CN115034160B - Calculation method for converting parameters into equivalent river channels based on Ma Sijing root method - Google Patents

Calculation method for converting parameters into equivalent river channels based on Ma Sijing root method Download PDF

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CN115034160B
CN115034160B CN202210745922.XA CN202210745922A CN115034160B CN 115034160 B CN115034160 B CN 115034160B CN 202210745922 A CN202210745922 A CN 202210745922A CN 115034160 B CN115034160 B CN 115034160B
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陈钢
王船海
俞悦
李宥霖
郑世威
张娉楠
马腾飞
曾贤敏
赵鹏轩
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Abstract

The invention discloses a calculation method based on Ma Sijing method parameters converted into equivalent river channels, (1) dividing a long river reach into n sub-river reach, and establishing parameters K of Ma Sijing total river reach Total (S) Parameter X Total (S) Parameter K of river reach i Parameter X i A relationship between; (2) Establishing a parameter K of Ma Sijing method river segments i Parameter X i Conversion relation with river width, water level ratio drop and section water depth of hydrodynamic model. The method can calculate the information of the section water depth, the river width, the water level ratio drop and the like of the river reach according to the parameter K, X in the Ma Sijing method, has the advantages of clear physical meaning, simple and convenient calculation method, wide applicable area and the like, realizes the expansion of the hydraulic elements of the river and improves the traditional hydrologic river confluence calculation mode.

