A Interpolation method of Global Climate Data

A Interpolation method of Global Climate Data

Teruyuki ITO, Ryosuke Shibasaki, Yoshiaki Honda
Shunji MURAI, Elegen. O. BOX Institute of Industrial Science
University of Tokyo 7-22-1, Roppongi, Minato-ku, Tokyo 106, Japan

Abstract
A variety of aerial global databases such as those of climate, vegetation, etc. are required for research and policy making for global environmental issues. However some kinds of data, such as temperature, precipitation, are point-based.

Since interpolation method of global climate data should be developed. The authors improved the conventional simple statistical interpolation method with some knowledge and made case study and discussion. Then some aspects of global GIS were defined.

Introduction
For research and policy making for the global environmental issues, a variety of databases such as those of climate, vegetation, topography ( elevation), land use, population distribution data, are required. Some of natural environmental data like climate data are point - Based data is indispensable.

Most of conventional interpolation methods like Kriging, are more suitable for handling data which are distributed with relatively high density and in local area, where the regional conditions are almost homogeneous. However global databases have to cover a variety of areas with different natural/socio economic conditions. And the distribution of point-based data available for interpolation tends to be much biased. With these reasons many of conventional interpolation methods cannot be effectively utilized.

Moreover, one global sphere, attentions should be paid to the calculation of distance area and direction. And a large size of data requires higher efficiency in interpolation works.

In this paper, the authors develop a interpolation method to develop more reliable global database more efficiently.

An Interpolation Method

1 Approaches for Interpolation
Approaches for interpolation can be roughly classified into these three classes.

Statistical Approach
Data are interpolated using only their spatial statistical characteristics. Kriging is a typical example. In case there are changes in the pattern of the occurrence of a phenomenon with no changes in the underlying mechanism, and no enough data are available to grasp the changes statistically, interpolation based on statistical approach may fail. One the other hand, the fact that only statistical information directly derived from the data eases the evaluation of the reliability of the interpolation. It could be concluded that a statistical approach is suitable for the interpolation of the data with high distribution density.
Model Based Approach
Interpolation can be conducted using a model which quantitatively describes the mechanism of a phenomenon. The parameters of the model can be determined from point-based data. Since a mechanism of a phenomenon is described explicitly in the interpolation, interpolated value can be obtained, which are consistent with the model of the mechanism, in spite of the observed data distribution. This approach is adequate for such kinds of data as can be successfully represented by a quantitative model. Short-term weather is an example which this approach can be successfully applied. However the reliability is an example which this approach can be successfully applied. However the reliability of interpolated value depends upon that of a model. In fact, there is no adequate model for a long term phenomenon like climate value. In these case, this approach cannot be used.
Knowledge Based Approach
When it is difficult to built a quantitative model to describe a phenomenon, but not so difficult to obtain quantitative knowledge on the characteristics of a phenomenon, these knowledge can be used for interpolation to improve the reliability. For example, climate conditions on the both sides of a huge mountain range may be quite difficult. Interpolation over the climatic boundary in the mountain range may provide the degraded results. When meteorological geographers draw the isohyet of mean temperature from point-based climate data, they might use their knowledge on climate divisions, etc.

Thus, knowledge based approach can be very flexible in handling a variety of data, although it is not so easy to collect and represent systematic and reliable knowledge.

2. Improvement of Interpolation Method
In this study, we developed an interpolation method for monthly mean temperature data as an example. This interpolation method is mainly based on statistical approach. It is because the spatial change of mean temperature is smaller than that of other climate data such as precipitation. The temperature usually change more in north-south ) latitude) direction than in east-west ( longitude) direction. This knowledge were taken into consideration. And altitude data were used, because altitude of observatory causes the deviation of temperature.

Case Study

1 Procedure of Interpolation

Data Set Used in This Study
Data set used in this study was collected in WMO (World Meteorological Organization, 1978), and by E.O.Box, and K. Iwasaki. It includes longitude, longitude, latitude and altitude of the observatory, and monthly mean temperature. The total number of observatory is 2974, and they are distributed shown in Fig. - 1, Furthermore, ETOPS (altitude data of global spherical surface ) was also used.

FIG - 1 Distribution of Observatories
Procedure of Interpolation
Procedure of interpolation is as follows (Fig-2);
- Ground level temperature of observatory are changed to sea level ones by using laps rate of temperature, o.60C/100m.
- Searching for neighboring observatories with search window. In usual interpolation, square window is used. However, in this study window is uses rectangular, which is elongated in east-west direction, because the variation of temperature in east-west direction is usually smaller. In this study, we set the ratio of rectangular window's sides be 1:3. ( Fig-3)
- For 4 nearest neighbors in search window, distances between points were calculated by trigonometry, regarding the globe as a sphere. (Fig-4)
- Interpolation by weighted mean method. (Fig-5)
FIG - 2 Flow of Interpolation of Monthly Temperature Data

FIG - 3 Concept of Search Window

FIG - 4 Distance on Shperical Surface

FIG - 5 Weighted Mean Method
Discussion
Comparing mean temperature image of January (Fig-6) with an isothermal map of January drawn by a meteorological geographer (Fig-7), it could be concluded that this interpolation method works quite well.

FIG - 6 Mean Temperature Image of January

FIG - 7 Isothermal Map of January
Between interpolated data using rectangular window and those using square window, large differences can be seen in the regions where the density of data distribution is low (Fig-8)

FIG - 8 Differential image between image of january using square window and it using rectangular window
Conclusion and Future Prospects
By adding a knowledge on the tendency of monthly mean temperature to relatively simple statistical method, we could obtain the quite good interpolated result. However, such a simple method may not work well in the interpolation of precipitation, which is also important climate data. It would be necessary incorporate the knowledge on the distribution of precipitation.

Global data are usually represented on latitude-longitude grid system, while in usual GIS, plane orthogonal coordinate system is used. Global GIS is required to have the functions to calculate the distance, the area, and direction of data represented on latitude-longitude grid system. Furthermore, on latitude-longitude grid system, the areas of pixel on the ground close to the equator are much large than those of pixels close to the pole. The differences of pixel sizes on the ground degrade the efficiency of data storage. Development of a coordinate system and efficient data representation methods based on its research subjects is one of the important research subjects.

References

Burroough, 1986; Principles od Geographical Information System for Land Resources Assessment, Claredon Press, London
Kazutaka Iwasaki (ed.), 1992; Precipitation and Temperature Distribution of the World, Division of Geography, Faculty of letters, Hokkaido University.