Patent Publication Number: US-10762774-B2

Title: Program, method, and apparatus for computing index on sediment disaster

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2018-38776, filed on Mar. 5, 2018, the entire contents of which are incorporated herein by reference. 
     FIELD 
     The embodiments discussed herein are related to a program, a method, and a computing unit for computing an index on sediment disasters. 
     BACKGROUND 
     In the field of sediment disaster, an index of how much similar rainfall was experienced in the past is calculated using short rainfall (short-term in several minutes to several hours) and long rainfall (long-term in several days to several weeks), and it is determined whether disaster may occur at the time of rainfall based on the computed index and the past disasters. An example of the index is an output value (an RBFN output value) obtained via a radial basis function network (RBFN) which is a neural network. 
     There is a known technique in the art for computing the probability of occurrence of disaster by obtaining a function for computing the probability of occurrence of disaster from the RBFN output value by a regression analysis and reading the obtained function and observation data obtained for each disaster occurrence factor. Examples include Japanese Laid-open Patent Publication No. 2004-003274, No. 2010-197185, No. 2010-271877, No. 2004-346653, and No. 2015-232537. 
     Sediment disaster is predicted based on, for example, the accumulated rainfall up to the present and past observation data. However, an increase in accumulated rainfall due to unexpected continuing rainfall and unexpected immediately following heavy rain may cause the accumulated rainfall to exceed a disaster critical line (CL). For this reason, the probability of exceeding the CL after a unit time (hereinafter referred to as “excess probability”) may be obtained in advance. 
     The above techniques take no account of the probability of unexpected continuing rainfall and unexpected immediately following heavy rain, so that the same RBFN value indicates the same disaster occurrence probability, that is, the same excess probability. 
     In one aspect, the influence of a precipitation zone is appropriately reflected to the probability of exceeding a critical line on the occurrence of disaster. 
     SUMMARY 
     According to an aspect of the embodiments, a method for computing an index on a sediment disaster, performed by a computer, the method includes: creating a computation model for computing the index on a sediment disaster at a specific point using information on a geometry of a precipitation zone at the specific point and long rainfall and short rainfall at the specific point, the information being created from past precipitation data accumulated in a storage unit; and computing the index on a sediment disaster using the computation model from the information on the geometry of the precipitation zone at the specific point, the information being created from the input precipitation data. 
     The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a graph illustrating determination of whether sediment disaster may occur using a critical line; 
         FIG. 2  is a graph illustrating critical lines; 
         FIG. 3  is a diagram for illustrating, in outline, a method for creating the critical line; 
         FIG. 4  is a graph illustrating an example of a decision diagram in the case of more than expected rainfall; 
         FIG. 5  illustrates a known method for obtaining CL excess probability; 
         FIG. 6  is a diagram illustrating an example of a linear precipitation zone; 
         FIGS. 7A and 7B  are graphs illustrating setting examples of a CL excess probability line; 
         FIGS. 8A and 8B  are diagrams for illustrating the relationship between the geometry of the precipitation zone and the continuity of rainfall; 
         FIG. 9  is a diagram illustrating an example of a rainfall distribution image in the sky; 
         FIG. 10A  is a graph illustrating the relationship between the long side of the precipitation zone and the rainfall; 
         FIG. 10B  is a graph illustrating the relationship between the long side of the precipitation zone and the soil water index; 
         FIG. 11  is a graph illustrating an example of the computation result of CL excess probability; 
         FIG. 12  is a diagram illustrating the hardware configuration of a computing unit; 
         FIG. 13  is a diagram illustrating an example of the functional configuration of the computing unit; 
         FIG. 14  is a flowchart for illustrating learning processing performed by a learning unit; 
         FIG. 15  is a flowchart for illustrating geometry-parameter computation processing performed by a geometry-parameter computing unit; 
         FIG. 16  is a flowchart for illustrating model creation processing performed by a model creating unit; 
         FIG. 17  is a flowchart for illustrating the entire CL-excess-probability-line creation processing performed by a CL-excess-probability-line creating unit; 
         FIG. 18  is a flowchart for illustrating update processing performed by an update unit; 
         FIG. 19A  is a diagram illustrating CL excess probability in a known technique in which a precipitation zone is not considered; 
         FIG. 19B  a diagram illustrating CL excess probability in the present embodiment obtained in consideration of the precipitation zone; 
         FIG. 20A  is a diagram illustrating different precipitation zones over the same target point; 
         FIG. 20B  illustrates graphs of examples of representation of CL-excess probability lines for the different precipitation zones in the known art; and 
         FIG. 20C  illustrates graphs of examples of representation of CL-excess probability lines for the different precipitation zones in the embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Embodiments of the present disclosure will be described hereinbelow with reference to the drawings. First, common sediment disaster prediction will be described.  FIG. 1  is a graph illustrating determination of whether sediment disaster may occur using a critical line. 
     A decision diagram  2   g  in  FIG. 1  for determining whether sediment disaster may occur is a graph illustrating soil water index on the horizontal axis and accumulated rainfall on the vertical axis. The decision diagram  2   g  illustrates a critical line (CL)  3  computed in advance and points  4  indicating the accumulated rainfall and the soil water index computed using observation data (rainfall) at past predetermined time intervals (every hour or the like). 
     The soil water index indicates the amount of moisture accumulated in the soil due to rainfall and is referred to as an index indicating sediment disaster risk. An example of the accumulated rainfall is a 60 minutes accumulated rainfall (mm/60 min). The accumulated rainfall is a value obtained by accumulating 10 minutes precipitation data obtained at a rainfall observation station for 60 minutes. At the plotted points  4 , changes in measured value are indicated by solid arrows, and changes in predicted value are indicated by dotted arrows. 
     The area enclosed by the CL  3 , the vertical axis, and the horizontal axis is a non-occurrence area where sediment disaster is less likely to occur. The area above the non-occurrence area corresponds to an occurrence area where sediment disaster is likely to occur. By referring to such a decision diagram  2   g , it is determined that sediment disaster is likely to occur when the predicted value reaches the occurrence area exceeding the CL  3 . 
       FIG. 2  is a graph illustrating critical lines. A decision diagram  2   h  illustrated in  FIG. 2  is a graph in which values are plotted based on past observation data. Referring to the decision diagram  2   h , the critical line and the occurrence/non-occurrence of landslides, which is an example of sediment disaster, will be described. 
