CN112861449A - Multi-river-section combined correction model based on flood forecast error inversion - Google Patents

Multi-river-section combined correction model based on flood forecast error inversion Download PDF

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CN112861449A
CN112861449A CN202110188466.9A CN202110188466A CN112861449A CN 112861449 A CN112861449 A CN 112861449A CN 202110188466 A CN202110188466 A CN 202110188466A CN 112861449 A CN112861449 A CN 112861449A
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梁忠民
黄一昕
胡义明
李彬权
王军
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Abstract

The invention discloses a multi-river-section combined correction model based on flood forecast error inversion, which comprises the following steps: representing a river course converging process of inflow in multiple river sections and intervals by means of a matrix equation of a Masjing's root method; simulating the evolution rule of flood forecasting errors of all sections and intervals based on the inversion theory of a power system; and forecasting the flood of the cross section of the outlet of the drainage basin by using the state variable after error correction so as to achieve the effect of forecasting and correcting. The method solves the problem of improving the flood forecasting precision of a complex river system, fully considers the problems of hydraulic connection in a river channel, the spatial composition of upstream incoming water, the time transmission of forecasting errors, the utilization of multi-source information and the like, accurately reflects the evolution of the flood forecasting errors in time and the transmission of the flood forecasting errors in space, further improves the river channel flood forecasting precision, and has a strong application prospect.

Description

Multi-river-section combined correction model based on flood forecast error inversion
Technical Field
The invention belongs to the technical field of river channel flood forecasting and real-time correction, and particularly relates to a multi-river-section combined correction model based on flood forecasting error inversion.
Background
Flood forecasting is an important non-engineering measure for flood control and disaster reduction. At present, flood forecasting, although well developed, still faces challenges: on one hand, because human cognition is limited, the absolutely accurate mathematical expression of a watershed hydrological model or a forecasting scheme cannot be obtained, so that the flow of the cross section of the watershed outlet is difficult to accurately simulate and forecast; on the other hand, under the combined action of climate change and human activities, the space-time pattern of the occurrence of hydrological events is variable, and the problem of intangible flood forecasting is increased. Therefore, in order to meet the higher requirements of the rapidly-developing economic society on flood forecasting, real-time correction is indispensable as the last precision guarantee of flood forecasting.
Methods and approaches for real-time correction are numerous. From the practical point of view, the single-point/single-section correction method is mainly used, namely, the forecast result is directly corrected and updated only by using the real-time information of the river outlet section. The method is easy to implement and widely applied in practice. However, for a natural complex river system, if only the convergence process of the masjing method of the drainage basin exit section or a single-section river channel is concerned, and other information of the upstream section and the upstream section is ignored, the evolution of the flood forecast error in time and the transmission of the flood forecast error in space cannot be reflected, and the forecast error of the upstream associated section which is not eliminated can limit the flood forecast real-time correction effect of the exit section.
Disclosure of Invention
The invention aims to solve the technical problem of providing a real-time correction model capable of improving the river channel flood forecasting precision of a complex river system.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a multi-river-section combined correction model based on flood forecast error inversion comprises the following steps:
step 1, dividing a river reach of a complex river system: in a natural river system, 1 long river section in the system is divided into n short river sections (fig. 2), and n +1 river section cross sections are obtained, wherein n is greater than 1, and the outlet cross section flow Q of the ith (i ═ 1, …, n) river section is obtainediComprises an upper cross-sectional inflow Qi-1And interval inflow qiThe flow forecasting error source of the river reach comprises an inflow forecasting error of an upper section and an inflow forecasting error of an interval;
step 2, establishing a matrix equation by the Masjing root method: according to the river reach division result in the step 1, adopting an Masjing root method matrix equation considering interval inflow to represent a river course converging process of multi-river reach and multi-interval inflow;
step 3, inflow forecasting error calculation: calculating inflow errors of all intervals and inflow errors of the upper section of the 1 st river reach in the river confluence evolution process;
step 4, constructing an inversion equation of the power system: according to the step 3, establishing a power system inversion equation of each inflow error, and calculating the forecast error:
step 5, jointly correcting the multi-river-section flow forecasting errors: and (3) establishing a multi-river-section flow error joint correction equation by combining the Masjing matrix equation in the step (2) and the power system inversion equation in the step (4):
Figure BDA0002944086130000021
in the formula (5), the reaction mixture is,
Figure BDA0002944086130000022
C0,C1,C2is the coefficient of the formula calculated by the Maskyo method of river reach, and C0+C1+C 21, wherein
Figure BDA0002944086130000023
Wherein K is the gradient of the storage and discharge relation curve, and x is the flow specific gravity coefficient;
in the formula (5), the reaction mixture is,
Figure BDA0002944086130000024
for the corrected upper section inflow forecasting value of the 1 st river reach at the time t + delta t,
Figure BDA0002944086130000025
the prediction value series of the lower section outflow of the 1 st to the nth river reach at the corrected t + delta t moment;
Figure BDA0002944086130000026
the measured inflow value of the upper section of the 1 st river reach at the time t,
Figure BDA0002944086130000027
a lower section outflow measured value series of the 1 st to the nth river reach at the time t;
Figure BDA0002944086130000028
the inflow forecast value of the upper section of the 1 st river reach at the moment of t + delta t before correction,
Figure BDA0002944086130000029
the prediction value series of the lower section outflow of the 1 st to the nth river reach at the moment of t + delta t before correction;
Figure BDA00029440861300000210
forecasting error of the inflow of the upper section of the 1 st river reach at the moment of t + delta t,
Figure BDA00029440861300000211
and (3) inputting the forecast error series for the interval from the 1 st river reach to the nth river reach at the moment of t + delta t.
