Abstract

Global warming mechanisms that cause changes in frequency and intensity of precipitation in the tropics are examined in climate model simulations. Under global warming, tropical precipitation tends to be more frequent and intense for heavy precipitation but becomes less frequent and weaker for light precipitation. Changes in precipitation frequency and intensity are both controlled by thermodynamic and dynamic components. The thermodynamic component is induced by changes in atmospheric water vapor, while the dynamic component is associated with changes in vertical motion. A set of equations is derived to estimate both thermodynamic and dynamic contributions to changes in frequency and intensity of precipitation, especially for heavy precipitation. In the thermodynamic contribution, increased water vapor reduces the magnitude of the required vertical motion to generate the same strength of precipitation, so precipitation frequency increases. Increased water vapor also intensifies precipitation due to the enhancement of water vapor availability in the atmosphere. In the dynamic contribution, the more stable atmosphere tends to reduce the frequency and intensity of precipitation, except for the heaviest precipitation. The dynamic component strengthens the heaviest precipitation in most climate model simulations, possibly due to a positive convective feedback.

1. Introduction

Anthropogenic influences on the earth’s climate have become more and more evident. The most pronounced climate change caused by human-induced forcings is global warming. Global warming has not only been projected by climate models (e.g., Meehl et al. 2007) but has also been seen in observations (e.g., Jones and Moberg 2003; Smith and Reynolds 2005; Trenberth et al. 2007). Under this global warming trend, changes in precipitation have also been found in both observations (e.g., Gu et al. 2007; Wentz et al. 2007) and climate model simulations (e.g., Held and Soden 2006; Meehl et al. 2007; Vecchi and Soden 2007). For global averages, precipitation tends to increase with the warming and its change is controlled by the global energy budget, a balance between latent heating and radiative cooling (e.g., Allen and Ingram 2002; Held and Soden 2006; Lambert and Allen 2009). Climate model simulations show an increased rate of global-mean precipitation of 1%–3% K−1 of surface warming (e.g., Held and Soden 2006; Vecchi and Soden 2007; Stephens and Ellis 2008), while observations show an increased rate with a much wider range among datasets. Wentz et al. (2007) estimated the increased rate in 1987–2006 of 7% K−1 of surface warming, which is close to the Clausius–Clapeyron thermal scaling. Adler et al. (2008), on the other hand, used the Global Precipitation Climatology Project (GPCP) (Adler et al. 2003) precipitation and the NASA Goddard Institute for Space Studies (GISS) surface temperature, and obtained a rate of 2.3% K−1 in 1979–2006. The discrepancy between the climate model simulations and the observations might be due to differences in periods that are used to calculate the increased rate of global precipitation (Liepert and Previdi 2009) since the changes in a shorter period could include not only a long-term trend but also an interdecadal variation.

On a regional basis, precipitation changes are more complicated and show an even poorer agreement among climate models (e.g., Allen and Ingram 2002; Neelin et al. 2006; Meehl et al. 2007), which might be due to changes in vertical velocity (Chou et al. 2009). To precisely project future precipitation changes on a regional basis, understanding mechanisms of the precipitation changes is very crucial (Muller and O’Gorman 2011). Chou and Neelin (2004) used a climate model with intermediate complexity to study the global warming mechanisms of tropical precipitation changes. They found that most positive precipitation anomalies over convective regions are induced by the “rich get richer” mechanism, in which increased water vapor destabilizes the atmosphere and further enhances precipitation over areas with strong convection. Negative precipitation anomalies over convective margins, on the other hand, are associated with the “upped ante” mechanism, in which a dry advection transports relatively dry air from areas outside convective regions and suppresses convection over the convective margins. These mechanisms are also found in more comprehensive climate models (Chou et al. 2006, 2009; Seager et al. 2010).

The studies discussed above all focus on changes in mean precipitation. The changes of frequency and intensity are also crucial to assess the global warming impacts (Trenberth et al. 2003); however, the changes in mean precipitation cannot tell us how precipitation frequency and intensity will change. For changes in precipitation frequency, previous studies show in observations that heavy precipitation tends to become more frequent, while light precipitation becomes less frequent (e.g., Fujibe et al. 2005; Goswami et al. 2006; Lau and Wu 2007; Qian et al. 2007; Trenberth et al. 2007; Allan and Soden 2008; Shiu et al. 2009). This tendency of changes in precipitation frequency has also been found in climate models (Sun et al. 2007). For changes in precipitation intensity, the intensity, particularly for precipitation extremes, tends to increase (e.g., Groisman et al. 2005; Alexander et al. 2006; Kharin et al. 2007; Trenberth et al. 2007; Min et al. 2011). In a warmer climate, water vapor in the atmosphere tends to increase, so increases in precipitation intensity are expected from a theoretical point of view if the associated atmospheric circulation does not change too much (Allen and Ingram 2002; Pall et al. 2007; O’Gorman and Schneider 2009; Gastineau and Soden 2011).

Previous studies discussed changes in precipitation frequency and intensity and also provided possible mechanisms for these changes, especially for changes in intensity of precipitation extremes. In this study, we analyze changes in precipitation frequency and intensity under global warming, particularly in the tropics (30°S–30°N). Climate model simulations used here are described in section 2, along with derivatives of equations to estimate thermodynamic and dynamic contributions to precipitation frequency and intensity. Changes in precipitation frequency and intensity from the ensembles of 10 climate models are shown in section 3. Mechanisms for changes in precipitation frequency and intensity are discussed in sections 4 and 5, respectively, followed by discussion and conclusions.

