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  • View in gallery

    (a) Equilibrium temperature profiles from cloud-system-resolving simulations with various surface elevations but the same surface albedo of 0.24. Colored dots indicate the surface temperature for the corresponding case; the black dashed line marks the theoretical estimate of surface temperature obtained from our cloud-free single-column model (see text for details), with its slope based on surface elevations of 0 and 6 km. (b) Upper-tropospheric (200–400-hPa averaged) saturation equivalent potential temperatures vs subcloud (25 hPa above surface) equivalent potential temperatures for the simulations shown in (a) (red circles) and for the simulations with different surface albedos discussed in section 6 (gray markers; crosses and triangles are for surface elevations of 0 and 4 km, respectively). The black solid one-to-one line corresponds to the strict quasi-equilibrium assumption.

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    (a) Theoretical moist pseudoadiabats starting from surface elevations of 0 (solid line) and 6 km (dashed line), together with the moist pseudoadiabatic lapse rate (colors). Numbers on the pseudoadiabats indicate the height (km) above each surface, with circles shown every 2 km. (b) The same pseudoadiabats as in (a), but plotted in height coordinates, with the vertical axis indicating the height above each surface. (c) Vertical profile of the temperature difference between moist pseudoadiabats over surfaces with surface pressures of 1000 and 500 hPa, starting at surface temperatures of 5° (blue) and 15°C (red). Note the greater temperature difference in the warmer climate, particularly in the upper troposphere.

  • View in gallery

    Elevated radiative forcing when the surface is elevated from 1000 to 500 hPa with a fixed albedo of 0.24, for each term in Eq. (14). The bar labeled RADD is for the addition of the four terms, and RNET is the net radiative forcing change with all the aforementioned effects and their interactions.

  • View in gallery

    (a) Vertical profiles of the temperature change from the case with an unchanged temperature profile T(z) to the case with a new pseudoadiabat, when the surface is elevated from 1000 to 500 hPa, with a fixed surface temperature of 28° (yellow) and 20°C (green). (b) The lapse-rate effect on OLR (i.e., LWLAPSE+H2O) after the removal of the temperature difference above a certain level; for example, the value at 100 hPa corresponds to the case with the removal of all temperature differences above the 100-hPa level in the radiative flux calculation. Yellow lines correspond to the case presented in Fig. 3. Both quantities are plotted in pressure coordinates of the elevated case (i.e., surface pressure = 500 hPa), and dots represent the 26 equispaced pressure levels in the offline radiative calculations. Note that the contribution of the stratosphere–upper troposphere to the lapse-rate effect becomes stronger in a warmer climate.

  • View in gallery

    Contributions to the net TOA radiative flux change (W m−2) when the surface is elevated from the reference level (surface pressure = 1000 hPa) to the target level indicated on the vertical axis while surface temperature is fixed at the value indicated on the horizontal axis. Contributions are from (a) shortwave, (b) longwave due to changes in carbon dioxide optical path, (c) longwave due to changes in water vapor optical path at a fixed lapse rate, and (d) longwave due to lapse-rate changes. Also shown are (e) the sum of (a)–(d), and (f) the net TOA radiative flux change including all aforementioned effects and their interactions. Positive values indicate a warming effect and negative values a cooling effect. The physical meaning of each term and the method of calculation are described in section 5.

  • View in gallery

    (a) Surface temperatures and (b) low-level equivalent potential temperatures over nonelevated surfaces (red) and over surfaces with 4-km elevation (blue), for a broad range of surface albedos, all from cloud-system-resolving simulations of radiative–convective equilibrium. Note the greater surface temperature drop and the weaker elevated heating effect in warmer climates (i.e., those with lower surface albedos).

  • View in gallery

    (a),(b) Vertical profiles of (a) temperature and (b) temperature anomaly with respect to the 1.5-km case (i.e., 850-hPa surface pressure; see main text) for the simulations with surface albedo of 0.2; the legend indicates the surface elevation used for each curve. (c),(d) As in (a) and (b). respectively, but without radiatively active clouds; the temperature anomaly is with respect to the additional 1-km case.

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The Physics of Orographic Elevated Heating in Radiative–Convective Equilibrium

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  • 1 Department of Geology and Geophysics, Yale University, New Haven, Connecticut
  • | 2 Department of Earth and Planetary Science, University of California, Berkeley, and Climate and Ecosystem Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California
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Abstract

Elevated heating of the atmosphere by large plateaus has been argued to influence regional climate in Asia and other regions, but the mechanisms that cause the troposphere to equilibrate at warmer temperatures over elevated terrain are not well understood. This paper quantitatively describes the physics that controls temperatures over elevated terrain in radiative–convective equilibrium (RCE). First, a cloud-system-resolving model (CSRM) is used to simulate RCE states over surfaces with various elevations. Then, a theory for the influence of surface elevation on temperatures in RCE is presented. Together with offline radiative transfer calculations, this theory is used to quantitatively attribute the magnitude of the elevated heating effect to top-of-atmosphere radiative flux changes caused by decreases in longwave absorption, shortwave scattering, and the moist lapse rate that occur as surface pressure drops. Sensitivity functions obtained through these offline calculations suggest that elevated heating is weaker in warmer climates, and additional CSRM simulations support this hypothesis. Under certain circumstances, even the sign of the elevated heating effect can change to produce cooler temperatures at a given pressure level as the surface is lifted in RCE.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Shineng Hu, shineng.hu@yale.edu

Abstract

Elevated heating of the atmosphere by large plateaus has been argued to influence regional climate in Asia and other regions, but the mechanisms that cause the troposphere to equilibrate at warmer temperatures over elevated terrain are not well understood. This paper quantitatively describes the physics that controls temperatures over elevated terrain in radiative–convective equilibrium (RCE). First, a cloud-system-resolving model (CSRM) is used to simulate RCE states over surfaces with various elevations. Then, a theory for the influence of surface elevation on temperatures in RCE is presented. Together with offline radiative transfer calculations, this theory is used to quantitatively attribute the magnitude of the elevated heating effect to top-of-atmosphere radiative flux changes caused by decreases in longwave absorption, shortwave scattering, and the moist lapse rate that occur as surface pressure drops. Sensitivity functions obtained through these offline calculations suggest that elevated heating is weaker in warmer climates, and additional CSRM simulations support this hypothesis. Under certain circumstances, even the sign of the elevated heating effect can change to produce cooler temperatures at a given pressure level as the surface is lifted in RCE.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Shineng Hu, shineng.hu@yale.edu

1. Introduction

Atmospheric temperature at a given height above sea level is expected to be warmer over an elevated surface than over a nonelevated surface (Molnar and Emanuel 1999, hereafter ME99), a phenomenon sometimes referred to as “elevated heating” (Ye and Wu 1998; Wu and Zhang 1998; Wu et al. 2007). Elevated heating by large plateaus has been argued to drive circulations that influence climate in a broad range of locations. The Bolivian Plateau in South America (Rao and Erdogan 1989), the Colorado Plateau in North America (Tao et al. 1999), and the Tibetan Plateau and the Zagros Plateau in Asia (Staff Members of Academia Sinica 1958; Zaitchik et al. 2007) have all been claimed to provide thermal forcings for regional monsoons. Even the meridional gradient in surface height on Mars is thought to produce an annual-mean thermally direct meridional circulation by providing elevated heating (Richardson and Wilson 2002).