     The CL  3  illustrated in the decision diagram  2   h  is a critical line that is appropriately set based on measured values at the occurrence of past landslides and measured values at the non-occurrence of landslides. The large circles indicate points at which landslides occurred after the next unit time, and the small circles indicate points at which no landslide occurred after the next unit time. 
     In the area between the CL  3  and a CL  3   a  set in the non-occurrence area, many values are present, but the number of actual landslides is only two. If the CL  3   a  is set, it is predicted for the values at which no landslide actually occurs that sediment disasters may occur, so that many predictions result in failure (the predictions fail). 
     In the area between the CL  3  and a CL  3   b  set in the occurrence area, less values are included than the values in the area between the CL  3  and the CL  3   a , but two landslides occurred actually. If the CL  3   b  is set, the two landslides that could be predicted using the CL  3  are missed. Compared to the CL  3 , there is a high possibility of missing the occurrence of landslides. 
       FIG. 3  is a diagram for illustrating, in outline, a method for creating a critical line CL. In  FIG. 3 , a response curved surface  5   b  is created by learning the occurrence and non-occurrence of landslides using past data  4  on accumulated rainfall and soil water indices as input data  5 . The response curved surface  5   b  is represented by the accumulated rainfall and soil water indices in the past data  4  and the output values of the radial basis function network (RBFN) (RBFN output values). Portions where no observation value is present are interpolated using the response curved surface  5   b  to define a critical line. 
     The response curved surface  5   b  is a three-dimensional curved surface represented by a graph  2   k  illustrating the soil water index on the x-axis, the RBFN output value on the y-axis, and the accumulated rainfall on the z-axis and created based on a frequency distribution of long periods of non-occurrence rainfall. 
     The RBFN is a technique for modeling the brain and neural network and computing human evaluation using a computer. The RBFN learns the relationship between the input and output from past data and outputs a value evaluating whether landslides may occur. As the RBFN output value approaches 1, landslides are less likely to occur, and as the RBFN output value approaches 0, landslides are likely to occur. 
     The response curved surface  5   b  is formed for each target point, such as a municipality (a precipitation station), using the RBFN to determine the CL  3 . In the learning phase using the RBFN, it is determined that areas where rain frequency is high in the past have low risk. In this example, the CL  3   a  and the CL  3   b  illustrated in  FIG. 2  are also illustrated for reference. On the response curved surface  5   b , the CL  3   a  is illustrated close to a RBFN output value of 1 with respect to the CL  3 , and the CL  3   b  is illustrated close to a RBFN output value of 0 with respect to the CL  3 . 
       FIG. 4  is a graph illustrating an example of a decision diagram in the case of more than expected rainfall. The decision on whether landslides may occur using the critical line is made based on expected rainfall, but actual rainfall may exceed expectations. 
     In  FIG. 4 , a point  4   a  close to the CL  3  is plotted in the non-occurrence area from the accumulated rainfall and the soil water index obtained based on a predicted rainfall for the next unit time. However, in the actual next unit time, a point  4   b  is plotted in the occurrence area across the CL  3  from the accumulated rainfall and the soil water index based on an actually measured rainfall. 
     The municipality at the target point normally takes different measures depending on whether the rainfall exceeds the CL  3 . If the excess over the CL  3  has not been predicted, the municipality may not contact the residents and prepare for disasters in advance. At least when the rainfall is close to the CL  3 , it is important for the municipality or the like to know in advance how much possibility that the rainfall exceeds the CL  3 . For that purpose, Laid-open Patent Publication No. 2010-271877 proposes a technique for computing CL excess probability that the rainfall exceeds the CL  3  determined for each municipality into the disaster occurrence area and illustrating the excess probability in the decision diagram  2   g.    
       FIG. 5  illustrates a known method for obtaining CL excess probability. A graph  5   g  of  FIG. 5  illustrates RBFN output value obtained by learning the past data  4  on the horizontal axis and CL excess probability on the vertical axis. In one example, the probability that the RBFN output value exceeds the CL after a unit time (CL excess probability) is calculated at the point in time the RBFN output value does not exceed the CL. For example, there are ten points in the past where the RBFN output value is 0.8, and when three of the ten points exceed the CL after the next unit time, the CL excess probability is 30%. 
     A regression model for obtaining CL excess probability for each RBFN output value is created. CL excess probability lines at which the CL excess probability is 25%, 50%, and 75% are obtained from the regression model. The CL excess probability is not limited to these values. The user, such as a municipality, may designate desired CL excess probability for reference. 
     The graph  2   g  in  FIG. 5  illustrates respective CL excess probability lines  3 - 1 ,  3 - 2 , and  3 - 3  of 25%, 50%, and 75% obtained from the regression model as dotted lines, thereby making it easy to understand the necessity of preparation for disasters. 
     The known technique described above allows the user to find the probability of exceeding the CL  3  in advance. However, this known technique statistically determines whether the RBFN value exceeds the CL  3  by performing a regression analysis using a RBFN output value immediately before the rainfall exceeds the CL  3 . Since the CL excess probability is computed only using the RBFN output value, the rainfall trend, such as whether the rain continues falling or stops, is not taken into consideration even with the same RBFN output value. Accordingly, even with different rainfall trends, the CL excess probability after the next unit time is unique if the RBFN value is the same. 
     The inventor has devised to obtain CL excess probability after a unit time in consideration of a linear precipitation zone in view of the fact that the linear precipitation zone is involved in the likelihood of continuation of rainfall and the likelihood of heavy rain. The linear precipitation zone will be first described. 
     The linear precipitation zone is crowded with multiple cumulonimbus clouds to cause concentrated heavy rain. The scale is normally from 20 to 50 kilometers wide and from 50 to 200 kilometers long, and the ratio of the long axis to the horizontal axis is about 3 to 1, but there is no set definition. If the linear precipitation zone is formed, heavy rain occurs, making it easy to cause sediment disasters. 
       FIG. 6  is a diagram illustrating an example of the linear precipitation zone. In  FIG. 6 , a linear precipitation zone  8   h  is formed from a mass of multiple cumulonimbus clouds appearing near the front. Representative examples include three types: a squall line type, a back building type, and a back and side building type. It is known that the linear precipitation zone  8   h  stays at the same point to cause long rainfall or the like, causing sediment disasters with a high possibility. 
     For example, the CL excess probability after a unit time may differ (change) between when the linear precipitation zone  8   h  is formed and when the linear precipitation zone  8   h  is not formed. Accordingly, the present embodiment improves the accuracy of CL excess probability by updating the CL excess probability line in real time based on the value of the latest geometry of the precipitation zone observed. 
