JP2003196670A - Erosion landform model generation device, erosion landform model generation method and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a device and a method capable of generating an erosion landform model more accurately in a shorter time compared with a conventional method. <P>SOLUTION: The erosion landform of a natural landform formed by erosion by flowing water is reproduced. For example, an initial digitized landform model h (x, y, 0) is generated based on data of the natural landform corresponding to a real region R or on an artificial model generated based on random numbers or the like, and an erosion function parameter is calculated based on the generated model. An erosion landform model h (x, y, t) is generated based on the calculated parameter, to thereby enable to execute, accurately in a shorter time, transition prediction of the erosion landform based on a characteristic held by the natural landform corresponding to the real landform. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to an erosion landform model generation device, an erosion landform model generation method, and a computer program. More specifically, the present invention relates to an erosion terrain model generation apparatus, an erosion terrain model generation method, and a computer program that reproduce changes in given given terrain due to erosion.

[0002]

2. Description of the Related Art As a conventionally known method for numerically creating a terrain model similar to natural terrain using a computer or the like, there is a method using a Fractional Brownian Surface. This method is based on a stochastic process that is irrelevant to the formation process of natural terrain, and it is possible to create a terrain model that looks like natural terrain. But,
This method cannot create topography such as canyons and rivers that are included in the natural topography. Topography such as canyons and rivers is mainly formed by the erosion of surface water currents. Therefore, it is necessary to incorporate the effects of erosion and river network formation processes in order to create a terrain model with characteristics closer to natural terrain.

[0003] The following are the main prior arts of a method for creating a topographic model that incorporates the effects of the erosion effect due to surface water flow and the river network formation process. (1) Differentiation of differential equations related to erosion and numerical solution. (2) A terrain erosion process or a river network formation process is simulated by a very simple decisive or probabilistic terrain formation rule.

[0004]

However, the above-described conventional erosion landform model creating method has the following problems. That is, in the case of the method of differentially calculating the differential equation regarding the erosion action described above in (1) and solving it numerically, the differential equation describing the erosion action is complicated, and it is necessary to create a large-scale erosion landform model from the relation of calculation time and the like. It is difficult to carry out with accuracy.

On the other hand, in the case of the method of simulating the terrain erosion process and the river network formation process by the very simple decisive or probabilistic terrain formation rule of the above (2), the terrain formation rule is usually very simple. It is suitable for modeling large-scale terrain, but its physical validity is unknown, and a general method for determining terrain formation rules that accurately approximates actual terrain erosion. Since it has not been developed, there is a problem that the accuracy of the created erosion topography model remains questionable.

Further, various parameters are involved in the formation process of erosion topography, and in order to obtain an accurate erosion topography model, these parameters must be estimated in advance by a method such as geological survey. This requires a lot of labor and time.

The present invention has been made to solve these problems, and to create an erosion landform model having a practically sufficient scale and accuracy from a given arbitrary initial landform in a relatively short time. With the goal.

[0008]

The first aspect of the present invention is as follows.
A erosion topography model generation device that generates an erosion topography model in a region having a topography shape, divides a region R to be an erosion topography model generation target into a plurality of blocks, and sets coordinate values corresponding to each block to grid point positions (x , Y), the initial digitized terrain model corresponding to the grid point is h (x, y;
0) initial digitized terrain model generation processing,
At the time t of the region R, a process based on the terrain erosion rule as an erosion action consisting of one or more processes is executed on the initial numerical terrain model, and the process based on the terrain erosion rule is repeatedly executed. An erosion terrain model generation apparatus having a calculation processing unit that executes a terrain erosion action simulation process for generating a digitized terrain model h (x, y; t).

Furthermore, in one embodiment of the erosion terrain model generation apparatus of the present invention, the process based on the terrain erosion rule assumes uniform precipitation in the region R as process 1, and assumes that each grid point at time t. Water volume s (x, y;
The process of adding a constant s ₁ to t), and as process 2, the running water at time t with the grid point (x, y) as the start point and the lowest point (x ′, y ′) in the adjacent grid points as the end point. Process for determining direction vector d (x, y; t) and process 3
Of moving the water quantity s (x, y; t) of the grid point (x, y) to the grid point indicated by the vector d (x, y; t), and the water quantity in the process 3 as the process 4. Formation process based on the movement of the
For a grid point that is a pond, remove the pond based on a certain condition, and as process 6, a grid point that is not a pond (x,
y) The process of determining the erosion amount E is included, and the arithmetic processing unit executes the processes 1 to 6 sequentially.

Further, in one embodiment of the erosion landform model generating apparatus of the present invention, the arithmetic unit executes processing for setting drainage conditions and water stopping conditions as boundary conditions for the region R, and It is characterized in that the process based on the terrain erosion rule is executed on the set region R.

Furthermore, in one embodiment of the erosion landform model generation device of the present invention, the erosion landform model generation device quantifies an erosion action by an initial numerical terrain model creation program for creating a numerical terrain model of the initial terrain. A boundary condition setting program that sets the boundary conditions when applying it to the terrain model, a storage device that stores the terrain erosion simulation program that creates the erosion terrain model by applying the terrain erosion rule that simulates the erosion effect on the digitized terrain model Have,
The arithmetic unit is configured to execute each program stored in the storage unit to generate a digitized terrain model of the region R.

Furthermore, in one embodiment of the erosion landform model generating apparatus of the present invention, the arithmetic unit is a constant, and the elevation value of the grid point (x, y) at time t is h (x, y;
t), the elevation value of the water surface at time t of the lowest grid point (x ', y') adjacent to the grid point (x, y) is h
_w (x ′, y ′; t), δh is the head difference δh = h (x, y; t) −h _w (x ′, y ′;
t), a, b are constants, and the amount of water at each grid point at time t is s (x, y; t), J = δh ^a-1 × [s (x, y;
t)] ^b , the erosion amount E of the grid point (x, y) at time t is calculated as E = C × δh × (J / (1 + J)), and the elevation value of the grid point (x, y) is calculated. To h (x, y; t
+1) = h (x, y; t) -E.

Further, in one embodiment of the erosion terrain model generation apparatus of the present invention, the process based on the terrain erosion rule is performed by calculating the water amount s (x, y; t) of each grid point due to uniform precipitation on the region R. A parameter s ₁ indicating the increase amount,
The configuration includes a parameter C as a coefficient value of a calculation formula of the erosion amount E of the grid point (x, y), and the parameter s ₁ and the parameter C are set based on the actual data of the real region R. It is characterized by

Further, in one embodiment of the erosion landform model generating apparatus of the present invention, the above formula: J = δh ^a-1 × [s
The parameter a in (x, y; t)] ^b is a grid point having a certain basin area taken out from the region R, and its altitude h (x, y) and head δh (x, y) = h _w. (X,
y) −h _w (x ′, y ′) is taken as a logarithmic log plot, and the plotted points are calculated by evaluating the power function that most closely approximates them.

