The classification of atmospheric circulation and weather patterns (WPs) is used in climate and meteorology researches since the beginning of these sciences, see El-Kadi and Smithson (1992), Yarnal et al. (2001), Huth et al. (2008) and Philipp et al. (2010) for reviews. The aim of these classifications is to define a limited number of typical synoptic meteorological situations for a given region. For instance, Kaufmann and Weber (1996) defined a classification over the Alpine region aiming at describing the typical Alps wind fields. In general, a circulation pattern classification is based only on geopotential fields, while a WP classification is based on one or more geopotential fields and some other relevant meteorological variables. Here, we focus on WP classification developed for heavy rainfall spatial explanation. This type of rainfall-based WP classification is able to provide information on heavy rainfall spatial distribution using geopotential information. Indeed, Littmann (2000) shows that geopotential fields can provide significant information on heavy rainfall events. Boé and Terray (2008) proposed a WP classification to explain winter rainfall fields in France, while Romero et al. (1999), Trigo and DaCamara (2000) and Martínez et al. (2008) classifications were focussed on rainfall description in Western Mediterranean region. Garavaglia et al. (2010) proposed a WP classification on France for the estimation of heavy rainfall quantiles based on a compound distribution. These classification methodologies follow a ‘bottom-up approach’: the ‘bottom’ part consists of the definition of a given number of classes based on daily rainfall fields over a given region which are then linked to geopotential information in the ‘up’ parts. Note that one of the main objective of these classifications is to be more focussed on ‘where does it rain’ information rather than on ‘how much does it rain’ information. An important motivation for using this type of classification is that the bottom-up approach, consisting in linking the rainfall information to the geopotential fields, could a priori be very interesting for the exploration of future climate scenarios, giving the fact that global circulation models are known to give more robust information on large scale features like geopotential than on small spatial scale phenomena like rainfall (Räisänen, 2007).
Traditionally, the geopotential height fields used in WPs classification are centred on the region for which the classification is done. Moreover, the spatial coverage of geopotential height fields is chosen depending on the available data and on the spatial extent of the region to be covered. However, the ‘optimal’ classification could a priori be defined on a geopotential field not centred on the region. We argue that the spatial extent, the position and the characteristics of geopotential height fields used to classify WPs on a given region are important choices when defining a classification.
The general aim of the paper is thus to introduce a WP classification useful for the description of Austrian heavy rainfall spatial distribution. The classification is based on a bottom-up approach. The classification process is improved via the definition of an optimization procedure for the choice of the geopotential information considered. A specific aim of the paper is thus to show that the optimization procedure is relevant for capturing physical information on synoptic situations responsible for heavy rainfall and that it can improve WP classification performances.
The optimization is based on the WP classification methodology introduced by Garavaglia et al. (2010) for France, including methodological choices that are inherited of previous works on quantitative precipitation forecasting, using the analogue method (Guilbaud and Obled, 1998; Obled et al., 2002; Bontron, 2004). Note that the geopotential grid used in the analogue method results from tests of different locations, sizes and characteristics (Obled et al., 2002). This methodology was shown to be useful for the definition of a rainfall compound distribution in France (Garavaglia et al., 2010) and was also applied to other domains (e.g. by Brigode et al. (2012) over British Columbia). All methodological hypotheses are listed and verified in this study. The proposed optimization procedure consists in finding the size, the location and the characteristics of the geopotential fields that better explain the spatial distribution of the rainfall on a given region. The definition of a WP classification over Austria is then presented. Several classifications were developed in the past for modelling rainfall over this region (Ehrendorfer, 1987; Matulla et al., 2003; Seibert et al., 2006).
Recently, numerous WP classifications have been defined over the region within the COST 733 action (harmonization and applications of weather types classifications for European regions; http://cost733.met.no/about_cost733.htm). The COST 733 action main objective is to ‘achieve a general numerical method for assessing, comparing and classifying weather situations in Europe, scalable to any European (sub)region with time scales between 12 h and 3 d and spatial scales of 200–2000 km, applicable for a number of applications’. The performances of the proposed classification are thus compared to the performances of COST 733 classifications.
The method used for the WP classification is summarized in Section 2. The rainfall and geopotential data used in the study are described in Section 3, while in Section 4, the results of the optimization for the definition of Austrian WPs are presented and discussed. Finally, some conclusions are drawn in Section 5.