       FIGS. 7A and 7B  are graphs illustrating examples of setting of the CL excess probability lines in the present embodiment.  FIG. 7A  illustrates CL excess probability lines  3   a - 1 ,  3   a - 2 , and  3   a - 3  in the case where the linear precipitation zone  8   h  is present. In the case where the linear precipitation zone  8   h  is present, heavy rain tends to occur. For that reason, in the present embodiment, the CL excess probability lines  3   a - 1 ,  3   a - 2 , and  3   a - 3  are set lower in the non-occurrence area. The CL excess probability lines  3   a - 1 ,  3   a - 2 , and  3   a - 3  are set away from the CL  3 . 
       FIG. 7B  illustrates CL excess probability lines  3   b - 1 ,  3   b - 2 , and  3   b - 3  in the case where the linear precipitation zone  8   h  is not present. In the case where the linear precipitation zone  8   h  is not present, heavy rain is less likely to occur. For that reason, in the present embodiment, the CL excess probability lines  3   b - 1 ,  3   b - 2 , and  3   b - 3  are set higher in the non-occurrence area. The CL excess probability lines  3   b - 1 ,  3   b - 2 , and  3   b - 3  are set close to the CL  3 . 
     In the case of a pattern  6   a  in  FIG. 7A  illustrating the transition of accumulated rainfall, the accumulated rainfall exceeds the CL excess probability line  3   a - 1  when the value at a point  4   e  reaches an accumulated rainfall  7   a . This allows the municipality or the like to recognize that the rainfall may exceed the CL  3  with a probability of 25% after the next unit time when the value at the point  4   e  is obtained. At a point  4   f  after the next unit time, the value does not exceed the CL  3 , but the point  4   f  is positioned above the CL excess probability line  3   a - 3 , so that the value may exceed the CL  3  after the next unit time with a probability of 75% or higher. 
     Under such circumstances, a predicted point  4   g  is above the CL excess probability line  3   a - 3  after the next unit time even below the CL  3 . This allows the municipality or the like to recognize that sufficient precaution has to be taken. 
     In contrast, in the case of a pattern  6   b  in  FIG. 7B  illustrating transition of accumulated rainfall, a point  4   p  with the same accumulated rainfall  7   a  as in  FIG. 7A  is lower than the CL excess probability line  3   b - 1 . A point  4   q  after the unit time next to the point  4   p  is above the same accumulated rainfall  7   b  as in  FIG. 7A  but is lower than the CL excess probability line  3   b - 1 . Thus, it may be determined that there is little probability of exceeding the CL  3  at both of the point  4   p  and the point  4   q.    
     A point  4   r  after the next unit time is positioned between the CL excess probability lines  3   b - 2  and  3   b - 3 . Therefore, there is a probability of 50% or higher and 75% or lower that the rainfall exceeds the CL  3 . After the next unit time, a point  4   s  is presented between the CL excess probability lines  3   b - 1  and  3   b - 2 . The accumulated rainfall at the point  4   s  is substantially the same as the accumulated rainfall at the point  4   q , but the soil water index is higher than the soil water index at the point  4   q , so that the point  4   s  is positioned over the CL excess probability line  3   b - 1 . 
     The predicted point after the unit time next to the point  4   s  is a point  4   t . The point  4   t  is lower than the CL excess probability line  3   b - 1 , but the point  4   s  above the CL excess probability line  3   b - 1  allows easy recognition of the probability of sediment disasters at 25% or more and 50% or less, thus allowing preparation for sediment disasters. 
     If a comparison is made between the pattern  6   a  in  FIG. 7A  and the pattern  6   b  in  FIG. 7B , the accumulated rainfall of the pattern  6   a  gradually increases, but the probability of sediment disasters is found out when the rainfall reaches the accumulated rainfall  7   a . For the pattern  6   b  in the case where the linear precipitation zone  8   h  is not formed, even if the accumulated rainfall increases in the early phase, the probability of sediment disasters is low even when the rainfall reaches the accumulated rainfall  7   b  over the accumulated rainfall  7   a.    
     In the present embodiment, in the case where the linear precipitation zone  8   h  is formed, heavy rain is likely to occur, as illustrated in  FIG. 7A , so that the CL excess probability is increased and varied in consideration of the influence of the heavy rain. That is, the CL excess probability is computed with higher accuracy. For example, geometry parameter representing the geometry of the linear precipitation zone  8   h  is created, and CL excess probability is obtained using the created geometry parameter and the RBFN output values. 
     Since the definition of the linear precipitation zone  8   h  has not been established yet, it is simply referred to as “precipitation zone”, and is explained in the following description. First, the relationship between the geometry of the precipitation zone and the continuity of rainfall will be described with reference to  FIGS. 8A and 8B . In  FIGS. 8A and 8B , precipitation zones  8   a  and  8   b  are formed along a front  8   f  and the flow of wind into an elongate shape, whose size may be approximately represented by the long side and the short side. Simply, the longer the long side, the wider area is given rainfall, and the longer the short side, the longer the rainfall lasts. 
     In this example, a target point or geographical location  9   p , such as a municipality, illustrated in  FIGS. 8A and 8B  represents the same point, and the precipitation zones  8   a  and  8   b  move in the same traveling direction  8   e  at the same speed. The difference in continuity of the rainfall according to the difference between the lengths of the short sides of the precipitation zones  8   a  and  8   b , with the long sides set at the same, will be described in outline. 
     The precipitation zone  8   a  in  FIG. 8A  is smaller in short side than the precipitation zone  8   b  in the  FIG. 8B . The target point  9   p  is exposed to rain for a moving distance  8   p  after entering the precipitation zone  8   a  until coming out of the precipitation zone  8   a.    
     The precipitation zone  8   b  in  FIG. 8B  is larger in short side than the precipitation zone  8   a  in  FIG. 8A . Accordingly, the target point  9   p  is exposed to rain for a moving distance  8   q  after entering the precipitation zone  8   b  until coming out of the precipitation zone  8   b , which is longer than the case of the precipitation zone  8   a , thereby providing a longer rainfall than the case of the precipitation zone  8   a.    
     Thus, it is posited that the probability of the occurrence of sediment disaster depends on the geometry of the precipitation zone and a method is found for computing CL excess probability using geometry parameter representing information on the geometry of the precipitation zone (hereinafter referred to as “geometry parameter”). 
     First, the geometry parameter will be described.  FIG. 9  is a diagram illustrating an example of a rainfall distribution image in the sky. In  FIG. 9 , a rainfall that may have low influence on sediment disasters is predetermined as a threshold so that weak rain areas are not detected, and a distribution of rainfalls higher than or equal to a fixed strength is created. An example of the fixed strength is 50 mm/3 h. 
     In a rainfall distribution image  7   g  illustrated in  FIG. 9 , a minimum circumscribed rectangle  7   c  enclosing a continuous detected area  7   d  is obtained. The following information is acquired from the obtained circumscribed rectangle  7   c . The information is generically referred to as geometry parameter. The obtained parameter includes:
         The ratio of the long side to the short side (aspect ratio)   Area   The long side of the circumscribed rectangle   The short side of the circumscribed rectangle.       

