General circulation models do not impose a fixed relative humidity. Assumptions built into the models directly govern the relative humidity only in the sparse set of grid boxes that are actively convecting, where the choice of convection scheme determines the humidity. In the case of moist convective adjustment, the relative humidity after convection is explicitly set to a predetermined profile, whereas the mass flux schemes compute a humidity profile based on microphysical assumptions of varying complexity. The relative humidity elsewhere is determined by explicitly resolved dynamical processes, and in fact undergoes marked spatial (e.g., Figure 7.1b,c) and temporal fluctuations. Nonetheless, all models studied to date produce a positive water vapour feedback consistent with the supposition that water vapour increases in such a way as to keep the relative humidity approximately unchanged at all levels (Held and Soden, 2000). The strength of the water vapour feedback is consistent amongst models, despite considerable differences in the treatment of convection and microphysics (Cess et al., 1990).
The "convective region" is potentially a source of modelling errors, since the evaporation of detrained precipitation and other poorly characterised and heavily parametrized processes are essential to the moistening of the atmosphere. Tompkins and Emanuel (2000) showed that in a single-column model, numerical convergence of the simulated water vapour profile requires a vertical resolution better than 25 mb in pressure (see also Emanuel and Zivkovic-Rothman, 1999). Thus, the apparent lack of sensitivity of water vapour feedback in current GCMs to the way convection is treated may be an artefact of insufficient vertical resolution. An alternative view is that the water vapour flux is vigorous enough to keep the convective region at a substantial fraction of saturation, so that the details of the moistening process do not matter much. In this case the convection essentially extends the boundary layer into the free troposphere, making condensed water abundantly available to evaporation, but in the form of droplets or crystals. Indeed, Dessler and Sherwood (2000) find that satellite observations of tropical water vapour can be understood without detailed microphysical considerations, even in the convective region. Radiosonde observations (Kley et al., 1997) and satellite UTH data (Soden and Fu, 1995) reveal free troposphere relative humidities of 50 to 70% throughout the convective region. Udelhofen and Hartmann (1995) find that moisture decays away from convective systems with a characteristic scale of 500 km, so that convection need not be too closely spaced to maintain a uniformly moistened region. As noted by Held and Soden (2000), the evidence for the opposite view, that convective region air becomes drier as temperature increases, is weak.
This moistening of large-scale tropical subsiding zones by large-scale advection is a process explicitly resolved in models, and in which one can have reasonably high confidence. Care must still be taken with the design of numerical advection methods to avoid spurious transport. In this regard, there has been notable progress since the SAR as models are increasingly using semi-Lagrangian and other advanced advection methods in place of spectral advection of water vapour (Williamson and Rasch, 1994). These methods virtually eliminate spurious transport arising from the need to adjust negative moisture regions, as commonly happens in spectral advection.
In the extra-tropics the ubiquitous large-scale synoptic eddies which dominate moisture transport are explicitly represented in GCMs, and there is reasonably high confidence in simulated mid-latitude water vapour feedback. The eddies maintain a fairly uniform monthly mean relative humidity of 30 to 50% throughout the year (Soden and Fu, 1995; Bates and Jackson, 1997).
Simulation of water vapour variations with natural climate fluctuations such as the annual cycle and El Niño can help provide tests of the verisimilitude of models but may not be sufficient for assessing climate change due to increases in greenhouse gases (Bony et al., 1995). Models are quite successful at reproducing the climatological free tropospheric humidity pattern (e.g., Figure 7.1b,c). Model-satellite comparisons of UTH are still at a rather early stage of development; the AMIP simulations did not archive enough fields to provide an adequate understanding of UTH, and there are problems in determining which model level should be compared to the satellite data. Also there are uncertainties in UTH retrievals (see Chapter 2). Caveats notwithstanding, the ensemble mean of the AMIP simulations shows a moist bias in UTH compared to satellite data, but this result is rendered uncertain by apparent inconsistencies in the computation of model relative humidities for intercomparison purposes. The models studied by AMIP (Bates and Jackson, 1997) appear to show little skill in reproducing the seasonal or interannual variations of convective region UTH, though many show significant correlations between simulated and observed sub-tropical and extra-tropical UTH fluctuations. The latter lends some confidence to the simulated water vapour feedback, as the dry sub-tropics and extra-tropics account for a large part of the feedback. Del Genio et al. (1994) found good agreement between the observed seasonal cycle of zonal mean UTH, and that simulated by the GISS model.
Humidity is important to water vapour feedback only to the extent that it alters OLR. Because the radiative effects of water vapour are logarithmic in water vapour concentration, rather large errors in humidity can lead to small errors in OLR, and systematic underestimations in the contrast between moist and dry air can have little effect on climate sensitivity (Held and Soden, 2000). Most GCMs reproduce the climatological pattern of clear-sky OLR very accurately (Duvel et al., 1997). In addition, it has been shown that the CCM3 model tracks the observed seasonal cycle of zonal mean clear-sky OLR to within 5 Wm-2 (Kiehl et al., 1998), the GFDL model reproduces tropical mean OLR fluctuations over the course of an El Niño event (Soden, 1997), and the collection of models studied under the AMIP project reproduces interannual variability of the clear-sky greenhouse parameter with errors generally under 25% for sea surface temperatures (SSTs) under 25°C (Duvel et al., 1997). Errors become larger over warmer waters, owing to inaccuracies in the way the simulated atmospheric circulation responds to the imposed SSTs (which may also not be accurate). The LMD model shows close agreement with the observed seasonal cycle of greenhouse trapping (Bony et al., 1995), but models vary considerably in their ability to track this cycle (Duvel et al., 1997).
Indirect evidence for validity of the positive water vapour feedback in present models can be found in studies of interannual variability of global mean temperature: Hall and Manabe (1999) found that suppression of positive water vapour feedback in the GFDL model led to unrealistically low variability. An important development since the SAR is the proliferation of evidence that the tropics during the Last Glacial Maximum were 2 to 5°C colder than the present tropics. Much of the cooling can be simulated in GCMs which incorporate the observed reduction in CO2 at the Last Glacial Maximum (see Chapter 8). Without water vapour feedback comparable to that currently yielded by GCMs, there would be a problem accounting for the magnitude of the observed cooling in the tropics and Southern Hemisphere.
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