SNOW HYDROLOGY (GEOG 4321): MODELING
Instuctor: Mark Williams
Telephone: 492-4794 or 492-8830
Primary approaches to modeling snowmelt are:
- ablation stakes
- regression analysis (linear or multiple)
- temperature index approach
- energy balance approach
Ablation stakes were the first approach consistently used to
model distributed snowmelt over some area of interest.
Ablation stakes are still widely used in glacial hydrology.
Essentially, stakes are placed in the snow and the distance
between the snow surface and top of the stake is noted.
The readings are repeated at some temperal frequency,
usually weekly to monthly.
The difference in depth between two readings is the amount
of snow depth lost over that time interval.
Density is measured or estimated as well.
Depth times the depth change provides SWE contribution to snow melt.
There may be an adjustment factor (guesstimate) for
losses to sublimation/ET.
- Provide estimated total discharge at a gaging site
- based on empirical regression equations
- SWE measurements at SnoTel and/or Snow Course sites
- annual or seasonal discharge at gaging site
- SWE is independent variable
- discharge is dependent variable
- get regression relationship "Q = b + (SWE)x"
- where Q is annual or seasonal discharge, b is the y-intercept,
x is the slope, and SWE is the measured value at the SnoTel/snow course.
- representative sites (get a high r^2).
- often only one SWE measurement station in basin.
- if more than one station, can run multiple regression.
- need long-term record, usually at least 10 years.
- Provides an estimate of total discharge from basin
- Provides a good index for water managers to use to make
water allocation decisions; when to open/close reservoirs, when
to honor senior/junior water rights, etc.
- minimum data requirements
- doesn't provide info on timing and magnitude of snowmelt
- doesn't provide info on factors such as peak discharge.
Peak discharge is needed for calculations such as the amount
of discharge needed to move sediments to improve trout habitat.
- cannot extrapolate past range of measurements
- Threshold effects may occur: small increase in SWE can
saturate soils and lead to increased runoff efficiency.
- assumes stationarity: climate boundary conditions can't change,
because then the regression equation will change.
Probably can't use in climate change scenarios.
Based on the concept that changes in air temperature provide
an index of snowmelt. Air temperature is a commonly measured
meterological variable, so a good choice from the standpoint
of data availability. Moreover, air temperature is a secondary
meteorological variable that provides an integrated measure
of heat energy, so a good choice from that standpoint as well.
- Day Air temperature = f(Rin, H, and LE)
- Night Air temperature = f(Lout, wind velocity)
- M = Mf (Ta - To)
- M = snowmelt (mm/day)
- Mf = degree day factor (mm/degreeC/day)
- Ta = air temp (degrees C); daily mean, daytime mean,
maximum daily Ta; user must decide
- To = threshold or base temperature (degreesC) above
which snow melt occurs, usually 0 degreesC.
- range is usually 1 mm/degreeC/day < Mf < 7 mm/degreeC/day
- The degree-day factor is the heart of the approach.
- The degree-day factor must be calibrated for each basin and may change
with elevation on the same time step and over time at the same point
within a basin.
Snowmelt Runoff Model (SRM) developed by Martinec and Rango
- Q = [C a T S ) + P] A
- Q = discharge
- c = runoff coefficient; essentially runoff efficiency or
what fraction of snowmelt gets converted to discharge.
Calibrate for each basin.
- a = degree day factor
- T = number of degree days
- S = ratio of snow covered area to total area, e.g. how much of
the basin has snow to melt.
- P = new precipitation which gets added in to the system
- A = basin area
- T, S, and P need to be measured (or estimated) daily
- a = 1.1 rhos/rhow is the initial estimate
if no calibration done, based on the concept that as the density
of snow increases (rhos), albedo decreases and liquid
water content increases, leading to more efficient melt for the
same number of degree days.
- This is a model based on empirical calibrations.
- However, the simple approach includes much of the physics involved
in snow melt. SRM thus provides a reasonable approximation to
modeling snowmelt over a basin. A major benefit of SRM is that only
a few parameters need to be measured, including air temperature,
snow-covered area, and new precipitation. These parameters are among
the easiest to obtain in snow hydrology.
ENERGY BALANCE MODELS
These models can be run at a point or be spatially distributed.
Essentially, these models run on measured data and transfer that
information based on first principles. This is in contrast to
empirical models such as SRM, which run on only a few measured
parameters and which rely on calibration parameters at the
heart of the model.
However, with energy balance models you sacrifice simplicity
for complicated measurements and complicated algorithms.
Your energy balance model is only as good as your measured data
and your understanding of the system.
Energy balance models are often run at a point
with measured meteorological variables.
These point measurements are then spatially distributed
using a variety of simplifying assumptions.
- areal extent of snow cover
- spatial distribution of SWE (a harder problem)
- distributed energy balance over a given area
- lags: through snowpack; through basin
- snow depletion (SCA; SWE) over time
General Modeling Approach. Each is usually a stand-alone submodel.
- Precipitation submodel
- Storage and spatial distribution of snow, SWE
- New precipitation
- Little information exists on the spatial distribution of SWE.
- An outstanding problem in snow hydrology.
- We have good tools for estimating snow covered area.
- Energy balance submodel
- calculate the energy balance of the snow surface
- Q = R + G + H + LE + A + dQ/dt
- Q = net energy
- R = net radiation
- G = ground heat flux
- H = sensible heat flux
- LE = latent heat flux
- A = advected energy (rain-on-snow)
- dQ/dt = change in internal snowpack energy
- since a surface has no volume, Q = zero.
- we understand snow/atmosphere energy transfers well from
first principles, so we can model this part well at a point if we
can measure the meteorological variables.
- where this gets tricky is that over a basin of interest, there are
usually few meteorological stations. Spatially distributing the
meteorological variables is difficult.
- Snowpack Model
- Another difficult problem
- We know little about liquid water retention and movement
- Essentially, once we melt snow at the surface of the snowpack,
we lose track of the snow.
- Snow Depletion Model
- We need to keep track of the change in SCA and SWE over time.
- Obviously, as the amount of SCA decreases with time, the
same amount of energy per unit area melts less snow because
there is less snow to melt.
- There are a number of good methods to estimate changes in SCA
with time, including remote sensing measurements and aerial photography.
With this information you can calculate areal depletion curves
(linear, exponential, etc).
- Again, our ability to estimate changes in the spatial distribution of SWE
over time is a challenge.