Thresholding Based Method for Rainy Cloud Detection with NOAA / AVHRR Data by Means of Jacobi Itteration Method

Thresholding based method for rainy cloud detection with NOAA/AVHRR data by means of Jacobi iteration method is proposed. Attempts of the proposed method are made through comparisons to truth data which are provided by Japanese Meteorological Agency: JMA which is derived from radar data. Although the experimental results show not so good regressive performance, new trials give some knowledge and are informative. Therefore, the proposed method suggests for creation of new method for rainfall area detection with visible and thermal infrared imagery data. Keywords—Jacobi itteration method; Multi-Variiate Regressive Analysis; AVHRR; Rainfall area detection; Rain Radar


INTRODUCTION
Rainfall area detection with satellite based visible and thermal infrared sensor data is tough issue because the visible and thermal infrared sensor data represent just cloud surface reflectance and temperature.In general, the rainy clouds which cause rainfall can be divided into two kinds, nimbostratus and cumulonimbus.The reflectance and the temperature at the top of the cumulonimbus are relatively high and extremely cold, respectively because the height of the cumulonimbus is quite high.On the other hand, the reflectance and the temperature of the nimbostratus are comparatively low and relatively warm, respectively because the height of the nimbostratus is comparatively low.Meanwhile, no rainy cloud types show very similar characteristics in terms of cloud top reflectance and temperature.Therefore, it is extremely difficult to discriminate between rain and no rain clouds.
There are 10 types of clouds which include four types of cumulus, cumulonimbus, stratus, stratocumulus in the lower cloud, three types of nimbostratus high-rise clouds and high cumulus clouds in the middle clouds, in the high-rise clouds three types of cirrus, cirrocumulus, and cirrostratus.Moreover, these clouds are overlapped sometime.Therefore, it is tough to discriminate rainy clouds by using only reflectance and temperature at the top of the clouds.
Microwave radiometer data represent cloud liquid in rainy cloud.Therefore, some methods for detecting rainy clouds with microwave radiometer data have been proposed already [1]- [9].On the other hand, limb sounding data also represent some extent of rainy clouds information.Therefore, some methods for rainy cloud detection based on limb sounding data have also been proposed so far [10]- [16].
The rainy cloud detection method proposed here is based on thresholding of visible and thermal infrared radiometer data by means of Jacobi iteration method.The proposed method is to be compared to the multiple linear regressive analyses by only using visible and thermal infrared data observed from space.In the method, Probability Density Function: PDF of the visible and thermal infrared data are calculated.Then the PDF is approximated with the best fit ideal normal distribution.After that, the visible and thermal infrared data are binarized (0 denotes no rain, and 1 means rain) with the most appropriate threshold determined by means of Jacobi iteration method.
The proposed method is described followed by experiments.The experimental results are validated with the posterior created weather maps by using rainfall radar data and the other meteorological data in the following section followed by conclusion with some discussions.

II. PROPOSED METHOD
A. Discrimination of Cloud Types Within 10 types of clouds, cumulonimbus and nimbostratus clouds are major concern because I intend to discriminate between rainy clouds and the clouds without rainfall.The cumulonimbus clouds are situated in the lower layer of the atmosphere while the nimbostratus clouds are situated in the middle layer of the atmosphere.Therefore, relatively low cloud top temperature and comparatively low cloud top reflectance of clouds have to be found with visible and thermal infrared radiometer data.By using visible and thermal infrared data, appropriate threshold which allows discriminate nimbostratus / cumulonimbus and the other clouds has to be determined.

B. Jacobi Iteration Method
The proposed method uses Jacobi iteration method.The Jacobi iteration method is expressed as follows, where k denotes iteration number while F k denotes summation of the PDF functions of the approximated normal distribution of S i (i=1 denotes rainy cloud while i=2 denotes non rainy clouds of visible and thermal infrared radiometer data.Namely, the PDF functions of visible and thermal infrared data are firstly created then the most appropriate approximation normal distribution functions are calculated.After that, cross point between two approximated normal distribution is determined by using Jacobi iteration method.This cross point is used for threshold for discrimination between rainy and non-rainy clouds.

C. Process Flow
Fig. 1 shows the process flow of the proposed method for discrimination of rainy and non-rainy clouds with visible and thermal infrared radiometer data.

