# Model help:TopoFlow-Evaporation-Energy Balance

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## TopoFlow-Evaporation-Energy Balance

This module is used as the evaporation 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 The location of the input files [-]
Output directory The location for the output files [-]
Site prefix [-]
Case prefix [-]
Number of steps Number of simulation steps [-]
Time step [sec]
alpha type Allowed input types: Scalar / Grid /Time_Series /Grid_Sequence [-]
alpha coefficient [-]
K_soil type Allowed input types: Scalar / Grid /Time_Series /Grid_Sequence [-]
K_soil thermal conductivity of soil [W / m / deg_C]
soil_x type Allowed input types: Scalar / Grid /Time_Series /Grid_Sequence [-]
soil_x reference depth in soil [m]
T_soil_x type Allowed input types: Scalar / Grid /Time_Series /Grid_Sequence [-]
T_soil_x temperature of soil at depth x [deg_C]
Parameter Description Unit
Save grid timestep time interval between saved grids [sec]
Save er grids toggle option to save grids of evap. rate [mm / hr]
Save er grids file file name for grid stack of evap. rate [mm / hr]
Save pixels timestep time interval between time series values [sec]
Save er pixels toggle option to save time series of evap. rate [-]
Save er pixels file file name for time series of evap. rate [mm / hr]

## Uses ports

• Meteorology
• Channels (surface water flow in a network of channels with trapezoidal cross-section)
• Snow (Snowmelt)
• Infil (Infiltration)
• Satzone (Subsurface flow in saturated zone)

## Provides ports

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

## Main equations

• Evaporation rate
 $\displaystyle{ ET=\left (1000 \ast Q_{et}\right) / \left (\rho_{water} \ast L_{v}\right) }$ (1)
• Energy flux used to evaporate water
 $\displaystyle{ Q_{et}=\left (Q_{SW} + Q_{LW} + Q_{c} + Q_{h}\right) }$ (2)
• Conduction energy flux
 $\displaystyle{ Q_{c}= K_{soil} \ast \left (T_{soil_x} - T_{surf} \right) \ast \left ( 100 / x \right) }$ (3)
• Sensible heat flux
 $\displaystyle{ Q_{h}= \rho_{air} \ast c_{air} \ast D_{h} \ast \left (T_{air} - T_{surf}\right) }$ (4)
• Bulk exchange coeff. (neutrally stable conditions)
 $\displaystyle{ D_{n}= u_{z} \ast \kappa^2 / LN [ \left ( z - h_{snow}\right) / z0_{air}] ^2 }$ (5)
• Bulk exchange coeff. for heat
 $\displaystyle{ D_{h}=\left\{\begin{matrix} D_{n} / \left (1 + \left (10 \ast Ri \right)\right) & stable: T_{air} \gt T_{surf} \\ D_{n} \ast [ 1 - \left ( 10 \ast Ri \right) ] & unstable: T_{air} \lt T_{surf} \end{matrix}\right. }$ (6)
• Richardson's number
 $\displaystyle{ Ri= g \ast z \ast \left (T_{air} - T_{surf} \right) / [ u_{z}^2 \left ( T_{air} + 273.15 \right) ] }$ (7)

## Notes

Notes on Input Parameters

If net total radiation has been measured, it can be entered as QSW and then QLW can be set to zero. Any meteorological variables entered here (such as Tair) are automatically shared with other other processes, such as Snowmelt and Precipitation.

Snow depth is tracked internally, and can increase from snowfall or decrease by melting, starting from its initial value. In the current version there is no mechanism for redistribution of snow.

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 use 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.

Notes on the Equations

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

Wherever (d > 0), evaporation results in a reduction in the surface flow depth. Wherever (d = 0), water is removed from subsurface storage. If the 1D Richards' equation is used for infiltration, then the evaporation rate is applied as a surface boundary condition and alters

In the equation for computing Dn, the reference height, z, is reduced by the computed snow depth, hsnow. It follows that z must be chosen so as to be greater than any possible snow depth.

## 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.