CN110619111B - Natural runoff series consistency correction method - Google Patents

Natural runoff series consistency correction method Download PDF

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CN110619111B
CN110619111B CN201910886292.6A CN201910886292A CN110619111B CN 110619111 B CN110619111 B CN 110619111B CN 201910886292 A CN201910886292 A CN 201910886292A CN 110619111 B CN110619111 B CN 110619111B
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杜军凯
卢琼
仇亚琴
李云玲
张象明
张海涛
孙素艳
郝春沣
赵红莉
冶运涛
张双虎
郭东阳
何君
郭旭宁
刘海滢
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China Institute of Water Resources and Hydropower Research
China Renewable Energy Engineering Institute
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Abstract

The invention discloses a method for correcting the consistency of a natural runoff series, which comprises five parts: the method comprises the following steps of I, checking the natural runoff and the time sequence mutability; II, analyzing the relation between rainfall and runoff; III, correcting the consistency of the natural runoff series based on a statistical method; IV, correcting the consistency of the natural runoff series based on a graphical method; and V, correcting the consistency of the natural runoff series by a comprehensive statistical method and a graphical method. The method designs a mapping conversion module, and provides a threshold judgment method suitable for standardizing the application range of the statistical correction method; the method integrates the graphic analysis and the statistical analysis, takes the graphic analysis result as the outer boundary condition of controllability, effectively solves the problems that the correction proportion exceeds 100 percent and the relative size relation of the natural runoff volume of the Fengchong and Kukui years after correction is disordered, and enriches the natural runoff consistency correction method system.

Description

Natural runoff series consistency correction method
Technical Field
The invention relates to the technical field of hydraulic engineering, in particular to a consistency correction technology of a natural runoff series, and specifically relates to a consistency correction method of a natural runoff series, which integrates a statistical method and a graphical method.
Background
Water resources are basic resources for the survival and development of human society, and China faces complex water problems such as little water (shortage of quantity), much water (flood disasters), water pollution (water pollution), muddy water (water and soil loss) and the like. The water resource evaluation work is carried out, the natural endowment condition and the evolution law of the water resource are mastered, the method is an important reference for scientifically coping with the water resource pressure and solving the water problem, and the method has important significance for guaranteeing the sustainable utilization of regional water resources.
The hydrology department typically uses long series of data to develop natural river runoff (i.e., surface water resource) evaluations. However, the hydrological process is a high-dimensional nonlinear system influenced by climate, terrain, geology, surface coverings, ground water dynamic changes and other underlying factors, and social water intake and use. With the passage of time, the climatic conditions such as precipitation, temperature, humidity, radiation, etc., and the underlying surface conditions such as land utilization (expansion of water areas due to urban expansion, reservoir construction), ground surface coverings (reclamation of farmlands, returning to forests, etc.), soil structures, geological structures, etc., are constantly changing. Among these, changes in the underlying surface have long-term effects, such as increased building and hardened surfaces due to expansion of the urban mass, formation of a wide surface of water from reservoir construction, and irreversible destruction of groundwater aquifers by coal mining. Therefore, even if the climate conditions reappear decades ago, the river runoff with the same amount as the historical amount cannot be generated under the current underlying surface conditions, because the underlying surface background conditions generated and converged in different periods are inconsistent. For related work such as water resource planning, configuration and scheduling, an evaluation result capable of accurately reflecting the current runoff capacity under the underlying surface condition is more required, and the problem of conversion of the natural runoff evaluation result under the historical underlying surface condition to the current underlying surface is involved.
The consistency correction technology of the natural runoff series is used for solving the problems, the consistency correction refers to that the background conditions of production and confluence of the historical underlying surface are corrected to be consistent with the existing underlying surface, the influence of the underlying surface change on the natural runoff is stripped through quantitative evaluation of the water resource effect caused by the underlying surface change, and therefore the long-term natural runoff series with consistency is obtained. The traditional natural runoff series consistency correction technology mainly depends on a mathematical statistics method, and comprises the following steps: (1) drawing a double accumulation curve of precipitation and runoff, and dividing a long-time series into two stages of a historical underlying surface and a current underlying surface by taking a point where the double accumulation curve has an obvious turn as a boundary; (2) and respectively establishing a rainfall-runoff function relationship of two periods, inputting the annual rainfall amount of the historical underlying surface into the rainfall-runoff relationship of the current underlying surface (moving the historical rainfall-runoff relationship diagram to the current relationship diagram), and outputting corrected runoff data so as to realize the conversion of the natural runoff series between the historical underlying surface and the current underlying surface.
