JP2003228646A - River condition simulation method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To highly precisely simulate change of a water level and a flow rate rivers due to an uncertain flow. <P>SOLUTION: As for the uncertain flow of rivers, a continuity equation and a motion equation from which a time item is omitted are solved by a shadow system difference calculus. In this case, a flow rate Q(ij) at each spot at each point of time is assumed in a step S4, and a water level H(ij) is calculated by using the motion equation in a step S5. Whether or not the flow rate conversion value of reservoir quantity associated with the water level and the flow rate changing quantity being the reservoir quantity of the flow rate are balanced is judged by using the continuity equation in a step S6, and when the flow rate is not balanced, the flow rate is assumed again, and the steps S4-S6 are repeated. In the step S4, the flow rate changing quantity is set by averaging the flow rate changing quantity obtained by the previous assumption and the flow rate changing quantity appearing in the water level change, and the flow rate is reassumed based on this. When the flow rate is balanced, the point of time is updated, and arithmetic processing is executed in the same way in a step S8. <P>COPYRIGHT: (C)2003,JPO

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for simulating river conditions, and more particularly, to appropriately simulate an unsteady flow of a river by using a computer to estimate an arbitrary point in a monitoring area and a water level and a flow rate after a predetermined time. The present invention relates to a method for simulating a river state.

[0002] Analyzing an irregular flow of a river due to a torrential rain, etc., examines a situation such as a flood due to a rise in the water level of the river,
And it is extremely important in drafting a river plan based on the verification. On the other hand, there is a strong demand for reduction of construction costs for public works, and therefore, cost reduction is also required for construction of river flood control systems. In such a situation, a simulation capable of accurately predicting a state quantity of water such as a water level and a flow rate of a river basin when a torrential rain occurs and when planning a river flood control system is important.

The present inventor has simulated a river system as an electric system, and omitted a time-varying term of velocity and a term of distance-varying velocity in the equation of motion. We have already found that by simulating the unsteady flow by the Wave method, the flood flow can be reproduced to a considerable extent. However, in the analogy to the electric system, the frictional resistance of the river channel, which changes according to the water level, changes due to the prolongation of the current conduction time,
This made it difficult to simulate unsteady flows in long river channels.

A method of analyzing an indeterminate flow by an implicit difference method using a continuous equation and an equation of motion of the indeterminate flow has already been proposed. In the implicit form solution, when calculating M cross sections, 2 (M-1) simultaneous equations must be solved after giving the initial condition and the upper and lower end conditions at the next time. . In this solution, the simultaneous equations are solved under the assumption that the value at the previous time point is used as the value outside the difference term, so strictly speaking, the condition of the motion equation at the next time point may not be satisfied .

The present invention has been made in view of the above-mentioned problems of the prior art, and has as its object to accurately simulate changes in water level and flow due to unsteady flow even in a long river. It is to provide a method of simulating unsteady flow.

[0006]

