CN112949046A - Method for calculating urban design double-peak rainstorm type - Google Patents
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Abstract
The invention provides a method for calculating a double-peak rainstorm type designed in a city, which comprises the steps of obtaining a virtual rain peak according to a main peak and a secondary peak of double-peak rainstorm in a field, calculating the rain amount of the virtual rain peak, obtaining a best-fit linear formula and a correlation coefficient according to the relationship between the rain amount of the virtual rain peak and the sum of the total rain amount, the secondary peak rain amount, the main peak rain amount and the secondary peak rain amount of the field, and finally obtaining the main peak rain amount and the secondary peak rain amount of the double-peak rainstorm through the fitted linear formula. The method provided by the invention is more accurate in solving the rainfall of the main peak and the secondary peak for the P & C rain type method, and meanwhile, the method is divided into two situations of the main peak being in front, the secondary peak being behind, the main peak being behind and the secondary peak being in front, so that compared with the P & C rain type method which is not distinguished, the method is more in line with the actual rainfall situation, an important way is provided for researching the double-peak rain type, and the diversity of the method for deducing the double-peak rain type is increased.
Description
Technical Field
The invention belongs to the field of urban design rainstorm research, and particularly relates to a method for calculating an urban design double-peak rainstorm type.
Background
The city promotes the social and economic development and simultaneously has negative influence on the natural ecological environment of the urban area, the urban forest coverage rate is reduced due to the urbanization, the trend of the greenhouse effect is increasingly intensified, the urban area has higher heat absorption rate due to the urbanization, the heat island effect is formed, and finally the extreme rainstorm weather events are obviously increased.
The urban design of the rainfall type of the double-peak rainstorm refers to the distribution condition of rainfall intensity or rainfall on a time scale, is an important basis for planning and designing an urban drainage system, and is key input data of urban rainfall runoff simulation calculation. Under the background of severe urban inland inundation disaster conditions in China, the method has important significance for deducing scientific urban design of the double-peak rainstorm type.
Since the short-duration single-peak rainstorm accounts for a large proportion of the total rainstorm, the current urban rainstorm flood research process mainly takes single-peak rainstorm as the main factor, and therefore, the research on the double-peak rainstorm is insufficient. With the intensive research, the proportion of the bimodal rainstorm in some regions is increased more than before, but at present, few methods for researching the bimodal rainstorm pattern exist, and the bimodal rainstorm pattern needs to be researched. The existing method for calculating the rainstorm type comprises a K & C rain type (Chicago rain type), a P & C rain type and a Huff rain type, and the three rain type methods are all directed at a single peak; the P & C rain pattern can be found to be a uniform double peak rain pattern, but has the following drawbacks: 1. the P & C rainfall pattern does not consider the influence of main and secondary peak rainfall on the calculation of urban design rainstorm rainfall pattern in the actual rainfall process, the actual rainfall process has time distribution nonuniformity, and the change rules of the main peak rainfall and the secondary peak rainfall are different; 2. the P & C rain type does not distinguish the situation that the main peak is in front and the secondary peak is in back or the main peak is in back and the secondary peak is in front, which is not in accordance with the actual situation.
The Chinese invention patent CN 107016178B discloses a method for calculating the type of rainstorm of urban design, firstly, sampling the rainstorm of a field and determining the rainstorm sample of the field; then dividing the scene rainstorm sample into a pre-peak rainstorm sample and a post-peak rainstorm sample according to the position of the maximum rainfall; calculating a rain peak coefficient of a field rainstorm sample and a proportion of rainfall of the field rainstorm sample to total rainfall of the field rainstorm sample based on a division result of the pre-peak rainstorm sample and the post-peak rainstorm sample, and respectively calculating a pre-peak rainstorm type and a post-peak rainstorm type based on a Huff rain type method according to time distribution characteristics of the pre-peak rainstorm sample and the post-peak rainstorm sample; combining the pre-peak rainstorm rain type and the post-peak rainstorm rain type to obtain a rain type of urban design rainstorm; the method fully considers the inconsistency of rainfall rules of the designed rainstorm before and after the rain peak, the obtained matching degree of the designed rainstorm type and the actual rainfall process is high, and the defect that the difference between the estimated raintype and the actual rainfall process is larger due to the fact that the change of the rain peak position along with the duration is not considered in the traditional method is overcome. The above patent is a calculation method based on a unimodal storm design, and is not suitable for bimodal stormwater.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a method for calculating a double-peak rainstorm model designed in an urban area, which comprises the steps of utilizing a double-peak rainstorm model to perform single peaking to obtain a virtual rain peak, then obtaining a virtual rain peak coefficient and a virtual rain peak rainfall formula through a method for restoring the double peak, calculating a main peak rainfall and a secondary peak rainfall of the double-peak rainstorm through linear relations between the virtual rain peak rainfall and the sum of the independent field secondary total rainfall, the main peak rainfall, the secondary peak rainfall and the main and secondary peak rainfalls respectively, finally calculating the double-peak rainstorm model by combining a P & C rainfall method, and drawing a rainfall process curve.
