A plot indicates that the incoming solar radiance, distributed over the Visible-Near IR, presents one curve for its measurement at the top of the atmosphere and a second, different (reduced intensities) after the irradiation reaches the Earth’s surface. The meaning of several thermal parameters - Heat Capacity; Thermal Conductivity and Diffusivity, and Thermal Inertia - is explored. A list of factors that influence variations in these parameters and the measured thermal radiances is outlined.

### Solar Irradiation as a Heating Mechanism

The amount of solar radiation reflected from land and sea surfaces, as well as the amount absorbed, depends partly on that portion of energy from the Sun that reaches these surfaces. In the Introduction, we stated that when we move from lower to higher wavelengths, this radiance rises rapidly to a peak at 480 nanometers (0.48 µm), then trails off to near zero through wavelengths out to about 3000 nanometers (3.0 µm). The plot below confirms that distribution and also shows many of the principal water, carbon dioxide, and oxygen absorption bands.

A thermal sensor detects radiant energy from a surface target, heated through radiation (solar insolation and sky radiance), convection (atmospheric circulation) and conduction (through the ground). Most sensed heat from surfaces has its origin in solar illumination, that varies with diurnal and seasonal changes, as well as cloud cover, but there is also a small, nearly constant, contribution from internal heat flux from Earth's interior (mostly from radioactive decay). Heat transfers into and out of near surface layers because of external heating by the thermal processes of conduction, convection, and radiation.

### Heat Capacity; Thermal Conductivity; Thermal Inertia

A primary objective of temperature measurements and related thermal responses is to infer something about the nature of the composition and other physical attributes of materials at the Earth's surface and, in its atmosphere. For any material, certain internal properties play important roles in governing the temperature of a body at equilibrium with its surroundings.

These properties include:

- Heat Capacity (C): The measure of the increase in thermal energy content (Q) per degree of temperature rise. It denotes the capacity of a material to store heat, and we give it cgs units of calories per cubic cm. per degree Centigrade (recall from physics that a calorie [cal] is the quantity of heat needed to raise one gram of water by one degree Centigrade). We calculate heat capacity as the ratio of the amount of heat energy, in calories, required to raise a given volume of a material by one degree Centigrade (at a standard temperature of 15° Centigrade) to the amount needed to raise the same volume of water by one degree Centigrade. A related quantity, specific heat (c), is defined as C = c/ρ (units are calories per gram per degree Centigrade) where ρ (rho) = density. This property associates Heat Capacity to the thermal energy required to raise a mass of one gram of water by one degree Centigrade.
- Thermal Conductivity (K): The rate at which heat passes through a specific thickness of a substance, measured as the calories delivered in one second across a one centimeter square area through a thickness of one cm at a temperature gradient of one degree Centigrade (units: calories per centimeter per second per degree Centigrade)
- Thermal Inertia (P): The resistance of a material to temperature change, indicated by the time dependent variations in temperature during a full heating/cooling cycle (a 24-hour day for Earth); defined as P = (Kc ρ )1/2 = c ρ (k)1/2. (The term k, related to conductivity K, is known as thermal diffusivity, and has units of centimeters squared per second; this parameter governs the rate of temperature change within a material; it is a measure of a substance's ability to transfer heat in and out of that portion that received solar heating during the day and cools at night). P is a measure of the heat transfer rate across a boundary between two materials. e.g., air/soil. Because materials with high P possess a strong inertial resistance to temperature fluctuations at a surface boundary, they show less temperature variation per heating/cooling cycle than those with lower thermal inertia.

In this chart, we show some characteristic values of these intrinsic thermal properties:

| Water | Sandy Soil | Basalt | Stainless Steel
--- | --- | --- | --- | ---
K | 0.0014 | 0.0014 | 0.0050 | 0.030
c | 1.0 | 0.24 | 0.20 | 0.12
d | 1.0 | 1.82 | 2.80 | 7.83
P | 0.038 | 0.024 | 0.053 | 0.168

9-5: Of the materials in this table, which will show the largest temperature fluctuation during a 24-hr heating/cooling cycle; which the smallest? ANSWER

9-6: We give here the values (without their units; see above) for Specific Heat; Thermal Conductivity; and Density (in that order) for these three rock types: Limestone: 0.17, 0.0048, 2.5; Sandstone: 0.47, 0.0125, 2.5; Shale: 0.391, 0.0042, 2.3. Calculate the Thermal Inertia P for each type. Are the P values different enough that, assuming a gray scale from 0 to 100, they would show up as sufficiently separable gray tones (assigned to each P value) on a black and white image of a target containing these three rocks? There is also a river passing through the scene; its values are 1.00, 0.0013, 1.0; will it show up as distinctly different? ANSWER

Interpreting thermal data and images of temperature distribution over an area is complex. In many instances, we must look for patterns of relative temperature differences rather than the absolute values, because of the many complex factors that make quantitative determinations difficult, such as:

- Number and distribution of different material classes in an instantaneous field of view
- Variations in the angle of thermal insolation relative to sensor position
- Dependency of thermal response on composition, density and texture of the materials
- Emissivities of the surface materials
- Contributions from geothermal (internal) heat flux; usually small and local
- Topographic irregularities including elevation, slope angle, and aspect (surface direction relative to the Sun's position)
- Rainfall history, soil-moisture content, and evaporative cooling effects near the surface
- Vegetation canopy characteristics, including height, leaf geometry, and plant shape
- Leaf temperatures as a function of evapotranspiration and plant stress
- Near surface (1 to 3 meters) air temperature; relative humidity; and wind effects
- Temperature history of the atmosphere above the surface zone
- Cloud-cover history (during heating/cooling cycle)
- Absorption and re-emission of thermal radiation by aerosols, water vapor, and air gases

9-7: All of the above factors play a role but some are more influential in determining the radiant temperatures than others. List, in your opinion, the five most important of these. ANSWER

Some factors have fixed or constant effects, while others vary with each sensor overpass. We may possibly correct for the influence of some of the variable factors, but this is difficult to do routinely. Measurements made at isolated individual points in a scene and extrapolated to the general scene have limited validity.

Primary Author: Nicholas M. Short, Sr. email: nmshort@ptd.net