CN113705855A - Hydrological prediction method based on incomplete beta function - Google Patents
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Abstract
The invention discloses a hydrological prediction method based on an incomplete beta function, which comprises the following steps of 1, analyzing and generalizing statistical characteristics and rules of hydrological elements; 2, judging the adaptability of the statistical characteristics of the hydrological factors and the incomplete beta function; 3, determining an adaptation line type and a parameter range of the incomplete beta curve and a calculation expression related to the hydrologic element statistical characteristic curve; 4, carrying out hydrological model calibration by utilizing historical actual measurement data or carrying out calculation fitting by combining geographic data to obtain curve parameters and a function expression; 5. and carrying out hydrological prediction according to the curve parameters and the function expression. The invention considers the statistical characteristics of the hydrological elements under the complex condition with the coexistence of multiple states, adopts the incomplete beta function curve with flexible and changeable line types to extract the statistical characteristics of the hydrological elements, realizes the line type classification matching of the statistical characteristic curve of the hydrological elements through the parameter range classification, can better meet the actual requirements of hydrological simulation and forecast, and has wide applicability.
Description
Technical Field
The invention relates to a hydrological prediction method, in particular to a hydrological prediction method based on an incomplete beta function.
Background
The hydrological factors are main factors constituting the hydrological situation of a certain place or area at a certain time, and include various hydrological variables and hydrological phenomena in a wide sense, and are not limited to precipitation, evaporation, runoff, water level, flow, water temperature, water quality, tension water storage capacity, free water storage capacity and the like. Analyzing the statistical characteristics of the hydrological elements in time and space is one of the important processes of hydrological simulation and forecasting.
Taking the soil water storage capacity of the drainage basin as an example, the spatial and temporal distribution difference of the soil water storage condition in the natural drainage basin is large, and the reasonable description of the soil water storage capacity is an important content for accurately simulating rainfall runoff. The water storage capacity curve method in the Xinanjiang model can effectively reflect the spatial distribution nonuniformity of the water storage capacity of the soil in the drainage basin, and the method is widely applied at home and abroad. The original Xinanjiang model adopts an exponential single parabolic function to describe a water storage capacity curve, the type of the function curve is single, and the soil moisture movement mode which changes along with the change of terrain, seasons and the like is difficult to meet. There is no clear boundary between different modes and there is a transition region, so using a single exponential function is sometimes insufficient to describe this complex soil water holding capacity distribution. Therefore, a new function expression method is needed to describe the spatial distribution of the soil water storage capacity more variously to improve the accuracy of the runoff yield calculation.
At present, in hydrologic element prediction, a description method for statistical characteristics of hydrologic elements is mostly performed by curve description and function expression. For example, hydrologic prediction is performed on basin tension water storage capacity by a double parabolic method. The specific prediction process is shown in Zhouyichun, A.W. Jayawarena, an improvement of a Xinan river production flow model by using a double parabolic soil water storage capacity curve, A.W. hydrofuge, A.hydronics (12), 38-43. The following disadvantages mainly exist: (1) the adopted curve line is single in shape, and the description of the statistical characteristics of the hydrological factors is not comprehensive. (2) The generalized function expression is complex and segmented, which makes the model calibration process more difficult. Taking a watershed soil water storage capacity curve as an example, most researches adopt a single-parabola curve type water storage capacity curve to carry out runoff production calculation, and a few researches adopt a sectional expression double-parabola type water storage capacity curve. The flexibility and diversity of the space distribution condition of the soil water storage capacity are required to be further improved, and the selection of a proper curve function expression is crucial in order to accurately calculate the yield and improve the hydrological forecasting precision.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems, the invention provides a hydrological prediction method based on an incomplete beta function, which can solve the technical problem that the single type curve of the existing prediction method is not enough to solve the situation of complex hydrological elements.
