A method for constructing extreme rainfall index based on multidimensional rainfall feature recognition

Abstract

The present invention discloses a method for constructing an extreme rainfall index based on multi-dimensional feature recognition of rainfall, which belongs to the technical field of meteorological disaster identification and assessment. The implementation method of the present invention is as follows: 1. Cutting the raster rainfall data according to the basin geographic data to obtain the basin rainfall data; 2. Extracting three-dimensional rainfall events from the basin rainfall data; 3. Constructing an extreme rainfall index, and using the Copula function to couple the rainfall duration, total rainfall and rainfall intensity to form an extreme rainfall index; 4. Multi-dimensional feature analysis of the dynamic evolution of rainfall events; Compared with the prior art, the present invention captures the three-dimensional dynamic development process of rainfall through three-dimensional rainfall event recognition, realizes the multi-dimensional analysis of the dynamic evolution of rainfall events, couples the multi-dimensional features of three-dimensional rainfall events through the Copula function, and constructs an extreme rainfall index that can analyze the multi-dimensional features of extreme rainfall in multiple dimensions, thereby solving the multi-dimensional dynamic evolution feature analysis of rainfall with spatiotemporal distribution variability.

Description

Technical Field

[0001] The present invention relates to a method for constructing an extreme rainfall index based on multi-dimensional rainfall feature recognition, belonging to the technical field of meteorological disaster recognition and assessment, and is applied to multi-dimensional rainfall feature analysis and extreme degree assessment. Background Art

[0002] Extreme rainfall and the secondary disasters such as floods, debris flows, and landslides caused by it have caused huge economic and property losses to human society and seriously affected life safety. In the past, most studies on rainfall at home and abroad simplified the continuous rainfall events in three-dimensional space and time to one-dimensional time or two-dimensional space for analysis and research, while the current rainfall indicators at home and abroad mostly use the classification method and percentile method to evaluate extreme rainfall events. The classification method divides rainfall into six levels: light rain, moderate rain, heavy rain, rainstorm, heavy rainstorm, and extremely heavy rainstorm according to a fixed threshold; the percentile method arranges the daily rainfall in one-dimensional time in ascending or descending order, and selects a percentile value as the threshold of extreme rainfall events.

[0003] Rainfall is a dynamic process, and traditional time series analysis of sites or single grids will lose key information in the development of rainfall events. The previous fixed threshold classification method rainfall index cannot reflect the spatiotemporal variability of rainfall distribution, and the rainfall index obtained by the traditional univariate percentile method can only capture one-sided information of rainfall events and cannot fully reflect the three-dimensional dynamic process of rainfall events.

[0004] Therefore, how to analyze the multi-dimensional dynamic evolution characteristics of precipitation with temporal and spatial distribution variability has become an urgent problem to be solved. Summary of the invention

[0005] The purpose of the present invention is to solve the technical problem of analyzing the multi-dimensional dynamic evolution characteristics of rainfall with temporal and spatial distribution variability, and to propose a method for constructing extreme rainfall indicators based on multi-dimensional rainfall feature recognition.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] The present invention provides a method for constructing an extreme rainfall index based on multi-dimensional rainfall feature recognition, which is applied to multi-dimensional rainfall feature analysis and extreme degree assessment, and comprises the following steps:

[0008] Step 1: Clip the raster rainfall data according to the basin geographic data to obtain the basin rainfall data;

[0009] Step 2: Extract three-dimensional rainfall events from the basin rainfall data;

[0010] Step 2.1: Identify single-day rainfall events in the basin rainfall data in time series order, and then obtain a single-day rainfall event set;

[0011] Step 2.1.1: Search for the grid point with the maximum rainfall value in the single-day rainfall data;

[0012] Step 2.1.2: Starting from the grid point with the maximum rainfall, a loop iteration method is used to search for grid points with non-zero rainfall within the range of equally spaced grid points to form a grid point set;

[0013] Step 2.1.3: Mark a collection of grid points as rainfall events t_m ;Reset the marked rainfall event grid points to zero;

[0014] Step 2.1.4: Repeat steps 2.1.1 to 2.1.3 to obtain a single-day rainfall event set;

[0015] Step 2.2: Construct a three-dimensional rainfall event set from the single-day rainfall event set in time series order;

[0016] Step 2.2.1: Compare the overlap of rainfall events on a daily basis for the set of single-day rainfall events; treat rainfall events with overlap greater than a threshold as the same rainfall event;

[0017] Step 2.2.2: Repeat step 2.2.1 to obtain a three-dimensional rainfall event set;

[0018] Step 2.3: Segment the three-dimensional rainfall event set into rainfall sub-events to form a rainfall sub-event set;

