Patent Publication Number: US-2019187248-A1

Title: Specific differential propagation phase apparatus and method using dual-polarization variables

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an apparatus and a method for estimating a specific differential phase using dual-polarization variables, and more specifically, to an apparatus and a method for estimating a specific differential phase using dual-polarization variables, which can estimate a specific differential phase on the basis of a self-consistent method using dual-polarization variables. 
     Background of the Related Art 
     A differential phase is a difference between horizontal and vertical propagation phases and is proportional to forward scattering characteristics of hydrometeor. It is general that a horizontal propagation phase shift is larger than a vertical propagation phase shift in a horizontally deflected hydrometeor such as raindrops. 
     In addition, in a non-meteorological echo, variation of a differential phase is absolutely greater than variation in precipitation due to a poor correlation between signals of horizontal polarization and vertical polarization. 
     Generally, a specific differential phase is calculated as a mean slope of range profiles measured across a path. 
     To measure a specific differential phase from a measured mean slope of range profiles, Golestani, et al. (1989) and Hubbert and Bringi (1995) used a filtering method. This method works well in a rainfall area, in which microphysical properties do not change abruptly like laminar flow type rainfall. However, the peak value of a specific differential phase is underestimated in an abrupt convective rainfall area, and the specific differential phase sometimes even has a negative value. It is known that this is misestimated, comparing with that the specific differential phase has a characteristic of increasing at all times. 
     In addition, since signals of an estimated specific differential phase change greatly, it may oscillate greatly even in an area showing a low rainfall rate (Wang and Chandrasekar 2009). Wang and Chandrasekar (2009) proposed an adaptive algorithm to reduce noise related to variation of a small segment and to reduce convenience of estimation in a large segment. 
     This method is configured to adjust a regression error through scaling for estimation of a specific differential phase. This method allows to obtain a specific differential phase having a comparatively improved peak value even in a weak rainfall area, as well as in a torrential area. 
     However, the method proposed by Wang and Chandrasekar (2009) is also based on a filtering method and is not effective in removing back scattering and solving the problem of negative value of the specific differential phase. 
     SUMMARY OF THE INVENTION 
     Therefore, the present invention has been made in view of the above problems, and it is an object of the present invention to provide an apparatus and a method for estimating a specific differential phase using dual-polarization variables, which can estimate precipitation more accurately by estimating an optimum specific differential phase on the basis of a self-consistent method using dual-polarization variables, instead of the existing filtering method, on hydrometeor such as rainfall. 
     The technical problems of the present invention are not limited to those mentioned above, and unmentioned other technical problems may be clearly understood by those skilled in the art from the following descriptions. 
     To accomplish the above object, according to one aspect of the present invention, there is provided a specific differential phase estimation apparatus using dual-polarization variables, the apparatus comprising: a memory for storing a specific differential phase estimation program for estimating a specific differential phase using the dual-polarization variables of an observation data received from a dual-polarization radar and a self-consistent calculation method; and a processor including: a horizontal attenuation calculation unit for calculating a plurality of horizontal attenuations {circumflex over (α)} h   _   ik (r) using an observed horizontal reflectivity Z h (r), an observed differential reflectivity Z dr (r), and an observed differential phase ϕ dp (r) received as observation data by executing the specific differential phase estimation program stored in the memory; a differential phase calculation unit for calculating (m×n) differential phases using the calculated (m×n) horizontal attenuations; a cost function calculation unit for calculating a cost function including a difference between each of the calculated (m×n) differential phases and the observed differential phase for each of the (m×n) differential phases; and a specific differential phase calculation unit for calculating a specific differential phase using a horizontal attenuation, corresponding to a minimum cost function among the calculated (m×n) cost functions, and a proportion variable corresponding to the minimum cost function, wherein the horizontal attenuation calculation unit calculates (m×n) horizontal attenuations {circumflex over (α)} ik (r) considering m proportion variables γ i  of a differential phase and a total horizontal attenuation, and n kappa variables k of the differential phase and a total differential attenuation. 
     The processor may further include a total differential phase calculation unit for calculating a difference of differential phase between a rainfall start point r 0  and a rainfall end point r m  from the observed differential phase as a total differential phase Δϕ dp (r), and the horizontal attenuation calculation unit may calculate the (m×n) horizontal attenuations using the observed horizontal reflectivity, the observed differential reflectivity, and the calculated total differential phase. 
     The horizontal attenuation calculation unit may calculate the horizontal attenuations using a following equation. 
     
       
         
           
             
               
                 
                   
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                     ^ 
                   
                   
                     h 
                      
                     
                         
                     
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                               Z 
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                               ′ 
                             
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                               ( 
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                           ] 
                         
                         b 
                       
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                     c 
                   
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                         10 
                         
                           
                             0.1 
                             · 
                             
                               γ 
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                            
                           
                             
                               μ 
                               k 
                             
                             · 
                             
                               
                                 Δφ 
                                 dp 
                               
                                
                               
                                 ( 
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                                 ) 
                               
                             
                           
                         
                       
                       - 
                       1 
                     
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                       ( 
                       
                         
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                           0 
                         
                         ; 
                         
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                               0.1 
                               · 
                               
                                 γ 
                                 i 
                               
                             
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                                 k 
                               
                               · 
                               
                                 
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                                  
                                 
                                   ( 
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                                   ) 
                                 
                               
                             
                           
                         
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                       ) 
                     
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                         h 
                       
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                         ( 
                         
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                           ; 
                           
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                 h 
               
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                 ( 
                 
                   
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                     m 
                   
                 
                 ) 
               
             
             = 
             
               
                 0.46 
                 · 
                 
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                   k 
                 
               
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                     0 
                   
                   
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                     m 
                   
                 
                  
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               Z 
                               h 
                               ′ 
                             
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                           ] 
                         
                         b 
                       
                        
                       
                         [ 
                         
                           
                             Z 
                             dr 
                             ′ 
                           
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                         ] 
                       
                     
                     c 
                   
                    
                   dr 
                 
               
             
           
         
       
       
         
           
             
               μ 
               k 
             
             = 
             
               
                 f 
                  
                 
                   ( 
                   
                     b 
                     , 
                     c 
                   
                   ) 
                 
               
               = 
               
                 b 
                 + 
                 
                   
                     k 
                     k 
                   
                   · 
                   c 
                 
               
             
           
         
       
     
     Here, i and k are indexes of the m proportion variables γ i  and n proportion variables μ k  respectively, {circumflex over (α)} h   _   ik (r) is a horizontal attenuation calculated for indexes i and k among (m×n) proportion variables, Z′ h (r) is an observed horizontal reflectivity, Z′ dr (r) is an observed differential reflectivity, ϕ dp (r) is an observed differential phase, and Δϕ dp (r) is a total differential phase, γ i  is a proportion variable of a differential phase and a total horizontal attenuation, μ k  is a proportion variable determined by a kappa variable and a constant according to a radar frequency, r 0  is a rainfall start point, and r m  is a rainfall end point. 
     The differential phase calculation unit may calculate the differential phase using a following equation. 
     
