substantially improve low-frequency variability attributes of simulated precipitation in the regional model over a simpler mean bias correction. These results raise questions about the nature of bias correction techniques that are required to successfully gain improvement in regional climate model simulations and show that more complicated techniques do not necessarily lead to more skillful simulation.

Verification and bias correction of ECMWF forecasts for Irish weather stations to evaluate their potential usefulness in grass growth modelling

ABSTRACTTypical weather in Ireland provides conditions favourable for sustaining grass growth throughout most of the year. This affords grass based farming a significant economic advantage due to the low input costs associated with grass production. To optimize the productivity of grass based systems, farmers must manage the resource over short time scales. While research has been conducted into developing predictive grass growth models for Ireland to support on‐farm decision making, short term weather forecasts have not yet been incorporated into these models. To assess their potential for use in predictive grass growth models, deterministic forecasts from the European Centre for Medium‐Range Weather Forecasts (ECMWF) were verified for lead times up to 10 days using observations from 25 Irish weather stations. Forecasts of air temperature variables were generally precise at all lead times, particularly up to 7 days. Verification of ECMWF soil temperature forecasts is limited, but here they were shown to be accurate at all depths and most precise at greater depths such as 50 cm. Rainfall forecasts performed well up to approximately 5 days. Seven bias correction techniques were assessed to minimize systematic biases in the forecasts. Based on the root mean squared error values, no large improvement was identified for rainfall forecasts on equivalent ECMWF forecasts, but the optimum bias corrections improved air and soil temperature forecasts greatly. Overall, the results demonstrated that forecasts predict observations accurately up to approximately a week in advance and therefore could prove valuable in grass growth prediction at farm level in Ireland.

Multivariate generalized Birnbaum—Saunders kernel density estimators

ABSTRACTIn this article, we first propose the classical multivariate generalized Birnbaum–Saunders kernel estimator for probability density function estimation in the context of multivariate non negative data. Then, we apply two multiplicative bias correction (MBC) techniques for multivariate kernel density estimator. Some properties (bias, variance, and mean integrated squared error) of the corresponding estimators are also investigated. Finally, the performances of the classical and MBC estimators based on family of generalized Birnbaum–Saunders kernels are illustrated by a simulation study.

Projections of future rainfall for the upper Ping River Basin using regression-based downscaling

The objective of this study was to use regression modelling, a form of statistical downscaling technique, to predict the daily rainfall occurrence and rainfall amounts for a small river basin, the upper Ping River Basin (UPRB) in northern Thailand. Daily historic (1960–2005) rainfall and a number of daily reanalysis variables (NCEP/NCAR) were used to create regression models that estimate the probabilities of rainfall occurrence (wet days) and amounts (rainfall depth) at each of 29 rain gauge stations located in and around the UPRB. The regression models were calibrated using historic (1960–1989) data and validated using historic (1990–2005) data. Regression models were later applied to historic (1960–2005) GCM outputs (MPI-ESM-LR model) which were adjusted to correspond to the selected reanalysis variables using the Nested Bias Correction (NBC) technique. Rainfall occurrence and amounts were predicted for the periods 2006–2050 and 2051–2100 for RCP2.6, RCP4.5, RCP8.5 scenarios. Results show that the effects of climate change vary considerably across the catchment, with significantly declines in both the number of wet days and rainfall depth in the wet- and especially the dry-season in the middle of the catchment but obviously increase slightly towards the northern part of the catchment. Since the stepwise regression was used to select the atmospheric variables to form the regression models for simulating rainfall occurrence and amount, different stations have their own predictors and can influence future rainfall to vary significantly between 29 rain gauge stations. If the top three predictors were selected to form the regression models for simulating rainfall occurrence and amount for all stations, the future rainfall characteristics possibly change and can be used to compare with those of presented in this study. It will show either atmospheric predictors or climate change scenarios would have more effect on future rainfall characteristics.

A GLOBAL FOOD DEMAND MODEL FOR THE ASSESSMENT OF COMPLEX HUMAN-EARTH SYSTEMS

Demand for agricultural products is an important problem in global change economics. Food consumption will shape and be shaped by global change through interactions with bioenergy and afforestation, two critical issues in meeting international goals. We develop a model of food demand for staple and nonstaple commodities that evolves with changing incomes and prices. The model addresses a long-standing issue in estimating food demands, the evolution of demand relationships across large changes in income and prices. We discuss the model, some of its properties and limitations. We estimate parameter values using pooled cross-sectional-time-series observations and Bayesian Monte Carlo method and cross-validate the model by estimating parameters using a subset of the observations and test its ability to project into the unused observations. Finally, we apply bias correction techniques borrowed from the Earth system modeling community and report results. We find that the demand for food rises rapidly as income initially increases from zero. Demand for staples peaks at under $1000 per person per capita. Nonstaple food demands increase steadily with income. While staples are an inferior good at per capita incomes greater than $1000, we see no evidence that there is a range of per capita income for which staples are Giffen goods.

