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  • View in gallery

    Zonal and monthly climatological averages of (shaded; PVU) and (contours, labeled in K; contour interval is 10 K) equatorward of 70° latitude from NCEP–NCAR reanalysis for (a) January and (b) July. The 1.5-PVU contour is drawn with a thick black line. (c),(d) As in (a),(b), but from the model control simulation (M-Ctrl). Data extrapolated to pressure levels beneath the surface pressure were excluded from the averages.

  • View in gallery

    As in Fig. 1, but for a cross section along 45°N. Points beneath the surface pressure are masked out with black boxes (these correspond to elevated topography).

  • View in gallery

    Mean surface temperature (K) in M-Ctrl for (a) January and (b) July. (c),(d) As in (a),(b), but for M-3; (e),(f) as in (a),(b), but for M-5; (g),(h) as in (a),(b), but for E-4, which has Eocene continental configuration.

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    As in Fig. 1, but for (a) January and terrestrial zonal mean and (b) January and oceanic zonal mean in M-Ctrl. (c),(d) As in (a),(b) but for M-3; (e),(f) as in (a),(b), but for M-5.

  • View in gallery

    As in Fig. 2, but for the cross section along 60°N for M-Ctrl in (a) January and (b) July. (c),(d) As in (a),(b), but for M-5.

  • View in gallery

    As in Fig. 4, but for July.

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    Annual cycle of the fraction of time that terrestrial points between 40° and 50°N have (0.15 PVU) as a function of height (pressure) in (a) M-Ctrl, (b) M-3, and (c) M-5.

  • View in gallery

    Fraction of days (from all model years in Table 1) in which (0.15 PVU) between 700 and 400 hPa in (a) M-Ctrl in January and (b) M-Ctrl in July. (c),(d) As in (a),(b) but for M-3; (e),(f) as in (a),(b), but for M-5.

  • View in gallery

    As in Fig. 8, but for (0.15 PVU), showing the fraction of time that vertical profiles have convectively neutral or superadiabatic lapse rates.

  • View in gallery

    Difference between Figs. 8 and 9, showing the contribution that structures consistent with slantwise convective adjustment make to the frequency of low R.

  • View in gallery

    Fraction of days for E-4 on which (0.15 PVU) between 700 and 400 hPa in (a) January and (b) July. (c),(d) As in (a),(b), but for . The positions of the soundings shown in Fig. 12 are marked with symbols (circle, square, triangle).

  • View in gallery

    Thermodynamic soundings for three points in E-4 in (a) January and (b) July; solid light gray lines are moist adiabats, solid dark gray lines are dry adiabats, and dashed dark gray lines are skewed isotherms. Locations for soundings are marked in Fig. 11; the circle is a site along west coast of North America, the square is a site over India, and the triangle is a site on the east coast of Australia.

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Thermal Stratification in Simulations of Warm Climates: A Climatology Using Saturation Potential Vorticity

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  • 1 Texas A&M University, College Station, Texas
  • | 2 University of New Hampshire, Durham, New Hampshire
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Abstract

The spatial and temporal distribution of stable and convectively neutral air masses is examined in climate simulations with carbon dioxide levels spanning from modern-day values to very high levels that produce surface temperatures relevant to the hottest climate of the past 65 million years. To investigate how stability with respect to slantwise and upright moist convection changes across a wide range of climate states, the condition of moist convective neutrality in climate experiments is assessed using metrics based upon the saturation of potential vorticity, which is zero when temperature profiles are moist adiabatic profiles along vortex lines. The modern climate experiment reproduces previously reported properties from reanalysis data, in which convectively neutral air masses are common in the tropics and locally at higher latitudes, especially over midlatitude continents in summer and ocean storm tracks in winter. The frequency and coverage of air masses with higher stabilities declines in all seasons at higher latitudes with warming; the hottest case features convectively neutral air masses in the Arctic a majority of the time in January and nearly universally in July. The contribution from slantwise convective motions (as distinct from upright convection) is generally small outside of midlatitude storm tracks, and it declines in the warmer climate experiments, especially during summer. These findings support the conjecture that moist adiabatic lapse rates become more widespread in warmer climates, providing a physical basis for using this assumption in estimating paleoaltimetry during warm intervals such as the early Eocene.

Denotes Open Access content.

Corresponding author address: Ryan A. Zamora, Department of Atmospheric Sciences, Texas A&M University, TAMU 3150, College Station, Texas 77843-3150. E-mail: zamora.raz@gmail.com.

Abstract

The spatial and temporal distribution of stable and convectively neutral air masses is examined in climate simulations with carbon dioxide levels spanning from modern-day values to very high levels that produce surface temperatures relevant to the hottest climate of the past 65 million years. To investigate how stability with respect to slantwise and upright moist convection changes across a wide range of climate states, the condition of moist convective neutrality in climate experiments is assessed using metrics based upon the saturation of potential vorticity, which is zero when temperature profiles are moist adiabatic profiles along vortex lines. The modern climate experiment reproduces previously reported properties from reanalysis data, in which convectively neutral air masses are common in the tropics and locally at higher latitudes, especially over midlatitude continents in summer and ocean storm tracks in winter. The frequency and coverage of air masses with higher stabilities declines in all seasons at higher latitudes with warming; the hottest case features convectively neutral air masses in the Arctic a majority of the time in January and nearly universally in July. The contribution from slantwise convective motions (as distinct from upright convection) is generally small outside of midlatitude storm tracks, and it declines in the warmer climate experiments, especially during summer. These findings support the conjecture that moist adiabatic lapse rates become more widespread in warmer climates, providing a physical basis for using this assumption in estimating paleoaltimetry during warm intervals such as the early Eocene.

Denotes Open Access content.

Corresponding author address: Ryan A. Zamora, Department of Atmospheric Sciences, Texas A&M University, TAMU 3150, College Station, Texas 77843-3150. E-mail: zamora.raz@gmail.com.

