Snow Water Equivalent
Snow Cover
Runoff Modeling
Lecture 6
By Ahmet Emre TEKELI
February 19, 2009
Snow Cover, SWE and Runoff
Modeling
• Introduction
• Snow Water Equivalent (SWE)
• Remote Sensing in Hydrological modeling
(snow dominated)
• Components of Snowmelt modeling
• Snowmelt Runoff Model (SRM)
Introduction
• Microwave radiation emitted from ground,
scattered in many directions by the snow
grains within the snowpack.
• Mw emission @
snowpack surface < ground.
• Factors; snowpack depth & water
equivalent, liquid water content, density,
grain size and shape, temperature,
stratification, snow state, land cover.
Introduction
Mw sensitive
to snow layer
snow extent,
snow depth
snow water equivalent
snow state (wet/dry)
Can be derived
Introduction
Snow Water Equivalent (SWE)
• A common snowpack measurement
instead of depth.
• Indicates the amount of water contained
within the snowpack.
• Thought as the depth of water that would
theoretically result if the entire snowpack
melted instantaneously.
• SWE= Snow Depth (SD) x Snow Density
Snow Water Equivalent (SWE)
•
•
•
•
•
•
Same depth yields different SWE due to density.
SD= 120” density 10%
SWE=120 * 0.1= 12’’
SD= 120” density 40%
SWE=120 * 0.4= 48’’
The density of new snow ranges from about 5% @ Tair
14° F, to about 20% @ Tair 32° F.
• After the snow falls its density increases due to
gravitational settling, wind packing, melting and
recrystallization.
• Typical values of snow density are 10-20% in the winter
and 20-40% in the spring.
Snow Water Equivalent (SWE)
• Same depth yields different SWE due to
density.
Snow Water Equivalent (SWE)
Snow Water Equivalent (SWE)
Snow pack
scattering
Due to scatterers within
the snow pack
&
increases with
thickness and
density
Deeper snow packs
Result lower TB
TB related to SWE
Snow Water Equivalent (SWE)
TB related to SWE
SWE = A+ B [ΔTB(f1,f2) ]
Where,
• f1 low scattering channel (commonly 18/19 GHz)
• f2 high scattering channel (commonly 37 GHz)
• A, B offset and slope of the regression
• The coefficients should be determined for
different climate and land cover conditions.
• Thus, no single global algorithm can estimate
snow depth and/or SWE under all snowpack and
land cover conditions.
Snow Water Equivalent (SWE)
• Water presence, alters the emissivity of
snow, and results higher brightness
temperatures
• For accurate SWE, snow should be in dry
conditions. Thus, prefer early morning
passes (local time)
Snow Water Equivalent (SWE)
• Depth hoar formation in bottom of the
snowpack (mainly in cold regions), will
increase the scattering and reduce surface
emission, resulting an overestimation of
snow depth and SWE.
Snow Water Equivalent (SWE)
Snow Water Equivalent (SWE)
• Snow pack changes in time, seasonal aging or
metamorphism changes microwave emission of
snow.
• To account for seasonal variability of mw emission
from snow, they should be compiled for entire
season, over several years.
Snow Water Equivalent (SWE)
Snow Water Equivalent (SWE)
• WHY?
• SWE provides important information for
water resources management and is a
major research topic in RS assessment of
snow cover and melt.
RS HYDROLOGY
• Runoff at the outlet of the watershed is an integrated
result of the spatially varying sub-parts of the whole
basin
• Similarity is a serious problem in basins with pronounced
topography, because of the high spatial variability of
hydrometeorological parameters in these regions.
• Hard/impossible to handle with classical terms
• Increase in satellite platforms and improvements in the
data transmission and processing algorithms, remote
sensing (RS) enables to handle these spatial variations.
• RS is gaining importance in distributed watershed
modeling by its spatial variation handling capacity.
RS HYDROLOGY
• The advances in RS and GIS enable new data to
scientific community. New data necessitate
improvements in hydrological modeling rather than using
the conventional methods.
• “Existing models are designed for a limited number of
types of input and may need to be made more flexible to
make optimum use of the range of possible inputs.”
(Hydalp,2000)
• New models would enable new input from RS & GIS and
provide better hydrological outputs, enabling the
understanding of the complex world.
• Thus, there will be mutual developments between RS,
GIS and hydrological modeling, leading improvements in
the other ones.