[0019] Step 2.3.1: Set the starting threshold and the ending threshold; take the three-dimensional rainfall event set curve that exceeds the starting threshold as the starting point of the rainfall sub-event; take the three-dimensional rainfall event set curve that is lower than the ending threshold as the ending point of the rainfall sub-event;

[0020] Step 2.3.2: The curve between the starting point of the rainfall sub-event and the ending point of the rainfall sub-event forms a rainfall sub-event;

[0021] Step 2.3.3: Repeat steps 2.3.1 to 2.3.2 until the three-dimensional rainfall event set is segmented into rainfall sub-events to form a rainfall sub-event set;

[0022] Step 2.4: Calculate the rainfall duration, total rainfall, and rainfall affected area of ​​each extracted rainfall event and obtain the rainfall intensity using the method shown in formula (1);

[0023] (1)

[0024] in, PRCP The total amount of rainfall m ³, represents the accumulated rainfall in space and time of a rainfall event; AThe rainfall area km ², refers to the union of all rainfall areas in a rainfall event, which can also be regarded as the projection of three-dimensional rainfall on the longitude and latitude of a two-dimensional plane; D Duration of rainfall d ; I The rainfall intensity mm / d .

[0025] Step 3: Construct extreme rainfall index, use Copula function to couple rainfall duration, total rainfall and rainfall intensity to form extreme rainfall index;

[0026] Step 3.1: Heavy rainfall event screening;

[0027] Step 3.2: Fit the marginal probability distribution of rainfall duration, total rainfall and rainfall intensity;

[0028] Step 3.2.1: Estimate the probability distribution parameters of rainfall duration, total rainfall and rainfall intensity;

[0029] Step 3.2.2: Conduct hypothesis testing on the probability distribution of rainfall duration, total rainfall and rainfall intensity using the method shown in formula (2);

[0030] (2)

[0031] in, is the empirical distribution function, is the theoretical cumulative distribution function to be tested, n is the sample length, when the actual observation value , is the confidence level, and 0.05 is used to reject H 0, otherwise accept H 0 null hypothesis, the data conforms to the theoretical distribution; at the same time, the smaller the KS, i.e., the Kolmogorov-Smirnov statistic, the better the cumulative probability distribution fit;

[0032] Step 3.2.3: Optimize the probability distribution of rainfall duration, total rainfall and rainfall intensity using the method shown in formula (3);

[0033] (3)

[0034] in, is the empirical distribution function, is the theoretical cumulative distribution function to be tested, n is the sample length; RMSE is expressed as the smaller the root mean square error, the better the cumulative probability distribution fit.

[0035] Step 3.3: Use the Copula function to couple the probability distribution of rainfall duration, total rainfall and rainfall intensity;

[0036] Step 3.3.1: Estimate the parameters of the Archimedean Copula function;

[0037] Step 3.3.2: Use the method shown in formula (4) to perform hypothesis testing on the probability distribution of the three-dimensional Copula function of rainfall duration, total rainfall and rainfall intensity;

[0038] (4)

[0039] in, is the theoretical Copula distribution function to be tested, The Cramer-von Mises hypothesis test (CVM test) is performed at a significance level of 5%. If the p-value corresponding to the statistic is greater than 5%, the test fails to reject the null hypothesis, that is, the data comes from the selected theoretical Copula function. ;

[0040] Step 3.3.3: Use the method shown in formula (5) to optimize the distribution of the Copula function;

[0041] (5)

[0042] in k is the number of model parameters, L The smaller the RMSE root mean square error and AIC Akaike information criterion, the better the Copula function fitting effect.

[0043] Step 3.4: Coupling through Copula function to form extreme rainfall index;

[0044] Step 3.4.1: Use the Copula function to calculate the probability of rainfall events as shown in formula (6);

[0045] (6)

[0046] in, is the cumulative distribution function of total rainfall; is the cumulative distribution function of rainfall intensity; is the cumulative distribution function of rainfall duration, function is the generator function of Archimedean Copula function;

[0047] Step 3.4.2: Use the probability value calculated by the Copula function as an extreme rainfall indicator.

[0048] Step 4: Multi-dimensional characteristic analysis of the dynamic evolution of rainfall events;

[0049] Step 4.1: Use equations (7) and (8) to obtain the centroid of the rainfall event on a daily basis ( X t , Y t ), use the centroids of the start date and the end date to construct the migration direction of the centroid;

[0050] (7)

[0051] (8)

[0052] in, PRCP i Indicates the rainfall event i The rainfall at each grid point, x i and y i The rainfall events are i The longitude and latitude coordinates of the rainfall grid points, X t and Y t The rainfall events are t The longitude and latitude coordinates of the day.

