A Bayesian hierarchical nonhomogeneous hidden Markov model for multisite streamflow reconstructions. Issue 10 (12th October 2016)

• Record Type: Journal Article
• Authors: Bracken, C.; Rajagopalan, B.; Woodhouse, C.
• Is Part Of: Water resources research. Volume 52:Issue 10(2016:Oct.)
• Page Start: 7837
• Page End: 7850
• Publication Date: 2016-10-12
• Subjects: streamflow reconstruction -- tree rings -- Gaussian Copula -- hidden Markov model; Hydrology -- Periodicals; 333.91
• DOI: 10.1002/2016WR018887
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: In many complex water supply systems, the next generation of water resources planning models will require simultaneous probabilistic streamflow inputs at multiple locations on an interconnected network. To make use of the valuable multicentury records provided by tree‐ring data, reconstruction models must be able to produce appropriate multisite inputs. Existing streamflow reconstruction models typically focus on one site at a time, not addressing intersite dependencies and potentially misrepresenting uncertainty. To this end, we develop a model for multisite streamflow reconstruction with the ability to capture intersite correlations. The proposed model is a hierarchical Bayesian nonhomogeneous hidden Markov model (NHMM). A NHMM is fit to contemporary streamflow at each location using lognormal component distributions. Leading principal components of tree rings are used as covariates to model nonstationary transition probabilities and the parameters of the lognormal component distributions. Spatial dependence between sites is captured with a Gaussian elliptical copula. Parameters of the model are estimated in a fully Bayesian framework, in that marginal posterior distributions of all the parameters are obtained. The model is applied to reconstruct flows at 20 sites in the Upper Colorado River Basin (UCRB) from 1473 to 1906. Many previous reconstructions are available for this basin, making it ideal for testing this new method. The results show some improvements over regression‐based methods in terms of validation statistics. Key advantages of the Bayesian NHMM over traditional approaches are a dynamic representation of uncertainty and the ability to make long multisite simulations that capture at‐site statistics and spatial correlations between sites. Key Points: A Bayesian hierarchical nonhomogeneous hidden Markov model (NHMM) for streamflow reconstruction is developed Flow is reconstructed from 1473 to 1997 at 20 sites in the Upper Colorado River Basin using tree‐ring covariates Results are in agreement with published regression‐based reconstructions