Abstract

Subdaily temperature and precipitation extremes in response to warmer SSTs are investigated on a global scale using the superparameterized (SP) Community Atmosphere Model (CAM), in which a cloud-resolving model is embedded in each CAM grid column to simulate convection explicitly. Two 10-yr simulations have been performed using present climatological sea surface temperature (SST) and perturbed SST climatology derived from the representative concentration pathway 8.5 (RCP8.5) scenario. Compared with the conventional CAM, SP-CAM simulates colder temperatures and more realistic intensity distribution of precipitation, especially for heavy precipitation. The temperature and precipitation extremes have been defined by the 99th percentile of the 3-hourly data. For temperature, the changes in the warm and cold extremes are generally consistent between CAM and SP-CAM, with larger changes in warm extremes at low latitudes and larger changes in cold extremes at mid-to-high latitudes. For precipitation, CAM predicts a uniform increase of frequency of precipitation extremes regardless of the rain rate, while SP-CAM predicts a monotonic increase of frequency with increasing rain rate and larger change of intensity for heavier precipitation. The changes in 3-hourly and daily temperature extremes are found to be similar; however, the 3-hourly precipitation extremes have a significantly larger change than daily extremes. The Clausius–Clapeyron scaling is found to be a relatively good predictor of zonally averaged changes in precipitation extremes over midlatitudes but not as good over the tropics and subtropics. The changes in precipitable water and large-scale vertical velocity are equally important to explain the changes in precipitation extremes.

1. Introduction

Recent reports from the Intergovernmental Panel on Climate Change (IPCC), including the Special Report on Extreme Events (SREX) and the Fifth Assessment Report (AR5), have stated that the intensity, frequency, and duration of extreme events may change in warmer climate (e.g., Seneviratne et al. 2012; Collins et al. 2013; Flato et al. 2013; Hartmann et al. 2013). Future changes of the extremes have been assessed using output of general circulation models (GCMs), such as those from phase 3 (CMIP3; Meehl et al. 2007; Orlowsky and Seneviratne 2012; Kharin et al. 2007) and phase 5 (CMIP5; Taylor et al. 2012; Sillmann et al. 2013a,b; Kharin et al. 2013) of the Coupled Model Intercomparison Project. Statistically, changes in the temperature or precipitation extremes can be identified as the shift or change in the shape of a corresponding probability distribution function (PDF; e.g., Seneviratne et al. 2012). In the case of a simple shift, the change in the mean can be a good predictor of the future extremes. However, the shape of PDF can also vary so that the mean and the extremes may not always covary (e.g., Hegerl et al. 2004; Schär et al. 2004; Ballester et al. 2010; Orlowsky and Seneviratne 2012).

The changes in temperature and precipitation extremes may be due to different physical mechanisms. Processes that affect surface and radiative fluxes may have significant influences on temperature extremes. For example, some results from GCMs suggest that the temperature extremes can be amplified by drier soils, especially in the northern midlatitudes (e.g., Seneviratne et al. 2006; Lenderink et al. 2007; Vidale et al. 2007; Fischer and Schär 2009; Fischer et al. 2012). Changes in snow cover may also strongly influence the cold extremes (e.g., Kharin et al. 2007; Orlowsky and Seneviratne 2012). Observations suggest that since the 1950s, most land areas have experienced a relative decrease of cold extremes and a relative increase of warm extremes (e.g., Seneviratne et al. 2012; Donat et al. 2013; Hartmann et al. 2013). Also, the changes of nighttime temperatures have been more significant than the changes of daytime temperatures (Ballester et al. 2010; Simolo et al. 2011; Donat and Alexander 2012; Hansen et al. 2012).

The GCMs generally can simulate the observed temperature extremes, better than one would expect from the models with horizontal grid spacing being too coarse to resolve individual clouds. In CMIP5 GCMs, for example, the intermodel spread is comparable to the uncertainty of observations (Sillmann et al. 2013a). Also, the models generally agree well with the sign of the future change (Sillmann et al. 2013b); that is, more warm extremes and less cold extremes are projected to occur with the future increase of CO2 (Solomon et al. 2007; Orlowsky and Seneviratne 2012; Seneviratne et al. 2012; Sillmann et al. 2013b; Collins et al. 2013).

In terms of the rainfall, although higher precipitation rates are generally expected in the warmer climate in response to increased evaporation, the mean and extreme rainfall rates have different physical constraints. The global mean precipitation is mostly constrained by the global energy budget, as the surface enthalpy fluxes, mostly evaporation, need to balance the net radiative cooling of the atmosphere (Allen and Ingram 2002; Trenberth et al. 2003; Held and Soden 2006). As a result, the simulated global mean precipitation increase is in the range from 1% to 3% per 1 K of global mean surface temperature increase. Unlike the global mean precipitation, the individual extreme precipitation events are expected to be less constrained by the global energy budget but more by the local availability of moisture, that is, by the Clausius–Clapeyron (CC) relation. Assuming constant relative humidity, the precipitable water is expected to scale with the surface temperature following the CC relation, which dictates the increase of water vapor by about 7% per 1 K increase of temperature. Based solely on that argument, one would expect that the CC relation would be a good predictor of the future changes in precipitation extremes. However, the CC relation may not be the only factor affecting the precipitation extremes. For example, it has been found that the CC relation tends to overestimate precipitation extremes over the high latitudes and underestimate in the tropics (Pall et al. 2007; O’Gorman 2012). Other factors such as the horizontal moisture flux convergence and the corresponding vertical motion may be equally important (O’Gorman and Schneider 2009a,b). Also, the relative importance of dynamic and thermodynamic (i.e., CC) constraints on precipitation may vary with latitude (Emori and Brown 2005; Li et al. 2011; Chou et al. 2012) and precipitation intensity (Allen and Ingram 2002; Pall et al. 2007; Pendergrass and Hartmann 2014).

Most previous findings on temperature and precipitation extremes have been based on daily averages. However, the temperature and precipitation rates can be strongly modulated by the diurnal cycle, especially over land. Also, precipitation extremes are often associated with mesoscale convective systems (MCSs) with a life span less than 24 h. Several regional studies on subdaily precipitation rates have shown more complex behavior and spatial patterns of precipitation than revealed by the daily rates (Lenderink and van Meijgaard 2008, 2010; Sen Roy 2009; Westra and Sisson 2011; Sen Roy and Rouault 2013). Note that the subdaily data from GCMs are typically not archived (Taylor et al. 2012).

