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.)

Suppose that the temperature record consists of the linear superposition of two parts — the WMGG part and everything else. The real distinction here is that these two parts are assumed to affect the Northern and Southern Hemispheres differently.  If the global mean response to the WMGG is G(t), assume that the Northern and Southern hemisphere responses are respectively (1+g)G and (1-g)G.  Similarly for the non-WMGG part, A(t), I’ll write the two hemispheric responses as (1+a)A and (1-a)A.  Here the constants g and a, controlling the pattern of the responses, are assumed to be independent of time, so that the two parts of the response are individually separable in space and time.  Given the Northern and Southern hemisphere mean temperatures, N(t) and S(t), I’ll just write

N(t) = (1+g)G(t) +(1+a)A(t),

S(t) = (1-g)G(t)+(1-a)A(t).

Assuming g and a are given we can solve for the global mean responses G and A:

G(t) =- [(1-a)*N(t) - (1+a)*S(t)]/(2*(a-g)),

A(t) =  [(1-g)*N(t) - (1+g)*S(t)]/(2*(a-g)).

For example, in the special case of a=1 — in which the non-WMGG part is confined to the Northern Hemisphere — then G = S/(1-g) — so the WMGG component is determined completely by the Southern Hemisphere only, being uncontaminated by the non-WMGG component there.

Using N(t) and S(t) from HadCRUT4.2.0.0 and varying g and a over ranges of interest I get the figures at the top.  Anomalies are computed from the mean of the first 60 years, starting in 1850, and smoothing with a running 9 year average.  (See figure immediately above.)  Each panel in the figure at the top of the post corresponds to one value of g (top: g = 0.10; mid: g = 0.20; bot: g = 0.25) and G(t) and A(t) are shown for three different values of a (0.5, 0.65, and 1.0 as indicated by the legend on the middle panel — the three values of a are the same in each panel ).  Also shown is the response to WMGG forcing using the GISS forcing estimate, normalizing by a multiplicative constant to agree with the value of Skeie et al 2011 of 2.83 W/m² in 2010, and then multiplied by (TCR)/(2xCO2), where (2xCO2) = 3.7 W/m².  The 6 black lines in the figure correspond to TCR = {1.0, 1.2, 1.4, 1.6, 1.8, 2.0}.  If you can ignore phase lags between forcing and response, you can think of TCR (the transient climate response) in this context as the just a multiplicative constant that you multiply the WMGG forcing by to get the global transient climate response to the WMGGs, in degrees C, normalized to refer to doubling of CO2.  The TCR implicitly takes into account ocean heat uptake as well as radiative feedbacks and (I feel that I have to repeat this whenever using this concept) should not be confused with the more familiar “climate sensitivity”, which requires the oceans to have equilibrated and the ocean heat uptake to relax to zero.

One can read off the value of g simulated by a set of CMIP5 models run with varying WMGGs as the only forcing agents in Fig. 4 of Friedman et al 2013.  I get about 0.15 or 0.20 eyeballing the figure.  Also, if you assume that the non-WMGG component is primarily aerosol forced, the same figure implies a value of a of about 0.5 .  (The figure also gives you a sense of how separable in time the responses are to WMGGs and aerosols in isolation.)   If mutidecadal natural variability dominates over aerosols, then I would expect a value of a closer to 1, or even greater than 1, since variability in the Atlantic overturning, in particular, should, if anything, cool the southern while warming the northern hemisphere. ( If the non-WMGG component consists of an aerosol part and an interannual variability part of comparable magnitude, and with different values of a, this kind of simple linear transformation will be of limited utility.)  If  there are other forcing agents (ie increased stratospheric water or tropical volcanoes) that result in a modest interhemispheric contrast in warming or cooling similar to the assumed structure of the WMGG response, these would find themselves lumped together with the WMGG component.  You don’t have to smooth, but interannual variability (ie ENSO) most likely would not project cleanly onto one or the other component, so I don’t see any advantage of leaving it in.

I have used these numbers and considerations in deciding which combinations of (g,a) to use in the plots, also keeping in mind that it makes no sense to allow g and a to get too close to each other, since the near-degeneracy would then result in a meaningless decomposition.

The idea here, which should be clear from the inclusion of the TCR-normalized WMGG forcing curves in the figures, is to use what we are relatively sure about — the time history and the radiative forcing from the WMGG’s — to constrain TCR. while assuming as little as possible about aerosol forcing and natural multi-decadal variability.

The panel at the top is a case with g approaching 0.  In this limit the non-WMGG component has to explain all of the interhemispheric difference, and since this component  is assumed to be Northern-centric the observed larger increase in the north requires global mean warming from this term, pushing the WMGG component down to a TCR value of 1.0 or so.  This is a picture that you might favor if you think, for other reasons, that the non-WMGG component is dominated by internal variability.

The middle panel has somewhat larger TCR, with the net non-WMGG component small near the present because the observed north/south ratio is similar to that implied by the assumed WMGG pattern in isolation.

In the bottom panel, the value of g is large enough to leave room for a substantial “aerosol” affect remaining at present, resulting in a larger TCR that depends more strongly on the value of a: a smaller a results in less difference  in the north-south ratios between the two patterns, producing more compensation.

These results will be sensitive to the input data set due to the role played by the relatively small interhemispheric differences.   You could propagate the observational error estimates provided along with the HADCRUT4 data set through this transformation, as well as use information about the distribution of a and g from individual models in the CMIP ensembles.  But the choice of the two hemispheric means for this analysis is arbitrary.  I am sure that one could be more systematic along the lines of the fingerprinting literature (but much of this literature assumes more about the aerosol forcing time dependence than I would prefer). And one could look in more detail at the assumption of negligible phase lag in the WMGG response over the past century needed when trying to constrain TCR.  I am thinking of this as being more exploratory than quantitative,  nudging readers of this blog to think beyond the global mean time series.

[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]

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:

1. 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);
2. the tendency for the subtropical dry zones and the mid-latitude storm tracks to move polewards with warming;
3. 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.

My exposure to this issue started some time ago listening to Suki Manabe discussing early coupled atmosphere-ocean model simulations in which the latitude of the Pacific intertropical convergence zone (ITCZ) was sensitive to the cloud cover in midlatitudes of the Southern Hemisphere — these were the days in which cloud cover was prescribed in the models so it was easy to manipulate.  By increasing the cloud cover in the South, well away from the tropical rainbelts themselves, one could move the ITCZ from south of the equator to north of the equator (where it is in reality).

In the late 80′s a flurry of work on Sahel rainfall and particularly the severe drought in the preceding decade, starting with Folland et al 1986, argued that much of the decadal variability in the Sahel  is tied to the differential warming of the hemispheres.  Relatively cool Northern Hemisphere, as in the 70′s, results in less Sahel rainfall, thinking of the Sahel as marking the northernmost extension of the ITCZ, or monsoonal rainfall, over Africa, which retreats due to the pull of the differential cooling of the Northern with respect to the Southern Hemisphere.  While there are other things going on in the Sahel, most recent research supports this picture of variations in interhemispheric temperature gradients, whether produced by variability in Atlantic overturning or aerosol forcing,  as being a big part of the Sahel drought picture.  I talk about this here, although that page is a bit dated.

