A method and system for testing the consistency of observed precipitation between the return period and the forecast period

Abstract

The present invention provides a method and system for testing the consistency of observed precipitation between the return period and the forecast period, including global precipitation site observed grid data; dividing the precipitation data within the spatial area for precipitation consistency testing into return period precipitation data and forecast period precipitation data; testing the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data, and if there are differences between the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data, it is determined that the precipitation consistency between the return period and the forecast period has changed; calculating the mean change and variance change of the return period precipitation data and the forecast period precipitation data based on the bootstrap method, and discriminating the type of precipitation consistency change between the return period and the forecast period according to the mean change and variance change. The present invention can determine whether the consistency of the time series of hydrological elements in different periods has changed, which is helpful for analyzing the time series system of hydrological elements over a long period of time.

Description

Technical Field

[0001] The present invention relates to the field of hydrological calculation, and more specifically, to a method and system for testing the consistency of observed precipitation between the return period and the forecast period. Background Art

[0002] Stationarity refers to the property that a natural system fluctuates within a range of invariant variability, and it is a fundamental concept throughout water resources engineering. System stationarity means that hydrological elements all have a probability density function that does not change with time, and at all times, all hydrological elements follow the same distribution. In the field of classical hydrological analysis, this property is also called consistency, which is a prerequisite for calculating traditional hydrological frequencies. Under the influence of human activities and natural climate, with the continuous occurrence of phenomena such as increasing carbon dioxide concentration, global warming, changes in land use, and changes in basin characteristics, precipitation and runoff undergo jumps and mutations, making hydrological elements no longer have consistency. In this case, traditional hydrological calculations based on the assumption of consistency will pose great risks to flood control safety, water resource utilization, and management. Therefore, the study of the consistency of hydrological elements is particularly important.

[0003] There is a existing rainfall frequency estimation method based on the analysis of hydrometeorological consistency regions. First, it divides the study area into multiple consistent regions according to the analysis of climate similarity and hydrological similarity, where the climate statistical characteristics of each rainfall station belonging to the same consistent region are similar and the statistical characteristic values of hydrological data are the same; then it uses the historical data of all rainfall stations in the consistent region to analyze the optimal dimensionless rainfall probability distribution curve of this consistent region, and further derives the rainfall frequency estimation values of each station.

[0004] However, the above method cannot distinguish whether the consistency of the time series of hydrological elements in different periods has changed under climate change conditions, resulting in inaccurate calculation results of rainfall frequency. Summary of the Invention

[0005] The present invention provides a method and system for testing the consistency of observed precipitation between the return period and the forecast period to solve the defect in the prior art that it is impossible to distinguish whether the consistency of the time series of hydrological elements in different periods has changed.

[0006] To solve the above technical problems, the technical solution of the present invention is as follows:

[0007] In the first aspect, the present invention proposes a method for testing the consistency of observed precipitation between the return period and the forecast period, including the following steps:

[0008] Select the spatial region and time range for precipitation consistency testing.

[0009] Obtain global precipitation station observation grid data; perform spatial dimension cropping on the global precipitation station observation grid data according to the selected spatial region to obtain precipitation data within the selected spatial region; divide the precipitation data within the selected spatial region into return period precipitation data and forecast period precipitation data according to the selected time range.

[0010] Examine the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data. If there are differences between the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data, it is determined that the precipitation consistency between the return period and the forecast period has changed.

[0011] Based on the bootstrap method, calculate the mean change and variance change of the return period precipitation data and the forecast period precipitation data, and determine the type of precipitation consistency change between the return period and the forecast period according to the mean change and variance change.

[0012] As a preferred solution, performing spatial dimension cropping on the global precipitation station observation grid data according to the selected spatial region to obtain precipitation data within the selected spatial region specifically includes:

[0013] Obtain the longitude vector in the global precipitation station observation grid data Its expression is as follows:

[0014]

[0015] where x i represents the longitude value of the i-th global precipitation station observation grid data, and p is the total length of the global precipitation station observation grid data in the longitude direction.

[0016] Obtain the longitude vector within the longitude range of the selected spatial region Its expression is as follows:

[0017]

[0018] where a represents the starting longitude of the selected spatial region, and b represents the ending longitude of the selected spatial region.

