Size Distribution Estimation Method using Reflected Laser Light Angle Dependency by Rain Droplets

Methods for size distribution estimation and rainfall type discrimination with estimated phase function using measured reflected laser light by rain droplet are proposed. Preliminary experiments are conducted with Laser ranging instrument and spectral radiometer for estimation of size distribution and rainfall type discrimination as well as phase function of scattering by rain drops. Through the experiments, it is found that rainfall type can be discriminated together with rain droplet size distribution estimation. Keywords—Rainfall; Laser ranging; Marshall Palmer distribution; Rayleigh scattering; Mie scattering; Phase function; Rain drpolet size distribution


I. INTRODUCTION
Land slide detection and prediction due to heavy rain is important.Therefore, not so small number of systems are proposed so far.It requires quit high sensitivity of a tiny slide (mm order) has to be detected for prediction.The proposed method ensures that such high sensitivity of a slide in the order of mm.Landslide is one of severe disaster.In order to monitor landslides, several methods have been proposed so far.One of the conventional land slide monitoring systems is to measure the resistance of the wire which is set at potential landslide steeply slopes.Although it is simple and cheap system, measurement accuracy is not so good in terms of the distance between two ends of the wire which depends on resistance.Therefore, it cannot be used for making caution for evacuation from the potential landslide area.Other wide variety of commercial off-the-shelf electronic and/or mechanical geotechnical and hydrologic sensors exist [1], [2].Meanwhile, satellite remote sensing imagery data is used for disaster relief due to landslide.It cannot be used for landslide warning system.There are so many previously proposed methods for detection of landslide areas such as differentiation with edge enhancing filters [3], texture feature extraction [4], vegetation index utilized land cover change detection method [5], 3D stereo pair of images utilized change detection method [6], etc.Also, satellite remote sensing based rainfall rate estimation methods are proposed and discussed [7]- [10].
It is well known that laser ranging instrument allows mm order of movement from several 10m far from the target.It, however, is affected by rainfall.Rain droplet reflect and scattered the laser light.Therefore, previous system utilized time diversity method.Namely, if rain droplets are situated in between laser ranging instrument and the target, received signal returned faster than that without rain droplet.Therefore, the longest time duration between laser light emission and receiving the return signal from the target corresponds to the distance between laser ranging instrument and the target.Thus, influence due to rain droplets can be reduced.Although the sensor network for landslide monitoring with laser ranging system avoiding rainfall influence on laser ranging by means of time diversity and satellite imagery data based landslide disaster relief is proposed already, rainfall rate estimation accuracy is not good enough.Another demand for land slide monitoring is that rain type discrimination and rain droplet size distribution estimation.Droplet size and rainfall rate can be estimated.Thus, land slide detection and prediction can be done accurately.
The proposed methods for size distribution estimation and rainfall type discrimination using measured phase function make land slide detection and prediction accurately.If not only distance measurements but also observation angle dependency on the measured scattered laser light due to rain droplets is measured, then optical property, scattering characteristics of the rain droplets is estimated together with rain droplet size.Thus rain type can be estimated together with rainfall rate.The method proposed here is to estimate for both rain type and rainfall rate.
The next section describes the proposed system followed by experiment.The experiments can be divided into two are intended to show the sensitivity of solar direct and diffuse pointing angle on the aerosol parameter estimations.Then concluding remarks are described with some discussions.

A. Research Background
F.Yoshino [11], Christian Matzler [12], and the others estimate parameters of droplet size distributions, stratiform (Marshall and Palmer), drizzling (Joss-Drizzle), thunderstorm (Joss-Thunderstorm) and realistic rainfall (Laws-Persons) by using Normalized distribution (Marshall-Palmer: MP, JossDrizzle: JD, Joss-Thunderstorm: JT and LP distributions).Typical parameters of these different types of rainfall are shown in Table 1.Droplet size distribution, on the other hand, is shown in Fig. 1. www.ijarai.thesai.orgFurthermore, (3) The parameters shown in Table 1 are estimated based on Rayleigh scattering assumption.Thunderstorm is characterized as relatively large "a" and comparatively small "b" while stratiform is characterized as relatively small "a" and comparatively large "b".These estimated results are coincident to Z-R Relation 1 which is estimated by Remko Uijlenhoet et al. [14].If we assume a certain drop size distribution (e.g., Marshall Palmer), the Z-R relation is for rain assuming a Marshal Palmer drop size distribution: (4) Next Mie scattering based Z-R Relation is estimated.In general, the number of droplets is decreasing in accordance with decreasing of droplet size [15].From Fig. 2, it is set that droplet size ranges from 1 to 6.4 mm while air temperature is assumed to be 20 degrees centigrade under the standard atmospheric pressure.Therefore, phase function P m ( ) of scattering property can be described as equation (5).
The Rayleigh scattering of phase function is illustrated in Fig. 4. On the other hand, if the droplet size is greater than Rayleigh limitation, the optical property can be described by Mie scattering theory.As shown in Fig. 5, forward scattering is dominant.
Mie scattering intensity is expressed as equation (6).
where i 1, i 2 denotes Mie scattering intensity function as the function of x of size parameter, , and ̃ of rain droplet refractive index.On the other hand, n(r) denotes the number of droplets of which the radius is r and is called as number of droplet particle size distribution in unit of 1/cm2 /μm.www.ijarai.thesai.org

C. Simulation
For the proposed method, observation wavelength of laser light is much smaller than rain droplet size.Therefore, rain droplet scattering property can be described by Mie scattering theory.Using MODTRAN 2 of software code of radiative transfer model, phase function can be calculated.Fig. 7 shows the phase function for rainfall rate of 1, 5, 10 and 15 mm/hour.