In order to achieve the purpose, the invention is realized by the following technical scheme:
the invention provides a method for calculating a urban design double-peak rainstorm type, which is characterized by obtaining a virtual rain peak according to a main peak and a secondary peak of a field-time double-peak rainstorm, obtaining a best-fit linear formula and a correlation coefficient according to the relation between the rain amount of the virtual rain peak and the sum of the total rain amount, the secondary peak rain amount, the main peak rain amount and the secondary peak rain amount of the field-time rainfall, and finally obtaining the main peak rain amount and the secondary peak rain amount of the double-peak rainstorm through the fitted linear formula.
In a preferred embodiment, the method for estimating the urban design bimodal rainstorm specifically comprises the following steps:
s1, selecting a plurality of field double-peak rainstorm samples according to historical measured rainfall data, and calculating to obtain the positions of a main peak and a secondary peak in the double-peak rainstorm field;
s2, obtaining a plurality of virtual rain peaks according to the main peak and the secondary peak of the multi-field secondary double-peak storm rain, and calculating to obtain a comprehensive virtual rain peak coefficient and a virtual rain peak rainfall;
s3, respectively carrying out linear fitting on the virtual rain peak rainfall obtained in the step S2 and the sum of the total rainfall, the secondary rain peak rainfall, the main rain peak rainfall and the secondary rain peak rainfall in the field to respectively obtain a linear formula and a correlation coefficient of the best fitting;
s4, selecting a double-peak rainstorm sample of a scene, calculating to obtain main peak rainfall and secondary peak rainfall by using the best-fit linear formula obtained in the step S3, and obtaining the partial rainfall and the distribution proportion except the main peak rainfall and the secondary peak rainfall by a P & C rain type method;
and S5, obtaining a rainstorm model according to the main peak position and the secondary peak position obtained in the step S1, the main peak rainfall and the secondary peak rainfall, and the partial rainfall except the main peak rainfall and the secondary peak rainfall and the distribution proportion obtained by the P & C rainfall model method.
In a preferred embodiment, the positions of the main peak and the secondary peak in the bimodal storm run are obtained in step S1 by counting the main peak position average, the secondary peak position average or the main peak position mode, and the secondary peak position mode in the bimodal storm run, where the main peak, the secondary peak position average and the main peak, and the secondary peak position mode are selected as the positions of the main peak and the secondary peak in the bimodal storm run because the main peak and the secondary peak have a higher probability of falling on the average and mode.
In a preferred embodiment, the integrated virtual rain peak coefficient calculation formula in step S2 is as follows:
wherein r isiVirtual rain peak coefficient, t, for each field of double peak rainstormi、tjRespectively the time of occurrence of the main peak and the secondary peak of the double-peak heavy rain, hi、hjRespectively the main peak rainfall and the secondary peak rainfall, T is the total historical duration of a rain fall, rjTo synthesize the virtual rain peak coefficient, i ═ j ═ 1, 2, 3 … … n, and n is the total rainfall field.
