1. Introduction
There is much more uncertainty in modeled projections of rainfall than surface air temperature under global warming scenarios, with disagreement among models regarding not only the local magnitude of the rainfall response but also its sign (Collins et al. 2013; Rowell 2012; Chadwick et al. 2013; Kharin et al. 2013; Langenbrunner et al. 2015; Woldemeskel et al. 2016; Pfahl et al. 2017), the tropics being the region of highest uncertainty (Chen et al. 2014). Given this uncertainty and the expectation that global warming will increase water shortage risks and the number of droughts and heavy precipitation events (IPCC 2018), greater understanding of model variation in rainfall response characteristics is essential in predicting and adapting to climate change.
Our documentation of the impact of fLS within control and global warming simulations adds to the literature regarding the response of the hydrological cycle to global warming and may help to further clarify uncertainties in model responses. How circulation and precipitation respond to greenhouse gas forcing has been the subject of numerous studies, which have led to some important observations and hypotheses. The “rich-get-richer” (or “wet-get-wetter”) hypothesis (Betts 1998; Neelin et al. 2003; Chou and Neelin 2004; Held and Soden 2006) links changes in precipitation to present-day rainfall distributions, with rainfall growing more intense deep within convective zones (hence “rich-get-richer”) and less intense at the margins of such zones. Neelin and collaborators have posited an “upped-ante” mechanism for these rainfall changes at the margins, wherein a warmer troposphere requires more moisture in the planetary boundary layer to maintain positive convective available potential energy (CAPE), while low-level inflow of dry air into the adjacent regions leads to less rainfall there. These effects have been considered with respect to the zonal mean (Held and Soden 2006), but the rich-get-richer mechanism struggles to fully account for modeled local rainfall changes in the tropics. Studies have shown that the mechanism may be problematic over land (Byrne and O’Gorman 2015; Kooperman et al. 2018a), and in phase 5 of the Coupled Model Intercomparison Project (CMIP5) ensemble, the spatial correlation between precipitation patterns for climatological rain and the representative concentration pathway 8.5 (RCP8.5) response was only 0.2 for the ensemble mean (Chadwick et al. 2013). Chadwick et al. (2013) draw on Held and Soden (2006) and Ma et al. (2012) in arguing that Neelin’s primarily thermodynamic mechanism is countered by the dynamical effect of a weaker tropical circulation leading to a reduced convective mass flux. Held and Soden (2006) argued from Clausius–Clapeyron scaling that the hydrological cycle will respond in several robust ways to global warming, beginning with a roughly 7% increase in column-integrated water vapor for each degree increase in global mean surface temperature. However, since the global-mean precipitation increases at a slower rate of around 2% K−1, there must be a decrease in convective mass flux, suggesting a slowdown of the tropical circulation in response to climate change. A weakening of the tropical circulation is a robust feature of climate projections, but there is not yet consensus on how this occurs (Ma et al. 2012). According to Vecchi and Soden (2007), in CMIP3 the weakening occurs mainly in the zonally asymmetric Walker circulation rather than in the zonally symmetric Hadley cells; however, Feldl and Bordoni (2016) write that a weakening or slowdown of the Hadley circulation is a robust feature of climate projections. Ma et al. (2012) have postulated the mean advection of stratification change (MASC) hypothesis to explain this modeled slowdown of the tropical circulation in both the Walker and Hadley cells (under MASC, climatological cooling/heating in regions of convection/subsidence counteracts the motion of these circulatory cells), while others have attributed the slowdown to an increase in gross moist stability (Chou and Neelin 2004; Chou et al. 2009; Chou and Chen 2010; Chou et al. 2013; Wills et al. 2017). Ultimately, Chadwick et al. (2013) find that the spatial signatures of the thermodynamic (rich-get-richer) and dynamic (circulation slowdown) effects largely cancel in CMIP5; Wills et al. (2016) also conclude from an analysis of precipitation minus evaporation that CMIP5 shows little spatial signature of the rich-get-richer mechanism.
A separate line of thinking, sometimes called the “warmer-get-wetter” hypothesis, attributes changes in rainfall under global warming primarily to sea surface temperature (SST) changes (Xie et al. 2010; Ma and Xie 2013). This is related to the weak temperature gradient theory, according to which temperatures in the tropical troposphere show high spatial uniformity due to a small Coriolis effect and fast gravity waves smoothing out inhomogeneities (Charney 1963, 1969; Sobel and Bretherton 2000), hence convection will be most sensitive to low-level SST variations. Meanwhile, Chadwick et al. (2013) argue that the spatial pattern of rainfall change is dominated by shifting convergence zones. None of these investigations into the precipitation response to greenhouse gas forcing, however, has emphasized the partitioning between convective and large-scale rain or explored the effect this structural constraint may have upon modeled rainfall projections.
Apart from global warming studies, some insight into the interaction between convective and large-scale parameterizations is provided by Frierson (2007), who analyzed the dependence of tropical rainfall and circulation patterns on the convection scheme. Using an aquaplanet model, Frierson (2007) used several different parameterization configurations, including large-scale rainfall only and large-scale rain in addition to a “simplified Betts–Miller” convection scheme. When only large-scale precipitation was permitted, Frierson (2007) found reduced zonal symmetry in the tropical rainfall distribution (which appeared as a collection of localized storms) along with a stronger Hadley circulation and an increase in small-scale eddies exporting latent heat from the tropics. When the convective parameterization scheme was active as well, the Hadley cell turned more slowly and zonal bands of rainfall appeared. We expect that the Frierson (2007) aquaplanet configuration will differ in important ways from the more realistic simulations we consider. However, the Frierson (2007) findings suggest a hypothesis: that a larger fLS reduces the efficiency of poleward energy transport by the mean meridional circulation, because fewer convective plumes means less energy is injected deep into the free troposphere. A corollary hypothesis is that model configurations with larger fLS will be associated with stronger zonally asymmetric circulations, hence greater monsoonal rainfall and greater energy export from the tropics via transient eddies.
In this paper, we will argue that the circulatory and precipitation effects of CO2 forcing can be greatly affected by the partitioning of convective and large-scale rainfall, although whether circulation and precipitation are enhanced or suppressed will depend on details of the model. Awareness of the impact of rainfall partitioning may allow for greater understanding of uncertainty in modeled rainfall projections. To this end, we use three climate model ensembles (described below) to explore connections between the partitioning of tropical rainfall and other variables, including projected precipitation patterns under global warming. In sections 2 and 3, we describe our ensembles and use them to explore the relationship between fLS, precipitation, and circulation both in control/historical climatologies and in the response to CO2 forcing. In section 4 we present hypotheses explaining our findings and comment on the relationship between modeled and observed rainfall. Section 5 summarizes and concludes the paper.
