1 layer emissivity
2703101a-0d2a-49a5-9804-cf01a6db1d9f
isee systems
iThink
0
5
0.000976562
Euler
Years
j/yr
joules/degrees K
joules/kilograms-degrees K
joules/meters^2-seconds
kilograms/meters^3
meters^2
seconds/years
This model is a "swamp model", which assumes that the whole of the Earth's surface is covered by a layer of water of a certain depth (in this case 1 meter). This is done to simplify the model, as the Earth's surface can then be considered to have uniform conditions.
Earth Energy reservoir is the amount of joules stored in the Earth's surface, which is a swamp in this case.
All reservoirs are in units of joules (J).
0
Solar_to_Earth
Layer_1_heat
to_Surface
Surface_heat
to_Atm_Layer_1
Earth_to_space
joules
All flows are in units of joules per year (J/yr).
The total energy striking the Earth's surface every year is determined by multiplying the value of the solar constant by the area of a disk with the same diameter as the Earth and by the fraction of energy that is not reflected back to outer space (1-albedo).
Solar_Constant*(1-Earth_Albedo)*Earth_Cross_Section
j/yr
top
85
Energy radiated from Earth's surface to the overlying atmosphere. All flows are in units of joules per year (J/yr).
emissivity*Earth_Surface_Area*Stefan_Boltzmann*Surface_Temperature^4
j/yr
top
81
Temperature = Earth_Energy (J) / Heat_Capacity (J/K)
Temperature is in units of degrees Kelvin (K).
Earth_Energy/Heat_Capacity
degrees K
The heat capacity = Water_Depth (m) * Earth_Surface_Area (m^2) * Water_Density (Kg/m^3) * Specific_Heat_Water (J/Kg*K)
Heat_Capacity is in units of joules per degrees Kelvin (J/K).
Water_Depth*Earth_Surface_Area*Water_Density*Specific_Heat_Water
joules/degrees K
left
188
This model is a "swamp model", which assumes that the whole of the Earth's surface is covered by a layer of water of a certain depth (in this case 1 meter). This is done to simplify the model, as the Earth's surface can then be considered to have uniform conditions.
The specific heat of water = 4218.0 joules per kilograms degrees Kelvin (J/Kg*K).
4218.0
joules/kilograms-degrees K
top
77
The percentage of incoming solar radiation that is reflected back into space (dimensionless).
One minus this fraction is multiplied by the solar constant and the cross section of the Earth to determine the amount of energy actually absorbed by Earth's surface.
For the Earth, the albedo = 30%, however this number can be changed to represent increases or decreases in cloud and ice cover.
0.3
This model is a "swamp model", which assumes that the whole of the Earth's surface is covered by a layer of water of a certain depth (in this case 1 meter). This is done to simplify the model, as the Earth's surface can then be considered to have uniform conditions.
The density of water = 1000.0 kilograms per meters cubed (Kg/m^3).
1000.0
kilograms/meters^3
top
73
This model is a "swamp model", which assumes that the whole of the Earth's surface is covered by a layer of water of a certain depth (in this case 1 meter). This is done to simplify the model, as the Earth's surface can then be considered to have uniform conditions.
The initial assumption of depth of the layer of water ("swamp") covering the Earth is 1.0 meter. This may be changed for experimentation.
1.0
meters
top
73
Earth_Surface_Area is in units of meters squared (m^2).
Area of a sphere = 4*PI*r^2
Earth_Surface_Area = 4*PI*(Earth_Radius^2)
4*PI*(Earth_Radius^2)
meters^2
266
The radius of the earth is 6371.0e3 meters (m).
6371.0e3
meters
top
81
Earth_Cross_Section is in units of meters squared (m^2).
Area of a circle = PI * r^2
Earth_Cross_Section = PI*(Earth_Radius^2)
PI*(Earth_Radius^2)
meters^2
305
3.15576e7 seconds per year (s/yr).
3.15576e7
seconds/years
top
58
The amount of solar radiation received each year by a square meter of Earth at the Earth's average distance from the Sun.
The solar constant is in units of Watts per meters squared (W/m^2), or joules per meters squared seconds (J/m^2s). Here we multiply by the number of seconds in a year to determine the number of joules per square meter received annually.
1368.0*Seconds_per_Year
joules/meters^2-seconds
295
Stefan_Boltzmann = The Stefan Boltzmann constant {5.67e-8 (J/m^2*s*K^4)} * Seconds_per_Year (s/yr). The S-B constant relates the energy contained in a black body to its temperature.
Stefan_Boltzmann is in units of (J/m^2*yr*K^4)
5.67e-8*Seconds_per_Year
283
Atm_Layer_1 reservoir contains the number of joules stored in the one-layer atmosphere adjacent to the Earth's surface.
