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Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 29 (2012) 1856 – 1861 www.elsevier.com/locate/procedia
2012 International Workshop on Information and Electronics Engineering (IWIEE)
Study on Shape and Formation Extrapolation Algorithm for Cloud of Storm Wang Ping, Liu Chang*, Liu Heng School of Electrical Engineer and Automation, Tianjin University ,Tianjin 300072, China
Abstract There is very important forecast information in shape and formation of storm. The job of extrapolating cloud’s shape and formation has not been realized well, up to now, because the cloud shape and formation are always very complicated and changeful. In this paper cloud images are decomposed into some levels and blocks to obtain a series of convex, regular, connected regions with single value, at first. Then for the every region two shape-formation extrapolation algorithms are proposed. One is based on scattering model and another based on local corrosionexpansion to fan-shaped regions. In the end, storm’s extrapolation image of holding its shape and formation has been successfully implemented. The test results show that this method make the similarity rate between both clouds of extrapolation and truth after 6 minutes is greater than 92%.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University of Science and Technology. Open access under CC BY-NC-ND license. Keywords:extrapolation for storm; shape and formation extrapolation; decomposition and composition of image; local corrosionandexpansion
1. Introduction Hail, heavy rain, wind and other meso-micro scale weather system are called storm weather in meteorology. This kind of weather systems develop quickly and have strong destructive force. Now in meteorological forecast, Doppler radar systems are used to detect them and one system can provides a set of echo images which can objectively reflect the type of storm clouds and the distribution of precipitation particles in storm clouds every six minutes for observer.
*
* Corresponding author. Tel.: +86-013821036818. E-mail address:
[email protected].
1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2012.01.226
WangAuthor Ping etname al. / /Procedia – 1861 ProcediaEngineering Engineering29 00(2012) (2011)1856 000–000
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In the reflectivity image of radar echoes 16 kinds of colors are used to represent 16 levels of reflectivity, generally, to reflect scale and density of the particles in the storm cloud[1]. In general, one storm system is composed of one or a few high reflective regions and other regions, the former are called the nuclear area, because every one is surrounded by the latter whose reflectivity reduce gradually from its nuclear area to its bound. For forecasting, two aspects must be considered, one is future location of the current cloud, the other is future shape and structure of it. Nearly half a century, among the extrapolation forecast methods, the cross-correlation method[2] and cell’s centre method[3] have been widely used[4-8]. They are both location extrapolation for sub-regions of current storm cloud through matching techniques. So, in the extrapolation result, the information about internal structure of the cloud and the distribution of precipitation particle in the cloud is almost lost. In this paper, a new extrapolation method is proposed, which provides not only internal structure of the extrapolation cloud but also the distribution of precipitation particle in the extrapolation cloud. 2. Inertia criteria in storm evolution Storm cloud is accompanied by specific physical fields such as pressure, humidity, temperature. So a storm system is a typical inertial system. Inertia criterion 1: in the procedure of storm evolution the precipitation particle scale, density, speed and direction of movement are not mutated. According to statistics, there are 88% of storms whose life are more than 30 minutes, 49% last 60 minutes[9], the inertia criteria of adjacent 6 minutes is established: Inertia criterion 2: Motion speed and motion direction, reflectance intensity and distribution of storm clouds, all linearly vary. 3. Shape extrapolation algorithm of storm cloud 3.1. Scattering model Set convex object F develops continuesly and to time t becomes an image with inscribed rectangle of nt and centre pct shown in figure1. Starting from upper right corner, label all boundary points counterclockwise, then obtain pi i=1,2,…,4(nt-1). A set of rays li (i=1,2,…,4(nt-1)) from pct to pi is known as scattering model used to extrapolate the shape of F. × nt
