This document discusses the details of using the DIRSIG image and data generation model to simulate thermal infrared sensing systems.

## Overview

The DIRSIG model includes the ability to model self-emission from surfaces and volumes in the scene. This self-emission arises from blackbody radiation of those surfaces and volumes having temperatures greater than absolute zero. Radiometric simulations in the mid-wave infrared (MWIR) from 3 → 5 microns and the long-wave infrared (LWIR) from 7 → 14 microns will require the temperature of every surface in the scene to be either assigned or modeled. This handbook was written to help users understand how to assign or model temperatures in DIRSIG for thermal simulations. It is intended to be friendly to those with little to no temperature modeling experience.

### Heat Transfer Basics

This section will attempt to summarize basic heat transfer, but the reader should be aware that entire books are devoted to the subject. Heat transfer is the energy transferred between an object and its environment due to a temperature difference between the two. There are three basic mechanisms for heat transfer: (1) convection, (2) conduction and (3) radiation. They are described individually for clarity, however in reality a given system will typically exhibit all three processes simultaneously.

As an example, consider a block of wood sitting on a stone slab. The block of wood can be either heated or cooled by air passing over it (convection), by the stone slab on which it is in contact (conduction) and finally by it absorbing photons from the Sun and other sources (radiation).

The following sections give a brief overview of the theory and relevant parameters for these mechanisms.

#### Convection

Convection is the heat transfer caused by the macroscopic movement of matter. Just as molecules of high temperature possess more kinetic energy, fluids of a high temperature are less dense than of low temperature. The difference in the density (and temperatures) within the fluid create the macroscopic convection currents. As a first example consider a pocket of air. The hot air (less-dense) rises due to buoyant forces and the colder air (more-dense) falls.

To be explicit, convection is really the combined heat transfer due to the macroscopic bulk movement and the random molecular motion. This can be demonstrated considering the example of a fluid in motion and its barrier, both at different temperatures. At the surface boundary, the velocity of the fluid is zero, and thus all of the heat transfer is due solely to the random molecular motion. As you go further from the boundary, the velocity of the fluid increases to some finite value and additionally, the temperature decreases.

The macroscopic heat transfer is due to the fact that the thermal boundary layer grows as the flow progresses in the x direction and heat in this layer is swept downstream and eventually to the fluid outside the boundary layer.

There are essentially two types of convection: forced and natural. The hot air example above is an example of natural convection. Air blowing over the earth as a result of atmospheric wind is an example of forced convection. However, both obey the same rate equation given below.

\begin{equation} q_\mathrm{conv} = h(T_a - T_b) \end{equation}

where h is the convection heat transfer coefficient and Ta and Tb represent the temperature gradient.

#### Conduction

Conduction is the mechanism described by heat transfer through a medium in direct contact with surfaces of different temperatures. The first requirement for conduction is that the medium is not moving. Thus the medium must be a rigid solid, or if fluid, it must have no circulating currents (note that circulation is sometimes referred to as the fourth heat transfer mechanism).

If there is no large-scale movement then the heat transfer must be at the molecular and atomic level. Recall that molecules and atoms at any temperature above absolute zero are in motion. The motion is measured by the kinetic energy of the atoms and molecules. Temperature is by definition the measure of the average kinetic energy. This kinetic energy is due to the motion of the atoms and molecules globally, as well as the internal molecular motion; rotational, vibrational, etc. When atoms or molecules collide, energy is transferred. In terms of temperature, hotter (faster) atoms lose some energy, while the (slower) cooler atoms gain energy. Conduction is defined as the transfer of the energy in this manner.

Consider a group of atoms with high kinetic energy isolated from a group of atoms at a lower temperature via an ideal thermal insulator. At this point nothing interesting happens. If however the thermal insulator is removed, the atoms begin colliding randomly with each other, and at some time t1 > t0, the atoms will reach an equilibrium temperature. Now consider replacing the thermal insulator with a material of some given thermal conductivity. Thermal conductivity is a material property which describes the rate at which the material conducts heat. All materials have some thermal conductivity as a perfect vacuum is the only ideal insulator.

We can now quantify the heat transfer rate in terms of the thermal conductivity, k, temperature difference, dT, and the direction of energy transfer dx.

\begin{equation} q_\mathrm{cond} = -k\frac{dT}{dx} \end{equation}

Radiation is the mechanism of heat transfer where electromagnetic energy is either absorbed from an external source by the object or emitted by the object into the environment. Remember that any object at a temperature above absolute zero will radiate energy. A perfect radiator, also known as a blackbody, has the characteristic that it is a perfect absorber and in turn a perfect emitter. Planck derived the equation of spectral radiant exitance from a blackbody. It is given by Planck’s equation below.

\begin{equation} M_{\lambda BB}= 2 \pi h c^2 \lambda^5 (e^\frac{hc}{\lambda k T} - 1)^{-1} \end{equation}

Integrating Planck’s Equation yields the total exitance from a blackbody. This is knows as the Stefan-Boltzmann equation. Note that the total energy is proportional to the Temperature of the blackbody raised to the fourth power.

\begin{equation} M = \sigma T^4 \end{equation}

where sigma is the Stefan-Boltzmann constant.

