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
Figure: State sequences for
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
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
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
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).