# Isaac Held's Blog

## 27. Estimating TCR from recent warming

GISTEMP annual mean surface temperatures (degrees C)
for the Northern and Southern Hemispheres.

Here’s an argument that suggests to me that the transient climate response (TCR) is unlikely to be larger than about 1.8C.  This is roughly the median of the TCR’s from the CMIP3 model archive, implying that this ensemble of models is, on average, overestimating TCR

## 26. Relative humidity in “cloud resolving” models

Time and spatially averaged relative humidity profiles from radiative-convective equilibrium simulations with cloud-resolving models.  The figure on the left is from Held et al, 1993 and shows results from two simulations differing by 5C  in the prescribed surface temperature. That on the right is from Romps 2011 and shows the result of changing the CO2 and adjusting surface temperatures to keep the net flux at the top of the atmosphere unchanged.  (Also shown on the right is the observed profile at a tropical western Pacific ARM site.)

Regarding water vapor or, equivalently, relative humidity feedback, we can think of theory/modeling as providing a “prior” which is then modified by observations (trends, interannual variability, Pinatubo response). My personal “prior” is that relative humidity feedback is weak. or, conversely, that the strength of water vapor feedback in our global models is about right.

In justifying this prior, I like to start with the rather trivial argument, already mentioned in the last post, that the amount of water vapor in the atmosphere cannot possibly stay unchanged as the climate cools since many regions will become supersaturated, including the upper tropical troposphere where most of the water vapor feedback is generated..  So to expect specific humidity to remain unchanged as the climate warms requires the present climate to be close to a distinguished point as a function of temperature  – the point at which water vapor stops increasing as temperatures increase.  Its not impossible that we do reside at such a point, but you’re going to have work pretty hard to convince me of that — it doesn’t strike me as a plausible starting point.

Of course, there is also the community’s collective experience with global atmospheric models over the past several decades.  Less familiarly, there is experience more recently with the kind of “cloud-resolving” models (CRMs) discussed in Posts #19-20. I am going to focus on the latter here. This will have the advantage of introducing what I consider to be the physical mechanism that could most plausibly alter the strength of water vapor feedback.

## 25. Relative humidity feedback

Some feedbacks in AR4 models, from Held and Shell 2012.  The three red columns on the right provide the traditional perspective:  the “Planck feedback”– the response to uniform warming of surface and troposphere with fixed specific humidity ($\lambda_T$), the lapse rate feedback at fixed specific humidity ($\lambda_L$), and the water vapor feedback ($\lambda_Q$).  The three blue columns on the left provide an alternative perspective — with the fixed relative humidity uniform warming feedback ($\tilde{\lambda}_T$), the fixed relative humidity lapse rate feedback, ($\tilde{\lambda}_L$), and the relative humidity feedback ($\tilde{\lambda}_H$).  The sum of the three terms, shown in the middle black column, is the same from either perspective.  Surface albedo and cloud feedbacks are omitted. Each model is a dot.

This is the continuation of the previous post, describing how we can try to simplify the analysis of climate feedbacks by taking advantage of the arbitrariness in the definition of our reference point, or equivalently, in the choice of variables that we use to describe the climate response. There is nothing fundamentally new here — it is just making explicit the way that many people in the field actually think, myself included.  And if  you don’t like this reformulation, that’s fine — it’s just an alternative language that you’re free to adopt or reject.

## 24. Arbitrariness in feedback analyses

This post is concerned with arbitrariness in the terminology we use when discussing climate feedbacks.  The choice of terminology has no affect on the underlying physics, but it can, I think, affect the picture we keep in our minds as to what is going on, and can potentially affect the confidence we have in this picture.

In feedback analyses of a climate response to some radiative forcing, we start with a reference response, the response “in the absence of feedbacks”, and then we look at how this reference response is modified by feedbacks.   An electrical circuit analogy often comes to mind, with the reference response analogous to the unambiguous input into a circuit.  But the choice of reference response in our problem is ultimately arbitrary.  The following is closely based on the introductory section of Held and Shell 2012.

