JP2015129397A - Calculation method of regression function for estimating flow rate of mountain river basin, selection method of the function, and annual average flow rate estimation method of mountain river basin - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a calculation method of a regression function for estimating a flow rate in which a river flow estimation method by a conventional basin ratio is corrected, and a flow rate of a mountain river with a flow rate unmeasured can be estimated accurately and efficiently.SOLUTION: A calculation method of a regression function for estimating a flow rate of a mountain river basin includes the steps of: calculating an area according to an elevation zone and the elevation according to the elevation zone of an examination river basin, based on a commercial topographic map; calculating a basin solid terrain relative area and a basin relative elevation by using these as input data; and calculating a water estimation flow rate by using mathcad (R) being technical calculation software from a measured value of the annual average flow rate of a flow gaging station basin corresponding to the measured value of the annual average flow rate in each flow gaging station basin, and the calculated solid terrain relative area and the elevation.

Description

1.1 Outline The present invention relates to a method for calculating a regression function for estimating a flow rate in a mountain river basin, a method for selecting the function, and a method for estimating an annual average flow rate in a mountain river basin.
In the present invention, instead of the conventional method for estimating the flow rate at the upstream river basin point of the mountainous river by calculating the basin area ratio (abbreviated as basin ratio) from the measured flow rate at the existing gauging station in the downstream or nearby river, The basin 3D solid terrain correlation area AEQ, the basin 3D solid terrain correlation elevation HEQ, and the basin 3D solid terrain correlation depth length WEQ are defined using the combination of these new indices. It introduces a new method for estimating the flow of small basin rivers.

  The basin area CA, which is conventionally used as an index to represent the size of the basin, is a uniquely determined index that can be measured on the topographic map as a projected area on the horizontal plane of the actual area surrounded by the target basin boundary. . Therefore, CA is a single index that represents only the planar characteristics of the basin. In general, the high altitude zone has a lot of precipitation, the vegetation is sparse, the surface gradient is steep, so there is little loss due to evapotranspiration, and the river flow from the unit basin area (called specific flow rate) More than the specific flow rate in the entire downstream basin.

1.2 Previous research and discussion
1.2.1 Previous research on basin three-dimensional landform indices 1) The following are the indices representing the average elevation of the basin: (a) Contour area method, (b) Contour line extension method, (c) Intersection method and (d) Height measurement integration Lists four laws. Among these, the indices considered related to the basin three-dimensional landform indices AEQ, HEQ, and WEQ proposed in this study are (a) the contour line area method and (d) the height measurement integration method.

(a) Contour line area method In a map depicting contour lines at a certain height difference, measure the band-like area a _i between each contour line with a planimeter, and add the average of the contour line heights h _i and h _{i + 1 on} both sides. Divide by total basin area (Σa _i ). Ie

In the inset of a method the article by (d) measuring the high integration, the surface of the basin and ACBDA, the highest elevation point B (E _B), the lowest elevation point A (E _A), the elevation difference H, basin The vertical projection area of A is assumed to be A ₀ (introductory figure 1.11). While obtaining a horizontal plane cutting the cross-sectional area a _{h =} CEDCs basin any elevation (E _{A +} h), increasing h △ h by sequentially measuring the cutting area corresponding thereto _{(a h + △ h),} h It is assumed that _i can be obtained by the following equation and the average altitude (E) can be estimated by equation (3).

  Using the method of (d) above, the area between the contour lines is measured, the altitude is plotted on the vertical axis, and the total area from the highest altitude to a certain altitude is plotted on the horizontal axis. (Reference figure 1.12), the value on the vertical axis corresponding to the midpoint of the horizontal axis in this figure is called the middle altitude. In other words, the basin area higher and lower than this position are the same altitude, usually slightly lower than the average altitude. It is more reasonable to use the relative altitude. Argued.

  In the previous studies, the reference value of the basin area is the midpoint of the horizontal axis, that is, half of the basin area, and the reference value of the basin height is the middle altitude corresponding to the reference value of the basin area. That is, the reference value of the basin area is first determined, and then the altitude corresponding to the reference value of the basin area is obtained from the area-altitude curve and set as the middle altitude. Therefore, the reference value of the basin height is a dependent variable of the reference value of the basin area, and the two reference values are not variables defined independently. Furthermore, this basin area is the projected area on the horizontal plane and not the actual basin area.

1.2.2 Previous Research and Considerations in Basin Hydrology Kirkby (Non-Patent Document 1) wrote in his book “New Hydrology” that “surface hydrology is characterized by facilitating the prediction of runoff rate and runoff. Is a wide variety of prediction formulas ”(p. 253), and“ the power of surface flow as topographical characteristics or terrain power generally depends on hydraulic characteristics, Because hydraulic parameters vary drastically in time and space, it is impossible to simply describe hydraulic characteristics of natural slopes ”(p. 130), and“ regions with different topography ” It should be borne in mind that there are differences in the results of research conducted in Japan, and none of the researchers have so far described the entire spill production mechanism ”(p.204), and“ Hydrology is characterized by ease of forecasting runoff rate and volume. “A wide variety of prediction formulas devised” (p. 253), “There is no true hydrological model” (p. 255), and “The last and most stringent test in model validation is its application. The results should be applicable to other locations, unmeasured basins, or under different land use conditions ”(p. 261). Yes.

In addition, Engman et al. (1971) concluded on a scale issue related to interdisciplinary water resources research: It is possible to integrate various fields of hydrology, geology, meteorology, and water quality up to a scale of about 100acre (≒ 0.4km ² ). Although there are difficulties in working with models in each field at this scale, this scale is a limit that can extend the level of current expertise. Perhaps this scale gives an indication of the upper limit of the hillside hydrological model ”(p.273).

The basin area of the applicable limit (upper limit) of the hillside slope hydrological model devised in Non-Patent Document 1 is about 0.4 km ² . On the other hand, for example, the basin area of water stations set up in mountainous rivers in Hokkaido is a minimum of 37.0 km ² (quasi-tag 45 Otaki Water Station) to a maximum of 2930 km ² ( )) (Non-Patent Document 2). The basin area 0.4 km ² is much smaller than this range. Therefore, the hydrological model proposed in the new hydrology cannot be adopted as it is.

Patents by the present inventor in this technical field include Patent Document 1 and Patent Document 2.
(1) Difference between the present invention and Patent Document 1 In Patent Document 1, three variables Aeq, Heq, and Kv are taken as variables of the optimal regression function of the mountain river flow, and the order of each variable is set to second order. In Patent Document 1, the basin topographic variables are only Aeq and Heq, and Kv is a geological variable.
(2) Differences between the present invention and Patent Document 2 In Patent Document 2, three variables of Aeq, Heq, and Seq are used as variables of the optimal regression function of the mountain river flow. Aeq, Heq, and Seq are not variables that are uniquely calculated at the same time by a single common formula.

Patent No. 4528348 Patent No. 5189704

Kirkby: New hydrology, translator representative Mikio Hino, Asakura Shoten, 1983. Flow rate handbook (Hokkaido Trade and Industry Bureau jurisdiction), Ministry of Trade and Industry, Energy Agency; 1996 edition New Energy Foundation Hydropower Headquarters: Small and Medium Hydropower Guidebook, 5th edition, p.54-56, February 2002

  Based on the idea that if a new basin terrain index that incorporates the basin's three-dimensionality can be introduced, the flow rate estimation will be closer to the true flow rate than the flow rate estimation using CA that represents only the planar characteristics of the basin. Completed the invention.

In the present invention, since the three-dimensional landform originally has a three-dimensional form, the three-dimensional landform index should be represented by a combination of three independent indices. Therefore, the AEQ is newly set as the index value of the basin area. Introduce a combination of three indicators, HEQ as the indicator value and WEQ as the reference value of the basin depth horizontal length. AEQ, HEQ, and WEQ are indicators that are uniquely determined in the basin. AEQ, HEQ, WEQ and the product WAPsum of these three indices are adopted as variables of regression function for watershed discharge estimation.
Specifically, the present invention comprises the following.

