1. Introduction
Reducing the uncertainties in predictions of future climate is one of the most pressing issues in atmospheric science today. Projections of surface warmings as large as 5.8°C over the next 100 years are based largely on the expectation of a positive water vapor feedback in the atmosphere (Cubasch et al. 2001). In most global climate models, an initial warming caused by additional CO2 and other greenhouse gases leads to enhanced evaporation at the surface and a general moistening of the atmosphere. Since water vapor is a strong infrared absorber, the added moisture causes further warming. The amplifying effect can be quite large, increasing the global average warming by 70%–90% compared to calculations that maintain fixed water vapor (Cess et al. 1990).
Observational studies have attempted to verify the positive water vapor feedback by examining the response of atmospheric humidity to changes in surface temperature caused by interannual variability, the annual cycle, volcanic eruptions, and the El Niño–Southern Oscillation (Chou 1994; Sun and Oort 1995; Inamdar and Ramanathan 1998; Blankenship and Wilheit 2001; Soden et al. 2002). Results have been inconclusive, however, with some studies yielding a positive feedback and others indicating a negative response. Aside from the analyses by Soden (1997), Soden and Fu (1995), and Yang and Tung (1998), which examined Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) mean humidities within a broad layer from 5 to 12 km, none of the empirically based feedback studies focused specifically on humidity in the upper troposphere (UT) of the Tropics (between about 10 and 14 km). It has been pointed out that water vapor radiative effects in this region are important for global climate (Pierrehumbert 1995; Held and Soden 2000).
There are several plausible mechanisms for creating a negative water vapor feedback in the UT (see, e.g., the review by Held and Soden 2000). One oft-cited mechanism invokes the drying effects of deep cumulus convection, arguing that the mean detrainment altitude of deep convection will be both higher and cooler in a warmer climate compared to the present. Because the water vapor content of air pumped into the UT by convection is governed by the saturation vapor pressure at the temperature of cloud detrainment, this would imply a reduced supply of water at warmer surface temperatures, leading to drying and a negative feedback on climate (Lindzen 1990). Here, we test the convective drying mechanism using a model specifically designed to examine the moisture content of the UT in the Tropics. Implications for the water vapor feedback are also examined using measurements of relative and specific humidities in the tropical UT from microwave and infrared limb-viewing instruments on board the Upper Atmosphere Research Satellite (UARS; Dessler et al. 1998).
2. Model physics
Equations (1), (2), and (3) are tightly interconnected: Mc is a function of QR and T, QR is a function of q and T, and q is a function of Mc and T. Recent work has shown that the above equations describe the present-day UT well. Folkins et al. (2002) inserted climatological profiles of q and T into Eqs. (1) and (2) to derive the corresponding climatological profile of Mc. This Mc profile was then used in Eq. (3) to derive a q profile. The derived q profile agreed well with the climatological q profile between about 11 and 14 km. This is further confirmed by more sophisticated trajectory models, in which water vapor at pressure levels of 146 and 215 mb—between 11 and 14 km—is well described by detrainment of saturated air and subsequent advection by the large-scale flow (Dessler and Sherwood 2000), and neglecting any contribution from the evaporation of condensate to the mean UT water vapor budget. In the midtroposphere below 10 km, water vapor predicted by Eq. (3) is drier than the observations, suggesting that vertical mixing or evaporation of cloud condensate plays an important role in the middle and lower troposphere (Renno et al. 1994; Folkins et al. 2002).
Solutions to the above three relations, which involve four unknowns (Mc, QR, T, and q), require an additional relationship and a boundary condition. Previous studies that used a similar 1D approach to radiative–convective equilibrium employed constraints on Mc, and forced radiative cooling to adjust to the resulting cumulus heating profile (Minschwaner and McElroy 1992; Sun and Lindzen 1993; Sinha and Allen 1994). Here, we adopt constraints on tropical temperatures, relying on the observation that the current tropical atmosphere is nearly moist adiabatic (Xu and Emanuel 1989; Williams et al. 1993) and is expected to remain so over a range of changing surface temperatures (Betts and Ridgway 1992). Given a specified mean surface temperature and relative humidity, the moist pseudoadiabatic profile is calculated. Model temperatures in the convective adjustment region are equal to this moist pseudoadiabat, reduced by a universal profile of buoyancy. The buoyancy profile is symmetric, set to zero at the top and bottom of the convective adjustment region, and reaches a maximum of 4 K at the midpoint.