       
         
           
             
               
                 
                   φ 
                   dp 
                   
                     c 
                      
                     
                         
                     
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                     _ 
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                   ( 
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                 2 
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                     ∫ 
                     
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                       0 
                     
                     r 
                   
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                             α 
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                           ( 
                           r 
                           ) 
                         
                       
                       
                         γ 
                         i 
                       
                     
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             ; 
             
               
                 γ 
                 
                   m 
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                   ma 
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     Here, i and k are indexes of the m proportion variables and n proportion variables respectively, ϕ dp   c   _   ik (r) is a differential phase calculated at indexes i and k among the (m×n) proportion variables, and γ i  is an i-th proportion variable among the m proportion variables. 
     The cost function calculation unit may calculate the (m×n) cost functions from a sum of results of obtaining a difference between each of the calculated (m×n) differential phases and the observed differential phase at every observation distance. 
     The cost function calculation unit may calculate a cost function using a following equation. 
     
       
         
           
             
               x 
               
                 i 
                 , 
                 k 
               
             
             = 
             
               
                 1 
                 N 
               
                
               
                 
                   ∑ 
                   
                     j 
                     = 
                     1 
                   
                   N 
                 
                  
                 
                    
                   
                     
                       
                         ( 
                         
                           
                             
                               φ 
                               dp 
                             
                              
                             
                               ( 
                               
                                 r 
                                 j 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               φ 
                               dp 
                               
                                 c 
                                 
                                   1 
                                    
                                   k 
                                 
                               
                             
                              
                             
                               ( 
                               
                                 r 
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                               ) 
                             
                           
                         
                         ) 
                       
                       · 
                       
                         
                           φ 
                           dp 
                         
                          
                         
                           ( 
                           
                             r 
                             j 
                           
                           ) 
                         
                       
                     
                     
                       Δφ 
                       dp 
                     
                   
                    
                 
               
             
           
         
       
     
     Here, i and k are indexes of the m proportion variables and n proportion variables respectively, X i,k  is a cost function at indexes i and k among the (m×n) proportion variables, j is an index of an observation distance, γ j  is an observation distance, ϕ dp (r j ) is a differential phase observed at j, and ϕ dp   c     ik   (r j ) is a differential phase calculated at j. 
     The specific differential phase calculation unit may calculate the specific differential phase using a horizontal attenuation corresponding to the minimum cost function and a proportion variable of the differential phase and the total horizontal attenuation corresponding to the minimum cost function. 
     Meanwhile, according to another embodiment of the present invention, there is provided a method of estimating a specific differential phase using specific differential variables of a specific differential phase estimation apparatus, the method comprising the steps of: (A) calculating a plurality of horizontal attenuations using an observed horizontal reflectivity Z h (r), an observed differential reflectivity Z dr (r), and an observed differential phase ϕ dp (r) inputted as observation data of a dual-polarization radar; (B) calculating (m×n) differential phases using the calculated (m×n) horizontal attenuations; (C) calculating a cost function including a difference between each of the calculated (m×n) differential phases and the observed differential phase for each of the (m×n) differential phases; and (D) calculating a specific differential phase using a horizontal attenuation, corresponding to a minimum cost function among the calculated (m×n) cost functions, and a proportion variable corresponding to the minimum cost function, wherein step (A) calculates (m×n) horizontal attenuations {circumflex over (α)} h   _   ik (r) considering m proportion variables γ i  of a differential phase and a total horizontal attenuation, and n kappa variables k of the differential phase and a total differential attenuation. 
     Step (A) may include the steps of: (A1) receiving the observed horizontal reflectivity, the observed differential reflectivity, and the observed differential phase as observation data of the dual-polarization radar; (A2) calculating a difference of differential phase between a rainfall start point r 0  and a rainfall end point r m  from the observed differential phase as a total differential phase Δϕ dp (r); and (A3) calculating the (m×n) horizontal attenuations using the observed horizontal reflectivity, the observed differential reflectivity, and the total differential phase. 
     Step (A3) may calculate the horizontal attenuations using a following equation. 
     
       
         
           
             
               
                 
                   
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                     ^ 
                   
                   
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                           [ 
                           
                             
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                               ′ 
                             
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                               ( 
                               r 
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                           ] 
                         
                         b 
                       
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                         [ 
                         
                           
                             Z 
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                             ( 
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                     c 
                   
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                     ( 
                     
                       
                         10 
                         
                           
                             0.1 
                             · 
                             
                               γ 
                               i 
                             
                           
                            
                           
                             
                               μ 
                               k 
                             
                             · 
                             
                               
                                 Δφ 
                                 dp 
                               
                                
                               
                                 ( 
                                 r 
                                 ) 
                               
                             
                           
                         
                       
                       - 
                       1 
                     
                     ) 
                   
                 
                 
                   
                     
                       I 
                       h 
                     
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                       ( 
                       
                         
                           r 
                           0 
                         
                         ; 
                         
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                       ) 
                     
                   
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                           10 
                           
                             
                               0.1 
                               · 
                               
                                 γ 
                                 i 
                               
                             
                              
                             
                               
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                                 k 
                               
                               · 
                               
                                 
                                   Δφ 
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                                  
                                 
                                   ( 
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                                   ) 
                                 
                               
                             
                           
                         
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                         h 
                       
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                         ( 
                         
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                           ; 
                           
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                         ) 
                       
                     
                   
                 
               
             
             ; 
           
         
       
       
         
           
             
               
                 I 
                 h 
               
                
               