RS HYDROLOGY
• However, there has always been, a trade off between the
scientific complexity and practical applicability
• The frontiers of snowmelt modelers, Vivan 1979 ,
developed regression equations. These equations
worked well under the circumstances similar to in which
the model is developed. However, in new situations, the
model may not be dependable.
• On the other extreme, a fully developed model in which
all the temporal and spatial variable parameters are
handled may demand large data amounts. Difficult to
calibrate the parameters and hard to understand the
physical background by end users and difficult to get the
input variables.
HYDROLOGIC MODELING
Inputs
Incoming water
Hydrological Modeling
nothing else than
transformation
Output
Discharges
Formulations vary from black box approaches to physically based models
with different degrees of spatial and temporal variability
HYDROLOGIC MODELING
• Formulations may depend to the type of the
precipitation i.e. on rainfall (liquid) or snowfall
(solid).
• When precipitation occurs as snowfall, the
discharge timing is not only a function of
precipitation timing, but also the heat supplied to
the snowpack either by temperature or by
radiation.
HYDROLOGIC MODELING
In either forms,
the total runoff volume is still
total precipitation minus
losses;
however,
snowfall is stored in
snowpack until warmer
weather allows the phase
change from snow/ice to
liquid (i.e. melting).
SNOWMELT MODELING
Snowmelt runoff modeling has four main
components;
1. Extrapolation of meteorological data
2. Point melt rate calculations
3. Integration of melt water over the snow
covered areas
4. Runoff Routing
SNOWMELT MODELING
Extrapolation of Meteorological
Data
• In snowmelt dominated basins, very hard if not
impossible to find meteorological stations in
adequate number and good quality with even
distribution.
• Existing stations mostly located in major valleys
rather than the more inaccessible high portions
of the basin, where most of the snow exist.
• Thus, a necessity to use data from a station
even though it may be a long distance away and
at a much lower elevation from the snowpack.
Extrapolation of Meteorological
Data
• Air temperature, mainly used for two purposes in the snowmelt
models.
• Both as threshold temperature, separating precipitation as rainfall or
snow and as critical temperature, used for estimating snowmelt
rates.
• May not to be same and both may be other than zero.
• Since air temperature alters with elevation, temperature lapse rates
must be used to convert the measured air temperature at the lower
station to the air temperature at the snowpack location.
• Although, most runoff models assume a fixed value for the lapse
rate, the actual value may be a varying value depending on the
present meteorological conditions.
• Often the temperature lapse rate, threshold and critical temperature
values are treated as calibration parameters (Hydalp, 2000) of the
model used.
Extrapolation of Meteorological
Data
• Distribution of precipitation from point stations to
the rest of the basin has been a problem in the
hydrology.
• Come up with, unrealistic and inaccurate results.
• Besides, the systematic under catch of snow by
most rain gauges especially under high wind
speeds has long been reported in literature such
as Sevruk (1983).
• Precipitation amount increases with elevation.
Extrapolation of Meteorological
Data
• Exists numerous methods from simple arithmetic
averaging, Theissen polygons to inverse distance
relations. These methods allow the extrapolation in a
horizontal plane (2D), disregarding the topography of the
area under study.
• Some methods such as De-trended Kriging (Garen,
2003) when distributing the meteorological variables
takes the topography into consideration.
• Preliminary study must be performed since some times,
distributing the variables in 2D may give better results
than distribution in 3D (Weibel et al., 2002).
Point Melt Rate Calculations
• The energy flux that a surface absorbs or emits
is dependent to the sum of the:
• Net all wave radiation (sum of net short (net
solar) and long wave (net thermal) radiation)
• Sensible heat transfer to the surface by turbulent
exchange from atmosphere
• Latent heat of condensation or evaporation
• Heat added by precipitation (if the temperature
of precipitation is different than the surface
temperature)
• Heat conducted from ground
Point Melt Rate Calculations
• Main discrepancy in applying
the energy balance is high
variability over time and over
the location
• Highly scientifically based
equipped automated stations
enable the application of the
energy based snowmelt
models at a point, there still
remains the extrapolation of
these measurements over the
basin.
Point Melt Rate Calculations
“It is rare for such
instrumentation to be
available at even a
single point in a basin,
and even then a
problem remains in
extrapolating the
measurements to other
parts of the basin”
(Hydalp, 2000).