## 23. Cumulative emissions

Schematic of three different idealized global warming scenarios.  The time period is roughly 1,000 years and each scenario starts with the CO2 increase and warming from the anthropogenic pulse of emission in the 20th and 21st centuries.  On the left, emissions are slowed so that CO2 is maintained at the level reached at the end of this pulse.  In the center, emissions are eliminated at the end of the pulse, resulting in slow decay of CO2.  On the right, CO2 levels are abruptly returned to pre-industrial levels –perfect geoengineering –  a scenario useful for isolating the recalcitrant component of warming discussed  in post #8.

If we stop emitting CO2 at some future time $T$ how would surface temperature evolve over the ensuing decades and centuries — ignoring all other forcing agents?  This question (or closely related questions) has been looked at using a number of models of different kinds,  including Allen et al, 2009, Matthews et al, 2009, Solomon et al, 2009, and Frolicher and Joos, 2010.   These models agree on a simple qualitative result: global mean surface temperatures stay roughly level for as long as a millennium, at the value achieved at the time $T$ at which emissions are discontinued, as illustrated schematically in the middle panels above.

Read the rest of this entry »

## 22. Ultra-fast responses

From Held and Zhao 2011, a simulation with an atmospheric model of the change in the number of tropical cyclones that form over each hemisphere and over the globe when sea surface temperatures (SSTs) are raised uniformly by 2C (labelled P2K), when the CO2 is doubled with fixed SSTs, and when SSTs and CO2 are increased together.

Suppose that we have a model of the climatic response to gradually increasing CO2, and we examine the globally-averaged incoming top-of-atmosphere flux, $N$, as a function of time (using a large ensemble of runs of the model to average out internal variability).  Letting $\delta$ refer to the difference between two climate states, for example the difference between the climates of 2100 and 2000 in a particular model, we end up looking at an expression like

$\delta N \approx \frac{\partial N}{\partial C} \delta C + \frac{\partial N}{\partial T}\delta T +\frac{\partial N}{\partial X}\delta X$

where $T$ is the global mean surface temperature and $X$ refers to all of the other things on which $N$ depends.  Here $C$ is the CO2 concentration, or, to the extend the useful range of this linearization,  log(CO2).  The forcing $F$ might be defined as $\frac{\partial N}{\partial C} \delta C$.  We typically go a step further and write $\delta X = \frac{\delta X}{\delta T} \delta T$  so that we can think of this last term as a feedback, modifying the radiative restoring strength,

$\beta = -\frac{\partial N}{\partial T} -\frac{\partial N}{\partial X}\frac{\delta X}{\delta T}$

i.e, so that $\delta N = F - \beta \delta T$.  While this is a formal manipulation that you can always perform if you want to,  it is obviously more useful when $\delta X$ is actually more or less proportional to $\delta T$.  Ideally, there is a causal chain:  $\delta C$ => $\delta T$ => $\delta X$. But what if the change in $X$ due to an increase in CO2 results from some other causal chain that doesn’t pass through the warming of the surface (or the warming of the strongly coupled surface-troposphere system)?

## 21. Temperature trends: MSU vs. an atmospheric model

Lower tropospheric MSU monthly mean anomalies, averaged over 20S to 20N, as estimated by Remote Sensing Systems – RSS (red) and the corresponding result from three realizations of the GFDL HiRAMC180 model (black) using HadISST1 ocean temperatures and sea ice coverage. Linear trends also shown. (Details in the post.)

