1. Introduction
Under global warming, not only the global-mean precipitation tends to increase (e.g., Allen and Ingram 2002; Held and Soden 2006; Meehl et al. 2007; Trenberth et al. 2007), but the frequency and intensity of precipitation also change. The increased mean precipitation is usually associated with changes in rainfall frequency and intensity. From a global point of view, light rainfall events occur less frequently and heavy rainfall events become more common in global warming simulations (Hennessy et al. 1997; Wilby and Wigley 2002; Tebaldi et al. 2006; Sun et al. 2007; Allan and Soden 2008; O’Gorman and Schneider 2009; Liu et al. 2009; Allan et al. 2010; Chou et al. 2012). The precipitation intensity also tends to become stronger (Groisman et al. 2005; Alexander et al. 2006; Kharin et al. 2007; Trenberth et al. 2007; Min et al. 2011; Chou et al. 2012), especially for the extremes. These tendencies of model simulations are consistent with observations (Fujibe et al. 2005; Goswami et al. 2006; Lau and Wu 2007; Qian et al. 2007; Trenberth et al. 2007; Allan and Soden 2008; Liu et al. 2009; Shiu et al. 2009), even though their magnitude is underestimated, relative to observations (Dai 2006; Sun et al. 2007; Allan and Soden 2008; Allan et al. 2010). This might be associated with the fact that precipitation on shorter time scales is not well simulated by climate models (Trenberth et al. 2003; Sun et al. 2007; O’Gorman and Schneider 2009; Allan et al. 2010; Lenderink and van Meijgaard 2010), and the observed variations could include both long-term trends and decadal oscillations (Easterling et al. 2000; Frich et al. 2002; Groisman et al. 2005; Allan et al. 2010; Gastineau and Soden 2011; Young et al. 2011).
In general, the thermodynamic component due to increased water vapor shows a positive contribution to changes in mean precipitation and the dynamic component due to changes in circulation tends to reduce mean precipitation (Emori and Brown 2005; Held and Soden 2006). For changes in extreme events, however, the increased rate of precipitation could exceed the Clausius–Clapeyron thermal scaling, which is around 7.5% K−1 (Trenberth et al. 2003; Sugiyama et al. 2010), so the dynamic contribution could be positive. This implies that the dynamic component could play an important role, particularly in the tropics. In other words, changes in precipitation extremes are sensitive to changes in vertical motion (Gastineau and Soden 2009; O’Gorman and Schneider 2009; Sugiyama et al. 2010), which might be associated with different cumulus parameterizations (Wilcox and Donner 2007). Chou et al. (2012) analyzed the changes in rainfall frequency and intensity in the tropics and further estimated the corresponding thermodynamic and dynamic contributions. In the thermodynamic contribution, increased water vapor is favorable for increasing precipitation frequency and intensifying rainfall intensity. In the dynamic contribution, the more stable atmosphere leads to a reduction in rainfall frequency and intensity for most rainfall events, except for the heaviest precipitation which might be due to a positive convective feedback (Trenberth et al. 2003; Sugiyama et al. 2010).
Similar to changes in mean precipitation, which show a strong spatial variation (Allen and Ingram 2002; Neelin et al. 2006; Allan and Soden 2007; Chou et al. 2007; Meehl et al. 2007; Wentz et al. 2007; Zhang et al. 2007; Chou et al. 2009), changes in the frequency and intensity of precipitation, which could be associated with changes mean precipitation, should also vary with space. The spatial variation of changes in mean precipitation is mainly associated with changes in vertical mass transport (Chou and Neelin 2004; Kumar et al. 2004; Chou et al. 2006; Seager et al. 2010), the dynamic component, while the thermodynamic contribution is relatively uniform in space. Several possible mechanisms that induce changes in mean precipitation have been proposed, such as the rich-get-richer mechanism for positive precipitation anomalies and the upped-ante mechanism for negative precipitation anomalies, by dividing the tropics into six major subregions (Chou et al. 2009). In the rich-get-richer mechanism, the increase of moisture at low levels enhances moisture transport by mean flow over convective regions (the thermodynamic part), so wet regions get wetter. The increased moisture also tends to reduce the gross moist stability. The reduced gross moist stability enhances upward motion in convective regions, providing a dynamic feedback that increases the precipitation (the dynamic part). In the upped-ante mechanism, the dry advection associated with inflow from the less-moistened subsidence regions into the convergence zones tends to suppress convection in the convective margins, weakening the corresponding upward motion and reducing precipitation.