Elevated heating has been studied most intensely over the Tibetan Plateau, where the great height and horizontal extent of that surface (4 km and 2.5 million km2, respectively) were long held to drive the large-scale South Asian summer monsoon [Flohn 1968; Hahn and Manabe 1975; Yanai et al. 1992; Molnar et al. 1993; for a thorough review, see Yanai and Wu (2006)]. The idea that the Tibetan Plateau’s elevated heating is strong enough to make it the dominant regional heat source has been recently challenged from both observational and modeling perspectives (Chakraborty et al. 2006; Boos and Kuang 2010; Nie et al. 2010; Ma et al. 2014), but the more fundamental question of what sets the magnitude of the Tibetan Plateau’s elevated heating still remains. More generally, how does elevated topography thermally interact with the atmosphere? This question is especially important in the tropics and subtropics, where topography can set the direction of the incident prevailing wind, and its answer is crucial to understanding the evolution of regional climate on geological time scales.

Answering this question requires a fundamental understanding of the physics of elevated heating by orography, and attaining such an understanding is the central goal of this study. We build on the work of ME99, who showed that temperatures at a given pressure level of the upper troposphere are warmer over elevated surfaces than over nonelevated surfaces in the theoretical state of radiative–convective equilibrium (RCE). In an RCE state, radiative cooling of the atmosphere is balanced by the latent heating of precipitating convection, and there are no temperature or moisture tendencies produced by large-scale flow. Although RCE is never achieved in the real atmosphere, it is nevertheless a conceptually useful state when theoretical and numerical models are employed to understand the radiative and convective physics that influence climate (Emanuel et al. 1994; Held et al. 2007; Romps 2011; Popke et al. 2013; Emanuel et al. 2014; Silvers et al. 2016). Indeed, atmospheric temperatures are sometimes relaxed toward the temperature of the RCE state of a particular column of the atmosphere as a method of forcing idealized simulations of planetary-scale circulations (e.g., Lindzen and Hou 1988; Satoh 1994; Schneider 2006), providing a clean separation between large-scale dynamics and the radiative–convective physics that can be studied in the context of RCE. Here we use the RCE framework to study the mechanism of elevated heating, viewing this as a necessary first step in understanding the complete interaction between radiation, moist convection, and large-scale dynamics over elevated topography.

A variety of mechanisms have been argued to be responsible for the influence of surface elevation on the temperature of the overlying atmosphere, although these have been discussed by only a few authors. Flohn (1953) argued that radiative heating of the surface by solar radiation increases as the surface is lifted because less scattering occurs in a thinner atmosphere, while radiative emission from the surface changes comparatively little. He reasoned that this should produce a warmer atmosphere over mountains than over adjacent nonelevated terrain. ME99 argued that this view is overly simplistic because the rate of atmospheric infrared cooling can change with surface elevation. They also noted that the vertically integrated mass of infrared absorbers might be reduced over an elevated surface, leading to cooling as the local greenhouse effect is reduced. This dependence of the column-integrated mass of infrared absorbers might produce a state dependence of the elevated heating effect, exemplified by two limiting regimes (ME99): (i) the nearly transparent (in the infrared) atmosphere of cold and dry climates would produce only a weak decrease of surface temperature as surface elevation rises, so temperatures at a given pressure level of the upper troposphere warm strongly as the surface rises; and (ii) in warm and moist climates with optically thick atmospheres, surface temperatures follow a moist adiabat as the surface is lifted, eliminating nearly all of the elevated heating effect. Although ME99 did find that surface temperature fell as the surface was lifted in their RCE simulations, they did not actually assess the roles played by changes in the vertically integrated mass of infrared absorbers, in clear-sky shortwave scattering (Flohn 1953), or in other processes.

Here we extend the work of ME99 by actually quantifying the influence of various processes on the magnitude of the elevated heating effect. This turns out to be more than a minor incremental effort because we discover that the largest influence on the magnitude of the elevated heating effect is a process not previously discussed: surface temperature drops when the surface is elevated because the moist adiabatic lapse rate decreases as surface elevation rises, leading to stronger longwave cooling of the upper troposphere. This lapse-rate effect is similar to the lapse-rate feedback discussed in the climate sensitivity literature for greenhouse gas–forced climate change (e.g., Cess 1975; Colman 2003) but is caused by the pressure dependence of the moist lapse rate rather than by its temperature dependence. We also document the magnitude of several radiative mechanisms by which changes in longwave absorption by greenhouse gases influence the magnitude of elevated heating; these mechanisms have been discussed in the planetary science literature as ways in which the thickness of a planetary atmosphere can affect its equilibrium temperature (e.g., Halevy et al. 2009; Pierrehumbert 2010), but they do not seem to have been discussed in previous studies of elevated heating by orography. Our study also extends the efforts of ME99 in a methodological sense: we simulate RCE states over surfaces of different heights using a cloud-system-resolving model (CSRM) in which moist convection is represented explicitly rather than parameterized (ME99 used a single-column model with parameterized convection), and we use offline radiative transfer calculations to better understand the radiative–convective mechanisms that govern the CSRM behavior.

This paper is organized as follows. The CSRM used in this study and the experimental setup are described in section 2. We discuss the elevated heating effect simulated by this model in section 3. We derive an index and present a theory for the elevated heating effect in section 4. Offline radiative calculations are conducted in section 5 to quantitatively assess this theory. We further investigate the elevated heating effect across a wide range of climates in section 6, where we also discuss the possibility that the elevated heating effect can change sign to become elevated cooling in certain circumstances. We discuss implications and possible directions for future work in section 7.

2. Numerical model details

We use a CSRM called the System for Atmospheric Modeling (SAM), version 6.3, which solves the anelastic equations of motion with prognostic liquid water moist static energy, total nonprecipitating water, and total precipitating water (Khairoutdinov and Randall 2003). We use a horizontal domain size of 96 km × 96 km with 3-km horizontal resolution and 64 vertical levels. This domain has approximately the same size as a single column of a typical global climate model (GCM), so our integrations can be viewed as representative of the state that would be achieved by a single column of a GCM in the absence of any grid-scale horizontal flow between GCM grid cells. Rotation is not included in the equations of motion. Insolation is set to the annual- and diurnal-mean value at 30°N on Earth (~364 W m−2). We use the radiative transfer scheme from the NCAR Community Climate Model (CCM3; Kiehl et al. 1998). The ozone profile is fixed with respect to the surface, and tropospheric temperatures are relatively insensitive to its changes: for the case with a surface albedo of 0.24 and a surface pressure of 500 hPa, we shifted the ozone profile downward by about 6 km (roughly the height of a 500-hPa surface) and found that equilibrium surface temperature only dropped by half a degree in response.

