Meteorologische Zeitschrift, Vol. 22, No. 3, 235–256 (October 2013) Open Access Article Ó by Gebru¨der Borntraeger 2013

A Central European precipitation climatology – Part I: Generation and validation of a high-resolution gridded daily data set (HYRAS)

Monika Rauthe*, Heiko Steiner, Ulf Riediger, Alex Mazurkiewicz and Annegret Gratzki

Deutscher Wetterdienst, Offenbach, Germany

(Manuscript received October 05, 2012; in revised form March 26, 2013; accepted March 26, 2013)

Abstract A new precipitation climatology (DWD/BfG-HYRAS-PRE) is presented which covers the river basins in Germany and neighbouring countries. In order to satisfy hydrological requirements, the gridded dataset has a high spatial resolution of 1 km2 and a daily temporal resolution that is based on up to 6200 precipitation stations within the spatial domain. The period of coverage extends from 1951 to 2006 for which gridded, daily precipitation fields were calculated from the station data using the REGNIE method. This is a combination between multiple linear regression considering orographical conditions and inverse distance weighting. One of the main attributes of the REGNIE method is the preservation of the station values for their respective grid cells. A detailed validation of the data set using cross-validation and Jackknifing showed both seasonally- and spatially-dependent interpolation errors. These errors, through further applications of the HYRAS data set within the KLIWAS project and other studies, provide an estimate of its certainty and quality. The mean absolute error was found to be less than 2 mm/day, but with both spatial and temporal variability. Additionally, the need for a high station network density was shown. Comparisons with other existing data sets show good agreement, with areas of orographical complexity displaying the largest differences within the domain. These errors are largely due to uncertainties caused by differences in the interpolation method, the station network density available, and the topographical information used. First climatological applications are presented and show the high potential of this new, high-resolution data set. Generally significant increases of up to 40% in winter precipitation and light decreases in summer are shown, whereby the spatial variability of the strength and significance of the trends is clearly illustrated. Keywords: Precipitation measurement, daily interpolation, climate, KLIWAS.

1 Introduction d for climate analyses in regions without any or with Our ecosystem and civilisation strongly depend on water only sparse measurements (e.g. BECKER et al., resources. It is therefore important to know not only how 2013; SCHNEIDER et al., 2013), d precipitation patterns have changed, but also how they for regional climate analyses and for pattern analyses on different spatial scales (e.g. JACOBEIT et al., 2009; are likely to evolve in the future. To project future ´ changes correctly, past regional and global patterns of HUNDECHA and BARDOSSY, 2005). precipitation have to be analysed and understood. Despite the rapid progress achieved in the last two decades in Over the past few decades changes in precipitation pat- estimating precipitation from radar and satellite observa- terns have been observed, but it is very difficult to differ- tions, gauge observations still play a critical role in doc- entiate between natural changes and those due to global umenting precipitation and their patterns due to their warming. Nevertheless, there is clear evidence supporting direct measurement method and lenghtly time series. an anthropogenic influence on precipitation and its distri- However, the stations for precipitation observations are bution due to climate change (SOLOMON et al., 2007). often irregularly spatially and temporally distributed, Since the 1990’s there have been numerous studies making climatological analyses more complicated. There focused on climatic variation in Central Europe, with are many reasons why interpolation to a regular grid is a much attention directly on Germany. The observation- prerequisite to such analyses: based studies have concentrated in the last years more and more on developing a set of indices or trends through d for the bias correction of climate models and their eval- use of historic meteorological observation databases (e.g. uation [e.g. BOE´ et al., 2007; BERG et al., 2012), ZOLINA et al., 2008; MOBERG and JONES, 2005; HUNDE- d for impact modelling, e.g. hydrological models e.g. CHA and BA´ RDOSSY, 2005; KLEINTANK et al., 2002; BRONSTERT et al., 2007; LENDERINK et al., 2007; FREI and SCHA¨ R, 1998). Changes in precipitation KRAHE et al., 2009), regimes, frequencies and extremes are found and sup- *Corresponding author: M. Rauthe, Deutscher Wetterdienst, Frankfurter Str. ported by an accumulating amount of evidence that sug- 135, 63067 Offenbach, e-mail: [email protected] gests they are the result of global warming (e.g. FREI

