Being a pedant, it's important to consider the thermal mass of the
roof, as this makes a big difference to temperature variation.
Variations, in turn, greatly increase perception of discomfort - a
draft is cold, a cave is merely cool.
On 11 Nov 2017 23:27, "John Harte" <[email protected]
<mailto:[email protected]>> wrote:
I assigned that problem as a homework assignment in a course I
teach.
2. Consider a house in a relatively hot, sunny location such as
Southern California.
a. To keep the house cool without air conditioning, and thereby
reduce energy demand, its inhabitants decide to do one of two
things:
i. They can paint the roof white, increasing its albedo from
0.1 to 0.8, or
ii. They can grow a green roof, using a productive species of
grass that will increase the albedo of the roof from 0.1 to 0.2
and that, if watered and fertilized adequately, will cool the
house by transpiration. The rate of transpiration can be
estimated from the following: for every kg of grass produced, 300
kg of water are transpired, and the grass grows with an overall
photosynthetic efficiency of 1%.
a. Ignoring the issue of water supply, which of these strategies
(i. or ii.) will result in a cooler house? (20 pts.)
Solution: 2. a. First, let?s examine the effect of painting the
roof white. We?ll assume an average solar flux on the roof of 250
watts/m^2 (if you assumed anything between 170 and 300 we will
accept it.). By changing the albedo from 0.1 to 0.8, the home is
avoiding the absorption of 0.7 (250) = *175 watts/m^2 *, *which is
the benefit of plan i.* For plan ii., we need to estimate NPP on
the roof first. At 1% of available energy, the plants are
converting 2.5 watts/m^2 to biomass. Over a year, this is (2.5
joules/sec-m^2 ) x (3.1 x 107 sec) = 77.5 x megajoules/m^2
incorporated into biomass. Using the conversion: of 16
megajoules(dry biomass) per kg, we find that biomass is produced
at an annual rate of 77.5/16 = 4.8 kg (dry biomass0/m^2 . Now
using the 300:1 ratio of transpired water to photosynthesized
biomass, we get 4.8 x 300 = 1450 kg(transpired water)/year.
Transpiring a kilogram of water requires about 2.4 x 10^6 joules
(see COW Appendix) and so each year about 2.4 x 10^6 x 1450 = 3.5
x 10^9 joules/m^2 annually are causing transpiration rather than
heating the house. Expressed in power units, this is 3.5 x 10^9
(joules/m^2 )/3.1 x 10^7 sec= *113 watts/m^2 , which is the
transpiration benefit of plan ii. *But there is also a small
albedo benefit of grass versus dark shingle, so we get an
additional benefit which is 1/7 of the plan i. benefit (due to an
albedo increase of 0.1 rather than 0.7), so now we have 113 +
(1/7) 175 = *138 watts/m^2 , which is the albedo benefit of plan
ii.* *So plan i. wins by a little. *
The problem went on to evaluate the added benefit if you burn the
grass on the roof for fuel.
I actually replaced my dark shingle roof this autumn with
light-colored composition shingle. It makes a huge difference!
John Harte
Professor of Ecosystem Sciences
ERG/ESPM
310 Barrows Hall
University of California
Berkeley, CA 94720 USA
[email protected] <mailto:[email protected]>
On Nov 11, 2017, at 2:22 PM, Russell Seitz
<[email protected] <mailto:[email protected]>> wrote:
How do green roofs, which cool by evapotransportation ( rooftop
lawns require water much as those on the ground do) compare in
cooling efficiency with higher albedo white roofs combined with
an equal volume of water spraying when the sun is high?
On Saturday, November 11, 2017 at 12:16:10 AM UTC-5, E Durbrow
wrote:
Perhaps, tangental. Seville planners think they can cool
their city despite significant temperature increase with
204-700 hectares of green roofs.
Summary:
https://www.sciencedaily.com/releases/2017/11/171110113938.htm
<https://www.sciencedaily.com/releases/2017/11/171110113938.htm>
Comment: My layperson?s understanding is that it is very
difficult to predict and simulate city-wide changes in
temperature when a modification (e.g. reflective roofs, green
space, etc) occurs. I though I remember that reading that
reflective roofs might have no effect on local temperature
(city?s micro-climate). Modelers, is this the case?
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