[0019] According to the longitude vector and the longitude vector Obtain the longitude vector in the global precipitation station observation grid data within the longitude range of the selected spatial region Its expression is as follows:

[0020]

[0021] Obtain the latitude vector in the global precipitation station observation grid data Its expression is as follows:

[0022]

[0023] Among them, y i represents the latitude value of the i-th global precipitation site observation grid data, and q = p, which is the total length of the global precipitation site observation grid data in the latitude direction.

[0024] Obtain the latitude vector within the longitude range of the selected spatial region Its expression is as follows:

[0025]

[0026] Among them, a' represents the starting latitude of the selected spatial region, and b' represents the ending latitude of the selected spatial region.

[0027] According to the latitude vector and the latitude vector Obtain the latitude vector in the global precipitation site observation grid data within the longitude range of the selected spatial region Its expression is as follows:

[0028]

[0029] According to the longitude vector containing the longitude information set X, and the latitude vector containing the latitude information set Y, calculate the spatial distribution S of the global precipitation site observation grid data within the selected spatial region, and its expression is as follows:

[0030] S = X × Y = {(x, y)|x ∈ X, y ∈ Y}

[0031] According to the global precipitation site observation grid data and the spatial distribution S, screen out the precipitation data within the selected spatial region.

[0032] As an optimal solution, in S3, use the two-sample Kolmogorov-Smirnov method to test the overall distributions of the return period precipitation data and the forecast period precipitation data, specifically including:

[0033] Extract the return period precipitation amount set of each grid point in the selected spatial region and the forecast period precipitation amount set where n represents the sample number of the return period precipitation amount set, and m represents the sample number of the forecast period precipitation amount set;

[0034] Calculate the return period empirical cumulative distribution function and the forecast period empirical cumulative distribution function Its expression is as follows:

[0035]

[0036] Calculate the maximum value KS of the distance between the empirical cumulative distribution function of the return period and the empirical cumulative distribution function of the prediction period at the same precipitation amount value nm , and its expression is as follows:

[0037]

[0038] where represents the supremum of the distance set ;

[0039] When the maximum value of the distance between the empirical cumulative distribution function of the return period and the empirical cumulative distribution function of the prediction period exceeds the significance threshold corresponding to the sample size mn, it is determined that there is a difference between the overall distributions of the precipitation data in the return period and the precipitation data in the prediction period.

[0040] As a preferred solution, in S4, calculate the mean change of the precipitation data in the return period and the precipitation data in the prediction period based on the bootstrap method, specifically including:

[0041] A-1: Randomly draw n samples with replacement from the precipitation amount set of the return period and calculate the mean of the n samples The expression is as follows:

[0042]

[0043] where g 1i is the i-th precipitation data in the return period;

[0044] A-2: Randomly draw m samples with replacement from the precipitation amount set of the prediction period and calculate the mean of the m samples The expression is as follows:

[0045]

[0046] where g 2i is the i-th precipitation data in the prediction period.

[0047] A-3: Calculate the mean consistency test statistic t according to the mean and the mean The expression is as follows:

[0048]

[0049] A-4: Repeat steps A-1 to A-3 for a preset number of times j, calculate j mean consistency test statistics, and use the j mean consistency test statistics to form an empirical distribution T, whose expression is as follows:

[0050] T = {t1, t2…t j}

[0051] A-5: According to the empirical distribution T, calculate the rejection region of the mean consistency test; the expression of the rejection region of the mean consistency test is:

[0052]

[0053] where α represents the restrictive index of the significance level of the input control parameter, which is a parameter that can be set; represents the mean consistency test statistic when the cumulative quantile of the empirical distribution T reaches ;

[0054] If the mean consistency test statistic t falls within the rejection region of the mean consistency test, it is determined that the mean between the precipitation data of the return period and the precipitation data of the forecast period has changed.

[0055] As an optimal solution, in S4, based on the bootstrap method, calculate the variance change of the precipitation data of the return period and the precipitation data of the forecast period, specifically including:

[0056] B-1: Randomly draw n samples with replacement from the precipitation data set of the return period and calculate the variance of the n samples The expression is as follows:

[0057]

[0058] B-2: Randomly draw m samples with replacement from the precipitation data set of the forecast period and calculate the variance of the m samples The expression is as follows:

[0059]

[0060] where g 2i is the i-th precipitation data of the forecast period.