(Claim 1)
A method of calculating a regression function for estimating an annual average discharge in a mountainous river basin using a computer system, the method of calculating the regression function,
Altitude area data (aj), which is the slope area of the mountainous area for each elevation zone (j) in the gauging basin, and elevation data by elevation zone (Hcj), which is the average elevation data for each elevation zone (j), Storing the depth length (wj) of the altitude zone (j) obtained by dividing the horizontal projected area of the altitude zone (j) by the average length of the elevation zone in the storage unit of the computer system;
Multiplying the altitude zone-specific area data (aj), elevation zone-specific elevation data (Hcj), and elevation zone depth (wj) for each elevation zone (j) stored in the storage unit, wj, aj , Hcj, the cumulative value of the product is WAPj.
Suppose that j = 0, 1, ..., jlast, and if WAP _{j is} the value of WAP _j in the final value jlast of _j , WAPsum
WAPsum is defined as WAPsum = AEA, HEQ, and WEQ by basin solid topography correlation area AEQ, basin solid topography correlation elevation HEQ, and basin solid topography correlation depth length WEQ.
(Wcj = Σwj, acj = Σaj)
WAP3j is calculated, and WEq, AEq, and Heq are calculated for wcj, acj, and Hcj where WPA3j's regressed value and WPAsum are approximately equal,
ζ = (AEq ・ HEq ・ WEq) / WAPsum
If the AEQ, HEQ, and WEQ values of points corresponding to WAPsum are regressed using the value of ζ,
Is calculated,
Measured value Qmean of annual average discharge in each watershed basin, the basin solid terrain correlation area (AEQ), the basin solid terrain correlation elevation (HEQ), and the basin solid depth (WEQ) of the corresponding watershed basin Using the regress function of each data and technical calculation software mathcad (registered trademark),
It calculates the regression function of the annual average discharge of mountain river basin that includes at least the basin three-dimensional terrain correlation area (AEQ), the basin three-dimensional terrain correlation elevation (HEQ), and the basin terrain depth (WEQ) in its variables. The calculation method of the regression function for the flow estimation of the mountainous river basin.

(Claim 2)
When the regress function is the following R function:
R = regress (M, Q, n) (8)
(Where M = augment (X, Y, Z), X = HEQ
Y = AEQ Z = WEQ);
The following interpolation function interp and regression value Qest _i are used to estimate the flow rate regression value at the basic data point obtained from the regression function for estimating the flow rate of mountainous rivers according to claim 1 or the flow rate at a planning point other than the basic data point. Is obtained by the regression function for estimating the flow of the mountainous river according to claim 1;
(Here, x, y, z are the same as X, Y, Z (HEQ, AEQ, WEQ))
The Qest is represented by the following polynomial with the number of variables being 3 and the order being 1.
(C0, c1, c2, and c3 are coefficients that change according to variables X, Y, and Z)
The annual mean flow Qmean regression function is calculated by replacing Q in the above formulas (8) and (8-1) with the estimated annual mean flow Qmean of each data point. A flow rate estimation method for estimating the flow rate.

(Claim 3)
A method for selecting a regression function for estimating a flow rate in a mountain river basin,
After calculating the regression function by the method according to claim 1 using the annual average flow rate measurement data at a group of water stations consisting of a number of water stations in a predetermined area as data (provided that m is at least (n + k)! / n! k! +2, where n is the number of independent variables and n is the order of the variables))
While extracting water station i0 (i0 = 1, 2,..., M) which is an arbitrary water station in the water station group as a verification point, the calculated regression function is applied. Calculate the estimated value of annual average flow rate at each water station in the water station group,
The estimated error rate of the estimated error that occurs between the estimated value and the measured value of the annual average flow at the water station is set as εin, and then the water station i0 is selected from the water station group consisting of the m stations. A regression function is newly calculated by the method according to claim 1, with the water station group consisting of the removed m-1 stations as a new data water station group.

By applying the calculated regression function, an estimated error rate εout between the estimated value of the annual average flow rate of the water station i0 and the measured value of the annual average flow rate of the water station i0 is calculated, and both estimated error rates εin and Let Δε be the difference from εout,
By extracting the water stations i0 as verification points one by one in order for i0 = 1, 2, ..., m, the difference Δε is calculated by the number m of water stations in the whole water station group. Calculate and set the verification error rate maxεout with the estimated error rate εout of the verification point that gives the maximum absolute value among these m differences Δε,
A method for selecting a regression function for estimating a flow rate in a mountainous river basin, wherein only a regression function whose verification error rate maxεout satisfies an acceptance criterion is output as a pass function.

(Claim 4)
The method of calculating the estimated value of the annual average discharge of the mountainous river basin using a computer system, and the method of calculating the estimated value of the annual average discharge of the mountainous river basin,
Area data (aj) by altitude zone, which is the slope area of the mountainous area for each altitude zone (j) in the basin where no flow measurement is performed, and by altitude zone, which is the average altitude data for each altitude zone (j) The storage unit of the computer system includes elevation data (Hcj) and a depth length (wj) of the elevation zone (j) obtained by dividing the horizontal projected area of the elevation zone (j) by the average length of the elevation zone Save to
Multiplying the altitude zone-specific area data (aj), elevation zone-specific elevation data (Hcj), and elevation zone depth (wj) for each elevation zone (j) stored in the storage unit, wj, aj , Hcj, the cumulative value of the product is WAPj.
Suppose that j = 0, 1, ..., jlast, and WAP _j value at the final value jlast of _j is WAPsum.
WAPsum is defined as WAPsum = AEQ / HEQ / WEQ by basin solid topography correlation area AEQ, basin solid topography correlation elevation HEQ and basin solid topography correlation depth length WEQ,
(Wcj = Σwj, acj = Σaj)
WAP3j is calculated as WEq, AEq, and HEq for wcj, acj, and Hcj where WPA3j's regressed value and WPAsum are approximately equal,
ζ = (AEq ・ HEq ・ WEq) / WAPsum
From this, the AEQ, HEQ, and WEQ values of the points corresponding to WAPsum are calculated by regression from the following formula,
Measured value Qmean of annual average discharge in each gauging basin, each basin 3D terrain correlation area (AEQ), basin 3D terrain correlation elevation (HEQ), basin 3D depth (WEQ) Applying the regression function calculated by the method of claim 1 or the pass function output by the method of claim 2 to calculate the estimated value of the annual average flow rate in the basin where the flow rate is not measured An annual average flow rate estimation method for mountainous river basins characterized by

(1) In the present invention, the regression function for estimating the annual average discharge in a mountainous river basin is represented by a single basin terrain index, which is originally a three-dimensional solid, and this WAPsum is then represented by a basin three-dimensional terrain. It is possible to estimate the mountain river flow more objectively and accurately by decomposing it unambiguously as a product of the three indicators of correlation area AEQ, correlation elevation HEQ, and correlation depth length WEQ, and using them as new variables. It becomes.
(2) Further, according to the method for selecting a regression function for estimating the flow rate in a mountainous river basin according to the present invention, the suitability of the regression function can be evaluated by calculating the verification error rate, so that the accuracy is higher. Estimates can be adopted.

(3) According to the method of calculating the estimated value of the annual average flow rate in the mountainous river basin according to the present invention, it is possible to estimate the mountainous river flow rate more objectively and accurately.
(4) Generally, the actual flow rate of a river flowing down a mountainous highland is larger than the estimated value calculated based on the measured flow rate at the downstream point by the conventional basin ratio calculation. Therefore, it has been found that development plans for mountainous highland rivers, which have been abandoned as having no economic so far, are often economically rich. Therefore, the present invention newly establishes a high-accuracy calculation method for the mountainous highland river flow.

(5) By applying the new calculation method, it helps to find excellent water resources development points that have been missed or abandoned. If the project to be developed is hydroelectric power generation, it can take part of the CO ₂ reduction plan, which is currently a common issue worldwide.

