Genspect

Making it happen

Genspect: How it Works

GENSPECT is a line-by-line radiative transfer code to calculate gas absorption and emissivity, emission and transmission for a wide range of atmospheric gases. GENSPECT is available as an online service and as a toolbox of components under MATLAB.

Line-by-Line Calculations

Most gases have emission spectra that may be described by databases of individual gas lines that collectively describe the spectral properties of a gas. Each line has a set of associated parameters that describe spectral behaviour over a variety of pressure and temperature regimes. The principal parameters are a central frequency and a line strength. Additionally, there are line-width parameters and other associated information describing temperature dependency and other variations. Line broadening is caused by a quantum mechanical effect that depends strongly on gas pressure and temperature. The determination of the line shape from first principles with the application of quantum mechanics is rarely attempted by line-by-line codes. The calculation would require accurate knowledge of the molecular potentials which are rarely well characterized. Instead, line-by-line codes prefer to adopt a simple parameterization.

Each line has two associated line-width parameters that describe the line shape at two extremes where the line-broadening behaviour is well understood. One parameter describes behaviour assuming only Lorentz broadening and one describes behaviour assuming only Doppler broadening. Lorentz broadening tends to be the dominant effect are higher pressures while Doppler broadening is more dominant at lower pressures (that might occur higher in the atmosphere). For typical temperatures and pressures the actual line shape is a combination of the two effects, and a convolution of the two shapes, called the Voigt profile, is used. Additional parameters, along with pressure, partial pressure and temperature parameters control the relative weighting of the convolution.

A line-by-line calculator takes the database of information and uses it to calculate the spectral properties of a particular gas over a particular spectral interval and regime. By summing the contributions of all the significant lines for every gas, at every spectral point, the spectral properties of a gas mixture can be determined. Further dividing up an atmosphere into a series of gas cells, the spectral properties of the whole atmosphere can be modeled. The line databases tend to be large and can contain in excess of 50,000 lines for a single gas species. Calculations therefore tend to be extra-ordinarily intensive and calculations are generally too slow to calculate the effect of every line on every calculation grid point.

Typically, algorithms reduce the calculation order by interpolating over regions where the line function varies slowly. Most algorithms employ somewhat arbitrary heuristics to divide the calculation space and to determine where interpolation is appropriate. These algorithms do not ensure the ultimate accuracy of the calculation and may incur interpolation errors of order 1% for a 0.005cm-1 grid, depending on the line-width parameters.

The GENSPECT Solution

GENSPECT employs a new computation algorithm that maintains a specified percentage-error tolerance for every computed absorption coefficient over the whole spectral domain of the computation. The approach employs a binary division of the spectral range, and calculations are performed on a cascaded series of grids, each with approximately twice the spectral interval of the previous one. Figure 1 illustrates this division in a simple 14 division calculation. Calculations are accelerated by employing linear interpolation and dividing line-function evaluations piecewise across this series of grids. Each line-function section is computed on the grid with the coarsest interval spacing, consistent with the specified error tolerance.

Figure 1: A simple 14 interval calculation, distributed over four grids

The calculation division is implemented rapidly by pre-computing where the Voigt-line function may be interpolated without a reduction in accuracy (see Figure 2).

Figure 2: Typical computation points near line center derived using pre-computed calculation divisions and rounded away from line center.

The user can select a required accuracy tolerance for the calculation (0.01%, 0.1%, or 1%), and the algorithm will compute spectral absorption coefficients to this accuracy using a near minimal number of computations. Figure 3 illustrates the typical interpolation error incurred for a calculation of HF with a 0.1% accuracy requirement.

Figure 3: HF calculation using the new algorithm and an accuracy requirement of 0.1%.

The use of a percentage error tolerance has a number of advantages. First, it allows the user to determine the appropriate balance between execution time and calculation accuracy. Where only a rough calculation of a system's radiative characteristics is required, a coarse 1% error tolerance might be adopted, directing the algorithm to interpolate more readily and reducing the execution time. Where a high-accuracy computation is required, a fine error tolerance may be adopted at the expense of execution speed. Second, it allows interpolation error to be quantified rigorously in an error analysis or budget. As spectroscopy advances the discrepancy between experimental results and theoretical comparisons is narrowing. A complex radiative model of a system or atmosphere may incur a number of small error contributions that can accumulate to degrade significantly the model performance. While many contributions to the model discrepancy cannot be accurately quantified, this code allows the user to vary the interpolation error in order to investigate, quantify and then eliminate its effect. Due to the nature of the line-function, codes that employ linear interpolation incur a one-sided error that tends to over-estimate the absorption coefficient. In applications such as atmospheric constituent retrieval, where free parameters are fitted to make model results match experimental observations, this type of error may be completely masked as a corresponding decrease in constituent concentration. Models employing line-by-line codes with a single or undefined error tolerance provide no means to investigate directly this effect in order to validate results.

GENSPECT calculations are performed on a spectral grid in wavenumber space [cm^-1] and generate absorption coefficient data in corresponding units of [molecule^-1(cm^-2) ^-1]. For further details describing how the calculation is performed see Quine, B. M. and J. R. Drummond, “GENSPECT: A line-by-line code with selectable interpolation error tolerance”, JQSRT, April, 2002.

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