Statistical Downscaling of Daily Temperature in Central Europe

Radan Huth Institute of Atmospheric Physics, Prague, Czech Republic

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Abstract

Statistical downscaling methods and potential large-scale predictors are intercompared for winter daily mean temperature in a network of stations in central and western Europe. The methods comprise (i) canonical correlation analysis (CCA), (ii) singular value decomposition analysis, (iii) multiple linear regression (MLR) of predictor principal components (PCs) with stepwise screening, (iv) MLR of predictor PCs without screening (i.e., all PCs are forced to enter the regression model), and (v) MLR of gridpoint values with stepwise screening (pointwise regression). The potential predictors include two circulation variables (sea level pressure and 500-hPa heights) and two temperature variables (850-hPa temperature and 1000–500-hPa thickness). The methods are evaluated according to the accuracy of specification (in terms of rmse and variance explained), their temporal structure (characterized by lag-1 autocorrelations), and their spatial structure (characterized by spatial correlations and objectively defined divisions into homogeneous regions).

The most accurate specification and best approximation of the temporal structure are achieved by the pointwise regression; the spatial structure is best captured by CCA. The best choice of predictors appears to be a pair of one circulation and one temperature predictor. Of the two ways of reproducing the original variance, inflation yields more realistic both temporal and spatial variability than randomization. The size of the domain on which predictors are defined plays a rather negligible role.

Corresponding author address: Radan Huth, Institute of Atmospheric Physics, Boční II 1401, 141 31 Praha 4, Czech Republic. Email: huth@ufa.cas.cz

Abstract

Statistical downscaling methods and potential large-scale predictors are intercompared for winter daily mean temperature in a network of stations in central and western Europe. The methods comprise (i) canonical correlation analysis (CCA), (ii) singular value decomposition analysis, (iii) multiple linear regression (MLR) of predictor principal components (PCs) with stepwise screening, (iv) MLR of predictor PCs without screening (i.e., all PCs are forced to enter the regression model), and (v) MLR of gridpoint values with stepwise screening (pointwise regression). The potential predictors include two circulation variables (sea level pressure and 500-hPa heights) and two temperature variables (850-hPa temperature and 1000–500-hPa thickness). The methods are evaluated according to the accuracy of specification (in terms of rmse and variance explained), their temporal structure (characterized by lag-1 autocorrelations), and their spatial structure (characterized by spatial correlations and objectively defined divisions into homogeneous regions).

The most accurate specification and best approximation of the temporal structure are achieved by the pointwise regression; the spatial structure is best captured by CCA. The best choice of predictors appears to be a pair of one circulation and one temperature predictor. Of the two ways of reproducing the original variance, inflation yields more realistic both temporal and spatial variability than randomization. The size of the domain on which predictors are defined plays a rather negligible role.

Corresponding author address: Radan Huth, Institute of Atmospheric Physics, Boční II 1401, 141 31 Praha 4, Czech Republic. Email: huth@ufa.cas.cz

1. Introduction

The performance of general circulation models (GCMs) at the local scale is often poor, which is particularly true for surface variables (Giorgi et al. 2001). The local-scale surface variables are, however, essential for assessing climate change impacts. On the other hand, GCM simulations of large-scale upper-air fields are generally considered quite reliable. The methodologies to bridge the gap between what is successfully simulated by GCMs and what is needed in climate impact research are generally referred to as downscaling. Among the approaches designed for this purpose, statistical downscaling methods appear to be those most widely used.

Statistical downscaling consists of seeking statistical relationships between the variables simulated well by GCMs (predictors) and the surface climate variables (predictands). Several statistical methods are applicable to description of these relationships. Multiple linear regression (MLR), based either directly on gridpoint data or on principal components (PCs) of predictor fields, and canonical correlation analysis (CCA) have been used most frequently. Recently, nonlinear methods have emerged, including multivariate splines (Corte-Real et al. 1995) and neural networks (e.g., Crane and Hewitson 1998; Wilby et al. 1998; Trigo and Palutikof 1999; Cavazos 2000).

Many recent studies have used large-scale circulation (geopotential height or sea level pressure) as the only predictor in specifying a variety of variables, including temperature (Hewitson 1994; Schubert and Henderson-Sellers 1997), precipitation (Noguer 1994; Corte-Real et al. 1995; Saunders and Byrne 1996; Busuioc et al. 1999), and sea level (Heyen et al. 1996). However, the assumption that changes in surface climate elements due to the enhanced greenhouse effect can be derived from changes in circulation only does not appear to be realistic because observed changes in circulation may not be a dominant agent in long-term surface climate trends (Widmann and Schär 1997; Hanssen-Bauer and Førland 1998; Huth 2001). The downscaling procedure based on circulation variables only, if applied to a future climate, may lead to an entirely unrealistic result of virtually no temperature change, although a direct GCM output indicates a warming by several degrees (Schubert 1998). More recent studies avoid that questionable assumption and include among predictors other variables such as free atmospheric temperature, or equivalently thickness (Kaas and Frich 1995; Cavazos 1997), and moisture variables (Crane and Hewitson 1998; Wilby et al. 1998).

Since downscaling approaches are numerous, a comparison of methods and potential predictors appears to be a useful exercise. In the first study of this kind related to daily temperature, Winkler et al. (1997) concentrated on a sensitivity of downscaling output to a definition of seasons and the form of the transfer function, but relied on circulation predictors only (sea level pressure and 500-hPa heights) and a single downscaling method (multiple linear regression), the evaluation being based on explained variance. Huth (1999, hereafter H99) compared the accuracy of specification of three linear downscaling methods and several large-scale circulation and temperature predictors in terms of root-mean-square error (rmse). However, the accuracy of specification is not the only criterion according to which the methods can be rated. Also important, but so far considered sporadically in downscaling studies, are the temporal structure of downscaled time series and the spatial structure of downscaled fields. The former has been investigated recently by Huth et al. (2001) from the point of view of prolonged extreme events (heat and cold waves), while the latter has been considered by Solman and Nuñez (1999) in terms of spatial correlations for monthly mean temperature in South America and by Easterling (1999) who examined the dependence of correlation between stations on their distance.

Since the predictors account only for a part of variance of the predictand, the variance of downscaled time series should be artificially enhanced in order to be reproduced properly. For this purpose, the inflation procedure, introduced by Karl et al. (1990), has been used most commonly. The inflation consists of increasing the temperature anomaly on each day by the same factor. However, the inflation implicitly assumes that all local variability originates from large-scale variability, which is not true. An alternative is to represent processes unresolved by the large-scale predictor(s) by adding to the downscaled series a noise with some predefined properties (randomization; von Storch 1999).