It is a functional block diagram of the flow volume calculation assistance system used for the flow volume estimation method of the mountainous river by embodiment of this invention. Figure (Fig. 2 (a)) showing the relationship between the basin area (horizontal area) surrounded by the contour line of the catchment basin and the ground surface area, and the plane area and slope area for each of the divided elevation zones (j) It is a figure (FIG.2 (b)) showing the relationship of these. It is a figure which shows the precipitation to an altitude zone. It is a figure which shows a center, Hidaka Mountains candidate basin district (shaded basin group). It is a figure which shows a western mountainous area candidate basin district (shaded basin group). It is a figure which shows a bill 59 Oku Biei water survey station and the Biei River upstream plan point.

Embodiments of the present invention will be described below.
FIG. 1 is a functional block diagram of a system (flow rate calculation support system) used in a mountainous river flow rate estimation method according to the present embodiment. Here, the flow rate calculation support system 1 includes an input unit 30 for inputting data such as a keyboard and an external storage device, a storage unit 20 for storing input data and data for various calculations, and input data. And an output processing unit 10 for executing river flow rate calculation processing, and an output unit 40 such as a printer or a display for outputting calculation results and plots to be described later. The flow rate calculation support system 1 can be realized by a general-purpose computer such as a personal computer.

  The calculation processing unit 10 of the flow rate calculation support system 1 includes input / output processing means 11 for executing input / output processing between the input unit 30 and the output unit 40, and basic data such as topographical features for obtaining a regression function. Basic data input means 12 to be input and stored in the basic data storage area 21 of the storage unit 20, regression function calculation support means 13 to support the calculation of the regression function using the input basic data, topographical model data of the calculation target point , The target data input means 14 for storing in the calculation target point data storage area 23 of the storage unit 20, the estimated flow rate calculation means 15 for calculating the estimated flow rate using the input calculation target point data and the regression function, and And a verification error rate calculating means 16 for calculating a verification error rate of the regression function to be applied. Each means 11-16 is realizable by a program as a function of CPU.

  Hereinafter, a method for estimating the flow rate of a mountainous river using the flow rate calculation support system 1 will be described.

<Basic data input processing>
First, the average elevation data Hc _j for each elevation zone j of the mountainous basin, the area data a _j for each elevation zone, the average length lj, and the horizontal projection area A _j for the elevation zone are obtained from the input unit 30 of the flow rate calculation support system 1. entering a depth length wj altitude band obtained by dividing the average length l _j. The input data is input and processed by the input / output processing unit 11 of the arithmetic processing unit 10 and stored in the basic data storage area 21 of the storage unit 20 via the basic data input unit 12.

  Next, using this basic data, the regression function calculation support means 13 calculates a watershed three-dimensional landform characteristic value. Hereinafter, the procedure of this calculation process will be described with reference to the drawings.

<Watershed three-dimensional landform characteristic value calculation processing>
2． A new index representing watershed characteristics and its calculation
2.1 Three-dimensional solid basin topographic characteristics WAPsum
The basin solid terrain is represented by a single terrain characteristic value WAPsum. The outline of WAPsum is as follows.
The basin area CA of a certain point in the river, for example, a water survey point, is surrounded by a continuous closed curve that starts from this point and connects the ridges that extend from both sides to the highest peak. Is defined as the vertical projected area of the area (basin) on the horizontal plane. All the river flow generated in this basin flows down to the above-mentioned fixed point without flowing into other basins. The closed curve that divides the basin is a three-dimensional space curve, and the surface area (hereinafter referred to as the actual basin area) of the three-dimensional curved surface surrounded by the space curve is different from the projected area on the horizontal plane (that is, the basin area). Therefore, the basin area measured on the topographic map is not equal to the actual basin area composed of solid slopes.

In the topographic map, several contour lines can be seen between the lowest elevation of the basin and the highest elevation. The altitude zone j is a basin portion surrounded by two contour lines among these contour lines. However, if there are further contour lines between these two contour lines, the average value of the lengths of all the contour lines is l _j . Furthermore, the actual surface area (slope area) between these contour lines is defined as the actual area a _j of the altitude zone j (Fig. 2). If ac is the sum of all the altitude zones of the actual area a _j , ac represents the actual basin area of the basin and has a value different from the plane basin area CA.

The basin shape that normally exists is a tilted colander-shaped shape surrounded by a closed curve. The actual area a _j of the basin having such a shape is small because the contour line length of the lowest elevation zone is small (because the contour line length that passes closest to the water survey point is short), the area is small, As the elevation rises, the contour line length of the elevation zone becomes longer, so the elevation zone area gradually increases. The area reaches the maximum value at a certain elevation zone, and when the elevation rises further, the elevation starts to decrease and reaches zero at the highest elevation point. It becomes. Therefore, if plotting the altitude zone average elevation Hc _j on the horizontal axis and the actual area a _j by elevation zone on the vertical axis, the curve represented by a _j is a mountain-shaped curve having one peak, and in some cases, a plurality of peaks with a maximum peak. It becomes a mountain-shaped curve with a small peak. On the other hand, naturally, the value of the altitude Hc _j of the altitude zone j is increasing as the altitude increases. a _j and Hc _j can be calculated from commercially available 1 / 50,000 topographic maps.

Now it is possible to determine the depth length w _j of this altitude band by dividing the horizontal projected area A _j of each elevation band j at an average length l _j of the altitude band.

l _ja and l _jb are the upper side length and the lower side length of the altitude zone j, respectively. The unit of A _j is km ² , l _j, l _ja , l _jb is km, and w _j is m.
Here, the cumulative value of the product of w _j , a _j , and Hc _j is set as WAP _j .
Suppose that j = 0, 1, ..., jlast, and WAP _j in the final value jlast of _j is WAPsum.
WAPsum = WAP _jlast
WAPsum is a topographic index value that represents the total potential of this basin.
And take the product of ac _j and Hc _j
Zc _j = ac _j・ Hc _j
, Zc _j indicates a kind of topographic index that the altitude zone j has.

2.2 Rationale for WAPsum setting Check the rationale for WAPsum setting below.
The total precipitation R _j to the altitude zone j with the projected area A _j on the horizontal plane is expressed as r _j per unit area of the horizontal plane.
R _j = r _j・ Aj
Is represented by (Figure 3).
Many altitude zones j are inclined with respect to the horizontal plane. If this inclination angle is θ _{j and the} actual slope area is a _j , a _j is larger than A _j
(Fig. 3). Actual area a _j altitude band despite the large consisting its horizontal area A _j, the total precipitation to this area a _j does not change remains formula R _j = r _j · Aj. This is because the precipitation r _j is measured as a value per unit horizontal area, and the horizontal area of the altitude zone with the actual area a _j is A _j (FIG. 3). The precipitation r _j changes according to the altitude H _j . Thus r _j is a function with H _j .
So now
r _j = c ₀ + c ₁・ H _j
Then, R _j is
R _j = (c ₀ + c ₁・ H _j ) ・ A _j
It becomes. Here, c ₀ and c ₁ are constants. Therefore, precipitation r _j and R _j can be expressed as a function of topographic characteristic values H _j and A _j . Substituting formula _{R j = (c 0 + c} 1 · H j) · to A _j of A _j obtained from equation (16) a _j cosθ _j,
R _j = (c ₀ + c ₁・ H _j ) ・ a _j・ cosθ _j
It becomes. R _j in the above formula does not include precipitation r _j .

Now, the specific gravity of water due to precipitation on the ground surface is 1, so if we put the mass of R _j as M _j
M _j = R _j
Thus, the mass M _j is a load applied to the altitude zone j. When this is the case, M _j is
M _j・ H _j = R _j・ H _j
Has the potential
Furthermore, from equation (15), WAPsum = WAP _jlast
Since w _j , a _j , and Hc are all values calculated based on the measured values on the topographic map, the WAPsum value calculated by Equation (17) for the given target basin is an eigenvalue of the basin. As a result, the basin total potential value WAPsum as a function of the terrain features w _j , a _{j, and} Hc _j without the precipitation r _j or R _j could be expressed as the basin eigenvalue.

2.3
Basin Topographic Values lj and WAPsum Calculation Formulas The following formulas are used to calculate the basin topographic values used in each section.
Calculation formulas of AEQ, HEQ, WEQ and AEq, HEq, WEq in the above formula will be described later. In the following, in the above calculation formula, the matters to be noted in calculating the length (average length) and width of each elevation zone are described.

