Worksheet #22, ATOC 3600,  November 14, 2000 NAME: ____________________ 1a. Suppose the radiative imbalance caused by increased atmospheric CO2 results in a 4 W m-2 warming. If all this energy goes into heating the atmosphere with no other changes, how quickly will the atmosphere warm. Note the radius of the Earth is 6.36 x 106 m and the area is 1.27 x 1014 m2. Total heating is 1.27 x 1014 m2 * 4 W m-2 Total reservoir is 5.0 J gram-1 J K-1 x 106 x 1015 gram  The rate at which the atmosphere warms is equal to the heating rate divided by the reservoir size or 1.01x10-8 degrees per second or 0.3oK per year. 1b. Now imagine that once the atmosphere has warmed 5 degrees, half of the radiative flux imbalance goes into heating the surface ocean, and a quarter of the imbalance goes into heating the land surface. How quickly does the surface ocean warm? How quickly does the land surface warm? For the ocean, the total heating is 2.54x1014 W and for the land the total heating is 1.27x1014 W.  The reservoir for the surface ocean is 15.2 J gram-1 K-1 x 107 x 1015 g  and for land is 4.0 J gram-1 K-1 x 104 x 1015 g  Thus the heating rate for the surface ocean is 1.67x10-9 degrees per second or  0.052 oK per year and for the land surface the rate is 0.27oK per day or 100oK per year. 1c. Eventually, the atmosphere and surface ocean warm to a point at which the entire radiative imbalance goes into heating the deep ocean. How quickly will the deep ocean warm?  Total heating is 1.27 x 1014 m2 * 4 W m-2 Total reservoir is 5.6 J gram-1 J K-1 x 109 x 1015 gram  The rate at which the atmosphere warms is equal to the heating rate divided by the reservoir size or 9.07x10-11 degrees per second or 2.86oK per every thousand years. 1d. Propose a change in low and high clouds that would  mitigate the radiative imbalance caused by the anthropogenic greenhouse warming discussed above. In order to cool  the globe most efficiently, should an increase in clouds occur in the tropics, in the midlatitudes, or at the poles? Is an increase in high clouds or low clouds most effective at mitigating global warming? In order to cool the globe most effectively, one would want to increase the reflection of solar radiation without decreasing the top of atmosphere longwave flux. Low clouds reflect more solar radiation while having a minimal impact on OLR as compared to high clouds. Also, in the tropics, low clouds reflect more sunlight than in midlatitudes and have less of an impact on OLR because the lower troposphere is already optically thick in the tropics due to water vapor. Thus tropical low clouds are ideal for cooling the globe.