1. Dynamic modeling of glaciated watershed processes: Retrospective analysis and future
predictions in the headwaters of the Zongo River, Bolivia
Chris Frans1, Erkan Istanbulluoglu1, Bibi Naz1*, Dennis Lettenmaier1, Thomas Condom2
1Department of Civil and Environmental Engineering, University of Washington, Seattle, WA, USA,
2IRD/UJF-Grenoble 1/CNRS/Grenoble-INP, Laboratorie d’etude des Transferts en Hydrologie et Environnement (LTHE)
*Now at Oak Ridge National Laboratory, Oak Ridge, TN, USA
1. Summary
In high-altitude regions the contribution of glacier melt to runoff is often critical to sustain water supply
throughout the year. The tropical glaciers of the South American Andes, whose melt contributes to water supply
and energy production, have retreated at unprecedented rates since the 1970’s. Loss of these ice reservoirs will
have critical implications to downstream densely populated areas. In this study we use a recently developed
glacio-hydrological model to evaluate the contribution of glacier melt to streamflow and track this contribution
in time with changing glacier area. A glacier model based on the shallow ice approximation (SIA), solving time-
evolving and spatially-distributed balance equations for glacier mass and momentum, is integrated within the
Distributed Hydrology Soil Vegetation Model (DHSVM). The model is used to simulate the glacio-hydrologic
behavior of the headwaters of the Zongo River during the historical period of 1985-2010. Model performance is
evaluated by comparing model predictions with observed glacier extent, mass balance, discharge, and terms of
the surface energy balance. Further, the modeling approach is used to predict this transitioning contribution of
glacier melt into the future using a stochastic statistical downscaling technique where multiple realizations of
future climate are produced using predictions from general circulation models (GCMs) and a weather generator
(AWE-GEN). The results of this study demonstrate the applicability of dynamic modeling, of both glacier and
watershed processes, for prediction of trends and uncertainties of streamflow in vulnerable high altitude areas
that rely on glacier melt.
Resumen
El agua de glaciares es un recurso importante para el suminstro de agua para consumo humano a lo largo del
año. Los glaciares tropicales de los Andes Sudamericanos han retrocedido a velocidades imprecedentes después
los setentas. La pérdida de estas reservas de agua tendrán consecuencias críticas en localidades altamente
pobladas localizadas aguas abajo. En este estudio usamos un modelo hidrológico-glacial recientemente
desarrollado para evaluar la contribución del glacial en la descarga del Río Zongo y para evaluar si dicha
contribución cambia con el retroceso del glaciar en la cabecera del río. Un modelo de procesos glaciales basado
en la aproximación de hielo superficial (SIA por sus siglas en Inglés), que resuelve las ecuaciones de balance de
masa que evolucionan a lo largo del tiempo, y que es espacialemente distribuida, fue integrado al modelo
hidrolócigo DSHVM (Distributed Hydrology Soil Vegetation Model). El modelo resultante fue evaluado contra
observaciones de la extensión del glaciar, balance de masa, descarga del río, y elementos del balance de energía.
Más tarde fue usado para simular los procesos hidrológicos-glaciares de las cabeceras del Río Zongo durante el
periodo histórico de 1985 a 2010. Este futuro también fue investigado a través de este modelo, usando
ensambles de datos generados por modelos climáticos globales (GCM por sus siglas en Inglés) y por el modelo
generador de variables meteorológicas AWE-GEN (Advanced Weather GENerator). Los resultados de este
estudio demuestran el uso del modelado dinámico de los procesos glaciares y los procesos hidrológicos en una
cuenca en conjunto, para predecir tendencias e incertidumbre en la descarga de ríos en zonas altas vulnerables
que dependen de agua de glaciares.
2. Study Location
4. Retrospective Analysis
3. Modeling Method
5. Future Predictions
6. Conclusions
• Retrospective (1987-2010) model simulations indicate that on average
glacier melt represented 31% of annual discharge from the watershed. This
value increases seasonally, up to 90% during dry years.
• An analysis of 11 CMIP5 RCP4.5 GCM outputs reveals that high altitude
air temperatures are expected to increase throughout the year, with the
highest increases of 3-4 degrees during the winter months by 2100.
• Initial results of future simulations indicate that glacier melt will both
increase and decrease seasonally in the near future with ongoing recession,
however will decline throughout the entire year in the latter half of the 21st
century.