0941-2948/2013/0436 $ 9.90 DOI 10.1127/0941-2948/2013/0436 Ó Gebru¨der Borntraeger, Stuttgart 2013 236 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS Meteorol. Z., 22, 2013 et al., 2006). In Germany and Central Europe there has change on waterways and navigation – searching for been a marked and significant increase in daily winter options of adaptation’’, www.kliwas.de). KLIWAS is part precipitation and a small and less significant decrease of the German Adaptation Strategy (DAS) and a collab- in the summer (e.g. ZOLINA et al., 2008; ALEXANDER orative programme of the German Meteorological Ser- et al., 2006). Without a doubt, the magnitudes and fre- vice (DWD), the Federal Institute of Hydrology (BfG), quencies of daily precipitation have become more the Federal Maritime and Hydrographic Agency (BSH) extreme in winter and generally less so in summer (e.g. and the Federal Waterways Engineering and Research ZOLINA et al., 2008; KLEINTANK et al., 2002), although Institute (BAW). Within the context of the KLIWAS there is evidence to suggest that extreme events in sum- research programme and the HYRAS pilot study funded mer in some places in Central Europe could be becoming by the BfG, the DWD developed gridded data sets of rel- more intense. Most studies that have investigated trends evant hydrological parameters on a daily basis for in the spring and autumn seasons also show similar but Germany and the neighbouring river basins. This paper less significant increases to those found in winter (e.g. focuses on the precipitation data set. The currently exist- HUNDECHA and BA´ RDOSSY, 2005). These results are also ing climatologies provide neither the full spatial coverage consistent with other Northern European countries, e.g. of German river basins needed for studies on potential for the United Kingdom (OSBORN and HULME,2002). consequences of climate change for navigation on As temperature rises, the likelihood of precipitation German waterways nor the spatial resolution down to falling as rain rather than snow also increases. This is 1 km and/or the daily temporal resolution needed for especially true in autumn and spring at the beginning hydrological modelling (e.g. SCHNEIDER et al., 2013; and end of the snow season and in areas where tempera- HAYLOCK et al., 2008, EFTHYMIADIS et al., 2006; tures are near freezing. Such changes are observed espe- SCHWARB, 2000, FREI and SCHA¨ R, 1998; MU¨ LLER cially over land in middle and high latitudes of the WESTERMEIER, 1995). Regarding hydrological studies Northern Hemisphere, leading to increased rains but the need for high-resolution precipitation data is always reduced snow pack and consequently diminished water in great demand. resources during summer (e.g. SOLOMON et al., 2007). In this article we present the DWD/BfG-HYRAS v2.0 Nevertheless, the often spotty and intermittent nature of precipitation data set (HYRAS-PRE) covering Germany changes in observed patterns for mean precipitation are and neighbouring river basins using as many of the avail- complex. As climate changes, several influences alter able rain-gauge observations as possible between 1951 precipitation amount, intensity, frequency and type and 2006. The data set is created using the REGNIE directly. Warming accelerates land surface drying and (‘‘REgionalisierte NIEderschlagsho¨he’’, engl. regionalised increases the potential incidence and severity of droughts. precipitation amount) method, which is comprehensively However, a well-established physical law (the Clausius- described for the first time. The REGNIE dataset for Clapeyron relation) determines that the water-holding Germany is well-known both in the hydrological and mete- capacity of the atmosphere increases by about 7% for orological communities. Studies on meteorological fore- every 1°C rise in temperature. This generally tends to casting (SCHWITALLA et al., 2008), on climate simulation cause increased precipitation intensities and the risk of (BELLPRAT et al., 2012; BERG et al., 2012; KOTLARSKI heavy rain and snow events (BERG et al., 2013; BENGTS- et al., 2012), hydrological (GRASSELT et al., 2008; SON et al., 2009; O’GORMAN and SCHNEIDER, 2009). PHOTIADOU et al., 2011) or ecological (TO¨ LLE et al., Fundamental theory, climate model simulations and 2012; SAMANIEGO et al., 2013) modelling have all used empirical evidence all confirm that warmer climates, REGNIE data. One of the research tasks within KLIWAS owing to increased water vapour, lead to more intense was to investigate how well this method could be adapted precipitation events even when the total annual precipita- and expanded to bordering river basins as well as to the tion is slightly reduced. When the overall precipitation Alpine region. Another research purpose was to elaborate amounts increase there are prospects for even stronger the uncertainties of such a gridded data set, which is given events. A warmer climate therefore increases risks of both here by an extensive validation of the data set. drought and floods but at different times and/or places. The decision to use the REGNIE method is based on The distribution and timing of floods and droughts is two aspects: As mentioned in the previous paragraph, the most profoundly affected by atmospheric circulation pat- REGNIE data for Germany are well-known and terns such as El Nin˜o, which triggers the NAO (North accepted, but not yet documented in detail. On the other Atlantic Oscillation), an important teleconnection pattern hand the combination of multiple linear regression for Europe. Some of these observed circulation changes (MLR) considering orography and inverse distance have been associated with climate change (e.g. JACOBEIT weighting (IDW) is very fast and numerically stable for et al., 2009; HAYLOCK and GOODESS, 2004). calculating highly resolved, daily precipitation fields To analyse the potential consequences of climate and carrying out an extended validation. It is known that change on inland and coastal waterways and to formulate an extensive number of interpolation methods exist appropriate strategies for adaptation to the future environ- which can be used with different modulations and with mental conditions, the German government launched the differences in e.g. including neighbouring stations, search research programme KLIWAS (‘‘Impacts of climate radius, sector screening and other calibrations. Often, Meteorol. Z., 22, 2013 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS 237 geostatistical approaches performs better than IDW, as well as multivariate rather than univariate techniques, although the results differ depending on network density and geographical region. In LY et al. (2011) external drift kriging with elevation did not improve the interpolation accuracy in comparison to IDW. Also in regions with a sparse network WAGNER et al. (2012) found that IDW and Kriging have nearly the same error quantities. In DIRKS et al. (1998) no improvements from Kriging instead of IDW were detected. Furthermore, the studies of HEWITSON and CRANE (2005) and HOFSTRA et al. (2008) have shown that the station density, the parameter to interpolate, complex topography or a less representa- tive station network leads to more sensitivity in the results than the choice of the interpolation method – espe- cially for highly variable, daily precipitation processes. This paper is the first part of a trilogy and gives an overview of the DWD/BfG-HYRAS-PRE data base. In Figure 1: Temporal distribution of the number of rain gauge the two following papers, which are in preparation, appli- stations between 1951 and 2006. Different colours indicate the cations of the data sets are presented. In the second paper contributions from the different institutions. an evaluation of the COSMO-CLM by comparison with HYRAS-PRE (BRIENEN et al., in preparation) can be found and in the third paper downscaling and bias correc- Institute, KNMI), Belgium (Royal Meteorological Insti- tion of regional climate projections using the HYRAS- tute, RMI), Luxembourg (LUX Airport and Centre de PRE data set will be introduced (PLAGEMANN et al., in Recherche Public Gabriel Lippmann), France (Me´te´o- preparation). The main focus in this paper is the descrip- France), Switzerland (MeteoSchweiz), Austria (Central tion of the data base and the gridding method of the Institution for Meteorology and Geodynamics (ZAMG) HYRAS-PRE data (Sections 2 and 3). In Section 4 some and Hydrographical Survey (HD)) and the Czech Repub- examples and climatological features of the data set are lic (Czech Hydrological Institute, CHMI). All available presented. The validation by means of cross-validation observations were used for the creation of the DWD/ and Jackknifing is described and the comparison with BfG-HYRAS-PRE data set. An overview of the total other data sets is shown in Section 5. A conclusion number of available stations and their temporal distribu- including an outlook is given in Section 6. tion is shown in Fig. 1. As can be seen, the total number of observations varies significantly over time, though off- sets are particularly prominent: 2 Description of the data base d a near-tripling of the number of Swiss stations in The selected time period and region were chosen specifi- 1961, cally to support the goals and aims laid out in the KLIWAS d about 1000 additional German stations in 1969, and research programme. The data used here extend more than d a strong increase of about 500 stations in Austria in 50 years from 1951 to 2006, nearly twice the minimum per- 1971. iod (i.e. 30 years) recommended for climatological investi- gations by the World Meteorological Organization. The The total maximum number of stations is about 6200 in data set includes all river basins within Germany as well the early 1990’s. To present the differences in spatial as data of most neighbouring countries with shared basins station distribution, the coverage in 1951 and 1991 is (i.e. Rhine, Danube and Elbe). This area is henceforth shown in Fig. 2. Note the significantly increased num- referred to as the KLIWAS domain. Rain gauge data from ber of stations in Switzerland, Austria and Eastern Ger- Poland for the Oder catchment areas were not yet available many for 1991 and the sparse density of available for this study, but it is planned to include them in a future stations in the Czech Republic for this study, which version of the HYRAS data set. remains relatively constant. Between 4000 and 6000 daily reports are available for any particular day of the reference period (1961–1990) in the HYRAS-PRE 2.1 Data collection data set. But in general it should be noted that spa- tially-variable observation networks have a significant Rain gauge data were required and obtained from a num- influence on climatic averages (WILLMOTT et al., ber of national meteorological services and other institu- 1991). There are still considerable inhomogeneities in tions. In addition to Germany, data were received from: the spatial coverage across our domain. It is also the Netherlands (Royal Netherlands Meteorological required to keep this variable density in mind when 238 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS Meteorol. Z., 22, 2013