The above object is achieved.
In accordance with the present invention, in the monitoring area of the river in an irregular flow condition
The water level and discharge at a specified point after a specified time
Implicit difference using continuous and motion equations
In the simulation method of calculating and estimating by the method
Are located at multiple locations including the upstream and downstream ends of the river area.
Point x₀, X₁, X_Two, ..., x_i, ..., x_m(However, the upstream end
Point x_i= X₀, Downstream end point x_i= X_mTo each)
Initial time t₀Water level and discharge at multiple locations
Initial water level H at each_{(i, 0)}And initial flow rate Q_{(i, 0)}age
A first step of setting and initial time t₀From the prescribed time
Interval t_nThe time t when the subsequent part is divided into n₁, T_Two, ..., t_j,
... t_nThe upstream end point x₀Flow rate Q_{(0, j)}Or water level H_{(0, j)}
And downstream end point x_mWater level H_(m,_j)The second to set
Steps and multiple points x_i(However, x₀Except)
Time t at each_i= T₁Flow Q at_{(i, j)}= Q_{(i, 1)}
And a continuity equation and a motion equation
As an expression, δA / δt + δQ / δx = 0 δH / δx + δ (v^Two/ (2g)) / δx + n^Twov^Two/ R
^4/3= 0 Where A: cross section t: time Q: Flow rate x: distance H: Water level v: flow rate (v = Q / A) g: acceleration of gravity n: Manning's roughness coefficient R: diameter Is the boundary condition set using the equation of motion in
Flow Q_{(0, j)}, Water level H_(m, _j), Each point x_iThe assumed flow of
Quantity Q_{(i, 1)}Is calculated by substituting_iTo
Time t_j= T₁Water level H_{(i, j)}= H_{(i, 1)}Calculate
4th step and each point x_i(However, x₀
T)₁Flow of storage for later water levels
Quantity conversion value dRh_iAnd flow rate change
Amount dRq_iA fifth step of calculating dRh_ias well as
dRq_iTo determine whether the difference is within a predetermined tolerance.
The sixth step, dRh_iAnd dRq_iIs acceptable
When not enclosed, flow rate Q_{(i, j)}= Q_{(i, 1)}Assuming another value
And a seventh step of repeatedly executing the fourth and fifth steps.
And dRh_iAnd dRq_iIs within the allowable range
Time t_TwoRepeat steps 3 to 7 for
And then at time t_Three, ..., t_nAbout 3rd to 7th
An eighth step of repeatedly executing the steps of
And a river state simulation method.

[0007] In one embodiment of river state simulation method according to the present invention described above, the flow rate variation DRQ _i is the flow rate conversion value DRH _i and storage amount regarding the flow rate of the storage amount about water level, the following equation DRH _i = _{1/2 · (A (i-1} , j) + A (i, j) -A (i-1, j-1) -A (i, j-1)) dx i / dt dRq i = 1/2・ (Q _{(i, j-1)} + Q _{(i, j)} −Q _{(i-1, j-1)} −Q _(i − _{1, j)} ) where A _{(i, j)} : at the point x _i time t _j in cross-sectional flow area dt: calculation time interval _{= t j -t j-1 dx} i: is calculated by calculation distance interval = x _i -x _i-1. The flow rate Q in the seventh step executed in the seventh step and the eighth step
_{(i, j) assumption, Q (i, j) =} dRq i -dRh i + Q (i-1, j-1) + Q (i-1, j)
It is calculated by -Q _{(i, j-1)} .

[0008] The present invention further provides a computer-readable storage medium for executing a river state simulation method for estimating a water level and a flow rate of a predetermined point in a monitoring area of a river in an irregular flow state after a predetermined time. A storage medium, which is a medium, wherein the river state simulation method is the method described above.

[0009]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Before describing the embodiments of the present invention, the principle of the present invention will be described. The method of simulating an indeterminate flow according to the present invention is a method of an implicit form, in which the time term in the equation of motion is omitted as being smaller than the other terms, and the equation of motion and the continuity equation of the irregular flow are implicitly represented by a difference method. It is configured to solve as At each time point, the equation of motion of unequal flow is strictly satisfied, and the continuous equation is satisfied by performing repeated calculations. As the calculation step, first, the river channel section and roughness coefficient are set, and the initial conditions and boundary conditions are set. All the flow rates at each point at the next time are assumed, and the corresponding water level is calculated by unequal flow calculation. , And if necessary, re-assume the flow rate by the proposed method, and approach the flow rate to a true value that satisfies the continuous equation. By using the implicit form, a large calculation time interval can be taken.

