Abstract

This paper examines the controls on global precipitation that are evident in the transient experiments conducted using coupled climate models collected for the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4). The change in precipitation, water vapor, clouds, and radiative heating of the atmosphere evident in the 1% increase in carbon dioxide until doubled (1pctto2x) scenario is examined. As noted in other studies, the ensemble-mean changes in water vapor as carbon dioxide is doubled occur at a rate similar to that predicted by the Clausius–Clapeyron relationship. The ratio of global changes in precipitation to global changes in water vapor offers some insight on how readily increased water vapor is converted into precipitation in modeled climate change. This ratio ɛ is introduced in this paper as a gross indicator of the global precipitation efficiency under global warming.

The main findings of this paper are threefold. First, increases in the global precipitation track increase atmospheric radiative energy loss and the ratio of precipitation sensitivity to water vapor sensitivity is primarily determined by changes to this atmospheric column energy loss. A reference limit to this ratio is introduced as the rate at which the emission of radiation from the clear-sky atmosphere increases as water vapor increases. It is shown that the derived efficiency based on the simple ratio of precipitation to water vapor sensitivities of models in fact closely matches the sensitivity derived from simple energy balance arguments involving changes to water vapor emission alone. Second, although the rate of increase of clear-sky emission is the dominant factor in the change to the energy balance of the atmosphere, there are two important and offsetting processes that contribute to ɛ in the model simulations studied: One involves a negative feedback through cloud radiative heating that acts to reduce the efficiency; the other is the global reduction in sensible heating that counteracts the effects of the cloud feedback and increases the efficiency. These counteracting feedbacks only apply on the global scale. Third, the negative cloud radiative heating feedback occurs through reductions of cloud amount in the middle troposphere, defined as the layer between 680 and 440 hPa, and by slight global cloud decreases in the lower troposphere. These changes act in a manner to expose the warmer atmosphere below to high clouds, thus resulting in a net warming of the atmospheric column by clouds and a negative feedback on the precipitation.

1. Introduction

Scientific discussion about long-term climate change induced by the buildup of greenhouse gases has predominantly focused on global warming. Although much uncertainty remains regarding the prediction of how much warming will occur through greenhouse gas buildup, the predominant public focus on global surface temperature as a metric of climate change is in part understandable given that both simple and complex theories exist that directly connect perturbations of radiative forcing associated with changing concentrations of greenhouse gases to global-mean surface temperature (e.g., North et al. 1981). Relatively long records of global surface temperature (Folland and Parker 1995), or proxies for it (Mann and Jones 2003), can also be constructed from diverse observations to provide a way of testing such theories. Changes to the characteristics of rainfall on both global and regional scales have recently been undergoing similar levels of scrutiny (e.g., Diaz et al. 1989; Dai et al. 1997; Sun et al. 2007; Allen and Ingram 2002; Trenberth et al. 2007) as the societal impacts of changes in precipitation have become more apparent (e.g., Watkins et al. 2007). Understanding how precipitation patterns and types are likely to change in the face of increasing carbon dioxide (e.g., Trenberth et al. 2003), as well as by other anthropogenic factors like pollution, is essential for understanding the scope of a looming planetary-scale water supply crisis (Clarke and King 2004).

Precipitation is highly variable over both space and time and inherently forms on scales that are typically much smaller than those resolved explicitly by existing models of the earth’s climate. Even annual precipitation, which is adequately measured by existing land-based rain gauge networks, is not well sampled over the ocean. These difficulties create great problems for measuring global- and regional-scale precipitation and are major challenges for determining climate trends. The recognition of these problems has long served as motivation for the development of satellite-based methods for observing the global distribution of precipitation. Measurement of precipitation from space however is challenging (Stephens and Kummerow 2007), and sustaining global-scale observations over time scales that are relevant to the climate change problem has not yet proven possible, as evidenced in recent studies that report on contradictory global trends in existing satellite-based precipitation observations (Wentz et al. 2007; Gu et al. 2007). Representing the inherent spatial variability and character of precipitation in global climate models is also fraught with many difficulties, and determining where and how much it rains or snows continues to be one of the most difficult and pressing challenges confronting weather and climate prediction.

Despite the difficulties associated with modeling, observing, and predicting changes in local- and global-scale precipitation, there appears to be robust physical controls on the global hydrological cycle that provide us with a basis for forming gross expectations as to how global precipitation might change in the context of climate change (e.g., Allen and Ingram 2002; Held and Soden 2006). Modeling studies suggest that atmospheric moisture increases with warming at a rate of approximately 7% K−1 primarily resulting from the Clausius–Clapeyron (CC) relation (e.g., Trenberth et al. 2007), and observations over oceans demonstrate a similar rate of change (e.g., Santer et al. 2007). Although there is an expectation that precipitation too should increase at approximately the same rate (e.g., Wentz et al. 2007), a number of studies, including the present study, point out that projected changes in precipitation by models occur at a much reduced rate (1–3% K−1).

This paper further examines the controls on global precipitation that are evident in the transient experiments conducted using coupled climate models collected for the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4; information available online at http://www.ipcc.ch). The experiments analyzed are those of a 1% increase in carbon dioxide per year to doubling. As has been known for some time (e.g., Stephens et al. 1994; Mitchell et al. 1987; Allen and Ingram 2002; and others), global precipitation is constrained by the energy balance of the atmosphere more so than by the availability of moisture, and the model analysis presented in this study demonstrates that it is through this control that the rate of precipitation increase in warming cannot be expected to keep pace with water vapor increases. This result thus raises questions about the above-mentioned data sources used to infer observed changes in precipitation.