A. Preliminary Experiment
The configuration of the preliminary experiment is illustrated in Fig. 8.      Therefore, there is peak at the laser wavelength.
On the other hand, Fig. 11 shows the measured phase function.By changing the angle between laser light directions and pointing angle of the spectral radiometer, phase function can be measured as shown in Fig. 12. www.ijarai.thesai.org

B. Experiment for the Different Rainfall Conditions
Experimental configuration is shown in Fig. 13.Red line shows the radiant flux without laser light (noise component).Therefore, it is found that MS-720 of spectral radiometer is so noisy for the wavelength is over 900 nm.On the other hand, blue and green lines show laser repetition cycle 1 and 3 seconds, respectively.There are some water vapor and O 2 absorption lines in the Fig. 14 of spectral radiant flux.Also, red laser light is not so dominant for the scattered light.Furthermore, 3 seconds repetition cycle response is a little bit greater than that for 1 second repetition cycle.Through the experiments, it is found that rainfall type can be discriminated with the measured phase function using laser light scattered by rain droplets.Also, it is found that rain droplet size distribution can be estimated with the same measured phase function.Furthermore, rainfall rate is also estimated with the response of the scattered laser light by rain droplets.
Further investigation is highly required for the experiments in real situations.Also, relation between rainfall rate and land slide has to be clarified.Although the sensor network for landslide monitoring with laser ranging system avoiding rainfall influence on laser ranging by means of time diversity and satellite imagery data based landslide disaster relief is proposed already, rainfall rate estimation accuracy is not good enough.

Fig. 2 .
Fig. 2. Mie scattering based backscattering coefficient and its approximated coefficientB.Optical PropertyOptical property of scattered laser light by rain droplet depends on droplet size.If the droplet size is smaller than Rayleigh limitation (λ/10 where λ denotes observation wavelength), the optical property can be described by Rayleigh scattering theory.As shown in Fig.3, forward and backward scattering components are almost same.

Fig. 7 .
Fig. 7. Phase function of rain droplets Therefore, it is possible to estimate rainfall rate using measured phase function.The phase function can be measured with reflected laser light intensity with the different observation angles.

Fig. 8 .
Fig. 8. Configuration of preliminary experiment Outlook of the laser ranging instrument used is shown in Fig.9 (a) while that of the spectral radiometer is shown in Fig.10, respectively.Meanwhile, major specifications of the laser ranging instrument LEICA DISTO A6 3 and the spectral radiometer MS-720 4 are shown in Table 2 and 3, respectively.

Fig. 9 .
Fig. 9. Outlook of laser ranging instrument and spectral radiometer used for the preliminary experiment Fig.10 (a) shows spectral response measured with the spectral radiometer under the rainy condition.The wavelength of the laser ranging instrument is 630 nm.
Fig. 10.Spectral response of the laser ranging instrument The preliminary experiment is conducted for no rainfall condition on January 14 and 20 in 2012.Meanwhile, Fig.10 (b) shows the spectral radiometer responses for artificial rainy condition of rainfall rate of 0, 2.3, 4.5, 9, 18, and 27 mm/hour.

Fig. 13 .
Fig. 13.Configuration of preliminary experiment Fig.14 shows the measured spectral radiant flux of the scattered laser light from the back for no rainfall condition.Red line shows the radiant flux without laser light (noise component).Therefore, it is found that MS-720 of spectral radiometer is so noisy for the wavelength is over 900 nm.On the other hand, blue and green lines show laser repetition cycle 1 and 3 seconds, respectively.There are some water vapor and O 2 absorption lines in the Fig.14of spectral radiant flux.Also, red laser light is not so dominant for the scattered light.Furthermore, 3 seconds repetition cycle response is a little bit greater than that for 1 second repetition cycle.

Fig. 14 .
Fig. 14.Spectral radiant flux of the scattered laser light from the back for no rainfall condition Fig.15 (a) shows the measured spectral radiant flux of the scattered laser light from the back for rainy condition.Rainfall rate for this case is 9 mm/hour.Red and green lines show laser repetition cycle 1 and 3 seconds, respectively.Through the comparison between Fig.14, it is found that the response for the 9mm/hour of the rainfall rate is a little bit lower than that for no rainfall condition obviously.Meanwhile, Fig.15 (b) and (c) shows the measured spectral radiant flux of the scattered laser light from the back for rainy condition.Rainfall rate for this case is 18 and 27 mm/hour, respectively.. Red and green lines show laser repetition cycle 1 and 3 seconds, respectively.Through the comparison between Fig.14, it is found that the response for the 18 and 27 mm/hour of the rainfall rate is a little bit lower than that for no rainfall condition obviously.
Fig. 15.Spectral radiant flux of the scattered laser light from the back for rainy conditionOn the other hand, Fig.16(a) and (b) shows the measured spectral radiant flux of the scattered laser light from the back for no rainy and rainy conditions.Laser repetition cycle is set at 1 second for Fig.16(a) while that for Fig.16 (b) is set at 3 seconds, respectively.Red, green, blue and violet lines in Fig.16show the cases of rainfall rate of 0, 9, 18, and 27 mm/hour, respectively.

TABLE I .
PARAMETERS FOR LP, MP, JD, JT DISTRIBUTIONS

TABLE III .
MAJOR SPECIFICATION OF MS-720