This paper is a follow-up of the H99 study. Its aims can be summarized in a few items: (i) to compare the performance of several linear downscaling methods and several sets of large-scale predictors in terms of the accuracy of specification, temporal structure, and spatial structure; (ii) to compare the performance of the two ways of reproduction of variance (inflation vs randomization); and (iii) to estimate the dependence of the downscaling output on the size of the domains on which the predictors and predictands are defined. The downscaling is performed for daily mean temperature in winter at a network of stations in central Europe.

2. Data

The study is carried out for eight winter seasons (December–February) from 1982–83 to 1989–90. Daily mean temperature data are collected at 39 stations in central and parts of western Europe (Austria, Belgium, Czech Republic, Germany, Slovakia, and Switzerland). The stations are located in northern midlatitudes in various orographic conditions, ranging from the sea coast to highlands, mountain valleys, and summits. The stations are listed in Table 1 together with their elevations; their locations are mapped in Fig. 1. (All the maps displayed indicate degrees of east longitude and degrees of north latitude.) The relative shortness of the dataset is given by the availability of data. We are aware of the limitations it poses, for example, concerning the stationarity of the predictor–predictand relationships.

The potential large-scale predictors include 500-hPa heights (HGT), sea level pressure (SLP), 850-hPa temperature (TEM), and 1000–500-hPa thickness (THI) defined on a 5° × 10° grid extending from 35° to 70°N and from 45°W to 45°E, which covers most of Europe and adjacent parts of the Atlantic Ocean and consists of 80 grid points. The source of large-scale data are the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalyses (Kalnay et al. 1996). We decided to increase the grid step relative to the original resolution of NCEP–NCAR products (2.5° × 2.5°) to reduce the amount of data as well as the redundancy in them because all the predictors exhibit high spatial correlations.

3. Downscaling methods

Three linear methods of statistical downscaling are evaluated in this study: (i) CCA prefiltered by principal component analysis (PCA), (ii) singular value decomposition (SVD) analysis, and (iii) MLR. The CCA and SVD methods are described and discussed in detail in Bretherton et al. (1992). They seek pairs of patterns, one from predictors and one from predictands, such that they share maximum correlation (CCA) or covariance (SVD). The higher-order (second, third, etc.) pairs (modes) maximize correlation/covariance not captured by the preceding pairs. To make CCA feasible, its predictors are usually prefiltered using PCA (Barnett and Preisendorfer 1987; Barnston and Ropelewski 1992).

We consider three different MLR models: (i) stepwise screening of PCs of the predictor field(s) (hereafter referred to as “stepwise regression”), (ii) MLR of predictor's PCs without screening, that is, all PCs being forced to enter the model (“full regression”), and (iii) stepwise screening of gridded values (“pointwise regression”). The MLR approach was developed and successfully applied several decades ago to the specification of surface temperature from midtropospheric circulation, mainly for the purpose of weather prediction, by Klein (1962). In stepwise screening, each potential predictor (PC or gridpoint value) is evaluated for its individual significance level before including it in the regression equation, and, after the addition, each variable within the equation is evaluated for its significance as part of the model. A variable is included (retained) in the equation if the corresponding significance level is lower than 10% (5%).

For each method, several variants of the number of PCs and the number of modes have been examined. In all models, both predictors and predictands are used in the form of normalized anomalies, that is, the means over the analyzed period were subtracted first from the values at each grid point/station, which were then divided by standard deviations.

Two methods of reproducing variance of temperature series are compared. The inflation consists in increasing the anomaly on each day by the ratio of standard deviations of the observed and downscaled series, which is identical to dividing by the correlation between the two series (Karl et al. 1990). This has been the most common way of handling the unexplained variance so far. An alternative to it is to represent the processes unresolved by the large-scale predictor by adding noise to the downscaled series (von Storch 1999). The observed series can then be considered as a sum of the downscaled series and the noise. In this study we add white noise, generated at each station separately, to the output from downscaling. Because white noise is by definition uncorrelated with the downscaled time series, its variance may be defined as the difference of variances of the downscaled and observed series. The same approach has been adopted by Wilby et al. (1999) and Zorita and von Storch (1999). We take the inflation as a standard approach, so wherever the method of enhancing the variance is not specifically stated, the inflation is used.

4. Accuracy of specification

a. Methodology

The accuracy of downscaled values has been quantified in terms of (i) the rmse of the downscaled values relative to the observed, (ii) mean absolute error, and (iii) percentage of variance explained (or, equivalently, correlation coefficient). The rating of methods and predictors is identical for the three measures of correspondence in most cases, so we use in the presentation of results just one of them. To obtain one number for each method to characterize its general performance, the values of the correspondence measures are averaged over the stations.

The downscaling methods are evaluated within the cross-validation framework, which allows an unbiased estimate of potential “predictability.” The cross validation consists in omitting one case in turn, building the statistical model on the remaining dataset, and applying the statistical model to the omitted case (Michaelsen 1987). Since time series of daily temperature exhibit considerable autocorrelation, the above procedure would lead to a positive bias in downscaling skill. To eliminate autocorrelation, one season is held out at a time instead of a single day, and the statistical model built on the remaining seven seasons is verified on the omitted period. All the statistical models are thus built eight times.

b. Rating of predictors

In H99, temperature predictors (850-hPa temperature and 1000–500-hPa thickness) have been shown, in terms of rmse, to be superior to the circulation predictors (sea level pressure and 500-hPa heights); and the combined predictors (one temperature and one circulation) to be superior to any single predictor. This holds not only for the pointwise MLR method as shown in H99, but also for any method yielding a reasonably good specification. Figure 2 illustrates these facts in terms of variance explained for the pointwise regression. In addition, it shows that all four combined predictors yield a level of performance very close to one another and explain about two-thirds of the daily temperature variance. The combination of SLP and 850-hPa temperature appears to be superior, but by a rather narrow margin. It explains 68.4% of the variance on average, the mean correlation coefficient being 0.825 and mean rmse 2.84°C.

