CN111831966B - Combined river channel water level forecasting method based on high-dimensional probability distribution function - Google Patents
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Abstract
The invention relates to the technical field of hydrologic forecasting, in particular to a combined river channel water level forecasting method based on a high-dimensional probability distribution function, which comprises the following steps: selecting a time sequence of river channel water levels in a certain period; using the edge distribution function F (X) of the water level data series at time t-1 and time t t‑1 ) And F (X) t ) Constructing a joint distribution probability function of water level variables, and screening three Copula models with minimum AIC values; inputting a water level variable data series X at a known t-1 moment by using a joint distribution probability function t‑1 Solving the conditional distribution probability of the water level variable data series at the moment t; converting the conditional distribution probability function into its inverse form, implemented as X t‑1 Obtaining t-time fitting water level data series X for input variables t The method comprises the steps of carrying out a first treatment on the surface of the And obtaining three optimal Copula model predicted values, setting the weight of each Copula function predicted value according to the AIC value, and calculating the weighted average value of the three Copula function predicted values to obtain the final predicted value. The invention can accurately forecast the river channel water level variable and other hydrologic variables, and has important application value.
Description
Technical Field
The invention relates to the technical field of hydrologic forecasting, in particular to a combined river channel water level forecasting method based on a high-dimensional probability distribution function.
Background
The hydrologic forecasting is to forecast hydrologic conditions in a certain period of time in the future according to the rules of various hydrologic processes in nature and motion and combining the currently acquired hydrologic meteorological data. The result of hydrologic forecasting provides service for reasonable utilization and protection of water resources, flood prevention and emergency, construction of hydraulic engineering, scheduling, application and management and industrial and agricultural safety production. Hydrologic theory is based on physical hydrologic processes because physical processes can scientifically and reasonably reflect actual hydrologic processes. Therefore, numerous physical hydrologic models are built to achieve the purpose of hydrologic forecasting. However, since there are too many uncertain factors in nature, it is difficult for the physical model to completely reflect the influence relationship between variables, resulting in an unsatisfactory effect of the physical model. In addition, physical models often require a large number of underlying surfaces and types of climate data, which are often difficult to obtain in their entirety in practice, thus limiting the application of the physical model.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a combined river channel water level forecasting method based on a high-dimensional probability distribution function.
In order to solve the technical problems, the invention adopts the following technical scheme:
the combined river channel water level forecasting method based on the high-dimensional probability distribution function comprises the following steps:
s1, selecting a time sequence of a water level variable in a certain period aiming at a certain hydrologic station to enable X to be the same as t-1 For the water level data series at time t-1, X t A water level data series at the time t;
s2, utilizing an edge distribution function F (X) of the water level data series at the time t-1 and the time t t-1 ) And F (X) t ) Based on the binary Copula function, constructing a joint distribution probability function of water level variables at the time t-1 and the time t, and screening three Copula models with minimum red-pool information quantity criterion AIC (AKAIKE INFORMATION CRITERION) values;
s3, inputting a water level variable data series X at a known t-1 moment by utilizing the joint distribution probability function constructed in the step S2 t-1 Solving a conditional distribution probability function of a water level variable data series at the moment t;
s4, further converting the conditional distribution probability function into an inverse function form thereof, therebyRealize X as t-1 Obtaining a fitting water level data series X at time t for an input variable t ；
S5, after three Copula model predicted values are obtained, setting the weight of each Copula function predicted value according to the AIC value, and calculating the weighted average value of the three Copula function predicted values to obtain a final predicted value.
According to the combined river channel water level forecasting method based on the high-dimensional probability distribution function, a plurality of coupler function types are introduced, dynamic weights are given according to the forecasting performance, and combined forecasting based on the dynamic weights is achieved; the method can accurately forecast the river channel water level variable, provides a scientific and effective method and means for preventing and controlling drought and flood disasters, and has important application value.
Preferably, in step S1, the forecast variable is the river water level, but the forecast variable of the present invention is not limited to the river water level, and can be extended to other hydrologic variables such as water flow, precipitation, soil humidity, etc., and the time scale of the time sequence includes hours, days, months, and years.
Preferably, in step S2, the type of the binary Copula function is selected from: a Gaussian copula function, a BB1 copula function, a BB6 copula function, a BB7 copula function, a BB8 copula function.