In general, the diurnal cycle of precipitation is not well simulated by most GCMs (Nesbitt and Zipser 2003; Dai 2001, 2006), which limits the robustness of GCMs in reproducing the extreme events. In addition, GCMs tend to overestimate light precipitation while underestimating heavy precipitation (e.g., Sun et al. 2006; Wilcox and Donner 2007; DeMott et al. 2007; Allan and Soden 2008), most likely due to the tendency of convective parameterizations to continuously deplete available convective energy in the boundary layer instead of allowing it to accumulate (DeMott et al. 2007). Consequently, the simulated precipitation extremes in GCMs may be too sensitive to a particular choice of a convective scheme, with the results that the intermodel differences are typically larger than the observed precipitation variability (Wilcox and Donner 2007). Increase of the model resolution tends to improve the precipitation statistics (Wehner et al. 2010; Endo et al. 2012; Kendon et al. 2012; Kopparla et al. 2013), but it has limited impact on the timing of precipitation maximum during the day (Dirmeyer et al. 2012), except when the grid spacing is reduced to just a few kilometers and the deep convection becomes explicitly resolved (Ban et al. 2014).

Superparameterization has been a relatively new approach to the explicit representation of deep convection in climate models without increasing grid resolution to cloud-resolving range (Khairoutdinov and Randall 2001). In the superparameterized approach, all cloud parameterizations in each grid column of a GCM, including convective parameterization, are replaced with a small-domain cloud-resolving model (CRM) with a grid spacing of just a few kilometers, which is suitable to explicitly represent deep convection. The resultant model, also called a multiscale modeling framework (MMF), has been shown to improve, relative to the conventionally parameterized GCMs, the diurnal cycle of precipitation (Khairoutdinov et al. 2005; Pritchard and Somerville 2009), precipitation intensity distribution (DeMott et al. 2007; Kooperman et al. 2016a,b), and even the eastward propagation of nocturnal MCSs over the central United States (Pritchard et al. 2011). It has also been demonstrated that the MMF can substantially improve the simulation of the geographic distribution of extreme precipitation in the United States relative to the standard version of the same model (Li et al. 2012).

In this study, we also use a superparameterized (SP) version of the Community Atmosphere Model (CAM) from the National Center for Atmospheric Research (NCAR) to simulate the statistics of daily and subdaily precipitation and temperature extremes. The SP-CAM results are compared to the results obtained by CAM with conventional parameterizations.

2. Methods

a. Model and simulation design

The SP-CAM is based on CAM, version 3.5, with the superparameterization derived from the System for Atmospheric Modeling (SAM; Khairoutdinov and Randall 2003). The details of SP-CAM, including the coupling between the superparameterization and host GCM, are described by Khairoutdinov et al. (2005). The superparameterization solves the nonhydrostatic equations of motion in an anelastic approximation in a two-dimensional domain with 32 columns and horizontal grid spacing of 4 km. A single-moment bulk microphysics scheme predicts several categories of precipitating and nonprecipitating water. The superparameterization is performed in each column of CAM, subcycling with its own short time step (20 s) within CAM’s own time step (30 min) in response to large-scale tendencies due to dynamics. The superparameterization computes the horizontally averaged precipitation rates, cloud statistics, large-scale tendencies due to cloud processes, and radiation heating rates. The CAM is run using T85 spectral truncation (approximately 1.4° × 1.4° latitude–longitude grid spacing) and 30 vertical levels.

Two simulations have been performed. In the control simulation (CTL), the sea surface temperature (SST) and sea ice are prescribed using the observed monthly climatology. In the perturbation time-slice experiment (PERT), the SST perturbation is added from NCAR’s fully coupled Community Earth System Model (CESM) run with approximately 1° × 1° spatial resolution following the IPCC AR5 representative concentration pathway 8.5 (RCP8.5) scenario (dataset has been provided by NCAR; C. Hannay 2014, personal communication). The monthly SST perturbation is obtained by subtracting the simulated monthly mean SSTs in the 2000–10 period from the 2090–2100 period, thus removing the mean SST bias with respect to the observed climatology. Also, in PERT, the equivalent CO2 level of 1090 ppm is prescribed to reproduce the RCP8.5 radiative forcing. Each SP-CAM simulation has been complemented with the simulation using the conventional CAM. All simulations have been run for 11 years with the first year discarded as the spinup. We realize that 10 years may be too short for collecting robust statistics for the extremes. However, we have been constrained by the high computational cost of running the SP-CAM (which is about a hundred times as expensive as CAM), especially running at T85 spectral truncation used by the host model. We believe that our results can still be representative as long as the contrast between present and future states is larger than the natural variability. That has been one of the reasons for using a rather extreme RCP8.5 scenario as it leads to relatively large changes in hydrological cycle by the end of the twenty-first century (van Vuuren et al. 2011). Also, we use the SSTs repeatedly in each simulated year, which should reduce the interannual variability due to, for example, ENSO or decadal oscillations. To test the robustness of our results, we computed the extreme statistics using only five years of each simulation and found that the statistics are quite similar to the statistics obtained from the 10-yr runs, both qualitatively and quantitatively. Because of the relatively short simulations in this pilot study, our focus has been on moderate or “routine” extremes that tend to occur year after year rather than “epic” rare events with a returning period of decades. The latter would require much longer simulations, which will be performed in the future.

For comparison to observations, we use one-degree daily (1DD) precipitation data from the Global Precipitation Climatology Project (GPCP) (Huffman et al. 2001) and 2-m temperature data from the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERAI; Dee et al. 2011) averaged over the 1997–2011 period. The GPCP 1DD data are derived from satellite and rain gauge observations, while the ERAI is one of the latest reanalysis products. Since the global observation and reanalysis are currently not available at a temporal resolution higher than 6 h, we verify the simulations using only daily output.

b. Definition of the extremes

Different definitions can be used to identify the extreme events. The extremes may be strictly based on the probability of occurrence (e.g., percentiles and return frequencies) or specific impact (e.g., absolute thresholds). Some events are considered extremes relative to moderate conditions that occur yearly, while others may refer to very rare events that typically return after several decades. A threshold used for the extremes may also depend on the choice of the reference period (e.g., Lorenz et al. 2010; Seneviratne et al. 2012). Definitions of the extremes found in the literature usually focus on different climate-related impacts, and therefore, direct comparison among different studies can be sometimes difficult to make.