[0010] The basic equation of the indeterminate flow is composed of a continuous equation and a motion equation. The continuity equation is derived from the law of conservation of mass. When the flowing water is incompressible and there is no lateral inflow, it is represented by the following equation (1). In addition, the equation of motion is expressed as equation (2) based on the law of conservation of energy. δA / δt + δQ / δx = 0 (1) -i + δh / δx + δ (v 2 / (2g)) / δx + n 2 v 2 / R 4/3 + 1 / g · δv / δt = 0 (2) However, A: passing Water cross section t: Time Q: Flow rate x: Distance i: River bed gradient h: Water depth v: Flow velocity (v = Q / A) g: Gravity acceleration n: Manning's roughness coefficient R: Diameter depth formula (2) Since 1 / g · δv / δt is small compared to the other terms, it is neglected, and −i + δh / δx is set to δH / δx using the water level H, and the equation (2) becomes δH / δx + δ (V ² / (2 g)) / δx + n ² v ² / R ^4/3 = 0 (3), and an equation of motion of unequal flow is obtained.

Next, let us consider solving equations (1) and (3) as basic equations. These equations include A, Q, H, v, and R as unknowns. Since A and R are functions of H and v is represented by Q and A, the basic unknowns are H, Q and The two. In the difference method using the indefinite flow implicit form, when the total number of calculation sections is m, at t _j = jΔt, the water level H _{(i, j)} and the flow rate Q
_{If (i, j)} is known, the upstream end flow rate Q _{(0, j + 1)} (or the water level H _{(0, j + 1)} ) and the downstream end water level at the time t _{j + 1} = (j + 1) Δt Knowing H _{(m, j + 1)} , it calculates the total hydraulic quantity at that time t _{j + 1} . Therefore, the number of unknowns is 2
(M-1). Since the equation is expressed by the difference equation between the equation of motion and the continuity equation between two adjacent cross sections, the number is 2 (m−1), and the number of unknowns and the number of equations match, so the basic equation Should be able to be solved.

The simulation method according to the present invention is executed by a computer including the operation steps shown in the analysis processing flow of FIG. 1. These operation steps are realized by software installed in the computer. The simulation method will be described in detail with reference to FIG. First, the target basin simulation rivers, is divided into m, which point x ₀ the point _{it, x 1, x 2, ...} , x i, ..., and x _m. However,
It is assumed that the upstream end point x _i = x ₀ and the downstream end point x _i = x _m . Further, the period from the initial time to a predetermined time after which the water level and the flow rate are to be estimated is divided into n, and each time is defined as t ₀ ,
_{t 1, t 2, ...,} t j, and ... t _n. However, the initial time t
_j = t ₀ , and a time point t _j = t _n after a predetermined time.

First, in steps S1 and S2, a river channel section and a roughness coefficient are set. The setting of the river cross section in step S1 is executed by incorporating the cross section shape of the river in the monitoring section into the calculation system. The setting of the roughness coefficient in step S2 is set so that the roughness coefficient of the river channel can be changed according to the cross-sectional shape. Next, in steps S3 and S4, initial conditions and boundary conditions are set. The initial conditions are as follows: the water level H _{(i, 0)} and the flow rate Q _{(i, 0)} at the initial time point t ₀ at all points x _i
It is equal to the actual water level and discharge of the target river, and the boundary condition is the upstream end discharge Q at time t _j (j = 1, 2,..., N).
_{(0, j)} and the downstream end water level H _{(n, j)} . In steps S3 and S4, these conditions are set as known values. Next, in step S5, j = 1 is set, and in step S6, the flow rate Q _{(i, 1 )} at time t ₁ , that is, Δt from the initial time t ₀ , that is, after = dt time, is set to the point x _i (i = 1, 2, 3, ..., m). Then, in step S7, with a flow rate of at time t ₁ the total point is assumed, the water level H _{(m, 1)} of the downstream end point x _m as a starting condition, each point in the range of x _m ~x ₁ The water level H _{(i, 1)} of x _i is obtained by equation (3). This step is also calculated by making a difference, but is well known and will not be described further in this specification.