                 ( 
                 
                   
                     r 
                     0 
                   
                   ; 
                   
                     r 
                     m 
                   
                 
                 ) 
               
             
             = 
             
               
                 0.46 
                 · 
                 
                   μ 
                   k 
                 
               
                
               
                 
                   ∫ 
                   
                     r 
                     0 
                   
                   
                     r 
                     m 
                   
                 
                  
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               Z 
                               h 
                               ′ 
                             
                              
                             
                               ( 
                               r 
                               ) 
                             
                           
                           ] 
                         
                         b 
                       
                        
                       
                         [ 
                         
                           
                             Z 
                             dr 
                             ′ 
                           
                            
                           
                             ( 
                             r 
                             ) 
                           
                         
                         ] 
                       
                     
                     c 
                   
                    
                   dr 
                 
               
             
           
         
       
       
         
           
             
               μ 
               k 
             
             = 
             
               
                 f 
                  
                 
                   ( 
                   
                     b 
                     , 
                     c 
                   
                   ) 
                 
               
               = 
               
                 b 
                 + 
                 
                   
                     k 
                     k 
                   
                   · 
                   c 
                 
               
             
           
         
       
     
     Step (B) may calculate the differential phase using a following equation. 
     
       
         
           
             
               
                 
                   φ 
                   dp 
                   
                     c 
                      
                     
                         
                     
                      
                     _ 
                      
                     
                         
                     
                      
                     ik 
                   
                 
                  
                 
                   ( 
                   r 
                   ) 
                 
               
               = 
               
                 2 
                  
                 
                   
                     ∫ 
                     
                       r 
                       0 
                     
                     r 
                   
                    
                   
                     
                       
                         
                           
                             α 
                             ^ 
                           
                           
                             h 
                              
                             
                                 
                             
                              
                             _ 
                              
                             
                                 
                             
                              
                             ik 
                           
                         
                          
                         
                           ( 
                           r 
                           ) 
                         
                       
                       
                         γ 
                         i 
                       
                     
                      
                     ds 
                   
                 
               
             
             ; 
             
               
                 γ 
                 
                   m 
                    
                   
                       
                   
                    
                   i 
                    
                   
                       
                   
                    
                   n 
                 
               
               ≤ 
               
                 γ 
                 i 
               
               ≤ 
               
                 γ 
                 
                   ma 
                    
                   
                       
                   
                    
                   x 
                 
               
             
           
         
       
     
     Step (C) may calculate the (m×n) cost functions from a sum of results of obtaining a difference between each of the (m×n) differential phases calculated at step (B) and the observed differential phase at every observation distance. 
     Step (C) may calculate a cost function using a following equation. 
     
       
         
           
             
               x 
               
                 i 
                 , 
                 k 
               
             
             = 
             
               
                 1 
                 N 
               
                
               
                 
                   ∑ 
                   
                     j 
                     = 
                     1 
                   
                   N 
                 
                  
                 
                    
                   
                     
                       
                         ( 
                         
                           
                             
                               φ 
                               dp 
                             
                              
                             
                               ( 
                               
                                 r 
                                 j 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               φ 
                               dp 
                               
                                 c 
                                 
                                   1 
                                    
                                   k 
                                 
                               
                             
                              
                             
                               ( 
                               
                                 r 
                                 j 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                       · 
                       
                         
                           φ 
                           dp 
                         
                          
                         
                           ( 
                           
                             r 
                             j 
                           
                           ) 
                         
                       
                     
                     
                       Δφ 
                       dp 
                     
                   
                    
                 
               
             
           
         
       
     
     Step (D) may calculate the specific differential phase using a horizontal attenuation corresponding to the minimum cost function and a proportion variable of the differential phase and the total horizontal attenuation corresponding to the minimum cost function. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram schematically showing a specific differential phase estimation apparatus using dual-polarization variables according to an embodiment of the present invention. 
         FIG. 2  is a graph showing an example of an observation data that an input unit has received. 
         FIG. 3  is a block diagram showing a processor according to an embodiment of the present invention. 
         FIG. 4  is a graph showing another example of an observation data that an input unit has received and an example of a calculated optimum specific differential phase. 
         FIG. 5  is a flowchart illustrating a method of estimating a specific differential phase using a specific differential phase estimation apparatus according to an embodiment of the present invention. 
     
    
    
       
     
       
         
           
               
             
               
                   
               
               
                 DESCRIPTION OF SYMBOLS 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 100: Specific differential phase estimation apparatus 
               
            
           
           
               
               
               
            
               
                   
                 110: Input unit 
                   
               
               
                   
                 120: Memory 
                 130: Processor 
               
            
           
           
               
               
            
               
                   
                 310: Preprocessing unit 
               
               
                   
                 320: Total differential phase calculation unit 
               
               
                   
                 330: Horizontal attenuation calculation unit 
               
               
                   
                 340: Differential phase calculation unit 
               
               
                   
                 350: Cost function calculation unit 
               
               
                   
                 360: Specific differential phase calculation unit 
               
               
                   
                   
               
            
           
         
       