The geographical distribution of the percentage of variance explained can be seen in Fig. 3. It shows at each station the combination of predictors for which the highest share of variance is explained, and the corresponding value. Three combinations of predictors, SLP+TEM, HGT+TEM, and HGT+THI, are each superior to the others at 10–13 stations. The variance explained ranges from 90.6% at Feurkogel, Austria, to only 37.4% at Klagenfurt, Austria. The highest shares of variance are explained at the elevated, especially mountain summit stations (Feurkogel and Sonnblick in Austria, Säntis and Davos in Switzerland, Štrbské Pleso in Slovakia, and Milešovka in the Czech Republic). The elevation dependence of the percentage of explained variance is underlined by its Spearman rank correlation with the elevation, which is equal to 0.350 (significant at the 5% level).

c. Rating of methods

The downscaling methods are intercompared for the combination of predictors HGT+TEM, with variance inflation employed. The results for other combinations of predictors are qualitatively the same.

First of all we discuss the number of PCs to enter the MLR and CCA methods. It is our intention to compare results of downscaling based on different numbers of PCs, so we do not confine ourselves to identifying only a single, hopefully the most appropriate number. In selecting the suitable numbers of PCs we followed the rule of O'Lenic and Livezey (1988): the PCs should be cut just behind a section with a small slope (shelf) on an eigenvalue versus PC-number diagram. Such a diagram, with a percentage of variance explained given in a logarithmic scale on the ordinate, is shown in Fig. 4 for the set of predictors (500-hPa heights and 850-hPa temperatures at grid points) and predictands (daily mean temperature at stations). In both diagrams, eight curves are displayed, one for each cross-validated sample. The numbers of PCs for which breaks between the shelves and steeper sections are (more or less) evident for the majority of cross-validated samples (3, 5, 7, 9, 11, and 15 PCs for the predictor, and 4, 7, 9, and 15 PCs for the predictand) are indicated by vertical lines. These numbers of PCs are selected to enter the statistical models.

Results for the MLR methods are displayed in Table 2. The accuracy of the downscaled values improves with the increasing number of PCs, but after PC 9 the improvements become negligible. However, even higher-order PCs may be relevant for regression models: for example, PC 15 (which may have been considered the least important) enters the regression equations as the fourth–sixth most informative predictor at the majority of stations. Note that more than a half of PCs is selected by the stepwise procedure as informative predictors in the regression equations (last column in Table 2). Differences between the stepwise and full regression are negligible, which implies that the addition of predictors carrying virtually no information does not deteriorate the accuracy.

The pointwise regression clearly outperforms the regressions based on PCs: it improves the rmse by more than 0.6°C relative to the most successful full regression model for 15 PCs. The saturated level of accuracy, to which the stepwise and full regression appear to converge with the increasing number of PCs, is far below the performance of the pointwise regression. The difference in performance of the pointwise and PC-based regressions does not seem to be explainable by different numbers of parameters to be estimated. The area-averaged rmse for the pointwise model with the number of variables constrained to 12 is 2.88°C, which is identical to the unconstrained pointwise regression. This above opinion is further supported by the results of Klein and Walsh (1983) who found the superiority of the pointwise regression to the PC-based regression with both models constrained to the same number of variables. The most likely reason for this superiority was suggested by Klein and Walsh (1983): Whereas the pointwise regression selects the grid points that maximize the explained variance of surface temperature, the PCs are designed to maximize the height variance, and necessarily contain some information irrelevant to the temperature variability.

In the CCA method, the addition of more canonical modes enhances the accuracy first, but after a certain number of modes, the accuracy starts to decline slightly. An example is shown in Table 3 where the mean rmse is presented for CCA with seven PCs of predictors and seven PCs of predictands: the accuracy is at maximum for four modes. The dependence of the accuracy on the number of PCs entering CCA is documented in Table 4. The higher the number of PCs, the more accurate the downscaled values. The accuracy is affected more by the predictor PCs than predictand PCs. The optimum number of canonical modes for each combination of the numbers of predictor and predictand PCs varies from two to five (numbers in parentheses in Table 4). The most accurate approximation, achieved for 15 predictor PCs, 15 predictand PCs, and 5 canonical modes (rmse of 3.55°C) is, however, far from the accuracy of the pointwise regression (rmse of 2.88°C).

The SVD method appears to be the least successful one. The lowest rmse, 3.64°C, is achieved for the solution with one SVD mode; it is worse than for the superior variant of any other method. With an increasing number of modes, the error increases rather rapidly, reaching rmse of 5.22°C for four modes.

If the white noise addition is employed to reproduce the variance instead of inflation, the rating of methods remains unchanged. The only difference is a considerably weaker agreement of downscaled values with observations, which is nevertheless an expected result. For example, the areally averaged correlation for the pointwise regression of HGT and TEM drops from 0.821 to 0.718, and rmse increases from 2.88° to 3.62°C.

d. Sensitivity to the domain size: Predictors

To examine the effect the size of the domain from which predictors are selected has on the accuracy of downscaled values, the calculations are repeated for predictors defined over a smaller area on a denser grid. For that purpose we use the grid with a 5° × 5° spacing, extending from 40° to 60°N and from 15°W to 25°E. The effect on the results comes mainly from the changed spatial extent of the domain, although the grid density is different as well. The latter effect is, however, of little importance because of high correlation among grid points. The results are shown in Table 5 for three methods. The number of predictor PCs for a small domain, 5, was selected so that it accounts for approximately the same share of variance as 11 PCs for a large domain.

The domain size does not affect areally averaged results of the pointwise regression. Although distant grid points are selected in regression equations quite commonly, they are successfully replaced with closer grid points that appear to carry almost identical information. The methods utilizing PCs as predictors behave in a different way: the approximation is better if predictors are taken from a smaller area. This is because in the PCs on a larger domain, due to their larger spatial extent, the relevant information is more likely to be diluted with noise from grid points (frequently remote) irrelevant to temperature at a particular station. The implicit inclusion of such grid points in the regression model cannot be avoided when PCs are regressed, but they are ignored in building the pointwise regression model.

Although the areally averaged error of the pointwise regression method is almost identical for both domains, nonnegligible differences exist at individual stations (Fig. 5). In terms of the percentage of variance explained, the difference varies from −5.8% at Holešov, Czech Republic, to +4.3% at Teplice, Czech Republic (the difference is positive for small domain yielding more accurate results). We can observe a tendency for the small domain to give better results at more elevated stations, whereas in lowlands, the large domain is preferable, although there are notable exceptions. For example, at lowland stations in eastern Germany and at Teplice (lowland station in northwest Czech Republic), the small domain is to be preferred.

e. Sensitivity to the domain size: Predictands

Unlike multiple regression, which calculates the downscaled values at individual stations independently, the CCA method (as well as SVD, which is not discussed here because of its poorer performance) treats the predictand variable as a field. Therefore, its performance may depend on the size of the domain on which the predictand is defined and on the density of stations. To examine this, the calculations are performed for 2 dense networks of stations over small domains: 9 stations in the center of the Czech Republic, and 10 stations in Belgium; their location is shown in Fig. 6.