Point Melt Rate Calculations
• Instead of measuring all components some approximations are
provided, called “parametric energy balance” methods.
• In here, some energy components are derived from available data.
• Such as;
Incident radiation, F(latitude, time of year, shading effects, cloud
cover and snow albedo).
Sensible heat= wind speed * air temperature
Precipitation heat supply = Rainfall rate * Rainfall temperature
• But still, extrapolating over the other parts of the basin ?.
• And additional assumptions about the seasonal variations of these
terms should be made.
Point Melt Rate Calculations
• Air temperature, common factor in all
energy balance equations except the net
radiation.
• However, there is generally a good
correlation between them (Hydalp, 2000).
• Temperature can be considered as the
driving factor for the day to day variations
of the heat supply to snowpack.
Integration of melt water over the
snow covered areas
• Depletion of snow cover takes place over
a period called “melting season” during
both incident solar radiance and air
temperatures increase.
• SC doesn’t disappear at the same time
everywhere in the basin.
• Even uniform melting, differences in initial
snow distribution, results variations.
(longer SC @ higher elevations)
Integration of melt water over the
snow covered areas
• Wrong runoff predictions even correct melt
rates are applied to faulty SC.
• High SC leads over estimation, low
underestimation.
• Dealing with SC there are two main
approaches, snow pack formation is
modeled or observed.
Integration of melt water over the
snow covered areas
Formation observed;
• Snow on the surface is monitored.
• May start with initialization of the melting
• RS may be helpful
• Actually one of the practical uses of RS in
hydrology since 1970’s
• Basis of Snowmelt Runoff Model (SRM)
Integration of melt water over the
snow covered areas
Formation modeled;
• Simulation starts at autumn before the
melt season.
• T and P, used to model the snow pack
growth and SWE instead of depth used
due to compaction of snow
• SC is given for areas where SWE>0
• Ground data useful for cal./val.
Runoff Routing
infiltration
percolation
Runoff Routing
• Simplified in
conceptual
terms, upper
and lower
stores for
fast and
slow flow.
Runoff Routing
• Stores can
provide
linear or
nonlinear
flow rates
Q = A.S
A not constant F(S or Q)
Runoff Routing
• Stores can be in
series, parallel or
both.
• Two or even
single may
provide good
approximations
for daily rainfall
runoff predictions
• An extra
snowpack model
may be needed.
Quality Assessment
Model Accuracy
• Mainly by comparing observed and simulated discharges
• May also compare SWE and SCA but mostly the hyrographs
are compared
Quality Assessment
Model Accuracy
• Goodness of fit (R2) • Volume Difference
Nash & Sutcliffe
Not Sleepy yet?
BREAK?
Snowmelt Runoff Model (SRM)
• Developped by Martinec in 1975 in Swiss Snow
and Avalanche Research Institute.
• Changed & developed with collaboration of
Albert Rango (US ARS),
Ralph Roberts (US ARS),
Michael Baumgartner (University of Bern)
Klaus Seidel (University of Zürich)
• Various versions exist.
http: // hydrolab.arsusda.gov/cgibin/srmhome
Snowmelt Runoff Model (SRM)
• Contrary to general purpose hydrological models
with extra snow modules,
• SRM, initially developed to predict the snowmelt
runoff
• Year around simulation capability was also
shown by Martinec et al., (1998).