2. Ensembles
We use three climate model ensembles in this study. The first is a single-model ensemble (SME) representing a Bayesian calibration of the National Center for Atmospheric Research (NCAR) Community Atmosphere Model, version 3.1 (CAM3.1), at a (T42) resolution of 2.8° × 2.8° with 26 vertical levels. A collection of 3336 fixed-SST experiments were computed with this model as part of a Markov chain Monte Carlo sampling via Multiple Very Fast Simulated Annealing (MVFSA), by varying 15 model parameters related to clouds and precipitation and running each parameter setting for four years. From the 3336 simulations, roughly half represented samples from the posterior distribution. These 1800 models were ordered based on a test statistic of model skill (Jackson et al. 2004, 2008; Yokohata et al. 2012; Jackson and Huerta 2016; Wagman and Jackson 2018), and every tenth model was used to create a 180-member ensemble. Each member of this ensemble performed as well as or better than the CAM3.1 default configuration. The parameter settings from these experiments were then used to conduct global warming experiments, running CAM3.1 coupled to a slab ocean for 40 years with modern CO2 levels and 40 years with doubled CO2, the last 20 years of each being averaged for analysis. The same calculated set of ocean heat fluxes was used for all experiments in both control and 2 × CO2 runs. For details on Bayesian calibration, the MVFSA sampling method, and the test statistic and observational records used in generating the CAM3.1 ensemble, see appendix A.
An updated version of the NCAR model, the Community Atmosphere Model, version 5.3 (CAM5.3), was used to create a second SME, at a 0.9° latitude by 1.25° longitude resolution with 30 vertical levels, with 98 members selected from 505 experiments using MVFSA sampling. Using a finite-volume dynamical core, these experiments were run for 4.5 years each, with the last 4 years averaged for analysis. The 2 × CO2 experiments made use of a “modified Cess” experiment design intended to reduce computational expense. In the original Cess experiment design, experiments are carried out with prescribed SSTs, which are uniformly increased for the 2 × CO2 experiments. In a modified Cess experiment, SSTs remain fixed, but for the 2 × CO2 experiments they are increased according to a predetermined spatial pattern, for example, one found by running a single 2 × CO2 experiment to equilibrium (Cess et al. 1990; Gettelman et al. 2012; B. M. Wagman and C. S. Jackson 2019, unpublished manuscript). The modified Cess experiments provide an efficient means to estimate cloud feedbacks in response to CO2 forcing. Here we are evaluating these same experiments for CO2-forced changes in precipitation. It is not clear how this experiment design affects the response relative to a coupled system model. For instance, where the CAM3.1 model and CMIP datasets show greater globally averaged precipitation responses for higher climate sensitivities, our CAM5.3 ensemble shows a slight decrease in rainfall response for higher sensitivities (Fig. S1 in the online supplemental material). Despite the questions we have about the modified Cess experiments, the spatial pattern of the response had features in common with the CMIP5 dataset and therefore we decided to include the CAM5.3 ensemble results as well. Again, see appendix A for additional details.
The CMIP5 data used here were taken from the “historical” simulations and the RCP8.5 (high emissions) experiments. We averaged precipitation data over the final 20-yr intervals: 1986–2005 for the historical experiments and 2081–2100 for the RCP8.5 scenarios. We were able to gather the necessary data from 33 CMIP5 models, which we regridded to match the CAM3.1 grid for comparison. We note that three of the 33 CMIP5 models had responses noticeably further from the mean response, but excluding these experiments does not greatly affect our results, so we kept them. Noteworthy differences between the two CAM and the CMIP5 ensembles are first, in the latter, CO2 is not specifically doubled but rather increased to a level consistent with the RCP8.5 scenario at year 2100, and second, the CMIP5 models include dynamic oceans whereas the CAM ensembles do not.
Our ensembles show different ranges of fLS. For the CAM3.1 ensemble, fLS ranges from roughly 3%–12% with an average of about 6%. (CAM3.1 also includes a shallow convective precipitation rate; however, this is included in the total convective rainfall rate. We comment briefly on the relationship between convective, shallow convective, and large-scale rain in the CAM3.1 ensemble below.) For the other ensembles, fLS values can be much larger: in CAM5.3, the range is from roughly 5%–60% (average ~ 29%), while for CMIP5, the range is from roughly 6%–53% (average ~19%, see Fig. S2, supplemental material). However, while fLS may exhibit a wide range of values, once the physical parameters of a particular climate model are set, the fraction of tropical large-scale rainfall is a relatively fixed property of that model: correlations between control and global-warming fLS are very high (of our three ensembles, the lowest correlation was ~0.98 for CMIP5), and fLS only changes by a few percent on average with global warming (Fig. S3, supplemental material). Hence we use the control (CAM) or historical (CMIP5) fLS for sorting ensemble members throughout this paper.
Our experimental design allows us to determine the parameters most closely correlated with fLS in our CAM ensembles. Because a number of parameters related to clouds and rainfall were perturbed in the CAM3.1 and CAM5.3 ensembles (15 and 7, respectively—a complete list is given in Table A1), it is difficult to tease apart the effects of individual parameters on fLS, and indeed this was not the original intention behind the construction of these ensembles. More careful studies of specific parameters have been carried out; the CAPE-consumption time-scale tau in particular has been studied in some detail in various settings (Mishra and Srinivasan 2010; Yang et al. 2013; Williamson 2013; Gustafson et al. 2014; Lin et al. 2016). In the CAM3.1 ensemble, fLS is most sensitive to changes in icritc (the cold ice autoconversion threshold, with a correlation with fLS of about 0.68), alfa (the initial cloud downdraft mass flux, correlation ~ 0.61), and, consistent with previous studies, tau (correlation ~ 0.50). These parameters are not necessarily independent of each other: we find that both tau and alfa are correlated with icritc (with coefficients of ~0.72 and ~0.44, respectively). Negative correlations with fLS are weaker, but the strongest is with c0, the precipitation efficiency, which determines how much condensate rains out; a less efficient rainout leaves more condensate in the atmosphere, allowing for more grid-scale rain later (Zhao 2014). In the CAM5.3 ensemble, fLS is most sensitive to changes in tau, with a correlation with fLS of ~0.84. The other parameters show much weaker correlations, starting with criqc (the maximum updraft condensate) at ~0.34. However, we discovered a very strong correlation (~0.92) in the CAM5.3 ensemble between fLS and the globally averaged 10-m wind speed. We speculate that this sensitivity to the surface wind, and the resultant effect on evaporation and precipitation, is a result of changes to the Zhang–McFarlane convection scheme, which was modified starting with CAM4 to include convective momentum transport (Richter and Rasch 2008; Neale et al. 2013). It is possible, however, that the causality runs in the opposite direction: less convection could lead to greater instability, higher levels of CAPE, and stronger surface winds. Other papers have looked at relationships between parameters and rainfall (Held et al. 2007; Williamson 2013, 2015; Ma et al. 2014; Gustafson et al. 2014), as well as the connection between rainfall partitioning and rainfall intensity (Kooperman et al. 2018b; O’Brien et al. 2016). Jackson et al. (2008) found evidence that larger values of tau are correlated to extreme rain events in CAM3.1, and we therefore expect that there would be a connection between rainfall intensity and fLS, but with only monthly averaged data we are unable to comment on that relationship in these experiments.