[0053] Step 4.2: Analyze the dynamic evolution of extreme rainfall;

[0054] Step 4.2.1: Use extreme rainfall indicators to screen three-dimensional extreme rainfall events in the basin;

[0055] Step 4.2.2: Analyze the temporal evolution characteristics of rainfall duration, total rainfall and rainfall intensity of extreme rainfall events;

[0056] Compared with the prior art, the present invention has the following effects:

[0057] The present invention captures the three-dimensional dynamic development process of rainfall through three-dimensional rainfall event recognition, realizes multi-dimensional analysis of the dynamic evolution of rainfall events, couples the multi-dimensional characteristics of three-dimensional rainfall events through Copula functions, and constructs an extreme rainfall index that can analyze the multi-dimensional characteristics of extreme rainfall in multiple dimensions. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A flowchart of the method for constructing extreme rainfall indicators based on multi-dimensional rainfall feature identification;

[0059] Figure 2 for Figure 1 A schematic diagram of the process for step 2 in Figure 1;

[0060] Figure 3 is the rainfall area change process of rainfall event 512_29;

[0061] Figure 4 It is the three-dimensional Copula function fitting graph;

[0062] Figure 5 It is the distribution map of the migration direction of rainfall centroid;

[0063] Figure 6 The rainfall evolution process of four extreme rainfall events in the Yellow River Basin;

[0064] Figure 7 The evolution of rainfall intensity during four extreme rainfall events in the Yellow River Basin;

[0065] Figure 8 The evolution of rainfall area in four extreme rainfall events in the Yellow River Basin;

[0066] Fig. 9 This is a comparison chart of the spatial coverage and total rainfall of extreme rainfall events under the extreme rainfall index identified based on multidimensional characteristics of rainfall and the P95 index. DETAILED DESCRIPTION

[0067] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below in conjunction with the accompanying drawings and examples. It should be noted that the implementation of the present invention is not limited to the following embodiments, and any form of modification or change made to the present invention will fall within the protection scope of the present invention.

[0068] In this embodiment, the Yellow River Basin is taken as an example, and GPM rainfall data and Yellow River Basin geographic data are used to identify and extract three-dimensional rainfall events in the Yellow River Basin, construct an extreme rainfall index based on rainfall multidimensional feature recognition, and analyze the dynamic evolution characteristics of three-dimensional rainfall events to illustrate the technical solution of the present invention. Example

[0069] like Figure 1 As shown, the method for constructing an extreme rainfall index based on multi-dimensional rainfall feature recognition in this embodiment has the following specific implementation steps:

[0070] Step 1: Clip the raster rainfall data according to the basin geographic data to obtain the basin rainfall data;

[0071] In the embodiment, the daily grid rainfall data of the Yellow River Basin from 2000 to 2021 is obtained using the Yellow River Basin geographical data and GPM rainfall data.

[0072] Step 2: Extract three-dimensional rainfall events from the basin rainfall data;

[0073] Step 2.1: Identify single-day rainfall events in the basin rainfall data in time series order, and then obtain a single-day rainfall event set;

[0074] Step 2.1.1: Search for the grid point with the maximum rainfall value in the single-day rainfall data;

[0075] Step 2.1.2: Starting from the grid point with the maximum rainfall, a loop iteration method is used to search for grid points with non-zero rainfall within the range of equally spaced grid points to form a grid point set;

[0076] Step 2.1.3: Mark a collection of grid points as rainfall events t_m ;Reset the marked rainfall event grid points to zero;

[0077] Step 2.1.4: Repeat steps 2.1.1 to 2.1.3 to obtain a single-day rainfall event set;

[0078] In the embodiment, for each layer of the three-dimensional matrix of rainfall data in the Yellow River Basin, the grid point with the largest rainfall is identified and assigned a sequence number n Mark all points with non-zero rainfall within a radius of two grid points with the same serial number n For each newly marked grid point, the marking process is repeated until there are no unmarked points with non-zero rainfall within a radius of two grid points. This process defines a rainfall event for that day. n After finding the rainfall event points, set the values ​​of these marked points to zero in the original three-dimensional rainfall matrix of the Yellow River Basin. Find the new grid point with the largest rainfall in the updated matrix and assign it a serial number n+ 1, and repeat the above steps until all values ​​in the original three-dimensional rainfall matrix are zero. The identified rainfall events are saved in a three-dimensional ordinal matrix.