[0061] B-3: Calculate the variance consistency test statistic u according to the variance and the variance The expression is as follows:

[0062]

[0063] B-4: Repeat steps B-1 to B-3 for a preset number of times j, calculate j variance consistency test statistics, and use the j variance consistency test statistics to form an empirical distribution U, whose expression is as follows:

[0064] U = {u1, u2…u j}

[0065] B-5: According to the empirical distribution U, calculate the rejection region of the variance consistency test; the expression of the rejection region of the variance consistency test is:

[0066]

[0067] where, represents the variance consistency test statistic when the cumulative quantile of the empirical distribution U reaches .

[0068] If the variance consistency test statistic u falls within the rejection region of the variance consistency test, it is determined that the variance between the precipitation data in the return period and the precipitation data in the forecast period has changed.

[0069] As a preferred solution, the global precipitation station observation grid data includes time, longitude data, latitude data, and observed precipitation data.

[0070] As a preferred solution, the method further includes separately plotting the overall distribution of the precipitation data in the return period, the overall distribution of the precipitation data in the forecast period, the mean change, and the variance change on different spatial schematic diagrams.

[0071] As a preferred solution, the method further includes plotting a first Sankey diagram and a second Sankey diagram. The types of precipitation consistency changes between the return period and the forecast period include simultaneous changes in the mean and variance, changes in the mean and no change in the variance, no change in the mean and changes in the variance, and no changes in both the mean and the variance.

[0072] The first Sankey diagram is used to show the proportion of the number of grids with mean changes and variance changes in the spatial area where precipitation consistency changes occur.

[0073] The second Sankey diagram is used to show the proportion of different types of precipitation consistency changes between the return period and the forecast period in the same grid in the spatial area where precipitation consistency changes occur.

[0074] As a preferred solution, the first Sankey diagram and the second Sankey diagram are respectively plotted using the Sankey module of Pyecharts.

[0075] Second aspect, this aspect also proposes a system for testing the consistency of observed precipitation between the return period and the forecast period, which is applied to the method for testing the consistency of observed precipitation between the return period and the forecast period described in any of the above solutions, and includes:

[0076] A data acquisition module, which is used to acquire global precipitation station observation grid data; perform cropping in the spatial dimension on the global precipitation station observation grid data to obtain precipitation data in the spatial area for precipitation consistency testing, and divide the obtained precipitation data in the spatial area for precipitation consistency testing into return period precipitation data and forecast period precipitation data.

[0077] A consistency testing module, which includes a consistency judgment unit and a consistency discrimination unit.

[0078] The consistency judgment unit is used to test the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data. If there are differences between the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data, it is determined that the precipitation consistency between the return period and the forecast period has changed.

[0079] The consistency discrimination unit is used to calculate the mean change and variance change of the return period precipitation data and the forecast period precipitation data based on the bootstrap method, and discriminate the type of precipitation consistency change between the return period and the forecast period according to the mean change and variance change.

[0080] Compared with the prior art, the beneficial effects of the technical solution of the present invention are as follows: By testing the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data in the global precipitation station observation grid data output by GPCC (Global Precipitation Climatology Centre), the present invention can determine whether the precipitation consistency between the two periods has changed, and further can determine whether the consistency of the hydrological element time series between the two periods has changed. And based on the bootstrap method, the mean change and variance change of the precipitation data in the two periods are calculated to explain the precipitation consistency change, and the type of precipitation consistency change is discriminated, which is helpful for analyzing the long-term hydrological element time series system. Description of the Drawings

[0081] Figure 1 It is a flowchart of the method for testing the consistency of observed precipitation between the return period and the forecast period in Embodiment 1.

[0082] Figure 2 It is a distribution diagram of the t-distribution and rejection region of the mean consistency test with 1000 samplings in Embodiment 2.

[0083] Figure 3 It is a distribution diagram of the u-distribution and rejection region of the variance consistency test with 1000 samplings in Embodiment 2.

[0084] Figure 4It is the schematic diagram of the consistency test method for the observed precipitation in the return period and the forecast period in Embodiment 3.