     
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The objects, other objects, features and advantages of the present invention can be easily understood through the following preferred embodiments related the accompanying drawings. However, the present invention is not limited to the embodiments described herein and may be embodied in other forms. Rather, the embodiments introduced herein are provided to make the content disclosed herein thorough and complete and to fully convey the scope of the present invention to those skilled in the art. 
     In addition, when it is mentioned that a first element (constitutional component) operates or is executed on a second element (constitutional component), it should be understood such that the element (constitutional component) operates or is executed in an environment in which the second element (constitutional component) operates or is executed or the element (constitutional component) operates or is executed directly or indirectly, through an interaction. 
     If it is mentioned that an element, a constitutional component, a device or a system includes a constitutional component configured of a program or software, it should be understood such that although it is not mentioned explicitly, the element, the constitutional component, the device or the system includes hardware (e.g., a memory, a CPU, etc.), other programs or software (e.g., an operating system, a driver needed for driving the hardware, etc.) needed for executing or operating the program or the software 
     In addition, if it is not specially mentioned in implementing an element (or constitutional component), it should be understood such that the element (or constitutional component) may be implemented in any form of software, hardware, or software and hardware. 
     In addition, the terms used in this specification are for the purpose of describing the embodiments and are not intended to limit the present invention. In this specification, singular forms include plural forms as well, unless the context clearly indicates otherwise. The terms “comprises” and/or “comprising” used in this specification mean that a constitutional element does not preclude the presence or addition of one or more other constitutional elements. 
     Hereinafter, the present invention will be described in detail with reference to the accompanying drawings. In describing the specific embodiments below, various specific contents are disclosed to describe the present invention more specifically and to help understanding of the present invention. However, those skilled in the art may recognize that the present invention may be used without these various specific contents. 
     It is mentioned in advance that, in some cases, the parts well-known in describing an invention and not greatly related to the invention are not described to avoid confusion generated without a particular reason. 
     Hereinafter, specific technical contents to be embodied in the present invention will be described in detail with reference to the accompanying drawings. 
     Those skilled in the art may easily infer that configurations of a specific differential phase estimation apparatus  100  using dual-polarization variables as shown in  FIG. 1  may be functionally and logically separated and it does not mean that each configuration should be distinguished as a separate physical device or created as a separate code. 
     Furthermore, the specific differential phase estimation apparatus  100  using dual-polarization variables may be installed in a certain data processing apparatus to implement the spirit of the present invention. 
     In addition, the specific differential phase estimation apparatus  100  using dual-polarization variables may be one among all electronic devices that can install and execute a program, such as a desktop personal computer (PC), a server, a laptop PC, a netbook computer and the like, or may be implemented in any one of the electronic devices. 
       FIG. 1  is a block diagram schematically showing a specific differential phase estimation apparatus  100  using dual-polarization variables according to an embodiment of the present invention. 
     Referring to  FIG. 1 , the specific differential phase estimation apparatus  100  using dual-polarization variables according to an embodiment of the present invention may include an input unit  110 , a memory  120 , and a processor  130 . 
     The input unit  110  may receive a plurality of dual-polarization variables including an observed horizontal reflectivity Z h (r), an observed differential reflectivity Z dr (r), and an observed differential phase ϕ dp (r) as observation data of a dual-polarization radar (not shown). 
       FIG. 2  is a graph showing an example of an observation data that an input unit  110  has received. 
       FIG. 2( a )  shows a ray profile of an observed horizontal reflectivity,  FIG. 2( b )  shows a ray profile of an observed differential reflectivity, and  FIG. 2( c )  shows a ray profile of an observed differential phase. 
     The memory  120  may include volatile memory and/or non-volatile memory. The memory  120  may store commands or data related to constitutional components, one or more programs and/or software, an operating system and the like to implement and/or provide operations, functions or the like provided by the specific differential phase estimation apparatus  100 . 
     The program stored in the memory  120  may include a specific differential phase estimation program for estimating a specific differential phase using dual-polarization variables of the observation data received from the dual-polarization radar (not shown) and the self-consistent calculation method. The specific differential phase estimation program may be implemented to include one or more modules. 
     For example, modules for implementing operations of a preprocessing unit  310 , a total differential phase calculation unit  320 , a horizontal attenuation calculation unit  330 , a differential phase calculation unit  340 , a cost function calculation unit  350 , and a specific differential phase calculation unit  360  may be stored in the memory  120 , or a module for implementing the operation of the preprocessing unit  310  and a module for implementing the operation of the other constitutional components  320  to  360  may be separately stored in the memory  120 , or one module for implementing the operations of these constitutional components  310  to  360  may be stored in the memory  120 . 
     The processor  130  controls general operation of the electronic device  200  by executing one or more programs stored in the specific differential phase estimation apparatus  100 . 
     For example, the processor  130  calculates a plurality of horizontal attenuations using an observed horizontal reflectivity Z h (r), an observed differential reflectivity Z dr (r), and an observed differential phase ϕ dp (r) received as observation data by executing the specific differential phase estimation program stored in the memory  120 , i.e., by executing commands of the program. That is, after calculating (m×n) horizontal attenuations {circumflex over (α)} h   _   ik (r) considering m proportion variables γ i  of a differential phase and a total horizontal attenuation, and n kappa variables k of the differential phase and a total differential attenuation, calculating (m×n) differential phases using the calculated (m×n) horizontal attenuations, and calculating a cost function including a difference between each of the calculated (m×n) differential phases and the observed differential phase for each of the (m×n) differential phases, the processor  130  may calculate a specific differential phase using a horizontal attenuation corresponding to a minimum cost function among the calculated (m×n) cost functions, and a proportion variable corresponding to the minimum cost function. 
       FIG. 3  is a block diagram showing a processor  130  according to an embodiment of the present invention. 
     Referring to  FIG. 3 , the processor  130  may include a preprocessing unit  310 , a total differential phase calculation unit  320 , a horizontal attenuation calculation unit  330 , a differential phase calculation unit  340 , a cost function calculation unit  350 , and a specific differential phase calculation unit  360 . 
     The preprocessing unit  310  reduces signal variation by smoothing the observation data received from the input unit  110 , i.e., the observed horizontal reflectivity Z h (r), the observed differential reflectivity Z dr (r), and the observed differential phase ϕ dp (r), and may perform a quality processing process by removing bad data having a large signal variation and a low signal-to-noise ratio. 
     The total differential phase calculation unit  320  may calculate a difference of differential phase between a rainfall start point r 0  and a rainfall end point r m  from the observed differential phase ϕ dp (r) among the quality processed observation data received from the preprocessing unit  310  as a total differential phase Δϕ dp (r). 
     Referring to  FIG. 2( c ) , the total differential phase calculation unit  320  may determine a point around 15 Km as the start point and a point around 22.5 km as the end point and calculate a difference of the observed differential phases between the two points as the total differential phase Δϕ dp (r). 
     The horizontal attenuation calculation unit  330  calculates a plurality of horizontal attenuations using the quality processed observation data, i.e., the observed horizontal reflectivity Z′ h (r), the observed differential reflectivity Z′ dr (r), and the calculated total differential phase Δϕ dp (r), in which (m×n) horizontal attenuations {circumflex over (α)} h   _   ik (r) may be calculated considering m proportion variables γ of the differential phase and the total horizontal attenuation, and n kappa variables k of the differential phase and the total differential attenuation. 
     The horizontal attenuation calculation unit  330  may calculate horizontal attenuations using [Equation 1]. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             α 
                             ^ 
                           
                           
                             h 
                              
                             
                                 
                             
                              
                             _ 
                              
                             
                                 
