Cumulative Distribution Function Transformation Research Articles

Response of Matching Degree between Precipitation and Maize Water Requirement to Climate Change in China

The synchronicity of rain and heat in the summer of China’s monsoon region provides sufficient water and heat resources for maize growth. However, the intra-annual distribution of precipitation and the probability of extreme precipitation have been inevitably altered by the ongoing climate change, thus affecting the matching degree between precipitation and crop water requirements (MDPCWR). Evaluating the extent to which the MDPCWR will change in the future is of great importance for food security and the sustainable management of water resources. In this study, considering that different growth stages of crops have different sensitivities to water stress, the AquaCrop model was used to calculate the MDPCWR more accurately. In addition, a cumulative distribution function-transform (CDF-t) method was used to remove the bias of 11 global climate models (GCMs) under two typical emission scenarios (SSP2-4.5 and SSP5-8.5) from phase six of the Coupled Model Intercomparison Project (CMIP6). A comprehensive investigation was conducted on how maize growth, water consumption, and the MDPCWR will respond to future climate change with CO2 concentration enrichment in the Huang–Huai–Hai (3H) region in China by driving a well-tested AquaCrop model with the bias-corrected GCMs outputs. The results indicate the following: (1) The CDF-t method can effectively remove seasonal bias, and it also performs well in eliminating the bias of extreme climate events. (2) Under the SSP2-4.5 scenario, the average maximum temperature will increase by 1.31 °C and 2.44 °C in 2021–2050 and 2051–2080, respectively. The average annual precipitation will increase up to 96.8 mm/year, but it will mainly occur in the form of heavy rain. (3) The increased maize evapotranspiration rate does not compensate for the decreased crop water requirement (up to −32 mm/year), due to a shorter growth cycle. (4) The farmland cultivation layer is not able to hold a significant amount of precipitation, due to the increased frequency of heavy rains, resulting in increased irrigation water requirements for maize over the next two periods, with the maximum value of 12 mm/year. (5) Under different scenarios, the projected future MDPCWR will decrease by 9.3–11.6% due to changes in precipitation patterns and crop water requirements, indicating that it will be more difficult for precipitation to meet the water demand of maize growing in the 3H region. The results can provide comprehensive information to understand the impact of climate change on the agricultural water balance and improve the regional strategy for water resource utilization in the 3H region.

Bias-Corrected CMIP5 Projections for Climate Change and Assessments of Impact on Malaria in Senegal under the VECTRI Model.

On the climate-health issue, studies have already attempted to understand the influence of climate change on the transmission of malaria. Extreme weather events such as floods, droughts, or heat waves can alter the course and distribution of malaria. This study aims to understand the impact of future climate change on malaria transmission using, for the first time in Senegal, the ICTP's community-based vector-borne disease model, TRIeste (VECTRI). This biological model is a dynamic mathematical model for the study of malaria transmission that considers the impact of climate and population variability. A new approach for VECTRI input parameters was also used. A bias correction technique, the cumulative distribution function transform (CDF-t) method, was applied to climate simulations to remove systematic biases in the Coupled Model Intercomparison Project Phase 5 (CMIP5) global climate models (GCMs) that could alter impact predictions. Beforehand, we use reference data for validation such as CPC global unified gauge-based analysis of daily precipitation (CPC for Climate Prediction Center), ERA5-land reanalysis, Climate Hazards InfraRed Precipitation with Station data (CHIRPS), and African Rainfall Climatology 2.0 (ARC2). The results were analyzed for two CMIP5 scenarios for the different time periods: assessment: 1983-2005; near future: 2006-2028; medium term: 2030-2052; and far future: 2077-2099). The validation results show that the models reproduce the annual cycle well. Except for the IPSL-CM5B model, which gives a peak in August, all the other models (ACCESS1-3, CanESM2, CSIRO, CMCC-CM, CMCC-CMS, CNRM-CM5, GFDL-CM3, GFDL-ESM2G, GFDL-ESM2M, inmcm4, and IPSL-CM5B) agree with the validation data on a maximum peak in September with a period of strong transmission in August-October. With spatial variation, the CMIP5 model simulations show more of a difference in the number of malaria cases between the south and the north. Malaria transmission is much higher in the south than in the north. However, the results predicted by the models on the occurrence of malaria by 2100 show differences between the RCP8.5 scenario, considered a high emission scenario, and the RCP4.5 scenario, considered an intermediate mitigation scenario. The CanESM2, CMCC-CM, CMCC-CMS, inmcm4, and IPSL-CM5B models predict decreases with the RCP4.5 scenario. However, ACCESS1-3, CSIRO, NRCM-CM5, GFDL-CM3, GFDL-ESM2G, and GFDL-ESM2M predict increases in malaria under all scenarios (RCP4.5 and RCP8.5). The projected decrease in malaria in the future with these models is much more visible in the RCP8.5 scenario. The results of this study are of paramount importance in the climate-health field. These results will assist in decision-making and will allow for the establishment of preventive surveillance systems for local climate-sensitive diseases, including malaria, in the targeted regions of Senegal.