The lower boundary of the model is an idealized representation of a land surface having a heat capacity equivalent to that of 1 m of water. Surface temperature is interactively computed based on a surface energy balance. Surface fluxes are based on bulk aerodynamic formulas with constant surface exchange coefficients and a constant surface wind speed of 7 m s−1. To represent the reduced evaporation that typically occurs over land compared to ocean, we multiply the latent heat flux by a constant fraction β = 0.5, similar to what was done in ME99. In reality, local feedbacks involving soil moisture and surface relative humidity changes might exist but are not explicitly considered in our idealized simulations. However, we did test model sensitivity to the surface evaporation fraction: substantial free-tropospheric cooling occurs when β is reduced below 0.25, as expected for a very dry climate, but there is little sensitivity to β for β ≥ 0.25.

In our CSRM simulations, we vary surface pressure, or equivalently surface elevation, at a prescribed surface albedo and compare the tropospheric temperatures after the system reaches an RCE state. That is, we conduct one simulation for each combination of surface pressure and surface albedo, presenting horizontal and time averages over the last 300 days when the system is in the equilibrium state. We refer to integrations by both surface height and surface pressure, with approximate heights of 0, 1, 2, 3, 4, and 6 km having surface pressures of, respectively, 1008, 890, 790, 710, 600, and 500 hPa. Further description of the experimental setup is provided in the relevant sections below.

3. Elevated heating in a CSRM

In the first set of experiments, we set surface albedo to 0.24 (near the observed mean for the Tibetan Plateau) and vary surface pressure from 1008 to 500 hPa by roughly 100-hPa increments, as mentioned above. We find that elevated heating, previously found in the RCE states of a single-column model (ME99), indeed exists in these CSRM simulations that explicitly represent three-dimensional moist convective processes (Fig. 1a). Specifically, surface temperature decreases with surface height, but at a rate of 2.2°C km−1 that is much slower than typical moist adiabatic lapse rates (6°–10°C km−1), consistent with the estimate of ME99. As a result, the troposphere is warmer over an elevated surface by as much as 20°C for a 5-km change in surface height, when compared at the same pressure level.

Fig. 1.
Fig. 1.

(a) Equilibrium temperature profiles from cloud-system-resolving simulations with various surface elevations but the same surface albedo of 0.24. Colored dots indicate the surface temperature for the corresponding case; the black dashed line marks the theoretical estimate of surface temperature obtained from our cloud-free single-column model (see text for details), with its slope based on surface elevations of 0 and 6 km. (b) Upper-tropospheric (200–400-hPa averaged) saturation equivalent potential temperatures vs subcloud (25 hPa above surface) equivalent potential temperatures for the simulations shown in (a) (red circles) and for the simulations with different surface albedos discussed in section 6 (gray markers; crosses and triangles are for surface elevations of 0 and 4 km, respectively). The black solid one-to-one line corresponds to the strict quasi-equilibrium assumption.

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0312.1

In a convecting atmosphere, upper-level temperature covaries with subcloud equivalent potential temperature θeb better than it does with surface temperature; this is a central tenet of the theory of convective quasi equilibrium (CQE; Emanuel et al. 1994). This can be expressed as
e1
where δ represents a variation in time or space, and is the saturation value of the equivalent potential temperature of the convecting layer ( depends only on temperature and thus provides an appropriately rescaled measure of temperature; also, for our purposes, equivalent potential temperature could be replaced by moist static energy or moist entropy). When variations in θeb and are equal rather than simply proportional, the relationship is referred to as strict quasi equilibrium (SQE). The CQE framework and the SQE assumption have been used extensively in studies of large-scale tropical and monsoon dynamics (Emanuel et al. 1994; Brown and Bretherton 1997; Neelin and Zeng 2000; Nie et al. 2010). Here we find that SQE holds when surface elevation is varied in simulations of RCE. In particular, Fig. 1b shows θeb plotted against averaged over an upper-tropospheric layer (200–400 hPa) for the same simulations plotted in Fig. 1a and for two additional sets of simulations where surface elevation is fixed at 0 km and then at 4 km while surface albedo is varied from 0.22 to 0.40. The points fall very close to the one-to-one line, consistent with the SQE hypothesis. The elevated heating effect can thus be characterized by the effect of surface elevation on θeb or on upper-tropospheric temperature: the two serve as nearly equivalent metrics. This provides a more convenient and insightful way to use surface air properties to think about the elevated heating effect: one does not need to compare the rate of surface temperature decrease with the moist adiabatic lapse rate but only assess whether θeb increases as surface elevation rises. As we discuss in the next section, these two views are equivalent. More generally, one might ask what controls the quantitative sensitivity of θeb to surface elevation. Is this sensitivity always positive, or might θeb decrease and the upper-troposphere cool as the surface is lifted?

4. Theory

a. Derivation of an elevated heating index

To answer these questions, we first define an elevated heating index (EHI), which is simply the sensitivity of θeb to surface elevation zs:
e2
In our model and in an atmosphere that can be described by a CQE framework, this index also represents the sensitivity of upper-tropospheric temperature to zs, as discussed above. Now we express the EHI in terms of other variables by first approximating the subcloud θeb as the surface air equivalent potential temperature θes:
e3
Here, qs is surface air specific humidity, Rd is the gas constant of dry air, cpd is the specific heat at constant pressure of dry air, Lυ is the latent heat of evaporation, p0 is a reference pressure (here taken to be 1000 hPa), and Ts is surface air temperature. Taking the logarithm of each side of Eq. (3) and then differentiating with respect to surface elevation, we obtain
e4
Specific humidity is related to vapor pressure by
e5
where ε is the ratio of the gas constants for dry air and water vapor, Hs is surface relative humidity (RH), and is the saturation vapor pressure of surface air, which depends only on Ts. Assuming that Hs does not change much with surface elevation (Sherwood et al. 2010), which is consistent with our simulations (not shown), changes in specific humidity can thus be due to surface pressure changes or saturation vapor pressure changes. Combining Eqs. (4) and (5), we find
e6
where part of the last term can be expressed as
e7
using hydrostatic balance and the ideal gas law. Substituting Eq. (7) into Eq. (6), we then find
e8
where we dropped the 1/Ts term in square brackets in Eq. (6) because it is more than an order of magnitude smaller than the term involving . Based on Eq. (8), we obtain the elevated heating index (defined as eb/dzs):
e9
which can be simplified as
e10
with A a dimensionless number, defined as
e11
The s subscript denotes a surface air property, but here and in subsequent offline radiative calculations, we neglect the air–ground temperature difference. The error introduced by this assumption is expected to be small; in our CSRM simulations, the change in air–ground temperature difference produced by surface lifting is about 10% of the change in surface temperature.
The coefficient A is positive definite and state dependent, being larger over high-elevation surfaces (i.e., larger θeb/Ts) and larger in warmer and moister climates. For example, A equals 2.1 for Ts = 15°C and ps = 1000 hPa and increases to 4.0 either when Ts increases to 32°C or ps decreases to 500 hPa. The variable is
e12
which has a similar expression to, and here will thus be interpreted as, the moist adiabatic lapse rate evaluated at surface conditions. The only difference with the standard moist lapse rate is the use of specific humidity qs instead of saturation specific humidity , but this has a relatively small effect on . More precisely, is better interpreted as the moist adiabatic lapse rate at the lifted condensation level (LCL) where the air parcel becomes saturated; in this case, the temperature Ts should be replaced with the temperature at the LCL and the EHI represents the sensitivity of θe at the LCL to surface elevation.