Further, in step 2, the matrix equation of the masjing root method of the multi-river-section multi-interval inflow is as follows:
Figure BDA0002944086130000031
in the formula (1), the reaction mixture is,
Figure BDA0002944086130000032
and
Figure BDA0002944086130000033
the inflow values of the upper section of the 1 st sub-river reach at the time t and the time t + delta t respectively,
Figure BDA0002944086130000034
and
Figure BDA0002944086130000035
the lower section outflow values of the 1 st to nth sub-river segments at the time t and the time t + delta t respectively,
Figure BDA0002944086130000036
interval inflow value of the 1 st to the nth sub-river reach at the time t + delta t, C1,0,C1,1,C1,2,…Cn-1,2,Cn,0,Cn,1,Cn,2The coefficients are calculated by the masjing root method of each river reach.
Further, in step 3, the inflow error of each interval and the inflow error of the upper section of the 1 st river section in the river confluence evolution process are as shown in formula (2):
Figure BDA0002944086130000037
in the formula (2), epsilon0 tFor the inflow error of the upper section of the 1 st river reach at the time t,
Figure BDA0002944086130000038
the measured inflow value of the upper section of the 1 st river reach at the time t,
Figure BDA0002944086130000039
the measured inflow value of the upper section of the 1 st river reach at the time point of t-delta t,
Figure BDA00029440861300000310
for the interval inflow error series of the 1 st to the nth river reach at the time t,
Figure BDA00029440861300000311
the interval from the 1 st to the nth river reach at the time t flows into the real value series,
Figure BDA00029440861300000312
the interval inflow forecast value series of the 1 st to the nth river reach at the time t,
Figure BDA00029440861300000313
for the inflow forecast value series of the upper sections of the 1 st to the nth river reach at the time t,
Figure BDA00029440861300000314
the measured values of the lower cross-sectional outflow at the 1 st to nth river reaches at time t,
Figure BDA00029440861300000315
the measured values of the lower section outflow of the 1 st to nth river reach at the time t-delta t are shown in the figure.
Further, the power system inversion equation of each inflow error in the step 4 is shown in formula (3):
Figure BDA0002944086130000041
in the formula (3), the reaction mixture is,
Figure BDA0002944086130000042
the upper section inflow error value a of the 1 st river reach at the time t + delta t, t, t-delta t, t-2 delta t0,1,a0,2,a0,3,a0,4,a0,5,a0,6,a0,7,a0,8,a0,9,a0,10Are the parameters of the inversion equation respectively,
Figure BDA0002944086130000043
Figure BDA0002944086130000044
interval inflow error series of each river reach at t + delta t, t, t-delta t, t-2 delta t1,1,a1,2,a1,3,a1,4,a1,5,a1,6,a1,7,a1,8,a1,9,a1,10，…，an-1,1,an-1,2,an-1,3,an-1,4,an-1,5,an-1,6,an-1,7,an-1,8,an-1,9,an-1,10，an,1,an,2,an,3,an,4,an,5,an,6,an,7,an,8,an,9,an,10Are all parameters of the inversion equation.
Further, the formula (3) is substituted for the formula (1), and the calculation parameter C of each sub-river section is considered0,C1,C2And (3) establishing a flow forecasting error calculation equation based on the matrix equation of the MasJinggen method:
Figure BDA0002944086130000045
and (3) solving an inverse matrix of the first matrix A at the left end of the formula (4), and then multiplying the inverse matrix on two sides of the equation to obtain the multi-river-section flow error joint correction equation after sorting. The prior art is referred to in the art for techniques not mentioned in the present invention.