1. Introduction

The vertical structure of temperature is a fundamental property of the atmosphere, and questions about its variability and of the physics that regulate it have been posed throughout the modern history of the field (e.g., Teisserenc de Bort 1902; Brunt 1933; Manabe and Wetherald 1967; Ramanathan and Coakley 1978; Held 1982; Schneider 2004). The frequency of upright (vertical) convection, combined with the large Rossby radius of deformation, and the comparatively slow time scale of subsequent radiative adjustments render moist adiabatic lapse rates nearly ubiquitous in the tropics and subtropics (Sarachik 1985; Chimonas and Rossi 1987; Xu and Emanuel 1989; Pierrehumbert 1995), but they are stable, on average, in middle and high latitudes (e.g., Stone and Carlson 1979). Yet observations have documented extensive seasonal, vertical, and meridional variability in the magnitude of the lapse rates in the extratropical troposphere (Rennick 1977; Stone and Carlson 1979; Juckes 2000; Frierson and Davis 2011), and both dynamical and convective processes influence it on distinct spatial and temporal scales. Either process may dominate locally and temporarily, while interactions between these processes may also jointly contribute to the mean stratification and its variability (e.g., Juckes 2000).

Large-scale eddies transport entropy poleward and upward in baroclinically unstable atmospheres, which results in elevated static stability and reduced meridional temperature gradients. Early work on the question of extratropical stability focused primarily on the role of dry dynamics, especially the possibility that baroclinic adjustment may control mean stratification (e.g., Stone 1978; Held 1982; Lindzen 1993). While there is significant evidence that eddies are effective at stabilizing the extratropical lower troposphere (e.g., Schneider and Walker 2006), there is further evidence that the atmosphere does not exist in a purely baroclinically neutral state (Valdes and Hoskins 1989; Barry et al. 2000). And a growing number of authors have argued that moist processes play an important role in the extratropical stratification problem (Juckes 2000; Frierson 2006; Pauluis et al. 2008; O’Gorman 2011; Frierson and Davis 2011), which has profound importance for polar amplification of climate change (Graversen et al. 2008; Abbot et al. 2009). Thus the frequency and distribution of convective processes at all latitudes—and in different climates—is important to understand.

Stone and Carlson (1979) showed that zonal mean tropospheric thermal stratification in the Northern Hemisphere was moist adiabatic equatorward of about 30°N only in January, but that this area expanded into middle latitudes during July. Chimonas and Rossi (1989) showed that convection was important to tropospheric stratification in midlatitude summers, and that connections to convection in remote locations may be important to midlatitude stratification in other seasons too. Korty and Schneider (2007; hereafter KS07) showed that convectively neutral air was frequent even at the highest latitudes over continents in July, and over the lower and middle troposphere in ocean storm tracks during winter. KS07 also showed that several regions in the middle and high latitudes with stable vertical lapse rates nevertheless showed moist adiabatic lapse rates along sloping angular momentum surfaces, showing that symmetric instabilities (Emanuel 1983a,b) may also contribute to the mean thermal stratification (Emanuel 1988, 2008). The process of slantwise moist convection is driven by symmetrically unstable slantwise displacements of moist air masses if moist entropy decreases upward along the slanted isosurfaces of absolute angular momentum (Bennetts and Hoskins 1979); convection may be driven by unstable displacements along the gravitational vector (upright convection), by symmetric instabilities (slantwise convection), or both. Case studies by Emanuel (1988) showed that the ascent regions of several extratropical cyclones exhibit approximately moist-adiabatic lapse rates along angular momentum surfaces.

The main objective of this paper is to examine how the climatology of extratropical stratification changes in simulations of significantly warmer climates. Diagnosing the magnitude and variability of stratification across different climates provides a body of evidence to test theories of what physical processes establish and maintain it (e.g., Held 1982; Lindzen 1993; Juckes 2000; Frierson 2006, 2008; Frierson and Davis 2011; O’Gorman 2011). Additionally, paleoclimate reconstructions may provide a means to test model results if vertically resolved temperature estimates can be established. Alternatively, assumptions about lapse rates are critical to paleoaltimetry, which estimates the elevation of topography in the geologic past by comparing terrestrial proxies of temperature with others from a nearby sea surface value (Forest et al. 1995, 1999; Forest 2007; Meyer 2007). Different assumptions about appropriate lapse rates yield very different estimates of altitude, so some understanding of its variability in climate simulations of these periods would be useful. Here we extend the work of KS07, who assessed the frequency and spatial distribution of convectively neutral extratropical lapse rates in modern reanalysis data, to its representation in global climate models and their simulations of climates spanning from modern-day conditions to the hotter climates relevant to the Eocene epoch.

We note at the outset that this paper diagnoses thermal structures consistent with those that adjustment by convective processes (both upright and slantwise) would produce, but that we do not assess their actual cause. We compare the frequency and geographic distribution of convectively neutral air masses in a modern-day global climate model simulation to its climatology in reanalysis products (reported by KS07, and reviewed here) and find the major properties to be reproduced. Although we identify regions in simulations of the coarse-resolution global model that have structures consistent with those produced by slantwise convective adjustment, such processes are not parameterized in its convective routines (although it is possible they could arise from synoptic-scale dynamics). We discuss some of the questions raised by that result at the end of the paper, but a proper analysis of slantwise motions in coarse-resolution models lies beyond the scope of this paper.

Our paper is organized as follows. Section 2 reviews the properties of saturation potential vorticity, its use as a diagnostic of extratropical lapse rates, and discusses our definitions to divide air masses between stable, moist-neutral, and superadiabatic cases. Section 3 compares the climatology of extratropical lapse rates in the modern-day control climate simulation with the results from reanalysis presented in KS07, and introduces the model experiments. Section 4 presents the results of how the distribution of stable and convectively neutral air masses change in warmer simulations forced with higher carbon dioxide levels. Section 5 compares these results to a simulation with Eocene epoch continental configurations and land surface characteristics. Section 6 summarizes the main findings and conclusions, and notes some questions raised by the results.