It is assumed that the altitude zone j includes n contour lines including the contour lines at both ends. The average length of this altitude zone is the average length of these n contour lines. That is,
n is a contour line with 50m intervals [Revision 12 A] is 6 (Revision 12 B) with a contour line of 3,20m, but the lowest elevation zone (including the water point) and the highest elevation zone [ It may be 3 or less or 6 or less.
Therefore, the main purpose of calculating the altitude zone length is to calculate the width of the altitude zone. If the width of the altitude zone is calculated using the value of l _j when n = 3 in the case of 50m interval contour lines and the value of l _j when n = 6 in the case of 20m interval contour lines, the purpose is Achieved. However, this method cannot be applied when the number of contour lines contained in the altitude zone is one or two.

The main purpose is to obtain each elevation width w _j with respect to the horizontal projected area of each elevation zone (measured separately as A _j ). Therefore, if there are only two contour lines in each elevation, the area of that elevation is
Divide by to find the average length of the altitude zone. In addition, if l _j contains only one contour line, the average length is obtained by dividing the area of the altitude zone by l ₁ . Further, the contour line length is measured by measuring the contour line length inside the basin boundary line. Therefore, although the length of the contour line connecting the basin boundary lines running on both sides is within the target basin, the circumference of the isolated contour line away from the basin boundary line is the distance between the isolated contour lines in the measurement of the target contour length l _k . There is no need to add circumferences. However, in the measurement of the basin area surrounded by the contour lines according to each elevation, it is necessary to consider the area surrounded by these isolated contour lines.

2.4
Calculation of basin topographic values for an example basin The following is an example of the WAPsum derived in the above and the specific calculation process for the related formulas, using the bill 59 Okumi Mine Gauge basin as an example.
Topographic map: 1/25000 Tokachidake, Shirokane Onsen, Mt. Tomlausi, Fujiyama The highest point in the basin: 2077m (Tokachidake), the lowest point: 580m (estimated water measuring point)
The results of measuring the basin area by contour line on the topographic map are shown in the following table. The interval between contour lines was based on every 100 m. The symbols used in the table represent the following values:
i: contour line counter, HC _i : elevation of contour line i (m), CA _i : basin area surrounded by contour line i (km ² ),
j: Elevation zone counter, HC _j : Elevation of contour line j (m), A _j : Horizontal bottom area of elevation zone j (km ² )
here
A _j = CA _{i + 1} -CA _i
A specific calculation program for various terrain characteristic values in the main basin is shown in Calculation Example 1-Calculation of the terrain characteristic values in the stag 59 Oku-Mine Water Station basin (Amendment 12). This program is “MathSoftEngineering &
Education, Inc .: mathcad13, September 2005 ”. In the calculation formula in the previous section, the measured values of altitude zone l _k are shown in Table 2, and the average of these l _k values is summarized. The calculated values of the value l _j are shown in the following Table 3. The value of l _j becomes part of the subsequent basin terrain characteristic value calculation, and various values calculated by applying the calculation formula in the previous section 2.3 together with this l _j. Together with it, it forms the whole of the basin values of the Okubimi Water Station (see Tables 4 and 2.4.1, 2.4.2).

2.4.1 Correlation area AEQ, correlation elevation HEQ, correlation depth length WEQ
As seen in the previous table and Calculation Example 1, WAPsum in the main basin = 26676019.740
It is calculated as km ⁴ and uniquely represents the three-dimensional solid property of the Okumi Pass basin. Therefore, the WAPsum value is an index that represents the basin characteristics more strictly than the basin area CA that shows only the plane characteristics of the basin conventionally used. The actual watershed is a three-dimensional solid. A combination of at least three mutually independent indicators is necessary to show this three-dimensional characteristic. Therefore, it is considered that an estimation value closer to true can be obtained by introducing an index value in which each of the three WAPsums is uniquely determined in place of only one WAPsum value for estimating the basin flow rate. However, the product of these three index values must be equal to WAPsum. Therefore, the following WAPsum is uniquely decomposed into products of three AEQs, HEQs, and WEQs.

Now for WAP _{j in} equation (4)
And
As can be seen by comparing the right side of equation (15) with the right side of equation (20), the former W _j is changed to Wc _j in the latter, and the former a _j is changed to ac _j in the latter, but Hc _j There is no change. Therefore, it can be seen that WAPsum = 26676019.7 which is the final value of WAP _j in Table 4 is between j = 2 and J = 3 in the WAP3 _j column. This position is the wc value at which WAPsum is approximately equal to the value obtained by regressing between WAP3 ₂ and WAP3 ₃ between j = 2 and j = 3.

Therefore, when this value is calculated for wc _j , WEq = 1479.3 (Attached program page 41)
Similarly for ac _j AEq = 15.7 (Attached program page 40)
For Hc _j , Heq = 829.8 (Attached program page 39)
Therefore, AEq.HEq.Weq = 19287388.5.
Therefore, the value of WAPsum is a value between WAP ₂ (j = 2) and WAP ₃ (J = 3). Therefore ζ = (AEq ・ HEq ・ WEq) / WAPsum
Ζ = (19287388.5 / 26676019.7 = 0.723
It becomes. If the value of ζ is used to regress the AEQ, HEQ, and WEQ values at the point corresponding to WAPsum
It becomes. Substituting the above AEq, HEq, Weq and ζ into this equation
AEQ = 17.506 HEQ = 924.6
WEQ = 1648.1
As required. The product of these three values is AEQ.HEQ.WEQ = 26,676,225.0.
The value of this product is almost the same as WAPsum = 26,676,019.7 obtained earlier. Therefore, as a conclusion, the final total value of wapj, that is, WAPsum, was uniquely decomposed into 3 of AEQ, HEQ, and WEQ.
WAPsum = AEQ ・ HEQ ・ WEQ

2.4.2 Calculation Example 1 Calculation of Topographic Characteristic Values for the Basin 59 Okumien Water Station Basin The following shows the calculation program for each of the above formulas, taking the Tag 59 Okumia Water Station Basin as an example:

2.4.3 Summary of topographic characteristics of Hidakayama basin group in the central west The method for calculating the characteristics of the Oku-Mine gauging basin in the previous section is applied to various basins in Hokkaido.
In this section, out of all basin groups in Hokkaido, 14-12 basin groups belonging to the Chuo Mountains, Nishikata Mountains and Hidaka Mountains are selected as trial target basin groups (see Figures 4, 5 and Table 6). .
The main reason for setting these basin groups as trial target groups is that the basin area is approximately 90 km ² or less in order to enable the estimation of the basin area below the basin area of the existing water station which is one of the objects of the present invention. It is in having chosen as a condition.
The calculation method of these basin specifications is the same as the calculation method of the Okumi irrigation watershed basin described above, so the description is omitted, and only the calculation results of the 12C gauging basin group are shown in Table 7:
○ indicates that the area is included, and X indicates that the area is not included.

3． Calculation of annual average discharge The purpose of this chapter is to select an optimal regression function with some or all of the basin indicators obtained in the previous chapter as variables. Prior to the theoretical development for this purpose, a flow rate estimation method based on a basin ratio which has been conventionally used will be described for comparison.
3.1 Target point flow rate calculation method based on the conventional method The basin ratio method is the ratio of the basin area of the target point to be considered and the basin area of the basin ratio calculation source station, that is, the basin ratio is a proportional constant. This is a proportional calculation method that estimates the flow rate at the target point by multiplying the measured flow rate by this basin ratio. Therefore, the basin ratio method regards the index of the three-dimensional solid basin as the ratio of the basin area on the two-dimensional horizontal projection plane, and does not represent the three-dimensionality of the natural basin.
In addition, in the watershed ratio method, the source water station is limited to one water station, so if the source water station changes, the estimated flow rate at the target point will also change. Therefore, the key point of the basin ratio method is to select which station is the optimal source station from among the multiple source stations.