In this study, we will analyze changes in tropical precipitation frequency and intensity and their association with changes in mean precipitation on a regional basis, in which the classification of regions is similar to that used in Chou et al. (2009). The effects of those mechanisms proposed in Chou et al., which were used to study changes in mean precipitation, on changes in regional rainfall frequency and intensity will also be examined. The datasets of climate model simulations, analysis methods and the classification of regions are described in section 2. Changes in regional precipitation frequency and intensity are shown in section 3. The thermodynamic and dynamic contributions to precipitation frequency and intensity are examined in sections 4 and 5, respectively. The mechanisms of changes in regional rainfall frequency and intensity are discussed in section 6, followed by conclusions.
2. Data and analysis methods
a. Data
The World Climate Research Programme (WCRP) Coupled Model Intercomparison Project phase 3 (CMIP3) multimodel dataset is used in this study. Both 20C3M and A1B emission scenarios are used. This simulated dataset can provide estimates of climate changes associated with anthropogenic forcing, which will be examined in the following analyses. The period of 1981–2000 is defined as current climate, while the period of 2081–2100 is future climate. To examine changes in rainfall frequency and intensity, daily precipitation is used. Other variables, such as surface latent heat flux, specific humidity, and horizontal velocity from 1000 to 200 mb, are used as well. Owing to data availability, only 10 models (Table 1) are chosen here. One realization of each model is examined.
List of the 10 coupled atmosphere–ocean climate model simulations in the A1B scenario from the CMIP3 archive.
b. Method
1) Calculating the frequency and intensity of precipitation
Compared to the amount of total rainfall, the accumulated precipitation attributed to events with intensity less than 0.1 mm day−1 is small (Chou et al. 2012), so we only consider the grid data in which precipitation is larger than 0.1 mm day−1. This criterion has been used in previous studies (e.g., Sun et al. 2007; Chou et al. 2012) as well. To calculate precipitation frequency, the spectrum interval of 1 mm day−1 is used here, except for the first bin which is between 0.1 and 1 mm day−1. Thus, the occurrence of precipitation is counted for each precipitation intensity bin in current and future climate, respectively. The frequency for each bin is the percentage over the whole domain in the entire 20-yr period: that is, the occurrence is divided by the total grid point number of the domain that we are interested in, six subregions in the tropics (30°S–30°N), which includes both precipitation and nonprecipitation events (days). This method has been used in Sun et al. (2007) and Chou et al. (2012).
To calculate precipitation intensity, precipitation events are first sorted by their magnitudes from light to heavy and then averaged for each percentile bin in current and future climate, respectively. A width of 1% is used for each bin for total precipitation events: that is, 1 ~ 100%. Since our interest is mainly in precipitation extremes, we further examine precipitation intensity for the last percent, the 99th percentile, with the bin width of 0.01%. This method has been used in Allen and Ingram (2002), O’Gorman and Schneider (2009), and Sugiyama et al. (2010).
In this study, we first compute precipitation intensity and frequency in current and future climate for each model, and then the changes due to global warming are normalized by its own global-mean surface temperature change. Most figures are shown as ensembles, and the standard deviation is calculated from these 10 models. A more detailed description on classifying precipitation frequency and intensity can be found in Chou et al. (2012).
2) Estimations of thermodynamic and dynamic contributions to the intensity of precipitation
3) Estimations of thermodynamic and dynamic contributions to the frequency of precipitation
A set of equations derived by Chou et al. (2012) is used here to estimate the thermodynamic and dynamic effects on rainfall frequency. Moisture convergence associated with vertical motion −ω∂pq is usually the main process that induces precipitation, which is particularly true for heavy precipitation (Schneider et al. 2010; Sugiyama et al. 2010). We use the vertical velocity at 500 hPa ω500mb to represent the corresponding vertical motion since most precipitation, extremes in particular, is associated with convection. Note that here we use grid-sized vertical motion to represent the updraft in convective systems, owing to the coarse resolutions used in GCMs. Since ∂pq and q always exist, with or without P ≠ 0, and vary 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.
