Latitude of ice margin as a function of a non-dimensional total solar irradiance in the diffusive energy balance climate model described byNorth 1975, for different values of the non-dimensional diffusion . Stable states are indicated by a thicker line.
When we were first starting out as graduate students, Max Suarez and I became interested in ice age theories and found it very helpful as a starting point to think about energy balance models for the latitudinal structure of the surface temperature. At about the same time, Jerry North had simplified this kind of model to its bare essence: linear diffusion on the sphere with constant diffusivity, outgoing infrared flux that is a linear function of surface temperature, and absorbed solar flux equal to a specified function of latitude multiplied by a co-albedo that is itself a function of temperature to capture the different planetary albedos for ice-free and ice-covered areas. Playing with this kind of “toy” model is valuable pedagogically – I certainly learned a lot by building and elaborating this kind of model — and can even lead to some nuggets of insight about the climate system.
The response of a 1km non-rotating doubly periodic model of radiative-convective equilibrium to an increase in surface temperature, in increments of 2K. Left: temperature, showing a moist-adiabatic response; Right: fraction of area with cloud at each height, showing an upward displacement of upper tropospheric clouds. From Kuang and Hartmann 2007.
The presence of cirrus clouds in the tropics warms the troposphere because infrared radiation is emitted to space from their relatively cold surfaces rather than the warmer temperatures below the clouds. The response of these clouds can be important as feedbacks to climate change. A reduction in the area covered by these high clouds would be a negative feedback to warming. [7/25/13: Several readers have pointed out that a reduction in the areas of high cloud cover would be a negative infrared feedback but a positive shortwave feedback and that the net effect could go either way.] An increase in the average height of these clouds with warming, resulting in a colder surface than would be the case if this height did not increase, would be a positive feedback. It is the latter that I want to discuss here. GCMs have shown a positive feedback due to increasing height of tropical cirrus since the inception of global modeling (e.g., Wetherald and Manabe, 1980). This is probably the most robust cloud feedback in GCMs over the years and is one reason that the total cloud feedbacks in GCMs tend to be positive. This increase in cloud top height has, in addition, a clear theoretical foundation, formulated as the FAT (Fixed Anvil Temperature) hypothesis by Hartmann and Larson, 2002.
Rough estimates of the WMGG (well-mixed greenhouse gas — red) and non-WMGG (blue) components of the global mean temperature time series obtained from observed (HADCRUT4) Northern and Southern Hemisphere mean temperatures and different assumptions about the ratio of the Northern to Southern Hemisphere responses in these two components. Black lines are estimates of the response to WMGG forcing for 6 different values of the transient climate response TCR (1.0, 1.2, 1.4, 1.6, 1.8, 2.0C).
How can we use the spatial pattern of the surface temperature evolution to help determine how much of the warming over the past century was forced by increases in the well-mixed greenhouse gases (WMGGs: CO2, CH4, N2O, CFCs), assuming as little as possible about the non-WMGG forcing and internal variability. Here is a very simple approach using only two functions of time, the mean Northern and Southern Hemisphere temperatures. (See #7, #27, #35 for related posts.)
Schematic of the response of tropical rainfall to high latitude warming in one hemisphere and cooling in the other or, equivalently, to a cross-equatorial heat flux in the ocean. From Kang et al 2009.
When discussing the response of the distribution of precipitation around the world to increasing CO2 or other forcing agents, I think you can make the case for the following three basic ingredients:
the tendency for regions in which there is moisture convergence to get wetter and regions in which there is moisture divergence to get drier (“wet get wetter and dry get drier”) in response to warming (due to increases in water vapor in the lower troposphere — post #13);
the tendency for the subtropical dry zones and the mid-latitude storm tracks to move polewards with warming;
the tendency for the tropical rainbelts to move towards the hemisphere that warms more.
There are other important elements we could add to this set, especially if one focuses on particular regions — for example, changes in ENSO variability would affect rainfall in the tropics and over North America in important ways . But I think a subset of these three basic ingredients, in some combination, are important nearly everywhere. I want to focus here on 3) the effect on tropical rain belts of changing interhemispheric gradients.
Lower panel: the observed (irrotational) component of the horizontal eddy sensible heat flux at 850mb in Northern Hemisphere in January along with the mean temperature field at this level. Middle panel: a diffusive approximation to that flux. Upper panel: the spatially varying kinematic diffusivity (in units of ) used to generate the middle panel. From Held (1999) based on Kushner and Held (1998).
