We consider discriminant analysis of land-cover categories based on multivariate geo-spatial data observed by artificial satellites or airborne sensors. The following contextual classification methods will be introduced through statistical treatment.
First, we discuss the intrinsic model, which was introduced to take the spatial correlation of the data into account. We derive the estimation procedure for unknown parameters and their distribu-tions under normality assumption. Then, we employ a penalized likelihood principle based on the penalty due to spatial configuration such that adjacent pixels belong to different categories. We com-pare the penalized likelihood method and Switzer's smoothing method through simulation study. It is shown that our method is superior to Switzer's method and to the ordinary non-contextual method based on the linear discriminant function.
Next, we assume that the categories follow a Markov random field (MRF), which is commonly used in image analysis. In this case, the MRF is based on the Mahalanobis distance for specifying the conditional distribution of the category given pixels in a neighborhood. Then, an adaptive clas-sification method based on the interactive conditional mode (ICM) algorithm is derived. We obtain the exact error rate of the classification of the center pixel given pixels in a local window, and it is shown that the ICM algorithm reduces the error rate in most cases. Finally, our adaptive ICM method is applied to the real data set provided by IEEE Geoscience and Remote Sensing Society for benchmark of classifications. We examine several models for the class-conditional densities and our contextual classification result shows the best performance.

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This paper aims to reveal the features of the spatial distribution of land use/land cover in China based on the statistical analysis on a set of county-level databases including area estimates from the 1-km resolution NOAA/AVHRR-derived monthly NDVI composite data as well as the population census data. The initial analysis based on 2, 374 county-level land use/land cover data disclose the mechanism of land type converting, and show the distributional features of China's land use/land cover are very different throughout the six administrative regions. After that, the author divides the six administrative regions into the four land cover types based on the results derived from canonical discriminant analysis, especially examines the regional distributions on cropland and forestland in terms of area coverage and area per capita at the county-level. As an integrated conclusion, it was demonstrated that China's spatial features of land use/land cover at the county level can be drawn based on the NOAA/AVHRR data for wide area monitoring, and the results of canonical discriminant analysis is meaningful for spatial classification of land use/land cover. On the other hand, it was also shown that the NOAA/AVHRR data are not suitable to monitor the land cover changes in a small area because of the restriction of low spatial resolution.

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Environmental data acquired by periodic or continuous measurements at many points are expressed in the spatio-temporal region. Therefore, it is necessary to combine a spatial analysis and a time-series analysis for characterizing data distribution. This study adopts geostatistics to construct a distribution model, which can consider spatio-temporal correlation structures peculiar to the regionalized data and has ability to predict the near future values. The concentration data of seven ion components, Na+, Mg2+, K+, Ca2+, C1-, SO2-4, and HCO-3 contented in the groundwater in the Kumamoto city area, southwest Japan, were chosen for a case study of hydrologic environmental related problem. These data were sampled two times per year between 1994 and 2000 at the 31 groundwater observation wells. Omnidirectional semivariograms of univariate and cross-semivariograms of two variates were made and approximated by polynomials. They clarified two features of correlation structures of the components, which are monotonous increase type and periodic change type of semivariances between data pair with increase of distance and time interval. Through the cross-validation from the two viewpoints, (1) temporal extrapolation capability of ordinary kriging and ordinary co-kriging and (2) validness for considering both the spatial and temporal directions, it was demonstrated that the kriging methods can estimate properly the ion component concentrations and produce less smoothing effect. The concentrations in four June times in 1994, 1996, 1998, and 2000 were estimated and characteristics of fluctuation patterns of each component were detected. A cluster analysis of the hexadiagrams using the seven ion component concentrations estimated in each observation year clarified the zones having similar water quality. The lithologies and groundwater flows in the shallow depths are regarded as influence factors on water quality. In addition, the temporal changes of water qualities were found to be interpretable by a combination of the precipitation and groundwater flows. Water management is specially required for the portions where the qualities are changeable.

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Various mathematical models have been developed to reveal the influence of pollution sources on natural environment. Among them, this paper states Chemical Mass Balance (CMB), which is a model to estimate source contribution rates based on the mass balance between certain materials at sources and those at a receptor site. As its solution, linear least-squares technique, that is, multiple regression has been widely used. The compositions of materials observed at sources and at a receptor site are assumed for independent and dependent variables, respectively. However, the observations at sources involve irregular variation as same as in that at a receptor site. Multiple regression cannot deal with such irregular variation. Other than this problem, existing methods involve several problems. To solve those problems, this paper proposes two kinds of functional relationship models for CMB. One is a model based on the mass, and another is a model based on the proportion. The use of multinomial and scaled Dirichlet distributions is also proposed to define the covariance structure in the later model. Finally, the proposed models are applied to actual dioxins data.

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One of the scientific objectives of the Tropical Rainfall Measuring Mission is to estimate monthly mean rainfall between approximately ±37°(latitude) and over 5°×5°(latitude-longitude) regions.The present study is motivated by the need to determine a relationship between radar reflectivity Z and rain rate R. The relationship, Z=ARB, where A(>0) and B are constants, is known as the Z-R relationship. It reduces to a linear relation between log Z and log R. The regression is widely used to determine the relationship. Other methods are the method of probability matching, the method of incomplete first-moment ratio matching, and the method of Lorenz curve matching.
The paper addresses the structural model approach to the determination of the relationship. It studies the maximum likelihood (ML) estimation under a normal assumption when some observations on either of the variables are missing. As a side condition for identifiability, it is assumed that the variance of the unobservable variable log R is known. This condition is adopted because it is known that a lognormal distribution provides a close fit to the frequency distribution for area-average rain rate, conditional on rain, measured in the tropical region and the shape parameter tends to be a constant if the rain is appropriately stratified by area, time and type. The paper gives an algorithm for having ML estimates and provides asymptotic variances and covariances of the ML estimators.

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