We further considered the effect of model resolution on fLS in our ensembles, since as resolution grows higher, grid cells become smaller, conceivably making it easier to reach the saturation threshold for the microphysics parameterization to generate large-scale rain. A number of studies have shown that resolution is important in determining fLS (Bacmeister et al. 2014; Kooperman et al. 2018b; O’Brien et al. 2016), but our experimental setup limits what we can conclude in this regard. Based on the CAM ensembles, wherein the higher-resolution CAM5.3 ensemble is capable of generating much larger fLS, we might conclude there is a connection, but would need to test each model independently at different resolutions to draw a robust conclusion. (We find that the CMIP5 ensemble, which includes a range of model resolutions, shows a weak relationship between horizontal resolution and fLS, with a correlation of 0.17 between them.)
3. Findings
Rainfall and circulation patterns within the CAM ensembles show clear and strong relationships with fLS, both within the control climatologies and in the response to CO2 forcing. In the first part of this section, we document the strong relationships between control and response spatial rainfall patterns and fLS, and we quantify their significance. In the second part, we discuss the important ways in which models show different or even opposite behavior with fLS, despite their shared strong correlations between fLS and rainfall and circulation.
a. Variations in rainfall and circulation with fLS
Despite the comparatively small range of fLS in our CAM3.1 ensemble, we find a fairly smooth transition between rainfall response patterns when binning response anomalies by fLS (Fig. 1; see Figs. S7–S9 of the supplemental material for the control precipitation for the three ensembles). The most dramatic transition is in the Pacific, where for smaller fLS (i.e., more convective rainfall) there is a greater increase in rainfall along the equator and comparatively less on the poleward flanks. These patterns are reversed across much of the Pacific in the high-fLS case, where there is less of an increase in rainfall in the deep tropics and less of a decrease in the subtropics. A connection between fLS and monsoonal circulations is evident as well: for low fLS, India dries in the response, while for large fLS, India gets wetter (this effect also shows up in the Fig. 1 anomalies). The highest-fLS experiments for the CAM3.1 ensemble are anomalous in some ways that we point out as necessary below. This anomalous behavior for the highest-fLS experiments illustrates the complexity and nonlinearity of the handoff from convective to large-scale rain and suggests the possibility of different kinds of equilibria as fLS rises.
Rainfall response (2 × CO2 minus control) anomalies for the CAM3.1 ensemble, averaged over five bins defined by a simple scheme based on the mean and standard deviation for fLS (Fig. S4, supplemental material). (from top to bottom) Bins contain 8, 42, 90, 9, and 16 experiments.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Rainfall response (2 × CO2 minus control) anomalies for the CAM3.1 ensemble, averaged over five bins defined by a simple scheme based on the mean and standard deviation for fLS (Fig. S4, supplemental material). (from top to bottom) Bins contain 8, 42, 90, 9, and 16 experiments.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Rainfall response (2 × CO2 minus control) anomalies for the CAM3.1 ensemble, averaged over five bins defined by a simple scheme based on the mean and standard deviation for fLS (Fig. S4, supplemental material). (from top to bottom) Bins contain 8, 42, 90, 9, and 16 experiments.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Locally the rainfall response with fLS can be substantial. In the deep tropical Pacific (0°, 160°W), the high-fLS experiments show on average 49% less of a response while the low-fLS experiments show on average 47% more. In the Caribbean (15°N, 60°W) the corresponding numbers are about 26% more for high fLS and 19% less for low fLS. In the Indian Ocean (15°S, 90°E), the corresponding numbers are about 31% less for high fLS and 14% more for low fLS.
In the CAM5.3 ensemble, we again find a smooth transition between bins; Fig. 2 includes only three bins due to the smaller sample size. The pattern is more complex for the CAM5.3 ensemble than for the CAM3.1 ensemble, due in particular to a zonal asymmetry over the Pacific. In CMIP5, again with three bins in Fig. 3, some areas, for example, the northern Pacific, show a transition, but overall the transition with fLS is less smooth than in the CAM ensembles. We expect this is due at least partly to small sample size and greater scatter among the CMIP5 models, several of which are noticeably different from the mean CMIP5 response, in addition to the dynamic oceans in CMIP5 models.
Rainfall response (2 × CO2 minus control) anomalies for the CAM5.3 ensemble, averaged over three bins defined by a simple scheme based on the mean and standard deviation for fLS (Fig. S5, supplemental material). (from top to bottom) Bins contain 27, 49, and 22 experiments.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Rainfall response (2 × CO2 minus control) anomalies for the CAM5.3 ensemble, averaged over three bins defined by a simple scheme based on the mean and standard deviation for fLS (Fig. S5, supplemental material). (from top to bottom) Bins contain 27, 49, and 22 experiments.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Rainfall response (2 × CO2 minus control) anomalies for the CAM5.3 ensemble, averaged over three bins defined by a simple scheme based on the mean and standard deviation for fLS (Fig. S5, supplemental material). (from top to bottom) Bins contain 27, 49, and 22 experiments.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Rainfall response (RCP8.5 minus historical) anomalies for the CMIP5 ensemble, averaged over three bins defined by a simple scheme based on the mean and standard deviation for fLS (Fig. S6, supplemental material). (from top to bottom) Bins contain 6, 22, and 5 experiments.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Rainfall response (RCP8.5 minus historical) anomalies for the CMIP5 ensemble, averaged over three bins defined by a simple scheme based on the mean and standard deviation for fLS (Fig. S6, supplemental material). (from top to bottom) Bins contain 6, 22, and 5 experiments.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Rainfall response (RCP8.5 minus historical) anomalies for the CMIP5 ensemble, averaged over three bins defined by a simple scheme based on the mean and standard deviation for fLS (Fig. S6, supplemental material). (from top to bottom) Bins contain 6, 22, and 5 experiments.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
The response anomaly maps shown in Figs. 1–3 are suggestive of a correlation between fLS and the precipitation response pattern, particularly within our CAM ensembles, but to quantify the importance of fLS for the response patterns and remove any dependence on an arbitrary binning scheme, we employ a standard analysis using empirical orthogonal functions. By the method described in appendix B, in which we define maps ΔR′ representing the effect of fLS on each ensemble’s precipitation response pattern (Fig. 4), we conclude that for the CAM3.1, CAM5.3, and CMIP5 ensembles, the respective ΔR′ patterns account for 13.6%, 35.6%, and 11.0% of the total precipitation response variance. We expect the dynamic oceans in CMIP5 models to contribute significantly to the response variance.