The percentile thresholds have been widely used in the past (e.g., Allen and Ingram 2002; Griffiths et al. 2005; Pall et al. 2007; Kenyon and Hegerl 2008, 2010; O’Gorman and Schneider 2009a,b; Ballester et al. 2010; Orlowsky and Seneviratne 2012), as they allow simpler comparison among different studies. The most frequently used threshold is the 90th percentile, which is also one of the major indices used in the IPCC report. However, the 90th percentile defines roughly 36 days as extremes each year on each grid, which is more than a month, and is close to the seasonal statistics. The 99.9th percentile is also commonly used in studies of precipitation extremes. But in our 10-yr simulation, if the 99.9th percentile is used, the sample size of the extremes is about 3.6 days (or ~30 cases for the 3-hourly output), which is too small. For 3-hourly extremes investigated in this study, the 99th percentile seems to be an optimal threshold for a 10-yr period as it virtually guarantees that the sample size is large enough to identify extreme cases that are distinct from the mean conditions of summer or winter.

Two methods of identifying the changes in extremes due to climate warming are used in this study. In the first method, the change in the intensity of the events with the same probability of occurrence is investigated. In this method, the percentile extremes are defined independently for each simulation on each grid. In the second method, the 99th (or the 1st) percentile from the CTL run is used to identify the change in frequency of the events in PERT run on the same grid. This method may introduce a bias toward the change in the intensity of extremes. For example, Sillmann et al. (2013b) found that the largest decreases and increases in temperature extremes, defined by 10% exceedance rate over 1961–90 period, are different from those defined by the annual maximum or minimum temperatures. Thus, the fixed threshold should only be used to examine the frequency change of the events, which are presently considered to be extreme but may no longer be considered extreme in the future because of, for example, mitigation.

For precipitation rate, a wet-day threshold is often used to exclude the nonprecipitating days from percentile estimates. The wet-day extremes are common in studies by the Expert Team on Climate Change Detection and Indices (ETCCDI; e.g., Frich et al. 2002; Kiktev et al. 2003; Alexander et al. 2006; Sillmann and Roeckner 2008; Orlowsky and Seneviratne 2012; Zhang et al. 2011; Collins et al. 2013; Kharin et al. 2013; Sillmann et al. 2013a,b). In our study, we use the wet-day threshold of 1 mm day−1 for daily data and 0.1 mm h−1 for 3-hourly data. As GCMs are notorious for producing large amount of precipitation in the form of drizzle, a wet-day threshold may arbitrarily exclude a certain number of rainy days, which, in turn, can affect the percentile threshold. To avoid this ambiguity, it is common to use all-day extremes, regardless of whether it was raining on a particular day or not. Each method has advantages and drawbacks, and we use both in this study as summarized in Table 1.

Table 1.

Indices and notations used in this study.

Indices and notations used in this study.
Indices and notations used in this study.

The PDFs of daily precipitation and temperature have also been computed. PDFs are calculated on the individual grid before the area-weighted averaging is done. To better illustrate the difference of the extremes, the PDFs are plotted on a log–log scale, but the areas below the curves are no longer proportional to the probabilities of occurrence. For the distribution functions of annual occurrence of 3-hourly wet-day precipitation extremes (see Fig. 3), the number of extremes on each grid column is identified and weighted by the grid area before all the extremes over the globe are used to calculate the distributions. The global distributions are then normalized by the total number of grid columns and years of simulation.

3. Results

a. Mean climatology

Simulated and observed daily PDFs of 2-m temperature over land (ocean temperatures are prescribed) and precipitation (global mean and in the 45°S–45°N belt) are shown in Figs. 1a and 1b, respectively. Both models generally reproduce the observed land-temperature PDF rather well, including a well-pronounced peak at about 25°C, although CAM tends to overestimate its frequency. The SP-CAM tends to overestimate the frequency of very cold events, colder than −60°C, which happen mostly over Antarctica. The spatial patterns of the daily temperature biases over land with respect to ERAI (Figs. 1c,d) show generally smaller biases for SP-CAM.

Fig. 1.

Model PDFs and spatial patterns compared to reanalysis (ERAI) and observations (GPCP and TRMM): (a) 2-m temperature PDF over land and (b) precipitation PDF, and (c),(d) model bias (model minus reanalysis) in daily 2-m temperature and (e)–(h) model bias (model minus observation) in daily precipitation for (c),(e),(g) SP-CAM and (d),(f),(h) CAM. Since TRMM only covers mid-to-low latitudes, comparisons against TRMM are limited to 45°S–45°N.

Fig. 1.

Model PDFs and spatial patterns compared to reanalysis (ERAI) and observations (GPCP and TRMM): (a) 2-m temperature PDF over land and (b) precipitation PDF, and (c),(d) model bias (model minus reanalysis) in daily 2-m temperature and (e)–(h) model bias (model minus observation) in daily precipitation for (c),(e),(g) SP-CAM and (d),(f),(h) CAM. Since TRMM only covers mid-to-low latitudes, comparisons against TRMM are limited to 45°S–45°N.

As for the precipitation, SP-CAM also seems to outperform CAM in simulating heavy rain rates (Fig. 1b), which is consistent with the previous studies (DeMott et al. 2007; Kooperman et al. 2016a). Relative to GPCP, SP-CAM tends to overestimate the frequency of the rates higher than about 40 mm day−1; however, when compared to TRMM, SP-CAM shows very good agreement, especially for heavy rain rates. The spatial pattern of mean precipitation bias with respect to GPCP and TRMM (Figs. 1e–h) shows substantial biases, especially over tropical oceans. Over the western Pacific and Maritime Continent, SP-CAM tends to produce too much rain, while the opposite is true for CAM. Over land, both SP-CAM and CAM generally do a good job with a notable exception of the Amazon region, where both models seem to have rather substantial dry biases. Note that these biases are quite similar to the biases documented in other SP-CAM studies using earlier versions of the model (e.g., Khairoutdinov et al. 2005). Consistent with the earlier studies (Khairoutdinov et al. 2005; Pritchard and Somerville 2009), our results confirm that SP-CAM simulates a reasonable diurnal cycle of precipitation over land (not shown). The consistency among studies using superparameterization with different resolutions suggests that the improvement of rainfall is not sensitive to the resolution of the GCMs.