The technical scheme is as follows: the technical scheme adopted by the invention is a hydrological prediction method based on an incomplete beta function, which comprises the following steps:
Step 2, judging the adaptability of the statistical characteristics of the hydrological factors and the incomplete beta function; the suitability of the statistical characteristic of the hydrological element and the incomplete beta function is judged by taking the hydrological element as a variable and the statistical characteristic value of the hydrological element as a function, and judging whether the statistical characteristic of the hydrological element meets an incomplete beta function expression, wherein the incomplete beta function expression is as follows:
wherein x is used to represent a variable of a hydrological element, fα,β(x) The statistical characteristic values used for representing the hydrological elements, alpha and beta are two parameters of the curve, and t represents time.
first class, α, β ∈ (0, 1);
when alpha is less than beta, the slope of the trend line is larger when alpha is larger;
when alpha is equal to beta, the upper and lower half-branches are centrosymmetric inverse S-shaped curves, and the larger alpha and beta are, the larger the gradient of the trend line is;
when alpha is larger than beta, the slope of the trend line is larger when beta is larger;
the second class, α, β ∈ (1, 100 ];
when alpha is less than beta, the slope of the trend line is larger when alpha is larger and the upper half is a main S-shaped curve;
when alpha is equal to beta, the upper half branch and the lower half branch are centrosymmetric S-shaped curves, and the larger the alpha and the beta are, the larger the gradient of the trend line is;
when alpha is larger than beta, the slope of the trend line is larger when beta is larger;
When alpha is less than beta, the parabola (the upper half branch of the S-shaped curve) is parabolic, the larger alpha is, the smaller beta is, and the larger the gradient of the trend line is;
when alpha is larger than beta, the parabola (the lower half branch of the S-shaped curve) is parabolic, the smaller alpha is, the larger beta is, and the larger the gradient of the trend line is;
a fourth class, α ═ β ═ 1; a straight line with a slope equal to 1.
Step 4, carrying out hydrological model calibration by utilizing historical actual measurement data or carrying out calculation fitting by combining geographic data to obtain curve parameters and a function expression; the method for calibrating the hydrological model by using the historical measured data or calculating and fitting by combining the geographic data is characterized in that calibration or calculation is adopted according to the model characteristics and the data completeness to determine the acquisition mode of the curve parameter values.
And 5, carrying out next hydrologic prediction according to the curve parameters and the function expression obtained in the step 4.
Has the advantages that: compared with the prior art, the invention has the following advantages: the invention adopts the incomplete beta function curve with flexible and changeable linear type to describe the statistical characteristics of the hydrological elements, has wider applicability compared with the prior single linear or sectional curve, improves the flexibility and diversity of the description function, can more comprehensively consider the statistical characteristics of the multi-state coexistence of the hydrological elements under the complex condition, improves the hydrological forecasting precision and can better meet the actual requirements of hydrological simulation and forecasting. The parameter range classification provided by the invention distinguishes curve line types, realizes classification matching of hydrologic element statistical characteristic curve line types, quickly determines parameter ranges, is simpler in model rating process, improves the efficiency of rating and parameter calculation, has smaller influence on a double-parameter function curve by different parameters and the same effect than a multi-parameter function curve, and has higher operability and reliability.
Drawings
FIG. 1 is a flow chart of a hydrological prediction method based on incomplete beta functions according to the present invention;
FIG. 2 is (a) a schematic representation of three line forms of a basin tension water holding capacity curve; (b) a basin tension water storage capacity graph converted from graph (a) based on an incomplete beta function;
FIG. 3 is a schematic diagram of different line types of incomplete beta function curves;
fig. 4 is a graph of the tensile water holding capacity curve and its production flow rate based on the partial beta function.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
The hydrological prediction method based on the incomplete beta function can be applied to different hydrological elements according to linear matching, and the statistical feature extraction method is introduced by taking the hydrological element of drainage basin tension water storage capacity as an example. The present embodiment is only for explaining the present invention, and does not limit the statistical application of hydrological elements of the present invention except for the watershed tension water storage capacity.
Fig. 1 is a flowchart of a hydrological prediction method based on an incomplete beta function according to the present invention, which includes the following steps:
the hydrological elements in the invention are hydrological elements in a broad sense, are main factors constituting the hydrological conditions of a certain place or area in a certain period of time, and comprise various hydrological variables and hydrological phenomena. Taking the drainage basin tension water storage capacity as an example, according to the hydrographic forecast historical data point drawing and experience summarization, the spatial distribution characteristic of the drainage basin tension water storage capacity can be statistically described as a parabola in the humid season, and the inverse S-shaped curve can more accurately and comprehensively describe the spatial distribution characteristic of the drainage basin tension water storage capacity in the dry season and the dry-wet transition period. Fig. 2(a) shows three line-type diagrams of the basin tension water storage capacity curve. W 'in the drawing'mIndicates the tensile water storage capacity (mm), W 'at a certain point in the flow field'mmDenotes the maximum point tension water storage capacity (mm) in the drainage area, and f denotes a tension water storage capacity of W 'or less'mArea of flow field (km)2) And F represents the basin area (km)2)。
Step 2, judging the adaptability of the statistical characteristics of the hydrological factors and the incomplete beta function:
according to the incomplete beta function expression of the statistical characteristics of the hydrological elements:
wherein x is used to represent a variable of a hydrological element, fα,β(x) The statistical characteristic values for representing the hydrological elements, α and β are two parameters of the curve. Fig. 3 is a schematic diagram of an incomplete beta function curve, and several line types drawn in the diagram are only examples and do not represent all line types of the incomplete beta function curve.