Preferably, in step S2, the AIC value of the Copula model is calculated according to the following formula:
wherein k is the number of parameters of the Copula function, N is the number of variable observations, c (U t，i ，U t-1，i I θ) represents U t，i ，U t-1，i And the parameter θ, i thereof is the i-th observation.
Preferably, in step S3, the conditional distribution probability F (X t ) The method comprises the following steps of:
s31, order U t-1 ＝F(X t-1 )，F(X t-1 ) Is X t-1 Is a function of the edge distribution of (a);
s32 for F (X) in step S31 t-1 ) Each value of (2) is obtained by using three Copula model functions which are selected to obtain corresponding conditional distribution probability:
F(U t |U t-1 )＝h(U t |U t-1 ；θ) (2)
wherein θ is U t 、U t-1 The parameters of the joint probability function of (2) can be calculated by the copula model, and the h function is a standard conditional distribution function.
In addition, the invention further provides a 3-dimensional conditional prediction model, and the formula can be expressed as follows:
F(U t |U t-1 ，U t-2 )＝h[h(U t |U t-2 )|h(U t-1 |U t-2 )] (3)
wherein U is t-2 Is X t-2 Edge distribution function of time series, X t-2 2 times forward;
s33, calculating the probability distribution value U of the variable to be predicted through the inverse function of the calculation formula (2) t ：
U t ＝h -1 (γ|U t-1 ；θ) (4)
For a 3-dimensional conditional prediction model, it can be written as:
U t ＝h -1 (h -1 (γ|h(U t-1 |U t-2 )|U t-1 ) (5)
wherein h is -1 As the inverse function of the h conditional function, γ is the probability value to be set, ranging from [0,1]A plurality of gamma values may be generated by a sampling algorithm and a plurality of U's may be generated for each specific water level data value to be predicted according to equation (4) t 。
In step S4, fitting water level data series X at time t t The method comprises the following steps of:
s41, assuming that the water level variable data series at the time t and the water level variable data series at the time t-1 obey the same distribution, and obtaining an inverse function of the edge distribution function according to the water level variable data series at the time t-1;
s42, inputting the conditional distribution probability obtained by fitting into an inverse function to obtain simulation data. Namely:
X t ＝F -1 (U t ) (6)
wherein X is t Representing the predicted value at time t, F -1 Representing an edge distribution function U t Is an inverse function of (2);
s43, generating n gamma values by a sampling algorithm according to the step S33, and obtaining n probability distribution values U at t moments according to the formula (4) t The predicted values X of the water level variable at n times t can be calculated by the formula (6) t . At this time, by taking the average value of n predicted valuesDefinition:
the water level data series at the time t is obtained by predicting the data value at the time t-1, namely the predicted value
Preferably, in step S5, the weight of each Copula function predicted value is calculated as follows:
wherein w is i Weights representing the i-th Copula function predictors, AIC 1 、AIC 2 、AIC 3 The AIC values of the 1 st, 2 nd and 3 rd Copula functions are shown, respectively.
Preferably, when the predicted value of the three Copula functions is Y 1 、Y 2 、Y 3 The final predicted value Y is calculated as follows:
Y＝Y 1 ×w 1 +Y 2 ×w 2 +Y 3 ×w 3 (9)。
preferably, after step S5, the accuracy of the final predicted value is evaluated using a fitness index comprising a root mean square error RMSE, a nash efficiency coefficient NSE and a decision coefficient R 2 。
Compared with the prior art, the invention has the beneficial effects that:
the invention utilizes the conventional Gaussian copula and BB novel copula function to forecast, and fits the water level data and the joint relation more comprehensively; providing a three-dimensional condition forecasting model to obtain higher forecasting sensitivity; introducing a plurality of copula types, and giving dynamic weights according to the predicted performances of the copula types, so that the combined forecast based on the dynamic weights is realized; the method can accurately forecast the river channel water level variable, provides a scientific and effective method and means for preventing and controlling drought and flood disasters, and has important application value.
Drawings
FIG. 1 is a schematic diagram of a combined river channel water level forecasting method based on a high-dimensional probability distribution function;
FIG. 2 is a graph of three best Copula probability densities for water levels at the daily scale fitted by the present invention;
FIG. 3 is a graph of three best Copula probability densities for water levels at the month scale fitted by the present invention;
FIG. 4 is a graph showing the comparison of measured and simulated values of water level at the daily scale predicted by the method of the present invention;
FIG. 5 is a graph showing the comparison of measured and simulated values of water level at the month scale predicted by the method of the present invention.
