heat radiating upward from roof http://people.csail.mit.edu/jaffer/SimRoof/Introduction

SimRoof: Introduction


In the tropics, the roof tends to be the dominant conduit of solar heat into single-story dwellings[60] (and warehouses). And, unless perched alone on a mountaintop, the roof is also the dominant source of radiative cooling. Roofs, then, are an important part of the thermal design for tropical buildings.

How can the performance of roof systems in hot humid climates be quantified?

One could simulate a dwelling with various roof designs through the same typical-meteorological-year, evaluating some criteria for thermal comfort inside the dwelling. Such an approach is fraught with difficulties:

Prior Work

Radiative cooling power of each sample even under the sun was estimated with the measured spectral reflectance, and meteorological data (OM institute, Japan) for each day in 1994 at Nagoya, Japan. The meteorological data include temperature, flux of direct normal solar radiation, global solar radiation, nocturnal radiation, and solar altitude hourly.

They present graphs of net radiative cooling during two 24 hour periods in Nagoya Japan. Unfortunately, they do not present statistics for radiative cooling throughout a year.

Nagoya is at 35°11'N latitude and receives 1.56 m of rain per year.

The DOE-2 Energy Use and Cost Analysis Software from Oak Ridge National Laboratory and Lawrence Berkeley National Laboratory is the basis for several applications:

The Roof Savings Calculator was developed as an industry-consensus roof savings calculator for commercial and residential buildings using whole-building energy simulations. It is built upon the DOE-2.1E engine for fast energy simulation and integrates AtticSim for advanced modeling of modern attic and cool roofing technologies. An annual simulation of hour-by-hour performance is calculated for the building properties provided based on weather data for the selected location. Annual energy savings reported are based upon heating and cooling loads and thus this calculator is only relevant to buildings with a heating and/or cooling unit.
The DOE Cool Roof Calculator Estimates Cooling and Heating Savings for Flat Roofs with Non-Black Surfaces[58]. It was developed by the U.S. Department of Energy's Oak Ridge National Laboratory (Version 1.2).

This version of the calculator is for small and medium-sized facilities that purchase electricity without a demand charge based on peak monthly load.

The DOE Cool Roof Calculator Estimates Energy and Peak Demand Savings for Flat Roofs with Non-Black Surfaces[59]. It was developed by the U.S. Department of Energy's Oak Ridge National Laboratory (Version 2.0).

This version of the calculator is for large facilities that purchase electricity with a demand charge based on peak monthly load.

All three programs compute comparisons between two roofs, one being a "black roof" in the case of CoolCalcEnergy and CoolCalcPeak. Because the black-roof and most existing roofs (asphalt shingle in particular) have high thermal-emissivity, and because roof performance is less sensitive to thermal-emissivity than to solar-reflectance[58], and because the CoolCalcEnergy (and CoolCalcPeak) model was tested against measurement only under cloudless conditions[58], these tools don't model downward thermal-infrared radiation and its variation.

Always comparing two (virtual) buildings also avoids the comfort issue[58]:

The implicit assumption is that the inside air temperature must be the same with and without radiation control. Estimates with the tool should be valid despite different thermostat set points during the heating and cooling seasons, as long as the same schedule is followed with and without radiation control. If, in practice, radiation control permits a higher cooling thermostat set point, the estimating tool will underpredict savings.

These three programs are tailored to north-American buildings with heating or cooling units, and not directly applicable to the passive tropical buildings of interest here.

SimRoof is more ambitious. It can be used to estimate how many people can occupy a passively cooled building comfortably at a given level of availability (electrically cooled buildings also have availability limits from their dependence on electricity).

The Component Approach

The approach here is to treat the roof as a thermal component with (radiative) power inputs and power outputs. Simulation through the typical-meteorological-year of Guam will allow estimation of the number of hours of roof cooling or heating at various times-of-day and weather conditions in the humid tropics. Simulation with other TMYs will produce estimations for other regions.

SimRoof deals only with low-slope roofs because low-slope roofs are exposed mostly to sky. To model high-slope roofs requires infrared characterization of the surrounds, losing the uniformity needed to treat the roof as a component.

Instead of simulating a building below it, the simulated temperatures of the roof are set to the hourly ambient (dry-bulb) temperatures from the typical-meteorological-year, limited by a maximum goal temperature. The roof being at or below ambient temperature eliminates convection processes, simplifying calculations (convection is modeled for solar-reflecting screens). All roofs will shed heat at a greater rate as their temperature rises above ambient. But under conditions where an uninsulated roof is suffering such a large net increase in heat (hence temperature) that convection becomes significant, the dwelling would be too hot to occupy.

Buildings in temperate zones may be called upon to maintain 40°C temperature differences from ambient (20°C vs −20°C). With such large differences, drafts and poor insulation can overwhelm the thermal properties of the roof.

If a roof starts out at ambient temperature, then it will warm or cool due only to radiation absorbed and emitted by it. It thus functions as a component independent of the walls, windows, and floor, no matter what their R-values are. This independence is mostly preserved even when the roof temperature differs from ambient by only a few degrees. Buildings in humid tropical zones will rarely need to maintain temperature differences of more than 10°C (27°C vs 37°C); so calculations at ambient temperature can be reasonably extrapolated to slightly cooler interiors (as controlled by the maximum-goal-temperature).

Although the roof may not dominate the solar heat gain and radiative heat loss of other types of buildings, characterizing the roof as a component in a specific climate allows it to be evaluated for reducing cooling costs in industrial, commercial, and retail space.


Although we don't know which combinations of temperature and humidity are comfortable for tropical dwellers, we do know that a roof which is unable to remove the heat (sensible + latent) produced by the occupants' bodies will be unable to maintain those comfortable conditions.

On the http://www.engineeringtoolbox.com website, the metabolic rates given by Persons and Metabolic Heat Gain for a sedentary adult male range from 100 W to 130 W; Met - Metabolic Rate gives a "reclining" rate of 83 W (presumably adult male); I can't find a metabolic rate for sleeping persons.

So the goal for a simple tropical roof is a net heat loss of (at least) 83 W per sleeping occupant and somewhat more for active occupants.

As this project has grown to encompass US subtropical deserts, the assumption that the interior temperature is near to the outdoor ambient temperature becomes unworkable. Dry-bulb temperatures there range up to 50°C, which can be lethal for humans (who have an internal temperature of 37°C).

The ENERGY STAR® Program Requirements for Programmable Thermostats Eligibility Criteria (Version 1.2) contains two tables:

Table 1: Programmable Thermostat Setpoint Temperatures
SettingSetpoint Temperature (Heat)Setpoint Temperature (Cool)
Daysetback at least 8°Fsetup at least 7°F
Sleepsetback at least 8°Fsetup at least 4°F

Table 2: Acceptable Setpoint Times and Temperature Settings
SettingTimeSetpoint Temperature
Setpoint Temperature
Wake6 a.m.70°F78°F
Day8 a.m.62°F85°F
Evening6 p.m.70°F78°F
Sleep10 p.m.62°F82°F

78°F is 25.6°C
82°F is 27.8°C
85°F is 29.4°C

For simulating desert locations the indoor temperature will be set to the minimum of the current (simulated) dry-bulb temperature and 27°C (300.15 K). Note that limiting the interior temperature to 27°C reduces the amount of radiative cooling available; warmer temperatures would radiate more.

Copyright © 2010, 2011 Aubrey Jaffer

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.
agj @ alum.mit.edu
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