Figure 2: Spatial distribution of precipitation stations from January 1951 (left) and 1991 (right). The red dots indicate the available stations. Elevation larger than 300 m is shown in yellow-green. interpreting the results of climatological analysies (e.g. time series are affected and become outliers. On the other SEVRUK, 2004). In this context it is also important to hand, a time series is called inhomogeneous if the varia- know that the station distribution with elevation is often tions are not only caused by natural variability (CONRAD sub-optimal in mountainous areas. More stations are and POLLACK, 1950). Inhomogeneities may be due to located in valleys than atop mountains because the sup- changes in the observer and/or observing practices, port and measurement conditions at high altitudes are changes in the instrumentation or changes in the mea- very difficult (e.g. SEVRUK, 1997). Furthermore, there surement environment (for more details see PETERSON are notable differences in the observing practices within et al., 1998). In combination with the natural variations and between the different networks (see for example of precipitation the climate change signal of the time ser- GROISMAN et al., 1991; FREI and SCHA¨ R, 1998; ZOLI- ies can be influenced by such interventions. An in-depth NA et al., 2008). On the one hand, various rain-gauge description and analysis of quality control and homoge- types are used and in the last decade automated opera- neity of precipitation data in Europe can be found in tion was introduced in most countries. On the other BLU¨ MEL et al. (2001) and GONZALEZ-ROUCO et al. hand, different measurement times are common: 8:00 (2001). In addition, the data quality varies between insti- UTC (NL), 6:30 UTC (CH) and 6:00 UTC (all other tutions (e.g. FREI and SCHA¨ R, 1998). Commonly, errone- KLIWAS countries, thus far known). In the following ous daily precipitation amounts (e.g. WIJNGAARD et al. analysis inconsistencies due to the different rain gauge (2003) proposed values less than 0.0 mm or greater than types and due to the different measurement times have 300 mm) are removed and inhomogeneities as well as been neglected to obtain the maximum data base for the inconsistencies flagged and corrected or removed. But gridded data set. an objective data control scheme for both types of errors is very difficult to implement, especially for precipitation because its large natural variability in time and space 2.2 Quality control makes it very difficult to separate inhomogeneities or out- liers from real extremes. Although automated control is By applying quality control checks, large errors in the still ongoing work (SCHERRER et al., 2011) we neverthe- time series can be detected and, if possible, corrected. less performed a uniform quality control of all precipita- Common errors are documented e.g. by WIJNGAARD tion data in the KLIWAS project for which control-rules et al. (2003) and ZURBENKO et al. (1996). Generally, and -results will be presented in the following subsec- there are two different types of errors in time series. tions. Some data providers perform their own quality On the one hand, there are errors from reading, coding control and/or provide homogenised time series, but and the encryption of the data, as well as problems with details of the individual methods used are not known in the data transfer itself. Typically, only single values of a most instances. Meteorol. Z., 22, 2013 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS 239

Table 1: Results of the homogeneity testing for each country. Only time series longer than 30 years were tested.

Country Useful Doubtful Suspect Total stations Institution Germany 2991 (90%) 138 (4%) 183 (6%) 3313 DWD Austria 454 (79%) 49 (8%) 72 (13%) 575 ZAMG and HD Netherlands 233 (84%) 24 (9%) 20 (7%) 277 KNMI Switzerland 192 (79%) 34 (14%) 18 (7%) 244 MeteoSchweiz Czech Republic 85 (90%) 2 (2%) 7 (8%) 94 CHMI France 47 (76%) 4 (6%) 11 (18%) 62 Me´te´o-France Belgium and Luxemburg 6 (53%) 8 (34%) 2 (13%) 16 RMIB & LUX & CRP Total 4008 (87%) 259 (6%) 313 (7%) 4580

Apart from these non-systematic errors, the precipita- values were then tested with the Standard Normal Homo- tion measurements are also affected by a bias in accuracy. geneity Test (ALEXANDERSSON, 1986), the Pettitt Test This bias depends on the precipitation type, the hydrome- (PETTITT, 1979), the Buishand Test (BUISHAND,1982) teor size, the wind speed and temperature as well as the and the von Neumann Test (VON NEUMANN, 1941). Each resulting evaporation errors. Generally, the true precipita- times series was tested against the null hypothesis that the tion amount is underestimated by at least 10% (or more) series is homogeneous with a significance level of 95%. (SEVRUK, 1982). Bias-corrected precipitation data are Two additional criteria were used to verify the inhomoge- often used in hydrological applications, but the calcula- neities: First, the inhomogeneities should not appear in tions for the bias correction require sufficient metadata the first or last five years of the time series, because of (e.g. position and exposition of the station). Up to now the potential to yield uncertain results in the tests. Sec- no bias correction has been applied in this data set. ond, inhomogeneities were neglected if the differences between the mean precipitation before and after the inho- mogeneity were smaller than 100 mm. Time series reject- 2.2.1 Outliers ing more than two of the four tests were classified as ‘‘suspect,’’ series rejecting two as ‘‘doubtful’’, and all Outliers were found by using the interquartile-adjusted other time series were classified as ‘‘useful’’ method described by EISCHEID et al., 1995. They define (WIJNGAARD et al, 2003). As Table 1 shows, about an outlier to be greater than a threshold depending on the 87% of the time series were declared as useful, which statistical properties of each individual rain gauge: is comparable to findings from other data sets e.g. the ECA data set (BEGERT et al., 2008; KLOK and TANK, y > y ¼ q þ f ðq q Þ; ð2:1Þ outlier threshold 50 75 25 2009). For the background field described in Section 3.1, th only stations with homogeneous time series were where qi is the i quantile, ðq75 q25Þ the interquartile range and f an arbitrary parameter. A value of f ¼ 15 included, whereas all values were used in the interpola- was specified from consultations with the extreme precip- tion process of the daily data to incorporate the largest itation maps for Germany (KOSTRA-DWD-2000, database possible. Due to the large effort required for MALITZ, 2000) and applied for all data series. To avoid such a voluminous daily data set, we refrained from using the removal of real extreme values, outliers were flagged relative homogeneity testing as described e.g. by PETER- and only removed if their values proved implausible in SON et al. (1998) and RHOADES and SALINGER (1993).In comparison to neighbouring stations or within the interpo- such tests the time series is tested against neighbouring lated field. stations, which has the additional benefit of detecting changes in a larger region e.g. caused by upgrades in the network. Most available gridded daily data sets are 2.2.2 Inhomogeneities based on non-homogenised time series (e.g. FREI and SCHA¨ R, 1998, HAYLOCK et al., 2008) because there are Four different homogeneity tests were performed on each general difficulties with the homogenisation process as observation time series longer than 30 years to identify well as large efforts required to homogenise all time ser- inhomogeneities caused by non-natural changes. Due to ies (VENEMA et al., 2012). the large daily variability, the tests were performed using yearly precipitation amounts. The selection and applica- 3 Interpolation method tion of the tests was based on WIJNGAARD et al. (2003), who used these tests for the European Climate The irregularly-spaced station observations were interpo- Assessment daily precipitation data sets (ECAD). Only lated to create a regularly-gridded precipitation data set, days with more than 1 mm precipitation were included DWD/BfG-HYRAS v2.0. In this paper, version 2.0 is in the calculation of the yearly precipitation amounts to presented, although we are currently working on further reduce the variability. The resulting time series of yearly improvements. The data set uses the Lambert Conformal 240 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS Meteorol. Z., 22, 2013

Conic Coordinate Reference of the European Terrestrial the homogeneity testing as ‘‘useful’’ (see Section 2.2.2). Reference System 1989 (ETRS89-LCC). As shown by About 4000 stations for the whole KLIWAS domain HEWITSON and CRANE (2005) and HOFSTRA et al. were included in these background fields. The first step (2008), the best interpolation method depends on several to calculating the background fields is a multiple linear factors such as the variable of interest, the desired resolu- regression (MLR). This regression was performed for tion of the gridded data set, the point accuracy of the each calendar month: interpolation method, the orographical complexity of the area of interest, the data quality and the density of yi ¼ a0xi0 þ a1xi1 þ a2xi2 þ a3xi3 þ a4xi4 þ a5xi5 þei 8 > > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > > : the observational network. For the HYRAS-PRE data regi set, the interpolation is based on a combination of multi- ð3:1Þ ple linear regression (MLR) and inverse distance weights

