A precipitation intensity-duration-frequency curve generation method and system

Abstract

The present invention discloses a precipitation intensity-duration-frequency curve generation method and system, the method comprising: reading site precipitation data and extracting annual maximum precipitation data; constructing a precipitation intensity-duration-frequency curve model according to the annual maximum precipitation data; processing the precipitation intensity-duration-frequency curve model based on a parameter estimation method to estimate distribution parameters; generating a site precipitation intensity-duration-frequency curve according to the distribution parameters. The system comprises: a data extraction module, a model construction module, a parameter estimation module and a curve generation module. By using the present invention, an IDF curve can be generated quickly and efficiently, which is helpful for the construction of urban drainage and flood prevention projects. As a precipitation intensity-duration-frequency curve generation method and system, the present invention can be widely used in the field of hydrological research.

Description

Technical Field

[0001] The present invention relates to the field of hydrological research, and in particular to a method and system for generating a precipitation intensity-duration-frequency curve. Background Art

[0002] The rainstorm intensity-duration-frequency (IDF) curve shows the relationship between rainstorm intensity and specific return period and duration. By analyzing the relationship between these three, the intensity of extreme rainstorm events under specific duration and return period can be estimated, and then the characteristics of extreme rainstorms can be evaluated. The rainstorm IDF curve can be used to determine the design rainstorm volume, and is one of the important bases for the design, operation, maintenance and management of various water conservancy infrastructure and municipal projects (such as sewers, drainage ditches, water collection pools, drainage pumping stations, bridges, etc.). Today, the IDF curve has become one of the most commonly used tools in the construction of urban drainage and flood control projects, and its application in various water resources management processes has been increasing. Therefore, the IDF curve has important practical significance.

[0003] The generation of IDF curves by traditional methods requires repeated parameter estimation according to different rainstorm durations and recurrence periods. The generation efficiency of IDF curves is low and it is no longer applicable to the current environment where IDF curves need to be updated frequently. Summary of the invention

[0004] In order to solve the above technical problems, the purpose of the present invention is to provide a precipitation intensity-duration-frequency curve generation method and system, which can quickly and efficiently generate IDF curves and contribute to the construction of urban drainage and flood control projects.

[0005] The first technical solution adopted by the present invention is: a method for generating a precipitation intensity-duration-frequency curve, comprising the following steps:

[0006] Read the site precipitation data and extract the annual maximum precipitation data;

[0007] Construct a precipitation intensity-duration-frequency curve model based on the annual maximum precipitation data;

[0008] Based on the parameter estimation method, the precipitation intensity-duration-frequency curve model is processed to estimate the distribution parameters;

[0009] Generate station precipitation intensity-duration-frequency curve based on distribution parameters.

[0010] Further, the step of reading the site precipitation data and extracting the annual maximum precipitation data specifically includes:

[0011] Read the site's historical precipitation data;

[0012] Based on the rolling window summation method, the largest set of rainstorm amounts is selected from the data of each duration each year according to the precipitation data of previous years to obtain the annual maximum precipitation data.

[0013] Furthermore, the step of constructing a precipitation intensity-duration-frequency curve model based on the annual maximum precipitation data specifically includes:

[0014] The generalized extreme value distribution is used to fit the annual maximum precipitation data, and the generalized extreme value distribution function related to the duration of heavy rain is constructed;

[0015] A precipitation intensity-duration-frequency curve model is constructed based on the generalized extreme value distribution function.

[0016] Furthermore, the generalized extreme value distribution function related to the duration of the rainstorm is expressed as follows:

[0017]

[0018] In the above formula, x represents the intensity of the rainstorm, d represents the duration of the rainstorm, represents the location parameter, σ0>0 represents the scale offset, ξ represents the shape parameter, θ represents the slope parameter, and η represents the curvature parameter.

[0019] Furthermore, the step of processing the precipitation intensity-duration-frequency curve model based on the parameter estimation method to estimate the distribution parameters specifically includes:

[0020] Based on the maximum likelihood estimation method, the log-likelihood function is constructed according to the precipitation intensity-duration-frequency curve model;

[0021] Based on the Newton iteration method, distribution parameters are estimated according to the log-likelihood function, and the distribution parameters include location parameter, scale parameter, shape parameter, slope parameter and curvature parameter.