In reality real objects are not perfect absorbers or emitters. We introduce emissivity as the ratio of the object’s spectral exitance to that of an ideal blackbody at the same temperature. From the equation it is obvious that the emissivity is a number between 0 and 1 and it can vary spectrally (as a function of wavelength).

An object is simultaneously absorbing and emitting with surrounding surfaces. Determination of the overall rate of heat transfer becomes complicated very quickly. A common example used in heat transfer is a small object completely surrounded by a larger surface (picture a ball hovering within a larger sphere). Whereas convection and conduction rely on a medium for heat transfer, radiation can occur in a vacuum. The heat transfer of the surface and surroundings is given in the following equation.

\begin{equation} q_\mathrm{rad} = \varepsilon \sigma {(T_o^4 - T_s^4)} \end{equation}

where e is the spectral emissivity, To is the temperature of the object and Ts is the temperature of the surroundings.

### Thermodynamic Properties

Materials in the world (solids, fluids, surface materials) have intrinsic thermodynamic properties that describe their thermal behavior. These properties are invariant to the heat transfer problem and will be important to understand when defining them in DIRSIG scenes. The units listed in the following table are SI units. The units required for temperature models can vary, depending on the model. It is important to always define thermal properties in the correct units.
 h Convection Heat Transfer Coefficient $\frac{W}{m^2 K}$ Defines the rate of heat transfer via Convection. This property is a surface-level property, as convection is a heat transfer mechanism that occurs at an interface between a solid and a fluid. k Thermal Conductivity $\frac{W}{m K}$ Defines the rate of heat transfer via Conduction. In addition to the temperature gradient, thermal conductivity has a direct effect on the rate of conductive heat transfer. This property can be thought of as "how well a material conducts heat". ε Thermal Emissivity Unitless The emission and absorption rate of thermal radiation is described by this property. This is a spectral property (changes value based on wavelength). The emissivity plays a role in the heat transfer problem (temperature prediction) as well as the radiance problem (thermal imagery). α Absorptivity Unitless Describes the ratio of the incoming solar radiation that is absorbed into the surface and converted to thermal energy. Cp Specific Heat $\frac{J}{kg K}$ Specific heat can be described as the amount of energy required to change one unit of mass by one degree. This property quantifies how much thermal energy is "stored" in an object. ρ Mass Density $\frac{kg}{m^3}$ The mass density (mass per unit volume) is used in thermal calculations to define the amount of mass into (or out of) which the heat is being transferred. Some advice for how to assign these parameters can be found in the guide to assigning thermodynamic properties.

The convection heat transfer coefficient h is difficult to parameterize in thermal models because it can depend on many factors. Surface roughness, fluid properties such as viscosity, stability (vertical temperature change), and humidity (of air) can affect the convection rate. This coefficient tends to be the largest source of uncertainty in temperature prediction models. Some models, such as MuSES allow the user to explicitly define h, while some models such as THERM calculate h at runtime based on a parameterization that depends on the problem conditions (e.g. Wind Speed).

### Temperature Prediction Approaches

While many complex modeling approaches exist, it is useful to think about temperature prediction as a balance between the three heat transfer mechanisms (convection, conduction, and radiation). By definition, an energy balance approach assumes $\Sigma E_{in} - \Sigma E_{out} = 0$, or the energy coming in is equal to the energy going out. When this is true the system is as thermodynamic equilibrium. The $E$ in this case accounts for the sum of all three heat transfer mechanisms. Solving this complex system of differential equations (each of which is dependent on knowing the temperature) is non-trivial, and is often approached using an iterative method of calculation. When setting up temperature models, it is useful to keep the underlying heat transfer physics in mind.

### Requirements for a Thermal Simulation

To perform a thermal simulation in DIRSIG, the simulation inputs must provide the following:

• Surfaces (and volumes) in the scene must have a temperature that drives self emission.

• Weather data must be available to drive predictive temperature models that are used.

• Surfaces (and volumes) in the scene must have optical properties that are valid in the appropriate wavelength regions (e.g., mid-wave and/or long-wave infrared).

• The DIRSIG5 scene database must be compiled to include the appropriate wavelength regions (e.g., mid-wave and/or long-wave infrared).

• The sensor must contain detectors that are sensitive in the appropriate wavelength regions (e.g., mid-wave and/or long-wave infrared).

• The DIRSIG5 convergence criteria should be adjusted to account for the lower radiances expected at these wavelengths.

## Temperature Model Options

When running a thermal simulation, every object in the scene acts as a source. The amount of thermal emission from each surface depends on the surface temperature. Because of this, accurately assigning or predicting surface temperatures will have a large impact on the accuracy of the simulation output. In DIRSIG there are options for either assigning temperatures or predicting temperatures. The "best" option will depend on the initial resources and project needs. The following sections, each option is described so users can make informed decisions when planning scene construction and/or modification. The computationally expensive calculations associated with most temperature prediction models are disabled by default. They are automatically enabled when a sensor with spectral coverage above 3 microns (e.g., a MWIR and/or LWIR sensor) is part of the simulation. The user can force the enabling of these calculations via the `--force_temperature_prediction` command-line option.