(IDW). This method, which is called REGNIE at the where xik are the k ¼ 1; ::; 5 explanatory variables at sta- DWD (‘‘REgionalisierte NIEderschlagsho¨he’’, engl. re- tion i with xi0 1, yi the response variable, aik the regres- gionalised precipitation amount), is composed of two sion coefficients at station i for the explanatory variables main steps. First, mean background fields are calculated k, ei the residuum and regi the result of the ‘‘pure’’ regres- (see Section 3.1) and second, the daily data are interpo- sion. The five explanatory variables consist of geographi- lated as a ratio of the total precipitation to the climatology cal longitude and latitude, height above sea level, (see Section 3.2). The assumption of this method is that exposition and mountain slope at the stations. The hillside the quantities of precipitation are partly determined by parameters are determined using the elevation data of the geographical factors (like altitude, aspect, and slope) Digital Elevation Model (GTOPO30) from the United and otherwise by daily atmospheric circumstances (like States Geological Survey USGS (1993). At the end of fronts or convection). Therefore, the background monthly the procedure, the regression and the residuum of each sta- climatology fields and their daily anomalies bring these tion were calculated for each calendar month as the mean aspects together. An overview of different interpolation of the period 1961–1990. Only stations with homoge- methods for meteorological data can be found in neous monthly time series were used. The use of MLR with respect to geographic and topographic factors has SZENTIMREY et al. (2007). As shown in previous studies, widely been demonstrated to add considerable value to using the ratio for the interpolation instead of the total spatial interpolation (AGNEW and PALUTIKOF, 2000; precipitation itself gives a better representation of the spa- VICENTE-SERRANO et al., 2003). The explanatory and tial distribution of precipitation, especially for orograph- response variables are known and the regression coeffi- ically complex areas (CHEN et al., 2002; XIE et al., cients can be calculated using the least squares method. 2007; HAYLOCK et al., 2008). The combination of All available (at least 60) stations in one area were used MLR with IDW is often used in meteorology (e.g. to calculate the coefficients for that respective area. One WIDMANN and BRETHERTON, 2000; PERRY and HOLLIS, of the main points of the regression is the classification 2005). In the studies of NALDER and WEIN (1998) and of different climatological areas to optimise the explained BROWN and COMRIE (2002) this combination was shown variance of the MLR. With a cluster analysis based on to yield the lowest errors for both temperature and precip- ANOVA (Analysis of Variance), these areas (named clus- itation. In contrast, HOFSTRA et al. (2008) found that global ters in the following) were identified. The clustering kriging was the best-performing method in their compari- method of Ward (WILKS, 2005) begins with n clusters son of six (global and local kriging, angular distance of size one and continues merging until all the observa- weighting, natural neighbour interpolation, thin plate tions are included in one cluster (so called agglomerative splines and conditional interpolation) for temperature, pre- clustering). The error sum of squares and coefficient of cipitation and pressure. As illustrated in Figures 1 and 2 the determination were stepwise computed. The combination station density in this study is very unequally distributed in of two observations that yield the smallest sum of squares time and space. The REGNIE method was developed to error formed the first cluster. Thus, at each step of the support hydrometeorlogical and hydrological applications algorithm, observations were combined in such a way as at DWD and has been used successfully for many years. to minimize the results of error from the squares. To The main advantage of the REGNIE method is that the achieve the optimum for the HYRAS dataset the whole measured precipitation amounts are conserved, which KLIWAS domain was divided into 30 clusters for every calendar month. Within each cluster the regression coeffi- means that, in contrast to other interpolation methods with cients were determined for all stations. The number of 30 smoothing (e.g. HAYLOCK et al., 2008), observed extreme regions is a good compromise between a too small scaled precipitation events as well as non-precipitation events can fragmentation and a well-explained variance in the differ- be found unchanged in the gridded field. ent regions. In Fig. 3 the distribution of the cluster is shown for September. The pattern of the clusters does 3.1 Background fields not differ strongly between the months. Only areas with pronounced orography (Alps or German Central Uplands) Interpolated background precipitation for the period and border areas of the KLIWAS domain show differences 1961–1990 was calculated using the stations that passed in clustering for different months. The explained variance Meteorol. Z., 22, 2013 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS 241

and the station i is dki and n the number of stations included for the interpolation. For the calculation, all sta- tions within a maximum distance of 20 km were included. If there were no stations within this radius, the radius was extended to 30 km. To obtain the monthly background field, the residuum was added to the result of the regres- sion for grid points without observations. Otherwise the regi and ei values calculated from Eq. 3.1 were used. Despite the larger extension of the KLIWAS domain there are two main differences between the gridding pro- cedure used in KLIWAS for the HYRAS-PRE data set and the standard REGNIE method used in the routine applications for Germany at DWD. Both lie in the calcu- lation of the background fields: First, slightly different elevation data were used. Second, the classification of the clusters, which were combined for linear regression, was based on a different spatial aggregation in the stan- dard REGNIE procedure for the German data set.

3.2 Daily data set The daily precipitation at grid points without stations was calculated using the following three step process:

d The daily precipitation at a station was divided by the Figure 3: Result of the cluster analysis for the stations (September). value of the background field of the appropriate Different colours indicate the different clusters. The attribution of month and grid point. the different clusters were calculated by the nearest neighbour d For grid points without stations, the dimensionless method with respect to the nearest station. The black lines indicate ratio was interpolated via distance-weighting (see the first order catchment areas. Equation 3.2) using the four closest stations. d The daily precipitation distribution was determined by of the MLR in the clusters is about 60% ± 20% (mean and multiplying the dimensionless ratio with the back- standard deviation). Regression coefficients and residua ground field. were applied separately for each cluster. The homoscedas- ticity of residua, tested by the Goldfeld-Quandt-Test for each cluster (GOLDFELD and QUANDT, 1965) revealed that For grid points with stations, the observed precipitation values were used. Note that due to the high spatial reso- about 60% of all clusters were homoscedastic with a sig- 2 nificance level of 95%. More than 80% of all residua were lution of 1 km , two stations could never be assigned to found to be within a range of ±10% deviation from the the same grid point. One basic consideration concerning observed station value, though the residua can reach the quality of gridded data sets is independent from the higher amounts in mountainous regions. Altogether, the gridding method: the density of the usable stations varies MLR model is less representative for stations in Alpine strongly, which influences the quality of the gridded data valleys, leeward areas or stow relief rainfall influenced set. For our method, the quality of the background fields regions, i.e. areas with mesoscale climates that are, spa- (Section 3.1) also plays an important role in the daily tially, highly-versatile. gridded data. Especially in areas of the KLIWAS domain To obtain the background field at grid points without where the precipitation is not dominated by orographic observations the residua of the MLR (ei) and the result of structures and local conditions, the regression coefficients the regression (regi) were interpolated using IDW. There- of the background field are less certain, e.g. in the North fore, the following distance metric was used: German Plain. Pn zk d2 k¼1 ki 4 Examples and climatology ~zi ¼ Pn ð3:2Þ 1 2 dki Many climate indices, which are important for hydrome- k¼1 teorological and hydrological applications, can be calcu- where ~zi is the interpolated value of ei or regi at the grid lated from the daily precipitation values. As a first point i, zk the ei or regi at the station k, which is calculated overview of the data set, two exemplary daily fields by Eq. 3.1. The distance between the centre of the grid k and some climatological features are discussed: first, 242 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS Meteorol. Z., 22, 2013

