SOM-Based Estimation of Meteorological Profiles. T. Tambouratzis. Department of Industrial Management and Technology, University of Pireaus,.
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SOM-Based Estimation of Meteorological Profiles T. Tambouratzis Department of Industrial Management and Technology, University of Pireaus, 107 Delighiorgi St, Pireaus 185 34, Greece e-mail tatiana(%un ipi.gr; tatiana@ipta. demokritos.gr
Abstract The task of estimating the meteorological profile of any location of interest within a specified area is undertaken. Assuming that the meteorological profiles of a sufficient number of representative reference locations within the specified area are available, the proposed methodology is based on (a) the organisation of the meteorological profiles of the reference locations employing a self-organising map (SOM) and (b) the classification of the most salient morphological characteristics of the reference locations. Subsequently, the meteorological profile of any novel location of interest is approximated by a weighted average of the meteorological profiles represented on the SOM for those reference locations whose morphological characteristics most closely match the morphological characteristics of the location of interest. The proposed methodology is evaluated by comparing the accuracy of meteorological profile estimation with that of existing estimation techniques as well as with the actual meteorological profiles of the locations of interest.
1 Introduction The estimation of the meteorological profile of any location of interest within a specified area is of obvious practical interest. Assuming that • the morphology of the area is available, and • the meteorological profiles of a sufficient number of representative reference locations within the specified area are known, various methods can be employed for the estimation of the meteorological profile of the location of interest (e.g. "adoption-adaptation" of the meteorological profile of the reference location that is closest to the location of interest, interpolation between the nearest reference locations). In this piece of research, a novel methodology is proposed which combines the construction of a selforganising map (SOM) that orders the meteorological profiles of the reference locations with the classification of the reference locations according to their most salient morphological characteristics. Given a novel location of
interest within the specified area, its meteorological profile is generated by: • classifying the location of interest into one of the morphological classes and, subsequently, • determining the meteorological profile represented on the SOM for those reference locations that most closely match the morphological characteristics of the location of interest. This paper is structured as follows: the area specified for meteorological profile estimation is described in section 2; the SOM employed for organising the meteorological profiles of the reference locations within the specified area as well as morphological classification of the Greek territory are presented in section 3; the experimental results as well as a comparison with existing estimation techniques and the actual meteorological profiles of the locations of interest are given in section 4; finally, section 5 concludes the paper.
2 The specified area The Greek territory has been used as the area on which the estimation of the meteorological profile of any location of interest is performed. 2.1 Meteorological parameters - profiles The meteorological profiles of 130 locations in the Greek territory are available; these locations (shown in Fig. 1) correspond to the weather stations maintained by the National Meteorological Service (EMY) of Greece. Each meteorological profile has been derived from 28 meteorological parameters1 which have been collected over a period of 43 years (from 1955 to 1997) at a given weather station. A single value per meteorological parameter (equalling the numeric average of the collected values over the 43 years) has been utilised for the
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describing monthly and yearly maximum, minimum and average temperature, barometric pressure and relative humidity, monthly and yearly average number of sunny and cloudy hours per day, monthly and yearly average levels of precipitation and snow, monthly and yearly average wind speed
174 174 generation of of the the meteorological meteorological profile profile of of the the given given generation weather station. station. weather
Greek territory territory can can be be determined, determined, the the meteorological meteorological Greek profiles of of only only 130 130 locations locations are are available. available. profiles
3 The Self-Organising Map (SOM)
Fig. 11 The The Greek Greek territory territory with with the the 130 130 weather weather stations stations Fig. maintained by by EMY; EMY; locations locations of of the the available available meteorological meteorological maintained profiles. profiles.