Further, in one embodiment of the erosion landform model generating apparatus of the present invention, the above formula: J = δh ^a-1 × [s
(X, y; t)] parameter b in ^b, h / ^{δh a}
And s ₀ are taken in a logarithmic plot, and the plotted points are calculated by evaluating the power function that most closely approximates them.

Further, a second aspect of the present invention is an erosion landform model generation method for generating an erosion landform model in an area having a terrain shape, in which an area R to be an erosion landform model generation target is divided into a plurality of blocks. , An initial digitized terrain model generation step of generating coordinate values corresponding to respective blocks as grid point positions (x, y) and an initial digitized terrain model corresponding to the grid points as h (x, y; 0), By performing a process based on a terrain erosion rule as an erosion action consisting of one or more processes on the initial numerical terrain model generated in the step, and repeating the process based on the terrain erosion rule. Digitized terrain model h (x, y; t) at time t in region R
Terrain erosion simulation processing step for generating
The method for generating an erosion landform model is characterized by executing

Furthermore, in one embodiment of the erosion terrain model generation method of the present invention, the process based on the erosion erosion rule assumes uniform precipitation in the region R as process 1, and assumes that each grid point at time t. Water volume s (x, y;
The process of adding a constant s ₁ to t), and as process 2, the running water at time t with the grid point (x, y) as the start point and the lowest point (x ′, y ′) in the adjacent grid points as the end point. Process for determining direction vector d (x, y; t) and process 3
Of moving the water quantity s (x, y; t) of the grid point (x, y) to the grid point indicated by the vector d (x, y; t), and the water quantity in the process 3 as the process 4. Formation process based on the movement of the
For a grid point that is a pond, remove the pond based on a certain condition, and as process 6, a grid point that is not a pond (x,
y) deciding the erosion amount E, and the terrain erosion effect simulation processing step includes the steps 1 to 6
Is performed sequentially.

Further, in one embodiment of the erosion landform model generation method of the present invention, the erosion landform model generation method further executes processing for setting drainage conditions and water stoppage conditions as boundary conditions for the region R. The terrain erosion effect simulation processing step includes a step of performing a process based on the terrain erosion rule on the region R in which the boundary condition is set.

Further, in one embodiment of the erosion terrain model generation method of the present invention, in the terrain erosion action simulation processing step, C is a constant, and a time t of a grid point (x, y).
Altitude value at h (x, y; t), grid point (x, y)
To the lowest grid point (x ', y') adjacent to the water surface at time t is h _w (x ', y'; t), and δh is the head difference δh = h (x at time t , Y; t)-
h _w (x ′, y ′; t), a and b are constants, and the amount of water at each grid point at time t is s (x, y; t), J = δh
^{When a-1} x [s (x, y; t)] ^b , the grid point (x,
y), the erosion amount E at time t is E = C × δh × (J /
(1 + J)), and the elevation value of the grid point (x, y) is calculated as h (x, y; t + 1) = h (x, y; t) -E. To do.

Further, in one embodiment of the erosion terrain model generation method of the present invention, the process based on the terrain erosion rule is performed by calculating the water amount s (x, y; t) of each grid point due to uniform precipitation on the region R. A parameter s ₁ indicating the increase amount,
A parameter C as a coefficient value of a calculation formula of the erosion amount E of the grid point (x, y), and the terrain erosion effect simulation processing step includes the parameter s ₁ and the parameter C.
It is characterized by including a step of setting and based on the actual data of the real area R.

Furthermore, in one embodiment of the method for generating an erosion landform model of the present invention, the above formula: J = δh ^a-1 × [s
The parameter a in (x, y; t)] ^b is a grid point having a certain basin area taken out from the region R, and its altitude h (x, y) and head δh (x, y) = h _w. (X,
y) -h _w (x ', y') is taken as a logarithmic log plot, and the plotted points are calculated by evaluating a power function that most closely approximates them.

Furthermore, in one embodiment of the method for generating an erosion landform model of the present invention, the above formula: J = δh ^a-1 × [s
(X, y; t)] parameter b in ^b, h / ^{δh a}
It is characterized in that a logarithmic plot of s ₀ and s ₀ is taken, and the plotted points are calculated by evaluating the power function that most closely approximates the power.

Further, a third aspect of the present invention is a computer program for executing an erosion landform model generation process for generating an erosion landform model in an area having a terrain shape, and an area R to be an erosion landform model generation target. Is divided into a plurality of blocks, the coordinate value corresponding to each block is defined as a grid point position (x, y), and the initial digitized terrain model corresponding to the grid point is generated as h (x, y; 0). A step based on a terrain erosion rule as an erosion action consisting of one or more processes is executed for the digitized terrain model generation step and the initial digitized terrain model generated in the step, and the terrain erosion rule based process is executed. The terrain erosion simulator for generating the digitized terrain model h (x, y; t) at the time t in the region R by repeatedly executing In computer program characterized by comprising a preparative process step.

In the present invention, an erosion terrain model is created by subjecting a given initial terrain to an erosion action defined by a simple rule and simulating a time change due to the erosion action of the terrain.

Although the terrain erosion rule used in the present invention is simple, it is derived by approximating a differential equation that describes the erosion action of natural terrain, and is physically valid. The erosion function included in the terrain erosion rule contains two main parameters, and these values create an erosion terrain model with various topographical features. Estimate the parameters of. These simple terrain erosion rules obtained from differential equations that describe erosion and the estimation of erosion functions by analyzing natural terrain data enabled the creation of large-scale and accurate erosion terrain models in a short time. .

The computer program of the present invention is, for example, a storage medium or communication medium provided in a computer-readable format for a general-purpose computer system capable of executing various program codes, such as a CD or FD. , MO, etc., or a computer program that can be provided by a communication medium such as a network. By providing such a program in a computer-readable format, processing according to the program is realized on the computer system.

Further objects, features and advantages of the present invention are as follows.
It will be clarified by a more detailed description based on embodiments of the present invention described below and the accompanying drawings. In this specification, the system is a logical set configuration of a plurality of devices, and is not limited to a device in which each configuration is provided in the same housing.

[0028]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below. First, a method of creating an erosion landform model according to the present invention will be described.

As shown in FIG. 1, the area where the topography is reproduced is R
far. Region R may be a real region or a fictitious region created on a computer. The region R is divided into square blocks, and the position of each block is represented by a set of two integers, that is, coordinates (x, y). This quantization is introduced for the sake of simplification of explanation, and it is not always necessary to use square blocks, and for example, other quantization configurations such as block division by equilateral triangles are applied. You may.

The digitized terrain model is a function that takes an elevation value on an integer grid point (x, y) in a two-dimensional space, and is realized by a two-dimensional array on a computer. In the present invention, since the digitized terrain model is developed over time according to the terrain erosion rule, the digitized terrain model at time t is represented by h (x, y;
t).

