1. Introduction
The global hydrological cycle and general circulation are constrained to adjust to each other by moisture availability (which varies with tropospheric temperature) as well as surface and top-of-the-atmosphere heat fluxes. Although global climate models are fairly consistent in their prediction of the strengthening of the hydrological cycle and weakening of circulation with global warming (Held and Soden 2006; Vecchi and Soden 2007), the regional patterns of precipitation changes in the future remain highly uncertain. This is because climate models projected future precipitation patterns that are fairly similar to the present day, with only small changes associated with the expansion of the Hadley cell and subtropical dry zones, that is, a poleward expansion of the mean state (Lu et al. 2007; Seager et al. 2007, 2010). Thus changes in precipitation pattern predicted by different models depend to a large degree on the precipitation pattern simulated by the models for the current climate. Studying the jet stream and its poleward shift in the future, Kidston and Gerber (2010) provided an example of how fidelity of a model’s simulation of the current climate may be related to its projection of climate change in the future. The fact that intermodel differences in the hydrological cycle of the present may be projected to carry into the future suggests that reducing uncertainties in the present-day modeled hydrological cycle would likely go a long way toward reducing the corresponding uncertainties in the projected hydrological cycle.
The adjustment of the hydrological cycle and circulation to radiative constraints takes place through moisture transport and diabatic heating. Therefore uncertainties in the hydrological cycle are likely to be related to uncertainties in diabatic heating that is almost always parameterized in global models. Despite its obvious importance, there is no direct way of measuring diabatic heating yet. It is often estimated from radar observations (Shige et al. 2004; Tao et al. 2006) or from wind and temperature fields as a residual from the energy budget (see Yanai et al. 1973; Hagos et al. 2010, and references therein). In the latter case, horizontal divergence is calculated from observed winds from which vertical velocity and subsequently heating are estimated. Divergence therefore can be reasonably used as a proxy for diabatic heating in evaluating models for it can be calculated using horizontal wind from both models and observations more directly than is possible for diabatic heating or even vertical velocity. By quantitatively assessing the uncertainties in tropical divergence and their relationships to those in the hydrological cycle, this study aims to provide some guidance to the development of the next-generation parameterizations.
2. Data
Three groups of datasets are analyzed in this study: GCM outputs, global reanalyses, and data from in situ soundings. They are listed in Table 1 along with brief descriptions and corresponding references. The GCMs included are the Hadley Centre Climate Model, version 3 (HadCM3), the Canadian GCM (CGCM3), and the National Center for Atmospheric Research Community Climate System Model, version 3 (CCSM3). These models were among the 24 GCMs used in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4; Meehl et al. 2007). One ensemble member of each GCM was rerun to generate 6-hourly data for the North American Regional Climate Change Assessment Program (NARCCAP) to develop regional climate change scenarios for North America using dynamical downscaling (Mearns et al. 2009). Although the Geophysical Fluid Dynamics Laboratory (GFDL) model was also used in NARCCAP, 6-hourly data are only available for a quadrant of the globe that covers the North American region, so it is not included in this study. The horizontal grid spacings (or equivalent for the spectral models CCSM3 and CGCM3) are 1.4° × 1.4°, 1.9° × 1.9°, 2.5° × 3.75° latitude × longitude, respectively, for CCSM3, CGCM3, and HadCM3. We utilize the 6-hourly winds and moisture data from the GCM model outputs that were written on each model’s native horizontal grid. The CGCM3 and HadCM3 model outputs have been vertically interpolated from 31 and 19 sigma levels, respectively, to 42 pressure levels. Model outputs for a 20-yr time period (1980–99) from the twentieth-century historical runs and a 20-yr future time period (2050–69) that used the IPCC Special Report on Emissions Scenarios (SRES) A2 emission scenario are used to study hydrological change under global warming.
Description of data.
Corresponding 20-yr data of wind and water vapor mixing ratio from the National Centers for Environmental Prediction (NCEP)/Department of Energy (DOE) global reanalysis (NCEP-2), the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40), and the 25-yr Japanese Reanalysis (JRA-25) are also included in the study. All the model and reanalysis datasets cover the entire globe. Divergence is also derived from soundings from field campaigns at four tropical locations. The field campaigns are the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE), the Kwajalein Experiment (KWAJEX), the Tropical Warm Pool International Cloud Experiment (TWP-ICE), and the Large-Scale Biosphere–Atmosphere Experiment in Amazonia (LBA). Divergence calculated from each of the soundings is representative of an area that approximates the resolution of typical GCMs, for a relatively short time period (see Table 1). All the datasets in this study have a temporal resolution of 6 hours except for ERA-40, which is daily.