2.2 Morphological Morphological characteristics characteristics -- classes classes 2.2 The morphological morphological characteristics characteristics deemed deemed as as most most salient salient The for classifying classifying any any location location of of interest interest within within the the Greek Greek for territory are are territory quantitative (and (and directly directly available), available), namely namely the the •• quantitative altitude, amplitude amplitude and and longitude longitude of of the the location, location, altitude, and and qualitative (derived), (derived), such such as as the the location location being being on on •• qualitative an island island (also (also specifying specifying the the approximate approximate island island an size and and the the proximity proximity to to other other islands islands or or the the size mainland) versus versus the the location location being being on on the the mainland mainland mainland) (also specifying specifying the the proximity proximity to to the the sea), sea), the the (also proximity of of the the location location to to rivers rivers and/or and/or lakes, lakes, the the proximity location being being on on aa plane plane versus versus the the location location being being location on aa mountain mountain (also (also specifying specifying highland highland and and on lowland plateaus). plateaus). lowland The classification classification of of the the Greek Greek territory territory according according The exclusively to to qualitative qualitative morphological morphological characteristics characteristics exclusively results into into 4,096 4,096 combinatorially combinatorially possible possible classes, classes, of of results which only only 55 55 are are observed observed in in the the 130 130 locations locations which corresponding to to the the weather weather stations stations of of Fig. Fig. 1. 1. corresponding Classification according according to to both both quantitative quantitative and and Classification qualitative morphological morphological characteristics characteristics is is detailed detailed in in qualitative section 3. 3. section For reasons reasons of of clarity clarity itit should should be be mentioned mentioned that, that, while while For the morphological morphological characteristics characteristics of of any any location location in in the the the
The main main sources sources of of inspiration inspiration for for the the SOM SOM [1] [1] are are the the The self-organisation of of the the neurons neurons in in biological biological brains brains and and self-organisation the emerging emerging topology topology preservation preservation such such that that similar similar the stimuli excite excite (and, (and, thus, thus, are are represented represented by) by) stimuli neighbouring neurons. neurons. neighbouring For meteorological meteorological profile profile estimation, estimation, two-dimensional two-dimensional For SOMs arranged arranged into into hexagonal hexagonal grids grids have have been been SOMs employed; the the sizes sizes of of the the grids grids range range from from 5x12 5x12 to to employed; 20x30 nodes. nodes. The The SOMTOOLBOX SOMTOOLBOX for for the the MATLAB MATLAB 20x30 environment has has been been used used [4]. [4]. The The training training procedure procedure environment comprises 1,000 1,000 and and 10,000 10,000 iterations iterations of of the the entire entire comprises training set set during during the the rough-training rough-training and and the the fine-tuning fine-tuning training phases, respectively. respectively. Following Following range range normalisation, normalisation, the the phases, 28-dimensional inputs (corresponding to the 28-dimensional inputs (corresponding to the meteorological profiles profiles of of the the locations locations of of Fig. Fig. 1) 1) have have meteorological been used used for for training. training. Cross-validation Cross-validation of of these these 130 130 been locations has has been been employed employed for for meteorological meteorological profile profile locations estimation. A A total total of of 130 130 tests tests have have been been performed performed estimation. where, in in each each test, test, 129 129 different different locations locations constitute constitute the the where, reference locations locations22.. reference
Fig. 2. 2. One One of of the the 11x22 11x22 SOMs SOMs employed employed for for organizing organizing the the Fig. meteorological profiles profiles of of the the Greek Greek territory. territory. meteorological The 12x22 12x22 SOM SOM (shown (shown in in Fig. Fig. 2) 2) with with range range The normalisation has has been been selected selected as as the the most most consistent consistent normalisation over the the 130 130 trials trials as as well well as as the the best best in in preserving preserving the the over distances of of the the original original meteorological meteorological profiles, profiles, i.e. i.e. in in distances ordering the the meteorological meteorological profiles profiles of of the the locations locations of of ordering Fig. 11 in in aa reasonable reasonable manner. manner. Fig. 22
the remaining remaining location location constitutes constitutes the the location location of of interest interest the large SOMs SOMs have have been been found found preferable preferable to to smaller smaller ones ones since since large they are are more more capable capable of of exposing exposing the the proximity proximity in in terms terms of of they meteorological profiles profiles between between the the 130 130 locations; locations; smaller smaller meteorological SOMs would would be be useful useful only only ifif the the aim aim were were to to ease ease computation computation SOMs (i.e. aa class class of of meteorological meteorological profiles profiles per per node) node) (i.e.
