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

Input

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	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]

Output

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

This will be something that the CSDMS facility will add

Provides ports

This will be something that the CSDMS facility will add

Main equations

Evaporation rate

[math]\displaystyle{ ET=\left (1000 Q_{et}\right) / \left (/rho_{water} 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} \left (T_{soil_x} - T_{surf} \right) \left ( 100 / x \right) }[/math]

(3)

Sensible heat flux

[math]\displaystyle{ Q_{h}= /rho_{air} c_{air} D_{h} \left (T_{air} - T_{surf}\right) }[/math]

(4)

Bulk exchange coeff. (neutrally stable conditions)

[math]\displaystyle{ D_{n}= u_{z} /kappa^2 / LN \left ( \left ( z - h_{snow}\right) / z0_{air}\right)^2 }[/math]

(5)

Bulk exchange coeff. for heat (stable: T_{air} > T_{surf})

[math]\displaystyle{ D_{h}= D_{n} / \left (1 + \left (10 Ri \right)\right) }[/math]

(6)

Bulk exchange coeff. for heat (unstable: T_{air} < T_{surf})

[math]\displaystyle{ D_{h}= D_{n} \left ( 1 - \left ( 10 Ri \right) \right) }[/math]

(7)

Richardson's number

[math]\displaystyle{ Ri= g z \left (T_{air} - T_{surf} \right) \left ( u_{z}^2 \left ( T_{air} + 273.15 \right) \right) }[/math]

(8)

Nomenclature

Symbol	Description	Unit
Q_SW	net shortwave radiation	[W / m²]
Q_LW	net longwave radiation	[W / m²]
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
z₀	surface roughness height (with no snow)	m
h0_snow	initial snow depth	m
/rho_air	density of the air	kg / m³
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 / m²
Q_c	conduction energy flux (between surf. and subsurf.)	W / m²
Q_h	sensible heat flux	W / m²
D_n	bulk exchange coeff. (neutrally stable conditions)	m / s
D_h	bulk exchange coeff. for heat	m / s
Ri	Rechardson's number	-

Notes

Note 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.

Note on equations

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: http://csdms.colorado.edu/wiki/Special:Upload
Create link to the file on your page: [[Image:<file name>]].

Developer(s)

Scott Peckham

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

Model help:TopoFlow-Evaporation-Energy Balance