Spectral quality requirements for effluent quantification

Based on simulated atmospheric and sensor effects, we identify spectral resolution and per-channel signal-to-noise ratio (SNR) requirements for thermal infrared spectrometers that allow effluent quantification to any desired precision. This work is based on the use of MODTRAN-4 to explore the effects of temperature contrast and effluent concentration on the spectral slopes of particular absorption features. These slopes can be estimated from remotely sensed spectral data by use of least-squares techniques. The precision of these estimates is based on two factors related to spectral quality: the number of spectral samples that lie along an absorption feature and the radiometric accuracy of the samples themselves. The least-squares process also calculates the slope estimation error variance, which is related to the effluent quantification uncertainty by the same function that maps the slope itself to effluent quantity. The effluent quantification precision is thus shown to be a function of the spacing between spectral channels and the per-channel SNR. The relationship between SNR, channel spacing and effluent quantification precision is expressed as an equation defining a surface of constant "difficulty." This surface can be used to evaluate parameter sensitivities of sensors in design, to appropriately task sensors, or to evaluate effluent quantification tasks in terms of feasibility.