The invention achieves the following beneficial effects: the multi-river-section combined correction model based on the flood forecasting error inversion can reflect the river channel converging process of multi-river-section linkage and multi-section inflow, can simulate the evolution rule of the flood forecasting errors of all sections and sections, solves the problem of correction of the flood forecasting errors of a complex river system, further improves the river channel flood forecasting precision, and has strong engineering significance.
Drawings
FIG. 1 is a flow chart of a multi-river-section joint correction model based on flood forecast error inversion according to the present invention;
fig. 2 is a schematic view of a complex multi-river-segment river system.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
As shown in figure 1 of the drawings, in which,
step 1, dividing 1 long river section in a system into 3 short river sections (from a level 1 river to a level 3 river) for a natural river system at the upstream of a large river crossing, and obtaining 4 river section sections (from a 0 th section to a 3 rd section, wherein the 0 th section is a river source section, and the 3 rd section is a river basin outlet section), so that the outlet section flow Q of the ith (i is 1,2, 3) river sectioniThe source comprises an upper cross-sectional inflow Qi-1And interval inflow qiCorrespondingly, the flow forecasting error source of the river reach also comprises an upper section inflow forecasting error and an interval inflow forecasting error;
step 2, according to the river reach division result in the step 1, adopting an Masjing root method matrix equation considering interval inflow to represent a river course converging process of multi-river reach and multi-interval inflow:
Figure BDA0002944086130000051
in the formula (1'), in the presence of a catalyst,
Figure BDA0002944086130000052
and
Figure BDA0002944086130000053
the upper section inflow of the 1 st sub-river reach at the time t and the time t + delta t respectively,
Figure BDA0002944086130000054
and
Figure BDA0002944086130000055
the 1 st to 3 rd sub-rivers of the t moment and the t + delta t moment respectivelyThe outflow from the lower section of the segment,
Figure BDA0002944086130000056
inflow of the interval from the 1 st to the 3 rd sub-river segment at time t + Δ t, C1,0,C1,1,C1,2,C2,0,C2,1,C2,2,C3,0,C3,1,C3,2Respectively calculating coefficients by the Masjing root method of each river reach;
step 3, calculating inflow errors in the river confluence evolution process, wherein the inflow errors comprise interval inflow errors of river reach and upper section inflow errors of the 1 st river reach, the interval inflow errors are not measured well, and the interval inflow error series are calculated according to the response of the interval forecast flow on the lower section of the section subtracted by the actually measured flow of the lower section of the river reach:
Figure BDA0002944086130000061
in the formula (2'),
Figure BDA0002944086130000062
for the inflow error of the upper section of the 1 st river reach at the time t,
Figure BDA0002944086130000063
is the measured value of the upper section inflow of the 1 st river reach at the time t,
Figure BDA0002944086130000064
the measured inflow value of the upper section of the 1 st river reach at the time point of t-delta t,
Figure BDA0002944086130000065
the interval inflow error series of the 1 st, 2 nd and 3 rd river reach at the time t,
Figure BDA00029440861300000612
the interval of the 1 st, 2 nd and 3 rd river reach at the time t flows into the real value series,
Figure BDA0002944086130000066
inflow forecast value series for intervals of 1 st, 2 nd and 3 th river reach at the time t,
Figure BDA0002944086130000067
inflow forecast value series of upper sections of 1 st, 2 nd and 3 th river reach at the time t,
Figure BDA0002944086130000068
the measured value series of the outflow of the lower section of the 1 st, 2 nd and 3 th river reach at the time of t-delta t;
step 4, establishing a power system inversion equation of each inflow error according to the step 3, and calculating the forecast error:
Figure BDA0002944086130000069
in the formula (3'),
Figure BDA00029440861300000610
the inflow error of the upper section of the 1 st river reach at the time t + delta t, t, t-delta t, t-2 delta t, a0,1,a0,2,a0,3,a0,4,a0,5,a0,6,a0,7,a0,8,a0,9,a0,10Are the parameters of the inversion equation respectively,
Figure BDA00029440861300000611
interval inflow error series of each river reach at t + delta t, t, t-delta t, t-2 delta t1,1,a1,2,a1,3,a1,4,a1,5,a1,6,a1,7,a1,8,a1,9,a1,10，a2,1,a2,2,a2,3,a2,4,a2,5,a2,6,a2,7,a2,8,a2,9,a2,10，a3,1,a3,2,a3,3,a3,4,a3,5,a3,6,a3,7,a3,8,a3,9,a3,10Are parameters of an inverse equation based on observationsThe data is obtained by solving the equation, and the result is shown in the table 1;
TABLE 1 Special solution of inversion equation parameters for each river section
Figure BDA0002944086130000071
Step 5, jointly correcting the multi-river-section flow forecasting errors: substituting formula (3') into formula (1'), considering that the calculation parameters of each sub-river reach are equal, and determining C0＝0.074，C1＝0.815，C2And (3) establishing a flow forecasting error calculation equation based on the matrix equation of the Masjing's method when the flow forecasting error calculation equation is 0.111:
Figure BDA0002944086130000072
in the formula (4'),
Figure BDA0002944086130000081