2. Data and analysis method

a. Data

The World Climate Research Programme (WCRP) Coupled Model Intercomparison Project phase 3 (CMIP3) multimodel dataset is used here. The A1B scenario is chosen for the twenty-first-century simulations, along with the 20C3M simulations. Ten climate models (Table 1) are chosen in this study because of data availability. One realization of each model is examined. The current climate is defined as the period from 1981 to 2000 and will be compared to future climate, which is defined as the period from 2081 to 2100. Most results shown here are multimodel ensembles. To obtain multimodel ensembles, we first calculate changes for each model, and then normalize them with changes in the global-mean surface temperature of its own before averaging the changes from 10 climate models. The standard deviation in each figure is calculated from these 10 climate models, so it is an intermodel standard deviation. Since we are interested in frequency and intensity of precipitation, daily data are used. We note that daily data still cannot exactly present precipitation intensity and frequency, such as hourly data, but it should be good enough to show the tendency of the changes due to global warming.

Table 1.

List of the 10 coupled atmosphere–ocean climate model simulations in the A1B scenario from the CMIP3 archive.

List of the 10 coupled atmosphere–ocean climate model simulations in the A1B scenario from the CMIP3 archive.
List of the 10 coupled atmosphere–ocean climate model simulations in the A1B scenario from the CMIP3 archive.

b. Precipitation frequency and intensity

Before calculating the frequency and intensity of precipitation, we first use 0.1 mm day−1 as a threshold to define a precipitation event, which has been used in previous studies (e.g., Sun et al. 2007). In other words, only daily precipitation greater than 0.1 mm day−1 is counted as one precipitation event. The precipitation amount accumulated from daily precipitation less than 0.1 mm day−1 is very small, less than 0.3% of total precipitation, so it does not affect the results in this study. The frequency of precipitation is a function of intensity bins, with an interval of 1 mm day−1 in this study. We note that the first intensity bin is between 0.1 and 1 mm day−1. For each intensity bin, the frequency of precipitation is the percentage of both precipitation and nonprecipitation events (days) cumulating in the tropics (30°S–30°N) for current and future climate, respectively. This definition is similar to that used in Sun et al. (2007). For the multimodel ensemble, we first calculate changes in the frequency of precipitation for each model, doing so by normalizing them with the changes in its global-mean surface temperature. Then we average them for each intensity bin.

To calculate the intensity of precipitation, we first rank the daily precipitation from light to heavy precipitation in the tropics for the current and future climate, respectively. For instance, the 99th percentile bin indicates the strongest percent of precipitation in the time–space cumulative distribution. We then calculate the intensity of precipitation by averaging precipitation over each percentile bin. The width for each percentile bin is 1%. To examine precipitation extremes, we further divide the strongest percentile bin, that is, the 99th percentile, equally into 100 intervals with a width of 0.01%. We next normalize changes in precipitation intensity for each percentile bin with changes in its global-mean surface temperature. This is similar to those used in previous studies, such as Allen and Ingram (2002), O’Gorman and Schneider (2009), and Sugiyama et al. (2010). The multimodel ensemble is an average of the 10 models for each percentile bin.

c. Moisture budget

To understand changes in precipitation intensity, a column-integrated water vapor budget is used, which can be written as

 
formula

where pressure velocity ω is assumed to be zero at the surface and at tropopause, and angle brackets denote a mass integration through the entire troposphere. Here v is horizontal velocity. Since P and E designate the latent heat release due to precipitation and evaporation, P is in energy units (W m−2, which, divided by 28, becomes mm day−1). The number 28 is obtained from ρL day−1, where ρ is the density of liquid water (=1 kg m−2 mm−1), L is latent heat per unit mass, and “day” is in seconds. For the same reason, specific humidity q is also in energy units by absorbing L. In (1) water storage in the atmosphere is neglected since it is relatively small. Contributions from the surface process due to topography (Seager et al. 2010) are also not included. The change in precipitation intensity P′ can be estimated by

 
formula
 
formula

where 〈···〉 denotes climatology in 1981–2000. Here 〈···〉′ represents the difference between the future and current climate (i.e., the future minus current climate). The nonlinear effect, such as transient, is neglected in (3). The second term on the right is the thermodynamic component, which is associated with changes in water vapor. The third term on the right is the dynamic component, associated with changes in vertical motion and tropical circulation. The last term on the right is changes in horizontal moisture advection.

The moisture budget discussed here is usually not balanced, even including the nonlinear term −〈ω′∂pq′〉 and other terms that we neglected, such as the transient in current climate, the water vapor storage in the atmosphere, and the surface effect associated with topography. The errors could come from various places (Seager et al. 2010). For instance, the interpolation from the original model hybrid atmospheric levels to standard pressure levels can contribute to the errors (Chou and Chen 2010). The errors can also be introduced by the transient since we calculate the moisture budget with daily output, not the output from each model time step. However, these errors will not alter our result, which will be discussed later.

The moisture budget (3) can be used to calculate contributions to intensity of precipitation, averaged for each percentile bin. Unlike the moisture budget for mean precipitation, discussed in our previous studies (e.g., Chou et al. 2006, 2009), in which means are temporal averages for each grid point, means discussed here, such as ω and q, are averaged over each percentile bin. We note that the nonlinear contribution from the variation within each percentile bin is neglected.

