# Hierarchical Modeling of Solar System Planets with Isca

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}with swirling vortices embedded within them, all visible from Earth and, with much more detail, from the recent Juno mission. Beyond Jupiter is Saturn, another gas giant, rather smaller, but surrounded by its beautiful and famous rings. Then, on to the ice giants, Uranus and Neptune, both unique in their own way. Uranus, for example, has an obliquity of 97${}^{\circ}$, meaning one of its poles points almost directly at the Sun at the solstice. Its atmosphere is a hydrogen–helium mix, with a nominal troposphere that in some respects is quite Earth-like: its temperature falls from about 320 K at its base to 53 K at its top, possibly containing both water and ammonia/methane clouds.

- There are so many planets that constructing a comprehensive model for each is simply infeasible.
- The observational data available for solar system planets are orders of magnitude less than that for Earth in terms of spatial and temporal coverage, even with modern missions to other planets such as the Venus Express or Juno. The data available for exoplanets are orders of magnitude less still. Thus, were we to choose to use a highly complex model to model a given planet, we would be in danger of having to make too many choices about important parameters and processes that are, at the very least, under-constrained by the observations. We would therefore run the risk of over-interpreting matches between model output and observations when the solutions could be highly non-unique, thus running the risk of “over-fitting” the data to the model.
- Although there is a diversity of planetary atmospheres, they obey the same physical laws. This, and the desire to understand as well as simulate (a desire that also holds for Earth) suggests that we should use models that take advantage of that commonality and build from there, with appropriate complexity for the problem at hand.

## 2. Isca, the Modeling Framework

- A spectral, primitive equation dynamical core in spherical co-ordinates.
- The shallow water equations on the sphere.
- The barotropic vorticity equation on the sphere [13].
- Optional inclusion of moisture and other tracers.

- A thermal relaxation scheme, in particular the Held–Suarez scheme and variants about it [14].
- A thermal relaxation scheme based on an analytic radiative-convective equilibrium state, with variable tropopause height depending on optical depth and other parameters, and a seasonal cycle.
- A thermal relaxation scheme based on an analytic radiative equilibrium state.
- A radiation scheme with two bands in the infra-red [17].
- The multi-band, comprehensive RRTM (Rapid Radiative Transfer Model) scheme [18].
- The multi-band, comprehensive SOCRATES scheme [19].

- A slab mixed-layer ocean, with or without Q-fluxes (that is, specified horizontal heat fluxes) to mimic heat transport (see e.g., [26]).
- Evaporative resistance over land, or a simple bucket model with evaporation dependent on how full the bucket is.
- Configurable land outlines, or land outline taken from a dataset (e.g., ERA-interim reanalysis for Earth [27]).
- Configurable topography, or topography taken from a dataset (for Earth or Mars).

## 3. Earth

#### 3.1. A Simple Thermal-Relaxation Model

#### 3.2. An Intermediate Complexity Model

#### 3.3. A More Comprehensive Model

## 4. Mars

#### 4.1. A Simple Model

#### 4.2. An Intermediate Complexity Model

#### 4.3. A More Comprehensive Model

#### 4.4. Comparison of Models and Observations

## 5. Jupiter

#### 5.1. A Simple Model

#### 5.2. An Intermediate Complexity Model

#### 5.3. Toward a More Comprehensive Model

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Zonal-mean zonal wind averaged over three winter months (March, April, and May (

**a**,

**b**) and December, January, and February (

**c**,

**d**)): (

**a**) sample model of Earth; (

**b**) intermediate-complexity model of Earth; (

**c**) high-complexity model of Earth; and (

**d**) JRA-55 reanalysis for 1958–2018.

**Figure 2.**Zonal winds at 250 hPa in our most realistic Earth model (

**a**,

**b**) and JRA-55 (

**c**,

**d**). The left column is averaged over December, January, and February, and the right column is averaged over June, July, and August.

**Figure 3.**Meridional overturning streamfunction in our most realistic Earth model (

**a**,

**b**) and from JRA-55 (

**c**,

**d**). The left column is averaged over December, January, and February, and the right column is averaged over June, July, and August.

**Figure 4.**Zonal-mean zonal wind for Mars averaged over the solar longitude range L

_{S}= 225°–315°, corresponding to a seasonal average centered on northern-hemisphere winter solstice at L

_{S}= 270°: (

**a**) Newtonian-cooling model of Mars, with radiative-equilibrium relaxation temperatures; (

**b**) grey radiation model of Mars; (

**c**) SOCRATES-radiation model of Mars with Martian topography included; and (

**d**) MACDA reanalysis from MY24-27 [40].

**Figure 5.**Zonal mean atmospheric temperatures in our most realistic Mars model (

**a**,

**b**) and MACDA (

**c**,

**d**). The left column is averaged over L

_{S}= 225°–315°, which is a seasonal average centered on northern-hemisphere winter solstice at L

_{S}= 270°, and the right column is averaged over L

_{S}= 45°–135°, which is a seasonal average centered on northern-hemisphere summer solstice at L

_{S}= 90°.