[0022] Further, the log-likelihood function expression is as follows:

[0023]

[0024] In the above formula, θ=(μ,σ,ξ), x represents the rainstorm intensity, n represents the number of observations, and y i =[1-(ξ / σ)(x-μ)], μ, σ, ξ represent the position parameter, scale parameter and shape parameter respectively.

[0025] Furthermore, the step of generating a precipitation intensity-duration-frequency curve of a station according to the distribution parameters specifically includes:

[0026] The specific duration and the corresponding non-exceedance probability are calculated according to the location parameter, scale parameter, shape parameter, slope parameter and curvature parameter, and the station precipitation intensity-duration-frequency curve is generated.

[0027] The second technical solution adopted by the present invention is: a precipitation intensity-duration-frequency curve generation system, comprising:

[0028] Data extraction module, used to read the site precipitation data and extract the annual maximum precipitation data;

[0029] Model building module, used to build a precipitation intensity-duration-frequency curve model based on the annual maximum precipitation data;

[0030] The parameter estimation module processes the precipitation intensity-duration-frequency curve model based on the parameter estimation method and estimates the distribution parameters;

[0031] The curve generation module is used to generate the precipitation intensity-duration-frequency curve of the station according to the distribution parameters.

[0032] The beneficial effects of the method and system of the present invention are as follows: the IDF curve model established by the present invention fully considers the correlation between the parameters in the generalized extreme value distribution and the duration of the rainstorm. In addition, the present invention only needs to estimate five distribution parameters to quickly obtain results using the generalized extreme value distribution related to the duration of the rainstorm, which can maximize the use of existing information and improve the generation efficiency of the IDF curve. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of steps of a method for generating a precipitation intensity-duration-frequency curve according to the present invention;

[0034] Figure 2 It is a schematic diagram of data extracted by a specific embodiment of the present invention;

[0035] Figure 3 is a schematic diagram of a rainstorm intensity-duration-frequency curve of a specific embodiment of the present invention;

[0036] Figure 4 It is a structural block diagram of a precipitation intensity-duration-frequency curve generation system of the present invention. DETAILED DESCRIPTION

[0037] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only provided for the convenience of explanation and description, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0038] like Figure 1As shown, the present invention provides a method for generating a precipitation intensity-duration-frequency curve, the method comprising the following steps:

[0039] S1, read the site precipitation data and extract the annual maximum precipitation data;

[0040] S1.1. Read the site's historical precipitation data;

[0041] S1.2. Based on the rolling window summation method, the largest set of rainstorm amounts is selected from the data of each period of each year according to the precipitation data of previous years to obtain the annual maximum precipitation data.

[0042] Specifically, the maximum annual rainfall over a selected duration is calculated. Taking a certain station as the research object, the rainfall data of the station are collected to obtain the hourly rainfall data of the station for a total of 15 years. The rainfall data used to generate the IDF curve must meet the following conditions: (1) The data should be hourly scale data. If the time scale is daily, the data must be downscaled first; (2) The number of years of data should be equal to or greater than 10 years. When the data is only 10 years or slightly higher than 10 years, the time series of the data must be continuous; (3) The data should be complete and there should be no missing values. The present invention cannot fill in or extrapolate missing data. The present invention provides a read.data() function to read and organize the site rainfall data. The function supports reading files in the comma-separated value file format (CSV). It should be noted that the content in the file should be organized by column, where the first and second columns should represent the date and rainfall amount respectively, and the date and rainfall amount should correspond one to one. Then, the annual maximum value method is used to sample the rainstorm data. The present invention provides the agg.max() function to extract the maximum annual rainstorm intensity. The maximum value can be obtained from the time series of the whole year or a specific month according to the research needs. Thus, a data frame can be obtained, which contains the annual rainstorm intensity maximum value "max.data" (unit: mm / hour), the rainstorm duration "duration" corresponding to the maximum value, the year "year", the month "months" and the station name "station". The specific data is as follows Figure 2 As shown, it is not listed separately here. The data frame can be used as the input of the function in step S3 below.