Especially, the digitized terrain model before the time evolution according to the terrain erosion rule, that is, the initial digitized terrain model is used as the initial digitized terrain model h (x, y; 0), and the time evolution is performed as necessary. The thing is called an erosion topography model. In the following description, the time t takes an integer value and represents the number of times the terrain erosion rule is applied to the given initial digitized terrain model. That is, the digitized terrain model to which the terrain erosion rule has been applied t times is denoted as h (x, y; t). However, the time t may be set so as to represent the physical elapsed time when the terrain erosion has been performed, if necessary.

At each grid point (x, y) in the region R, the elevation value h
In addition to (x, y; t), water volume s (x, y; t), water depth w
Give (x, y; t). A grid point where the water depth w (x, y; t) is not 0 is called a pond. Water surface elevation h _w at each grid point
(X, y; t) is h _w (x, y; t) = h (x, y;
t) + w (x, y; t).

The water flow direction vector d on each grid point is determined by the relationship between the elevation of the water surface of each grid point and the surrounding grid points.
(X, y; t) is determined. These quantities are also h (x,
Similar to y; t), it is realized by a two-dimensional array or the like.

The time evolution due to the erosion of the digitized terrain model represented by the altitude value h (x, y; t) is performed by repeating a series of procedures 1 to 6 described below.

(Process 1) Uniform precipitation A constant s ₁ is added to the water amount s (x, y; t) at each grid point.

(Process 2) Determination of Flowing Direction Vector For each grid point (x, y), the elevation of the water surface of the nearest grid point is examined and the lowest one is selected. This is (x ',
y '). The flowing water direction vector d (x, y; t) at the grid point (x, y) is a vector having the point (x, y) as the starting point and the point (x ', y') as the ending point. Figure 2
The example shown in (a) is an example of setting a flowing water direction vector based on a grid point to which a square block is applied, and the example shown in FIG. 2 (b) is an example of setting a flowing water direction vector based on a grid point to which a triangular block is applied. is there.

(Process 3) The water quantity s (x, y; t) at the flowing water grid point (x, y) is converted into a vector d.
Move to the lattice point pointed to by (x, y; t). New (x,
The amount of water s (x, y; t + 1) in y) is given by the total amount of water moved from the surrounding grid points to (x, y).

(Process 4) h _w (x, y;
When t) ≦ h _w (x ′, y ′; t), it is unnatural that the water at the grid point (x, y) flows to (x ′, y ′). Therefore, in such a case, a pond is formed as follows: w (x, y; t) = _hw (x ', y'; t) -h (x, y; t) + ε (Equation 1) .

Here, ε is a small constant, and it is desirable to set it to about 1% of the difference between the maximum value and the minimum value of the altitude of the initial digitized terrain model. Water volume s at the grid point where the pond is newly formed
(X, y; t) does not move.

(Process 5) Removal of pond For a grid point that is a pond, h (x, y; t)> h
_{If w} (x ', y'; t), then the pond is removed with w (x, y; t) = 0.

(Process 6) The erosion amount E of the grid point (x, y) which is not the erosion pond due to running water is determined by the following equation. E = C × δh × (J / (1 + J)) (Equation 2)

Here, C is a constant and δh is a head δh = h.
(X, y; t) -h _w (x ', y'; t), and J
Is J = δha ^-1 × [s (x, y; t)] ^b (Equation 3).

The erosion amount E is subtracted from the altitude value of the grid point (x, y) to obtain a new altitude value. h (x, y; t + 1) = h (x, y; t) -E (Equation 4)

However, when the lattice point is a pond, it is assumed that there is no erosion effect and h (x, y; t + 1) = h (x, y; t).

A process for sequentially and collectively executing the series of processes (1) to (6) described above is called a terrain erosion rule. Given initial digitized terrain model, ie
Initial digitized terrain model h (x, y; 0) at t = 0
By repeatedly applying the terrain erosion rule to the arbitrary number of times (t times), an erosion terrain model of an arbitrary phase can be obtained.

[0046] When the procedure terrain erosion rules (Process 6) erosion amount E is J is ^{small, E = C × δh a ×} s b ...... ( Equation 5), and the differential unquantized (Formula 4) writing in the equation becomes (∂h / ∂t) = -C × δh a × s b ...... ( equation 6).

On the other hand, in the simplest case, the erosion effect by the surface water flow is the unquantized continuous coordinates (x,
y), time t, and the two-dimensional elevation value function h (x, y; t), (∂h / ∂t) = -constant × ∇ · (vector F) ... (Equation 7) it is conceivable that.

Here, (vector F) is the field of the flow of the deposit caused by the erosion action. In addition, the amount E of deposits generated by erosion at each point is based on the gradient magnitude | ∇h | at each point and the water flow rate s, and a power relation E = | ∇h | ^a × s ^b …… (equation 8) It is considered to be determined by

When the rate of erosion is sufficiently slow and the amount of sediment produced does not exceed the sediment transport capacity of surface flow, ∇ · (vector F) on the right side of (Equation 7) is a point (x, y). It is determined by the amount E of the deposit generated at (∂h / ∂t) = − constant × | ∇h | ^a × s ^b (Equation 9).

This has the same shape as (Equation 6). Further, when the terrain is represented by a quantized quantized terrain model, it can be considered that the flow of the surface flow is directed to the lowest one of the closest grid points. Thus, the terrain erosion rules used in the present invention are based on the knowledge about the erosion action of natural terrain.

Although it is possible to use (Equation 5) instead of (Equation 2) as the erosion amount E in the procedure of the terrain erosion rule (Process 6), in this case, the erosion amount E according to (Equation 5) is It should be noted that very few grid points in R can take very large values. When the erosion amount E takes a large value, after performing the procedure (process 6), the altitude h (x, y; t + 1) of the starting point (x, y) of the flowing water direction vector d (x, y; t) is the end point. It may be lower than the altitude h _w (x ', y'; t) of the water surface of (x ', y').

This is an unnatural result that cannot occur due to the erosion of natural terrain. As a method of avoiding such a situation, the increment Δt of the time t is set to a real number,

[0053] h (x, y; t + Δt) = H (x, y; t)-[Delta] t * E (Equation 10) There is a way to.

The time increment Δt is h (x, y; t + 1) <h _{w at the} grid point where the maximum erosion amount E is in the area R.
It is set so as not to be (x ', y'; t + 1). However, in the case of this method, the erosion amount E in (Equation 5) may take a very large value even on a very small number of grid points, so the value of Δt must be made extremely small, It takes a very long time to create an erosion topography model.

On the other hand, in the case of the erosion amount E of (Equation 2) used in the procedure (Process 6), the erosion amount E when the value of J is large deviates from the accurate (Equation 8), but the erosion amount is Since the number of grid points that take extremely large values is very small, (Equation 2)
Even if the erosion amount E of is used, there is almost no effect on the morphology of the entire erosion topography model.

Moreover, since the erosion amount E of (Equation 2) does not take a value larger than the constant C, the increment of the time t can be made constant, and the erosion landform model can be created in a relatively short time. Is possible.

