CN111242472B - Basin similarity degree identification method based on Copula empirical density function - Google Patents
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Abstract
The invention discloses a basin similarity degree identification method based on a Copula empirical density function, which comprises the following steps of: collecting data series of actually measured rainfall, air temperature and flow of a research basin, and calculating an early rainfall Index (API) and a runoff depth value (R); constructing a bivariate Copula empirical density function based on API-R relation of each research basin, and drawing a Copula empirical density function graph; based on a preset threshold value, selecting corresponding areas in a Copula empirical density function graph of API-R to calculate the dissimilarity degree of rainfall-runoff relation among the drainage basins, and identifying the similarity degree of the drainage basins. According to the method, the correlation of the rainfall-runoff process of the drainage basin is analyzed based on the Copula empirical density function, the confluence similarity index between the drainage basins is quantitatively estimated, the similarity degree between the drainage basins can be better identified, and the precision of model parameter transplantation is further improved.
Description
Technical Field
The invention belongs to the technical field of hydrology, and particularly relates to a basin similarity degree identification method based on a Copula empirical density function.
Background
Under the conditions of different hydrometeorology subareas and underlying surfaces, the rainfall-runoff process of a basin is complex and changeable, and the current hydrologic field cannot form a unified theory and generalized conclusion. The data-free area lacks actual measurement data to carry out model calibration, and the flood forecasting problem of the area is one of the difficulties and the key points of the international hydrological study. The international hydrological scientific association initiated an international hydrological decade program named "Prediction in Ungouged bases (PUB)" in 2003, vigorously developed hydrological studies in data-free areas, and achieved fruitful results. In China, a large amount of research is also carried out to solve the problem of flood forecasting in medium and small watershed data shortage areas, and methods such as unit line area synthesis, landform instantaneous unit lines, reasoning formulas and the like are gradually introduced into the flood forecasting research in data-free areas. Model parameter migration among similar flow domains is a commonly adopted method for solving the problems of data-free area model application and flood forecasting at present. The mining of the similarity mechanism of the basin product confluence and the identification of the space product confluence similar area are the premise of parameter regionalization and data starvation area parameter derivation based on the space similarity. At present, a general basin similarity analysis criterion still cannot be made internationally. Most basin similarity cluster analysis methods depend on the geographical spatial position of the basin, and only select the basin underlying surface features or the hydrological meteorological statistics as the feature factors for similarity identification, so that the basin cluster analysis results are very sensitive to initial values, the number of the feature factors and the spatial distance of the basin, the basin cluster analysis results are not unique, high uncertainty is provided, and the time-space variability of the basin and the actual process of basin convergence are generally difficult to consider.
Aiming at the problems, the inventor needs to solve the problem of how to fully consider the time-space dynamic change in the process of performing the basin similarity analysis, select a proper variable and a proper method to perform the identification of the degree of the basin similarity, and reduce the uncertainty of the basin similarity measurement.
Disclosure of Invention
The invention aims to: in order to obtain a stable and reliable basin similarity measurement criterion, the invention provides a basin similarity degree identification method based on a Copula empirical density function.
The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a basin similarity degree identification method based on a Copula empirical density function comprises the following steps:
step 2, constructing a bivariate Copula empirical density function of each research basin based on the API-R relation, and drawing a Copula empirical density function graph;
and 3, selecting areas related to rainfall and runoff depth in a Copula empirical density function graph based on a binary variable API and R, calculating the dissimilarity of rainfall-runoff relation among the drainage basins, and identifying the degree of similarity of the drainage basins.
Further, the step 1 specifically includes:
step 1.1, collecting and calculating average precipitation, air temperature and flow data of day-by-day observation surfaces of about 10 years of a research basin; the specific age can be any age selected from 5 to 15 years.
