# Vertical atmospheric profiles measured with lidar

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Vertical atmospheric profiles measured with lidar G. J. Kunz

Physics Laboratory TNO, P.O. Box 96864, 2509 JG The Hague, The Netherlands. Received 23 December 1982. 0003-6935/83/131955-03$01.00/0. 1983 Optical Society of America. Lidar provides a unique method for the remote sensing of

the atmosphere in homogeneous and inhomogeneous situa-tions. When homogeneous atmospheres are considered, both the extinction coefficient and the backscatter coefficient can be calculated from the lidar signal by means of the slope method provided the lidar system has been calibrated abso-lutely.1 When an inhomogeneous atmosphere is probed, the deduction of the extinction coefficient and the backscatter coefficient from the lidar signal becomes less straightforward because the two quantities have to be determined from one single equation. To solve the problem, at least one more equation is required. This can be derived from the total transmission over the lidar path or from an assumed relation between the extinction coefficient and the backscatter coef-ficient; see, e.g., Kohl2 and Quenzel.3 However, even in that case the extinction coefficient and/or the backscatter coeffi-cient can only be inferred from the lidar signal if a boundary condition is known.

The purpose of this Letter is to present a method for mea-suring the boundary condition with the lidar system itself and to demonstrate the applicability on vertical profile measure-ments.

A description of the lidar equation and methods for solving it have been given in Refs. 1-10. It seems that a lack of an accurate input boundary condition is the main problem in applying the proposed methods. We propose to measure this boundary condition for the vertical structure with the lidar system itself in the lower part of the atmosphere, which is assumed to be homogeneous. This assumption has proved to be valid in the great majority of cases, i.e., in the absence of local aerosol sources and excluding extreme low-visibility cases, where patches of fog might occur. Next the vertical profile is calculated from a vertical lidar measurement for heights higher than the reference height by means of the

1 July 1983 / Vol. 22, No. 13 / APPLIED OPTICS 1955

Fig. 1. Vertical atmospheric extinction profile for two wavelengths calculated from lidar measurements with a low-altitude boundary

condition.

Fig. 3. Vertical atmospheric extinction profiles for two wavelengths calculated with the Klett method from the same lidar signals as used in F'ig. 1. Two different boundary conditions per wavelength have

been used.

Fig. 2. Vertical atmospheric extinction profile for two wavelengths calculated from lidar measurements with a low-altitude boundary condition. The maximum height is limited by a cloud base at ~800-m

height.

Fig. 4. Vertical atmospheric extinction profiles for two wavelengths calculated with the Klett method from the same lidar signals as used

in Fig. 2.

traditional solution of the lidar equation assuming a linear relation between extinction and backscatter. The advantage of this low-level boundary condition is that both the extinction coefficient and the backscatter coefficient can be inferred accurately over the total range of the lidar, e.g., by means of the slope method. Vertical extinction profiles have been generated routinely since Apr. 1982 using this approach.

Two examples of these profiles, deduced from lidar mea-surements at two wavelengths and processed utilizing the low-altitude boundary condition, are presented in Figs. 1 and

2. Equipment limitations forced us to construct the vertical profiles from multiple elevation measurements up to the maximum angle allowed by the system. Both profiles have been composed from lidar measurements at elevation angles of 2, 7, 15, and 35. The boundary extinction coefficient has been calculated by means of the slope method from the 2 measurement.

The results of the evaluation of the same lidar signals using the Klett method (solving the traditional lidar equation from the far end) are presented in Figs. 3 and 4. Although we re-

1956 APPLIED OPTICS / Vol. 22, No. 13 / 1 July 1983

alize that the large optical depth condition has not been fulfilled, this method remains one of the very few practical options to extract the vertical profile from lidar measurements. The boundary conditions were deduced with the slope method from seemingly homogeneous atmospheric layers over different intervals at the high-altitude part of the lidar signals recorded at maximum elevation. Selecting the boundary value in this way is about the only practical approach. Other methods will provide other boundary conditions resulting in different profiles, which emphasize this main problem. Lidar returns from true vertically homogeneous layers unfortunately cannot be discerned from certain vertically inhomogeneous layers which generate the same backscatter signature (e.g., Kohl2). The boundary conditions are shown in the figures. Note that the profiles in Figs. 1 and 2 were built up from low to high altitude, and Figs. 3 and 4 were built up from high to low altitude.

It should be noted that both methods provide, of course, the same results when the necessary boundary values are known exactly. However, Klett's method is more suited for high optical densities where the boundary conditions are unknown. The method presented is more suited for low optical densities with measured low-altitude boundary conditions.

In conclusion the feasibility has been demonstrated to infer vertical atmospheric profiles from vertical lidar measurements by inverting the lidar equation with an accurately measured boundary condition at low altitude. This boundary condition at low elevation has been determined with the same lidar system. Routinely obtained results at 0.69- and 1.06-m wavelengths indicate that meaningful profiles could be acquired. Multiangle measurements offer the additional possibility of checking the path integrated extinction coefficient with the transmission losses calculated from different elevation measurements; see Fernald. et al.8 It is pointed out that the Klett method could be used to iterate the far end boundary condition until a profile is obtained in agreement with the measured near-end extinction. Note, however, that exactly the same profile is acquired without iteration by inverting the lidar equation directly using the near-end extinction as proposed here.

The author is endebted to C. W. Lamberts for stimulating all lidar work and J. Holsbrink who performed most of the vertical lidar measurements.

References 1. R. T. H. Collis, Adv. Geophys. 13, 113 (1969). 2. R. H. Kohl, J. Appl. Meteorol. 17, 1034 (1978). 3. H. Quenzel, Atmos. Environ. 9, 587 (1975). 4. W. Hitschfeld, and J. Bordan, J. Meteorol. 11, 58 (Feb. 1954). 5. E. W. Barret and 0. Ben-Dov, J. Appl. Meteorol. 6, 500 (1967). 6. W. Viezee, J. Appl. Meteorol. 8, 274 (1969). 7. P. A. Davis, Appl. Opt. 8, 2099 (1969). 8. F. G. Fernald, B. M. Herman, and J. A. Reagan, J. Appl. Meteorol.

11,482(1972). 9. J. D. Spinhirne, J. A. Reagan, and B. M. Herman, J. Appl.

Meteorol. 19,426(1980). 10. J. D. Klett, Appl. Opt. 20, 211 (1981).

1 July 1983 / Vol. 22, No. 13 / APPLIED OPTICS 1957