models for the atmosphere with ocean models. Here, theclimate tends to drift unless one applies so-called flux corrections. Examples of such corrections are given for all the leading models ( 4 ). The corrections have to be applied on a latitude-by-latitude basis, and the magnitude of the correction can be as large as 100 W·m-2. As can be understood from our discussion of the realistic nature of the greenhouse effect, these dynamic fluxes do not represent systematic biases independent of the CO2 forcing; rather they are essential to calculating the response to increased CO2. The issue is not that the forcing due to CO2 is buried within these larger uncertainties, but rather whether we can reckon the response reliable.
The role of water vapor is nonlinear. Assuming 80% relative humidity in a 2-km boundary layer, and a fixed relative humidity above the boundary layer, Fig. 1 shows how, for a given temperature distribution, outgoing long-wave radiative flux varies as one perturbs the relative humidity above the boundary layer [ Fig. 1 was calculated using the radiative transfer code ( 5 ); a similar calculation appears in ref.6 ]. One sees that the effect of a 5% change in relative humidity depends on the base humidity being perturbed. For low base humidities, a 5% change is associated with about 5 W·m-2. For high base humidities, the change is about half of this. For purposes of comparison, the 4 W·m-2, which a doubling of CO2 is expected to produce, is roughly equivalent to a 4–8% change in relative humidity. Note that uncertainties in measurements of humidity are on the order of 20% or more, though things appear to have improved over the past 2 years. We shall look at the improved data soon. However, it is again clear that we are dealing with uncertainties and errors that are large compared with the climatic impact of CO2. Here too, these errors occur in a field that is crucial to calculating the response to CO2, since the water vapor feedback is essentially responsible for the model predictions of large warming due to increasing CO2. Clearly, even superficial agreement between observations and model-derived water vapor would be inadequate to establish the model feedback.
This potentially important positive feedback was first identified by Manabe and Wetherald ( 7 ). Using a simple one-dimensional radiative–convective model, they found that assuming constant relative humidity led to a significantly enhanced response to increased CO2 over what would have been obtained with fixed specific humidity. The point, simply, is that with fixed relative humidity, specific humidity must increase with warming. Upper-level water vapor (above 2–3 km in the tropics) dominates the radiative role of water vapor, despite the fact that most of the atmosphere’s water vapor is found below 800 millibars [1 millibar (mb) = 100 Pa] ( 8 ). Of course, given the nonlinearity of the radiative effect of water vapor, the average radiative response to water vapor is not equal to the response to an average water vapor, and, therefore, one-dimensional studies are inappropriate. However, the results of the above one-dimensional studies remain indicative of general properties.
The most useful way of viewing feedbacks is by means of the formula
where fi is the ith feedback factor. For fixed relative humidity, the water vapor feedback factor is about 0.4. This turns out to be much larger than the factors due to clouds and snow in present models. However, as may be seen from the formula, the addition of smaller factors on top of the 0.4 due to water vapor rapidly increase the response. Without the water vapor feedback the impact of model cloud and snow feedbacks would be small ( 2 ).
It is worth reviewing the basis for the assumption of constant relative humidity in ( 7 ). It is based on the crudely observed picture from ref. 9 reproduced in Fig. 2 . It was argued in ( 7 ) that the overall relative humidity varied only between about 30% and 50%, and that the pattern was similar for both winter and summer, suggesting that the atmosphere was attempting to maintain a given relative humidity regardless of temperature. There were, of course, very few measurements available for ref. 9. However, subsequent analyses of radiosonde data showed a fairly similar picture ( 10 ). Unfortunately, the radiosonde data have proven extremely unreliable ( 11 ). In particular, radiosonde data tended to replace readings of very low humidity with relative humidities of 20%. Nevertheless, these primitive observations received a certain amount of credibility insofar as they were consistent with humidities predicted in general circulation models (GCMs). However, recently, the 183-GHz channel on the SSM/T-2 satellite has provided detailed data on the global distribution of relative humidity. Fig. 3 shows a global daily map for relative humidity between 500 and 300 mb for May 5, 1995. We see hugely more variability