Step 1.2, adopting a Degree-day snow melting calculation method, distinguishing the snowfall and the rainfall in the drainage basin according to the collected average rainfall and air temperature data of the observation surface in the drainage basin, and estimating the effective rainfall; when the air temperature data is lower than the snow melting critical temperature, the average precipitation of the observation surface is regarded as the snowfall, and the flow is not produced; when the temperature data is higher than the snow melting critical temperature, rainfall is determined as rainfall at the moment, snow begins to melt at the same time, and the snow melting amount is as follows:
Snowmelt(t)＝DD·(T(t)-Tt)T(t)＞Tt (1)
wherein t is the calculation time, in days, Snowmelt (t) is the snow melting amount, DD is the daily snow melting rate, T (t) is the observed air temperature, and Tt is the critical air temperature for snow melting;
when the snow melting amount is less than the snow accumulation amount, the effective rainfall amount capable of forming runoff is as follows:
P(t)＝Pobs(t)+min(Snowmelt(t)，Snow(t)) (2)
wherein P (t) is the effective rainfall at the time t, Pobs (t) is the observed rainfall at the time t, and snow (t) is the snowing amount at the time t;
step 1.3, constructing an early-stage rainfall index model based on the effective rainfall obtained in step 1.2, and calculating day-by-day API values:
API(t+1)＝P(t+1)+α·API(t) (3)
in the formula, API (t +1) and API (t) are API values at t +1 and t, respectively; p (t +1) is effective rainfall at the moment of t + 1; alpha is an attenuation coefficient, and is generally between 0.8 and 0.9 according to experience; the API value at the initial time is assumed to be a 0;
step 1.4, calculating the daily observation runoff depth of the research basin:
wherein R (t) is the daily radial depth (mm) calculated at the current time, and Q (t) is the measured daily average flow (m) 3 (s) Area is the basin Area (km) 2 )。
Further, in the step 2, constructing a bivariate Copula empirical density function of each research basin based on the API-R relationship, and drawing a Copula empirical density function diagram, specifically including the following steps:
step 2.1, selecting a basin to be subjected to similarity identification, calculating an API and an R value of each basin, respectively, forming samples S { (API (T), R (T), T ═ 1, …, T) } from the API and R data of which the total time period number of any one basin is T, arranging the samples S from small to large according to API values, converting the samples S into level data, and calculating the level value of each API:
in the formula, V API (t) is the rating value of API at time t, Ord API (T) is a ranking number of the API in a descending order, and T is the total time interval number;
and then arranging the samples S from small to large according to the values of R, converting the samples S into grade data, and calculating the grade value of each R:
in the formula, V R (t) is the rank value, Ord, at time T R (T) is the ranking number of R in the order from small to large, and T is the total time interval number;
step 2.2, converting the sample S into grade data S 'through formulas (5) and (6), calculating a Copula empirical density function by utilizing S', uniformly dividing a two-dimensional interval [0,1] × [0,1] into L × L regular grids, wherein the positions of the grids are represented by (r, c), r is more than or equal to 1 and less than or equal to L, c is more than or equal to 1 and less than or equal to L, and r is the position of the grid, counted from left to right on the horizontal coordinate; c is the position of the grid from bottom to top on the ordinate, so the empirical frequency corresponding to each grid (r, c) is:
in the formula, |, the total number of elements falling within the grid (r, c) meeting the condition is taken as the empirical frequency Q corresponding to the grid (r, c) rc L is the grid width, r, c is the grid position;
thus, the Copula empirical density corresponding to each grid can be calculated as:
in the formula (I), the compound is shown in the specification,
copula empirical density function for grid location (r, c), L grid width, Q rc An empirical frequency corresponding to the grid position (r, c);
and 2.3, drawing a Copula empirical density function graph according to the calculation result.
Further, in the step 3, selecting areas related to rainfall and runoff depth in a Copula empirical density function graph based on a binary variable API and R, calculating the dissimilarity degree of the rainfall-runoff relation between the drainage basins, and identifying the drainage basin similarity degree, wherein the method comprises the following steps:
and 3.1, in the river basin runoff generation process, the correlation between rainfall and runoff during flood is high, the runoff generation in drought seasons is greatly influenced by other factors, and the correlation between the rainfall and the river basin is low. Therefore, the basin similarity analysis is more reasonable by only selecting Copula empirical density function values in a period with larger rainfall and runoff;
firstly, analyzing the correlation degree of rainfall-runoff according to the empirical density function diagram of each basin, and generally selecting a part with the maximum rainfall and runoff value of 20%, namely a fifth area in the upper right corner of the empirical density function diagram:
in total
Calculating the dissimilarity degree of the drainage basin by each grid;
step 3.2, calculating the dissimilarity index between every two drainage basins aiming at the selected areas:
in the formula D ij To the degree of dissimilarity between the two watersheds numbered i and j,
and
for empirical density values of basin i and basin j at grid (r, c) locations, the grid area selected is:
and 3.3, if the dissimilarity index value between the drainage basins is smaller than a preset threshold value, the hydrological responses of the two drainage basins are similar.