Equation (10) is the central result of this subsection, and it intuitively but quantitatively shows the dependence of EHI on the relative magnitudes of the moist adiabatic lapse rate and dTs/dzs: the upper-tropospheric temperature will be higher over an elevated surface than over a nonelevated surface only if the surface temperature Ts decreases, as zs rises, more slowly than temperature along a moist adiabat (e.g., Fig. 1a). As is discussed above, the term A in Eq. (10) is a proportionality constant that gives the quantitative rate at which θeb changes with surface height, and it modulates the magnitude of the elevated heating effect simply because here EHI is defined using θeb; if we instead define EHI using upper-tropospheric temperature, the term A will disappear. The terms that control the sign and magnitude of the elevated heating effect are thus the moist adiabatic lapse rate and dTs/dzs. The former is easy to estimate given a background climate state, but what controls the sign and magnitude of dTs/dzs?

b. Two complementary perspectives on elevated heating

When considering how tropospheric temperatures in general respond to surface lifting, one could start by assuming the surface initially either (i) maintains the same temperature it had in the nonelevated case or (ii) decreases its temperature by following the same pseudoadiabat, with respect to sea level, that existed in the nonelevated case. In either case, surface and tropospheric temperatures will subsequently adjust to a new RCE state, and the details of this adjustment help us understand the mechanisms that set dTs/dzs. The two cases correspond to the two extremes depicted in ME99 and will be referred to as the (i) optically thin and (ii) optically thick limits, respectively. In the first limiting scenario, the atmosphere does not interact with radiation, so surface temperature is determined only by insolation, surface albedo, and surface emissivity (i.e., it does not change with surface elevation). In the second case, the atmosphere is optically thick and the RCE moist adiabat remains independent of surface elevation; longwave emission from the lower troposphere does not penetrate to the upper troposphere, so surface lifting has no effect on upper-tropospheric radiative balance. We assume the actual troposphere lies between these limiting cases so that temperatures will evolve toward a new RCE state after the initial lifting.

If Ts was preserved during lifting [case (i)], the initial state will be too warm compared to the final RCE state, and TOA radiative flux changes produce cooling. As stated in the introduction, these radiative flux changes might be caused by reductions in the column-integrated mass of infrared absorbers (ME99), but the contribution of this and other changes to the net radiative flux change has not been quantified.

If Ts was decreased during lifting along a pseudoadiabat [case (ii)], the initial state will be too cool and subsequent radiative changes will produce warming. This is because the warm lower troposphere will have been replaced by a cooler lifted surface so that, if the atmosphere is not strictly in the optically thick limit, OLR will decrease and thus warm the column. This method thus produces “elevated heating” after the initial lifting, providing a useful way of thinking about the phenomenon. However, changes in humidity, the column-integrated mass of dry air, and other atmospheric properties will complicate the response.

As we will show, these two approaches must produce the same final RCE state (assuming multiple equilibria do not exist). We will focus on the first approach (i.e., conducting the initial lifting following the optically thin limit) because it allows us to more easily assess the contributions from different physical mechanisms, including some not discussed by previous studies (Flohn 1953; ME99). However, we will also discuss insights from the second approach (the optically thick limit) below.

c. Surface temperature dependence on surface height

We now present a theory for the value of dTs/dzs, a quantity sometimes termed the terrestrial lapse rate (Forest et al. 1995; Meyer 2007), and explain how the effect of surface elevation on top-of-atmosphere (TOA) radiative fluxes sets the magnitude, and even the sign, of elevated heating. We use a traditional climate sensitivity framework (Cess et al. 1990; Held and Soden 2000 and references therein),
e13
where R is the net radiative flux at TOA and is the net climate feedback parameter of the radiative–convective system, representing the sensitivity of TOA radiation to surface temperature changes. In a traditional climate sensitivity calculation (e.g., Cess et al. 1990), such as for a doubling of CO2, the radiative forcing is imposed, so R can be viewed as the external forcing. Here there is another step in the chain of causation, since R is set by the radiative changes that occur as a consequence of the surface lifting. Although the changes in R and Ts that occur in response to a surface lifting occur simultaneously, we conceptually partition them into two parts: first, the surface is lifted without any change in surface temperature and both radiation and moist convection adjust to the new surface elevation; then, surface temperature adjusts to the altered net TOA radiation. These two conceptual parts of the response are represented by the numerator and denominator of Eq. (13), respectively, and we now discuss them in sequence.
We decompose the numerator of the right-hand side of Eq. (13) into shortwave and longwave components and further separate the latter into changes associated with CO2, H2O, and lapse-rate effects. We want to emphasize again that surface temperature is fixed as the surface is lifted, but for brevity we drop the subscript Ts on partial derivatives below:
e14
In the second line of Eq. (14), τ represents the optical depth of a given constituent, and T represents tropospheric temperature that is controlled by the moist adiabatic lapse rate given a fixed surface temperature. The four terms on the right-hand side of Eq. (14) represent the effect of surface elevation on, respectively, (i) incoming shortwave radiation (ISR) due to changes in clear-sky scattering and absorption by air (labeled in the third line as SW), (ii) outgoing longwave radiation (OLR) due to changes in the optical depth of carbon dioxide (LWCO2), (iii) OLR due to changes in the amount of longwave absorption by a given mass of water [e.g., the pressure broadening of water vapor’s absorption lines (LWH2O)], and (iv) OLR due to changes in both the atmospheric lapse rate and the associated vapor pressure needed to keep a fixed RH profile (LWLAPSE+H2O).

The first two terms are relatively straightforward to understand. The third water vapor term might seem counterintuitive because it assumes a fixed mass of total precipitable water due to use of the same profiles of T(z), RH(z), and thus es(z); it represents changes in absorption due only to pressure effects. The last (fourth) term includes the effects of changes in tropospheric temperature as well as the changes in water vapor that accompany the lapse-rate changes, assuming fixed relative humidity. Cloud radiative effects are highly uncertain and not included in Eq. (14) but will be discussed later. To be clear, these four terms represent the effect of changes in surface height on TOA radiation at fixed surface temperature; the resulting change in surface temperature is then found using Eq. (13) as in a traditional climate sensitivity calculation.