                             
                              
                             ik 
                           
                         
                          
                         
                           ( 
                           r 
                           ) 
                         
                       
                       = 
                       
                         
                           
                             
                               
                                 
                                   [ 
                                   
                                     
                                       Z 
                                       h 
                                       ′ 
                                     
                                      
                                     
                                       ( 
                                       r 
                                       ) 
                                     
                                   
                                   ] 
                                 
                                 b 
                               
                                
                               
                                 [ 
                                 
                                   
                                     Z 
                                     dr 
                                     ′ 
                                   
                                    
                                   
                                     ( 
                                     r 
                                     ) 
                                   
                                 
                                 ] 
                               
                             
                             c 
                           
                            
                           
                             ( 
                             
                               
                                 10 
                                 
                                   
                                     0.1 
                                     · 
                                     
                                       γ 
                                       i 
                                     
                                   
                                    
                                   
                                     
                                       μ 
                                       k 
                                     
                                     · 
                                     
                                       
                                         Δφ 
                                         dp 
                                       
                                        
                                       
                                         ( 
                                         r 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                         
                           
                             
                               I 
                               h 
                             
                              
                             
                               ( 
                               
                                 
                                   r 
                                   0 
                                 
                                 ; 
                                 
                                   r 
                                   m 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   10 
                                   
                                     
                                       0.1 
                                       · 
                                       
                                         γ 
                                         i 
                                       
                                     
                                      
                                     
                                       
                                         μ 
                                         k 
                                       
                                       · 
                                       
                                         
                                           Δφ 
                                           dp 
                                         
                                          
                                         
                                           ( 
                                           r 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                              
                             
                               
                                 I 
                                 h 
                               
                                
                               
                                 ( 
                                 
                                   r 
                                   ; 
                                   
                                     r 
                                     m 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ; 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         I 
                         h 
                       
                        
                       
                         ( 
                         
                           
                             r 
                             0 
                           
                           ; 
                           
                             r 
                             m 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         0.46 
                         · 
                         
                           μ 
                           k 
                         
                       
                        
                       
                         
                           ∫ 
                           
                             r 
                             0 
                           
                           
                             r 
                             m 
                           
                         
                          
                         
                           
                             
                               
                                 
                                   [ 
                                   
                                     
                                       Z 
                                       h 
                                       ′ 
                                     
                                      
                                     
                                       ( 
                                       r 
                                       ) 
                                     
                                   
                                   ] 
                                 
                                 b 
                               
                                
                               
                                 [ 
                                 
                                   
                                     Z 
                                     dr 
                                     ′ 
                                   
                                    
                                   
                                     ( 
                                     r 
                                     ) 
                                   
                                 
                                 ] 
                               
                             
                             c 
                           
                            
                           dr 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       μ 
                       k 
                     
                     = 
                     
                       
                         f 
                          
                         
                           ( 
                           
                             b 
                             , 
                             c 
                           
                           ) 
                         
                       
                       = 
                       
                         b 
                         + 
                         
                           
                             k 
                             k 
                           
                           · 
                           c 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     γ 1 ≤γ i ≤γ m , γ l =minimum value of γ, γ m =maximum value of γ 
     μ 1 ≤μ k ≤μ n , μ l =minimum value of μ, μ h =maximum value of μ 
     In Equation 1, i and k are indexes of m proportion variables γ i  and n proportion variables μ k  respectively, {circumflex over (α)} h   _   ik (r) is a horizontal attenuation calculated for indexes i and k among the (m×n) proportion variables, Z′ h (r) is an observed horizontal reflectivity, Z′ dr (r) is an observed differential reflectivity, ϕ dp (r) is an observed differential phase, and Δϕ dp (r) is a total differential phase. When i and k are expressed as an equation or a matrix in the present invention, they are expressed as ‘ik’ or ‘i,k’. 
     In addition, γ i  is a proportion variable of the differential phase and the total horizontal attenuation, μ k  is a proportion variable determined by a kappa variable k and parameter constants (b, c), the parameter constants (b, c) are constants according to a radar frequency, r 0  is a rainfall start point, and r m  is a rainfall end point. The kappa variable k may be a proportion variable expressing statistical reliability of the differential phase and the total differential attenuation. 
     In an embodiment of the present invention, the range of the proportion variables γ i  and μ k  is defined by the frequency of the dual-polarization radar (not shown), and if the frequency increases, the start value and the end value of the proportion variables are changed. Generally, if the frequency increases, the start value and the end value of the proportion variables are increased. A range of the proportion variables γ i  and μ k  may be defined as shown below. 
     γ 1 ≤γ i ≤γ m , γ l =minimum value of γ, γ m =maximum value of γ 
     μ 1 ≤μ k ≤μ n , μ l =minimum value of μ, μ h =maximum value of μ 
     Each of the proportion variables γ i  and μ k  defined as described above may have a step set to be independent from the others so that its value may change independently. Accordingly, the proportion variables γ i  and μ k  may have one or more values according to the set step within the range defined for the proportion variables γ i  and μ k . 
     That is, proportion variable γ i  has a step defined to repeat m times within the defined range, and proportion variable μ k  has a step defined to repeat n times within the defined range. 
     Accordingly, it may be that 0&lt;i&lt;m+1 and 0&lt;k&lt;n+1, and i and k, which are repetition indexes of the proportion variables, are expressed as an integer. When i and k are set to repeat as many times as m and n in maximum respectively, the proportion variables (γ i , μ k ) for calculating the horizontal attenuation may be defined as shown below. 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       
                         γ 
                         1 
                       
                        
                       
                         μ 
                         1 
                       
                     
                   
                   
                     … 
                   
                   
                     
                       
                         γ 
                         1 
                       
                        
                       
                         μ 
                         n 
                       
                     
                   
                 
                 
                   
                     ⋮ 
                   
                   
                     ⋱ 
                   
                   
                     ⋮ 
                   
                 
                 
                   
                     
                       
                         γ 
                         m 
                       
                        
                       
                         μ 
                         1 
                       
                     
                   
                   
                     … 
                   
                   
                     
                       
                         γ 
                         m 
                       
                        
                       
                         μ 
                         n 
                       
                     
                   
                 
               
               ] 
             
               
           
         
       
     
     For example, if the range of the proportion variable γ i  is γ 1 ≤γ i ≤γ m =0.2≤γ i ≤0.3 and the repetition step is 0.1, the proportion variable γ i  may be as shown in Table 1. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 Index, i 
                   
               
            
           
           
               
               
               
            
               
                   
                 1 
                 2 
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                 γ i   
                 0.2 
                 0.3 
               
               
                   
               
            
           
         
       
     
     In addition, if the range of the proportion variable μ k  is μ 1 ≤μ k ≤μ n =0.3≤μ k ≤0.5 and the repetition step is 0.05, the proportion variable μ k  may be as shown in Table 2. 
     
