Optimal vector interpolation of asynoptic spatial survey of vector quantities for interpolating ADCP water velocity measurements

Abstract

In fields of study such as geophysics and hydraulics, many random variables are vector quantities, not scalars. Vector quantities require statistical techniques that are independent of choice of coordinate system. In this research a new optimal vector interpolation method, suitable for interpolation of asynoptically measured spatial vector fields, was developed and tested. The new method was compared to scalar interpolation by kriging. The test data were spatial Acoustic Doppler Current Profiler (ADCP) surveys of depth average fluvial water velocity in reaches upstream and downstream of a bridge. The interpolation procedures were evaluated by interpolating the fields with various amounts of data removal, and comparing to the actual measured field using a vector correlation coefficient previously developed by Crosby et al. (1993). The new optimal vector interpolation method was superior to kriging when all data were utilized (upstream reach) and for data removal rates of up to 30% (downstream reach).