Based on Eqs. (5) and (8), the thermodynamic and dynamic contributions to precipitation frequency can be estimated, respectively. We note that the estimations are also more accurate for precipitation extremes, as they are for precipitation intensity.
c. Classification of subregions
To examine the variation of rainfall frequency and intensity on a regional basis, as well as the corresponding mechanisms, the classification of subregions in Chou et al. (2009) is used here. The definition of each area is described in Table 2. The subregion domains are defined by monthly data; hence, the subregions vary with the seasons. Areas I, IIa, and IIb are over climatologically ascending regions, defined as areas with 
Definition of six subregions in the tropics.
Summary of six subregions, using the MIROC3.2(hires) (CCSR33.2H) model as an example, which are shaded with precipitation anomalies in December. Thick solid (dashed) curves denote the boundary of convergence zones in the period of 1981–2000 (2081–2100). Dark (light) blue shading in subset II is for the area IIa (IIb) and dark (light) red shading in subset IV is for the area IVa (IVb) (adapted from Chou et al. 2009).
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
3. Changes in precipitation frequency and intensity
Before examining the detailed changes in precipitation frequency and intensity for different strengths of precipitation, the averaged changes are first examined. Figure 2 illustrates the changes for 10 models in six subregions in the tropics (30°S–30°N). In the regions with decreased mean precipitation, which are areas I, IVa, and IVb, rainfall events become less frequent in a warmer climate in all 10 models, ranging from −20% to a little less than zero. In the regions with increased mean precipitation (areas IIa, IIb, and III), on the other hand, the frequency tends to increase for most models. The frequency in areas IIa and III increases in all 10 models, ranging from a little greater than zero to 10%, while that in area IIb is inconsistent between models and the changes are relatively small (Fig. 2a). Changes in precipitation intensity show a similar tendency. In regions with decreased mean precipitation (areas I, IVa, and IVb), precipitation becomes weaker in all models, ranging from −25% to a little less than zero. However, it is intensified in regions with increased mean precipitation (areas IIa, IIb, and III), with changes ranging from 5% to a little greater than 40%. The magnitude of changes in intensity are usually greater than those in frequency, and the changes in intensity between increased and decreased mean precipitation regions are more distinct than those in frequency. Overall, the decrease of mean precipitation in areas I, IVa, and IVb is contributed to both from less frequent rainfall events and from weakened precipitation intensity. The increase in mean precipitation in areas IIa and III, on the other hand, is associated with more frequent and heavier rainfall events. In area IIb the increased mean precipitation is mainly contributed to by intensified rainfall events. Although the changes in frequency and intensity are slightly varied among 10 models in each area, the tendencies between different models are quite consistent. Thus, only ensemble results from 10 models in six subregions are shown in the following analysis.
Tropical averages of changes in (a) precipitation frequency and (b) intensity in six subregions (denoted by different colors) vs changes in global surface temperature (x axis) for 10 CMIP3 coupled GCMs. The changes (%) are differences between 2081–2100 and 1981–2000 relative to 1981–2000.
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
The frequency distribution with specific precipitation intensity is further investigated and shown in Fig. 3. For current climate, in all six subregions, precipitation frequency reduces as its intensity increases (Fig. 3a), and it seems that the frequency distribution is sorted into two categories: convective regions (I, IIa, and IIb) and nonconvective regions (III, IVa, and IVb). There are relatively less light rainfall events and more medium and heavy rainfall events in convective regions, while there are more light rainfall events and less medium and heavy rainfall events in nonconvective regions. The frequency distinction of light rain between the convective and nonconvective regions is relatively small. The frequency distinction of heavier precipitation (with intensity greater than 10 mm day−1), on the other hand, is more obvious with the difference being about 10 times larger in convective than in nonconvective regions.
(a) Precipitation frequency (%) in six subregions 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 (% K−1) in (b),(c) are normalized by the changes in global-mean surface temperature. 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 of 10 climate models.
