Model help:TopoFlow-Meteorology

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TopoFlow-Meteorology

The module is the meteorology process component for a D8-based, spatial hydrologic model

Model introduction

This component reads a variety of variables for the atmosphere and for the land surface from input files or as simple scalars. It then computes many additional variables, such as vapor pressure, e_air, and net shortwave (solar) radiation, Q_SW, using built-in shortwave and longwave radiation calculators that are based on celestial mechanics and widely-used empirical relationships. These additional variables are needed by the Snowmelt → Energy Balance and Evaporation → Energy Balance components. Direct, diffuse and back-scattered radiation fluxes are all modeled. Properties of the atmosphere (e.g. precipitation rate, P, air temperature, T_air, relative humidity, RH, and dust attenuation, γ), are used as well as surface/topographic properties (e.g. slope angle, aspect angle and surface albedo). The approach used here closely follows the one outlined in Appendix E of Dingman (2002). However, instantaneous vs. day-integrated radiation fluxes are used and the optical air mass is modeled using the widely used method of Kasten and Young (1989).

Model parameters

Input 1

Input 2

Input 3

Output 1

Output 2

Parameter	Description	Unit
Components 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 step	meteorology time step	sec
ρ H2O type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
ρ H2O	density of water	kg/m3
Cp_air type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
Cp air	heat capacity of air	J/kg/K
ρ_air type:	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
ρ air	density of air	kg/m3
Precipitation rates type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
Precipitation rates		mm/yr
PRECIPITATION ONLY toggle	toggle to turn off all variable updates except precipitation

Parameter	Description	Unit
T_air type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)	-
T_air	temperature of air	degree C
T_surf type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
T_surf	temperature of surface	degree C
RH type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
RH	relative humidity
p0 type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
p0	atmospheric pressure	mbar
uz type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
uz	wind velocity at height z	m / s
z type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
z	wind reference height	m
z0_air type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
z0_air	surface roughness length scale for wind	m

Parameter	Description	Unit
albedo type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
albedo	surface albedo in [0,1]
emissivity type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
emissivity	surface emissivity in [0,1]
dust atten. type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
dust attenuation	dust attenuation factor in [0,0.3]
cloud factor type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
cloud factor	cloudiness factor in [0,1]
canopy factor type	allowed input types (Scalar/Grid/Time_Series/Grid_Sequence)
canopy factor	canopy coverage factor in [0,1]
slope grid file	flat binary, row-major file with grid of 4-byte slopes
aspect grid file	flat binary, row-major file with grid of 4-byte aspects
time zone offset	time zone offset from GMT
start month
start_day
start_hour

Parameter	Description	Unit
Save grid timestep	time interval between saved grids	sec
Save e_air grids toggle	option to save grids of vapor pressure (in air)	-
Save e_air grids file	filename for grid stack of vapor pressure (in air)	mbar
Save e_surf grids toggle	option to save grids of vapor pressure (at surface)	-
Save e_surf grids file	filename for grid stack of vapor pressure (surf)	mbar
Save Qn_SW grids toggle	option to save grids of net short wave radiation	-
Save Qn_SW grids file	filename for grid stack of short wave radiation	W / m2
Save Qn_LW grids toggle	option to save grids of net longwave radiation	-
Save Qn_LW grids file	filename for grid stack of net longwave radiation	W / m2
Save em_air grids toggle	option to save grids of air emissivity
Save em_air grids file	filename for grid stack of air emissivity in [0,1]

Parameter	Description	Unit
Save pixels timestep	time interval between time series values	sec
Save e_air pixels toggle	option to save time series of sat. vapor pressure (in air)	-
Save e_air pixels file	filename for time series of sat. vapor pressure (in air)	mbar
Save e_surf pixels toggle	option to save time series of sat. vapor pressure (at surface)	-
Save e_surf pixels file	filename for time series of sat. vapor pressure (surf)	mbar
Save Qn_SW pixels toggle	option to save time series of net shortwave radiation	-
Save Qn_SW pixels file	filename for time series of short wave radiation	W / m2
Save Qn_LW pixels toggle	option to save time series of net longwave radiation	-
Save Qn_LW pixels file	filename for time series of net longwave radiation	W / m2
Save em_air pixels toggle	option to save time series of air emissivity
Save em_air pixels file	filename for time series of air emissivity in [0,1]