(top) Average response of the CAM3.1 ensemble to a doubling of atmospheric CO2. (bottom) ΔR as defined by Eq. (B1), showing the effect of fLS. High fLS has the effect of counteracting much of the ensemble mean response.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
(top) Average response of the CAM3.1 ensemble to a doubling of atmospheric CO2. (bottom) ΔR as defined by Eq. (B1), showing the effect of fLS. High fLS has the effect of counteracting much of the ensemble mean response.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
(top) Average response of the CAM3.1 ensemble to a doubling of atmospheric CO2. (bottom) ΔR as defined by Eq. (B1), showing the effect of fLS. High fLS has the effect of counteracting much of the ensemble mean response.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
We can also quantify the linearity of the transition from the low-fLS pattern to the high-fLS pattern by projecting onto ΔR′ each of the response anomalies (Ai ⋅ ΔR′) as in Fig. 5. For the two CAM ensembles, this produces fairly linear plots. For the CAM3.1 ensemble, the correlation is ~0.75, with the somewhat anomalous behavior of the highest-fLS experiments (mentioned above) evident in the graph. For the CAM5.3 ensemble, the correlation is ~0.95 and the transition is smoother. For the smaller CMIP5 ensemble, a smooth transition is less apparent in the maps of Fig. 3, but in this calculation some linearity is still evident with a correlation of ~0.61 (as noted above, the CMIP5 dataset includes several models that are noticeably far from the mean response; these models bring down the correlation slightly). To quantify these results’ dependence on the high- and low-fLS cutoffs, we carried out the same calculation while varying the number of experiments in the high and low bins separately from two to 30 experiments each. Over all 841 calculations, the average correlation for the CAM3.1 ensemble is ~0.72 with a standard deviation of ~0.06. Over the same calculations for the CAM5.3 ensemble, the average correlation is ~0.96 with standard deviation <0.01. We therefore conclude that the changing spatial patterns of the rainfall response with fLS is a robust result that does not depend strongly on the binning scheme.
In black: the dot product of rainfall anomalies αi = Ai ⋅ ΔR′ [see Eq. (B3)] vs fLS. (from left to right) The CAM3.1 ensemble (r = 0.75), the CAM5.3 ensemble (r = 0.95), and the CMIP5 dataset (r = 0.61). (Note that the p values for all of the scatterplot correlations given throughout this paper are very small, P < 0.001, and henceforth we only report the correlations.) The linearity of these data points gives an indication of how smoothly the response varies between extremes with fLS. For the CAM5.3 ensemble, we have also included the contribution to the total (black) data from convective rain only (red) and large-scale rain only (blue). In this case, fitting the total, convective, and large-scale rain α values using linear regression indicates that large-scale rain makes up roughly 77% of the total pattern, with convective raining making up the remaining 23%. (For the CAM3.1 ensemble and the CMIP5 dataset, convective rain dominates the total pattern.)
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
In black: the dot product of rainfall anomalies αi = Ai ⋅ ΔR′ [see Eq. (B3)] vs fLS. (from left to right) The CAM3.1 ensemble (r = 0.75), the CAM5.3 ensemble (r = 0.95), and the CMIP5 dataset (r = 0.61). (Note that the p values for all of the scatterplot correlations given throughout this paper are very small, P < 0.001, and henceforth we only report the correlations.) The linearity of these data points gives an indication of how smoothly the response varies between extremes with fLS. For the CAM5.3 ensemble, we have also included the contribution to the total (black) data from convective rain only (red) and large-scale rain only (blue). In this case, fitting the total, convective, and large-scale rain α values using linear regression indicates that large-scale rain makes up roughly 77% of the total pattern, with convective raining making up the remaining 23%. (For the CAM3.1 ensemble and the CMIP5 dataset, convective rain dominates the total pattern.)
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
In black: the dot product of rainfall anomalies αi = Ai ⋅ ΔR′ [see Eq. (B3)] vs fLS. (from left to right) The CAM3.1 ensemble (r = 0.75), the CAM5.3 ensemble (r = 0.95), and the CMIP5 dataset (r = 0.61). (Note that the p values for all of the scatterplot correlations given throughout this paper are very small, P < 0.001, and henceforth we only report the correlations.) The linearity of these data points gives an indication of how smoothly the response varies between extremes with fLS. For the CAM5.3 ensemble, we have also included the contribution to the total (black) data from convective rain only (red) and large-scale rain only (blue). In this case, fitting the total, convective, and large-scale rain α values using linear regression indicates that large-scale rain makes up roughly 77% of the total pattern, with convective raining making up the remaining 23%. (For the CAM3.1 ensemble and the CMIP5 dataset, convective rain dominates the total pattern.)
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
The CAM5.3 ensemble shows a larger response anomaly amplitude than the CAM3.1 ensemble or the CMIP5 dataset; we believe the reasons for the larger spread with respect to the CAM3.1 ensemble are twofold. First, while the adjusted parameters for the CAM5.3 ensemble are not all the same as those for the CAM3.1 ensemble, those parameters that are adjusted in both ensembles (e.g., tau, rhminl) range more broadly for the CAM5.3 ensemble (see Table A1). Hence a wider range of responses may be expected for the CAM5.3 ensemble. Second, the large-scale rain rate in the CAM5.3 ensemble shows more sensitivity to these adjustments than in the CAM3.1 ensemble. In Fig. 5, the vertical spread for the CAM3.1 ensemble is due almost entirely to variation in convective rainfall, while for the CAM5.3 ensemble, both convective and large-scale rain contribute to the overall spread, with large-scale rain contributing more (as shown in Fig. 5, large-scale rain makes up about 77% of the overall pattern, with convective rain making up for the remaining 23%). Hence the greater sensitivity of the large-scale rainfall in the CAM5.3 ensemble contributes to an overall larger amplitude of response anomaly. The CMIP5 ensemble follows the pattern of the CAM3.1 ensemble, with a greater contribution from convective rain to the total spread in response anomaly.
Neither CAM ensemble shows a strong signature of the rich-get-richer mechanism between 30°S and 30°N. For the CAM3.1 ensemble, the largest spatial correlation between control rainfall P and the 2 × CO2 response ΔP in this region is close to 0.5, but the average spatial correlation is ~0.12, while for the CAM5.3 ensemble, the largest correlation is less than 0.25 with a similar average of ~0.12. In the zonal mean, the ensemble-mean correlations between P and ΔP are ~0.47 and ~0.41, respectively. [For our 33-member CMIP5 dataset, we find, consistent with Chadwick et al. (2013), that the ensemble-mean spatial correlation between P and ΔP is close to 0.3. However, in the zonal mean, the ensemble-mean correlation between P and ΔP rises to about 0.73.] Nevertheless, the spatial patterns of both control and 2 × CO2 rainfall do show a relationship with fLS. As fLS increases in the control experiments, the spatial correlation between large-scale and convective rain (between 30°S and 30°N and globally as well) grows more positive, as shown in Fig. 6. In the CAM5.3 ensemble, this effect appears to saturate as fLS gets large, but for the CMIP5 ensemble, which has a similar range of fLS, this is less clear. Judging by Fig. 6, large-scale and convective rain tend to be active in different areas for low fLS, while for larger fLS they tend to work in tandem. The same effect is observed for the 2 × CO2 experiments, as demonstrated in the supplemental material, Fig. S10.
