Francesc Rocadenbosch,1,2,*
M. Nadzri Md. Reba,1,2
Michaël Sicard,1,2
and Adolfo Comerón1
1Remote Sensing Laboratory (RSLAB), Department of Signal Theory and Communications, Universitat Politècnica de Catalunya, Campus Nord, Jordi Girona 1-3, 08034 Barcelona, Spain (http://www.tsc.upc.edu/rslab)
2Institute for Space Studies of Catalonia–Aeronautics and Space Research Center, Universitat Politècnica de Catalunya, Barcelona, Spain
We present an analytical formulation to compute the total-backscatter range-dependent error bars from the well-known Klett’s elastic-lidar inversion algorithm. A combined error-propagation and statistical formulation approach is used to assess inversion errors in response to the following error sources: observation noise (i.e., signal-to-noise ratio) in the reception channel, the user’s uncertainty in the backscatter calibration, and in the (range-dependent) total extinction-to-backscatter ratio provided. The method is validated using a Monte Carlo procedure, where the error bars are computed by inversion of a large population of noisy generated lidar signals, for total optical depths and typical user uncertainties, all of which yield a practical tool to compute the sought-after error bars.
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B. Total backscatter error bar (case , calibration point)
Follow Subsection 2C for the forward variant. Upper/lower error bar is sign, respectively.
Table 2
Estimated Mean Relative Error and Dispersion on Backscatter Analytical Error Bars for Different Optical Depths and Signal-to-Noise Ratios at Calibration Range [Error Source (ii) , Only]
Errors without/within brackets correspond to and , respectively. Positive/negative mean values indicate error bar over/underestimation.
Table 3
Estimated Mean Relative Error and Dispersion on Backscatter Analytical Error Bars for Different Optical Depths and Relative Error p in Assumed Total Lidar Ratio Eq. (14) [Error Source (ii) , Only]a
Errors without/within brackets correspond to (10%) and (50%), respectively. Underlined values correspond to divergent backscatter inversions (see text).
Tables (3)
Table 1
Summary Table to Compute Total-Backscatter Analytical Error Bars in Klett’s Backward Inversion Method Due to Error Sources (i–iv) in Subsection 3Ba
B. Total backscatter error bar (case , calibration point)
Follow Subsection 2C for the forward variant. Upper/lower error bar is sign, respectively.
Table 2
Estimated Mean Relative Error and Dispersion on Backscatter Analytical Error Bars for Different Optical Depths and Signal-to-Noise Ratios at Calibration Range [Error Source (ii) , Only]
Errors without/within brackets correspond to and , respectively. Positive/negative mean values indicate error bar over/underestimation.
Table 3
Estimated Mean Relative Error and Dispersion on Backscatter Analytical Error Bars for Different Optical Depths and Relative Error p in Assumed Total Lidar Ratio Eq. (14) [Error Source (ii) , Only]a
Errors without/within brackets correspond to (10%) and (50%), respectively. Underlined values correspond to divergent backscatter inversions (see text).