Has the beneficial effects that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the basin similarity degree identification method based on the Copula empirical density function provided by the invention is characterized in that a binary Copula empirical density function is constructed and a density function graph is drawn by calculating the early rainfall index and runoff depth of a basin, the similarity degree is calculated and identified by calculating the dissimilarity degree of rainfall-runoff relations among basins, the inter-basin similarity measurement based on the dynamic change process of the basin is realized, a stable similarity identification method is provided for parameter regional analysis based on basin spatial similarity, and a similarity analysis result is provided for flood forecasting research in a data-free area. The watershed similarity analysis factor selected by the method considers the influence of snow melting in a cold period on runoff production, can effectively reflect the space-time variability and the hydrological response process of the watershed, selects a Copula empirical density function to carry out rainfall-runoff relation analysis, can well describe the correlation among variables without being influenced by marginal distribution, ensures the objective rationality and stability of the result, can provide a good measurement criterion for watershed similarity identification, and further promotes the deep development of watershed parameter regionalization and data-free regional hydrological model application research.
Drawings
FIG. 1 is a schematic diagram of the computational flow of the present invention.
FIG. 2 is a graph of the Copula empirical density function calculated by the present invention.
FIG. 3 is a diagram of empirical density function of highly dependent portions of variables selected in the present invention.
Fig. 4 is a schematic diagram illustrating the calculated dissimilarity between the designated watershed and other watersheds.
FIG. 5 is a schematic diagram of the high similarity watershed calculated in the present invention.
FIG. 6 is a schematic diagram of the low similarity watershed calculated in the present invention.
FIG. 7 is a diagram illustrating the dissimilarity index of 50 domains calculated by the present invention.
Detailed Description
The invention is further described below with reference to the figures and the specific embodiments.
As shown in fig. 1, a basin similarity degree identification method based on Copula empirical density function includes the following steps:
step 2, constructing a bivariate Copula empirical density function based on the API-R relation of each research basin, and drawing a Copula empirical density function graph;
and 3, selecting areas related to rainfall and runoff depth in a Copula empirical density function graph based on a binary variable API and R, calculating the dissimilarity of rainfall-runoff relation among the drainage basins, and identifying the degree of similarity of the drainage basins.
Further, the step 1 specifically includes:
step 1.1, collecting and calculating average precipitation, air temperature and flow data of day-by-day observation surfaces of about 5 to 15 years of a research basin; the specific age can be any number of years selected from 5 to 15 years.