The model data used in this study are briefly described in the following section together with the simple procedures developed for analysis of these data. Section 3 reviews the changes to column water vapor associated with the resultant global warming of the models offering a context for the following analysis. A nondimensional ratio of the changes in global-mean precipitation to changes in global-mean water vapor is introduced in this section. This ratio ɛ serves as a proxy for global precipitation efficiency, because it is a measure of how much the predicted increase in water vapor is converted to increased precipitation. Section 4 then reviews the changes in cloud amount that relate to the moisture changes described in section 3. The associated changes in atmospheric cloud radiative heating are also introduced in section 4, and it is shown how these changes are related to changes in the vertical structure of clouds, with decreased middle-level and low clouds and slightly increased high clouds producing the predicted heating. Section 5 examines the basic energy controls on the model hydrological cycle formulated in terms of the ɛ ratio introduced in section 3. This section shows that the rate at which radiation is emitted from the atmosphere by water vapor establishes a basic reference limit on this ratio with values that are substantially below that expected from the implied CC increase in water vapor. This section further illustrates how the cloud radiative feedbacks associated with changes in radiative heating related to changes in vertical cloud structure further reduce the ratio from the upper clear-sky emission limit, and in this way act as a negative feedback on global precipitation. The paper concludes with a discussion of these results that appear to contradict the recent observational studies that suggest a value of ɛ ought to be nearly unity.

2. Data and methodology

The data used in this study are those of coupled climate models archived by the World Climate Research Programme’s (WCRP’s) Coupled Model Intercomparison Project, phase 3 (CMIP3) multimodel dataset (available online at http://www-pcmdi.llnl.gov/; see also Meehl et al. 2007). The focus of this particular study is directed toward addressing the nature of changes that occur under predicted global warming resulting from a 1% yr−1 increase in carbon dioxide over 70 yr from present at which point in time CO2 is doubled from initial levels [referred to by the Program for Climate Model Diagnosis and Intercomparison (PCMDI) as the 1pctto2x scenario]. This allows us to not only study the differences in the hydrological cycle before and after the carbon dioxide change, but also to study the evolution of the system in order to shed more light on the physical mechanisms involved. We consider only one realization from each of the 21 models under this scenario,1 which are listed in Table 1.

Table 1.

PCMDI AR4 model simulations for which data were available, used in this analysis. Asterisks indicate that the model was used for the emission limit analyses of sections 5 and 6.

PCMDI AR4 model simulations for which data were available, used in this analysis. Asterisks indicate that the model was used for the emission limit analyses of sections 5 and 6.
PCMDI AR4 model simulations for which data were available, used in this analysis. Asterisks indicate that the model was used for the emission limit analyses of sections 5 and 6.

It is important to note that not all models contribute to all calculated quantities studied in this paper when relevant data are missing. These missing data also limit the number of models that can be used for the analysis in section 5. To obtain self-consistent results, only seven models, highlighted with an asterisk in Table 1, are used in those analyses because they were the only models to have available, realistic data for each field necessary to calculate clear- and all-sky column radiative energy fluxes as well as cloud radiative forcing fluxes.

Our analyses consider averages over 1–10 and 61–70 yr in order to mitigate contributions of year-to-year variability. Differences between these averages illustrate how the atmospheric states change from initial values as the models approach a doubling in carbon dioxide concentrations. To present robust geographical responses of models, maps of the ensemble means of data exclude values outside of one standard deviation to remove possible effects of model outliers. The responses presented, however, do not change significantly when values within two standard deviations of the mean are included (not shown). Globally averaged quantities are derived using appropriate equal area weighting of model gridpoint data.

3. Water vapor and precipitation changes in global warming simulations

In studying the factors that control precipitation changes in global warming it is relevant to first consider changes to water vapor for context. The following simplistic arguments illustrate how precipitation changes might relate to the water vapor increases that are uniformly predicted by the climate models considered in this study. It is commonly argued that precipitating weather systems of all kinds feed mostly on the moisture that already resides in the atmosphere (e.g., Trenberth 1998), primarily through low-level convergence of this moisture in the vicinity of weather systems. Therefore, changes to the availability of atmospheric moisture, through projected water vapor increases resulting from global warming, can be expected to lead directly to changes in this moisture convergence and hence precipitation intensity. It is through these arguments that the rate of precipitation increase might follow the rate of water vapor increase.

The CC relationship for saturated vapor pressure presents a much-discussed basis for understanding the predicted changes to atmospheric water vapor under global warming. This relationship is given by

 
formula

where L is the latent heat of vaporization, R is the gas constant, and es is the saturation vapor pressure at the surface associated with the surface temperature Ts. It has been assumed for some time that the column total water vapor in the atmosphere follows the behavior expected from this relationship. This expectation is confirmed in the study of Stephens (1990) and others (e.g., Wentz and Schabel 2000; Trenberth et al. 2005) in the analysis of satellite data. Many other studies (e.g., Held and Soden 2006) also underscore this key point, arguing that the changes in column-mean water vapor under global warming closely follow a projected CC increase of approximately 7% K−1 given the associated increase in surface temperature.