When applying the terrain erosion rule to the digitized terrain model, it is necessary to set appropriate boundary conditions in advance each time. This boundary condition is set on the boundary of the region R or on a grid point in the region R as necessary. Typical boundary conditions are as follows.

(Boundary condition 1) Drainage condition At the grid point (x, y) of the boundary, the altitude h (x, y;
t) is fixed at a sufficiently low value, and the amount of water s (x, y;
t) and the water depth w (x, y; t) are always 0. The amount of water s (x, y; t) flowing into this boundary will be removed. When the region R includes a region corresponding to the ocean, it is preferable to use this condition for the region. For example,
The boundary having the drainage condition is the boundary condition line 30 shown in FIG.
It is set as 1.

(Boundary condition 2) At the grid point (x, y) of the water stopping condition boundary, the altitude h (x, y;
t) is fixed at a sufficiently high value, and the water volume s (x, y;
t) and the water depth w (x, y; t) are always 0. The amount of water s (x, y; t) in the region R exceeds this boundary and the region R
Can't flow out. For example, the boundary having the water stop condition is set like the boundary condition line 302 shown in FIG.

In addition to this, it is possible to set appropriate boundary conditions such as periodic boundary conditions according to the purpose of creating the erosion topography model.

By drawing the flow direction vector d (x, y; t) of each grid point (x, y) in the process of creating the erosion landform model, a pattern similar to a natural river network with complicated bifurcation Can be obtained. This is called a river network model attached to the erosion topography model. Figure 4 shows an example of a river network model. Each of the branched lines shown in FIG. 4 corresponds to the flowing direction vector d (x, y; t) of each grid point (x, y), and the flowing direction is formed along the branch. Become.

This river network model is an aggregate of the flow direction vectors d (x, y; t) determined by the terrain erosion rule. Therefore, in the initial stage of creating the erosion topography model, the shape changes every time the topography erosion rule is applied. However, if the terrain erosion rule is repeated a sufficient number of times and erosion terrain is developed on the digitized terrain model, the shape of the river network model hardly changes. This state is called the steady state of the river network model.

The watershed area at the grid point (x, y) is defined as the flow direction vector d (x, y; upstream of the grid point (x, y).
It is defined as the number of grid points connected through t). When the river network model is in a steady state, grid points (x,
The watershed area of y) is the water volume s (x, y; t) at the grid point.
It is necessary to note that it is proportional to.

The terrain erosion rules include parameters s ₁ , C,
a and b are included. Of these, s ₁ and C are amounts relating to the amount of precipitation and the speed of terrain erosion, and must be determined based on surveys of the amount of precipitation in region R. That is, the parameter s ₁ is the amount of water s (x, x at each grid point based on the occurrence of uniform precipitation in the above (Process 1).
It is a constant s ₁ that is set as an increment with respect to y; t). In addition, the parameter C is the grid point (x,
It is a coefficient set in the calculation formula (see Formula 2) of the erosion amount E of y). When these parameters are assumed for an actual area, they can be determined based on a survey of precipitation in the actual area R, etc., so that the actual progress of erosion can be simulated more appropriately.

The parameters a and b are quantities relating to the nature of the erosion action. The larger the value of a, the more stable the slope of the land becomes. The larger the value of b, the narrower the valley is formed. It becomes the setting of the terrain erosion tendency. The correspondence between the setting of the parameters a and b and the specific terrain shape when the terrain erosion rule based on the set parameters is executed is as follows. Setting a small: The topography becomes steeper as it approaches the summit. Larger setting of a: The terrain shape has a constant slope from the summit to the foot. Setting b to a small value: The terrain shape covers the entire valley. Large setting of b: A fine valley is formed, and the valley has a terrain shape that does not cover the entire area.

As described above, the processing for collectively executing the above-mentioned series of processes (1) to (6), that is, the terrain erosion rule, for the region R in which predetermined boundary conditions such as drainage condition and water stop condition are set. It is possible to simulate the change of the topographical shape due to the continuous erosion of the terrain by repeating the above process any number of times.

[Hardware Configuration Example] Next, with reference to the block diagram of FIG. 5, a hardware configuration example of the erosion terrain model generation apparatus used for executing the above-mentioned terrain erosion rule and creating the erosion terrain model. Explain. The erosion landform model generation device shown in FIG. 5 includes a calculation device 101, an input device 102, an output device 103, a control device 104, and a storage device 1.
50, which are connected to each other by a data bus line 171 and an address bus line 172.

As shown in FIG. 5, the storage device 150 stores an initial digitized terrain model creation program section 151 in which a program for creating a digitized terrain model of initial terrain is stored.
A boundary condition setting program unit 152 that stores a program for setting boundary conditions when applying erosion to a numerical terrain model, and creates a erosion terrain model by applying terrain erosion rules that simulate erosion to the numerical terrain model. Program for storing terrain erosion simulation program 153, which stores the numerical terrain erosion simulation program, the numerical terrain erosion model storage unit 154, which stores the numerical terrain model for initial numerical terrain and the erosion terrain created by this device The river network model storage unit 155 that stores the river network model that is created at the same time as the simulation, and the water flow amount that temporarily stores various quantities such as the water flow volume necessary for terrain erosion simulation The control unit 156 includes a control program unit 157 in which a control program such as an OS is stored.

The arithmetic unit 101 comprises a CPU as a processor means, a RAM, a ROM etc. as a memory means, and executes each program stored in the storage device 150. When executing the program, the storage device 15 is executed.
Each model stored in 0 is applied, and the input device 10
Initial condition setting value input from 2, each parameter s ₁ ,
The terrain erosion rule shown in the above processes 1 to 6 is executed based on the value of C, a, b, or the number of times the terrain erosion rule is repeated or the time (t).

The input device 102 is composed of, for example, an input file, a digitizer, a mouse, a keyboard, a light pen, etc., and an initial digitized terrain model h as an initial condition.
Input (x, y; 0) or set value of boundary condition,
The parameters s ₁ , C, a, b, the number of times the terrain erosion rule is repeated, the time (t), etc. are input.

The output device 103 is, for example, an output file, C
A two-dimensional or three-dimensional shape display of the initial digitized terrain model h (x, y; 0) input from the input device 102, which includes an RT display, a printer, a network relay device, etc., and is stored in the storage device 150 by the arithmetic device 101. A numerical terrain model h (x, x, which is generated by repeating the terrain erosion rule based on the execution of each stored program
y; t) is displayed.

The control unit 104 is composed of a CPU as a processor unit, a RAM and a ROM as a memory unit, and the mutual data of the arithmetic unit 101, the input unit 102, the output unit 103, and the storage unit 150 of the erosion landform model generator. Input / output control, processing sequence control, etc. are executed.

The basic operation of the erosion terrain model generation processing executed using the erosion terrain model generation apparatus shown in FIG. 5 will be described with reference to the flowchart of FIG.