     The target data from which the geometry parameter is to be obtained may be any of the following data.
         Data on target time (target time: the latest value at the time of execution, the individual times at the time of learning)   Prediction data (30 minutes after the target time, for example, one hour later)   Past data (30 minutes before the target time, for example, one hour ago)   Time-series change data (for example, the difference between n minutes before the target time and the target time)       

     How the geometry parameter obtained as described above is to be used will be described. Referring to  FIGS. 10A and 10B , the respective relationships between the geometry of the precipitation zone and the rainfall and the soil water index will be described.  FIGS. 10A and 10B  respectively illustrate the rainfall and the soil water index in a municipality in a precipitation zone with accumulated rainfall equal to or higher than 50 mm/3 h. 
     The graph in  FIG. 10A  illustrates the relationship between the long side of the precipitation zone and the rainfall. The graph in  FIG. 10B  illustrates the relationship between the long side of the precipitation zone and the soil water index. Both the rainfall and the soil water index in the graphs exhibit low relationship. For example, using the long side of the precipitation zone to correct the value of precipitation may not improve the accuracy because of the low relationship. 
     However, it is found that if the geometry parameter is used in addition to the RBFN output values to determine the CL excess probability, there is a relationship between the RBFN output values and the geometry parameter. An approximate curve model to determine the CL excess probability is derived as 
     
       
         
           
             
               
                 
                   
                     