Detailed Description
The invention is further described below in connection with the following detailed description. Wherein the drawings are for illustrative purposes only and are shown in schematic, non-physical, and not intended to be limiting of the present patent; for the purpose of better illustrating embodiments of the invention, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the size of the actual product; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
Examples
Fig. 1 shows an embodiment of a method for forecasting a combined river channel water level based on a high-dimensional probability distribution function, which comprises the following steps:
s1, selecting a time sequence of a water level variable in a certain period aiming at a certain hydrologic station to enable X to be the same as t-1 For the water level data series at time t-1, X t A water level data series at the time t; in this embodiment, the step is illustrated by taking the time t-1 as an example, but the method is not limited thereto, and the method can be further extended to more time-lag series as input variables;
s2, utilizing an edge distribution function F (X) of the water level data series at the time t-1 and the time t t-1 ) And F (X) t ) Based on a binary Copula function, constructing a joint distribution probability function of water level variables at the time t-1 and the time t, and screening three Copula models with minimum red pool information quantity criterion AIC values;
s3, inputting a water level variable data series X at a known t-1 moment by utilizing the joint distribution probability function constructed in the step S2 t-1 Solving a conditional distribution probability function of a water level variable data series at the moment t;
s4, further converting the conditional distribution probability function into an inverse function form thereof, thereby realizing the following X t-1 Obtaining a fitting water level data series X at time t for an input variable t ；
S5, selecting three models with the best performance effect from the plurality of copula models to further form a combined prediction model, wherein the copula models selected in the embodiment are not limited to three, and other numbers of copula models can be set according to actual requirements. That is, after obtaining three Copula model predicted values, setting the weight of each Copula function predicted value according to the size of the AIC value, and calculating the weighted average value of the three Copula function predicted values to obtain the final predicted value.
In step S1, the forecast variable is the river water level, but the forecast variable of this embodiment is not limited to the river water level, and may be extended to other water level variables, such as water flow, precipitation, and soil humidity, and the time scale of the time sequence includes hours, days, months, and years.
In step S2, the type of the binary Copula function is selected from: a Gaussian copula function, a BB1 copula function, a BB6 copula function, a BB7 copula function, a BB8 copula function.
In step S2, the AIC value of the Copula model is calculated according to the following formula:
wherein k is the number of parameters of the Copula function, N is the number of variable observations, c (U t ，U t-1，i I θ) represents U t，i ，U t-1，i And the parameter theta, i of the joint density function c is the ith observation value; in this embodiment, the AIC values of the Copula functions are all smaller than 0, and the smaller the AIC values, the higher the fitting degree of the Copula model.
In step S3, the conditional distribution probability F (X t ) The method comprises the following steps of:
s31, order U t-1 ＝F(X t-1 )，F(X t-1 ) Is X t-1 (i.e., 1 moment lag 1 forward) of the edge distribution function;
s32 for F (X) in step S31 t-1 ) Each value of (2) is obtained by using three Copula model functions which are selected to obtain corresponding conditional distribution probability:
F(U t |U t-1 )＝h(U t |U t-1 ；θ) (2)
wherein θ is U t 、U t-1 The parameters of the joint probability function of (2) can be calculated by the copula model, and the h function is a standard conditional distribution function.
In addition, the invention further provides a 3-dimensional conditional prediction model, and the formula can be expressed as follows:
F(U t |U t-1 ，U t-2 )＝h[h(U t |U t-2 )|h(U t-1 |U t-2 )] (3)
wherein U is t-2 Is X t-2 (i.e., 2 forward time instants: lag 2) time sequenceAn edge distribution function of the columns; the embodiment can be implemented under actual requirements according to the three-dimensional condition prediction model;
s33, calculating the probability distribution value U of the variable to be predicted through the inverse function of the calculation formula (2) t For a 2-dimensional conditional prediction model, it can be written as:
U t ＝h -1 (γ|U t-1 ) (4)
for a 3-dimensional conditional prediction model, it can be written as:
U t ＝h -1 (h -1 (γ|h(U t-1 |U t-2 )|U t-1 ) (5)
wherein h is -1 As the inverse function of the h conditional function, γ is the probability value to be set, ranging from [0,1]A plurality of gamma values can be generated through a sampling algorithm, and the number of the gamma values can be taken as 200; then, for each data value (i.e., each specific water level data value to be predicted) a plurality of U's can be generated according to equation (4) t ，U t The number of (2) is equal to the gamma value.