[0085] Figure 5 It is the schematic diagram of the first Sankey diagram in Embodiment 3.

[0086] Figure 6 It is the schematic diagram of the second Sankey diagram in Embodiment 3.

[0087] Figure 7 It is the architecture diagram of the consistency test system for the observed precipitation in the return period and the forecast period in Embodiment 4. Specific implementation manners

[0088] The accompanying drawings are only for illustrative purposes and cannot be construed as a limitation to this patent;

[0089] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0090] Embodiment 1

[0091] This embodiment proposes a consistency test method for the observed precipitation in the return period and the forecast period. Refer to Figure 1 , Figure 1 which is the flowchart of the consistency test method for the observed precipitation in the return period and the forecast period, and includes the following steps:

[0092] S1: Select the spatial region and time range for the precipitation consistency test.

[0093] S2: Obtain the observed grid data of global precipitation stations; perform spatial dimension cropping on the observed grid data of global precipitation stations according to the selected spatial region to obtain the precipitation data within the selected spatial region; divide the precipitation data within the selected spatial region into return period precipitation data and forecast period precipitation data according to the selected time range.

[0094] S3: Test the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data. If there are differences between the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data, it is determined that the precipitation consistency between the return period and the forecast period has changed.

[0095] When it is determined that the precipitation consistency between the return period and the forecast period has changed, calculate the mean change and variance change of the return period precipitation data and the forecast period precipitation data based on the bootstrap method, and determine the type of precipitation consistency change between the return period and the forecast period according to the mean change and variance change.

[0096] By examining the overall distribution of return period precipitation data and forecast period precipitation data in the global precipitation station observation grid data output by GPCC (Global Precipitation Climatology Centre), it is possible to determine whether the precipitation consistency has changed between the two periods, and further whether the consistency of the hydrological element time series has changed between the two periods. Based on the bootstrap method, the mean change and variance change of the precipitation data in the two periods are calculated to explain the change in precipitation consistency, and the type of change in precipitation consistency is discriminated. This helps to analyze the long-term hydrological element time series system, overcoming the problems of difficult handling, complex solution methods, and one-sided analysis angles in the consistency problem in hydrological frequency calculation and statistical post-processing methods.

[0097] Example 2

[0098] In this example, using the open-source Python language platform, taking the observed precipitation between the return period (1982 - 2010) and the forecast period (2010 - 2019) in the GCM (Global Climate Model) forecast as an example, based on statistical tests and visualization methods, improvements are made on the return period and forecast period observed precipitation consistency test method proposed in Example 1.

[0099] S1: Select the spatial region and time range for precipitation consistency test.

[0100] In this example, the spatial region and time range for precipitation consistency test are selected with a time period in the format of "year - month - day" to "year - month - day" as an input string and a spatial region of ["longitude range", "latitude range"].

[0101] S2: Obtain the global precipitation station observation grid data; crop the global precipitation station observation grid data in the spatial dimension according to the selected spatial region to obtain the precipitation data within the selected spatial region; divide the precipitation data within the selected spatial region into return period precipitation data and forecast period precipitation data according to the selected time range.

[0102] In this example, the global precipitation station observation grid data GPCC.nc output by GPCC (Global Precipitation Climatology Centre) is used as the input data, including information such as time, longitude data, latitude data, and observed precipitation data. The Dataset function of the open-source third-party library netcdf in python and the load_mfdataset of xarray are used to read the time, longitude data, latitude data, and observed precipitation data in the GPCC.nc file.

[0103] In this embodiment, the global precipitation station observation grid data is cropped in the spatial dimension according to the longitude data and latitude data of the selected spatial region to obtain the precipitation data within the selected spatial region, which specifically includes:

[0104] Use load_mfdataset to read all the longitude information in the global precipitation station observation grid data, and represent it with the longitude vector as shown in the following expression:

[0105]

[0106] where x i represents the longitude value of the i-th global precipitation station observation grid data, and p is the total length of the global precipitation station observation grid data in the longitude direction;

[0107] Obtain the longitude vector within the longitude range of the selected spatial region as shown in the following expression:

[0108]

[0109] where a represents the starting longitude of the selected spatial region, and b represents the ending longitude of the selected spatial region.