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     In Eq. 1, x is RBFN output value, and y is a geometry parameter. “a”, “b” and “c” are coefficients. 
       FIG. 11  is a graph illustrating an example of the computation result of CL excess probability. In  FIG. 11 , a graph  9   g  illustrates the RBFN output value on the x-axis, the CL excess probability on the y-axis, and the geometry parameter on the z-axis. The geometry parameter includes four parameters, as described above and is represented in multiple dimensions. In this example, the long side is illustrated as an example. 
     In the graph  9   g  in  FIG. 11 , the CL excess probability increases as the RBFN output value decreases and the long side increases. Thus using Eq. 1 allows correcting the CL excess probability according to the geometry of the precipitation zone using the geometry parameter. 
     A computing unit that implements the above embodiment has the hardware configuration illustrated in  FIG. 12 .  FIG. 12  illustrates the hardware configuration of the computing unit. In  FIG. 12 , the computing unit  100  is an information processing apparatus controlled by a computer and includes a central processing unit (CPU)  11 , a main storage  12 , an auxiliary storage  13 , an input device  14 , a display device  15 , a communication interface (I/F)  17 , and a drive unit  18 , which are connected via a bus B. 
     The CPU  11  corresponds to a processor that controls the computing unit  100  according to programs stored in the main storage  12 . The main storage  12  includes a random access memory (RAM) and a read only memory (ROM), and stores or temporarily stores the programs to be executed by the CPU  11  and data for use in processing in the CPU  11  and data obtained by the processing in the CPU  11 . 
     An example of the auxiliary storage  13  is a hard disk drive (HDD). The auxiliary storage  13  stores data, such as programs for executing various processes. Part of the programs stored in the auxiliary storage  13  are loaded to the main storage  12  and executed by the CPU  11 , so that the various processes are implemented. The main storage  12 , the auxiliary storage  13 , and an external storage that may be accessed by the computing unit  100  are collectively referred to as a storage unit  130 . 
     The input device  14  includes a mouse, a keyboard, and so on, and is used for the user to input various pieces of information for processing performed by the computing unit  100 . The display device  15  displays various pieces of information under the control of the CPU  11 . The input device  14  and the display device  15  may be a user interface, for example, an integrated touch panel. The communication I/F  17  performs communication via a wired or wireless network. The communication via the communication I/F  17  is not limited to the wired or wireless communication. 
     The drive unit  18  interfaces a storage medium  19  (for example, a compact disc read-only memory [CD-ROM]) set in the drive unit  18  and the computing unit  100  with each other. 
     The programs for implementing processing to be performed by the computing unit  100  are provided to the computing unit  100  using the storage medium  19 , such as a CD-ROM. The storage medium  19  stores programs for implementing various processes according to the present embodiment, to be described later. The programs stored in the storage medium  19  are installed in the computing unit  100  via the drive unit  18 . The installed programs are executed by the computing unit  100 . 
     The storage medium  19  storing the programs is not limited to the CD-ROM but may be one or more computer-readable non-transitory, tangible media with a structure. The computer-readable storage media may include portable recording media, such as a digital versatile disk (DVD) and a universal serial bus (USB) memory, and a semiconductor memory, such as a flash memory. 
       FIG. 13  is a diagram illustrating an example of the functional configuration of the computing unit  100 . In  FIG. 13 , the computing unit  100  mainly includes a learning unit  200  and a CL-excess-probability-line creating unit  300  for processing. The learning unit  200  and the CL-excess-probability-line creating unit  300  are implemented by the programs installed in the computing unit  100  causing the CPU  11  of the computing unit  100  to execute. In  FIG. 13 , the solid lines indicate the relationship between the processing units, and the broken lines indicate the relationship between the processing units and data. 
     The storage unit  130  stores precipitation data  132 , soil water indices  133 , RBFN output values  134 , geometry parameter  135 , excess data  136 , settings  137 , model coefficient data  138 , and so on. 
     The learning unit  200  is a processing unit for creating a model for computing CL excess probability. The learning unit  200  includes a soil-water-index computing unit  210 , an RBFN-output-value computing unit  220 , an excess-data extraction unit  230 , a geometry-parameter computing unit  240 , and a model creating unit  250 . 
     The soil-water-index computing unit  210  is a processing unit for computing the soil water indices  133  for all past rainfalls with reference to all or part of the precipitation data  132 . The computed soil water indices  133  are stored in the storage unit  130 . 
     The RBFN-output-value computing unit  220  is a processing unit for computing the RBFN output values  134  with reference to all or part of the past precipitation data  132 . Accumulated rainfall is calculated for each target past precipitation data  132 . The RBFN output value  134  is computed from the soil water index and the accumulated rainfall in each precipitation data  132  and is stored in the storage unit  130 . In the storage unit  130 , the soil water index and the accumulated rainfall are associated with each RBFN output value  134 . 
     The excess-data extraction unit  230  is a processing unit for extracting an RBFN output value  134  that exceeds the CL after a unit time from a non-excess state. An RBFN output value  134  that exceeds the CL after the next unit time is extracted as the excess data  136  from the RBFN output values  134  computed by the RBFN-output-value computing unit  220  using a CL threshold for the RBFN output values, which is indicated by the settings  137 , and is stored in the storage unit  130 . 
     The geometry-parameter computing unit  240  is a processing unit for computing four kinds of value on the geometry of the precipitation zone using a threshold for extracting the geometry, which is a threshold for the precipitation data  132 , which is indicated by the settings  137 . The geometry parameter  135  indicating the calculated four kinds of value is stored in the storage unit  130 . The four kinds of value are
         The ratio of the long side to the short side   Area   The long side of the circumscribed rectangle   The short side of the circumscribed rectangle.       

