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/m2 (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/m2, 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/m2 to biomass. Over a year, this is (2.5 joules/sec-m2) x (3.1 x 107 sec) = 77.5 x megajoules/m2 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/m2. 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 106 joules (see COW Appendix) and so each year about 2.4 x 106 x 1450 = 3.5 x 109 joules/m2 annually are causing transpiration rather than heating the house. Expressed in power units, this is 3.5 x 109 (joules/m2)/3.1 x 107 sec= 113 watts/m2, 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/m2, 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] > On Nov 11, 2017, at 2:22 PM, Russell Seitz <[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? > > -- > You received this message because you are subscribed to the Google Groups > "geoengineering" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/geoengineering > <https://groups.google.com/group/geoengineering>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "geoengineering" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/geoengineering. For more options, visit https://groups.google.com/d/optout.
