Martin Widmann

Precipitation downscaling under climate change: Recent developments to bridge the gap between dynamical models and the end user

Precipitation downscaling improves the coarse resolution and poor representation of precipitation in global climate models and helps end users to assess the likely hydrological impacts of climate change. This paper integrates perspectives from meteorologists, climatologists, statisticians, and hydrologists to identify generic end user (in particular, impact modeler) needs and to discuss downscaling capabilities and gaps. End users need a reliable representation of precipitation intensities and temporal and spatial variability, as well as physical consistency, independent of region and season. In addition to presenting dynamical downscaling, we review perfect prognosis statistical downscaling, model output statistics, and weather generators, focusing on recent developments to improve the representation of space-time variability. Furthermore, evaluation techniques to assess downscaling skill are presented. Downscaling adds considerable value to projections from global climate models. Remaining gaps are uncertainties arising from sparse data; representation of extreme summer precipitation, subdaily precipitation, and full precipitation fields on fine scales; capturing changes in small-scale processes and their feedback on large scales; and errors inherited from the driving global climate model.

The Effective Number of Spatial Degrees of Freedom of a Time-Varying Field

The authors systematically investigate two easily computed measures of the effective number of spatial degrees of freedom (ESDOF), or number of independently varying spatial patterns, of a time-varying field of data. The first measure is based on matching the mean and variance of the time series of the spatially integrated squared anomaly of the field to a chi-squared distribution. The second measure, which is equivalent to the first for a long time sample of normally distributed field values, is based on the partitioning of variance between the EOFs. Although these measures were proposed almost 30 years ago, this paper aims to provide a comprehensive discussion of them that may help promote their more widespread use. The authors summarize the theoretical basis of the two measures and considerations when estimating them with a limited time sample or from nonnormally distributed data. It is shown that standard statistical significance tests for the difference or correlation between two realizations of a field (e.g., a forecast and an observation) are approximately valid if the number of degrees of freedom is chosen using an appropriate combination of the two ESDOF measures. Also described is a method involving ESDOF for deciding whether two time-varying fields are significantly correlated to each other. A discussion of the parallels between ESDOF and the effective sample size of an autocorrelated time series is given, and the authors review how an appropriate measure of effective sample size can be computed for assessing the significance of correlations between two time series.

Statistical Precipitation Downscaling over the Northwestern United States Using Numerically Simulated Precipitation as a Predictor

This study investigates whether GCM-simulated precipitation is a good predictor for regional precipitation over Washington and Oregon. In order to allow for a detailed comparison of the estimated precipitation with observations, the simulated precipitation is taken from the NCEP‐NCAR reanalysis, which nearly perfectly represents the historic pressure, temperature, and humidity, but calculates precipitation according to the model physics and parameterizations. Three statistical downscaling methods are investigated: (i) local rescaling of the simulated precipitation, and two newly developed methods, namely, (ii) downscaling using singular value decomposition (SVD) with simulated precipitation as the predictor, and (iii) local rescaling with a dynamical correction. Both local scaling methods are straightforward to apply to GCMs that are used for climate change experiments and seasonal forecasts, since they only need control runs for model fitting. The SVD method requires for model fitting special reanalysis-type GCM runs nudged toward observations from a historical period (selection of analogs from the GCM chosen to optimally match the historical weather states might achieve similar results). The precipitationbased methods are compared with conventional statistical downscaling using SVD with various large-scale predictors such as geopotential height, temperature, and humidity. The skill of the different methods for reconstructing historical wintertime precipitation (1958‐94) over Oregon and Washington is tested on various spatial scales as small as 50 km and on temporal scales from months to decades. All methods using precipitation as a predictor perform considerably better than the conventional downscaling. The best results using conventional methods are obtained with geopotential height at 1000 hPa or humidity at 850 hPa as predictors. In these cases correlations of monthly observed and reconstructed precipitation on the 50-km scale range from 0.43 to 0.65. The inclusion of several predictor fields does not improve the reconstructions, since they are all highly correlated. Local rescaling of simulated precipitation yields much higher correlations between 0.7 and 0.9, with the exception of the rain shadow of the Cascade Mountains in the Columbia Basin (eastern Washington). When the simulated precipitation is used as a predictor in SVD-based downscaling correlations also reach 0.7 in eastern Washington. Dynamical correction improves the local scaling considerably in the rain shadow and yields correlations almost as high as with the SVD method. Its combination of high skill and ease to use make it particularly attractive for GCM precipitation downscaling.