However, the existing statistical correction method has certain defects, and cannot completely meet the requirement of the consistency correction work of the natural runoff series, and particularly has larger defects when the condition of drastic change of the underlying surface is treated. The concrete points are as follows: (1) when the inflection point year is determined, the subjective randomness is high, and the support of quantitative analysis is lacked; (2) when the relation between rainfall and runoff scattering points is relatively disordered, a mathematical method cannot be directly applied to directly fit a rainfall-runoff relation line, a rainfall-runoff relation graph must be determined by depending on expert experience, and the condition that how to reasonably use the relation graph lacks systematic ground specifications and errors are too large is easily caused; (3) unreasonable conditions exist in the correction result, and the runoff is negative after correction in part of years, so that the objective fact is not met; the relative magnitude relation of the runoff before and after correction is disordered, and the situation that the natural runoff is smaller than the result after correction in dry water after correction in rich water exists.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defects of the conventional statistical correction method in the process of processing the natural runoff consistency correction problem, and provides a natural runoff series consistency correction technology integrating a graphical method and a statistical method. The purpose of the invention is realized by the following technical scheme:
a method for correcting the consistency of a natural runoff series, which comprises five parts: the method comprises the following steps of I, checking the natural runoff and the time sequence mutability; II, analyzing the relation between rainfall and runoff; III, correcting the consistency of the natural runoff series based on a statistical method; IV, correcting the consistency of the natural runoff series based on a graphical method; v, correcting the consistency of the natural runoff series by a comprehensive statistical method and a graphical method;
the specific steps of the identification of natural runoff and the time series mutability test comprise:
1-1: converting the measured runoff data measured day by day into an annual scale according to the long-series hydrological test results after the hydrological measurement station is integrated, and obtaining measured runoff data A measured year by year;
1-2: according to the development and utilization conditions of watershed water resources, by combining agricultural, industrial and domestic water consumption, reservoir storage variables, interval flood diversion quantity and interval water diversion quantity, obtaining various reduction components in a catchment range above a hydrological test section, and checking the natural runoff of a measuring station according to a formula (1) to obtain the reduction runoff as data B;
R＝R1+R2+R3+R4±R5±R6±R7(1)
in the formula: r is reduction runoff;R1the measured runoff is measured; r2The water consumption of agriculture is obtained; r3Industrial water consumption; r4The water consumption of life is obtained; r5The water diversion amount across the drainage basin is positive; r6The water quantity which can not return after flood diversion is divided into positive water quantity from the station; r7The value is positive when the storage capacity of the reservoir is increased;
1-3: testing the mutability of the natural runoff time sequence by adopting a PETTITT test method, and determining the year corresponding to the maximum value of the test statistic as a mutation point of the natural runoff series to obtain data C;
1-4: dividing the natural runoff long-time sequence into two sections according to the mutation point detection result, and respectively obtaining natural runoff series data D of the historical underlying surface and natural runoff series data E of the current underlying surface;
II, analyzing the relationship between rainfall and runoff, which specifically comprises the following steps:
2-1: according to the meteorological monitoring result in the catchment range above the hydrological test section, obtaining surface rainfall data F of the historical underlying surface and surface rainfall data G of the current underlying surface in the same time sequence with the natural runoff by adopting a Thiessen polygon method or other spatial interpolation and spread algorithms;
2-2: obtaining the precipitation-runoff relational expression y of the historical underlying surface as F (x) and the precipitation-runoff relational expression y of the current underlying surface as G (x), and enabling the decisive coefficient R of the expressions2＞0.7；
The specific steps of the consistency correction of the natural runoff series based on the statistical method comprise:
3-1: arranging the rainfall data F of the historical underlying surface of each year in an ascending order, and calculating the attenuation coefficient of a statistical correction method corresponding to the rainfall data F point by point, namely the relative variation of the rainfall-runoff relation y (F) (x) of the historical underlying surface obtained in the previous step and the rainfall-runoff relation y (G) (x) of the current underlying surface, as shown in formula (7):
Figure BDA0002207386100000031
in the formula, P*For a given year of face rainfall, #*Is the natural runoff attenuation coefficient of the corresponding year;
3-2: establishing a functional relation psi-P between the attenuation coefficient vector and the surface rainfall vector under the condition of the historical underlying surface by adopting a least square method fitting method (see formula (6)), namely obtaining the attenuation coefficient corresponding to the rainfall on any surface of the historical underlying surface as shown in a formula (8), and further calculating a natural runoff attenuation quantity series based on a statistical method as shown in a formula (9);
ψ＝k(P) (8)
ΔR＝k(P)*F(P) (9)
in the formula, delta R is a natural runoff attenuation series based on a statistical method, P is a surface rainfall series, k is an attenuation coefficient series corresponding to the surface rainfall, and F (P) is a rainfall runoff relation function of a historical underlay surface;
3-3: calculating the attenuation of the natural runoff of the historical underlying surface year by year according to the formulas (7) to (9), and determining the corrected natural runoff series based on a statistical correction method by combining the natural runoff series before the correction of the historical underlying surface:
Rmod＝R-ΔR (10)
in the formula, RmodThe corrected natural runoff quantity series is R, and delta R is a natural runoff attenuation quantity series based on a statistical method;
IV, the concrete steps of the consistency correction of the natural runoff series based on the graphical method comprise:
4-1: and (3) calculating the distance between two curves based on the relation curves of the rainfall and the runoff of the historical underlying surface and the current underlying surface, wherein the difference value is the natural runoff attenuation series based on the graphical method, and the calculation method is shown in formula (11).