[0079] Step 2.2: Construct a three-dimensional rainfall event set from the single-day rainfall event set in time series order;

[0080] Step 2.2.1: Compare the overlap of rainfall events on a daily basis for the set of single-day rainfall events; treat rainfall events with overlap greater than a threshold as the same rainfall event;

[0081] Step 2.2.2: Repeat step 2.2.1 to obtain a three-dimensional rainfall event set;

[0082] In the embodiment, Figure 2 In the generalized scenario shown, it is assumed that 1_1 to 7_215 single-day rainfall events are identified in step 1, and a three-dimensional rainfall event that is continuous in time and space is aggregated in step 2 as shown in Figure 3As shown in the second row of orange events in the Yellow River Basin single-day rainfall event set. t Each serial number in the day serial number matrix M , identify the next day ( t+ 1) Middle and t The day number is m The rainfall events overlapped over m All events that are half the area of ​​the rainfall event or half the area of ​​the test rainfall event. t +1 The rainfall event numbers that meet the requirements on the day are included in the collection L :{ l 1 , l 2 , …, l n},for L Each serial number in the next day ( t +2) and repeat the process until the next day ( t + n ) has no event with an overlap area greater than the threshold with the event of the previous day, and these rainfall events are marked as t_m , classified as the same rainfall event. Record the occurrence time of all events involved in this round of marking t and its serial number m , while looping through all days and sequence numbers, make sure to skip these processed events to avoid duplication.

[0083] Step 2.3: Segment the three-dimensional rainfall event set into rainfall sub-events to form a rainfall sub-event set;

[0084] Step 2.3.1: Set the starting threshold and the ending threshold; take the three-dimensional rainfall event set curve that exceeds the starting threshold as the starting point of the rainfall sub-event; take the three-dimensional rainfall event set curve that is lower than the ending threshold as the ending point of the rainfall sub-event;

[0085] Step 2.3.2: The curve between the starting point of the rainfall sub-event and the ending point of the rainfall sub-event forms a rainfall sub-event;

[0086] Step 2.3.3: Repeat steps 2.3.1 to 2.3.2 until the three-dimensional rainfall event set is segmented into rainfall sub-events to form a rainfall sub-event set;

[0087] In the embodiment, for Figure 2 In the generalized scenario shown in the figure, let the starting threshold be 2 grid areas and the ending threshold be 10 grid areas. Then the events aggregated in step 2.2 will be divided into two parts: event 1_2 marked in orange and event 1_3 marked in blue. For the Yellow River Basin, the starting threshold is H 1 is 1.6% of the Yellow River basin area, the termination threshold H2 is 30% of the Yellow River Basin area. In each extracted rainfall event, if the area is less than H 1 point a and Point b There exists an area greater than H 2, it is determined that this rainfall event needs to be segmented. The original starting point of this rainfall event is used as the starting point of the first segment of the rainfall event to be segmented. H 1 point c If there is an area smaller than b and c The minimum area point d , then d The point is taken as the end point of the first rainfall segment. If there is no point, b The point is taken as the end point, and the same segmentation process is performed for the remaining rainfall events after clipping until all sub-events do not meet the segmentation conditions. The rainfall sub-event is treated as a rainfall event.

[0088] Step 2.4: Calculate the rainfall duration, total rainfall, and rainfall affected area of ​​each extracted rainfall event and obtain the rainfall intensity using the method shown in formula (1);

[0089] (1)

[0090] in, PRCP The total amount of rainfall m ³, represents the accumulated rainfall in space and time of a rainfall event; A The rainfall area km ², refers to the union of all rainfall areas in a rainfall event, which can also be regarded as the projection of three-dimensional rainfall on the longitude and latitude of a two-dimensional plane; D Duration of rainfall d ; I The rainfall intensity mm / d .

[0091] In the embodiment, using the Yellow River Basin rainfall data obtained in step 1, a total of 111926 rainfall events are extracted. In step 2.3, rainfall events similar to 512_29 will be segmented, such as Figure 3As shown. According to the rules of the segmentation step, rainfall event 512_29 is segmented into four parts: day 1 to day 17, day 18 to day 101, day 102 to day 192, and day 193 to day 216. The three-dimensional rainfall event recognition method effectively captures the evolution and development of the rainfall affected area and rainfall amount of this rainfall event. Table 1 shows the statistical characteristics of all extracted rainfall event related parameters. Among all rainfall events, the variability in the distribution of total rainfall and rainfall area is significant, while the variability in the distribution of rainfall intensity and rainfall duration is not very significant, but it can still be observed. Events with rainfall intensity less than 0.22 account for 50.89% of all events, while rainfall events lasting more than one day account for 10.86% of all rainfall events.