Uses ports

• Snow (Snowmelt)

Provides ports

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

Main equations

Equations Used to Compute Longwave Radiation

• Net longwave radiation

<math> Q_{LW} = \left (LW_{in} - LW_{out}\right ) </math>

(1)

• Incoming longwave radiation (using Stefan-Bolzman law)

<math> LW_{in} = \varepsilon_{air} \cdot \sigma \cdot \left (T_{air} + 273.15 \right )^4 </math>

(2)

• Outgoing longwave radiation (using Stefan-Bolzman law)

<math> LW_{out} = \varepsilon_{surf} \cdot \sigma \cdot \left (T_{surf} + 273.15 \right )^4 + \left ( 1 - \varepsilon_{surf} \right ) \, LW_{in} </math>

(3)

• Saturation vapor pressure, Brutsaert (1975) method

<math> e_{sat} = 0.611 \cdot \exp [\left ( 17.3 \cdot T \right ) / \left ( T + 237.3 \right )] </math>

(4)

• Saturation vapor pressure, Satterlund (1979) method

<math> e_{sat} = \frac{10^\left[11.4 - (2353 / (T + 273.15)) \right]}{1000} </math>

(4)

• Vapor pressure of air

<math> e_{air} = e_{sat} \cdot RH </math>

(5)

• Emissivity of air

<math> \varepsilon_{air} = \left[\left (1 - F \right ) \, 1.72 \, \left[e_{air}/ \left (T_{air} + 273.15 \right ) \right]^ \left ({\frac{1}{7}} \right ) \, \left (1 + 0.22 \cdot C^2 \right ) \right] + F </math>

(6)

Equations Used to Compute Shortwave Radiation

• Day angle or fractional year

<math> \Gamma = 2 \, \pi \, \left ( J - 1 \right ) / 365 </math>

(1)

• Earth orbit eccentricity correlation

<math> \begin{align} E_{0} &= \left ( r_{0} / r \right )^2 \\ &= 1.000110 + 0.034221 \cdot \cos \left ( \Gamma \right ) + 0.001280 \cdot \sin \left ( \Gamma \right ) + \\ & \qquad \qquad \qquad 0.000719 \cdot \cos \left ( 2 \, \Gamma \right ) + 0.000077 \cdot \sin \left ( 2 \, \Gamma \right ) \end{align} </math>

(2)

• Declination of the sun at a given latitude

<math> \begin{align} \delta &= \left( 180 / \pi \right) \, [ 0.006918 - 0.399912 \cdot \cos \left( \Gamma \right) + 0.070257 \cdot \sin \left( \Gamma \right) - \\ & \qquad \qquad \qquad \qquad 0.006758 \cdot \cos \left( 2 \, \Gamma \right) + 0.000907 \cdot \sin \left( 2 \, \Gamma \right) - \\ & \qquad \qquad \qquad \qquad 0.002697 \cdot \cos \left( 3 \, \Gamma \right) + 0.00148 \cdot \sin \left( 3 \, \Gamma \right) ] \end{align} </math>

(3)

• Zenith angle

<math> \theta = \arccos [\sin \left ( \Lambda \right ) \, \sin \left ( \delta \right ) + \cos \left ( \Lambda \right ) + \cos \left ( \Lambda \right ) \, \cos \left (\delta \right ) \, \cos \left ( \omega \, t_{h} \right )] </math>

(4)

• Sunrise offset, horizontal plane (hours before true solar noon)

<math> T_{hr} = - {\frac{ \arccos \left[- \tan \left( \Lambda \right) \, \tan \left ( \delta \right ) )\right] }{\omega}} </math>

(5)

• Sunset offset, horizontal plane (hours after true solar noon)

<math> T_{hs} = + {\frac{ \arccos \left[- \tan \left ( \Lambda \right ) \, \tan \left ( \delta \right ) \right]}{\omega}} </math>

(6)

• Instantaneous extraterrestrial radiation flux on a horizontal plane

<math> k_{ET}^' = I_{sc} \, E_{0} \, [\cos \left ( \delta \right ) \, \cos \left ( \Lambda \right ) \, \cos \left ( \omega \, t \right ) + \sin \left ( \delta \right ) \, \sin \left ( \Lambda \right )] </math>