Motivated by the previous post and Fu et al 2011 I decided to look in a bit more detail at the vertical structure of the tropical temperature trends in a model that I have been studying and how they compare to the trends in the MSU/AMSU data.  The model is an atmosphere/land model using as boundary condition the time-evolving sea surface temperatures and sea ice coverage from HadISST1.  It is identical to the model that generates the tropical cyclones discussed in Post #2 (and the animation of outgoing infrared radiation in Post #1).  It has the relatively high horizontal resolution, for global climate models, of about 50km.  Three realizations of this model, starting with different initial conditions, for the period covering 1979-2008, have been provided to the CMIP5 database, and it is these three runs that I will use in this discussion.  The model also has prescribed time-evolving well-mixed greenhouse gases, aerosols (including stratospheric volcanic aerosols), solar cycle, and ozone.  The atmospheric and land states are otherwise predicted.

## 20. The moist adiabat and tropical warming

Results from a high resolution model of horizontally homogeneous radiative-convective equilibrium, Romps 2011.  Left: equilibrium temperature profiles for 3 values of CO2 compared to an observed tropical profile.  Right: the temperature differences compared to the response to doubling CO2 in an ensemble of CMIP3 global climate models.

As a moist parcel of air ascends it cools as it expands and does work against the rest of the atmosphere.  If this were the only thing going on, the temperature of the parcel would decrease at 9.8K/km.  But once the water vapor in the parcel reaches saturation some of this vapor condenses and releases its latent heat, compensating for some of the cooling (you get about 45K of warming from latent heat release when a typical parcel rises from the tropical surface to the upper troposphere).   A warmer parcel contains more water vapor when it becomes saturated, so it condenses more vapor as it rises, and temperature decreases with height more slowly.  That is, the moist adiabatic lapse rate, $- \partial T/\partial z$, decreases with warming.

To say something about the warming of the tropical atmosphere, rather than that of a moist adiabat, we need to argue that the tropical troposphere is close to a moist adiabat and remains close as it warms.  The upper troposphere will then warm more than the lower troposphere.  This is precisely what happens in our global climate models. The consistency or inconsistency of this prediction with observations, particularly the Microwave Sounding Unit (MSU) temperatures, is a long-standing and important issue  A failure of the upper troposphere to warm as much as anticpated by this simple argument would signal a destabilization of the tropics — rising parcels would experience a larger density difference with  their environment, creating more intense vertical accelerations — affecting all tropical phenomena involving deep convection.  I like to refer to warming following the moist adiabat as the most “conservative” possible — having the least impact on tropical meteorology.

## 19. Radiative-convective equilibrium

Animation of horizontally homogeneous non-rotating radiative-convective equilibrium courtesy of Caroline Muller.  The model is SAM (System for Atmospheric Modeling) the principal architect of which is Marat Khairoutdinov.  Transparent shading is condensate concentration; colors on the surface indicate near-surface air temperature.  See text for further description.

The starting point for most of my thinking regarding climate sensitivity is the simple 1-dimensional radiative-convective model introduced by Suki Manabe and Dick Wetherald in 1967.  See also Manabe and Strickler, 1964.  For an early review of this kind of modeling, see Ramanathan and Coakley, 1978. Sadly, Dick Wetherald passed away very recently; although it is a very small gesture, I would like to dedicate this post to his memory.

## 18. Noise, TOA fluxes and climate sensitivity

A model configuration used to study how temperature variations in the equatorial Pacific force temperature variations in other ocean basins and the land. Figure courtesy of Gabriel Lau.

Consider a simple energy balance model for the oceanic mixed layer (+ land + atmosphere) with temperature $T$ and effective heat capacity $c$.  The net downward energy flux at the top-of-atmosphere $R$ is assumed to consist of a radiative relaxation, $- \beta T$, plus some noise, $N$.  With imposed flux from the deep ocean to the mixed layer, $S$:

$c \frac{dT}{dt} = R + S = -\beta T + N + S$

The assumption is that there is no external radiative forcing due to volcanoes or increasing CO2, etc. Can we use a simple one-box model like this to connect observations of interannual variability in $R$ and $T$ to climate sensitivity?