3. Analysis
a. Divergence profiles
Horizontal divergence 
Figure 1 shows the divergence profiles at the updraft and downdraft points for all the models and the reanalyses averaged over the 20 years and over latitudinal bands between 25°S and 25°N. The most obvious differences among the divergence profiles from the models and reanalyses are the strength of shallow divergent circulation and the strength of deep circulation. Specifically shallow divergent circulation is strongest in CCSM3 followed by CGCM3 and by contrast, shallow circulation is essentially absent in HadCM3 and all the global reanalyses. Furthermore CCSM3 has stronger deep divergent circulation in comparison to the other models and all the reanalyses.
Divergence (day−1) at updraft and downdraft points averaged between 25°N and 25°S and over the 20 years.
Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00058.1
Figure 1 also shows the distinct separation between deep and shallow divergence. In all the models and reanalyses, the peak shallow divergence (convergence) in the updraft (downdraft) points is below 400 hPa. This enables further partitioning of the divergence fields into deep and shallow according to the level of their peak. Therefore, as a next step in the analysis, shallow and deep divergence profiles are identified by the levels of peak divergence (convergence) for the updraft (downdraft) points. This enables direct comparison of the shallow and deep components of the divergence from the datasets as well as calculation of shallow and deep circulations and their contributions to the hydrological cycle. For this study, a point is defined as a point of shallow divergence if both peak divergence and peak convergence are below 400 hPa.
Figure 2 shows the deep and shallow divergence at updraft and downdraft points averaged over the tropics between 25°S and 25°N and averaged over the 20 years. In addition to the obvious differences in the amounts of divergence, the models also differ in the profiles of the deep divergence. Specifically the pressure levels of zero divergence (which is the level of maximum upward vertical velocity) at updraft points vary (Fig. 2a). The level of zero divergence for the NCEP-2 and ERA-40 reanalyses is about 400 hPa, while that of HadCM3, JRA-25, and CGCM3 is about 300 hPa and that of CCSM3 is 250 hPa. There is also a corresponding intermodel difference among the levels at which divergence is zero (the levels of maximum downward vertical velocity) at the downdraft points (Fig. 2b).
Divergence (day−1) over updraft and downdraft points partitioned into deep and shallow. All are averaged zonally, between 25°N and 25°S and over the 20 years.
Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00058.1
Similar analysis is performed on the divergence derived from the in situ soundings (Fig. 3). There is also significant uncertainty in the level at which deep divergence changes sign (peak vertical velocity), which is about 350 hPa for TOGA COARE, 390 hPa for LBA, 450 hPa for TWP-ICE, and 490 hPa for KWAJEX. One has to keep in mind that direct comparison of the magnitude of the divergence from the soundings with those of the models or reanalyses is not warranted because the former correspond to a very limited area and time window. However, one can at least compare the level of peak vertical velocity or maximum diabatic heating. Although one should not read too much into the differences in the magnitude of shallow divergence among the soundings for they correspond to different time periods and locations, all the soundings have significant shallow divergence, with peaks that range between 900 and 500 hPa. The differences in the levels of peak shallow divergences might have implications for regional variations. In contrast, as noted above, among the global models and reanalyses, only CCSM3 and CGCM3 produced significant shallow divergence circulation.
Divergence from in situ soundings (day−1) over updraft points (a) total, (b) deep, and (c) shallow averaged over their respective periods (Table 1).
Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00058.1
Once the average deep divergences for updraft and downdraft points in the tropics are calculated they are integrated vertically to calculate the mean vertical velocity 
(a) The pressure level (hPa) of minimum pressure vertical velocity vs pressure vertical velocity (Pa s−1) over points of updraft and (b) that of maximum pressure vertical velocity vs pressure vertical velocity (Pa s−1) over points of downdraft. The dashes in (a) represent the level of peak vertical velocity from each in situ sounding.
Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00058.1
The dashes in Fig. 4a mark lines of constant low-level mass convergence. The models (except HadCM3) lie within the range of mass convergence of NCEP-2 and ERA-40. If two models lie parallel to the convergence lines, they have similar mass fluxes (CGCM3 and CCSM3) even though the magnitudes of their peak vertical velocity and their pressure levels differ. Otherwise, they disagree in their low-level mass convergence (HadCM3 and CCSM3).
b. Divergent circulation and global warming
As discussed in the introduction, tropical divergent circulation is projected to weaken under global warming because radiative constraints do not allow precipitation to increase at the pace of the atmospheric column water vapor. Another consequence of global warming is the increase in the depth of the divergent circulation, which depends on the surface temperature, lapse rate and emission height (Schneider et al. 2010). Both the weakening and deepening of the circulation are consistent with the overall weakening of low-level convergence in the tropics that counteracts the increase in moisture convergence due to increased moisture availability.
Figure 5 shows the magnitude and level of peak mean vertical velocity from the present (1980–99) and future (2050–69) model simulations over updraft (Fig. 5a) and downdraft (Fig. 5b) regions. As noted above, in all three models global warming leads to the weakening of the updraft vertical velocity and deepening of the level of maximum updraft. This is also true for the downdraft vertical velocity except for HadCM3, where it appears to have slightly increased. An important point to note is the fact that the intermodel differences in the magnitude as well as level of peak vertical velocity remain more or less unchanged under global warming. In other words, uncertainties in the projected profile and strength of divergent circulation mainly follow from the respective uncertainties in the present-day simulations.
(a) The pressure level (hPa) of minimum pressure vertical velocity vs pressure vertical velocity (Pa s−1) over points of updraft and (b) that of maximum pressure vertical velocity vs pressure vertical velocity (Pa s−1) over points of downdraft; “−P” and “−F” refer to the 1980–99 and 2050–69 means, respectively.
Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00058.1
c. Divergent circulation and the hydrological cycle
In section 3b, we showed that tropical divergence in global models and reanalyses differ in the amount of shallow and deep divergence and the depth of the deep divergence. In this section, the contributions of the shallow and deep divergence to the hydrological cycle are calculated for each model. This is done by first calculating the divergence circulation associated with deep and shallow divergence as categorized above. The technique for separating shallow and deep circulation is presented here briefly. Its mathematical foundations are discussed in detail in Hagos and Zhang (2010) in the context of the African monsoon study.
In a physical sense, the above two equations mean that the divergent wind at a point is a linear combination of the divergent wind contributed by the divergence at every point on the globe and one can partition the global divergence field in anyway, solve the equation for each partition, and add them to find the total divergent wind field. Here we partitioned the global divergence field into shallow and deep and calculate the corresponding parts of the total divergent circulation.
The rhs terms in Eq. (9) represent the contributions to net precipitation from moisture convergence by deep divergent circulation, shallow divergent circulation, and advection by nondivergent circulation. These terms are calculated at the temporal resolution of the model or reanalysis (daily for ERA-40 and 6-hourly for all others) and averaged over the 20 years.
Before continuing with the analysis of the contributions of the various forms of circulation to the hydrological cycle, the accuracy of estimating the net precipitation from vertically integrated moisture convergence [Eq. (7)] is evaluated by comparing the result from the finite difference calculation [rhs of Eq. (7)] with the actual 
Comparisons between zonal mean P − E (mm day−1) from CCSM estimated from the moisture budget [Eq. (6)] and model output. Both are averaged over the 20 years.
Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00058.1
Figure 7 shows comparison of the 20-yr-averaged zonal mean 
(a) Zonal mean P − E in (mm day−1) from the models 1980–99 mean (solid) and 2050–69 mean (dashed) from the IPCC SRES A2 run and (b) 2050–69 mean minus 1980–99 mean.
Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00058.1
Figure 8 shows the zonal mean of 
(a) Zonal and 20-yr mean P − E (mm day−1) and the contributions of (b) deep divergent circulation, (c) shallow divergent circulation, and (d) nondivergent circulation.