Step 1.2, adopting a Degree-day snow melting calculation method, distinguishing the snowfall and the rainfall in the drainage basin according to the collected average rainfall and air temperature data of the observation surface in the drainage basin, and estimating the effective rainfall; when the air temperature data is less than the critical temperature of snow melting, the average precipitation of the observation surface is regarded as snow falling, and the flow production is not carried out; when the temperature data is greater than the snow melting critical temperature, rainfall is determined as rainfall at the moment, snow begins to melt at the same time, and the snow melting amount is as follows:
Snowmelt(t)＝DD·(T(t)-Tt)T(t)>Tt (1)
wherein t is the calculation time, in days, Snowmelt (t) is the snow melting amount, DD is the daily snow melting rate, T (t) is the observed air temperature, and Tt is the critical air temperature for snow melting;
when the snow melting amount is less than the snow accumulation amount, the effective rainfall amount capable of forming runoff is as follows:
P(t)＝Pobs(t)+min(Snowmelt(t),Snow(t)) (2)
wherein P (t) is the effective rainfall at the time t, Pobs (t) is the observed rainfall at the time t, and snow (t) is the snowing amount at the time t;
step 1.3, constructing an early-stage rainfall index model based on the effective rainfall obtained in step 1.2, and calculating day-by-day API values:
API(t+1)＝P(t+1)+α·API(t) (3)
in the formula, API (t +1) and API (t) are API values at t +1 and t, respectively; p (t +1) is effective rainfall at the moment of t + 1; alpha is an attenuation coefficient, and is generally between 0.8 and 0.9 according to experience; the API value at the initial time is assumed to be a 0;
step 1.4, calculating the daily observation runoff depth of the research basin:
wherein R (t) is the daily radial flow depth (mm) calculated at the current moment, and Q (t) is the measured daily average flow (m) 3 (s) Area is the basin Area (km) 2 )。
Further, in the step 2, constructing a bivariate Copula empirical density function of each research basin based on the API-R relationship, and drawing a Copula empirical density function diagram, specifically including the following steps:
step 2.1, selecting a basin to be subjected to similarity identification, calculating an API and an R value of each basin, respectively, forming samples S { (API (T), R (T), T ═ 1, …, T) } from the API and R data of which the total time period number of any one basin is T, arranging the samples S from small to large according to API values, converting the samples S into level data, and calculating the level value of each API:
in the formula, V API (t) is the rating value of API at time t, Ord API (T) is a ranking number of the API in a descending order, and T is the total time interval number;
and then arranging the samples S from small to large according to the values of R, converting the samples S into grade data, and calculating the grade value of each R:
in the formula, V R (t) is the rank value, Ord, of time R at t R (T) is the ranking number of R in the order from small to large, and T is the total time interval number;
2.2, converting the sample S into grade data S 'through formulas (5) and (6), calculating a Copula empirical density function by utilizing S', uniformly dividing a two-dimensional interval [0,1] x [0,1] into L x L regular grids, wherein the positions of the grids are represented by (r, c), r is more than or equal to 1 and less than or equal to L, c is more than or equal to 1 and less than or equal to L, and r is the position of the grid, counted from left to right on the horizontal coordinate; c is the number from bottom to top of the ordinate, where the grid is located, so the empirical frequency corresponding to each grid (r, c) is:
in the formula, | · | statistic is the total number of elements falling within the grid (r, c) meeting the condition, and is taken as the empirical frequency Q corresponding to the grid (r, c) rc L is the grid width, r, c is the grid position;
thus, the Copula empirical density corresponding to each grid can be calculated as:
in the formula (I), the compound is shown in the specification,
copula empirical density function for grid location (r, c), L grid width, Q rc An empirical frequency corresponding to the grid position (r, c);
and 2.3, drawing a Copula empirical density function graph according to the calculation result.
Further, in the step 3, selecting areas related to rainfall and runoff depth in a Copula empirical density function graph based on a binary variable API and R, performing dissimilarity calculation of rainfall-runoff relations between watersheds, and identifying the watershed similarity degree, wherein the method comprises the following steps:
and 3.1, in the river basin runoff merging process, the relevance between rainfall and runoff is high in the flood period, the runoff yield in the drought season is greatly influenced by other factors, and the relevance between the rainfall and the river basin is low. Therefore, the basin similarity analysis is more reasonable by only selecting Copula empirical density function values in a period with larger rainfall and runoff;
firstly, analyzing the correlation degree of rainfall-runoff according to the empirical density function diagram of each basin, and generally selecting a part with the maximum rainfall and runoff value of 20%, namely a fifth area in the upper right corner of the empirical density function diagram:
in total
Calculating the basin dissimilarity degree of each grid;
step 3.2, aiming at the selected area, calculating the dissimilarity index between every two drainage basins:
in the formula, D ij To the degree of dissimilarity between the two watersheds numbered i and j,
and
selecting grid areas as follows for empirical density values of the drainage basin i and the drainage basin j at the grid (r, c) positions:
and 3.3, if the dissimilarity index value between the drainage domains is smaller than a preset threshold value, the hydrological responses of the two drainage domains are similar.