• These findings demonstrate the potential of this coupled glacio-
hydroloigcal physics based modeling as a powerful tool for the prediction
of glaciated watershed processes in the context of water resources.
• Further analysis of uncertainty is required to strengthen the confidence in
model predictions
DHSVM
Glacier Dynamics Model
Watershed Hydrologic
Processes
Accumulation and Ablation
Surface
Mass
Balance
Dynamic Ice Flow in Response to Surface Mass Balance
Change in
Glacier thickness
and Area
Melt
Streamflow
Coupling of Models
Ice
Snow
Bedrock/
Soil
1
12
2 ( )
( , ) ( )
2
nn
mice xy n m m
xy ice xy
A g S
D H S H C g S H
n





  

( ) ice n
xy xy
water
bS
D S
t



    

nb IWE SWE   
Glen’s Flow Law Weertman Sliding Law
Non-linear Ice Diffusion
Momentum Diffusivity
A S O N D J F M A M J J A
-100
-50
0
50
100
150
Month
Wattsm-2
Surface Energy Balance (Elev. 5050 m, WY 2000)
SWnet
LE
SH
LWnet
Normalized Difference
Snow Index (NDSI)
(Landsat 4-5 TM scenes)
Headwaters of the Zongo River
• Located 30 km north of La Paz (-16.25, -68.1)
• 14 drainage area
• Runoff is intercepted and routed to reservoir for
hydro-electricity production
• Glacier extent decreased 54% from 1987-2010
(Huayna Potosi, left)
• Distinct seasonality: wet and warm Nov. to
March, dry and cold May through August.
• Accumulation occurs during the wet season
while ablation occurs throughout the year.
2
km
Distributed Hydrology Soil Vegetation
Model (DHSVM, Wigmosta et al., 1994)
• Fully distributed physically based
hydrology model
• Sub-daily timesteps
• Two layer energy balance snow/ice
accumulation and melt model
UBC Glacier Dynamics Model (Garry
Clarke, UBC; Jarosch et al., 2013)
• Based on shallow ice approximation
• Solves time-evolving balance equations
for glacier mass and momentum
• Spatially distributed
• Monthly time-step
• Forced with mass balance calculated by
DHSVM model
The glacier dynamics model is integrated in the DHSVM hydrology model. DHSVM is run at subdaily timesteps, simulating all
hydrologic processes, including snow accumulation and melt, snow densification to ice, and glacier ice ablation. Mass balance for
each gridcell covered with a glacier is provided to the glacier dynamics model at a monthly time-step. Flow of ice is calculated in
response to surface mass balance fluctuations. The thickness and extent of glacier ice is updated accounting for the simulated
dynamic ice flow [Naz et al. (in review)].
Model Inputs
• 50 meter Digital Elevation Model (DEM,
ASTER GDEM)
• Hourly air temperature, relative humidity, wind
speed, incoming incoming shortwave and
longwave radiation, precipitation
-Source: Modern Era Retrospective Analysis
for Research and applications
(MERRA,NASA) bias corrected using hourly
GLACIOCLIM observations.
• Soil Depth (estimated)
• Bed Topography (estimated, Clarke et al. 2013)
• Land Cover (Texas A&M University)
• Soil classes (estimated)
• Hourly solar shading and skyview maps
(estimated from DEM)
• Initial ice thickness (estimated with glacier
dynamics model)
Step 1: Spin-up to steady state matching
oldest satellite derived extent (1987)
Step 2: 30 year spin-up with current climate to
thin glaciers to transient state (iterate length of
spin-up to match observed recession)
Glaciological Simulation
-8000
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
4900
5000
5100
5200
5300
5400
5500
5600
5700
Elevation (m)
MassBalance(mmw.e.)
Simulated and Observed Mass Balance: Zongo Glacier 1992-2009
Simulated Annual
Simulated Mean Annual
Observed
(1991-2009)
1985 1990 1995 2000 2005 2010
-25
-20
-15
-10
-5
0
Year
Balance(mw.e.)