     The model creating unit  250  is a processing unit for determining the coefficients of the approximate curve model (Eq. 1) and includes a division-interval determination unit  260  and an approximate-curved-surface computing unit  270 . 
     The division-interval determination unit  260  is a processing unit for determining the number of divisions of the geometry parameter  135  and the number of divisions of the RBFN output values  134 . The number of divisions may be determined using Sturges&#39; rule but is not limited to the Sturges&#39; rule. Sturges&#39; rule:
 
 k =log 2    N+ 1  [Eq. 2]
 
     When Eq. 2 is used, the number of divisions, k, may be obtained by setting the number of pieces of the excess data  136  to n. The interval (division interval) of division by the number of divisions, k, is obtained by dividing the values from a minimum value to a maximum value by the number of divisions, k, for both of the geometry parameter  135  and the RBFN output value  134 . For the geometry parameter  135 , the number of divisions, k, is obtained for each of the four kinds of value. 
     The geometry parameter  135  and the RBFN output value  134  may be divided using the number of divisions, k, set in the settings  137  in advance. The number of divisions, k, Sturges&#39; rule, or another rule may be set in the settings  137  so that the division-interval determination unit  260  may obtain the division interval using the number of divisions determined for processing corresponding to the settings  137 . 
     The approximate-curved-surface computing unit  270  is a processing unit for computing an approximate curved surface representing the CL excess probability. First, the approximate-curved-surface computing unit  270  computes a CL excess probability for each of grids formed by the number of divisions, k, in multiple dimensions formed from the geometry parameter  135  (four dimensions), the RBFN output values  134 , and the CL excess probability. The CL excess probability at each grid may be obtained by 
     
       
         
           
             
               
                 
                   
                     Number 
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                     of 
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                     CL 
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                     excess 
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                     data 
                   
                   
                     Number 
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                     of 
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                     total 
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                     precipitation 
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                     data 
                   
                 
               
               
                 
                   [ 
                   
                     Eq 
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                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     The approximate-curved-surface computing unit  270  computes the approximate curved surface using the CL excess probability at each grid. The settings  137  include the approximate curve model (Eq. 1). The approximate-curved-surface computing unit  270  determines coefficients a, b, and c with which the approximate curve model (Eq. 1) most approximates the CL excess probability at each grid. The model coefficient data  138  indicating the obtained coefficients a, b, and c is stored in the storage unit  130 . 
     The settings  137  include:
         A threshold for extracting the geometry   A threshold for CL   The number of divisions (a numerical value or an equation)   Approximate curve model (an equation)   Display interval of probability line (for example, 25% intervals).       