The denominator of Eq. (13) can be determined in multiple ways. First, we double CO2 concentrations in one of our CSRM simulations that has a surface albedo of 0.24 and a surface pressure of 500 hPa and estimate the climate feedback λ from the CO2 doubling–induced abrupt changes in TOA radiative fluxes and the equilibrium surface temperature changes. Although the value of λ might be expected to depend on the details of how R is perturbed, we find good quantitative agreement between values of λ obtained through different radiative forcings. In the next section, we present an alternate estimate of λ calculated for a change in the TOA shortwave induced by varying surface albedo; this turns out to be nearly identical to that produced by CO2 doubling. We emphasize that here λ is an equilibrium climate feedback parameter; the global-mean transient climate sensitivity has been shown to vary in time as regions with different surface heat capacities warm at different rates, but even that complication can be explained by assuming climate feedbacks that are linear and constant in time for a particular region (Armour et al. 2013). The value of λ for our simple RCE system additionally seems to have little sensitivity to the nature of R, although we have not sampled very dry states or a large range of basic state temperatures.

5. Mechanistic attribution with offline radiative calculations

Now we use offline radiative calculations to estimate each term in Eq. (14), thereby understanding what sets the magnitude of the elevated heating effect. We use a single-column radiative–convective toolkit called the Climate Modeling and Diagnostics Toolkit (CliMT; Caballero 2012) to quantitatively attribute the net TOA radiative flux change to the processes represented by each term. Like other single-column models, CliMT has no horizontal degrees of freedom; it is vertically discretized into 26 equispaced pressure levels. We take the approach of imposing vertical profiles of temperature, humidity, and CO2 in the model, then use CliMT to conduct offline radiative transfer calculations to obtain TOA radiative fluxes. To ease comparison with our CSRM results, we chose the same NCAR CCM3 radiative scheme for CliMT as used in our CSRM (although some details of that scheme’s implementation may differ).

We estimate the various partial derivatives in Eq. (14) based on TOA radiative fluxes from a large ensemble of CliMT simulations with different surface temperatures and surface elevations. We start with a set of simulations having nonelevated surfaces (i.e., surface pressure = pref = 1000 hPa) and vertical temperature profiles that are moist pseudoadiabatic from the specified surface temperature up to the tropopause, defined as the level at which the pseudoadiabat reaches −100°C, with a constant stratospheric temperature of −100°C prescribed above. We used a moist pseudoadiabat starting from the surface instead of from the LCL for the sake of simplicity and consistency with our derivation of the EHI, but we expect similar results if a dry adiabat is used below the LCL, as long as the LCL is not very high. The relative humidity profile mimics that in the CSRM simulations and is fixed for all climate sensitivity calculations here: it has a surface value of 69%, local maxima of 87% and 90% at altitudes of 1 and 15 km above the surface, respectively, a local minimum of 60% at 8 km, is zero above 21 km, and is piecewise linear in between. There are no cloud–radiative interactions. Surface albedo is tuned for each surface temperature to obtain an RCE state (i.e., one in which the net TOA radiative flux is zero). We refer to this as the reference state, with one reference state existing for each value of surface temperature examined. We lift the surface until its pressure drops to ptarget, then calculate how the TOA radiative flux R changes as a result of that lifting while Ts is held constant [this gives in Eq. (13), and it is the climate feedback parameter λ that determines how Ts responds to this change in R after equilibration]. This is done for many combinations of Ts and ptarget (listed in section 6); for each combination, we perform several versions of this calculation to find the various total and partial derivatives in Eq. (14):

  1. Estimating the first term in Eq. (14), , is straightforward: it is simply the net ISR change at TOA, relative to the reference state, when the surface is elevated while Ts and the CO2 mixing ratio are fixed but other quantities are allowed to change. In particular, the lapse rate is allowed to change (Fig. 2a shows the pressure dependence of the moist lapse rate) and vapor pressure is modified to maintain fixed RH(z). Changes in clear-sky shortwave absorption by water vapor are included in this estimate but are typically about a factor of 4 smaller than the changes due to scattering by dry air.
  2. The second term, which represents the influence of changes in CO2 optical depth on OLR, is estimated by comparing OLR in two configurations that differ only in their CO2 concentrations. Each has the same Ts and T(z) (with z indicating the height above each surface) as the reference state and uses a lifted surface (with surface pressure ptarget). One of these configurations uses the same CO2 mixing ratio as the reference state, while the mixing ratio in the other is increased by a factor of ( pref/ptarget)2 to obtain the same CO2 optical path as the reference state. Note that the column-integrated mass of CO2 changes by pref/ptarget, but the optical path of CO2 changes quadratically because of the pressure broadening of absorption lines (Pierrehumbert 2010). Since water vapor absorption features are also broadened by pressure, we multiplied the vapor pressure in both configurations by a scale factor in order to hold the water vapor optical path constant. We determined this scale factor by varying it iteratively until the OLR difference with the reference state was less than 0.001 W m−2; the factor turns out to be slightly greater than unity.
  3. The third term represents the influence of modified water vapor absorption while CO2 optical path, Ts, T(z), and RH(z) are all held constant. This is estimated by comparing OLR for two cases, each with lifted surfaces and with the CO2 scaled by ( pref/ptarget)2 to obtain the same CO2 optical path as the reference state. In one case, the vapor pressure is set to be the same as in the reference case, while in the other it is scaled by the same factor described in (ii) above to compensate for changes in pressure broadening. Alternatively, the third term can also be estimated by comparing two cases with different surface pressures but with the same profiles of Ts, T(z), RH(z), and CO2 optical depth [i.e., scaled by ( pref/ptarget)2]. These two approaches are equivalent and are simply different representations of the derivatives in the third term.
  4. The fourth term, which represents the effect of changes in lapse rate and accompanying changes in vapor pressure, is estimated by comparing OLR in two cases, each with lifted surfaces with the same Ts and with CO2 scaled by ( pref/ptarget)2 to obtain the same CO2 optical path as the reference state. One case uses the same T(z) and vapor pressure as the reference state, while in the other T(z) is modified so that lapse rates are moist adiabatic at the modified surface pressure; vapor pressure is also changed to maintain constant RH(z).
Fig. 2.
Fig. 2.

(a) Theoretical moist pseudoadiabats starting from surface elevations of 0 (solid line) and 6 km (dashed line), together with the moist pseudoadiabatic lapse rate (colors). Numbers on the pseudoadiabats indicate the height (km) above each surface, with circles shown every 2 km. (b) The same pseudoadiabats as in (a), but plotted in height coordinates, with the vertical axis indicating the height above each surface. (c) Vertical profile of the temperature difference between moist pseudoadiabats over surfaces with surface pressures of 1000 and 500 hPa, starting at surface temperatures of 5° (blue) and 15°C (red). Note the greater temperature difference in the warmer climate, particularly in the upper troposphere.

