Model help:TopoFlow-Evaporation-Energy Balance
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
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
[math]\displaystyle{ ET=\left (1000 \ast Q_{et}\right) / \left (\rho_{water} \ast L_{v}\right) }[/math] (1)
- Energy flux used to evaporate water
[math]\displaystyle{ Q_{et}=\left (Q_{SW} + Q_{LW} + Q_{c} + Q_{h}\right) }[/math] (2)
- Conduction energy flux
[math]\displaystyle{ Q_{c}= K_{soil} \ast \left (T_{soil_x} - T_{surf} \right) \ast \left ( 100 / x \right) }[/math] (3)
- Sensible heat flux
[math]\displaystyle{ Q_{h}= \rho_{air} \ast c_{air} \ast D_{h} \ast \left (T_{air} - T_{surf}\right) }[/math] (4)
- Bulk exchange coeff. (neutrally stable conditions)
[math]\displaystyle{ D_{n}= u_{z} \ast \kappa^2 / LN [ \left ( z - h_{snow}\right) / z0_{air}] ^2 }[/math] (5)
- Bulk exchange coeff. for heat
[math]\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. }[/math] (6)
- Richardson's number
[math]\displaystyle{ Ri= g \ast z \ast \left (T_{air} - T_{surf} \right) / [ u_{z}^2 \left ( T_{air} + 273.15 \right) ] }[/math] (7)
Symbol | Description | Unit |
---|---|---|
Q_{SW} | net shortwave radiation | [W / m^{2}] |
Q_{LW} | net longwave radiation | [W / m^{2}] |
T_{air} | air temperature | deg C |
T_{surf} | surface (snow) temperature | deg C |
T_{soil_x} | soil temperature at depth x | deg C |
x | reference depth in soil | m |
K_{soil} | thermal conductivity of soil | W / (m deg_C ) |
u_{z} | wind velocity at height z | m / s |
z | reference height for wind (above land surface) | m |
z_{0} | surface roughness height (with no snow) | m |
h0_{snow} | initial snow depth | m |
ρ_{air} | density of the air | kg / m^{3} |
c_{air} | specific heat of air | J /kg |
L_{v} | latent heat of vaporization, water (2500000) | m / m |
g | gravitational constant, Earth = 9.81 | m / s ^{2} |
κ | von Karman's constant, equals to 0.41 | - |
ET | evaporation rate | mm / sec |
Q_{et} | energy flux used to evaporate water | W / m^{2} |
Q_{c} | conduction energy flux (between surf. and subsurf.) | W / m^{2} |
Q_{h} | sensible heat flux | W / m^{2} |
D_{n} | bulk exchange coeff. (neutrally stable conditions) | m / s |
D_{h} | bulk exchange coeff. for heat | m / s |
Ri | Rechardson's number | - |
ρ_{water} | density of the water | kg / m^{3} |
Notes
Notes on Input Parameters
If net total radiation has been measured, it can be entered as Q_{SW} and then Q_{LW} can be set to zero. Any meteorological variables entered here (such as T_{air}) 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 D_{n}, the reference height, z, is reduced by the computed snow depth, h_{snow}. 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:
- Upload file: https://csdms.colorado.edu/wiki/Special:Upload
- Create link to the file on your page: [[Image:<file name>]].
See also: Help:Images or Help:Movies
Developer(s)
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.
Links
Related Help Pages
- Model help:TopoFlow-Evaporation-Priestley_Taylor
- Model help:TopoFlow-Evaporation-Read_File
- Model help:TopoFlow-Meteorology
Model Metadata