(7)

• Dew point temperature

<math> T_{dew} = {\frac{ \ln \left ( e\right ) + 0.4926}{0.0708 - 0.00421 \, \ln \left ( e \right )}} </math>

(8)

• Precipitable water content

<math> W_{p} = 1.12 \, \exp \left ( 0.0614 \, T_{dew} \right ) </math>

(9)

• Optical air mass (from Kasten and Young, 1989)

<math> M_{opt} = 1 / [\cos \left ( \theta \right ) + 0.50572 \, \left ( 96.07995 - \theta \right ) ^ \left (-1.6364 \right )] </math>

(10)

• Total atmospheric transmissivity

<math> \tau = \exp \left[ -0.124 - 0.0207 \, W_{p} - \left (0.0682 + 0.0248 \, W_{p} \right ) \, M_{opt} \right] </math>

(11)

• Instantaneous direct radiation flux

<math> k_{dir}^ ' = \tau \, k_{ET}^ ' </math>

(12)

• Scattering attenuation

<math> \gamma_{s} = 1 - \exp \left [ -0.0363 - 0.0084 \, W_{p} - \left (0.0572 + 0.0173 \, W_{p} \right ) \, M_{opt} \right ] + \gamma_{dust} </math>

(13)

• Instantaneous diffuse radiation flux

<math> k_{dif}^ ' = 0.5 \, \gamma_{s} \, k_{ET} ^ ' </math>

(13)

• Instantaneous global radiation flux

<math> k_{global}^' = k_{dir}^' + k_{dif}^' </math>

(14)

• Backscattered radiation flux

<math> k_{bs}^' = 0.5 \, a \, \gamma_{s} \, k_{global}^' </math>

(15)

• Longitude offset for sloped topography

<math> \Delta \Omega = \arctan \left[{\frac{\sin \left ( \beta \right ) \, \sin \left ( \alpha \right )}{\cos \left ( \beta \right ) \, \cos \left ( \Lambda \right ) - \sin \left ( \beta \right ) \, \sin \left ( \Lambda \right ) \, \cos \left ( \alpha \right )}} \right] </math>

(16)

• Equivalent latitude for sloped topography

<math> \Lambda_{eq} = \arcsin \left[ \sin \left (\beta \right ) \, \cos \left ( \alpha \right ) \, \cos \left ( \Lambda \right ) + \cos \left ( \beta \right ) \, \sin \left ( \Lambda \right ) \right] </math>

(17)

• Sunrise offset for sloped topography

<math> T_{sr} = - {\frac{ \arccos \left[ - \tan \left ( \Lambda_{eq} \right ) \, \tan \left ( \delta \right ) \right] - \Delta \Omega}{\omega}} </math>

(18)

• Sunset offset for sloped topography

<math> T_{ss} = + {\frac{ \arccos \left[ - \tan \left ( \Lambda_{eq} \right ) \, \tan \left ( \delta \right ) \right] - \Delta \Omega}{\omega}} </math>

(19)

• Instantaneous extra-terrestrial radiation flux for sloped topography

<math> k_{ET} = I_{sc} E_{\theta} \left[ \cos \left ( \delta \right ) \cos \left ( \Lambda_{eg} \right ) \cos \left ( \omega \, t_{h} + \Delta \Omega \right ) + \sin \left ( \delta \right ) \sin \left ( \Lambda_{eg} \right ) \right] </math>

(20)

• Instantaneous clear sky radiation for sloped topography

<math> k_{cs} = \tau \, k_{ET} + k_{dif}^' + k_{bs} ^' </math>

(21)

• Net shortwave radiation for sloped topography

<math> Q_{SW} = k_{cs} </math>

(21)

• Earth rotation rate

<math> \Omega = 2 \, \pi \, {DPY}_{sidereal} </math>

(22)