Description

Calculation method for converting parameters into equivalent river channels based on Ma Sijing root method
Technical Field
The invention relates to a hydrologic river channel converging calculation method, in particular to a calculation method for converting parameters into equivalent river channels based on Ma Sijing method.
Background
Ma Sijing is mainly applied to river confluence algorithm, and is proposed by McCarthy in 1938 for the first time. Ma Sijing is a hydrologic method for river course flood calculation, and is different from solving the Saint Vinan equation set, and the method is simple and easy to operate, is suitable for confluence simulation of hilly areas, but can only forecast section flow. The main parameters of the Ma Sijing method are K and X, wherein the physical meaning of K is the propagation time of a river segment in steady flow, and X consists of river channel wedge storage factors and regulation storage factors. Ma Sijing, the calculation process is simple and convenient, the required data is less, and the precision can meet the requirements of general scientific research and engineering. However, the traditional Ma Sijing method can only forecast the section flow, and along with the new requirement of 'four pre-measures' in the construction of the national digital twin river basin, a new challenge is provided for flood forecasting, including forecasting the information of river channel water level, flow rate and the like.
Currently, ma Sijing root method calculation mainly has the following problems: (1) Ma Sijing method parameters K, X are all constant, the required flow is in straight line distribution characteristics in a calculation period and along-path change, and the real river channel condition is difficult to reflect; (2) Ma Sijing methods output single results, only simulate the flow information of the river outlet section, need more data support for the acquisition of other elements in the river, and have higher requirements on the integrity of the river data.
Disclosure of Invention
The invention aims to: aiming at the problems, the invention provides a calculation method for converting the Ma Sijing method parameters into the equivalent river, which realizes the expansion of the hydraulic elements of the river and improves the traditional hydrologic river confluence prediction mode.
The technical scheme is as follows: the technical scheme adopted by the invention is a calculation method for converting parameters into equivalent river channels based on Ma Sijing method, which comprises the following steps:
1) Dividing the long river reach into N sub-river reach, and establishing parameters K of Ma Sijing method total river reach Total (S) Parameter X Total (S) Parameter K of river reach i Parameter X i A relationship between;
dividing a long river reach into N sub-river reach, and establishing Ma Sijing method total river reach K Total (S) 、X Total (S) And divide river reach K i 、X i Relationship:
Figure BDA0003717467250000011
Figure BDA0003717467250000012
let K of each partial river reach 1 ＝K 2 ＝…＝K N ，X 1 ＝X 2 ＝…＝X N The following relationship is:
Figure BDA0003717467250000021
wherein L is the length of the river segment, and L is the length of the total river segment.
2) Establishing a parameter K of Ma Sijing method river segments i Parameter X i Conversion relation with river width, water level ratio drop and section water depth of hydrodynamic model;
(1) let hydraulic radius r=r (H), binermannin formula
Figure BDA0003717467250000022
And wave velocity-river length propagation time relation (l=k i αu) is the following relationship:
Figure BDA0003717467250000023
wherein u is the flow rate, n is the roughness, i 0 For water surface ratio drop, l is river segment length, alpha is average flow velocity conversion wave velocity coefficient, K i Is Ma Sijing method parameters, and H is the section water depth.
(2) Let cross-sectional area a=f (H), manning's formula
Figure BDA0003717467250000024
And the flow formula (Q=f (H) u) is combined to obtain the section flood peak flow Q:
Figure BDA0003717467250000025
the H bias in formula (5) results in:
Figure BDA0003717467250000026
(3) and constructing an equivalent river channel by using a simultaneous characteristic river length calculation formula and a flow weight formula in a Ma Sijing method.
Substituting (6) into the characteristic river length formula
Figure BDA0003717467250000027
Obtaining:
Figure BDA0003717467250000028
formulating (7) with flow weight
Figure BDA0003717467250000029
And (3) simultaneous obtaining:
Figure BDA00037174672500000210
in the formula, l' is the characteristic river length, namely the equivalent river length.
(4) Establishing the water surface ratio drop i 0 And Ma Sijing parameters. The following modifications are obtained from formula (5):
Figure BDA0003717467250000031
substituting formula (9) into formula (8) to obtain:
Figure BDA0003717467250000032
where f '(H) is the partial derivative of the cross-sectional area function f (H) to H, and R' is the partial derivative of the hydraulic radius function R (H) to H.
(5) Obtaining Ma Sijing-root-method river segment dividing parameter K of general section shape i Parameter X i And a hydrodynamic model B,i 0 The conversion relationship between H and H is expressed by the following equations (4), (5) and (10):
Figure BDA0003717467250000033
the equation (10) is deformed to obtain a calculation formula of the equivalent river length l':
Figure BDA0003717467250000034
the beneficial effects are that: compared with the prior art, the method provided by the invention can be used for dividing the river reach parameter K according to Ma Sijing methods i Parameter X i Calculating the section water depth H, the river width B and the water surface ratio drop i of the river reach 0 Etc. The invention realizes the expansion of the river hydraulic elements, improves the traditional hydrologic river confluence calculation mode, is favorable for realizing the flow velocity and flow field process simulation, and provides a new method for converting the traditional Ma Sijing method into the hydrodynamic model calculation. The method has the advantages of clear physical meaning, simple and convenient calculation method, wide applicable area and the like.
Drawings
FIG. 1 is a schematic illustration of a river segment;
FIG. 2 is a schematic view of a rectangular channel;
FIG. 3 is a schematic view of a symmetric parabolic channel.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 2, when the cross section of the river channel is rectangular, the calculation method based on Ma Sijing method parameter conversion into an equivalent river channel is applied to calculate, and the method specifically comprises the following steps:
(1) As shown in FIG. 1, a long river is divided into N sub-river segments, and Ma Sijing total river K is established Total (S) 、X Total (S) And divide river reach K i 、X i Relationship:
Figure BDA0003717467250000041
Figure BDA0003717467250000042
let K of each partial river reach 1 ＝K 2 ＝…＝K N ，X 1 ＝X 2 ＝…＝X N The following relationship is:
Figure BDA0003717467250000043
wherein L is the length of the river segment, L is the length of the total river segment, and K, X is Ma Sijing method parameters.
(2) Establishing a parameter K of Ma Sijing method river segments i Parameter X i I is reduced by the ratio of the water surface to the river width B of the hydrodynamic model 0 Conversion relation between section water depth H:
(1) as can be seen, the hydraulic radius r=h, the cross-sectional water depth area relationship f (H) =bh, f' (H) =b
(2) Substituting the relation in the step (1) into the formula (10) to obtain the water surface ratio drop i 0 ：
Figure BDA0003717467250000044
Wherein:
Figure BDA0003717467250000045
(3) will i 0 =dh is taken into formula (4), yielding a section water depth H:
Figure BDA0003717467250000046
(4) obtaining the river width B from the formula (5):
Figure BDA0003717467250000047
(5) obtaining the parameter K of Ma Sijing method river segments with rectangular sections i Parameter X i And hydrodynamic model B, i 0 The conversion relationship between H is as follows:
Figure BDA0003717467250000051
wherein:
Figure BDA0003717467250000052
the hydrodynamic model river width B and the water surface ratio drop i obtained by the conversion are utilized 0 The section water depth H can be predicted hydrodynamically.
Example 2
As shown in fig. 3, when the river section shape is a symmetrical parabola, the calculation method based on Ma Sijing method parameter conversion into an equivalent river is applied to calculate, and the method specifically comprises the following steps:
(1) Dividing a long river reach into N sub-river reach, and establishing Ma Sijing method total river reach K Total (S) 、X Total (S) And divide river reach K i 、X i Relationship, as in equation (3).
(2) Establishing a parameter K of Ma Sijing method river segments i Parameter X i I is reduced by the ratio of the water surface to the river width B of the hydrodynamic model 0 Conversion relation between section water depth H:
(1) supposing river width
Figure BDA0003717467250000053
The relation between the water passing area and the section water depth is as follows:
Figure BDA0003717467250000054
/>
then
Figure BDA0003717467250000055
Beta is the coefficient of the characteristic parabolic curve and needs to be additionally obtained
(2) Substituting the relation in the step (1) into the formula (10) to obtain the water surface ratio drop i 0 ：
Figure BDA0003717467250000056
Wherein:
Figure BDA0003717467250000057
(3) will i 0 =dh is taken into formula (4), yielding a section water depth H:
Figure BDA0003717467250000058
(4) the formula for calculating β is given by formula (5):
Figure BDA0003717467250000061
river width B:
Figure BDA0003717467250000062
(5) obtaining the parameter K of Ma Sijing method river segments with parabolic sections i Parameter X i And hydrodynamic model B, i 0 The conversion relationship between H is as follows:
Figure BDA0003717467250000063
wherein:
Figure BDA0003717467250000064
/>