### Data-Driven Temperatures (data-driven)

The data-driven temperature solver should be used when temperature data is available as an input to the simulation. Temporally varying temperature can be provided to produce temperatures that change over time.

### Temperature Map (data-driven)

A Temperature Map can be used to apply temperature data to an object. This type of map is applied similarly to other property maps. This allows the temperature assignment to vary spatially across the surface of the object.

### Balfour (predictive, empirical fit)

The Balfour temperature prediction model [Balfour] uses empirical methods to estimate temperature. The model inputs are derived from thermal imagery data. The end result is a 5-term polynomial of weather data and empirically derived coefficients.

### THERM (predictive, physics-driven)

THERM has been the workhorse temperature prediction model for DIRSIG for decades. A physics-based, energy balance model is used to predict the surface temperature based on intrinsic thermodynamic properties of the materials combined with provided weather data. THERM is a 1-dimensional slab model that takes into account the three heat transfer mechanisms: conduction, convection, and radiation to estimate the equilibrium surface temperature. Advice and helpful tips on how to assign the thermodynamic properties for THERM can be found in this guide.

### MuSES (predictive, physics driven)

The MuSES temperature prediction package is developed and maintained by ThermoAnalytics, Inc. MuSES is a high-fidelity temperature prediction model that calculates internal and external temperatures in full 3D and accounts for complicated heat transfer mechanisms such as internally generated heat and internal circulation. This model is recommended when very realistic thermal signatures are necessary for in-scene targets. MuSES is not capable of modeling full scenes and is usually combined with another temperature solver for the background geometry. See the appropriate section of the Temperature Solvers manual for more information about incorporating MuSES results into DIRSIG.

## Weather Model Options

A thermal simulation also needs weather to drive the heat transfer calculations. The temperature model and atmosphere can both be affected by the defined weather conditions. However, these weather conditions are independent of each other. For example, There is nothing in DIRSIG that will stop a simulation from running with summer-like weather in the temperature model and winter-like weather in the atmosphere model. It is up to the user to ensure the weather that drives the atmosphere and the weather that drives the temperature model are similar enough to give physically realistic results.

### THERM Weather

The ThermWeather Plugin brings compatibility for the legacy THERM weather files to DIRSIG5. The old THERM weather file format is fully described in the ThermWeather plugin manual. This plugin allows the use of legacy weather data files from other simulations, creation of new hypothetical weather files via DIRSIG’s Weather Data Generator in the GUI, and import of external data using the makewth utility, which can convert CSV weather data or data from NSRDB (see below) to the THERM weather file format.

### NSRDB Weather

The National Solar Radiation Database (NSRDB) provides near-global coverage of weather data. The NsrdbWeather Plugin provides the ability to use NSRDB files in DIRSIG5 sims. The NsrdbWeather Plugin has the advantage of reading in a full year of weather data (versus ThermWeather’s 48 hours of data). This extended weather coverage prevents users from inadvertently running thermal simulations with weather from the wrong part of the year.

## Surface and Bulk Optical Properties

Any surface (or volume) in the scene that has a temperature greater than absolute zero will produce self emission. The spectral graybody radiance from the surface (or volume) is a function of the temperature (discussed previously) and the spectral emissivity. The DIRSIG material subsystem provides a wide variety of surface properties and bulk properties. For surface materials, the model will compute the complementary reflectance or emissivity from the other, so the user does not need to explicitly provide a spectral emissivity property for a material. As long as the spectral reflectance is defined in the MWIR and/or LWIR wavelength region, the corresponding spectral emissivity will be computed. When using a BRDF model, the directional hemispherical emissivity (DHE) will be computed from the directional hemispherical reflectance (DHR) as DHE = 1 - DHR. The DHR is automatically computed computed by hemispherically integrating the BRDF at a given view geometry.

## Scene Compilation

As part of the scene compilation process performed by the scene2hdf tool, the spectral optical properties of all the materials in the scene are resampled to a unified spectral range and resolution. In order to generate an input scene HDF for DIRSIG5 that includes the appropriate spectral coverage options must be employed. Please refer to this section of the `scene2hdf` manual for the options to specify the spectral range and sampling of a scene during compilation.

## Sensor Considerations

To collect thermal imagery during the simulation, the sensor(s) modeled in the simulation need to include spectral coverage in the MWIR and/or LWIR wavelengths regions.

## Convergence Considerations

The radiance threshold used in the default convergence criteria in DIRSIG5 are optimized for reflective region (VIS, NIR and SWIR from 0.4 → 2.5 micron) simulations. In these regions, the magnitude of the absolute radiance is significantly higher than in the MWIR and LWIR. As a result, the absolute radiance threshold should be adjust to account for the difference. As outlined in this table, it is suggested that the radiance threshold be reduced to `1e-08` for a MWIR and/or LWIR simulation:

`\$ dirsig5 --convergence=20,100,1e-08 thermal.jsim`

## References

• [Balfour] Balfour, L. S. (1995, June). Simple thermal model for natural background elements. In 9th Meeting on Optical Engineering in Israel (Vol. 2426, pp. 79-84). SPIE.