Modified, threshold-based circulation type classification for Central Europe, on the basis of Lityński’s classification

The classification of atmospheric states into separate circulation types is a well-known tool for describing and analysing climate conditions. The main idea behind this is to move from continuous information about an atmospheric state (e.g., the pressure field on a given day) towards discrete information. This involves ordering individual atmospheric states and assigning them to groups of types with certain similarities. This is how a circulation type catalogue is created – each type is described with a value on a nominal scale. The main advantage of such an approach is clearly that circulation type catalogues are easy to use and that classification results can be compared at different locations and times, as well as the ability to analyse how different climate elements depend on atmospheric circulation. However, moving from continuous to discrete information entails a certain amount of information loss concerning the atmospheric state, which can make it difficult to interpret results. On the one hand, we thus want to develop the simplest catalogue of types; while on the other, we need to retain as much information as possible on the state of atmosphere. As a result, a number of classifications are being developed worldwide that seek to find an optimal method for classifying atmospheric circulation types – one that would be simple yet, at the same time, provide the most important information about the climate elements’ variability. This results in existing classifications differing from one another, mainly in the number of types. European circulation type classifications are characterised by the large variation in the number of types: ranging from 13, (Péczely 1983) up to 40 (Schüepp 1979) or even 80 different predefined types (as in the classification developed by the Central Institute of Meteorology in Vienna). Most of the classifications used in Europe have between 9 and 40 types, while the most popular ones are those with 9, 18, or 27 types (Philipp et al. 2010).

According to Philipp et al. (2010), circulation type classification schemes can be divided into two main groups: subjective and automated. Subjective classifications include the very well-known Grosswetterlagen classification (Hess & Brezowsky 1952; Gerstengarbe & Werner 2005), the Péczely (1983) classification, and the Polish ones by Osuchowska-Klein (1991) and Niedźwiedź (1981). The second type of classification methods, the automated or numerical methods, have the advantage of being independent of the individual experience of the observer; meaning that every researcher obtains the same results with the same data. These methods can be further divided into threshold-based methods (Schüepp 1979; Beck et al. 2007) and those in which the possible types are not defined prior to classification, such as principal component analyses (Buishand & Brandsma 1997; Esteban et al. 2006), leader-based algorithms (Lund 1963), and optimisation algorithms (Enke & Spekat 1997; Petisco et al. 2005). All three of these are based on the idea of identifying ‘natural’ types, without any presumptions or thresholds. A major drawback with such an approach, and especially of optimisation algorithms, is the fact that it requires the use of a large data set right from the beginning. Moreover, adding new data may entail changes to the previously defined catalogue. Of course, at some point in this process all objects are assigned to their nearest cluster, and reassignment is no longer necessary, so convergence to an optimum is reached. However, this would result in not being able to update the catalogue without changing the previously designated types. A catalogue in which set types are stable over time would seem to be more useful: such a catalogue can be established using threshold-based methods. In this case, certain threshold values, as wel las tine number of all possible circulation types, are determined in advance. This group includes, for example, the Polish classifications by Lityński (1969), Ustrnul (1997), and Piotrowski (2009), as well as the Swedish classification by Linderson (2001), and the British one by Jenkinson and Collison (1977), which was based on the Lamb classification (1950).

In the original work by Lityński (1969), the author outlines the main underlying principles of his method, that is, the method for constructing the zonal index, W_s; the meridional index, W_p; and the cyclonicity in Poland index, C_p. Lityński proposed dividing the distribution of the values of each index into three equally-likely classes. As a result, the frequency of each class under each index should amount to 33.33%, and all possible class combinations of the three indices produce 27 circulation types: 9 cyclonic types, 9 gradientless types, and 9 anticyclonic types.