ΔR'＝F(P)-G(P) (11)
In the formula, delta R' is a natural runoff decrement series based on a graphical method, and other symbols have the same meanings as the above;
4-2: and (3) calculating the attenuation amount of the natural runoff of the historical underlying surface year by year according to the formula (11), and determining the corrected natural runoff series based on a graphical correction method by combining the runoff series before correction, as shown in a formula (12).
Rmod＝R-ΔR' (12)
V, the specific steps of the natural runoff series consistency correction of the comprehensive statistical method and the graphical method comprise:
5-1: using the delta R 'obtained by the graphical method as a controllable outer boundary condition, wherein the delta R is not more than or equal to the delta R' in the natural runoff volume correction, namely the runoff volume correction in a single year should not exceed the moving distance of a rainfall-runoff relation line, and obtaining a corrected natural runoff series based on the comprehensive method, which is shown as a formula (13) and a formula (14);
Figure BDA0002207386100000041
Rmod＝R-Rtmp(14)
5-2: and combining the determined natural runoff after the historical underlay surface is corrected with the current underlay surface to obtain the natural runoff long series consistency correction result.
Further, in the steps 1-3, the data C is obtained by specifically adopting the formulas (2) to (5),
Figure BDA0002207386100000042
Figure BDA0002207386100000043
k(t)＝Max1≤t≤N|Ut,N| (4)
Figure BDA0002207386100000044
in the formula of Ut,NFor test statistics, PbK (t) is a significance probability value of Ut,NMaximum value of the sequence, t being Ut,NThe position, x, corresponding to the maximum value k (t) in the sequencejFor the runoff volume of the jth year, N represents the series length, i.e., the number of input annual runoff volume data.
Further, the specific operation method of step 2-2 is as follows:
2-2-1: respectively establishing rainfall runoff relations under different underlying surface conditions by adopting a least square method, wherein the rainfall runoff relations comprise a regression equation y (F) (x) of surface rainfall F and natural runoff D of a historical underlying surface and a regression equation y (G) (x) of E and G under the current underlying surface condition, and the regression equations are written into the following forms:
Figure BDA0002207386100000051
note the book
Figure BDA0002207386100000052
Then least squares estimates of the regression equation coefficients
Figure BDA0002207386100000053
In the formula: y is natural runoff, namely a dependent variable; b is a regression coefficient; x is a surface rainfall matrix, namely an independent variable; n is the length of the dependent variable vector; p is the number of independent variables, and when a single independent variable is used, p is 1; selecting a unary linear regression or a high-order polynomial regression according to the fitting condition of the regression equation;
2-2-2: checking whether the regression equations y ═ f (x) and y ═ g (x) obtained in step 2-2-1 satisfy R (x)2If the requirement is more than 0.7, the established statistical rainfall-runoff relation is considered to be reliable, and a directly fitted mathematical relation is available;
2-2-3: if the statistical relationship between the rainfall series to be processed and the surface rainfall series does not meet the requirements of the step 2-2-2, analysis is carried out by combining a rainfall-runoff relation curve submitted by a hydrological testing department (an obtaining way is that the rainfall-runoff relation curve is generally attached when the hydrological testing department submits a testing result, or the hydrological testing department can draw by hand and uniformly pass through all data points by using a smooth line as much as possible; selecting 10-15 data points from a rainfall-runoff relation curve drawn in a graph, and reading the abscissa and ordinate values of the points;
2-2-4: aiming at the data points obtained in the step 2-2-3, a least square method fitting method (see formula (6)) is used for obtaining a regression equation y of the relation between the historical underlying surface and the current underlying surface empirical rainfall-runoff, wherein the regression equation y is lambda1(x) And y ═ λ2(x) Ensuring the deterministic coefficient R of the regression equation2＞0.7；
2-2-5: when a function equation directly fitted by using the series of the surface rainfall and the runoff quantity is available, representing the rainfall-runoff relation of the historical underlying surface and the current underlying surface by analytical expressions y (f) (x) and y (g) (x); otherwise, the analytical formula y ═ λ is selected1(x) And y ═ λ2(x) As a representative; and (3) recording the relation expression of the rainfall-runoff of the historical underlying surface finally determined through the 4 steps as follows: and the relational expression of y ═ F (x) and the current rainfall-runoff of the underlying surface is recorded as: g (x).