[0110] According to the longitude vector and the longitude vector Use the.isel method to obtain the longitude vector in the global precipitation station observation grid data within the longitude range of the selected spatial region as shown in the following expression:

[0111]

[0112] Use load_mfdataset to read all the longitude information in the global precipitation station observation grid data, and represent it with the latitude vector as shown in the following expression:

[0113]

[0114] where y i represents the latitude value of the i-th global precipitation station observation grid data, and q = p, which is the total length of the global precipitation station observation grid data in the latitude direction;

[0115] Obtain the latitude vector within the longitude range of the selected spatial region as shown in the following expression:

[0116]

[0117] Among them, a' represents the starting latitude of the selected spatial region, and b' represents the ending latitude of the selected spatial region.

[0118] According to the latitude vector and the latitude vector Obtain the latitude vector in the global precipitation station observation grid data within the longitude range of the selected spatial region Its expression is as follows:

[0119]

[0120] According to the longitude vector The set of longitude information X it contains, and the latitude vector The set of latitude information Y it contains, calculate the spatial distribution S of the set X and the set Y as the global precipitation station observation grid data within the selected spatial region, and its expression is as follows:

[0121] S = X × Y = {(x, y)|x ∈ X, y ∈ Y}

[0122] According to the global precipitation station observation grid data and the spatial distribution S, use the broadcasting interface of the numpy function in xarray, and filter out the precipitation data within the spatial distribution S through the.sel method.

[0123] In this embodiment, according to the selected time range, use the.isel method to divide the precipitation data within the selected spatial region into return period precipitation data and forecast period precipitation data, and store them in the xarray.Dataarray format.

[0124] S3: Examine the overall distributions of the return period precipitation data and the forecast period precipitation data. If there are differences between the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data, it is determined that the precipitation consistency between the return period and the forecast period has changed.

[0125] In this embodiment, use the two-sample Kolmogorov-Smirnov method to examine the overall distributions of the return period precipitation data and the forecast period precipitation data. First, use the K-S test to determine whether the overall distributions of the return period precipitation data and the forecast period precipitation data have changed and whether they are equal. If the K-S test believes that there are no differences in the overall precipitation distributions in the two periods, it is considered that the impacts of natural changes and human activities on the hydrological cycle have not caused the precipitation between the return period and the forecast period to lose consistency; if the K-S test believes that there are differences in the overall precipitation distributions in the two time periods, it can be considered that natural changes and human activities have caused the precipitation between the return period and the forecast period to lose consistency.

[0126] When it is determined that the precipitation consistency between the return period and the forecast period has changed, calculate the mean change and variance change of the precipitation data in the return period and the precipitation data in the forecast period based on the bootstrap method, and determine the type of change in the precipitation consistency between the return period and the forecast period according to the mean change and variance change. Specifically, it includes:

[0127] Extract the precipitation data set of the return period for each grid point in the selected spatial region and the precipitation data set of the forecast period where n represents the number of samples in the precipitation data set of the return period, and m represents the number of samples in the precipitation data set of the forecast period;

[0128] Calculate the empirical cumulative distribution function of the return period and the empirical cumulative distribution function of the forecast period The expressions are as follows:

[0129]

[0130]

[0131] Calculate the maximum value KS of the distance between the empirical cumulative distribution function of the return period and the empirical cumulative distribution function of the forecast period at the same precipitation value nm , and the expression is as follows:

[0132]

[0133] where, represents the supremum of the distance set ;

[0134] When the maximum value of the distance between the empirical cumulative distribution function of the return period and the empirical cumulative distribution function of the forecast period exceeds the significance threshold Pr(KS nm <KS nm,α ) corresponding to the sample number mn, it is determined that there is a difference in the overall distribution of the precipitation data in the return period and the overall distribution of the precipitation data in the forecast period.

[0135] In this embodiment, if it is determined that the precipitation between the return period and the forecast period loses consistency, analyze the loss of precipitation consistency between the return period and the forecast period through the mean consistency test based on Bootstrap and the variance consistency test based on Bootstrap, and determine the type of change in the precipitation consistency between the return period and the forecast period.