Temperatures are calculated in this way from the surface upward to the altitude where the radiative equilibrium lapse rate becomes subadiabatic. We define this level to be the top of convection, which closely coincides with the zero net radiative cooling level. Air above this altitude is rising as part of the mean stratospheric circulation; temperatures here are calculated to provide a balance between net radiative heating and dynamical cooling with an ascent rate of 1/40 km day−1, consistent with current estimates of vertical velocities in the tropical lower stratosphere (Dessler et al. 1996). Rates of radiative heating and cooling [Eq. (2)] throughout the troposphere are calculated using the National Center for Atmospheric Research (NCAR) Community Climate Model 2 (CCM2) radiation model (Briegleb 1992a,b). The model is maintained on a fixed-pressure grid, with 300 levels from the surface to approximately 30 km and a mean layer thickness of 100 m. This fine vertical resolution is necessary to capture small changes in the maximum height of convective detrainment and in vertical gradients of the subsidence mass flux in the UT. Three additional model levels are included to extend the model up to the stratopause.
3. Results
Model temperatures corresponding to three different values of surface temperature and 85% surface relative humidity (Liu et al. 1991) are displayed in Fig. 1. Mean temperatures from Truk, in the Federated States of Micronesia (FSM), which are typical of the Pacific warm pool region, are quite similar to our model case with 301-K surface temperature. We note that the inclusion of dynamical cooling by the Brewer–Dobson circulation is crucial to adequately simulate the height and cold temperature of the tropopause, a problem that has long plagued tropical radiative–convective models (Mahlman 1997). In addition, the calculated convective top appears roughly 2 km below the cold point, similar to observations. The model also shows that increasing surface temperatures lead to a higher and warmer convective top and cold point tropopause.
By specifying details of the profile of Mc, previous radiative–convective model studies of the tropical water vapor feedback did not incorporate the full coupling of Eqs. (1)–(3) into their analyses. In so doing, these models might have missed important responses in the UT to climate forcings. In contrast, our model allows Mc to freely adjust, and instead constrains the temperature profile to remain close to the moist adiabat. The model uses the temperature profiles described above and iteratively solves Eqs. (1)–(3) to produce QR, Mc, and q profiles that are consistent with each other and with the temperature distribution over the altitude range between 11 and 14 km. Below this, we assume an exponential increase in the water vapor mixing ratio between the value predicted at 11 km and the lifted condensation level. Stratospheric water vapor is fixed by the calculated temperature of the tropopause (assuming 75% relative humidity at the cold point).
Ozone is another important radiatively active gas, and it is calculated above the top of convection by assuming a balance between production via ultraviolet photolysis of O2 and upward transport of ozone-poor air from below (Dessler et al. 1996). Tropospheric ozone is determined by the detrainment of air with a value of 20 ppbv, coupled with a net production rate of 1 ppbv day−1. Unless otherwise noted, CO2 is set to a current mean value of 360 ppmv.
Figure 1 shows how the calculated subsidence flux, which by mass conservation must equal the net upward flux in cumulus convection, responds to changes in surface temperature. As the surface warms, convection penetrates to higher altitudes and the mass flux becomes larger near the top, consistent with larger net rates for radiative cooling in the UT. However, the subsidence rate becomes smaller in the middle troposphere. This result is related to a decrease in temperature lapse rate between about 5 and 10 km, as expected on the basis of a near-moist-adiabatic temperature profile. In addition, the fractional increase in radiative cooling with surface warming is smaller in the middle troposphere in comparison to the UT.
Water vapor profiles are shown in Fig. 2 along with tropical mean observations. As with the case of temperatures and in agreement with Folkins et al. (2002), we find that model UT water vapor with 301-K surface temperature agrees well with the present tropical atmosphere. Our results further show an increasing water vapor mixing ratio as the surface warms, contrary to the convective drying hypothesis. The response seen in our model is the net of two opposing effects. Warming of the UT, in the absence of any other changes, leads to increases in the moisture content of convective detrainment and higher water vapor mixing ratios. In contrast, raising the altitude of detrainment in a fixed temperature profile leads to reduced moisture detrainment and smaller UT mixing ratios. It must be noted that the changes in temperature and detrainment level are linked through Eqs. (1)–(3) and cannot vary independently. Based on our results, warming dominates over higher detrainment, leading to increasing UT water vapor with surface temperature and a positive climate feedback. Clearly, the consistency between Mc, QR, and q is an important part of the model, as is the high vertical resolution required to capture the large gradients in Mc and q in the UT.
