Modelling surface mass balance and
water discharge of tropical glaciers
The case study of three glaciers in La Cordillera
Blanca of Perú
Presented by: MSc. Maria Fernanda Lozano
Supervised by: Prof. Dr. rer. nat. Manfred Koch
Content

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Problem statement
Objectives
Study area
Available data (temperature,
precipitation, mass balance
measurements, radiation data)
Filling data gaps
Methods


Energy balance Model
Temperature Index Model
Modelling mass balance under
climate change simulation by REMO
Problem statement
Changes in climate
Alteration of
mass balance
Front advance or
Retreatment
Changes in discharge
Identification of causes what will happen
Energy balance
models
Temperature Index
models
Not large records
Data gaps
Estimation of
Future discharge
Objectives


Contribute to the understanding of glacier climate
interaction in tropical areas.
Foresee the possible variation on surface water discharge
due to climate change.
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Evaluate historical trends of hidroclimatic time series.
Fill the gaps in time series
Simulate the dynamic of the mass balance and runoff with a Energy
Balance Model (4 years)
Simulate runoff of the glaciers with a Temperature Index model.
Examine the sensitivity of stream-flow of surface water resources
under future climate scenarios of global warming
Study Area
Study Area
Available data
Temperature
Precipitation
Relative humidity
Wind Speed
Discharge
Total
Number of Stations
Station
over 4000 Stations in
(Santa)
m.a.s.l
Glaciers
52
10
5
90
11
4
6
5
4
18
4
1
12
6
5
Available data
Time series available in glaciers
Time series available in related basins
Glacier Artesonraju
Variables
Radiation, wind and relative humidity
Mass balance
Temperature
Precipitation
Discharge
Relative Humidity
Wind Speed
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Variables
Radiation
Mass balance
Temperature
Precipitation
Discharge
Relative Humidity
Wind Speed
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Variables
Radiation
Mass balance
Temperature
Precipitation
Discharge
Relative Humidity
Wind Speed
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Basin Artesoncocha
Variable
Temperature
Precipitation
Discharge
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 0 1 2 3 4 5 6 7 8
Variable
Temperature
Precipitation
Discharge
Wind Speed
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 0 1 2 3 4 5 6 7 8
Variable
Temperature
Precipitation
Discharge
Relative Humidity
Wind Speed
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 0 1 2 3 4 5 6 7 8
Variable
Temperature
Precipitation
Discharge
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 0 1 2 3 4 5 6 7 8
Variable
Temperature
Precipitation
Discharge
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 0 1 2 3 4 5 6 7 8
Variable
Temperature
Precipitation
Discharge
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 0 1 2 3 4 5 6 7 8
Basin Paron
Glacier Yanamarey
Basin Querococha
Glacier Uruashraju
Basin Olleros
Basin Quilcay
Glacier Shallap
Variables
Radiation
Mass balance
Temperature
Precipitation
Discharge
Relative Humidity
Wind Speed
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Variables
Radiation
Mass balance
Temperature
Precipitation
Discharge
Relative Humidity
Wind Speed
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Basin Llanganuco
Glacier Huarapasca
Temperature and precipitation
Mean Daily T emperature vs Elevation
Monthly Temperature Artesonraju
°C
-5
4
1.0
5
0
1.5
6
°C
oC
7
5
2.0
8
2.5
9
10
10
Monthly Temperature Querococha
3500
4000
4500
5000
5500
Jan Feb Mar Apr May Jun
Jul Aug Sep Oct
Nov Dec
Jan Feb Mar Apr May Jun
Jul Aug Sep Oct Nov Dec
m.a.s.l
Monthly Precipitation Querococha
Monthly Precipitation Artesonraju
mm
100
100
200
150
mm
4.0
3.5
50
3.0
3800
4000
4200
4400
4600
4800
5000
0
0
2.5
mm
200
300
4.5
250
5.0
400
300
Mean Daily Precipitation vs Elevation
5200
Jan Feb Mar Apr May Jun
Elevation (m.a.s.l)
Jul Aug Sep Oct Nov Dec
Jan Feb Mar Apr May Jun
Jul Aug Sep Oct Nov Dec
Temperature and precipitation
-5.5
oC
-5.0
-4.5
Reanalysis North
1970
1980
1990
2000
Year
1000
800
600
mm
1200
1400
Querococha
1970
1980
1990
Year
2000
Mass balance measurements
ELA
Artesonraju
Uruashraju
Yanamarey
2003
5000
4850
-5
4900
-4
4950
-3
m.w.e
m.a.s.l
-2
-1
5050
0
5100
Mass Balance
2004
2005
Time
2006
2007
Artesonraju
Uruashraju
Yanamarey
2003
2004
2005
Time
2006
2007
Retreatment of the Yanamarey glacier since
1948.