John Chiang and collaborators have emphasized the importance of this mechanism for paleoclimate as well as higher frequency climate variations in a series of papers, see this recent review (Chiang and Friedman, 2012).  Another paper that affected my own work on this issue was that of Broccoli et al 2006, which helped shift the picture of the underlying dynamics from one focused on surface energy balances and changes in tropical ocean temperatures to one focused on the requirements of atmospheric  energy balance.  Two former students of mine, Sarah Kang and Dargan Frierson, have picked up on this energy balance perspective in more recent work, starting with Kang et al 2008.

Sarah has focused on a setup in which one takes an atmospheric model of the type used for climate simulations and couples it to a “slab ocean” of uniform depth with no ocean currents, which just provides some heat capacity and a saturated surface.  Starting with the case in which there is no heat flux through the bottom of the slab ocean, the resulting climate  is independent of longitude and symmetric about the equator, with most tropical precipitation confined to a sharp ITCZ located over the equator (the solid line in the lower panel).  The model determines its own surface temperature, and the energy flowing into the slab will be zero everywhere if you average long enough.  (One of the nice things about this setup is that, unlike models in which surface temperatures are prescribed,  you never have to worry about generating a double ITCZ.)  Heat is then added poleward of 40N in one hemisphere and the same amount is removed from the other hemisphere (as pictured in the upper left panel.) .  This is equivalent to prescribing a cross-equatorial heat flux in the ocean underneath the slab (upper right).  No heat is being input or extracted equatorward of 40 degrees.  After the model equilibrates, the ITCZ has moved into the warmed hemisphere.  The larger the heating, the larger the displacement of the ITCZ.  The lower panel shows the precipitation from simulations in which the peak in the imposed subpolar heating/cooling is 10, 20 and 40 W/m².

One way of thinking about this is to focus on how the surface temperatures in the tropics are affected by the extratropical heat sources/sinks, assuming that the ITCZ will follow the warmest surface temperatures. But I prefer a perspective based on the atmospheric energy budget, as in the papers by Broccoli et al and Kang et al linked to above.

Before the system is disturbed, the northward heat flux F  in the atmosphere is zero at the equator and has some slope in latitude as pictured below. The Hadley cells, symmetric about the equator, have poleward flow in the upper troposphere and equatorward flow near the surface, with rising motion mostly confined to the ITCZ.  These cells transport energy in the direction of their upper tropospheric flow.  In response to the high latitude heating and cooling, the atmosphere tries to resist the resulting interhemispheric asymmetry by transporting energy across the equator from the heated to the cooled hemisphere.  In this setup, you can equivalently talk about how much of the prescribed oceanic flux is compensated by an atmospheric flux in the opposite direction.  In the schematic at the top of the post, the fraction of the flux that is compensated is denoted by C.  Putting aside how C is determined, we can estimate the new latitude of  the “energy flux equator” where the atmospheric flux vanishes.  (See sketch below.)  If simple Hadley cells continue to dominate the horizontal energy fluxes in the tropics, with most of the rising motion in a sharp ITCZ, then the ITCZ will need to be close to this energy flux equator so that energy flows away from this latitude in both directions.

But how do you estimate C?  Start by ignoring any responses in clouds.  Part of the input of energy into the warmed hemisphere is balanced more or less locally by an increase in the energy radiated away to space and the rest is transported to low latitudes.  I picture the transport as a diffusive process (post #37), with a diffusivity that weakens as one approaches the tropics, where the mean meridional circulation (the Hadley cell) takes over a lot of the energy transport.  The subtropical heating/cooling by midlatitude storms creates a problem because the tropical atmosphere can’t sustain large horizontal temperature gradients. If the change in the net radiation at the top of the atmosphere is primarily a function of tropospheric temperature (ie if clouds don’t change), then the changes in this net radiation  have to be very uniform with latitude across the tropics. So the key from this perspective is the extent to which the eddy diffusive-like fluxes in midlatitudes manage to extract or input energy into the subtropics of each hemisphere, which the circulation must then redistribute.

As discussed in the Kang et a papers linked to above, if we either fix clouds in the GCM or use an idealized moist GCM with no clouds, this degree of compensation at the equator, C, seems to be of the order of 25-40%, a value you can get from a simple diffusive model with the diffusivity tuned to the atmospheric fluxes in the control climate.  If you use the standard AM2 model that was used in our contribution to the CMIP3/AR4 database, you get something like 80%, but this number can be changed by manipulating the closure scheme for moist convection.  It’s not the convection per se that matters, but the effect of the convection scheme on the cloud feedbacks — the response of clouds to this extratropical heating/cooling perturbation and the effect of these changes on the top-of-atmosphere (TOA) balance.  It is still the TOA that matters here, because the net surface fluxes are prescribed — one can only change the net atmospheric poleward fluxes if the TOA fluxes change.  (It is this emphasis on the TOA fluxes that distinguishes this perspective from those focusing on surface temperatures.)

There are two distinct kinds of cloud feedbacks that come into play.  First, there can be changes in clouds in the high latitude regions which are directly being heated or cooled.  These modify the heating/cooling that the atmosphere feels, so they effectively renormalize the forcing.  But in addition, once the tropical circulation is modified clouds in the tropics will react to these changes in circulation to alter the energy transports needed to homogenize the tropical temperatures.  For example, the strength of the subsidence  increases in the tropics and subtropics of the cooled hemisphere, which might result in an increase in low level cloudiness (due to the suppression of vertical mixing of vapor into the upper troposphere)– a positive feedback on the initial cooling.  (The movement of the ITCZ would also directly generate changes in long and shortwave fluxes at the TOA, but these tend to cancel — the effects of shallow clouds are often dominant.)  So this is a hard problem to get right quantitatively, as are all cloud-related issues it seems.  But the qualitative effect is clear.

This mechanism is important when thinking about the tropics during past glacial periods, given the large cooling associated with Northern ice sheets.  It is important for the response to aerosol forcing that preferentially cools the Northern Hemisphere.  It is important for the response to variations in the Atlantic meridional overturning, which directly modifies the cross-equatorial ocean flux.  And it can be important for understanding the mean climatology, as indicated by the reference above to Suki Manabe’s early experience with coupled atmosphere-ocean models (see also Hwang and Frierson, 2013 and Marshall et al 2013).

[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]

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.

We can choose to be the steady state global mean temperature in some control climate and reinterpret the temperature as the departure from this reference so that

If we are using this equation to model the time averaged north-south temperature gradients we can think of as the absorbed solar flux with its global mean removed.  But the equation is linear and we can also think of it as modeling the temperature response to some perturbation in the energy input, for example that due to aerosol forcing or changes in ocean heat uptake or ocean heat redistribution.

We can talk about an atmospheric radiative relaxation time scale, — which might be 45 days or so if we choose for example — and a diffusive time scale for temperature variations on the length scale of .  For a diffusivity of , which we’ll see is the order of magnitude of interest, the two time scales would be equal for , or about   degrees of latitude.  Let’s call this length scale .  The atmospheric response to perturbations on scales smaller than  would be spread over the distance in this model. If the ocean redistributes heat from latitude A to latitude B, and if A and B are within of each other, we might expect the atmospheric transport to closely compensate for this oceanic transport; if the heating and cooling are more widely separated than , the heating/cooling will be balanced more by radiation to space with atmospheric transport playing less of a role.