p4 p3 p2 p 1
F
nt
p4( nt −1)
t2
t3
t1
pct
nt
(a)
(b)
Fig.1 (a) Scattering model, (b) Illustration of algorithm based on scattering mode
3.2. Extrapolation algorithm based on scattering mode (1) Obtain segmentation image of last time, Ft1, by region growing method. (2) Get tracking result of current time, Ft2, by centre tracking and correlation coefficient method. (3) Let centre of Ft1be pc(t1), centre of Ft2 be pc(t2), then the future centre pc(t3) of F can be deduced by
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linear extrapolation method. (4) Let the boundary points of Ft1 and Ft2, which fall into rays li(i=1,…,4(nt-1)), be pFli(t1) and pFli(t2), calculate ∆i=pFli(t1)−pFli(t2), deduce 4(nt-1) boundary points of F in t3: pFli(t3)= pFli(t2)+∆i shown in figure3. (5) Take 4(nt-1) points pFli(t3) as corners, polygon Ft2 can be deduced through them. Generally, the nuclear region area is more than 50 points in radar reflectivity image (distance between 2 points is 1km), let parameter of scattering model nt=7, so the number of rays is 24. Obviously, extrapolation method based on scattering model becomes inaccurate with increase of the area, so it should be applied to a small area. The form of clouds vary differently, this algorithm is more suited to the objective whose shape is like lumpy. 4. Corrosion expansion method of fan-shaped edge 4.1. Extension/ retraction region detection Let convex object F becomes Ft1 at time t1 and Ft2 at time t2, t2 is the next time of t1, their centres and boundary point sets are pc(t1), Pb1={pb1(i)} and pc(t2), Pb2={pb2(i)} respectively. Let background value be 0, others is 1, pc(t1) coincides with pc(t2), the synthetic image of Ft1 and Ft2 is F12, the value in the pixel of F12 is as follows: ⎧1 ⎪ f12 ( pi ) = f t2 ( pi ) − f t1 ( pi ) = ⎨0 ⎪ −1 ⎩
pi－extension pi－Background overlapping point
(1)
pi－Retraction point
here, the region S made of extension/retraction points and the non-change region S% shown in fig 2. stretching region pc (t1 )
Ft1
pc (t2 )
non-change region
Ft2
non-change region pc
contractive region stretching region
F12
Fig.2 Illustration of extension/retraction area local
4.2. Calculating the scale of extension/retraction Let Si is an extension/retraction region, if the pixels of (p∈Si∪p∈Pb1) is N1, the pixels of p∈Si∪p∈ Pb2) is N2 and the pixels p∈Si is N, then the scale D of extension/retraction is D=
N 0.5( N1 + N2 )
4.3. Take fan-shaped regions (1) Search critical point set Pl={pl, k=1,2,……}of extension/retraction area as follows: when pb1(i)∈Pb1 and pb2(i)∈Pb2, if {f12[pb1(i)]≠0}∪{pb1(i)∈Pb2} or {f12[pb2(i)]≠0}∪{pb2(i)∈ Pb1}, then pb1(i)∈Pl or pb2(i)∈Pl . (2) Get fan-shaped regions ASi, i=1,2,…… through drawing lines from pc to all critical points.
(2)
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4.4. Local corrosion/expansion to fan-shaped regions (1) Put marks of non-processing for two rays of ASi ; (2) Get corrosion/expansion information of F12; (3) Set scale d of structure element and times n of corrosion/expansion processing as follows: ⎧ D, D ≤ 2 D d ⎨= n int( +0.5) = 2 , D > 2 2 ⎩
(3)
(4) Iterate corrosion expansion, n times, a set of new fan-shaped regions ASi′ , i=1,2,…… are formed. In the end, combine sub-regions {ASi′} and non-change regions {S%i} into an extrapolated image Ft3 of Ft2. 5. Synthetic extrapolation base on layer-images When using above two extrapolation methods the image F must ①be convex;②be the same in pixel values of it. Firstly, do multi-level decomposition for a storm image: For a radar reflectivity image, 16 colors represent -5,0,5,10,…,65dbz respectively. For the reflectivity intensity of a storm cloud, outermost one starts from 25dbz, and it reaches 55dbz(or bigger) from outer to inner step by step. So the images are decomposed into 6 levels and the ever level’s value large than and equal to 25dbz or 30dbz……. Secondly, do multi-block decomposition for one layer-image in order for every block to meet above condition ①. Then do the choice and synthesis of two shape extrapolation schemes: For a sub-block Ωi, if area S(Ωi)≥γ (γ equals 100), corrode or expand partially fan-shaped regions of Ωi, otherwise use the scattering model. The extrapolation result of Ti=25dbz is used