The most important difference from the large domain is in the number of PCs necessary to explain the temperature variance. Whereas the first PC over the large domain explains about three-fourths of the total variance, over the small domains it explains 96%–97%. It is loaded highly positively everywhere, while the second PC (accounting for about 1% of total variance in the central Czech Republic and about 1.7% in Belgium) carries the information on a west–east temperature contrast. Table 6 compares the performance between the predictand domains for the stations included both in the large and small networks: Hradec Králové belongs to the central Czech stations, the other three stations being in Belgium. The smaller predictand domain results in a slightly better approximation than the large one, even if one PC only is involved; however, the performance of CCA still remains far behind pointwise regression. The inclusion of information on the west–east temperature contrast, contained in the second PC, has a very small effect on the accuracy of downscaled values.

5. Temporal and spatial structure

Both temporal and spatial structures were examined for the time series obtained from statistical models built on the whole analyzed period, that is, without cross validation. The temporal structure of downscaled temperatures is characterized by their persistence (lag-1 autocorrelations); the spatial structure is examined by means of correlation maps and by dividing the domain into regions using principal component analysis.

a. Persistence

First let us examine the area-averaged persistence, shown in Table 7 together with deviations from its observed magnitudes. Among all the methods considered, the pointwise regression with inflation yields the area-averaged persistence closest to the observations. If the white noise addition is used to reproduce variance, the day-to-day variability is enhanced considerably, resulting in unrealistically low lag-1 autocorrelations. All other methods overestimate the persistence. The inclusion of higher-order PCs of predictors, which tend to describe processes on smaller spatial and temporal scales, leads to a slight decrease in the area-averaged persistence: this holds both for the full regression and CCA. The effect of including higher-order PCs of predictands and higher-order canonical modes in the CCA method is not so straightforward: some PCs and modes are conducive to a decrease of the overall persistence, others to its increase. The pointwise regression with inflation is best also in approximating the spatial distribution of persistence (not shown).

b. Interstation correlations

Thirty-nine sets of correlation maps could have been produced in order to verify the ability of downscaling methods to reproduce the spatial structure of daily temperature fields. Here we present the maps of correlations with Norderney, the station located at the northwest corner of the domain, for observations and six downscaling methods (Fig. 7). Correlation maps based on other stations lead to analogous results.

In observations, correlations tend to gradually decrease with an increasing distance. Some irregularities occur in mountainous areas where close lowland (valley) and elevated (mountain) stations exhibit considerable differences in their link with the distant station of Norderney. Three such pairs of stations are listed in Table 8: Zürich and Säntis in Switzerland, Poprad and Štrbské Pleso in Slovakia, and Teplice and Milešovka in the Czech Republic. In the first two pairs, stations with lower elevation are correlated more strongly with Norderney. In contrast, in the Czech pair, the lowland Teplice station is more decoupled from surrounding stations because of its isolated position in a relatively deep valley with frequent temperature inversions, which inhibit surface conditions from being influenced by the free atmosphere.

The basic geographical features in the field of spatial correlations are reproduced by all the downscaling methods: the decrease with increasing distance, low values on the eastern and southern flanks of the domain (stations Košice, Slovakia, and Klagenfurt, Austria) and at Austrian and Swiss mountain stations (Feurkogel, Sonnblick, Säntis), and relatively high values at lowland and valley stations in the Alpine region (Basel, Zürich, Davos, Reutte). If only one predictor PC or canonical mode is used in the statistical model, all stations undergo identical temporal variations, and correlations between all station pairs are equal to 1. Adding more PCs and canonical modes to the downscaling equations results in lowering the magnitude of correlations. However, the decline of correlations with distance is too flat in the neighborhood of the base station because of a dominance of one PC/mode and little effect of other PCs/modes, as can be seen in Fig. 7 for both the full regression and CCA. This flatness of the correlation field is extreme for the full regression of 3 PCs and still strongly pronounced for the full regression of 11 PCs.

All the methods that employ the variance inflation overestimate spatial correlations at all stations. This is in accord with the findings of Easterling (1999) for monthly values. The overestimation is most severe for the full regression of 3 PCs: even rather remote stations of Teplice and Milešovka correlate with Norderney by as much as 0.999 (see Table 8). Spatial correlations are reproduced most closely by CCA and the correspondence is better for more modes involved. CCA with seven modes outperforms the pointwise regression everywhere except for the seven stations nearest to Norderney where the regression is marginally better. The differences between the paired lowland/mountain stations are reproduced by all methods to a satisfactory degree for the Swiss and Slovak stations (Table 8). For the Czech pair, only CCA with seven modes captures its different behavior.

The pointwise regression with white noise underestimates spatial correlations at the majority of stations. The underestimation is largest at sites close to the base station. A slight overestimation only appears at four stations with the largest share of variance explained, that is, with the smallest amounts of added white noise. It is only these four stations (Säntis, Davos, Sonnblick, and Feurkogel) where the overestimation of correlations produced by the pointwise regression is not outweighed by the added white noise (which is uncorrelated among stations).

c. Regionalization

One of the common tasks in climatological research is to divide a research domain into regions within which the analyzed climate element varies similarly in time (this is frequently referred to as regionalization). In this section we examine to what extent the divisions of stations based on the time course of daily temperature agree between observations and the downscaling methods. We employ the rotated principal component analysis as a regionalization tool (Richman and Lamb 1985; Gong and Richman 1995). In this method, each PC is identified with one region and the stations are assigned to that region for whose PC they have the highest loading. PCA is based on the correlation matrix and the “Direct Oblimin” method of oblique rotation was used.

Results of regionalization are shown in Fig. 8. Four regions are identified in observations. The largest region encompasses the lowlands and plains in the northwest up to Bavaria (the southeastern part of Germany) and the western part of the Czech Republic. The second and third region involve more continental stations in a more hilly terrain in the east and southeast (Slovakia, east of the Czech Republic, eastern Austria), and in the south (southern Germany, Switzerland). A separate group (although not geographically coherent) is composed of the five most elevated stations: Säntis and Davos in Switzerland, Sonnblick and Feurkogel in Austria, and Štrbské Pleso in Slovakia.