[0092] Table 1 Statistical characteristics of rainfall event parameters

[0093] variable average value variance Standard Deviation median Maximum Minimum <![CDATA[PRCP(m 3 )]]> 75.3 <![CDATA[1.83×10 7 ]]> <![CDATA[4.28×10 3 ]]> 0.0695 <![CDATA[4.72×10 5 ]]> 0.0093 <![CDATA[A(km 2 )]]> <![CDATA[2.40×10 3 ]]> <![CDATA[7.34×10 8 ]]> <![CDATA[2.71×10 4 ]]> <![CDATA[2.03×10 2 ]]> <![CDATA[7.95×10 5 ]]> 92.38 I(mm / d) 0.54 3.05 1.75 0.22 66.73 0.03 D(d) 1.25 6.79 2.61 1 252 1

[0094] Step 3: Construct extreme rainfall index, use Copula function to couple rainfall duration, total rainfall and rainfall intensity to form extreme rainfall index;

[0095] Step 3.1: Heavy rainfall event screening;

[0096] In the embodiment, the rainfall events with the largest and second largest annual rainfall amount, affected area and rainfall duration in the Yellow River Basin are marked as heavy rainfall events.

[0097] Step 3.2: Fit the marginal probability distribution of rainfall duration, total rainfall and rainfall intensity;

[0098] Step 3.2.1: Estimate the probability distribution parameters of rainfall duration, total rainfall and rainfall intensity;

[0099] In the embodiment, Exponential Distribution, Generalized ExtremeValue Distribution, Gamma Distribution, LognormalDistribution, Weibull Distribution, Generalized ParetoDistribution and Pearson Type III Distribution are used, and the maximum likelihood estimation method is used to perform parameter estimation on the probability distribution of rainfall duration, total rainfall and rainfall intensity of each heavy rainfall event.

[0100] Step 3.2.2: Conduct hypothesis testing on the probability distribution of rainfall duration, total rainfall and rainfall intensity using the method shown in formula (2);

[0101] (2)

[0102] in, is the empirical distribution function, is the theoretical cumulative distribution function to be tested, n is the sample length, when the actual observation value , is the confidence level, and 0.05 is used to reject H 0, otherwise accept H 0 null hypothesis, the data conforms to the theoretical distribution; at the same time, the smaller the KS, i.e., the Kolmogorov-Smirnov statistic, the better the cumulative probability distribution fit;

[0103] Step 3.2.3: Optimize the probability distribution of rainfall duration, total rainfall and rainfall intensity using the method shown in formula (3);

[0104] (3)

[0105] in, is the empirical distribution function, is the theoretical cumulative distribution function to be tested, n is the sample length; RMSE is expressed as the smaller the root mean square error, the better the cumulative probability distribution fit.

[0106] In the embodiment, in the Yellow River Basin, for rainfall duration, among all distributions that pass the KS test, i.e., Kolmogorov-Smirnovtest, the exponential distribution has the lowest RMSE value, so the exponential distribution is selected to fit the rainfall duration. For the total rainfall, among the three distributions with the smallest RMSE values, i.e., the Pearson III distribution, the Weibull distribution, and the gamma distribution, the difference between the maximum and minimum RMSE values ​​does not exceed 5.5%, but the KS statistic of the Pearson III distribution is 31% lower than that of the gamma distribution, so the Pearson III distribution is selected to fit the total rainfall. For rainfall intensity, the minimum values ​​of the RMSE value and the KS statistic both appear in the generalized extreme value distribution, so the generalized extreme value distribution is selected to fit the rainfall intensity.

[0107] Step 3.3: Use the Copula function to couple the probability distribution of rainfall duration, total rainfall and rainfall intensity;

[0108] Step 3.3.1: Estimate the parameters of the Archimedean Copula function;

[0109] In this embodiment, the probability distribution of rainfall duration, total rainfall and rainfall intensity is coupled by using Clayton Copula function, Gumbel Copula function and Frank Copula function. The parameters of the three-dimensional symmetrical structure Copula function are estimated by using the maximum likelihood estimation method, where the probability density function of the three-dimensional Clayton Copula function is expressed as:

[0110]

[0111] In the formula is the relevant parameter of the Clayton Copula function, and its generator function is When ρ→0, the random variable , and Will become independent.

[0112] The probability density function expression of the three-dimensional Gumbel Copula function is:

[0113]

[0114] In the formula is the relevant parameter of Gumbel Copula, and its generator function is .

[0115] The probability density function expression of the three-dimensional Frank Copula function is:

[0116]

[0117] In the formula is the relevant parameter of the Frank Copula function, and its generator function is .

[0118] Step 3.3.2: Use the method shown in formula (4) to perform hypothesis testing on the probability distribution of the three-dimensional Copula function of rainfall duration, total rainfall and rainfall intensity;

[0119] (4)

[0120] in, is the theoretical Copula distribution function to be tested, The Cramer-von Mises hypothesis test (CVM test) is performed at a significance level of 5%. If the p-value corresponding to the statistic is greater than 5%, the test fails to reject the null hypothesis, that is, the data comes from the selected theoretical Copula function. .

[0121] Step 3.3.3: Use the method shown in formula (5) to optimize the distribution of the Copula function;

[0122] (5)

[0123] in k is the number of model parameters, L The smaller the RMSE root mean square error and AIC Akaike information criterion, the better the Copula function fitting effect.