2. Diagnostic properties of saturation potential vorticity

Assessing stability with respect to moist convection requires computing saturation equivalent potential temperature (details on its definition and calculation follow below), which is constant on moist adiabats. Convective motions result from buoyancy against restorative forces, dominantly gravity, but in strongly rotating systems where centrifugal forces are significant there may arise symmetric instabilities along vortex lines tilted away from the vertical. Although symmetric instabilities are not explicitly parameterized in global models, we do not wish a priori to assume that they are absent or negligible (they can arise as solutions to the primitive equations). Thus we look for places where the gradient of along vortex lines is zero, and we therefore use the properties of saturation potential vorticity for our diagnosis.

The term P* is defined in analogy to Ertel’s (1942) potential vorticity P by replacing the dry potential temperature with (cf. Schubert et al. 2001). Unlike Ertel’s P, it is not materially conserved in unsaturated air,1 so its utility is fundamentally different. Here P* is defined as follows:
e1
where is the specific volume, is Earth’s angular velocity vector, and u is the wind vector. The saturation equivalent potential temperature , which is the equivalent potential temperature a parcel would have if it were saturated at the same temperature and pressure, is a thermodynamic state variable uniquely determined by temperature T and pressure p alone; it is defined as follows:
e2
Here po is a reference pressure (1000 hPa); pd is the partial pressure of dry air, which is the difference between total pressure p and the saturation vapor pressure e*; Rd is the gas constant for dry air; cpd and cl are the heat capacities for dry air and water, respectively; rt is the total water mixing ratio; r* is the saturation mixing ratio;2 and L is the latent heat of vaporization or sublimation, depending on temperature (Emanuel 1994, p. 120). We follow the technique outlined in KS07 to compute , which involves first computing an effective saturation vapor pressure e* and latent heat L using the relations of Simmons et al. (1999). These relations are based on saturation over ice and sublimation for temperatures below −23°C, on saturation over liquid water and vaporization for temperatures above 0°C, and on a quadratic interpolation for values in between. The values of these quantities are then used in (2) to compute .
Upright or vertical convection occurs when unstable parcels are buoyant against the gravitational vector. Slantwise moist convection occurs when displaced parcels embedded in rotating flows are buoyant along vortex lines parallel to a tilted angular momentum surface M, defined by
e3
where is the planetary angular velocity, a is the planetary radius, u is the zonal component of the wind, and ϕ is the latitude. The restoring forces against these slantwise convective motions are the combination of the gravitational and centrifugal vectors, a symmetric instability. Because angular momentum surfaces are parallel to the absolute vorticity vector (Frisius 2005; KS07), P* given by (1) will be zero everywhere that is constant along the surface. Thus the utility of (1) is fundamentally different from Ertel’s P: (1) is not a conservative dynamical tracer in unsaturated air, but rather it can be used to assess stability because its sign differs if increases, decreases, or remains constant along angular momentum surfaces. Note that P* will take the same sign as f everywhere that increases upward, indicating stable temperature profiles along angular momentum surfaces; conversely, P* will take the sign opposite of f where decreases along angular momentum surfaces, indicating conditionally unstable conditions; and it is zero where is constant.
Following KS07, we invoke the hydrostatic, traditional, and thin shell approximations in computing individual terms in (1).3 Thus, expanding (1) in pressure coordinates then yields four terms:
e4
Here is the Coriolis parameter, is the vertical component of relative vorticity, and all other variables have their usual meaning. The largest term in (4), , will be zero when vertical temperature profiles are moist adiabatic. In general, the second and fourth terms are smaller by a factor of the Rossby number, and the first term is usually an order of magnitude smaller than those (see KS07); these terms become significant in situations where vortex lines depart from the vertical. We include all four terms in our analysis, but we address whether a simpler analysis of just upright convection (using just the third term) would yield similar results in section 4c.
Like and , the meaning of the sign of will change between hemispheres. To give our analysis a single interpretation globally, and to facilitate comparison with our analysis of upright convection only (which depends on the sign of ), we define a modified version of , which we call R, by multiplying it by the factor Ω/f (or, equivalently, dividing by :
e5
The sign of R differs depending on the thermal structure of the air mass, and its meaning is universal globally: it is zero wherever profiles on vortex lines are moist adiabatic, positive where they are stable, and negative where they are supermoist adiabatic (a situation commonly found in desert air and boundary layers). To separate all profiles that are nearly moist adiabatic from those that are decidedly stable, we look for cases when R is smaller than the threshold PVU (1 PVU = 10−6 K m2 kg−1 s−1), which is 10% of the value used to define the dynamical tropopause. (The dynamical tropopause is taken to be the 1.5-PVU surface of P, Ertel’s potential vorticity, but in stratospheric air.) Thus we classify air masses based on the following criteria:
  • When , profiles on vortex lines are stable.
  • When (i.e., when , profiles on vortex lines are (nearly) moist adiabatic.
  • When , profiles on vortex lines are supermoist adiabatic, as is common in deserts and boundary layers, for example.
Our primary concern in this paper will be the division surrounding , to see whether profiles of stable to moist convection change in coverage or frequency with warming. By dividing by , we depart from the methodology used by KS07, but the quantitative differences that arise in the extratropics from our different thresholds are very small in practice because (and hence R) rapidly increases from zero in stable air. Introducing the latitude dependence offers advantages of a cleaner comparison with the analysis of upright convection in isolation (section 4c) and removes a bias that painted all equatorial latitudes as convectively neutral, regardless of the actual underlying profile ( as , but is equally difficult to pass at all latitudes off of the equator).