Table 2 summarizes the global response of mean temperature to prescribed SST warming. The global mean temperature change for SP-CAM is 4.18°C, which is closer than CAM to the CMIP5 multimodel mean of 3.7°C for RCP8.5 scenario (Collins et al. 2013). Over land, the SP-CAM and CAM produce mean warming of about 5.03° and 5.37°C, respectively, which is within the range of 3.4°–6.2°C reported in IPCC AR5. Both models show about 35%–45% larger warming over land relative to the ocean.

Table 2.

Changes between PERT and CTL in mean and extreme temperatures over the globe, land, and ocean. The last column is the ratio of changes between land and ocean. All calculations are based on 3-hourly temperature.

Changes between PERT and CTL in mean and extreme temperatures over the globe, land, and ocean. The last column is the ratio of changes between land and ocean. All calculations are based on 3-hourly temperature.
Changes between PERT and CTL in mean and extreme temperatures over the globe, land, and ocean. The last column is the ratio of changes between land and ocean. All calculations are based on 3-hourly temperature.

b. Extremes in SP-CAM versus CAM

The differences between SP-CAM and CAM in simulated temperature and precipitation extremes, based on 3-hourly data, are shown in Fig. 2. SP-CAM tends to simulate colder warm extremes (Fig. 2a) and colder cold extremes (Fig. 2c) over most of the land. It is particularly true for the cold extremes over North America and Europe, where SP-CAM is 5°–10°C colder than CAM. Over land, SP-CAM tends to simulate larger warming of cold extremes over the United States and western Europe. However, the changes in temperature extremes are generally comparable between CAM and SP-CAM (Figs. 2b,d). Since SP-CAM resolves convection explicitly, it tends to simulate stronger precipitation events, especially over maritime tropics where convection is the most prominent (Fig. 2e). In terms of the changes in precipitation extremes, SP-CAM changes tend to be 50%–100% larger than that simulated by CAM; for example, east of the Rockies over the continental United States (CONUS), changes in SP-CAM are 2–5 times as large, which may be due to the amplified summertime mesoscale convective systems (Kooperman et al. 2014).

Fig. 2.

Differences between SP-CAM and CAM in terms of (a),(b) warm extremes, (c),(d) cold extremes, and (e),(f) precipitation extremes. (left) The absolute difference between SP-CAM and CAM in the CTL run and (right) the changes between PERT and CTL in SP-CAM normalized by the changes in CAM. All panels are based on 3-hourly data.

Fig. 2.

Differences between SP-CAM and CAM in terms of (a),(b) warm extremes, (c),(d) cold extremes, and (e),(f) precipitation extremes. (left) The absolute difference between SP-CAM and CAM in the CTL run and (right) the changes between PERT and CTL in SP-CAM normalized by the changes in CAM. All panels are based on 3-hourly data.

Figure 3 shows globally averaged distributions of annual precipitation extremes and the changes in the distributions for all-day and wet-day cases. The amount distribution is correlated to frequency distribution by multiplying the frequency by the specific rain rate over 3-h duration in each bin. Thus, the relative change in amount and frequency are identical in Figs. 3g,h. For the all-day cases (Fig. 3a), the extremes in SP-CAM occur more frequently at higher rain rates, which is consistent with the aforementioned tendency of SP-CAM to produce rain at heavier rates than CAM. In the warmer climate, both SP-CAM and CAM tend to increase frequency and amount for all-day rain rates (Figs. 3a,c). However, CAM simulates larger increases in rainfall amount due to extremes at lighter rain rates and smaller increases at heavier rain rates (Fig. 3e). Differences between the two models are also apparent in terms of relative change as a result of the imposed warming (Fig. 3g). In SP-CAM, the heavy-rain extremes tend to increase their frequency more than light-rain extremes, which is consistent with several previous studies (Allen and Ingram 2002; Pall et al. 2007; Pendergrass and Hartmann 2014). In contrast, in CAM, the increase occurs rather uniformly over most of the rates. The results are qualitatively similar for the wet-day extremes (Figs. 3b,d,f,h).

Fig. 3.

Distributions of annual (a),(b) occurrence and (c),(d) amount of precipitation extremes at different rain rates on a grid. (e),(f) The absolute changes in the annual amount (PERT − CTL) and (g),(h) relative changes in frequency and amount (PERT/CTL). Precipitation extremes are defined as the cases that exceed the 99th percentile of the CTL run, and the global statistics are normalized by the number of grid columns, years of simulation, and bin width ΔR. (left) Extremes of all-day precipitation and (right) extremes of wet-day precipitation (>0.1 mm h−1); all panels are based on 3-hourly precipitation.

Fig. 3.

Distributions of annual (a),(b) occurrence and (c),(d) amount of precipitation extremes at different rain rates on a grid. (e),(f) The absolute changes in the annual amount (PERT − CTL) and (g),(h) relative changes in frequency and amount (PERT/CTL). Precipitation extremes are defined as the cases that exceed the 99th percentile of the CTL run, and the global statistics are normalized by the number of grid columns, years of simulation, and bin width ΔR. (left) Extremes of all-day precipitation and (right) extremes of wet-day precipitation (>0.1 mm h−1); all panels are based on 3-hourly precipitation.

c. Temperature extremes

Furthermore, we will discuss only the extremes as simulated by the SP-CAM. It has been known that the changes in temperature extremes and mean values are closely correlated (Schär et al. 2004; Griffiths et al. 2005; Seneviratne et al. 2012). SP-CAM results support that notion as can be seen in Figs. 4a,c,e. As was mentioned above and found in many previous studies, the land in general and the Arctic in particular tend to warm more than the ocean (Fig. 4a). In terms of the extremes, the biggest change is for the cold extremes. Significant warming of cold extremes, more than 10°C, is found over high- and midlatitude landmasses (Fig. 4e). In comparison, the model predicts a large increase of the warm extremes over Amazonia, North America, Europe, Sahel, and southern Africa (Fig. 4c). It is interesting that although the changes in temperature extremes (Figs. 4c,e) show a similar pattern to the changes in mean temperature (Fig. 4a), there is a relatively small amplification of warm extremes over middle and high latitudes. At the same time, the change in warm extremes is relatively larger than the change in cold extremes over low-latitude continents (Fig. 4b). Globally, the range of temperatures tends to become narrower in the warmer climate, but the local temperature distributions can broaden over mid-to-low latitudes over continents (Fig. 4b).