Later, the source material used for establishing circulation types, and the algorithm for calculating the thresholds of index classes underwent a change (Pianko-Kluczyńska 2007; Philipp et al. 2010). At present, the Polish weather service uses the following principles for this classification: data from the NCEP/NCAR reanalysis of sea level pressure at 12:00 UTC are used (Kalnay et al. 1996) instead of the synoptic charts used by Lityński. Since reanalyses constitute grid data, the method for calculating the values of the W_s, W_p, and C_p indices has also undergone a change. The grid point, which is taken as the central point, is the one closest to Warsaw, that is, φ=52.5°N, λ=20°E. The zonal index, W_s, is determined as a horizontal zonal pressure gradient on the basis of a formula originally proposed by Lityński (1969). It amounts to the difference between the spatially averaged sea level pressure at parallels φ-12.5° and φ+12.5° within the λ-20° to λ+15° section, with a 5° step (where φ and λ are the coordinates of the central point). This difference is then divided by 25 (the number of degrees between the parallels) in order to produce the pressure gradient (Equation 1):

Ws=125⋅(P(φ<!-- f -->−<!-- - -->12.5o,λ<!-- ? -->−<!-- - -->20o)+P(φ<!-- f -->−<!-- - -->12.5o,λ<!-- ? -->−<!-- - -->15o)+⋯<!-- ? -->+P(φ<!-- f -->−<!-- - -->12.5o,λ<!-- ? -->+15o)8−<!-- - -->P(φ<!-- f -->+12.5o,λ<!-- ? -->−<!-- - -->20o)+P(φ<!-- f -->+12.5o,λ<!-- ? -->−<!-- - -->15o)+⋯<!-- ? -->+P(φ<!-- f -->+12.5o,λ<!-- ? -->+15o)8$$\begin{array}{} \displaystyle W_s=\frac{1}{25}\cdot (\frac{P_{(\varphi-12.5^{\text o},\lambda-20^{\text o})}+P_{(\varphi-12.5^{\text o},\lambda-15^{\text o})}+\cdots+P_{(\varphi-12.5^{\text o},\lambda+15^{\text o})}}{8}-\\ \displaystyle \,\,\,\frac{P_{(\varphi+12.5^{\text o},\lambda-20^{\text o})}+P_{(\varphi+12.5^{\text o},\lambda-15^{\text o})}+\cdots+P_{(\varphi+12.5^{\text o},\lambda+15^{\text o})}}{8} \end{array} $$(1)

The W_s index, as defined in this way, takes positive values for western circulation (western air mass advection) and negative ones for eastern circulation (eastern air mass advection).

The meridional index, W_p, is determined as a horizontal meridional pressure gradient. As with the W_s index, it equals the difference between spatially averaged sea level pressure at meridians λ+15° and λ-20° with in the φ-12.5° to φ+12.5 section with a 5° step (Equation 2):

Ws=135⋅(P(φ<!-- f -->−<!-- - -->12.5o,λ<!-- ? -->+15o)+P(φ<!-- f -->−<!-- - -->7.5o,λ<!-- ? -->+15o)+⋯<!-- ? -->+P(φ<!-- f -->+12.5o,λ<!-- ? -->+15o)6−<!-- - -->P(φ<!-- f -->−<!-- - -->12.5o,λ<!-- ? -->−<!-- - -->20o)+P(φ<!-- f -->−<!-- - -->7.5o,λ<!-- ? -->−<!-- - -->20o)+⋯<!-- ? -->+P(φ<!-- f -->+12.5o,λ<!-- ? -->−<!-- - -->20o)6$$\begin{array}{} \displaystyle W_s=\frac{1}{35}\cdot (\frac{P_{(\varphi-12.5^{\text o},\lambda+15^{\text o})}+P_{(\varphi-7.5^{\text o},\lambda+15^{\text o})}+\cdots+P_{(\varphi+12.5^{\text o},\lambda+15^{\text o})}}{6}-\\ \displaystyle \frac{P_{(\varphi-12.5^{\text o},\lambda-20^{\text o})}+P_{(\varphi-7.5^{\text o},\lambda-20^{\text o})}+\cdots+P_{(\varphi+12.5^{\text o},\lambda-20^{\text o})}}{6} \end{array} $$(2)

The W_p index, as defined in this way, takes positive values for southern circulation (southern air mass advection) and negative ones for northern circulation (northern air mass advection).