According to the Small and Medium Hydropower Guidebook (Non-Patent Document 3), it is stipulated that an existing water station in the vicinity of the target point and having a basin ratio in the range of 0.5 to 1.5 should be selected as the source water station. However, as a matter of fact, this rule can be applied, and there are only a few sites that can specify the calculation source gauging station for the flow rate of the small basin plan target river in the upper mountainous river, and there are many planning sites that cannot be specified. For these points, it is stipulated that a new water survey station will be newly established in the vicinity and water measurement will be started for several years. For this reason, the cost and time required are large.
Conversely, there are cases where there are multiple watersheds adjacent to the target basin, all of which have existing water stations that are within the specified basin ratio. However, the estimated flow rate at the target point calculated from the basin ratio differs greatly from each of these multiple calculation source gauging stations, and there are cases in which it is difficult to determine which one is the calculation source gauging station for the target point.

Therefore, in the case of the basin ratio method, it is necessary to investigate the topography, geography, geology, weather, vegetation status, etc. of the target point basin and the candidate calculation source gauging basin, and specify the calculation source gauging station. Requires years of experience and intuition, and there are no established rules. Therefore, the basin ratio calculation method is an incomplete method with no universal applicability as a target point flow rate estimation method. In order to eliminate this imperfection, it is necessary to introduce a regression function with the basin indicators newly calculated in the previous chapter as variables.
The flow rate estimation method based on the catchment ratio is as follows:
The ratio of the basin area of the target point t (basin area CAt) to the basin area of the source water station i (basin area CA _i ), that is, the basin ratio CAratio is
Therefore, if the measured flow rate at source water station i is Q _i , the flow rate Q _t at the target point _t is calculated by the following formula:
Qt: = CAratio ・ Qi

3.2 Calculation of annual average flow rate by multivariate regression function
3.2.1 Calculation of multivariate regression function The calculation method of the flow regression function employed in the present invention is as follows. The following formulas show regression functions using the three primary variables of HEQ, AEQ, and WEQ for simplification of expression. When the variable number includes variables other than these three variables, and when the order is second or higher Can be applied by appropriately modifying the variable terms in the following equations.
When the number of variables is other than three, the following two cases are considered: (1) When the variables are 1, 2 and (2) When the variables are 4 or more.
(1) When there are one or two variables x, y, and z in formula (5-1) below are only x (when the number of variables is one)
x, y, x is x, y (when there are two variables)
(2) When the number of variables is 4 or more x, y, and z in the following formula (5-1) change as x, y, z, u. In this case, it is possible to adopt variables other than the terrain variables, for example, geographic variables, geological variables,..., But in the present invention, when the number of variables is four or more, it is excluded.
Note that the degree is expressed as follows in 3.2.2 Equivalent Polynomial: deg is the degree, deg = 1 when the order is first order, deg = 2 when it is second order, etc. To do.

The calculation algorithm of the trivariate regression function when the variable order is n = 1 and the objective variable is the annual mean flow Qmean is a commercially available software mathcad (MathSoftEngineering & Education, Inc .: mathcad11 User's Guide, April 2003, p365) Is given by the following equations. Here Qmean is the observed value of annual average flow at each water station that is the data point. Let M be the matrix of basin specification values;
M = augment (X, Y, Z)
here
X = HEQ, Y = AEQ, Z = WEQ
Next
R = regress (M, Q, n)
far. Here, regress is a built-in function of mathcad and means a regression function. This equation includes the flow variable Q other than the basin specification matrix M, which is basic data, and its order n. Therefore, when Q and n change, the value of R changes even if the basic data M is constant.
Next, an interpolation function interp and a regression value Qest _i for estimating the flow rate regression value at the basic data point or the flow rate at the planning point other than the basic data point by applying this function R are given by the following equations.
The regression function of the annual mean flow Qmean can be obtained by substituting Qmean for the equation R = regress (M, Q, n) and Q in the above equation (23-1). x, y, z are the same basic data as X, Y, Z (HEQ, AEQ, WEQ).
The next section shows an application example of these trivariate A1 regression functions in the central west Hidaka Mountains gauging station group.

3.2.2 Equivalent polynomial:
The built-in functions augment, regress, and interp included in the above algorithm are not common, so if Qest is expressed as a normal polynomial p (X, Y, Z), the following equation is obtained (MathSoftEngineering &
Education, Inc .: mathcad11 User's Guide, April 2003, p.310).
In this case, since the number of variables nvars = 3 and the degree of variables deg = 1, the term number Nterms of the polynomial p (x, y, z) is
It becomes 4 terms by. The polynomial p is given by
X, y, z in this formula are given values with the same basic data as HEQ, AEQ, WEQ of X, Y, Z and (23-2) of the previous formula M = augment (X, Y, Z), Only the values of c ₀ , c _1, c ₂ , c ₃ change according to the objective variable. The fact that the regression value by equation (23-2) and the calculated value by polynomial (25) match has been confirmed for many example points. However, if the variable order is large, the number of significant digits of the coefficient c must be 12 or more.

3.2.3 Relationship between the number of data required for regression function calculation, the number of variables, and the order In the case of the regress function that is a regression function, the number m of input data values is
Must be satisfied (Non-Patent Document 3). Here, k is the number of independent variables, n is the order of the variables, and m is the number of data. K and n in this equation correspond to nvar and deg in equation (24), respectively, and the value on the right side corresponds to Nterms in equation (24). Therefore, if the value on the right side of Equation (26) is m ′, m ′ indicates the number of data necessary to find the solution of the k-ary n-ary simultaneous equations. Accordingly, in the case of the regression function formula, the number of data m required must be larger than the number of data required to solve the simultaneous equations, so the following formula is obtained.
Furthermore, the required number of data Nterms2 when applying the verification error rate (discussed in this paper) that is separately considered is as follows.
The following table shows the calculated value of Nterms2, which is the number of data required to solve the k-ary n-order regression function including verification regression.

  In general, when the number of variables is constant, the regression accuracy of the regression function itself increases as the order of the variable increases. On the other hand, an arbitrary design point with a basin specification that is different from the basin specification used for calculating the regression function. If a regression function with higher-order variables is applied to the flow rate estimation (even if the specification value at the arbitrary point is within the change range of the specification used as the data for calculating the regression function), May appear. On the other hand, increasing the number of meaningful and effective variables is also effective in improving the regression accuracy. For example, if the number of variables is 2 from the following table, the minimum number of data required to solve the binary and cubic simultaneous regression function is 12, whereas if the number of variables is 3, the ternary quadratic simultaneous system The minimum number of data required to solve the regression function is also 12. Therefore, it is necessary to consider which of the two-dimensional cubic function and the three-dimensional quadratic function should be adopted. Furthermore, even if the number of variables increases to 9 elements, the minimum required number of data in the case of 9-element linear simultaneous regression function remains 12 and does not change. Therefore, in the selection of the optimal regression function, it is necessary to fully examine the adopted variables, their combinations, and the order of the variables based on the number of water measurement data available within the target mountainous gauging station group.

3.2.4 Calculation of regression error rate Statistics often focus on the difference between individual measurements and the average of all measurements, but this is a calculation method used when the true value of all measurements is unknown. Therefore, the average value and the true value are different. The difference between the measured value and the average value is called deviation.
Since the object of examination in the present invention is the measured flow rate at each water station and the return flow rate with respect to this measured flow rate, the difference is the difference between the return flow rate and the measured flow rate at each water station. This difference is called an error. The difference between the average value of the return flow at all stations and the flow rate return at each station is not considered as an error.
In the following, the definition formulas of specifications relating to errors used in the present invention are shown.

Error of measured value Q _i of regression value Qest _{i in} equation (23-2), Calculation formulas for error rate, average error rate, maximum error rate, variance, standard error rate:
error
erri = Qesti-Qi
Error rate:
Average error rate:
Maximum error rate:
maxε = Maximum error rate | ε _i |
dispersion:
Here, Ndata is the number of water stations as data, and variance var (ε) is the difference between the error rate ε _{i and} the average value εmean.
Standard error rate:
Represented by
Since the standard error rate sterr (ε) is an average value of the variation of the regression error with respect to the measured value of each data point, it is a basic index for checking the suitability of the assumed regression function. Further, the maximum error rate maxε is an index for judging whether or not the assumed water station group includes water stations that are not appropriate to be included in the water station group.