Figure 4: Daily precipitation field for December 16, 2005: HYRAS-PRE (left) and RADOLAN (right). The black lines and the white lines indicate the first-order catchment areas and country bounderies, respectively. the precipitation characteristics in the KLIWAS domain Here, the RADOLAN product shows greater detail and, second, two results of trend analyses. in the local structures e.g. in the western and northern part of the area, which are not detected by the HY- RAS-PRE data. It is not surprising that in this case the 4.1 Event-based comparison with radar- differences between the two methods are much larger. based precipitation data One of the largest advantages of the HYRAS-PRE prod- uct is the direct measurement of the required variable, Figures 4 and 5 show two examples of daily precipita- although only the precipitation events that are actually tion. For a qualitative comparison, daily fields of precip- recorded by a station can be included. In contrast, the itation from weather radar are also shown (named radar is able to scan the whole area and record all small RADOLAN). The RADOLAN method combines the events if there are no obstacles. Mountains, for example, reflectivity from radar with rain gauge measurements can lead to a partial shadowing of the radar beam (so- (for more details see WINTERRATH et al., (2012). A fron- called partial beam blockings), and ground and fixed ech- tal event from December 16, 2005 is shown in Fig. 4. oes can falsely simulate precipitation where none has The general weather situation was characterised by the fallen. Additionally, if the heavy rain is directly above arriving low pressure system ‘‘Dorian,’’ which caused the radar the measurements are falsified (e.g. in Hamburg very high daily precipitation amounts of up to 100 mm for the example in Fig. 5) because the water on the in the North-Alpine region. The precipitation area cov- radome corrupts the radar signal of the precipitation ered most of the KLIWAS domain with maxima in and leads to an overestimation. regions of higher elevation. In the RADOLAN product, These two examples show that the radar with calibra- the spatial distribution is very similar to the HYRAS- tion from ground precipitation stations is a good alterna- PRE data. However, there are local differences and the tive to analyse single precipitation events with high intensity of the precipitation can be seen to vary. Larger temporal resolution (see also SCHUURMANS et al., differences between both methods can be found in the 2008; WINTERRATH et al., 2012). However, Radar pre- second example. The daily precipitation amounts of June cipitation climatology at DWD is still under development 25, 2005, were mostly generated by convection (Fig. 5). and time series remain too short for some climate appli- The dominating weather event in this case was the storm cations. There is thus still a need for high resolution pre- ‘‘Theo,’’ which was responsible for local hail and heavy cipitation climatologies based solely on surface precipitation in Saxony and Bavaria. For very small areas, measurements, such as e.g. in the KLIWAS research daily precipitation amounts clearly exceeded 100 mm. programme. Meteorol. Z., 22, 2013 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS 243

Figure 5: Daily precipitation field for June 25, 2005: HYRAS-PRE (left) and RADOLAN (right). The black lines and the white lines indicate the first-order catchment areas and national frontiers, respectively.

4.2 Climatology From the HYRAS-PRE data set a number of climatolog- ical studies were performed (e.g. calculation of climate indices). The main focus of this paper is the description of the method and the validation; therefore only a few aspects of the climatological results will be presented here. In Fig. 6 the yearly mean precipitation from 1971–2000 is shown to give an overview of the mean characteristics in the KLIWAS domain. As can be seen in the figure, the mean precipitation is very inhomoge- neous. In the Alps as well as in the Black Forest the yearly precipitation sum tops 2000 mm and exceeds this value in the higher mountain areas. In contrast only pre- cipitation sums of less than 700 mm are reached in the eastern part of the domain, the Elbe basin. In the western regions yearly precipitation amounts up to 1000 mm are common. Apart from these larger scale patterns, the German Central Uplands (e.g. Bavarian Forest, Harz, Ore Mountains, Eifel) are characterised by larger values than the surrounding areas. Furthermore, the Upper Rhine Rift with Vosges and Black Forest is a very prom- inent spatial structure of the mean precipitation with low precipitation amounts in the valley and higher values in Figure 6: Yearly precipitation sum for the HYRAS-PRE data set: the mountainous areas on either side. This strong vari- mean from 1971–2000. The black lines indicate the first order ability is a challenge for the gridding procedure. catchment areas. The results of a trend analysis performed for precipi- tation data in the winter and summer seasons, respec- the mean precipitation of second-order catchment areas, tively, are presented in Fig. 7. We calculated the linear which are one of the concerted spatial division of the trends and their significances between 1952–2005 for KLIWAS project. In contrast to studies of the cooperative 244 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS Meteorol. Z., 22, 2013

Figure 7: Linear trends (top) in % for 1952–2005 for the average amount of precipitation received in a catchment area in the summer months June, July and August (left) and in winter months November, December and January (right). Trends which are smaller than ±4% are grey shaded. Significance levels of the calculated trends (bottom) in the summer (left) and winter (right). project KLIWA (climate change and its impact to water (left part of Fig. 7) with decreases up to 20% observed. resource management, www.kliwa.de), in which trends However, only in the northwest of the domain (excluding of the hydrological half years in the catchment areas of the coastal region) are the decreases significant. These Southern Germany were investigated between 1931– results are generally consistent with other studies for 2010 (KLIWA, 2011), here, the trends on the meteorolog- Germany and Western Europe, where summer trends ical seasons were examined. In Fig. 7 the trends (top) and are also less significant than in winter (e.g. KLIWA, their significance levels (bottom) are shown for summer 2011; ZOLINA et al., 2008; MOBERG and JONES, 2005). and winter. There is a decline in summer precipitation The region has also experienced notable decreases Meteorol. Z., 22, 2013 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS 245 in the frequency of heavy precipitation events of more values (WILKS, 2005). Due to the large computation time than 10, 20 and 30 mm, respectively (not shown). These needed to calculate the daily gridded data set over such a results, in combination with the decline in maximum large area, we randomly removed 20% of the stations in observed values, which are also observed in Germany each recalculation instead of removing every single sta- and the western half of Central Europe, imply that hea- tion for each calculation and repeating the calculation. vier events are occurring less frequently there. In contrast This percentage of 20% is an acceptable compromise to summer, the mean precipitation is generally increasing between a reduction in computation time and a sufficient (20–40%) in winter months (right part of Fig. 7) across conservation of the interpolation quality and is based on the majority of Germany and Central Europe, while rela- test results (not shown). This procedure was repeated five tively weak, non-significant decreases of magnitudes less times to ensure, on average, that every station was statis- than about 10% have occurred in the southern Alpine tically removed once. To calculate the interpolation error, regions of the domain. There is a tendency for larger rel- the removed station values were compared with the inter- ative changes toward the northwest of Central Europe polated values calculated without these stations. For all (i.e. most of Germany) were the trends are highly signif- interpolation error calculations more than 20 values per icant. Trends are also strong across the German Central day with precipitation are necessary to ensure stable Uplands from the Meuse and Mosel basins in the west cross-validation results. To condense the results, we took to the Elbe basin in the Czech Republic (east), although the mean of the differences to determine the mean error with somewhat lower significance values. Again, it must per day. It must be noted that only daily precipitation val- be mentionend that the station density varies with time ues (PREC) exceeding 1 mm per day were investigated (see Fig. 1) and outliers and inhomogeneities may still to avoid the distortion of the results by small precipitation exist in the station data. Both can influence the trends, amounts. The smaller values (PREC < 1 mm/day) were but due to averaging in time and space the trends and analysed with scores based on contingency tables. About their signs are very robust. Furthermore, we have pre- 60% of all days in the station data are so called dry days formed station data analyses which have shown the sim- with PREC less than 1 mm/day. ilar trend results for the mean precipitation (not shown). Fig. 8a shows a pronounced seasonal cycle for the Comparable results were also found e.g. by ZOLINA et al. mean absolute error (MAE, see Equation A.1 in Appen- (2008). dix A) of each calendar month. The median is smaller than 1.5 mm/day between October and April and approaches 2.5 mm/day in summer. The seasonal cycle 5 Validation is caused by different seasonal precipitation amounts and also by the different dominating precipitation mech- The quality of the data set was analysed using the meth- anisms. In summer, the total precipitation is generally lar- ods described in Sections 5.1 to 5.3. First, the results of a ger and the precipitation patterns are more patchy due to cross-validation are presented. By means of these error convection than in winter. Different quantiles (10%, 25%, measures the users of the data set are able to assess the 75% and 90%) are also presented in Fig. 8. The upper interpolation error, i.e. the quality of the data set and its quantiles show that the errors can exceed two times the reliability for different regions and seasons. Second, Jack- mean. As can be seen from the lower quantiles, there knifing results show the general influence of the station are also many days with smaller MAE. density on the gridded dataset. Third, a comparison with With this error measure, however, it is not possible to other existing climatologies allows one to identify the differentiate if the gridded precipitation amounts are sys- characteristics of the data sets. These validation results tematically under- or overestimated compared to the sta- enable the assessment of uncertainties due to the gridded tion values. From the mean relative error (MRE) (see data set in such applications as e.g. evaluation of climate Equation A.2 in Appendix A) shown in Fig. 8b it can models, bias correction of climate models, and hydrolog- be seen that the majority of MRE values are positive. ical impact modelling. This means that the station precipitation amounts are smaller than the gridded values: there is an overestima- 5.1 Cross-validation tion of precipitation in the gridded field due to a reduc- tion of stations in the gridding procedure. In summer As mentioned already in Section 2, the number and spa- months the overestimation is larger: more than 75% of tial distribution of stations, on which the gridding is the MRE values are greater than zero, which means that based, essentially influences the quality of a data set. the 25%-quantile can be found above zero. This could be We applied the method of cross-validation to estimate caused by the dominance of convective precipitation the interpolation error. During the cross-validation, one events with large precipitation amounts, which are highly or several station values were removed from the sample localised. Summer precipitation is more often smoothed and the field was recalculated. Afterwards, the results out in the surrounding grid cells than in winter, where of the reduced sample field were compared with those the precipitation patterns generally have a larger extent. of the full sample or the calculated values of the reduced In winter, more than half of the days show an underesti- data product were compared directly with the removed mation. We assume that the larger-scale precipitation 246 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS Meteorol. Z., 22, 2013