The full regression of three predictor PCs does not provide any classification at all: the same PC dominates at all stations; that is, the stations are assigned to a single region covering the whole domain (not shown). The full regression of 11 predictor PCs produces 3 regions: the elevated stations are correctly grouped together, but the other 2 regions do not correspond to observations; the large one (denoted by circles) involves all remaining stations but 3 in the southeast and east (denoted by crosses). The large region is oversized because of the overestimation of correlations between stations across the whole domain, and especially in its northwestern part, as shown in Fig. 7. The pointwise regression yields the same regionalization regardless of what method of variance reproduction is used (with an exception of station Holešov, which is assigned to the eastern region after inflation but to the large northwestern region after white noise addition). Only three regions are produced by that method, the large one (denoted by circles) joining the observed large northwest region, the southern region, and a part of the eastern region. The Štrbské Pleso station is incorrectly assigned to the eastern region, not among the elevated stations. The best regionalization is achieved by CCA, resulting in four regions for both four and seven canonical modes. If four modes are retained in CCA, the border between the northwestern and eastern regions is placed too far east, and Štrbské Pleso is misassigned. CCA with seven modes produces regionalization that is identical with observations.

6. Discussion and conclusions

The main conclusions of this paper can be summarized in the following items. They apply to central and western Europe in winter; the potential for their validity to be extended to other areas should be proved. Nevertheless, it is likely that in general they are transferable at least to northern midlatitude continental areas.

  1. Large-scale free-atmosphere temperature variables are more informative predictors of local surface daily mean temperature than large-scale circulation fields. The best results are achieved if a pair of predictors, one temperature and one circulation based, is used.

  2. In the accuracy of specification (regardless of whether expressed in terms of rmse, mean absolute error, or correlation coefficient), the stepwise regression of gridded data (referred to as “pointwise regression”) is by far the best. It outperforms the regression of predictors' principal components (both with and without stepwise screening), canonical correlation analysis, as well as singular value decomposition. Worth mentioning is the absence of overfitting in most statistical models after higher-order PCs, frequently suspected for being little important and containing noise rather than relevant signal, are added.

  3. The magnitude and spatial distribution of lag-1 autocorrelations are best approximated by the pointwise linear regression. All the other methods overestimate the persistence. The situation may be even worse for summer temperatures, for which the pointwise linear regression itself produces time series that are too persistent (Huth et al. 2001).

  4. The spatial structure of the surface temperature field is characterized in two ways: by correlation maps and by dividing the analyzed area into regions within which temperature covaries similarly. In both respects, CCA appears to be the best method. Nonetheless, all the downscaling methods (including CCA) overestimate the spatial correlations.

  5. The effect of the size of the domain on which predictors are defined is only marginal. A denser network of stations on a smaller domain tends to result in a more accurate specification if the CCA method is applied. The density of stations and the size of predictand's domain have naturally no effect if the pointwise regression is used.

  6. A comparison of two approaches to reproducing the original variance in downscaled series indicates that the variance inflation performs better than the addition of white noise. The latter results in a lower correspondence between downscaled and observed values, a strong underestimation of persistence, and to a general underestimation of spatial correlations.

The final aim of downscaling studies is a construction of site-specific time series for a future, changed climate, with use of outputs from general circulation models (GCMs). From this point of view, the predictors selected for downscaling must fulfill more demands than only to provide the best approximation of the observed predictands after the downscaling is applied to the observed predictors. There are at least two such additional demands. First, the predictors should be well simulated by the GCM; if they are not, we can have no confidence in surface variables derived from them (e.g., Palutikof et al. 1997). Second, the variables selected as predictors must be predictors not only of natural variability within the ranges of the present climate, but also of climate change. This is impossible to prove on the observed data; instead, one should resort to a GCM output and compare the GCM-simulated climate change with that derived from downscaling (Busuioc et al. 1999; Murphy 2000). The agreement between the two does not necessarily mean that the downscaling relationship will hold under the changed climate and that the selected variable(s) is (are) a good predictor of climate change (because of the imperfection of GCM itself); it rather hints that the selected predictor(s) may not be a bad choice.

The study underlines the necessity of validating more characteristics of downscaled variables than only the degree to which they fit observations. We show that different downscaling methods may be most satisfactory for different characteristics. Therefore, the selection of the downscaling method should be suited to the aims of the study. If, for example, the time structure is of primary importance (including prolonged extreme events such as cold or heat waves), which is frequently the case of impact studies, for example, on agriculture (Dubrovský et al. 2000), the pointwise regression method should be selected. If the aim is in regionalization, it would perhaps be better to choose the CCA method, although its performance in terms of correspondence measures is not as good as that of the pointwise regression.

Acknowledgments

The study was supported by the Grant Agency of the Czech Republic under Project 205/99/1561 and by the Grant Academy of the Czech Academy of Sciences under Project A3042903. Thanks are due to I. Auer, M. Beniston, A. Berger, A. Kästner, M. Lapin, E. Nieplová, R. Schweitzer, C. Tricot, and M. Wolek for the provision of the data and an assistance in acquiring them. The NCEP–NCAR reanalyses were obtained from the University of Colorado, Boulder, Colorado. The datasets were preprocessed by N. Klimperová.

REFERENCES

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    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., and C. F. Ropelewski, 1992: Prediction of ENSO episodes using canonical correlation analysis. J. Climate, 5 , 13161345.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., C. Smith, and J. M. Wallace, 1992: An intercomparison of methods for finding coupled patterns in climate data. J. Climate, 5 , 541560.

    • Search Google Scholar
    • Export Citation
  • Busuioc, A., H. von Storch, and R. Schnur, 1999: Verification of GCM-generated regional seasonal precipitation for current climate and of statistical downscaling estimates under changing climate conditions. J. Climate, 12 , 258272.

    • Search Google Scholar
    • Export Citation
  • Cavazos, T., 1997: Downscaling large-scale circulation to local winter rainfall in north-eastern Mexico. Int. J. Climatol., 17 , 10691082.

    • Search Google Scholar
    • Export Citation
  • Cavazos, T., . 2000: Using self-organizing maps to investigate extreme climate events: An application to wintertime precipitation in the Balkans. J. Climate, 13 , 17181732.

    • Search Google Scholar
    • Export Citation
  • Corte-Real, J., X. Zhang, and X. Wang, 1995: Downscaling GCM information to regional scales: A non-parametric multivariate regression approach. Climate Dyn., 11 , 413424.

    • Search Google Scholar
    • Export Citation
  • Crane, R. G., and B. C. Hewitson, 1998: Doubled CO2 precipitation changes for the Susquehanna basin: Down-scaling from the GENESIS general circulation model. Int. J. Climatol., 18 , 6576.

