Entropy and kriging approach to rainfall network design

Abstract

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.

Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy

“…In this study, we use the exponential model to fit the semi-variogram from the measurements of rainfall [24]:…”

“…Therefore the rainfall information of the two rain gauge stations can become two variables x1 and x2. Corresponding to Equation (3), the joint entropy of two variables is [24]:…”

“…The joint entropy that can measure the amount of information of the joint events is derived by Equation (7) with conditional probability [24]:…”

“…After confirming the first station, which has the greatest entropy value, the rest are selected and added one at a time, according to the inferiority of the system and overlapped information. To minimize the system's uncertainty, the standardization of determining the second most important station in the sequence is set as [24]:…”

“…Applications to groundwater quality monitoring networks, stream gauge networks, and water distribution networks have increased in recent years. The methods used in network research related to entropy include least square methods and entropy [4], kriging [5], information entropy [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], and combined kriging and information entropy [23][24][25]. In particular, the information entropy approach has been widely adopted since the 1970s for hydrologic data collection network design and uncertainty evaluation [26][27][28][29][30][31][32][33].…”