As introduced in the previous section, a rainfall days classification is first generated as the ‘bottom’ steps. This classification is then linked to different geopotential informations implementing the ‘up’ steps.
2.1. The bottom part of the classification: generating one rainfall classification
This first part of the classification process is the ‘bottom’ part, only dealing with rainfall information. The main objective of this part is to identify a limited number of typical rainfall classes characterized by similar heavy rainfall spatial patterns.
The first step consists of the selection of a ‘rainy days’ subpopulation. Suppose that a meteorological dataset is available and is composed of n rainfall series observed on a given region at daily resolution. Each day j is thus characterized by a rainfall vector of size n. The rainy days can be selected using an average rain depth threshold (e.g. all the days with > 5 mm of spatial average precipitation are considered as rainy days) or using a fixed proportion of all the observed days (e.g. the 20% days with the highest rain depth are then considered as rainy days). The need of a classification more focussed on ‘where does it rain’ information than on ‘how much does it rain’ information is fulfilled by the use of the ‘shapes’ of the rainfall fields. These rainy day shapes, named Rj, are defined in a rainy days space of dimension n and obtained with the normalization of each rainy day rainfall field by each day average precipitation depth.
In a second step, a hierarchical ascendant classification is performed on the Rj vectors previously identified. The classes are generated using Ward's (1963) method, which chooses iteratively the grouping presenting the minimum intra-class inertia (Cheng and Wallace, 1993). The final number of rainfall classes (NRC, which contains all the rainfall classes and one non-rainy class) is determined by looking at the intra-class inertia evolution as a function of the number of classes. Finally, the NRC rainfall classes gather days characterized by rainfall fields with similar spatial distribution.
2.2. The first ‘up’ steps: optimization of the geopotential information used
The ‘up’ steps consist now in moving into the geopotential height space and finding optimal geopotential information explaining the rainfall generating processes coming from the synoptic scale.
First, the rainfall classes and the non-rainy class centroids are projected onto the geopotential height space. Like for the rainfall fields, geopotential field shapes are used and are thus previously estimated with the normalization of each geopotential field by each day average geopotential height. Each day j is thus characterized by a geopotential field vector , where m indicates the dimension of the geopotential field space. The centroid of the rainfall class A is defined as the mean geopotential field vector of the nA days composing the class, named in the defined geopotential space.
The geopotential height space can be composed of different geopotential fields at different heights (e.g. 500, 700 and 1000 hPa, etc.) and recorded at different times (e.g. 0, 12 and 24 h, etc.) on several geographic locations (i.e. different grid points). For example, the geopotential height space of day j can be described by a vector G, composed of two different height fields estimated on 500 grid points. The geopotential space used by Garavaglia et al. (2010) is characterized by a vector G440, because the geopotential space is defined at two heights (700 and 1000 hPa), for two times per day (0 and 24 h) and on 110 points grid covering a spatial extent of around 106 km2. Note that a principal component analysis (PCA) of each potential space is implemented in order to reduce the number of dimensions of this space to 10. All the optimization procedure tends to find the optimal geopotential field space m onto which the rainfall class centroids are projected.
2.3. The final ‘up’ steps: reattribution of each day to one WP
The last classification step consists in reattributing each day (considered as rainy or not) to a given WP in estimating the Euclidian distances between the considered day and the class centroids. The considered day is then attributed to the WP witch is the closest one. Note that some ‘no rainy days’ can thus be considered as members of a rainy WP if they are closer of a rainy WP centroid in the considered geopotential space.
Finally, our classification is no more driven by the prior rainfall information but by the geopotential field information. Finding rainfall data set with good spatial and temporal coverage and good data quality over a specific area is harder than geopotential information. Thus, classifications can be easily extended using only other geopotential data set, like National Oceanic and Atmospheric Administration (NOAA) 20th Century Reanalysis (6 hourly geopotential height fields from 1871 to 2011, Compo et al., 2011) or EMULATE reanalyses (daily mean sea-level pressure reconstructions over Europe for the period 1850–2003, Ansell et al., 2006).