In a preferred embodiment, the virtual rain peak rainfall calculation method in step S2 is as follows:
when the main peak is in front and the secondary peak is in back in the double-peak heavy rain type, the rain amount H of the virtual rain peakiSatisfy Hi＝hi×yi+hj×yjAnd hj＜Hi＜hj+hi，yi、yjSatisfies the following conditions: a is more than 0 and less than or equal to yi≤1、0＜b≤yjLess than or equal to 1, wherein hi、hjRespectively, the main peak rainfall and the secondary peak rainfall, yi、yjRespectively a main peak coefficient and a secondary peak coefficient, a and b respectively are the minimum value of the main peak coefficient and the secondary peak coefficient, and the position x of the main peakiThe closer to the virtual rain peak, the peak rain amount h of the main peakiCorresponding coefficient yiThe larger, and xiAnd yiIs a linear relation, the position x of the secondary peakjThe closer to the virtual rain peak, the lower the secondary peak rainfall hjCorresponding coefficient yjThe larger, xjAnd yjIs a linear relationship, and xiAnd yiIs a linear relationship, xjAnd yjIn a linear relationship, the calculation formula is obtained according to the above conditions as follows:
xk＝rjn
wherein r isjFor synthesizing the virtual rain peak coefficient, n is the number of time periods, xkThe time interval corresponding to the comprehensive virtual rain peak coefficient;
when x isi∈[1，xk]，yiIs calculated by the formula
When x isj∈[xk，n]，yiIs calculated by the formula
When the main peak is in front, the value range of the main peak coefficient is [ a,1 ], the value range of the secondary peak coefficient is [ b,1), and the rainfall H of the virtual rain peakiThe calculation formula is as follows:
in a preferred embodiment, the virtual rain peak rainfall calculation method in step S2 is as follows:
when the secondary peak is in front of the main peak and the main peak is behind the secondary peak in the double-peak heavy rain type, the rainfall of the virtual rain peak is HiSatisfy Hi＝hi×yi+hj×yjAnd hj＜Hi＜hj+hi，yi、yjSatisfies the following conditions: a is more than 0 and less than or equal to yi≤1、0＜b≤yjLess than or equal to 1, wherein hi、hjRespectively, the main peak rainfall and the secondary peak rainfall, yi、yjRespectively a secondary peak coefficient and a main peak coefficient, a and b respectively are the minimum value of the main peak coefficient and the secondary peak coefficient, and the position x of the secondary peakiThe closer to the virtual rain peak, the lower the peak-to-peak rainfall hiCorresponding coefficient yiThe larger, and xiAnd yiIs a linear relation, the main peak position xjThe closer to the virtual rain peak, the main peak rainfall hjCorresponding coefficient yjThe larger, xjAnd yjIs a linear relationship, and xiAnd yiIs a linear relationship, xjAnd yjIn a linear relationship, the calculation formula is obtained according to the above conditions as follows:
xk＝rjn
wherein r isjFor synthesizing the virtual rain peak coefficient, n is the number of time periods, xkThe time interval corresponding to the comprehensive virtual rain peak coefficient;
when x isi∈[1，xk]，yiIs calculated by the formula
When x isj∈[xk，n]，yiIs calculated by the formula
When the main peak is in front, the value range of the main peak coefficient is [ a,1 ], the value range of the secondary peak coefficient is [ b,1), and the rainfall H of the virtual rain peakiThe calculation formula is as follows:
in a preferred embodiment, the least square method is used to obtain the best fit linear formula and the correlation coefficient of the virtual rain peak rainfall and the sum of the total rainfall, the secondary rainfall, the main rainfall and the secondary rainfall of the rainfall in the session respectively in step S3,
the least square method formula is as follows:
the correlation coefficient formula is as follows:
in a preferred embodiment, when the main peak position average and the secondary peak position average are used to calculate the positions of the main peak and the secondary peak in a double-peak rainstorm run, a group of rainstorm patterns is obtained, when the main peak position mode and the secondary peak position mode are used to calculate the positions of the main peak and the secondary peak in the double-peak rainrun, another group of rainstorm patterns is obtained, the two groups of rainstorm patterns are compared with the measured value, and the rainstorm pattern determined by the main peak and the secondary peak position with good attaching degree of the rainstorm patterns is selected as the final rainstorm pattern.
In a preferred embodiment, the P & C rain-type process comprises the steps of:
dividing each rainstorm into n small segments, sequencing and numbering the time segments, wherein the large rainfall corresponds to the small numbers, namely each rainstorm has n serial numbers;
averaging the serial numbers corresponding to each time interval, and taking the value from small to large to correspond to the rainstorm intensity of the time interval from large to small;
calculating the ratio of the rainfall capacity of each rainstorm in each time interval to the total rainfall capacity, and taking an average value;
and fourthly, forming a rainfall process curve on the premise of the maximum possible sequence determined in the step 2 and the distribution proportion determined in the step 3.
P&The C rain type method is that all the rainfalls of the same period of time except the main peak and the secondary peak are added and compared with the total rainfall, and then the sum of proportions is distributed and normalized, wherein the proportion of the distribution of each period of time is ki，i＝1,2,…,n。
The invention has the following beneficial effects:
(1) the invention provides a method for calculating a double-peak rainstorm type designed in a city, which comprises the steps of obtaining a virtual rain peak according to a main peak and a secondary peak of double-peak rainstorm in a field, calculating the rain amount of the virtual rain peak, obtaining a best-fit linear formula and a correlation coefficient according to the relationship between the rain amount of the virtual rain peak and the sum of the total rain amount, the secondary peak rain amount, the main peak rain amount and the secondary peak rain amount of the field, and finally obtaining the main peak rain amount and the secondary peak rain amount of the double-peak rainstorm through the fitted linear formula.