Further, step V further includes a correction effect evaluation: constructing a statistical index NSE for inspection aiming at the problem of consistency of runoff series before and after correction, as shown in a formula (15), sequencing natural runoff quantity before the correction of a historical underlying surface in a descending order aiming at the problem of sequencing confusion of rich and withered years before and after the correction, taking out 5 values with the largest annual runoff quantity, recording corresponding years, carrying out the same operation on the corrected series, and calculating the mismatching degree S of the rich water year according to the formula (16); taking out the 5 most withered years for comparison, and calculating the mismatching degree V of the withered water years; the criteria evaluated were NSE as large as possible, S and V as small as possible;
Figure BDA0002207386100000061
Figure BDA0002207386100000062
Figure BDA0002207386100000063
NSE→max,S→min,V→min (18)
in the formula: NSE is the Nash coefficient of the natural runoff series before and after correction, O is the natural runoff series after correction of the historical underlying surface, Q is the natural runoff series before correction of the historical underlying surface, k is the series length, OiAnd QiRespectively the runoff volume after the correction and before the correction in the ith year,
Figure BDA0002207386100000064
the average runoff is evenly averaged for years before correction; s is the nonmatch of full-water years, TjSorting the natural runoff quantity before correction into the years corresponding to the runoff quantity of j in a descending order, TjThe years corresponding to the runoff with j are sorted in descending order after the repair; (ii) a V is the mismatching degree of the dry year.
The invention has the beneficial effects that:
1) the method designs a mapping conversion module, and provides a threshold judgment method suitable for standardizing the application range of the statistical correction method; the method integrates the graphic analysis and the statistical analysis, takes the graphic analysis result as the outer boundary condition of controllability, effectively solves the problems that the correction proportion exceeds 100 percent and the relative size relation of the natural runoff volume of the Fengchong and Kukui years after correction is disordered, and enriches the natural runoff consistency correction method system.
2) The method provides a new determination method for determining the inflection point year, and supports quantitative analysis.
Drawings
The invention is described in further detail below with reference to the figures and the specific embodiments.
FIG. 1 is a flow chart of a method according to an embodiment of the present invention.
FIG. 2 is year-by-year measured runoff data for a hydrological test section used in the present invention.
FIG. 3 is a graph showing year-by-year reduced water volume data within a certain water collection range of a hydrological test section used in the present invention.
Figure 4 is a graph of year-by-year natural runoff data within a certain hydrological test section catchment range for use in the present invention.
FIG. 5 shows the results of a series of mutations in the natural runoff of a hydrological test section according to the present invention.
FIG. 6 is the classification of the underlying surface of the invention for the history and current situation of the natural runoff series of a hydrological test section.
Fig. 7 is annual surface rainfall data within a certain hydrological test section catchment range as used in the present invention.
FIG. 8 shows the relationship between rainfall runoff obtained by the present invention according to the series of data of natural runoff and surface rainfall by using the least square fitting method.
FIG. 9 is a functional relation between the rainfall runoff under the conditions of the historical underlay surface and the current underlay surface of a certain hydrological test section established according to the rainfall-runoff relation line.
FIG. 10 is a statistical-based calculation of natural runoff attenuation according to the present invention.
FIG. 11 is a series comparison of natural run-off before and after a statistical-based correction of a historical underlying surface of the present invention.
FIG. 12 is a graphical calculation based on the natural runoff attenuation of the present invention.
FIG. 13 is a graphical method based comparison of natural run off series before and after a historical underlying surface modification of the present invention.
FIG. 14 is a graph of the amount of natural runoff attenuation calculated by the present invention based on a synthetic method.
FIG. 15 is a series comparison of natural run-off before and after the revision of the historical underlay surface based on the synthetic method of the present invention.
FIG. 16 shows the results of the present invention in correcting the consistency of the natural runoff for a hydrological test cross-section using the recommended method.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Aiming at the problems of correction distortion, failure of a statistical correction method and disordered relative magnitude relation of natural runoff before and after correction in the process of correcting consistency of the natural runoff, a hydrological test section in a northern area is selected as a representative example to be analyzed, actual measurement runoff and reduction water quantity data in 1956-2015 are from statistical results of a hydrological department, and precipitation data are from actual measurement data of the hydrological department and a meteorological department. Example calculations were mainly performed by Excel and MATLAB.
The method comprises the following specific steps of natural runoff verification and time series mutability test:
1-1: according to the long-series hydrological test results after the hydrological measurement station is integrated, the daily actual measurement runoff data is converted into annual scale, and the annual actual measurement runoff data in 1956-2015 is obtained, and is shown in figure 2.
1-2: according to the development and utilization conditions of water resources in a drainage basin, by combining agricultural, industrial and domestic water consumption, reservoir storage variables, interval flood diversion quantity and interval water diversion quantity, all reduction components in a catchment range above a hydrological test section are obtained, the natural runoff of a measuring station is verified according to the following formula, the reduced water quantity is shown in a graph 3 in 1956-2015 year by year, and the natural runoff data is shown in a graph 4 in 1956-2015 year.
R＝R1+R2+R3+R4±R5±R6±R7(1)
In the formula: r is reduction runoff; r1The measured runoff is measured; r2The water consumption of agriculture is obtained; r3Industrial water consumption; r4The water consumption of life is obtained; r5The water diversion amount is the water diversion amount across the basin (interval), and the diversion amount is positive; r6The water quantity which can not return after flood diversion is divided into positive water quantity from the station; r7The value is positive when the storage capacity of the reservoir is increased.