2.4. Cramér–von Mises test for classification evaluation
Numerous criteria exist for evaluating classification performance. The Cramér–von Mises test (Anderson, 1962), named Cramér further, is typically used as a ‘basic’ tool to check the discriminating power of a WP classification in terms of rain/no rain occurrence (Bárdossy et al., 1995; Stehlik and Bárdossy, 2003; Bliefernicht and Bárdossy, 2007; Garavaglia et al., 2010). The Cramér coefficient can be estimated for each available rainfall series with a contingency table, constructed with the considered WP classification (vector with one WP for each day) and a vector of rain/no rain occurrence (vector with, for each day, either 0 if the rain average is null or 1 if rainfall is observed). Thus, the Cramér performances of each classification and each rainfall series are estimated as follows:
where χ2 is the result of a classical dependence χ2 test between the WP classification and the rain/no rain occurrence vector and nd is the number of classified days. This score ranges between 0 (no dependence between the classification and the observed rain/no rain occurrence) and 1 (absolute dependence). To focus on heavy precipitation, the Cramér coefficient can be estimated on a sub-sample population of heavy rainfall composed of the days with a precipitation amount greater than a given threshold. The performances of each WP classification produced are thus evaluated using this type of score qualifying their discriminating power in terms of rain/no rain occurrence. Figure 1 presents an example of the evaluation of one hypothetical classification in three classes with the Cramér test. The considered classification is thus compared with a rain/no rain vector generated from the observed rainfall record studied. A threshold T can then be fixed in order to test the discriminating power of the classification in terms of heavy rainfall.
The two archives used in this study are (1) information on rainfall fields (needed for the identification of Austrian rainfall classes) and (2) information on the synoptic scale (required for the projection of these classes onto the geopotential height space). WP classifications defined in the COST action 733 are finally used for analyzing WP classification performances.
3.1. Rainfall fields
The Austrian daily rainfall field is obtained from the European Climate Assessment and Data (ECA&D) reanalyses data set (Haylock et al., 2008) providing daily precipitation amounts (calculated as the sum of rainfall at 18 UT of the current day and rainfall at 06 UT of the next day) with a resolution of 0.5° × 0.5° for the period 1950–2008. A sub-domain of 300 000 km2 is extracted to cover the Austrian territory (from 9.25°E to 17.25°E and from 46.25°N to 49.25°N) and consists thus of 119 rainfall reanalysis series. This grid is shown with red points in Figure 2.
3.2. Geopotential fields
The geopotential height space is characterized by daily geopotential height fields at 700 and 1000 hPa. These fields, provided by the National Center for Environmental Prediction (NCEP) and National Center for Atmospheric Research (NCAR) reanalysis (Kalnay et al., 1996), are defined on a 2.5° resolution grid for 247 points in Western Europe, at 00 and 24 UT. Thus, each day is described by four geopotential fields defined on 247 points. The NCEP–NCAR grid is shown with black points in Figure 2.
3.3. COST733 WP classifications
Numerous WP classifications have been defined within COST 733 action and are available and could be downloaded on the COST 733 wiki website (http://geo23.geo.uni-augsburg.de/cost733wiki/). 76 COST 733 classifications defined two at a time on the domains D06 (Alps, from 3° to 20°E and from 41° to 52°N) and D07 (Central Europe, from 3° to 26°E and from 43° to 58°N) have been extracted in order to compare these classifications and the Austrian WP classification defined here with a ‘bottom-up’ approach. Note that these classifications have been defined with different methodologies and are characterized by different number of WPs (from 7 to 13 classes for the D06 domain and from 8 to 13 for the D07 domain).
4.1. The ‘bottom’ steps: hierarchical ascendant classification of the rainy days
In this section, some first illustrations of the ‘bottom’ steps, which results in the definition of one Austrian rainfall classification, are presented. Following the steps depicted in the Section 2, we defined a rainy day as a day with a total rainfall amount greater than the 80th percentile of the total population.