First, in step S101, an initial digitized terrain model is created. For example, when simulating the change of the terrain based on the erosion of the real region R, the data created from the numerical map of the natural terrain may be input. The map is divided into rectangular block areas shown in FIG. 1, and the respective altitude data are input as the initial digitized terrain model h (x, y; 0). Alternatively, in the case of performing a simulation based on an artificial arbitrary terrain, the artificially created terrain data using random numbers may be used.

Next, in step S102, boundary conditions for applying the terrain erosion rule to the digitized terrain model are set. As the boundary condition, the drainage condition, the water stoppage condition, and the like described above are set on the boundary of the region R or the region corresponding to the ocean.

Next, in step S103, the terrain erosion rule is applied to the digitized terrain model for which the boundary conditions are fixed.
This topographical erosion rule adds a constant s ₁ to the series of procedures of the above-described processes 1 to 6, that is, (process 1) uniform precipitation water amount s (x, y; t) at each grid point. (Process 2) Determination of water flow direction vector Let the water flow direction vector d (x, y; t) be a vector having a point (x, y) as a start point and a point (x ', y') as an end point. (Process 3) The water volume s (x, y; t) at the flowing water grid point (x, y) is represented by the vector d.
Move to the lattice point pointed to by (x, y; t). (Process 4) Formation of pond Formation of a pond based on the movement of the amount of water in Process 3. (Process 5) Pond removal For a grid point that is a pond, removal of the pond based on certain conditions. (Process 6) The erosion amount E of the grid point (x, y) which is not an erosion pond due to running water is determined. Execute each process.

Next, in step S104, it is determined whether or not the erosion landform model is completed. This is a step of determining whether or not the terrain erosion rule corresponding to a preset number of times of terrain erosion rule execution or time (t) has been executed, and it seems that the terrain erosion rule has not been applied the required number of times. For example, the process returns to step S103, and the above-described processes 1
Repeat the Terrain Erosion Rule of 6. If the terrain erosion rule is repeated as many times as necessary, step S11
Proceed to 05 to output the erosion topography model h (x, y; t).

In the step S104 for judging whether or not the erosion landform model is completed, for example, the following judgment criteria can be considered.

(1) To specify the time when the terrain erosion rule is applied, for example, estimating the change of the terrain after 10,000 years due to the erosion action. In this case, the parameters s relating to precipitation and erosion rate
₁ and C are evaluated in advance by some method, and the number of years after which the change in the numerical terrain model corresponds to the change in the natural terrain when the terrain erosion rule is applied to the numerical terrain model,
It is necessary to estimate in advance.

(2) When completed when the eroded landform is fully developed. In this case, the steady state of the river network model associated with the erosion topography model can be used for the determination.

At the initial stage of generation of the erosion terrain model, most of the flow direction vectors d (x, y) forming the river network model change every time the terrain erosion rule is applied. However, as mentioned above, as the number of times the erosion erosion rules are applied increases, the number of water flow direction vectors that cause changes decreases, and in terrain with sufficient terrain erosion rules, the ratio of the water flow direction vectors that cause changes is extremely high. Becomes smaller.

Therefore, a plurality of river network models before and after applying the terrain erosion rule are stored in the river network model storage unit 155 of the erosion terrain model generation apparatus shown in FIG. 5, and the running water changed by comparing them. It is also possible to evaluate the ratio of the direction vector and determine that the erosion landform model is completed when it becomes less than a certain value.

[Setting of Parameters] Next, a method of estimating the parameters in the erosion function used in the above-described erosion landform model generation method from the analysis of natural landforms will be described.

The topography of the region R for which the erosion function is to be estimated is quantized using blocks such as squares and equilateral triangles as in the method described in the procedure for generating the erosion topography model. The digitized terrain model of natural terrain is created by storing the elevation value of each grid point (x, y) in a two-dimensional array or the like. This is referred to as h (x, y).

When the river network model is in a steady state, the elevation of each grid point of the erosion topography model due to erosion is h (x, y; t) = constant × t ^γ × h ₀ (x, y) (Equation 11) and changes according to

| ∇h ₀ | ^a × s ^b = constant × h ₀ (Equation 12) is obtained. Here, h ₀ (x, y) is a function of only the coordinates (x, y) and does not change with time.

Numerical terrain model h of natural terrain to be analyzed
For (x, y), only the process (2) and the process (4) for generating the erosion landform model are repeated. From the vector d (x, y) obtained by this operation, a river network model associated with the digitized terrain model of natural terrain is created. Assuming that this river network model is in a steady state, the water volume s (x, y; t) at the grid point (x, y) is substituted by the watershed area s ₀ (x, y).

If the watershed area s ₀ is constant in (Equation 12), | ∇h ₀ | = constant × h ₀ ^{(1 / a)} (Equation 13) holds, so that Only the grid points with a certain catchment area are extracted from the inside, and the altitude h
(X, y) and head δh (x, y) = h _w (x, y) −h _w
Take a log-log plot of (x ', y').

The parameter a is obtained by evaluating the power function that best approximates the plotted points by a method such as the least square method.

Parameter a obtained in (Equation 12)
Is substituted, (h ₀ / | ∇h ₀ | ^a ) = constant × s ₀ ^b (Equation 14) holds for all grid points of the given digitized terrain model.

Therefore, ^a logarithmic plot of h / δh ^a and s ₀ is taken, and similarly to the case of the parameter a, the power function that best approximates the plotted points by the method such as the least square method can be evaluated. , The parameter b is obtained.

A method of directly storing data such as a numerical map (50 m mesh) issued by the Geospatial Information Authority of Japan in an array can be used to create a digitized terrain model of natural terrain to be analyzed. In such a digital map, a grid along the longitude and latitude lines of the earth is used for quantization of the terrain, and rectangles having different lengths in the longitude and latitude directions are sometimes used for quantization.

When the range of the region R to be analyzed is extremely wide, the rectangular area is different between the north end and the south end of R. However, unless the range of R is too wide, the quantization by this rectangle does not affect the method described above, and the analysis can be performed in a practically sufficient range.
However, in the case of quantization by a rectangle, instead of the drop δh, the gradient | ∇h | = [h _w (x, y) −h _w (x ′, y ′)] /
It is necessary to use | vector d (x, y) |.

An example of the hardware configuration of the erosion function parameter calculation device used for the above-described erosion function parameter setting will be described with reference to the block diagram of FIG. The erosion function parameter calculation device includes an arithmetic device 301, an input device 302,
It has an output device 303, a control device 304, and a storage device 350, which are mutually connected by a data bus line 371 and an address bus line 372.

As shown in FIG. 7, the storage device 350 stores a numerical terrain model creation program unit 351 in which a program for creating a numerical terrain model of natural terrain is stored, and a program for creating a river network model used for analysis. Is stored, a river network model creation program unit 352 is stored, a numerical terrain model analysis program unit 353 is stored that stores a program for analyzing a numerical terrain model, and a numerical terrain model of natural terrain is analyzed. A digitized terrain model storage unit 354, a river network model storage unit 355 in which a river network model used for analysis is stored, and a quantified terrain model analysis program for temporarily storing an amount such as a basin area or a terrain slope. A basin area storage unit 356 and a control program unit 357 that stores a control program such as an OS are provided.