Citation: Journal of Climate 25, 1; 10.1175/JCLI-D-11-00058.1
The differences among the total zonal mean hydrological cycles among the models and reanalyses are reflected in the vertically integrated moisture convergence associated with deep divergent circulation. In comparison, the contributions of shallow divergent circulations and nondivergent circulations to the intermodel differences in the hydrological cycle are small. The nature of the relationship between the uncertainties in the zonal mean hydrological cycle (Fig. 8a) can now be explained in the context of uncertainty in the strength and profile of vertical velocity (Fig. 4). Since low-level convergence is proportional to the maximum vertical velocity, other things being equal, models with stronger vertical velocity would have stronger convergence and stronger hydrological cycle. For example, HadCM3 and CGCM3 have similar vertical velocity profile, but both updraft and downdraft vertical velocities of HadCM3 are stronger (Fig. 4) and, hence, it has stronger 
In most cases however, the effect of the strength of the circulation on convergence and 
4. Discussion
In this study the nature of uncertainties in tropical divergent circulations and their relationships to uncertainties in the hydrological cycle are assessed using data from three global models, three global reanalyses, and four in situ measurements in the tropics. The main sources of uncertainties identified are the strengths of shallow and deep divergence and the depth of the deep divergent circulation. For a more robust comparison, the grid points were partitioned into updraft and downdraft points. Figures 4a,b show the level and magnitude of peak vertical velocity at updraft and downdraft points averaged over 20 years zonally and between 25°S and 25°N. Of the three global models and three global reanalyses, only NCEP-2 and ERA-40 have divergence profiles that lie within the range of the uncertainty of the soundings; JRA-25 and all the global models have their peak vertical velocity near or above 300 hPa, which is well above the levels between 500 and 350 hPa indicated by the soundings. However, the latter group has a stronger vertical velocity. The weak low-level convergence they would otherwise have by virtue of the height of their peak vertical velocity is for the most part compensated for by the fact that they have stronger vertical velocity both in the updraft and downdraft points (Figs. 4a,b).
In the tropics and subtropics, deep divergent circulation is the largest contributor to moisture convergence that balances 
Although large differences exist among the profile of deep divergence in different global models and reanalyses, the effect of the differences is not obvious because, as noted above, the models with large peak vertical velocity (CCSM3, CGCM3, JRA-25, and HadCM3) also have it at higher level (≤300 hPa) such that their low-level convergence is comparable to the ones that have weaker peak vertical velocity at the lower levels (≥350 hPa, NCEP-2, and ERA-40). For example, the peak upward velocity for HadCM3 is about 50% larger than that of NCEP-2, but that does not translate to a 50% difference in moisture convergence because of the difference in their profiles. If the levels of peak vertical velocity are comparable, however, the difference in the magnitude of peak vertical velocity is manifested in the moisture convergence. For example, HadCM3 and CGCM3 have comparable levels of peak vertical velocity, but HadCM3 has a stronger updraft and therefore has a stronger hydrological cycle. If the magnitudes of vertical velocity are comparable but differ in profile (CCSM3 is deeper than JRA-25), the differences in profiles affect the hydrological cycle (JRA-25 has a stronger hydrological cycle). Overall, however, since most of the models lie along lines of constant low-level mass convergence (Fig. 4a), the differences in the profiles do not have as large an impact on the hydrological cycle.
In summary, both the magnitude and profile of deep vertical velocity, (or equivalently divergence or diabatic heating), pose a constraint on the hydrological cycle through convergence. Currently, neither global models nor global reanalyses produce consistent diabatic heating profiles as inferred from the large differences in their divergence profiles, hence, the uncertainties in their hydrological cycles. Therefore reducing uncertainties in the vertical profile of divergence (vertical velocity or diabatic heating) using observations will at least reduce uncertainty in the overall strength of the divergent circulation or the hydrological cycle, if not necessarily both. Hagos et al. (2010) showed that the structure of the diabatic heating for the deep mode are quite consistent among different estimates based on the Tropical Rainfall Measuring Mission (TRMM) products, reanalysis products, and soundings, so they may offer some guidance to constrain the deep divergent circulation that provides the primary contribution to moisture convergence or P − E in the tropics.
Acknowledgments
The authors thank Dr. Jin-Ho Yoon for his comments and suggestions. This work is supported by the U.S. Department of Energy under the Investigation of the Magnitudes and Probabilities of Abrupt Climate Transitions (IMPACTS) Project. The Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy under Contract DE-AC06-76RLO1830.
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