Projected Future Flooding Pattern of Wabash River in Indiana and Fountain Creek in Colorado: An Assessment Utilizing Bias-Corrected CMIP6 Climate Data

Climate change is considered one of the biggest challenges around the globe as it has been causing alterations in hydrological extremes. Climate change and variability have an impact on future streamflow conditions, water quality, and ecological balance, which are further aggravated by anthropogenic activities such as changes in land use. This study intends to provide insight into potential changes in future streamflow conditions leading to changes in flooding patterns. Flooding is an inevitable, frequently occurring natural event that affects the environment and the socio-economic structure of its surroundings. This study evaluates the flooding pattern and inundation mapping of two different rivers, Wabash River in Indiana and Fountain Creek in Colorado, using the observed gage data and different climate models. The Coupled Model Intercomparison Project Phase 6 (CMIP6) streamflow data are considered for the future forecast of the flood. The cumulative distribution function transformation (CDF-t) method is used to correct bias in the CMIP6 streamflow data. The Generalized Extreme Value (L-Moment) method is used for the estimation of the frequency of flooding for 100-year and 500-year return periods. Civil GeoHECRAS is used for each flood event to map flood extent and examine flood patterns. The findings from this study show that there will be a rapid increase in flooding events even in small creeks soon in the upcoming years. This study seeks to assist floodplain managers in strategic planning to adopt state-of-the-art information and provide a sustainable strategy to regions with similar difficulties for floodplain management, to improve socioeconomic life, and to promote environmental sustainability.

A support vector machine-based method for improving real-time hourly precipitation forecast in Japan

• Improved real-time hourly precipitation forecast accuracy using machine learning. • Investigated the use of CDF-transform for short-range forecast bias correction. • Provided forcing data for the next step to enhance flood early warning accuracy. Real-time precipitation forecast facilitates water management and water-associated disaster early warning. However, numerical weather prediction (NWP) models provide precipitation forecasts with bias. This study proposed to combine support vector machine (SVM) regression with quantile-based bias correction method to improve real-time 39-hour precipitation forecasts in Japan. Five methods were compared and evaluated against observations, which include SVM regression, quantile mapping (QM), cumulative distribution function transform (CDFt), and the combination of SVM and QM (or CDFt). Results indicated that the combination of SVM and CDFt (i.e., SVM-CDFt) generally provided the highest accuracy with good computational efficiency. SVM alone improved the spatial representation of hourly precipitation with a correlation coefficient increased from 0.387 to 0.490 in January and from 0.235 to 0.296 in July in the cross-validation experiment. However, SVM underestimated the variability of hourly precipitation and heavy precipitation events. QM and CDFt perform well in correcting the bias in modeled precipitation, while they have limited capability in correcting the rainband location. Combining SVM and quantile-based method took advantage of both approaches, providing a more consistent variability with observations and better predicted extreme precipitation events, although overestimation of rainfall area was witnessed. The simple concept, high computational efficiency, as well as evident improvement in forecast accuracy make the combined cases, especially the SVM-CDFt method, beneficial for real-time precipitation forecast and flood early warning.