       
         
           
               
               
             
               
                   
                 TABLE 2 
               
             
            
               
                   
                   
               
               
                   
                 Index, k 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 1 
                 2 
                 3 
                 4 
                 5 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 μ k   
                 0.3 
                 0.35 
                 0.4 
                 0.45 
                 0.5 
               
               
                   
                   
               
            
           
         
       
     
     Since m and n are 2 and 5, respectively, in Table 1 and Table 2, i has indexes of 1 and 2, and k has indexes of 1 to 5. Accordingly, if ten proportion variables (γ i ,μ k ) according to the combination of the repetition indexes i and k are defined with reference to Table 1 and Table 2, it is as shown below. 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       
                         γ 
                         1 
                       
                        
                       
                         μ 
                         1 
                       
                     
                   
                   
                     
                       
                         γ 
                         1 
                       
                        
                       
                         μ 
                         2 
                       
                     
                   
                   
                     
                       
                         γ 
                         1 
                       
                        
                       
                         μ 
                         3 
                       
                     
                   
                   
                     
                       
                         γ 
                         1 
                       
                        
                       
                         μ 
                         4 
                       
                     
                   
                   
                     
                       
                         γ 
                         1 
                       
                        
                       
                         μ 
                         5 
                       
                     
                   
                 
                 
                   
                     
                       
                         γ 
                         2 
                       
                        
                       
                         μ 
                         1 
                       
                     
                   
                   
                     
                       
                         γ 
                         2 
                       
                        
                       
                         μ 
                         2 
                       
                     
                   
                   
                     
                       
                         γ 
                         2 
                       
                        
                       
                         μ 
                         3 
                       
                     
                   
                   
                     
                       
                         γ 
                         2 
                       
                        
                       
                         μ 
                         4 
                       
                     
                   
                   
                     
                       
                         γ 
                         2 
                       
                        
                       
                         μ 
                         5 
                       
                     
                   
                 
               
               ] 
             
             = 
             
                 
               
                 [ 
                 
                   
                     
                       
                         ( 
                         
                           0.2 
                            
                           
                               
                           
                            
                           0.3 
                         
                         ) 
                       
                     
                     
                       
                         ( 
                         
                           0.2 
                            
                           
                               
                           
                            
                           0.35 
                         
                         ) 
                       
                     
                     
                       
                         ( 
                         
                           0.2 
                            
                           
                               
                           
                            
                           0.4 
                         
                         ) 
                       
                     
                     
                       
                         ( 
                         
                           0.2 
                            
                           
                               
                           
                            
                           0.45 
                         
                         ) 
                       
                     
                     
                       
                         ( 
                         
                           0.2 
                            
                           
                               
                           
                            
                           0.5 
                         
                         ) 
                       
                     
                   
                   
                     
                       
                         ( 
                         
                           0.3 
                            
                           
                               
                           
                            
                           0.3 
                         
                         ) 
                       
                     
                     
                       
                         ( 
                         
                           0.3 
                            
                           
                               
                           
                            
                           0.35 
                         
                         ) 
                       
                     
                     
                       
                         ( 
                         
                           0.3 
                            
                           
                               
                           
                            
                           0.4 
                         
                         ) 
                       
                     
                     
                       
                         ( 
                         
                           0.3 
                            
                           
                               
                           
                            
                           0.45 
                         
                         ) 
                       
                     
                     
                       
                         ( 
                         
                           0.3 
                            
                           
                               
                           
                            
                           0.5 
                         
                         ) 
                       
                     
                   
                 
                 ] 
               
             
           
         
       
     
     The proportion variables (γ i , μ k ) like this may be defined in advance considering the parameter constants and the kappa variable according to a radar frequency. 
     Accordingly, the horizontal attenuation calculation unit  330  may calculate horizontal attenuations for ten proportion variables by substituting each of the ten (m×n=2×5=10) proportion variables (γ i ,μ k ) in Equation 1. 
     Meanwhile, the differential phase calculation unit  340  may calculate differential phases using Equation 2 shown below. 
     
       
         
           
             
               
                 
                   
                     
                       
                         φ 
                         dp 
                         
                           c 
                            
                           
                               
                           
                            
                           _ 
                            
                           
                               
                           
                            
                           ik 
                         
                       
                        
                       
                         ( 
                         r 
                         ) 
                       
                     
                     = 
                     
                       2 
                        
                       
                         
                           ∫ 
                           
                             r 
                             0 
                           
                           r 
                         
                          
                         
                           
                             
                               
                                 
                                   α 
                                   ^ 
                                 
                                 
                                   h 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   ik 
                                 
                               
                                
                               
                                 ( 
                                 r 
                                 ) 
                               
                             
                             
                               γ 
                               i 
                             
                           
                            
                           ds 
                         
                       
                     
                   
                   ; 
                   
                     
                       γ 
                       
                         m 
                          
                         
                             
                         
                          
                         i 
                          
                         
                             
                         
                          
                         n 
                       
                     
                     ≤ 
                     
                       γ 
                       i 
                     
                     ≤ 
                     
                       γ 
                       
                         ma 
                          
                         
                             
                         
                          
                         x 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 2, i and k are indexes of the m proportion variables and n proportion variables respectively, ϕ dp   c   _   ik (r) is a differential phase calculated at indexes i and k among the (m×n) proportion variables, and γ i  is the i-th proportion variable among the m proportion variables. 
     Referring to Equation 2, the differential phase calculation unit  340  may calculate (m×n) differential phases ϕ dp   c   _   ik (r) using (m×n) horizontal attenuations α h   _   ik (r), which is calculated for each index of the proportion variables using Equation 1, and the proportion variable γ i . 
     The cost function calculation unit  350  may calculate a cost function including a difference between each of the (m×n) differential phases ϕ dp   c   _   ik (r) calculated by the differential phase calculation unit  340  and the observed differential phase ϕ dp (r) for each of the (m×n) differential phases. 
     If the differential phases of all the proportion variables, i.e., (m×n) differential phases, are calculated, the cost function calculation unit  350  may calculate cost functions using Equation 3 shown below. 
     