According to the comparison analysis of the basin tension water storage capacity curve and the incomplete beta function curve, the three line types of the basin tension water storage capacity curve can be judged to be matched with the incomplete beta function.
the parameter range of the incomplete beta function is divided into the following four types according to the actual application requirement and the curve shape:
first class, α, β ∈ (0, 1);
when alpha is less than beta, the slope of the trend line is larger when alpha is larger;
when alpha is equal to beta, the upper and lower half-branches are centrosymmetric inverse S-shaped curves, and the larger alpha and beta are, the larger the gradient of the trend line is;
when alpha is larger than beta, the slope of the trend line is larger when beta is larger.
The second class, α, β ∈ (1, 100 ];
when alpha is less than beta, the slope of the trend line is larger when alpha is larger and the upper half is a main S-shaped curve;
when alpha is equal to beta, the upper half branch and the lower half branch are centrosymmetric S-shaped curves, and the larger the alpha and the beta are, the larger the gradient of the trend line is;
when alpha is larger than beta, the slope of the trend line is larger when beta is larger.
When alpha is less than beta, the parabola (the upper half branch of the S-shaped curve) is parabolic, the larger alpha is, the smaller beta is, and the larger the gradient of the trend line is;
when alpha is larger than beta, the parabola (the lower half branch of the S-shaped curve) is larger, the smaller alpha is, the larger beta is, and the slope of the trend line is larger.
A fourth class, α ═ β ═ 1; a straight line with a slope equal to 1.
According to the formula (1) and the significance of hydrological elements in the model, obtaining a functional expression of a basin tension water storage capacity curve based on the incomplete beta function:
wherein W'mIndicates the water storage capacity (mm), W 'at a certain point in the flow field'mmDenotes the maximum point water storage capacity (mm) in the drainage area, and f denotes a water storage capacity of W 'or less'mArea of flow field (km)2) And F represents the basin area (km)2) And alpha and beta are two parameters of the curve, W'mmIs one of the model parameters.
Thereby converting the three line-type watershed tension water storage capacity curves shown in fig. 2(a) into the watershed tension water storage capacity curve based on the incomplete beta function shown in fig. 2 (b).
According to fig. 2(b), the parameter pairs of the incomplete beta function to which equation (2) is fitted are β 0 α ═ 0.75, and β ═ 0.23, respectively; β 1 α ═ 1.3, β ═ 0.5; β 2 α ═ 3.1, β ═ 2. Further, the parameter ranges of the three adaptation line types can be determined as follows: a first class of α, β ∈ (0, 1) and α > β; of the third kindAnd a second class of α, β ∈ (1, 100)]。
FIG. 4 is a diagram showing a specific tension water storage capacity curve and its output flow rate based on incomplete beta function, and the curve parameter range is alpha, beta epsilon (1, 100) according to classification]In combination with production, the parameter range can be reduced to alpha, beta epsilon (1, 50)]. : w 'in FIG. 4'm、W′mmF and F have the same meanings as in FIG. 2, W'mmIs one of the parameters of the model,is the average water storage of the early stage basin, A is the corresponding ordinate value of the average water storage of the early stage basin, PE is net rain, and R is the output.
Taking the model of Xinanjiang as an example, the hydrological model deduces a runoff calculation formula of the runoff production model according to the formula (2):
when PE + A < W'mm,
When PE + A is more than or equal to W'mm
Wherein the content of the first and second substances,representing the mean tensile water holding capacity (mm) of the basin,the mean tensile water storage capacity (mm) at the early stage of the watershed is shown, and a represents the corresponding ordinate value in fig. 4 of the mean tensile water storage capacity at the early stage of the watershed.The method is one of initial conditions of the model and can be determined according to the average tension water storage volume value obtained by hydrological features, experience or early calculation of the watershed.
