Kriging technique for river flood representation

Abstract

The kriging technique is a geostatistical estimation method developed for mining applications some thirty years ago. It can be used to interpolate the value of a given property based on the value of the same properties at various experimental points.

The solution of this system is a set of coefficients that can then be used to interpolate the function at any given point by a simple scalar product with the covariance of each sample point.

In a civil engineering project, the natural ground surface is often the most important feature. It is generally described by a set of data from various sources and precision such as contour lines digitized from existing maps, bathymetric cross sections or surveys. For design purposes, these points may be replaced by a mathematical function representing the ground surface. It is then very easy to represent a cross section, calculate a volume relative to another surface, calculate the intersection of two surfaces or generate the contour lines incorporating all the available data. The relative precision of the input data points may be taken into account through the nugget effect. If it is zero at a given point, the surface will go through this point. This method has been used to represent the ground surface of a rural area on the north shore of Lac St. Jean. The purpose of the study was to simulate the flooding process resulting from the failure of an upstream dam. The water profile along the valley at variant time step was obtained using the NWS Dambreak Flood Forecasting Model. This 1-D water profile was then extended laterally to obtain a water surface also represented by its mathematical equation. The evolution of the Hooded area at various times after failure corresponds to the intersection of the ground with the various water surfaces. The intersection of two surfaces is easily determined by substraiting their corresponding elevation on a regular grid and evaluating the contour at elevation zero.