Figure 1 offers a closer examination of the relationship between the column water vapor predicted from the CC relationship and the model-predicted water vapor. Figure 1a is the global distribution of the percentage increase in water vapor per degree warming calculated from the CC relation using the ensemble-mean model surface–700-hPa mean layer temperature averaged over the first 10 yr of integration. This layer-mean temperature is taken to characterize the boundary layer temperature where most of the water vapor resides and thus is broadly characteristic of the column water vapor (CWV). The global-mean value of the fractional rate of increase with precipitation calculated using layer-mean temperatures is 6.7% K−1. Calculated in this way, we interpret the results of this figure as representing the contribution to the rate of increase of model water vapor per degree warming that would occur purely through thermodynamic controls on water vapor under the common assumption that relative humidity remains fixed. This assumption of fixed relative humidity is validated by the results of Dai (2006), among others.

Fig. 1.

(a) The projected rate of the relative percent change of column water vapor per degree increase of temperature amount derived from CC, assuming the multimodel ensemble-mean boundary layer temperature. Units are % K−1. The global-mean value of this sensitivity is 6.7% K−1. (b) The difference between the actual model-projected rate of change of column water vapor and that derived from the CC relationship (a) in units of % K−1. (c) The change in ensemble-mean winds from 1–10 to 61–70 yr. Contours indicate changes in wind speed (m s−1) and vectors represent the vector difference in winds at selected locations.

Fig. 1.

(a) The projected rate of the relative percent change of column water vapor per degree increase of temperature amount derived from CC, assuming the multimodel ensemble-mean boundary layer temperature. Units are % K−1. The global-mean value of this sensitivity is 6.7% K−1. (b) The difference between the actual model-projected rate of change of column water vapor and that derived from the CC relationship (a) in units of % K−1. (c) The change in ensemble-mean winds from 1–10 to 61–70 yr. Contours indicate changes in wind speed (m s−1) and vectors represent the vector difference in winds at selected locations.

A similar quantity to that of Fig. 1a can also be derived from the ensemble mean of the ratio of model-predicted column water vapor changes divided by the respective surface temperature increases of each model. The difference between this sensitivity and that derived from CC is shown in Fig. 1b. This difference reveals how most models moisten over oceans at rates that slightly exceed the simple thermodynamic increase as embodied in the CC relationship, and that this enhanced moistening is substantial in some regions. Differences between real-world-observed water vapor and water vapor derived from this specific form of the CC relationship reveal atmospheric circulation influences on water vapor (Stephens 1990). In an analogous way, the differences shown in Fig. 1b reveal the influence of changes in the atmospheric circulation on the model water vapor increases. To underscore this point, Fig. 1c shows the model ensemble-mean changes in surface wind speed and velocity (arrows). This figure suggests that the increased midlatitude westerlies over the southern oceans poleward of about 40°S drive the increased water vapor through evaporation associated with these stronger winds. The extensive area of enhanced moistening over the tropical Pacific Ocean appears to be related to enhanced moisture convergence into this region. These results are also consistent with Vecchi and Soden (2007), who show that these regions of moistening beyond that predicted by the CC relation are also regions where the vertical velocity is changing in connection to a weakening of the tropical Walker circulation.2

The global- and ensemble-mean sensitivity of the AR4 models is 7.4% K−1, which slightly exceeds that derived from CC as shown in Fig. 1a (6.7% K−1), implying a modest change in relative humidity in the models. It is usually assumed that the relative humidity changes that occur in climate change are small, and that on the whole the water vapor feedback in models is interpreted through a mechanism that inherently is structured around assumptions of fixed relative humidity. However, we will show the potential importance of even small changes to relative humidity that are evident in Figs. 2a,b. The geographic changes in layer-mean surface–500-hPa relative humidity (Fig. 2a) are small but nevertheless are coherent in structure, showing wide-scale decreases of relative humidity in the subtropics and increases in regions that could be anticipated from the difference maps of Fig. 1b. The increases are confined to the tropical regions and the mid- to higher latitudes, and decreases in relative humidity exist in broad regions of the subtropics and some regions of the tropical atmosphere. Figure 2b shows the changes in ensemble-mean relative humidity in the layer above 500 hPa. Increases in relative humidity of the upper troposphere are more broadly spread, with the largest increases coupled to regions of increased lower-tropospheric relative humidity. Upper-tropospheric drying occurs in regions of the subtropics where increases to subsidence presumably occur, as found in Vecchi and Soden (2007).

Fig. 2.

(a) The absolute change in 1000–500-mb relative humidity (%) from 1–10 to 61–70 yr. (b) The absolute change in 0–500-mb relative humidity (%) from 1–10 to 61–70 yr. (c) The absolute change in precipitation rate (mm day−1) from 1–10 to 61–70 yr.

Fig. 2.

(a) The absolute change in 1000–500-mb relative humidity (%) from 1–10 to 61–70 yr. (b) The absolute change in 0–500-mb relative humidity (%) from 1–10 to 61–70 yr. (c) The absolute change in precipitation rate (mm day−1) from 1–10 to 61–70 yr.

