|
It is well known that in water-droplet clouds sounded with a monostatic lidar the variation of the Stokes vector of a sounding beam I0(I, QO, (JO, J/O) j due to the multiple scattering effects. In this case the polarization components of lidar return signal can be inferred only from the solution of the radiative transfer equation in its vector form. This equation can be solved by the Monte-Carlo method developed in Refs. 1-3 as applied to the problems of this type. Let us consider the salient features of the mathematical model. Nonstationary radiation flux, whose polarization state is defmed as I0(I, Q°, (JO, J/O) 10(1, 1, 0, 0) , is propagated within the given cone of directions ço and is incident on a plane-parallel cloud layer with the given optical properties. The desired functionals (polarized and cross-polarized components of the lidar return signal) II = (I + Q) 2 and I = (I — Q) 2 are estimated for a set of detectors with the field-of-view angles I Lfl* I = sin0 dO dco and spatial resolution l — Atc. The location of a monostatic lidar is specified by the radius of its circular orbit Re H0 (Re 5 the Earth's radius). The cloud layer of thickness zh is at the altitude h0 above the earth surface, its optical characteristics are determined by the scattering phase matrix S and the extinction coefficient ext( For convenience of interpretation the results will be given for a set of the parameters n = H0tan(l/2cor) aext, characterizingthe boundary conditions of illumination. All estimates refer to the wavelength X = 0.69 jm and the receiver aperture 1/2çO O.3 1O rad. The scattering phase matrices of water-droplet clouds were for Deirmendjian's Cl and C2 clouds.4 For the model of crystal clouds, the phase matrices were used, calculated by Liou et a!.5 for ice plates and columns of hexagonal form. The typical values of the depolarization ratio of singly scattered radiation ôk fell within the range 0.4 < ôk < 0.6. Its most probable value was 0.45. The given model was preliminary tested based on the numerical experiments compared with the field measurements of polarization characteristics of the lidar return signal performed in Refs. 6 and 7. Before proceeding to an analysis of the possibilities of polarization method of sounding, it is desirable to 'consider the feasibility of recording the lidar return components (i-) and 11(r) using the lidar located at the altitude H0 - 200 km above the earth surface. Figure 1 shows the results of calculation of the lidar return components I (r) and 11(r) recorded by a detector in sounding of the water-droplet and crystal stratus clouds. It was assumed that clouds were at the altitude h0 = 0.5 km above the earth surface, the lidar was located at the altitude H0 = 200 km, and the cloud thickness was h — 200 m. The extinction coefficient was aext 25 km1 throughout the cloud thickness, and was assumed to be horizontally homogeneous. The ratio of the signals 11(r) and I1(r) (see Fig. 1) coming from the top of the water-droplet cloud was about two orders of magnitude, decreasing slightly with the increase of the depth of the sounded layer. The maximum of 11(r) was formed at the depth r = 1. The lidar return intensity (r), for the pulse energy W = 1 J and pulse duration 10 ns was about 106 W/m2. In the case of crystal clouds the lidar return intensities 111(r) and 11(r) coming from the top of clouds differ by no more than half the order of magnitude due to the fact that the lidar return signal of the first multiplicity of scattering is partially depolarized.
|