The calculated increase in water vapor mixing ratio is not large enough to preserve the relative humidity at a fixed value, as shown in Fig. 2. We find that relative humidity in the UT decreases with increasing surface temperature, on the order of 3%–5% per degree of surface warming. Thus, aspects of the drying mechanisms outlined by Lindzen (1990) are operating in the UT of our model, but not sufficiently to overcome the influence of the Clausius–Clapeyron relation.
Fractional changes in both specific and relative humidities are quantified in Fig. 3. The fractional change in specific humidity increases from 0.1 K−1 at the base of the UT to a maximum of about 0.3 K−1 near the highest level of convective detrainment. The corresponding fractional changes in relative humidity are −0.2 to −0.05 K−1. A similar trend of decreasing RH with warmer temperature was found by Sun and Oort (1995) using radiosonde observations at altitudes slightly below the UT.
In contrast to these results, the mesoscale model study by Larson and Hartmann (2003) indicated a small increase in UT relative humidity with surface temperature of about +1% RH per degree of warming. The cloud resolving model used by Tompkins and Craig (1999), however, indicated a decrease in relative humidity between 10 and 12 km, which was roughly −2% RH per degree surface warming. The different behavior is likely related to details of the cumulus parameterizations used in these models, which included schemes for simulating high clouds and cloud microphysics. Both models also employed much coarser vertical resolution in the UT, with about four model levels between 11 and 14 km, compared to the ∼30 UT levels used in the present study.
The water vapor feedback shown in Fig. 3 is also weaker than that found in a number of general circulation models (GCMs), where relative humidity is found to be nearly invariant throughout the troposphere (Cess et al. 1990; Soden et al. 2002). In comparison to the equilibrium model of the tropical UT presented here, GCMs are confronted with a substantial number of complexities, such as the need to account for surface fluxes, precipitation, evaporation, and long-range transport of water vapor. A detailed discussion of the parameterizations used to represent the physics of moist convection in GCMs is beyond the scope of this paper [some of the more popular schemes are discussed in Emanuel (1994)], and specific causes for the different behavior are difficult to pinpoint. Sun and Held (1996) have postulated that relative humidities in general circulation models may be overly constrained by the strength of vertical mixing that occurs during convective adjustment.
The humidity feedback in our model can also be quantified by the standard measure of response to a doubling of CO2. In the absence of any change in water vapor, we find a tropical surface warming of 0.8 K for a fixed net radiative flux at the top of the model atmosphere. Inclusion of the feedbacks from Eqs. (1)–(3) produces a larger warming of 1.2 K. Water vapor mixing ratios increase by 20%–50% in the UT, with maximum changes at the top of the model convective outflow near 140 mb (the mean cloud-top level moves up ∼200 m in the 2 CO2 simulation). The vertical profile of change in water vapor is consistent with the GCM feedback study by Colman (2001); however, the magnitude of fractional changes are smaller than the values of 40%–80% found by Colman (2001). On the other hand, maintaining a constant model profile of relative humidity produces larger UT mixing ratio increases, on the order of 60%–75% for doubled CO2. The stronger water vapor feedback leads to a larger surface warming of 1.6 K, which is 30% larger than calculated when relative humidity is not constrained to be constant.
4. Model sensitivities
It is important to note that this is not a study of convective parameterizations, but rather our focus is on the mean state of the larger tropical area in the upper troposphere that is not involved in deep convection. While the details of convective downdrafts, entrainment, and precipitation are clearly important to modeling the tropical atmosphere at the cloud and mesoscale level, here we treat convection as a “black box” that impacts the larger tropical domain in three ways, all of which are supported by previous analyses: (i) convection maintains a nearly neutral moist-adiabatic mean temperature, (ii) it provides a net mass detrainment in the UT to balance the flux divergence, and (iii) it detrains saturated air to supply moisture. Nevertheless, our model results may be expected to be sensitive to assumptions regarding the choice of values for certain model parameters, or the neglect of condensate evaporation and the radiative effect of clouds.