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
Changes in precipitation frequency in warmer climate are shown in Fig. 3b. There are distinctive differences in the changes of precipitation frequency between both convective and nonconvective regions. We first examine changes in convective regions. In area I, where mean precipitation decreases as climate warms, there are more light rain events but less medium and heavy rain events. In areas IIa and IIb, where mean precipitation increases in warmer climate, on the other hand, there are less light rain events but more medium and heavy rain events. In nonconvective regions, changes in precipitation frequency also vary with region. Precipitation in area III occurs more frequently for entire intensity bins, except for light rain events. In areas IVa and IVb, precipitation is less frequent for almost entire precipitation intensity bins. The variation of precipitation frequency between regions is easier to see in Fig. 3c, especially for heavier precipitation. It appears that the distributions of changes in frequency in six regions can also be classified into two categories: increased and decreased mean precipitation regions. In areas IIa, IIb, and III, where mean precipitation increases in warmer climate, the increase in precipitation frequency is evident as precipitation intensity increases. However, the change is relatively small and tends to decrease slightly for almost every precipitation intensity bin in areas I, IVa, and IVb where mean precipitation decreases. According to Fig. 3, the increased mean precipitation in areas IIa, IIb, and III may be partially attributed to increased frequency of medium and heavy rainfall events, while the decreased mean precipitation in areas I, IVa, and IVb are associated with a reduced frequency of medium and heavy rainfall events. Although the difference in the changes in frequency for light rain is apparent between six regions, the difference in the relative change in precipitation frequency between regions for heavy precipitation is more remarkable.
In addition to frequency, changes in regional mean precipitation may be due to changes in precipitation intensity as well. The distribution of precipitation intensity is shown in Fig. 4. In current climate (Fig. 4a), two groups can be distinguished for precipitation intensity: convective (areas I, IIa, and IIb) and nonconvective regions (areas III, IVa, and IVb). In areas I, IIa, and IIb precipitation intensity rises rapidly when intensity is greater than the 90th percentile and the intensity for the last 1% is close to 60 mm day−1. In areas III, IVa, and IVb more than 70% of rainfall events are quite small, and precipitation intensity increases slowly between the 70th and 90th percentiles and then rises up sharply for the last 2%–3%. The intensity for the heaviest 1% is close to 40 mm day−1. As climate warms, precipitation intensity in areas I, IVa, and IVb weakens for all percentile bins, with a range from 10% to less than zero (Fig. 4b). On the other hand, rainfall in areas IIa, IIb, and III is intensified for all percentile bins with a magnitude as strong as about 12% (Fig. 4b).
As in Fig. 3 but for precipitation intensity (mm day−1) (a) in 1981–2000 for percentiles from 1% to 100%, (b) relative changes with respect to 1981–2000 (% K−1). The interval of each percentile bin is 1%. The changes in (b) are normalized by the changes of global-mean surface temperature. The solid curves are multimodel ensemble means, and the dashed curves indicate one standard deviation of 10 climate models.
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
To investigate precipitation extremes, the last one percentile is further divided into 100 bins (Fig. 5) with a bin interval of 0.01%. In nonconvective regions the intensity is from 20 to around 100 mm day−1; in convective regions it is from 40 to around 160 mm day−1. The intensity of the extremes in areas I, IVa, and IVb is reduced for almost all percentile bins ranging from −6% to a little less than zero, except for the extremes above the 99.7 percentile in area I and the 99.99 percentile in area IVa. In areas IIa, IIb, and III, extremes strengthen, from around 6% to 16%, which is slightly greater than the Clausius–Clapeyron thermal scaling of 7.5% K−1.
As in Fig. 4 but for precipitation intensity and the corresponding −〈ω∂pq〉′ in the last 1% bin (the 99th percentile), with an interval of 0.01%: (a) precipitation intensity in 1981–2000, (b) relative changes (% K−1) in precipitation intensity with respect to 1981–2000, and (c) relative changes (% K−1) in −〈ω∂pq〉′ with respect to 1981–2000.
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
Overall, the increased mean precipitation in areas IIa, IIb, and III can be attributed to intensified rainfall events, while the decreased mean precipitation in areas I, IVa, and IVb is associated with weakened rainfall events. In a warmer climate, the strengthened rainfall intensity is expected if the vertical motion associated with convection is unchanged or changes little, due to increased water vapor in the atmosphere—the thermodynamic contribution. However, changes in precipitation intensity show a strong spatial variation. This implies that changes in vertical motion—the dynamic contribution—must contribute to changes in precipitation intensity and make the difference spatially.