[0136] In this embodiment, analyze the grid points at the same longitude and latitude. For each grid, denote as the precipitation data set of all the same months on this grid for the return period, as the precipitation data set of all the same months on this grid for the forecast period, where It is the result of multiple simple random samplings from the overall distribution of the precipitation data of the return period. It is the result of multiple simple random samplings from the overall distribution of the precipitation data of the return period.

[0137] In this embodiment, based on Bootstrap, the mean change of the precipitation data of the return period and the precipitation data of the prediction period is calculated, specifically including:

[0138] A-1: Randomly draw n samples with replacement from the precipitation data set of the return period and calculate the mean of the n samples The expression is as follows:

[0139]

[0140] where g 1i is the precipitation data of the i-th return period;

[0141] A-2: Randomly draw m samples with replacement from the precipitation data set of the prediction period and calculate the mean of the m samples The expression is as follows:

[0142]

[0143] where g 2i is the precipitation data of the i-th prediction period;

[0144] A-3: Calculate the mean consistency test statistic t according to the mean and the mean The expression is as follows:

[0145]

[0146] A-4: Repeat steps A-1 to A-3 to the preset number of times j, calculate j mean consistency test statistics, and form an empirical distribution T using the j mean consistency test statistics. The expression is as follows:

[0147] T = {t1, t2…t j}, j > 1000

[0148] A-5: Calculate the rejection region of the mean consistency test according to the empirical distribution T; the expression of the rejection region of the mean consistency test is:

[0149]

[0150] where α represents the restrictive index of the significance level of the input control parameter and is a parameter that can be set; Indicates that the cumulative quantile of the empirical distribution T reaches when the mean consistency test statistic is used.

[0151] α is the significance index in the input control parameters, a number between 0 and 1, which represents the strictness of the statistical test. By controlling the value of α according to user needs, the probability of making a Type I error in the statistical test judgment can be controlled. According to academic convention, α = 0.05.

[0152] As Figure 2 shown, Figure 2 is the t-distribution and rejection region distribution map of the mean consistency test statistic for 1000 samplings. If the mean consistency test statistic t falls within the rejection region of the mean consistency test, it is considered that the probability that the means of the return period precipitation data and the forecast period precipitation data are equal is less than α, that is, there is a probability of more than 95% that the means between the return period precipitation data and the forecast period precipitation data change.

[0153] In this embodiment, the variance change of the return period precipitation data and the forecast period precipitation data is calculated based on the bootstrap method, specifically including:

[0154] B-1: Randomly draw n samples with replacement from the return period precipitation dataset and calculate the variance of the n samples The expression is as follows:

[0155]

[0156] B-2: Randomly draw m samples with replacement from the forecast period precipitation dataset and calculate the variance of the m samples The expression is as follows:

[0157]

[0158] where g 2i is the i-th forecast period precipitation data;

[0159] B-3: Calculate the variance consistency test statistic u according to the variance and the variance The expression is as follows:

[0160]

[0161] B-4: Repeat steps B-1 to B-3 to a preset number of times j, calculate j variance consistency test statistics, and form an empirical distribution U using the j variance consistency test statistics. The expression is as follows:

[0162] U = {u1, u2…u j}, j > 1000

[0163] B-5: Calculate the rejection region of the variance consistency test according to the empirical distribution U; the expression of the rejection region of the variance consistency test is:

[0164]

[0165] where represents the variance consistency test statistic when the cumulative quantile of the empirical distribution U reaches .

[0166] As Figure 3 shown, Figure 3 is the distribution diagram of the 1000 - time sampling statistic u and the rejection region of the variance consistency test. If the variance consistency test statistic u falls within the rejection region of the mean consistency test, it is considered that the probability that the means of the precipitation data in the return period and the precipitation data in the forecast period are equal is less than α, that is, there is a probability of more than 95% that the means between the precipitation data in the return period and the precipitation data in the forecast period change.