Figure 3 includes an estimate of the uncertainty in our results obtained by varying the range of model constraints. While some of these changes produced large differences in the profiles of subsidence mass flux, radiative heating and cooling, ozone mixing ratios, and water vapor, our primary interest is on the net effect of these changes on the calculated water vapor sensitivity, (dq/q)/dTs, shown in Fig. 3. The maximum percent changes in sensitivity with respect to the standard model case are listed in Table 1.
a. Lapse rate
As discussed in section 2, model temperatures are constrained wherever convective adjustment is required by using a universal buoyancy profile referenced to a moist pseudoadiabat. Buoyancy is zero at the lifted condensation level (LCL) and at the convective top (computed in each case to be where the radiative equilibrium lapse rate becomes less than the moist pseudoadiabat). The free parameter is the maximum buoyancy, ΔT, assumed to lie at the midpoint between the LCL and convective top. Our standard model employs ΔT = 4 K, which provides good agreement with the present mean thermal state.
Calculations were also made using ΔT = 2 K and ΔT = 8 K, intended to represent extreme limiting cases in mean convective available potential energy. Since there is a large effect on the temperature lapse rate in the UT, we find that changing ΔT also impacts the calculated subsidence mass flux (by almost a factor of 2) and water vapor mixing ratios (by about 20%). However, changes in the sensitivity of UT water vapor to surface warming [(dq/q)/dTs] are much smaller (2%–4%). These latter changes are listed in Table 1 (the ΔT column).
b. Middle-tropospheric water
Water vapor mixing ratios in the middle troposphere are determined by interpolating between the amount calculated at the bottom of the UT (about 230 mb), and the input value at the surface (determined by surface temperature and relative humidity). This interpolation assumes ln(q) = a ln(p) + b, and is designed to implicitly account for moistening effects of shallow convection and evaporation of condensate.
Through the equations of radiative transfer, water vapor mixing ratios in the middle troposphere have a small but non-negligible effect on heating rates in the UT, which may then feed back on subsidence rates and calculated water vapor profiles. We tested this sensitivity by employing two other interpolation schemes that cover a range of extreme distributions in the middle troposphere: q = apα, where α = 2.7 or 4.7 (the log–log interpolation in the standard model case is very nearly equivalent to α = 3.7). These extremes were equivalent to changing water vapor mixing ratios in the midtroposphere by factors of 2 and 0.5. Corresponding changes in the UT water vapor sensitivity were between 3% and 10% (Table 1, α column).
c. Brewer–Dobson circulation
The strength of upwelling near the tropical tropopause and in the lower stratosphere is important in the thermal equilibrium of these regions. We calculate water vapor based on the temperature of the cold-point tropopause, and model ozone is determined through a balance between vertical transport and photochemical production. Therefore, changes in the model upwelling rate will impact temperature, water vapor, and ozone in the lower stratosphere, leading to changes in radiative cooling rates in the UT as discussed above.
We increased the upwelling rate by a factor of 2, and also reduced the upwelling rate by a factor of 0.5. Very large changes in lower-stratospheric water vapor and ozone were found (up to a factor of 6). The net effect on UT water vapor feedback (Table 1, B–D column) was much smaller.
d. Clouds
Clouds are known to have a large impact on both longwave and shortwave radiation. Our standard cases assume a clear model atmosphere, which is applicable to a large fraction of the tropical subsiding regions but may not be entirely appropriate for a tropical mean. The largest impact would be on UT cooling rates, which could lead to changes in subsidence and resulting water vapor. To address this possibility, a series of calculations were performed that considered cloudy skies. A 1-km-thick cloud was placed just below the calculated convective top, with cloud fraction of 8% and liquid water path of 3 g m2. We note that there are practical limits to the magnitude of the radiative heating/cooling perturbation in our model; the simple assumption of subsidence heating balanced by radiative cooling will break down if there is net heating, or if cooling is much greater than a few Kelvins per day.