[0043] S2. Construct a precipitation intensity-duration-frequency curve model based on the annual maximum precipitation data;

[0044] S2.1. Use the generalized extreme value distribution to fit the annual maximum precipitation data and construct the generalized extreme value distribution function related to the duration of heavy rain;

[0045] S2.2. Construct a precipitation intensity-duration-frequency curve model based on the generalized extreme value distribution function.

[0046] The IDF curve describes the mathematical relationship between rainstorm intensity, rainstorm duration and annual frequency (i.e., non-exceedance probability). For a given rainstorm duration d, return period T, and maximum rainstorm intensity i(d,T) at a specific location, the general form of the IDF curve can be expressed as:

[0047]

[0048] In the above formula, a(d,T) and i(d,T) are functions related to the duration of the rainstorm d and the return period T; θ and η are parameters that need to be estimated (θ>0, 0<η<1). Formula (1) indicates that within a given return period, the intensity of the rainstorm decreases as the duration of the rainstorm increases. In addition, the relationship between the cumulative distribution function (CDF) of the maximum rainstorm intensity and the return period T can be expressed as:

[0049]

[0050] Generally, the time series of measured rainstorm data rarely exceed 100 years. When the set recurrence period is large, it is necessary to use the extreme value distribution to fit the rainstorm extremes of each large recurrence period. Therefore, it is necessary to select an appropriate extreme value distribution to model the maximum rainstorm intensity within a certain rainstorm duration range.

[0051] The present invention adopts generalized extreme value distribution to build a model, thereby achieving the fitting of heavy rain data.

[0052] The specific cumulative distribution function form of the generalized extreme value distribution is:

[0053]

[0054] In the formula, the domain of F(x) is The position parameter μ∈R, the scale parameter σ>0, and the shape parameter ξ∈R. When μ=0, σ=1, it is called the standard form.

[0055] The location parameter μ represents the shift of the distribution in each direction on the horizontal axis; the scale parameter σ represents the distribution of the distribution and defines the location where most of the distribution is located. As the scale parameter increases, the distribution will become more dispersed; the shape parameter ξ is called the extreme value indicator, which indicates the location of most of the data, controls the tail of the distribution, and affects the distribution. ξ=0 is the Gumbel distribution, that is, the extreme value type I; ξ<0 is the Fréchet distribution, that is, the extreme value type II; ξ>0 is the Weibull distribution, that is, the extreme value type III. Among them, the Gumbel probability distribution curve is light-tailed, and the Fréchet probability distribution curve has a longer tail than the Gumbel probability distribution curve, which is right heavy-tailed, which means that the possibility of large extreme values ​​in the Fréchet distribution is greater than that in the Gumbel distribution; and the Weibull probability distribution curve is also heavy-tailed, but it indicates that there is an upper limit to the variable value, and the maximum value cannot exceed a fixed value.

[0056] In fact, the most general expression of IDF relationship is:

[0057]

[0058] In the formula, the rainstorm intensity quantile q p Equivalent to the non-exceedance probability p, ω, ν, θ, η are all non-negative coefficients, νη ≥ 1. For the generalized extreme value distribution, its location parameter μ and scale parameter σ are related to the duration of the rainstorm, while the shape parameter ξ is independent of the duration of the rainstorm. Their respective relationships can be expressed as:

[0059] σ(d)=σ0(d+θ) -η (5)

[0060] μ(d)=μ·σ(d) (6)

[0061] ξ(d)=const (7)

[0062] The dependence of the location parameter μ and the scale parameter σ on the rainstorm duration is described by the slope parameter θ and the curvature parameter η, where θ>0, 0<η<1, which represent the rainstorm duration offset and the rainstorm duration index, respectively. In addition, σ0>0 represents the scale offset, which indicates the scale parameter of the generalized extreme value distribution when d=1-θ. The reparameterized location parameter Combining equations (2) and (4) we can obtain the generalized extreme value distribution related to the duration of heavy rain. Its distribution function is:

[0063]

[0064] In the above formula, x represents the intensity of the rainstorm, d represents the duration of the rainstorm, represents the location parameter, σ0>0 represents the scale offset, ξ represents the shape parameter, θ represents the slope parameter, and η represents the curvature parameter.