[0167] To prove the effectiveness of the above - mentioned method, the following mathematical proof is given:

[0168] First, focus on the magnitude relationship between the statistics θ1 and θ2 of the overall distributions F1 and F2 of the precipitation data in the return period and the precipitation data in the forecast period:

[0169] θ = T(F)

[0170] where θ = {θ1, θ2}, F = {F1, F2}, and T(·) is the function for calculating the statistic θ

[0171] is the sample of the overall distribution F1:

[0172]

[0173] is the sample of the overall distribution F2:

[0174]

[0175] is the data 's empirical distribution, is the data 's empirical distribution,

[0176] Using the plug - in estimation method, using the empirical distribution of and the empirical distribution of to calculate the estimator

[0177]

[0178] Extract bootstrap samples of the same size from the empirical distribution and and

[0179]

[0180] A bootstrap sample refers to a sample of the same size as the original sample obtained by simple random sampling from the empirical distribution g * .

[0181] Based on the bootstrap sample g * , the empirical distribution and the statistic calculation function T(·), the bootstrap distribution corresponding to the bootstrap sample can be written For different statistics, the statistical calculation functions are different, and the resulting bootstrap distributions are different.

[0182] For the mean consistency test: the bootstrap distribution is:[[]]

[0183]

[0184] For the variance consistency test: the bootstrap distribution is:[[]]

[0185]

[0186] When conducting the variance consistency test and the mean consistency test, it is necessary to calculate the sample estimation distribution:[[]]

[0187]

[0188] Obtain the statistic t corresponding to the statistical test. Thus, the mathematical rigor of the above-mentioned K-S test, mean consistency test, and variance consistency test is proved.

[0189] According to the principle of the bootstrap method, it can be considered that: the bootstrap sample distribution is a reasonable estimate of the ideal bootstrap distribution R(g,F).

[0190] Proved by the law of the iterated logarithm, the difference between the overall distributions of the two precipitation data decreases as the number of sampling times i increases. When i is greater than 1000 times, the effect is relatively stable. Therefore, when ensuring that the number of repeated sampling times i is sufficient, it can be ensured that g * → the approximation process of g will not produce large errors; when ensuring that the sample sizes n and m are greater than or equal to 30, it can be ensured The error generated during the approximation process is relatively reasonable.

[0191] The present invention introduces the Bootstrap method into the statistical inference of mean and variance, and can effectively play a role in the face of populations with any distribution, overcoming the narrow application range of traditional statistical test methods.

[0192] Based on the open-source Python language platform, the present invention docks with the international data storage standard adopted by the National Center for Atmospheric Research in the United States, facilitating applications in different countries, different systems, and different platforms.

[0193] Example 3

[0194] This example makes improvements on the basis of the return period and forecast period observed precipitation consistency test method proposed in Example 2, as Figure 4 shown, Figure 4 is the schematic diagram of the return period and forecast period observed precipitation consistency test method in this example.

[0195] In this example, the third-party libraries of Python, cartopy, Mpl_toolkits, and Matplotlib are used to visualize the precipitation consistency discrimination in the entire spatial region, and some case points are selected to draw schematic diagrams.

[0196] In this example, the overall distribution of return period precipitation data, the overall distribution of forecast period precipitation data, the mean change, and the variance change are respectively plotted on three spatial schematic diagrams.

[0197] Furthermore, the ax.pcolormesh method is used to draw the spatial schematic diagram of the K-S test results. When the p-value calculated by the K-S test is smaller, the distribution difference is more significant, and the possibility of changes in the consistency of hydrological elements is greater. The ccrs.PlateCarree() function in cartopy is used to call the geoaxes object of matplotlib to control the projection type of the spatial schematic diagram of the K-S test results.

[0198] Furthermore, the ax.pcolormesh method is used to draw the spatial schematic diagram of the mean consistency test results. When the p-value calculated by the mean consistency test is smaller, the mean difference is more significant, the possibility of changes in the mean of hydrological elements is greater, and the more likely reason for the destruction of the hydrological element consistency is the mean change. The ccrs.PlateCarree() function in cartopy is used to call the geoaxes object of matplotlib to control the projection type of the spatial schematic diagram of the mean consistency test results.

[0199] Furthermore, the ax.pcolormesh method is used to draw the spatial schematic diagram of the variance consistency test results. The smaller the result of the variance consistency test, the greater the possibility of changes in the variance of hydrological elements, and the more likely the reason for the destruction of hydrological element consistency is variance change. The ccrs.PlateCarree() function in cartopy is used to call the geoaxes object of matplotlib to control the projection type of the spatial schematic diagram of the variance consistency test results.