Validation of Mesoscale Precipitation in the NCEP Reanalysis Using a New Gridcell Dataset for the Northwestern United States

Abstract Precipitation fields from the National Centers for Environmental Prediction (NCEP) reanalysis are validated with high-resolution, gridded precipitation observations over Oregon and Washington. The NCEP reanalysis is thought of as a proxy for an ideal GCM that nearly perfectly represents the synoptic-scale pressure, temperature, and humidity but does not resolve the complex topography of this region. The authors’ main goal is to understand how useful precipitation fields from such a model are for estimating temporal variability in local precipitation. The gridded observations represent area-averaged precipitation on a 50-km grid and have daily temporal resolution. They are calculated with a newly developed scheme, which explicitly takes into account the effect of the topography on precipitation. This gridding method profits from the already existing, high-resolution climatologies for the monthly mean precipitation in the United States, obtained from the Precipitation–Elevation Regressions on Indep...

Skill, correction, and downscaling of GCM-simulated precipitation

AbstractThe ability of general circulation models (GCMs) to correctly simulate precipitation is usually assessed by comparing simulated mean precipitation with observed climatologies. However, to what extent the skill in simulating average precipitation indicates how well the models represent temporal changes is unclear. A direct assessment of the latter is hampered by the fact that freely evolving climate simulations for past periods are not set up to reproduce the specific evolution of internal atmospheric variability. Therefore, model-to-real-world comparisons of time series of daily, monthly, or annual precipitation are not meaningful. Here, for the first time, the authors quantify GCM skill in simulating precipitation variability using simulations in which the temporal evolution of the large-scale atmospheric state closely matches that of the real world. This is achieved by nudging the atmospheric states in the ECHAM5 GCM, but crucially not the precipitation field itself, toward the 40-yr European Ce...

Historical SAM Variability. Part I: Century-Length Seasonal Reconstructions*

Seasonal reconstructions of the Southern Hemisphere annular mode (SAM) index are derived to extend the record before the reanalysis period, using station sea level pressure (SLP) data as predictors. Two reconstructions using different predictands are obtained: one [Jones and Widmann (JW)] based on the first principal component (PC) of extratropical SLP and the other (Fogt) on the index of Marshall. A regional-based SAM index (Visbeck) is also considered.These predictands agree well post-1979; correlations decline in all seasons except austral summer for the full series starting in 1958. Predictand agreement is strongest in spring and summer; hence agreement between the reconstructions is highest in these seasons. The less zonally symmetric SAM structure in winter and spring influences the strength of the SAM signal over land areas, hence the number of stations included in the reconstructions. Reconstructions from 1865 were, therefore, derived in summer and autumn and from 1905 in winter and spring. This paper examines the skill of each reconstruction by comparison with observations and reanalysis data. Some of the individual peaks in the reconstructions, such as the most recent in austral summer, represent a full hemispheric SAM pattern, while others are caused by regional SLP anomalies over the locations of the predictors. The JW and Fogt reconstructions are of similar quality in summer and autumn, while in winter and spring the Marshall index is better reconstructed by Fogt than the PC index is by JW. In spring and autumn the SAM shows considerable variability prior to recent decades.

VALUE - A Framework to Validate Downscaling Approaches for Climate Change Studies

VALUE is an open European network to validate and compare downscaling methods for climate change research. VALUE aims to foster collaboration and knowledge exchange between climatologists, impact modellers, statisticians, and stakeholders to establish an interdisciplinary downscaling community. A key deliverable of VALUE is the development of a systematic validation framework to enable the assessment and comparison of both dynamical and statistical downscaling methods. In this paper, we present the key ingredients of this framework. VALUEs main approach to validation is user- focused: starting from a specific user problem, a validation tree guides the selection of relevant validation indices and performance measures. Several experiments have been designed to isolate specific points in the downscaling procedure where problems may occur: what is the isolated downscaling skill? How do statistical and dynamical methods compare? How do methods perform at different spatial scales? Do methods fail in representing regional climate change? How is the overall representation of regional climate, including errors inherited from global climate models? The framework will be the basis for a comprehensive community-open downscaling intercomparison study, but is intended also to provide general guidance for other validation studies.