     In the above learning processing, the learning unit  200  obtains the precipitation data  132  in advance at the first learning. At the second learning from then on, computations of the soil water index  133 , the RBFN output value  134 , and the geometry parameter  135  may be performed only for the uncomputed portion of the precipitation data  132 . 
     The CL-excess-probability-line creating unit  300  is a processing unit for creating a CL excess probability line corresponding to the latest rainfall situation using the approximate curve model (Eq. 1) created by the learning unit  200  and includes a data receiving unit  310 , a soil-water-index computing unit  210 , an RBFN-output-value computing unit  220 , a geometry-parameter computing unit  240 , and an update unit  350  for processing. The processing units in the CL-excess-probability-line creating unit  300  similar to the processing units in the learning unit  200  are given the same reference numbers, and detailed descriptions will be omitted. 
     The data receiving unit  310  is a processing unit for receiving precipitation data  132   w  from a weather-data distribution source  400  in events at predetermined intervals and accumulates the precipitation data  132   w  in the storage unit  130 . The decision diagram  2   g  using the soil water indices and the RBFN output values obtained by using the precipitation data  132   w  is created by the soil-water-index computing unit  210  and the RBFN-output-value computing unit  220  and is displayed on a user screen G 95  of the display device  15 . 
     The update unit  350  is a processing unit for updating the CL excess probability line displayed on the decision diagram  2   g  and includes an excess-probability computing unit  360  and a display unit  370 . The excess-probability computing unit  360  is a processing unit for computing a cross-sectional expression using the geometry parameter  135  of the precipitation zone based on the precipitation data  132   w  in the approximate curve model (Eq. 2) obtained from the settings  137  and the model coefficient data  138  by the geometry-parameter computing unit  240 . 
     The display unit  370  is a processing unit for computing CL excess probability lines based on the probability-line display intervals specified by the settings  137  using the cross-sectional expression computed by the excess-probability computing unit  360 . The computed CL excess probability lines are displayed on the decision diagram  2   g  on the user screen G 95  to update the decision diagram  2   g . In one example, CL excess probability lines of 25%, 50%, and 75% are displayed on the decision diagram  2   g.    
     In the present embodiment, the CL excess probability lines are updated based on the latest precipitation data  132   w . This allows the user to determine whether the rainfall exceeds the CL  3  according to changes in rainfall situation. The learning processing performed by the learning unit  200  will be described with reference to  FIGS. 14 to 16 , and the CL-excess-probability-line creation processing performed by the CL-excess-probability-line creating unit  300  will be described with reference to  FIGS. 17 and 18 . 
       FIG. 14  is a flowchart for illustrating the learning processing performed by the learning unit  200 . Referring to  FIG. 14 , in the learning unit  200 , first, the soil-water-index computing unit  210  computes the soil water indices using all or part of the past precipitation data  132  (step S 211 ), and the RBFN-output-value computing unit  220  computes the RBFN output values using all or part of the past precipitation data  132  and soil water indices  133  (step S 212 ). 
     The excess-data extraction unit  230  inputs a threshold of the RBFN values (step S 213 ). The threshold is an RBFN output value for the CL  3 . When the threshold of the RBFN is input, the excess-data extraction unit  230  extracts data in which the RBFN output value does not exceed the CL  3  and exceeds the CL  3  at the next time as the excess data  136  (step S 214 ). 
     Next, the geometry-parameter computing unit  240  performs geometry parameter computation processing for specifying a precipitation zone whose rainfall is equal to or higher than the geometry extraction threshold of the settings  137  from the precipitation data  132  and computing the geometry parameter  135  from the geometry of the specified precipitation zone (step S 215 ). The computed geometry parameter  135  is stored in the storage unit  130 . 
     The model creating unit  250  performs model creation processing (step S 216 ), and the learning processing ends. 
       FIG. 15  is a flowchart for illustrating the geometry-parameter computation processing performed by the geometry-parameter computing unit. In  FIG. 15 , the geometry-parameter computing unit  240  creates geographical rainfall distribution using the rainfall in the precipitation data  132  at each time (step S 231 ). 
     The geometry-parameter computing unit  240  extracts areas in which rainfall is equal to or higher than the threshold for extracting the geometry from the created rainfall distribution (step S 232 ) and allocates a circumscribed rectangle with a minimum area to the extracted areas (step S 233 ). 
     The geometry-parameter computing unit  240  stores the extracted areas, the short side and the long side of the circumscribed rectangle, and the aspect ratio as the geometry parameter  135  in the storage unit  130  (step S 135 ) and terminates the geometry-parameter computation processing. The storage unit  130  stores the geometry parameter  135  on each time. 
       FIG. 16  is a flowchart for illustrating the model creation processing performed by the model creating unit  250 . In  FIG. 16 , the division-interval determination unit  260  of the model creating unit  250  determines the number of divisions of the geometry parameter  135  based on the number of excess data (step S 251 ). The division-interval determination unit  260  determines the number of divisions of the RBFN output values based on the number of excess data (step S 252 ). 
     The division-interval determination unit  260  then determines an interval value for each parameter (step S 253 ). The four kinds of value of the geometry parameter  135  and the RBFN output values correspond to the parameters. The interval value is set for each of the four kinds of value of the geometry parameter  135 . The interval value is obtained by dividing the values at the individual times from the minimum value to the maximum value by the number of divisions. 
     Next, the approximate-curved-surface computing unit  270  finds CL excess probability=the number of excess data/the number of total data for each of the grids partitioned by the interval value (step S 254 ). The CL excess probability is computed in a six-dimensional space defined by the four kinds of value of the geometry parameter, the RBFN output values, and the CL excess probability. Therefore, if the geometry of the precipitation zone differs, different CL excess probability is obtained even if the RBFN is the same. 
     The approximate-curved-surface computing unit  270  creates an approximate curve (an approximate curved surface) model (Eq. 1) for representing the CL excess probability at each grid (step S 255 ). Thus, the coefficients a, b, c of the approximate curve model (Eq. 1) is obtained. The obtained coefficients a, b, c are stored in the storage unit  130  as the model coefficient data  138 . Thereafter, the model creating unit  250  ends the model creation processing. 
       FIG. 17  is a flowchart for illustrating the entire CL-excess-probability-line creation processing performed by the CL-excess-probability-line creating unit  300 . In  FIG. 17 , the data receiving unit  310  of the CL-excess-probability-line creating unit  300  obtains current precipitation data  132  (step S 310 ). The data receiving unit  310  obtains the current precipitation data  132  from the weather-data distribution source  400 . 
     The soil-water-index computing unit  210  computes soil water indices using all or part of the past precipitation data  132  (step S 311 ). The RBFN-output-value computing unit  220  computes RBFN output values using all or part of the past precipitation data  132  and the past soil water indices  133  (step S 312 ). The display unit  370  plots the current accumulated rainfall and the current soil water index on the decision diagram  2   g  (step S 313 ). 