1-3: writing a MATLAB program, testing the natural runoff time series mutation by adopting a PETTITT test method, and determining the year corresponding to the maximum value of the test statistic as the mutation point of the natural runoff series, wherein the mutation point is 1998 in the example and is shown in figure 5.
Figure BDA0002207386100000081
Figure BDA0002207386100000082
k(t)＝Max1≤t≤N|Ut,N| (4)
Figure BDA0002207386100000083
In the formula of Ut,NFor test statistics, PbK (t) is a significance probability value of Ut,NMaximum value of the sequence, t being Ut,NThe position, x, corresponding to the maximum value k (t) in the sequencejFor the runoff volume of the jth year, N represents the series length, i.e., the number of input annual runoff volume data.
1-4: according to the mutation point test result, the natural runoff long-time sequence is divided into two sections, and natural runoff series data D and E of the historical underlying surface and the current underlying surface are obtained respectively, namely two periods of 1956-1997 and 1998-2015 are shown in FIG. 6.
II, carrying out rainfall-runoff relation fitting under different underlying surface conditions:
2-1: according to the meteorological monitoring result in the catchment range above the hydrological test section, an MATLAB or VBA program is compiled, and the surface rainfall data F and G of the historical underlying surface and the current underlying surface which have the same time sequence with the natural runoff are obtained by adopting a Thiessen polygon algorithm, and are shown in figure 7.
2-2: obtaining the precipitation-runoff relational expression y of the historical underlying surface as F (x) and the precipitation-runoff relational expression y of the current underlying surface as G (x), and enabling the decisive coefficient R of the expressions2＞0.7；
2-2-1: and respectively establishing rainfall runoff relations under different underlying surface conditions by adopting a least square method, wherein the rainfall runoff relations comprise a regression equation y (F) (x) of the surface rainfall F and the natural runoff D of the historical underlying surface, and a regression equation y (G) (x) of E and G under the current underlying surface condition, and the figure 8 is shown.
Figure BDA0002207386100000091
Note the book
Figure BDA0002207386100000092
The minimum of two of the regression equation coefficientsMultiplying the estimated value
Figure BDA0002207386100000093
In the formula: y is natural runoff, namely a dependent variable; b is a regression coefficient; x is a surface rainfall matrix, namely an independent variable; n is the length of the dependent variable vector; p is the number of independent variables, and when a single independent variable is used, p is 1; selecting a unary linear regression or a high-order polynomial regression according to the fitting condition of the regression equation;
2-2-2: checking whether the regression equations y ═ f (x) and y ═ g (x) obtained in 2-2-1 satisfy R2If the requirement is more than 0.7, the established statistical rainfall-runoff relation is considered to be reliable, and a statistical correction method can be used because R of a fitting equation in the graph 82<0.7, indicating that a direct fit mathematical relationship is not available.
2-2-3: if the statistical relationship between the rainfall series to be treated and the surface rainfall series does not meet the requirement of 2-2-2, analyzing by combining a rainfall-runoff relation curve drawn by an expert experience graph; selecting 10-15 points from a rainfall-runoff relation curve drawn in a graph, and reading the abscissa and ordinate values of the points;
2-2-4: aiming at the data points obtained in the previous step, a least square method fitting method (see the above) is used for obtaining an analytical expression y ═ lambda of the empirical precipitation-runoff relation between the historical underlying surface and the current underlying surface1(x) And y ═ λ2(x) Ensuring the deterministic coefficient R of the analytic expression2See FIG. 9 for > 0.7.
2-2-5: and (3) recording the relation expression of the rainfall-runoff of the historical underlying surface finally determined through the 4 steps as follows: and the relational expression of y ═ F (x) and the current rainfall-runoff of the underlying surface is recorded as: g (x).
III, correcting the consistency of the natural runoff series based on a statistical method, comprising the following specific steps:
3-1: and (3) arranging the rainfall data F of the historical underlying surface in an ascending order, and calculating the attenuation coefficient of the statistical correction method corresponding to the rainfall data F point by point, namely the relative variation of the relationship y between the rainfall and the runoff of the historical underlying surface obtained in the previous step, namely F (x), and the relationship y between the rainfall and the runoff of the current underlying surface, namely G (x), which is shown in formula (7).
Figure BDA0002207386100000101
In the formula, P*For a given year of face rainfall, #*Is the natural runoff attenuation coefficient of the corresponding year.
3-2: a least square method fitting method (see the above) is adopted to establish the function relation psi-P of the attenuation coefficient vector and the surface rainfall vector under the condition of the historical underlying surface, so that the attenuation coefficient corresponding to the rainfall of any surface of the historical underlying surface can be obtained, and further, the natural runoff attenuation quantity series based on a statistical method is obtained, and the figure 10 is shown.
