Negative Feedbacks

November 3, 2007 Estimations of Water Feedback in USA Locations in July (See feedback.xls, and feedback1a.xls below) I think I finally got a semi-quantitative handle on the effects of water on temperature. I say semi-quantitative, because the analyses are based on correlations between empirical data, and the correlations are not perfect. However, I think they are sufficient to conclude without any doubt that both water vapor and clouds have significant negative effects on temperature. I think I can finally explain why it is 5 degrees C hotter in July in Daggett, CA than in Birmingham AB. As before, my approach involves comparing 30-year average temperature, humidity, and solar radiation data for various locations in the USA. Water Vapor Feedback Since temperature is closely related to latitude and altitude, it is problematical to compare different locations, due to variations in these parameters. In order to “account” for these differences, I adjusted the data in the following way. To account for altitude effects, I adjusted temperatures using standard lapse rates. Since there is no way to know exactly what the average lapse rate is for any given location, I simply used an average rate of 5.5 degrees/km, derived from the average of the average moist lapse rate (4.9 degrees/km) and the dry lapse rate (6.2 deg/km). This constant was multiplied by the elevations in km. To account for the effects of latitude, I divided the locations into nine 3-5 degree latitude “bands,” and assumed that solar insolation at the top of the atmosphere is constant within the 3-5 degree bands. It was necessary to use latitude bands to provide a sufficient number of locations (data points) for each band. For the locations falling into each band, I then plotted the following: (1) relative humidity vs. temperature; (2) relative humidity vs. “adjusted” temperature (adjusted for lapse rate as described above); and (3) absolute humidity vs. “adjusted” temperature. The plots are shown in the spreadsheets to the right of the data. A linear relationship was assumed for all plots. In the case of the plots of relative humidity with unadjusted temperature, the trends in all latitude bands showed a negative correlation of temperature with increasing humidity. The correlation coefficients (R2) varied from 0.00 to 0.84 for the nine latitude bands, with the higher coefficients corresponding to latitude bands in which nearly all locations were at similar elevations. In the case of the plots of relative humidity against adjusted temperatures, the correlation coefficients improved greatly. They ranged from 0.52 to 0.85 for the nine latitude bands. Again, all trends showed a decrease in temperature with increasing relative humidity. The differences between these plots and those

using unadjusted temperature demonstrate the importance of altitude on the relationships. In the case of the plots of absolute humidity against adjusted temperatures, the correlation coefficients ranged from only 0.05 to 0.34, with most being around 0.2. However, again, all trends showed a decrease in temperature with an increase in absolute humidity. As expected, the slopes of the trend lines differed between latitude bands, so I also plotted the slopes against latitude for the 9 relative humidity/adjusted temperature curves and for the 9 absolute humidity/adjusted temperature curves (shown below the data). These plots showed linear relationships between the slope of the humidity temperature curves and latitude. Using these plots, I estimated the effects of relative humidity and absolute humidity on temperature at different latitudes. The relative humidity plot shows that a 1% increase in relative humidity decreases temperature of from 0.14 to 0.32 degrees C, in going from 20 to 60 degrees latitude (R2 = 0.61). The absolute humidity plot shows that each 1 g/m3 increase in absolute humidity decreases temperature by from 0.26 to 1.03 degrees C in going from 20 to 60 degrees latitude (R2 = 0.54). Cloud feedback. To estimate the effects of cloud feedbacks, I assumed that the amount of solar radiation received by each location in a latitude band is an inverse measure of cloudiness., since the total radiation at the top of the atmosphere is relatively constant for each band. I then plotted adjusted temperature against solar insolation for each latitude band, obtaining correlation coefficients that varied from 0.13 to 0.86. As with the humidity data, I also plotted the slopes of these curves against latitude to obtain a measure of variation with latitude. The resulting plot has a correlation coefficient of 0.16 and shows that a decrease of 1 kwh of insolation (more clouds) results in a decrease in temperature of 1.36 to 2.3 degrees C in moving from 20 to 60 degrees in latitude. Other observations. I noticed that those western locations situated directly adjacent to the Pacific Ocean were always outliers in the plots, presumably due to the chilling effect of the Pacific marine influence and onshore winds. Thus, I left those locations out in the second spreadsheet (negative feedback1a.xls). Omitting these locations greatly improved correlations between absolute humidity and adjusted temperature, between relative humidity and adjusted temperature, and between solar insolation and adjusted temperature. It also had have some effect the final feedback quantification results. Omitting the locations had little effect on the relationships between solar insolation and temperature.

How do the predictions agree with reality? Not bad, if one uses the absolute humidity/corrected temperature relationships! For example, there is an actual adjusted July temperature difference of 7 degrees C between Daggett, CA and Birmingham, AB. If one uses the absolute humidity/corrected temperature relationship for the relevant 35 degree latitude (based on data that includes West Coast locations), one obtains a 5.8 degree difference between the locations (4.5 degrees, if West Coast locations are omitted). If one then uses the “cloudiness” data (same whether West Coast data are included or not), one obtains another 4.8 degree difference between the locations. The total would then be 10.6 degrees (West Coast included) or 9.3 degrees (West Coast data excluded), which is higher than the actual 7 degree difference. Thus, the effects are not additive. In fact, one would not expect the negative feedbacks for humidity and for cloudiness to be additive, since increased water vapor feedback undoubtedly also decreases the amount of solar insolation received at ground level. Moreover, cloudiness is associated with higher humidity, confounding the situation. However, the calculations are certainly in the ballpark. The relative humidity/corrected temperature relationship, on the other hand, overpredicts the temperature difference between Daggett and Birmingham. Using data from this analysis to calculate the relative humidity-caused negative feedback expected between these locations, one obtains a 10 degree difference (even without any “cloudiness” effects). Obviously, the use of the relative humidity relationship over estimates the true effects. Thus, it appears that the absolute humidity/corrected temperature relationship is better.