       
         
           
             
               
                 
                   
                     
                       
                         x 
                         
                           1 
                           , 
                           1 
                         
                       
                       = 
                       
                         
                           1 
                           N 
                         
                          
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             N 
                           
                            
                           
                              
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         φ 
                                         dp 
                                       
                                        
                                       
                                         ( 
                                         
                                           r 
                                           j 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         φ 
                                         dp 
                                         
                                           c 
                                           11 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           r 
                                           j 
                                         
                                         ) 
                                       
                                     
                                   
                                   ) 
                                 
                                 · 
                                 
                                   
                                     φ 
                                     dp 
                                   
                                    
                                   
                                     ( 
                                     
                                       r 
                                       j 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 Δφ 
                                 dp 
                               
                             
                              
                           
                         
                       
                     
                     ; 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         x 
                         
                           i 
                           , 
                           k 
                         
                       
                       = 
                       
                         
                           1 
                           N 
                         
                          
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             N 
                           
                            
                           
                              
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         φ 
                                         dp 
                                       
                                        
                                       
                                         ( 
                                         
                                           r 
                                           j 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         φ 
                                         dp 
                                         
                                           c 
                                           
                                             1 
                                              
                                             k 
                                           
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           r 
                                           j 
                                         
                                         ) 
                                       
                                     
                                   
                                   ) 
                                 
                                 · 
                                 
                                   
                                     φ 
                                     dp 
                                   
                                    
                                   
                                     ( 
                                     
                                       r 
                                       j 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 Δφ 
                                 dp 
                               
                             
                              
                           
                         
                       
                     
                     ; 
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         x 
                         
                           m 
                           , 
                           n 
                         
                       
                       = 
                       
                         
                           1 
                           N 
                         
                          
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             N 
                           
                            
                           
                              
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         φ 
                                         dp 
                                       
                                        
                                       
                                         ( 
                                         
                                           r 
                                           j 
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         φ 
                                         dp 
                                         
                                           c 
                                           mn 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           r 
                                           j 
                                         
                                         ) 
                                       
                                     
                                   
                                   ) 
                                 
                                 · 
                                 
                                   
                                     φ 
                                     dp 
                                   
                                    
                                   
                                     ( 
                                     
                                       r 
                                       j 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 Δφ 
                                 dp 
                               
                             
                              
                           
                         
                       
                     
                     ; 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 3, i and k are indexes of m proportion variables and n proportion variables respectively, X i,k  is a cost function calculated at indexes i and k among (m×n) proportion variables, j is an index of an observation distance, γ j  is an observation distance, ϕ dp (r j ) is a differential phase observed at j, and ϕ dp   c     ik   (r j ) is a differential phase calculated at j. N is the maximum number of distances observed in the total observation distance range. For example, if the total observation distance range is 10 to 20 km and the observation step is 1 km, it means observation of every 1 km, and N may be 10 or 11 according to setting of a user. 
     Referring to Equation 3, the cost function calculation unit  350  may obtain a difference between each of the (m×n) differential phases ϕ dp   c     ik   (r j ) calculated by the cost function calculation unit  350  and the observed differential phase ϕ dp (r j ) at every observation distance, and calculate (m×n) cost functions from a sum of results obtained at every observation distance. That is, the cost function calculation unit  350  may calculate (m×n) cost functions corresponding to the repetition indexes i and k, and this can be expressed as a matrix shown below. 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       X 
                       
                         1 
                         , 
                         1 
                       
                     
                   
                   
                     … 
                   
                   
                     
                       X 
                       
                         1 
                         , 
                         n 
                       
                     
                   
                 
                 
                   
                     ⋮ 
                   
                   
                     ⋱ 
                   
                   
                     ⋮ 
                   
                 
                 
                   
                     
                       X 
                       
                         m 
                         , 
                         1 
                       
                     
                   
                   
                     … 
                   
                   
                     
                       X 
                       
                         m 
                         , 
                         n 
                       
                     
                   
                 
               
               ] 
             
               
           
         
       
     
     Meanwhile, the specific differential phase calculation unit  360  may calculate a specific differential phase using the horizontal attenuation corresponding to a minimum cost function among the (m×n) cost functions calculated by the cost function calculation unit  350 , and the proportion variable corresponding to the minimum cost function. This is since that the minimum cost function means a differential phase, the difference of which from the observed differential phase is smallest, among the (m×n) differential phases calculated by the cost function calculation unit  350  and therefore means that they are most similar to each other. 
     The specific differential phase calculation unit  360  may confirm the horizontal attenuations {circumflex over (α)} h   _   ik (r) used for calculating the minimum cost function and the proportion variable γ j  of the differential phase and the total horizontal attenuation, and calculate an optimum specific differential phase using Equation 4 shown below. 
     
       
         
           
             
               
                 
                   [ 
                   
                     
                       
                         K 
                         dp 
                       
                        
                       
                         ( 
                         r 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             α 
                             ^ 
                           
                           
                             h 
                              
                             
                                 
                             
                              
                             _ 
                              
                             
                                 
                             
                              
                             ik 
                           
                         
                          
                         
                           ( 
                           r 
                           ) 
                         
                       
                       
                         γ 
                         i 
                       
                     
                   
                   ] 
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     Referring to Equation 4, the specific differential phase calculation unit  360  may calculate the specific differential phase using the horizontal attenuations {circumflex over (α)} h   _   ik (r) and the proportion variable γ j  corresponding to the confirmed minimum cost function. 
     For example, if the minimum cost function is X 3,4  among the (m×n) cost functions 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       X 
                       
                         1 
                         , 
                         1 
                       
                     
                   
                   
                     … 
                   
                   
                     
                       X 
                       
                         1 
                         , 
                         n 
                       
                     
                   
                 
                 
                   
                     ⋮ 
                   
                   
                     ⋱ 
                   
                   
                     ⋮ 
                   
                 
                 
                   
                     
                       X 
                       
                         m 
                         , 
                         1 
                       
                     
                   
                   
                     … 
                   
                   
                     
                       X 
                       
                         m 
                         , 
                         n 
                       
                     
                   
                 
               
               ] 
             
             , 
           
         
       
     
     the specific differential phase calculation unit  360  may calculate an optimum specific differential phase as shown in Equation 5 by substituting the horizontal attenuation {circumflex over (α)} h   _   34 (r) used for calculating the minimum cost function X 3,4  and the proportion variable γ 3  into Equation 4. 
     