(2) The method for calculating the urban design double-peak heavy rain type is more accurate in solving the rainfall of the main peak and the secondary peak for the P & C rain type, and meanwhile, the method is divided into two situations, namely the situation that the main peak is in front of the main peak, the situation that the secondary peak is behind the main peak and the situation that the secondary peak is in front of the main peak, and the situation that the secondary peak is behind the main peak.
Drawings
FIG. 1 is a flow chart of a method for estimating a city design twin peak rainstorm type according to the present invention;
FIG. 2 shows the coefficient y of the main and sub-peak when the main peak is before and the sub-peak is afteri、yjAnd the primary and secondary peak positions xi、xjA relationship diagram of (1);
fig. 3 is a schematic diagram showing the linear relationship between the 1.5-hour double-peak rainstorm peak rainfall and the total rainfall in the session of the rain in example 1 when the fitting is optimal, wherein a is 0.5 and b is 0.5;
fig. 4 is a linear relationship diagram of the virtual rain peak rainfall of the bimodal rainstorm at 1.5 hours and the main peak rainfall at 0.5 and 0.5;
fig. 5 is a linear relationship diagram of the peak rainfall and the sub-peak rainfall of the double-peak heavy rain in 1.5 hours when a is 0.5 and b is 0.5;
fig. 6 is a linear relation diagram of the virtual rain peak rainfall of the double-peak heavy rain at 1.5 hours when a is 0.5 and b is 0.5 and the sum of the main peak rainfall and the secondary peak rainfall;
FIG. 7 shows a bimodal rainstorm pattern of 1.5 hours per market and a total measured rainfall of 20mm in example 1.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
In the description herein, reference to the description of the terms "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present disclosure. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The present embodiment provides a method for estimating a double-peak rainstorm type for city design, as shown in the flowchart of fig. 1, including the following steps:
s1, selecting a plurality of field double-peak rainstorm samples according to historical measured rainfall data, and calculating to obtain the positions of a main peak and a secondary peak in the double-peak rainstorm field.
Specifically, in step S1, the positions of the main peak and the secondary peak in the bimodal storm run are obtained by counting the main peak position average, the secondary peak position average or the main peak position mode, and the secondary peak position mode in the bimodal storm run, where the main peak, the secondary peak position average, the main peak, and the secondary peak position mode are selected as the positions of the main peak and the secondary peak in the bimodal storm run because the main peak and the secondary peak have a high position probability of falling on the average and the mode.
And S2, obtaining a plurality of virtual rain peaks according to the main peak and the secondary peak of the multi-field secondary double-peak storm rain, and calculating to obtain a comprehensive virtual rain peak coefficient and a virtual rain peak rainfall.
The comprehensive virtual rain peak coefficient calculation formula is as follows:
wherein r isiVirtual rain peak coefficient, t, for each field of double peak rainstormi、tjRespectively the time of occurrence of the main peak and the secondary peak of the double-peak heavy rain, hi、hjRespectively the main peak rainfall and the secondary peak rainfall, T is the total historical duration of a rain fall, rjTo synthesize the virtual rain peak coefficient, i ═ j ═ 1, 2, 3 … … n, and n is the total rainfall field.
The virtual rain peak rainfall calculation method is divided into two cases as follows:
when the main peak is in front and the secondary peak is in back in the double-peak heavy rain type, the rain amount H of the virtual rain peakiSatisfy Hi＝hi×yi+hj×yjAnd hj＜Hi＜hj+hi，yi、yjSatisfies the following conditions: a is more than 0 and less than or equal to yi≤1、0＜b≤yjLess than or equal to 1, wherein hi、hjRespectively, the main peak rainfall and the secondary peak rainfall, yi、yjRespectively a main peak coefficient and a secondary peak coefficient, a and b respectively are the minimum value of the main peak coefficient and the secondary peak coefficient, and the position x of the main peakiThe closer to the virtual rain peak, the peak rain amount h of the main peakiCorresponding coefficient yiThe larger, and xiAnd yiIs a linear relation, the position x of the secondary peakjThe closer to the virtual rain peak, the lower the secondary peak rainfall hjCorresponding coefficient yjThe larger, xjAnd yjIs a linear relationship, and xiAnd yiIs a linear relationship, xjAnd yjIn a linear relationship, the calculation formula is obtained according to the above conditions as follows:
xk＝rjn formula (3)
Wherein r isjFor synthesizing the virtual rain peak coefficient, n is the number of time periods, xkThe time interval corresponding to the comprehensive virtual rain peak coefficient;
when x isi∈[1，xk]，yiIs calculated by the formula
When x isj∈[xk，n]，yiIs calculated by the formula
When the main peak is in front, the value range of the main peak coefficient is [ a,1 ], the value range of the secondary peak coefficient is [ b,1), and the rainfall H of the virtual rain peakiThe calculation formula is as follows:
when the major peak is before and the minor peak is after: coefficient of primary and secondary peaks yi、yjAnd the primary and secondary peak positions xi、xjThe relationship diagram of (A) is shown in FIG. 2.