ψ＝k(P) (8)
ΔR＝k(P)*F(P) (9)
In the formula, delta R is a natural runoff attenuation series based on a statistical method, P is a surface rainfall series, k is an attenuation coefficient series corresponding to the surface rainfall, and F (P) is a rainfall runoff relation function of a historical underlay surface.
3-3: the attenuation amount of the natural runoff of the historical underlying surface is calculated year by year according to the expressions (7) to (9), the corrected natural runoff series based on the statistical correction method is determined by combining the natural runoff series before the historical underlying surface is corrected, the calculation method is shown in an expression (10), and the calculation result is shown in a figure 12.
Rmod＝R-ΔR (10)
In the formula, RmodThe corrected natural runoff quantity series is R, and delta R is a natural runoff attenuation quantity series based on a statistical method;
IV, the specific steps of the consistency correction of the natural runoff series based on the graphical method are as follows:
4-1: and (3) calculating the distance between the two curves based on the relation curves of the rainfall and the runoff of the historical underlying surface and the current underlying surface, wherein the difference value is the natural runoff attenuation series based on the graphical method, the calculation method is shown in the formula (11), and the calculation result is shown in the figure 12.
ΔR'＝F(P)-G(P) (11)
In the formula, the delta R' is a natural runoff decrement series based on a graphical method, and other symbols have the same meanings as the above.
4-2: calculating the attenuation of the natural runoff of the historical underlying surface year by year according to the formula (11), determining the corrected natural runoff series based on a graphical correction method by combining the runoff series before correction, wherein the calculation method is shown as the formula (12),
the calculation results are shown in FIG. 13. Rmod＝R-ΔR' (12)
V, correcting, executing and checking the consistency of the natural runoff series based on the comprehensive method:
5-1: and (3) taking the delta R 'obtained by the graphical method as a controllable outer boundary condition, wherein the delta R is required to be less than or equal to the delta R' in the natural runoff volume correction, namely the runoff volume correction in a single year should not exceed the moving distance of a rainfall-runoff relation line, and obtaining a natural runoff volume attenuation series (see figure 14) based on the synthetic method and a corrected natural runoff volume series (see figure 15), see formula (13) and formula (14).
Figure BDA0002207386100000111
Rmod＝R-Rtmp(14)
And (6) evaluating the correction effect. And (5) aiming at the consistent problem of runoff series before and after correction, constructing a statistical index NSE for inspection, and obtaining a formula (15). Aiming at the problem of disordered sequencing of the rich and lean years before and after correction, the natural runoff quantity before the correction of the historical underlying surface is arranged in a descending manner, the 5 maximum annual runoff quantity values are taken out, the corresponding years are recorded, the same operation is carried out on the corrected series, and the mismatching degree S of the rich water years is calculated according to the formula (16). Similarly, the worst 5 years are taken out for comparison, and the mismatching degree V of the dry year is calculated. The criteria for evaluation are that NSE is as large as possible and S and V are as small as possible.
Figure BDA0002207386100000112
Figure BDA0002207386100000121
Figure BDA0002207386100000122
NSE→max,S→min,V→min (18)
In the formula: NSE is the Nash coefficient of the natural runoff series before and after correction, O is the natural runoff series after correction of the historical underlying surface, Q is the natural runoff series before correction of the historical underlying surface, k is the series length, OiAnd QiRespectively the runoff volume after the correction and before the correction in the ith year,
Figure BDA0002207386100000123
the average runoff is evenly averaged for years before correction; s is the nonmatch of full-water years, Tj、T'jRespectively sorting the years corresponding to the runoff with j before and after correction in descending order; v is the mismatching degree of the dry year.
The comparison of the Nash efficiency coefficients before and after the correction by different methods is shown in table 1, the comparison before and after the correction by different methods for 5 years with the highest abundance is shown in table 2, the comparison before and after the correction by different methods for 5 years with the lowest abundance is shown in table 3, and according to the formula (18), the correction effect of the comprehensive method is obviously better than that of the single method.
TABLE 1 correction of the front and rear Nash efficiency coefficient contrast by different methods
Correction by statistical method Graphical solution correction Comprehensive method correction
NSE 0.335 0.627 0.753
TABLE 2 comparison of before and after correction for 5 years of best abundance by different methods
Figure BDA0002207386100000124
TABLE 3 comparison of pre-and post-correction for 5-year-cumtest with different methods
Figure BDA0002207386100000125
Figure BDA0002207386100000131
5-2: the inspection indexes provided in the above steps are used to compare and optimize the correction results of different methods, and the determined natural runoff after the historical underlay surface correction is combined with the current underlay surface, so that the natural runoff length series consistency correction result can be obtained, which is shown in fig. 16.
Finally, it should be noted that the above is only for illustrating the technical solution of the present invention and not for limiting, and although the present invention is described in detail with reference to the preferred arrangement, it should be understood by those skilled in the art that the technical solution of the present invention (such as the application of various formulas, the sequence of steps, etc.) can be modified or equivalently replaced without departing from the spirit and scope of the technical solution of the present invention.

