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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 19, issue 6 | Copyright
Hydrol. Earth Syst. Sci., 19, 2925-2942, 2015
https://doi.org/10.5194/hess-19-2925-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 24 Jun 2015

Research article | 24 Jun 2015

TopREML: a topological restricted maximum likelihood approach to regionalize trended runoff signatures in stream networks

M. F. Müller and S. E. Thompson M. F. Müller and S. E. Thompson
  • Department of Civil and Environmental Engineering, Davis Hall, University of California, Berkeley, CA, USA

Abstract. We introduce topological restricted maximum likelihood (TopREML) as a method to predict runoff signatures in ungauged basins. The approach is based on the use of linear mixed models with spatially correlated random effects. The nested nature of streamflow networks is taken into account by using water balance considerations to constrain the covariance structure of runoff and to account for the stronger spatial correlation between flow-connected basins. The restricted maximum likelihood (REML) framework generates the best linear unbiased predictor (BLUP) of both the predicted variable and the associated prediction uncertainty, even when incorporating observable covariates into the model. The method was successfully tested in cross-validation analyses on mean streamflow and runoff frequency in Nepal (sparsely gauged) and Austria (densely gauged), where it matched the performance of comparable methods in the prediction of the considered runoff signature, while significantly outperforming them in the prediction of the associated modeling uncertainty. The ability of TopREML to combine deterministic and stochastic information to generate BLUPs of the prediction variable and its uncertainty makes it a particularly versatile method that can readily be applied in both densely gauged basins, where it takes advantage of spatial covariance information, and data-scarce regions, where it can rely on covariates, which are increasingly observable via remote-sensing technology.

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We introduce TopREML as a method to predict runoff signatures in ungauged basins using linear mixed models with spatially correlated random effects. The nested nature of streamflow networks is accounted for by allowing for stronger correlations between flow-connected basins. The restricted maximum likelihood framework provides best linear unbiased predictions of both the predicted flow variable and its uncertainty as shown in Monte Carlo and cross-validation analyses in Nepal and Austria.
We introduce TopREML as a method to predict runoff signatures in ungauged basins using linear...
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