Although the changes in relative humidity are small, they appear to exert an important influence on changes to the hydrological cycle. The ensemble-mean distribution of precipitation change is shown in Fig. 2c and comparison to Fig. 2a underscores how the distribution of precipitation change in the tropics and in the southern oceans, to a large degree, mirrors the change in lower-atmospheric relative humidity in these regions. However, the relationship between the precipitation changes and the relative humidity is not sufficient to wholly describe the model-simulated changes because climate change also includes an effect on the ratio of the global-mean precipitation sensitivity to the global-mean water vapor sensitivity. These changes, which represent a proxy for the efficiency of the global atmosphere’s conversion of increased water vapor into increased precipitation, are explored below.

Figure 3 provides a slightly different perspective on the results of Fig. 1 by showing the differences in global-mean column water vapor ΔW as a function of the global-mean surface temperature ΔTs for all models studied. In the previous section we noted that the global-mean sensitivity deduced from the individual models is approximately 7.4% K−1, slightly exceeding the CC inferred global-mean value by 0.7% K−1. Figure 3 also contrasts the change in precipitation as a function ΔTs. The sensitivity of precipitation to changes in surface temperature is approximately 2.3% K−1 (also Held and Soden 2006). We introduce the following nondimensionalized ratio of the precipitation sensitivity to water vapor sensitivity:

 
formula

where W and P are global-mean values of column water vapor and precipitation, respectively, and ΔP and ΔW are the increased precipitation and column water vapor related to global warming, respectively. This ratio is a simple and convenient proxy of the atmosphere’s efficiency in converting increased global-mean water vapor into increased global-mean precipitation. It also provides a simple way of examining the disparity between the scaling of precipitation that might be expected from CC alone (hereafter ɛCC = 1) and the actual changes predicted by models. Figure 4a shows this quantity for individual models, indicating a range from 0.09 to 0.25, substantially below ɛCC = 1.

Fig. 3.

The relative changes in column water vapor amount and precipitation rate, expressed as percentage changes, as functions of global temperature change derived from the AR4 models. The change in column water vapor derived assuming the CC relationship (see text for explanation) corresponds to an increase of 7.4% K−1. The sensitivity of global precipitation rate changes to temperature changes is approximately 2.3% K−1. The discrepancy between these two sensitivities indicates that the ratio of precipitation sensitivity to water vapor sensitivity in these models must be much less than unity. Note: Not all models had both column water vapor and precipitation data.

Fig. 3.

The relative changes in column water vapor amount and precipitation rate, expressed as percentage changes, as functions of global temperature change derived from the AR4 models. The change in column water vapor derived assuming the CC relationship (see text for explanation) corresponds to an increase of 7.4% K−1. The sensitivity of global precipitation rate changes to temperature changes is approximately 2.3% K−1. The discrepancy between these two sensitivities indicates that the ratio of precipitation sensitivity to water vapor sensitivity in these models must be much less than unity. Note: Not all models had both column water vapor and precipitation data.

Fig. 4.

(a) The change in the global-mean precipitation efficiency as defined by the nondimensionalized ratio of the precipitation sensitivity to the column water vapor sensitivity. (b) The global change in recycling or residence time for water vapor in the atmosphere in days, illustrating the slowing of the atmospheric branch of the hydrological cycle slows under global warming.

Fig. 4.

(a) The change in the global-mean precipitation efficiency as defined by the nondimensionalized ratio of the precipitation sensitivity to the column water vapor sensitivity. (b) The global change in recycling or residence time for water vapor in the atmosphere in days, illustrating the slowing of the atmospheric branch of the hydrological cycle slows under global warming.

Because the time scale of cycling water in the atmosphere is also dictated broadly by the ratio of the total water vapor in the atmosphere to precipitation rate (e.g., Trenberth 1998), the reduced sensitivity of precipitation relative to the sensitivity of water vapor also implies that the time scale of cycling water through the atmosphere must also be increased in these global warming experiments (Bosilovich et al. 2005). This is confirmed in Fig. 4b, showing the change in residence time of water vapor in the atmosphere. The reduced residence time, and thus the implied slowing of the atmospheric branch of the hydrological cycle, has been noted in other contexts, such as in those studies that examine the change in the character of precipitation with more intense storms occurring in a warmed climate with longer periods between events (Tselioudis and Rossow 2006; Kharin and Zwiers 2005; Groisman et al. 2005). Held and Soden (2006) also note how the model convective mass fluxes are also reduced under global warming, and Vecchi and Soden (2007) outline changes in model-predicted vertical velocity, both of which are also consistent with a slowing of this branch of the hydrological cycle.

4. Cloud and radiative heating changes in global warming simulations

Figures 5 and 6, respectively, show the changes in global cloud amount and atmospheric column radiative heating resulting from these cloud changes. These ensemble-mean results include only the seven models indicated in Table 1. The pressure ranges defined by the International Satellite Cloud Climatology Project (ISCCP; Schiffer and Rossow 1983) for high, middle, and low cloud are also applied in this study. Figure 5 reveals small increases in high clouds over the eastern tropical Pacific and at higher latitudes, as well as decreases in high clouds over a broad region centered on the Maritime Continent. There are also small but widespread decreases of low clouds between 30°–60°N and 30°–60°S, consistent with slight decreases in relative humidity observed in the lower troposphere (Fig. 2a). The largest changes in cloudiness, however, are the wide-scale decreases of midlevel clouds, particularly in the midlatitudes and over the Maritime Continent.