For percentage changes, the water vapor budget (2) can be rewritten as

 
formula

since evaporation and horizontal moisture advection are relatively small and the residual is proportional to −〈ωpq〉′. We will demonstrate this with examples in section 5. In this study, we examine the thermodynamic and dynamic contributions to precipitation intensity, so the vertical moisture advection in (4) can be further divided into

 
formula

We note that the denominators are slightly different between the right and left of (5). Actually, the thermodynamic and dynamic contributions are physically better represented by the terms on the right of (5). The thermodynamic contribution, the first term on the right of (5), is similar to that used in O’Gorman and Schneider (2009) but with the specific humidity instead of the saturation specific humidity. However, both estimations should be close to each other, as pointed out by Sugiyama et al. (2010). The second term on the right of (5), the dynamic contribution, is a relatively more direct measurement for the dynamic contribution than that used in O’Gorman and Schneider. The dynamic contribution estimated in (5) considers changes in vertical velocity at all levels, unlike those used in Emori and Brown (2005) and Sugiyama et al., which consider changes in vertical velocity only at 500 hPa.

d. Estimation of thermodynamic and dynamic contributions to frequency

Moisture convergence associated with vertical motion −〈ωpq〉 is usually the main process that induces precipitation, which is particularly true for heavy precipitation (Schneider et al. 2010; Sugiyama et al. 2010). Within one precipitation intensity bin, the corresponding vertical motion is usually a probability distribution function, not a fixed number. We use the vertical velocity at 500 hPa ω500 to represent the corresponding vertical motion since most precipitation, extremes in particular, is associated with convection. We note that this assumption might not be suitable for light precipitation since −〈ωpq〉 is not the dominant process for light precipitation, but it can still be used to estimate those changes associated with −〈ωpq〉. For a given intensity of precipitation Pi, the frequency of the corresponding vertical velocity at 500 hPa for strength at ωj500 can be written as gi(ωj500), a probability distribution function of the vertical velocity. Since ∂pq and q always exist, with or without P ≠ 0, and varies relatively little within one precipitation intensity bin, the frequency of precipitation for a given precipitation intensity bin Pi should be equal to the sum of the frequency of the corresponding vertical motion at 500 hPa in the same precipitation intensity bin:

 
formula

The subscript and superscript i refers to the ordering of precipitation intensity bins and the subscript j is the ordering of intensity bins of vertical velocity at 500 hPa.

Under global warming, when surface temperature warms up 1 K, water vapor increases from q to (1 + γ)q, where γ is the fractional change of water vapor per 1 K of surface temperature increase. Assuming that γ is relatively constant in the vertical:

 
formula
 
formula

This implies that weaker vertical velocity is required to generate the same intensity of precipitation in warmer climate, that is, , because of the increased water vapor. Assuming the distribution of the corresponding vertical motion for each precipitation intensity bin does not change under global warming, the frequency of precipitation in the future will be equal to the frequency of precipitation in the current climate that is associated with −〈ω/(1 + γ)∂pq〉, that is, P/(1 + γ). Thus,

 
formula

where denotes precipitation frequency associated with the thermodynamic component (superscript t) in the future climate (subscript “1”) and the subscript “0” denotes current climate. In other words, the frequency of Pi in the future climate will be similar to the frequency of Pi/(1 + γ) in the current climate if only considering changes in water vapor. The percentage of changes in frequency, that is, with respect to the frequency in current climate, can then be written as

 
formula

According to (10), the change in precipitation frequency induced only by changes in water vapor, that is, the thermodynamic component, can be estimated from the frequency in current climate, as long as the change in water vapor is known.

We next estimate the dynamic contribution to the frequency of precipitation. First, we calculate the frequency of vertical velocity at 500 hPa ω500 associated with precipitation events in the tropics (30°S–30°N) for the current and future climate, respectively, as a function of vertical velocity intensity. The width of each intensity bin is 0.01 Pa s−1 in this study. Under global warming, the normalized change in the frequency of vertical velocity at 500 hPa for a given intensity ωj500 is

 
formula

normalized by the frequency of ωj500 in the current climate, that is, f0(ωj500). We assume that the normalized change in the frequency of the vertical velocity Δf(ωj500) is similar to the normalized change for each precipitation intensity bin Pi: . We note that gi is the probability distribution function of the vertical velocity for only one precipitation intensity bin, that is, Pi. Thus, the contribution of the dynamic component to the frequency of precipitation for the precipitation intensity bin Pi can be written as

 
formula

where the superscript d denotes the dynamic contribution.

Based on (10) and (12), the thermodynamic and dynamic contributions to the precipitation frequency, Δft and Δfd, can be estimated. For the thermodynamic contribution, we assume that the distribution of vertical velocity is unchanged and focus only on changes in water vapor. For the dynamic contribution, on the other hand, we assume that water vapor does not change, but vertical velocity varies with surface temperature. Here we did not consider the contribution from the nonlinear effect, such as when both water vapor and vertical velocity change simultaneously. We want to reemphasize that (10) and (12) are more suitable for heavier precipitation, which is dominated by −〈ωpq〉.