• Applied over 100 basins in 25 countries @
altitudes 32-60 oN & 33-54oS
with basin sizes varying from <1 to 120 000 km2
documented in about 80 scientific references
(Seidel and Martinec, 2004)
SnowMelt Runoff Model
Physically
based
Semi
Distributed
Deterministic
Same input same output
SnowMelt Runoff Model
• SRM , based on degree day method, can
be used to simulate/forecast the snowmelt
runoff
SRM
Simulate daily flows
in snowmelt season
or year around
Provide short term
and
long term forecasts
Analyze the effect of
climate change
Snowmelt Runoff Model (SRM)
Basin is divided in to elevation zones
Precp. & Temp extrapolated from base and snowmelt in each zone computed
SCA values are provided to determine melting area information
Losses from evap and ground water handled
Runoff from all zones summe up before routing
Total amount routed by single store
SnowMelt Runoff Model
• Basic snowmelt model
Qn+1 = [cSn . an (Tn + Tn) Sn + cRn . Pn] (A.10000/86400) (1-kn+1) + Qn kn+1
Snow melt
Rainfall
Q : Basin discharge
n
: Day indicator
T
: Air temperature
P
: Precipitation falling as rain
S
: Snow covered area
A
: Zonal area
kn+1: Recession coefficient
an : Degree day factor
csn,crn : correction for losses due to snowmelt and rainfall
Flow
Recession
SnowMelt Runoff Model
• Basic snowmelt model
Qn+1 = [cSn . an (Tn + Tn) Sn + cRn . Pn] (A.10000/86400) (1-kn+1) + Qn kn+1
Snow melt
Rainfall
uses
3 Variables
Flow
Recession
7 Parameters
SnowMelt Runoff Model
Variables (Inputs)
Temperature
Precipitation
Meteorological Stations
Snow Covered
Area %
Aerial Photos
or
Measured
Forecasted
Satellite Data
SnowMelt Runoff Model
Variables (Inputs)
SnowMelt Runoff Model
Variables (Inputs) T & P
T or P; either from single station or from separate sites for
each zone.
Single/synthetic station; T and P lapse rates are needed to
extrapolate values. LR can be variable seasonally.
P type (snow/rain) f(Tcrit)
Snow on no SCA temporary snow pack, becomes Q as
sufficient melt conditions
Rain on snow pack, becomes Q if ripe snow exist
Rain on no SCA direct runoff
Melting effect of rain is neglected
SnowMelt Runoff Model
Variables (SCA)
Time series of daily SCA, snow depletion
curves(SDC) or conventional depletion
curves (CDC), is needed
Initially ground observations and aerial
photos, used. Recently satellite images
are utilized.
MODIS
SCA
NOAA
AVHRR
MODIS
AQUA & TERRA
Image Processing
Snow covered area determination
MODIS
NOAA/AVHRR
NOAA
AVHRR
April
May
June
MODIS
MODIS
MOD10A1
MOD10A2
Daily Snow Cover
8 Daily Snow Cover
1/10/12/26
April
1/10/12/26
2004_089 2004_137
21/22
May
22
2004_097 2004_145
June
11/12/13/
14/25/30
12/13
2004_105 2004_153
2004_113 2004_161
2004_121 2004_169
2004_129 2004_177
Snow Covered Area (SCA) Determination
100.0
Zone E (L.B.)
Zone E (U.B.)
90.0
80.0
70.0
SCA (%)
60.0
50.0
40.0
30.0
20.0
10.0
0.0
1-Apr
8-Apr
15-Apr
22-Apr
29-Apr
6-May
13-May 20-May
Date
27-May
3-Jun
10-Jun
17-Jun
24-Jun
1-Jul
8-Jul
Snow Covered Area (SCA) Determination
• The discrete points can connected by
decreasing gradients linearly.
Snow Covered Area (SCA) Determination
• Or by exponential equation.
Snow Covered Area (SCA) Determination
100.0
Zone E (L.B.)
Zone E (U.B.)
90.0
80.0
70.0
SCA (%)
60.0
50.0
40.0
30.0
20.0
10.0
0.0
1-Apr
8-Apr
15-Apr
22-Apr
29-Apr
6-May
13-May 20-May
Date
27-May
3-Jun
10-Jun
17-Jun
24-Jun
1-Jul
8-Jul
SnowMelt Runoff Model
• Disappearing patterns expected to be
same year to year.
• Although, differences in winter
accumulations and melting conditions may
vary, a family of CDC’s might be expected
for a basin, zone, all similar in shape but
timing varying f(initial SWE) (Hydalp,2000)
SnowMelt Runoff Model
Variables (Inputs)
Temperature
Precipitation
Snow Covered
Area %
SnowMelt Runoff Model
Runoff Coefficients (cs,cr)
Degree Day Factor (a)
Temperature Lapse Rate ()
7Parameters
Critical Temperature (Tcrit)
Rainfall Contributing Area
Time Lag (L)
Recession Coefficient
SnowMelt Runoff Model
SnowMelt Runoff Model
Degree day factor
Converts the number of degree days
(temperature values above a certain base
temperature) (oC d) into snowmelt depths
M(cm)
M= a*T
Comparing the degree day values with the
daily decrease of snow water equivalent.