Fig. 4.

Changes between PERT and CTL in (a) mean temperature, (c),(d) warm extremes, (e),(f) cold extremes, and (b) cold extremes normalized by warm extremes. In (a),(c),(e), the absolute changes in intensity of mean temperature and extremes defined by the 99th percentile and 1st percentile in each run. In (d),(f), the relative changes in frequency of extremes defined by the percentile thresholds in CTL run. All panels are based on 3-hourly SP-CAM temperature, and the blank areas in (f) do not have future temperatures below the CTL threshold.

Fig. 4.

Changes between PERT and CTL in (a) mean temperature, (c),(d) warm extremes, (e),(f) cold extremes, and (b) cold extremes normalized by warm extremes. In (a),(c),(e), the absolute changes in intensity of mean temperature and extremes defined by the 99th percentile and 1st percentile in each run. In (d),(f), the relative changes in frequency of extremes defined by the percentile thresholds in CTL run. All panels are based on 3-hourly SP-CAM temperature, and the blank areas in (f) do not have future temperatures below the CTL threshold.

In PERT, the warm temperature extremes, as defined using the threshold based on the 99th percentile of the CTL, become several times more frequent (Fig. 4d). For example, over North America and Eurasia, the temperature extremes become 3–10 times more frequent. The large changes over the ocean are due to small temperature variability; thus, a small change in mean would result in significant relative changes in the frequency of the extremes. At the same time, the cold extremes defined as temperatures below the 1st percentile of the CTL are not found at most places in PERT, except for the midlatitudes (Fig. 4f), which means that in a warmer climate the present cold extremes become very unlikely.

Note that the changes in warm and cold extremes may be due to different physical mechanisms. The warm extremes over land are most likely influenced by the soil moisture feedback. For example, the temperature extremes are amplified by the drier soil especially in the midlatitudes (Seneviratne et al. 2006; Lenderink et al. 2007; Vidale et al. 2007; Fischer and Schär 2009; Fischer et al. 2012). Dry soil limits latent heat flux and enhances sensible heat flux, so the warming of air is greater (Betts et al. 1996; Zhou and Geerts 2013). As a result, the changes in warm extremes are larger over land. The changes in cold extremes are mainly associated with the changes in snow and ice cover; therefore, they are more prominent over middle and high latitudes.

d. Precipitation extremes

Studies based on daily rates generally suggest that the precipitation extremes increase faster than the mean precipitation (Allen and Ingram 2002; Collins et al. 2013; Kharin et al. 2013; Sillmann et al. 2013a,b), which is also true for 3-hourly precipitation rates used in this study. Table 3 summarizes the changes in mean and extreme precipitation, both for SP-CAM and CAM. For SP-CAM, the mean precipitation increases with global mean temperature at the rate of about 2.0% K−1, while the extreme precipitation tends to increase at a much faster rate of 5.0% K−1 for all-day extremes and 6.3% K−1 for wet-day extremes, which is closer to 7% K−1 dictated by the CC relation. It is usually explained by the notion that mean precipitation is mostly constrained by radiative cooling, which does not have to scale with the CC relation, while the extreme precipitation is more constrained by the moisture availability and, hence, should scale more closely with the CC relation. Note that the extremes in Table 3 tend to increase more over ocean than over land, which is explained by higher moisture availability over the ocean and relatively limited transport of moisture from the oceans to the land.

Table 3.

Fractional changes between PERT and CTL in mean and extreme precipitation (% K−1) over the globe, land, and ocean. All calculations are based on 3-hourly precipitation.

Fractional changes between PERT and CTL in mean and extreme precipitation (% K−1) over the globe, land, and ocean. All calculations are based on 3-hourly precipitation.
Fractional changes between PERT and CTL in mean and extreme precipitation (% K−1) over the globe, land, and ocean. All calculations are based on 3-hourly precipitation.

The widely accepted wet-get-wetter and dry-get-drier paradigm (Held and Soden 2006) seems to be also applicable to the changes in precipitation extremes, as demonstrated by Fig. 5. The precipitation extremes tend to decrease over regions of small precipitation extremes, which may vary for different definitions of extremes. Also, the increases in extremes seem to be close to those dictated by the CC relation. This behavior will be discussed in more detail below. In terms of the relative change in the frequency of extreme events in PERT using the thresholds from the CTL, the frequency tends to increase significantly over many regions. For example, over the United States, the frequency of the extreme precipitation events increases by 50%–100%.

Fig. 5.

Changes between PERT and CTL in intensities of (a),(b) mean precipitation, (c),(d) precipitation extremes, and (e),(f) relative changes in frequencies of precipitation extremes that exceed 99th percentile of the CTL run. (left) All-day precipitation and (right) wet-day precipitation (>0.1 mm h−1). The blank areas do not have sample size that is large enough to define wet-day extremes, and all panels are based on 3-hourly SP-CAM precipitation.

Fig. 5.

Changes between PERT and CTL in intensities of (a),(b) mean precipitation, (c),(d) precipitation extremes, and (e),(f) relative changes in frequencies of precipitation extremes that exceed 99th percentile of the CTL run. (left) All-day precipitation and (right) wet-day precipitation (>0.1 mm h−1). The blank areas do not have sample size that is large enough to define wet-day extremes, and all panels are based on 3-hourly SP-CAM precipitation.

e. Difference between 3-hourly and daily extremes

The changes in subdaily temperature and precipitation extremes mentioned above are consistent with the changes in previous studies on daily extremes (e.g., Seneviratne et al. 2012; Collins et al. 2013; Kharin et al. 2013; Sillmann et al. 2013a,b). For example, the cold extremes usually warm up more than warm extremes with significant contrasts between land and ocean, between tropics and higher latitudes, etc. Also, relative to the mean change, the precipitation extremes and their frequency tend to increase more over wet regions and decrease more over dry regions. In our study, we also find important qualitative and quantitative differences between 3-hourly and daily extremes.