The number of rainfall classes, and consequently the number of WPs, is here chosen by looking at the intra-class inertia evolution in the dendrogram as a function of the number of classes (Figure 3). Each difference D1 is estimated as the absolute value of the difference between the intra-class inertia estimated for n + 1 rainfall classes and the inertia estimated for n classes. The intra-class inertia evolution suggests the choice of four rainfall classes and one non-rainy class. Note that, to ensure a significant number of observations in each class and define a simple operational classification, we should consider a parsimonious number of classes (typically fewer than ten classes). For instance, in the ‘French classification’ described in Garavaglia et al. (2010), this number is thereby fixed to eight classes (seven rainy classes and one non-rainy class). Moreover, the previous works on Austrian rainfall classification result in a number of classes never higher than seven (Matulla et al., 2003; Seibert et al., 2006).
The choice of five classes (four rainy classes and one non-rainy class) is also comforted by the visual analysis of the rainfall fields characterizing the five classes and reported in Figure 4. Indeed, we can observe that class 1 is characterized by a rainfall spatial distribution centred in the north-western part of Austria, in the north-eastern for class 2, in the southeast for class 3, in the southwest for class 4 and class 5 is the non-rainy class.
4.2. On the ‘up’ part optimization (geopotential fields position and spatial extent)
In this section, we search the optimal geopotential space in terms of classification general performances. Following Garavaglia et al. (2010), we first defined the geopotential space as constituted by four geopotential height fields for each day: the 700 and 1000 hPa fields at 0 and 24 h. Three different sizes of geopotential height grid are chosen. The first one is of size 3.0 × 106 km2 as used for the French WPs classification and further named ‘Size 1’ (S1). A second size of approximately 0.6 × 106 km2 is chosen to cover the Austrian territory entirely, named ‘Size 2’ (S2). The last one is of size around 0.9 × 106 km2, named ‘Size 3’, (S3), which is a compromise between S1 and S2. About 403 different classifications of weather types are generated, by moving the location of the centre of grids characterized by these three different spatial extents over Europe. Considering the spatial extent of the data set used in this study, the S1 centre grid can thus be positioned in 88 locations, S2 in 165 and S3 in 150. The five rainfall classes are projected onto each different geopotential space of dimension 216 (54 geopotential measure points × 2 heights × 2 measure hours), 60 (15 geopotential measure points × 2 heights × 2 measure hours) and 80 (20 geopotential measure points × 2 heights × 2 measure hours), respectively, resulting in different WP classifications. The performances of each WP classification are evaluated by the Cramér test estimated over the whole rainy days population (named Cramér0 hereafter) and over the heavy rainfall sub-sample exceeding a threshold, as depicted in Section 2. This threshold T is chosen here as 20 mm. This choice is coherent with the previous results of Seibert et al. (2006) who used the mean precipitation 98th percentile of seven rainfall regions in Austria as a criterion for selecting ‘heavy precipitation days’ and found a threshold around 20 mm d−1. This ‘heavy Cramér’ coefficient is further named ‘Cramér20 coefficient’. Figure 5 presents the Cramér0 and the Cramér20 coefficients for each grid of geopotential heights (from S1 to S3 from top to bottom) and for each position of the grid. Thus, each coloured point represents the barycentre of one grid and the colours correspond to the mean Cramér performances obtained on all the Austrian rainfall reanalyses considered (blue points). Finally, the black box represents for each grid size and for each coefficient the location of the best geopotential height spatial extent.
First, note that the geopotential grids centred on Austria are not the best grids in terms of Cramér0 and Cramér20, for all three sizes. The best performances are obtained for grids located in the South and in the West of Austria. Then, the west–east flux appears to have a major role in the Austrian rainfall processes. Thus, the more the geopotential grid centre moves away latitudinally from Austria the poorer the performances are in terms of rain/no rain occurrence. On the contrary, a geopotential grid with very distant longitudinal locations offers some reasonable performances in terms of rain/no rain occurrence. For the S1 size, e.g. a classification based on a geopotential grid distant approximately from only 200 km North of Vienna (centred near Dresden) offers a Cramér0 coefficient < 0.30, whereas another classification based on a grid distant from > 4000 km (centred off the Bretagne coast and thus 20 times more distant than the precedent one), is characterized by a Cramér0 coefficient > 0.40. This tendency is more clearly observable for the S2 grid, with a clear latitudinal threshold of both Cramér coefficients: grid centre locations over 55°N and under 37.5°N lead to WP classifications with poor performances in terms of Austria rain/no rain occurrence. These results are coherent with those of previous studies focussing on Austrian heavy precipitations. Ehrendorfer (1987) stated that an important part of heavy rainfall events in Austria is due to West and south-west circulations. Moreover, Matulla et al. (2003) showed that the back trajectories for heavy precipitation days in Austria are coming mostly from West and south-west, like the dramatic Elba flood in 2002. It is important to note that eastern or northern circulations can equally generate heavy rainfalls. Nevertheless, the best quantity of heavy rainfall information in Austria is obtained when looking at the south-west geopotential height fields.