3.3 Example of calculation of annual average basin discharge In this section, the regression function of the basin discharge is calculated by using the topographic parameters of the actual basin introduced in Section 2.4.
3.3.1 Calculation Example 1 Central West Hidaka 12C Water Station Group The method for calculating the regression function of the basin discharge is as described in the previous section 3.2. Applying this calculation method, the flow regression of 14D group, 13A group, 13B group and 12C group in the central west Hidaka Mountains was performed. As a result, the summary table of the regression results of the 12C basin group obtained as the optimal basin group is shown in the following Table 9 (the attachment of the calculation process of other basin groups is omitted).
According to this result, the case of the univariate WAPsum 9th-order equation and the case of the trivariate AEQ, HEQ, and WEQ 2nd-order equations are acceptable and all others are unacceptable.
Therefore, the 9th order equation in the case of univariate is considered an abnormal order (according to Mathcad, the 4th order or less is normal and the 6th order or more is rarely used). The optimal regression variable combination is a trivariate AEQ, HEQ, or WEQ. It becomes a quadratic equation.

3.4 Applicable conditions of the flow regression function The following restrictions exist when applying the regression function obtained above to the estimation of the basin flow without measurement:
That is, the regression function can be regressed only on variable values within the range of the upper and lower limits of the variable given as its characteristic (ie, the regression function is not suitable for extrapolation). Therefore, the regression function applied to the flow rate estimation of a new planned point where the flow rate is not measured must have the variable value of the planned point within the upper and lower limits of the variable.

When selecting the regression function of the river flow rate in the mountain gauging station group selected for examination, the standard error rate and the maximum error rate defined in the previous section are used as a guide for determining whether the candidate regression function is appropriate or inappropriate. The limit range is defined as follows.
First class standard error rate: sterr <2.5% Maximum error rate: maxε <5%
Level 2 standard error rate: sterr <5% Maximum error rate: maxε <10%
Class 3 standard error rate: sterr <10% Maximum error rate: maxε <20%
Each class is subject to the simultaneous establishment of the standard value for the standard error rate and the standard value for the maximum error rate.
Regression functions with errors that exceed these tolerance limits cannot be adopted. In the case of a regression function with an error exceeding the allowable limit, it is necessary to recalculate the regression function by changing either the number of initially assumed data (number of water stations) and the number of variables (number of variables) or both. is there. Here, the change in the number of data and the change in the variable number are interrelated. In general, it is desirable that the applicable range of the regression function is as wide as possible. Therefore, if the number of data is increased, the number of variables can be increased accordingly, and as a result, the regression error rate can be reduced. However, if the increase in the number of data cannot be expected even if the number of data is increased, the increase in the number of data may conversely increase the regression error rate.

Four. Estimating the flow rate at a new planned site
4.1 Calculation of Watershed Characteristic Values for the Biei River Upstream AAA Project Three sites were planned as candidates for the new plan site upstream of the Tag 59 Okubibi Water Station. The calculation results of the basin characteristic value at the Biei River upstream planning point, which is one of the points, are as shown in the following table. In addition, in FIG. 6, a basin diagram of the bill 59 Okubi water survey station [left side section] and the Biei River upstream plan point (right side section) is shown.
The method for calculating this characteristic value is the same as the method for calculating the watershed characteristic value of Okubimine Water Station in section 2.4 above.

Summary of topographical calculation results Calculation program accommodation source and program name:
/ Hydraulic / basin terrain / basin terrain multi-element specifications / central mountains / basin terrain multi-element regression by plan point /
“BieiA New Bieigawa River Basin Topographical Plural Regression AAA Proposal. Xmcd”
bieiA New Biei River plan AAA plan basin specifications calculation plan water level: 750m
WAPsum = 12972722.05695
HEq = 982.73719
AEq = 8.9491825
WEq = 1068.28566
AEq ・ HEq ・ WEq = 9395245.1
ζ = (AEq ・ HEq ・ WEq) / WAPsum
ζ = 0.724231
AEQ = 9.965315 HEQ = 1094.321818 WEQ = 1189.583754
AEQ ・ HEQ ・ WEQ = 12972722.05695
Conclusion: WAPj's maximum sum WAPsum was uniquely resolved to be equal to the product of the three values of AEQ, HEQ, and WEQ.

4.2 Calculation of the Regression Function for Estimating the Flow of the Biei River Upstream AAA Project The Biei River upstream AAA plan site is within the coverage of the Chuo West Hidaka 12C Basin Group, which is the optimal basin group estimated in the previous section 3.3. The regression function applied to the AAA plan site is a quadratic expression of trivariate AEQ, HEQ, and WEQ determined as optimal in the study of the Biei River upstream basin group.
The calculation program for each of the above formulas for this basin is shown below:

4.3 Flow Calculation at the Biei River Upstream AAA Planned Point In this section, the regression function based on the quadratic formula of AEQ, HEQ, and WEQ selected in the previous section 4.2 is applied to the Biei River planned AAA point to estimate the flow rate:
Comparison with the measured flow rate at the downstream Okubimi gauging station:
Measured value of annual average flow rate at Okubimi Water Station: Qmeant59 = 4.84
cub.m / s
Planned basin area: CAbieiAAA = 39.1sq.km
Okumi Passage basin area Cat59 = 69.95sq.km
The estimated flow rate at the planned location when using the basin area ratio is

4.81 * 39.1 / 69.95 = 2.70542
Therefore, the calculated flow rate by applying the regression function is compared to the estimated flow rate by the basin ratio.
Double the size.

Five. Universality of the proposed regression function The above results show the usefulness of the multivariate regression function according to the present invention, and overlooked that the current flow condition in the upstream area is good. It has the effect of promoting development planning in mountain rivers that have been neglected as being economically rare.
This leads to hydropower development in mountain rivers and contributes to the promotion of the creation of clean energy that generates no CO2.
The flow rate regression function calculation proposed in the present invention requires the terrain specifications of the basin and the flow rate measurement data of the existing water station as basic data. Of these, the terrain specifications of the basin can be read in the 200,000, 50,000 and 25,000 topographic maps published by the Geospatial Information Authority of Japan. These topographic maps are generally available for purchase.

The flow rate data is described in the flow rate manual edited by the Ministry of International Trade and Industry and Agency for Natural Resources and Energy. This handbook is a record of surveys of water stations under the direct control of the Ministry of International Trade and Industry under Article 101 of the Electricity Business Act and designated water stations under Article 102 of the Act. The flow manual is not available for general sale, but it is publicly available and can be freely viewed at the National Diet Library (Class Library 517.3 Tu7835, etc.).
Furthermore, the personal computer software mathcad frequently used in the present invention is widely used in Western countries and is commercially available software that can be generally purchased in Japan. Therefore, the calculation of the flow rate regression function is not limited to specific data or software owners, and can generally be performed.
Therefore, the mountain river flow rate calculation by the multivariate regression function proposed in the present invention has universality and generality.

6． Conclusion As a method for estimating the flow rate of a small basin upstream of a mountain river, instead of the conventional method of estimating the basin area ratio (abbreviated as basin ratio) from the measured flow rate at an existing gauging station in the downstream or nearby river, We first examined the representation of the basin topography index, which is a three-dimensional solid, by only one index WAPsum, and then expressed this WAPsum as three basin three-dimensional landform correlation area Aeq, correlative elevation HEQ, and correlative depth length WEQ. A new method is introduced to apply a regression function of annual average flow rate that is uniquely decomposed as a product of

  The basin area CA conventionally used as an index representing the size of the basin is an index measured on the topographic map as a planar area of the region surrounded by the target basin boundary. Therefore, the basin ratio is a single index that is calculated based only on the planar characteristics of the basin, whereas the combination of the above new variables has three basic terrain variables since the basin terrain is essentially a three-dimensional solid terrain. The basin conditions are captured from a more complete perspective including the combination of Therefore, the regressive flow rate by this new variable regression function can estimate the flow rate closer to the true value than the estimated flow rate by the basin ratio.