The optimal bias correction for daily extreme precipitation indices over the Yangtze-Huaihe River Basin, insight from BCC-CSM1.1-m

Due to the considerable biases of model simulation, bias correction is a widely used method to reduce the model biases. It is necessary to evaluate the performance of multiple bias corrections before selecting the optimal one. In this study, four statistical bias correction methods, i.e., the linear scaling (LS), quantile mapping (QM), distribution mapping (DM), and cumulative distribution function transform (CDFt), are introduced to correct the simulated of daily precipitation in Yangtze-Huaihe River Basin (YRB) in China from BCC-CSM1.1-m model. Furthermore, we evaluate their performance in reproducing the probability distribution of observed summer daily precipitation as well as the precipitation extremes. Results show that BCC-CSM1.1-m exhibits systematic biases in simulating the daily precipitation, especially for the tail of the distribution. The bias corrected simulation can significantly reduce the systematic biases. Among them, QM has the most significant improvement in simulating the probability distributions of daily precipitation with Brier scores (BS) dropping to 0 and while the significance scores (Sscore) rise to 1 quickly. For the domain averages and spatial consistency of extreme precipitation, QM, CDFt, and LS have well simulation capabilities in the total precipitation and moderate rainy days. Meanwhile, only QM can reduce the biases of the rainfall days, precipitation intensity, and 95% quantile precipitation simultaneously. For example, the relative errors for 95% quantile precipitation are reduced from −57.8% in raw simulation to −2.76% in bias corrected simulation, and the spatial correlation coefficients are increased from −0.12 to 0.64. It is noted that the continuous dry days, are failed to be well corrected. The DM, based on the Gamma distribution, is less effective in characterizing the probability distribution of model-simulated precipitation, especially for the heavy precipitation. We believe that the QM and CDFt are the optimal methods used for applying the bias corrections in the extreme precipitation in the YRB.

Superensembles of raw and bias‐adjusted regional climate models for Mediterranean region, Turkey

AbstractFor regional‐scale studies on climate change and relevant impact assessment, the projections of regional climate models (RCMs) are used due to their advantage of high resolution and better representation of the local climate relative to the global climate models. However, direct use of RCM outputs is prone to uncertainties and biases that may significantly diminish the accuracy of results. EURO‐COordinated Regional Downscaling EXperiment (CORDEX) initiative that is a part of the global Coordinated Regional Downscaling Experiment Project provides high‐resolution RCM projections for the European domain and bias‐adjusted regional projections under the “CORDEX‐Adjust” Project for climate change impact assessment studies. This study aims to perform a multi‐model analysis of precipitation data using bias‐adjusted and raw/non‐bias adjusted CORDEX RCMs to obtain an evaluation of their representativeness for local climate conditions and adequacy to be used for climate change impact assessment. For this purpose, the analysis focuses on four CORDEX RCMs and their 12 bias‐adjusted versions generated with cumulative distribution function transformation, quantile mapping, and distribution‐based scaling methodologies. For the analysis in total, 16 hindcast results of raw and bias‐adjusted RCMs, and three superensembles (SEs) generated through multiple linear regression are compared for their performance regarding their goodness of fit to the ground‐based precipitation monitoring data from eight meteorological stations in the Mediterranean region in Turkey. The analysis verified that the skill of individual simulations including the bias‐adjusted outputs is significantly variable in spatial and temporal means. On the other hand, SE formed by using all 16 hindcast outputs has the highest skill for the representation of variability in precipitation in time as well as for the reproduction of annual climatology at all stations, although potential drawbacks concerning seasonality and the range of anomaly may still exist which might be significant depending on the specific aim of impact assessment.

