## SNOW HYDROLOGY (GEOG 4321): MODELING

### PRIMARY APPROACHES

Primary approaches to modeling snowmelt are:

1. ablation stakes
2. regression analysis (linear or multiple)
3. temperature index approach
4. energy balance approach

### ABLATION STAKES

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.

### REGRESSION MODELS

• 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.
• requirements:
• 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.
• Uses:
• 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.
• simple
• 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.

### TEMPERATURE-INDEX METHODS

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)

Approach:

• 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.

Important factors:

• 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.

1. 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.
2. Energy balance submodel
• calculate the energy balance of the snow surface
• Q = R + G + H + LE + A + dQ/dt
• Q = net energy
• 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.
3. 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.
4. 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.