3. Model experiments and comparison to reanalysis

Our primary objective in this work is to classify how the frequency and spatial coverage of stable and convectively neutral air masses change in warmer climate simulations, which necessitates first showing that a coarse-resolution global climate model can reproduce the properties of the climatology seen in reanalysis products. We consider a series of experiments performed with NCAR’s Community Atmospheric Model version 3 (CAM3) in which carbon dioxide levels are successively doubled to very high levels (see Table 1). The experiments were conducted at T42 spatial resolution (~2.5° latitude by 2.5° longitude horizontal resolution) and were described in detail by Sherwood and Huber (2010), Williams et al. (2009), and Caballero and Huber (2010, 2013). Briefly, the set of experiments examined here were extended from previously equilibrated low-resolution coupled ocean–atmosphere experiments and were extended forward using either a slab ocean with prescribed ocean heat transport (S) or with fixed sea surface temperatures (F) taken from the earlier coupled run.

Table 1.

Properties of experiments performed with CAM3 are examined here. The naming convention uses M for modern geography and land surface properties, E for Eocene geography and land surface properties, and the number for the number of doublings of CO2 concentration from preindustrial-era levels (actual values given under CO2 column); the Control case uses 1990 levels of CO2. Simulations were extended from lower-resolution coupled runs with the atmospheric model and a slab ocean (S) or with fixed SST (F). Global and annual mean SST (°C), tropical (30°S to 30°N) and annual mean SST (°C), and the number of years of simulation output included in the analysis are given.

Table 1.

We examine four climate experiments, three of which feature modern-day geography (M) and one additional case with continental configuration appropriate to the early Eocene epoch (E) ~56–48 million years ago (Mya), which was the warmest interval of the past 65 million years (Huber and Caballero 2011). The modern experiments use a slab ocean, while the Eocene experiment uses an ocean with fixed sea surface temperatures. The control case, M-Ctrl, uses 1990 levels of carbon dioxide (355 ppm) with aerosol forcing, land surface properties, and solar constant appropriate to modern times. The high CO2 experiments in this series retain these parameter choices except for increasing CO2 concentrations to 23 and 25 times preindustrial era levels (M-3 and M-5, respectively), yielding cases with much warmer surface conditions to study how the lapse rate climatology evolves. The land surface and vegetation is not interactive in these simulations, and terrestrial ice sheets over Antarctica and Greenland remain in all cases in the M series, regardless of how hot the atmosphere becomes. A case with Eocene continental configuration and 24 times preindustrial era levels of CO2 (E-4) is examined in section 5. The Eocene case does not include modern aerosol levels or modern land surface characteristics (importantly, it includes no ice), and it uses the solar constant and other parameters from the preindustrial era; see Caballero and Huber (2010, 2013) for further details. Given the different set of boundary conditions, the E-4 case offers a test of whether any changes in M-3 and M-5 are robust responses to warmer climates, or specific to modern-day boundary conditions. All simulations were run for several thousand years to statistical equilibrium, and data here are taken from output at the end of each experiment. The value of was computed from daily mean temperatures. We emphasize here that these high CO2 levels are used merely as the tool to generate the hot climates examined here; other models with larger climate sensitivity may achieve similarly high surface temperatures using CO2 levels lower than those required in CAM3 (cf. Lunt et al. 2012).

As summarized in Table 1, this experimental setup enabled us to explore a wide temperature range from the modern-day control simulation, through intermediate warming, and into exceedingly hot conditions. The latter cases include CO2 levels higher than seen at any time after the early Paleogene (Archer et al. 2009). Huber and Caballero (2011) showed that there is a good match between proxies of the warm early Eocene and temperatures in the E-4 simulation, even though the CO2 levels from that time are uncertain. CAM3 has a lower climate sensitivity than many other global climate models, meaning that a model with a higher one could achieve the same temperatures as produced by E-4 with lower CO2 levels than required do to so here. Caballero and Huber (2013) also showed there exists a nonlinear temperature dependence with each CO2 doubling, with linear increases initially and a much stronger sensitivity in the hottest simulations (M-5 and E-5). This increase not only raises the overall global mean temperature, but also weakens the meridional temperature gradient as described further in Huber and Caballero (2011) and Lunt et al. (2012). The consequences of these changes on thermal stratification will be explored here.

Figure 1 shows the zonal mean (solid lines) and (shaded) for January (left) and July (right) in both reanalysis (top) and the model control run (bottom). The reanalysis data are the same examined in KS07 (NCEP–NCAR reanalysis; Kalnay et al. 1996), and the technique follows the practice in KS07: data were averaged into daily means between 1970 and 2004 on pressure surfaces, and was computed at each grid point (spaced every 2.5° latitude by 2.5° longitude over 17 vertical pressure levels between the surface and lower stratosphere). Note that was calculated at model interface levels in order to compute the vertical derivative embedded in (1). Unlike KS07, in Fig. 1 (and all subsequent figures) we choose to exclude all pressure levels beneath the surface, which eliminates artificial lapse rates that arise from extrapolation techniques (i.e., assumptions of dry adiabatic lapse rates); it also means, however, that data near the surface in the zonal mean come from an unequal distribution of points: the majority of data for p > 900 hPa are oceanic boundary layers, while higher altitudes lie above a mixture of terrestrial and maritime locations.

Fig. 1.
Fig. 1.

Zonal and monthly climatological averages of (shaded; PVU) and (contours, labeled in K; contour interval is 10 K) equatorward of 70° latitude from NCEP–NCAR reanalysis for (a) January and (b) July. The 1.5-PVU contour is drawn with a thick black line. (c),(d) As in (a),(b), but from the model control simulation (M-Ctrl). Data extrapolated to pressure levels beneath the surface pressure were excluded from the averages.

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

The modern climate control simulation (M-Ctrl) captures the distribution and structure of the zonal mean properties in the NCEP–NCAR reanalysis as reported in KS07 and reproduced here in Figs. 1 and 2. Note that because we have adjusted values by a latitude-dependent threshold [defined by (5) in section 2], the plots of R differ slightly from those of found in KS07 (contrast Fig. 1a herein with Fig. 4f of KS07, Fig. 1b herein with Fig. 6f of KS07, Fig. 2a herein with Fig. 5a of KS07, and Fig. 2b herein with Fig. 7a of KS07). These slight differences highlight the effect of equalizing the ability for identical nearly moist-neutral profiles to pass a common threshold, regardless of the latitude at which they occur; qualitatively the change is unimportant to the interpretation of our results.