[0124] In the embodiment, it can be seen from the fitting result table 2 that the maximum p value of the Cramer-von Mises hypothesis test, i.e., the CVM test, appears in the Frank Copula function, and the Frank Copula function is the smallest in both RMSE and AIC values. Therefore, the Frank Copula function is selected to couple the three variables of rainfall duration, total rainfall, and rainfall intensity of the rainfall event in the Yellow River Basin. Figure 4 The three-dimensional Copula function is displayed through a slice diagram of three-dimensional data. The colors from red to green reflect the distribution of the three-dimensional function values.

[0125] Table 2 Three-dimensional Copula distribution function fitting results

[0126] Copula Function Types parameter CVM Statistics P-value RMSE AIC Frank 19.3841 0.2285 0.2112 0.0705 -222.4686 Gumbel 4.6136 0.2780 0.1559 0.0777 -211.9417 Clayton 4.4227 0.4387 0.0582 0.0977 -166.8755

[0127] Step 3.4: Coupling through Copula function to form extreme rainfall index;

[0128] Step 3.4.1: Use the Copula function to calculate the probability of rainfall events as shown in formula (6);

[0129] (6)

[0130] in, is the cumulative distribution function of total rainfall; is the cumulative distribution function of rainfall intensity; is the cumulative distribution function of rainfall duration, function is the generator function of Archimedean Copula function;

[0131] In the embodiment, the index value of each three-dimensional rainfall event calculated according to the research method represents the probability that the total rainfall amount, rainfall duration and rainfall intensity are all less than the corresponding values ​​of the three rainfall event components in the event, that is:

[0132]

[0133] Through the optimal calculation of marginal probability distribution and three-dimensional Copula function, the calculation formula of extreme rainfall index based on multidimensional rainfall feature identification in the Yellow River Basin is obtained as follows:

[0134]

[0135] in, is the cumulative distribution function of total rainfall; is the cumulative distribution function of rainfall intensity; is the cumulative distribution function of rainfall duration;

[0136] Step 3.4.2: Use the probability value calculated by the Copula function as the extreme rainfall indicator;

[0137] Step 4: Multi-dimensional characteristic analysis of the dynamic evolution of rainfall events;

[0138] Step 4.1: Use equations (7) and (8) to obtain the centroid of the rainfall event on a daily basis ( X t , Y t ), use the centroids of the start date and the end date to construct the migration direction of the centroid;

[0139] (7)

[0140] (8)

[0141] in, PRCP i Indicates the rainfall event i The rainfall at each grid point, x i and y i are the longitude and latitude coordinates of the ith rainfall grid point of the rainfall event, X t and Y t The rainfall events are t The longitude and latitude coordinates of the day.

[0142] In the embodiment, Figure 5 The distribution of the migration directions of the rainfall centroids of these three-dimensional rainfall events is shown. It can be seen that the migration paths of the three-dimensional rainfall events in the Yellow River Basin are mainly concentrated in the northeast and southwest directions: rainfall events with azimuths ranging from 0° to 90° account for 34.26% of the total rainfall events; rainfall events with azimuths ranging from 180° to 270° account for 25.76%. In addition, despite the presence of rainfall exceeding 4.5×10 5 m 3 However, the rainfall of most rainfall events is distributed within 2.25×105 m 3 the following.

[0143] Step 4.2: Analyze the dynamic evolution of extreme rainfall;

[0144] Step 4.2.1: Use extreme rainfall indicators to screen three-dimensional extreme rainfall events in the basin;

[0145] Step 4.2.2: Analyze the temporal evolution characteristics of rainfall duration, total rainfall and rainfall intensity of extreme rainfall events;

[0146] In the embodiment, Table 3 shows the characteristic data of four extreme rainfall events identified by the extreme rainfall index based on the multi-dimensional rainfall feature recognition when the 75th percentile of the three-dimensional Copula cumulative probability distribution function is taken as the extreme event threshold.

[0147] Table 3 Four extreme rainfall events during the study period were selected using the new extreme rainfall index

[0148] Event Number D A Start Date Termination Date PRCP I Index value 1274_14 154 <![CDATA[7.95×10 5 ]]> 2003-04-13 2003-09-13 <![CDATA[3.24×10 5 ]]> 2.6465 0.7858 4538_19 156 <![CDATA[7.95×10 5 ]]> 2012-04-01 2012-09-03 <![CDATA[3.05×10 5 ]]> 2.4582 0.7584 6744_16 207 <![CDATA[7.95×10 5 ]]> 2018-04-08 2018-10-31 <![CDATA[4.17×10 5 ]]> 2.5354 0.8169 7446_38 232 <![CDATA[7.95×10 5 ]]> 2020-03-05 2020-10-22 <![CDATA[4.72×10 5 ]]> 2.5570 0.8324

