A Non-Homogenous Hidden Markov Model to Generate Future PMDI Time Series in order to Inform Water Supply Planning and Generate Streamflow Ensembles

A major challenge in framing and conducting long-term planning studies in the interconnected watersheds of the Western United States is the uncertainty in spatial and temporal hydrological patterns. The region exhibits strong climate variability on a variety of time scales at different regions [1]. Thus, the distribution of hydrological variability has spatial and temporal differences. This causes for some places impacted more by problems associated with variance tolerance than other places [2]. Hence, developing a water infrastructure network resilient to extreme events (e.g., droughts) which requires a robust understanding of spatio-temporal hydrological patterns is very important.

In this study, paleoclimate time series of modified Palmer drought severity index (PMDI) [3] and temperature records [4] are leveraged together with observed data to better understand the long-term climatic variability for future challenges. A non-homogenous hidden Markov model (NHMM) of PMDI is used in order to capture realistic spatial patterns of PMDI variability, their temporal distribution, and transitions between states in these sequences across the Western U.S including the Colorado River and interconnected watersheds linked by interbasin transfers and shared demand nodes (e.g., Rio Grande, Sacramento-San Joaquin) [5]. The developed model is used to generate plausible future scenarios by using temperature output from a general circulation model (GCM) to improve future reliability of water supply and reduce vulnerability [6]. Principle component analysis (PCA) and k-means clustering methods are used to compact the data set prior to fitting the NHMM in order to preserve the regional variability [7]. The NHMM model generates an ensemble of future regional PMDI for any projected temperature sequence. These ensembles can be used to inform water supply planning and to generate streamflow ensembles that preserve long term spatio-temporal variability.

References:

[1] National Research Council. (2007). Colorado River Basin water management: Evaluating and adjusting to hydroclimatic variability. National Academies Press.

[2] Anderies, J. M. (2015). Managing variance: key policy challenges for the Anthropocene. Proceedings of the National Academy of Sciences, 112(47), 14402-14403.

[3] Cook, E. R., Seager, R., Heim Jr, R. R., Vose, R. S., Herweijer, C., & Woodhouse, C. (2010). Megadroughts in North America: Placing IPCC projections of hydroclimatic change in a long-term palaeoclimate context. Journal of Quaternary Science, 25(1), 48-61.

[4] Wahl, E.R. and J.E. Smerdon. 2012. Comparative performance of paleoclimate field and index reconstructions derived from climate proxies and noise-only predictors. Geophys. Res. Lett., 39, L06703, doi:10.1029/2012GL051086.

[5] Zucchini, W., & MacDonald, I. L. (2009). Hidden Markov models for time series: an introduction using R. Chapman and Hall/CRC.

[6] Voldoire, A., E. Sanchez-Gomez, D. Salas y Mélia, B. Decharme, C. Cassou, S.Sénési, S. Valcke, I. Beau, A. Alias, M. Chevallier, M. Déqué, J. Deshayes, H. Douville, E. Fernandez, G. Madec, E. Maisonnave , M.-P. Moine, S. Planton, D.Saint-Martin, S. Szopa, S. Tyteca, R. Alkama, S. Belamari, A. Braun, L. Coquart, F. Chauvin (2011) : The CNRM-CM5.1 global climate model : description and basic evaluation, Clim. Dyn., accepted, DOI:10.1007/s00382-011-1259-y.

[7] Wilks, D. S. (2011). Statistical methods in the atmospheric sciences (Vol. 100). Academic press.