3. Changes in precipitation frequency and intensity

Figure 1 shows changes in the frequency and intensity of precipitation, which are differences between 2081–2100 and 1981–2000. The results in Fig. 1 are tropical averages of every precipitation event at a given grid point for the entire year. The changes in frequency are all negative among the 10 climate models, ranging from −5% to a little less than zero (Fig. 1a). The changes in intensity, on the other hand, show consistent increases among these 10 climate models, ranging from 2% to 11% (Fig. 1b). In other words, precipitation tends to be less frequent but stronger in the tropics under global warming.

Fig. 1.

Tropical averages of changes in precipitation (a) frequency and (b) intensity with respect to changes in global surface temperature (x axis) for 10 CMIP3 coupled GCMs. The changes (%) are differences between 2081–2100 and 1981–2000 with respect to 1981–2000.

Fig. 1.

Tropical averages of changes in precipitation (a) frequency and (b) intensity with respect to changes in global surface temperature (x axis) for 10 CMIP3 coupled GCMs. The changes (%) are differences between 2081–2100 and 1981–2000 with respect to 1981–2000.

We further examine changes in frequency for different precipitation intensities, with a bin interval of 1 mm day−1. Figure 2a shows precipitation frequency in 1981–2000 from the multimodel ensembles for the entire year in the tropics (30°S–30°N). The frequency decreases quickly as the corresponding precipitation intensity increases, so most precipitation events are with very light rain. In the future warmer climate (2081–2100), the frequency for medium and heavy precipitation increases, while light precipitation becomes less frequent (Fig. 2b). Since the decrease in light precipitation is much stronger than the increase in medium and heavy precipitation, the frequency for the entire spectrum of precipitation events tend to decrease, consistent with the result shown in Fig. 1a. When considering changes in percentage, however, the result becomes quite different. As precipitation intensity increases, percentage changes in frequency become larger. The frequency for 100 mm day−1 can increase as high as 35% per 1 K of surface temperature warming, but only around 10% for 50 mm day−1. For light precipitation, the changes are even less, only around −2%. In other words, the most noticeable change in precipitation frequency is the increase of heavy precipitation, even though the change in the number of precipitation events is the smallest for heavy precipitation.

Fig. 2.

Precipitation frequency (a) in 1981–2000 for precipitation intensity from 0.1 to 100 mm day−1, (b) differences between 2081–2100 and 1981–2000, and (c) relative changes, with respect to 1981–2000. The changes in (b) and (c) are normalized by the change in global-mean surface temperature; units are % for (a) and % K−1 for (b) and (c). The interval of each precipitation intensity bin is 1 mm day−1. The solid curves are multimodel ensemble means and the dashed curves indicate one standard deviation.

Fig. 2.

Precipitation frequency (a) in 1981–2000 for precipitation intensity from 0.1 to 100 mm day−1, (b) differences between 2081–2100 and 1981–2000, and (c) relative changes, with respect to 1981–2000. The changes in (b) and (c) are normalized by the change in global-mean surface temperature; units are % for (a) and % K−1 for (b) and (c). The interval of each precipitation intensity bin is 1 mm day−1. The solid curves are multimodel ensemble means and the dashed curves indicate one standard deviation.

We next examine changes in precipitation intensity for different percentile bins, with a bin interval of 1% (Fig. 3). The insets of Fig. 3 show the intensity for heavy precipitation, the last 1%, that is, the 99th percentile, with a 0.01% bin interval. We note that the intensity in climate models is not as strong as in observations at ground stations (e.g., Allan and Soden 2008; Dai 2006), even for the 99.99th percentile bin, which is around 150 mm day−1 (or 6 mm h−1), compared to, for instance, around 35 mm h−1 observed in Taiwan, a subtropical area in which the heaviest precipitation is often related to typhoons (J.-Y. Tu 2011, personal communication). We note that precipitation intensity for the observed 99.99th percentile bin might vary from region to region. This discrepancy between models and observations is mainly due to the coarse spatial resolution used in climate models. Under global warming, precipitation intensity tends to increase for almost every percentile bin, except for the light precipitation which weakens slightly (Fig. 3c). The intensification of precipitation is usually less than 4% except for the 99th percentile bin. For the heaviest precipitation—the 99.99th percentile bin—precipitation intensity can be enhanced to as high as around 9% for the ensemble, with a variation ranging from 1% to 16% among climate models (see the inset of Fig. 3c).

Fig. 3.

Precipitation intensity (a) in 1981–2000 for percentile from 1% to 100% (mm day−1), (b) differences between 2081–2100 and 1981–2000 (mm day−1 K−1), and (c) relative changes with respect to 1981–2000 (% K−1). The interval of each percentile bin is 1%. Insets are for the last one-percentile bin (the 99th percentile), with a 0.01% interval. The changes in (b) and (c) are normalized by the change of global-mean surface temperature. The solid curves are multimodel ensemble means and the dashed curves indicate one standard deviation.

Fig. 3.

Precipitation intensity (a) in 1981–2000 for percentile from 1% to 100% (mm day−1), (b) differences between 2081–2100 and 1981–2000 (mm day−1 K−1), and (c) relative changes with respect to 1981–2000 (% K−1). The interval of each percentile bin is 1%. Insets are for the last one-percentile bin (the 99th percentile), with a 0.01% interval. The changes in (b) and (c) are normalized by the change of global-mean surface temperature. The solid curves are multimodel ensemble means and the dashed curves indicate one standard deviation.