When the secondary peak is in front of the main peak and the main peak is behind the secondary peak in the double-peak heavy rain type, the rainfall of the virtual rain peak is HiSatisfy Hi＝hi×yi+hj×yjAnd hj＜Hi＜hj+hi，yi、yjSatisfies the following conditions: a is more than 0 and less than or equal to yi≤1、0＜b≤yjLess than or equal to 1, wherein hi、hjRespectively, the main peak rainfall and the secondary peak rainfall, yi、yjRespectively a secondary peak coefficient and a main peak coefficient, a and b respectively are the minimum value of the main peak coefficient and the secondary peak coefficient, and the secondary peakPosition xiThe closer to the virtual rain peak, the lower the peak-to-peak rainfall hiCorresponding coefficient yiThe larger, and xiAnd yiIs a linear relation, the main peak position xjThe closer to the virtual rain peak, the main peak rainfall hjCorresponding coefficient yjThe larger, xjAnd yjIs a linear relationship, and xiAnd yiIs a linear relationship, xjAnd yjIn a linear relationship, the calculation formula is obtained according to the above conditions as follows:
xk＝rjn formula (3)
Wherein r isjFor synthesizing the virtual rain peak coefficient, n is the number of time periods, xkThe time interval corresponding to the comprehensive virtual rain peak coefficient;
when x isi∈[1，xk]，yiIs calculated by the formula
When x isj∈[xk，n]，yiIs calculated by the formula
When the main peak is in front, the value range of the main peak coefficient is [ a,1 ], the value range of the secondary peak coefficient is [ b,1), and the rainfall H of the virtual rain peakiThe calculation formula is as follows:
and S3, respectively carrying out linear fitting on the virtual rain peak rainfall obtained in the step S2 and the sum of the total rainfall, the secondary rain peak rainfall, the main rain peak rainfall and the secondary rain peak rainfall in the field to respectively obtain a linear formula and a correlation coefficient of the best fitting.
The method specifically comprises the steps of obtaining a best fit linear formula and a correlation coefficient of virtual rain peak rainfall and the sum of the total rainfall, the secondary rainfall, the main rainfall and the secondary rainfall of the rainfall in the field by using a least square method, wherein the least square method formula is as follows:
the correlation coefficient formula is as follows:
s4, selecting a double-peak rainstorm sample of a scene, calculating to obtain a main peak rainfall and a secondary peak rainfall by using the best-fit linear formula obtained in the step S3, and obtaining the partial rainfall and the distribution proportion except the main peak rainfall and the secondary peak rainfall by a P & C rain model method.
The P & C rain type method comprises the steps of:
dividing each rainstorm into n small segments, sequencing and numbering the time segments, wherein the large rainfall corresponds to the small numbers, namely each rainstorm has n serial numbers;
averaging the serial numbers corresponding to each time interval, and taking the value from small to large to correspond to the rainstorm intensity of the time interval from large to small;
calculating the ratio of the rainfall capacity of each rainstorm in each time interval to the total rainfall capacity, and taking an average value;
and fourthly, forming a rainfall process curve on the premise of the maximum possible sequence determined in the step 2 and the distribution proportion determined in the step 3.
P&The C rain mode is defined as the storm in all periods except the main peak and the secondary peakAdding rainfall of each time interval of rain, comparing with total rainfall, and normalizing by distributing proportion ki,i＝1,2,…,n。
And S5, obtaining a rainstorm model according to the main peak position and the secondary peak position obtained in the step S1, the main peak rainfall and the secondary peak rainfall, and the partial rainfall except the main peak rainfall and the secondary peak rainfall and the distribution proportion obtained by the P & C rainfall model method.
Example 1
The method for calculating the double-peak rainstorm type in a certain city by using the release comprises the following steps:
(1) and dividing the double-peak rainstorm according to the measured rainfall data of 14 rainfall sites in a certain city from 2009 to 2018.
(2) Samples were selected according to the rainfall duration of each time of double-peak rainstorm, and in this example, 19 time of double-peak rainstorm samples were selected as samples for 1.5 hours.
