# Model help:TopoFlow-Snowmelt-Energy Balance

## TopoFlow-Snowmelt-Energy Balance

This module is the snowmelt process component (Energy Balance method) for a D8-based, spatial hydrologic model

## Model introduction

This process component is part of a spatially-distributed hydrologic model called TopoFlow, but it can now be used as a stand-alone model.

## Model parameters

Parameter Description Unit
Component status Enabled/Disabled
Input directory -
Output directory -
Site prefix file prefix for the study site -
Case prefix file prefix for the model scenario -
Number of steps Number of time steps -
Time steps timestep for snowmelt process sec
Cp_snow type allowed input type (Scalar/Grid/Time_series/Grid_Sequence) -
Cp_snow heat capacity of snow J/kg/K
ρ_snow type allowed input type (Scalar/Grid/Time_series/Grid_Sequence) -
ρ_snow density of snow kg / m3
c0 type allowed input type (Scalar/Grid/Time_series/Grid_Sequence) -
c0 degree-day coefficient mm/day/deg C
T0 type allowed input type (Scalar/Grid/Time_series/Grid_Sequence) -
T0 reference temperature deg C
h0_snow type allowed input type (Scalar/Grid/Time_series/Grid_Sequence) -
h0_snow depth of snow m
h0_swe type allowed input type (Scalar/Grid/Time_series/Grid_Sequence) -
h0_swe depth of snow water equivalent (SWE) m
Parameter Description Unit
Save grid timestep time interval between saved grids sec
Save mr grids toggle option to save grids of snow meltrate
Save mr grids file filename for grid stack of snow meltrate m / s
Save hs grids toggle option to save grids of snow depth
Save hs grids file filename for grid stack of snow depth m
Save sw grids toggle option to save grids of snow water equivalent
Save sw grids file filename for grid stack of snow water equivalent m
Save cc grids toggle option to save grids of cold content
Save cc grids file filename for grid stack of cold content J / m2
Parameter Description Unit
Save pixels timestep time interval between time series values sec
Save mr pixels toggle option to save time series of snow meltrate
Save mr pixels file filename for time series of snow meltrate m / s
Save hs pixels toggle option to save time series of snow depth
Save hs pixels file filename for time series of snow depth m
Save sw pixels toggle option to save time series of snow water equivalent
Save sw pixels file filename for time series of snow water equivalent m
Save cc pixels toggle option to save time series of cold content
Save cc pixels file filename for time series of cold content J / m2

## Uses ports

• Meteorology (for air temperature, T_air, etc.)

## Provides ports

• Snow (snowmelt)
• Configure (tabbed dialog GUI to change settings)
• Run (only if used as the Driver)

## Main equations

• Meltrate
 $\displaystyle{ M= \left ( 1000 \ast Q_{m}\right) / \left ( \rho_{water} \ast L_{f}\right) }$ (1)
• Max possible meltrate
 $\displaystyle{ M_{max}= \left ( 1000 \ast h_{snow} / dt\right) \ast \left ( \rho_{water} / \rho_{snow}\right) }$ (2)
• Change in snow depth
 $\displaystyle{ dh_{snow}= M \ast \left ( \rho_{water} / \rho_{snow}\right) \ast dt }$ (3)
• Energy flux used to melt snow
 $\displaystyle{ Q_{m}= Q_{SW} + Q_{LW} + Q_{h} + Q_{e} - Q_{cc} }$ (4)
• Sensible heat flux
 $\displaystyle{ Q_{h}= \rho_{air} \ast c_{air} \ast D_{h} \ast \left (T_{air} - T_{surf} \right) }$ (5)
• Latent heat flux
 $\displaystyle{ Q_{e}= \rho_{air} \ast L_{v} \ast D_{e} \ast \left ( 0.662 / p_{0} \right ) \ast \left ( e_{air} - e_{surf} \right ) }$ (6)
• Bulk exchange coefficient
 $\displaystyle{ D_{n}= \kappa^2 \ast u_{z} / LN [ \left ( z - h_{snow}\right) / z0_{air}]^2 }$ (7)
• Bulk exchange coefficient for heat
 $\displaystyle{ D_{h}= \left\{\begin{matrix} D_{n} / [1 + \left (10 \ast Ri \right) ] & stable: T_{air} \gt T_{surf} \\ D_{n} \ast [ 1 - \left ( 10 \ast Ri \right)] & unstable: T_{air} \lt T_{surf} \end{matrix}\right. }$ (8)
• Bulk exchange coefficient for vapor
 $\displaystyle{ D_{e}= D_{h} }$ (9)
• Richardson's number
 $\displaystyle{ Ri= g \ast z \ast \left (T_{air}- T_{surf} \right) / [ u_{z}^2 \left ( T_{air} + 273.15 \right)] }$ (10)
• Initial cold content
 $\displaystyle{ E_{cc} [ 0 ] = h0_{snow} \ast \rho_{snow} \ast c_{snow} \ast \left (T_{0} - T_{snow} \right) }$ (11)
• Vapor pressure of air
 $\displaystyle{ e_{air}= e_{sat} \left ( T_{air} \right) \ast RH }$ (12)
• Vapor pressure at surface
 $\displaystyle{ e_{surf}= e_{sat} \left ( T_{surf} \right) }$ (13)
• Saturation vapor pressure (mbar), Brutsaert (1975)
 $\displaystyle{ e_{sat}=6.11 \ast exp [ \left (17.3 \ast T\right) /\left (T + 237.3 \right) ] }$ (14)

## Notes

Notes on Input Parameters

For each variable, you may choose from the droplist of data types. For the "Scalar" data type, enter a numeric value with the units indicated in the dialog. For the other data types, enter a filename. Values in files must also have the indicated units.

Single grids and grid sequences are assumed to be stored as RTG and RTS files, respectively. Time series are assumed to be stored as text files, with one value per line. For a time series or grid sequence, the time between values must coincide with the timestep provided.

Note: If net total radiation has been measured, it can be entered as QSW and then QLW can be set to zero in the Meteorology component that this component uses.

Notes on the Equations

All variables and their units can be seen by expanding the Nomenclature section above.

The cold content of the snow pack, Ecc, represents an energy deficit that must be overcome before snow begins to melt. First, Qnet is computed as the sum of all energy fluxes (the Q's). Wherever (Qnet < 0 and hsnow > 0) the snow cools and the cold content increases. Similarly, wherever (Qnet > 0 and hsnow > 0) the snow warms and the cold content decreases. In both cases the cold content changes according to: Ecc = [Ecc - (Qnet * dt)] and we have M=0 as long as (Ecc > 0). However, if warming continues long enough to consume the cold content (so that Ecc drops to zero), then the snow begins to melt (M > 0). In this case the meltrate is given by M = Qnet / (ρwater * Lf).

## Examples

An example run with input parameters, BLD files, as well as a figure / movie of the output

Follow the next steps to include images / movies of simulations:

## References

Brutsaert, W. (1975) On a derivable formula for long-wave radiation from clear skies, Water Resources Research, 11, 742-744.

Dingman, S.L (2002) Physical Hydrology, 2nd ed., Prentice Hall, New Jersey. (see Chapter 7, pp. 285-299)

Schlicting, H. (1960) Boundary Layer Theory, 4th ed., McGraw-Hill, New York, 647 pp.

Zhang, Z., D.L. Kane and L.D. Hinzman (2000) Development and application of a spatially-distributed Arctic hydrological and thermal process model (ARHYTHM), Hydrological Processes, 14, 1017-1044.

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