Taking 50 MOPEX watersheds in the United states as an example, the data of day-to-day rainfall, flow and temperature in 1970-1979 of research watersheds adopts historical observation data provided by the United states geological survey bureau (USGS). The method specifically comprises the following steps:
step one, collecting and researching actually measured precipitation and flow data series of the basin, and calculating an early rainfall index API and a runoff depth value R. The method specifically comprises the following steps:
1) collecting and calculating the average precipitation, air temperature and flow data of observation surfaces of 50 research basins;
2) distinguishing the river basin snowfall from the rainfall according to the rainfall and air temperature data and estimating the effective rainfall by adopting a Degree-day snow melting calculation method; when the air temperature is lower than the snow melting critical temperature, the snowfall is observed and is considered as snowfall, and the flow is not produced; when the air temperature is higher than the snow melting critical temperature, the rainfall is determined as rainfall in the day, the accumulated snow starts to melt, and the accumulated snow melting amount is as follows:
Snowmelt(t)＝DD·(T(t)-Tt)T(t)>Tt (1)
in the formula, t is the calculation time; snowmelt (t) is the amount of snow melt; DD is the daily snow melt rate; t (t) is an observed air temperature; tt is the critical temperature for snow to melt.
In this study, the critical temperature for melting snow is 0 ℃ and the daily snow melting rate is 4.5 mm/day.
When the snow melting amount is less than the snow accumulation amount, the effective rainfall amount capable of forming runoff is as follows:
P(t)＝Pobs(t)+min(Snowmelt(t),Snow(t)) (2)
wherein, P (t) is effective rainfall, Pobs (t) is observed rainfall, snow (t) is current snowfall;
3) constructing an early rainfall index model, and calculating day-by-day API values:
API(t)＝P(t)+α·API(t-1) (3)
in the formula, API (t) and API (t-1) are API values of the current time t and the previous time t-1 respectively; p (t) is effective rainfall at the current moment; alpha is an attenuation coefficient, and is generally between 0.8 and 0.9 according to experience;
the attenuation coefficient α in this study was 0.85.
4) And (3) calculating the daily observation runoff depth of the research basin:
wherein, R (t) is the daily radial flow depth (mm) calculated at the current moment; q (t) is the measured daily average flow (m) 3 S); area is the basin Area (km) 2 )；
Step two, constructing a bivariate Copula empirical density function based on the API-R relation of each research basin, and drawing a Copula empirical density function graph, which specifically comprises the following steps:
1) and selecting the basin to be subjected to similarity identification, and respectively calculating the API and R value of each basin. The API with total time period T and R data of any basin may form samples S { (API (T), R (T), T ═ 1, …, T) }, the samples S are first arranged from small to large according to API values, and are converted into level data, and the level value of each API is calculated:
in the formula, V API (t) is the rating value of API at time t, Ord API (T) is a ranking number of the API in a descending order, and T is the total time interval number;
and then arranging the samples S from small to large according to the values of R, converting the samples S into grade data, and calculating the grade value of each R:
in the formula, V R (t) is the rank value, Ord, at time T R (T) is the ranking number of R in the order from small to large, and T is the total time interval number;
2) the sample S is converted into rank data S 'by equations 5 and 6, and the Copula empirical density function is calculated using S'. And uniformly dividing the two-dimensional interval [0,1] × [0,1] into L × L regular grids, wherein the positions of the grids are represented by (r, c), wherein r is the number from left to right of the horizontal coordinate, the positions of the grids are, c is the number from bottom to top of the vertical coordinate, and the positions of the grids are. Thus, the empirical frequency for each grid (r, c) is:
in the formula, Q rc Is the empirical frequency corresponding to the grid (r, c), L is the grid width; and r and c are grid positions.
Thus, the Copula empirical density corresponding to each grid can be calculated as:
in the formula (I), the compound is shown in the specification,
copula empirical density function of grid location (r, c), L grid width, Q rc The empirical frequency corresponding to the grid location (r, c).
The grid width in this study was set to 25, i.e. the two-dimensional space was evenly divided into a 25 x 25 regular grid.
3) And drawing a Copula empirical density function graph (shown in figure 2) according to the calculation result.