(3) The average value of the main peak position and the average value of the secondary peak position or the mode of the main peak position and the mode of the secondary peak position in the double-peak storm scene are counted to obtain the positions of the main peak and the secondary peak in the double-peak storm scene, and the result is shown in table 1:
TABLE 1
As can be seen from Table 1, when the main peak is before and the secondary peak is after, the positions of the main peak and the secondary peak are found to be 3, 7 and 2, 6; when the main peak is behind and the secondary peak is in front, the positions of the main peak and the secondary peak are 5, 2, 6 and 2.
(4) Calculating the virtual rain peak coefficient r of the 19-field double-peak rainstorm sample according to the field double-peak rainstorm sample by using the formula (1)iUsing the formula (2) to pass through the virtual rain peak coefficient riCalculating a 19-field double-peak rainstorm comprehensive virtual rain peak coefficient rj，rj＝0.39。
(5) Calculating the position time interval of the comprehensive rain peak coefficient through a formula (3), wherein n is 9 according to the extracted data of the rainstorm of 1.5 hours by 10 minutes, and finally x is obtainedk＝3.5。
(6) For a and b, taking any value within (0, 1), xkSubstituting 3.5 and 9 into the formulas (4), (5), (6) and (7) for fitting until the obtained a and b maximize the correlation coefficient between the virtual rain peak rainfall and the total rainfall, as shown in fig. 3, when R is equal to2＝0.8851，a＝0.5、b＝0.5。
The main and secondary peak coefficients are as follows:
xi∈[1，3.5]，yi＝0.2xi+0.3
xj∈[3.5，9]，yj＝-00909xj+1.3182
this gives:
when the main peak is in front, the peak rainfall of the virtual rain peak is as follows:
Hi＝(0.2xi+0.3)hi+(yj＝-0.0909xj+1.3182)hj
when the main peak is at the back, the peak rainfall of the virtual rain peak is as follows:
Hi＝(0.2xi+0.3)hj+(-yj＝-0.0909xj+1.3182)hi
when a is 0.5 and b is 0.5, the fitting obtains a linear relation diagram of the virtual rainfall of the double-peak heavy rain and the main peak rainfall for 1.5 hours, as shown in fig. 4, when R is2＝0.8759；
When a is 0.5 and b is 0.5, the fitting obtains a linear relation diagram of the peak rainfall and the sub-peak rainfall of the 1.5-hour double-peak heavy rain virtual rain, as shown in fig. 5, when R is2＝0.7662；
When a is 0.5 and b is 0.5, the fitting obtains a linear relation diagram of the rainfall of the virtual rain peak of the 1.5-hour double-peak heavy rain and the sum of the rainfall of the main peak and the secondary peak, as shown in fig. 6, when R is2＝0.9224；
(7) In 19-field double-peak rainstorm, a single-field rainfall with a total rainfall of 20mm in 1.5 hours is selected as an example, the total rainfall is taken as 20mm into a fitting formula shown in fig. 3, 4, 5 and 6, and the main and secondary peak rainfalls are calculated, wherein in the linear relation between the double-peak rainstorm virtual rainfall and the secondary peak rainfall shown in fig. 5, the correlation coefficient is the lowest, so that the correlation coefficient is omitted, and the main peak rainfall is 5.8mm and the secondary peak rainfall is 3.3mm through calculation shown in fig. 3, 4 and 6.
(8) And (3) for the distribution proportion of the rainfall in the independent field of rainfall except the primary peak and the secondary peak selected in the step (7), when the primary peak is in front and the secondary peak is in back, the positions of the primary peak and the secondary peak are 3, 7, 2 and 6 are obtained in the table 1 in the step (3), after final calculation is carried out by utilizing the two positions, and after comparison with an actual measurement value is carried out, when the positions of the primary peak and the secondary peak are 2 and 6, the rain type fitting degree is better.
Where the main peak is in front, the secondary peak is in back, and the positions of the main peak and the secondary peak are 2 and 6, the distribution ratio is as shown in table 2:
TABLE 2
When the main peak is at the back and the secondary peak is at the front, the positions of the main peak and the secondary peak are 5, 2 and 6, 2, which are obtained in the table 1 of the step (3), and after the final calculation is carried out by utilizing the two positions and compared with the measured value, the rain-type fitting degree is better when the positions of the main peak and the secondary peak are 5, 2.
Wherein when the main peak is at the back and the secondary peak is at the front, and the positions of the main peak and the secondary peak are 5 and 2, the distribution ratio is as shown in table 3:
TABLE 3
The rainfall of each time interval can be obtained by subtracting the rainfall of the main peak and the secondary peak from the total rainfall of 20mm and multiplying the obtained value by the ratio of each time interval, and the rainfall of each time interval can be obtained together with the estimated position of the main peak and the secondary peak and the rainfall.