Forecasting of Future Flooding and Risk Assessment under CMIP6 Climate Projection in Neuse River, North Carolina

Hydrological extremes associated with climate change are becoming an increasing concern all over the world. Frequent flooding, one of the extremes, needs to be analyzed while considering climate change to mitigate flood risk. This study forecast streamflow and evaluate risk of flooding in the Neuse River, North Carolina considering future climatic scenarios, and comparing them with an existing Federal Emergency Management Agency study. The cumulative distribution function transformation method was adopted for bias correction to reduce the uncertainty present in the Coupled Model Intercomparison Project Phase 6 (CMIP6) streamflow data. To calculate 100-year and 500-year flood discharges, the Generalized Extreme Value (L-Moment) was utilized on bias-corrected multimodel ensemble data with different climate projections. Out of all projections, shared socio-economic pathways (SSP5-8.5) exhibited the maximum design streamflow, which was routed through a hydraulic model, the Hydrological Engineering Center’s River Analysis System (HEC-RAS), to generate flood inundation and risk maps. The result indicates an increase in flood inundation extent compared to the existing study, depicting a higher flood hazard and risk in the future. This study highlights the importance of forecasting future flood risk and utilizing the projected climate data to obtain essential information to determine effective strategic plans for future floodplain management.

An intercomparison of multiple statistical downscaling methods for daily precipitation and temperature over China: present climate evaluations

In this study, we use four statistical downscaling methods to statistically downscale seven Coupled Model Intercomparison Project (CMIP5) Global Climate Models (GCMs) and project the changes in precipitation and temperature over China under RCP4.5 and RCP8.5 emission scenarios. The four statistical downscaling methods are bias-correction and spatial downscaling (BCSD), bias-correction and climate imprint (BCCI), bias correction constructed analogues with quantile mapping reordering (BCCAQ), and cumulative distribution function transform (CDF-t). Though large inter-model variability exists in the distribution and magnitude of changes in projected precipitation, particularly for wet spell length (CWD), all downscaling methods generally project a consistent enhancement of precipitation in both summer and winter over most parts of China. For the arid and semiarid Northwest China, the shortened dry spell length (CDD) is accompanied by the pronouncedly intensified very wet days (R95p), as well as the increase in maximum 5-day precipitation amount (Rx5day). In contrast, southeastern regions may experience more consecutive dry days and more severe wet precipitation extremes. The projected changes from different downscaling techniques are fairly similar for temperature, apart from the diurnal temperature range for BCSD. Warming is projected across the whole domain with larger magnitude over the north and in winter under RCP8.5. More summer days and fewer frost days would appear in the future. The bias correction components of downscaling methods cause a higher degree of agreement among models, and the downscaled results generally retain the main climate change signal of the driving models.

Evaluation and improvement of tail behaviour in the cumulative distribution function transform downscaling method

The cumulative distribution function transform (CDFt) downscaling method has been used widely to provide local‐scale information and bias correction to output from physical climate models. The CDFt approach is one from the category of statistical downscaling methods that operates via transformations between statistical distributions. Although numerous studies have demonstrated that such methods provide value overall, much less effort has focused on their performance with regard to values in the tails of distributions. We evaluate the performance of CDFt‐generated tail values based on four distinct approaches, two native to CDFt and two of our own creation, in the context of a “Perfect Model” setting in which global climate model output is used as a proxy for both observational and model data. We find that the native CDFt approaches can have sub‐optimal performance in the tails, particularly with regard to the maximum value. However, our alternative approaches provide substantial improvement.

A bias-corrected CMIP5 dataset for Africa using the CDF-t method – a contribution to agricultural impact studies