[0065] Combining formula (3), the quantile of the rainstorm intensity of the generalized extreme value distribution related to the rainstorm duration can be expressed as:

[0066]

[0067] Where q d,p is the non-exceedance probability, which is also equivalent to the IDF relationship. The parameters θ and η represent the curvature of the IDF curve at the short duration and the slope at the long duration in the double logarithmic coordinate diagram, respectively. The present invention uses this generalized extreme value distribution related to the rainstorm duration to simultaneously simulate the maximum annual rainstorm intensity of a single station within a series of specific rainstorm durations. The use of this distribution can reduce the number of parameters that need to be estimated. Only five parameters need to be estimated to obtain the distribution of all rainstorm durations and all quantiles related to the corresponding durations through formula (7). For the general generalized extreme value distribution, in order to obtain the same result, it is necessary to first estimate the three parameters under several rainstorm durations according to (Formula 2), and then estimate the three parameters of each quantile according to formula (3).

[0068] S3. Based on the parameter estimation method, the precipitation intensity-duration-frequency curve model is processed to estimate the distribution parameters;

[0069] S3.1. Based on the maximum likelihood estimation method, the likelihood function is constructed according to the precipitation intensity-duration-frequency curve model;

[0070] S3.2. Based on Newton's iteration method, estimate distribution parameters according to the likelihood function, wherein the distribution parameters include location parameter, scale parameter, shape parameter, slope parameter and curvature parameter.

[0071] Specifically, commonly used parameter estimation methods include Maximum Likelihood Estimation (MLE), least squares method and linear moment estimation method. The present invention uses the maximum likelihood estimation method to construct a likelihood function based on the generalized extreme value distribution function, and then estimates the parameters of the generalized extreme value distribution. And this estimate is unbiased, asymptotically normal, and asymptotically valid under the assumption.

[0072] Assume {x i} is an independent and identically distributed set that follows a generalized extreme value distribution, then the n observations {x1,...x n The likelihood function of} is:

[0073]

[0074] in, Therefore, formula (4) can be expressed as:

[0075]

[0076] Let z i =(x i -μ) / σ,y i =1+ξz i , thus obtaining:

[0077]

[0078] So its log-likelihood function is:

[0079]

[0080] In the above formula, θ=(μ,σ,ξ), x represents the rainstorm intensity, n represents the number of observations, and y i =[1-(ξ / σ)(x-μ)], μ, σ, ξ represent the position parameter, scale parameter and shape parameter respectively.

[0081] Take the first-order inverse of θ in equation (7), and let The obtained likelihood equations are nonlinear equations, and Newton's method can be used to obtain the maximum likelihood estimates of the parameters.

[0082] S4. Generate the precipitation intensity-duration-frequency curve of the station based on the distribution parameters.

[0083] Step S3 of the present invention is performed according to the result of step S2. After the parameter estimation is completed (step S2), five parameters of the generalized extreme value distribution can be obtained, namely, location parameter μ, scale parameter σ, shape parameter ξ, slope parameter θ and curvature parameter η. The parameters obtained after fitting are then used to calculate the specific duration and the corresponding non-exceedance probability, and finally generate an IDF curve.

[0084] Specifically, the present invention provides a plot.idf() function to generate an IDF curve, such as Figure 3 As shown. The default duration "durs" used to calculate quantiles in the function is 1 hour, 2 hours, 6 hours, 12 hours, 18 hours and 24 hours, and the default non-exceedance probability "probs" used to generate the IDF curve is They are 0.5, 0.8, 0.9, 0.95, 0.98 and 0.99.

[0085] like Figure 4 As shown, a precipitation intensity-duration-frequency curve generation system comprises:

[0086] Data extraction module, used to read the site precipitation data and extract the annual maximum precipitation data;

[0087] Model building module, used to build a precipitation intensity-duration-frequency curve model based on the annual maximum precipitation data;

[0088] The parameter estimation module processes the precipitation intensity-duration-frequency curve model based on the parameter estimation method and estimates the distribution parameters;

[0089] The curve generation module is used to generate the precipitation intensity-duration-frequency curve of the station according to the distribution parameters.