The rain patterns of the two positions of the main peak before, the secondary peak after and the main peak after and the secondary peak before are calculated by using the tables 2 and 3, and compared with the measured value, the rain pattern fitting degree is better when the main peak is before and the secondary peak is after, and only the estimation result of the distribution of the rain amount in the 20mm field of rainfall time period of 1.5 hours and the rain amount process curve (rain pattern graph) of the main peak before and the secondary peak after are given.
When the main peak is in front and the secondary peak is in back, the rainfall is distributed for a 20mm rainfall period of 1.5 hours, and the estimated value (fitting value) and the measured value marking result are shown in table 4:
TABLE 4
The instantaneous rainfall corresponding to the midpoint time point of each time interval obtained by fitting in table 4 is the total rainfall of the time interval, for example, 1.5mm corresponds to the total rainfall under 0-10min when the time interval is 1 in table 4, then the instantaneous rainfall at 5min is 1.5mm, and the results are shown in the table:
TABLE 5
The design rainstorm pattern for a 20mm rainfall session over a 1.5 hour period is plotted according to table 5 as shown in fig. 7.
The method for calculating the urban design bimodal rainstorm rainfall includes the steps of enabling a main peak and a secondary peak of a plurality of fields of secondary bimodal rainstorms to be assumed to form a virtual rain peak, calculating the rain amount of the virtual rain peak, obtaining a best-fit linear formula and a correlation coefficient according to the relation between the rain amount of the virtual rain peak and the sum of the total rain amount of the field of secondary rainstorms, the rain amount of the secondary peak, the rain amount of the main peak and the rain amount of the secondary peak, and finally obtaining the rain amount of the main peak and the rain amount of the secondary peak of the bimodal rainstorms through the fitted linear formula.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and is not intended to limit the practice of the invention to these embodiments. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (8)
1. A method for calculating a double-peak rainstorm type for urban design is characterized in that a virtual rain peak is obtained according to a main peak and a secondary peak of double-peak rainstorm of a field, the rain amount of the virtual rain peak is calculated, a best-fit linear formula and correlation coefficients are obtained according to the relation between the rain amount of the virtual rain peak and the sum of the total rain amount of the field, the secondary peak rain amount, the main peak rain amount and the secondary peak rain amount, and finally the main peak rain amount and the secondary peak rain amount of the double-peak rainstorm are obtained through the fitted linear formula.
2. The method for estimating the urban design bimodal rainstorm according to claim 1, characterized by comprising the following steps:
s1, selecting a plurality of field double-peak rainstorm samples according to historical measured rainfall data, and calculating to obtain the positions of a main peak and a secondary peak in the double-peak rainstorm field;
s2, obtaining a plurality of virtual rain peaks according to the main peak and the secondary peak of the multi-field secondary double-peak storm rain, and calculating to obtain a comprehensive virtual rain peak coefficient and a virtual rain peak rainfall;
s3, respectively carrying out linear fitting on the virtual rain peak rainfall obtained in the step S2 and the sum of the total rainfall, the secondary rain peak rainfall, the main rain peak rainfall and the secondary rain peak rainfall in the field to respectively obtain a linear formula and a correlation coefficient of the best fitting;
s4, selecting a double-peak rainstorm sample of a scene, calculating to obtain main peak rainfall and secondary peak rainfall by using the best-fit linear formula obtained in the step S3, and obtaining the partial rainfall and the distribution proportion except the main peak rainfall and the secondary peak rainfall by a P & C rain type method;
and S5, obtaining a rainstorm model according to the main peak position and the secondary peak position obtained in the step S1, the main peak rainfall and the secondary peak rainfall, and the partial rainfall except the main peak rainfall and the secondary peak rainfall and the distribution proportion obtained by the P & C rainfall model method.
3. The method of claim 2, wherein the positions of the main peak and the secondary peak in the double-peak rainstorm are determined by counting the average of the main peak positions, the average of the secondary peak positions, or the mode of the main peak positions and the mode of the secondary peak positions in the double-peak rainstorm.
4. The method of claim 2, wherein the calculation formula of the integrated virtual rainpeak coefficient in step S2 is as follows:
wherein r isiVirtual rain peak coefficient, t, for each field of double peak rainstormi、tjRespectively the time of occurrence of the main peak and the secondary peak of the double-peak heavy rain, hi、hjRespectively the main peak rainfall and the secondary peak rainfall, T is the total historical duration of a rain fall, rjTo synthesize the virtual rain peak coefficient, i ═ j ═ 1, 2, 3 … … n, and n is the total rainfall field.