for the corrected upper section inflow forecasting value of the 1 st river reach at the time of t + delta t,
Figure BDA0002944086130000082
forecasting value series for outflow of lower section of each river reach at the corrected t + delta t moment;
Figure BDA0002944086130000083
is the measured value of the inflow of the section on the 1 st river reach at the time t,
Figure BDA0002944086130000084
the measured value series of outflow of the lower section of each river reach at the time t;
Figure BDA0002944086130000085
the forecast value of the upper section inflow of the 1 st river reach at the moment of t + delta t before correction,
Figure BDA0002944086130000086
for predicting outflow values of lower sections of various river reach at t + delta t moment before correction；
Figure BDA0002944086130000087
Forecasting error of the inflow of the upper section of the 1 st river reach at the moment of t + delta t,
Figure BDA0002944086130000088
for the interval inflow forecasting error series of each river reach at the time of t + delta t, an inverse matrix is solved for a first matrix A at the left end of the equation (4), then the inverse matrix is multiplied on the left side of the equation, and a multi-river reach flow error joint correction equation is obtained after the arrangement:
Figure BDA0002944086130000089
in the formula (5'),
Figure BDA00029440861300000810
Figure BDA00029440861300000811
equation (5') is written in vector form as follows:
Q(t+Δt)＝ΗQ(t)+P[q(t+Δt)+ε(t+Δt)] (6)
h in formula (6) ═ a (a)TA)-1ATB and P ═ aTA)-1ATAll the parameters are coefficient matrixes, Q (t + delta t) is a section flow prediction value vector at the moment of t + delta t, Q (t) is a section flow measured value vector at the moment of t, Q (t + delta t) is a section flow prediction value vector at the moment of t + delta t, and epsilon (t + delta t) is a section flow prediction error prediction value vector at the moment of t + delta t.
Step 6, adopting the peak flow relative error delta QmAbsolute error at peak time Δ T, relative error at radial depth δ R and deterministic coefficient DCThe 4 basic indexes quantify the real-time correction result of the multi-river-section combined correction model, and the improvement degree of flood forecasting precision before and after real-time correction is evaluated.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (5)

1. A multi-river-section combined correction model based on flood forecast error inversion is characterized by comprising the following steps:
step 1, dividing a river reach of a complex river system: for a natural river system, dividing 1 long river section in the system into n short river sections to obtain n +1 river section cross sections, wherein n is more than 1, and the outlet cross section flow Q of the ith river sectioniComprises an upper cross-sectional inflow Qi-1And interval inflow qiI is 1, …, n, the flow forecasting error source of the river reach comprises the upper section inflow forecasting error and the interval inflow forecasting error;
step 2, establishing a matrix equation by the Masjing root method: according to the river reach division result in the step 1, adopting an Masjing root method matrix equation considering interval inflow to represent a river course converging process of multi-river reach and multi-interval inflow;
step 3, inflow forecasting error calculation: calculating inflow errors of all intervals and inflow errors of the upper section of the 1 st river reach in the river confluence evolution process;
step 4, constructing an inversion equation of the power system: according to the step 3, establishing a power system inversion equation of each inflow error, and calculating the forecast error;
step 5, jointly correcting the multi-river-section flow forecasting errors: and (3) establishing a multi-river-section flow error joint correction equation by combining the Masjing matrix equation in the step (2) and the power system inversion equation in the step (4):
Figure FDA0002944086120000011
in the formula (5), the reaction mixture is,
Figure FDA0002944086120000012
C0,C1,C2horse in river reachCoefficient of formula calculated by the Sijing root method, and C0+C1+C21, wherein
Figure FDA0002944086120000013
Wherein K is the gradient of the storage and discharge relation curve, and x is the flow specific gravity coefficient;
in the formula (5), the reaction mixture is,
Figure FDA0002944086120000014
for the corrected upper section inflow forecasting value of the 1 st river reach at the time t + delta t,
Figure FDA0002944086120000021
the prediction value series of the lower section outflow of the 1 st to the nth river reach at the corrected t + delta t moment;
Figure FDA0002944086120000022
the measured inflow value of the upper section of the 1 st river reach at the time t,
Figure FDA0002944086120000023
a lower section outflow measured value series of the 1 st to the nth river reach at the time t;
Figure FDA0002944086120000024
the inflow forecast value of the upper section of the 1 st river reach at the moment of t + delta t before correction,
Figure FDA0002944086120000025
the prediction value series of the lower section outflow of the 1 st to the nth river reach at the moment of t + delta t before correction;
Figure FDA0002944086120000026
forecasting error of the inflow of the upper section of the 1 st river reach at the moment of t + delta t,
Figure FDA0002944086120000027
1 st to nth at time t + Δ tAnd (4) entering a forecast error series in the interval of the river reach.