4. Thermodynamic contribution
When considering the entire tropical region, the thermodynamic component tends to increase precipitation frequency and intensity. However, the strong spatial variation of changes in precipitation might imply that the thermodynamic component could vary with space. Here, we would like to examine the thermodynamic contribution to different subregions.
a. Frequency
To understand the thermodynamic effect on regional changes in precipitation frequency, the vertical integral of total column water vapor (CWV) is first investigated here. The CWV distribution versus precipitation intensity over six subregions in 1981–2000 is shown in Fig. 6a. CWV increases slowly as precipitation intensity increases in all six regions. The distribution is similar between six subregions, but they can still be classified into two categories: convective regions (I, IIa, and IIb) and nonconvective regions (III, Iva, and IVb). The amount of CWV in convective regions is slightly greater than that in nonconvective regions, with a maximum of about 60 mm in convective and 50 mm in nonconvective regions. When the earth warms up, CWV increases similarly in all six regions, with a range of 7%–9% K−1 (Fig. 6b), except for very heavy rainfall, which shows strong variance. This is due to less data, especially in nonconvective regions. The thermodynamic contribution to changes in precipitation frequency Δft, estimated from (5), is shown in Fig. 6c. Evidently, Δft is positive and increases with rainfall intensity in all six subregions. Its magnitude is a little less than 10% for light rainfall and increases to around 60% for heavy rainfall. There are no apparent differences between six subregions. Overall, the thermodynamic contribution to precipitation frequency is positive, and no clear spatial variation is found even when CWV varies between convective and nonconvective regions.
As in Fig. 3 but for column-integrated water vapor (CWV) and the thermodynamic contribution: (a) CWV (mm) in 1981–2000, (b) relative changes (% K−1) in CWV with respect to 1981–2000, and (c) the thermodynamic contribution (% K−1) to precipitation frequency.
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
b. Intensity
Based on the analysis of the moisture budget, changes in moisture convergence associated with vertical motion −〈ω∂pq〉 are the dominant source for precipitation intensity and show a similar distribution to the corresponding changes in precipitation intensity (Chou et al. 2012). The contributions from horizontal advection, evaporation, and residual terms are all relatively small, especially for heavy precipitation. Here, we focus only on changes for the 99th percentile of precipitation when (2) is more applicable.
For heavy precipitation, positive −〈ω∂pq〉′ is found in areas IIa, IIb, and III, which corresponds to positive precipitation anomalies (Fig. 5). For areas with negative mean precipitation anomalies, −〈ω∂pq〉′ is not as consistent as in the positive mean precipitation anomaly areas. In area I, changes in −〈ω∂pq〉 are relatively small and increase slowly with the precipitation percentile, with a maximum of around 4% (Fig. 5c). In areas IVa and IVb, −〈ω∂pq〉′ is negative for almost every percentile, except for precipitation intensity greater than the 99.97 percentile (Fig. 5c). Compared to Fig. 5b, −〈ω∂pq〉′ is slightly greater than the relative change of precipitation in I, IIa, IIb, and III, but the distribution of −〈ω∂pq〉′ for the entire 99th percentile in each subregion is still relatively similar to changes in precipitation intensity. This implies that −〈ω∂pq〉′ can be used to estimate changes in precipitation intensity in six subregions.
For the thermodynamic contribution 
As in Fig. 5 but for CWV (a) in 1981–2000, (b) relative changes (% K−1) with respect to 1981–2000, and (c) relative changes (% K−1) in −〈ω∂pq′〉 with respect to 1981–2000.