The tropical (30°S–30°N) spatial correlation r between convective (PC) and large-scale (PLS) components of rainfall vs fLS for the control/historical experiments for the three ensembles. The correlation becomes more positive as fLS increases; the same trend applies globally as well, with even higher correlations for all three ensembles (not shown). We believe these correlations are meaningful even at small fLS, because as maps of the CAM3.1 ensemble large-scale rain shows (Fig. S11, supplemental material), small amplitude is still consistent with a coherent spatial pattern.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
The tropical (30°S–30°N) spatial correlation r between convective (PC) and large-scale (PLS) components of rainfall vs fLS for the control/historical experiments for the three ensembles. The correlation becomes more positive as fLS increases; the same trend applies globally as well, with even higher correlations for all three ensembles (not shown). We believe these correlations are meaningful even at small fLS, because as maps of the CAM3.1 ensemble large-scale rain shows (Fig. S11, supplemental material), small amplitude is still consistent with a coherent spatial pattern.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
The tropical (30°S–30°N) spatial correlation r between convective (PC) and large-scale (PLS) components of rainfall vs fLS for the control/historical experiments for the three ensembles. The correlation becomes more positive as fLS increases; the same trend applies globally as well, with even higher correlations for all three ensembles (not shown). We believe these correlations are meaningful even at small fLS, because as maps of the CAM3.1 ensemble large-scale rain shows (Fig. S11, supplemental material), small amplitude is still consistent with a coherent spatial pattern.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
b. Differing dependence on fLS in CAM3.1 and CAM5.3
We have shown that our CAM ensembles and the CMIP5 dataset show strong and systematic variations with fLS; however, despite these strong correlations, there are important ways in which the models differ in their dependence on fLS. In the CAM3.1 control simulations, as fLS grows the annual mean convective rain rate tends to decrease at all latitudes, and especially in the tropics. Large-scale rain shows less systematic variation with fLS, except in the tropics and subtropics where it increases slightly (but with considerable percentage changes) and consistently with fLS (Fig. 7). However, large-scale rain is unable to make up for the loss of convective rain, with the possible exception of the highest-fLS experiments: as fLS gets into the higher range for the CAM3.1 ensemble (7%–13%), there is a more substantial increase in large-scale rain in the deep tropics and along the intertropical convergence zone (ITCZ). In the CAM5.3 ensemble, the situation is different, again with a substantial decrease in convective rain (about 50%) as fLS rises, but with more-than-compensating increases in large-scale rain, hence the total amount of rainfall increases slightly (Fig. 8). In the CAM3.1 ensemble, therefore, as parameter settings inhibit the convective parameterization, moisture that is not used up by the convective subroutine may or may not flow to other areas, which then see more large-scale rain, but for the most part we simply see less convective rain, hence fLS increases. In the CAM5.3 ensemble, parameter settings that inhibit convective rain ultimately allow for even more large-scale rain, increasing the amount of total rainfall.
(top) (from left to right) The zonal mean convective, large-scale, and shallow rain rates for the CAM3.1 ensemble divided into three bins by fLS similar to Fig. 2 (blue, fLS < 0.041; red, 0.041 < 0.073; black, fLS > 0.073). The shading behind each line shows one standard deviation for each bin. While convective rain falls off gradually with rising fLS, the large-scale rainfall gradually rises until the highest-fLS experiments show a more abrupt increase. A similar pattern holds for the shallow convection, except the lower-fLS experiments largely overlap. (bottom) (from left to right) The tropical average convective, large-scale, and shallow rain rates for the CAM3.1 ensemble vs fLS. Again it is evident that the shallow convection exhibits an abrupt increase for sufficiently high fLS.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
(top) (from left to right) The zonal mean convective, large-scale, and shallow rain rates for the CAM3.1 ensemble divided into three bins by fLS similar to Fig. 2 (blue, fLS < 0.041; red, 0.041 < 0.073; black, fLS > 0.073). The shading behind each line shows one standard deviation for each bin. While convective rain falls off gradually with rising fLS, the large-scale rainfall gradually rises until the highest-fLS experiments show a more abrupt increase. A similar pattern holds for the shallow convection, except the lower-fLS experiments largely overlap. (bottom) (from left to right) The tropical average convective, large-scale, and shallow rain rates for the CAM3.1 ensemble vs fLS. Again it is evident that the shallow convection exhibits an abrupt increase for sufficiently high fLS.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
(top) (from left to right) The zonal mean convective, large-scale, and shallow rain rates for the CAM3.1 ensemble divided into three bins by fLS similar to Fig. 2 (blue, fLS < 0.041; red, 0.041 < 0.073; black, fLS > 0.073). The shading behind each line shows one standard deviation for each bin. While convective rain falls off gradually with rising fLS, the large-scale rainfall gradually rises until the highest-fLS experiments show a more abrupt increase. A similar pattern holds for the shallow convection, except the lower-fLS experiments largely overlap. (bottom) (from left to right) The tropical average convective, large-scale, and shallow rain rates for the CAM3.1 ensemble vs fLS. Again it is evident that the shallow convection exhibits an abrupt increase for sufficiently high fLS.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
The zonal mean (left) convective, (middle) large-scale, and (right) total rain rates for the CAM5.3 ensemble binned by fLS according to the scheme described in the supplemental material accompanying Fig. S5 (blue, fLS < 0.13; red, 0.13 < fLS < 0.46; black, fLS > 0.46). The shading behind each line shows one standard deviation for each bin.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
The zonal mean (left) convective, (middle) large-scale, and (right) total rain rates for the CAM5.3 ensemble binned by fLS according to the scheme described in the supplemental material accompanying Fig. S5 (blue, fLS < 0.13; red, 0.13 < fLS < 0.46; black, fLS > 0.46). The shading behind each line shows one standard deviation for each bin.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
The zonal mean (left) convective, (middle) large-scale, and (right) total rain rates for the CAM5.3 ensemble binned by fLS according to the scheme described in the supplemental material accompanying Fig. S5 (blue, fLS < 0.13; red, 0.13 < fLS < 0.46; black, fLS > 0.46). The shading behind each line shows one standard deviation for each bin.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Upon investigating the spatial patterns of the large-scale rainfall in the CAM3.1 ensemble, it became apparent that the large-scale rain grows steadily in the tropics and subtropics as fLS rises while convective rain falls with fLS in both regions (this can be seen in the top middle panel of Fig. 7). We subsequently found that fLS correlates well with relative humidity throughout the tropics, but especially strongly in the subtropics. Between 10° and 30°N and 10° and 30°S, respectively, the correlations between fLS and the zonal-mean, column-averaged relative humidity are ~0.83 and ~0.85 (see Figs. S15 and S16, supplemental material). We proceeded to explore the source of the moisture associated with the large-scale rainfall in the subtropical Pacific. In annual averages, we find that, averaged over the Pacific Ocean (130°–260°E), averaged between 15° and 20°N for the Northern Hemisphere (NH) and between 20° and 25°S for the Southern Hemisphere (SH), and averaged between 500 and 700 mb, there are several variables correlated with fLS (Fig. 9): VQ (the product of the meridional wind and specific humidity), the cloud fraction, and the vertical pressure velocity omega. These relationships, which are evident seasonally as well, are most evident for fLS < 0.08 (shown in blue in Fig. 9), where the correlation between VQ and fLS is 0.63 in the NH and 0.72 for the SH. Within this region, there are also fairly strong correlations with cloud fraction and omega (see the supplemental comments accompanying Figs. S16–S18 for explanations of how we arrived at our averaging regions). This set of correlated variables suggests that for CAM3.1 parameter settings that give less rainout from the convective parameterization, more moisture is being detrained at midlevels in the tropics. We see nearly identical patterns, but with slightly stronger correlations, in the 2 × CO2 experiments (not shown).