For the case of cloudy sky, the modeled changes in subsidence mass fluxes and water vapor mixing ratios were up to a factor of 2. Clouds also produced the largest impact on water vapor sensitivity (11%) compared with all of the model changes discussed here (Table 1, cloud column).
e. Surface relative humidity
Table 1 (RHo column) shows maximum differences in UT water vapor sensitivity for surface relative humidities of 70% and 95%. The standard model assumes 85%.
f. Ice evaporation
The only apparent way to produce a negative feedback in the tropical UT is to assume a large present-day moisture source from evaporation of ice, and then decrease this source to zero as the atmosphere warms. We tested this scenario by including a maximum realistic evaporation source in our present-day model case, with ice evaporation declining to zero at warmer surface temperatures. For the present-day atmosphere, τ can be as short as 2 days and the model will still predict water vapor at the upper limit of observed values. We then assume that τ becomes infinite with a 2-K surface warming. Changes in UT humidity are reduced to nearly zero with this drastic assumption, although the model still fails to produce an overall negative feedback.
5. Observations of UT water vapor
One of the best opportunities to test our model calculations is provided by UT humidity measurements made from the Microwave Limb Sounder (MLS) and from the Halogen Occultation Experiment (HALOE). Both instruments are located on the UARS satellite, which was launched in late 1991. In general, both datasets contain a more uniform spatial sampling in the Tropics and higher sensitivity in the UT compared with standard radiosonde observations. We will focus on interannual variations in monthly mean relative and specific humidities, and how these may vary with the mean sea surface temperature (SST) in tropical convective regions.
For MLS, the data used here are upper-tropospheric humidity (UTH) version 4.90 at 215 mb, which span a 5.5-yr period from January 1992 to June 1997. These are relative humidities with respect to ice (% RHi) retrieved from observed limb radiances near 203 GHz (Read et al. 2001). The mean precision of a single measurement at 215 mb in the Tropics is about 15% RHi, and although the microwave observations are relatively unaffected by aerosol, haze, or thin cirrus, there do exist cases where moderately thick cirrus or convective clouds can elevate measurements to values well above 100% RHi. On the other hand, it is clear that supersaturation can occur in the UT (Jensen et al. 1999) and even subsaturated air may produce measured values in excess of 100% due to random errors. The recommended threshold for probable contamination of MLS UT water vapor by clouds is 120% RHi (Read et al. 2001).
We computed monthly mean values of UT humidity between 20°S and 20°N, which encompasses both rising and subsiding branches of the Walker and Hadley circulations, in order to provide a meaningful estimate of the overall tropical feedback (e.g., Lau et al. 1996). Area-weighted averaging was applied to avoid possible biases from uneven spatial sampling. This bias was only an issue for 10% of the months, as most mean values were computed using between 2000 and 10 000 MLS measurements distributed nearly uniformly in latitude and longitude. Even with perfectly uniform sampling, however, there is a possibility for artificial variations arising from month-to-month changes in the number of observations contaminated by cloud. These typically composed between 5% and 10% of the available tropical measurements within any given month, and their spatial distribution correlated well with areas of low monthly mean outgoing longwave radiation (OLR), confirming a high likelihood that these humidities were artificially enhanced by clouds. We therefore excluded measurements greater than 120% RHi so that the monthly means provided a better representation of mean conditions in the subsiding, nonconvective tropical regions simulated by our radiative–convective model.
Figure 4 shows the time series of monthly mean humidity along with the mean seasonal variation computed by averaging over each month of the year. Seasonal means vary between about 44% and 47% RHi, with a clear maximum in March. Note that the model results near 200 mb are in good agreement with this range of values (Fig. 2). Also indicated in Fig. 4 are monthly mean SST, spatially averaged over all areas of the Tropics (±20° latitude) where monthly mean OLR was less than 250 W m−2. These data are designed to represent the mean SST within convective regions of the tropical oceans,
Interannual variations in RH and
As discussed previously, our model calculations predict an overall increase in UT water vapor mixing ratios at warmer surface temperatures, corresponding to a positive feedback situation. Modeled relative humidity shows a small decrease, however, where [d(RH)/RH]d(
Alternatively, we may expect that the time for equi-librium between changes in
Shown also in Fig. 6 are the results from our model calculations along with two extremes representing a case of constant relative humidity feedback, and the case of zero feedback (constant specific humidity). Despite the large degree of variability and uncertainty in the measured correlation, the observations indicate that the present relationship between tropical-mean UT water vapor and convective-mean SST is constrained between the cases of constant relative and specific humidities, a result that is consistent with the model results presented here. The RH variations in Fig. 6 that appear to be independent of SST could be driven by interannual variations in other variables, such as those discussed in section 4, that are capable of producing perturbations to the mean UT humidity budget.
