# Isaac Held's Blog

## 48. Increasing vertically integrated water vapor over the oceans

Percentage changes in total water vapor, vertically integrated and averaged over 20S-20N over the oceans only, comparing the RSS microwave satellite product (red) to the output of an atmospheric model running over prescribed SSTs (HADISST).

This is a continuation of the discussion in the previous post regarding the increase in water vapor near the surface and within the boundary layer more generally as the ocean surface warms.  Models very robustly maintain more or less constant relative humidity in these lower tropospheric layers over the oceans as they warm, basically due to the constraint imposed by  the energy balance of the troposphere on the strength of  the hydrological cycle, and the tight coupling between the latter and the low level relative humidity over the oceans.  Do we have observational evidence for this behavior?  The answer is a definitive yes, as indicated by the plot above of microwave measurements of total column water vapor compared to model simulations of the same quantity.  These are monthly means of water vapor integrated in the vertical.  The observations are  RSS Total Precipitable Water Product V7.  The model is the 50km resolution version of GFDL’s HiRAM discussed in previous posts (on hurricane simulations , MSU trends , and land surface temperature trends)  which uses observed SSTs and sea ice extent from HADISST1. for the lower boundary condition. Data are monthly means, deseasonalized by removing each month’s climatology defined by averaging over 1988-2007, and plotted as percentage changes from the climatological average over the same domain.  The model results plotted are the spread of three realizations with different initial conditions (these are the runs from this model deposited in the CMIP5 database).

## 47. Relative humidity over the oceans

The change in near surface relative humidity averaged over CMIP5 models over the 21st century in the RCP4.5 scenario.  Dec-Jan-Feb is on the left and June-July-Aug on the right. From Laine et al, 2014.

We expect the amount of water vapor in the atmosphere to increase as the atmosphere warms.  The physical constraints that lead us to expect this are particularly strong in the atmospheric boundary layer over the oceans.   The relative humidity (RH — the ratio of the actual vapor pressure to the saturation value) at the standard height of 2 meters  is roughly 0.80 over the oceans.  At typical temperatures near the surface, the fractional increase in the saturation vapor pressure per degree C warming is about 7%.  So RH would decrease by about the same fraction, amounting to roughly 0.06 per degree C of warming if the water vapor near the surface did not increase at all.  Why isn’t it possible for RH to decrease by this seemingly modest amount?

## 46. How can outgoing longwave flux increase as CO2 increases?

Evolution in time of fluxes at the top of the atmosphere (TOA) in several GCMs running the standard scenario in which CO2 is increased at the rate of 1%/yr until the concentration has quadrupled.

A classic way of comparing one climate model to another is to first generate a stable control climate with fixed CO2 and then perturb this control by increasing CO2 at the rate of 1%/yr.  It takes 70 years to double and 140 years to quadruple the concentration.  I am focusing here on how the global mean longwave flux at the TOA changes in time.

For this figure I’ve picked off a few model simulations from the CMIP5 archive (just one realization per model), computed annual means and then used a 7 yr triangular smoother to knock down ENSO noise, and plotted the global mean short and long wave TOA fluxes as perturbations from the start of this smoothed series. The longwave ($L$) and shortwave ($S$) perturbations are both considered positive when directed into the system, so $N = L +S$ is the net heating.  The only external forcing agent that is changing here is CO2, which (in isolation from the effects of the changing climate on the radiative fluxes) acts to heat the system by decreasing the outgoing longwave radiation (increasing $L$).  But in most of these models, L is actually decreasing over time, cooling the atmosphere-ocean system.  It  is an increase in the net incoming shortwave ($S$) that appears to be heating the system –  in all but one case.  This qualitative result is common in GCMs.  I have encountered several confusing discussions of this behavior recently, motivating this post.  Also, the ESM2M model that is an outlier here is very closely related to the CM2.1 model that I have looked at quite a bit, so I am interested in its outlier status.

## 45. Dynamic retardation of tropical warming

Observed (HADCRUT4) surface temperature trends from 1980-2010, compared to the estimate of the forced response over this time frame obtained from the multi-model mean of the CMIP5 models.  From Knutson et al 2013.

