Elastic retrievals

Retrieval of aerosol optical properties from elastic lidar signals.

Todo

Implement iterative retrieval (Di Girollamo et al. 1999)

elastic_retrievals.klett_backscatter_aerosol(range_corrected_signal, lidar_ratio_aerosol, beta_molecular, index_reference, reference_range, beta_aerosol_reference, bin_length, lidar_ratio_molecular=8.73965404)

Calculation of aerosol backscatter coefficient using Klett algorithm.

The method also calculates aerosol backscatter above the reference altitude using forward integration approach.

Parameters

range_corrected_signalfloat.

The range corrected signal.

lidar_ratio_aerosolfloat.

The aerosol lidar ratio.

beta_moleculararray_like

The molecular backscatter coefficient. (m^-1 * sr^-1)

index_referenceinteger

The index of the reference height. (bins)

reference_rangeinteger

The reference height range. (bins)

beta_aerosol_referencefloat

The aerosol backscatter coefficient on the reference height. (m^-1 * sr^-1)

bin_lengthfloat

The vertical bin length. (m)

lidar_ratio_molecularfloat

The molecular lidar ratio. Default value is \(8 \pi/3\) which is a typical approximation.

Returns

beta_aerosol: float

The aerosol backscatter coefficient. (m^-1 * sr^-1)

Notes

We estimate aerosol backscatter using the equation.

\[\beta_{aer}(R) = \frac{A}{B-C} - \beta_{mol}(R)\]

where

\[ \begin{align}\begin{aligned}A &= S(R) \cdot exp(-2\int_{R_{0}}^{R} [L_{aer}(r)-L_{mol}] \cdot \beta_{mol}(r) dr)\\B &= \frac{S(R_0)}{\beta_{aer}(R_{0})+\beta_{mol}(R_0)}\\C &= -2 \int_{R_0}^{R} L_{aer}(r) \cdot S(r) \cdot T(r, R_0) dr\end{aligned}\end{align} \]

with

\[T(r,R_0) = exp(-2\int_{R_0}^{r}[L_{aer}(r')-L_{mol}] \cdot \beta_{mol}(r') \cdot dr')\]

and

• \(R\) the distance from the source,

• \(R_0\) the distance between the source and the reference region,

• \(\beta_{aer}\) the aerosol backscatter coefficient,

• \(\beta_{mol}\) the molecular backscatter coefficient,

• \(S(R)\) the range corrected signal,

• \(P\) the signal due to particle and molecular scattering,

• \(L_{aer}\) the aerosol lidar ratio (extinction-to-backscatter coefficient),

• \(L_{mol}\) the molecular lidar ratio.

Note that lidar_ratio_molecular should correspond to the beta_molecular i.e. they should both correspond to total or Cabannes signal.

References

Ansmann, A. and Muller, D.: Lidar and Atmospheric Aerosol Particles, in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere, vol. 102, edited by C. Weitkamp, Springer, New York., 2005. p. 111.