The probabilistic characteristics and the forecasts for precipitation on the basis of a special transformation of the initial data, which makes it possible to reveal patterns in observations, are briefly discussed. Patterns in data analysis can be used to improve the accuracy and speed of forecasting. Moreover, pattern's methodology is a convenient approach to the solution of various climatological problems. The issues of testing the Markov property of data, probabilistic and neural network forecasting for statistical observations without involvement of any additional information about meteorological conditions are investigated. The initial data is volumes of daily precipitation observed during 60 years. The best accuracy for neural networks trained on patterns based on sequences of «D» (dry days, i.e. without precipitations) and «W» (wet ones, i.e. with any nonzero volume) is 97% for one-day and 89% for two-day forecasts. Few directions for further investigations are suggested. The paper continues the author's research in the fields of creation of mathematical models and data mining algorithms for meteorological observations.
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In: K. E. Samouylov, L. A. Sevastianov, D. S. Kulyabov (eds.): Selected Papers of the VIII Conference “Information and Telecommunication Technologies and Mathematical Modeling of High-Tech Systems”, Moscow, Russia, 20-Apr-2018, published at http://ceur-ws.org
Precipitation is an important parameter for meteorological models (see, for example,
papers [
In this paper, the probabilistic characteristics and the forecasts for precipitation on
the basis of a special transformation of the initial data, which makes it possible to reveal
patterns in observations, are briefly discussed. Patterns in data analysis can be used
to improve the accuracy and speed of forecasting. Moreover, pattern’s methodology
is a fairly common tool in the solution of various climatological problems. This paper
continues the previous author’s research in the fields of creation mathematical models
and data mining algorithms for meteorological observations [
The volumes of daily precipitation observed during 60 years in Potsdam are the initial data. Let’s consider transformation of non-negative data according to the following rule: if any positive value was observed in the -th day, it is replaced () () by one (̃︀daily = 1), otherwise the value of ̃︀daily equals zero. Thus, the initial series consisting of continuous values becomes discrete, taking two possible values {0, 1}. This simplification makes it possible to analyze the presence or absence of precipitation irrespective of their volume. Thus, any sequence of dry (without precipitations) and wet (with any nonzero volume) days can be represented as a «0–1» (or «D–W») chain (the pattern).
For each pattern within the historical data it is possible to determine the frequencies
of appearance as the ratio of the number of such sets of fixed length to the total
number of possible chains (obviously 2 ). In fact, these are the probabilities according
to the classical definition. Within the framework of the research, observations for 60
years for Potsdam were analyzed for the values of the parameter from 1 to 14. For
each set, the frequencies (probabilities) were obtained, the pattern with a maximum
value was determined [
In the most of the papers devoted to the statistical analysis of meteorological data,
it is assumed that the duration of the period of precipitation, measured in days (that
is, the number of successive wet days), has the geometric distribution. Perhaps, these
assumptions are based on the classical interpretation of the geometric distribution in
terms of Bernoulli’s tests as the distribution of the number of successive wet days
(«success») to the first day without precipitation («failure»). With the use of patterns,
it was demonstrated [
3.
Using the data on frequencies (probabilities) for patterns, it is possible to calculate the values of the conditional probability of occurrence in the future of certain combinations,
Probability, pattern's length N=5 DDDDD DDDDW DDDWD DDDWW DDWDD DDWDW DDWWD DDWWW DWDDD DWDDW DWDWD DWDWW DWWDD nDWWDW rDWWWD eDWWWW tt WWDDDDDDWD aWDDWD PWDDWW WDWDD WDWDW WDWWD WDWWW WWDDD WWDDW WWDWD WWDWW WWWDD WWWDW
WWWWWWWWWD that is, to obtain probabilistic forecasts for certain events. For example, if current observations is «Wet-Wet-Dry-Dry» (that is, there were precipitations for two days in a row, on the next two days volumes were equal zero), the following statements can be formulated as: «The probability of precipitation through 2 days in Potsdam at current observations is 0,3961, and the probability of precipitation absence through 2 days is 0,6039». Unlike the standard practice for data analysis, when the predicted window should not exceed the size of input observations, this rule can be violated for historical values.
As an alternative forecasting tool, feed-forward neural networks with several hidden
layers and various activation functions were used [
For the chosen architecture of the neural network, there is no overfitting: the error value is the same for both the training part and for the test part, which does not participate directly in the process of building the neural network. Thus, we can expect that the model will work correctly not only for the training part, but also for real data.
Fig. 2 demonstrates an example of the accuracy of precipitation prediction for the next day taking into account the month of data. The numerical values of the corresponding forecast errors are indicated in Table 2.
January February
March April May June
July h t n o M August September
October November December 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
value ̃︀d(a)ily is assigned a zero value.
For the analysis of the probabilistic behavior of the precipitation process and the forecasting, it is suggested to use the chains of events (patterns) extracted from the data. High accuracy for neural networks forecasting is demonstrated, wherein the analysis is based solely on basic statistical data without any additional information about meteorological conditions.
Working with patterns is of interest in terms of verification ensemble of forecasts.
Also, this methodology can be used to predict the behavior of the moment characteristics
of finite normal mixtures of probability distributions [
As one of the directions for further research, it is possible to propose a transition from the binary model of the discretization of events to base- numeral system. It could allow to solve more complex forecasting tasks, for example, to predict the amount of precipitation in terms of falling into pre-selected ranges of values. That is, if any positive value was observed in -th day, it is replaced by from the range 1, . . . , − 1 (̃︀d(a)ily = ) corresponding to the precipitation volume partition by − 2 intervals; otherwise, the
To maximize the automation of the research process, the developed forecasting
methods will be integrated into the service of stochastic data analysis [
The research was supported by the Russian Foundation for Basic Research (project No 17-07-00851) and the Ministry of Education and Science of the Russian Federation (No 538.2018.5). The author is grateful to Corresponding Member of the Russian Academy of Sciences Prof. S. K. Gulev for provided data, to Prof. V. Yu. Korolev for useful discussions within the framework of joint studies of meteorological phenomena and V. Kuzmin for training of neural networks.