Claims (4)

1. A method for correcting the consistency of a natural runoff series is characterized by comprising five parts: the method comprises the following steps of I, checking the natural runoff and the time sequence mutability; II, analyzing the relation between rainfall and runoff; III, correcting the consistency of the natural runoff series based on a statistical method; IV, correcting the consistency of the natural runoff series based on a graphical method; v, correcting the consistency of the natural runoff series by a comprehensive statistical method and a graphical method;
the specific steps of the identification of natural runoff and the time series mutability test comprise:
1-1: converting the measured runoff data measured day by day into a year scale to obtain measured runoff data A measured year by year;
1-2: obtaining each reduction component in a catchment range above a hydrological test section, and checking the natural runoff of the measuring station according to the formula (1) to obtain the reduction runoff as data B;
R＝R1+R2+R3+R4±R5±R6±R7(1)
in the formula: r is reduction runoff; r1The measured runoff is measured; r2The water consumption of agriculture is obtained; r3Industrial water consumption; r4The water consumption of life is obtained; r5The water diversion amount across the drainage basin is positive; r6The water quantity which can not return after flood diversion is divided into positive water quantity from the station; r7The value is positive when the storage capacity of the reservoir is increased;
1-3: testing the mutability of the natural runoff time sequence by adopting a PETTITT test method, and determining the year corresponding to the maximum value of the test statistic as a mutation point of the natural runoff series to obtain data C;
1-4: dividing the natural runoff long-time sequence into two sections according to the mutation point detection result, and respectively obtaining natural runoff series data D of the historical underlying surface and natural runoff series data E of the current underlying surface;
II, analyzing the relationship between rainfall and runoff, which specifically comprises the following steps:
2-1: according to the meteorological monitoring result in the catchment range above the hydrological test section, obtaining surface rainfall data F of the historical underlying surface and surface rainfall data G of the current underlying surface in the same time sequence with the natural runoff by adopting a Thiessen polygon method or other spatial interpolation and spread algorithms;
2-2: obtaining the precipitation-runoff relational expression y of the historical underlying surface as F (x) and the precipitation-runoff relational expression y of the current underlying surface as G (x), and enabling the decisive coefficient R of the expressions2＞0.7；
The specific steps of the consistency correction of the natural runoff series based on the statistical method comprise:
3-1: arranging the face rainfall data F of the historical underlying surface of each year in an ascending order, and calculating the attenuation coefficient of a statistical correction method corresponding to the face rainfall data F point by point, namely the relative variation of the relationship y between the rainfall and the runoff of the historical underlying surface obtained in the previous step, namely F (x), and the relationship y between the rainfall and the runoff of the current underlying surface, namely G (x), as shown in the formula (7):
Figure FDA0002419364430000021
in the formula, P*For a given year of face rainfall, #*Is the natural runoff attenuation coefficient of the corresponding year;
3-2: establishing a function relation psi-P of the attenuation coefficient vector and the surface rainfall vector under the condition of the historical underlying surface by adopting a least square fitting method, wherein the function relation psi-P is shown as (8), namely the attenuation coefficient corresponding to the rainfall of any surface of the historical underlying surface can be obtained, and further a natural runoff attenuation quantity series based on a statistical method is obtained, wherein the formula is shown as (9);
ψ＝k(P) (8)
ΔR＝k(P)*F(P) (9)
wherein, Delta R is a natural runoff attenuation series based on a statistical method, P is a surface rainfall series, k (P) is an attenuation coefficient function taking the surface rainfall P as an independent variable, and F (P) is a rainfall runoff relation function of a historical underlay surface;
3-3: determining a corrected natural runoff series based on a statistical correction method:
Rmod＝R-ΔR (10)
in the formula, RmodThe corrected natural runoff quantity series is R, and delta R is a natural runoff attenuation quantity series based on a statistical method;
IV, the concrete steps of the consistency correction of the natural runoff series based on the graphical method comprise:
4-1: calculating the distance between two curves based on the relation curves of rainfall and runoff of the historical underlying surface and the current underlying surface, wherein the difference value is the natural runoff attenuation series based on a graphical method, and the calculation method is shown as formula (11):
ΔR'＝F(P)-G(P) (11)
in the formula, delta R' is a natural runoff decrement series based on a graphical method, and other symbols have the same meanings as the above;
4-2: calculating the attenuation amount of the natural runoff of the historical underlying surface year by year according to the formula (11), and determining the corrected natural runoff series based on a graphical correction method by combining the runoff series before correction, wherein the formula (12) is shown:
Rmod＝R-ΔR' (12)
v, the specific steps of the natural runoff series consistency correction of the comprehensive statistical method and the graphical method comprise:
5-1: using the delta R 'obtained by the graphical method as a controllable outer boundary condition, wherein the delta R is not more than or equal to the delta R' in the natural runoff volume correction, namely the runoff volume correction in a single year should not exceed the moving distance of a rainfall-runoff relation line, and obtaining a corrected natural runoff series based on the comprehensive method, which is shown as a formula (13) and a formula (14);
Figure FDA0002419364430000031
Rmod＝R-Rtmp(14)
5-2: and combining the determined natural runoff after the historical underlay surface is corrected with the current underlay surface to obtain the natural runoff long series consistency correction result.
