Selection of multiple donor gauges via Graphical Lasso for estimation of daily streamflow time series

A fundamental challenge in estimations of daily streamflow time series at sites with incomplete records is how to effectively and efficiently select reference or donor gauges from an existing gauge network to infer the missing data. While research on estimating missing streamflow time series is not new, the existing approaches either use a single reference streamflow gauge or employ a set of "ad-hoc" reference gauges, leaving a systematic selection of reference gauges as a long-standing open question. In this work, a novel method is introduced that facilitates systematical selection of multiple reference gauges from any given streamflow network. The idea is to mathematically characterize the network-wise correlation structure of a streamflow network via graphical Markov modeling, and further transforms a dense network into a sparsely connected one. The resulted underlying sparse graph from the graphical model encodes conditional independence conditions among all reference gauges from the streamflow network, allowing determination of an optimum subset of the donor gauges. The sparsity is discovered by using the Graphical Lasso algorithm with an L1-norm regularization parameter and a thresholding parameter. These two parameters are determined by a multi-objective optimization process. Furthermore, the graphical modeling approach is employed to solve another open problem in gauge removal planning decision (e.g., due to operation budget constraints): which gauges to remove would statistically guarantee the least loss of information by estimations from the remaining gauges? Our graphical model-based method is demonstrated with daily streamflow data from a network of 34 gauges over the Ohio River basin.