The bottom panel in the figure at the top is the eddy sensible heat flux, , in January at 850 hPa, in the lower troposphere but above the planetary boundary layer, where is the horizontal wind and a prime denotes the deviation from the mean seasonal cycle — computed from 4 times daily NCEP-NCAR reanalysis.  The overline is a time average over all Januarys.  Most of this flux is associated with midlatitude storms.  Also shown by the contours is the mean temperature field for that month. The black splotches are where the surface protrudes above this pressure surface.

(Actually, before plotting the flux, we decompose it into a a part that has zero divergence on this surface and a part that has zero curl  –this Helmholtz decomposition is unique on the sphere– and retain only the latter part, since we are only interested in the divergence of the flux here.  If you don’t do this, the flux is not as cleanly directed downgradient.)

The fluxes in the middle panel are generated with the same mean gradients and with the spatially varying diffusivity shown in the upper panel.  The result is evidently in the right ballpark.  The kinematic diffusivity has the dimensions of (length)²/(time), or velocity times length.  One could try to develop a theory for the relevant length and time scales or one could estimate them from observations in different ways.  Here we do the latter, and take the shortcut of just looking at the streamfunction of the flow.  The atmospheric flow is approximately non-divergent in the horizontal, so can be described by a streamfunction . (Ignoring spherical geometry, the rotational zonal (eastward) component of the wind and meridional (poleward) component are related to by .)  So has units of velocity times length, the same as kinematic diffusivity.  We compute the standard deviation of the eddy streamfunction, and allow ourselves a single constant of proportionality that provides the best fit of the form   where is uniform in space. (The plot uses .)  This may seem a bit arcane, but it is just a way to avoid having to estimate length and time scales separately.  This approach was motivated by Holloway 1986, who used this same procedure with satellite data of sea level fluctuations (sea level is proportional to the streamfunction of a geostrophic current) to estimate horizontal transport due to ocean eddies.

A fascinating question for me, ever since I entered the field, is how the magnitude and structure of this diffusivity is determined. (In Held 1999, I discuss why turbulent diffusion might actually be a better approximation for the atmosphere, at least for the transport of sensible heat in the lower troposphere,  than for typical shear or convectively driven turbulence studied in the laboratory.)  We expect this effective diffusivity to change as the climate changes, since the diffusivity must be determined by some aspect of the large-scale environment giving rise to these storms.  In particular, most theories have this diffusivity increasing with the magnitude of the north-south temperature gradient, making it harder to change this gradient than one might otherwise guess.

The values of the diffusivity in the middle of the oceanic storm tracks rise above . It is the large value in midlatitudes, where north-south temperature gradients are strongest, that are most important for understanding the mean equator-to-pole temperature difference on Earth. A value of   is more or less what you need in this simple diffusive model to get reasonable north-south temperature profiles (see North et al 1981), depending on the vertical level at which you think it’s most appropriate to diffuse the temperature field.  From the previous discussion, we get the sense from this simple diffusive picture that north-south heat transport couples different latitudes within the same hemisphere rather strongly.  In addition to the effective turbulent diffusivity, which is a key to north-south transport, there are strong zonal winds mixing even more strongly in longitude within a hemisphere.  Too local a perspective is a common mistake when first being exposed to the climate change problem — ie, expecting the temperature response to reflect the spatial structure of the CO2 radiative forcing or of the water vapor feedback..

But my motivation in bringing up this topic is a concern about the opposite tendency to ignore the difficulty that the atmosphere has in communicating temperature responses from extratropical latitudes of one hemisphere to extratropical latitudes of the other. A diffusivity of 2-3 x 10⁶ m²/s, if uniform over the sphere, is not large enough to mix from pole to pole in an atmospheric radiative relaxation time.   The effective diffusivity gets small as one enters the tropics — one can see a bit of this reduction in the figure — seemingly making it harder still to communicate between hemispheres, but this is potentially misleading because the large scale overturning (the “Hadley Cell”) is very efficient at destroying temperature contrasts across the tropics.  This effect is sometimes mimicked in diffusive models by using a large diffusivity in the tropics, which can be confusing since this diffusivity would not be relevant for passive tracers.  In addition the strong tendency for the tropical circulation to wipe out horizontal temperature gradients applies to deep temperature perturbations in the free troposphere, from which the surface can be protected by structure in the atmospheric boundary layer.  In any case, the signal still has to move through the tropics, which provide a large area to radiate it away to space, so the difficulty in getting much of a signal to reach extratropical latitudes in the opposite hemisphere remains.  GCMs provide an essential tool for navigating this complexity.   (But uncertain cloud feedbacks, the familiar wild card when discussing global sensitivity, can also come into play in this problem.)

When thinking about aerosol forcing, which is heavily tilted to the Northern Hemisphere, no one is surprised if the response is strongly tilted to the Northern Hemisphere as well.  But consider the concept of (global mean) transient climate response (TCR), discussed in several earlier posts.  The TCR is dependent on the efficiency of heat uptake by the oceans.  Much of this heat uptake occurs in the North Atlantic and in the Southern Ocean.   Consider two models, identical except for the Southern Ocean heat uptake.  The one that warms more slowly in the Southern Ocean will have a smaller TCR, which is fine, but would the warming in the extratropical Northern hemisphere be substantially smaller?  I don’t think so.  I am not aware of a simulation addressing this specific question in the literature.

A paper by Stouffer 2004 (Fig 5 in particular) is informative.  This paper describes very long simulations of the response to doubling and halving of CO₂ in a coupled atmosphere-ocean model (5,000 years — long enough for this  model to approach its new equilibrium quite closely ).  In the 2 x CO₂ case at year 200 the Southern Hemisphere (SH) as a whole, held back in large part by the Southern Ocean, has reached about 40% of its final temperature response.  Meanwhile the Northern Hemisphere (NH)  has achieved over 80% of its equilibrium response.  Even if all of the NH disequilibrium is due to the lack of warming in the Southern Hemisphere, which is unlikely, there is little room left for the rest of the SH warming to affect the NH — implying that a change in the SH relaxation time would have only a small effect on the NH in this model.

Thinking in terms of the global mean temperature in isolation can be valuable and it can also be misleading.  I tried to argue in Post #7 that neither of the usual arguments for focusing on the global mean — reduction in noise and the connection to the global mean energy balance –  is very compelling. (To think about one way in which the energy balance can get divorced from the mean temperature, just make in this simple diffusive model a function of latitude.) It is seductive to focus on the global mean temperature response; whenever I do I have to continually remind myself not to be misled into thinking that the Northern and Southern Hemispheres, in particular, are more strongly coupled than they actually are.

(Thanks to Sarah Kang, Paulo Ceppi, Yen-Ting Hwang and Dargan Frierson for discussions on closely related topics.)

[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]

(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.