Figure 6 compares daily and 3-hourly temperature and precipitation extremes. One can see that the changes in the 3-hourly warm temperature extremes are somewhat smaller than the changes in daily extremes, while the changes in 3-hourly cold extremes are slightly larger (Figs. 6a,c). The changes in daily and 3-hourly temperature extremes are quite similar over the regions where the diurnal temperature range (DTR) is small, such as over the oceans, while being farther apart over the snow-free land, where the DTR can be quite large as a result of the prominent diurnal cycle (Figs. 6b,d). Physically, the warm extremes (T99m) are mainly related to the dryness of the soil (e.g., Seneviratne et al. 2006; Lenderink et al. 2007; Vidale et al. 2007; Fischer and Schär 2009; Fischer et al. 2012), while cold extremes (T01m) are more influenced by less persistent snow and ice cover (e.g., Kharin et al. 2007; Orlowsky and Seneviratne 2012). However, other processes, which can influence surface energy balance, may also have an impact on temperature extremes.

Fig. 6.

Changes between PERT and CTL in the intensity of subdaily (a),(b) warm extremes, (c),(d) cold extremes, and (e),(f) precipitation extremes normalized by the changes in daily extremes. The same percentile level is used to define both daily and subdaily extremes based on SP-CAM simulations. The zonal averages are presented in (a),(c),(e), and global patterns are shown in (b),(d),(f).

Fig. 6.

Changes between PERT and CTL in the intensity of subdaily (a),(b) warm extremes, (c),(d) cold extremes, and (e),(f) precipitation extremes normalized by the changes in daily extremes. The same percentile level is used to define both daily and subdaily extremes based on SP-CAM simulations. The zonal averages are presented in (a),(c),(e), and global patterns are shown in (b),(d),(f).

Figure 7 shows various impacts on temperature extremes including the changes in cloud cover, which is rarely examined in previous studies. Since the subdaily soil moisture is not available, we relate the soil moisture in the hottest and coldest months to the warm and cold extremes in this study. Changes in soil moisture and cloud cover in snow-free regions have different influences on the DTR. By changing the heat content of the soil, the increased soil moisture in a warmer climate results in a smaller increase in daytime temperature (correlated with 3-hourly T99m in summer) but a larger increase in nighttime temperature (included in daily T99m in summer), and vice versa. At the same time, the increased summertime cloud cover leads to similar changes in 3-hourly and daily warm extremes as what the increased soil moisture does, since the surface receives less solar radiation during the day but more longwave radiation during the night. Therefore, changes in daily warm extremes dominate over the regions with both increased soil moisture and cloud cover in summer (Figs. 6b and 7a,c). Over the regions where the soil moisture and cloud cover have opposite changes, the stronger change dominates. Similarly, the dominant changes in 3-hourly cold extremes over the tropical continents (Fig. 6d) are primarily due to the increased cloud cover in winter (Fig. 7d), as the 3-hourly T01m is correlated with the larger increases in nighttime temperature over those areas. Compared with the increase in cloud cover, decreased soil moisture has limited influence on cold extremes (Figs. 7b and 6d). The presence of the snow cover in winter (blank region over land in Fig. 7b) reduces the DTR; hence, the changes in daily and 3-hourly T01m are quite similar over the mid-to-high-latitude continents (Fig. 6d). In general, the largest difference between daily and 3-hourly temperature extremes is found mainly over the regions where the soil moisture and cloud cover change significantly. The daily temperature extremes might overemphasize the remaining part of each day beyond the hottest and coldest hours. Qualitatively, though, the 3-hourly and daily temperature extremes are found to be quite similar.

Fig. 7.

Changes between PERT and CTL in the (a),(b) volumetric soil moisture and (c),(d) total cloud fraction correlated to temperature extremes over land. (left) The hottest summer month (July in Northern Hemisphere and January in Southern Hemisphere) and the warm extremes and (right) the coldest winter month (January in Northern Hemisphere and July in Southern Hemisphere) and the cold extremes. The blank areas over land in (a),(b) are covered by snow in both CTL and PERT runs.

Fig. 7.

Changes between PERT and CTL in the (a),(b) volumetric soil moisture and (c),(d) total cloud fraction correlated to temperature extremes over land. (left) The hottest summer month (July in Northern Hemisphere and January in Southern Hemisphere) and the warm extremes and (right) the coldest winter month (January in Northern Hemisphere and July in Southern Hemisphere) and the cold extremes. The blank areas over land in (a),(b) are covered by snow in both CTL and PERT runs.

Changes in 3-hourly precipitation extremes are generally larger than the changes in daily extremes (Figs. 6e,f). As will be discussed further, the precipitation extremes (>99th percentile) with larger intensities have larger changes. The 3-hourly precipitation extremes tend to be more intense than daily extremes because of the relatively short duration of the extreme precipitation events. Note that the differences shown in Figs. 6e,f are not the absolute magnitude of 3-hourly and daily extremes. Instead, they are the differences between the fractional changes in 3-hourly and daily precipitation extremes.

Table 3 shows that the global-mean changes in 3-hourly all-day and wet-day precipitation extremes are about 5.0% and 6.3% K−1, respectively. In comparison, the corresponding changes in daily extremes are smaller, that is, 4.7% and 5.6% K−1, respectively. These estimates are calculated based on global mean values, as regionally averaged relative changes can be quite large, especially over dry regions where the rain rates are small.

f. Change in precipitation with different intensities

As mentioned above, our results suggest that in a warmer climate, precipitation tends to increase more over wet regions than over dry regions. Figure 8a shows the fractional change in global precipitation rate at different percentiles. The change in precipitation is positive and increases for large precipitation percentiles, while the change becomes negative for percentiles smaller than the 90th percentile, which suggests that the increases in precipitation extremes happen mostly at the expense of lighter precipitation. The shift of the rainfall toward heavier precipitation is consistent with CMIP5 models (Pendergrass and Hartmann 2014). Also, the asymptote of changes at the highest percentiles is consistent with the daily SP precipitation at a coarser resolution by Kooperman et al. (2016b). Figure 8b shows the zonal-mean change in precipitation percentiles with latitude. For a given percentile, the sign of the change can be different for different latitudes, which is consistent with Pall et al. (2007) using a traditional GCM. For example, the precipitation rate for the 99th percentile tends to increase more significantly over the tropics and midlatitude storm tracks where the rain rates are larger at that percentile level.