An effective post-processing of the North American multi-model ensemble (NMME) precipitation forecasts over the continental US

The North American multi-model ensemble (NMME) forecast system provides valuable information for climate variables at different lead times over the globe. A Bayesian ensemble post-processing approach based on Copula functions (COP-EPP) is employed to bias-correct the NMME precipitation forecast from 11 models (totaling 128 ensemble members). The study is conducted over the Continental United States (CONUS) for the hindcast period of 1982–2010 at lead-0, and the forecast period of 2012–2015 at four different lead times of lead-0 to lead-3 and the results are verified using deterministic and probabilistic measures. COP-EPP is compared with a widely-used bias-correction technique, the Quantile Mapping (QM). Although the NMME forecasts show to be more accurate across the eastern United States, large bias is found over the great plains of the central US. However, QM and COP-EPP present significant improvements over the NMME forecasts, with COP-EPP proving to be more reliable and accurate across the CONUS. In addition, COP-EPP substantially improves the temporal and spatial variability of the intra-seasonal NMME forecasts, even at lead-3.

Downscaling RCP8.5 daily temperatures and precipitation in Ontario using localized ensemble optimal interpolation (EnOI) and bias correction

A novel method for daily temperature and precipitation downscaling is proposed in this study which combines the Ensemble Optimal Interpolation (EnOI) and bias correction techniques. For downscaling temperature, the day to day seasonal cycle of high resolution temperature of the NCEP climate forecast system reanalysis (CFSR) is used as background state. An enlarged ensemble of daily temperature anomaly relative to this seasonal cycle and information from global climate models (GCMs) are used to construct a gain matrix for each calendar day. Consequently, the relationship between large and local-scale processes represented by the gain matrix will change accordingly. The gain matrix contains information of realistic spatial correlation of temperature between different CFSR grid points, between CFSR grid points and GCM grid points, and between different GCM grid points. Therefore, this downscaling method keeps spatial consistency and reflects the interaction between local geographic and atmospheric conditions. Maximum and minimum temperatures are downscaled using the same method. For precipitation, because of the non-Gaussianity issue, a logarithmic transformation is used to daily total precipitation prior to conducting downscaling. Cross validation and independent data validation are used to evaluate this algorithm. Finally, data from a 29-member ensemble of phase 5 of the Coupled Model Intercomparison Project (CMIP5) GCMs are downscaled to CFSR grid points in Ontario for the period from 1981 to 2100. The results show that this method is capable of generating high resolution details without changing large scale characteristics. It results in much lower absolute errors in local scale details at most grid points than simple spatial downscaling methods. Biases in the downscaled data inherited from GCMs are corrected with a linear method for temperatures and distribution mapping for precipitation. The downscaled ensemble projects significant warming with amplitudes of 3.9 and 6.5 °C for 2050s and 2080s relative to 1990s in Ontario, respectively; Cooling degree days and hot days will significantly increase over southern Ontario and heating degree days and cold days will significantly decrease in northern Ontario. Annual total precipitation will increase over Ontario and heavy precipitation events will increase as well. These results are consistent with conclusions in many other studies in the literature.

The effect of GCM biases on global runoff simulations of a land surface model

Abstract. Global climate model (GCM) outputs feature systematic biases that render them unsuitable for direct use by impact models, especially for hydrological studies. To deal with this issue, many bias correction techniques have been developed to adjust the modelled variables against observations, focusing mainly on precipitation and temperature. However, most state-of-the-art hydrological models require more forcing variables, in addition to precipitation and temperature, such as radiation, humidity, air pressure, and wind speed. The biases in these additional variables can hinder hydrological simulations, but the effect of the bias of each variable is unexplored. Here we examine the effect of GCM biases on historical runoff simulations for each forcing variable individually, using the JULES land surface model set up at the global scale. Based on the quantified effect, we assess which variables should be included in bias correction procedures. To this end, a partial correction bias assessment experiment is conducted, to test the effect of the biases of six climate variables from a set of three GCMs. The effect of the bias of each climate variable individually is quantified by comparing the changes in simulated runoff that correspond to the bias of each tested variable. A methodology for the classification of the effect of biases in four effect categories (ECs), based on the magnitude and sensitivity of runoff changes, is developed and applied. Our results show that, while globally the largest changes in modelled runoff are caused by precipitation and temperature biases, there are regions where runoff is substantially affected by and/or more sensitive to radiation and humidity. Global maps of bias ECs reveal the regions mostly affected by the bias of each variable. Based on our findings, for global-scale applications, bias correction of radiation and humidity, in addition to that of precipitation and temperature, is advised. Finer spatial-scale information is also provided, to suggest bias correction of variables beyond precipitation and temperature for regional studies.

Multiplicative bias correction for discrete kernels

In this paper, we prove that two multiplicative bias correction techniques (MBC) can be applied for discrete kernels in the context of probability mass function estimation. First, some properties of the MBC discrete kernel estimators (bias, variance and mean integrated squared error) are investigated. Second, the popular cross-validation technique is adapted for bandwidth selection. Finally, a simulation study and a real data application for discrete data illustrate the performance of the MBC estimators based on dirac discrete uniform and triangular discrete kernels.