Fig. 2.
Fig. 2.

As in Fig. 1, but for a cross section along 45°N. Points beneath the surface pressure are masked out with black boxes (these correspond to elevated topography).

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

Stable lapse rates in the zonal mean, indicated by areas in white where (where PVU), are confined to areas poleward of about 50°S and 40°N in January, but retreat out of Northern Hemisphere middle latitudes during July. Values of are approximately constant equatorward of 20° latitude throughout the troposphere, a signature of the well-known dominance of convectively neutral lapse rates in this region. Figures 1a and 1c show a small difference in the extent of air masses where is negative (shaded dark gray) in the middle troposphere of the Southern Hemisphere subtropics in January (summer), but the values in both the model and in reanalysis are similar to one another, near the threshold in this area. Negative values can be found where lapse rates are less stable than moist adiabats, as is common in desert areas during summer, for example. These regions pull the zonal mean toward lower values than is commonplace elsewhere. The other major departure from KS07 comes from our treatment of the highest p levels, which here exclude all points from the averages below the surface. This is the reason that the high values near 20°N at the surface in July reported in KS07 are lower in Fig. 1b (and Fig. 1d) here. Data between 40° and 60°N for p > 950 hPa are mostly oceanic air (stable in July), while points above it include both terrestrial boundary layers and oceanic air. This is why the lines slope poleward and upward at the surface: they are stable in marine boundary layers in summer. This can be more clearly seen in Fig. 2, which shows cross sections along 45°N.

One of the most impressive distinctions in KS07 was the difference between the seasonal extremes over land and over ocean. The cross section depicted in Fig. 2 shows that while the zonal mean is stable at this latitude in January, the Pacific and Atlantic sectors feature air masses with convectively neutral properties in the time mean. Stable air dominates in January over Eurasia and North America. The model reproduces the distribution seen in reanalysis quite well. In July, maritime air masses have stable lapse rates below about 700 hPa, while continental locations feature lapse rates, in many instances less stable than moist adiabatic. The control simulation again reproduces the properties seen in the reanalysis, and we conclude that it is able to capture the important variations reported in KS07.

In the remainder of the paper we turn attention to how the properties seen in both the reanalysis and M-Ctrl change with warming climates. In Fig. 3, we show the very large range of surface temperatures produced across the experiments examined in subsequent sections. As reported in Table 1, the global and annual mean temperature is ~5°C hotter in M-3 than in M-Ctrl, and M-5 is an additional ~11°C hotter than the intermediate case. These differences are amplified in polar latitudes, with temperatures over the Arctic ~10°C higher in M-3 than in M-Ctrl, and as much as 25° to 30°C warmer in M-5. July surface temperatures in part of the Arctic exceed 305 K in M-5, and are above freezing even in January. The M-3 case features tropical sea surface temperatures (SSTs) ~5°C warmer than in M-Ctrl, while they are ~15°C higher in M-5 (see Table 1). The Eocene geography case (E-4) produces temperatures that compare favorably with the latest synthesis of proxies from the early Paleogene (Caballero and Huber 2013), with temperatures warmer than the average of M-3 and M-5. [The Eocene cases, which do not include terrestrial ice distributions or modern continental configurations, are about 5°C warmer than their modern geography counterparts; see Caballero and Huber (2013) for further details.]

Fig. 3.
Fig. 3.

Mean surface temperature (K) in M-Ctrl for (a) January and (b) July. (c),(d) As in (a),(b), but for M-3; (e),(f) as in (a),(b), but for M-5; (g),(h) as in (a),(b), but for E-4, which has Eocene continental configuration.

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

4. Saturation potential vorticity in simulations of warmer climates

We now examine how the mean state and variability of lapse rate properties change across the climate experiments described in the previous section. We computed the values of and from daily mean data in each of the years for which output at this temporal resolution or higher was available (see Table 1). The role of moist convection in the tropics is well established in the modern climate, and our primary interest here is on how the frequency of stable and neutral air masses changes in middle and high latitudes. We examine the mean state properties over land and over ocean of the two seasonal extremes first, followed by analysis of the temporal variability of both and of vertical convective neutrality across the climate experiments. We consider the partitioning between upright and slantwise contributions in section 4c.

a. Seasonal extremes

As seen in Fig. 2, the climatology of lapse rates differs over land and ocean, with low values most common in middle latitudes over land in summer and over ocean in winter. Therefore, here we examine the changes with climate separately for terrestrial and marine environments. Figure 4 shows the climatology of and broken into separate zonal averages for all grid points over land (left panels) and for all points over ocean (right panels) for the three climate experiments with modern-day geography during January. (The lack of any land between 55° and 70°S leads to the band of empty data in the right panels of Fig. 4.) The region with over land expands poleward from about 35°–40°N in M-Ctrl, to 40°–50°N in M-3. Air masses feature lapse rates more stable than moist adiabatic over land in January at high latitudes in M-5, but advection of maritime air masses with from the North Sea and Bearing Sea lowers the stability in the middle troposphere, as depicted in Figs. 5a and 5b, which contrast cross sections along 60°N for M-Ctrl and M-5 in January.

Fig. 4.
Fig. 4.

As in Fig. 1, but for (a) January and terrestrial zonal mean and (b) January and oceanic zonal mean in M-Ctrl. (c),(d) As in (a),(b) but for M-3; (e),(f) as in (a),(b), but for M-5.

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

Fig. 5.
Fig. 5.

As in Fig. 2, but for the cross section along 60°N for M-Ctrl in (a) January and (b) July. (c),(d) As in (a),(b), but for M-5.

