WO2011018578A1

WO2011018578A1 - Method for approximating meteorological variables

Info

Publication number: WO2011018578A1
Application number: PCT/FR2010/051686
Authority: WO
Inventors: Martin Fischer
Original assignee: Metnext
Priority date: 2009-08-13
Filing date: 2010-08-10
Publication date: 2011-02-17
Also published as: FR2949157A1

Abstract

The invention relates to a method for approximating a meteorological variable, such as the temperature at any point of a region in the world, from a small number of indicators obtained in said region, said method including analyzing (12) main components of meteorological data recovered in a significant number of stations in the region, defining (18) indices which are weighted averages of data in a small number of stations and which show a strong correlation to the time series of the first main components, the correlations between the indices being small and the vectors formed with the weight for calculating the indices being orthogonal or nearly orthogonal, and approximating (20) the values of the meteorological variable by means of a weighted linear combination of said indices.

Description

Method for approximating meteorological variables

The invention relates to a method for approximating a weather variable such that, for example, the temperature at any point in a region of the world, such as Europe for example, from a small number of indicators obtained in this region.

When it is necessary to process a large number of random variables, it is known to use a mathematical method of principal component analysis (or EMI), this method of searching in a multidimensional space for directions that represent at best between variables.

If this method is applied to the processing of data such as meteorological variables (temperature, wind speed, precipitation, ...) recorded at a large number of points in a given region, for example in several dozen installed weather stations in Europe, over a period of time comprising a large number of measurements, for example from several tens to several hundreds, we obtain principal components, the first of which explains most of the vahance of all the data that can be obtained. express by a single linear combination of data. The second major component accounts for the second largest portion of the data variance, and so on. The N first principal components therefore explain most of the variance of the set of data that can be expressed by N linear combinations of the data.

In the case of meteorological data, it is often found that the first three or four major components account for a large percentage, for example 80%, of the total variance of the data. The optimal choice to define linear indices best suited to measure the evolution of all data would be therefore to use the first N main components. In practice, however, it would be too complicated to use these principal components as clues to approximate a temperature or other meteorological variable at any point in a region. This approach would require the use of data from many, for example, several tens or hundreds of meteorological stations in this region.

The object of the invention is in particular to provide a simple and effective solution to this problem.

To this end, it proposes a method for approximating a meteorological variable, such as, for example, the temperature in a region of the world, for example in Europe, characterized in that it consists of:

to record and record values of this variable and / or anomalies of this variable on one or on given periods in a number of locations in this region and to perform a principal component analysis of the recorded values of this variable and / or anomalies of this variable;

identifying from the results of this analysis groups of locations in which the variations of the values of the variable have similar behavior, and choosing a location in each group so that the values of the variable at this location represent an approximation major components of the above analysis in a minimum number of locations; and

approximating a value of the variable or an anomaly of the variable at any point in the region by a weighted linear combination of indices, these indices being weighted averages of the values of the variable at the selected locations so that the indices show a good correlation with the time series of the principal component analysis, that the correlations between the indices are weak and that the vectors formed by the weights used for each index are orthogonal or almost orthogonal. These criteria ensure that the indices represent a good approximation of the first principal components, the invention thus making it possible:

- approximating the value of the weather variable and / or an anomaly of that variable at any point in the region using a weighted linear combination of indices,

- to determine or estimate very quickly, with good accuracy, a value or an anomaly of a weather variable at any point in a given region from a minimum number of weighted indices (this number being 3 to the whole of Europe if the invention is applied to temperature anomalies),

- to monitor or quantify variations of this variable in a region of the world, for example Europe, by measuring only a very small number of indices.

By definition, an anomaly of a variable is the difference between an actual value of this variable and the climatological value (the climatological value being the normal value for the period considered, determined from the statements of the values of the variable previously made).

According to another characteristic of the invention, the groups of locations correspond to the geographical zones having the highest amplitudes in the first principal components of the aforementioned analysis.

In the case of temperatures, a principal component analysis of daily and monthly temperature anomalies in Europe leads to the following structure:

the first main component comprises a single pole or monopole,

the second and third main components are dipoles. In Europe, the center of variability of the monopoly structure is Central Europe. The centers of the dipole corresponding to the second main component are Eastern Europe on the one hand and South-West Europe plus the Mediterranean West on the other, and the centers of activities corresponding to the third main component are the Mediterranean Basin and North West Europe.

If the analysis is applied to the temperature anomalies in Europe, the selected locations are the cities of Nuremberg in Germany (Central Europe), Leba in Poland (Eastern Europe), Vigo in Spain (South West Europe). and Mediterranean West), Amsterdam in the Netherlands (North West Europe) and Pescara in Italy (Mediterranean Basin).

The indices are calculated as follows: (ind1, ind2, ind3) = (tanoi, tano2, ..., tano5) ^* A

The vector (tanoi, ..., tanoδ) contains the temperature anomalies in the five selected locations - Nuremberg, Vigo, Pescara, Leba, Amsterdam (in that order), "A" is a 5 x 3 dimensional matrix that contains the weights, and the vector (ind1, ind2, ind3) contains the three indices computed for a given moment. In general, if "n" indices ind1, ..., indn must be calculated from "m" time series ts1, ... tsm at "m" locations, the formula is: (ind1, .... indn ) = (ts1, ... tsm) ^* A

A being a matrix of dimension mx n. Column n of matrix A contains the weights to compute the index n from the data in the m locations. The weighting coefficients of the indices that are used to approximate a temperature or anomaly of temperature at any point in a region are calculated by multi-step regression.