27-
Morrena cubierto
de hielo, producto
de pequeñas avalanchas
0907
GLACIAR YANAMAREY
1948
27
06-1
15-1100
09-
0806
28-09
-95
Y-1 8
-0
84
6-
Y-1 6
Y-9
1948
1986
Derrumbe ocurrido en el mes de
junio 2007
23/01/09
01
6-
0994
-9
1
31-
-99
1096
23-
-1
0
08-0905
-0
2
0-04
02-0903
170702
23-10
1097
02-
907
22
28
2
9-9
93
0-
03
2409- 10-89
088
2
20- 4-09- 8
058
86 7
5
-8
5
9-0
-0
-1
30
14
5-83
20-05-82
05-0
76
5-0
-80
1
-8
-05
5
-0
06
29-12-98
21
10
-0
1993
2001
2009
Glacier front variation in glaciers of the
Cordillera Blanca
VARIACIONES DEL FRENTE DE LOS GLACIARES MONITOREADOS EN LA CORDILLERA
BLANCA
0
-100
-200
-400
-500
-600
-700
-800
-900
ALPAMAYO
BROGGI
URUASHRAJU
YANAMAREY
GAJAP
PASTORURI
2005
2006
2007
2008
Años
98
99
2000
01
02
03
2004
91
92
93
94
95
96
97
84
85
86
87
88
89
90
77
78
79
80
81
82
83
68
70
71
72
74
1976
-1000
1948
Retroceso (m)
-300
Energy data in Artesonraju
Longwave incoming radiation
200 250 300 350
Wm-2
300
200
100
Wm-2
400
Shortwave incoming radiation
2004
2004
2005
2006
2007
2008
2005
2006
2007
2008
2009
2008
2009
2009
Time
Time
Artesama
Longwave emitted radiation
310
290
300
Wm-2
150
50
0
Wm-2
250
320
Shortwave reflected radiation
2004
2005
2006
2007
2008
2004
2009
2005
2006
Time
Time
Artesama
Station
2007
Swin (Wm )
Min
110.00
1st Q
182.40
Median
227.50
Mean
234.60
3rd Q
282.60
Max
408.80
SD
65.76
VAR
4325.37
Swref (Wm-2)
-2
6.97
60.56
91.01
95.64
126.50
248.14
48.23
2326.76
-2
194.30
254.20
290.70
280.60
311.10
369.40
36.36
1322.31
-2
287.70
303.90
309.70
308.50
313.50
320.00
6.80
46.27
-2
-38.79
44.26
80.68
87.87
123.02
266.38
56.51
3193.47
Lwatm (Wm )
Lwsurf (Wm )
Rnette (Wm )
Filling gaps in time series
Multilinear regression

STL

Harmonic analysis
300
100
100
350
data
5
4
3
200
2010
300
0
-50
ATRSwinc
245
2000
240
1990
150
2006
2007
2008
2004
2005
2006
2000
2010
2009
2008
2009
Data with interpolated gaps
0.4
1990
2008
Time
ACF
1980
2007
2009
time
1970
0.3
400
years
Multilinear regression method
200
ATRSwinc
0.2
1980
1990
2000
2010
years
0
1970
0.0
100
0.4
0.1
0.6
0.8
ATRSwinc
1.0
300
Nash Coefficient-Filled Temperature Artesonraju
Nash Coefficient
100
-50 0 50
-150
2
2005
1
2004
-1 0
T oC
3
4
5
remainder
Filled Temperature Artesonraju
150
230
years
235
1980
trend
1970
250
seasonal
50
2
1
-1 0
T oC
200
Original Temperature Artesonraju
400
400
Initially interpolated data
0
5
10
15
20
Lag
25
30
2004
2005
2006
2007
Time
Energy balance model (Hock)
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Distributed model.
Works in a subdiurnal or diurnal
temporal resolution.
Solves the energy balance
equation on the glacierized area
(calculation per each grid of
DTM).
Calculates water discharge from
the melting of three areas (firn,
snow and ice) and the liquid
precipitation.
Accounts for the spatial
distribution of topographic
shading.
Calculates individual energy
balance components
ACCUMULATION:

Precipitation
(temperature)
ABLATION

Melting and Sublimation
QM / S  G  G ( )   L   L  QG  QH  QL  QR
QM
M
L f w
Energy balance model (Hock)
Main station
Extrapolation
1.Interpolation of G directly
Gs/Ics

Amounts of diffuse radiation

Cloud Cover
Global
radiation
Gg=Icg*(Gs/Ics)
2. Separating G into direct and diffuse
radiation considering terrain effects