Abstract. The objective of this paper is to present a new dataset of bias-corrected CMIP5 global climate model (GCM) daily data over Africa. This dataset was obtained using the cumulative distribution function transform (CDF-t) method, a method that has been applied to several regions and contexts but never to Africa. Here CDF-t has been applied over the period 1950–2099 combining Historical runs and climate change scenarios for six variables: precipitation, mean near-surface air temperature, near-surface maximum air temperature, near-surface minimum air temperature, surface downwelling shortwave radiation, and wind speed, which are critical variables for agricultural purposes. WFDEI has been used as the reference dataset to correct the GCMs. Evaluation of the results over West Africa has been carried out on a list of priority user-based metrics that were discussed and selected with stakeholders. It includes simulated yield using a crop model simulating maize growth. These bias-corrected GCM data have been compared with another available dataset of bias-corrected GCMs using WATCH Forcing Data as the reference dataset. The impact of WFD, WFDEI, and also EWEMBI reference datasets has been also examined in detail. It is shown that CDF-t is very effective at removing the biases and reducing the high inter-GCM scattering. Differences with other bias-corrected GCM data are mainly due to the differences among the reference datasets. This is particularly true for surface downwelling shortwave radiation, which has a significant impact in terms of simulated maize yields. Projections of future yields over West Africa are quite different, depending on the bias-correction method used. However all these projections show a similar relative decreasing trend over the 21st century.

Improved Bias Correction Techniques for Hydrological Simulations of Climate Change*

Abstract Global climate model (GCM) output typically needs to be bias corrected before it can be used for climate change impact studies. Three existing bias correction methods, and a new one developed here, are applied to daily maximum temperature and precipitation from 21 GCMs to investigate how different methods alter the climate change signal of the GCM. The quantile mapping (QM) and cumulative distribution function transform (CDF-t) bias correction methods can significantly alter the GCM’s mean climate change signal, with differences of up to 2°C and 30% points for monthly mean temperature and precipitation, respectively. Equidistant quantile matching (EDCDFm) bias correction preserves GCM changes in mean daily maximum temperature but not precipitation. An extension to EDCDFm termed PresRat is introduced, which generally preserves the GCM changes in mean precipitation. Another problem is that GCMs can have difficulty simulating variance as a function of frequency. To address this, a frequency-dependent bias correction method is introduced that is twice as effective as standard bias correction in reducing errors in the models’ simulation of variance as a function of frequency, and it does so without making any locations worse, unlike standard bias correction. Last, a preconditioning technique is introduced that improves the simulation of the annual cycle while still allowing the bias correction to take account of an entire season’s values at once.

A new method to improve estimation of uncertain parameters in the Ensemble Kalman filter by re-parameterization employing prior statistics correction

The Ensemble Kalman Filter (EnKF) is a Monte Carlo based method to assimilate the measurement data sequentially in time. Although, EnKF has some advantages over the other Kalman based methods to deal with non-linear and/or high dimensional reservoir models, it also suffers from deficiency in estimation of non-Gaussian parameters. In this work, we propose a re-parameterization method to handle non-Gaussian parameters via Ensemble Kalman Filter framework. For this purpose, concept of cumulative distribution function transformation has been used. In addition, the statistics of prior information have been aggregated in the state vector in order to capture the prior uncertainties of non-Gaussian parameters. To evaluate the performance of the new method, three estimation examples have been implemented. These examples are designed to evaluate the performance of the proposed method to estimate both local and global parameters. The performance of method in handling non-Gaussian prior as well as capturing the prior uncertainty has been assessed. The results revealed that, the proposed method handled both non-Gaussian prior and capturing of the prior uncertainties of the local and global parameters quite efficiently. Compared to previously conducted researches, new algorithm would considerably reduce the number of required ensemble members to converge to the appropriate solution. Standard ensemble Kalman filter and normal score transformation have been also implemented for each setup; the obtained results show that the new proposed method outperforms the other alternate methods.

Approach for modelling stochastically dependent renewable energy‐based generators using diagonal band copula

This study presents a novel algorithm for modelling stochastically dependent renewable energy-based generators. To examine and model the stochastic dependence between renewable energy power outputs and system demand, all different random variables corresponding to wind speeds, solar irradiance and system demand are transformed to a common domain ‘the rank/uniform domain’ by applying the cumulative distribution function transformation. The rank correlation is first used to examine stochastic dependence and then, diagonal band copula is employed for considering the multivariate stochastic dependence. Finally, Monte Carlo method is utilised to accurately obtain the most likelihood values of the wind power, photovoltaic power and system demand. The rationale behind the proposed model is to include the probabilistic model into deterministic planning problems. The proposed algorithm is implemented in MATLAB environment and the results and comparisons show the accuracy of the proposed modelling algorithm.