Fig. 5.

The changes in (a) low (p ≥ 680 mb), (b) midlevel (680 mb > p ≥ 440 mb), and (c) high (p < 440 mb) cloud amount (%) for selected models, as indicated in Table 1.

Fig. 5.

The changes in (a) low (p ≥ 680 mb), (b) midlevel (680 mb > p ≥ 440 mb), and (c) high (p < 440 mb) cloud amount (%) for selected models, as indicated in Table 1.

Fig. 6.

The changes in (a) longwave, (b) shortwave, and (c) net cloud radiative forcing (W m−2) for selected models, as indicated in Table 1.

Fig. 6.

The changes in (a) longwave, (b) shortwave, and (c) net cloud radiative forcing (W m−2) for selected models, as indicated in Table 1.

The changes in cloud vertical structure implied in the results of Fig. 5 impose important influences on the radiative budget of the atmospheric column. This influence can be measured by the contribution of clouds to the column radiative heating as introduced by Cnet in (5) below. Figure 6 presents Cnet and the individual long- and shortwave components that define it. The decreases in middle-level clouds, and to a lesser extent lower clouds, induce a net column warming by proportionally exposing the higher clouds above to the warmer lower atmosphere. This results in a broad increase in the longwave contribution to Cnet, especially in midlatitudes where the heating pattern mirrors the pattern of change in midlevel clouds. A tongue of strong heating also exists over the tropical mid- to eastern Pacific resulting from the small increases of high clouds there.

5. Global energy controls on precipitation

It is obvious from the results of Fig. 3 that more influential controls on global precipitation exist in models other than those of moisture availability alone. While the latter might influence regional changes in precipitation to some degree, as noted in the comparison of the changes to low-level relative humidity (Fig. 2a) and precipitation (Fig. 2c), increased water vapor governs the changes to global precipitation in a more indirect but significant way. As noted earlier, it has been understood for some time that the global hydrological cycle and global atmospheric energy budget are intimately linked and that changes to atmospheric energy, more so than changes to water variability, control the hydrological cycle on the global scale (Stephens et al. 1994; Stephens 2005; Mitchell et al. 1987; Allen and Ingram 2002).

We now examine this energy-based control in the context of the ratio ɛ introduced in section 3. We start by first considering the atmospheric energy balance of the form

 
formula

where Rnet,atm is the net radiative energy loss from the atmosphere that occurs as a result of the fact that the emission of radiation from the atmosphere exceeds the absorption of radiation by the atmosphere. This net radiative loss is balanced by the input of energy from convective processes that transport both sensible (S) and latent (LP) heat from the surface and deposit it in the atmosphere, where P is the surface precipitation and L is the latent heat of vaporization. In general, the larger of these two turbulent contributions is the latent heating associated with evaporation of water from the surface, mostly over the world’s oceans. This simple balance between radiation losses and heat added from the surface and mixed into the atmosphere by convection constitutes a general state of radiative convective equilibrium (e.g., Goody and Walker 1972; Manabe and Strickler 1964). In this state, the net radiative flux at the top of the atmosphere is zero, and thus Rnet,atm = Rnet,sfc, where Rnet,sfc is the net radiative flux at the surface (positive downward). Thus, in a state of radiative convective equilibrium, the atmospheric energy balance as expressed by (3a) is equivalent to the surface energy balance

 
formula

The relationship between the changes to atmospheric radiative cooling, namely, ΔRnet,atm (and therefore changes to the surface radiation balance) and changes to precipitation ΔP, then follows as (e.g., Stephens 2005)

 
formula

where positive values of ΔRnet,atm correspond to increased emission of infrared radiation from the atmosphere (i.e., more radiative cooling), ΔS is the change in sensible heating, and LΔP is the corresponding change in latent heating of the atmosphere determined by a change in precipitation of amount ΔP. Figure 7 illustrates the energy balance of the perturbed state and shows the changes to the global- and annual-mean atmospheric net radiation (ΔRnet,atm) of individual models versus the respective changes in latent heating (LΔP). This figure indicates that the changes in sensible heating, on the whole, are smaller than the other two components and generally are negative. This decrease in sensible heating is the result of the increased infrared opacity of the atmosphere associated with increased water vapor levels in the atmosphere, which, in a general state of radiative equilibrium, acts to reduce the air–sea temperature difference at the surface (e.g., Goody 1964) thereby inhibiting the sensible heat flux.

Fig. 7.

The relationship between changes in latent heating (LΔP) vs changes in atmospheric column cooling (ΔRnet) for the AR4 models. The dotted line represents the linear relationship between the two quantities, and the offset between that line and the solid line representing a one-to-one correspondence reflects the contribution of sensible heating to the energy balance.

Fig. 7.

The relationship between changes in latent heating (LΔP) vs changes in atmospheric column cooling (ΔRnet) for the AR4 models. The dotted line represents the linear relationship between the two quantities, and the offset between that line and the solid line representing a one-to-one correspondence reflects the contribution of sensible heating to the energy balance.