       
         
           
             
               
                 
                   
                     
                       K 
                       dp 
                     
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                       ( 
                       r 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           α 
                           ^ 
                         
                         
                           h 
                            
                           
                               
                           
                            
                           _ 
                            
                           
                               
                           
                            
                           34 
                         
                       
                        
                       
                         ( 
                         r 
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                       γ 
                       3 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     The calculated optimum specific differential phase can be used for calculating precipitation, i.e., for predicting rainfall. 
       FIG. 4  is a graph showing another example of an observation data that an input unit  110  has received and an example of a calculated optimum specific differential phase. 
     Referring to  FIG. 4 , for example, the specific differential phase calculated considering the differential phase observed at an observation distance between 30 km and 68 km does not have a negative differential phase value, and the problem of underestimating the peak value is solved, and although it is not shown, the back scattering is also removed. 
       FIG. 5  is a flowchart illustrating a method of estimating a specific differential phase using a specific differential phase estimation apparatus  100  according to an embodiment of the present invention. 
     Since the specific differential phase estimation method of  FIG. 5  can be implemented by the specific differential phase estimation apparatus  100  described with reference to  FIGS. 1 to 4 , detailed description is omitted. 
     Referring to  FIG. 5 , the specific differential phase estimation apparatus  100  receives a plurality of dual-polarization variables including an observed horizontal reflectivity Z h (r), an observed differential reflectivity Z dr (r), and an observed differential phase ϕ dp (r) as observation data of a dual-polarization radar (not shown) (step S 410 ). 
     The specific differential phase estimation apparatus  100  may reduce signal variation by smoothing the received observation data, perform a quality processing process by removing bad data having a large signal variation and a low signal-to-noise ratio, and calculate a difference of differential phase between a rainfall start point r 0  and a rainfall end point r m  from the observed differential phase among the quality processed observation data as a total differential phase Δϕ dp (r). 
     The specific differential phase estimation apparatus  100  may calculate a plurality of horizontal attenuations using the quality processed observation data, i.e., the observed horizontal reflectivity, the observed differential reflectivity, and the total differential phase calculated at step S 420 , in which (m×n) horizontal attenuations {circumflex over (α)} h   _   ik (r) may be calculated considering m proportion variables γ i  of the differential phase and the total horizontal attenuation and n kappa variables k of the differential phase and the total differential attenuation. Step S 430  may be calculated as shown in Equation 1. 
     The specific differential phase estimation apparatus  100  may calculate (m×n) differential phases using the (m×n) horizontal attenuations calculated for each index of the proportion variables at step S 430  and the proportion variables (step S 440 ). Step S 440  may be calculated as shown in Equation 2. 
     In addition, the specific differential phase estimation apparatus  100  may calculate a cost function including a difference between each of the (m×n) differential phases calculated at step S 440  and the observed differential phase for each of the (m×n) differential phases (step S 450 ). Step S 450  may be calculated as shown in Equation 3. 
     The specific differential phase estimation apparatus  100  may confirm a horizontal attenuation corresponding to a minimum cost function among the (m×n) cost functions calculated at step S 450 , and a proportion variable corresponding to the minimum cost function (step S 460 ), and calculate an optimum specific differential phase using the confirmed horizontal attenuation used for calculating the minimum cost function, and the confirmed proportion variable of the differential phase and the total horizontal attenuation (step S 470 ). Step S 470  may be calculated as shown in Equation 4. 
     Meanwhile, those skilled in the art may easily understand that the method of estimating a specific differential phase using dual-polarization variables of the specific differential phase estimation apparatus  100  according to the present invention can be provided in a recording medium that can be read through a computer as a program of commands for implementing the method is tangibly implemented. 
     That is, the method of estimating a specific differential phase using dual-propagation variables of the specific differential phase estimation apparatus  100  according to the present invention may be implemented in the form of a program that can be performed through various computing means and recorded in a computer-readable recording medium, and the computer-readable recording medium may include program commands, data files, data structures and the like independently or in combination. The computer-readable recording medium includes magnetic media such as a hard disk, optical media such as CD-ROM and DVD, and hardware devices specially configured to store and perform program commands, such as ROM, RAM, flash memory, USB memory and the like. 
     Accordingly, the present invention also provides programs stored in the computer-readable recording medium executed on a computer which controls the specific differential phase estimation apparatus  100 , to implement the method of estimating a specific differential phase using dual-polarizations of the specific differential phase estimation apparatus  100 . 
     According to the present invention, there is an effect of estimating precipitation more accurately by estimating an optimum specific differential phase on the basis of a self-consistent method using dual-polarization variables, instead of the existing filtering method, on hydrometeor such as rainfall. 
     In addition, according to the present invention, the problem of underestimating a peak value generated when an existing filtering method is applied can be solved, and the back scattering can be removed, and furthermore, the problem of misestimating a specific differential phase as a negative value can be solved. 
     In addition, according to the present invention, the specific differential phase estimation apparatus is almost not affected by the bias effect of a radar system, which gives an influence to the observed reflectivity and differential reflectivity, and is not much sensitive to variation of a temperature and rainfall model (drop size distribution, DSD). 
     In addition, according to the present invention, since a further better convergence is conducted to estimate an optimum specific differential phase, accuracy of calculating the specific differential phase can be enhanced considerably. 
     The effects of the present invention are not limited to those mentioned above, and unmentioned other effects may be clearly understood by those skilled in the art from the following descriptions. 
     Meanwhile, although the preferred embodiments for exemplifying the spirit of the present invention have been described above, the present invention is not limited to the configuration and operation as is described and shown like this, and those skilled in the art may easily understand that a plurality of modifications and changes can be made on the present invention without departing from the spirit of the present invention. Accordingly, all the proper modifications, changes and equivalents should be considered as falling within the scope of the present invention. Accordingly, the true scope of the present invention should be defined by the spirit of the appended claims.