Figure 8: Results for the cross-validation of the mean daily precipitation averaged over each month and the KLIWAS domain: Monthly distribution of (a) the mean absolute error (MAE) in mm/d, (b) the mean relative error (MRE) in %, (c) the correlation (COR) and (d) the bias score (BSC). The black line is the median, grey the mean and the red and yellow lines are the 25% and 75% quantiles and the 10% and 90% quantiles, respectively. induced by frontal systems can be better interpolated with days with precipitation smaller than 1 mm/day are under- our gridding method and the underestimation of up to estimated. This feature is slightly stronger in summer and 25% of the MRE values is due to smoothing effects. With winter seasons than in spring and autumn. the comparison between the MRE and MAE, it is possi- To analyse the spatial distribution of the cross-valida- ble to separate the effects of the seasonal dependence of tion errors they were also calculated as averages over sec- the total precipitation from the effects of different precip- ond-order catchments areas. The mean of the MAE and itation patterns. The MRE is defined such that the sea- MRE are shown in Fig. 9. We want to emphasise that sonal dependence of the total precipitation amount is the individual daily interpolation errors can differ enor- removed by the normalisation. On account of the remain- mously, as can be seen in the quantile values in Fig. 8. ing seasonal cycle in the MRE, the precipitation patterns The largest MAE exists in the Alps and other mountain- due to different precipitation mechanisms influence the ous areas. In flat and coastal areas, the error is smaller error measures more than the total precipitation amount. because of less orographic complexity, which can signif- The correlation (see Equation A.3 in Appendix A) icantly influence the processes of precipitation genera- shows large values for all months, which implies that tion. In the eastern part of the KLIWAS domain, total the spatial distribution is well-reproduced in the gridded precipitation is generally lower and the MAE conse- data over all seasons (see Fig. 8c). However, from the quently smaller. The MRE, in which the dependence of spread of the correlation and the larger values in winter the total precipitation amount is removed by the normal- than in summer, one may induce that the type of precip- isation, shows values between 2and6% in most parts itation largely influences the quality of the interpolation of the KLIWAS domain. This implies that the precipita- result (i.e. frontal events are much more precisely repro- tion is often underestimated in the daily gridded data. duced than convective events). Further investigations Only in the Alps are there areas with overestimations have shown that the correlation decreases with height up to 2%. Here, the MRE is clearly smaller because (not shown), but it must be noted that the station density the total precipitation amount is generally larger than in and their representativity are also lower in mountainous the rest of the area. The unclear patterns in the Czech areas than in lowland areas. republic and in some parts of Austria are perhaps due For precipitation amounts smaller than 1 mm/day the to the lower number of available measurements (see bias score (BSC) (see Equation A.4 in Appendix A) was Fig. 2). The spatial distribution of the correlation is very calculated. This score compares the frequency of events uniform; only in the south-east are the values smaller (not in the gridded field with the frequency of events in the shown). This could be attributed to different reasons: station data. More than 90% of the calculated BSC values First, there are lower total precipitation amounts and a are smaller than one (see Fig. 8d), indicating that in the lower number of precipitation events. Second, the precip- station data, more values less than 1 mm/day exist than itation mechanism may be different because large precip- in the interpolated precipitation values. The gridding pro- itation events in this area are mostly caused by more cedure tends to interpolate more precipitation across the continental processes, which means that a large part of area than is measured, which means that the number of the total precipitation is not caused by Atlantic low Meteorol. Z., 22, 2013 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS 247

Figure 9: Different error measures of the cross-validation calculated as the mean for the whole time period (1951–2005) and catchments areas of the second order: mean absolute error (MAE) in mm/day (left) and mean relative error (MRE) in % (right). pressure systems. Furthermore and as mentioned above, the lower station density in the Czech Republic and in some parts of Austria places a probabilistic limit on the likeliness of event observation.