The arithmetic unit 301 is composed of a CPU as a processor means, a RAM, a ROM etc. as a memory means, and executes each program stored in the storage device 350. When the program is executed, the storage device 35 is executed.
Applying each model stored in 0, or based on the initial condition setting value, the number of repetitions of the terrain erosion rule or the value of the time (t) input from the input device 302, the processes 1 to 6 described above are performed. Implement terrain erosion rules.

The input device 302 is composed of, for example, an input file, a digitizer, a mouse, a keyboard, a light pen, etc., and inputs an initial condition, a boundary condition set value, the number of times the terrain erosion rule is repeated or a time (t), etc. .

The output device 303 is, for example, an output file, C
A two-dimensional or three-dimensional shape display of the initial digitized terrain model h (x, y; 0) input from the input device 302, which is composed of an RT display, a printer, a network relay device, etc., and is stored in the storage device 350 by the arithmetic device 301. A numerical terrain model h (x, x, which is generated by repeating the terrain erosion rule based on the execution of each stored program
y; t) is displayed.

The control device 304 is composed of a CPU as a processor means, a RAM and a ROM as a memory means, and the mutual data of the arithmetic device 301, the input device 302, the output device 303, and the storage device 350 of the erosion landform model generator. Input / output control, processing sequence control, etc. are executed.

When the natural terrain is analyzed and subsequently the eroded terrain model is created by using the quantified terrain model of the natural terrain as the initial quantified terrain model, the erosion terrain model generation device described with reference to FIG. 5 is used. It is also possible to configure a device having both functions of the erosion function parameter calculation device shown in FIG. 7.

Erosion function parameter estimation performed by using the erosion function parameter calculation device shown in FIG.
The basic operation of the calculation processing of the parameters a and b will be described with reference to the flowchart of FIG.

First, in step S201, natural terrain data is input. This can be done by inputting data created from a numerical map of natural terrain, and as described above, data such as a numerical map (50 m mesh) issued by the Geographical Survey Institute can be applied.

Next, in step S202, an initial digitized terrain model h (x, y; 0) is created based on the data input in step S201.

Next, in step S203, a river network model associated with the digitized terrain model is created. The river network model is a model composed of vectors connecting grid points as described above with reference to FIG.

Next, in step S404, the digitized terrain model created in step S402 and step S402 are used.
Analyze the topography from the river network model created in 403,
The parameters a and b are evaluated. As the parameter a, based on (Equation 13) described above, only the grid points having a certain basin area are extracted from the given numerical map,
The altitude h (x, y) and the drop δh (x, y) = h
It is calculated by taking a log-log plot of _w (x, y) -h _w (x ', y') and evaluating a power function that best approximates the plotted points by a method such as the least square method. Parameters b, based on the aforementioned equation (14), h / δh ^a
And the logarithmic plot of s ₀ are taken, and similarly to the case of the parameter a, it is calculated by evaluating the power function that best approximates the plotted points by a method such as the least square method.

In step S205, step S204
It outputs the parameters a and b acquired in.

The parameter a set by the above method,
By executing the above-described erosion terrain model creation process (FIG. 6 flow) by applying b, a more accurate terrain erosion simulation that reflects the actual substance of the region R becomes possible.

[Specific Usage Example] Next, a specific usage example of the above-described erosion landform model simulation of the present invention will be described.

(1) Computer Graphics By displaying the erosion landform model created by the above-described erosion landform model generation method on the display in time series, it can be used as a background image of, for example, a simulation game or a movie. The terrain model creation method used so far is the Fractional Brown
Ian Surface is used, and it is completely different from the actual terrain erosion process. By using the erosion landform model created by the erosion landform model generation method of the present invention, a more realistic image can be created. Also, by setting the parameter of the erosion function to a value different from the actual topography, it is possible to create an image of the topography that gives an unrealistic impression.

FIG. 9 shows an example of a system configuration for executing computer graphics processing for displaying the erosion landform model created by the erosion landform model generation method on the display in time series. CPU (Central processing Unit) 501 is
Various application programs and OS (Operating)
System) is actually executed. Specifically, for example, execution of a game program using an erosion image as a background image,
Further, an initial numerical terrain model creation program, boundary condition setting program section, and terrain erosion model for creating an erosion terrain model that simulates erosion effects on the numerical terrain model are created for the above-described erosion terrain model generation processing. Execution of the simulation program, in addition, the numerical terrain model creation program that is executed when calculating the erosion function parameters, the river network model creation program that creates the river network model used for analysis, and the analysis of the numerical terrain model Digitalized terrain model analysis program, and O
The control program such as S is executed.

A ROM (Read-Only-Memory) 502 is a C
A program executed by the PU 501 or fixed data as a calculation parameter is stored. RAM (Random A
The ccess memory) 503 is used as a storage area and a work area for programs executed in the processing of the CPU 501 and parameters that change appropriately in the program processing.

The host bus 504 is connected to the PCI (Peripheral Component Internet / Interfac) via the bridge 505.
e) It is connected to an external bus 506 such as a bus.

The keyboard 508 is operated by the user to input various commands to the CPU 501, and the pointing device 509 is operated by the user when the position on the screen of the display 510 is specified, the command is specified, and the like. The display 510 is, for example, a CRT, a liquid crystal display, or the like, and displays various kinds of information by text or images. HDD (Hard Disk Drive) 511
Drives a hard disk as an information storage medium and executes a program or data read from the hard disk or a program or data write to the hard disk.

The drive 512 is a flexible disk, CD-ROM (Compact Disc ReadOnly Memory), M
O (Magneto optical) disc, DVD (Digital Versat
ile Disc), a magnetic disk, a semiconductor memory or the like, which is a drive for performing recording / reproduction of the removable recording medium 513, and executes reproduction of a program or data from each removable recording medium 513 and storage of a program or data in the removable recording medium 513.

When the program or data recorded in each storage medium is read and executed or processed by the CPU 501, the read program or data is the interface 507, the external bus 506, or the bridge 50.
5, R connected, for example, via the host bus 504
Supply to AM503.

The keyboard 508 to the drive 512 are connected to the interface 507, and the interface 507 is connected to the CPU 501 via the external bus 506, the bridge 505, and the host bus 504.

The communication unit 514 is a communication unit for executing communication via the Internet or the like, communicates with an external device via a connected router, and packetizes the data supplied from the CPU 501, HDD 511, etc., and transmits it. Alternatively, it executes a process of receiving a packet via a router. The communication unit 514 is connected to the CPU 501 via the external bus 506, the bridge 505, and the host bus 504.