Fig. 8.

Changes between PERT and CTL in (a) globally averaged precipitation, (b) zonally averaged precipitation, and grid-scale precipitation at different percentiles over (c) land and (d) ocean. Changes in (c),(d) are sorted by the Rm on the grids from the light to the heavy for land and ocean, respectively, and the average precipitation over land and ocean is indicated by the vertical black line. All panels are based on 3-hourly SP-CAM precipitation.

Fig. 8.

Changes between PERT and CTL in (a) globally averaged precipitation, (b) zonally averaged precipitation, and grid-scale precipitation at different percentiles over (c) land and (d) ocean. Changes in (c),(d) are sorted by the Rm on the grids from the light to the heavy for land and ocean, respectively, and the average precipitation over land and ocean is indicated by the vertical black line. All panels are based on 3-hourly SP-CAM precipitation.

The changes in precipitation sorted by the mean rainfall in each grid box are shown in Figs. 8c and 8d over the land and ocean, respectively. This is a relatively new perspective to evaluate the changes in precipitation with different intensities at different locations. One can see that for the rain rates above the global average, the changes in precipitation are positive at percentiles higher than 95% for both land and ocean, and the fractional changes at upper percentiles are larger with heavier mean precipitation. For mean rain rates smaller than the global average, the rates increase over land but decrease over ocean for virtually all percentiles >50%. It might be related to larger warming over land and, as a result, stronger thermally induced circulation between land and ocean with increased convergence of moisture over land.

4. Discussion

a. The Clausius–Clapeyron scaling

Precipitation extremes are usually associated with relatively short-lived events, which are strongly influenced by the availability of moisture. If the relative humidity remains approximately constant (as suggested by many GCM simulations) in the warmer climate, the precipitation extremes should respond to the increased amount of precipitable water. It is, therefore, tempting to use a simple CC scaling to estimate the response of extreme precipitation to global warming (Allen and Ingram 2002). However, as has been discussed in the previous section, precipitation extremes defined using different percentiles may have different rates of change for a given warming. Also, the changes in precipitation extremes may be regionally different even at the same percentile level. The notion that the CC scaling may not be a good predictor of the change in extreme precipitation, especially on the regional scale, has been common (e.g., Pall et al. 2007; O’Gorman and Schneider 2009a,b; Lenderink and van Meijgaard 2008, 2010; Singh and O’Gorman 2014). This notion is well illustrated by Fig. 9a, which compares the changes in the zonally averaged 3-hourly precipitation extremes and corresponding precipitable water with the CC prediction. One can see that the CC scaling is indeed a rather poor predictor of the extreme precipitation change for most latitudes. In particular, the CC scaling tends to overestimate the changes over the subtropics and high latitudes while grossly underestimating the changes over tropics. The CC scaling seems to work better for midlatitudes, which is consistent with some previous studies (e.g., Pall et al. 2007). However, even for midlatitudes, the noisy pattern in Fig. 9b suggests that the CC scaling, being a relatively good predictor for zonally averaged extremes, still is not a good predictor of the extremes on a regional scale. Looking at the precipitable water (Figs. 9c,d) as a proxy for water availability, it is again clear that moisture alone may not well predict the extremes.

Fig. 9.

Changes between PERT and CTL in precipitation extremes compared with (a),(b) CC prediction, (c),(d) precipitable water (pw), and (e),(f) vertical velocity (omega) at 500 mb during the precipitation extremes (R99m). The zonal changes and average of the parameters are shown in (a),(c),(e). The global distribution of the changes are shown in (b),(d),(f), and the areas with decreased all-day precipitation extremes are hatched in (f). All panels are based on 3-hourly data from SP-CAM.

Fig. 9.

Changes between PERT and CTL in precipitation extremes compared with (a),(b) CC prediction, (c),(d) precipitable water (pw), and (e),(f) vertical velocity (omega) at 500 mb during the precipitation extremes (R99m). The zonal changes and average of the parameters are shown in (a),(c),(e). The global distribution of the changes are shown in (b),(d),(f), and the areas with decreased all-day precipitation extremes are hatched in (f). All panels are based on 3-hourly data from SP-CAM.

b. Dynamic constraint on precipitation extremes

Besides the thermodynamics, the dynamics should also be considered in order to explain the response of the extremes to warming. For example, the horizontal moisture convergence and the corresponding vertical velocity should correlate with precipitation. This is well illustrated by considering the zonal-mean vertical velocity shown in Fig. 9e, regional patterns of precipitation extremes in Fig. 5c, and the vertical velocity at 500 mb (1 mb = 1 hPa) in Fig. 9f. Similar to the CC constraint, the influence of the dynamic constraint on precipitation also varies over different latitudes, but it is most significant over tropics (Emori and Brown 2005; Li et al. 2011).

Both the magnitude and the change of the constraints are important. Over the high latitudes, where precipitable water is small, changes in vertical velocity have a relatively small effect on precipitation extremes (Figs. 9a,c,e). Thus, precipitation extremes are more sensitive to moisture constraint at high latitudes. In contrast, over the tropics, where precipitable water is abundant, changes in vertical velocity may have a larger effect on precipitation extremes. This notion may explain the “super CC” scaling of the precipitation extremes over the equator. In addition, the dominance of the dynamic constraint is illustrated by the southward shift and broadening of the ascending branch of the Walker cell over the eastern Pacific, leading to dramatic changes in Rm99 (Figs. 5c,d and 9e).

c. Physical influences on precipitations with different intensities

Although the thermodynamic and dynamic constraints are discussed separately, they are not always independent. For example, the increased water vapor due to surface warming tends to slow down the atmospheric circulation to keep vertical moisture advection and precipitation in balance with the radiative cooling, at least over large temporal and spatial scales (Held and Soden 2006). For the extreme precipitation, the relationships between these constraints can be even more complicated, and it may be difficult to clearly quantify the contribution from the given constraint. It can be revealing to look at the response of precipitation to a certain combination of the constraints as shown in Fig. 10, where precipitation over given latitudes is binned by the vertical velocity at the 500-mb level (Fig. 10a). Such velocity has been commonly used as a discriminator of the large-scale circulation regime (Bony et al. 1997). The average precipitation (BR) is then compared to heavy precipitation (BR99+) in each bin, which is defined by the 99th percentile of precipitations in that bin. Note that the average and 99th percentile in each bin shown in Fig. 10 are not necessarily equivalent to the mean and extreme precipitation discussed in the previous sections.