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

The right panels of Fig. 4 show that the area of low during January expands poleward with warming across the range of simulations: midtroposphere stable air can be found as far south as ~40°N in M-Ctrl, but only to 50°N in M-3. Figure 4f shows that air expands into the Arctic Ocean in January in M-5 in the time mean. Subtropical stable air can be found in the lower troposphere between about 700 and 850 hPa in all three climates (as indicated by the poleward bend of lines) over the oceans; this is consistent with the trade wind inversions reported in KS07. The poleward expansion of winter convectively neutral air is much stronger over the oceans than over land. Even partitioning the data into separate zonal averages for land and ocean masks some further variability (not shown). Profiles along meridians on the west coasts of continents show winter neutral layers much farther poleward than the mean; they share more in common with the oceans to their west. Profiles along the east coasts of continents are stable farther equatorward in winter. Similarly, the poleward reach of neutral air expands from west to east across ocean basins in winter.

The M-5 case features special tropical dynamics, which were documented by Caballero and Huber (2010): an increase in momentum convergence from tropical eddies disrupts the modern balance with momentum divergence by the zonal mean circulation, leading to equatorial superrotation (westerlies along the equator) and strong vertical shears at low latitudes. The contribution from the term in (4) to the full value of is strongly negative in the M-5 case between 20° and 45°N in January, despite the fact that contours are approximately vertical; a separate analysis of upright convection will be presented in section 4c.

The extent of stable air in the Northern Hemisphere is much smaller in July than in January (Stone and Carlson 1979; KS07), and Fig. 6 shows the mean conditions in July across the climate experiments. As in Fig. 4, the left panels are means above terrestrial locations and the right panels are averages above ocean. The important differences from January include a poleward retreat of stable air (), especially over continents. Less stable air expands poleward from M-Ctrl to M-3 and M-5 over land. There is also an expansion of convectively neutral air over high-latitude oceans in the warmer climates.

Fig. 6.
Fig. 6.

As in Fig. 4, but for July.

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

The zonal average of maritime air shows a maximum in between 700 and 800 hPa in the subtropics, which produces a dipole in with a stable layer below 800 hPa and negative values of above. This is a convolution of two processes. First, there is a stable layer in the lower troposphere associated with the trade inversion. This can be seen also in the Southern Hemisphere subtropics by a poleward tilt in the contours between 700 and 800 hPa. Second, in the Northern Hemisphere, some advection of very high air from adjacent deserts such as the Sahara to oceanic regions raises the mean higher. This becomes more pronounced in the warmer climates, where surface temperatures in July reach very high levels (Fig. 3f).

b. Temporal variations

Given the changes in the mean state seasonal extremes across the climate experiments presented in the last section, we turn now to an analysis of their temporal variability. We examine both the change in the annual cycle of stability across the climate changes as well the frequency of lower stability air masses in each climate. Regions with stable lapse rates in the time mean may still experience lower stability intermittently.

Figure 7 shows the annual cycle of the frequency of at terrestrial locations averaged between 40° and 50°N as a function of height. Stable air () is common during winter from November to March in M-Ctrl, although as many as a third to a half of days and locations exhibit lower stability. This shows that although both the zonal mean and zonal average over land is stable during winter at these latitudes, a sizable fraction of the time lapse rates are lower. From April to October, more than 70% of days and locations over land in this latitude band show lower stability, indicating that more stable lapse rates are rare during summer. This pattern expands to a month earlier and lingers a month longer in M-3, while the frequency of higher stabilities in winter declines. In the warmest case, low values of are common in the middle troposphere throughout the year, with stable air dominating only in the lower troposphere from November to February. Regions below 700 hPa are most effectively stabilized by baroclinic waves (Schneider and Walker 2006), and higher lapse rates () can be found around 800 hPa a majority of the time in winter even in the hottest M-5 case.

Fig. 7.
Fig. 7.

Annual cycle of the fraction of time that terrestrial points between 40° and 50°N have (0.15 PVU) as a function of height (pressure) in (a) M-Ctrl, (b) M-3, and (c) M-5.

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

The frequency of less stable lapse rates increases from M-Ctrl to M-3 and M-5 over land in middle latitudes during winter in the free troposphere, and the changes in frequency can be seen at higher latitudes as well. Figure 8 shows the frequency of days in January (left) and July (right) for which in the middle troposphere, which we take here to be pressure levels between 400 and 700 hPa. In M-Ctrl, lapse rates are always stable in January over Siberia and the Hudson Bay region in January, and are stable a majority of the time over the Arctic in July. These areas show an increase in days with lower stability in both seasons at M-3 and in M-5; by July in M-5 much of the Arctic shows lower stability at least 70% of the time.

Fig. 8.
Fig. 8.

Fraction of days (from all model years in Table 1) in which (0.15 PVU) between 700 and 400 hPa in (a) M-Ctrl in January and (b) M-Ctrl in July. (c),(d) As in (a),(b) but for M-3; (e),(f) as in (a),(b), but for M-5.

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

January lapse rates above Northern Hemisphere oceans are less stable than over continents at the same latitude in all three climates. The frequency of over midlatitude oceans is larger in the eastern Pacific and eastern Atlantic than on the western sides of the basin, consistent with the orientation of oceanic storm tracks. This difference is larger in M-Ctrl and in M-3 than in M-5, where the pattern becomes more zonally homogenous over midlatitude oceans. The pattern in the middle troposphere shows less difference between land and ocean in July, although as seen earlier maritime locations remain stable over oceans at lower altitudes (Fig. 6).

One interesting aspect in several panels of Fig. 8 is a band of slightly less frequent low- air within 20° latitude of the equator. Lapse rates are known to be approximately moist adiabatic throughout the tropics, but observations of the tropical atmosphere show there is often a narrow band of stability surrounding the freezing level (which occurs between 600 and 500 hPa in the M-Ctrl run) associated with melting of ice particles (Johnson et al. 1996). This appears to be the reason for the reduced frequency of convectively neutral air around 20° latitude at 550 hPa in KS07 (cf. Fig. 9 of KS07), but the approach used in that paper (a constant threshold for , rather than for R) masked this effect nearer to the equator where with f.

c. Upright convective neutrality

Until now we have considered signatures of convective adjustment along vortex lines, which are most often vertical but in strongly rotating systems may tilt away from the gravitational vector. If the condition of slantwise-convective neutrality (as distinct from upright-convective neutrality) is rare, a simpler analysis involving only the vertical derivative of rather than would suffice. As noted in KS07, the largest term in (1) is , which is generally an order of magnitude larger than the next largest terms in subtropical, middle, and high latitudes. In this section we explore where and when is constant with pressure (height), a defining property of moist adiabats. We again note that while slantwise-convective motions are not explicitly parameterized in global models, they could arise as solutions to the primitive equations. However, our analysis is merely diagnostic, and we do not analyze the root cause of any such structures in this paper.