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
5. Dynamic contribution
a. Frequency
Since water vapor always exists in the atmosphere with or without precipitation, how frequently precipitation occurs should be closely related to the occurrence of the corresponding vertical motion. The intensity of vertical velocity at 500 hPa and its frequency in six subregions is shown in Fig. 8. Generally, weaker vertical motion occurs more frequently than a stronger one (Fig. 8a); thus, the probability distribution of ω500mb tends to have a frequency peaking at weak subsidence in both convective and nonconvective regions. The upward (downward) motion is predominant in convective (nonconvective) regions, with a higher percentage of upward (downward) motion and a lower percentage of downward (upward) motion (Fig. 8a). In warmer climate, weaker vertical motion (both upward and downward) with the magnitude close to zero occurs more frequently, while stronger vertical motion occurs less frequently in almost all six subregions except in areas IIa and III (Fig. 8b). In areas IIa and III, which are dominated by a positive precipitation anomaly, upward motion occurs more frequently, while downward motion occurs less (Figs. 8b,c). Although there are great variances in the occurrence of vertical velocity, the relative change is the most evident for the strongest vertical motion. Overall, both strong ascents and descents become less frequent over areas with reduced mean precipitation. Over areas with increased mean precipitation, upward motion occurs more and downward motion becomes less, except over area IIb where both ascents and descents are less frequent, for the strength within ±0.4 Pa s−1. For the greater strength of vertical motion, both ascents and descents become more frequent.
Frequency of vertical velocity ω at 500 hPa associated with precipitation frequency in six subregions: (a) averages in 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 x axis is intensity bins of vertical velocity at 500 hPa with an interval of 0.01 Pa s−1. The solid curves are multimodel ensemble means, and the dashed curves indicate one standard deviation of 10 climate models.
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
Based on changes in the frequency distribution of ω500mb over different regions, we further estimate the dynamic contribution to changes in rainfall frequency, shown in Fig. 9. In general, the magnitude of the dynamic contribution becomes larger with precipitation intensity. In regions with negative mean precipitation anomalies, areas I, IVa, and IVb, a negative dynamic contribution to precipitation frequency is found. In regions with positive mean precipitation anomalies, areas IIa, IIb, and III, a positive dynamic contribution is found for almost all corresponding precipitation intensities in areas IIa and III, but only for heavy precipitation greater than 90 mm day−1 and light precipitation less than 5 mm day−1 in area IIb. Overall, the dynamic contribution shows a positive relation with changes in mean precipitation for almost all subregions, except for area IIb. In other words, the dynamic component, not the thermodynamic component, is the controlling factor for determining the direction of changes in precipitation frequency.
Dynamic contribution to changes in precipitation frequency for precipitation intensity from 0.1 to 100 mm day−1 in six subregions.
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
b. Intensity
We next estimate the dynamic contribution to changes in precipitation intensity. The intensity of ω500mb versus precipitation intensity percentiles is shown in Figs. 10 and 11 . Weak downward motion corresponds to light precipitation, especially over subsidence regions (areas III, IVa, and IVb). Vertical motion becomes upward and stronger when precipitation intensity increases (Fig. 10a). For extreme events vertical motion is upward and strengthened with rainfall intensity in all six regions (Fig. 11a). Changes in ω500mb vary with regions and become larger with precipitation intensity. In regions with negative mean precipitation anomalies, especially areas I and IVa, anomalous downward motion is found for almost every precipitation percentile bin, even for the very heavy precipitation events (Fig. 11b). In area IVb both downward motion for light and medium precipitation and upward motion for heavy precipitation is reduced. In areas IIa and III, where mean precipitation increases, the corresponding upward motion is strengthened for all precipitation percentiles, especially for extreme events. However, in area IIb upward motion weakens even though mean precipitation anomalies are positive, except for the 99th percentile. Here the dynamic contribution to changes in precipitation intensity is estimated only for precipitation extremes. A positive dynamic contribution, which is associated with strengthened ascending motion, increases rainfall intensity in areas IIa, IIb, and III (Fig. 11d) where mean precipitation increases. On the other hand, a negative dynamic contribution, which is associated with weakened upward motion, reduces rainfall intensity in areas I, IVa, and IVb where mean precipitation decreases. Thus, the dynamic contribution to the intensity of precipitation extremes has a positive relation with changes in mean precipitation. The dynamic contribution is consistent with the changing rate of ω500mb, shown in Fig. 11c. In other words, changes in ω500mb can be used to examine the dynamic contribution, such as in Vecchi and Soden (2007), O’Gorman and Schneider (2009), and Sugiyama et al. (2010).
The vertical velocity at 500 hPa associated with precipitation intensity percentile from 1% to 100% in six subregions: (a) averages in 1981–2000 (Pa s−1) and (b) differences between 2081–2100 and 1981–2000 (Pa s−1 K−1).