The interest results from the figure in the left panel above.  This model’s forced response agrees very well with the observed surface temperatures averaged over the North Atlantic, so in this model one doesn’t need to invoke internal multidecadal variability to match these observations.  (The forced response is estimated by averaging over multiple realizations of the model with different initial conditions).  Zhang et al list several aspects of this simulation that seem problematic, exemplified by the upper right panel, which shows a time series of the ocean heat content down to 700m over this same region.  (observations from Levitus, 2009). The model does not produce the upward trend in this N. Atlantic heat content.  If one removes the anthropogenic aerosol forcing from the model (green line) it fits these observations better.

[The flatness of the heat content in the N. Atlantic in this model is intriguing. Based on discussions with my colleagues Rong Zhang and Mike Winton,  this seems to be a consequence of an AMOC  (Atlantic Meridional Overturning Circulation) which builds in strength when the aerosol cooling is strong, trying to balance a part of the cooling at the surface with warm waters advected in from the tropics, but also -- by a process that is not particularly straightforward  -- cools the subsurface waters.  It's as if  and (where   is the mean temperature between the bottom of the mixed layer and 700m) resulting in out phase with for sinusoidal fluctuations, and with these out-of-phase near surface and subsurface temperatures compensating in the total heat content — or something like that.  But there is no particular reason to expect close compensation.]

Another problematic aspect of the N.Atlantic simulation is the co-variability of temperature and salinity.  Decadal scale temperature and salinity variations in the subpolar Atlantic tend to be positively correlated in observations.  In particular, the cold period in the 70′s was marked by a fresh subpolar Atlantic.  This is what one expects when the AMOC  is weak, with less transport of more saline waters from the subtropics and more export of fresh waters from the Arctic.  The model does not show this correlation, and in the 70′s  it has relatively high salinity (presumably due to the stronger AMOC mentioned in the previous paragraph).  Our understanding of AMOC variability is admittedly limited, but the temperature-salinity correlations point towards there being a substantial internal component to the observations.  These Atlantic temperature variations affect the evolution of Northern hemisphere and even global means (e.g., Zhang et al 2007).  So there is danger in overfitting the latter with the forced signal only.

Our lab has a model, CM3 (Donner et al, 2011), that also has strong indirect aerosol effects and that produces simulations of the past century that share many of the features of HAD-GEM2-ES discussed here, including the nice fit to the N. Atlantic SSTs.  So this issue is naturally a hot topic of conversation in our lab. The issue has been around for a while.  For example,  Rotstayn and Lohmann 2002 made a case that strong aerosol forcing could explain the Sahel drought of the 70′s by cooling the N. Atlantic. The same qualitative behavior is seen in many models, but we are left with the quantitative question of how big the aerosol effect is.

Differences of opinion make life interesting and always force us to sharpen our arguments. And there remain strong differences of opinion on the relative importance of AMOC variability and aerosol forcing for the non-monotonic variation of North Atlantic surface temperatures and all the phenomena that we think are affected by it (including hurricanes and African rainfall).  But I remain skeptical that one can make a compelling case for aerosol dominance by focusing only on SSTs, without simultaneously considering salinities and sub-surface temperatures that are better able to distinguish between forced and free variations.

(conversations with Rong Zhang, Mike Winton, and Yi Ming have helped me think about this issue)

[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]

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.

In post #32, the focus was on the annual mean land temperatures averaged over the Northern Hemisphere.  If you look at the model simulations in different seasons, in this prescribed SST/ice context, you see a lot more variation from realization to realization in winter than in summer due to internal atmospheric variability.  If we are interested in confronting models with the observed spatial structure of trends over land, it helps to look at the system in such a way as to minimize the influence of internal variability.  Focusing on summer is one way to get started. The idea to focus on Asia in addition is partially to try to maximize the influence of the forcing agents as opposed to the SST influence, but our AMIP simulations suggest that the spatial structure of the summertime trends is also less noisy over Asia than over N. America.  There are more systematic ways of doing this, needless to say, but I think looking at Asia in summer might be a good way to get a feeling for whether this is worth pursuing.

The figure at the top of this post shows the spatial mean of 2m land temperatures in June-July-August over Asia (35E-170W, 7N-83N) from CRUTEM4 in green. As in #32, the AMIP simulations from 17 models  in the CMIP5 archive are first averaged over all available realizations for each model, and anomalies are computed from the mean over the 1979-2008 period.  The shading in the figure on the right shows the 25%-75% range of this ensemble of model anomalies.

The figure on the upper left shows the result from one of our atmosphere/land models, HiRAM C180.  To confuse matters the shading here indicates the spread among three realizations,  a measure of internal variability.    The figure on the lower left is generated with the same model but including only SST and ice extent variations, holding the forcing agents fixed.

The temperature trends in the CMIP5 ensemble are very close to the observational estimate, while the C180 model’s trend (upper left) is a bit high — one anomalously cold season,  in ’83 near the start of this time series, seems to be partly to blame.  With forcing variations removed (lower left), the C180 model trend is reduced by more than 40%.

It is nice to see the cooling due to Pinatubo appear so clearly in the summer of ’92 (the eruption was in June ’91).  It is well simulated by the models without any additional smoothing or removal of ENSO effects. Of course, some of this is coming from the observed SST response, which is imposed here.  From the “attribution” implied by the figures on the left above, it seems that about 1/2 to 2/3 of the cooling over Asia in the summer of ’92 is communicated from the ocean, the rest coming directly from the volcanic forcing.

Putting the summertime trends over Asia in a global context, here is the observed spatial pattern of 30 year June-July-Aug trends as well as the results from the mean of the CMIP5 ensemble and the mean of our 3 C180 realizations.

The numbers on the color scale are in degrees C/30 yrs.  In the OBS=CRUTEM4 plot, white means that we felt that too much data was missing to compute a trend; gray, as in the other plots, means that the absolute value of the trend is less than 0.5C/30yrs.  The relatively small summer trends in this 30 year period in the eastern half of the US and in a curious slash through central Asia are some of the interesting discrepancies between these observational estimates and the mean of these model ensembles.

Decomposing the C180 model result over Asia into a part due to the SSTs and sea ice alone and the remainder, which we interpret as due to varying forcing agents, we get this:

I have focused this plot on Asia because that seems to be where the model decomposition is particularly robust across the different realizations.  (The analogous figure over N. America seems to be more strongly distorted by sampling of internal atmospheric variability.)  We need more realizations to look at this decomposition carefully across the globe and to test the assumption of linear superposition.  It is interesting that the response to SSTs and sea ice extent has weak cooling in Northern Asia.  Over the Arctic in summer near surface temperatures are tightly constrained to be close to the melting temperature of sea ice, so to the extent that diffusion from the Arctic is relevant this would tend to minimize the warming in adjacent land, but this mechanism would not produce cooling. Cooling is most likely related to moistening of the soil, perhaps due to increase in Spring snowfall or summer rains.  To what extent is this pattern robust across models?  (A number of other modeling centers have simulations relevant for this kind of decomposition but they are not in the CMIP5 archive.)