5.2 Jackknifing The influence of station density was investigated using the Jackknifing method described in (WILKS, 2005). Stepwise, more and more stations used in the interpola- Figure 10: Mean absolute error (MAE) in mm/day calculated with tion were iteratively removed from the data set to demon- the Jackknifing method and averaged over each month and the strate the evolution of the error. For the calculation of the KLIWAS domain. Different densities of stations (10%–70%) are used for the calculation and indicated by different colours, where error measures, the data of the field with fewer stations e.g. 10% means that 10% of the stations were removed before were compared with the full analysis for daily precipita- recalculating the gridded data set. tion (greater than 1 mm/day only). It is possible to esti- mate the minimum number of stations required for a certain error, but the error itself always depends on the noted that seasonal differences are smaller than the differ- quality of the full data product. As shown in Fig. 1, ences due to the reduction of the stations by 50%. From the number of stations is not constant over time these results it is clear that a reduced station density (1951 – 2006). Therefore the number of stations is increases the MAE very quickly. reduced relative to the full data product. Note that the For the months January and July the spatial distribu- reduction steps are 5% and 10%, respectively. The error tion of the MRE is shown in Fig. 11 for reductions of increases with the reduction level almost linearly, which 10%, 50% and 70%. As mentioned above, the errors gen- means that the increase of the MAE between the 10% erally increase with the reduction in station density, and 20% station reductions relative to the total number although there are strong dependencies on the location, of stations has approximately the same magnitude as i.e. the geographical conditions as well as the total station the increase between 60% and 70%. A seasonal influence density available in the surrounding area. In all cases the can be seen in all levels of reduction, with the largest effects of single stations are clearly visible by strongly mean absolute error in summer and the smallest values increasing or decreasing errors (named bull’s eye pat- from October to April (see Fig. 10). The values of terns). In the comparison of the seasons, the larger summer are nearly double those in winter. It has to be errors in summer are also visible as in the results of the 248 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS Meteorol. Z., 22, 2013

Figure 11: Mean relative error (MRE) in %/day calculated using Jackknifing for different station densities (10%, 50% and 70%) for January (top) and July (bottom). 10% means that 10% of the stations were removed before recalculating the gridded data set. cross-validation. The main point of this analysis, how- possible to determine a minimum station density. ever, is the spatial distribution: a reduction of only 10% Because all results are relative to the full data set, it is causes large negative MREs in the Alpine region, which therefore necessary to compare the product based on rain dominate the errors of the whole KLIWAS domain and gauge data with other independent data sets. Unfortu- indicate an underestimation of the precipitation. In con- nately satellite data do not yet have the required quality trast to these results, a stronger reduction of station den- and radar data time series are still too short for climato- sity produces (apart from the Alpine region for up to 50% logical studies. Additionally, there are large uncertainties reduction) positive MREs. The precipitation is overesti- in the algorithms for converting radiometric measure- mated in comparison to the full data product, which ments into precipitation rates at the surface (e.g. KRAJEW- means that the precipitation measured at a station is dis- SKI et al. (2010). At the moment, only the comparison persed into the surrounding area. The different behaviour with other gridded data sets is possible for investigating in the Alpine region may be due to the complex orogra- climatological features (see next section). phy, which strongly influences the background field. Fur- thermore, the reduced station density in the Czech Republic contributes to larger errors than in the rest of 5.3 Comparison with existing climatologies the area. The reduction of 70% imposingly demonstrates that with such a low network density, the generation of a Although several climatologies currently exist for high resolution gridded field is futile. Generally, the need Europe, the HYRAS data set was developed specially for a high station density is evident, although it is not to address the requirements of the KLIWAS research Meteorol. Z., 22, 2013 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS 249

Table 2: Data sets used for comparisons with main characteristics and references.

Data set Region Spatial resol. Period Temporal resol. References HYRAS-PRE v2.0 KLIWAS domain 1 km 1951–2006 daily this publication EOBS v6.0 Europe 25 km 1950–2011 daily HAYLOCK et al. 2008 DWD_MONTHLY Germany 1 km 1891–present monthly MU¨ LLER-WESTERMEIER 1995 1 ¨ ALPIMP Alpine region 6 degree 1971–1990 monthly mean EFTHYMIADIS et al. 2006 FREI &SCHAR 1998 1 PRISM Larger Alpine region 48 degree 1971–1990 monthly mean SCHWARB 2000 SCHWARB et al. 2001 programme with a high spatial and temporal resolution across the KLIWAS domain. Nevertheless, the HYRAS-PRE data set was compared with other data sets to gain insight into the variability of regionalised precip- itation data sets based on different interpolation methods, spatial resolutions and topographic data. First, the precip- itation distribution of the whole KLIWAS domain is pre- sented in this section. Second, we focus on two regions for the comparison, (i) the Alps and (ii) Germany as a whole. A description of the data sets used can be found in Table 2.

5.3.1 Precipitation distribution Figure 12: Probability density functions (PDF) of the daily The probability density functions or histograms of the precipitation amounts in mm for the KLIWAS domain for the time daily precipitation amounts provide information on how period 1951–2006 based on station data, the HYRAS-PRE and the well the relative intensities of the daily precipitation EOBS data set. The calculations for the gridded data sets are based amounts are reproduced in the gridded field. In Fig. 12, on their original spatial resolution. the distributions for the station data, the HYRAS-PRE data set and also for the EOBS data set are shown (HAYLOCK et al., 2008). For the different classes, which underestimated. This results in a strong overestimation arealsousedbyCHEN et al. (2008), the daily precipita- with more than three times more events up to 1 mm. tion values of the station and gridded data were counted The non-precipitation events are similar to those in the and scaled by the total number of events. Note that the station data set, which can be due to coarse resolution. the original spatial resolution of each gridded data set More than one station can be found inside a grid point is used in the calculation. The main characteristics of and therefore the smoothing of small precipitation values the station and the HYRAS-PRE data are generally very into the surrounding field occurs less frequently. The similar and differences are generally only found for results show that the high spatial resolution plays an precipitation amounts smaller than 3 mm. The station important role for heavy precipitation events and that data show more non-precipitation events, while the the conservation of the station values within the gridded HYRAS-PRE data set shows more precipitation events field enables the analysis of such events. Nevertheless, in the following two classes with larger amounts up to the distinction between non-precipitation and small pre- 3 mm. This behaviour can be explained by the gridding, cipitation events is blurred in the gridded data set, which where relatively frequent small precipitation amounts are has also been documented for other gridding procedures smoothed and spread out over the surrounding grid cells (e.g. CHEN et al., 2008). This feature of the gridded data without stations, causing an underestimation of non- must be considered when analysing, for example, both precipitation events and an overestimation of small pre- dry and wet days. cipitation values. With our method it is only possible to create grids with no precipitation if there is a measure- ment with 0 mm/day at the grid point, or if all surround- 5.3.2 Alpine region ing stations included in the interpolation show no precipitation. In contrast to the high resolution of the In the KLIWAS domain the Alpine region, due to its HYRAS-PRE data set (1 km), the EOBS data are based complex orography, is the most ambitious region for on a 25 km grid. With the coarser resolution, precipita- the regionalisation (see also DUMOLARD, 2007). All tion events with daily amounts larger than 10 mm are available data sets in this region, i.e. ALPIMP (EFTHYMI- not resolved and events between 1 and 10 mm are clearly ADIS et al., 2006), PRISM (SCHWARB, 2000)andE-OBS 250 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS Meteorol. Z., 22, 2013

Figure 13: Comparisons of monthly mean values between HYRAS-PRE and other data sets (1971–1990) for the Alpine region (top, a+b) and Germany (bottom, c+d). On the left side (a+c) the monthly mean precipitation in mm/month is shown and on the right side the mean absolute error (MAE) in mm/month (b+d). Note the different y-axis for the monthly mean precipitation.