In step S4, fitting water level data series X at time t t The method comprises the following steps of:
s41, assuming that the water level variable data series at the time t and the water level variable data series at the time t-1 obey the same distribution, obtaining an inverse function of an edge distribution function according to the water level variable data series at the time t-1, and restoring data by using the inverse function;
s42, inputting the conditional distribution probability obtained by fitting into an inverse function to obtain simulation data. Namely:
X t ＝F -1 (U t ) (6)
wherein X is t Representing the predicted value at time t, F -1 Representing an edge distribution function U t Is an inverse function of (2);
s43, generating n gamma values according to the step S33 through a sampling algorithm, wherein the n available values are 200; according to equation (4), then, n probability distribution values U at time t can be obtained t The predicted values X of the water level variable at n times t can be calculated by the formula (6) t . At this time, by taking n predicted valuesAverage value ofDefinition:
then the average value of t time is predicted by using the data of t-1 timeFor the finally obtained predictive value +.>
In step S5, three models (or a plurality of models may be set according to actual requirements) with the best performance are selected from the plurality of copula models to further compose a combined prediction model. The weight of each Copula function predictor is calculated as follows:
wherein w is i Weights representing the i-th Copula function predictors, AIC 1 、AIC 2 、AIC 3 The AIC values of the 1 st, 2 nd and 3 rd Copula functions are shown, respectively.
When the predicted value of the three Copula functions is Y 1 、Y 2 、Y 3 The final predicted value Y is calculated as follows:
Y＝Y 1 ×w 1 +Y 2 ×w 2 +Y 3 ×w 3 (9)。
after step S5, the accuracy of the final predicted value is evaluated using a fitness index comprising a root mean square error RMSE, a nash efficiency coefficient NSE and a decision coefficient R 2 。
In order to verify the prediction effect of the method of the present embodiment, the present embodiment selects water level data of a hydrological station from 1989 to 2011 to test (mainly taking a 2-dimensional prediction model as an example, a 3-dimensional prediction model may be implemented according to the 3-dimensional prediction formula provided by the present invention under actual requirements), and includes the following steps:
converting the data at time t and time t-1 into edge distribution functions, respectively, and using the edge distribution F (X t-1 ) And F (X) t ) Constructing a joint distribution probability function of water level variables at the time t-1 and the time t based on a binary Copula function; the types of the Copula functions are selected from Gaussian Copula functions, BB1 Copula functions, BB6 Copula functions, BB7 Copula functions and BB8 Copula functions, parameters and AIC values of the Copula types obtained through calculation are shown in table 1, the Copula types selected by the daily scale are BB1 Copula functions, BB6 Copula functions and BB7 Copula functions, three functional diagrams are shown in FIG. 2, and the Copula models selected by the monthly scale are BB1 Copula functions, BB6 Copula functions and BB8 Copula functions, and three functional diagrams are shown in FIG. 3.
TABLE 1 copuia function fitting case
Constructing a conditional distribution function of a water level variable data series at the time t-1 and a water level variable data series at the time t by using the selected Copula model;
based on the three screened optimal Copula models, a condition prediction model is established by utilizing the condition distribution function of the invention, and the water level prediction values of the three models are respectively obtained;
and calculating weights of the three model predicted values according to the AIC, obtaining a weighted average value of the predicted water level values, and taking the weighted average value as a final predicted value of the embodiment.