The remainder (on the right in the figure), which we interpret as due to forcing variations, is also interesting. The cooling or lack of warming over the southern half of the continent is presumably due in large part to aerosols.  I don’t think Pinatubo torques the trend very much since it occurs close to the middle of this time period, but that needs to be checked. There does seem to be some potential for constraining aspects of the anthropogenic aerosol forcing with this approach.

Aerosols have not been a focus of the model development leading to this HiRAM model series  (these models include the same prescribed aerosol distributions as in our earlier AM2/CM2 model series and include no indirect effects due to aerosol-cloud interactions).  In these models we have focused instead on moving to higher resolution and simulating tropical storms statistics.  Our lab’s aerosol and atmospheric chemistry modeling research has instead been directed towards our AM3/CM3 branch of models, which is driven by emissions rather than prescribed concentration fields.  We are just getting started on a development path designed in part to combine the best aspects of HiRAM and AM3 so that, among other things, we can study the influence of aerosols (including Saharan dust) on tropical storms.  A quick inspection of AM3 AMIP simulations suggests a decomposition between forcing and SST components different from that described above. (Thanks to Yi Ming for a look at the AM3 results and to Bruce Wyman for generating the figures in this post.)

[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]

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.

In that post you can find an animation of the model output and some comparisons with observations. Here’s a reprise of the figure on the seasonal cycle of hurricane frequency in the different ocean basins

This version of the model, which has about 50km horizontal resolution, seems to do a very good job at simulating the frequency of tropical cyclones  -  (max winds > 17m/s) and the fraction of these storms of hurricane strength (> 33 m/s),  but does not simulate very strong (cat 3-5) storms, although the intensity distribution looks better if you look at minimum pressure rather than maximum winds.  I have been impressed by the quality of this simulation and similar simulations in other models.  We also have a 25 km version that produces quite similar results. Yet many in the tropical cyclone research community remain skeptical that a model with 25-50km grid size can simulate the physics of TC formation.

When we first described these results in  Zhao et al 2009 we knew very little about their sensitivity to model parameters.  We still don’t,  because the model is computationally expensive.  Why work with a model that is so resource-consuming?  It’s a tension that is always present in climate modeling: do you use increasing computer resources to create higher resolution models with the idea that improvements in the simulation will make the higher computational burden worthwhile, or do you stop with a more modest model that allows you to vary parameters systematically?  If one is interested in phenomena that are difficult to resolve in typical global models, such as tropical cyclones. the choice is pretty obvious — you need to push the resolution to build a case for the credibility of the simulations.

A recent paper Zhao etal 2012 describes the sensitivity of TC and hurricane frequency in this model to two parameters — one of  these is shown in the figure at the top.  The parameter is part of the sub-grid closure scheme for moist convection in the model.  The plot shows the average number of TCs per year on the whole globe (one of the dashed lines), as well as the number of TCs of hurricane strength (the other dashed line).  For convenience it also redundantly shows the fraction of TCs that are of hurricane strength (solid line with scale on the right).  We run a 20 year simulation for each of 5 values of ; the “error bars” are the standard deviation of the 20 yearly values . As increases the total number of TCs and hurricanes first increases and then decreases.  The fraction of TCs that reach hurricane strength, a crude measure of average intensity, increases monotonically with .

In the tropics a lot of the vertical transport takes place in plumes generated by moist gravitational instability that extend from near the surface to just beneath the tropopause.  The dominant horizontal scale of these plumes might be of the order of one or a few kilometers — although direct simulation of the turbulent entrainment into and detrainment out of these plumes, which affects their buoyancy, requires still smaller scales.  If you don’t have a sub-grid scale convection scheme in your model, “plumes” will still occur  but in a distorted way on the scale of the model grid.  In reality convection occurs even though the average conditions over, say, a 50 km square are not conducive to the generation of gravitational  instability — due to spatial variability on smaller scales.   Closure schemes for moist convection are based on an explicit or implicit picture of what is going on within a grid box that determines if convective plumes are triggered, how much mass is transported to the upper troposphere within the plumes, etc.  In the case of the closure scheme used here, when is  small deep convection occurs relatively easily; when it is large the convection is more inhibited.

It happens that the value we chose to use was , close to the value that produces the maximum number of TCs. The main reason for this choice was the model’s top-of-atmosphere energy balance, which is sensitive to , varying by more than 10 W/m2 over this range of values, due mostly to changes in low cloud.  It is hard to find other ways of counteracting such large changes to rebalance the model.  And the model becomes quite noisy on the grid scale at the higher values of examined.  It was these considerations, rather than systematic examination of storm statistics vs. , on which the initial choice of this parameter value was based.

The other parameter we have examined directly controls the grid-scale noise in the model, especially in the tropics. (The horizontal flow on each model level can be decomposed into rotational and divergent components — the parameter controls the strength of the damping of the divergent component only, which affects the flow primarily in the tropics.)

As   increases this damping of small scales increases and one might expect the number of TCs, which after all are only marginally resolved by the grid, to decrease,  But the opposite occurs — the number of TCs increases as the small scale damping increases in strength.  The intensity as measured by the fraction of TCs that become hurricanes stays about the same.  In fact it is hard to find anything in the simulation that is affected by this parameter other than the number of TCs that the model generates — and explicit measures of how noisy the model tropics is close to the grid scale. Our interpretation of this result is that it is the competition for a resource (the evaporation of water at the surface) that is the key — if you have too may little nascent disturbances trying to grab their share it becomes difficult for vortices of TC strength to form. We think that this dependence on the noise level is also responsible for the reduction in storm counts at large .  (Other effects are dominant at small .)

These dependencies are still under investigation.   But it should be clear that the kind of results displayed in Post #2 are not entirely “first principles” simulations of TC statistics, and the picture could change as we move to finer and finer resolution, especially to the point of resolving some of the deep plumes dominating moist convective turbulence in the tropics.  Are we justified in using this model as a tool to ask how hurricane statistics respond to warmer SSTs/increasing greenhouse gases?

I put a lot of weight on results such as the seasonal cycle figure above. The simulations hold together remarkably well. Nothing has been done to try to tune these seasonal cycles.   I don’t know how to quantify my level of confidence based on the quality of the simulations, but I would argue that tropical cyclone projections with this class of model should  be taken seriously despite legitimate concerns about dependence on the treatment of sub-grid scale processes.

[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]

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.

The figure at the top summarizes the variation in the Northern Hemisphere mean surface air temperature over land in these CMIP5 AMIP runs. (The figures in this post were generated by my colleague Bruce Wyman.) We compute annual and hemispheric means from the monthly averages in the archive. We first average over all available realizations for each of 17 models. (We have left out two of our own models from this ensemble simply because we generated this figure to have something to compare our results with — adding a couple more models would have little impact on this figure.)    The observations, in green, are taken from CRUTEM4. The model results are interpolated to the observational grid and the model results treated in the same way as the observations after that point (including discarding model results at grid points where monthly averaged data is missing.)  Anomalies are computed, for each model and the observations, from the mean over the same 1979-2008 period.  The shading in the figure indicates the middle half –the 25%-75% percentiles — of the resulting ensemble of values. (Sometimes it is important to focus on the model outliers and the full spread, but here we do the opposite and focus on the core of the model distribution.) The land warming trend in these models is about 15% smaller on average than the observed trend over this period.  An example of a study that looks at land temperature trends in earlier AMIP simulations (but extending over the full 20th century)  in this way is Scaife et al 2009 . I would like to see more work along these lines.