Selecting a corresponding area in a Copula empirical density function graph of API-R for calculating the dissimilarity degree of rainfall-runoff relation between drainage basins based on a preset threshold, and identifying the similarity degree of the drainage basins, wherein the steps are as follows:
1) in the river basin confluence process, the relevance between rainfall and runoff is high during flood, and the rainfall in drought seasons is greatly influenced by other factors and has low relevance to the rainfall in the river basin. Therefore, the basin similarity analysis is more reasonable by only selecting Copula empirical density function values in a period with larger rainfall and runoff. Firstly, analyzing the correlation degree of rainfall-runoff according to the empirical density function graphs of all watersheds, selecting a threshold value, and extracting corresponding data in the empirical density function graphs. Usually, the 20% area with the maximum rainfall and runoff (one fifth part of the upper right corner in the empirical density function chart) is selected for calculationI.e. the position of the first grid in the lower left corner is
In total
A grid. The selection result is shown in fig. 3, and 5 × 5-25 grid areas in the upper right corner of the empirical density map are selected for performing basin rainfall runoff correlation analysis.
2) And (3) calculating the dissimilarity index between every two drainage basins aiming at the selected area:
in the formula, D ij The degree of dissimilarity between the two watersheds numbered i and j,
and
selecting the empirical density values of the drainage basin i and the drainage basin j at the grid (r, c) position
To L.
Fig. 4 shows dissimilarity-based indices of watershed a and watershed B, C, D. FIG. 5 shows the results of high and low similarity obtained from the Copula empirical density function.
3) The smaller the dissimilarity among the stream domains is, the more similar the stream domains are, and accordingly, the identification of the similarity degree among the stream domains can be carried out. Fig. 6 shows the calculation results of the dissimilarity index of 50 watersheds. Blue indicates small dissimilarity, indicating that the domains are similar, while red indicates large dissimilarity between the domains. Fig. 7 shows the correlation of dissimilarity with watershed spatial distance.
It should be noted that the various features described in the above embodiments may be combined in any suitable manner without departing from the scope of the invention. The invention is not described in detail in order to avoid unnecessary repetition.
The foregoing shows and describes the general principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (2)
1. A basin similarity degree identification method based on a Copula empirical density function is characterized by comprising the following steps:
step 1, collecting data of observation rainfall, air temperature and flow of a research basin, and calculating an early rainfall index API and a runoff depth value R;
step 2, constructing a bivariate Copula empirical density function based on the API-R relation of each research basin, and drawing a Copula empirical density function graph;
step 3, selecting areas related to rainfall and runoff depth in a Copula empirical density function graph based on a binary variable API and R, calculating the dissimilarity of rainfall-runoff relation among the drainage basins, and identifying the degree of similarity of the drainage basins;
the step 1 specifically includes:
step 1.1, collecting and calculating average precipitation, air temperature and flow data of an M-year day-by-day observation surface of a research basin;
step 1.2, adopting a Degree-day snow melting calculation method, distinguishing the snowfall and the rainfall in the drainage basin according to the collected average rainfall and air temperature data of the observation surface in the drainage basin, and estimating the effective rainfall; when the air temperature data is less than the critical temperature of snow melting, the average precipitation of the observation surface is regarded as snow falling, and the flow production is not carried out; when the temperature data is greater than the snow melting critical temperature, rainfall is determined as rainfall at the moment, snow begins to melt at the same time, and the snow melting amount is as follows:
Snowmelt(t)＝DD·(T(t)-Tt)T(t)＞Tt (1)
wherein t is the calculation time, in days, Snowmelt (t) is the snow melting amount, DD is the daily snow melting rate, T (t) is the observed air temperature, and Tt is the critical air temperature for snow melting;
when the snow melting amount is less than the snow accumulation amount, the effective rainfall amount capable of forming runoff is as follows:
P(t)＝Pobs(t)+min(Snowmelt(t),Snow(t)) (2)
wherein P (t) is the effective rainfall at the time t, Pobs (t) is the observed rainfall at the time t, and snow (t) is the snowing amount at the time t;