One-Dimensional CCA and SVD, and Their Relationship to Regression Maps

Abstract The canonical correlation analysis (CCA) and singular value decomposition (SVD) approaches for estimating a time series from a time-dependent vector and vice versa are investigated, and their relationship to multiple linear regression (MLR) and to regression maps is discussed. Earlier findings are reviewed and combined with new aspects to provide a systematic overview. It is shown that regression maps are proportional to canonical patterns and to singular vectors and that the estimate of a time-dependent vector from a time series does not depend on whether CCA, SVD, or component-wise regressions are used. When a time series is linearly estimated from a time-dependent vector, it is known that CCA is equivalent to MLR. It is demonstrated that an estimate for the time series based on a time expansion coefficient of the regression map that is calculated by orthogonal projection is identical to an SVD estimate, but different from the CCA and MLR estimate. The two approaches also lead to different corr...

Stochastic Model Output Statistics for Bias Correcting and Downscaling Precipitation Including Extremes

Precipitation is highly variable in space and time; hence, rain gauge time series generally exhibit additional random small-scale variability compared to area averages. Therefore, differences between daily precipitation statistics simulated by climate models and gauge observations are generally not only caused by model biases, but also by the corresponding scale gap. Classical bias correction methods, in general, cannot bridge this gap; they do not account for small-scale random variability and may produce artifacts. Here, stochastic model output statistics is proposed as a bias correction framework to explicitly account for random small-scale variability. Daily precipitation simulated by a regional climate model (RCM) is employed to predict the probability distribution of local precipitation. The pairwise correspondence between predictor and predictand required for calibration is ensured by driving the RCM with perfect boundary conditions. Wet day probabilities are described by a logistic regression, and precipitation intensities are described by a mixture model consisting of a gamma distribution for moderate precipitation and a generalized Pareto distribution for extremes. The dependence of the model parameters on simulated precipitation is modeled by a vector generalized linear model. The proposed model effectively corrects systematic biases and correctly represents local-scale random variability for most gauges. Additionally, a simplified model is considered that disregards the separate tail model. This computationally efficient model proves to be a feasible alternative for precipitation up to moderately extreme intensities. The approach sets a new framework for bias correction that combines the advantages of weather generators and RCMs.

Comparison of GCM‐ and RCM‐simulated precipitation following stochastic postprocessing

In order to assess to what extent regional climate models (RCMs) yield better representations of climatic states than general circulation models (GCMs), the output of each is usually directly compared with observations. RCM output is often bias corrected, and in some cases correction methods can also be applied to GCMs. This leads to the question of whether bias-corrected RCMs perform better than bias-corrected GCMs. Here the first results from such a comparison are presented, followed by discussion of the value added by RCMs in this setup. Stochastic postprocessing, based on Model Output Statistics (MOS), is used to estimate daily precipitation at 465 stations across the United Kingdom between 1961 and 2000 using simulated precipitation from two RCMs (RACMO2 and CCLM) and, for the first time, a GCM (ECHAM5) as predictors. The large-scale weather states in each simulation are forced toward observations. The MOS method uses logistic regression to model precipitation occurrence and a Gamma distribution for the wet day distribution, and is cross validated based on Brier and quantile skill scores. A major outcome of the study is that the corrected GCM-simulated precipitation yields consistently higher validation scores than the corrected RCM-simulated precipitation. This seems to suggest that, in a setup with postprocessing, there is no clear added value by RCMs with respect to downscaling individual weather states. However, due to the different ways of controlling the atmospheric circulation in the RCM and the GCM simulations, such a strong conclusion cannot be drawn. Yet the study demonstrates how challenging it is to demonstrate the value added by RCMs in this setup.