[0090] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0091] A precipitation intensity-duration-frequency curve generating device:

[0092] at least one processor;

[0093] at least one memory for storing at least one program;

[0094] When the at least one program is executed by the at least one processor, the at least one processor implements the precipitation intensity-duration-frequency curve generation method as described above.

[0095] The contents of the above method embodiments are all applicable to the present device embodiments. The functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0096] A storage medium stores processor-executable instructions, wherein the processor-executable instructions are used to implement a precipitation intensity-duration-frequency curve generation method as described above when executed by the processor.

[0097] The contents of the above method embodiments are all applicable to the present storage medium embodiments. The functions specifically implemented by the present storage medium embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0098] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A method for generating a precipitation intensity-duration-frequency curve, characterized in that: The following steps are involved: Read the site precipitation data and extract the annual maximum precipitation data; Construct a precipitation intensity-duration-frequency curve model based on the annual maximum precipitation data; Based on the parameter estimation method, the precipitation intensity-duration-frequency curve model is processed to estimate the distribution parameters; Generate station precipitation intensity-duration-frequency curves based on distribution parameters; The step of processing the precipitation intensity-duration-frequency curve model based on the parameter estimation method to estimate the distribution parameters specifically includes: Based on the maximum likelihood estimation method, the log-likelihood function is constructed according to the precipitation intensity-duration-frequency curve model; Based on the Newton iteration method, the distribution parameters are estimated according to the log-likelihood function, wherein the distribution parameters include location parameter, scale parameter, shape parameter, slope parameter and curvature parameter; The log-likelihood function expression is as follows: In the above formula, θ=(μ,σ,ξ), x represents the rainstorm intensity, n represents the number of observations, and y i =[1-(ξ / σ)(x-μ)], μ, σ, ξ represent the position parameter, scale parameter and shape parameter respectively.

2. The method for generating a precipitation intensity-duration-frequency curve according to claim 1, characterized in that: The step of reading the site precipitation data and extracting the annual maximum precipitation data specifically includes: Read the site's historical precipitation data; Based on the rolling window summation method, the largest set of rainstorm amounts is selected from the data of each duration each year according to the precipitation data of previous years to obtain the annual maximum precipitation data.

3. The method for generating a precipitation intensity-duration-frequency curve according to claim 2, characterized in that: The step of constructing a precipitation intensity-duration-frequency curve model based on the annual maximum precipitation data specifically includes: The generalized extreme value distribution is used to fit the annual maximum precipitation data, and the generalized extreme value distribution function related to the duration of heavy rain is constructed; A precipitation intensity-duration-frequency curve model is constructed based on the generalized extreme value distribution function.

4. The method for generating a precipitation intensity-duration-frequency curve according to claim 3, characterized in that: The generalized extreme value distribution function related to the rainstorm duration is expressed as follows: In the above formula, x represents the intensity of the rainstorm, d represents the duration of the rainstorm, represents the location parameter, σ0>0 represents the scale offset, ξ represents the shape parameter, θ represents the slope parameter, and η represents the curvature parameter.

5. The method for generating a precipitation intensity-duration-frequency curve according to claim 4, characterized in that: The step of generating a station precipitation intensity-duration-frequency curve according to the distribution parameters specifically includes: The preset duration and the corresponding non-exceedance probability are calculated according to the location parameter, scale parameter, shape parameter, slope parameter and curvature parameter, and the station precipitation intensity-duration-frequency curve is generated.

6. A precipitation intensity-duration-frequency curve generation system, characterized in that: The method for generating a precipitation intensity-duration-frequency curve according to claim 1 comprises: Data extraction module, used to read the site precipitation data and extract the annual maximum precipitation data; Model building module, used to build a precipitation intensity-duration-frequency curve model based on the annual maximum precipitation data; The parameter estimation module processes the precipitation intensity-duration-frequency curve model based on the parameter estimation method and estimates the distribution parameters; The curve generation module is used to generate the precipitation intensity-duration-frequency curve of the station according to the distribution parameters.

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