Then, the process proceeds to step S8,
It is determined whether the flow rate Q _{(i, 1)} assumed in step 6 and the water level H _{(i, 1)} obtained in step S7 satisfy Expression (1) (whether the flow rate is balanced). . If you are satisfied (affirmative decision YES), it becomes the solution of simultaneous equations, estimates of flow rate and water level in each point x _i at time t ₁ is determined. In step S8, when it is determined that the expression (1) is not satisfied (NO in step S8), the process returns to step S6, re-assumes the flow rate Q ₍₁ , _j) , and repeats steps S7 and S8. Es This is repeated until an affirmative determination YES is obtained in step S8. The method assumes a flow rate Q at a point x ₁ in step S6 _{(i, 1),} and for the determination method in step S8, the flow rate Q at time t _j at the point x _i
The assumption method of _{(i, j)} and the judgment method using its continuous equation will be described below.

If an affirmative determination is obtained in step S8, the process proceeds to step S10 via step S9 to set "j = j + 1", and then to step S6.
Returning to, assume Q _{(i, 2)} at the point x _i at the next time point t ₂ . Then, until the affirmative determination is obtained at time t ₂ in step S8, it executes the processing in step S6 to S8. In this way, steps S6 to S10 are repeated while updating the time point t _j. However, when the negative determination NO of “j <n?” Is obtained in step S9, the process proceeds to step S11 and is obtained. The water level H _{(i, j)} and the flow rate Q _{(i, j)} are displayed on the monitor screen of the computer, and the information is printed and output as necessary. At this time,
Summarize the water level and discharge at each point and each point in the calculation results,
A water level time curve and a flow time curve, as well as a curve showing the relationship between the water level and the flow rate at the flow observation point, are output, and the results are compared with the actual measurement results to examine the validity of the calculation.

In the course of the calculation, the unequal flow calculation in step S7 has a changing point where the flow rate changes at the center of the calculation section unlike the unequal flow calculation of the constant flow.
This is the unequal flow calculation that is usually performed. Taking the above into consideration, it is important how to reassume the flow rate Q _{(i, j)} in step S6 _, and how to assume the flow rate Q _{(i, j)} will be described below. I do. The continuity equation, when the difference of the time t _j-1 and the time point t _j at a point x _i-1 and the point x _i, can be expressed as follows. 1/2 (A _{(i-1, j)} + A _{(i, j)} -A _{(i-1, j-1)} -A _{(i, j-1)} ) / dt + 1/2. (Q _{( i, j-1)} + Q _{(i, j)} -Q _{(i-1, j-1)} -Q _(i - _{1, j)} ) / dx = 0 (4) where A _{(i, j) is a} point cross-sectional flow area of the time t _j in x _i dt: calculation time interval _{= t j -t j-1 dx} i: calculated distance interval = x _i -x _i-1

These two points x_i-1, X_ieach
Two time points t_j-1, T_jWater level H _{(i, j-1)}, H_{(i, j)},
H_{(i-1, j-1)}, H_{(i-1, j)}And flow rate Q_{(i, j-1)}, Q_{(i, j)}, Q
_{(i-1 , j-1)}, Q_{(i-1, j)}Is known, the water level is
From the relationship, the converted value of the amount of storage between them
Difference value dRh_iIs expressed by the following equation (5)
Can be. dRh_i = 1/2 · (A_{(i-1, j)}+ A_{(i, j)}-A_{(i-1, j-1)}-A_{(i, j-1)}) Dx_i/ Dt                                                             (5) Similarly, because of the relationship between flow rates, the flow storage between them
Flow rate change amount dRq_iIs given by the following equation (6).
Can be expressed as dRq_i = 1/2 · (Q_{(i, j-1)}+ Q_{(i, j)}−Q_{(i-1, j-1)}−Q_(i―_{1, j)}) (6)

When the relation of the above equation (4) is established, the relation of dRh _i = −dRq _i (7) should be established. However, when the water level H and the flow rate Q include an error, the relation (7) is obtained. The formula does not hold. Note that the storage amount means the amount of change in the flow rate in the calculation distance section in the calculation time interval in the flow-down process. Therefore, in step S8, the flow rate change amount DRQ _i is the flow rate conversion value DRH _i and flow storage amount of the storage amount about water level
Is calculated from Expressions (5) and (6), and it is determined whether or not these deviations are within an allowable error range. If it is within the allowable error range, the process proceeds to step S9, and if it is outside the allowable error range, the process proceeds to step S6.