4. Mechanisms for frequency change

a. Thermodynamic contribution

In a warmer climate, relative humidity does not vary too much, so water vapor in the troposphere increases—roughly following the Clausius–Clapeyron thermal expansion of saturated water vapor (Allen and Ingram 2002; Held and Soden 2006; Stephens and Ellis 2008; Trenberth et al. 2003; Vecchi and Soden 2007; Wentz et al. 2007). Figure 4 shows column-integrated water vapor for different precipitation intensity bins. In the current climate, total column-integrated water vapor is ~35 mm (kg m−2) for light precipitation, but increases as the corresponding precipitation becomes stronger (Fig. 4a). This increase of column-integrated water vapor with respect to precipitation intensity has been discussed in previous studies (e.g., Bretherton et al. 2004; Neelin et al. 2009). It reaches around 60 mm for precipitation intensity at 100 mm day−1, but with a flatter slope. This implies that precipitation increases sharply when column-integrated water vapor reaches a critical value (Neelin et al. 2009). Changes in column-integrated water vapor also increase with precipitation intensity (Fig. 4b). The associated percentage changes are around 7%–8% for almost every intensity, varying within a relatively narrow range (Fig. 4c).

Fig. 4.

As in Fig. 2, but showing column-integrated water vapor for different precipitation intensity bins; units are (a) mm, (b) mm K−1, and (c) % K−1.

Fig. 4.

As in Fig. 2, but showing column-integrated water vapor for different precipitation intensity bins; units are (a) mm, (b) mm K−1, and (c) % K−1.

Based on the changes shown in Fig. 4, we can estimate the impact of the increased water vapor, the thermodynamic contribution, on precipitation frequency via (10), and the result is shown in Fig. 5a. The thermodynamic contribution is positive for all intensity bins and increases as precipitation intensity increases. It is ~40% for heavy precipitation, but only ~10% for light precipitation. This positive thermodynamic contribution is expected. In the future warmer climate, weaker vertical velocity is required to generate the same intensity of precipitation because of enhanced water vapor. Vertical velocity (at 500 hPa) usually becomes more frequent as its amplitude decreases (Fig. 6a). We note that (10) is a good approximation only for heavy precipitation, which is dominated by the moisture convergence associated with vertical motion, that is, −〈ωpq〉. Compared to changes in frequency for heavy precipitation (Fig. 2c), the result in Fig. 5a implies that the thermodynamic component should be the dominant mechanism for changes in frequency.

Fig. 5.

As in Fig. 2, but showing (a) the thermodynamic and (b) the dynamic contributions to precipitation frequency for different precipitation intensity bins; unit is % K−1.

Fig. 5.

As in Fig. 2, but showing (a) the thermodynamic and (b) the dynamic contributions to precipitation frequency for different precipitation intensity bins; unit is % K−1.

Fig. 6.

Frequency of vertical velocity ω at 500 hPa associated with precipitation events (a) for the period 1981–2000 (%), (b) the differences between 2081–2100 and 1981–2000 (% K−1), and (c) relative changes with respect to 1981–2000 (% K−1). The numbers in (b) and (c) are normalized by the change in global-mean surface temperature. The x axis is intensity bins of vertical velocity at 500 hPa with a 0.01 Pa s−1 interval. The solid curves are multimodel ensemble means and the dashed curves indicate one standard deviation.

Fig. 6.

Frequency of vertical velocity ω at 500 hPa associated with precipitation events (a) for the period 1981–2000 (%), (b) the differences between 2081–2100 and 1981–2000 (% K−1), and (c) relative changes with respect to 1981–2000 (% K−1). The numbers in (b) and (c) are normalized by the change in global-mean surface temperature. The x axis is intensity bins of vertical velocity at 500 hPa with a 0.01 Pa s−1 interval. The solid curves are multimodel ensemble means and the dashed curves indicate one standard deviation.

b. Dynamic contribution

As the atmosphere warms, the frequency of vertical velocity also changes. Figure 6 shows the frequency of vertical velocity at 500 hPa corresponding with a precipitation event. We note that the vertical velocity associated with nonprecipitating events is not included here. It is interesting that precipitation is not always associated with upward motion at 500 hPa (Fig. 6a). In fact, the distribution of frequency for downward motion is similar to that for upward motion, but less frequent. The weaker the vertical motion is, the more frequently it occurs. This is true for both upward and downward motion. Under global warming, changes in the frequency of vertical velocity have a relatively symmetric tendency between upward and downward motions (Fig. 6b). Weaker ascent and descent tend to be more frequent, while stronger ascent and descent become less frequent. In terms of changes in percentage, the frequency of weaker vertical motion increases around 1%, but the frequency of stronger vertical motion can decrease as much as 7% (Fig. 6c). The redistribution of frequency of vertical velocity implies a possible weakening of the mean tropical circulation, associated with changes in atmospheric stability (Held and Soden 2006; Vecchi and Soden 2007; Chou and Chen 2010).