**Figure 6.**Surface pressure in our most realistic Mars model (

**a**,

**b**) and MACDA (

**c**,

**d**). The left column is averaged over L

_{S}= 225°–315° which is a seasonal average centered on northern-hemisphere winter solstice at L

_{S}= 270°, and the right column is averaged over L

_{S}= 45°–35°, which is a seasonal average centered on northern-hemisphere summer solstice at L

_{S}= 90°.

**Figure 7.**Zonal-mean zonal wind for Jupiter with prescribed deep-jet profiles: (

**a**) 1.5-layer shallow-water model of Jupiter, with prescribed deep jets (u

_{2}) with meridional wavenumber n = 26; (

**b**) grey radiation model of Jupiter, with prescribed jets at 14.5 bars (u

_{2}), with profiles in blue shown at the same time as those in (

**a**), where the deep jets are shown with n = 12; and (

**c**) zonal-mean zonal-winds plotted as a function of pressure as an average between 10,770 and 10,800 days of the same simulation shown in (

**b**). Solid contours are positive values. Values of “days” in (

**a**,

**b**) are the time in Earth days in the simulations shown.

**Figure 8.**Zonal-mean zonal wind for Jupiter with prescribed deep-jet profiles. Data are from the same simulations as in Figure 7, but showing Isca’s ability to well-simulate Jupiter’s well-known zonal symmetry in the presence of zonally-symmetric deep jets. (

**a**) The 1.5-layer shallow-water model averaged between 10,770 and 10,800 days. (

**b**) Grey radiation model of Jupiter, zonal-winds shown at 1 bar pressure level.

**Table 1.**Parameters for each of the runs shown in the present work. E-S, E-I, and E-C are the simple, intermediate, and complex models of Earth described in Section 3. M-S, M-I, and M-C are the Mars models described in Section 4. J-S and J-I are the simple and intermediate models of Jupiter from Section 5. Other short-hand used are Prim., meaning primitive-equation dynamics; SW, meaning shallow-water dynamics; SBM, meaning the simplified Betts–Miller convection scheme; ${\tau}_{\mathrm{Conv}}$, being the timescale for convective relaxation; and ${t}_{30}$, being the wall-time in minutes taken to run 30-Earth-days in this configuration using ${N}_{procs}$ processors. None of the model configurations displayed in this paper use Q-fluxes. All of the parameters below may be easily changed as desired.

Planet | E-S | E-I | E-C | M-S | M-I | M-C | J-S | J-I |
---|---|---|---|---|---|---|---|---|

Dynamics | Prim. | Prim. | Prim. | Prim. | Prim. | Prim. | SW | Prim. |

Rad. Scheme | Newt. Relax | Grey | Socrates | Newt. Relax | Grey | Socrates | N/A | Grey |

Seasons | Y | Y | Y | Y | Y | Y | N | N |

Number of levels | 30 | 25 | 40 | 25 | 25 | 25 | 1.5 | 60 |

Horiz. resolution | T42 | T42 | T42 | T42 | T42 | T42 | T341 | T213 |

Surf. Pressure (hPa) | 1013.25 | 1013.25 | 1013.25 | 6.1 | 6.1 | 6.1 | N/A | 15,000 |

Rot. Rate (${10}^{-5}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{s}}^{-1}$) | 7.29 | 7.29 | 7.29 | 7.12 | 7.12 | 7.12 | 17.6 | 17.6 |

Radius (km) | 6376 | 6376 | 6376 | 3396 | 3396 | 3396 | 69,911 | 69,911 |

Ocean depth | 20 m | 20 m | 20 m | N/A | N/A | N/A | N/A | N/A |

Land depth | N/A | N/A | 2 m | 2 m | 2 m | 2 m | N/A | N/A |

Fixed SSTs | N | N | Y | N | N | N | N | N |

Topography | N | N | Y | N | N | Y | N/A | N |

Conv Scheme | None | SBM | SBM | None | None | None | N/A | Dry |

${\tau}_{\mathrm{Conv}}$ (s) | N/A | 7200 | 7200 | N/A | N/A | N/A | N/A | 21,600 |

${t}_{30}$, ${N}_{procs}$ | 2.4, 16 | 1.2, 16 | 6.3, 16 | 14.5, 16 | 8, 16 | 16.4, 32 | 7, 32 | 124, 64 |

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**MDPI and ACS Style**

Thomson, S.I.; Vallis, G.K. Hierarchical Modeling of Solar System Planets with Isca. *Atmosphere* **2019**, *10*, 803.
https://doi.org/10.3390/atmos10120803

**AMA Style**

Thomson SI, Vallis GK. Hierarchical Modeling of Solar System Planets with Isca. *Atmosphere*. 2019; 10(12):803.
https://doi.org/10.3390/atmos10120803

**Chicago/Turabian Style**

Thomson, Stephen I., and Geoffrey K. Vallis. 2019. "Hierarchical Modeling of Solar System Planets with Isca" *Atmosphere* 10, no. 12: 803.
https://doi.org/10.3390/atmos10120803