For example, in the apparatus of FIG. 9, when the game program using the erosion image as the background image is executed, the image data generated by the above-described erosion landform model generation processing is applied as the background image and displayed on the display. You can create realistic images. Also, by setting the parameter of the erosion function to a value different from the actual topography, it is possible to create an image of the topography that gives an unrealistic impression.

(2) Civil engineering simulation. Furthermore, the erosion function parameters are set using the erosion function parameter calculation device described with reference to FIG. 7, and the erosion topography model generation device described with reference to FIG. By simulating
When conducting a business involving large-scale topographical changes such as dam construction and land reclamation, it is possible to more accurately predict the influence of those changes on the surrounding topography. Even if the change in topography over many years does not pose a problem, by accurately knowing the erosion function, it is possible to estimate the amount of sediment produced by erosion. This can be applied to, for example, evaluation of dam life.

(3) Geological analysis. The parameters of the erosion function are considered to depend on the geology of the eroded land. Analyzing the difference between the erosion function parameter calculated using the erosion function parameter calculation device described with reference to FIG. 7 and the model created by the erosion topography model generation processing based on the set parameter, and the actual erosion action This makes it possible to improve the accuracy of the parameters of the erosion function, which is determined by the geology of the land.
By clarifying the relationship between the geology and the erosion function, it will be possible to know the rough geological structure in the future simply by analyzing the digital map and the like, without conducting a geological survey.

The present invention has been described in detail above with reference to the specific embodiments. However, it is obvious that those skilled in the art can modify or substitute the embodiments without departing from the scope of the present invention. That is, the present invention has been disclosed in the form of exemplification, and should not be limitedly interpreted. In order to determine the gist of the present invention, the section of the claims described at the beginning should be taken into consideration.

The series of processes described in the specification can be executed by hardware, software, or a combined configuration of both. When executing the processing by software, the program recording the processing sequence is installed in the memory in the computer incorporated in the dedicated hardware and executed, or the program is stored in a general-purpose computer capable of executing various processing. It can be installed and run.

For example, the program can be recorded in advance in a hard disk or a ROM (Read Only Memory) as a recording medium. Alternatively, the program may be a floppy (registered trademark) disc or a CD-ROM (Compact Disc).
Read Only Memory), MO (Magneto optical) disk,
It can be temporarily or permanently stored (recorded) in a removable recording medium such as a DVD (Digital Versatile Disc), a magnetic disk, or a semiconductor memory. Such a removable recording medium can be provided as so-called package software.

The program is installed in the computer from the removable recording medium as described above, is wirelessly transferred from the download site to the computer, or is wired to the computer via a network such as LAN (Local Area Network) or the Internet. Then, the computer can receive the program thus transferred and install it in a recording medium such as a built-in hard disk.

The various processes described in the specification are
The processing may be executed not only in time series according to the description, but also in parallel or individually according to the processing capability of the device that executes the processing or the need.

[0126]

As described above, according to the configuration of the present invention, it is possible to simulate the transition of natural topography formed by the erosion action of flowing water, and the actual region R
Initial digitized terrain model based on natural terrain of the above, or initial digitized terrain model based on arbitrary data such as random number h
By applying the terrain erosion rule consisting of a plurality of processes to (x, y; 0), the erosion terrain model h (x, y; t) generated by the erosion processing is more accurate than the conventional method. It can be created in a shorter time.

According to the configuration of the present invention, the initial digitized terrain model h (x, y; 0) is created based on the natural terrain data corresponding to the real area R, and based on the created model. By calculating the erosion function parameters and creating the erosion topography model based on the calculated parameters, it is possible to predict the transition of the erosion topography that accurately reflects the characteristics of the natural topography corresponding to the actual topography. Therefore, it becomes possible to create a highly accurate erosion topography model in a shorter time.

Further, by applying the erosion landform model creating process of the present invention as an image of a game program, a more realistic and powerful image can be provided. Also,
It can also be effectively used in fields such as civil engineering and geological analysis.

[Brief description of drawings]

FIG. 1 is a diagram illustrating a setting process of a region R in an erosion landform model generation device of the present invention.

FIG. 2 is a diagram illustrating a process of setting a flowing water direction vector in the erosion landform model generation device of the present invention.

FIG. 3 is a diagram illustrating a boundary condition setting process in the erosion landform model generation device of the present invention.

FIG. 4 is a diagram illustrating a river network model generated by the erosion landform model generation device of the present invention.

FIG. 5 is a block diagram showing a configuration example of an erosion landform model generation device of the present invention.

FIG. 6 is a flowchart illustrating processing in the erosion landform model generation device of the present invention.

FIG. 7 is a block diagram showing a configuration example of an erosion function parameter calculation device of the present invention.

FIG. 8 is a flowchart illustrating processing in the erosion function parameter calculation device of the present invention.

FIG. 9 is a diagram showing a configuration example of a computer graphics processing device to which the device of the present invention is applied.

[Explanation of symbols]

101 arithmetic unit 102 input device 103 Output device 104 control device 150 storage devices 171 data bus line 172 address bus line 151 Initial digitized terrain model creation program section 152 Boundary condition setting program section 153 Terrain erosion simulation program section 154 Digitized terrain model storage 155 River network model storage 156 Flow rate storage 157 Control program section 301 arithmetic unit 302 Input device 303 Output device 304 control device 350 storage device 371 data bus line 372 address bus line 351 Digitized Terrain Model Creation Program Section 352 River Network Model Creation Program Department 353 Digitalized Terrain Model Analysis Program Section 354 Digitized terrain model storage 355 River network model storage 356 Basin area storage 357 Control program section

Claims (16)