According to the changes in the frequency of vertical velocity, we can estimate the dynamic contribution to precipitation frequency via (12), and the result is shown in Fig. 5b. The dynamic contribution is negative for all precipitation intensity bins. The negative dynamic contribution is associated with the more stable atmosphere in the warmer climate. For light precipitation, the dynamic contribution is slightly negative. For heavy precipitation, on the other hand, the dynamic contribution is around −4%. Variations in the dynamic contribution among climate models are large, ranging from −12% to +5% for heavy precipitation. Compared to the thermodynamic contribution, the dynamic contribution to precipitation frequency is smaller, even for the climate model with the strongest dynamic contribution. Thus, the increase in precipitation frequency is, indeed, mainly controlled by the thermodynamic component, that is, the enhancement of water vapor, consistent with the study of Gastineau and Soden (2011).

5. Mechanisms for intensity change

Unlike precipitation frequency, we use the vertically integrated water vapor budget, which has been used to examine changes in mean precipitation (e.g., Chou and Neelin 2004; Chou et al. 2006; Chou and Tu 2008; Tan et al. 2008), to examine mechanisms that control precipitation intensity. We first examine the water budget (1) for 1981–2000. For consistency, all terms shown in Fig. 7 are in energy units. Figure 7a shows the distribution of precipitation intensity for different percentile bins, which is same as in Fig. 3a but in energy units, but becomes millimeters per day, divided by 28 (see section 2c for details). The moisture convergence associated with vertical motion −〈ωpq〉 shows a similar distribution to the corresponding precipitation intensity, but its value is negative for the first 60 percentile bins (Fig. 9b). This implies that subsidence dominates the large-scale environment here. Horizontal moisture advection −〈v · q〉 is always negative—a dry advection—and reaches a minimum at the 99th percentile bin, ~60 W m−2 (Fig. 3c). Evaporation is positive for all percentile bins with a roughly constant value ~120 W m−2.

Fig. 7.

As in Fig. 3a, but showing water vapor budget [Eq. (1) in the text] in 1981–2000 for (a) precipitation, (b) −〈ωpq〉, (c) −〈v · q〉, (d) evaporation E, and (e) the residual for different precipitation percentile bins; units are W m−2 K−1 (see details in the text).

Fig. 7.

As in Fig. 3a, but showing water vapor budget [Eq. (1) in the text] in 1981–2000 for (a) precipitation, (b) −〈ωpq〉, (c) −〈v · q〉, (d) evaporation E, and (e) the residual for different precipitation percentile bins; units are W m−2 K−1 (see details in the text).

The balance of the water vapor budget is examined next. For heavy precipitation, the moisture convergence associated with vertical motion −〈ωpq〉 contributes to more than a half of precipitation. Horizontal moisture advection −〈v · q〉 is relatively small and negative, so it only reduces precipitation intensity slightly. For the heaviest precipitation, the 99.99th percentile bin, horizontal moisture advection decreases sharply (increases in magnitude) and roughly cancels out the positive contribution of evaporation to precipitation intensity (see the insets of Figs. 7c,d). Thus, the residual becomes the major contribution to the remaining part of precipitation intensity. The distribution of the residual (Fig. 7e) is similar to that of vertical moisture advection −〈ωpq〉. The residual is associated with various processes, such as the transient term accumulated from each model time step, the interpolation between the original model levels and standard pressure levels and a surface boundary effect (Seager et al. 2010). For light precipitation, on the other hand, vertical moisture advection is negative, so it cannot be a dominant process to contribute to precipitation intensity, such as in heavy precipitation. Horizontal moisture advection is relatively small. Thus, the dominant process affecting precipitation intensity is evaporation. Overall, heavy precipitation is mainly induced by convection associated with −〈ωpq〉, while light precipitation is more related to evaporation.

Figure 8 shows changes in the water vapor budget (2). Figure 8a shows changes in precipitation, which is the same as in Fig. 3b but in energy units. Changes in precipitation intensity tend to increase as precipitation intensity increases. For the terms on the right of (2), the distribution of −〈ωpq〉′ has the most similar distribution to changes in precipitation intensity. Similar to −〈ωpq〉 shown in Fig. 7b, −〈ωpq〉′ is negative for the first 60 percentile bins, becomes positive afterward, and sharply increases for the last 5 percentile bins. Changes in horizontal moisture advection −〈v · q〉′, which are also similar to −〈v · q〉 shown in Fig. 7c, are negative and small, less than 4 W m−2 in magnitude for most percentile bins. The negative −〈v · q〉′ is associated with the upped ante mechanism (Chou and Neelin 2004; Chou et al. 2009). Changes in evaporation are also small, less than 3 W m−2, but positive.

Fig. 8.

As in Fig. 7, but for anomalies of water vapor budget [Eq. (2) in the text].

Fig. 8.

As in Fig. 7, but for anomalies of water vapor budget [Eq. (2) in the text].

For light precipitation, changes in vertical moisture advection −〈ωpq〉′ tend to be negative, which could be associated with the rich-get-richer mechanism over the descent regions (Chou and Neelin 2004; Chou et al. 2009), with a reversed sign, since the thermodynamic component tends to be negative due to downward motion—which should be the main source for negative −〈ωpq〉′. However, a detailed examination of −〈ωpq〉′ and its contribution to light precipitation should be done before drawing any conclusions since convection might not be the dominant process for light precipitation. Other processes, such as boundary layer process and evaporation, could be more important. Horizontal moisture advection is very small, while changes in evaporation are slightly positive. Thus, negative −〈ωpq〉′ tends to be cancelled out by positive changes in evaporation. Overall, the terms in the water vapor budget for light precipitation are all very small and comparable with each other.