Let’s consider the simplest atmospheric model with diffusive horizontal transport on a sphere:
Here is the energy input into the atmosphere as a function of latitude , is the outgoing infrared flux linearized about some reference temperature , is the heat capacity of a tropospheric column per unit horizontal area , and is a kinematic diffusivity with units of (length)2/time. Think of the energy input as independent of time and, for the moment, think of as just a constant.
(Left) Sea surface temperature averaged over the North Atlantic (75-7.5W, 0-60N), in the HADGEM2-ES model (ensemble mean red; standard deviation yellow) compared with observations (black), as discussed in Booth et al 2012. (Right) Upper ocean (< 700m) heat content in this model averaged over the same area, from Zhang et al 2013 ( green = simulation with no anthropogenic aerosol forcing, kindly provided by Ben Booth.)
A paper by Booth et al 2012 has attracted a lot of attention because of the claim it makes that the interdecadal variability in the North Atlantic is in large part the response to external forcing agents, aerosols in particular, rather than internal variability. This has implications for estimates of (transient) climate sensitivity but it also has very direct implications for our understanding of important climate variations such as the recent upward trend in Atlantic hurricane activity (linked to the recent rapid increase in N.Atlantic sea surface temperatures) and drought in the Sahel in the 1970′s (linked to the cool N. Atlantic in that decade). I am a co-author of a recent paper by Rong Zhang and others (Zhang et al 2013) in which we argue that the Booth et al paper and the model on which it is based do not make a compelling case for this claim.
Anomalies in near surface air temperature over land (1979-2008) averaged over Asia and the months of June-July-August from CRUTEM4 (green) — and as simulated by atmosphere/land models in which oceanic boundary conditions are prescribed to follow observations (gray shading). See text and Post #32 for details.
This is a follow up to Post #32 on Northern Hemisphere land temperatures as simulated in models in which sea surface temperatures (SSTs) and sea ice extent are prescribed to follow observations. I am interested in whether we can use simulations of this “AMIP” type to learn something about how well a climate model is handling the response of land temperatures to different forcing agents such as aerosols and well-mixed greenhouse gases. If a model forced with prescribed SST/ice boundary conditions and prescribed variations in the forcing agents does a reasonably good job of simulating observations, we can then ask how much of this response is due to the SST variations and how much is due to the forcing agents (assuming linearity). If the response to SST variations is robust enough, we have a chance to subtract it off and see if different assumptions about aerosol forcing, in particular, improve or degrade the fit to observations.
Globally integrated, annual mean tropical cyclone (TC) and hurricane frequency simulated in the global model described in Post #2, as a function of a parameter in the model’s sub-grid moist convection closure scheme, from Zhao etal 2012.
It is difficult to convey to non-specialists the degree to which climate models are based on firm physical theory on the one hand, or tuned (I actually prefer optimized) to fit observations on the other. Rather than try to provide a general overview, it is easier to provide examples. Here is one related to post #2 in which I described the simulation of hurricanes in an atmospheric model.
Anomalies in annual mean near surface air temperature over land (1979-2008), averaged over the Northern Hemisphere, from CRUTEM4 (green) and as simulated by an ensemble of atmosphere/land models in which oceanic boundary conditions are prescribed to follow observations.
As discussed in previous posts, it is interesting to take the atmosphere and land surface components of a climate model and run it over sea surface temperatures (SSTs) and sea ice extents that, in turn, are prescribed to evolve according to observations. In Post #2 I discussed simulations of trend and variability in hurricane frequency in such a model, and Post #21 focused on the vertical structure of temperature trends in the tropical troposphere. A basic feature worth looking at in this kind of model is simply the land temperature – or, more precisely, the near-surface air temperature over land. How well do models simulate temperature variations and trends over land when SSTs and ice are specified? These simulations are referred to as AMIP simulations, and there are quite a few of these in the CMIP5 archive, covering the period 1979-2008.
Relative humidity evolution over one year in a 50km resolution atmospheric model
in the upper (250hPa) and lower (850hPa) troposphere.
In their 1-D radiative-convective paper of 1967, Manabe and Wetherald examined the consequences for climate sensitivity of the assumption that the tropospheric relative humidity (RH) remains fixed as the climate is warmed by increasing CO2. In the first (albeit rather idealized) GCM simulation of the response of climate to an increase in CO2, the same authors found, in 1975, that water vapor did increase throughout the model troposphere at roughly the rate needed to maintain fixed RH. The robustness of this result in the world’s climate models in the intervening decades has been impressive to those of us working with these models, given the differences in model resolution and the underlying algorithms, a robustness in sharp contrast to the diversity of cloud feedbacks in these same models.