# In-Situ Testing of Methane Emissions from Landfills Using Laser Absorption Spectroscopy
## 2 Methodology  
### Principle of TDLAS  
TDLAS is one of the most common techniques to analyze the properties and constituents of gases, such as concentration, temperature, pressure, and flow velocity [27]. TDLAS measures the wavelength-dependent absorption of light through a gas medium. Figure 1 shows the principle of TDLAS. The technique usually employs a tunable-wavelength diode laser as the light source. The wavelength of the diode laser emission is scanned over the absorption peak of the target gas; then, the photodiode is used to detect the light signal absorbed by the target gas to get the absorption spectrum. The gas concentration can be obtained by analyzing the absorption spectrum of the laser after passing through the gas. The laser is eye-safe. Beer-Lambert law is used to describe the attenuation of laser intensity after passing through the gas:  
\[I(v)=I_{0}(v)\exp[-\alpha(v)I]=I_{0}(v)\exp[-\sigma(v)Nl] \tag{1}\]  
where \(v\) is the photon frequency (Hz); \(I(v)\) is the light intensity after passing through the gas (candela, cd); \(I_{0}(v)\) is the light intensity before passing through the gas (cd); \(\alpha(v)\) is the absorption coefficient (m\({}^{-1}\)); \(\sigma(v)\) is the attenuation cross-section of a gas molecule (m\({}^{2}\)/molecule); \(N\) is the number density of gas molecular (molecule/m\({}^{3}\)); \(L\) is the effective absorption path (m). The attenuation cross-section in Equation (1) consists of absorption cross-section and scattering cross-section:  
\[\sigma(v)=\sigma_{abs}(v)+\sigma_{sca}(v) \tag{2}\]  
where \(\sigma_{abs}(v)\) is the absorption cross-section of a gas molecule (m\({}^{2}\)/molecule); \(\sigma_{sca}(v)\) is the scattering cross-section of a gas molecule (m\({}^{2}\)/molecule). During the testing of methane emissions, pure gas is generally detected. There is no scattering effect caused by solid particles, and thus the scattering cross-section is ignored. Gas absorption cross-section can be further expressed as:  
\[\sigma_{abs}(v)=S(T)\varphi(v) \tag{3}\]  
where \(S(T)\) represents the absorption line strength of a gas molecule (m/molecule); \(\varphi(v)\) represents the normalized linear function (m). The absorption line strength of gas molecules depends on the population number of the low-state molecules and their transition probability. The population number of the low-energy molecules follows the Boltzmann distribution. The absorption line strength \(S(T)\) at a certain temperature \(T\) can be expressed as:  
\[S(T)=S(T_{0})\frac{Q(T_{0})}{Q(T)}\exp\biggl{[}-\frac{hcE}{K_{B}}\biggl{(} \frac{1}{T}-\frac{1}{T_{0}}\biggr{)}\biggr{]}\frac{1-\exp\biggl{(}\frac{hc \gamma_{0}}{K_{B}T_{0}}\biggr{)}}{1-\exp\biggl{(}\frac{hc\gamma_{0}}{K_{B}T_{ 0}}\biggr{)}} \tag{4}\]  
where \(T_{0}\) is a given temperature (K); \(S(T_{0})\) is the absorption line strength under the given temperature \(T_{0}\) (m/molecule); \(Q(T)\) is the overall partition function of gas molecules; \(Q(T_{0})\) is the overall partition function under the given temperature \(T_{0}\); \(h\) is the [PERSON] constant (J-s); \(c\) is the light speed (m/s); \(E\) is the energy of the low-state molecules (J); \(K_{B}\) is the Boltzmann constant (J/K); \(v_{0}\) is the line center frequency of molecular transition (Hz). The absorption spectrum of gas is generated by the transition between energy levels of gas molecules after absorbing photon energy. Since the energy level has a certain width, the resulting absorption spectrum also has a width. When the pressure is equal or greater than the standard atmospheric pressure, the collision broadening is much greater than the  
Figure 1: Schematic diagram of tunable diode laser absorption spectroscopy (TDLAS). Doppler broadening in the absorption spectrum. In this study, the gas concentration is measured under the standard atmospheric pressure.