step 1.3, constructing an early-stage rainfall index model based on the effective rainfall obtained in step 1.2, and calculating day-by-day API values:
API(t+1)＝P(t+1)+α·API(t) (3)
in the formula, API (t +1) and API (t) are API values at t +1 and t respectively; p (t +1) is effective rainfall at the moment of t + 1; alpha is an attenuation coefficient; the API value at the initial time is assumed to be a 0;
step 1.4, calculating the daily observation runoff depth of the research basin:
wherein R (t) is the daily radial flow depth (mm) calculated at the current moment, and Q (t) is the measured daily average flow (m) 3 (s) Area is the basin Area (km) 2 )；
In the step 3, areas related to rainfall and runoff depth in a Copula empirical density function diagram based on binary variables API and R are selected, the dissimilarity degree of the rainfall-runoff relation between the drainage basins is calculated, and the drainage basin similarity degree is identified, wherein the method comprises the following steps:
step 3.1, firstly, analyzing the correlation degree of rainfall-runoff according to the empirical density function diagram of each basin, and selecting a part with the maximum rainfall and runoff value of 20%, namely a fifth area at the upper right corner in the empirical density function diagram:
in total
Calculating the basin dissimilarity degree of each grid;
step 3.2, aiming at the selected area, calculating the dissimilarity index between every two drainage basins:
in the formula D ij To the degree of dissimilarity between the two watersheds numbered i and j,
and
for empirical density values of basin i and basin j at grid (r, c) locations, the grid area selected is:
and 3.3, if the dissimilarity index value between the drainage domains is smaller than a preset threshold value, the hydrologic responses of the two drainage domains are similar.
2. The method for identifying the basin similarity degree based on the Copula empirical density function according to claim 1, wherein in the step 2, a bivariate Copula empirical density function based on an API-R relationship is constructed for each research basin, and a Copula empirical density function graph is drawn, and the method specifically comprises the following steps:
step 2.1, selecting a basin to be subjected to similarity identification, calculating an API and an R value of each basin, respectively, forming samples S { (API (T), R (T), T ═ 1, …, T) } by the API and R data of which the total time period number of any basin is T, first arranging the samples S from small to large according to API values, converting the samples S into level data, and calculating a level value of each API:
in the formula, V API (t) is the API rank value, Ord, at time t API (T) is a ranking number of the API in a descending order, and T is the total time interval number;
and then arranging the samples S from small to large according to the R values, converting the samples S into grade data, and calculating the grade value of each R:
in the formula, V R (t) is the rank value, Ord, at time T R (T) is the ranking number of R in the order from small to large, and T is the total time interval number;
step 2.2, converting the sample S into grade data S 'through formulas (5) and (6), calculating a Copula empirical density function by utilizing S', uniformly dividing a two-dimensional interval [0,1] × [0,1] into L × L regular grids, wherein the positions of the grids are represented by (r, c), r is more than or equal to 1 and less than or equal to L, c is more than or equal to 1 and less than or equal to L, and r is the position of the grid, counted from left to right on the horizontal coordinate; c is the number from bottom to top of the ordinate, where the grid is located, so the empirical frequency corresponding to each grid (r, c) is:
in the formula, | · | statistic is the total number of elements falling within the grid (r, c) meeting the condition, and is taken as the empirical frequency Q corresponding to the grid (r, c) rc L is the grid width, r, c is the grid position;
thus, the Copula empirical density corresponding to each grid can be calculated as:
in the formula (I), the compound is shown in the specification,
copula empirical density function of grid location (r, c), L grid width, Q rc An empirical frequency corresponding to the grid position (r, c);
and 2.3, drawing a Copula empirical density function graph according to the calculation result.
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| CN109543147A (en) * | 2018-10-26 | 2019-03-29 | 西安理工大学 | A kind of method of the non-linear quick diagnosis of Basin Rainfall runoff relationship and classification, Reasons |
| CN109710883A (en) * | 2018-12-25 | 2019-05-03 | 河海大学 | A kind of runoff yield excess area rainfall runoff counts description method |
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| CN109543147A (en) * | 2018-10-26 | 2019-03-29 | 西安理工大学 | A kind of method of the non-linear quick diagnosis of Basin Rainfall runoff relationship and classification, Reasons |
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