Ordinary kriging as a tool to estimate historical daily streamflow records

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 covariance 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 covariance 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.

Transferring measured discharge time series: Large‐scale comparison of Top‐kriging to geomorphology‐based inverse modeling

“…Several observation‐based approaches found in the literature rely on geostatistical techniques to spatially interpolate variables measured in the stream network [ Skøien et al ., ; Isaak et al ., ; Müller and Thompson , ; Farmer , ]. Topological kriging (or Top‐kriging) of a variety of variables was recently compared to several other methods.…”

“…Kriging has sometimes also been used to interpolate runoff time series. Farmer [] used ordinary kriging at a daily time step, whereas Skøien and Blöschl [] extended their topological kriging technique for this purpose at an hourly time step. Viglione et al .…”

Reducing the Uncertainty of Radiata Pine Site Index Maps Using an Spatial Ensemble of Machine Learning Models

“…Geostatistical models have been widely used for predicting spatially continuous variables based only on geospatial locations. Ordinary kriging (OK) is one of the most widely used geostatistical methods [2,15,[61][62][63], in which the value for an unsampled point is estimated based on the weighted average of observed neighbouring points within a given area [63]. The neighborhood was restricted to include only the 100 nearest neighbours.…”

Review "Ordinary kriging as a tool to estimate historical daily streamflow records"

“…In this case, one can denote non-stationarity as the variogram diverge and never reach the "sill", while non-stationarity might not be seen from the covariance. I think the mathematical notations and equations (1), (2), (3) and (4) (L25 P4) are formally incorrect as they refer to the covariance, rather they should refer to semivariances of the increment z(x + h) − z(x), both theoretical or experimental (see for examples, Cressie, 1993;Journel and Huijbregts, 1978). Although there is a way to employ the covariance matrix too, which derives from the optimization of the prediction variance, the author did not report the correct one.…”