Figure 9 shows the frequency of upright convection by assessing how often PVU. This is the same threshold used to assess upright convection in KS07 [equivalently, the largest term in (4) is multiplied by the same factor Ω/f used to define (5)], and it will be met wherever changes less than 2.1 K per 100 hPa. (Strictly speaking, moist adiabatic lapse rates would have no change in with pressure at all, but we allow small departures to assess the frequency of lapse rates that are approximately moist adiabatic.) As with the frequency of low values in Fig. 8, the frequency of approximately moist adiabatic vertical lapse rates outside of the tropics increases in both seasonal extremes in the warmer climate experiments, becoming widespread even in the Arctic during July of M-5.

Fig. 9.
Fig. 9.

As in Fig. 8, but for (0.15 PVU), showing the fraction of time that vertical profiles have convectively neutral or superadiabatic lapse rates.

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

One interesting aspect of Fig. 9 is that the frequency of moist neutral lapse rates in the tropics, although common, is not unity. This arises because of the small, often subtle stable layer found near the freezing level, which in the M-Ctrl simulation occurs between 600 and 500 hPa in the tropics. Values of tend to be slightly lower at 600 hPa (just below the freezing level) and slightly higher at 500 hPa (just above it) than at other altitudes, which is consistent with observations from Johnson et al. (1996) from melting and freezing processes. Both Fig. 8 and Fig. 9 show the frequency over the 700–400-hPa layer, which includes three midpoint levels at which and were computed (650, 550, and 450 hPa); the freezing level occurs within this band in M-Ctrl and M-3 but rises to a higher altitude in M-5, which is why the frequency of increases low latitudes of the M-5 case.

While there are many qualitative similarities between Figs. 8 and 9, indicating that upright convection is the dominant contribution to the earlier analysis of low values of there are also several important differences. Figure 10, which shows the difference between Figs. 8 and 9, separates the additional contributions that slantwise-convective motions make to the total cases of low stability. The midlatitude Pacific and Atlantic storm tracks have substantially higher frequency of low than of low in January of M-Ctrl, and Fig. 10 indicates that slantwise-convective processes may contribute to a majority of the cases with low R here. For example, along the central coast of China in January of M-Ctrl, upright convection is infrequent (~0.25 of all days), but low values of R are present on most of them. These processes add at least 0.25 to the January frequency of low occurrences at the origin of the North Atlantic and North Pacific storm tracks, and locally more than 0.5. The contribution of slantwise motions to the frequency of convective neutrality in the Southern Hemisphere storm belts is similarly large, and does not decline as much during summer as the Northern Hemisphere tracks do. Outside of the storm tracks, there is generally a much smaller difference between the frequency of low R in Fig. 8 and the frequency of low in Fig. 9 in middle and high latitudes of M-Ctrl, ranging from about 0.05 to 0.3.

Fig. 10.
Fig. 10.

Difference between Figs. 8 and 9, showing the contribution that structures consistent with slantwise convective adjustment make to the frequency of low R.

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

An interesting feature revealed by Fig. 10 is that the contribution from slantwise terms to the total frequency of low stability appears to decline significantly with warming (while the total coverage of increases). The decline during summer, which already featured a smaller contribution from slantwise convection than in winter, is especially large. The decline (in all seasons) in the additional contribution to low stability made by slantwise convection suggests that the expansion of convectively neutral air in the warmer simulations is caused by increases in upright convection, rendering the need to consider slantwise motions of lesser importance in the hotter cases. However, there is evidence that representations of slantwise processes in coarse-resolution models differs from those with finer resolution (KS07 showed that oceanic regions had lower frequencies of in the higher-resolution North American Regional Reanalysis than in the coarser NCEP–NCAR product), so this result should be viewed cautiously.

Given that upright convection is the dominant contribution to low values outside of storm tracks, and given that frequency of convectively neutral air masses increases in the warmer climate simulations, there are potential applications to paleoaltimetry methods for the early Eocene (cf. Forest 2007). We introduce in the next section the results from an experiment with Eocene continental configuration and land surface characteristics to compare with the results from increasing CO2 only.

5. Eocene boundary conditions

As seen in Figs. 3g and 3h, the E-4 case produces surface temperatures warmer than M-3 and broadly comparable to (but slightly cooler than) those in M-5. Caballero and Huber (2013) showed that this simulation produces the best match to the latest proxies of surface temperatures from the early Eocene epoch, and we consider here how the climatology of lapse rates in it differs from the modern world. Note that E-4 includes no terrestrial ice, which means the altitude of the surface in Antarctica and Greenland is lower than in the M-series, and temperatures over Antarctica are considerably warmer; they remain above 270 K in both seasonal extremes, supporting an ice free world with polar temperatures above freezing. The E-4 case offers a test of whether the changes with warming reported in the previous section are also seen with different boundary conditions.

Figure 11 shows the frequency of in January (Fig. 11a) and July (Fig. 11b); Figs. 11c and 11d show the frequency of lower vertical stability in which (as in Fig. 9 for the modern cases). The frequencies of both low and low are qualitatively similar to M-5, although both are slightly lower than the corresponding frequency in M-5 in Arctic latitudes in January. Lower stabilities are more common over Antarctica and Greenland than in M-5 with the ice sheets removed. The frequency of low over Australia is lower than in M-5 owing to its higher latitude in the Eocene.

