SimRoof: Lambertian Model for Tropics

	http://people.csail.mit.edu/jaffer/SimRoof/Tropics/Lambertian
	SimRoof: Lambertian Model for Tropics

Lambertian Model

A flat Lambertian emitter radiates uniformly over the whole hemisphere.

A coarse Lambertian dataset doing 450 radiative-transfer integrations and storing 675 net-flow values has:

ray-angle (6): 7.5°, 22.5°, 37.5°, 52.5°, 67.5°, 82.5°
ceiling-height (12+1): 3.58 m, 12.6 m, 28.0 m, 57.9 m, 117 m, 237 m, 479 m, 966 m, 1.95 km, 3.93 km, 7.93 km, 16.0 km, unlimited
dry-bulb temperature (5): 12.7°C, 18.7°C, 24.7°C, 30.7°C, 36.7°C
precipitable-water (5): 10 mm, 23.75 mm, 37.5 mm, 51.25 mm, 65 mm
atmospheric-pressure (3): 95 kPa, 100 kPa, 105 kPa
atmospheric-transparency (41004): ~1312123÷32

The ceiling-heights are parametrized using a hyperbolic-sine curve (sinh) to compensate for the exponentially decreasing humidity with altitude. The γ parameter in troposphere.pdf scales sinh to make steps in each integration have roughly the same increment. This graph shows the thermal-infrared inflow integration through 65 mm to 10 mm of preciptable water with γ=10.

The net flow for clouds at multiple altitudes is calculated simultaneously with the cloudless radiative-transfer integration (with respect to altitude).

The graph on the left shows the net infrared radiative transfer (NIRT) over the range of ceiling-heights with ground-level at 25°C and 100 kPa and with 65 mm (upper curve) to 10 mm (lower curve) of precipitable-water. The extra crosses on the right edge are the unlimited-ceiling NIRTs. The graph on the right shows it sliced the other way: lines of constant ceiling-heights (unlimited ceiling at the bottom) with precipitable-water on the abscissa.

Plot of radiative transfers versus Ceiling Height for various Precipitable Water at ap=100000 dbt=24.7
Decreasing the increment between the lower precipitable-water steps would improve interpolation accuracy.

The next pair of graphs shows the dependence of NIRT on ceiling-height and dry-bulb-temperature.

Plot of radiative transfers versus Ceiling Height for various Dry Bulb Temperature at ap=100000 pw=37.5

The next pair of graphs shows the dependence of cloudless NIRT on precipitable-water and dry-bulb-temperature.

Plot of radiative transfers versus Dry Bulb Temperature for various Precipitable Water at ap=100000 ch=16001

Finally, the dependence of NIRT on ground-level atmospheric-pressure is so small for the atmospheric-pressure range among the tropical TMY3 datasets that it can be ignored:

Plot of radiative transfers versus Ceiling Height for various Atmospheric Pressure at dbt=24.7 pw=37.5
The cool-roof page shows the results of running this model with Guam TMY3 data.

I am a guest and not a member of the MIT Computer Science and Artificial Intelligence Laboratory. My actions and comments do not reflect in any way on MIT.
		SimRoof
	agj @ alum.mit.edu	Go Figure!