Excerpts from Evidence for Negative Water Feedback
by Clive Best
Abstract: Positive linear climate feedback for combined water effects is shown to be incompatible with the Faint Sun Paradox. In particular, feedback values of ~2.0 W/m2K-1 favored by current GCM models lead to non physical results at solar radiation levels present one billion years ago. A simple model is described whereby Earth like planets with large liquid water surfaces can self-regulate temperature for small changes in incident solar radiation. The model assumes that reflective cloud cover increases while normalized greenhouse effects decrease as the sun brightens. Net water feedback of the model is strongly negative. Direct evidence for negative water feedback is found in CRUTEM4 station data by comparing temperature anomalies for arid regions (deserts and polar regions) with those for humid regions (mainly saturated tropics). All 5600 weather stations were classified according to the Köppen-Geiger climatology . Two separate temperature anomaly series from 1900 to 2011 were calculated for each region. A clear difference in temperature response is observed. Assuming the difference is due to atmospheric water content, a water feedback value of -1.5 +/- 0.8 W/m2K-1 can be derived.
The Faint Sun Paradox was first proposed by Carl Sagan  who pointed out that the geological evidence that liquid oceans existed on Earth 4 billion years ago appears incompatible with a solar output 30% dimmer than today.
The sun is a main sequence star whose output is known to increase slowly with age. The total change in solar radiation over this long period turns out to be huge ~ 87 W/m2. It has been argued that an enhanced greenhouse effect due to very high CO2 and/or CH4 concentrations could resolve this paradox . However, recent geological evidence does not support CO2 as being responsible but instead the authors propose a greater ocean surface leading lower albedo as a likely solution . Others have suggested that high cirrus clouds effectively warmed the Earth . Although the atmosphere must have been very different before photosynthesis began, the presence of large liquid oceans still implies that clouds and water vapor played a similar role in the Earth’s energy balance then, as they do today.
Figure 1: Past temperatures extrapolating backwards from today (T=288ºK) assuming different linear feedback values.
It is apparent that a simple linear positive feedback of +2 leads to unphysical results. The basic problem is that if the temperature falls sufficiently so that 4σT3= F then a singularity occurs ~1.5 billion years ago. Instead a negative feedback value of -2 W/m2K-1 is more compatible both with current temperatures and with the Faint Sun Paradox..
IV. CRUTEM4 ANALYSIS
Water vapor feedback in recent climate data have been investigated by studying differences between regions with very low atmospheric water vapor (Deserts and Polar) and those regions with very large water vapor content (Tropical Wet regions). The latest CRUTEM4 data  consisting of 5500 individual station data covering global land areas has been studied. Each station was classified by indexing its geographic location against the Köppen-Geiger climate classification .
“ARID” stations are defined as those with precipitation values ‘W’ or with climate ‘E’ in . These are situated either in deserts or in polar areas having the lowest atmospheric water column on Earth . “WET” stations are defined as those within fully humid Tropical areas – Climate ‘A’ and precipitation ‘f’ in . These are situated in tropical rain forests or year-round humid climates having the highest atmospheric water column on Earth . Global anomalies have been calculated for both stations ARID and WET stations independently using the same algorithm as used for CRUTEM4. The results are shown in Figure 4.
Figure 4: Temperature anomalies for ARID(DRY) stations in red and WET stations in blue. The smooth curves are FFT smoothed curves. The black dashed curve is an FFT smooth to the full CRUTEM4 global temperature anomalies.
There is a clear trend in the data that ARID stations warm faster and cool faster than WET stations. They respond stronger to changes in external forcing. The WET humid stations respond less than both the ARID stations and the global average.
Climate change is complex and global so it is reasonable to assume that both anthropogenic and natural forcing are reflected in the temperature anomaly data. For a given forcing DS the consequent change in temperature anomaly is gDT where g is a gain factor. The period between 1900 and 2005 is used to measure the temperature rise for each region DT1 and DT2 as given in Table 1. DS is assumed to be global in extent.
Table 1 : Temperature changes for ARID and WET regions and their ratio. Errors on DT are derived from differences between the FFT smooth and a linear fit.
|1900-2005||1.1 +/-0.1 ºK||0.8+/- 0.1 ºK||1.4 +/- 0.2|
Heat inertia effects due to nearby oceans may cause tropical climates to react slower than desert regions, but not over such long periods. If positive feedbacks from increased water evaporation lead to enhance warming then this should be apparent in the tropics, and this is not observed. In fact the opposite is the case implying a negative feedback. Under the assumption that net water feedback F is present only for the WET stations (taking F=0 for ARID stations) then F can be measured from the data:
DT1/DT2 = 1 – G0F , where DT1 = G0DS and DT2 = G0 (DS+FDT2)
For G0-1 = 3.75W/m2K gives Water Feedback F = – 1.5 +/- 0.8 W/m2K-1
This is compatible with the value needed to resolve the Faint Sun Paradox. As has been pointed out by Lindzen  and others, much of the Earth’s heat is transported bodily through evaporation and convection to the upper atmosphere where IR opacity is low and can then escape to space. Therefore water feedback effects depend mostly on the water vapor content of the upper atmosphere. Increased evaporation, convection and consequent rain out could then result in lower humidity in the upper atmosphere. This is a possible mechanism for negative feedbacks in the tropics. Such effects would be largely absent in ARID areas, which have no local sources of evaporation.
Read the entire analysis here, it is well worth your time, well written, and easy to comprehend.
h/t to Scott Gates