The figure below shows the same result for one of our models, the 50km resolution HiRAM model described in Posts 2 and 21. The shading means something different in this figure. We have three realizations of this model in the archive and the shading shows the spread across these three runs, so it gives you some feeling for the internal variability generated in this statistic by a model with prescribed ocean temperatures and sea ice.  This atmospherically-generated internal variability is washed out by averaging over multiple realizations in the figure above.  This particular model also underestimates the observed linear warming trend over this period by about 15%. (The grid in this model has the topology of a cube: the “C180″” in the figure indicates that there are 180×180 points on each face of the cube.)

I failed to mention that in these AMIP simulations, in addition to the observed variations in SST and sea ice, one also typically prescribes time-varying “forcing agents”– well-mixed greenhouse gases, aerosols, ozone, solar cycle variations in incoming flux.  In some AMIP models aerosol and ozone variations might be predicted, given emissions of precursors, but in the particular model that produces the results above these are all prescribed.  (There are no interannual variations in land surface properties such as the type of vegetation in our model at all, and no urban heat island effects.) What happens if you keep all of these forcing agents fixed and vary only the lower boundary condition – the SST and sea ice. The figure below shows what you get from three realizations of this type in the same model. This tells you how much of the land temperature variation and trend is “forced” by the observed changes in ocean boundary conditions versus changes in the forcing agents themselves.  In this model, the warming trend over Northern Hemisphere land is reduced by about 30% when holding these forcing agents fixed.  Assuming that this is a linear superposition, 70% of the model trend is generated by the communication of the observed  oceanic warming to the land.

You have to be a little careful in interpreting this decomposition. Part of the SST and sea ice variation is itself due to the changing forcing, of course. But there are still important things one can learn by comparing this kind of simulation with observed land warming.  Suppose that all of of the land warming is just communicated from the ocean, with no direct dependence on forcing agents.  Then one can use this fit to analyze what one might call the degree of redundancy of the land temperature record. I use the word redundancy with some reluctance, because it has the connotation of irrelevant whereas I actually mean just the opposite. Redundant climate records are precisely what we need!

On the other hand, to the extent that one can isolate the directly forced component, one can try to use it in attribution studies aimed at seeing whether or not a particular model has, say, the right mix of greenhouse gas and aerosol forcing.  For this purpose the hemispheric mean doesn’t give us too much to work with., but there is a lot more information than this in the spatial and seasonal structure of this directly forced component.  In particular,  one can increase the amplitude of this component by focusing on regions, such as Central Asia, where the oceanic influence is weaker. But it also helps to focus on those regions and times of year when internal (atmospherically-generated) variability is at a minimum (ie summer).

This kind of decomposition of land temperature trends has not received a lot of attention.  There are more papers that use AMIP simulations to attribute trends in the atmospheric circulation in this way, such as Deser and Phillips 2009.  It would be helpful if this kind of decomposition were available for multiple models in the CMIP5 archive. It would, in particular, be useful to know how robust the spatial and seasonal structure of the fixed “forcing” component is — the more robust this component, the more likely that one can subtract it cleanly from the observed variations and use the remainder to constrain forcing or sensitivity, at least over land.

The value of these AMIP simulations is that one can look in much more detail at the time evolution of the discrepancy between model and observations than is possible when working with a fully coupled model.  Consider, for example, the difference between the models’ and CRUTEM4 values in the last few years of this period. Is this due to problems with the land observations, the SSTs and sea ice driving the atmospheric model (we use HADISST), or the models themselves?  One interesting point, which I also failed to mention above, is that when one prescribes sea ice in these kinds of AMIP simulations one often just varies ice extent and not thickness, due to the lack of an observational basis for prescribing thickness. ( In contrast, fully-coupled climate models invariably try to simulate thickness variations directly).  Could these AMIP models be missing some warming over land due to this deficiency, especially in the last few years of the simulations?

Note added Jan 10:  An early paper that introduces the use of AMIP simulations for detection attribution studies that I was not aware of is Folland et al 1998.

[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]

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.

The animation above shows the evolution of RH on the 250hPa pressure surface in the upper troposphere and on the 850hPa surface in the lower troposphere  in a GCM (this is the same ~50km resolution model as discussed in several previous posts).  The loop covers one year with each frame showing a daily mean.  (This makes the animation a bit jumpy — I don’t have the a higher time resolution version of this field readily available.)  The brightest white is 100% relative humidity and darkest black 0%. Values less than 10% in the upper panel are common, in subsidence regions within the tropics or in stratospheric intrusions at higher latitudes. Air parcel trajectories cut though these pressure surfaces in complex ways and are difficult to visualize, these parcel trajectories being the key to understanding the resulting relative humidities. These animations can be useful in discussions with those unfamiliar with GCMs, who might mistakenly think that RH is fixed by fiat in these models.  The result that RH distributions remain more or less unchanged in warmer climates is an emergent property of these models.  Is it possible to construct a GCM that keeps the amount of water vapor itself more or less unchanged as the climate warms, rather than roughly following the saturation vapor pressure?  It would be nice to have such a model, which we could then analyze to see if it  provides as convincing a simulation of other aspects of the atmospheric circulation as do our existing GCMs.  But  no one has constructed such a model to my knowledge.

GCMs do simulate modest changes in the distribution of RH in response to increasing CO2.  In fact, there is actually considerable similarity across models in the pattern of RH change that is simulated, primarily reflecting an upward stretching of the troposphere and poleward expansion of the subtropical dry zones.  Here’s a figure from  Sherwood et al 2010 showing the mean relative humidity response, per degree C global surface warming, in the CMIP3 models, using the idealized scenario of a 1%/year increase in CO₂ and comparing the climate at the time of doubling to the control:

Shading means that 16 of the 18 models being averaged over agree on the sign.  Averaging different models together reduces the amplitudes of the changes seen in individual models, but highlights the robust part of these changes.  You can look at the individual model results in the paper; individual models have larger amplitudes and more spatial structure in the pattern of the response,but they never approach the magnitude needed to compete with the temperature dependence of the saturation vapor pressure (more than 10%/C in the upper tropospheric regions of prime importance for water vapor feedback.)

Differences between the climatological RH in different models can be substantial,  and the biases in  these models compared to various observational estimates can be substantial as well (see, for example, the recent paper of Risi etal 2012 which also has quite a few references to other papers discussing these biases). Are these biases large enough to detract from our confidence in the robustness of the basic result that RH doesn’t change that much with warming? The situation is similar to that described in Post #26 on high-resolution simulations of radiative-convective equilibrium in small domains — different models simulate very different RH distributions associated with differences in the way that the convection is organized, but each model when warmed hold its RH distribution nearly fixed because the convective organization is effectively unchanged.