as a basic image which is covered by extrapolation one of Ti=30dbz to obtain their synthetic image which is covered by extrapolation one of Ti=35dbz, and so on. In the end, do the progressive extrapolation: T1 and T2, two actual storm cloud images at an interval of 6 minutes, are used to obtain their extrapolation image T3’ which will appear later 6m than T2, and then using T2 and T3’ to obtain their extrapolation image T4’ which will arrive at 12m behind T2, and so on. 6. Testing 100 radar reflectivity images which are from 6 sets of time series are used to test this paper method and algorithm with evaluation indicators as follows: Set the actual image at t3 to F(t3), F12(t3) is the extrapolation result for F(t3), their core-areas are Sh(t3) and Sh12(t3), other areas are S50(t3),…,S25(t3) and S50h(t3),…,S25h(t3), in short, S6,…,S1 and S6h,…,S1h. (1) Similarity between Si and Si12 with ρ1 about core-region area and ρ2 about other-region areas
ρ1 =
min{S h (t3 ), S h12 (t3 )} max{S h (t3 ), S h12 (t3 )}
ρ2 =
1 n min{S i , S i12 } , ∑ n i =1 max{S i , S i12 }
n≤6
(4)-(5)
(2) Similarity between F and F 12 with ρ3 about high intensity area and ρ4 about low intensity area
ρ3 =
=i
ni 40,45,50, ≥ 55dbz ni + ni′
∑
ρ4 =
ni i = 25,30,35dbz ni + ni′
∑
(6)-(7)
Here, the number of point p whose intensity meets “R(p)≥i” is ni in both F12 and F, the number of p is ni’ which is only in F12 or F. (3) Synthesis of above 4 similaritirs
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Consider high intensity information is always worth more than low intensity information, so deduce a synthetic similarity ρ from weighted sum of ρi, i＝1,2,3,4, the value is k={k1,k2,k3,k4}={0.4,0.2,0.3,0.1}.
= ρ
4
4
= k ρ , ∑k ∑
i i =i 1 =i 1
i
(8)
1
Figure 3 is the illustration of 6 minutes extrapolation. Table 1 is the assessment data for extrapolation algorithm based on test samples. So far as the test samples are concerned, the average similarity between the actual storm image and its extrapolation after 6 minutes is greater than 92%. And with the increase of extrapolation time the average similarity will reduce, but still greater than 80% with extending the extrapolation time to 18 minutes.
(b)
(a)
(d)
(c)
Fig.3 Comparsion between an actual storm image and its extrapolation. (a)the actual image of t1; (b)the actual image later 6m than t1; (c)the actual image later 12m than t1; (d)the extrapolation image of (c) by (a) and (b) Table 1. Evaluation indicators extrapolation time(minutes) Similarity/run time(second) data
6
ρ1
ρ2
0.964
0.933
6
ρ3 0.919
18
ρ /run time
ρ4 0.914
12
0.94/0.87
0.90/1.51
0.81/2.43
7. Conclusion For storm cloud’s reflectivity images with multi-value, irregular shape and irregular distribution, this paper decompounds the image to 6 level sub-images firstly and disassembles the every level image into more sub-blocks, then presents two shape extrapolation algorithms and a strategy of optimizing the two algorithms. Doing it this way make the extrapolation images of storm clouds hold not only the fine detail of ditribution of the precipitation particles within them but also the shape of the boundary of every level sub-image of them. Using this paper’s technique, more and useful forecast information will be provided for weathermen. Acknowledgements This work is sponsored by Tianjin Natural Science Foundation(09JCYBJC07500). References [1]Yu xiaoding.Application of doppler radar.Beijing：Meteorological press,2006.1 [2]Rinehart R. E., et al. Three Dimension storm motion detection by conventional weather radar. Nature, 1978,273:287-289 [3]Crane R.K., Automatic Cell Detection and Tracking. IEEE Trans.Geosci.Electron.,1979.GE-17:250-262 [4]Mueller C.K., et al. NCAR Auto-Now cast system, Weather and Forecasting,2003,18:545-561 [5]Golding B.W., Nimrod: A system for generating auto- mated very short range forecasts,Meteor,Appl.,1998, 5:1-16 [6]Johnson J.T., et al. The Storm Cell Identification and Tracking Algorithm: an enhanced WSR-88D algorithm. Weather and
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[7]Zhu ping,Li Sehngchen,Xiao jianshe.Application of radar extrpolation.Meteorology,2008,34(7):3-9 [8]Lan hongping, Sun xiangping,. Study on automatic recognition and track technology.Meteorology,2009,35(7):101-111 [9]Wilson J.W., et al. Nowcasting thunder storms: a status report. Bull.Am.Meteorol. Soc.,1998,79:2079-2099.
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