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0312.1

To directly compare with the conditions used in our main set of CSRM experiments, we now show in Fig. 3 our offline estimates of each term in Eq. (14) for a change in ps from 1000 to 500 hPa and a surface albedo of 0.24, which has a corresponding RCE surface temperature of about 28°C for the nonelevated surface. Using the offline calculations described in items (i) and (ii) above, we find that the increase in absorbed shortwave radiation due to reduced clear-sky scattering is nearly equal to the increase in outgoing longwave radiation due to the reduction in CO2 optical path [i.e., SW ≈ LWCO2 in Eq. (14); note that CO2 optical depth increases quadratically with ps, rather than linearly, because of pressure broadening of its absorption lines]. The water vapor line breadth term [LWH2O, the calculation of which is described in item (iii) above] has a cooling effect of similar magnitude to each of the previous two terms and arises from the fact that a given vertical profile of water vapor pressure has a smaller optical depth when surface pressure is reduced. The largest term LWLAPSE+H2O, as far as we know, has not been considered by previous studies of elevated heating and so will now be discussed in detail.

Fig. 3.
Fig. 3.

Elevated radiative forcing when the surface is elevated from 1000 to 500 hPa with a fixed albedo of 0.24, for each term in Eq. (14). The bar labeled RADD is for the addition of the four terms, and RNET is the net radiative forcing change with all the aforementioned effects and their interactions.

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0312.1

The LWLAPSE+H2O term in Eq. (14) represents enhanced longwave cooling that results from the reduction in moist adiabatic lapse rate that occurs as ps drops. It can be understood by considering what happens to R as the surface is elevated with surface temperature and relative humidity fixed. Since vapor pressure depends only on temperature and since ps decreases, the water vapor mixing ratio increases and thus the moist adiabatic lapse rate is reduced (Fig. 2a). That is, as ps decreases there is less dry air to be heated by condensation of a given mass of water. As a result, air temperature above the elevated surface will be warmer than air temperature the same distance above the nonelevated surface (e.g., Fig. 2b, where height is referenced in kilometers relative to each surface). The vertically integrated effect of this dependence of the moist adiabatic lapse rate on surface pressure produces a much warmer troposphere above the elevated surface (again, at a given altitude relative to each surface). For surface temperatures of 5°–15°C, a reduction of surface pressure from 1000 to 500 hPa produces a temperature contrast as large as 10°–30°C at altitudes of 10–15 km (Fig. 2c).

This increase of air temperature at a given altitude above the surface increases OLR, cooling the column. Some of this cooling is offset by the reduction in OLR that occurs as water vapor pressure increases in the warmer upper troposphere, where relative humidity has been argued to stay roughly constant as the lapse-rate changes (Sherwood et al. 2010). This lapse-rate effect, including the associated water vapor changes, is analogous to that which occurs as CO2 is increased over a nonelevated surface (Soden and Held 2006). As in that well-known scenario, our calculations show that the net effect of the change in lapse rate is an increase in OLR with surface elevation (i.e., the temperature effect dominates). For the particular case of lifting the surface from 1000 to 500 hPa, the temperature part of the lapse-rate effect accounts for −48.1 W m−2 while the associated water vapor effect is +36.7 W m−2, yielding a total lapse-rate effect of −11.4 W m−2. This net lapse-rate effect is larger than any of the other terms discussed above or mentioned in ME99, and, unlike the other terms, it involves both moist convective and radiative processes rather than radiation alone. One could categorize the terms in Eq. (14) differently and add together all the contributions from greenhouse gas changes (LWCO2, LWH2O, and the water vapor component of LWLAPSE+H2O), yielding a positive value that would cancel much but not all of the temperature component of LWLAPSE+H2O. Note that, as the atmospheric column cools in response to the TOA radiative changes, its pseudoadiabatic lapse rate will adjust accordingly; our framework does not impose an artificially low lapse rate over elevated surfaces.

For this particular case of lifting the surface from 1000 to 500 hPa with a surface temperature of 28°C, we further investigate which levels the lapse-rate effect comes from using offline radiative calculations (yellow lines in Fig. 4). Because of the lapse-rate change, the whole troposphere is much warmer, and this temperature difference extends to the lower stratosphere. Note that the upper-level warming is realized by a lifted “tropopause” in offline radiative calculations, mimicking the fact that, in the CSRM simulations, the warming always extends to the lower stratosphere before it gradually vanishes with height in the presence of the basic-state ozone heating (not shown). Next we eliminate the temperature difference above a certain level in our offline calculation and study its effect on LWLAPSE+H2O (Fig. 4b). We find that about 60% of the lapse-rate effect comes from the lower stratosphere–upper troposphere (e.g., above 100 hPa). However, the contribution from the lower stratosphere–upper troposphere shrinks in colder and drier climates. For example, when for a surface temperature of 20°C, the elimination of air temperature changes above 150 hPa has little effect on the magnitude of LWLAPSE+H2O, and the contribution from the mid- and lower troposphere dominates (Fig. 4b). Note that the nonmonotonic changes with height in Fig. 4b occur because of nonlinear radiative interactions among different vertical levels.

Fig. 4.
Fig. 4.

(a) Vertical profiles of the temperature change from the case with an unchanged temperature profile T(z) to the case with a new pseudoadiabat, when the surface is elevated from 1000 to 500 hPa, with a fixed surface temperature of 28° (yellow) and 20°C (green). (b) The lapse-rate effect on OLR (i.e., LWLAPSE+H2O) after the removal of the temperature difference above a certain level; for example, the value at 100 hPa corresponds to the case with the removal of all temperature differences above the 100-hPa level in the radiative flux calculation. Yellow lines correspond to the case presented in Fig. 3. Both quantities are plotted in pressure coordinates of the elevated case (i.e., surface pressure = 500 hPa), and dots represent the 26 equispaced pressure levels in the offline radiative calculations. Note that the contribution of the stratosphere–upper troposphere to the lapse-rate effect becomes stronger in a warmer climate.

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0312.1

The sum of all four of these individual effects [(i)–(iv) above] is −20.9 W m−2 for our surface lifting from 1000 to 500 hPa. Nonlinearities are slight: simulation in CliMT of the net change in R produced by the same surface lifting while Ts is fixed has a magnitude that is only about 1 W m−2 smaller (cf. black and gray bars in Fig. 3).

To predict the change in surface temperature caused by the surface lifting, we combine this net change in R with the climate feedback parameter λ. As mentioned in the previous section, a doubled-CO2 CSRM simulation yielded an estimate of λ = 2.5 W m−2 K−1. Although one might think that the climate feedback on a CO2 doubling could differ substantially from the feedback on a surface lifting, it is important to remember that a change in surface elevation alters surface temperature partly through a change in CO2 optical depth. To test if the climate feedback parameter is sensitive to the details of how the TOA radiative fluxes are perturbed, we separately estimated λ in CliMT using two different approaches with the same background state as in the CSRM (surface albedo = 0.24; surface pressure = 500 hPa). In the first approach, we doubled CO2 concentrations just like we did in the CSRM, while in the second approach we examined the surface temperature change caused by a change in surface albedo. The latter provides an estimate of λ based on a shortwave rather than a longwave forcing. We obtained a nearly identical value of λ for these two independent approaches using CliMT: 2.0 W m−2. The modest differences in λ obtained from the CSRM and from CliMT are expected, given their totally different treatments of convection and the suppressed cloud–radiation interaction in CliMT.