Next, the reassumement in step S6 will be described. First, the flow rate change amount is calculated by calculating the flow rate change value dRq _i obtained by the above assumption and the flow rate conversion value of the storage amount appearing in the water level change (that is, the flow rate change amount appearing in the water level change).
It is set to the average value of the -dRh _i. That is, equation (6)
In the left-hand side of _{dRq i (dRq i -dRh i)} / 2
Set to. Based on this _{setting, dRq i -dRh i = (Q} (i, j) + Q (i, j-1)) - ((Q (i-1, j) + Q (i-1, j-1)) ( 8) can be obtained, when deforming the equation _{(8), Q (i, j) =} dRq i -dRh i + Q (i-1, j-1) + Q (i-1, j) -Q (i _{, j-1)} (9) In step S6, based on equation (9),
Flow rate Q _{(i, j)} of all points x _i at a certain time t _j sequentially seek to set the obtained flow rate of assumed values. Then, in step S7, the flow rate Q _{(i, j)} of the obtained each point x _i using the boundary condition H of the downstream end point x _{m
Under (m, j)} (set in step S4), H _{(i, j)} at time t _j is obtained.

When the flow rate Q _{(0, j)} is given (condition setting) as the upstream end condition, the above-described calculation is performed, but the water level H _{(0, j)} may be given. Even in this case, unless the flow rate at the upstream end is given, the flow rate at each point toward the downstream cannot be reset. In this case, the flow rate at the upstream end is assumed, and the assumed flow rate is given as (9)
The flow rate at each point is reset according to the equation, and it is checked whether the water level at the upstream end obtained in step S7 falls within the allowable range of the condition setting. If the calculated upstream water level is not within the predetermined error range for the given water level, the upstream flow rate is reset.

Hereinafter, the case where the upstream end condition requires the water level will be described in detail. The simulation method in this case is performed by executing a program including the calculation steps shown in the analysis processing flow of FIG. 2 on a computer. This method is different from the analysis processing flow shown in FIG. In step S4, the water level H (0, j) is set instead of the flow rate Q (0, j) at the upstream end. Step S6 ′ for assuming the flow rate at the upstream end is added before step S6. Step S8 'for checking the degree of coincidence of the water level at the upstream end is added after the step of Step S8. Assuming the upstream end flow rate in step S6 ′, the first time is set using the amount of rise of the upstream end water level from the previous time as an index,
For the second and subsequent times, the difference between the given water level at the upstream end and the calculated water level is set as an index. The check of the upstream end water level in step S8 'is performed N times (about 20 times) when the calculated water level at the upstream end is stabilized by the calculations in steps S6 to S8.
After the repetition of In this check, if the upstream end given water level and the calculated water level do not fall within the predetermined error range, the process returns to step S6 ', and the upstream end flow rate is reassumed.

Using the simulation method of the present invention,
Explain the transition of the approximation degree due to the change of the flow rate assumption in the simulation at the time when about 10 steps were performed in the section of about 70 km downstream of the river A without a large tributary (that is, almost no inflow from the tributary). I do. Note that this simulation is performed under the condition that the water level is given as an actually measured value at both the downstream end and the upstream end, and the separation distance δx between two adjacent points is approximately 2 k
m, time interval δt = 1 hour. As a result unsteady flow calculations were calculated level H _{(i, j)} and the flow rate Q _{(i, j)} and for each point x _i and each time point t _j.