Cumulative Mass Balance: Zongo Glacier 1986-2010
Simulated
Hydrological (Soruco et al. 2009)
Adjusted Glaciological
(Soruco et al. 2009)
19951990
20102005
Demonstrating the performance of the
modeling approach (a,b) simulated mass
balance is compared with observations
(GLACIOCLIM, Soruco et al., 2009), (c)
modeled mean monthly surface energy
fluxes are compared with observations
digitized from Communidad Andina
(2007), and (d-g) comparing modeled
I.W.E with glacier extent derived from
Landsat satellite imagery.
(a)
(b)
(c)
(d)
(g)(f)
(e)
Hydrologic Simulation
Stochastic Downscaling of CMIP5 RCP4.5 GCM Output using an hourly
weather generator (Advanced WEather GENerator AWE-GEN) [Fatichi et al. 2011]
1)EstimateAWE-GEN
parameters from
historical observations
2) Calculate statistical
properties of GCM model
outputs
3) Calculate PDFs of factors
of change for each climate
statistic using Bayesian
approach with GCM
output and observations
5) Extend precipitation
statistics to finer time
scales
4) Estimate mean factors of
change from PDFs
6) Calculate new AWE-
GEN parameters from
future statistics obtained
in steps 4,5 (parameters
are calculated for each
decade to represent
transitional climate)
7) AWE-GEN construction
of future climate forcing
Factors of Change (170 PDFs total):
Temperature FUT = Future time period
Precipitation HIST= Historic time period
S(h) = Precipitation statistic at aggregation hour interval h
Precipitation Statistics: Mean, Variance, Skewness, Frequency of non-precipitation
Coefficient of Variation (annual)
, ,
( )FUT OBS GCM FUT GCM HIST
mon mon mon monT T T T  
,
,
( ) ( )
( ) ( )
FUT GCM FUT
OBS GCM HIST
S h S h
S h S h

Sept-90 Sept-91 Sept-92 Sept-93 Sept-94 Sept-95 Sept-96 Sept-97 Sept-98
0
200
400
600
literssec
-1
DHSVM Qtotal
DHSVM Qglacier ObservedALPACA
CANAL
0 2 4 6
0
0.1
0.2
0.3
0.4
T [°C]
Factor of Change for Air Temperature
pdf T
T GCMs
5 10 15 20 25
0
0.2
0.4
0.6
0.8
Pr [mm]
Frequency
Mean Precipitation (June)
pdf HIST
pdf FUT
0.4 0.6 0.8 1 1.2 1.4
0
0.1
0.2
0.3
0.4
Factor of Change
Factor of Change for Mean Precipitation
pdf FC
FC GCMs
-10 -5 0 5 10
0
0.1
0.2
0.3
0.4
Ta [°C]
Frequency
Monthly Air Temperature (June)
pdf HIST
pdf FUT
Downscaling Steps: Example visualizations of downscaling steps:
J F M A M J J A S O N D
0
1
2
3
4
5
6
Month
T[°C]
Ta500hPa
Factors of Change 2080-2100
BCC-CSM1
ACCESS1
CanESM2
CCSM4
CNCRM
CSIRO-Mk3.6
GFDL-CM3
INMCM4
MIROC5
MRIGCM
NORESM1
J F M A M J J A S O N D
0
0.5
1
1.5
2
2.5
Precip. Factors of Change 2080-2100
Month
[FUT/HIST]
Hourly time series of Ta,
SWin, RH, Wind, Precip.,
Cloud Cover (2011-2100)
J F M A M J J A S O N D
-4
-2
0
2
4
6
8
[°C]
Monthly Air Temperature
HIST
2080-2100
J F M A M J J A S O N D
0
50
100
150
200
[mm]
Monthly Precipitation
HIST
2080-2100
0
2
4
mm
0
500
1000
Wm-2
-5
0
5
C
Ta
SW
in
PPT
Predicted Glacier Response 2011-2100
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
0
200
400
600
800
Discharge(literssec-1
)
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
0
200
400
600
800
Water Year
Simulated ObservedZongo Proglacial
Stream
Sept-93 Sept-94 Sept-95 Sept-96
0
100
200
300
400
500
literssec-1
Sept-03 Sept-04 Sept-05 Sept-06 Sept-07 Sept-08 Sept-09
Qtotal
Qglacier
Observed
Proglacial Stream (Monthly)
7. References
Clarke, Garry K. C., Faron S. Anslow, Alexander H. Jarosch, Valentina Radić, Brian Menounos, Tobias Bolch, Etienne Berthier, 2013: Ice
volume and subglacial topography for western canadian glaciers from mass balance fields, thinning rates, and a bed stress
model. J. Climate, 26, 4282–4303.