One can try to shed light on this robustness in global models by turning to the fruit fly model that I discussed in Post #28 — a dry ideal gas atmosphere on a sphere forced by relaxing temperatures to a specified “radiative equilibrium” field and relaxing near surface winds to zero.  Galewsky et al 2005 add a simple water-like passive tracer to this model — a tracer that does not interact with the flow or the temperatures.  It just has a specified source at the surface (“evaporation”) and a sink that exists only when the water vapor pressure rises above a saturation value that is a function of temperature, in which cases it just resets the vapor pressure to saturation, with the water vapor that disappears in this process thought of as “precipitation”.  The resulting time mean relative humidity is shown on the right.  The left panel is just the mean simulation from the AR4 models lifted form the Sherwood et al paper.

In the figure on the right, the bold lines are the mean potential temperature, or isentropic,  surfaces. Outside of the tropics, one can think of the air trajectories as tending to align along these surfaces.  Also shown with lighter lines (harder to see) are the streamlines of the mean meridional circulation — the time and zonally averaged circulation in the latitude-height plane, indicating mean upward motion at the equator and downward motion in the subtropics.

The most obvious feature that this model captures qualitatively is the subtropical dry zones. Air parcels in these driest areas have either been carried down and warmed due to compression by the mean subtropical subsidence after losing most of their water in upward motion near the equator — or they have traveled down the midlatitude isentropic surfaces after having condensed most of their water during an earlier poleward and upward excursion.  (The point of this paper was to think about how to quantify the relative importance of these two classes of trajectories.)  Differences with the comprehensive models on the left are due in part to the absence of realistic boundary layer mixing spreading the evaporated water upwards, the absence of  a seasonal cycle and monsoons that move subtropical dry zones and wash out the minima in the annual mean figure shown on the left, and the distortion of the vertical structure of the outflow from the tropical rising motion.  (In the dry model, this outflow is spread over a broad layer of the troposphere, whereas in more realistic models with moist convection this outflow is confined more sharply to a layer near 200mb, causing the dry zone to be displaced upwards compared to the passive water model.)  The bottom line is just that the atmospheric flow is what prevents this model atmosphere from becoming saturated everywhere – by wringing water out of parcels of rising/cooling air and then bringing these parcels back down so their relative humidity drops as they warm.

Suppose you warm this dry model.  There is an interesting special case that Tim Merlis and I have been discussing recently.  The relaxation to “radiative equilibrium” temperatures replaces radiative transfer in this model, so you  warm the model climate by warming these radiative equilibrium temperatures. Suppose also that the saturation vapor pressure is exactly exponential in temperature so that it increases by a fixed percentage for a uniform increase in temperature.  And then increase the evaporation by the same fraction.  One can show that the solution in this warmer climate will have exactly the same relative humidity as the original one — water vapor will increase everywhere by this same factor.  This is admittedly a very special situation –  it works only for the passive case,  so that the water vapor equation is linear, and is modified if the warming is non-uniform, but it provides a simple foundation for thinking about more complicated situations. (This is somewhat misleading — see the first comment and response below). I think more could be done with this passive-water fruit-fly model, helping us think about what kinds of changes in relative humidity can be generated by non-uniform warming and a changing mix of trajectories — without the added complexity of latent heat release and moist convection.

I’ll discuss some observed RH trends in upcoming posts.

[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]

Percentage change in the precipitation falling on days within which the daily precipitation is above the pth percentile (p is horizontal axis) as a function of latitude and averaged over longtitude, over the 21st century in a GCM projection for a business-as-usual scenario, from Pall et al 2007.

(I have added a paragraph under element (1) below in response to some off-line comments — Aug 15)

When I think about global warming enhancing “extremes”,  I tend to distinguish in my own mind between different aspects of the problem as follows (there is nothing new here, but these distinctions are not always made very explicit):

1) increases in the frequency of extreme high temperatures that result from an increase in the mean of the temperature distribution without change in the shape of the distribution or in temporal correlations

The assumption that the distribution about the mean and correlations in time do not change certainly seems like an appropriately conservative starting point.  But if you look far out on the distribution, the effects on the frequency of occurrence of days above a fixed high temperature, or of consecutive occurrences of very hot days (heat waves), can be surprisingly large.  Just assuming a normal distribution, or playing with the shape of the tails of the distribution, and asking simple questions of this sort can be illuminating.  I’m often struck by the statement that “we don’t care about the mean; we care about extremes” when these two things are so closely related (in the case of temperature). Uncertainty in the temperature response translates directly into uncertainty in changes in extreme temperatures in this fixed distribution limit.  It would be nice if, in model projections, it was more commonplace to divide up the responses in extreme temperatures into a part due just to the increase in mean and a part due to everything else.  It would make it easier to see if there was much that was robust across models in the “everything else” part. And it also emphasizes the importance of comparing the shape of the tails of the distributions in models and observations.  Of course from this fixed-distribution perspective every statement about the increase in hot extremes is balanced by one about decreases in cold extremes.

(Added Aug 15)  The discussion of this topic is often confused by the fact that people are asking different questions.  Suppose we consider days that exceed some fixed temperature that is on the tail of the distribution of daily temperatures.  If the mean temperature warms by , while holding the distribution about the mean fixed, this number could increase dramatically, depending on the shape of the distribution, even if is much smaller than the width of the distribution.  In this case, the mean warming is contributing a small fraction of the temperature anomaly in these extreme warm events even though the probability of these events has increased a lot (see Otto et al, 2012 for a discussion of the Russian heat wave along these lines).  If we redefined our criterion for a very hot day by upping the criterion by the small amount we would go from a description of what is going on as one in which the “number of very hot days increases dramatically” to one in which “the number of very hot days does not change but they are on average warmer”:  .  My gut reactions to these two descriptions of the same physical situation are rather different.  The goal has to be to relate these changes to impacts (things we care about) to decide what our level of concern should be, rather than relying on these emotional  reactions to the way we phrase things.

2) increases in extreme precipitation that result from an increase in atmospheric moisture, this increase in turn resulting from the increase in saturation vapor pressure resulting from warming — without changes in the winds that are converging moisture into the region of interest during these extreme precipitation episodes;

There is an important sense in which the increase in high precipitation events is more basic, and more robust, than the changes in the mean precipitation.  Some expectations for the latter are discussed in Post #13-14 and include regions of increasing and regions of decreasing mean precipitation.  Changes in extremely high precipitation events seem to be simpler — we expect them to increase nearly everywhere.  It is precisely when one is strongly converging water into some region, creating a lot of precipitation, that the upper bound on the water vapor in the atmosphere comes into play most strongly. irrespective of what the time mean humidity is doing.  If you think of the dominant term that is trying to increase water vapor mixing ratios in regions of strong upward motion as , and assume that the atmosphere is saturated over some depth, then the rain rate would be determined by integrating over the layer within which condensation is preventing  supersaturation. Since the saturation mixing ratio at a given pressure is just a function of temperature, and the temperature profile would be moist adiabatic, we have a straightforward null hypothesis connecting the warming and changes in these precipitation extremes, just as we do for temperature extremes.