For heavy precipitation, particularly the 99th percentile bin (see the insets of Fig. 8), changes in precipitation intensity are mainly associated with changes in vertical moisture advection −〈ωpq〉′, which contributes to more than half of precipitation intensity. Horizontal moisture advection and evaporation are much smaller than −〈ωpq〉′ with a strong cancellation between them. The residual is slightly smaller than −〈ωpq〉′. The variation of the residual is roughly proportional to −〈ωpq〉′ (Figs. 8b,e), so the fractional changes in precipitation intensity can be estimated by the fractional changes in −〈ωpq〉′, such as in (4), even when the residual contributes to more than one-third of changes in precipitation intensity. The insets of Figs. 3c and 9a do show similar distributions in and for the 99th percentile bin. This provides evidence for the balance in (4). In other words, −〈ωpq〉′ can be used to examine mechanisms that induce changes in heavy precipitation, such as in O’Gorman and Schneider (2009) and Sugiyama et al. (2010), even when P′ ≠ −〈ωpq〉′. We note that the term −〈ωpq〉′ cannot be used to estimate changes in mean precipitation since evaporation, which shows a different distribution, is important in the water vapor budget for mean precipitation (Chou and Chen 2010).

Fig. 9.

Relative changes between 2081–2100 and 1981–2000, with respect to 1981–2000 for (a) −〈ωpq〉, (b) , and (c) in the 99th percentile bin, with a 0.01% interval [Eq. (5) in the text]. The numbers are normalized by the change of global-mean surface temperature; units are % K−1.

Fig. 9.

Relative changes between 2081–2100 and 1981–2000, with respect to 1981–2000 for (a) −〈ωpq〉, (b) , and (c) in the 99th percentile bin, with a 0.01% interval [Eq. (5) in the text]. The numbers are normalized by the change of global-mean surface temperature; units are % K−1.

Changes in vertical moisture advection can be further divided into the thermodynamic component and the dynamic component , which are associated with changes in water vapor and vertical velocity, respectively. Figure 9 shows percentage changes in (5) for the heaviest precipitation, the 99th percentile bin. Vertical moisture advection increases about 4% at the 99th percentile bin, gradually increases with percentiles, and reaches about 9% at the 99.99th percentile bin (Fig. 9a). This is about the same as changes in precipitation intensity shown in the inset of Fig. 3c. For the thermodynamic contribution (Fig. 9b), the change is ~6%—slightly smaller than changes in column-integrated water vapor, which is about 7%–8% (Fig. 10b). The rate of , which increases more slowly than changes in column-integrated water vapor, has been discussed in O’Gorman and Schneider (2009) and Sugiyama et al. (2010). In other words, changes in column-integrated water vapor slightly overestimate the thermodynamic contribution.

Fig. 10.

As in Fig. 9, but for (a) the vertical velocity at 500 hPa and (b) the column-integrated water vapor.

Fig. 10.

As in Fig. 9, but for (a) the vertical velocity at 500 hPa and (b) the column-integrated water vapor.

For the dynamic contribution, tends to decrease at the 99th percentile bin at a rate within −2% per 1 K of surface warming, and becomes slightly positive for the heaviest precipitation, less than 2% (Fig. 9c). The dynamic contribution is roughly consistent with changes in vertical velocity at 500 hPa (Fig. 10a). This implies that the vertical velocity at 500 hPa can be used to estimate the dynamic contribution, such as in Emori and Brown (2005) and Sugiyama et al. (2010). We note that changes in vertical velocity become different from the dynamic contribution at higher latitudes (not shown). The reduction of ascent at 500 hPa is consistent with the weakening of the tropical circulation found in climate models, which is associated with changes in atmospheric stability (Held and Soden 2006; Vecchi and Soden 2007; Chou and Chen 2010). The dynamic component varies a lot among climate models, and this variation becomes greater as the precipitation percentile increases, ranging from −3% to 10% for the heaviest precipitation. Thus, the greatest discrepancy for changes in precipitation intensity among climate models could be due to differences in the dynamic component (O’Gorman and Schneider 2009; Sugiyama et al. 2010), which could be associated with different cumulus parameterizations used in climate models. This discrepancy becomes smaller at midlatitudes, especially for higher percentile bins, such as the 99.9th percentile bin (not shown), implying that changes in precipitation intensity at midlatitudes are relatively robust among climate models (O’Gorman and Schneider 2009).

Overall, changes in vertical moisture advection −〈ωpq〉′ are dominated by changes in water vapor, not changes in vertical velocity. In other words, changes in precipitation intensity are mainly associated with the thermodynamic component, not the dynamic component, which is consistent with previous studies (Allan and Soden 2008; Emori and Brown 2005; O’Gorman and Schneider 2009; Sugiyama et al. 2010).

6. Discussion and conclusions

Under global warming, changes in precipitation are inevitable. For simplicity, mean precipitation is commonly examined, instead of precipitation frequency and intensity, which are two main factors determining mean precipitation. We aim to examine changes in precipitation frequency and intensity in the tropics where convection dominates and understand mechanisms that induced these changes. Here we derived a set of equations that can directly estimate the thermodynamic and dynamic contributions not only to precipitation intensity, which has been discussed frequently, but also precipitation frequency. The focus here is only on the CMIP3 global warming simulations (the A1B scenario).