In a particular embodiment of the invention, the principal component analysis is performed on daily data and on monthly data of temperature anomalies.

To compute indices from daily temperature anomalies, the components of matrix A are:

[, l] [, 2] [, 3]

[1,] -0.12025594 0.10184922 0.01330028

[2,] -0.02738203 0.11979894 0.18362434

[3,] -0.05001196 0.12851656 -0.29182618

[4,] -0.08329636 -0.33201439 -0.02303887

[5,] -0.09309122 0.06122933 0.10620130 To calculate indices from standard monthly data (variance = 1), the components of matrix A are:

Ml [, 2] [, 3]

[1,] -0.19551935 0.2798633 -0.10141862

[2,] -0.04701654 0.4602554 -0.29874588

[3,] -0.11156334 0.2875479 0.61925407

[4,] -0.18758694 -0.6903224 -0.02383865

[5,] -0.15033798 0.1400668 -0.20446550

The invention also proposes temperature indices which are determined by execution of the method described above and which are intended for an estimation of the temperature or a temperature anomaly at any point in Europe, these temperature indices. characterized in that they are three in number and include:

a weighted average of the temperature anomalies according to the coefficients of the first column of the matrix A; a weighted average of the temperature anomalies according to the coefficients of the second column of matrix A and

a weighted average of the temperature anomalies according to the coefficients of the third column of the matrix A.

The invention will be better understood and other characteristics, details and advantages thereof will appear more clearly on reading the description which follows, given by way of example with reference to the appended drawing, which represents a flowchart of the main steps. of the process according to the invention.

The embodiment which will now be described concerns the approximation of temperatures and temperature anomalies at any point in Europe during a given period, for example from October to April of the year. next.

The first step 10 of the method according to the invention is to record temperatures and / or temperature anomalies at different points in the region. For example, measurements can be made regularly in about 90 weather stations in Europe.

The next step 12 of the above according to the invention consists of a principal component analysis of all the temperature and temperature anomalies that were found in step 10.

If a principal component temperature analysis is carried out between October 2003 and the end of April 2009, the first main component represents about 73% of the total temperature variation in Europe, whereas the second component The main component represents 5.7% of this total variance, the third main component represents 4.7% of this total variance and the fourth main component 3.3% of this total variance, when the analyzes concern daily temperatures. If the analyzes are made on monthly temperatures, the corresponding values for the first four main components are respectively 89.5%, 3.7%, 2.5% and 1, 1%.

The same pattern structures are dominant for the monthly analysis and the daily analysis.

When the principal component analysis is done on the recorded values of temperature anomalies in the October-April period, the first main component is 51.9% of the total variance, the second main component is 10.1% of this variance. total variance, the third major component at 8.8% and the fourth largest component at 4.9% of the total variance.

In the case of monthly analyzes, the corresponding values are 69.4% for the first main component, 10.7% for the second main component, 5.8% for the third main component and 4.1% for the fourth component. main.

The first three main components of monthly temperature anomalies account for about 86% of the total temperature variance in Europe.

These different analyzes give quite consistent results: in winter, the maximum variability is in southern Germany and Poland. The second and third main components show dipole structures with a principal oriented gradient of

Southwest to Northeast and Southeast to Northwestern, respectively.

The next step 14 of the method according to the invention consists in grouping meteorological stations having similar behaviors in terms of temperature variations or variations of the meteorological anomalies and selecting in each group a meteorological station which will be the representative of the group considered to obtain a minimum number of stations characterizing the temperature models in Europe. We can thus identify five groups of locations, which correspond globally to the principal components mentioned above (step 16):

- South West Europe and the Mediterranean West, including Spain, Portugal and South West France;

the Mediterranean basin, including Italy and South-East France;

North West Europe including England, the Netherlands, Belgium and the North of France;

- Central Europe, including Germany and Eastern Europe

France ;

Eastern Europe, including Poland and eastern Germany.

The geographic areas of these five groups are those with the highest amplitudes of the first three major components:

South West Europe and the Mediterranean West correspond to the maximum of the second main component;

the Mediterranean basin corresponds to the maximum of the third main component;

North West Europe corresponds to the maximum of the third main component;

Central Europe corresponds to the maximum of the first main component;

- Eastern Europe corresponds to the maximum of the second main component.

This grouping is consistent with the fact that the first principal component is a monopole (all the elements of the first principal component have the same sign) while the second and third principal component are dipoles (each dipole being defined by two associated regions, the signs of the elements of each of these principal components being opposed).

The next step 18 of the method according to the invention consists in defining temperature indices as weighted averages of the temperatures or anomalies of the temperatures or standardized anomalies of the temperatures at the selected locations which will represent, in a simplified way, modes of variation of temperature. in the aforementioned groups. Simplified indices must show a high correlation with the time series of the principal component analysis, the correlations between the indices must be weak and the three vectors formed by the weights of each index must be orthogonal or almost orthogonal.