B. Truth Data Used
As a truth data of rainfall areas, radar data derived rainfall areas which is provided by Japanese Meteorological Agency: JMA is used.Fig. 3 shows the radar data derived rainfall areras of image which consists of 500km by 500km (the pixel consists 2.6km by 2.6km).Black areas show the rainfall areas with 1 to 4mm/hr of rainfall rate while hatched areas shows the rainfall areas with less than 1mm/hr of rainfall rate.These visible and thermal infrared imagery data are extracted from the NOAA/AVHRR imagery data.Also, the cloud analysis information image which is acquired at 18:00 on that day provided by JMA and weather map at 12:00, noon on that day is shown in Fig. 5 as reference data for rainfall areas.① to ④ in Fig. 5     On the other hand, Fig. 9 shows the extracted rainfall areas with NOAA/AVHRR of visible and thermal infrared imagery data.White square box in the Fig. 9 shows the corresponding area of interest with the rain radar derived rainfall areas.Through comparisons between rainfall radar data derived rainfall rate image and the extracted rainfall areas with NOAA/AVHRR data based on the proposed method, it is found that the extracted rainfall areas with NOAA/AVHRR data based on the proposed method shows relatively heavily rainfall areas.The extracted rainfall areas with NOAA/AVHRR data based on the proposed method is corresponding to the rainfall areas with rainfall rate of 2 to 4 mm/hr.

E. Alternative Method for Rainfall Area Detection
As described before, there is the alternative method of rainfall area detection, multiple linear regressive analyses: MLRA based method.Namely, rainfall radar data derived rainfall rate is approximated with the NOAA/AVHRR of visible and thermal infrared radiometer data through the MLRA.Fig. 11 (a) shows the scatter plots of the rainfall rate

Fig. 1 .
Fig. 1.Process flow of the proposed method for discrimination between rainy and non-rainy clouds with visible and thermal infrared data

Fig. 2 .
Fig. 2. NOAA/AVHRR of visible and thermal infrared data of Tohoku, Japan which is acquired on February 12 1997 is used for the experiments Fig.2 shows the visible and the thermal infrared imagery data used for the experiments.The images consists of 512 by 512 pixels (the pixel represent 2.2km by 2.2km ground surface areas).Radiometric resolution of visible channel is 0.1% of

Fig. 3 .
Fig. 3. Radar data derived rainfall areas which is observed at 10:00 in the morning on February 12 1997 Also, Fig.4 shows the imagery data which are used for multiple linear regressive analysis (Radar data on the right, Visible channel of imagery data in the middle, and Thermal infrared imagery data on the left, respectively) which are acquired on February 12 1997.

Fig. 4 .
Fig. 4. Imagery data which are used for multiple linear regressive analysis (Radar data on the right, Visible channel of imagery data in the middle, and Thermal infrared imagery data on the left, respectively) which are acquired on February 12 1997 (a) denotes cumulus clouds while ⑤ and ⑥ areas denote non rainy areas.The eastern portion of Japanese island, in particular, Hokkaido and Tohoku, there are relatively large cloudy areas.Particularly, ① area shows rainfall areas.
Fig.5.Cloud analysis information image which is acquired at 18:00 on that day and weather map at 12:00, noon on that day are shown in Fig.5as reference data for rainfall areas

Fig. 6 .
Fig. 6.Histograms of rainy (S1) and non-rainy (S2) cloud areas of thermal infrared channel of imagery data and the approximate PDF functions for the histograms for both rainy and non-rainy cloud areas It is found that histograms of rainy and non-rainy clouds are very close for the thermal channel of data while those are relatively distinguishable for the visible channel of data.

Fig. 7 (
Fig.7 (a) shows the binarized image of the visible channel of data while Fig.7 (b) shows that of the thermal infrared

Fig. 7 .
Fig. 7. Binarized images of the visible and the thermal infrared channels of data which are acquired on February 12 1997

Fig. 8 .
Fig. 8. Rainfall radar image and the rainfall rate extracted image with rain fall radar data

Fig. 9 .Fig. 10 .
Fig. 9. Extracted rainfall areas with NOAA/AVHRR of visible and thermal infrared imagery data (White square box shows the corresponding area of interest with the rain radar derived rainfall areas)