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Application and Evaluation of a Snowmelt Runoff Model in the Tamor River Basin,
Eastern Himalaya using a Markov Chain Monte Carlo Data Assimilation Approach
Prajjwal K.
1Graduate
1†
Panday ,
Christopher A.
1
Williams ,
2 Biospheric
School of Geography, Clark University, Worcester, MA 01610;
†Corresponding
Karen E.
1
Frey ,
Sciences, NASA Goddard Space Flight Center, Greenbelt, MD 20771
author: [email protected]
Markov Chain Monte Carlo (MCMC)
INTRODUCTION
 Previous studies have drawn attention to substantial hydrological changes taking place in
mountainous watersheds where hydrology is dominated by cryospheric processes.
Snowmelt modeling, an important tool for understanding such changes, is particularly
challenging in mountainous terrain owing to scarcity of observations and uncertainty of
model parameters across space and time (Pellicciotti et al., 2012).
 A thorough assessment of hydrologic processes, patterns, and trends requires
minimization of uncertainties in modeling and available input data. This study utilizes a
Markov Chain Monte Carlo (MCMC) data assimilation approach coupled with a
conceptual, degree-day snowmelt runoff model applied in the Tamor River basin in the
eastern Nepalese Himalaya to:

Examine and evaluate the performance of the model

Investigate issues of model parameter sensitivity and uncertainty

Evaluate model performance with two alternative input precipitation datasets

Provide a guide to constrain parameters and provide uncertainty bounds in
snowmelt contributions to runoff
(a)
(b)
Sensitivity / Uncertainty Analyses  Figure 6 shows overall model parameter
 This study utilizes a MCMC data assimilation approach to examine and evaluate the
performance of SRM. The MCMC approach is one of several data assimilation
techniques (Zobitz et al., 2011) which iteratively adjusts the model parameters to yield the
best match between the observed and modeled streamflows.
 Experimental runs were also carried out by setting snow runoff coefficients to zero such
that snowmelt contributions were neglected in the simulation.
 Additional sensitivity and uncertainty analyses were conducted via ensemble streamflow
simulations to identify parameters that control model performance and uncertainties in
modeled streamflow and total input contributions.
 Gridded precipitation data (APHRODITE; Yatagai et al., 2009) was also used to drive
SRM to determine the reliability of the dataset for snowmelt runoff modeling.
 Average annual precipitation at the Lungthung
station was ~2484 mm for the 1996–2006 period.
 Monthly streamflow at the Majhitar station
averaged 256 m3/s annually during the same period
(Figure 3).
 Optimization using MCMC increased model fit
(Nash-Sutcliffe ~0.80, annual volume bias <2%)
(Figure 4).
Snowmelt Runoff Model (SRM)
Qn+1 = [csn . an (Tn + ΔTn) Sn + crn . Pn] A(10000/86400) (1−kn+1) + Qn kn+1
Q
cs
T
a
S
=
=
=
=
=
Average daily discharge at day n+1 [m3s-1]
Runoff coefficient to snowmelt
cr
Degree days [°C]
P
Degree-day factor [cm°C-1d-1]
k
Ratio of snow covered area to total area
Figure 3. Average monthly streamflow and total
monthly precipitation from 1996 to 2006 at Majhitar
2002–03
 The modeling of the streamflow at Majhitar station was based on the SRM which is a
conceptual, deterministic, degree-day hydrologic model (Martinec et al., 2008). It
simulates and forecasts daily runoff resulting from snowmelt and precipitation across
elevation zones from hydro-meteorological input data and snow cover data.
=
=
=
Runoff coefficient to rainfall
Precipitation [cm]
Recession coefficient
2003–04
2004–05
2005–06
 Logically constraining the prior parameter
ranges provided models with better fit and
parameters that were physically plausible when
varied across seasons and elevations.
 Some of the most sensitive parameters (such as
lapse rate and x and y coefficients) were
constrained well by MCMC as they exhibited a
narrow, unimodal distribution (Figure 5).
Figure 4. Time series and scatter plots of observed
and modeled streamflows using observed precipitation
 The model was able to reproduce the
hydrograph well even when snowmelt
