# Thermal Imaging

**Dimensioning of an hydraulic system**

**for water bombing from an aircraft**

**Thermal imaging**

Thermal imaging gives the temperature differences in each point on the ground and thus allows to describe thermally the area. The temperature distribution helps us to analyse the burned areas and gives us valuable information to be able to control the fire by water bombing.

Indeed, when water is dropped to extinguish a fire, the temperature before and after the drop gives the cooling of the ground. This cooling is due to a heat exchange between the hot ground and the cold water, and is proportional to the quantity of water which arrived on this spot.

By monitoring the temperature distribution, we could anticipate the quantity of water to drop on each spot of the area to extinguish the fire.

**Introduction**

Fire propagates through the combustion of fuels consisting of live and dead plant material. Fuel temperature must be high enough to volatilize and ignite these materials. Once ignition has occured, the energy released through combustion raises the temperaure of adjacent fuels.

By measuring thermal emission within multiple channels, remote sensing can be used to determine the dominant temperature of a fire.

To that end, we have to seperate the spectral contribution of fire and the spectral contribution of the cooler background.

The total spectral radiance measured by a sensor imaging a fire daylight will be a combination of emitted radiance and reflected solar radiance. Atmospheric absorption and scattering of both emitted and reflected radiance (path radiance) must also be accounted.

We use the following notation:

- $r$ for reflected solar radiance

- $Pr$ for reflected solar path radiance

- $e$ for emitted radiance

- $Pe$ for emitted path radiance

The total radiance at a specific wavelength is:

$L_{\lambda t}=L_{\lambda r}+L_{\lambda Pr}+L_{\lambda e}+L_{\lambda Pe}$ (1)

Emitted radiance is a function of temperaure, emissivity, and atmospheric absorption and scattering. The mitted spectral radiance of a blackbody can be calculated using Planck's equation:

$L_{\lambda}= \frac{2hc^2}{\lambda^5 (exp(\frac{hc}{k \lambda T})-1)}$ (2)

with $h$ Planck's constant and $k$ Boltzmann's constant.

We take the integral of equation (2) to have the total radiance of a blackbody:

$L=\frac{2k^4 \pi^4 T^4}{15 h^3 c^2}$ (3)

This equation shows that, **as temperature increases, the total emitted radiance increases**.

We take the derivative of this equation to identify the wavelenght of peak radiance:

$\lambda_{max}=\frac{a}{T}$ with $a=2.898 . 10^{-3} Km$ (4)

This equation shows that, **as temperature increases, the pic radiance shifts to shorter wavelenghts**.

**As the temperature of the combusting fuels increases, the energy radiated by the fire increases and shifts to shorter wavelenghts. This demonstrates that spectral shape is an indicator of the temperature of an emitting body.**

AVIRIS, Airbone Visible Infrared Imaging Spectrometer, collects 224 channels across an approximate spectral ange of 370-2510 nm and was used to estimate fire properties and background properties for the 2003 Simi Fire in Southern California, USA.

**Methods**

AVIRIS use the atmospheric radiative transfer model MODTRAN to model the expected solar path radiance and remove it from the image. It also use radiative transfer modeling and assume that emitted radiance and emitted path radiance are interdependent and combined into a single term: $L_{\lambda m}$.

Two modeling assumptions were made following Dozier (1981):

- the fire is assumed to be a blackbody emitter

- the fire is assumed to have a single temperature within each AVIRIS image pixel

Equation (1) can now be expressed as a linear mixing model:

$L_{\lambda m}=f_r L_{\lambda r}+f_{et} L_{\lambda et}+f_s L_s+\epsilon$ (5)

where $f_r$ is the reflected solar radiance fraction, $f_{et}$ the fractional area, $L_s$ the shade radiance, $f_s$ the shade radiance fraction. The term regarding shade radiance allows the reflected solar radiance fraction and the fire fractional area to vary independently, hence, the model equation can be solved using singular value decomposition.

$\epsilon$ is an error term that accounts for any differences in spectral shape between the measured radiance $L_{\lambda m}$ and the sum of the other radiances.

Equation (5) is a **three-endmember linear spectral mixing model**. We use MESMA, Multiple Endmember Spectral Mixture Analysis to determine the best combination of a reflected solar radiance endmember, an emitted radiance endmember and a shade endmember to fit each image spectrum. The best combination is determined by using **spectral libraries** for reflected solar radiance endmember and for emitted radiance endmember and calculating the magnitude of the error term $\epsilon$.

The spectral librairies contains endmembers selected for six classes chosen based on their fuel characteristics and include four vegetation classes.

**Results**

An example of a model fit for an unsatured image spectrum is shown on this figure:

*Example fit for an unsaturated AVIRIS spectrum*

A total of 606 endmember combinations were tested for each pixel, with 101 emitted radiance endmembers and 6 reflected solar radiance endmembers.

The modeled endmembers were used to map fire temperature and land cover type within the AVIRIS scene.

The following images show the masked fire temperature and fire fractional area. In these images the fire is moving from left to right. The temperatures are higher within the fire front, where the fire is burning into new fuels.

*Retrieved temperature ranging from 500 to 1500K (a) and fire fractional area ranging from 0 to 1 (b)*

Simultaneous fire and fuel information extracted using hyperspectral data could provide the basis for eventual real-time complex fire spread modeling. This modeling could help us to determine the quantity of water to drop on the fire to extinguish it in each burned area.

**As a consequence, the spots of water bombing from aircrafts and the quantity of water dropped could be anticipated in order to extinguish the fire quickly and effectively.**

Source : "Wildfire temperature and land cover modeling using hyperspectral data" from sience direct