(HAYLOCK et al., 2008), are listed with the version, tem- Between these two data sets the mean absolute error poral and spatial resolution, period and references in (MAE) is smaller than 5 mm/month (Fig. 13b). The Table 2. For the comparison, the common period of MAE between the HYRAS-PRE data set and both 1971–1990 and the ALPIMP grid were used. In Alpine climatologies is also small with 5–10 mm/month. Fig. 13a the monthly mean values are shown. The sea- The largest differences between the data sets occur when sonal behaviour of all data sets is very similar. The largest compared to the EOBS data set, where the MAE is larger precipitation amounts of more than 120 mm can be found than 10 mm/month. For all data sets there is no clear sea- in June and small values less than 85 mm between Octo- sonal cycle in the MAE. We also investigated the spatial ber and May. The EOBS data set shows smaller precipi- correlation (not shown) between the data sets, which tation amounts during all months. We assume that the (excluding the EOBS data) are larger than 0.95, whereas coarser resolution of all investigated data sets and the par- the values for the comparisons with the EOBS data are tially reduced station density in some data sets are the between 0.7 and 0.9. In spite of the good agreement in main reasons for this. The strongest similarity between the mean values there are systematic differences between the data sets can be found between the PRISM and the the HYRAS-PRE data set and, for example, the PRISM ALPIMP data sets. Both use additional weightings in data set. As seen in Fig. 14, the HYRAS-PRE data set the interpolation method to take into account elevation, shows smaller mean yearly precipitation sums in the distance and angular information between the stations. Eastern and Southern Alps of about 100 mm, but larger Meteorol. Z., 22, 2013 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS 251

Figure 14: Differences between the HYRAS-PRE and the PRISM data set for the yearly precipitation sum on the PRISM grid of about 2 km: mean of 1971–1990.

amounts in the Western part of the area. A similar pattern in the spatial distribution of the differences is found in the comparison between daily values of the HYRAS-PRE and EOBS data set (see Fig. 15). In addition, the HY- RAS-PRE data set shows smaller values in the valleys and larger ones atop mountains compared to PRISM. The observed differences could be due to different station Figure 15: Differences between the HYRAS-PRE and EOBS data density, interpolation method and topographic data and set based on daily fields on the EOBS grid of 25 km: mean of 1971– 2000. are an indicator for the uncertainty for the gridded precip- itation data set. 6 Summary and outlook 5.3.3 Germany A precipitation climatology covering Germany and Since most of the KLIWAS domain covers Germany the neighbouring river basins, the DWD/BfG-HYRAS v2.0 HYRAS-PRE data set was compared with other data sets precipitation data set (HYRAS-PRE), was successfully of Germany. In Fig. 13c a comparison of monthly mean developed at the DWD. In contrast to other existing data values between the HYRAS-PRE, EOBS (HAYLOCK sets, the high spatial and temporal resolution as well as et al., 2008) and the DWD_MONTHLY climatology the domain are unique and necessary for the hydromete- (MU¨ LLER-WESTERMEIER, 1995) is shown. The analysed orlogical and hydrological applications in the KLIWAS period is 1971–1990 and the common grid is the EOBS project. Within the project and beyond, the HYRAS- grid. The differences between the data sets are small and PRE data set can be used for the bias correction of regio- not as clear as in the Alps. For all months, the HYRAS- nal climate model output, hydrological modelling, studies PRE data show the largest precipitation values, which of precipitation climatology and other hydrologically-rel- can be explained by the higher station density and the evant indicators. The first successful application of the gridding method with station precipitation amount con- data sets was produced by BERG et al. (2012). servation. The seasonal variation is smaller than in the It has been observed that the REGNIE method pre- Alpine region and the monthly sums vary between 50 sented in this paper works particularly well with a dense and 100 mm. The MAE is small with 5 to 12 mm/month station network. A slight variation of the station density (see Fig. 13d). An investigation of the whole (1951– or the relocation of stations influences the quality of 2006) period shows similar results. The average correla- the gridded data only marginally. In contrast to other pro- tion of daily precipitation amounts (not shown) between cedures, this method reproduces the observed daily the HYRAS-PRE and the EOBS data set for the precipitation amounts in the respective grid cells, which 1951–2006 period is about 0.8, which means that the data includes heavy precipitation as well as non-precipitation sets aggregated on a coarse resolution result, on average, events. Performing a detailed validation enabled the in fields of similar precipitation amounts with similar spa- quantification of the interpolation errors with respect to tial structures. The mean daily differences confirm this time and region, which is important information for all (see Fig. 15). The differences in Germany are smaller following applications. Generally, the results of the than 10 mm/day for most grid points. cross-validation showed that precipitation greater than 252 M. Rauthe et al.: A Central European precipitation climatology – Part I: HYRAS Meteorol. Z., 22, 2013

1 mm/day is more often than not overestimated and that Bulding and Urban Development (BMVBS). The small precipitation amounts are mostly underestimated in DWD/BfG-HYRAS-PRE data set was created during the gridded field. Furthermore, the results of the Jackknif- the HYRAS project, funded by the Federal Institute of ing procedure demonstrated the importance of high sta- Hydrology (BfG), and the KLIWAS research pro- tion density. In comparison with other data sets, a gramme. We are indebted to the following institutes for general agreement of the precipitation amount and the providing daily precipitation data: Royal Netherlands spatial distribution was found. Larger differences were Meteorological Institute, De Bilt; Royal Meteorological found in more orographically complex areas. These dif- Institute of Belgium, Brussels; Administration des Ser- ferences are indicative of the uncertainties due to the dif- vices Techniques de l’Agriculture, LUX Airport and ferences in station density, interpolation method and Centre de Recherche Public Gabriel Lippmann, Luxem- topographic data. Additionally, the advantages in high bourg; Me´te´o-France, Toulouse; Federal Office of Mete- spatial resolution and high station density were also dem- orology and Climatology MeteoSwiss, Zu¨rich; onstrated. Within the KLIWAS project, the data are deliv- Zentralanstalt fu¨r Meteorologie und Geodynamik, Wien; ered to impact modellers in different resolutions: 1x1 km2 The Ministry of Life, Austria; Czech Hydrometeorologi- and 5x5 km2. These analyses are in progress and an eval- cal Institute, Prague. The E-OBS data set is from the EU- uation of a potential added value of the high resolution FP6 project ENSEMBLES (http://ensembles-eu.metof- dataset will be carried out in due time. fice.com) and the data providers in the ECA&D project In the future, more detailed climatological studies are (http://eca.knmi.nl). With many thanks we acknowledge planned; only the first results were presented in this MeteoSwiss and ETH Zu¨rich for providing access to paper. We found a clear increase in winter precipitation the gridded Alpine precipitation climatology (PRISM) of up to 40% (1952–2005) and indications of light and the Climate Reseach Unit from the University of East decreases in summer precipitation. Both results varied Anglia for the precipitation data set for the Greater Al- in the trend magnitude and their significance across the pine Region (ALPIMP). 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Appendix A Correlation:

PN The following error measures were used to quantify the ðxi xÞðyi yÞ quality of the data set for precipitation values greater than COR ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii¼1 ðA:3Þ 1mm: PN PN 2 2 Mean absolute error: ðxi xÞ ðyi yÞ i¼1 i¼1 1 XN MAE ¼ jx y jðA:1Þ where N is the number of values, x the value of the grid- N i i i i¼1 ded field, yi the observation at the station and x and y the mean of gridded and station values, respectively. To quantify the precipitation amounts below 1 mm, Mean relative error: the bias score was used: 1 XN x MRE ¼ ð100 i 100ÞðA:2Þ hits þ false alarms N y BSC ¼ ðA:4Þ i¼1 i hits þ misses