A similar analysis of water vapor mixing ratios was done using HALOE measurements at 215 mb. These are version 19 data retrieved from observations of solar occultation at infrared wavelengths (Russell et al. 1993). We consider data obtained after 1993 to avoid any impact of volcanic aerosol extinction from the 1991 eruption of Mount Pinatubo. As above, individual measurements were area averaged by month within ±20° latitudes; however, the nature of the HALOE observations does not provide the same number of measurements as for MLS (on the order of 100 as compared to 5000). The monthly averaging period was therefore extended ±10 days to adjoining months, which provided more reliable means with a small smoothing effect on the time series. In addition, the observations are impacted by cloud extinction so that HALOE 215-mb humidities are necessarily biased toward drier tropical regions free from convection and/or cirrus clouds, similar to the Stratospheric Aerosol Gas Experiment II (SAGE II) dataset (Rind et al. 1993). The impact of this bias on the amplitude of observed interannual variations in mean values is difficult to assess, but it could be comparable to the magnitude of the mean dry bias in HALOE water vapor at 215 mb, which is approximately a factor of 2 in comparison with MLS.
Figure 7 shows the correlation between interannual variations in monthly mean UT water vapor and
This constraint was investigated using 200-mb temperatures archived in the NCEP–NCAR reanalysis (Kalnay et al. 1996). We used the period 1992–99, which overlaps both of the MLS and HALOE observing times analyzed previously. As before, monthly means within ±20° latitude were computed with the annual cycle removed to highlight interannual variations. Displayed in Fig. 8 are the 200-mb temperature variations plotted versus
The quantitative agreement between MLS, HALOE, and NCEP data suggests that the feedback is better understood than indicated by the uncertainty in the individual MLS or HALOE fits. The reason is that the MLS and HALOE data are not expected to have any common systematic errors, so that errors in one fit would have to be matched by errors of similar magnitude and sign in the other dataset in order to produce the same result. Such a constraint reduces the uncertainty of the conclusion from the combined dataset.
The MLS and HALOE observations can also be applied individually to compute temperature changes for the limiting cases of constant specific and relative humidities. For the decreasing RH with
6. Conclusions
The radiative–convective model described here and applied to the mean state of nonconvecting regions of the Tropics, contains two fundamental constraints that are almost certain to be applicable to any future climate: a tropical temperature profile that is near moist adiabatic, and a balance in the UT between net radiative cooling, clear-sky subsidence, and the water vapor abundance. The calculated changes in UT water vapor are not dependent on any parameterizations of surface heat and moisture fluxes, and are only weakly impacted by any reasonable assumptions regarding evaporation of cloud condensate. Equilibrium states of the model show that increases in the detrainment height of deep convection and warmer detrainment temperatures lead to increases in the mixing ratio of UT water vapor with increasing surface temperature. The change in water vapor near 215 mb is between 8.5 and 9.5 ppmv K−1 increase in surface temperature. On the other hand, the modeled increases in moisture with surface temperature are not enough to preserve constant relative humidity. The calculated decrease in relative humidity at 215 mb is between −4.0% and −8.4% RHi K−1.
Observations of interannual variations in tropical-mean HALOE water vapor and convective-mean SST also support the existence of a positive water vapor feedback in the UT, with an implied moistening of 3.0 ± 1.2 ppmv K−1 at 215 mb. Furthermore, observations of interannual variations in MLS relative humidity and SST show decreases in mean relative humidity with increasing mean SST, on the order of −4.8% ± 3.4% RHi K−1. Both results are consistent with variations in 200-mb temperature and SST from the NCEP–NCAR reanalysis. These observations provide evidence (at the 95% confidence level) that the present climate regime operates between the limiting cases of constant specific and constant relative humidities in the tropical UT. This feedback can be understood in terms of the modeled balance between radiative cooling, clear-air subsidence, and convective detrainment.
The simulated feedback is found to be sensitive to uncertainties arising from possible changes in clouds and lapse rate, and from the evaporation of condensate. One measure of the modeled uncertainty is obtained by varying the range of fixed model parameters used to represent these quantities. We find that the resulting uncertainty is within the limits imposed by current observations of UT humidity and SST. On the other hand, the model can be forced to produce results beyond these limits by artificially changing the cloud amount, lapse rate, and condensate evaporation as the climate changes. Even under the most extreme assumptions regarding these processes, however, we find that the model is unable to produce a negative feedback simulation.