In the late 80’s, Mark Cane, Steve Zebiak and colleagues wrote a series of papers – Zebiak and Cane 1987 is one of the first – about a simple oscillatory atmosphere-ocean model of the tropical Pacific, with the goal of capturing the essence of ENSO evolution and providing dynamical predictions of ENSO. In 1996 Clement et al subjected this model’s surface temperatures to a forced warming tendency and showed that it then evolves towards a state that favors La Nina, and a cold Eastern Pacific, over the warm El Nino state.

## 44. Heat uptake and internal variability — part II

I’m returning to an argument discussed in post #16 regarding the decomposition of the global mean warming into a part that is forced and a part that is due to internal variability. I am not looking here for the optimal way of doing this decomposition. I am just interested in getting a better feeling for whether an increasing ocean heat content over time is a “smoking gun” for the forced component being dominant, a term Jim Hansen and others have used in this context.  I’ll assume that we know that the heat flux has been into, not out of, the earth system (ie the oceans) averaged over the period in question, which could be the last half century or any period longer than a decade or two to insure that we can think in terms of a transient climate sensitivity (or transient climate response TCR) for the forced component.  (AR5 WG1 Ch. 3 has a synthesis of the observations of ocean heat content).  We’ll think in the most traditional terms, focusing on the global mean energy balance at the top of the atmosphere (TOA). Everything is considered to be a small perturbation from a control climate,  and the assumption is that we can just linearly superpose the forced component of this perturbation and the component due to internal variability.

Animation of near-surface wind speeds in rotating radiative-convection equilibrium, following Zhou et al, 2014.

I have discussed models of non-rotating radiative-convective equilibrium (RCE) in previous posts.  Given an atmospheric model one idealizes it by throwing out the spherical geometry, land-ocean configuration and rotation, creating a doubly-periodic planar geometry re-entrant in both x and y, while also removing any horizontal inhomogeneities in the forcing and boundary conditions.  In the simplest case, surface temperatures are specified and the surface is assumed to be water-saturated. The result is an interesting idealized explicitly fluid dynamical system for studying how the climate — especially that of the tropical atmosphere — is maintained by a balance between destabilization through radiative fluxes and stabilization through turbulent moist convection.  There is a lot that we don’t understand about this setup, which still contains all of the complexity of latent heat release and cloud formation.  But even though we don’t understand the non-rotating case very well, it is interesting to re-introduce rotation while maintaining horizontal homogeneity.  Adding rotation has a profound influence on the results — the model atmosphere fills up with tropical cyclones!  Some colleagues suggest referring to this system as TC World;  others suggest Diabatic Ekman Turbulence.  I’m going to stick with Rotating Radiative-Convective Equilibrium, or Rotating RCE for short.

## 42. Aqua-planet hurricanes and the ITCZ

Zonal (east-west) wind in the lower troposphere (850mb) in two simulations with a 50km resolution atmospheric model with zonally symmetric boundary conditions.  Only $180^\circ$ of longitude within the tropics (30S-30N) is shown. The ITCZ is located at $3^\circ N$ in the upper panel and $8^\circ N$ in the lower panel.  Simulations described in Merlis et al 2013. (White, Black) => winds from the (west, east). 6 frames/day for 100 days.

The frequency of formation of hurricanes/typhoons has mostly been studied in the past by trying to develop “genesis indices” – empirical relations between the frequency of storm genesis and the larger scale circulation and thermodynamic structure of the atmosphere. But there is an ongoing transition, picking up steam in a number of atmospheric modeling groups around the world, to using global atmospheric models that simulate hurricanes directly to study how genesis is controlled. One goal of this work is to understand how hurricane frequency responds to the warming resulting from increasing greenhouse gases. Posts #2, 10, and 33 describe some of our recent efforts at GFDL along these lines. That work uses models in a comprehensive setting, with a seasonal cycle and realistic distribution of continents. But Tim Merlis, Ming Zhao, Andrew Ballinger and I have started looking at analogous simulations with global models in more idealized settings.