[0149] Figure 6 The changes in rainfall amount, rainfall intensity and rainfall area of ​​these four extreme rainfall events are shown. Figure 6 The rainfall shown in the figure is the daily rainfall of each rainfall event, not the cumulative rainfall up to that day. From the daily rainfall process diagram of these four rainfall events, it can be observed that the daily rainfall of each event shows a trend of change from low to high and then falling back. Among them, the peak rainfall of 1274_14 and 4538_19 occurred in the late stage of the event, while the peaks of 6744_16 and 7446_38 were closer to the center of the rainfall event. The changes in rainfall area of ​​these four events also showed significant fluctuations, but the amplitude of their rise and fall was not as large as the amplitude of the change in rainfall. The change in rainfall intensity is mainly affected by the fluctuation of rainfall, and its trend is basically consistent with the change in rainfall.

[0150] In order to further demonstrate the superiority of the present invention, the traditional P 95 The index is compared with the extreme rainfall index based on rainfall multidimensional feature recognition proposed in the present invention to verify the effect of the present invention.

[0151] The extreme rainfall index based on multidimensional rainfall feature recognition is compared with the traditional extreme rainfall index P 95 The comparison between the spatial coverage of detecting extreme rainfall and the total rainfall amount is shown in Table 4 and Fig. 9 The new extreme rainfall index and the traditional P 95 The statistical results of the indicator on the total rainfall and the number of rainfall grid points in each extreme rainfall event. As shown in Table 4, P 95Traditional rainfall indices ignore many rainfall sub-events that contribute to extreme rainfall events, while the new rainfall index can identify these effects. From the perspective of daily rainfall, this index is better than the traditional P 95 The recognition rate of extreme rainfall indicators has been improved by more than 90 times. In terms of the evolution characteristics of extreme rainfall, the new method can analyze the development process of various rainfall elements, such as Figures 6 to 8 As shown, the development patterns of various extreme rainfall elements can be analyzed.

[0152] Rainfall events are a continuous process, but traditional rainfall indicators can only identify isolated grid points where rainfall exceeds historical percentiles. In contrast, the new extreme rainfall index can capture the entire process and reconstruct the complete evolution of rainfall events. The new extreme rainfall index can reflect the various characteristics of extreme rainfall, and the rainfall analysis method proposed in this paper can effectively analyze the dynamic change characteristics of rainfall events.

[0153] Table 4 New index and P 95 Comparison of spatial coverage of index precipitation events and total extreme rainfall

[0154] Event Number <![CDATA[More than P 95 lattice points]]> <![CDATA[Rainfall exceeding P 95 (m 3 )]]> Number of grid points for three-dimensional rainfall events <![CDATA[Total rainfall of three-dimensional rainfall event (m 3 )]]> <![CDATA[P 95 Grid / 3D Event Grid]]> <![CDATA[P 95 Rainfall / 3D event rainfall total]]> 1274_14 442 3.32 627572 324 0.0704% 1.0230% 4538_19 1319 8.62 585322 305 0.2253% 2.8274% 6744_16 1757 13.2 786794 417 0.2233% 3.1725% 7446_38 3078 20.8 879723 472 0.3499% 4.4134%