Nomenclature

Symbol	Description	Unit
ρH2O	density of water	kg / m^3
Cpair	heat capacity of air	J / kg / K
ρair	density of air	kg / m^3
precip. rate	precipitation rate	mm / hr
Tair	air temperature	deg C
Tsurf	surface temperature	deg C
p0	atmospheric pressure	mbar
z	reference height for uz	m
uz	wind velocity at reference height	m / s
z0	surface roughness length scale for wind	m
albedo	surface albedo	unitless, in [0,1]
emair = εair	emissivity of air	unitless, in [0,1]
dust atten.	dust attenuation factor	unitless, typically in [0,0.3]
cloud factor	cloud factor	unitless, in [0,1], 0 for no clouds
canopy factor	forest canopy factor	unitless, in [0,1], 0 for no canopy
slope	topographic slope = rise/run	unitless or m/m, in [0, infinity]
slope grid file	as flat binary, row-major file with 4-byte floats	radians
aspect angle	aspect angle	radians measured CW from due North ##### CHECK
aspect grid file	as flat binary, row-major file with 4-byte floats	radians measured CW from due North ##### CHECK
time zone offset	offset from Greenwich Mean Time (GMT); <0 for east of prime meridian, >0 otherwise	hours
start month	start month for solar radiation calculations	month number
start day	start day for solar radiation calculations	day of the month number
start hour	start hour for solar radiation calculations	decimal hours, 24-hour clock
h	height above mean sea level	m
R	mean earth radius	m
Mopt	optical air mass	unitless, greater than 1
emsurf = εsurf	emissivity of the surface (e.g. snow)	unitless, in [0,1]
σ	Stefan-Boltzman constant, equal to 5.67e-8	Watts / (m2 K4)
C	the fraction of sky covered by clouds	unitless, in [0,1]
F	the fraction of sky covered by forest canopy	unitless, in[0,1]
Isc	solar constant, equal to 1367	Watts / m2
J	Julian day	decimal days (J =1 at midnight on January 1)
Γ	day angle or fractional year	radians
E0	Earth orbit eccentricity correction	unitless
Λ	latitude for a given point on the earth's surface	radians
Λdegree	latitude for a given point on the earth's surface	degrees
δ	declination of the sun	degrees
ω	Earth angular velocity, equals to 0.2618 (15 degrees per hour)	radians/hour
θ	zenith angle	radians
th	number of hours before (-) or after (+) true solar noon (TSN)	hours
T	temperature, measured	degrees Celsius
RH	relative humidity, measured	unitless, in [0,1]
γdust	dust attenuation (default is 0.08; typically < 0.2)	unitless
α	aspect angle, measured clockwise from north	radians
β	slope angle, equal to atan(slope)	radians
DPY	Earth days per year, equals to 365.2425	days
DPYsidereal	Earth days per year (sidereal), equals to 366.2425	days
angle	Earth tilt angle, equals to 23.4397	degrees
e (in shortwave radiation equations)	Earth orbit eccentricity, equal to 0.016713	unitless

Output

Symbol	Description	Unit
eair	vapor pressure of air	mbar
esurf	vapor pressure at the surface	mbar
QnSW	net shortwave radiation	W / m^2
QLW	net longwave radiation, equals to LWin - LWout	W / m^2
emair	air emissivity	unitless, in [0,1] ##### CHECK
LWin	incoming longwave radiation	W/m^2
LWout	outgoing longwave radiation	W/m^2
esat = e*	saturation vapor pressure	mbar
Thr	sunrise offset	hours before true solar noon (TSN)
Ths	sunset offset	hours after true solar noon (TSN)
k' ET	instantaneous extraterrestrial radiation flux on a horizontal plane	Watts / m2
esat	saturated vapor pressure	kPa
e	vapor pressure	kpa
Tdew	dew point	degree Celsius
Wp	precipitation water content	cm
Mopt	optical air mass (from Kasten and Young, 1989)	meters #### CHECK
τ	total atmospheric transmissivity	unitless, in [0,1]
kdirect '	instantaneous direct radiation flux	Watts / m2
γs	scattering attenuation	unitless ### CHECK
kdiffuse'	instantaneous diffuse radiation flux	Watts/m2
kglobal'	instantaneous global radiation flux	Watts/m2
kbs'	backscattered radiation flux	Watts/m2
ΔΩ	longitude offset for sloped topography	radians
Λeq	equivalent latitude for sloped topography	radians
noon_offset	noon offset for sloped topography, equal to - ΔΩ / ω	hours
Tsr	sunrise offset for sloped topography	hours
Tss	sunset offset for sloped topography	hours
day_length	day length for sloped topography, equal to Tss - Tsr	hours
kET'	instantaneous extraterrestrial radiation flux for sloped topography	Watts/m2
kcs	instantaneous clear sky radiation	Watts/m2
Ω	earth rotation rate	radians/year

Notes

Notes on Input Parameters

For each input 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.