Acknowledgments
The first author acknowledges support through a Goddard Visiting Fellowship in Earth Sciences administered through the University of Maryland, Baltimore County, and hosted by the NASA Goddard Space Flight Center. Other support comes from a NASA EOS/IDS grant and a New Investigator Program grant, both to the University of Maryland. W. Read provided the MLS humidity data used in Fig. 2. We acknowledge useful discussions with I. Folkins, D. Kirk-Davidoff, M. Schoeberl, P. Forster, J. Coakley, P. Newman, S. Sherwood, and W. Read, and beneficial comments from two anonymous reviewers.
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(a) Model thermal structure for 299-, 301-, and 303-K surface temperatures (dashed, solid, and dotted curves, respectively). Short horizontal lines denote the calculated top of convection. Squares are 1998–2000 means of daily radiosonde observations from Truk, FSM. (b) Calculated rates of clear-air subsidence corresponding to three values of surface temperature
Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1272:WVFITT>2.0.CO;2
(a) Model specific humidities for surface temperatures of 299, 301, and 303 K (dashed, solid, and dotted curves, respectively). Data at altitudes below 146 mb are version 4.90 MLS UTH data (Read et al. 2001), averaged between 25°N and 25°S over the period 1992–99. Error bars are based on estimated accuracies. Water vapor at 100 mb represents the annual average H2O entry value for the stratosphere (Dessler and Kim 1999). Horizontal lines represent the UT layer where water vapor is explicitly calculated. (b) Relative humidities corresponding to the three values of surface temperature
Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1272:WVFITT>2.0.CO;2
Sensitivity of relative (dashed) and specific (solid) humidity to changes in surface temperature. Sensitivity is determined by (dX/X)/dTs, where Ts is surface temperature and X is either relative or specific humidity. The dotted curves indicate the maximum possible range of sensitivities through variation of assumed model parameters
Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1272:WVFITT>2.0.CO;2
(a) Monthly mean MLS relative humidity with respect to ice at 215 mb (xs) averaged between ±20° lat. (b) Monthly mean SST (triangles) averaged between ±20° lat and over regions where monthly mean OLR was less than 250 W m−2. Error bars on both sets of data represent the standard error of monthly means (typically 0.5% RHi and 0.05 K, respectively). Solid curves show repeating annual cycles computed from monthly means
Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1272:WVFITT>2.0.CO;2
(a) Monthly mean, deseasonalized MLS relative humidity variations (xs). (b) Deseasonalized SST variations (triangles)
Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1272:WVFITT>2.0.CO;2
Relationship between MLS UT relative humidity variations at 215 mb and NCEP SST variations (xs). Data are monthly means between ±20° lat over the period 1992–97 with annual cyles removed, SST means are limited to regions with OLR < 250 W m−2, and a 1-month phase lag is applied between humidity and SST variations. The shaded region is a linear least squares fit with uncertainty (95% confidence limit), the dashed line is the relationship calculated using the radiative–convective model, and the two dotted lines represent the cases of constant relative and specific humidities in the model
Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1272:WVFITT>2.0.CO;2
Relationship between HALOE UT specific humidity variations at 215 mb and NCEP SST variations (xs). Data are monthly means between ±20° lat over the period 1993–99 with annual cycles removed, SST means are limited to regions with OLR < 250 W m−2, and a 1-month phase lag is applied between water vapor and SST variations. The shaded region is a linear least squares fit with uncertainty, the dashed line is the relationship calculated using the radiative–convective model, and the two dotted lines represent the cases of constant specific and relative humidities in the model
Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1272:WVFITT>2.0.CO;2
Relationship between NCEP temperature variations at 200 mb and SST variations (xs). Data are monthly means between ±20° lat over the period 1992–99 with annual cycles removed, SST means are limited to regions with OLR < 250 W m−2, and a 1-month phase lag is applied between 200-mb temperature and SST. The shaded region is a linear least squares fit with uncertainty, and the dashed line is the temperature relationship implied by the MLS relative humidity and HALOE specific humidity variations shown in Figs. 6 and 7
Citation: Journal of Climate 17, 6; 10.1175/1520-0442(2004)017<1272:WVFITT>2.0.CO;2
Changes in water vapor sensitivity with variations in model parameters