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  1. Modeling Rainfall Data over the Bhakra Region using a Multivariate Non-homogenous Hidden Markov Model Shammunul Islam1, Andrew W. Robertson2 1 MA in Climate and Society Candidate, Class of 2014 2 Senior Research Scientist, Head of Climate Group, IRI Abstract: We have used a Bayesian non-homogenous Hidden Markov model (NHMM) to model the spatial dependence of precipitation in Himalayan Bhakra region of Nortwest (NW) India. We have classified rainfall into 3 hidden states and looked at the variability of rainfall in terms of these states. For the summer season, we have found the seasonal cycle to be significantly affecting rainfall while El Niño Southern Oscillation (ENSO)and Indian Ocean Dipole (IOD) to be insignificantly affecting rainfall. Likewise, for the winter season we find a similar pattern. Data and model: We have used daily rainfall data from 1984- 2004 over the Bhakra basin, one of the largest reservoir in northwest India. For ENSO indicator, we have considered NINO3.4 index which is the average sea surface temperature (SST) anomalies over the region between 5°N to - 5°S and between 170°W to - 120°W. Again, for IOD indicator, we used Dipole Mode Index (DMI) which is the difference between sea surface temperature (SST) anomalies in the western (50°E to 70°E and 10°S to 10°N) and eastern (90°E to 110°E and 10°S to 0°S) equatorial Indian Ocean. Both of these indices were extracted from the IRI data library. We have considered June, July, August and September as the summer season and December, January, February and March as the winter season. We consider winter rainfall as it meets irrigation demand in northwest India at that time and brings lower temperatures conducive to wheat development (Yadav et al. 2012). Hidden Markov Model (HMM) have been used before for simulating rainfall variability (for example, Greene et al. 2008). NHMM further allows the inclusion of meteorological or climatic variables as exogenous variables. We denote Yt,s as the observed time series of rainfall observed for s=15 stations of Bhakra region. Yt is a a non- homogeneous Markov model (NHMM) with hidden process Z which can take at any step any one of 3 values(figure in the left panel).The Markov transition property between state t-1 and state t is given by qt- 1,t and matrix Qt denotes the set of all of these properties. There are two covariate processes Xt and Wt. We here consider seasonal cycle, ENSO and IOD as exogenous variables and investigate how they affect rainfall. Figure: State sequences for summer Figure: State sequences for winter Results: As we can see from the panel above, the top figure shows the evolution of daily rainfall classified into the three hidden states (ordered from driest (S1) to wettest (S3)) drawn with Bayesian sampling. The bottom figure shows the average seasonal evolution of the occurrence of these three states. For the summer season (left figure), July-August period remains mainly wet or somewhat wet with intermittent dry state throughout the period. We can also observe that at the beginning and at the end of a year, this region remains mainly dry or somewhat dry corresponding to state 1 or state 2. For winter considering DJFM (right figure in the middle panel), the region remains mainly dry with a very few number of days falling in somewhat dry or wet state. Surprisingly, more days fall into wettest state (state 3) than the middle state (state 2), indicating that winter storms tend to be intense. At the end of February and March, we find more days falling into state 3 signifying heavy rainfall in those days. The top figure shows that both probability of rainfall and mean daily intensity both increases with states. For summer, we further find that none of the transition probabilities between states are significantly impacted by ENSO or the IOD. Here, the seasonal cycle affects rainfall through the emission distribution but ENSO and IOD don’t affect significantly. Implications: Understanding the rainfall dynamics in Bhakra region will help practical water management and hence will help in terms of agriculture also. As NHMM model clusters states with respect to spatial and temporal characteristics, these states provide us a way of identifying larger scale weather patterns and climatic conditions that affect the moisture transport. References: Yadav RK, Rupa Kumar K, Rajeevan M (2012) Characteristic features of winter precipitation and its variability over northwest India. Journal of Earth System Science 121(3):6111-623. Greene, A., M., A. W. Robertson, and S. Kirshner, 2008: Analysis of Indian monsoon daily rainfall on subseasonal to mutidecadal time-scales using a hidden Markov model. Q. J. of the Roy. Meteor. Soc., 134 (633), 875-887. Introduction: This paper analyses local precipitation in Bhakra basin in NW India. It aims to shed some light on weather and climatic conditions associated with precipitation over this region. This work is done under the project Decadal Prediction and Stochastic Simulation of Hydroclimate Over Monsoonal Asia and is supported by Department of Environment (DOE).