5. The method for estimating the urban design bimodal rainstorm according to claim 2, wherein the method for calculating the amount of the virtual rain peak rain in the step S2 is as follows:
when the main peak is in front and the secondary peak is in back in the double-peak heavy rain type, the rain amount H of the virtual rain peakiSatisfy Hi＝hi×yi+hj×yjAnd hj＜Hi＜hj+hi，yi、yjSatisfies the following conditions: a is more than 0 and less than or equal to yi≤1、0＜b≤yjLess than or equal to 1, wherein hi、hjRespectively, the main peak rainfall and the secondary peak rainfall, yi、yjRespectively a main peak coefficient and a secondary peak coefficient, a and b respectively are the minimum value of the main peak coefficient and the secondary peak coefficient, and the position x of the main peakiThe closer to the virtual rain peak, the peak rain amount h of the main peakiCorresponding coefficient yiThe larger, and xiAnd yiIs a linear relation, the position x of the secondary peakjThe closer to the virtual rain peak, the lower the secondary peak rainfall hjCorresponding coefficient yjThe larger, xjAnd yjIs a linear relationship, and xiAnd yiIs a linear relationship, xjAnd yjIn a linear relationship, the calculation formula is obtained according to the above conditions as follows:
xk＝rjn
wherein r isjFor synthesizing the virtual rain peak coefficient, n is the number of time periods, xkThe time interval corresponding to the comprehensive virtual rain peak coefficient;
when x isi∈[1，xk]，yiIs calculated by the formula
When x isj∈[xk，n]，yiIs calculated by the formula
When the main peak is in front, the value range of the main peak coefficient is [ a,1 ], the value range of the secondary peak coefficient is [ b,1), and the rainfall H of the virtual rain peakiThe calculation formula is as follows:
6. the method for estimating the urban design bimodal rainstorm according to claim 2, wherein the method for calculating the amount of the virtual rain peak rain in the step S2 is as follows:
when the secondary peak is in front of the main peak and the main peak is behind the secondary peak in the double-peak heavy rain type, the rainfall of the virtual rain peak is HiSatisfy Hi＝hi×yi+hj×yjAnd hj＜Hi＜hj+hi，yi、yjSatisfies the following conditions: a is more than 0 and less than or equal to yi≤1、0＜b≤yjLess than or equal to 1, wherein hi、hjRespectively, the main peak rainfall and the secondary peak rainfall, yi、yjRespectively a secondary peak coefficient and a main peak coefficient, a and b respectively are the minimum value of the main peak coefficient and the secondary peak coefficient, and the position x of the secondary peakiThe closer to the virtual rain peak, the lower the peak-to-peak rainfall hiCorresponding coefficient yiThe larger, and xiAnd yiIs a linear relation, the main peak position xjThe closer to the virtual rain peak, the main peak rainfall hjCorresponding coefficient yjThe larger, xjAnd yjIs a linear relationship, and xiAnd yiIs a linear relationship, xjAnd yjIn a linear relationship, the calculation formula is obtained according to the above conditions as follows:
xk＝rjn
wherein r isjFor synthesizing the virtual rain peak coefficient, n is the number of time periods, xkThe time interval corresponding to the comprehensive virtual rain peak coefficient;
when x isi∈[1，xk]，yiIs calculated by the formula
When x isj∈[xk，n]，yiIs calculated by the formula
When the main peak is in front, the value range of the main peak coefficient is [ a,1 ], the value range of the secondary peak coefficient is [ b,1), and the rainfall H of the virtual rain peakiThe calculation formula is as follows:
7. the method as claimed in claim 2, wherein the step S3 is performed by using a least square method to obtain a best-fit linear formula and correlation coefficients of the virtual rain peak rainfall and the sum of the total rainfall, the secondary rainfall, the main rainfall, and the main rainfall and the secondary rainfall of the rainstorm in the field.
8. The method of claim 3, wherein the positions of the main peak and the secondary peak in the double-peak rainstorm are calculated using the average of the positions of the main peak and the average of the positions of the secondary peaks to obtain a set of rainstorm patterns, the positions of the main peak and the secondary peak in the double-peak rainstorm storm are calculated using the mode of the main peak and the mode of the secondary peak to obtain another set of rainstorm patterns, and the two sets of rainstorm patterns are compared with the measured value to select the rainstorm pattern with the determined positions of the main peak and the secondary peak of the rainstorm pattern having good fitting degree as the final rainstorm pattern.
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