The loss of radiant energy from the atmosphere Rnet,atm can also be conveniently separated into two components (e.g., Stephens 2005)—one resulting from the clear-sky contribution to this net emission (Rnet,clr) and the second resulting from changes associated with the absorption and emission by clouds Cnet as presented in Fig. 6. Thus, we write

 
formula

where a positive value of Cnet corresponds to a heating of the column and thus a reduction of the radiative loss of the column. The clear-sky term, of the order of 100 W m−2, is the dominant contribution and its change can be directly related to W (e.g., Stephens et al. 1994). The cloud term Cnet is much less certain and cannot simply be predicted by water vapor changes. Recent global estimates of this quantity using new satellite observations indicate that it is less than 10 W m−2 (Stephens et al. 2008). To first order, Rnet,clr varies proportionally with W according to a power law that owes its existence to the properties of the bulk absorption (and emission) of radiation by strongly absorbing gases, like water vapor. The relation between the absorption and absorption path is referred to as the curve of growth. A crude but adequate approximation of this curve of growth relation between water vapor and Rnet,clr is

 
formula

where c0 represents the limit of column cooling by all other greenhouse gases in the absence of water vapor and b = 0.5 under the “square root law” approximation (e.g., Goody and Yung 1995). We tabulate values of a, b, and c0 derived from a curve fit to the data obtained for all climate models with sufficient data and for which the fit converged to a single, physically reasonable solution. These parameters, along with the calculated standard deviations in those parameter fits, are provided in Table 2 for each successful model fit.

Table 2.

Retrieved parameters of the curve fit to the clear-sky atmospheric emission vs column water vapor curves. Sigma represents the standard deviation in the parameters as returned from the curve-fitting routine. Models not appearing on this list either had insufficient data for calculation or the curve fit did not converge to a physically reasonable value.

Retrieved parameters of the curve fit to the clear-sky atmospheric emission vs column water vapor curves. Sigma represents the standard deviation in the parameters as returned from the curve-fitting routine. Models not appearing on this list either had insufficient data for calculation or the curve fit did not converge to a physically reasonable value.
Retrieved parameters of the curve fit to the clear-sky atmospheric emission vs column water vapor curves. Sigma represents the standard deviation in the parameters as returned from the curve-fitting routine. Models not appearing on this list either had insufficient data for calculation or the curve fit did not converge to a physically reasonable value.

We now consider three separate approximations to illustrate the behavior of ɛ as a function of the changes to different energy balance terms in (4) and (5). Consider first the idealized state of balance governed purely by clear-sky emission and absorption and latent heating:

 
formula

and thus

 
formula

where we explicitly ignore the contributions changes by ΔCnet and ΔS for the time being. From (6), we infer

 
formula

and combining (8) with (7) and (2), we obtain

 
formula

which we will refer to as the water vapor emission limit on the efficiency. In this case, the ratio of precipitation sensitivity to water vapor sensitivity is determined by the exponent of the curve of growth relationship (6) and the normalized magnitude of the growth of emission itself, defined from the difference between the atmospheric emission devoid of water vapor (c0) and the atmospheric emission containing the present-day amounts of water vapor (Rnet,clr). The reference limit defined in this way is shown in Fig. 8, including errors bars to denote the range of values possible given the uncertainty of the curve fits to the data. This figure illustrates that reference limit closely approximates to the actual efficiency derived using (2) above. That is to say, the global changes in precipitation of the models analyzed closely follow the change in emission as governed by water vapor changes alone.

Fig. 8.

A comparison of the model-predicted precipitation efficiency ɛ to estimates of the emission limit derived from changes in the radiative balance of model atmospheres for selected models. (from left to right) The bars represent the water vapor emission limit based solely on changes in clear-sky column cooling for selected models, the predicted precipitation efficiency, the emission limit when including only the radiative effects of clouds, the emission limit when including only the effect of including sensible heating, and the emission limit when including both clouds and sensible heating. The ensemble-mean relationships appear in the rightmost set of bars. The error bars on the water vapor emission limit indicate the uncertainty in this limit resulting from uncertainty from the curve fit parameters b and co (see Table 2).

Fig. 8.

A comparison of the model-predicted precipitation efficiency ɛ to estimates of the emission limit derived from changes in the radiative balance of model atmospheres for selected models. (from left to right) The bars represent the water vapor emission limit based solely on changes in clear-sky column cooling for selected models, the predicted precipitation efficiency, the emission limit when including only the radiative effects of clouds, the emission limit when including only the effect of including sensible heating, and the emission limit when including both clouds and sensible heating. The ensemble-mean relationships appear in the rightmost set of bars. The error bars on the water vapor emission limit indicate the uncertainty in this limit resulting from uncertainty from the curve fit parameters b and co (see Table 2).

Now, we consider the contribution of clouds by considering the all-sky energy balance,

 
formula

and its perturbed form

 
formula

Using Eqs. (5) and (6), we obtain

 
formula

and, on rearrangement with some simplification,

 
formula

The additional term that appears in (12) compared to (9) represents the direct effects of cloud feedbacks on precipitation through the contribution of ΔCnet on the net atmospheric energy balance. Because ΔCnet is positive (Fig. 6), the heating of clouds acts to further reduce the efficiency below the water vapor emission limit. Figure 8 illustrates how this contribution is indeed nonnegligible and is an important factor in establishing the overall global precipitation efficiency.