For both hemispheres, (left) VQ, (middle) cloud fraction, and (right) vertical pressure velocity omega in the CAM3.1 ensemble, averaged annually, over the Pacific (130°–260°E), and between 500 and 700 mb, vs fLS. (top) The Northern Hemisphere quantities are averaged from 15° to 20°N, and (bottom) the Southern Hemisphere quantities are averaged from 20° to 25°S (see supplemental material for details). Except for the highest-fLS experiments (with fLS > 0.08, in red), these three variables show correlations of varying strength with fLS, suggesting that midlevel detrainment of moisture from the deep tropics, and subsequent condensation in the subtropics, may play a role in weakening the mean meridional circulation.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
For both hemispheres, (left) VQ, (middle) cloud fraction, and (right) vertical pressure velocity omega in the CAM3.1 ensemble, averaged annually, over the Pacific (130°–260°E), and between 500 and 700 mb, vs fLS. (top) The Northern Hemisphere quantities are averaged from 15° to 20°N, and (bottom) the Southern Hemisphere quantities are averaged from 20° to 25°S (see supplemental material for details). Except for the highest-fLS experiments (with fLS > 0.08, in red), these three variables show correlations of varying strength with fLS, suggesting that midlevel detrainment of moisture from the deep tropics, and subsequent condensation in the subtropics, may play a role in weakening the mean meridional circulation.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
For both hemispheres, (left) VQ, (middle) cloud fraction, and (right) vertical pressure velocity omega in the CAM3.1 ensemble, averaged annually, over the Pacific (130°–260°E), and between 500 and 700 mb, vs fLS. (top) The Northern Hemisphere quantities are averaged from 15° to 20°N, and (bottom) the Southern Hemisphere quantities are averaged from 20° to 25°S (see supplemental material for details). Except for the highest-fLS experiments (with fLS > 0.08, in red), these three variables show correlations of varying strength with fLS, suggesting that midlevel detrainment of moisture from the deep tropics, and subsequent condensation in the subtropics, may play a role in weakening the mean meridional circulation.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Along with these differences in rainfall behavior we find corresponding effects on the modeled tropical circulation, another way in which the models differ with fLS. In the CAM3.1 ensemble, increasing fLS in the CAM3.1 ensemble correlates with reductions in circulation and meridional fluxes of total (meridional mean, stationary, and transient eddy) potential energy and total sensible and latent heat. In the CAM3.1 control experiments, as fLS grows we find reductions in the circulation of moist static energy, particularly in DJF (see Fig. S13, supplemental material). The Pacific-averaged (130°–260°E) vertical wind at 900 mb along the ITCZ (~5°N) weakens in DJF and JJA by about 70% in both cases as fLS rises to ~0.08. On the other hand, in the CAM5.3 ensemble the circulation strengthens with fLS. On the ITCZ (about 6°N in this ensemble), the annual- and zonal-mean pressure velocity omega strengthens (omega grows more negative) until about fLS = 0.35 at which point the effect seems to saturate (Fig. 10), similar to the behavior of the CAM5.3 ensemble’s spatial correlations between convective and large-scale rainfall in Fig. 6. This effect is further borne out by inspection of the streamfunctions, which show increasing transport via the mean meridional circulation for the CAM5.3 ensemble (Fig. 11). Approximate seasonal meridional energy transport calculations are consistent with a strengthening of the Hadley circulation with increasing fLS, showing that the Hadley cell is carrying more potential (sensible and latent heat) energy at higher (lower) levels as fLS rises (Fig. S14, supplemental material). Note that this does not imply total energy export from the tropics is increasing, since greater high-level energy outflow is offset by greater low-level inflow.
The CAM5.3 ensemble vertical pressure velocity (omega) at 800 mb on the ITCZ (approximately 6°N) grows stronger with fLS, similar to what was observed in Frierson (2007). The vertical average follows a roughly similar pattern. The effect seems to saturate as fLS gets large, similar to the behavior of the CAM5.3 ensemble’s spatial correlations between convective and large-scale rainfall in Fig. 6.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
The CAM5.3 ensemble vertical pressure velocity (omega) at 800 mb on the ITCZ (approximately 6°N) grows stronger with fLS, similar to what was observed in Frierson (2007). The vertical average follows a roughly similar pattern. The effect seems to saturate as fLS gets large, similar to the behavior of the CAM5.3 ensemble’s spatial correlations between convective and large-scale rainfall in Fig. 6.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
The CAM5.3 ensemble vertical pressure velocity (omega) at 800 mb on the ITCZ (approximately 6°N) grows stronger with fLS, similar to what was observed in Frierson (2007). The vertical average follows a roughly similar pattern. The effect seems to saturate as fLS gets large, similar to the behavior of the CAM5.3 ensemble’s spatial correlations between convective and large-scale rainfall in Fig. 6.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Maximum values of the annual-mean streamfunctions ψ for the CAM3.1 (blue) and CAM5.3 (red) ensembles. Note that the upper horizontal axis refers to CAM3.1 and the lower horizontal axis refers to CAM5.3. Consistent with Fig. 10, the CAM5.3 ensemble ψ show increasing maxima as fLS rises with a correlation of 0.82. For the CAM3.1 ensemble, maximum ψ values decrease with fLS, although the correlation is weaker at −0.50. (Maximum values correspond to the northern branch of the mean meridional circulation, which shows up more clearly in the annual mean.)
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Maximum values of the annual-mean streamfunctions ψ for the CAM3.1 (blue) and CAM5.3 (red) ensembles. Note that the upper horizontal axis refers to CAM3.1 and the lower horizontal axis refers to CAM5.3. Consistent with Fig. 10, the CAM5.3 ensemble ψ show increasing maxima as fLS rises with a correlation of 0.82. For the CAM3.1 ensemble, maximum ψ values decrease with fLS, although the correlation is weaker at −0.50. (Maximum values correspond to the northern branch of the mean meridional circulation, which shows up more clearly in the annual mean.)
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Maximum values of the annual-mean streamfunctions ψ for the CAM3.1 (blue) and CAM5.3 (red) ensembles. Note that the upper horizontal axis refers to CAM3.1 and the lower horizontal axis refers to CAM5.3. Consistent with Fig. 10, the CAM5.3 ensemble ψ show increasing maxima as fLS rises with a correlation of 0.82. For the CAM3.1 ensemble, maximum ψ values decrease with fLS, although the correlation is weaker at −0.50. (Maximum values correspond to the northern branch of the mean meridional circulation, which shows up more clearly in the annual mean.)