Through the above steps, the evaluation analysis of the final predicted value obtained in this example is as follows in table 2:
TABLE 2 model predictive effects of the invention
As can be seen from table 2, the simulation effect of the water level data on the daily scale is good, and the simulation effect of the water level data on the monthly scale is relatively poor. As can be seen from fig. 4 and fig. 5, the measured value and the simulation value of the daily water level data are relatively close, and the simulation effect is good; and the measured value of the lunar scale water level data deviates from the simulation value, so that the simulation effect is relatively poor. This is because the larger the daily-scale water level data amount is, the more the data amount inputted when the model is calibrated, the more representative the model is obtained, and the closer to the actual situation is, and therefore, the RMSE value is smaller, NSE, R 2 The model prediction effect is good because of larger size; the data quantity to be referred in the process of establishing the monthly scale model is relatively limited, the representativeness is poor, the forecasting effect is inferior to that of the daily scale model, but the RMSE value is smaller, so that the forecasting effect of the invention is fair. Therefore, in the combined water level forecasting method of the embodiment, the selected data volume should be as large as possible when the water level forecasting is performed, so as to improve the model forecasting precision and achieve a good forecasting effect. In addition, selecting different copula types may also have a certain influence on the prediction result, so the invention proposes to give a certain weight according to the specific performance by introducing a plurality of copula types, thereby realizing the combined prediction based on the weight. Although only a 2-dimensional conditional combination prediction model is adopted in the embodiment of the invention, the invention provides a specific calculation formula of the 3-dimensional conditional combination prediction model at the same time, and if more input variables are used as prediction factors, the prediction accuracy can be further improved.
It is to be understood that the above examples of the present invention are provided by way of illustration only and not by way of limitation of the embodiments of the present invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are desired to be protected by the following claims.
Claims (5)
1. A combined river channel water level forecasting method based on a high-dimensional probability distribution function is characterized by comprising the following steps:
s1, selecting a time sequence of a water level variable in a certain period aiming at a certain hydrologic station to enable X to be the same as t-1 The water level data series at the time t-1, and Xt is the water level data series at the time t;
s2, utilizing an edge distribution function F (X) of the water level data series at the time t-1 and the time t t-1 ) And F (X) t ) Based on a binary Copula function, constructing a joint distribution probability function of water level variables at the time t-1 and the time t, and screening three Copula models with minimum red pool information quantity criterion AIC values;
s3, inputting a water level variable data series X at a known t-1 moment by utilizing the joint distribution probability function constructed in the step S2 t-1 Solving a conditional distribution probability function of a water level variable data series at the moment t;
s4, converting the conditional distribution probability function into an inverse function form of the conditional distribution probability function so as to realize the condition of X t-1 Obtaining a fitting water level data series X at time t for an input variable t ；
S5, after three Copula model predicted values are obtained, setting the weight of each Copula function predicted value according to the AIC value, and calculating the weighted average value of the three Copula function predicted values to obtain a final predicted value;
in step S2, the type of the binary Copula function is selected from: a Gaussian copula function, a BB1 copula function, a BB6 copula function, a BB7 copula function, a BB8 copula function;
in step S2, the AIC value of the Copula model is calculated according to the following formula:
wherein k is the number of parameters of the Copula function, N is the number of variable observations, c (U t，i ，U t-1，i I θ) represents U t，i ，U t-1，i And its parameter θ;
in the step S3, the conditional distribution probability of the water level variable data series at the moment t is calculated according to the following steps:
s31, order U t-1 ＝F(X t-1 )，F(X t-1 ) Is X t-1 Is a function of the edge distribution of (a);
s32 for F (X) in step S31 t-1 ) Each value of (2) is obtained by using three Copula model functions which are selected to obtain corresponding conditional distribution probability:
F(U t |U t-1 )＝h(U t |U t-1 ；θ) (2)
wherein θ is U t 、U t-1 The parameters of the joint probability function are calculated through a copula model function, and the h function is a standard conditional distribution function;
providing a 3-dimensional conditional prediction model expressed as:
F(U t |U t-1 ，U t-2 )＝h[h(U t |U t-2 )|h(U t-1 |U t-2 )](3)
wherein U is t-2 Is X t-2 Edge distribution function of time series, X t-2 2 times forward;
s33, calculating an edge distribution function U of the water level variable to be predicted through an inverse function of a calculation formula (2) t ：
U t ＝h -1 (γ|U t-1 ；θ) (4)
For a 3-dimensional conditional prediction model, then we express:
U t ＝h -1 (h -1 (γ|h(U t-1 |U t-2 )|U t-1 )) (5)
wherein h is -1 As the inverse function of the h conditional function, γ is the probability value to be set, ranging from [0,1]Generating a plurality of gamma values by a sampling algorithm, and generating a plurality of U's for each specific water level data value to be predicted according to formula (4) t ；
In step S4, fitting water level data series X at time t t The method comprises the following steps of:
s41, assuming that the water level variable data series at the time t and the water level variable data series at the time t-1 obey the same distribution, and obtaining an inverse function of the edge distribution function according to the water level variable data series at the time t-1;
s42, inputting the fitted conditional distribution probability into an inverse function of a predicted variable distribution function to obtain simulation data; namely:
X t ＝F -1 (U t ) (6)
wherein X is t Representing the predicted value at time t, F -1 Edge distribution function U representing water level variable at time t t Is an inverse function of (2);
s43, generating n gamma values through a sampling algorithm according to the step S33, and obtaining n probability distribution values U at t moments according to the formula (4) t Calculating through formula (6) to obtain n predicted values X of water level variable at t moments t The method comprises the steps of carrying out a first treatment on the surface of the At this time, by taking the average value of n predicted valuesDefinition:
the water level data series at the time t is obtained by predicting the data value at the time t-1, namely the predicted value
2. The method for predicting the water level in a combined river based on a high-dimensional probability distribution function as defined in claim 1, wherein in step S1, the time scale of the time series includes hours, days, months and years.