Fig. 10.

Binned (a)–(d) precipitation and (e)–(h) pw by omega at 500 mb over different latitudes. (a) BR and BR99+ in each bin and (e) the corresponding pw are shown for 40°–70°N. Differences between mean and heavier rainfall conditions are shown for each parameter over (b),(f) the Northern Hemisphere latitudes between 40° and 70°N, (c),(g) the tropics between 25°S and 25°N, and (d),(h) the Southern Hemisphere latitudes between 40° and 70°S. All panels are based on the 3-hourly SP-CAM CTL run.

Fig. 10.

Binned (a)–(d) precipitation and (e)–(h) pw by omega at 500 mb over different latitudes. (a) BR and BR99+ in each bin and (e) the corresponding pw are shown for 40°–70°N. Differences between mean and heavier rainfall conditions are shown for each parameter over (b),(f) the Northern Hemisphere latitudes between 40° and 70°N, (c),(g) the tropics between 25°S and 25°N, and (d),(h) the Southern Hemisphere latitudes between 40° and 70°S. All panels are based on the 3-hourly SP-CAM CTL run.

In the Northern Hemisphere, midlatitude precipitation strongly depends on vertical velocity and precipitable water as expected (Figs. 10a,e). Not surprisingly, both BR and BR99+ increase with increasing large-scale ascent and precipitable water. From the dynamical point of view, a strong ascent is accompanied by the large-scale convergence, which enhances the moisture available for the formation of rain. The influences of the constraints on precipitation can also be seen by looking at the difference between BR and BR99+ (Figs. 10b,f). For the given vertical velocity, the prominent difference between the BR and BR99+ is mostly due to the large difference in precipitable water. Besides vertical velocity and precipitable water, the low-level wind shear may influence the mesoscale organization of moist deep convection into different mesoscale structures, which can also affect the precipitation rates (Weisman and Klemp 1982; Houze 1994; Anber et al. 2014). However, the CRM domain in SP-CAM is oriented north–south. Therefore, the clouds in SP-CAM respond only to the meridional wind shear, which is generally quite small at low levels. As a result, the influence of wind shear is not discussed in this study.

The influences of the constraints may also vary with the latitude. Precipitation is less sensitive to precipitable water over tropics as the moisture is abundant there, and the change in moisture is relatively small compared to the existing moisture (Fig. 10g). In contrast, precipitation is more sensitive to the precipitable water over higher latitudes where the moisture is relatively limited (Figs. 10f,h). The dependence of the constraints on latitude is generally consistent with the previous studies (Emori and Brown 2005; Li et al. 2011).

5. Conclusions

In this paper, we presented the statistics of precipitation and temperature extremes as simulated by the SP-CAM, in which all parameterizations of clouds are replaced by the superparameterization. The 10-yr control simulation with prescribed climatological SSTs has been contrasted against the simulation in which SSTs are perturbed by the late twenty-first-century SST pattern derived from the coupled simulation forced by the RCP8.5 emission scenario. The SP-CAM results are complemented with the results obtained using CAM with conventional parameterizations. In addition to the analysis of daily extremes commonly used in previous studies of the extremes, the emphasis of this study has been on less commonly studied 3-hourly extremes. The subdaily extremes can be particularly common over land, where convection is strongly modulated by the diurnal cycle and where heavy precipitation is often due to summertime convective systems with a life span shorter than a single day. Our use of the SP-CAM has been motivated by the previous findings that SP-CAM can simulate a more realistic diurnal cycle of precipitation over land and precipitation intensity distribution compared to conventional CAM.

In this study, the SP-CAM does seem to reproduce the frequency of the heavy rain rates derived from TRMM and GPCP observations rather well. In terms of the extremes defined by the 99th-percentile rates, the SP-CAM predicts stronger precipitation extremes than CAM, with the largest differences over tropical and subtropical regions where convection is more active. In terms of the response of precipitation extremes to warmer SSTs, CAM predicts a uniform increase of frequency of precipitation regardless of the rain rate, while SP-CAM predicts a monotonic increase of frequency with increasing rain rate. Over the CONUS, east of the Rockies, the precipitation extremes in SP-CAM simulations in response to SST warming tend to be 2–5 times as strong as those predicted by CAM.

In terms of the temperature, SP-CAM tends to simulate somewhat colder warm extremes and colder cold extremes than CAM. The biggest response to the warmer SSTs is found for cold seasons when cold extremes tend to warm up by as much as 10°C in both models. At the same time, both models suggest that the frequency of the warm extremes, defined as subdaily temperatures exceeding the present 99th percentile, becomes several times as high. For example, over North America, the frequency of heat events is predicted to increase by 3–10 times over the present.

In response to the warmer SSTs, the subdaily precipitation extremes tend to increase more than mean precipitation, consistent with the earlier studies. The wet-get-wetter and dry-get-drier paradigm is found to be applicable to extreme precipitation in this study. We also found the decrease of precipitation at lower percentiles, which suggests that the extremes increase at the expense of lighter rain rates.

In many respects, the changes in subdaily and daily temperature extremes in response to warmer SSTs are similar, except for the regions with significant changes in soil moisture and cloud cover over land. In comparison, the subdaily precipitation extremes change more than daily extremes. This can be explained by the notion that the subdaily extremes are usually associated with relatively vigorous but short-lived convective events, while daily extremes are mostly associated with long-lived synoptic-scale events.

Our results suggest that broadly, over midlatitudes, in a zonally averaged sense, the increase of 3-hourly extremes tends to follow the CC constraint. In contrast, over tropics and subtropics, the CC scaling alone fails to explain the change in precipitation extremes in response to warmer SSTs. However, even over midlatitudes, the CC scaling is found to be a poor predictor of the extremes on regional scales. The changes in precipitable water and large-scale vertical velocity have been found to be equally important to changes in precipitation extremes in warmer climate.

Acknowledgments

This work has been supported in part by the U.S. Department of Energy through Grant DESC0012488 and by the National Science Foundation through Grants AGS-1418309 and AGS-1048918. All computations have been performed at NCAR on the Yellowstone supercomputer.

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Footnotes

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