Step 4, carrying out hydrological model calibration by utilizing historical actual measurement data or carrying out calculation fitting by combining geographic data to obtain curve parameters and a function expression:
wherein the hydrological model is selected and applied according to actual requirements. And (3) improving a production flow calculation formula in the Xinanjiang model program according to the formula (5) and the formula (6), and then carrying out parameter calibration on the model through an automatic optimization algorithm. The purpose of parameter calibration is mainly to obtain parameters of a basin tension water storage capacity curve, so that the simulation result of the production flow is used as a main object for evaluating the simulation effect to weaken the influence of different and identical effects caused by the calibration of the runoff process so as to quickly and effectively obtain curve parameters.
And 5, carrying out hydrological prediction according to the obtained curve parameters and the function expression.
According to the curve parameters and the function expression obtained in the previous steps, the corresponding numerical value of the basin tension water storage capacity in a future period of time can be obtained on the function, and hydrologic prediction is carried out on the basin tension water storage capacity. The calculation method of the invention is used for obtaining the hydrological parameter function expression.
Claims (5)
1. A hydrological prediction method based on an incomplete beta function is characterized by comprising the following steps:
step 1, analyzing and generalizing statistical characteristics and rules of hydrological factors;
step 2, judging the adaptability of the statistical characteristics of the hydrological factors and the incomplete beta function;
step 3, determining an adaptation line type and a parameter range of the incomplete beta curve and a calculation expression related to the hydrologic element statistical characteristic curve;
step 4, carrying out hydrological model calibration by utilizing historical actual measurement data or carrying out calculation fitting by combining geographic data to obtain curve parameters and a function expression;
and 5, carrying out hydrological prediction according to the curve parameters and the function expressions obtained in the step 4.
2. The method according to claim 1, wherein the method comprises: the hydrological elements in step 1 are generalized hydrological elements, which are main factors constituting the hydrological conditions of a certain place or area in a certain period of time, including various hydrological variables and hydrological phenomena.
3. The method according to claim 1, wherein the method comprises: the step 2 of judging the suitability of the statistical characteristic of the hydrological element and the incomplete beta function is to use the hydrological element as a variable, use the statistical characteristic value of the hydrological element as a function, and judge whether the statistical characteristic of the hydrological element meets an expression of the incomplete beta function, where the expression of the incomplete beta function is as follows:
wherein x is used to represent a variable of a hydrological element, fα,β(x) The statistical characteristic values used for representing the hydrological elements, alpha and beta are two parameters of the curve, and t represents time.
4. The method according to claim 1, wherein the method comprises: the parameter ranges of the incomplete beta function in the step 3 are divided into the following four types:
first class, α, β ∈ (0, 1);
when alpha is less than beta, the slope of the trend line is larger when alpha is larger;
when alpha is equal to beta, the upper and lower half-branches are centrosymmetric inverse S-shaped curves, and the larger alpha and beta are, the larger the gradient of the trend line is;
when alpha is larger than beta, the slope of the trend line is larger when beta is larger;
the second class, α, β ∈ (1, 100 ];
when alpha is less than beta, the slope of the trend line is larger when alpha is larger and the upper half is a main S-shaped curve;
when alpha is equal to beta, the upper half branch and the lower half branch are centrosymmetric S-shaped curves, and the larger the alpha and the beta are, the larger the gradient of the trend line is;
when alpha is larger than beta, the slope of the trend line is larger when beta is larger;
When alpha is less than beta, the parabola (the upper half branch of the S-shaped curve) is parabolic, the larger alpha is, the smaller beta is, and the larger the gradient of the trend line is;
when alpha is larger than beta, the parabola (the lower half branch of the S-shaped curve) is parabolic, the smaller alpha is, the larger beta is, and the larger the gradient of the trend line is;
a fourth class, α ═ β ═ 1; a straight line with a slope equal to 1.
5. The method according to claim 1, wherein the method comprises: in the step 4, the hydrological model calibration is performed by using the historical measured data, or calculation fitting is performed by combining the geographic data, and the calibration or calculation is adopted according to the model characteristics and the data completeness to determine the acquisition mode of the curve parameter values.
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