In turn, the C_p index indicates whether the domain is influenced by a cyclonic, anticyclonic, or gradientless circulation. It is determined by the sea level pressure at the central grid point (in hPa);inthiscase, φ=52.5°N, λ=20°E.

The algorithm for determining the thresholds of the circulation index classes has also undergone a change. The mean value x̄ and the standard deviation σ are determined for each index, and for each of the months during the whole available time period. Means and standard deviations are calculated on the basis of an increasingly longer period each year; for example, the mean value for January 1948 is calculated on 31 daily values, while the mean value for January 2003 – is based on 1,736 daily values (all 56 Januaries during the period 1948 to 2003). Based on such values for x̄ and σ, the thresholds of the three classes (negative, indifferent, and positive) are determined so that the distribution of these classes is close to being equally-likely (the indifferent class is contained between the lower threshold, t_l = x̄ -0.433σ, and the upper threshold, t_u = x̄ +0.433σ). Threshold values established in this way are then assigned to the middle dates of each month (the 16th day for 31-day months, the 15th day for 30-day months, and the 14th day for February). For days that are between the middle dates of two adjacent months, the threshold values are linearly interpolated (Pianko-Kluczyńska 2007). At the end, each day is assigned to a circulation type according to its classified index value. Circulation types are defined as combinations of all three index classes. Combining the three classes of W_s and the three classes of W_p results in nine advection types (e.g., W_s = negative and W_p = positive for type SE; W_s = indifferent, and W_p = indifferent for type 0 – no advection). Including the three C_p classes results in a further subdivision of advection types into 27 types according to their cyclonicity characteristics (e.g., W_s = negative, W_p = positive, and C_p = positive for SE anticyclonic type).

Lityński’s classification of atmospheric circulation types is one of the most important classifications used in climatological studies in Poland. The researchers who use it usually define it as an equally-likely classification – in reality, however, it differs from the equally-likely division. This paper proposes a number of small modifications to the algorithm currently in use for establishing atmospheric circulation types. The aim, therefore, is to compare the proposed algorithms, and indicate which one produces a catalogue of circulation types in which the division into three classes of the distribution of the values (of the three indices, W_s, W_p, and C_p) is closest to being equally-likely; thus actually fulfilling the principles of Lityński’s original classification.

In order to prepare circulation type catalogues, data originating from the NCEP/NCAR reanalysis on sea level pressure at 12:00 UTC for each day from 1948 to 2015 were used. The variants, which are described below, were compared for the period 1986 to 2015 (30 years). This circulation type classification is calculated for a spatial domain of a specified size. The central grid point, which is specified by the coordinates φ and λ, and the corner points of the domain are shown in Figure 1. In this paper the classification is carried out only for the grid point that is the closest to Warsaw, but the domain can be freely moved to any point in the European middle latitudes. Therefore, the data for the area 40–65^ºN and 0–35^ºE were used, and the grid point, φ=52.5°N, λ=20°E was taken as the central point of the domain.

Figure 1

Five variants of the classification scheme were prepared. Their main underlying principles are described below.

ORG: the classification currently used by the Polish weather service. In this classification, the W_p and W_s indices are determined using a 5° step, and the thresholds of the three index classes are defined based on the above-described algorithm, which was introduced by Pianko-Kluczyńska (on the basis of all the material available at a given time; the lower threshold t_l = x̄ -0.433σ and the upper threshold t_u = x̄ +0.433σ).

In all variants the calculated threshold values are assigned to the middle date of each month. For days that are between the middle dates of two adjacent months, the threshold values are linearly interpolated.