[Claims] 1. An erosion topography model generation device for generating an erosion topography model in an area having a topography shape, wherein an area R to be an erosion topography model generation target is divided into a plurality of blocks, and coordinate values corresponding to each block are calculated. The initial digitized terrain model generation process for generating the initial digitized terrain model corresponding to the lattice point as h (x, y; 0) as the grid point position (x, y), and the initial digitized terrain model Then, a process based on the terrain erosion rule as an erosion action consisting of one or more processes is executed, and the process based on the terrain erosion rule is repeatedly executed to obtain a numerical terrain model h (x, An erosion terrain model generation device having a terrain erosion effect simulation process for generating y; t) and an arithmetic processing unit for executing 2. The process based on the terrain erosion rule assumes uniform precipitation in a region R as process 1, and a constant s ₁ is added to the water amount s (x, y; t) at each grid point at time t. In addition to the process, as the process 2, the flow direction vector d (x, y) at time t starting from the grid point (x, y) and ending at the lowest point (x ′, y ′) in the adjacent grid points. ; T) determination process, and as process 3, the water amount s (x, y at the grid point (x, y)
y; t) is moved to a grid point indicated by the vector d (x, y; t), process 4 is a pond formation process based on the movement of the amount of water in the process 3, and process 5 is a pond. For a grid point that is a constant condition, and a process 6 for determining a erosion amount E of a grid point (x, y) that is not a pond, which is the process 6. The erosion landform model generation device according to claim 1, wherein steps 1 to 6 are executed sequentially. 3. The arithmetic unit executes processing for setting drainage conditions and water stoppage conditions as boundary conditions for the region R, and based on the terrain erosion rule for the region R for which the boundary condition is set. The erosion landform model generation device according to claim 1, wherein the device is configured to execute a process. 4. The erosion terrain model generation device is an initial numerical terrain model creation program for creating a numerical terrain model of initial terrain, and boundary condition setting for setting boundary conditions when applying erosion action to the numerical terrain model. program,
It has a storage device that stores a terrain erosion simulation program that creates a erosion terrain model by applying terrain erosion rules simulating erosion to a digitized terrain model, and the arithmetic unit stores each stored in the storage device. The erosion terrain model generation device according to claim 1, wherein the erosion terrain model generation device is configured to execute a program to generate a digitized terrain model of the region R. 5. The computing device is configured such that C is a constant, an elevation value of a grid point (x, y) at a time t is h (x, y; t), and the grid is adjacent to the grid point (x, y) and has the lowest grid. The elevation value of the water surface at time t at the point (x ′, y ′) is h _w (x ′, y ′; t), and δh is the head difference δh = h (x, y; t) − at the time t. h _w (x ',
y ′; t), a and b are constants, and the amount of water at each grid point at time t is s (x, y; t), and J = δh ^a-1 × [s (x, y; t)] ^b Then, the erosion amount E of the grid point (x, y) at time t is E = C ×
δh × (J / (1 + J)) is calculated, and the altitude value of the grid point (x, y) is calculated as h (x, y; t + 1) = h (x, y; t) -E. The erosion landform model generation device according to claim 1, wherein 6. The process based on the terrain erosion rule comprises:
The parameter s ₁ indicating the increase amount of (x, y; t) and the parameter C as the coefficient value of the calculation formula of the erosion amount E of the grid point (x, y) are included, and the parameter s ₁ and the parameter C are included. And the real area R
The erosion landform model generation device according to claim 1, wherein the erosion landform model generation device is configured to be set based on the actual data of. 7. The above formula: J = δh ^a-1 × [s (x, y;
t)] ^b is the parameter a: A grid point having a certain basin area is extracted from the region R, and its altitude h (x, y) and head δh (x, y) = h.
_{w (x, y) -h w} (x ', y') takes the log-log plot of claim, characterized in that is configured to calculate the evaluation of power function that best approximates the points plotted 5 The erosion terrain model generation device described in. 8. The above formula: J = δh ^a-1 × [s (x, y;
parameter b in t)] ^b, h / δh take log-log plot of ^a and s _0, claim 7, characterized in that is configured to calculate the evaluation of power function that best approximates the points plotted The erosion terrain model generation device described in. 9. A method of generating an erosion landform model for generating an erosion landform model in an area having a terrain shape, in which an area R targeted for erosion landform model generation is divided into a plurality of blocks, and coordinate values corresponding to each block are calculated. An initial digitized terrain model generation step for generating an initial digitized terrain model corresponding to the grid point as h (x, y; 0) as a grid point position (x, y); and the initial numeric value generated in the step. The digitized terrain at time t of the region R is executed by executing a process based on the terrain erosion rule as an erosion action consisting of one or more processes on the digitized terrain model and repeatedly executing the process based on the terrain erosion rule. Model h (x,
y; t), a terrain erosion effect simulation processing step, and: 10. The process based on the terrain erosion rule assumes uniform precipitation in a region R as process 1, and sets a constant s ₁ to the water amount s (x, y; t) at each grid point at time t. In addition to the process, as the process 2, the flow direction vector d (x, y) at time t starting from the grid point (x, y) and ending at the lowest point (x ′, y ′) in the adjacent grid points. ; T) determination process, and as process 3, the water amount s (x, y at the grid point (x, y)
y; t) is moved to a grid point indicated by the vector d (x, y; t), process 4 is a pond formation process based on the movement of the amount of water in the process 3, and process 5 is a pond. For a grid point that is, a pond removal process based on a constant condition and a process 6 for determining an erosion amount E of a grid point (x, y) that is not a pond are included. The method according to claim 9, further comprising: performing the processes 1 to 6 sequentially. 11. The erosion terrain model generation method further includes a step of setting a drainage condition and a water stoppage condition as boundary conditions for the region R, and the terrain erosion effect simulation processing step, The erosion terrain model generation method according to claim 9, wherein a process based on the terrain erosion rule is executed on the region R in which the boundary condition is set. 12. The terrain erosion simulation processing step uses C as a constant, and an altitude value at time t of a grid point (x, y) as h (x, y; t) and a grid point (x, y). The elevation value of the water surface of the adjacent lowest grid point (x ′, y ′) at time t is h _w (x ′, y ′; t), and δh is the drop δh = h (x, x of adjacent grid points at time t. y; t) _{-w w} (x ',
y ′; t), a and b are constants, and the amount of water at each grid point at time t is s (x, y; t), and J = δh ^a-1 × [s (x, y; t)] ^b Then, the erosion amount E of the grid point (x, y) at time t is E = C ×
δh × (J / (1 + J)) is calculated, and the altitude value of the grid point (x, y) is calculated as h (x, y; t + 1) = h (x, y; t) -E. The erosion landform model generation method according to claim 9, wherein 13. The process based on the terrain erosion rule comprises:
The terrain erosion effect simulation processing step includes a parameter s ₁ indicating an increase amount of (x, y; t) and a parameter C as a coefficient value of a calculation formula of the erosion amount E of the grid point (x, y). Represents the parameter s ₁ and the parameter C in the real region R
10. The method for generating an erosion landform model according to claim 9, further comprising the step of setting based on the actual data of. 14. The above formula: J = δh ^a-1 × [s (x, y;
t)] ^b is the parameter a: A grid point having a certain basin area is extracted from the region R, and its altitude h (x, y) and head δh (x, y) = h.
_The logarithmic plot of _w (x, y) -h _w (x ', y') is taken, and the plotted points are calculated by evaluation of a power function that most closely approximates them. Erosion topography model generation method. 15. The above formula: J = δh ^a-1 × [s (x, y;
The parameter ^b in t)] ^b is calculated by taking a log-log plot of h / δh ^a and s ₀ and evaluating a power function that most closely approximates the plotted points. Erosion topography model generation method. 16. A computer program for executing erosion topography model generation processing for generating an erosion topography model in a region having a topography, wherein an area R to be an erosion topography model generation target is divided into a plurality of blocks, and An initial digitized terrain model generating step of generating coordinate values corresponding to the blocks as grid point positions (x, y) and initial digitized terrain models corresponding to the grid points as h (x, y; 0); A region based on the terrain erosion rule as an erosion action including one or more processes is executed on the initial digitized terrain model generated in step, and the process based on the terrain erosion rule is repeatedly executed to thereby obtain the region R. Digitized terrain model h (x,
y; t), a terrain erosion simulation processing step, and a computer program.