Hui-Chung Yeh

Entropy and kriging approach to rainfall network design

Hydrological data are the basic ingredients for planning, constructing, and operating of hydraulic structures. A well-designed rainfall network can accurately provide and reflect the information of rainfall in a catchment. However, in past studies, the required number and optimal location of rain gauge stations have yet to produce a satisfactory result. A more accurate design is required. Hence, in this study, a proposed model composed of kriging and entropy with probability distribution function is introduced to relocate the rainfall network and to obtain the optimal design with the minimum number of rain gauges. The ordinary kriging is used to generate rainfall data of potential locations where rain gauge stations may be installed. The information entropy based on probability is used to measure the uncertainty of rainfall distribution. The probability distribution function will be introduced to fit the statistical characteristics of data of the rain gauges. By calculating the joint entropy and the transferable information, the relocated rain gauges are prioritized and the minimum number and location of the rain gauges in the catchment can be obtained to construct the optimal rainfall network to replace the existing rainfall network.

Estimation of River Pollution Index in a Tidal Stream Using Kriging Analysis

Tidal streams are complex watercourses that represent a transitional zone between riverine and marine systems; they occur where fresh and marine waters converge. Because tidal circulation processes cause substantial turbulence in these highly dynamic zones, tidal streams are the most productive of water bodies. Their rich biological diversity, combined with the convenience of land and water transports, provide sites for concentrated populations that evolve into large cities. Domestic wastewater is generally discharged directly into tidal streams in Taiwan, necessitating regular evaluation of the water quality of these streams. Given the complex flow dynamics of tidal streams, only a few models can effectively evaluate and identify pollution levels. This study evaluates the river pollution index (RPI) in tidal streams by using kriging analysis. This is a geostatistical method for interpolating random spatial variation to estimate linear grid points in two or three dimensions. A kriging-based method is developed to evaluate RPI in tidal streams, which is typically considered as 1D in hydraulic engineering. The proposed method efficiently evaluates RPI in tidal streams with the minimum amount of water quality data. Data of the Tanshui River downstream reach available from an estuarine area validate the accuracy and reliability of the proposed method. Results of this study demonstrate that this simple yet reliable method can effectively estimate RPI in tidal streams.

An Anisotropic Spatial Modeling Approach for Remote Sensing Image Rectification

Abstract Rectification of a remote sensing image is commonly done by applying polynomial regression models to image coordinates and map coordinates of ground control points. A major drawback of the polynomial regression model is that it does not capture the random characteristic of terrain elevation. In fact, the distortion of a remote sensing image is attributed to the variation of terrain elevation and orbital parameters, the variations being random in nature. A more effective approach of remote sensing image rectification is a stochastic approach that takes into account the spatial variation structure of terrain elevation. This article presents an anisotropic spatial modeling approach of image rectification using ordinary kriging estimation. By considering the residuals of polynomial trend mapping as anisotropic random fields, the proposed approach models separately the spatial variation structures of the residuals in X and Y directions, and employs the ordinary kriging method for spatial interpolation of the residual random fields. By means of a cross validation procedure, residuals of image rectification by the polynomial trend mapping, the multiquadric interpolation function, and the ordinary kriging approaches are compared. The ordinary kriging approach yields smallest variances and root-mean-squared of mapping errors.

A path radiance estimation algorithm using reflectance measurements in radiometric control areas

A new algorithm of path radiance estimation based on measurements of surface reflectance at radiometric control areas (RCAs) is proposed. Path radiance estimates of the proposed RCA-based method were compared against estimates of other methods including the dark object subtraction (DOS) method, the multi-band regression (MBR) technique and the covariance matrix method (CMM). The RCA-based method is superior to other methods based on three qualitative assessment criteria and a quantitative assessment based on measurements of molecule and aerosol optical depths (AODs) available from the Aerosol Robotic Network (AERONET) and Moderate Resolution Imaging Spectroradiometer (MODIS) data archive. Asphalt-paved surface, which could be easily identified in most images, was also found to be a good choice for RCAs. The DOS method and the CMM tend to overestimate path radiances. Although in our study the MBR technique and the RCA-based method seem to perform equally well, estimates of the MBR technique may be less reliable.

Rainfall Network Optimization Using Radar and Entropy

In this study, a method combining radar and entropy was proposed to design a rainfall network. Owing to the shortage of rain gauges in mountain areas, weather radars are used to measure rainfall over catchments. The major advantage of radar is that it is possible to observe rainfall widely in a short time. However, the rainfall data obtained by radar do not necessarily correspond to that observed by ground-based rain gauges. The in-situ rainfall data from telemetering rain gauges were used to calibrate a radar system. Therefore, the rainfall intensity; as well as its distribution over the catchment can be obtained using radar. Once the rainfall data of past years at the desired locations over the catchment were generated, the entropy based on probability was applied to optimize the rainfall network. This method is applicable in remote and mountain areas. Its most important utility is to construct an optimal rainfall network in an ungauged catchment. The design of a rainfall network in the catchment of the Feitsui Reservoir was used to illustrate the various steps as well as the reliability of the method.

A new approach to selecting a regionalized design hyetograph by principal component analysis and analytic hierarchy process

Designing storm hyetographs is the essential element of hydrologic modeling analysis and storm water drainage design. In order to reasonably use storm hyetograph design in an un-gauged area, a regional representative hyetograph from an alternative and uniform area must be found. A new approach is proposed in this study to select a regional design storm hyetograph using principal component analysis (PCA) and analytic hierarchy process (AHP). The proposed approach combines both PCA and cluster analysis techniques. Furthermore, the AHP method is also used to establish the regional design hyetograph. A case study applied in the area of northern Taiwan shows that our method can successfully categorize the area into three homogenous zones. A representative regional hyetograph can be obtained by selecting the largest priority vector or by the weighted average of rain gauges in each zone.