SimRoof: Lambertian Model for Deserts

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

Lambertian Model

A flat Lambertian emitter radiates uniformly over the whole hemisphere.

Computing this Lambertian model entails 1008 radiative-transfer integrations and stores 2184 net-flow values:

ray-angle (6): 7.5°, 22.5°, 36°, 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 (7): −10°C, 0.1°C, 10.2°C, 20.3°C, 26.85°C, 40.5°C, 50.6°C
precipitable-water (8): 0 mm, 4.5 mm, 9 mm, 18 mm, 27 mm, 36 mm, 45 mm, 54 mm
atmospheric-pressure (3): 88.3 kPa, 96 kPa, 103.7 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 54 mm to 0 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=96000 dbt=26.85

The next pair of graphs shows the dependence of NIRT on ceiling-height and dry-bulb-temperature. For dry-bulb temperatures above 27°C, the model's radiator (roof) temperature does not follow (staying at 27°C). This causes heat inflow (warming, not cooling) at ambient temperatures above 27°C,

Plot of radiative transfers versus Ceiling Height for various Dry Bulb Temperature at ap=96000 pw=36

Plot of radiative transfers versus Dry Bulb Temperature for various Ceiling Height at ap=96000 pw=36

The next pair of graphs shows the dependence of cloudless NIRT on precipitable-water and dry-bulb-temperature. Dry-bulb temperatures above 27°C result in reduced NIRT.

Plot of radiative transfers versus Dry Bulb Temperature for various Precipitable Water at ap=96000 ch=16001

Plot of radiative transfers versus Precipitable Water for various Dry Bulb Temperature at ap=96000 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 could be ignored:

Plot of radiative transfers versus Ceiling Height for various Atmospheric Pressure at dbt=26.85 pw=36

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!