On regression analysis of spatial proportional data with zero/one values

Proportions including exact zero and/or one values observed at spatial locations in a study area are often encountered in environmental and ecological studies. In this paper, we propose a new spatial beta-Bernoulli mixture model that combines a beta distribution and a Bernoulli distribution. The beta component links the original response on the open unit interval (0,1) to covariates via regression and is flexible to capture a variety of shapes of the data distributions. Further, the Bernoulli component models the probability of zero/one values with regression. In addition, we propose a novel spatial generalized Tobit model which extends an existing spatial Tobit model by applying an inverse beta cumulative distribution function transformation. A composite likelihood approach is developed for parameter estimation by maximizing a pairwise likelihood function for each model. The standard errors of the parameter estimates are obtained via the inverse of the Godambe information matrix. A simulation study is conducted to evaluate the performance of the proposed models and methods, followed by an ecological data example. Connections among the spatial beta-Bernoulli mixture model, the spatial generalized Tobit model, and the spatial Tobit model are explored using both simulated and real data.

An evaluation of single-site statistical downscaling techniques in terms of indices of climate extremes for the Midwest of Iran

Seven single-site statistical downscaling methods for daily temperature and precipitation, including four deterministic algorithms [analog model (ANM), quantile mapping with delta method extrapolation (QMD), cumulative distribution function transform (CDFt), and model-based recursive partitioning (MOB)] and three stochastic algorithms [generalized linear model (GLM), Conditional Density Estimation Network Creation and Evaluation (CaDENCE), and Statistical Downscaling Model–Decision Centric (SDSM–DC] are evaluated at nine stations located in the mountainous region of Iran’s Midwest. The methods are of widely varying complexity, with input requirements that range from single-point predictors of temperature and precipitation to multivariate synoptic-scale fields. The period 1981–2000 is used for model calibration and 2001–2010 for validation, with performance assessed in terms of 27 Climate Extremes Indices (CLIMDEX). The sensitivity of the methods to large-scale anomalies and their ability to replicate the observed data distribution in the validation period are separately tested for each index by Pearson correlation and Kolmogorov–Smirnov (KS) tests, respectively. Combined tests are used to assess overall model performances. MOB performed best, passing 14.5 % (49.6 %) of the combined (single) tests, respectively, followed by SDSM, CaDENCE, and GLM [14.5 % (46.5 %), 13.2 % (47.1 %), and 12.8 % (43.2 %), respectively], and then by QMD, CDFt, and ANM [7 % (45.7 %), 4.9 % (45.3 %), and 1.6 % (37.9 %), respectively]. Correlation tests were passed less frequently than KS tests. All methods downscaled temperature indices better than precipitation indices. Some indices, notably R20, R25, SDII, CWD, and TNx, were not successfully simulated by any of the methods. Model performance varied widely across the study region.

A Polynomial Logistic Distribution and its Applications in Finance

The importance of Logistic distribution has been widely recognized in many applied areas such as, demography, population studies, finance, agriculture, etc. Since its introduction as a model, much attention has been paid to the study of several generalizations of it, which would offer additional flexibility when data fitting is chased. In the present paper we introduce and develop a natural generalization of the Logistic distribution by considering a probability model whose logit cumulative distribution function transformation is of polynomial type. The performance of the model's fitting to financial data, using different parameter estimation methods, is also investigated.