    • Search Google Scholar
    • Export Citation
  • Dubrovský, M., Z. Žalud, and M. Št'astná, 2000: Sensitivity of CERES-Maize yields to statistical structure of daily weather series. Climatic Change, 46 , 447472.

    • Search Google Scholar
    • Export Citation
  • Easterling, D. R., 1999: Development of regional climate scenarios using a downscaling approach. Climatic Change, 41 , 615634.

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    • Export Citation
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    • Export Citation
  • Hanssen-Bauer, I., and E. J. Førland, 1998: Long-term trends in precipitation and temperature in the Norwegian Arctic: Can they be explained by changes in atmospheric circulation patterns? Climate Res., 10 , 143153.

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    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Huth, R., 1999: Statistical downscaling in central Europe: Evaluation of methods and potential predictors. Climate Res., 13 , 91101.

  • Huth, R., . 2001: Disaggregating climatic trends by classification of circulation patterns. Int. J. Climatol., 21 , 135153.

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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and Coauthors. 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Karl, T. R., W. C. Wang, M. E. Schlesinger, R. W. Knight, and D. Portman, 1990: A method of relating general circulation model simulated climate to the observed local climate. Part I: Seasonal statistics. J. Climate, 3 , 10531079.

    • Search Google Scholar
    • Export Citation
  • Klein, W. H., 1962: Specification of monthly mean surface temperatures from 700 mb heights. J. Appl. Meteor., 1 , 154156.

  • Klein, W. H., and J. E. Walsh, 1983: A comparison of pointwise screening and empirical orthogonal functions in specifying monthly surface temperature from 700 mb data. Mon. Wea. Rev., 111 , 669673.

    • Search Google Scholar
    • Export Citation
  • Michaelsen, J., 1987: Cross-validation in statistical climate forecast models. J. Climate Appl. Meteor., 26 , 15891600.

  • Murphy, J., 2000: Predictions of climate change over Europe using statistical and dynamical downscaling techniques. Int. J. Climatol., 20 , 489501.

    • Search Google Scholar
    • Export Citation
  • Noguer, M., 1994: Using statistical techniques to deduce local climate distributions. An application for model validation. Meteor. Appl., 1 , 277287.

    • Search Google Scholar
    • Export Citation
  • O'Lenic, E. A., and R. E. Livezey, 1988: Practical considerations in the use of rotated principal component analysis (RPCA) in diagnostic studies of upper-air height fields. Mon. Wea. Rev., 116 , 16821689.

    • Search Google Scholar
    • Export Citation
  • Palutikof, J. P., J. A. Winkler, C. M. Goodess, and J. A. Andresen, 1997: The simulation of daily temperature time series from GCM output. Part I: Comparison of model data with observations. J. Climate, 10 , 24972513.

    • Search Google Scholar
    • Export Citation
  • Richman, M. B., and P. J. Lamb, 1985: Climatic patterns analysis of three- and seven-day summer rainfall in the central United States: Some methodological considerations and a regionalization. J. Climate Appl. Meteor., 24 , 13251343.

    • Search Google Scholar
    • Export Citation
  • Saunders, I. R., and J. M. Byrne, 1996: Generating regional precipitation from observed and GCM synoptic-scale pressure fields, southern Alberta, Canada. Climate Res., 6 , 237249.

    • Search Google Scholar
    • Export Citation
  • Schubert, S., 1998: Downscaling local extreme temperature changes in south-eastern Australia from the CSIRO Mark2 GCM. Int. J. Climatol., 18 , 14191438.

    • Search Google Scholar
    • Export Citation
  • Schubert, S., and A. Henderson-Sellers, 1997: A statistical model to downscale local daily temperature extremes from synoptic-scale atmospheric circulation patterns in the Australian region. Climate Dyn., 13 , 223234.

    • Search Google Scholar
    • Export Citation
  • Solman, S. A., and M. N. Nuñez, 1999: Local estimates of global climate change: A statistical downscaling approach. Int. J. Climatol., 19 , 835861.

    • Search Google Scholar
    • Export Citation
  • Trigo, R. M., and J. P. Palutikof, 1999: Simulation of daily temperatures for climate change scenarios over Portugal: A neural network model approach. Climate Res., 13 , 4559.

    • Search Google Scholar
    • Export Citation
  • von Storch, H., 1999: On the use of “inflation” in statistical downscaling. J. Climate, 12 , 35053506.

  • Widmann, M., and C. Schär, 1997: A principal component and long-term trend analysis of daily precipitation in Switzerland. Int. J. Climatol., 17 , 13331356.

    • Search Google Scholar
    • Export Citation
  • Wilby, R. L., T. M. L. Wigley, D. Conway, P. D. Jones, B. C. Hewitson, J. Main, and D. S. Wilks, 1998: Statistical downscaling of general circulation model output: A comparison of methods. Water Resour. Res., 34 , 29953008.

    • Search Google Scholar
    • Export Citation
  • Wilby, R. L., L. E. Hay, and G. H. Leavesley, 1999: A comparison of downscaled and raw GCM output: Implications for climate change scenarios in the San Juan River basin, Colorado. J. Hydrol., 225 , 6791.

    • Search Google Scholar
    • Export Citation
  • Winkler, J. A., J. P. Palutikof, J. A. Andresen, and C. M. Goodess, 1997: The simulation of daily temperature time series from GCM output. Part II: Sensitivity analysis of an empirical transfer function methodology. J. Climate, 10 , 25142532.

    • Search Google Scholar
    • Export Citation
  • Zorita, E., and H. von Storch, 1999: The analog method as a simple statistical downscaling technique: Comparison with more complicated methods. J. Climate, 12 , 24742489.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Location of stations used in the study. For their names refer to Table 1. Degrees of east longitude on x axis and degrees of north latitude on y axis (for this and other map figures)

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1731:SDODTI>2.0.CO;2

Fig. 2.
Fig. 2.

Percentage of variance explained, averaged over 39 stations, for different predictors and their combinations. All for pointwise MLR

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1731:SDODTI>2.0.CO;2

Fig. 3.
Fig. 3.

Percentage of variance explained, maximum among the four combined predictors. The most successful combination of predictors is indicated by symbols: star (HGT+TEM), cross (HGT+THI), circle (SLP+TEM), square (SLP+THI)

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1731:SDODTI>2.0.CO;2

Fig. 4.
Fig. 4.

Percentage of variance explained (y axis) by 20 leading PCs for (top) the predictor (HGT+TEM) and (bottom) predictand (Tsfc, daily mean temperature at stations). The numbers of PCs selected for the further analysis are indicated by vertical lines

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1731:SDODTI>2.0.CO;2

Fig. 5.
Fig. 5.