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175 qualitative morphological characteristics); the resulting 27 morphological classes are shown in Fig. 4. The relatively high degree of agreement between locationgrouping and morphological classification (Figs. 3 and 4, respectively) underlies the fact that the morphological characteristics of any location largely affect its meteorological profile. The morphological classes are not as continuous as are the groups resulting from the Umatrix; this can also be seen in Fig. 5 which further illustrates the assignment of the SOM nodes into the 27 morphological classes. However, the similarity of the (range-normalised) meteorological profiles between locations assigned to the same class is high. Hence, some understanding of the relationship between meteorological parameters and morphological characteristics is established.
Fig. 3. The mapping of the 11x22 SOM on the Greek territory into five groups created by the U-matrix.
Fig. 5 The assignment of the nodes of the SOM of Fig. 2 into the 27 morphological classes of Fig. 4.
4 Experimental results - comparison with existing methods
Fig. 4 The 27 morphological classes of the Greek territory.
The organisation accomplished by the SOM of Fig. 2 as well as the five groups created by its U-matrix (Fig. 3) have been employed in order to configure the morphological classification of the 130 locations of the Greek territory (according to both quantitative and
In each of the 130 trials, the meteorological parameters and hence the meteorological profile - of the remaining location (the location of interest) are assumed unknown. However, the morphological characteristics of the location of interest are available, whereby they can be employed in order to classify the location into one of the 27 morphological classes of Fig. 4. Subsequently, an estimation of the meteorological profile of the location of interest can be performed from the reference locations of the same morphological class that lie in the same closed area of Fig. 4. The estimation is based on the weighted average of the meteorological profiles of the reference locations involved, where the weights have been determined according to the similarity between reference
176 location and location of interest in terms of the three quantitative morphological characteristics. The proposed methodology for estimating the meteorological profiles of the locations of interest has been found superior to that of • Simply adopting the meteorological profile of the nearest reference location. This approach ignores the fact that, although the two locations are near each other, the morphological characteristics of the reference location and the location of interest may differ significantly. • Adopting and adapting the meteorological profile of the nearest reference location (e.g. adiabatic lapse rate normalization of temperature [5]). This approach takes into account the differentiation of the morphological characteristics between the reference location and the location of interest but is quite complicated to implement and not always accurate. • Interpolating between the nearest reference locations. As for the simple adaptation, the fact that the morphological characteristics of one or more of the reference locations and the location of interest may differ significantly - although the locations are near each other - is ignored.
5 Conclusions A novel methodology is proposed for the estimation of the meteorological profile of any location of interest within a specified area. Assuming that the morphology of the area is available, and that the meteorological profiles of a sufficient number of representative reference locations within the area are known, the methodology employs * a self-organising map where the meteorological profiles of the reference locations have been ordered, and * the morphological classification of the reference locations. Subsequently, The meteorological profile of a location of interest within the specified area is generated by: # classifying the location of interest into one of the morphological classes and, subsequently, • determining a weighted average of the meteorological profiles represented on the SOM for those reference locations that belong to the same morphological class of Fig. 4. The proposed methodology has been found superior to existing estimation techniques and consistently close to the actual meteorological profiles.
References [1] Kohonen, T. (1997) Self-Organising Maps, 2nd ed. Springer-Verlag, Berlin. [2] Kornaros, G. (1999) Climatic Data of the Stations of the Hellenic National Meteorological Service (period 1955-1997), Vols. 1 & 2. National Meteorological Service (E.M.Y.), Athens, Greece (in Greek). [3] Tambouratzis, T., Tambouratzis G. (2003) Meteorological data mining employing Self-Organising Maps. In: Pearson, D.W., Steele, N.C., Albrecht R.F. (eds) Proceedings of the "International Conference on Artificial Neural Networks and Genetic Algorithms 2003", Roanne, France, April 23rd-25th, 2003, Artificial Neural Nets and Genetic Algorithms, Springer, Wien, pp. 149-152 [4] Vesanto, J., Himberg, J., Alhoniemi, E. & Parhankangas, J. (2000). "SOM Toolbox for Matlab 5". Report A57. SOM Toolbox Team, Helsinki University of Technology, Finland (available at http://www.cis.hut.fi/proiects/somtoolbox). [5] Watson, B.G., Maclver, D.C. (1995) Bioclimate Mapping of Ontario. Environment Canada and Ministry of Natural Resources of Ontario.