Given this value of λ (i.e., 2.5 W m−2 K−1) the net change in R of −20.9 W m−2 in response to a surface lifting from 1000 to 500 hPa is expected to cool the surface by about 8.4 K. This explains about 65% of the 13-K surface temperature drop found in our CSRM (Fig. 1a, where the black dashed line represents our linearized estimate). The remaining one-third of the temperature drop simulated in the CSRM might come from the full complexity of those simulations: for example, cloud radiative effects, relative humidity changes, deviation of temperatures from moist adiabatic, air–ground temperature difference changes, and radiative transfer details that differ from those of our offline calculations. Note that if we use the CliMT estimate of λ, this climate sensitivity framework can precisely predict the surface temperature dependence on surface elevation in the idealized offline calculations with CliMT (i.e., no cloud radiative effect, fixed relative humidity profile, temperatures following moist adiabats, and no air–ground temperature difference).

We now use offline radiative calculations to illustrate the equivalence of the two approaches described in section 4b. We again choose a nonelevated surface with albedo of 0.24 and temperature of 28°C and then elevate this surface to 500 hPa. In one case, we fix surface temperature during lifting (Ts,ref = 28°C), and in the other, we set the temperature of the elevated surface to the air temperature that existed at 500 hPa in the nonelevated case (Ts,ref = 5°C). In both cases, a moist pseudoadiabat (with a minimum of −100°C) and a fixed relative humidity profile are assumed. We then calculate the TOA radiative flux change ∆RTOA and estimate the subsequent surface temperature change, ∆Ts,est = ∆RTOA/λ, using the climate feedback parameter λ (~2.0 W m−2 K−1). In both cases, the estimated equilibrium surface temperature Ts,est agrees well with the final equilibrium surface temperature Ts,eq simulated by the full single-column model (Table 1). A single equilibrium solution is found for Ts,eq with no evidence for multiple equilibria. The small discrepancy between the estimated and final equilibrium surface temperature mainly results from the varying climate feedback parameter in different climate states.

Table 1.

Comparison of the two approaches to calculating orographic elevated heating. Offline calculations are performed for the case with surface albedo of 0.24 and with a surface lifted from 1000 to 500 hPa. The equilibrium surface temperature for the nonelevated case is about 28°C. The value Ts,ref represents the reference surface temperature assumed in either approach after the surface is elevated; ∆RTOA represents the TOA radiative flux change after the surface lifting, and it can then be used to estimate surface temperature change ∆Ts,est using climate feedback; Ts,est is the estimated equilibrium surface temperature (i.e., Ts,est = Ts,ref + ∆Ts,est); and Ts,eq represents the final equilibrium surface temperature simulated by the full single-column model (a single equilibrium solution is found for Ts,eq with no evidence for multiple equilibria). Details are discussed at the end of section 5.

Table 1.

6. Elevated heating across a wide range of climates

We now use our offline radiative–convective calculations together with additional CSRM simulations to characterize the elevated heating effect over a broad range of surface temperatures and surface elevation changes. We begin by repeating the complete set of offline radiative–convective calculations described in the previous section for every Ts between 0° and 40°C, with an interval of 1°C, and for every target surface pressure between 500 and 990 hPa, with an interval of 10 hPa. This allows the magnitude of each term in Eq. (14) to be plotted as a function of Ts and target surface pressure (Figs. 5a–d). For every Ts and ptarget combination, we also calculate the net change in R that includes all effects and their interactions [i.e., the surface is lifted and the lapse rate is allowed to change while Ts, CO2 mixing ratio, and RH(z) are fixed]. The sum of all individual terms [(i)–(iv) above] is very nearly equal to this net change in R (cf. Figs. 5e and 5f; also see Fig. 3), which shows that the various effects are additive with small nonlinearities; this also lends confidence to our methodology.

Fig. 5.
Fig. 5.

Contributions to the net TOA radiative flux change (W m−2) when the surface is elevated from the reference level (surface pressure = 1000 hPa) to the target level indicated on the vertical axis while surface temperature is fixed at the value indicated on the horizontal axis. Contributions are from (a) shortwave, (b) longwave due to changes in carbon dioxide optical path, (c) longwave due to changes in water vapor optical path at a fixed lapse rate, and (d) longwave due to lapse-rate changes. Also shown are (e) the sum of (a)–(d), and (f) the net TOA radiative flux change including all aforementioned effects and their interactions. Positive values indicate a warming effect and negative values a cooling effect. The physical meaning of each term and the method of calculation are described in section 5.

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0312.1

The results show that the net change in shortwave has an opposite sign but similar magnitude to the change in OLR that is caused by the modified CO2 optical path. The shortwave term increases with surface temperature because of the larger ISR associated with the smaller surface albedo required to achieve a warmer RCE reference state (Fig. 5a). It is thus important to remember that the surface temperature dependence of each term shown in Fig. 5 may differ if surface temperature is altered by a forcing other than surface albedo; for example, the shortwave term may not increase in magnitude if the climate state is warmed by an increase in greenhouse gas concentrations.

The change in OLR due only to pressure-induced changes in water vapor absorption has the same sign and roughly the same magnitude as the CO2-driven OLR changes. These two terms have little sensitivity to Ts and scale near linearly with the change in surface pressure (Figs. 5b,c).

The fourth term, which includes all effects of changes in lapse rate, is relatively weak in cold climates but is much stronger than any of the other terms for large changes in surface pressures in warm climates (Fig. 5d). Its sensitivity to Ts is much larger than, and of opposite sign to, that of the shortwave change (Figs. 5a,d). We emphasize again that the lapse-rate term includes the direct effect of temperature (e.g., OLR increases as the surface is lifted because the upper troposphere warms as the moist lapse rate decreases) as well as the compensating effect of moisture (e.g., a reduced lapse rate and fixed RH require an increase in upper-tropospheric vapor pressure and thus a reduction in OLR). Unlike the shortwave term, the temperature dependence of the lapse-rate term is expected to hold regardless of what causes the change in climate state, as long as the vertical temperature profile is strongly constrained by moist convection.

The combined effects of these four terms, , is negative and increases in magnitude as the climate warms (Figs. 5e,f), causing an increase in the magnitude of dTs/dzs given a constant climate feedback λ. However, the actual dTs/dzs change will be affected by the state dependence of λ (e.g., dependence on background temperature or surface elevation), the value of which involves large uncertainty due to cloud–radiative feedbacks and which might furthermore be model dependent. This is an important topic in and of itself, but we leave it for future investigation. At the same time, the moist lapse rate is smaller in warmer climates (Fig. 2a), which directly controls the last term on the right-hand side of Eq. (10). Both factors (i.e., a more negative dTs/dzs and a less positive Γms) work together to decrease the EHI. The exact value of EHI in our definition is also dependent on the coefficient A in Eq. (11), but, as we will show later, the state dependence of the EHI is dominated by changes in .