Ig=Icg*(Is/Ics)

the radio of global radiation to top of the
atmosphere G/IToA
Is=Gs-Ds
Direct radiation
Diffuse radiation
Energy balance model (Hock)
Extrapolation
Snow Albedo Variable:

Assumed constant
according to the surface

Number of days since last snowfall

Air temperature
Albedo

Variable for snow and
ice.
Ice Albedo Variable:
Assumed increase of 3%(100m-1)
Account for the tendency of debris to
accumulate towards the glacier.
Energy balance model (Hock)
Main station
Long inc.
radiation
Lsky:
Lterrain:
Extrapolation
It requires the estimation of Lo at climate
station and it is assumed invariant for all grids.
Linc in each grid is calculated as the sum
of Lsky and Lterrain in each grid.
Long out.
radiation
Direct measurements of longwave
outgoing radiation
EL s TS4  TS4
Linear decrease with increasing elevation
when surface temperature is negative,
if temperature is 0 Lout is spatially constant
Energy balance model (Hock)
Calculated from the aerodynamic approach
Sensible
heat
QH  c p 
k2
 u z Tz  T0 
ln z / z0 w ln z / z0T 
Qh proportional to Temperature (Tz) and
Wind speed (zu)
L
Latent heat of evaporation or
sublimation
ρ
density of air
Po mean atmospheric pressure at
the sea level
Cp specific heat capacity of air
k
Calculated from the aerodynamic approach
Latent
heat
Karman´s constant
To surface temperature
Eo vapor pressure of the surface
QL  L 
0.63230
k

 u z ez  e0 
P0
ln z / z0 w  ln z / z0e 
2
QL proportional to vapour pressure (ez)
and Wind speed (zu)
Zow, zoT and zoe
are the roughness lengths fro
logarithmic profiles of wind
speed, temperature and water
vapor
Energy balance model (Hock)
Conditions
 Daily resolution
 No separation of direct
and diffuse radiation
 Albedo constant
 Snow water equivalent
interpolated with linear
interpolation.
Qmeas
Qcalc
0.0
0.5
m3/s
1.0
1.5
Discharge
2004.5
2005.0
Time
Artesoncocha (r2=0.64)
2005.5
Temperature Index Model (Hock)

Melting is related to the positive air temperatures and the amount of time that this
temperature exceeds the melting point.

This relation uses a factor of proportionality (DDF) which shows the decrease of
water content in the snow cover or ice by 1°C above freezing in 24 hours.
Melt=(DDF/24)*T(timestep)
Melt=0
Melt=(MF/24+ rsnow/ice*I)*T(timestep) T>0
Melt=0
T<=0
Melt=(MF+rsnow/ice*I*Globs/Is)*T(timestep) T>0
Melt=0
T<=0



DDF= Degree day factor mm/oCdía
MF= Melt factor mm/h K
rsnow/ice= radfactorice mm m2/WhK
T>0
T<=0
Incorporates clear sky solar radiation (I)
accounts for the spatial topographic
variability
Incorporates global measured radiation
Which account for deviations on clear sky
conditions
Temperature Index Model (Hock)
Discharge
0.8
0.6
0.4
0.2
m3/s
1.0
1.2
1.4
r2
fm ice
4
5
6
7
8
9
8
0.5605
9
0.6044
0.6166
0.648
0.6617
0.6622
0.6512
0.6504
0.6712
0.6739
0.6631
0.648
10
0.637
0.6715
0.6812
0.6724
0.6499
0.616
11
0.6578
0.6801
0.6777
0.657
0.6226
0.5769
12
0.6665
0.6756
0.6606
0.6277
0.5811
0.5232
13
0.6633
0.6581
0.6298
0.5841
0.525
0.4548
14
0.6482
0.6274
0.5853
0.5264
0.4544
0.3717
15
0.621
fm ice
1
2
3
4
13
0.2384
0.526
0.6312
0.6633
14
0.2791
0.5489
0.6347
0.6482
15
0.3134
0.5642
0.6282
0.621
0.5719
0.6116
0.5816
16
2004.4
2004.6
2004.8
2005.0
Time
Artesoncocha
2005.2
2005.4
2005.6
fm snow
Simulation of glacier discharge in future
scenarios of climate change
MPI Regional Climate Model Remo

Horizontal Resolution 50Km x 50 Km (0.44°x 0.44°)

Variables: Temperature, surface pressure, horizontal wind
components, precipitation and humidity.

Domain. South América

Time step: 240 s

Forcing Data: ERA Interim

Simulation Period: 1989-2008

Future Simulation: until 2100 (in process)
THANK YOU
Mass Balance
Year of positive mass balance
Year of negative mass balance