FIGS. 3 and 4 show the case where the flow rate assumption is made once in the flow rate estimation simulation, and FIG.
The water level obtained in the case where the number of times has been performed is shown in comparison with the actual water level in the river A (actual measurement H). 3 and 4 show:
To understand the calculation process, the water level H _{(i, 0)} as the initial value
And the flow rate Q _{(i, 0),} the water level H _{(i, 1)} and the flow rate Q _{(i, 1)} in the calculation process at the next time point t ₁ , and the flow rate conversion value dRh and The flow rate change amount-dRq is also displayed. As described above, the degree of improvement in the degree of approximation by repeating the assumption of the flow rate Q is described in (5).
Storage amount dRh related to water level change shown in equation (6) and equation (6)
It can be checked by seeing the match / mismatch between the flow rate change amount and the flow rate change amount-dRq, which is the storage amount related to the flow rate change.
And, in FIG. 3, the values of dRh and -dRq are multiplied by 10 to facilitate comparison.

According to the graph of FIG. 3, -dRq and dRh at the beginning, that is, at the time of the first assumption, are significantly different. However, according to the graph of FIG. The values almost coincide with each other, and it can be seen that the degree of approximation is improved by performing the repeated calculation. By looking at the difference between the flow rates Q _{(i, 1)} shown in FIGS. 3 and 4, it is possible to know the change in the assumed value of the longitudinal flow rate in the approximation process. Note that, through a real machine test of the simulation method of the present invention, the time change term 1 / of the speed in the equation (2) is obtained.
When g · δv / δt was calculated, it was about 5 × 10 ⁻⁶ or less. Therefore, it was also proved that the assumption that the time change term of the speed was omitted was appropriate.

As described above, the simulation method according to the present invention comprises the following steps: a) deleting the speed-time change term in the equation of motion of equation (2); and b) balancing the storage amount in each section for each period. Is determined based on the deviation of the flow rate conversion value of the storage amount calculated based on the equations (5) and (6). C) If the balance is not achieved, the equation is determined based on the equation (9). Thus, the assumed flow rate at each point is changed so that the storage amount can be balanced. Therefore,
ADVANTAGE OF THE INVENTION According to this invention, it is possible to simulate the water level and the flow rate of a river with high accuracy while performing simple calculations.

At this time, the water level and flow rate at each point and each time point of the calculation result are summarized, and a water level time curve, a flow time curve,
Furthermore, a curve or the like indicating the relationship between the water level and the flow rate at the flow rate observation point is output, and comparison with the actual measurement result is performed, so that the validity of the calculation can be examined. For example, below the calculation results, each time water level and each time flow rate of the calculation results at the water level observation point and flow rate observation point in the monitoring section are compared with the actually measured time water level and time flow rate. Sex can be considered. If the results do not match, correct the roughness coefficient and recalculate. In the simulation method according to the present invention, corresponding to the set roughness coefficient,
Based on the given initial conditions and boundary conditions, the water level and discharge at each point in time and at each point are determined.If the results are different from the actually measured values to be verified, as described above, It is necessary to change the roughness coefficient. In this sense, it can be said that the simulation method according to the present invention is a method for verifying the roughness coefficient of a river channel. Also,
Based on the calculation results, the relationship between the water level and discharge is created and compared with the measured values to verify the validity of the calculation, and the relationship between the water level and discharge and the loop, etc., which cannot be clearly understood by actual measurement alone Can be clarified. As a result, the accuracy of estimating the actual flow rate during a flood can be improved. Therefore, by using the verified roughness coefficient, it can be useful for river flood control planning.

[Brief description of the drawings]

FIG. 1 is a flowchart for explaining processing of a first embodiment by a computer in a river state simulation method according to the present invention.

FIG. 2 is a flowchart for explaining processing of a second embodiment by a computer in the river state simulation method according to the present invention.

FIG. 3 is a graph showing a test result when a water level and a flow rate of a certain river are estimated by actually using the river state simulation method of the present invention, and a graph showing a result when a flow rate assumption is performed only once; It is.

FIG. 4 is a graph showing test results when a water level and a flow rate of a certain river are estimated by actually using the river state simulation method of the present invention, and is a graph showing a result when a flow rate assumption is performed 20 times; is there.

