You are welcome to use this model for your own research, but please acknowledge the source in any resulting publications, and include a reference to the above paper. Thanks!

- Depth-dependent thermophysical parameters
- Eclipses
- Endogenic heat flow
- Subsurface penetration of sunlight (solid-state greenhouse)
- Cooling by sublimation of various volatiles
- Arbitrary time variation of insolation (new in April 2006)

- No temperature-dependent thermophysical parameters
- Just calculates diurnal, not seasonal, temperatures (though seasonal temperatures could be calculated by brute force, using an appropriate time variation in insolation).
- Sublimation cooling is comet-like: no re-condensation of volatiles
- Thermal radiation from the surface only

- Solid-state greenhouse calculation may be buggy: calculated diurnal profiles are different from those published by Urquhart and Jakosky 1996, JGR 101, 21169-21176

Diurnal surface temperature variations are controlled by the thermal inertia, sqrt((thermal conductivity)*(density)*(heat capacity)), not by these parameters individually. However, the length scale of the subsurface temperature variations is determined by the skindepth, which combines these quantities differently: sqrt((thermal conductivity)/((angular velocity of rotation)*(density)*(specific heat))). Thermal inertia thus does not uniquely determine the skindepth. If only the thermal inertia is specified in the model, a default specific heat and density are assumed in order to calculate the skindepth and thus the depth scale of the model, though the surface temperature profile does not depend on the values chosen unless other parameters are specificed that explicitly specify the vertical length scale of the model, such as the sunlight penetration depth SUNDEPTH or the slab depth array ZARR.

Thermal conductivity is not specified directly, but is derived from the thermal inertia and the assumed or specified density and specific heat.

Parameters such as the number and thickness of subsurface slabs, and the number of timesteps per rotation, have default values that give accurate and stable results in most situations for vertically homogeneous models. For situations with minimal diurnal temperature variation (high thermal inertias, low temperatures, and/or rapid rotation), the model can be speeded up by decreasing NTINC, or a higher value of NTINC can be specified to avoid numerical instability for very large diurnal variability.

Note that the top slab is by default half the thickness of deeper slabs. This is because the model tracks temperature at the center of each slab, except for the surface temperature which by definition has to be the temperature at the TOP of the slab.

The model reports the quality of the thermal balance at the end of each run. For zero endogenic heat flow and zero subsurface penetration of sunlight (i.e., no solid-state greenhouse), thermal balance is achieved when the deep temperature equals the mean surface temperature. However, large variations in deep temperature generally produce only small variations in surface temperature- the "Total energy in/out" value is a better guide to the accuracy of the results than the surface/deep temperature discrepancy.

thermprojrs,tsurf,tod,rhel=9.0,alb=0.5,rot=10.0,emvty=0.9,ti=1e4 plot,tod/!dtor,tsurfDepth-dependent parameters: low-thermal-inertia layer over high-thermal-inertia layer. Time resolution (NTINC) is increased over default value to maintain numerical stability:

tiarr=[1e4+indgen(5),1e5+indgen(20)] zarr=[0.02*(1+indgen(5)),1+0.1*(1+indgen(20))] thermprojrs,tsurf,tod,rhel=9.0,alb=0.5,rot=10.0,emvty=0.9,ti=tiarr,zarr=zarr,ntinc=10000 plot,tod/!dtor,tsurfUse of CORRFAC to improve thermal balance convergence in the case of a solid-state greenhouse model:

Poor convergence:

thermprojrs,tsurf,tod,rhel=9.0,alb=0.5,rot=10.0,emvty=0.9,ti=1e4,sundepth=0.2,nrun=5 ... Energy Conservation Report at end of each run: Mean Mean Total Net Power Mean Power In Power Out Energy Out Surf. Deep Run W m-2 W m-2 In/Out W m-2 Temp. Temp. ----------------------------------------------------------- 0 2.700e+00 2.450e+00 0.9075 -2.498e-01 79.73 108.12 1 2.700e+00 2.457e+00 0.9101 -2.427e-01 79.81 109.71 2 2.700e+00 2.465e+00 0.9131 -2.346e-01 79.90 111.48 3 2.700e+00 2.473e+00 0.9161 -2.264e-01 79.99 113.28 4 2.700e+00 2.482e+00 0.9192 -2.182e-01 80.08 115.08Convergence improved:

thermprojrs,tsurf,tod,rhel=9.0,alb=0.5,rot=10.0,emvty=0.9,ti=1e4,sundepth=0.2,nrun=5,corrfac=6 ... Energy Conservation Report at end of each run: Mean Mean Total Net Power Mean Power In Power Out Energy Out Surf. Deep Run W m-2 W m-2 In/Out W m-2 Temp. Temp. ----------------------------------------------------------- 0 2.700e+00 2.450e+00 0.9075 -2.498e-01 79.73 108.12 1 2.700e+00 2.574e+00 0.9533 -1.261e-01 81.06 135.35 2 2.700e+00 2.669e+00 0.9885 -3.094e-02 82.02 156.25 3 2.700e+00 2.697e+00 0.9989 -2.952e-03 82.30 162.38 4 2.700e+00 2.700e+00 1.0000 1.979e-05 82.33 163.03 --------------For the latest version, see http://www.boulder.swri.edu/~spencer/thermprojrs/

Report bugs or suggestions for improvements to:

John Spencer

Southwest Research Institute

1050 Walnut St., Suite 400

Boulder, CO 80302

spencer@boulder.swri.edu

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