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
As in Fig. 5 but for (a) vertical velocity ω at 500 hPa in 1981–2000 (Pa s−1), (b) differences between 2081–2100 and 1981–2000 (Pa s−1 K−1), (c) relative changes with respect to 1981–2000 (% K−1), and (d) relative changes in −〈ω′∂pq〉 with respect to 1981–2000 (% K−1).
Citation: Journal of Climate 25, 24; 10.1175/JCLI-D-12-00096.1
6. Discussion
In Chou et al. (2009), several mechanisms for changes in regional mean precipitation have been proposed. Using the similar classification of subregions, we can further examine the impacts of these mechanisms on the thermodynamic and dynamic contributions to precipitation frequency and intensity. Since the atmospheric water vapor increases everywhere due to the increase of temperature, the thermodynamic contribution to precipitation frequency and intensity is positive and relatively uniform in space. Thus, the spatial variation of changes in precipitation frequency and intensity that is induced by the mechanisms proposed by Chou et al. (2009) should be mainly associated with the dynamic contribution.
In area I, which is dominated by the upped-ante mechanism, both precipitation frequency and intensity are reduced. The horizontal gradient of the increased water vapor creates a dry advection and reduces mean precipitation in convective margins. The dry advection, which is associated with the upped-ante mechanism, not only weakens the corresponding upward motion but also reduces its frequency. This further decreases the frequency and intensity of precipitation. In other words, the upped-ante mechanism is responsible for changes in precipitation frequency and intensity in area I, while the positive thermodynamic contribution is secondary.
In area IIa, which is dominated by the dynamic part of the rich-get-richer mechanism, which is the anomalous gross moist stability mechanism (Chou and Neelin 2004), both precipitation and intensity increase. The increased water vapor in the lower troposphere destabilizes the atmosphere, so the corresponding upward motion becomes stronger and occurs more frequently. Thus, the dynamic contribution associated with the rich-get-richer mechanism is positive to both precipitation frequency and intensity. In addition to the positive dynamic contribution, the positive thermodynamic contribution further enhances precipitation frequency and intensity.
In area IIb, which is dominated by the effect of convection depth, both precipitation frequency and intensity increase, as those in area IIa, but with relatively smaller amplitudes. In a warmer climate convection tends to deepen. The deepening of convection increases atmospheric stability (Chou and Chen 2010), that is, positive gross moist stability anomalies, so the corresponding upward motion generally weakens and becomes less frequent except for heavy precipitation. Thus, the dynamic contribution is negative to the frequency and intensity of most precipitation. For precipitation extremes, the dynamic contribution is slightly positive to both precipitation frequency and intensity, which might be related to a positive feedback of latent heat release (Sugiyama et al. 2010). Unlike those in area I, the magnitude of the negative dynamic contribution here is smaller than that of the positive thermodynamic contribution, so the changes in precipitation frequency and intensity are still positive. Overall, both deepening of convection and the upped-ante mechanism induce negative dynamic contributions, but the contributions induced by the upped-ante mechanism are stronger and more consistent throughout the entire range of precipitation.
In area III, a climatological subsidence region, which is mainly associated with an oceanic feedback via surface heat flux, precipitation frequency and intensity show strong enhancement. An increase of surface heat fluxes from oceans to the atmosphere, due to relatively warmer sea surface temperature, tends to create a favorable environment for convection, so the occurrence of the corresponding upward motion and its intensity increase. Thus, the associated dynamic contribution is positive and further enhances precipitation frequency and intensity, which have already been strengthened by the thermodynamic component.
In area IVa, a climatological nonconvective region dominated by longwave radiation cooling and cold horizontal advection, precipitation frequency and intensity decrease. Both radiation cooling and cold advection suppress convection, so the corresponding dynamic contribution is negative to precipitation frequency and intensity. The dynamic contribution is clearly stronger than the thermodynamic contribution, so the overall precipitation frequency and intensity changes are negative for all strengths of precipitation.
In area IVb, another climatological nonconvective region, which is the counterpart of area IIb and is dominated by warm horizontal advection, both precipitation frequency and intensity are reduced. The increased atmospheric stability, as in area IIb, suppresses convection, causing a decrease in precipitation frequency and intensity, particularly for precipitation extremes. The warm horizontal advection, on the other hand, might induce weak anomalous upward motion, so reduction of the descent that is associated with lighter precipitation is found in area IVb (Fig. 10). In other words, both ascents (associated with heavier precipitation) and descents (associated with lighter precipitation) in area IVb weaken.