The Cramér0 and Cramér20 performance differences between the optimal grids of each size are non-significant (>0.45 for the Cramér0 and > 0.14 for the Cramér20) and we do not use these scores for the choice of the optimal grid. In order to cover a larger area and maximizing the potential geopotential information of our classification, we choose as optimal one a S1 grid (around 3 × 106 km2). The optimal grid is approximately centredd on the Western Alps and thus not centering on the Austrian region (first line and first column black box of Figure 5).
4.3. Which geopotential information to be used in our WP classification?
In this section, we analyse the influence of the choice of geopotential information used in our ‘up’ steps on the classification performances. Note that we fixed in the precedent optimization procedure the geopotential space as constituted by four geopotential height shape fields for each day: the 700 and 1000 hPa fields at 0 and 24 h, following Garavaglia et al. (2010) methodology. We used now one grid size (S3 size) and we projected for each location the five rainfall classes onto geopotential spaces with different characteristics: using the shapes or the absolute values of the fields, using fields at 700 hPa, 1000 hPa or both and using geopotential fields at 0 h, 0 h or 24 h.
Figure 6 presents the Cramér0 (first column) and Cramér20 (second column) performances obtained for the 150 locations of S3 grid, using five different geopotential spaces for the five rainfall class projections.
The first main result is that the two Cramér coefficients present the same ‘evolution tendencies’. Thus, Cramér0 and Cramér20 performances are clearly higher when shapes of geopotential height fields are considered (boxplot E) than when absolute geopotential fields are used (boxplot A). Similarly, using geopotential height fields at 700 and 1000 hPa (boxplot E) add significant rainfall information compared to using geopotential height fields at 700 hPa (boxplot C) or at 1000 hPa (boxplot B). Finally, the classifications considering a geopotential height data couple (0 and 24 h, boxplot E) perform better than those considering a single geopotential height field for each day (0 h, boxplot D). These results are coherent with the findings of Obled et al. (2002) and Bontron (2004) in a precipitation forecasting context and validate the general applicability of the methodology used in Garavaglia et al. (2010).
4.4. Final Austrian WP classification illustration
In this section, we illustrate the final Austrian WP classification defined with the ‘optimal geopotential space’: four geopotential shape fields (700 and 1000 hPa at 0 and 24 h) defined on an area of 3 × 106 km2 centred on the Western Alps.
Figure 7 presents the mean geopotential heights (1000 hPa at 0 h) and ratio between the mean precipitation amount and the general precipitation amount (considering all WP) for each of the five Austrian WPs.
The general patterns observed on the Austrian territory with the five rainfall classes are also identified at a larger scale with the five WPs, characterized by rainfall spatial distribution centred in the north-western part of Western Europe for WP1, in the eastern for WP2, in the south-eastern for WP3, in the south-western for WP4 and the WP5 is the anticyclonic WP. Logically, the spatial distribution of each WP is no more concentred on the Austrian area, due to the Austrian rainfall classes projection into a larger geopotential space. Moreover, rainfall classes were identified on a rainy days sub-sample, while WPs are constructed attributing each day to a WP, anticyclonic or not. Thus, WPs can contain days with no rain observed on Austria and rainy days on the northern part of Austria can have the same type of atmospheric circulation that a rainy day in the central part of Germany.
The evolution of each five clusters occurrence frequency, from the five original rainfall classes to the five final WPs, is presented in the Table I.
Table I. Evolution of the classes occurrence percentages from the five original rainfall classes to the five final WPs
Rainfall classes (%)
Class 5 (non-rainy)
Note that the number of days attributed to the anticyclonic WP (WP5) is lower than the number of days of the ‘non-rainy’ class (RC5), meaning that several Austrian non-rainy days are classified into the different non-anticyclonic WPs. At the same time, the frequencies of occurrence of each WP are higher. This tendency has a limited impact on the desired discriminating power of our classification: the rainy days characterized by heavy rainfall in a particular area are always regrouped in the same class.