Claims (5)

1. the calculation method for converting the Ma Sijing-root-method parameters into the equivalent river channel is characterized by comprising the following steps of:
(1) Dividing the long river reach into N sub-river reach, and establishing parameters K of Ma Sijing method total river reach Total (S) Parameter X Total (S) Parameter K of river reach i Parameter X i A relationship between;
(2) Establishing a parameter K of Ma Sijing method river segments i Parameter X i Conversion relation with river width, water surface ratio drop and section water depth of hydrodynamic model is as follows:
Figure FDA0004100811480000011
wherein R is a hydraulic radius, and the hydraulic radius R and the river width B have a functional relation of R=g (B), i 0 The water surface ratio is reduced, n is the roughness, l is the river segment length, alpha is the average flow velocity conversion wave velocity coefficient, K i 、X i For Ma Sijing method river segments, Q is the section flow, f (H) is the section area function, H is the section water depth, f '(H) is the section area function f (H) to determine the bias of H, and R' is the hydraulic radius function R (H) to determine the bias of H.
2. The method for calculating the equivalent river course based on Ma Sijing root method parameters according to claim 1, wherein the method comprises the following steps: establishing the parameters K of Ma Sijing method segments in the step (2) i Parameter X i The conversion relation between the water depth and the river width, the water surface ratio drop and the section water depth of the hydrodynamic model comprises the following steps:
(21) Let the hydraulic radius R=R (H), the Lismann formula and the wave velocity-river length propagation time relation to obtain the hydraulic radius R, the water surface ratio drop i 0 And Ma Sijing root method for dividing river reach parameter K i Relationship between:
Figure FDA0004100811480000012
wherein n is the roughness, l is the river segment length, and alpha is the average flow velocity conversion wave velocity coefficient;
(22) Let section area a=f (H), H be the section water depth, combine the manning formula with the flow formula to obtain the expression of section flood peak flow Q:
Figure FDA0004100811480000013
(23) And (4) solving the bias of the flow expression in the step (22) on the H, substituting the bias into a characteristic river length formula, and combining with a flow weight formula to obtain the flow weight formula:
Figure FDA0004100811480000014
wherein f '(H) is the partial derivative of the cross-sectional area function f (H) to H, and R' is the partial derivative of the hydraulic radius function R (H) to H;
(24) Establishing a water surface ratio drop i by combining two formulas in the step (22) and the step (23) 0 Relationship with Ma Sijing parameters to obtain Ma Sijing method parameters K of general cross-section shape i 、X i Conversion relation with hydrodynamic model river width, water surface ratio drop and section water depth.
3. The method for calculating the equivalent river course based on Ma Sijing root method parameters according to claim 1, wherein the method comprises the following steps: step (2) also comprises establishing a parameter K of Ma Sijing method segments i Parameter X i The conversion relation with the equivalent river channel length l' is as follows:
Figure FDA0004100811480000021
wherein R is hydraulic radius, i 0 For the water surface ratio drop, f (H) is a cross-sectional area function, H is a cross-sectional water depth, f '(H) is a cross-sectional area function f (H) for deflecting H, and R' is a hydraulic radius function R (H) for deflecting H.
4. The method for calculating the equivalent river course based on Ma Sijing root method parameters according to claim 1, wherein the method comprises the following steps: establishing the parameters K of Ma Sijing method segments in the step (2) i Parameter X i The conversion relation with the river width, the water level ratio and the section water depth of the hydrodynamic model is as follows for a river reach with a rectangular section:
Figure FDA0004100811480000022
wherein:
Figure FDA0004100811480000023
wherein B is river width, i 0 The water surface ratio is reduced, H is the section water depth, n is the roughness rate, l is the river segment length, alpha is the average flow velocity conversion wave velocity coefficient, and Q is the section flood peak flow.
5. The method for calculating the equivalent river course based on Ma Sijing root method parameters according to claim 1, wherein the method comprises the following steps: establishing the parameters K of Ma Sijing method segments in the step (2) i Parameter X i The conversion relation with the river width, the water level ratio and the section water depth of the hydrodynamic model is as follows for the river reach with the parabolic section:
Figure FDA0004100811480000031
wherein:
Figure FDA0004100811480000032
wherein B is river width, i 0 The water surface ratio is reduced, H is the section water depth, n is the roughness rate, l is the river segment length, alpha is the average flow velocity conversion wave velocity coefficient, and Q is the section flood peak flow.
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