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
We note here a further observation specific to the CAM3.1 ensemble that is not evident in the CAM5.3 ensemble. In Fig. 7, we see large increases in both large-scale and shallow rain in the highest-fLS experiments, as both seem to “turn on” abruptly for small convective rain rates. Spatially, the increase is largely in the areas where these rainfall types were already present; an exception is east of the Maritime Continent, where both large-scale and shallow rain increase suddenly in an area where lower-fLS experiments show very little (see Figs. S11 and S12, supplemental material). Shallow convection is present in both CAM ensembles, but we only have the data for the CAM3.1 ensemble; nevertheless, the CAM5.3 ensemble does not show such abrupt rainfall changes with fLS.
4. Discussion
Our findings in our CAM ensembles demonstrate the considerable impacts that small differences in model parameterizations can have on control climatologies and on a model’s response to global warming. However, our results also demonstrate that different models will not necessarily respond in the same way to such differences in parameterization. The CAM5.3 ensemble shows similarities to what Frierson (2007) observed in his aquaplanet model, where more large-scale rain was associated with a stronger Hadley circulation and more rainfall. We believe that a similar mechanism may be at work here, and for the same reasons Frierson (2007) supposes: a faster circulation makes up for a less efficient energy transport from the tropics caused by fewer convective plumes carrying moist static energy upward.
The CAM3.1 ensemble shows very different behavior with increasing fLS, most notably a weakening Hadley circulation, which requires a different explanation. We noted above that for parameter settings inhibiting convective rainout in the CAM3.1 ensemble, and therefore yielding higher fLS, moisture deposited in the midtroposphere by deep convection is being detrained to the subtropics at midlevels. We hypothesize that when this moisture condenses in the subtropics, the resulting diabatic heating (which would be associated with upward motion) counteracts the descending branch of the Hadley cell, weakening the downward motion. We refer to this as the “short-circuit mechanism” (Fig. 12).
Under the “short-circuit hypothesis,” parameter settings that give less convective rainfall in the tropics result in greater midlevel moisture transport from the tropics, resulting in condensation in the subtropics and counteracting the downward motion of the Hadley cell’s descending branch.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Under the “short-circuit hypothesis,” parameter settings that give less convective rainfall in the tropics result in greater midlevel moisture transport from the tropics, resulting in condensation in the subtropics and counteracting the downward motion of the Hadley cell’s descending branch.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
Under the “short-circuit hypothesis,” parameter settings that give less convective rainfall in the tropics result in greater midlevel moisture transport from the tropics, resulting in condensation in the subtropics and counteracting the downward motion of the Hadley cell’s descending branch.
Citation: Journal of Climate 32, 19; 10.1175/JCLI-D-18-0833.1
It is worth emphasizing the dramatic impact condensation in the subtropics has on the vertical winds in these regions: in Fig. 9, the magnitude of omega averaged between 500 and 700 mb varies by large fractions as fLS rises from its lowest value up to fLS ≈ 0.08. In the NH, omega varies by about 290% of the mean, while in the SH it varies by about 130%. These large reductions in the downward vertical wind strength are also observed seasonally. Subtropical large-scale condensation provides a plausible mechanism for what we observe in the CAM3.1 ensemble and highlights the remarkable sensitivity of the subtropics to condensation. This sensitivity may represent an important component of uncertainty in modeled rainfall responses to CO2 forcing. We note that the ratio of midlevel detrainment to deep convection in the control climate has also been speculated to relate to the low cloud feedback (Sherwood et al. 2014).
That slight variations in how rainfall is partitioned in climate models can have such dramatic effects on the modeled climate suggests more attention be paid to the ratio and distribution of convective and large-scale rain. Some efforts have touched on this topic (Kyselý et al. 2016; Storer et al. 2015; Liu et al. 2018); in particular, Yang et al. (2013) attempt to optimize a set of CAM5 parameters such that the model would agree with the conclusion of Schumacher and Houze (2003) that about 40% of tropical rainfall is stratiform based on Tropical Rainfall Measuring Mission (TRMM) data. Either implicitly or explicitly, such studies typically assume that model-world convective and large-scale rain correspond to real-world convective and stratiform rain, but we question this assumption. Indeed, because fLS is an artifact of climate model construction, it has no exact observational counterpart, and it is unclear how observational categories such as “convective” and “stratiform” rain correspond to modeled convective and large-scale rainfall. The Schumacher and Houze (2003) analysis of the TRMM data, for example, refers to high-level stratiform clouds in the tropics originating from deeply penetrating convective clouds. It is not clear that the CAM large-scale rain variable always corresponds to this type of rain, particularly when considering that anvil-type clouds, which would fall into the category analyzed by Schumacher and Houze (2003), are not explicitly represented in climate models.
There are various ways convective and stratiform rain can be distinguished in observations, including various algorithms (Rulfová and Kyselý 2013) or by studying isotope ratios within the rainfall (Aggarwal et al. 2016). Huaman and Schumacher (2018) distinguish convective from stratiform rain based on strength of vertical motion and type of raindrop growth (with shallow and deep convection distinguished by echo-top height). Based on such features of the various rainfall types, Huaman and Schumacher (2018) extract latent heating profiles from radar data—in this case by combining TRMM Precipitation Radar (PR) with CloudSat Cloud Profiling Radar (CPR) data—to try to gain information on the vertical latent heating profile in the east Pacific. The TRMM PR is able to capture higher-level precipitation, but struggles with low-level shallow precipitation and has a threshold of 0.4 mm h−1, hence it may underestimate low-level latent heating. The CloudSat CPR is better able to capture this low-level data, provided there is not too much attenuation due to heavy rain events.
Better understanding of how such observed rainfall types compare with those of model-world convective and large-scale rain could help us to get the fraction of large-scale rain right in models; however, satellite data still may not give a complete picture. Difficulties and possible errors in satellite measurements prompt Huaman and Schumacher (2018) to recommend more in situ observations to improve reanalysis datasets. There is room for improvement in representing the tropical circulation in reanalysis as well (Stachnik and Schumacher 2011). As alternative or complementary approaches, it may be possible, first, to repartition rainfall from models in a way that allows better comparison with existing observations. However, because we have no direct diagnostic for the altitude at which convective or large-scale rain forms in a given region, it is difficult to disentangle quantities better corresponding to observations from our two-dimensional rainfall data. Hence it may be useful to have a model diagnostic carrying more information about where rainfall is generated. A second thought is prompted by the fact that models do not explicitly represent processes such as mesoscale convective systems (MCSs), which may be missed by the deep convective scheme. We speculate that some fraction of the rainfall currently handled by the large-scale routine may be more properly processed by a MCS parameterization.
5. Summary and conclusions
We have shown that the fraction of large-scale rainfall in the tropics is strongly correlated with several aspects of global climate model behavior, including the rainfall response to CO2 forcing and tropical circulation strength, but that these correlations are complex, running in different directions depending on model details. These initial findings highlight additional issues worthy of further consideration, including the need for more information about the vertical distribution of large-scale condensation in climate models. A direct diagnostic for convective and large-scale condensation would allow for more detailed analysis of the sources of rainfall in models, which would in turn allow for both greater understanding of the effects of model rainfall partitioning and better comparison between observations and model behavior.
