http://people.csail.mit.edu/jaffer/SimRoof/PerfectLambertian
	SimRoof: Lambertian Perfromance Limits

• Introduction
• Sites
• Weather
• Net Radiative Transfer
• Lambertian Perfromance Limits
  • Limit Cases
  • Perfect Lambertian in the Tropics
  • Perfect Lambertian in the Southwestern US Deserts
  • Analysis
• CoolRoof
• Roof Convection
• Solar Screen Model
• Solar Screen Performance
• Thermal Infrared Optics (footnotes and supplemental information)

Limit Cases

A flat Lambertian emitter radiates uniformly over the whole hemisphere.

Note: In a scatter-plot two points at identical locations look no different from one point at that location. In order to reduce this effect, SimRoof dithers Typical Meteorological Year (TMY3) data values by up to half their resolution (as measured when the TMY3 file is read).

The top left plot shows the maximum diurnal radiative cooling at ambient temperature versus the simultaneous solar irradiance in Guam. Notice that the solar range is ten times the radiative cooling range. A perfect CoolRoof would reflect all solar radiation while having a thermal-infrared emissivity of one. It would have the hourly cooling distribution shown in the top right plot.

Available Cooling vs Solar Irradiance	Perfect CoolRoof
Solar Irradiance	Totally Absorbing Roof

The bottom left plot shows the hourly distribution of solar irradiance impinging on a horizontal roof. The bottom right plot shows the net heating of a perfectly absorbing and emissive roof.

Next we examine the first, tenth, median, ninetieth and ninety-ninth percentiles of available cooling versus solar radiance and time:

Available Cooling vs Solar Irradiance	Perfect CoolRoof

The "Perfect CoolRoof" graph shows that:

• The roof will provide more than 7 W/m² of cooling 99% of the time;
• the roof will provide more than 22 W/m² of cooling 90% of the time;
• the roof will provide more than 60 W/m² of cooling 50% of the time (the median);
• the roof will provide more than 80 W/m² of cooling only 10% of the time;
• the roof will provide more than 90 W/m² of cooling only 1% of the time.

For a perfect CoolRoof in Guam, the radiative cooling available varies little with time-of-day. We can plot availability versus ambient temperature:

Available Cooling vs Temperature	Histogram of Ambient Temperature

This histogram shows that performance below 23°C is unimportant because there are few such hours.

Perfect Lambertian at Other Sites

The limit cases discussed above are for the 912120TY TMY3 (Guam). The links below are to pages with scatter-plots, for each tropical or southwestern US desert TMY3 in Class I or II, of hourly net-infrared-radiative-transfer (NIRT) versus time of day and diurnal (daytime) NIRT versus dry-bulb-temperature. They are in order of increasing distance from the equator.

Some of the NIRT-vs-DBT plots show vertical banding. Most of the TMY3 datasets seem to include temperature measurements with different precisions. A precision of 1° Fahrenheit is common, so the temperature values are dithered by 5/9°C.

• Perfect Lambertian in the Tropics
• Perfect Lambertian in the Southwestern US Deserts

Analysis

The tropical locations have wide variation in the amount of Lambertian radiative-cooling possible. At 99% availability, Lanai, Hawaii has less than 7 W/m², while Mercedita, Puerto Rico has 20 W/m². At 90% availability, Hilo International Airport, Hawaii has 11 W/m² of cooling, while several sites have 40 W/m².