Difference in percentage of variance explained between small and large predictor domain for pointwise regression and HGT and TEM predictors. Positive values (crosses as station symbols) indicate that downscaling from the small domain is more accurate. Negative values (squares as station symbols) indicate that downscaling is less accurate

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1731:SDODTI>2.0.CO;2

Fig. 6.
Fig. 6.

Station locations in dense networks over small domains: Belgium and central Czech Republic. Stations indicated by stars are common with the large network

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1731:SDODTI>2.0.CO;2

Fig. 7.
Fig. 7.

Spatial correlations with the station of Norderney for observations and six downscaling methods. In the map for observations, Norderney is localized with a square, and the stations, referred to in Table 8, have gray stars

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1731:SDODTI>2.0.CO;2

Fig. 8.
Fig. 8.

Assignment of stations to regions (denoted by crosses, circles, triangles, and stars) for observations and selected downscaling methods

Citation: Journal of Climate 15, 13; 10.1175/1520-0442(2002)015<1731:SDODTI>2.0.CO;2

Table 1.

List of stations used in the study. Altitudes are in meters above mean sea level. The stations are marked in Fig. 1 with the numbers in the left column. The international country codes are used: CZ—Czech Republic, SK—Slovakia, DE—Germany, CH—Switzerland, AT—Austria, BE—Belgium

Table 1.
Table 2.

Performance (in terms of areally averaged rmse, in °C) of stepwise and full regression for different numbers of PCs of predictors. The last row shows results for the pointwise regression. The range of the number of variables selected in the stepwise regression models is in the last column

Table 2.
Table 3.

Areally averaged rmse (in °C) for different numbers of modes in CCA with 7 PCs of predictor and 7 PCs of predictand

Table 3.
Table 4.

Areally averaged rmse for CCA with different combinations of the numbers of predictor and predictand PCs. Results are only shown for the number of canonical modes (indicated in parenthesis) that yields the lowest rmse. The omitted values were not calculated

Table 4.
Table 5.

Comparison of rmse (in °C) between large and small predictor domains for pointwise regression, full regression, and CCA, all for HGT and TEM as predictors. For CCA, the number of predictor/predictand PCs is shown

Table 5.
Table 6.

Comparison of percentage of explained variance for CCA between the large and small predictand domains for selected stations. HGT and TEM are used as predictors. Methods are described by the number of predictor/predictand PCs and the number of canonical modes. Pointwise regression is shown for reference

Table 6.
Table 7.

Lag-1 autocorrelations (×1000) averaged over all stations for different downscaling methods (persistence) and their difference from observations (bias)

Table 7.
Table 8.

Correlations (×1000) with Norderney (Germany) for pairs of close mountain/lowland stations in observations and selected downscaling methods

Table 8.
Save
  • Barnett, T. P., and R. Preisendorfer, 1987: Origins and levels of monthly and seasonal forecast skill for United States surface air temperatures determined by canonical correlation analysis. Mon. Wea. Rev., 115 , 18251850.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., and C. F. Ropelewski, 1992: Prediction of ENSO episodes using canonical correlation analysis. J. Climate, 5 , 13161345.

    • Search Google Scholar
    • Export Citation
  • Bretherton, C. S., C. Smith, and J. M. Wallace, 1992: An intercomparison of methods for finding coupled patterns in climate data. J. Climate, 5 , 541560.

    • Search Google Scholar
    • Export Citation
  • Busuioc, A., H. von Storch, and R. Schnur, 1999: Verification of GCM-generated regional seasonal precipitation for current climate and of statistical downscaling estimates under changing climate conditions. J. Climate, 12 , 258272.

    • Search Google Scholar
    • Export Citation
  • Cavazos, T., 1997: Downscaling large-scale circulation to local winter rainfall in north-eastern Mexico. Int. J. Climatol., 17 , 10691082.

    • Search Google Scholar
    • Export Citation
  • Cavazos, T., . 2000: Using self-organizing maps to investigate extreme climate events: An application to wintertime precipitation in the Balkans. J. Climate, 13 , 17181732.

    • Search Google Scholar
    • Export Citation
  • Corte-Real, J., X. Zhang, and X. Wang, 1995: Downscaling GCM information to regional scales: A non-parametric multivariate regression approach. Climate Dyn., 11 , 413424.

    • Search Google Scholar
    • Export Citation
  • Crane, R. G., and B. C. Hewitson, 1998: Doubled CO2 precipitation changes for the Susquehanna basin: Down-scaling from the GENESIS general circulation model. Int. J. Climatol., 18 , 6576.

    • Search Google Scholar
    • Export Citation
  • Dubrovský, M., Z. Žalud, and M. Št'astná, 2000: Sensitivity of CERES-Maize yields to statistical structure of daily weather series. Climatic Change, 46 , 447472.

    • Search Google Scholar
    • Export Citation
  • Easterling, D. R., 1999: Development of regional climate scenarios using a downscaling approach. Climatic Change, 41 , 615634.

  • Giorgi, F., and Coauthors. 2001: Regional climate information—Evaluation and projections. Climate Change 2001: The Scientific Basis, J. T. Houghton et al., Eds., Cambridge University Press, 583–638.

    • Search Google Scholar
    • Export Citation
  • Gong, X., and M. B. Richman, 1995: On the application of cluster analysis to growing season precipitation data in North America east of the Rockies. J. Climate, 8 , 897931.

    • Search Google Scholar
    • Export Citation
  • Hanssen-Bauer, I., and E. J. Førland, 1998: Long-term trends in precipitation and temperature in the Norwegian Arctic: Can they be explained by changes in atmospheric circulation patterns? Climate Res., 10 , 143153.

    • Search Google Scholar
    • Export Citation
  • Hewitson, B., 1994: Regional climates in the GISS general circulation model: Surface air temperature. J. Climate, 7 , 283303.

  • Heyen, H., E. Zorita, and H. von Storch, 1996: Statistical downscaling of monthly mean North-Atlantic air-pressure to sea level anomalies in the Baltic Sea. Tellus, 48A , 312323.

    • Search Google Scholar
    • Export Citation
  • Huth, R., 1999: Statistical downscaling in central Europe: Evaluation of methods and potential predictors. Climate Res., 13 , 91101.

  • Huth, R., . 2001: Disaggregating climatic trends by classification of circulation patterns. Int. J. Climatol., 21 , 135153.

