Framework for idealized climate simulations with spatiotemporal stochastic clouds and planetary-scale circulations

In climate predictions, clouds are the leading source of uncertainty. This is partly because, to simulate the fluid dynamics of climate over the entire globe, a large grid spacing must be used, so clouds are a subgrid-scale parametrization rather than a resolved feature. Here, a framework is investigated with finer grid spacing of $O\left(1\right)$ or $O\left(10\right)\mathrm{km}$ so that some clouds are not subgrid-scale; instead, clouds evolve on the numerical grid. This cloud evolution is achieved using stochastic modeling. Hence, the framework is idealized in the sense that the full fluid dynamics of cloud circulations is still not resolved, and simplified vertical structures are used. Nevertheless, the fluid dynamics model includes evolving clouds that interactively adjust in size, shape, lifetime, and regional coverage. In addition, different cloud types are included with different roles in the climate system, including deep convective clouds and also boundary-layer clouds such as shallow cumulus and stratocumulus clouds. Other basic aspects of the idealized climate system are planetary-scale circulations (e.g., Walker circulation) and radiation. With these ingredients (evolving clouds, planetary-scale circulations, and radiation), the framework has the potential for idealized investigations of climate change with interactive cloud–radiative feedback of individual clouds. Here, the formulation of the model equations is presented, and numerical simulations are shown to illustrate the model dynamics and climate change.

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Figure 1

Schematic diagram of cloud regimes and associated large-scale circulations. Deep convective clouds are associated with the ascending branch of the Walker circulation, and shallow clouds are associated with the descending branch of the Walker circulation. Used with permission from Ref. [8].

Figure 2

Comparison of precipitation from (a) observational data and (b) stochastic model. Note that a stochastic model will not reproduce the exact same locations of individual cloud clusters in observational data on a particular day. The statistics, though, can be compared and are similar (in terms of, for instance, power spectral density and the pdf of cloud cluster area). Used with permission from the American Meteorological Society [21].

Figure 3

Stochastic model representation [panels (e)–(h)] of four types of shallow cloud organization, as seen from satellite in panels (a)–(d). Yellow lines indicate areas of $5^{\circ }$ longitude by $5^{\circ }$ latitude. The model domain size is also $5^{\circ }$ by $5^{\circ }$. Used with permission from Ref. [22].

Figure 4

Schematic diagram of the vertical structures of the atmospheric model variables. The height labels $s, t$, and $m$ correspond to the surface of the Earth, the top of the atmospheric boundary layer, and the midtroposphere. Adapted and used with permission from the American Meteorological Society [41].

Figure 5

Illustrations of circulation cells that arise from the vertical structures from Fig. 4. Top: A deep circulation cell arises from $u_1$ and $w_1$. Gray shading indicates deep convective clouds associated with upward motion, as in the Walker circulation cells of Fig. 1. Bottom: Boundary-layer convergence from $u_b$ can create a circulation cell in concert with free-tropospheric, barotropic $u_0,w_0$. Bottom panel is used with permission from the American Meteorological Society [41].

Figure 6

Schematic diagram of the physical processes related to the atmospheric boundary layer, including interactions with the ocean, free troposphere, and radiation. Used with permission from Ref. [36].

Figure 7

The mean climate state (i.e., time-averaged quantities) from the simulation with standard parameters. (A) Ocean temperature. (B) Shallow cloud fraction, from boundary-layer cloud indicator, ${\sigma }_b$. (C) Deep convective cloud fraction, from free-tropospheric cloud indicator, ${\sigma }_f$. (D) Column water vapor, from summation of $q_{tb}$ and $q_f$.

Figure 8

Snapshots of (A), (B) shallow clouds and (C), (D) deep convective clouds. Two snapshots are shown for each quantity, one at the time of 8 years and one at the time of 10 years. White color indicates the presence of cloud, and black color indicates the absence of cloud. The domain has been rotated counterclockwise by ${90}^{\circ }$ to fit on the page, and the western warm pool region appears in the bottom and the eastern cold pool region appears on the top.

Figure 9

Space-and-time evolution plot of model variables (meridionally averaged) from the simulation with standard parameters during the last two years: (A) Ocean temperature. (B) Shallow cloud fraction. (C) Deep convective cloud fraction. (D) Total column water vapor.

Figure 10

The mean climate state (i.e., time-averaged quantities), as in Fig. 7, except from the climate-change simulation with enhanced longwave absorptivity parameters $a_{lb}^0=0.288$ and $a_{lf}^0=0.48$. The climate state here has an expanded warm pool region in the western part of the domain, associated with more deep convection (C) and more moisture (D) in comparison to the standard simulation in Fig. 7.

Figure 11

Mean climate states in the standard simulation versus climate-change scenario, presented as functions of the zonal coordinate $x$ after a time-average and meridional-average. (A) Ocean temperature, (B) shallow cloud fraction, (C) deep cloud fraction, and (D) column water vapor.

Figure 12

Time series of domain-averaged quantities, and comparison between the standard simulation and the climate-change simulation: (A) ocean temperature, (B) boundary layer temperature, (C) free-tropospheric temperature, (D) shallow cloud fraction, and (E) deep convective cloud fraction.

Figure 13

Sensitive study involving the two cloud albedo parameters $A_b$ and $A_f$. Statistics of model variables are time-averaged and meridionally averaged. Solid lines show the simulation result with standard parameters, dashed lines show results under modification $\pm \mathrm{\Delta }{A}_b$ of the shallow cloud albedo, and dash–dot lines show results under modification $\pm \mathrm{\Delta }{A}_f$ of the deep convective cloud albedo. The adjustment values are $\mathrm{\Delta }{A}_b=\mathrm{\Delta }{A}_f=0.05$.