2. The flood forecast error inversion-based multi-river-section joint correction model of claim 1, wherein: in the step 2, the matrix equation of the Maskyo method of inflow in multiple river sections and multiple intervals is as follows:
Figure FDA0002944086120000028
in the formula (1), the reaction mixture is,
Figure FDA0002944086120000029
and
Figure FDA00029440861200000210
the inflow values of the upper section of the 1 st sub-river reach at the time t and the time t + delta t respectively,
Figure FDA00029440861200000211
and
Figure FDA00029440861200000212
the lower section outflow values of the 1 st to nth sub-river segments at the time t and the time t + delta t respectively,
Figure FDA00029440861200000213
interval inflow value of the 1 st to the nth sub-river reach at the time t + delta t, C1,0,C1,1,C1,2,…Cn-1,2,Cn,0,Cn,1,Cn,2The coefficients are calculated by the masjing root method of each river reach.
3. The flood forecast error inversion-based multi-river-section joint correction model of claim 1, wherein: in the step 3, inflow errors of each interval and inflow errors of the upper section of the 1 st river reach in the river confluence evolution process are shown as the following formula (2):
Figure FDA00029440861200000214
in the formula (2), the reaction mixture is,
Figure FDA00029440861200000215
for the inflow error of the upper section of the 1 st river reach at the time t,
Figure FDA00029440861200000216
the measured inflow value of the upper section of the 1 st river reach at the time t,
Figure FDA0002944086120000031
the measured inflow value of the upper section of the 1 st river reach at the time point of t-delta t,
Figure FDA0002944086120000032
for the interval inflow error series of the 1 st to the nth river reach at the time t,
Figure FDA0002944086120000033
the interval from the 1 st to the nth river reach at the time t flows into the real value series,
Figure FDA0002944086120000034
the interval inflow forecast value series of the 1 st to the nth river reach at the time t,
Figure FDA0002944086120000035
for the inflow forecast value series of the upper sections of the 1 st to the nth river reach at the time t,
Figure FDA0002944086120000036
the measured values of the lower cross-sectional outflow at the 1 st to nth river reaches at time t,
Figure FDA0002944086120000037
the measured values of the lower section outflow of the 1 st to nth river reach at the time t-delta t are shown in the figure.
4. The flood forecast error inversion-based multi-river-section joint correction model of claim 1, wherein: and 4, a power system inversion equation of each inflow error in the step 4 is shown as the formula (3):
Figure FDA0002944086120000038
in the formula (3), the reaction mixture is,
Figure FDA0002944086120000039
the upper section inflow error value a of the 1 st river reach at the time t + delta t, t, t-delta t, t-2 delta t0,1,a0,2,a0,3,a0,4,a0,5,a0,6,a0,7,a0,8,a0,9,a0,10Are the parameters of the inversion equation respectively,
Figure FDA00029440861200000310
Figure FDA00029440861200000311
interval inflow error series of each river reach at t + delta t, t, t-delta t, t-2 delta t1,1,a1,2,a1,3,a1,4,a1,5,a1,6,a1,7,a1,8,a1,9,a1,10，…，an-1,1,an-1,2,an-1,3,an-1,4,an-1,5,an-1,6,an-1,7,an-1,8,an-1,9,an-1,10，an,1,an,2,an,3,an,4,an,5,an,6,an,7,an,8,an,9,an,10Are all parameters of the inversion equation.
5. The method according to claim 1The multi-river-section combined correction model for flood forecast error inversion is characterized in that: in the step 5, the formula (3) is substituted for the formula (1), and the calculation parameter C of each sub-river course is considered0,C1,C2And (3) establishing a flow forecasting error calculation equation based on the matrix equation of the MasJinggen method:
Figure FDA0002944086120000041
and (3) solving an inverse matrix of the first matrix A at the left end of the formula (4), and then multiplying the inverse matrix on two sides of the equation to obtain the multi-river-section flow error joint correction equation after sorting.
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