3. The method for predicting the water level in a combined river channel based on a high-dimensional probability distribution function according to claim 1, wherein in step S5, the weight of each Copula function predicted value is calculated according to the following formula:
wherein w is i Weights representing the i-th Copula function predictors, AIC 1 、AIC 2 、AIC 3 The AIC values of the 1 st, 2 nd and 3 rd Copula functions are shown, respectively.
4. The method for forecasting the water level of a combined river channel based on a high-dimensional probability distribution function according to claim 3, wherein when the forecast value of three Copula functions is Y 1 、Y 2 、Y 3 The final predicted value Y is calculated as follows:
Y＝Y 1 ×w 1 +Y 2 ×w 2 +Y 3 ×w 3 (9)。
5. the method for combined channel water level prediction based on high-dimensional probability distribution functions according to claim 3, wherein after step S5, accuracy of final predicted value is evaluated using fitness index including root mean square error RMSE, nash efficiency coefficient NSE and decision coefficient R 2 。
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| CN112665680B (en) * | 2020-11-18 | 2024-05-14 | 贵州电网有限责任公司 | Small hydropower station front cell water level measuring method and measuring system |
| CN112415635B (en) * | 2020-11-19 | 2022-03-29 | 中山大学 | Gamma and Gaussian distribution coupled monthly scale rainfall forecast correction method |
| CN114741435A (en) * | 2022-06-13 | 2022-07-12 | 长江水利委员会长江科学院 | Method for determining water supply guarantee level of control station and related device thereof |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106202788A (en) * | 2016-07-20 | 2016-12-07 | 中国水利水电科学研究院 | A kind of tide flood combined probability analysis method based on Copula function and application thereof |
| CN107622162A (en) * | 2017-09-22 | 2018-01-23 | 江西省水利科学研究院 | A kind of rating curve calculation method based on Copula functions |
| CN109344993A (en) * | 2018-08-23 | 2019-02-15 | 江西省水利科学研究院 | A kind of river flood-peak stage forecasting procedure based on conditional probability distribution |
| CN110020792A (en) * | 2019-03-20 | 2019-07-16 | 三峡大学 | Based on flood flood peak-magnanimity, high rock-fill dam construction is passed the flood period Risk Forecast Method in combination |
-
2020
- 2020-05-21 CN CN202010434730.8A patent/CN111831966B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106202788A (en) * | 2016-07-20 | 2016-12-07 | 中国水利水电科学研究院 | A kind of tide flood combined probability analysis method based on Copula function and application thereof |
| CN107622162A (en) * | 2017-09-22 | 2018-01-23 | 江西省水利科学研究院 | A kind of rating curve calculation method based on Copula functions |
| CN109344993A (en) * | 2018-08-23 | 2019-02-15 | 江西省水利科学研究院 | A kind of river flood-peak stage forecasting procedure based on conditional probability distribution |
| CN110020792A (en) * | 2019-03-20 | 2019-07-16 | 三峡大学 | Based on flood flood peak-magnanimity, high rock-fill dam construction is passed the flood period Risk Forecast Method in combination |
Non-Patent Citations (1)
| Title |
|---|
| 基于G-H copula函数的秦淮河流域洪水风险分析;高玉琴;叶柳;赖丽娟;;水资源与水工程学报(01);第172-177页 * |
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