The thermodynamic and dynamic contributions to precipitation frequency and intensity shown here are different from those found in Chou et al. (2009), which focuses on mean precipitation, especially over climatologically descending areas: III, IVa, and IVb. Over climatologically ascending regions convection dominates, so both daily means and climatology behave alike. For instance, the vertical motions associated with daily precipitation events and climatological mean flow are both upward. Unlike those in the ascending regions, nonprecipitating events dominate the climatologically descending regions. Even though the mean flow is downward over these regions, the gridscale vertical motion associated with daily precipitation could be upward, such as those for heavy precipitation. This difference in vertical motion creates different thermodynamic and dynamic contributions to the frequency and intensity of precipitation and mean precipitation, especially for heavy precipitation. In this study, in which daily data were analyzed, the thermodynamic contribution to the frequency and intensity of precipitation extremes is positive everywhere, including in climatologically descending regions. On the other hand, the thermodynamic contribution to mean precipitation is positive only over the climatologically ascending regions. Over the climatologically descending regions, the thermodynamic contribution to mean precipitation is negative, due to the climatologically downward motion: that is, 
7. Conclusions
Similar to changes in mean precipitation, changes in precipitation frequency and intensity should also show a strong spatial variation. By classifying the tropics into six subregions (Chou et al. 2009), we first examined changes in precipitation frequency and intensity and the relationship of the changes between mean precipitation and the corresponding frequency and intensity of precipitation on a regional basis. We further examined the effects of those mechanisms proposed in Chou et al. (2009) on these changes associated with precipitation through the thermodynamic and dynamic contributions. We note that the results shown here are all from climate models, which may underestimate the changes in precipitation frequency and intensity, particularly for precipitation extremes, but the tendency of these changes should be similar. The summary of these findings is shown in Table 3.
Summary of changes in mean precipitation, frequency, and intensity of precipitation and the corresponding mechanisms. In the dynamic contribution only precipitation extremes are shown here for precipitation intensity (Fig. 11d), while all precipitation events are shown for precipitation frequency.
In general, the increase (decrease) of mean precipitation is mainly associated with increases (decreases) in the frequency and intensity of precipitation for almost all magnitudes of precipitation. Two dominant contributions for these changes in precipitation frequency and intensity are the thermodynamic component, associated with the increased water vapor in the atmosphere due to the warming, and the dynamic component, related to changes in the tropical circulation. The thermodynamic contribution is positive to both precipitation frequency and intensity, particularly for precipitation extremes, and does not vary with space, which differs from the contribution to mean precipitation over the climatologically descending regions, which is negative (Chou et al. 2009). The dynamic contribution, on the other hand, shows a strong spatial variation.
The increases in precipitation frequency and intensity are more dominated by the thermodynamic component. The dynamic component can either further enhance, via the rich-get-richer mechanism and ocean feedback, or slightly reduce, via the effect of convection depth, precipitation frequency, and intensity. The dynamic contribution associated with the rich-get-richer mechanism and the ocean feedback does not change signs with the strength of precipitation, but the effect of convection depth does vary with the strength of precipitation (Table 3). Decreases in precipitation frequency and intensity, on the other hand, are more related to the dynamic component than the thermodynamic contribution. The dynamic contribution associated with the upped-ante mechanism, longwave radiation cooling, cold horizontal advection, and the effect of convection depth tends to reduce precipitation frequency and intensity, while warm horizontal advection slightly enhances precipitation frequency and intensity.
In this study, we have demonstrated that the dynamic contribution is clearly the main cause for inducing the spatial variation of changes in precipitation frequency and intensity. The dynamic contribution is associated with changes in tropical circulation, which should be related to atmospheric stability. From a global point of view, it is generally believed that atmospheric stability will increase under global warming. However, how atmospheric stability will change on a regional basis is an interesting and important question, which will be examined in the future.
Acknowledgments
This work was supported by the National Science Council Grants NSC99-2111-M-001-003-MY3 and NSC100-2621-M-492-001. 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.
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