Fatichi, Simone, Valeriy Y. Ivanov, and Enrica Caporali. "Simulation of future climate scenarios with a weather generator." Advances in
Water Resources34.4 (2011): 448-467.
Comunidad Andina (2007), Is it the end of snowy heights? Glaciers and Climate change in the Andean Community. General
Secretariat of the Andean Community .
GLACIOCLIM database http://www-lgge.ujf-grenoble.fr/ServiceObs/ Last accessed 12/1/2012.
AH, Jarosch. "Restoring mass conservation to shallow ice flow models over complex terrain." The Cryosphere 7.24 (2013): 229-240.
Naz, B. S., Frans, C. D., Clarke, G. K. C., Burns, P., and Lettenmaier, D. P.: Modeling the effect of glacier recession on streamflow
response using a coupled glacio-hydrological model, Hydrol. Earth Syst. Sci. Discuss., 10, 5013-5056, doi:10.5194/hessd-10-5013-
2013, 2013.Soruco
Wigmosta, Mark S., Lance W. Vail, and Dennis P. Lettenmaier. "A distributed hydrology‐vegetation model for complex terrain." Water
resources research 30.6 (1994): 1665-1679.
We would like to thank Pat Burns for his production of the Landsat glacier extent estimates.
Importance of Glacier Dynamics
No Dynamics with Dynamics
Comparing simulations (1985-
2010) (a) without and (b) with
glacier dynamics highlights
the importance of representing
the dynamic redistribution of
ice over longer periods of
time.
4
6
8
10
12
x 10
7
[m3
]
2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
10
15
20
25
30
[%]
Glacier Volume
Glacier Extent
Predicted Hydrologic Response 2011-2100
Glacio-Hydrologic Simulations of 8 Future Climate Realizations:
2040 2060 2080 2100
(a)
(b)
(c) (d) (e) (f)
Modeled evolution of glacier (a)
volume, (b) extent, and (c-f) spatial
changes of ice water equivalent (I.W.E.).
(a) (b)
S O N D J F M A M J J A
0
200
400
600
800
literssec-1
S O N D J F M A M J J A S O N D J F M A M J J A
Total Discharge Glacier Melt Discharge
Dry
2005
Mean
1987-2010
Wet
2009
All Watershed Discharge
The model was calibrated to
optimize both streamflow and
cumulative mass balance of
Zongo glacier. Simulated
daily (monthly) discharge of
the proglacial stream is
shown at right (below).
Nash Sutcliffe efficiency
values for monthly flow
range from 0.4-0.7 for the
different locations and
periods of record in the
watershed. On average
glacier melt contributes 40%
of total monthly watershed
discharge but can represent
nearly 90% of total discharge
during low flows in dry years
(left).
1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
0
500
1000
[mm]
S O N D J F M A M J J A
0
50
100
150
[mm]
S O N D J F M A M J J A
2030-2050 2080-2100
1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
0
200
400
600
800
1000
1200
1400
mm
S O N D J F M A M J J A
0
50
100
150
200
mm
S O N D J F M A M J J A
Glacier Melt Total Runoff
Total Runoff
Glacier Melt
1987-2010
Total Runoff
1987-2010
Glacier Melt
2030-2050 2080-2100
1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
0
200
400
600
800
1000
1200
1400
mm
S O N D J F M A M J J A
0
50
100
150
200
mm
S O N D J F M A M J J A
Glacier Melt Total Runoff
Total Runoff
Glacier Melt
1987-2010
Total Runoff
1987-2010
Glacier Melt
2030-2050 2080-2100
S O N D J F M A M J J A
-60
-40
-20
0
20
40
60
[%]
S O N D J F M A M J J A
-60
-40
-20
0
Total Runoff
Glacier Melt
2030-2050 2080-2100
Changes in Watershed Runoff
Initial predictions indicate
decreased (increased) runoff
in summer (winter) in the
near future (2030-2100)
through changes in glacier
melt .
In the far future (2080-2100), decreased runoff is predicted throughout the
year (up to -36%), through drastic declines in glacier melt contribution.