# Isaac Held's Blog

## 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.