Advanced Tutorial

Revision as of 18:06, 29 July 2017

Parameter Dependent Variables

The Heat Transfer between surfaces and the atmosphere has been proving to depend on the temperature of the materials on the surface.

See Section 3.2.1 of Kieffer (2013) (Online Article) or Download PDF

Seasonal Dependant Parameters

Albedo and dust opacity (ALBEDO and TAUD) have the capability of being input as a 2 x n array, where n is the number of seasons desired. The first column contains all the values of albedo or dust opacity. The second column contains all the seasons that correspond to albedo or dust value. The season corresponding to a particular albedo or dust opacity must be in the same row as the albedo or dust value. These will be input by KRC together. You can use as many values for albedo or dust opacity as desired.

Example

Start davinci as normal and then create an array with the command cat2(). Set this command equal to a variable to input into KRC later. The cat2() command allows you to create your own array (visit DavinciWiki for more information).

Note: All data type values within cat2() must match. Therefore, even if you are using integers with floating point values, you must add decimal points (even just zeros) to your integer values.

>davinci
dv>

dv> albedoArray = cat2(.23//45.00,.25//90.00,.24//135.00,.25//180.00,.24//225.00,.23//270.00,.23//315.00)
2x7x1 array of float, bsq format [56 bytes]
0.2300000042    45.00000000   
0.2500000000    90.00000000   
0.2399999946    135.0000000   
0.2500000000    180.0000000   
0.2399999946    225.0000000   
0.2300000042    270.0000000   
0.2300000042    315.0000000   

The same can be done with dust opacity. Once the array is created, use this variable in place of any single value you might normally input for ALBEDO or TAUD.

Temperature Dependent Parameters

It has been proved that conductivity and specific heat are affected by temperature.

The parameter LofkT determines whether or not these temperature-dependent parameters will be used in the calculations.

Set LofkT = "T" to use temperature-dependent parameters.

When LofkT = "T", KRC requires the conductivity temperature-dependent coefficients (ConUp0, ConUp1, ConUp2, and ConUp3 and ConLo0, ConLo1, ConLo2, and ConLo3) and specific heat temperature-dependent coefficients (SphUp0, SphUp1, SphUp2, and SphUp3 and SphLo0, SphLo1, SphLo2 and SphLo3) that define the third order temperature-dependence relationship of conductivity and specific heat (see Temperature-Dependent Parameters).

Davinci has the built-in function materials_krc() which automatically calculates these coefficients for the user.

However, these coefficients can be calculated by the user with the materials_krc() function.

Example

Start davinci as normal, and type the materials_krc() command to bring up a menu of input/output for the command.

>davinci
dv>

dv> materials_krc()

Calculates the coefficients for T-dependent specific heat, conductivity, and Density
Also returns the standard K/rho/Cp for those materials
Returns a structure with various coefficients

$1 = Define the material thermal inertia

$2 = "basalt" or "H2O" or "CO2", material physical properties (Default="basalt")
Options:
    porosity = set the material porosity, 0.-1. (Default=0.4 if below I=315,
        otherwise overwrites input porosity to vary from 0.4 @ I=315 to 0 @ I=2207 (bedrock))

    layer = specify the upper(Up)/lower(Lo) layer (Default="Up")
s.piqueux 4/29/13

To manually determine the coefficients, the first two arguments must be input. The porosity and layer are optional, but require porosity=value between 0 and 1 and layer="Up" or "Lo" (with the quotes).

dv>materials_krc(200,"basalt",porosity=.3,layer="Up")
struct, 4 elements
    req: struct, 11 elements
        INERTIA: 200   
        SphUp0: 554.3699951   
        SphUp1: 214.6999969   
        SphUp2: -37.52399826   
        SphUp3: 13.62800026   
        SPEC_HEAT: 595.5549927   
        DENSITY: 2065.000000   
        ConUp0: 0.03999998048   
        ConUp1: 0.01780755445   
        ConUp2: 0.007334869355   
        ConUp3: 0.001111081685   
    COND: 0.03252505884   
    compositon: "basalt"
    porosity: 0.3000000119   

Other Bodies

KRC uses a coding system called PORB to model bodies in the Solar System other than Mars

For an in depth understanding of PORB see Planetary Orbit (PORB) General User’s Guide or the The KRC Planetary ORBit (PORB) System Advanced Design Guide

Planets

KRC can be applied to non-tidally locked, rocky Planets:

• Mars
• Earth
• Venus
• Pluto

Comets

List of available Comets

Asteroids

List of available Asteroids

Multi-Material Surfaces

Davinci and KRC both use one material as the default. However, two materials may be specified.

Changing Material Thickness

Multi-Layer Surfaces

It is important at this point to understand the distinction between layers and materials.

• Layers:

• KRC is designed to function as a multi-layered model. The purpose of this is to create model stability.

Understanding Model Stability and Convergence

Model stability is a feature of modeling used to ensure the values generated by KRC are physically possible as well as accurate. The model stability is based on certain convergence factors of KRC. The convergence factors use temperature to determine model stability. As thermal energy reaches the surface of Mars the heat that is able to penetrate into the surface begins to diminish. This is known as Heat Diffusivity. It is governed by the Heat Flow Equation which depends on conductivity, specific heat, density, time and depth. As depth and time increase the diffusion of heat increases. Therefore, less heat will penetrate into deep layers of the surface. The diurnal temperature of a layer is assumed to have a range of variability. This variability decreases with depth and time. Therefore, at a certain depth the diurnal temperature variation of a certain layer is 0. If the temperature of a layer is determined to be constant over more than one day, or very small, the model is considered to be stable.

i.e. When the daily temperature changes in a layer is 0, that layer is assumed to be the bottom-most layer. The model stops adding layers and the model is said to have converged and become stable.

There are other factors used in convergence and model stability. See Kieffer (2013) for more.

Changing Layer Thickness

Including Frost

Linked Runs

Jumped Perturbations

Atmospheric Parameters

Adequately Scale Dust Opacity