SnowMelt Runoff Model
• Snow pillows, snow lysimeters.
SnowMelt Runoff Model
• In case of no data;
can be used.
Shows a daily variation, expected as some
energy terms are neglected.
SnowMelt Runoff Model
• But, when averaged for a few days,
become more stable.
SnowMelt Runoff Model
• As snow ages, snow water content and
hence density increases, albedo
decreases.
• All these, favor melting, leading increased
ddf.
SnowMelt Runoff Model
• Ddf will maintain its popularity since
temperature is tentatively, a good measure of
energy flux, in addition to easy to measure and
forecast (Martinec and Rango, 1986).
SnowMelt Runoff Model
Critical Temperature (Tcrit)
• determine the type of precipitation
• i.e. either rainfall and contribute to runoff
immediately (T > Tcrit)
• or snowfall (T < Tcrit) and lead to
accumulation of snowpack and a delayed
runoff
• Thus, new snowfalls are kept in storage
until warm days allow the melting.
SnowMelt Runoff Model
Critical Temperature
• Tcrit from +3 in April to 0.75 oC in July is
reported (WinSRM, 2005) where as +1.5
to 0 oC is reported by US Army Corps of
Engineers (1956).
• Sharp rainfall runoff peaks may be missed
by SRM due to the determination of
temperature values being less than the
Tcrit.
SnowMelt Runoff Model
• Value may be changed, but daily values used, and
rain can occur during the warmer or colder period of
the day.
SnowMelt Runoff Model
Temperature Lapse Rate
• Defines a temperature gradient across the watershed, used
in extrapolating temperature values from a given station.
• SRM accepts a single, basin wide temperature lapse rate
or zonal temperature lapse rates.
• Higher temperature lapse rates for winter and lower values
for the summer months are expected (Hydalp, 2000).
• The depletion of snow cover may represent requirement of
the value change of the lapse rate.
• High temperatures from extrapolation by a LR value but no
change in snow areal extent is , then probably no
appreciable snowmelt is taking place (WinSRM, 2005) and
the LR should be modified accordingly.
SnowMelt Runoff Model
SnowMelt Runoff Model
Runoff Coefficients
• Explain, differences between the basin runoff and the
available precipitation (either snowfall or rainfall)
• Account for the volume of water, which does not leave
the basin, F(the site characteristics, such as soil type,
soil depth, elevation, slope, aspect, vegetation type and
vegetation density) (Levick, 1998).
• SRM uses two runoff coefficients cs and cr related to
snow melting and rainfall respectively. The two values
are expected to be different from each other due to their
characteristics.
SnowMelt Runoff Model
Runoff Coefficients
• In the early melt period, frozen soil early has lower
infiltration and storage capacities.
• Spring will thaw the soil and snow melt will soak in the
soil, leading a drop in the runoff coefficients.
• As soil becomes saturated, the values will increase
again.
• Thus, monthly variations in runoff coefficients are
expected and can be explained by an analysis of the
seasonal changes in vegetation and climate (Levick,
1998, Kaya 1999).
SnowMelt Runoff Model
SnowMelt Runoff Model
Time Lag
•
•
•
•
Indicates the time delay between the daily rise
in temperature and runoff production.
Used for time wise matching of the observed
and calculated peaks in the simulation mode.
Hydrographs of past years and the daily
fluctuating character of the snowmelt enable
the predetermination of the time lag value.
Value can be modified by comparing the timing
of simulated hydrograph peaks with the
observed hydrograph peaks.
SnowMelt Runoff Model
SnowMelt Runoff Model
Recession Coefficient
•
•
•
Represents the daily melt water production
that immediately appears in runoff.
Analysis of historic discharge data may be a
starting point.
Recession from a high discharge is relatively
steeper than from a low discharge, which is a
commonly observed situation (Seidel and
Martinec, 2004).
SnowMelt Runoff Model
Rainfall Contributing Area
•
•
•
•
•
If the snow is dry and deep, the snow largely retains
the rainfall.
Thus, the rainfall directly affecting the runoff values are
reduced by the ratio of NO SCA/ Total Area of the zone.
As snow softens and ripens, it becomes ready to
release the same amount of water as entering to the
snowpack.
In this case, rainfall falling on the whole area directly
affects the hydrograph.
The user determines the date of change of the snow
condition during the model runs.
SnowMelt Runoff Model
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