The influence of sensible heating on ɛ can be deduced in an analogous way by considering the balance

 
formula

and its perturbed form

 
formula

where cloud effects on the radiance balance are ignored. Following the same steps used to develop (12) we obtain

 
formula

Because ΔS < 0 (Fig. 9 below), the second term on the right-hand side of (15) is positive. Thus, reductions in sensible heat flux act to enhance the efficiency ɛ illustrated in Fig. 8. This is a simple and obvious result: for a given amount of radiative cooling any decrease in sensible heating must be offset by an increase in precipitation to provide balance.

Fig. 9.

A summary of the key findings of this study. Absolute (Abs) changes in quantities (filled bars) correspond to the scale at the bottom of the figure and relative percentage (Rel) changes in quantities (hatched bars) refer to the scale at the top.

Fig. 9.

A summary of the key findings of this study. Absolute (Abs) changes in quantities (filled bars) correspond to the scale at the bottom of the figure and relative percentage (Rel) changes in quantities (hatched bars) refer to the scale at the top.

6. Summary and discussion

Figure 9 summarizes the key results and findings of this study. It presents ensemble- and global-mean changes in selected model properties. Certain aspects of the results shown have also been noted in other studies. For example, the increase in column-integrated water vapor occurs at a rate that resembles a Clausius–Clapeyron (CC) relationship (e.g., Held and Soden 2006) and at a rate that resembles observations (Willett et al. 2007; Santer et al. 2007). Although the majority of the water mass increase occurs below 500 hPa (Fig. 9), the proportional increase of upper-tropospheric water vapor is substantially greater than that of the lower atmosphere. Given that upper-tropospheric water vapor has a disproportionately large influence on the water vapor feedback (Held and Soden 2000), the potential influences of the change in upper-tropospheric water vapor on the modeled greenhouse effects and the water vapor feedback are topics that warrant further research. Figure 9 also indicates that the absolute global-mean change in lower-atmosphere RH is small but is composed of coherent, compensating small regional increases and decreases (Fig. 2a). The regional changes to precipitation correlate significantly to regional changes in lower-atmospheric RH (Fig. 2c, and discussion). As noted by others (e.g., Held and Soden 2006; Seager et al. 2007; Allan and Soden 2007), the ensemble model results indicate that wet areas gain in precipitation and dry areas are prone to more droughts. The relevance of the association between the circulation and water vapor on precipitation is also noted in Meehl et al. (2005).

The main results of this study can be summarized as follows:

  • (i) Model-predicted water vapor increases per degree of warming occur at a rate that is more than 3 times the respective rate of increase of precipitation (Fig. 3). This result has many implications, two of which are examined. The result clearly points to the influence of factors other than water vapor alone on global precipitation. As a consequence of these controls, it takes longer for the increasing water vapor in the model atmosphere to cycle through the atmosphere, implying a slowing of the atmospheric branch of the hydrological cycle (Figs. 4b and 9). Furthermore, the ratio of global changes in precipitation to global changes in water vapor offer some insight on how readily increased water vapor is converted into precipitation in modeled climate change. This ratio ɛ is introduced as a gross indicator of the global precipitation efficiency under global warming (Fig. 4a).

  • (ii) Increases in the global precipitation track increases in atmospheric radiative energy loss (Fig. 7) and the ratio of precipitation sensitivity to water vapor sensitivity is primarily determined by changes to this atmospheric column energy loss. A reference limit to this ratio ɛwυ is introduced as the rate at which the emission of radiation from the clear-sky atmosphere increases as water vapor increases. It is shown in Fig. 8 that the derived efficiency based on the simple ratio of precipitation-to-water vapor sensitivities in fact closely matches the sensitivity derived from simple energy balance arguments involving changes to water vapor emission alone. That is, as water vapor increases, the atmosphere cannot emit radiation at a large enough rate to support precipitation matching the rate of increase in water vapor.

  • (iii) Although the rate of increase of clear-sky emission is the dominant factor in changing the energy balance of the atmosphere (Fig. 9) and in establishing the efficiency ɛ, there are two important and offsetting processes that contribute to ɛ in the model simulations studied: One involves a negative feedback through cloud radiative heating (Fig. 9), which acts to reduce the efficiency (Fig. 8); the second is a global reduction in sensible heating (Fig. 9) that counteracts the effects of the cloud feedback and increases ɛ.

  • (iv) The negative cloud radiative heating feedback occurs through reductions of cloud amount in the middle troposphere, defined by the layer between 680 and 440 hPa, and by slight global cloud decreases in the lower troposphere. These changes act in a manner that exposes the warmer atmosphere below to high clouds, thus resulting in a net warming of the atmospheric column by clouds and a negative feedback on the precipitation.

Although the global-scale influences on precipitation, the main topic of this paper, appear to have little direct relevance to the important topic of understanding the character of precipitation change and its regional consequences, the results of this paper nevertheless provide a context for developing a broader understanding of this topic. The results explain why the rate at which water is cycled through the atmospheric hydrological cycle must reduce in global warming. There are other indicators that this “slowing” of the atmospheric branch of the hydrological cycle is occurring in models, such as in the analysis of Held and Soden (2006), who note the reduced convective mass fluxes of models. This slowing of the cycle appears to manifest itself through a combination of less frequent but more intense storm events in models (Tselioudis and Rossow 2006; Kharin and Zwiers 2005; Pall et al. 2007).