contributions were excluded from
simulations.
(a) Elevation range 2500–4000 m
(b) Elevation range 4000–5500 m
(c) Elevation range > 5500 m
Figure 2. Snow cover depletion curves from MODIS 8-day snow cover 500-m resolution product from 2002–
2006 across different elevation zones
 Model simulated streamflow using the
interpolated precipitation data
(APHRODITE) decreased the fractional
contribution from rainfall compared to
simulations using observed precipitation.
Figure 6. Streamflow ensemble simulations using
observe precipitation at Lungthung station.
 The study shows a total snowmelt
contribution to be 29.7 ± 2.9% of annual
discharge averaged across the 2002–06
hydrological years which includes 4.2 ±
0.9% from new snow onto previously snowfree areas, where as 70.3 ± 2.6% is
attributed to rainfall contributions (Figure 7).
 On average, the elevation zone in the 4000–
5500 m range contributes the most to basin
runoff, averaging 56.9 ± 3.6% of all
snowmelt input and 28.9 ± 1.1% of all
rainfall contribution to runoff.
Figure 7. Cumulative curves of computed daily
snowmelt depths, melted precipitation in the form of
snow, and rainfall depths.
CONCLUSION
 This study has shown that a snowmelt runoff model based on degree-day factors has
skill in simulating daily streamflow in a mountainous environment with limited
coverage of hydrometeorological measurements.
 Coupling the SRM with an MCMC approach provided a good fit to observed
streamflows but still failed to capture peak discharge during the summer monsoon
months.
 Model performance in simulating the hydrograph is strongly sensitive to recession
coefficient and lapse rate, but exhibited little sensitivity to runoff coefficients, critical
temperature that determines the phase of precipitation, and degree-day factor that
estimates melt depth.
 The experimental run identified that the hydrograph does not constrain estimates of the
fractional contributions of total outflow coming from snowmelt versus rainfall, but that
this derives from the degree day melting model.
 This study provides a useful guide for how to constrain model parameters, provide
uncertainty bounds in snowmelt contributions to runoff, analyze effects of input
precipitation, and examine overall model uncertainty in Himalayan basins.
MODIS Snow Cover
 Ratio of snow covered area to total area for each of the four elevation zones was
derived using the 8-day MODIS snow cover data (Figure 2).
 Model is most sensitive to x and y
coefficients (required to compute recession
coefficient) and lapse rate.
Sensitivity and Uncertainty Analyses
 Long term annual temperatures (1970–2006) at the
Taplejung station averaged 13.6°C.
METHODOLOGY
uncertainty as 5% and 95% confidence
intervals. This shows that parameter
uncertainty alone cannot explain the total
error in the model. The unaccounted
uncertainty could arise from uncertainty in
input precipitation data.
 Prior ranges for the parameters of SRM were varied seasonally (snowmelt/monsoon
period and snow accumulation period), or annually across elevation zones. The MCMC
was run with three chains (10000 iterations/chain) and the set of accepted parameters
from the final set of iterations was used to determine parameter distributions.
RESULTS
Figure 1. a) Tamor River basin in the eastern
Nepalese Himalaya and b) Area-elevation curve for
the Tamor basin
& Molly E.
2
Brown
REFERENCES
 Martinec, J., et al. (2008). Snowmelt Runoff Model (SRM) user’s manual. Gomez-Landsea E,
Bleiweiss MP (eds). New Mexico State University.
 Pellicciotti, F., et al. (2012). Challenges and uncertainties in hydrological modeling of remote Hindu
Kush-Karakoram-Himalayan (HKH) basins: Suggestions for calibration strategies: Mountain Research
and Development, 32: 39–50.
 Yatagai, A., et al. (2009). A 44-year daily gridded precipitation dataset for Asia based on a dense
network of rain gauges. Sola,5: 137–140.
Figure 5. Posterior parameter distributions for the
2002–03 hydrological year as histograms.
 Zobitz, J., et al. (2011). A primer for data assimilation with ecological models using Markov Chain
Monte Carlo (MCMC). Oecologia: 1–13.
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