=Paper=
{{Paper
|id=Vol-2177/paper-01-a005
|storemode=property
|title=
Investigation of Parameters of Meteorological Models Based on Patterns
|pdfUrl=https://ceur-ws.org/Vol-2177/paper-01-a005.pdf
|volume=Vol-2177
|authors=Andrey K. Gorshenin
}}
==
Investigation of Parameters of Meteorological Models Based on Patterns
==
https://ceur-ws.org/Vol-2177/paper-01-a005.pdf
4
UDC 004.032.26
Investigation of Parameters of Meteorological Models Based
on Patterns
Andrey K. Gorshenin
Federal Research Center “Computer Science and Control” of RAS
44-2 Vavilov str., Moscow, 119333, Russian Federation
Email: agorshenin@frccsc.ru
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.
Key words and phrases: precipitation, patterns, forecast, neural networks, deep learn-
ing, probabilistic forecasting.
Copyright © 2018 for the individual papers by the papers’ authors. Copying permitted for private and
academic purposes. This volume is published and copyrighted by its editors.
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
Gorshenin Andrey K. 5
1. Introduction
Precipitation is an important parameter for meteorological models (see, for example,
papers [1–3]), so the development of an adequate mathematical models (including
probabilistic and statistical) and the creation of software tools for processing a significant
amount of accumulated observations using modern methods are in demand. In this case,
probabilistic approaches can be used to solve forecasting problems (see, for example,
paper [4]) as well as neural networks that are very effective in a wide range of application
areas (see, for example, papers [5–7]). Moreover, at present, the research of various
precipitation processes in the context of global warming and climate change problems is
quite popular (see, for example, [8–11]).
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 [12–15].
2. Investigation of the probabilistic characteristics of precipitation based
on patterns
The volumes of daily precipitation observed during 60 years in Potsdam are the
initial data. Let’s consider transformation of non-negative data 𝑉𝑑𝑎𝑖𝑙𝑦 according to
the following rule: if any positive value was observed in the 𝑖-th day, it is replaced
(𝑖) (𝑖)
by one (𝑉̃︀daily = 1), otherwise the value of 𝑉̃︀daily 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 𝑁 to the total
number of possible chains (obviously 2𝑁 ). 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 𝑁 from 1 to 14. For
each set, the frequencies (probabilities) were obtained, the pattern with a maximum
value was determined [12]. Fig. 1 demonstrates an example of frequencies for patterns
of length 𝑁 = 5. The numerical values of the corresponding probabilities are indicated
in Table 1.
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 [12] that the sequence of wet and dry days is not even Markovian,
so using Bernoulli’s scheme based on independence of data is incorrect. Alternative
probabilistic models are proposed in the papers [14, 15].
3. Forecasts for precipitation based on patterns
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,
6 ITTMM—2018
Probability, pattern's length N=5
DDDDD
DDDDW
DDDWD
DDDWW
DDWDD
DDWDW
DDWWD
DDWWW
DWDDD
DWDDW
DWDWD
DWDWW
DWWDD
Pattern
DWWDW
DWWWD
DWWWW
WDDDD
WDDDW
WDDWD
WDDWW
WDWDD
WDWDW
WDWWD
WDWWW
WWDDD
WWDDW
WWDWD
WWDWW
WWWDD
WWWDW
WWWWD
WWWWW
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
Probability
Figure 1. Probabilities/frequencies for patterns with length that equals 5
Table 1
Probabilities/frequencies for patterns with length that equals 5
Pattern Probability Pattern Probability
DDDDD 0,21 WDDDD 0,05
DDDDW 0,05 WDDDW 0,02
DDDWD 0,02 WDDWD 0,01
DDDWW 0,04 WDDWW 0,02
DDWDD 0,02 WDWDD 0,01
DDWDW 0,01 WDWDW 0,01
DDWWD 0,02 WDWWD 0,01
DDWWW 0,04 WDWWW 0,02
DWDDD 0,03 WWDDD 0,04
DWDDW 0,01 WWDDW 0,02
DWDWD 0,01 WWDWD 0,01
DWDWW 0,01 WWDWW 0,02
DWWDD 0,02 WWWDD 0,04
DWWDW 0,01 WWWDW 0,02
DWWWD 0,02 WWWWD 0,04
DWWWW 0,04 WWWWW 0,08
Gorshenin Andrey K. 7
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 [12]. The patterns are used as the
training sets. However, the frequency of each of the sets is not used explicitly, and the
corresponding procedures are implemented in the hidden layers of the neural network.
As a result of the work, a forecast is obtained for the following 1 − 2 days. The best
obtained prediction accuracy for a neural network with a sigmoid activation function
and two hidden layers was 82% for a one-day and 74% for a two-day forecast (with
"PHP"implementation). The adding of hidden layer, the changing of the activation
function to the rectifier, the increasing of a size of the input sample and the use of the
deep learning library Keras (with Python implementation) lead to enhance the forecast
accuracy for the same data to 97% for one-day and to 89% for two-day forecasts.
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.
Monthly 1-day precipitation forecast
January
February
March
April
May
Month
June
July
August
September
October
November
December
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Accuracy
Figure 2. Accuracy of the monthly 1-day precipitation forecast
8 ITTMM—2018
Table 2
Monthly 1-day precipitation forecast errors
Month Error (1-day)
January 1,1%
February 1,5%
March 2%
April 1,2%
May 2%
June 2,2%
July 1,9%
August 4,2%
September 3,5%
October 3,6%
November 5,6%
December 5,7%
4. Conclusions
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 [16] to determine the trend direction
within the framework of modeling of physical experiments [17]. Such data are different
from observations considered in this work (for example, there is no a seasonal factor),
but in general the task seems to be quite similar, although the architecture of neural
network should be modified.
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-𝑘 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
(𝑖)
value was observed in 𝑖-th day, it is replaced by 𝑗 from the range 1, . . . , 𝑘 − 1 (𝑉̃︀daily = 𝑗)
corresponding to the precipitation volume partition by 𝑘 − 2 intervals; otherwise, the
(𝑖)
value 𝑉̃︀daily is assigned a zero value.
To maximize the automation of the research process, the developed forecasting
methods will be integrated into the service of stochastic data analysis [18–20] as a special
tool for data mining.
Acknowledgments
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.
Gorshenin Andrey K. 9
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