As an example, the regression functions of 12C gauging stations in central, west, and Hidaka Mountains in Hokkaido are compared and selected. As a result of applying it to the estimation of the flow rate at the planned location, an estimated value of 4.5 cubic meters per second per year was obtained. This is equivalent to 1.7 times the basin ratio estimated value from the existing water station downstream by the conventional method, which is 2.7 cubic meters per second. In other words, it shows the possibility that the planned point where the development plan has been postponed due to the low flow rate will rise, and by applying this new method, there is no water station in the nearby river, or Of the rivers with planning points that are far from the downstream, it is possible to find rivers with high development prospects and new planning points.

In particular, after the accident at the Fukushima nuclear power plant, it is discussed whether or not the whole nuclear power plant will continue in Japan, and the study of introducing a pollution-free power plant that should replace nuclear power generation is an urgent issue.
However, thermal power generation that has the ability to replace nuclear power is limited in capacity expansion due to the large amount of CO ₂ generated, so it cannot be said that it has sufficient replacement capacity. Furthermore, power resources such as wind power, solar heat, and geothermal power are limited in their capacity and stability, so they do not have sufficient nuclear replacement capacity.
Small hydropower resources in the upper mountainous areas that have not been taken up as considerations for these problems can contribute to the solution by cooperating with the wind power, solar heat, geothermal power generation and the like. Furthermore, the flow estimation method based on the regression function proposed in the present invention is a general method, and is not limited to the planned basin of the above application example, but is developed for water resources such as hydropower, industrial water, and agricultural water in general river basins. It can also be applied to flow estimation for planning.

  By using the new combination index, in the case of the conventional basin ratio method, the costs and water surveys for a considerable number of new gauging stations that were necessary for grasping the flow rate of the new planned site without applicable gauging gauging stations. Not only is the period unnecessary, but the effect of promoting the prospecting of promising water resources in the upper mountainous area, which has been overlooked by the basin ratio method that has been adopted in the past, is significant. This means the discovery of new water resources in the upper mountainous areas.

(Claim 1)
Using a computer system, the regression function for estimating the average annual rate of mountainous river basin a resulting Ru method, Ru give regression function method,
Altitude area data (aj), which is the slope area of the mountainous area for each elevation zone (j) in the gauging basin, and elevation data by elevation zone (Hcj), which is the average elevation data for each elevation zone (j), Storing the depth length (wj) of the altitude zone (j) obtained by dividing the horizontal projected area of the altitude zone (j) by the average length of the elevation zone in the storage unit of the computer system;
Multiplying the altitude zone-specific area data (aj), elevation zone-specific elevation data (Hcj), and elevation zone depth (wj) for each elevation zone (j) stored in the storage unit, wj, aj , Hcj, the cumulative value of the product is WAPj.
Suppose that j = 0, 1, ..., jlast, and if WAP _{j is} the value of WAP _j in the final value jlast of _j , WAPsum
on the other hand
(Wcj = Σwj, acj = Σaj)
Wc3j is calculated as wcj, acj and Hcj where WAP sum is equal to the WAP 3j regression value, and the obtained wcj, acj and Hcj are WEq, AEq and HEq respectively.
In order to represent the basin characteristics in three dimensions, we introduced the basin three-dimensional terrain correlation depth length WEQ, the basin three-dimensional terrain correlation area AEQ, and the basin three-dimensional terrain correlation elevation HEQ,
WAPsum is defined as WAPsum = AEQ, HEQ, WEQ by basin solid terrain correlation depth length WEQ, basin solid terrain correlation area AEQ, basin solid terrain correlation elevation HEQ,
ζ = (AEq · HEq · WEq ) / WAPsum far transfected, AEQ · HEQ · WEQ = ( AEq · HEq · WEq) / ζ next, the point corresponding to WAPsum using the value of the zeta AEQ, HEQ, WEQ From the following equation ,
Measured value Qmean of annual average discharge in each watershed basin, the basin solid terrain correlation area (AEQ), the basin solid terrain correlation elevation (HEQ), and the basin solid depth (WEQ) of the corresponding watershed basin Using the regress function of each data and technical calculation software mathcad (registered trademark),
Estimate the annual average discharge of a mountain river basin that includes at least the basin three-dimensional terrain correlation area (AEQ), the basin three-dimensional terrain correlation elevation (HEQ), and the basin terrain depth (WEQ) in the regress function. following regress characterized Rukoto give functions, method of obtaining the regression function for the flow rate estimation of mountainous river basin for.
regress function: R = regress (M, Q, n)
(Here, M is the basic data, M = augment (X, Y, Z), X = HEQ Y = AEQ Z = WEQ, Q is the flow rate, and n is the order of the variable constituting the regress regression function)

(Claim 2)
The following interpolating function interp and the regression value Qesti are obtained by the regress function for estimating the flow of mountainous rivers according to claim 1, and the flow for estimating the flow at the basic data point or the flow at the planning point other than the basic data point. An estimation method, wherein the flow rate estimation method ;
(Here, x, y, z are the same as X, Y, Z (HEQ, AEQ, WEQ))
The Qest is represented by the following polynomial with the number of variables being 3 and the order being 1.
(C0, c1, c2, and c3 are coefficients that change according to variables X, Y, and Z)
The regression function of annual average flow Qmean formula R = regress (M, Q, n), by obtaining by replacing the estimated flow rate Qmean annual average flow rate is the data point the Q of the (8-1), A flow rate estimation method for estimating the flow rate at a basic data point or the flow rate at a planned point other than the basic data point.

(Claim 4)
The method of calculating the estimated value of the annual average discharge of the mountainous river basin using a computer system, and the method of calculating the estimated value of the annual average discharge of the mountainous river basin,
Area data (aj) by altitude zone, which is the slope area of the mountainous area for each elevation zone (j) in the basin where no flow measurement is performed, and elevation by elevation zone, which is the average elevation data for each elevation zone (j) Data (Hcj) and the depth length (wj) of the elevation zone (j) obtained by dividing the horizontal projection area of the elevation zone (j) by the average length of the elevation zone in the storage unit of the computer system Save and
Multiplying the altitude zone-specific area data (aj), elevation zone-specific elevation data (Hcj), and elevation zone depth (wj) for each elevation zone (j) stored in the storage unit, wj, aj , Hcj, the cumulative value of the product is WAPj.
Suppose that j = 0, 1, ..., jlast, and if WAP _{j is} the value of WAP _j in the final value jlast of _j , WAPsum
on the other hand
(Wcj = Σwj, acj = Σaj)
As calculated the WAP3j, WAP 3j regression values and WAP sum and is equal in terms of WCJ, acj, seeking Hcj, and WCJ, acj, respectively Hcj Weq, Aeq, and HEq obtained,
In order to represent the basin characteristics in three dimensions, we introduced the basin three-dimensional terrain correlation depth length WEQ, the basin three-dimensional terrain correlation area AEQ, and the basin three-dimensional terrain correlation elevation HEQ,
WAPsum is defined as WAPsum = AEQ, HEQ, WEQ by basin solid terrain correlation depth length WEQ, basin solid terrain correlation area AEQ, basin solid terrain correlation elevation HEQ,
If ζ = (AEq, HEq, WEq) / WAPsum , then AEQ, HEQ, WEQ = (AEq, HEq, WEq) / ζ, and the AEQ, HEQ, WEQ of the point corresponding to WAPsum using the value of ζ If you regress the value
Measured value Qmean of annual average discharge in each gauging basin, each basin 3D terrain correlation area (AEQ), basin 3D terrain correlation elevation (HEQ), basin 3D depth (WEQ) the applies pass function selected by the method according to the regression function or claim 3 obtained by the method of claim 1 wherein, the point where the flow measurement is not performed the annual average flow estimate of the basin operation An annual average flow rate estimation method for mountainous river basins characterized by