[0155] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for constructing extreme rainfall index based on multi-dimensional rainfall feature recognition, characterized by: The following steps are included: Step 1: Clip the raster rainfall data according to the basin geographic data to obtain the basin rainfall data; Step 2: Extract three-dimensional rainfall events from the basin rainfall data; Step 2.1: Identify single-day rainfall events in the basin rainfall data in time series order, and then obtain a single-day rainfall event set; Step 2.1.1: Search for the grid point with the maximum rainfall value in the single-day rainfall data; Step 2.1.2: Starting from the grid point with the maximum rainfall, a loop iteration method is used to search for grid points with non-zero rainfall within the range of equally spaced grid points to form a grid point set; Step 2.1.3: Mark the grid point set as rainfall event t_m; reset the marked rainfall event grid points to zero; Step 2.1.4: Repeat steps 2.1.1 to 2.1.3 to obtain a single-day rainfall event set; Step 2.2: Construct a three-dimensional rainfall event set from the single-day rainfall event set in time series order; Step 2.2.1: Compare the overlap of rainfall events on a daily basis for the set of single-day rainfall events; treat rainfall events with overlap greater than a threshold as the same rainfall event; Step 2.2.2: Repeat step 2.2.1 to obtain a three-dimensional rainfall event set; Step 2.3: Segment the three-dimensional rainfall event set into rainfall sub-events to form a rainfall sub-event set; Step 2.3.1: Set the starting threshold and the ending threshold; take the three-dimensional rainfall event set curve that exceeds the starting threshold as the starting point of the rainfall sub-event; take the three-dimensional rainfall event set curve that is lower than the ending threshold as the ending point of the rainfall sub-event; Step 2.3.2: The curve between the starting point of the rainfall sub-event and the ending point of the rainfall sub-event forms a rainfall sub-event; Step 2.3.3: Repeat steps 2.3.1 to 2.3.2 until the three-dimensional rainfall event set is segmented into rainfall sub-events to form a rainfall sub-event set; Step 2.4: Calculate the rainfall duration, total rainfall, and rainfall affected area of ​​each extracted rainfall event and obtain the rainfall intensity using the method shown in formula (1); Where PRCP is the total rainfall m 3 , represents the accumulated rainfall in space and time of a rainfall event; A is the rainfall area km 2 , refers to the union of all rainfall areas in a rainfall event, which can also be regarded as the projection of three-dimensional rainfall on the longitude and latitude of a two-dimensional plane; D is the rainfall duration d; I is the rainfall intensity mm / d; Step 3: Construct extreme rainfall index, use Copula function to couple rainfall duration, total rainfall and rainfall intensity to form extreme rainfall index; Step 3.1: Heavy rainfall event screening; Step 3.2: Fit the marginal probability distribution of rainfall duration, total rainfall and rainfall intensity; Step 3.2.1: Estimate the probability distribution parameters of rainfall duration, total rainfall and rainfall intensity; Step 3.2.2: Conduct hypothesis testing on the probability distribution of rainfall duration, total rainfall and rainfall intensity using the method shown in formula (2); in, is the empirical distribution function, F(x) is the theoretical cumulative distribution function to be tested, n is the sample length, when the actual observed value D>D(n,α), α is the confidence level, which is 0.05 in the present invention to reject H0, otherwise accept the original hypothesis H0, and the data conforms to the theoretical distribution; at the same time, the smaller the KS, i.e., the Kolmogorov-Smirnov statistic, the better the cumulative probability distribution fit; Step 3.2.3: Optimize the probability distribution of rainfall duration, total rainfall and rainfall intensity using the method shown in formula (3); in, is the empirical distribution function, F(x) is the theoretical cumulative distribution function to be tested, and n is the sample length; RMSE means that the smaller the root mean square error, the better the cumulative probability distribution fit; Step 3.3: Use the Copula function to couple the probability distribution of rainfall duration, total rainfall and rainfall intensity; Step 3.3.1: Estimate the parameters of the Archimedean Copula function; Step 3.3.2: Use the method shown in formula (4) to perform hypothesis testing on the probability distribution of the three-dimensional Copula function of rainfall duration, total rainfall and rainfall intensity; Where C is the theoretical Copula distribution function to be tested, For the empirical distribution function, the Cramer-von Mises hypothesis test (CVM test) is performed at a significance level of 5%. If the p-value corresponding to the statistic is greater than 5%, the test fails to reject the null hypothesis, that is, the data comes from the selected theoretical Copula function C; Step 3.3.3: Use the method shown in formula (5) to optimize the distribution of the Copula function; AIC=2k-2lnL (5) Among them, k is the number of model parameters, L is the likelihood function, and the smaller the RMSE root mean square error and AIC Akaike information criterion, the better the Copula function fitting effect; Step 3.4: Coupling through Copula function to form extreme rainfall index; Step 3.4.1: Use the Copula function to calculate the probability of rainfall events as shown in formula (6); Among them, F(PRCP) is the cumulative distribution function of total rainfall; F(I) is the cumulative distribution function of rainfall intensity; F(D) is the cumulative distribution function of rainfall duration, and the function is the generator function of Archimedean Copula function; Step 3.4.2: Use the probability value calculated by the Copula function as the extreme rainfall indicator; Step 4: Multi-dimensional characteristic analysis of the dynamic evolution of rainfall events; Step 4.1: Use equations (7) and (8) to obtain the centroid of the rainfall event on a daily basis (X t ,Y t ), use the centroids of the start date and the end date to construct the migration direction of the centroid; Among them, PRCP i represents the rainfall at the ith grid point of the rainfall event, x i and i are the longitude and latitude coordinates of the ith rainfall grid point of the rainfall event, X t and Y t are the longitude and latitude coordinates of the rainfall event on day t, respectively; Step 4.2: Analyze the dynamic evolution of extreme rainfall.

2. The method for constructing an extreme rainfall index based on multi-dimensional rainfall feature recognition according to claim 1, characterized in that: Step 4.2 is implemented as follows: Step 4.2.1: Use extreme rainfall indicators to screen three-dimensional extreme rainfall events in the basin; Step 4.2.2: Analyze the temporal evolution characteristics of rainfall duration, total rainfall and rainfall intensity of extreme rainfall events.

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