     The geometry-parameter computing unit  240  performs the geometry-parameter computation processing (step S 314 ). The update unit  350  performs the update processing (step S 315 ). The update unit  350  repeats the processing from step S 310  to S 315  at every update interval of the decision diagram  2   g . Since the geometry-parameter computation processing performed by the geometry-parameter computing unit  240  is illustrated in  FIG. 15 , a detailed description thereof will be omitted. 
       FIG. 18  is a flowchart for illustrating the update processing performed by the update unit  350 . In  FIG. 18 , the excess-probability computing unit  360  of the update unit  350  obtains a cross-sectional expression  3   p  of the approximate curved surface using the computed values of the geometry parameter  134  (step S 331 ). 
     The excess-probability computing unit  360  obtains the approximate curve model (Eq. 1) from the settings  137 , sets the values of the coefficients a, b, c obtained from the model coefficient data  138  in the approximate curve model, and specifies an approximate curve model to be used. 
     The excess-probability computing unit  360  obtains the cross-sectional expression  3   p  of the approximate curved surface by applying the geometry parameter  135  obtained by the geometry-parameter computing unit  240  at step S 314  in  FIG. 17  to the variable y of the specified approximate curve model. 
     The display unit  370  updates the CL excess probability line using the cross-sectional expression  3   p  of the approximate curved surface (step S 335 ). The display unit  370  obtains an RBFN output value corresponding to the value of the display interval of the probability line designated by the settings  137  from the cross-sectional equation  3   p  of the approximate curved surface. The display unit  370  computes the CL excess probability lines at the display intervals of the probability line based on the data on the accumulated rainfall and the soil water index corresponding to the obtained RBFN output value. Examples of the CL excess probability lines are lines of CL excess probability of 25%, 50%, and 75%. The display unit  370  displays the obtained CL excess probability lines on the decision diagram  2   g  displayed. Thus, the display of the CL excess probability lines is updated, and the update processing ends. 
       FIGS. 19A and 19B  illustrate examples of the CL excess probability depending on whether a precipitation zone is taken into consideration.  FIGS. 19A and 19B  respectively illustrate the results of computing the probability of exceeding the CL at the RBFN of 0.8 in the case where the long side of the precipitation zone is taken out of and into consideration using the probability distribution of actual data. 
       FIG. 19A  illustrates CL excess probability in a known technique in which the precipitation zone is not considered. In  FIG. 19A , the long side is plotted on the z-axis, but the geometry of the precipitation zone is not taken into consideration. Therefore, there is no change in CL excess probability due to a difference in the length of the long side. For example, if the RBFN output value is the same, the same CL excess probability is obtained. 
     In contrast,  FIG. 19B  illustrates CL excess probability in the present embodiment obtained in consideration of the precipitation zone. The CL excess probability depends on the length of the long side of the precipitation zone, so that different CL excess probabilities are obtained even if the RBFN output value is the same. 
     In the case where the long side is less than 100 km and the RBFN is equal to or greater than 0.8 and less than 0.85, two of 22 points exceed the CL at the next time in the actual data. Therefore, the CL excess probability is 2/22=0.10. Referring to  FIG. 19A , the CL excess probability is 0.20, which is an overestimate. In contrast, in  FIG. 19B , the CL excess probability is 0.09, which is substantially equal to the actual data. 
     If the long side is equal to or longer than 200 km and less than 400 km, and the RBFN is equal to or greater than 0.8 and less than 0.85, seven of 16 points exceed the CL at the next time, and the CL excess probability is 7/16=0.44. Referring to  FIG. 19A , the CL excess probability is 0.20, which is an underestimate. In contrast, in  FIG. 19B , the CL excess probability is 0.44, which is equal to the CL excess probability in actual data. 
     In  FIG. 19A  in which the geometry of the precipitation zone is not considered, there is no difference in CL excess probability depending on the length of the long side, the CL excess probability is uniformly 0.20. Thus, the use of the present embodiment increases the accuracy of CL excess probability. 
     Next, an example in which the indication of the CL excess probability line for the same target point changes depending on whether the present embodiment is applied.  FIGS. 20A to 20C  are diagrams illustrating comparative examples of the CL excess probability line in different precipitation zones. 
       FIG. 20A  illustrates two precipitation zones  10   e  and  10   f  having different geometries formed over the same target point  9   p .  FIGS. 20B and 20C  respectively illustrate examples of the decision diagram  2   g  indicating the probability that the rainfalls in the precipitation zones  10   e  and  10   f  exceed the CL.  FIGS. 20B and 20C  illustrate CL excess probability lines  3   c - 1 ,  3   c - 2 , and  3   c - 3  of 25%, 50%, and 75% by way of example, but this is given for mere illustrative purposes. 
       FIG. 20B  illustrates an example of CL excess probability lines in the case where the present embodiment is not applied. A decision diagram  2   g - 1  corresponds to a display example in the case of the precipitation zone  10   e . A decision diagram  2   g - 2  corresponds to a display example in the case of the precipitation zone  10   f . There is no difference in the display interval of the CL excess probability lines  3   c - 1 ,  3   c - 2 , and  3   c - 3  between the decision diagram  2   g - 1  and the decision diagram  2   g - 2 . The CL excess probability lines  3   c - 1 ,  3   c - 2 , and  3   c - 3  are displayed at the same intervals regardless of the geometry of the precipitation zone. 
     In contrast,  FIG. 20C  illustrates a display example of CL excess probability lines in the case where the present embodiment is applied. A decision diagram  2   g - 3  corresponds to a display example in the case of the precipitation zone  10   e . A decision diagram  2   g - 4  corresponds to a display example in the case of the precipitation zone  10   f . The display interval of the CL excess probability lines  3   c - 1 ,  3   c - 2 , and  3   c - 3  differs between the decision diagram  2   g - 1  and the decision diagram  2   g - 2 . The CL excess probability lines  3   c - 1 ,  3   c - 2 , and  3   c - 3  are displayed at different intervals between the precipitation zone  10   e  and the precipitation zone  10   f  according to the geometry of the precipitation zone. 
     Thus, the present embodiment allows appropriate evaluation of CL excess probability by considering the geometry of the precipitation zone. In the present embodiment, the index used is the probability of exceeding the critical line (CL) (critical-line excess probability). This is given for mere illustrative purposes. Any similar information may be used as the index. The approximate curve model described above is an example of a computation model. The learning unit  200  is an example of a creating unit. The CL-excess-probability-line creating unit  300  is an example of a computing unit or a computation display unit. The computing unit  100  is an example of a display device. 
     It is to be understood that the present disclosure is not limited to the disclosed embodiments and that various modifications and changes may be made without departing from the scope of the claims. 
     All examples and conditional language provided herein are intended for the pedagogical purposes of aiding the reader in understanding the invention and the concepts contributed by the inventor to further the art, and are not to be construed as limitations to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although one or more embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.