Therefore, when this value is obtained for wc _j , WEq = 1479.3 (Attached program page 32)
Similarly for ac _j AEq = 15.7 (Attached program page 31)
For Hc _j , Heq = 829.8 (Attached program page 30)
Therefore, AEq.HEq.Weq = 19287388.5.
Therefore, the value of WAPsum is a value between WAP ₂ (j = 2) and WAP ₃ (J = 3). Therefore ζ = (AEq ・ HEq ・ WEq) / WAPsum
Ζ = (19287388.5 / 26676019.7 = 0.723
It becomes. If the value of ζ is used to regress the AEQ, HEQ, and WEQ values at the point corresponding to WAPsum
It becomes. Substituting the above AEq, HEq, Weq and ζ into this equation
AEQ = 17.506 HEQ = 924.6 WEQ = 1648.1
As required. The product of these three values is AEQ.HEQ.WEQ = 26,676,225.0.
The value of this product is almost the same as WAPsum = 26,676,019.7 obtained earlier. Therefore, as a conclusion, the final total value of wapj, that is, WAPsum, was uniquely decomposed into 3 of AEQ, HEQ, and WEQ.
WAPsum = AEQ ・ HEQ ・ WEQ

4.3 Flow Calculation at the Biei River Upstream AAA Planned Point In this section, the regression function based on the quadratic formula of AEQ, HEQ, and WEQ selected in the previous section 4.2 is applied to the Biei River planned AAA point to estimate the flow rate:
QmeanestbieiAAA = f (AEQAAA, HEQAAA, WEQAAA)
QmeanestbieiAAA: = 4.49987
Comparison with the measured flow rate at the downstream Okubimi gauging station:
Measured value of annual average flow rate at Okubimi Water Station: Qmeant59 = 4.84 cub.m / s
Planned basin area: CAbieiAAA = 39.1sq.km
Okumi Passage basin area Cat59 = 69.95sq.km
The estimated flow rate at the planned location when using the basin area ratio is
4.81 * 39.1 / 69.95 = 2.70542
Therefore, the calculated flow rate by applying the regression function is compared to the estimated flow rate by the basin ratio.
Double the size.

Claims (4)

A method of calculating a regression function for estimating an annual average discharge in a mountainous river basin using a computer system, the method of calculating the regression function,
Altitude area data (aj), which is the slope area of the mountainous area for each elevation zone (j) in the gauging basin, and elevation data by elevation zone (Hcj), which is the average elevation data for each elevation zone (j), Storing the depth length (wj) of the altitude zone (j) obtained by dividing the horizontal projected area of the altitude zone (j) by the average length of the elevation zone in the storage unit of the computer system;
Multiplying the altitude zone-specific area data (aj), elevation zone-specific elevation data (Hcj), and elevation zone depth (wj) for each elevation zone (j) stored in the storage unit, wj, aj , Hcj, the cumulative value of the product is WAPj.
Suppose that j = 0, 1, ..., jlast changes, and if WAP _j is the value of WAP _j in the final value of jlast, jlast,
WAPsum is defined as WAPsum = AEA, HEQ, and WEQ by basin solid topography correlation area AEQ, basin solid topography correlation elevation HEQ, and basin solid topography correlation depth length WEQ.
(Wcj = Σwj, acj = Σaj)
As WAP3j is calculated, WEq, AEq, and Heq are obtained for wcj, acj, and Hcj where WPA3j's regressed value and WPAsum are approximately equal, respectively, and AEA, HEQ, and WEQ are obtained from the following equations,
ζ = (AEq ・ HEq ・ WEq) / WAPsum
If the AEQ, HEQ, and WEQ values of points corresponding to WAPsum are regressed using the value of ζ,
Calculated
Measured value Qmean of annual average discharge in each watershed basin, the basin solid terrain correlation area (AEQ), the basin solid terrain correlation elevation (HEQ), and the basin solid depth (WEQ) of the corresponding watershed basin Using the regress function of each data and technical calculation software mathcad (registered trademark),
It calculates the regression function of the annual average discharge of mountain river basin that includes at least the basin three-dimensional terrain correlation area (AEQ), the basin three-dimensional terrain correlation elevation (HEQ), and the basin terrain depth (WEQ) in its variables. The calculation method of the regression function for the flow estimation of the mountainous river basin.
When the regress function is the following R function:
R = regress (M, Q, n)
(Where M = augment (X, Y, Z), X = HEQ Y = AEQ Z = WEQ);
The following interpolation function interp and regression value Qest _i are used to estimate the flow rate regression value at the basic data point obtained from the regression function for estimating the flow rate of mountainous rivers according to claim 1 or the flow rate at a planning point other than the basic data point. Is obtained by the regression function for estimating the flow of the mountainous river according to claim 1;
(Here, x, y, z are the same as X, Y, Z (HEQ, AEQ, WEQ))
The Qest is represented by the following polynomial with the number of variables being 3 and the order being 1.
p (x, y, z) = c0 · x + c1 · y + c2 · x + c3
(C0, c1, c2, and c3 are coefficients that change according to variables X, Y, and Z)
Replace the regression function of the annual average flow Qmean with the above formula R = regress (M, Q, n), Q in (5-1), (5-2) with the estimated flow Qmean of the annual average flow that is each data point A flow rate estimation method for estimating the flow rate at a planned point other than the basic data point.
A method for selecting a regression function for estimating a flow rate in a mountain river basin,
After calculating the regression function by the method according to claim 1, using the annual average flow rate measurement data in a group of water stations consisting of a number of water stations in a predetermined area as data,
While extracting water station i0 (i0 = 1, 2,..., M), which is an arbitrary water station in the water station group, as a verification point, the calculated regression function is applied. Calculate an estimated value of the annual average flow rate of each water station in the water station group,
The estimated error rate of the estimated error that occurs between the estimated value and the measured value of the annual average flow at the water station is set as εin, and then the water station i0 is selected from the water station group consisting of the m stations. A regression function is newly calculated by the method according to claim 1, with the water station group consisting of the removed m-1 stations as a new data water station group.
By applying the calculated regression function, an estimated error rate εout between the estimated value of the annual average flow rate of the water station i0 and the measured value of the annual average flow rate of the water station i0 is calculated, and both estimated error rates εin and Let Δε be the difference from εout,
The difference Δε is calculated by the number m of water stations in all the water stations by extracting the water stations i0 as verification points one by one in order for i0 = 1, 2, ..., m. Of these m differences Δε, the verification error rate maxεout is defined as the estimated error rate εout of the verification point that gives the maximum absolute value,
A method for selecting a regression function for estimating a flow rate in a mountainous river basin, wherein only a regression function whose verification error rate maxεout satisfies an acceptance criterion is output as a pass function.
The method of calculating the estimated value of the annual average discharge of the mountainous river basin using a computer system, and the method of calculating the estimated value of the annual average discharge of the mountainous river basin,
Area data (aj) by altitude zone, which is the slope area of the mountainous area for each altitude zone (j) in the basin where no flow measurement is performed, and by altitude zone, which is the average altitude data for each altitude zone (j) The storage unit of the computer system includes elevation data (Hcj) and a depth length (wj) of the elevation zone (j) obtained by dividing the horizontal projected area of the elevation zone (j) by the average length of the elevation zone Save to
Multiplying the altitude zone-specific area data (aj), elevation zone-specific elevation data (Hcj), and elevation zone depth (wj) for each elevation zone (j) stored in the storage unit, wj, aj , Hcj, the cumulative value of the product is WAPj.
Suppose that j = 0, 1, ..., jlast changes, and if WAP _j is the value of WAP _j in the final value of jlast, jlast,
WAPsum is defined as WAPsum = AEA, HEQ, and WEQ by basin solid topography correlation area AEQ, basin solid topography correlation elevation HEQ, and basin solid topography correlation depth length WEQ.
(Wcj = Σwj, acj = Σaj)
WAP3j is calculated, and WEq, AEq, and Heq are calculated for wcj, acj, and Hcj where WPA3j's regressed value and WPAsum are almost equal, respectively, and the Aeq, HEQ, and WEQ values of the points corresponding to WAPsum are To return from
ζ = (AEq ・ HEq ・ WEq) / WAPsum
Measured value Qmean of annual average discharge in each gauging basin, each basin 3D terrain correlation area (AEQ), basin 3D terrain correlation elevation (HEQ), basin 3D depth (WEQ) Applying the regression function calculated by the method of claim 1 or the pass function output by the method of claim 2 to calculate the estimated value of the annual average flow rate in the basin where the flow rate is not measured An annual average flow rate estimation method for mountainous river basins characterized by