Since it is clear that is dominated by the lapse-rate term in the warmest climates (Fig. 5d), we now discuss the physics and implications of this effect in greater detail. The OLR change can be linearized as 4σT3ΔT, with σ the Stefan–Boltzmann constant, T the effective emission temperature, and ΔT the change in temperature at the emission level due to the lapse-rate change. As climate warms, the lapse-rate change ΔT that occurs as the surface is lifted becomes larger in the upper troposphere–lower stratosphere (e.g., Fig. 4a). This increases the OLR change, making dTs/dzs more negative in warmer climates and reducing the magnitude of elevated heating (Figs. 4b, 5d).

To confirm the hypothesis that elevated heating weakens in warmer climates, we conduct additional tests using the cloud-system-resolving model. Because of computational resource limits, we are not able to explore the wide range of surface temperatures and elevations examined in the offline radiative calculations. Instead, we prescribe surface albedos that range from 0.22 to 0.40 to control the background climate state, and we elevate the surface from 0 km (i.e., 1000-hPa surface pressure) to 4 km (600-hPa surface pressure). We find that the decrease in Ts that occurs as the surface is lifted is larger at lower albedos (Fig. 6a). Also, we find that a given surface lifting produces a smaller increase in in warmer climates, which confirms that elevated heating is indeed reduced in warmer climates in our CSRM (Fig. 6b). As for the first set of simulations described in section 3, SQE holds for these simulations, and thus is a good indicator of upper-tropospheric temperature (Fig. 1b). These additional CSRM simulations thus confirm our hypothesis, motivated by our theory and offline calculations, that elevated heating is weaker in warmer climates.

Fig. 6.
Fig. 6.

(a) Surface temperatures and (b) low-level equivalent potential temperatures over nonelevated surfaces (red) and over surfaces with 4-km elevation (blue), for a broad range of surface albedos, all from cloud-system-resolving simulations of radiative–convective equilibrium. Note the greater surface temperature drop and the weaker elevated heating effect in warmer climates (i.e., those with lower surface albedos).

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0312.1

Can the elevated heating effect approach zero or even change sign to become elevated cooling? As shown by Eq. (10), the sign of the EHI is determined by the relative magnitudes of the decrease in surface temperature dTs/dzs and the moist adiabatic lapse rate . As illustrated in Fig. 6a, the former term increases in magnitude and the latter term decreases in warmer climates. Therefore, if the magnitude of dTs/dzs exceeds that of , elevated cooling will occur.

To achieve a warmer climate state, we set the surface albedo to 0.2 in the CSRM, which is lower than any of the values shown in Fig. 6. At this surface albedo, the system with a nonelevated surface reaches a runaway greenhouse regime because the net downward solar radiation exceeds the upper limit of OLR the system can emit (Ingersoll 1969). A runaway greenhouse state is also achieved for surface elevations of 1 km (i.e., 890-hPa surface pressure) at this albedo. However, when we elevate the surface to 1.5 km (i.e., 850-hPa surface pressure), the system achieves an RCE state. Further increasing the surface elevation to 2 km (i.e., 790-hPa surface pressure) produces an RCE state with a cooler troposphere than that in the case with surface elevation of 1.5 km (Figs. 7a,b). Although the temperature at a given pressure level drops by less than 1 K when we lift the surface from 1.5 to 2 km, this clearly shows that one cannot universally expect tropospheric warming as surface elevation increases. In very warm and moist climates, the lapse-rate effect in Eq. (14) dominates to produce elevated cooling. This elevated cooling effect (i.e., negative EHI) persists when the CSRM simulations are repeated without radiatively active clouds, showing that it is not dependent on uncertain cloud radiative effects (Figs. 7c,d).

Fig. 7.
Fig. 7.

(a),(b) Vertical profiles of (a) temperature and (b) temperature anomaly with respect to the 1.5-km case (i.e., 850-hPa surface pressure; see main text) for the simulations with surface albedo of 0.2; the legend indicates the surface elevation used for each curve. (c),(d) As in (a) and (b). respectively, but without radiatively active clouds; the temperature anomaly is with respect to the additional 1-km case.

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0312.1

A possible explanation for this elevated cooling can be found in the perspective of the optically thick limit. In our CSRM simulations, ground temperature is higher than that of the immediately overlying air (i.e., a ground temperature discontinuity exists). In hot, moist climates, OLR might increase in response to surface lifting as radiation from the higher surface penetrates the overlying atmosphere, thus cooling the column.

7. Discussion

Elevated heating produced by the rise of orography has been widely invoked as a forcing for thermally direct circulations that influence regional climate in Earth’s tropics and subtropics (e.g., Staff Members of Academia Sinica 1958; Wu et al. 2007). It has also been argued to set some characteristics of the general circulation of the Martian atmosphere (Richardson and Wilson 2002). Yet, despite its importance, the physics of elevated heating has not been well understood. For example, no theory existed for the quantitative sensitivities of surface temperature and upper-tropospheric temperature to surface elevation, even in the idealized state of radiative–convective equilibrium.

Here we built on the work of ME99, who used parameterized convection to simulate radiative–convective equilibrium states over surfaces of different elevations. It is intuitive that elevated heating will occur if surface temperature decreases with surface elevation more slowly than the lapse rate of the nonelevated case (barring large compensating changes in air–ground temperature difference); we used a formalization of this idea together with a climate sensitivity framework to understand the radiative–convective processes that set the magnitude and sign of the elevated heating effect. In particular, we showed that the magnitude and sign of the elevated heating effect are set by top-of-atmosphere radiative changes dominated by the sensitivity of the moist adiabatic lapse rate to surface height. Based on the quantitative characteristics of this lapse-rate feedback, we hypothesized that surface temperature should decrease more rapidly with surface elevation in warmer climates, and thus elevated heating should be weaker in warmer climates. This hypothesis is supported by offline radiative calculations and is further confirmed by cloud-system-resolving simulations. In a sufficiently warm climate, elevated heating can even change sign to become elevated cooling.

Much work remains to be done to connect our results with real climate states where large-scale dynamics interact with radiative–convective processes, and where surface albedo and soil moisture may be influenced by surface elevation. For instance, observations show a faster warming trend during the last 50 years over the Tibetan Plateau compared with its lower-elevation surroundings (e.g., Mountain Research Initiative EDW Working Group 2015). This observed trend might be taken to suggest that elevated heating increases in magnitude in warmer climates, which would contradict our RCE findings. However, the enhanced warming trend at high elevations might be caused primarily by changes in the large-scale circulation, land surface drying, surface albedo reductions due to the melting of snow and ice cover, aerosol changes, and more. We will quantitatively explore in a separate work how changes in surface albedo can potentially compensate for the elevated heating effect (Hu and Boos 2017) and hope that other idealized modeling and observational analyses will help in understanding the more general interactions between large-scale dynamics, land surface hydrology, and the radiative–convective physics of elevated heating.

Acknowledgments

We acknowledge support from National Science Foundation Grants AGS-1253222 and AGS-1515960, Office of Naval Research Grant N00014-15-1-2531, and the Yale University Faculty of Arts and Sciences High Performance Computing facility. We thank Peter Molnar, Mark Brandon, and Yiqi Zheng for helpful discussions.

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