For DEMs with pixel geometry and bounding box given in terms of Geographic coordinates, the latitude and longitude of each pixel is used in the calculations. For DEMs with a "fixed-length" pixel geometry (e.g. UTM coordinates), which tend to span smaller areas, the dialog prompts for a single lat/lon pair to be used in the calculations.

In the calculation, the timestep between frames in the new grid sequence (RTS file) should typically be about one hour and should match the timestep that will be used to model the Snowmelt or Evaporation processes. The number of frames in the RTS file will depend on the start and stop times, as well as the timestep. The start time, stop time and timestep should match those used to create the new shortwave radiation file with extension "*.Qn-SW".

Notes on the Equations

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

time zone: Boundaries of time zones can be very irregular and a time zone map should be consulted if you are unsure. The time zone is not simply a function of the longitude. You can select an adjacent time zone to include the effect of Daylight Savings Time. Time zones with non-integer offsets from GMT are not yet supported.

slope: Topographic slopes (not slope angles) are specified as dimensionless numbers [m/m]. A RiverTools grid (RTG file) with extension "_slope.rtg", "_mf-slope.rtg" or "_dinf-slope.rtg" can be used.

aspect: Aspect is specified as an angle measured in radians counter-clockwise from due east (the standard convention). A RiverTools grid (RTG file) with extension "_mf-angle.rtg" or "_dinf-angle.rtg" can be used for the (continuous-angle) aspect grid.

Q_SW is set to zero between the times of local sunset and local sunrise, so frames in the RTS file that correspond to nighttime hours will contain only zeros.

Notes on the Equations to Compute Longwave Radiation

The value 237.3 in Brutsaert's equation for em_air is not a misprint.

Notes on the Equations to Compute Shortwave Radiation

The declination of the sun reaches its lowest value of -23.5 degrees on the Winter Solstice (Dec. 21/22) and reaches its highest value of 23.5 degrees on the Summer Solstice(June 21/22). It is zero for both the Vernal Equinox (Mar. 20/21) and the Autumnal Equinox (Sept. 22/23). The value of 23.4397 degrees is the fixed tilt angle of the Earth's axis from from the plane of the ecliptic.

The equation for declination of the sun is a Fourier series expansion that is supposed to have a maximum error of 0.0006 radians (less than 3 arcminutes). This should be double-checked. The equation shown here can also be found at: http://en.wikipedia.org/wiki/Declination, and is derived in the paper called "Fourier series representation of the position of the sun", by J.W. Spencer (1971), of CSIRO.

If (abs(lat_deg) gt 66.5) we are above Arctic circle or below Antarctic circle. This can also happen if lat_deg is an "equivalent latitude" for sloped topography. In this case, the absolute value of the argument to ACOS can exceed one and there is either no sunrise or no sunset at the given location. If the argument to ACOS is less than -1, it is set to -1. If it is greater than 1 it is set to 1.

True solar noon (TSN) for a given location is the time when the sun reaches its highest point above the horizon. At this time, the zenith angle attains its minimum value for the day and the sun is said to be "on the meridian." In order to compute the clock time at which true solar noon occurs, we start with the number 12, then add the following three corrections:

(1) ΔT_c is the time difference between true solar noon and local clock noon, without accounting for any arbitrary time zone adjustments. It is computed from the so-called Equation of Time and is related to the figure-8-shaped "analemma". See: http://en.wikipedia.org/wiki/Equation_of_time and Whitman, A.M. (2003) A Simple Expression for the Equation of Time (online document: http://www58.homepage.villanova.edu/alan.whitman/eqoftime.pdf.

(2) ΔT_tz is computed as the (signed) difference between the local longitude and the longitude at the center of the local time zone, divided by 15. The Earth turns through 15 degrees of longitude in one hour. The longitude at the center of a time zone is given by its GMT offset (and integer between -12 and 12) times 15.

(3) ΔT_dst is a correction for Daylight Savings Time, generally an integer.

Sunrise and sunset occur when zenith angle, θ, is equal to π/2, so cos(θ) = 0. Using the equation for the zenith angle we can then solve for time offsets (e.g. sunrise and sunset offsets) as t_h, in hours.

