Statistical and geostatistical analysis of rainfall in central Japan
Introduction
Water is essential for all living things including human beings, and hence one of the most important resources. All necessary water for life on land originates for rain. Estimation of precipitation, accordingly, is very important for assessing water resources. The result of the assessment contributes to not only water supply but also making plans to keep the environmental conditions. Many environmental problems are caused by water pollutions in rivers, lakes and sea. The estimation of precipitation is also important for predicting natural hazards caused by heavy rain.
To estimate precipitation properly, it is necessary to have optimally distributed locations of rain gauges, and to apply an appropriate technique for the estimation. We have used geostatistical approach to overcome the problem. In geostatistical approach, the variogram can suggest how to optimally set rain gauges, and the kriging should be able to estimate precipitation. Many papers have tried to apply geostatistics to these themes. For example, Delhomme and Delfiner (1973) draw a variogram of water heights (measured in rain gauges) after rain showers in the Kadjemeur basin in Tchad (Central Africa), and simulated rainfalls, although it is unbelievable that the variogram increased linearly. Takara and Oka (1992) applied variogram and kriging to rainfall in Yasu Basin, Central Japan using data of only nine stations. Lynch and Schulze (1995) compared daily rainfalls estimated by interpolation techniques of inverse distance weight, Schäfer, Thiessen, SACLANT (1979) and kriging using data of 90 rain gauges in the province of KwaZulu-Natal (ca. 10,735 km2), South Africa, and concluded that variograms needed to be analyzed for before the kriging technique was used, though variograms were not shown. Lynch (1998) estimated daily rainfalls using data of 27 automatic weather stations in the winter rain region (ca. 15,000 km2), South Africa, by interpolation techniques of inverse distance weight, root mean square error, Schäfer, regression, spline and kriging, and compared the estimates with data of 159 daily rainfall stations. The conclusion is that kriging did not produce better estimates of the daily rainfall surfaces, though variograms are not also shown. Çetin and Tülücü (1998) calculated variograms of monthly precipitations in Eastern Mediterranean Region, and showed that ranges changed from 25 to 270 km depending on months. Pardo-Igúzquiza (1998) compared the areal average climatological rainfall mean estimated by the classical Thiessen method, ordinary kriging, cokriging and kriging with an external drift (the first two methods used only rainfall information, while the latter two used both precipitation data and orographic information) in the Guadalhorce river basin in southern Spain, and concluded that kriging with an external drift seemed to give the most coherent results in accordance with cross-validation statistics and had the advantage of requiring a less demanding variogram analysis than cokriging. Campling et al. (2001) analyzed temporal and spatial rainfall patterns to describe the distribution of daily rainfall across a medium-sized (379 km2) tropical catchment, and concluded that although distinct wet season phases could be established based on the temporal analysis of daily rainfall characteristics, the interpolation of daily rainfall across a medium-sized catchment based on spatial analysis was better served by using the global rather than the wet season phase climatological variogram model.
All of the previous papers introduced above aim to estimate rain precipitations accurately. It is said really that this is the final goal of the geostatistical application for rainfall. Before the estimation, however, spatial and temporal continuities of rainfall should be revealed clearly. Accordingly, this paper aims to comprehend spatial and temporal continuities of rainfall, especially special continuities of hourly, daily, monthly and annual precipitations on the basis of their variograms.
Section snippets
Data and areas
Japan Meteorological Agency has established an automated meteorological observation system named AMeDAS (Automated Meteorological Data Acquisition System). AMeDAS has 1536 stations in the whole area of Japan (377,800 km2). Each station records precipitation and other meteorological data such as temperature, velocity of wind, and so on at every hour. The station density is about 1/250 station/km2 (41 stations in 100×100 km2). If the stations are arranged on a tetragonal grid, the average distance
Statistical distribution models
First, basic statistics were obtained from hourly, daily, monthly and annual precipitation data in the Chubu and Kanto districts (simply, Chubu and Kanto, respectively), and the Chubu–Kanto total area (ChuKan) combining both districts. The combination of the district and the dealt duration (i.e. hour, day, month and year) gives 12 categories (e.g. Hour-Chubu, Year-Kanto, and so on). Many statistical models have been proposed for rainfall (e.g. Suda, 1990; Hosking and Wallis, 1997; Toyama and
Spatial continuity of long term precipitations
Annual precipitation data should give fundamental information for assessing water resources. In order to examine if the station density of the AMeDAS is dense enough to know the spatial continuity of rainfall, experimental variograms (exactly, semivariograms) of annual precipitations were calculated by a program written in MS-Excel/VBA (Shoji, 2002a, Shoji, 2002c). A lag tolerance of ±10 km (i.e. a circle with the radius of 10 km) is applied for calculating omnidirectional variograms, considering
Temporal continuity of long term precipitations
In order to know the temporal continuity of rainfall, experimental variograms of hourly precipitations observed through a year (’99) were calculated. A lag tolerance of ±1 h is applied avoiding extreme variation in variograms, although the time interval in measurement is 1 h. Temporal variograms were obtained at all stations (170 in Chubu, 81 in Kanto, and totally 243, because eight stations belong to both districts).
Fig. 10 shows temporal variograms, which are selected from 243 variograms. The
Spatial correlation of short term rainfall
It is necessary to estimate accurately rainfall in a short term for predicting natural hazards such as flood, landslide and others. AMeDAS records precipitation with a time interval of 1 h. In order to know the spatial continuity of rainfall in a short term, experimental variograms of hourly precipitations has been calculated. The data studied came from August 13 to 14, 1999, because the rain caused a severe flood in Kanto.
Fig. 14 shows averaged hourly precipitation at Time t from 01 JST on
Conclusions
Statistical and geostatistical analyses of rainfall in the mountainous Chubu and plain Kanto districts in central Japan indicate the following features: (1) hourly, daily and annual precipitations show lognormal distributions independently of the districts, while only monthly precipitations show exponential distributions, and Weibull distribution illustrate hourly and daily precipitations excellently, and monthly precipitations well in both cases including and excluding zero data; (2) spatial
Acknowledgments
We would like to thank Emeritus Prof. Ryuji Kimura of The University of Tokyo, Dr. Y. Suda of Keio High School, and Dr. Chang-Jo F. Chung of Geological Survey of Canada for their critical reading of the manuscript and valuable suggestions.
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