Paper Summary: The Transition to Double-Celled Circulations in Mock-Walker Simulations
One way clouds add uncertainty to climate projections is through their interactions with the atmosphere’s circulation. On the one hand, large-scale circulation cells are the main control on the spatial distribution of cloud types in the tropics: deep convective clouds are found in the rising branches of the Walker and Hadley circulations, and low clouds in the marine boundary layers beneath the descending branches. On the other hand, the strengths and spatial structures of these circulation cells are strongly influenced by convective transports of heat, moisture and momentum, by the release of latent heat in moist convection, and by the reflection, absorption and emission of radiation by clouds. These two-way interactions are still poorly understood, in part because we don’t have well established modeling set-ups that can resolve cloud-scale processes while also representing the key features that drive the circulations (SST gradients and differential rotation).
In this paper, Tim Cronin and I looked into the usefulness of “mock-Walker” simulations for studying cloud-circulation interactions. Mock-Walker simulations use high enough resolutions to (partially) resolve convection, and are run in long-channel or 2D domains, with SSTs varying in the long dimension. This forces the convection to aggregate in one portion of the domain (the “warm pool”), generating a circulation that looks something like what we see over the tropical Pacific. Mock-Walker simulations have been around for 30 years (at least since Raymond 1994) but have been relatively understudied compared to other models of the tropical atmosphere, like small-scale Radiative-Convective Equilibrium (though they are the focus of Phase 2 of RCEMIP).
This project took many twists and turns – because there was so much to look into and because we found these simulations to be frustratingly hard to understand. In the end, we focused on the tendency of mock-Walker simulations to form two vertically-stacked circulation cells, with outflow from the warm pool in the mid-troposphere, as the mean SST of the simulations is increased (compare top and bottom rows):
Figure 1: Mean relative humidities (colored contours) and streamfunctions (black contours) for the mock-Walker simulations (left three columns) and the ERA5 data (rightmost column).
We weren’t the first to see this behavior, but we showed that the transition from single- to double-celled circulations is robust to the use of 2D or 3D geometries and to the use of different microphysics schemes. The transition occurs right around the observed mean SST of 300K and is favored by the use of larger zonal SST gradients (i.e., it’s more prevalent in La Nina conditions than in El Nino conditions).
By comparison, monthly reanalysis data favor single-celled circulations, though there are hints of a double-cell when the tropical east Pacific is anomalously dry (bottom right panel of Figure 1). Comparing the simulations with the reanalysis data also shows that mock-Walker simulations tend to be exceptionally dry over the cold pool, with relative humidities approaching 0%. So there seems to be a link between low relative humidities and double-celled circulations.
Why do mock-Walker simulations transition to double-celled circulations at warm temperatures? This turns out to be a tricky question and we weren’t able to give a complete explanation. The vertical velocities over the cold pool (ɷ) are largely set by radiative-subsidence balance:
ɷ = Q / S
So if we had models for the radiative cooling Q and the stability S we could explain the transition (Yano et al proposed an explanation based on the vertical profile of convective heating, but we wanted to steer clear of this).
In the supplement we combined the one-dimensional simple spectral model (SSM1D) for atmospheric radiative cooling of Jeevanjee and Fueglistaler (2020) with an assumption of moist adiabatic stratification to obtain an equation for ɷ. This suggests that vertical variations in relative humidity are important, as ɷ would otherwise increase monotonically with height. It also suggests ɷ is more sensitive to relative humidity variations at warmer temperatures, consistent with the simulations. But SSM1D assumes vertically-uniform relative humidity, and incorporating variable relative humidity into SSM1D is hard because radiative cooling depends on both the relative humidity at each level and on the water vapor path above it. The stability also isn’t very moist adiabatic over the cold pools of these simulations.
So this approach has some promise, but the simulations have clear departures from the simple picture of the tropical atmosphere its based on A full theory for the double-cell transition would also need to model the horizontal moisture and temperature fluxes, and how these affect Q and S.
Previous studies have eliminated the double-cell by fixing the radiative cooling to a prescribed profile that is constant in most of the troposphere. However, we showed that this does produce a double-cell at warm enough SSTs (see third column of Figure 1). This is easier to explain: if Q is constant then ɷ just depends on the inverse stability, and S develops a mid-tropospheric maximum at warmer surface temperature (this is also discussed in the supplement), eventually producing a mid-tropospheric minimum in ɷ.
Figure 2: Mean relative humidities (colored contours) and streamfunctions (black contours) in the mock-Walker simulations with smaller domain sizes (top row), with mean winds (middle row) and with the moisture source (bottom row)
Finally, we tried several other strategies for eliminating the double cell transition, including reducing the domain size and adding mean winds. The most successful approach (suggested by Guy Dagan, one of the paper’s reviewers) was adding a moisture source which is activated whenever the relative humidity drops below 50%. The moisture source succeeds in eliminating the double-celled circulation at the control mean SST of 300K, but the transition still occurs at 305K (see bottom row of Figure 2), likely due to the stability maximum again. So this set-up is promising, but we didn’t investigate whether the moisture source distorts the warm pool convection, nor how/whether it should be adjusted under warming.
In summary, mock-Walker simulations have some potentially important differences with the observed atmospheric flow over the tropical Pacific: the extreme dryness over the cold pool and the tendency for the simulations to form double-celled circulations. The relevance of the transition from a single- to a double-celled circulation in warmer climates for the real tropical atmosphere is still unclear, but these simulations suggest several different mechanisms by which the transition could occur. It seems worth investigating Walker circulations further -- either to rule out such strong circulation changes or to determine that they are physically plausible. We didn’t discuss it in the paper, but the transition dominates the response of mock-Walker simulations to warming (e.g., cloud feedbacks), so it could have a substantial impact on Earth’s climate sensitivity if it occurred in the real world.