According to the invention, these indices are the following: (ind1, ind2, ind3) = (tanoi, tano2, ..., tano5) ^* A

The vector (tanoi, ..., tanoδ) contains the temperature anomalies in the five selected locations, Nuremberg, Vigo,

Pescara, Leba, Amsterdam (in that order), A is a 5 x 3 matrix containing the weights, and the vector (ind1, ind2, ind3) contains the three indices calculated for a given moment.

To compute indices from daily temperature anomalies, the components of matrix A are: [, 1] [, 2] [, 3]

[1,] -0.12025594 0.10184922 0.01330028

[2,] -0.02738203 0.11979894 0.18362434

[3,] -0.05001196 0.12851656 -0.29182618

[4,] -0.08329636 -0.33201439 -0.02303887

[5,] -0.09309122 0.06122933 0.10620130 To calculate the indices from the monthly temperature anomalies, the components of matrix A are:

Ml [, 2] [, 3]

[1,] -0.19551935 0.2798633 -0.10141862

[2,] -0.04701654 0.4602554 -0.29874588

[3,] -0.11156334 0.2875479 0.61925407

[4,] -0.18758694 -0.6903224 -0.02383865

[5,] -0.15033798 0.1400668 -0.20446550

These three indices make it possible to measure the importance of the dominant spatial modes of temperature in Europe. It is thus possible to cover with these three temperature indices temperature anomalies everywhere in Europe.

The use of temperature anomalies, instead of total temperatures, makes these indices universal in Europe. They are also well suited for very cold countries such as Poland for example, as for countries with relatively mild winters, such as Spain or Italy.

The index ind1 measures the large-scale temperature anomaly in Europe.

The ind2 index measures the North-East / South-West temperature gradient and therefore the importance of the second main component of the temperature anomalies.

The index ind3 measures the importance of the third main component.

The indices according to the invention make it possible to estimate temperature anomalies and complete temperatures or total temperatures throughout Europe. Indices can have positive or negative values. Temperatures at any point in Europe can be represented by a linear combination of these three indices, with a weighting of each index.

The weights (or weights) for each index and for a specific location can be calculated from a multivariate regression. They have constant values over time, which can be positive or negative.

Claims

1. Method for approximating a meteorological variable such as, for example, the temperature in a region of the world, for example in Europe, characterized in that it consists of:

approximating a value of the variable or an anomaly of the variable at any point in the region by a weighted linear combination of indices, these indices being weighted averages of the values of the variable at the selected locations so that the indices show a good correlation with the time series of the principal component analysis, that the correlations between the indices are weak and that the vectors formed by the weights used for each index are orthogonal or almost orthogonal.

2. Method according to claim 1, characterized in that the groups of locations correspond to the geographical areas having the highest amplitudes in the first major components of the aforementioned analysis.

3. Method according to claim 1 or 2, characterized in that the first main component comprises a single pole.

4. Method according to one of the preceding claims, characterized in that the second and third main components are dipoles.

5. Method according to one of claims 1 to 4, characterized in that for the temperature anomalies in Europe, the selected locations are five in number and are located in Nuremberg (Central Europe), Vigo (South-West of France). Europe and Mediterranean West), Pescara (Mediterranean Basin), Leba (Eastern Europe) and Amsterdam (North West Europe).

6. Method according to claim 5, characterized in that the temperature indices in Europe for the selected locations are weighted averages of the temperature anomalies according to the formula

(ind1, ind2, ind3) = (tanoi, .... tano5) ^* A

A being a matrix whose components are, for normalized daily temperature anomalies:

[, l] [, 2] [, 3]

[1,] -0.12025594 0.10184922 0.01330028

[2,] -0.02738203 0.11979894 0.18362434

[3,] -0.05001196 0.12851656 -0.29182618

[4,] -0.08329636 -0.33201439 -0.02303887

[5,] -0.09309122 0.06122933 0.10620130 and are, for monthly temperature anomalies:

[, l] [, 2] [, 3]

[1,] -0.19551935 0.2798633 -0.10141862

[2,] -0.04701654 0.4602554 -0.29874588

[3,] -0.11156334 0.2875479 0.61925407

[4,] -0.18758694 -0.6903224 -0.02383865

[5,] -0.15033798 0.1400668 -0.20446550

7. Method according to one of the preceding claims, characterized in that the weighting coefficients of the indices used to determine a variable value or an anomaly of the variable at a certain point in Europe are computed by multivalve regression.

8. Method according to one of the preceding claims, characterized in that the principal component analysis is performed on daily data and on monthly data anomalies of the variable.

9. Temperature indices, determined by execution of the method according to one of the preceding claims and intended for an estimation of the temperature or a temperature anomaly at any point in Europe, characterized in that they are at number of three and include weighted averages of temperature anomalies with positive and / or negative weights so that the indices obtained show a strong correlation with the time series of the principal component analysis, that the correlations between the indices are low and that the vectors formed by the weights are orthogonal or nearly orthogonal.