  • Huth, R., J. Kyselý, and M. Dubrovský, 2001: Time structure of observed, GCM-simulated, downscaled, and stochastically generated daily temperature series. J. Climate, 14 , 40474061.

    • Search Google Scholar
    • Export Citation
  • Kaas, E., and P. Frich, 1995: Diurnal temperature range and cloud cover in the Nordic countries: Observed trends and estimates for the future. Atmos. Res., 37 , 211228.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and Coauthors. 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Karl, T. R., W. C. Wang, M. E. Schlesinger, R. W. Knight, and D. Portman, 1990: A method of relating general circulation model simulated climate to the observed local climate. Part I: Seasonal statistics. J. Climate, 3 , 10531079.

    • Search Google Scholar
    • Export Citation
  • Klein, W. H., 1962: Specification of monthly mean surface temperatures from 700 mb heights. J. Appl. Meteor., 1 , 154156.

  • Klein, W. H., and J. E. Walsh, 1983: A comparison of pointwise screening and empirical orthogonal functions in specifying monthly surface temperature from 700 mb data. Mon. Wea. Rev., 111 , 669673.

    • Search Google Scholar
    • Export Citation
  • Michaelsen, J., 1987: Cross-validation in statistical climate forecast models. J. Climate Appl. Meteor., 26 , 15891600.

  • Murphy, J., 2000: Predictions of climate change over Europe using statistical and dynamical downscaling techniques. Int. J. Climatol., 20 , 489501.

    • Search Google Scholar
    • Export Citation
  • Noguer, M., 1994: Using statistical techniques to deduce local climate distributions. An application for model validation. Meteor. Appl., 1 , 277287.

    • Search Google Scholar
    • Export Citation
  • O'Lenic, E. A., and R. E. Livezey, 1988: Practical considerations in the use of rotated principal component analysis (RPCA) in diagnostic studies of upper-air height fields. Mon. Wea. Rev., 116 , 16821689.

    • Search Google Scholar
    • Export Citation
  • Palutikof, J. P., J. A. Winkler, C. M. Goodess, and J. A. Andresen, 1997: The simulation of daily temperature time series from GCM output. Part I: Comparison of model data with observations. J. Climate, 10 , 24972513.

    • Search Google Scholar
    • Export Citation
  • Richman, M. B., and P. J. Lamb, 1985: Climatic patterns analysis of three- and seven-day summer rainfall in the central United States: Some methodological considerations and a regionalization. J. Climate Appl. Meteor., 24 , 13251343.

    • Search Google Scholar
    • Export Citation
  • Saunders, I. R., and J. M. Byrne, 1996: Generating regional precipitation from observed and GCM synoptic-scale pressure fields, southern Alberta, Canada. Climate Res., 6 , 237249.

    • Search Google Scholar
    • Export Citation
  • Schubert, S., 1998: Downscaling local extreme temperature changes in south-eastern Australia from the CSIRO Mark2 GCM. Int. J. Climatol., 18 , 14191438.

    • Search Google Scholar
    • Export Citation
  • Schubert, S., and A. Henderson-Sellers, 1997: A statistical model to downscale local daily temperature extremes from synoptic-scale atmospheric circulation patterns in the Australian region. Climate Dyn., 13 , 223234.

    • Search Google Scholar
    • Export Citation
  • Solman, S. A., and M. N. Nuñez, 1999: Local estimates of global climate change: A statistical downscaling approach. Int. J. Climatol., 19 , 835861.

    • Search Google Scholar
    • Export Citation
  • Trigo, R. M., and J. P. Palutikof, 1999: Simulation of daily temperatures for climate change scenarios over Portugal: A neural network model approach. Climate Res., 13 , 4559.

    • Search Google Scholar
    • Export Citation
  • von Storch, H., 1999: On the use of “inflation” in statistical downscaling. J. Climate, 12 , 35053506.

  • Widmann, M., and C. Schär, 1997: A principal component and long-term trend analysis of daily precipitation in Switzerland. Int. J. Climatol., 17 , 13331356.

    • Search Google Scholar
    • Export Citation
  • Wilby, R. L., T. M. L. Wigley, D. Conway, P. D. Jones, B. C. Hewitson, J. Main, and D. S. Wilks, 1998: Statistical downscaling of general circulation model output: A comparison of methods. Water Resour. Res., 34 , 29953008.

    • Search Google Scholar
    • Export Citation
  • Wilby, R. L., L. E. Hay, and G. H. Leavesley, 1999: A comparison of downscaled and raw GCM output: Implications for climate change scenarios in the San Juan River basin, Colorado. J. Hydrol., 225 , 6791.

    • Search Google Scholar
    • Export Citation
  • Winkler, J. A., J. P. Palutikof, J. A. Andresen, and C. M. Goodess, 1997: The simulation of daily temperature time series from GCM output. Part II: Sensitivity analysis of an empirical transfer function methodology. J. Climate, 10 , 25142532.

    • Search Google Scholar
    • Export Citation
  • Zorita, E., and H. von Storch, 1999: The analog method as a simple statistical downscaling technique: Comparison with more complicated methods. J. Climate, 12 , 24742489.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Location of stations used in the study. For their names refer to Table 1. Degrees of east longitude on x axis and degrees of north latitude on y axis (for this and other map figures)

  • Fig. 2.

    Percentage of variance explained, averaged over 39 stations, for different predictors and their combinations. All for pointwise MLR

  • Fig. 3.

    Percentage of variance explained, maximum among the four combined predictors. The most successful combination of predictors is indicated by symbols: star (HGT+TEM), cross (HGT+THI), circle (SLP+TEM), square (SLP+THI)

  • Fig. 4.

    Percentage of variance explained (y axis) by 20 leading PCs for (top) the predictor (HGT+TEM) and (bottom) predictand (Tsfc, daily mean temperature at stations). The numbers of PCs selected for the further analysis are indicated by vertical lines

  • Fig. 5.

    Difference in percentage of variance explained between small and large predictor domain for pointwise regression and HGT and TEM predictors. Positive values (crosses as station symbols) indicate that downscaling from the small domain is more accurate. Negative values (squares as station symbols) indicate that downscaling is less accurate

  • Fig. 6.

    Station locations in dense networks over small domains: Belgium and central Czech Republic. Stations indicated by stars are common with the large network

  • Fig. 7.

    Spatial correlations with the station of Norderney for observations and six downscaling methods. In the map for observations, Norderney is localized with a square, and the stations, referred to in Table 8, have gray stars

  • Fig. 8.

    Assignment of stations to regions (denoted by crosses, circles, triangles, and stars) for observations and selected downscaling methods

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