Precipitation and temperature space–time variability and extremes in the Mediterranean region: evaluation of dynamical and statistical downscaling methods

This study evaluates how statistical and dynamical downscaling models as well as combined approach perform in retrieving the space–time variability of near-surface temperature and rainfall, as well as their extremes, over the whole Mediterranean region. The dynamical downscaling model used in this study is the Weather Research and Forecasting (WRF) model with varying land-surface models and resolutions (20 and 50 km) and the statistical tool is the Cumulative Distribution Function-transform (CDF-t). To achieve a spatially resolved downscaling over the Mediterranean basin, the European Climate Assessment and Dataset (ECA&D) gridded dataset is used for calibration and evaluation of the downscaling models. In the frame of HyMeX and MED-CORDEX international programs, the downscaling is performed on ERA-I reanalysis over the 1989–2008 period. The results show that despite local calibration, CDF-t produces more accurate spatial variability of near-surface temperature and rainfall with respect to ECA&D than WRF which solves the three-dimensional equation of conservation. This first suggests that at 20–50 km resolutions, these three-dimensional processes only weakly contribute to the local value of temperature and precipitation with respect to local one-dimensional processes. Calibration of CDF-t at each individual grid point is thus sufficient to reproduce accurately the spatial pattern. A second explanation is the use of gridded data such as ECA&D which smoothes in part the horizontal variability after data interpolation and damps the added value of dynamical downscaling. This explains partly the absence of added-value of the 2-stage downscaling approach which combines statistical and dynamical downscaling models. The temporal variability of statistically downscaled temperature and rainfall is finally strongly driven by the temporal variability of its forcing (here ERA-Interim or WRF simulations). CDF-t is thus efficient as a bias correction tool but does not show any added-value regarding the time variability of the downscaled field. Finally, the quality of the reference observation dataset is a key issue. Comparison of CDF-t calibrated with ECA&D dataset and WRF simulations to local measurements from weather stations not assimilated in ECA&D, shows that the temporal variability of the downscaled data with respect to the local observations is closer to the local measurements than to ECA&D data. This highlights the strong added-value of dynamical downscaling which improves the temporal variability of the atmospheric dynamics with regard to the driving model. This article highlights the benefits and inconveniences emerging from the use of both downscaling techniques for climate research. Our goal is to contribute to the discussion on the use of downscaling tools to assess the impact of climate change on regional scales.

Probabilistic downscaling of GCM scenarios over southern India

AbstractThe cumulative distribution function transform (CDF‐t) is used to downscale daily precipitation and surface temperatures from a set of Global climate model (GCM) climatic projections over southern India. To deal with the full annual cycle, the approach has been applied by months, allowing downscaled projections for all seasons. First, CDF‐t is validated over a historical period using observation from the Indian Meteorological Department (IMD). Resulting high resolution fields show substantial improvements compared to original GCM outputs in terms of distribution, seasonal cycle and monsoon means for arid, semi‐arid and wetter regions of the subcontinent. Then, CDF‐t is applied to GCM large‐scale fields to project rainfall and surface temperature changes for the 21st century under the IPCC SRES A2 scenario. The results obtained show an increase of rainfall, mostly during the monsoon season, while winter precipitation is reduced, and suggest a widespread warming especially in the winter and post‐monsoon season. Copyright © 2012 Royal Meteorological Society

Using Copulas for Modeling Stochastic Dependence in Power System Uncertainty Analysis

The increasing penetration of renewable generation in power systems necessitates the modeling of this stochastic system infeed in operation and planning studies. The system analysis leads to multivariate uncertainty analysis problems, involving non-Normal correlated random variables. In this context, the modeling of stochastic dependence is paramount for obtaining accurate results; it corresponds to the concurrent behavior of the random variables, having a major impact to the aggregate uncertainty (in problems where the random variables correspond to spatially spread stochastic infeeds) or their evolution in time (in problems where the random variables correspond to infeeds over specific time-periods). In order to investigate, measure and model stochastic dependence, one should transform all different random variables to a common domain, the rank/uniform domain, by applying the cumulative distribution function transformation. In this domain, special functions, copulae, can be used for modeling dependence. In this contribution the basic theory concerning the use of these functions for dependence modeling is presented and focus is given on a basic function, the Normal copula. The case study shows the application of the technique for the study of the large-scale integration of wind power in the Netherlands.