Many of these equations are from Dingman, Appendix E. In his notation, a lower-case "k" indicates an instantaneous radiation flux. In expressions for "k", the argument "t_h" is the number of hours before (t_h < 0) or after (t_h > 0) true solar noon. Upper-case "K" then indicates the integral of "k" when t_h is allowed to vary from the sunrise offset to the sunset offset. Primes on "k" or "K" indicate values for a horizontal plane which must be corrected (as explained by Dingman) for sloped topography. For example, the sunrise and sunset times for a given location depend on the slope and aspect of the local topography.

The equation for k_ET' is similar to Dingman, App. E, E-25, but his was integrated over one day and this one is instantaneous. Need to double check that integrating the equation here over one day gives his equation E-25. Note that ω has units of radians/hour and ΔΩ (longitude offset) has units of radians. See the TopoFlow source code file: solar_funcs.py, which is imported by met_base.py.

TopoFlow provides two methods for computing the saturated vapor pressure, e_sat = e^*, as a function of temperature, T. One is from Brutsaert (1975) (and used in Dingman) and the other is from Satterlund (1979). Liston (1995, EnBal) uses the Satterlund method. When plotted, the two curves look almost identical for T between -40 and 20, but start to separate from one another for T > 20..

By definition, the relative humidity is the ratio of the actual vapor pressure to the saturated vapor pressure. That is, RH = e_a / e_a ^*. However, relative humidity is generally measured and used together with an equation for saturated vapor pressure to compute the vapor pressure as a function of temperature.

Optical air mass, M_opt is a dimensionless number that gives the relative path length (greater than 1) that radiation must travel through the atmosphere as the result of not entering at a right angle. The equation for optical air mass used here is from Kasten and Young (1989) and depends on latitude, declination and time of day. Instead of this equation, Dingman plots a family of curves in his Figure E-4 (p. 605) for *average daily* optical air mass. It would be interesting to integrate the equation given for M_opt over one day and compare the two by creating a contour plot.

Typical clear-sky values for γ_dust are between 0 and 0.2. See Dingman, p. 604-605.

The following variables are considered as input parameters (to be provided) that are used to compute many others: latitude (lat_deg), longitude (lon_deg or Λ), temperature (T), relative humidity (RH), slope angle (α), aspect angle (β), albedo, dust attenuation, cloudiness, canopy cover, solar constant (I_sc}), and various attributes of Earth such as angular velocity, tilt angle, eccentricity of orbit, days per year and perihelion.

A table of typical surface albedos is given by Dingman, Table D-2 on page 584.

The Earth orbit eccentricy *correction*, E₀, depends on the day angle, Γ, while the Earth orbit eccentricity is computed as: e = (b-a)/a, where a and b are the semi-major and semi-minor axes of the elliptical orbit.

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)

Scott Peckham

References

Dingman, S.L (2002) Physical Hydrology, 2nd ed., Prentice Hall, New Jersey. (see Appendix E)

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

Kasten and Young (1989) Revised optical air mass tables and approximation formula. Applied Optics, 28 (22): 4735~4738. (for the optical air mass equation)

Liston, G. *******

Marks and Dozier (1992) Climate and Energy exchange at the Snow Surface in the Alpine Region of the Sierra Nevada 1. Meteorological Measurements and Monitoring. Water Resources Research, 28(11), 3029~3042.

Whitman, A.M. (2003) A simple expression for the equation of time, online document, http://www58.homepage.villanova.edu/alan.whitman/eqoftime.pdf. Also see: http://en.wikipedia.org/wiki/Equation_of_time

Links

Related Help Pages

• Model help:TopoFlow-Snowmelt-Energy_Balance
• Model help:TopoFlow-Evaporation-Energy_Balance
• Model help:TopoFlow-Snowmelt-Degree-Day
• Model help:TopoFlow-Evaporation-Priestley_Taylor
• Model help:Gc2d

Model Metadata

• Model:TopoFlow-Meteorology
• Model:TopoFlow-Snowmelt-Energy_Balance
• Model:TopoFlow-Evaporation-Energy_Balance
• Model:TopoFlow-Snowmelt-Degree-Day
• Model:TopoFlow-Evaporation-Priestley_Taylor
• Model:TopoFlow