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A novel algorithm is introduced to improve estimations of daily streamflowtime series at sites with incomplete records based on the concept ofconditional independence in graphical models. The goal is to fill in gaps ofhistorical data or extend records at streamflow stations no longer in operationor even estimate streamflow at ungauged locations. This is achieved by firstselecting relevant stations in the hydrometric network as reference (donor)stations and then using them to infer the missing data. The selection processtransforms fully connected streamflow stations in the hydrometric network intoa sparsely connected network represented by a precision matrix using a Gaussiangraphical model. The underlying graph encodes conditional independenceconditions which allow determination of an optimum set of reference stationsfrom the fully connected hydrometric network for a study area. The sparsity ofthe precision matrix is imposed by using the Graphical Lasso algorithm with anL1-norm regularization parameter and a thresholding parameter. The twoparameters are determined by a multi-objective optimization process. Inaddition, an algorithm based on the conditional independence concept ispresented to allow a removal of gauges with the least loss of information. Ourapproaches are illustrated with daily streamflow data from a hydrometricnetwork of 34 gauges between 1 January 1950 and 31 December 1980 over the OhioRiver basin. Our results show that the use of conditional independenceconditions can lead to more accurate streamflow estimates than the widely usedapproaches which are based on either distance or pair-wise correlation.

Estimation of daily streamflow from multiple donor catchments with Graphical Lasso