Furthermore, the full climatic response to CO2 forcing will include ocean dynamics. The effects of sea surface temperature anomalies on rainfall anomalies could not be addressed within the context of our single-model ensembles, but the CMIP5 results suggest they may be important. The importance of SST anomalies to precipitation responses has been explored (Xie et al. 2010), although not with a focus on the partitioning of rainfall between convective and large-scale rain. Additionally, we are uncertain about the applicability of the modified Cess experiment design, with fixed SSTs, to this particular research question. More study is necessary to determine whether our CAM5.3 experiments, initially intended to study cloud responses to global warming, can be justifiably extended to this analysis.
It is further worth noting that the CAM3.1 and CAM5.3 models contain different dynamical cores. It is reasonable to expect that the choice of dynamic core will affect moisture transport in the tropics and hence the differences in model output we have identified could be at least partially attributable to choice of dynamical core. This could be tested through using, for example, the CAM3.1 dynamical core with the CAM5.3 physics, a type of experiment we have not carried out. Even so, this may be difficult due to model retuning.
Another question that might be profitably pursued is the possible existence of multiple equilibria as fLS changes. As noted above, in the CAM3.1 ensemble, experiments at the higher end of the fLS distribution exhibit nonlinear behavior in both large-scale and shallow rainfall suggestive of a threshold crossing. Such behavior illustrates the complexity of the handoff from convective to other types of rain, and further study may provide insight into new types of model behavior and perhaps suggest tropical mechanisms for abrupt climate change.
Finally, because slight changes in fLS can have dramatic effects on the modeled precipitation response to global warming, there is a need to study in greater detail whether this fraction is hitting the appropriate target and what the appropriate target is. The few studies that have investigated this ratio, for example, Yang et al. (2013), have typically assumed modeled convective and large-scale rain correspond to observed convective and stratiform rainfall, as described, for instance, by Schumacher and Houze (2003) based on TRMM data, but we believe the relationship is more complicated. More study is needed to assess how the different types of model rainfall correspond to different types of real-world precipitation, because we have found that relatively small differences in the location and type of rain that occurs in the tropics can have profound impacts on the structure of a model’s response to CO2 forcing.
Acknowledgments
We thank Phil Rasch, Courtney Schumacher, Pedro di Nezio, and Dargan Frierson for helpful discussions. We further thank three anonymous referees for their constructive criticism and helpful comments. Funding for this project was provided by the U.S. Department of Energy, Office of Science, Biological and Environmental Research Awards DE-SC0016401 and DE-SC0006985, and the NSF Collaboration in Mathematical Geosciences program, award OCE 0415738. Prepared by LLNL under Contract DE-AC52-07NA27344.
APPENDIX A
Ensemble Construction
This appendix discusses the construction of the CAM3.1 and CAM5.3 ensembles used in this study, starting with a description of Bayesian calibration of climate models and the MVFSA sampling method, based on Sen and Stoffa (1996), Jackson et al. (2004), Jackson et al. (2008), and Jackson and Huerta (2016). We then detail the test statistics employed for each CAM ensemble and the observational data used to evaluate those test statistics.
a. Bayesian calibration and MVFSA
We generate samples from the posterior distribution using an approximate Markov chain Monte Carlo (MCMC) sampling algorithm MVFSA (Jackson et al. 2004). At each step through parameter space, the Markov chain uses Metropolis–Hastings sampling (Metropolis et al. 1953; Hastings 1970) to select values for uncertain model parameters as well as Gibbs sampling (Gelfand et al. 1992) to select values for a precision hyper-parameter that accounts for sources of uncertainty affecting the gap between models and data such as model biases (Jackson and Huerta 2016). One of the primary sources of inefficiency in any MCMC sampling algorithm is due to a nonideal step size. MVFSA mitigates this source of inefficiency by using an iteration-dependent Cauchy distribution to gradually reduce step size over the course of the calibration (Ingber 1989). By deploying multiple Markov chains in parallel and exercising convergence criteria that are tied to a problem’s uncertainty space dimensionality, MVFSA is able to summarize important aspects of the posterior distribution with relatively few integrations of a computationally expensive numerical model (Villagran et al. 2008). Among those that use Bayesian calibration strategies for large-scale numerical codes, it is rather unusual to sample the posterior distribution directly using MCMC sampling. The more common approach is to develop a statistical emulator of one’s numerical model based on a designed set of experiments such as a Latin-hypercube structure. However, developing emulators of high-dimensional model output can be prohibitively difficult. The advantage of direct sampling, if it can be managed, is that it allows one to make use of sophisticated test statistics of model performance that account for skill in capturing observed dependencies in space and across multiple fields (Mu et al. 2004; Nosedal-Sanchez et al. 2016). We have found this to be a favorable trade-off especially if one only needs to generate an ensemble that spans a range of outcomes that is useful for exploring specific science questions.
b. Model skill test statistic
Names and descriptions of the perturbed parameters for the CAM ensembles, along with the files/subroutines in which they are found and their default values and ranges within the MVFSA sampling (Wagman 2018). For the CAM3.1 ensemble, the names of the physics files are given (i.e., \physics\filename.F90). For the CAM5.3 ensemble, the parameterization scheme is given.
Various sources of observational data were used in evaluating the test statistics for the two CAM ensembles. For the CAM3.1 ensemble, observational data were drawn from Willmott and Matsuura (2000) (2 m air temperatures), ERA-40 data (vertically averaged air temperature and relative humidity, sea level pressure, and 300-mb zonal winds), Yu et al. (2008) (ocean latent heat fluxes), Clouds and the Earth’s Radiant Energy System (CERES2) data (long- and shortwave cloud forcing), Global Precipitation Climatology Project (GPCP) data (precipitation), and ERS-2 data for the 5°S–5°N Pacific Ocean wind stress (Yokohata et al. 2012). For the CAM5.3 ensemble, GPCP data were used for rainfall; ERA-Interim reanalysis for temperature, humidity, wind speeds, and sea level pressure; CERES data for shortwave and longwave cloud forcings; and Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) for cloud fractions (Wagman 2018).
APPENDIX B
EOF Calculations
This appendix describes the steps of our empirical orthogonal function (EOF) analysis to arrive at the results accompanying Figs. 4 and 5. The goals of these calculations are to find the proportion of the total variance of the mean precipitation response attributable to fLS and to see how linearly the response patterns vary with fLS. The total variance within a field can be calculated by an eigenvalue decomposition of its covariance matrix, so we begin by vectorizing the responses for each ensemble member (i.e., turning each 2D map into a 1D array) to obtain a matrix of dimension (i, j) where i indexes the ensemble member and j indexes the ith member’s vectorized response map. We then calculate the covariance matrix and decompose it into EOFs via the standard eigenvalue problem. We truncate the evaluation at 10 EOFs. Each eigenvalue λk (k = 1, …, 10) quantifies the variance explained by its corresponding EOF, and the total variance within the response field is the sum
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