In terms of tropical averages, 10 climate models that we examined show consistent results. Negative changes in frequency range from −5% to slightly less than zero, while positive changes in intensity range from 2% to 11% per 1 K of warming. In terms of different precipitation intensities, precipitation frequency increases for heavier precipitation but decreases for lighter precipitation. For heavy precipitation, for example, 100 mm day−1, the increase in frequency can reach as high as 35% for an ensemble average. Changes in precipitation intensity also show a similar pattern as found in precipitation frequency, but with smaller amplitudes. For light precipitation the intensity decreases slightly. For heavy precipitation, on the other hand, the intensity increases consistently among climate models, with an amplitude of around 4% per 1 K warming. For the heaviest precipitation, the 99.99th percentile bin, the increase can reach around 9% for the ensemble, which is slightly stronger than what the Clausius–Clapeyron thermal scaling at a constant relative humidity indicates, with a variation ranging from 2% to 16% among climate models. This implies that the corresponding ascending motion could increase for the heaviest precipitation in some models. In other words, there might be a positive feedback via the convection-latent-release process to the heaviest precipitation (e.g., Richter and Xie 2008; Trenberth 2011), even though the global environment tends to suppress atmospheric circulation (Emori and Brown 2005; Held and Soden 2006; Vecchi and Soden 2007).

Two main mechanisms for changes in precipitation have been discussed in previous studies (e.g., Emori and Brown 2005; Held and Soden 2006; Chou et al. 2009; Seager et al. 2010). The first one is the thermodynamic contribution associated with changes in water vapor. The second mechanism is the dynamic contribution related to changes in vertical velocity. By assuming that vertical moisture advection −〈ωpq〉 is the main process to produce precipitation, we derived a set of simple equations to directly estimate the thermodynamic and dynamic contributions to precipitation frequency and intensity. This assumption is appropriate for heavy precipitation, which is dominated by convective processes. However, it cannot explain the total changes for light precipitation since light precipitation is usually controlled by other processes such as the boundary layer process and evaporation. Nevertheless, these equations can still be used to explain part of the changes in precipitation frequency and intensity.

Using these equations, we examined the CMIP3 global warming simulations (the A1B scenario). In the examination of precipitation frequency, most changes in frequency are induced by the thermodynamic component, which has a positive impact for every precipitation percentile bin. For heavy precipitation, the increase can be as high as 40% per 1 K of warming. The positive thermodynamic contribution is consistently found in all 10 climate models analyzed here. The dynamic component, on the other hand, has a relatively weak negative impact on precipitation frequency for most precipitation intensity bins due to the more stable atmosphere. The dynamic contribution is negative for all percentile bins, but varies greatly among climate models, ranging from −12% to +5% for heavy precipitation. Thus, the dynamic contribution is relatively inconsistent among climate models.

In the examination of precipitation intensity, we focus on heavy precipitation, the last one percentile bin. Here we derived an equation to directly estimate the thermodynamic and dynamic contributions. The thermodynamic contribution is slightly smaller than changes in column-integrated water vapor, which roughly follows the Clausius–Clapeyron thermal scaling at 7% per 1 K of warming. The dynamic contribution ranges from −2% to 2%, roughly consistent with changes in vertical velocity at 500 hPa. The dynamic component tends to weaken precipitation intensity most of the time. However, we do see positive dynamic contributions that are usually associated with a faster increased rate of precipitation intensity, which can sometimes exceed 7%. A positive convective feedback could be in place for the heaviest precipitation. However, when and how the local convective feedback can overcome the large-scale influence, which tends to suppress convection, should be further examined in the future.

Changes in precipitation frequency and intensity are intimately linked. For instance, the precipitation distribution could shift toward more intense events, so both frequency and intensity change. In this study, we found that the precipitation distribution indeed shifts toward more intense events, that is, more and stronger intense precipitation events, mainly due to the thermodynamic contribution. The enhanced water vapor tends to increase precipitation frequency and intensity. The dynamic component, on the other hand, slightly decreases precipitation frequency and reduces precipitation intensity except for the heaviest precipitation events. Thus, both thermodynamic and dynamic components can enhance the intensity of the heaviest precipitation.

In this study, we only focus on examining climate model simulations. Many studies (e.g., Allan and Soden 2007; Chou et al. 2007; Wentz et al. 2007; Zhang et al. 2007; Allan and Soden 2008; Liu et al. 2009) show that climate models tend to underestimate changes in precipitation even though the tendency of the changes is mostly consistent between climate models and observations. Thus, an examination of observed precipitation is necessary and should be compared to the model results shown here. We are planning to examine it in the near future. Moreover, the results shown here are from an entire tropical point of view. On a regional basis, the thermodynamic contribution might not vary too much, but the dynamic contribution should show a strong spatial dependence, such as that found in mean precipitation (Chou et al. 2009). Examination of the thermodynamic and dynamic contributions to regional precipitation is an ongoing work that we will discuss in a separate study.

Acknowledgments

This work was supported by the National Science Council Grants NSC99-2111-M-001-003-MY3, NSC98-2625-M-492-011, and NSC99-2111-M-415-001. We acknowledge the modeling groups, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the WCRP’s Working Group on Coupled Modelling (WGCM), for their roles in making available the WCRP CMIP3 multimodel dataset. Support of this dataset is provided by the Office of Science, U.S. Department of Energy. Comments from two anonymous reviewers were very helpful in improving the quality of this paper.

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