All reservoirs are in units of joules (J).
0
Surface_heat
to_Atm_Layer_1
Layer_1_heat
to_Surface
Layer_1_heat
to_Space
joules
Energy radiated by Earth's atmosphere back to the surface. All flows are in units of joules per year (J/yr).
emissivity*Layer_1_Area*Stefan_Boltzmann*(Atm_Layer__1_temp^4)
j/yr
Energy radiated by Earth's atmosphere to outer space. All flows are in units of joules per year (J/yr).
emissivity*Layer_1_Area*Stefan_Boltzmann*(Atm_Layer__1_temp^4)
j/yr
Layer 1 temp is in units of degrees Kelvin (K).
Layer_1_temp = Atm_Layer_1/Heat_Capacity_Layer_1
Atm_Layer_1/Heat_Capacity_Air
degrees K
Heat_Capacity_Layer_1 = Layer_1_Depth (m) *Layer_1_Area (m^2) * Air_Density (Kg/m^3) * Specific_Heat_Air (J/Kg*K)
Heat_Capacity is in units of joules per degrees Kelvin (J/K).
Layer_1_Depth*Layer_1_Area*Air_Density*Specific_Heat_Air
279
Layer_1_Radius = The radius of the earth in meters (m) + the thickness of the atmosphere layer in meters (m).
Layer_1_Radius = 6371.0e3+Layer_1_Depth
6371.0e3+Layer_1_Depth
top
77
Layer_1_Area is in units of meters squared (m^2).
Area of a sphere = 4*PI*r^2
Layer_1_Area = 4*PI*(Layer_1_Radius^2)
4*PI*(Layer_1_Radius^2)
This is the depth (or thickness) of the layer of atmosphere 1 in meters (m).
The initial assumption of depth of atmosphere layer 1 is 10,000.0 meters. This may be changed for experimentation.
10.0e3
meters
top
99
The density of air = 1.3 kilograms per meters cubed (Kg/m^3).
1.3
kilograms/meters^3
top
73
The specific heat of air = 750.0 joules per kilograms degrees Kelvin (J/Kg*K).
750.0
joules/kilograms-degrees K
top
65
(1-emissivity)*Earth_Surface_Area*Stefan_Boltzmann*Surface_Temperature^4
j/yr
0.773
Heat_Capacity
Earth_Surface
Area
Stefan_Boltzmann
310
Solar_Constant
Earth_Cross
Section
Stefan_Boltzmann
top
99
Stefan_Boltzmann
top
73
Layer_1
Area
295
Earth_Albedo
Solar_to_Earth
Water_Depth
Heat_Capacity
Water_Density
Heat_Capacity
Specific_Heat
Water
Heat_Capacity
Earth_Surface
Area
Heat_Capacity
Earth_Radius
Earth_Surface
Area
Earth_Radius
Earth_Cross
Section
Earth_Energy
Surface_Temperature
Surface_Temperature
Surface_heat
to_Atm_Layer_1
Seconds_per_Year
Stefan_Boltzmann
Seconds_per_Year
Solar_Constant
Surface_Temperature
Surface_heat
to_Atm_Layer_1
Surface_heat
to_Atm_Layer_1
Solar_to_Earth
Solar_to_Earth
Atm_Layer_1
Atm_Layer_
1_temp
Atm_Layer_
1_temp
Layer_1_heat
to_Surface
Atm_Layer_
1_temp
Layer_1_heat
to_Space
Layer_1
Depth
Heat_Capacity_Air
Layer_1_heat
to_Surface
Layer_1_heat
to_Space
Heat_Capacity_Air
Atm_Layer_
1_temp
Layer_1_heat
to_Space
Layer_1
Area
Layer_1_heat
to_Surface
Layer_1
Radius
Layer_1
Area
Air_Density
Heat_Capacity_Air
Specific_Heat
Air
Heat_Capacity_Air
Layer_1
Area
Heat_Capacity_Air
Layer_1
Depth
Layer_1
Radius
Surface_Temperature
Earth_to_space
Earth_to_space
Earth_to_space
emissivity
Surface_heat
to_Atm_Layer_1
emissivity
Layer_1_heat
to_Space
emissivity
Layer_1_heat
to_Surface
emissivity
Earth_to_space
0
blue
true
1
red
true
bottom
1 Layer Atmosphere Model (Earth Energy Model 3)
Here the model has been modified through the addition of an atmosphere composed of one layer with vairable emissivity.
Based on the following reading:
Few, A.A., 1996, System Behavior and System Modeling, Sausalito, CA: University Science Books, p. 27-37.
Harte, J., 1988, Consider a Spherical Cow, Sausalito, CA: University Science Books, p. 69-72, p. 160-167.
0