## 41. The hiatus and drought in the U.S.

Correlation between seasonal mean precipitation  (Dec-Jan-Feb) and sea surface temperatures in the eastern equatorial Pacific (Niño 3.4: 120W-170W and 5S-5N) in observations (GPCP) and in a free-running coupled atmosphere-ocean model (GFDL’s CM2.1), from Wittenberg et al 2006.  Green areas are wetter in El Niño and drier in La Niña winters; red areas are drier in El Niño and wetter in La Niña.

(Sept 30: I have moved a few sentences around to make this read better, without changing anything of substance.)

It is old news to farmers and water resource managers in the southern tier of the continental US that La Niña is associated with drought, especially with rainfall deficits in the winter months.  Since the major El Niño event of 1997-8, our climate system has been reluctant to generate El Niño at the expected frequency and instead the Pacific has seen several substantial La Niña events with mostly near neutral conditions in between.  This La Niña flavor to the past 15 years has been identified as causing at least part of the hiatus in global warming over this same period by simple empirical fitting and more recently by Kosaka and Xie 2013, in which a climate model is manipulated by restoring temperatures to observations in the eastern equatorial Pacific.  I find the excellent fit obtained in that paper compelling, having no free parameters in the sense that this computation was not contemplated while the model, GFDL’s CM2.1, was under development, and the model was not modified from the form in which it was frozen back in 2005.   The explanation for the hiatus must, in appears, flow through the the equatorial Pacific. (I have commented on this paper further here.) These authors mention briefly an important  implication of this connection – the extended drought in the Southern US and the hiatus in global mean warming are related.

## 40. Playing with a diffusive energy balance model

Latitude of ice margin as a function of a non-dimensional total solar irradiance $q$ in the diffusive energy balance climate model described by North 1975, for different values of the non-dimensional diffusion $d$.  Stable states are indicated by a thicker line.

When we were first starting out as graduate students, Max Suarez and I became interested in ice age theories and found it very helpful as a starting point to think about energy balance models for the latitudinal structure of the surface temperature.  At about the same time, Jerry North had simplified this kind of model to its bare essence: linear diffusion on the sphere with constant diffusivity, outgoing infrared flux that is a linear function of surface temperature, and absorbed solar flux equal to a specified function of latitude multiplied by a co-albedo that is itself a function of temperature to capture the different planetary albedos for ice-free and ice-covered areas.  Playing with this kind of “toy” model is valuable pedagogically –  I certainly learned a lot by building and elaborating this kind of model — and can even lead to some nuggets of insight about the climate system.

## 39. FAT

The response of a 1km non-rotating doubly periodic model of radiative-convective equilibrium to an increase in surface temperature, in increments of 2K.  Left: temperature, showing a moist-adiabatic response; Right: fraction of area with cloud at each height, showing an upward displacement of upper tropospheric clouds. From Kuang and Hartmann 2007.

The presence of cirrus clouds in the tropics warms the troposphere because infrared radiation is emitted to space from their relatively cold surfaces rather than the warmer temperatures below the clouds. The response of these clouds can be important as feedbacks to climate change.  A reduction in the area covered by these high clouds would be a negative feedback to warming.  [7/25/13:  Several readers have pointed out that a reduction in the areas of high cloud cover would be a negative infrared feedback but a positive shortwave feedback and that the net effect could go either way.]  An increase in the average height of these clouds with warming, resulting in a colder surface than would be the case if this height did not increase, would be a positive feedback.  It is the latter that I want to discuss here.  GCMs have shown a positive feedback due to increasing height of tropical cirrus since the inception of global modeling (e.g., Wetherald and Manabe, 1980).  This is probably the most robust cloud feedback in GCMs over the years and is one reason that the total cloud feedbacks in GCMs tend to be positive.  This increase in cloud top height has, in addition, a clear theoretical foundation, formulated as the FAT (Fixed Anvil Temperature) hypothesis by Hartmann and Larson, 2002.