The figure at the top of the page, from Pall et al (2007) illustrates this nicely.  Take each grid point in a GCM and create a histogram of daily precipitation.  Look at the change in total precip above the p-percentile of precip values, for a particular scenario by the end of the 21st century.  To create a smooth zeroth-order picture, sum the p-percentile precip at each point over longitude and then compute the fractional change in the precip amount — as a function of p and of latitude. I like this plot because of the way it distinguishes between the subtropics (where mean precip is decreasing) and subpolar latitudes (where the mean is increasing) — but it does have the disadvantage, if I am interpreting it correctly, that these averaged results are dominated by the high precip regions at that latitude.  In subpolar latitudes, precip is increasing in both heavy and light precip events.  In the subtropics there is an increase in very heavy precip events (above the 90-95th percentile of daily values) but a decrease when the rainfall values are light. It is the latter that is evidently causing the reduction in the mean, along with an increase in the frequency of dry days not evident in this plot. SREX (Ch. 3) has a summary of observations of trends in extreme precipitation and a lot of references.

3) changes in the frequency or severity of storms or lower frequency climate anomalies, such as droughts,  resulting from changes in atmospheric or oceanic circulations on large scales.

An example might be a poleward shift in the Atlantic storm track increasing the frequency of extreme wind and extreme surface wave events on the poleward flank, and decreasing these same extreme events on the equatorward flank of the storm track. These changes in extremes do not result from any subtle change in the underlying dynamics of the storms or waves — the robustness of the changes in extremes depends entirely on the robustness of the large-scale storm track shift.

Another example is the constructive superposition of la Nina and global warming-induced drought over the southern tier of the continental US.  Radiative forcing due to increased well-mixed greenhouse gases expands the subtropics and shifts the midlatitude storm tracks polewards in a variety of models of different levels of complexity.  El Nino has the opposite effect, especially over and downstream of the Pacific, where it shifts the jet and storm track equatorwards.  So the opposite phase of the ENSO cycle, la Nina events, tends to reduce precipitation especially in the southern tier of the continental US (see here).  See also this analysis by Bergman et al 2010 of the connections between Pacific ocean temperatures and medieval megadroughts.  The la Nina response adds to the simulated effect of the greenhouse gases (here).  See also Lau et al 2008 for discussion related to this superposition.  By the same token, some of the effects of El Nino events on North America due to the changes in atmospheric circulation might be ameliorated. Even if the meteorology turns out to be basically a linear superposition, impacts of various kinds — forest fires, agricultural, etc, — will remain a source of strong nonlinearities.  It is the existence of these nonlinearities in impacts that makes this constructive interference for US drought between la Nina and warming important, even if the effects of warming on the ENSO variability itself turn out to be modest.

Finally, we have–

4) Changes in the intensity of storms.

There is a tempting hand-waving argument that storms will intensify because there would be more heat of condensation released in rising air, creating more buoyancy and stronger upward motion,  but there are a variety of reasons why this is not a convincing argument. In any case, you have to distinguish between extratropical storms and tropical cyclones — these have such different dynamics that they present us with two very different sets of problems.  I’ll try to get back to some of these eventually.  My point here is just to emphasize that, as outlined above,  there are reasons to expect changes in extremes that do not depend on these changes in storm intensity.

[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]

Animation of the sea surface temperature in a coupled climate model under development at GFDL,
the ocean component having an average resolution of roughly 0.1 degree latitude and longitude.
Click HERE for the animation.
(Visualization created by Remik Ziemlinski; model developed by T. Delworth, A. Rosati, K. Dixon, W. Anderson using MOM4 as the oceanic code base.)

As models gradually move to finer spatial resolution we naturally expect to gradually improve our simulations of atmospheric and oceanic flows.  But things get especially interesting when one  passes thresholds at which new phenomena are simulated that were not present in anything like a realistic form at lower resolution.  The animation illustrates what happens after one passes through an important oceanic threshold, allowing mesoscale eddies to form, filling the oceanic interior with what we refer to as geostrophic turbulence. At resolutions too coarse to simulate the formation of these eddies, flows in ocean models tend to be quite laminar except for some relatively large scale instabilities of intense currents of the kind seen in the snapshot north of the equator in the Eastern Pacific. (For a transition comparably fundamental in atmospheric models, one has to turn to the point at which global models begin to resolve the deep convective elements in the tropical atmosphere — see for example Post #19).

When one makes the transition to a mesoscale eddy-resolving ocean model, one is in a sense just catching up with standard-resolution atmospheric models — the eddy production process involved is essentially identical to the process, referred to as baroclinic instability,  that generates midlatitude cyclones and anticyclones in the atmosphere.  The difference is that the scale at which eddies are generated by this process is much smaller in the ocean than in the atmosphere.

[Theory tells us that a key scale is where is the vertical scale of the flow, is the Coriolis parameter (twice the angular velocity of the Earth multiplied by the sin of latitude), and is the “reduced gravity”, the gravitational acceleration multiplied by the factional change over the vertical scale in the potential density (the density of a parcel when carried adiabatically from its ambient pressure to a reference pressure). The bottom line is that the reduced gravity is much smaller in the ocean than in the atmosphere.]

Just as for the high resolution atmospheric simulations animated in posts #1 and #2 , it is a challenge to confront these simulations with observations in the most informative way.  One observational constraint that has been especially useful for a first look at the quality of the mesoscale eddy field is the estimate of kinetic energy in the surface flow provided by satellite altimetry.   (The horizontal gradient of sea surface height provides an estimate of surface currents through the geostrophic relation.) Here’s a comparison of this model with an observational estimate, described in Delworth et al 2011.  Note that the color scale is logarithmic — . The geostrophic relation breaks down near the equator.

Among many aspects of these eddy-resolving simulations that are worthy of close study — mesoscale eddies are known to interact with convection  in key regions of deep- water formation; eddies and vortices forming around the Cape of Good Hope appear to be important for the saltiness of  the Atlantic; and, perhaps most importantly, these eddies help set the strength and structure of the Antarctic Circumpolar Current and its sensitivity to changes in wind and thermal forcing  — this being a a key region for heat and carbon uptake.  Eddy heat transport across the circumpolar current could play a crucial role in regulating how fast the waters around Antarctica warm.  Lower resolution ocean models include closure schemes for the fluxes associated with these mesoscale eddies, but these remain relatively crude (I can say this because I have spent some time trying to develop these theories in both atmospheric and oceanic contexts, as illustrated here.)  There is little doubt that direct simulation is better than any existing closure schemes.

On the other hand, these oceanic eddies are not as dominant as they are in the atmosphere.  This is at least in part because the basin geometry creates north-south currents that  play a significant role in oceanic north-south heat transport, unlike the atmosphere where poleward heat flux is dominated by eddies.  (The latitude band of the Drake passage is distinct in this regard, with no meridional coast along which boundary currents can form, making the dynamics in the Circumpolar Current more atmosphere-like.  But we’ll have to stay tuned to see how our overall perspective on  the role of the oceans in climate change is altered by these eddy resolving ocean models — a problem that is being tackled at a number of modeling centers around the world.

Note: The calendar indicator in the lower left corner of the animation seems to be off.

[The views expressed on this blog are in no sense official positions of the Geophysical Fluid Dynamics Laboratory, the National Oceanic and Atmospheric Administration, or the Department of Commerce.]