2. The method for correcting the consistency of a natural runoff series according to claim 1, wherein the method comprises the following steps:
in the step 1-3, the data C is obtained by specifically adopting the formulas (2) to (5),
Figure FDA0002419364430000032
Figure FDA0002419364430000033
k(t)＝Max1≤t≤N|Ut,N| (4)
Figure FDA0002419364430000036
in the formula of Ut,NFor test statistics, PbK (t) is a significance probability value of Ut,NMaximum value of the sequence, t being Ut,NThe position, x, corresponding to the maximum value k (t) in the sequencejFor the runoff volume of the jth year, N represents the series length, i.e., the number of input annual runoff volume data.
3. The method for correcting the consistency of a natural runoff series according to claim 1, wherein the method comprises the following steps:
the specific operation method of the step 2-2 comprises the following steps:
2-2-1: respectively establishing rainfall runoff relations under different underlying surface conditions by adopting a least square method, wherein the rainfall runoff relations comprise a regression equation y (F) (x) of surface rainfall F and natural runoff D of a historical underlying surface and a regression equation y (G) (x) of E and G under the current underlying surface condition, and the regression equations are written into the following forms:
Figure FDA0002419364430000034
note the book
Figure FDA0002419364430000035
Then least squares estimates of the regression equation coefficients
Figure FDA0002419364430000041
In the formula: y is natural runoff, namely a dependent variable; b is a regression coefficient; x is a surface rainfall matrix, namely an independent variable; n is the length of the dependent variable vector; p is the number of independent variables, and when a single independent variable is used, p is 1; selecting a unary linear regression or a high-order polynomial regression according to the fitting condition of the regression equation;
2-2-2: checking whether the regression equations y ═ f (x) and y ═ g (x) obtained in step 2-2-1 satisfy R (x)2If the requirement is more than 0.7, the established statistical rainfall-runoff relation is considered to be reliable, and a directly fitted mathematical relation is available;
2-2-3: if the statistical relationship between the rainfall series to be treated and the surface rainfall series does not meet the requirements of the step 2-2-2, analyzing by combining the rainfall-runoff relationship curve submitted by the hydrological testing department; selecting 10-15 data points from a rainfall-runoff relation curve drawn in a graph, and reading the abscissa and ordinate values of the points;
2-2-4: aiming at the data points obtained in the step 2-2-3, obtaining a regression equation y lambda of the relation between the historical underlying surface and the current underlying surface empirical rainfall-runoff by using a least square method fitting method1(x) And y ═ λ2(x) Ensuring the deterministic coefficient R of the regression equation2＞0.7；
2-2-5; when a function equation directly fitted by using the series of the surface rainfall and the runoff quantity is available, representing the rainfall-runoff relation of the historical underlying surface and the current underlying surface by analytical expressions y (f) (x) and y (g) (x); otherwise, the analytical formula y ═ λ is selected1(x) And y ═ λ2(x) As a representative; the relation expression of the rainfall-runoff of the historical underlying surface finally determined through the steps is recorded as follows: and the relational expression of y ═ F (x) and the current rainfall-runoff of the underlying surface is recorded as: g (x).
4. The method for correcting the consistency of a natural runoff series according to claim 1, wherein the method comprises the following steps:
and step V also comprises correction effect evaluation: constructing a statistical index NSE for inspection aiming at the problem of consistency of runoff series before and after correction, as shown in a formula (15), sequencing natural runoff quantity before the correction of a historical underlying surface in a descending order aiming at the problem of sequencing confusion of rich and withered years before and after the correction, taking out 5 values with the largest annual runoff quantity, recording corresponding years, carrying out the same operation on the corrected series, and calculating the mismatching degree S of the rich water years according to the formula (16); taking out the 5 most withered years for comparison, and calculating the mismatching degree V of the withered water years; the criteria evaluated were NSE as large as possible, S and V as small as possible;
Figure FDA0002419364430000051
Figure FDA0002419364430000052
Figure FDA0002419364430000053
NSE→max,S→min,V→min (18)
in the formula: NSE is the Nash coefficient of the natural runoff series before and after correction, O is the natural runoff series after correction of the historical underlying surface, Q is the natural runoff series before correction of the historical underlying surface, k is the series length, OiAnd QiRespectively the runoff volume after the correction and before the correction in the ith year,
Figure FDA0002419364430000054
the average runoff volume of years before correction is carried out; s is the nonmatch of full-water years, TjSorting the natural runoff quantity before correction into the years corresponding to the runoff quantity of j in a descending order, TjThe years corresponding to the runoff with j are sorted in descending order for the corrected natural runoff; v is the mismatching degree of the dry year.
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