Claims (4)

[Claims] 1. A predetermined place in a monitoring area of a river in an unsteady flow state.
The water level and flow rate of the point after a predetermined time are
By implicit difference method using continuity equation and equation of motion
In the simulation method for calculating and estimating, Multiple points x including the upstream and downstream ends of the target area of the river
₀, X₁, X_Two, ..., x_i, ..., x_m(However, upstream end point
x_i= X₀, Downstream end point x_i= X_mTo each)
Initial time t₀Water level and discharge at multiple locations
Initial water level H in_{(i, 0)}And initial flow rate Q_{(i, 0)}Set as
A first step of determining Initial time t₀From the specified time t_nWhen the last is divided into n
Point t₁, T_Two, ..., t_j, ... t_nThe upstream end point x₀Flow rate
Q_{(0, j)}Or water level H_{(0, j)}And downstream end point x_mWater in
Rank H_(m,_j)A second step of setting Multiple points x_i(However, x₀Except for each)
Time t_i= T₁Flow Q at_{(i, j)}= Q_{(i, 1)}The third assuming
Steps and As a continuous equation and an equation of motion, δA / δt + δQ / δx = 0 δH / δx + δ (v^Two/ (2g)) / δx + n^Twov^Two/ R
^4/3= 0 Where A: cross section t: time Q: Flow rate x: distance H: Water level v: flow rate (v = Q / A) g: acceleration of gravity n: Manning's roughness coefficient R: diameter Is the boundary condition set using the equation of motion in
Flow Q_{(0, j)}, Water level H_(m, _j), Each point x_iThe assumed flow of
Quantity Q_{(i, 1)}Is calculated by substituting_iTo
Time t_j= T₁Water level H_{(i, j)}= H_{(i, 1)}Calculate
A fourth step, Each point x_i(However, x₀Time)
t₁Flow rate conversion value dRh of stored amount related to water level after_iAnd flow
Flow rate change amount dRq, which is the storage amount related to the amount_iCalculate
A fifth step; dRh_iAnd dRq_iWhether the difference is within a predetermined tolerance
A sixth step of determining whether dRh_iAnd dRq_iFlow rate Q when the difference between
_{(i, j)}= Q_{(i, 1)}Assuming a different value for the fourth and fifth scans.
A seventh step of repeatedly performing the steps; dRh_iAnd dRq_iIs within an allowable range, the time t
_Two, The third to seventh steps are repeatedly performed, and the
Later time t_Three, ..., t_n3rd to 7th steps
And an eighth step of repeatedly executing
River state simulation method. 2. The river state simulation method according to claim 1, wherein a flow rate conversion value dR of the storage amount related to the water level.
flow rate change amount dRq, which is a storage amount related to h _i and flow rate
_i is given by the following formula: dRh _i = 1/2 · (A _{(i-1, j)} + A _{(i, j)} −A _{(i-1, j-1)
-A (i, j-1)} ) dx i / dt dRq i = 1/2 · (Q (i, j-1) + Q (i, j) -Q (i-1, j-1)
_{-Q (i - 1, j)} ) _However, A _{(i, j):} cross-sectional flow area of the time t _j at a point x _i dt: calculation time interval _{= t j -t j-1 dx} i: calculated distance interval = X _i -x _{i -1} . 3. The simulation method according to claim 2, wherein the assumption of the flow rate Q _{(i, j)} in the seventh step executed in the seventh step and the eighth step is as follows: Q _{(i, j)} = _{dRq i -dRh i + Q (i} -1, j-1) + Q (i-1, j)
-A river state simulation method characterized by calculating by Q _{(i, j-1)} . 4. A storage medium storing a computer-readable program for executing a river state simulation method for estimating a water level and a flow rate of a predetermined point in a monitoring area of a river in an unsteady flow state after a predetermined time. A storage medium, wherein the river state simulation method is the method according to any one of claims 1 to 3.