This study raises the following very important question as well: Are observed changes in global precipitation consistent with a rate of change that mirrors both the observed and modeled changes of water vapor, or are they consistent with the notion that the growth of precipitation, controlled by energetics, should be constrained for reasons mentioned in this paper? Strong evidence exists to suggest that the observed water vapor content of the atmosphere is increasing at rates similar to that projected by climate models, at least over oceans (e.g., Trenberth et al. 2005; Santer et al. 2007). A number of studies suggest that the frequency of intense precipitation (e.g., the frequency of very heavy precipitation or the upper 0.3% of daily precipitation events) has increased over half of the land area of the globe (e.g., Groisman et al. 2005). The studies of Fu et al. (2006), Mitchell et al. (1987), and Lu et al. (2007) also suggest that the areal extent of regions of the subtropics that come under the influence of broad-scale subsidence might also be expanding in time, broadly consistent with the model-drying tendency in the subtropics as implied in Fig. 2. This result appears to have been confirmed in the study of Allan and Soden (2007) who find that precipitation is observed to have decreased in descending regimes that typically define dry climatic regions between 30°N and 30°S. Although we expect the broad changes in precipitation distribution are shaped by changes to the large-scale circulation, Emori and Brown (2005) suggest that the noted precipitation increases by more intense storms in models is governed by thermodynamics rather than changes in atmospheric circulation.

Still, the results of a number of recent studies seem to conflict with the results presented in this study. For example, Gu et al. (2007) analyze 27 yr of Global Precipitation Climatology Project (GPCP) data, as do Allan and Soden (2007), and find a trend in the tropical precipitation over oceans that is more similar to the stated water vapor trend (i.e., ɛ ≈ 1) than the projected trends of climate models. Zhang et al. (2007) report on analysis of 75 yr of surface rain gauge data and note that observed regional changes of both signs are larger than the modeled changes. Wentz et al. (2007) recently reported on a study that merges different global precipitation data sources, including GPCP, with their own microwave-based precipitation estimates, together with inferences on evaporation, and they estimate a change in global precipitation of 6% K−1, which again implies ɛ → 1.

At first glance, it would appear from these studies that the models significantly underestimate the increase in precipitation suggested from observations. These observationally based studies seem to suggest that the rate of increase of precipitation ought to be similar to the rate of increase of water vapor, that is, ɛ ≈ 1, yet the robust, physical constraints described in this paper suggest that ɛ < 1 is to be expected and, in fact, is much closer to the values predicted by models. Feedbacks could occur in the real climate system that changes the nature of the constraints discussed in this paper, increasing ɛ toward the CC value, although it is difficult to see how these feedbacks could alter the energy balance enough to push ɛ to unity. For example, cloud changes could occur that are the reverse of those shown in Fig. 5; substantial decreases in high cloud and increases in low cloud could add to the water vapor–induced atmospheric cooling. This analysis suggests this feedback would have to approximately quadruple the magnitude of the water vapor–based cooling perturbation for ɛ → 1, and this seems unrealistic given that the net global radiative heating of the atmosphere by clouds in the present climate is almost an order of magnitude smaller than that resulting from water vapor (Stephens et al. 2008).

This brings the focus on the observation studies themselves and, in particular, a focus on the uncertainties related to the observing systems in those studies. The observations reported in most of these studies are not global, restricted to over land (e.g., Zhang et al. 2007), or limited to the tropics (Allan and Soden 2007), and thus can neither confirm nor refute the results of this paper. The only truly near-global (land + ocean) data source of precipitation is that of GPCP, and much care is needed in interpreting any trend in these data as Gu et al. (2007) caution. GPCP data are a heterogeneous mix of satellite data of different types and sensitivities to precipitation (based on infrared and microwave radiances) as well as surface rain gauge data (Huffman et al. 1997), and the uncertainty in the precision of these data has yet to be established. Gu et al. (2007) note that “the global linear change of precipitation is near zero” (we estimate it as less than 1% K−1 based on their trends); however, Wentz et al. (2007), using their own satellite microwave-based product over oceans combined with the overland GPCP, arrive at a conflicting result with precipitation changes approaching 6% K−1. This merely highlights the inconsistencies in the global data sources themselves and, coupled with the difficulties that arise from calculating decadal-scale trends with data that span a relatively short time period, serves as reminder that trends in these data should be treated cautiously at this time.

Acknowledgments

The authors wish to thank the three anonymous reviewers whose comments helped refine this study a great deal. This work was supported by NASA Contract NNG04GB97G and the U.S. Department of Energy Atmospheric Radiation Measurement Program under Grant DE-FG03-94ER61748. We acknowledge the modeling groups for making their simulations available for analysis, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the CMIP3 model output, and the WCRP’s Working Group on Coupled Modelling (WGCM) for organizing the model data analysis activity. The WCRP CMIP3 multimodel dataset is supported by the Office of Science, U.S. Department of Energy.

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Footnotes

Corresponding author address: Dr. Graeme L. Stephens, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371. Email: stephens@atmos.colostate.edu

1

Run 1 is used in all cases except for the National Center for Atmospheric Research (NCAR) Parallel Climate Model, version 1 (PCM1), where run 2 is used because it includes an entire model integration in one file.

2

Vecchi and Soden (2007) study the changes in the Special Report on Emission Scenarios (SRES) A1B of the IPCC AR4 models. This corresponds to a doubling of equivalent carbon dioxide between 2000 and 2100, after which time the radiative forcings are held constant.