We carried out an evaluation of classification schemes in order to decide which variant results in a catalogue of circulation types where the distribution of index values in the three classes is the closest to being equally-likely. The comparison was made by calculating the mean absolute error (MAE). It was adopted as a way of measuring, for each classification scheme, how close the distribution of values (of an individual index) within the three classes, was to being equally-likely, as shown in Equation 3: MAE=19∑<!-- ? -->i=19|Ti−<!-- - -->Ei|$$\begin{array}{} MAE=\frac{1}{9}\sum_{i=1}^{9}|T_i-E_i| \end{array} $$ (3)

The empirical frequency of each of the nine classes is indicated by E; while T indicates reference values (i.e., the theoretical equally-likely frequency [33.33%]); i means the subsequent class; and in each classification scheme there are 9 classes (three classes for the W_s index, three for W_p, and three for C_p). The MAE is expressed in percentage points, and the lower its value the closer the distribution of values in the three classes (for each index) is to being equally-likely.

This paper compares the different variants of circulation type classification by Lityński. Five different variants of the classification algorithm that were based on different underlying principles, were compared. This made it possible to indicate which algorithm generates a catalogue of circulation types in which the division into three classes of the distribution of the values of the W_s, W_p and C_p indices is the closest to being equally-likely. During 1986–2015, the MOD20 classification differed from the ORG classification in more than 19% of cases. In subsequent variants of the classification algorithm, the differences in the frequencies of each class (in relation to individual circulation indices) became smaller and smaller. Ultimately, the use of the MOD20 classification resulted in generating a catalogue of circulation types in which the division of the distribution of the values in the W_s, W_p and C_p indices into three classes was the closest to being equally-likely.

MOD20 is a threshold-based classification. In general, threshold-based methods perform surprisingly well in comparison to more complicated algorithms (Huth 2010). The relative simplicity of the MOD20 classification algorithm is its big advantage, in contradiction to methods using principal component analysis or optimisation methods. Even though, in recent times, computing time and algorithm complexity no longer constitute a problem, by having a simpler method, it is also easier to understand what exactly is being produced by the classification algorithm. According to Beck and Philipp (2010) the original Lityński classification (ORG) is one of the threshold-based methods that produces the best results in Central Europe.

The advantage of the MOD20 classification is its use of the empirical distribution of index values – the percentiles 33 and 67 – instead of the theoretical distribution x̄ ±0.433σ. In this classification scheme, the thresholds are calculated based on of the last 20 years, which is the optimum balance between the stability of the percentiles and circulation types. The presented MOD20 circulation type classification has 27 predefined types, which is the number of types frequently used in European classifications (Philipp et al. 2010). Owing to this, each synoptic situation can be classified clearly and there are no unclassified or transitional situations. With such an approach, the catalogue of types is easy to use. On the other hand, it should be remembered that indeterminate situations also occur in nature, and these have to be assigned to a certain type anyway. The MOD20 classification scheme is automated and makes it possible to do recalculations, so it is applicable to different regions and time periods. However, it has certain limitations. It may not give proper results in regions of certain topography, for example, mountain basins, where atmospheric circulation and the advection of air masses are determined mostly by local factors. On the other hand, it is a macroscale classification, so it provides information concerning a very big area around a central grid point. Even though it is calculated for a given point, it defines the atmospheric circulation pattern for a domain of a hundred square kilometres. The MOD20 classification should be used for data from 1967 onwards (i.e., for the years that have the whole preceding fixed-length period on which thresholds are calculated). A major limitation of the MOD20 classification scheme is its use of the moving period on which the thresholds are calculated. This can lead to a situation where two days, for example, at the beginning and at the end of a long time period, that have the same values of the three indices, may be classified differently. A solution to this problem would be to establish a fixed period on which the thresholds are calculated, for example, 1951–2000. Yet it should be remembered that the output catalogue of circulation types would be decreasingly equally-likely after the year 2000. Additionally, other changes to the ways for calculating thresholds (e.g., calculating them for each day separately, instead of calculating for the middle dates of months and interpolating the results) or to the classification scheme itself, could be introduced. This should be the subject of future research.

The algorithm for generating atmospheric circulation types according to the MOD20 method (with the thresholds based on either moving 20 year period or the fixed period, 1951–2000) is available at MATLAB File Exchange’s web page.