Fig. 11.
Fig. 11.

Fraction of days for E-4 on which (0.15 PVU) between 700 and 400 hPa in (a) January and (b) July. (c),(d) As in (a),(b), but for . The positions of the soundings shown in Fig. 12 are marked with symbols (circle, square, triangle).

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

Given that the frequency of moist adiabatic lapse rates rises in the E-4 simulations (compared to M-Ctrl), the assumption that lapse rates in the past were moist adiabatic (Meyer 2007) is well justified and more advanced methods, such as the paleoenthalpy method (Forest 2007), are in keeping with our results. Figure 12 shows soundings for three sites in both seasonal extremes: one along the west coast of North America (circle); one over India (square), which was near the equator during the early Eocene; and a third over the east coast of Australia (triangle), which was in the Southern Hemisphere midlatitudes during the early Eocene; the specific sites of the three soundings are indicated by the symbols on the maps in Fig. 11. The soundings from India (on the equator) are moist adiabatic ( constant with height) in both months, and the one from Australia is moist adiabatic above the boundary layer during January (summer); in July it is close to moist adiabatic between 700 and 500 hPa, but is stable below. The profile in western North America is moist adiabatic in January, but superadiabatic (less stable than a moist adiabat) in July. In regions where is constant with height, the fact that it is a thermodynamic state variable (a unique function of temperature and pressure) might be used to calculate the height for nearby terrestrial proxies of temperature whose altitude is unknown (if the assumption of moist neutrality holds there too). If an independent proxy for SST is available with knowledge of the mean sea level pressure for the Eocene, then the pressure of a nearby coastal site with the same is uniquely determined, and its altitude could be identified by calculating the column mean temperature and using the hypsometric equation to find the thickness of the layer. The regions where such an approach might work and the errors associated with such a methodology are worth examining more carefully, especially as the profiles show more varied structure than the free troposphere above; see Meyer (2007) for further discussion.

Fig. 12.
Fig. 12.

Thermodynamic soundings for three points in E-4 in (a) January and (b) July; solid light gray lines are moist adiabats, solid dark gray lines are dry adiabats, and dashed dark gray lines are skewed isotherms. Locations for soundings are marked in Fig. 11; the circle is a site along west coast of North America, the square is a site over India, and the triangle is a site on the east coast of Australia.

Citation: Journal of Climate 29, 14; 10.1175/JCLI-D-15-0785.1

6. Summary

We have shown that the frequency and coverage of convectively neutral air masses increase in simulations of warmer climates with high CO2. The simulation of the modern control climate replicates the important features found in reanalysis data: an increase in the frequency of convectively neutral air during summer over extratropical continents and in ocean storm tracks during winter, where the contribution from slantwise convection may also be of greater importance than elsewhere. The simulations of warmer climates show an expansion of convectively neutral air masses in both winter and summer, as well as an increase in the length of the season during which these air masses may dominate in the midlatitudes. The hottest case (M-5) shows that even the Arctic has nearly universal coverage of low air during July, and on about half of days during January. This increase in low air was also seen in the case with Eocene continental configuration and land surface properties. Differences at specific sites are largely attributable to their changed latitude; for example, air masses frequencies more common to middle latitudes over Australia in the E-4 case. Yet the overwhelming similarity between the future cases with high CO2 and the Eocene case, despite very different boundary conditions, demonstrates that the expansion of moist neutral air masses and its diagnosis using the saturation potential vorticity framework is a robust feature of the warmer climate simulations.

Slantwise convection generally adds a small additional amount of time to the frequency of low air in the extratropics, but it is of larger importance to winter ocean storm tracks where it may be of comparable relevance to upright convective processes. However, as KS07 noted, horizontal resolution affected the quantitative representation of convectively neutral air over the ocean in reanalysis products, where data were more limited. This should be kept in mind here too: slantwise convection is not an explicitly parameterized process, although it can arise in solution to the primitive equations. The horizontal resolution of the simulation might affect the specific quantity of low air masses reported here, although the qualitative similarities between high- and coarse-resolution reanalysis data over oceans reported in KS07 encourages us to expect that general circulation model simulations of other climates with different resolutions would be qualitatively similar to what we report here.

We note one additional caveat: like all global models of its resolution, CAM3 parameterizes deep convection, and it would be worth revisiting this analysis of modern-day and warming experiments in a cloud-resolving model that handles convection explicitly. Additionally, while we have identified regions with temperatures structures consistent with slantwise convective adjustment, a proper and extensive test of both coarse-resolution and convective-resolving models’ ability to generate such convective motions in a realistic way remains for future work.

The increase in coverage of convectively neutral air at high latitudes in the hottest climates has a number of potential consequences, from the potential to apply convective quasi-equilibrium theory of land–ocean warming contrasts at higher latitudes (Byrne and O’Gorman 2013) to the generation and vertical propagation of Rossby waves into the stratosphere in hot climates (Korty and Emanuel 2007). It also raises the possibility that tropical cyclones might operate in such climates in locations inhospitable to them today. Tropical storms are presently confined to low latitudes not by any specific SST (their relationship to SST is itself variable with climate; Emanuel 1987; Royer et al. 1998), but by the latitude at which subtropical lapse rates become stable owing to the trade inversion (e.g., Korty et al. 2012). How simulations of these climates treat such storms may teach us something about their ability to tackle questions of hurricanes and climate; we plan to take up the question of how the large-scale changes reported here may affect such systems in a separate paper.

Acknowledgments

We thank two anonymous reviewers for providing helpful comments on an earlier draft of the manuscript, including the suggestion to present the results with a latitude-dependent threshold for . This work was supported by National Science Foundation Grants ATM-1064013 and EAR-1445404.

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1

It is nearly conserved in cold air and stratospheric air masses, however, where it asymptotes to P (Emanuel 2008).

2

We do not consider liquid water content in our analyses, so rt equals r* in (2).

3

These approximations eliminate several small terms involving the horizontal component of the Coriolis force and derivatives of the vertical velocity.

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