Ordinary kriging as a tool to estimate historical daily streamflow records

William H Farmer

doi:10.5194/hess-20-2721-2016

Abstract

Abstract. Efficient and responsible management of water resources relies on accurate streamflow records. However, many watersheds are ungaged, limiting the ability to assess and understand local hydrology. Several tools have been developed to alleviate this data scarcity, but few provide continuous daily streamflow records at individual streamgages within an entire region. Building on the history of hydrologic mapping, ordinary kriging was extended to predict daily streamflow time series on a regional basis. Pooling parameters to estimate a single, time-invariant characterization of spatial semivariance structure is shown to produce accurate reproduction of streamflow. This approach is contrasted with a time-varying series of variograms, representing the temporal evolution and behavior of the spatial semivariance structure. Furthermore, the ordinary kriging approach is shown to produce more accurate time series than more common, single-index hydrologic transfers. A comparison between topological kriging and ordinary kriging is less definitive, showing the ordinary kriging approach to be significantly inferior in terms of Nash–Sutcliffe model efficiencies while maintaining significantly superior performance measured by root mean squared errors. Given the similarity of performance and the computational efficiency of ordinary kriging, it is concluded that ordinary kriging is useful for first-order approximation of daily streamflow time series in ungaged watersheds.

Highlights

One of the most fundamental problems confronting the fields of hydrology and water resources management is the prediction of hydrologic responses in ungaged basins (PUB) (Sivapalan et al, 2003)
The primary goal of this work is to demonstrate that simple geostatistical techniques can provide predictions of daily streamflow time series at ungaged sites that are superior to those produced by the single-index, transfer-based techniques
The estimation of daily streamflow records at ungaged sites is a fundamental problem of water resources management and assessment

Summary

Introduction

One of the most fundamental problems confronting the fields of hydrology and water resources management is the prediction of hydrologic responses in ungaged basins (PUB) (Sivapalan et al, 2003). The primary goal of this work is to demonstrate that simple geostatistical techniques can provide predictions of daily streamflow time series at ungaged sites that are superior to those produced by the single-index, transfer-based techniques. This work is concerned with the latter, which rely on transferring information from an index site or set of index sites to an ungaged site by the means of a statistical relationship These techniques include ungaged applications of record reconstruction techniques like the drainage-area ratio method (see Asquith et al, 2006), the maintenance of variance extension (Hirsch, 1979, 1982), and nonlinear spatial interpolation using flow duration curves (Fennessey, 1994; Hughes and Smakhtin, 1996). A portion of this work is dedicated to contextualizing geostatistical techniques within these traditional approaches

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