The Austrian WPs classification has been checked on a particular region in the North of Austria, the Kamp catchment at Zwettl in Niederösterreich. This catchment was particularly studied after the August 2002 extraordinary floods which happened in this region (Komma et al., 2007; Merz and Blöschl, 2008). The spatial rainfall record observed on this catchment (from 1976 to 2006) contains significant heavy rainy days, like events in August 2002 which lead to major floods of the Kamp river. Thus, we have tested the classification on this rainfall record and provided interesting results (not shown here): the major rainfall records (containing August 2002 and other summer events: 52 mm on 6 August 1985, 115 mm on 7 August 2002, 81 mm on 12 August 2002, etc.) are regrouped in one particular WP, the WP2. Moreover, observed synoptic situations of these particular events showed similarities with the mean synoptic situation of the WP2, characterized by a continental depression. The Austrian WP classification can thus provide interesting perspectives for heavy rainfall estimation on this particular catchment as for other ones.
Our final Austrian WP classification is based on rainfall classes identified on Austrian rainy days but is at the end only driven by a geopotential height fields information at a larger scale. This classification can be daily updated by using geopotential height reanalyse dataset.
4.5. Performances of WP classifications
The performances of the proposed WP classification (named further ‘Austrian bottom-up classification’) are compared in terms of Cramér20 score on the Austrian daily rainfall reanalyses used in this study, to the performances of 76 COST 733 classifications. Each of the 76 COST classifications is defined on two spatial domains: D06 (Alps, from 3° to 20°E and from 41° to 52°N) and D07 (Central Europe, from 3° to 26°E and from 43° to 58°N). Figure 8 presents (1) the spatial extent of the Austrian bottom-up classification domain (red colour) and the two COST 733 classification domains (black colour for the D06 and blue colour for the D07) and (2) Cramér20 score for each of the 157 classifications (76 COST 733 classifications × 2 spatial domains + 1 Final Austrian bottom-up classification + 4 bottom-up classifications with different geopotential information used in the ‘up’ steps of the classification).
For each classification, the Cramér20 score plotted in Figure 8(b) is estimated as the average Cramér20 score estimated on the 119 Austrian ECA&D reanalyses points. Performances of the Austrian bottom-up classification are similar to the best performing COST 733 D06 (Alps) classifications in terms of Cramér20 and are better than all the COST 733 D07 (Central Europe) classifications. Finally, the final Austrian bottom-up classification performs better than the bottom-up classifications using less geopotential information, showing that considering geopotential height fields shapes at both 700 and 1000 hPa and at 0 and 24 h improves significantly the classification performances.
In this article, a parsimonious (only five classes) and discriminating (contrasted classes in terms of rainfall and geopotential fields) Austrian WP classification, useful for spatial heavy rainfall description is proposed. The five classes are originated from rainfall information but the final classification is only driven by a geopotential height fields information (grid of around 3 × 106 km2, centred on the Western Alps). Updating the classification is then easy to perform by using long geopotential height reanalyse dataset or future geopotential height fields from general circulation models, which are more robust data sources than punctual (in time and space) rainfall record informations.
This type of classification can lead to different applications, as extreme flood estimation on a particular catchment (using WP classification as a sub-sample tool for the characterization of the rainfall risk, SCHADEX (Paquet et al., 2006) approach) or characterization of future climatic evolution (using WP classification as an evaluation tool of the future climate model predictions). Moreover, we investigated the optimal spatial extent, the position and the characteristics of the geopotential fields to be taken into account for a rainfall-based WP classification. We show that the choice of the spatial extent and the position of the centre of the geopotential heights is an important issue. It is possible that the optimal geopotential field is not centred on the studied region and potentially do not exactly cover the studied region. The performances of the WP classification using optimized geopotential height spatial extent and size are shown to be good in comparison with COST 733 WP classifications where the geopotential height field is fixed a priori as two different domains. Moreover, the location of the optimal geopotential fields can be explained from the physical and climatic phenomena leading to heavy rainfall. In addition to the identification of the ‘optimal’ WP classification, this approach allows the general comprehension of the synoptic processes involved in the precipitation over the studied region.