[0200] Furthermore, in the above three spatial schematic diagrams, the ax.gridlines method is used to draw the longitude and latitude grid lines, and the cticker.LongitudeFormatter() method in the third-party library cartopy is used to make the longitude and latitude labels. The fig.add_axes method is used to add a subplot for controlling the position of the colorbar; the position of the colorbar is set through the fig.colorbar method, the tick positions are set using the cbar.set_ticks method, and the tick label display content is set. Finally, through the savefig method of matplotlib.figure.Figure, the three visualized spatial schematic diagrams of hydrological consistency discrimination data are saved to the specified path.

[0201] In this embodiment, after three statistical tests of the K-S test, the mean consistency test, and the variance consistency test, the relationship between the three statistical tests among all spatial grid points is reflected through a Sankey diagram. The Sankey diagram includes a first Sankey diagram and a second Sankey diagram.

[0202] Furthermore, as Figure 5 shown, Figure 5 is a schematic diagram of the first Sankey diagram. The first Sankey diagram shows the proportion of the number of grids with mean change and variance change in the spatial area where precipitation consistency changes occur.

[0203] Furthermore, as Figure 6 shown, Figure 6 is a schematic diagram of the second Sankey diagram. The second Sankey diagram shows the proportion of different types of precipitation consistency changes in the same grid for different return periods and forecast periods in the spatial area where precipitation consistency changes occur, that is, the grid points are divided into four categories according to the mean and variance change conditions of the grid points, including both mean and variance change, mean change and variance unchanged, mean unchanged and variance change, and both mean and variance unchanged, so as to analyze and explain the proportion of consistency changes that can be explained under the combined action of mean change and variance change.

[0204] During the visualization process of this embodiment, the Python program can automatically match the same observation time and forecast time, avoiding the cumbersome manual adjustment process.

[0205] Embodiment 4

[0206] This embodiment proposes a system for the consistency of observed precipitation between the return period and the forecast period. Refer to Figure 7 , Figure 7 which is the architecture diagram of the system for testing the consistency of observed precipitation between the return period and the forecast period, including a data acquisition module and a consistency test module. The consistency test module includes a consistency judgment unit and a consistency discrimination unit.

[0207] In the specific implementation process, the data acquisition module acquires the observed grid data of global precipitation stations; performs cropping on the spatial dimension of the observed grid data of global precipitation stations to obtain the precipitation data of the spatial area for precipitation consistency test, and divides the obtained precipitation data of the spatial area for precipitation consistency test into return period precipitation data and forecast period precipitation data.

[0208] The consistency judgment unit tests the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data. If there are differences between the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data, it is judged that the precipitation consistency between the return period and the forecast period has changed.

[0209] The consistency discrimination unit calculates the mean change and variance change of the return period precipitation data and the forecast period precipitation data based on the bootstrap method, and discriminates the type of precipitation consistency change between the return period and the forecast period according to the mean change and variance change.

[0210] By testing the overall distribution of the return period precipitation data and the overall distribution of the forecast period precipitation data in the observed grid data of global precipitation stations output by GPCC (Global Precipitation Climatology Centre), it is judged whether the precipitation consistency between the two periods has changed, and further whether the consistency of the hydrological element time series between the two periods has changed. And based on the bootstrap method, the mean change and variance change of the precipitation data in the two periods are calculated to explain the precipitation consistency change, and the type of precipitation consistency change is discriminated, which is helpful for analyzing the long-term hydrological element time series system, and overcomes the problems such as difficult to handle, complex solution method and one-sided analysis angle in the hydrological frequency calculation and statistical post-processing method of the consistency problem.

[0211] The terms describing the positional relationship in the drawings are only for illustrative purposes and should not be construed as a limitation of this patent;

[0212] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, rather than limitations on the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the claims of the present invention.

Claims

1. A method for testing the consistency of observed precipitation between the return period and the forecast period, characterized in that, It includes the following steps: Select the spatial region and time range for precipitation consistency test; Obtain global precipitation station observation grid data; crop the global precipitation station observation grid data in the spatial dimension according to the selected spatial region to obtain precipitation data within the selected spatial region; According to the selected time range, divide the precipitation data within the selected spatial region into return period precipitation data and forecast period precipitation data, including: Obtain the longitude vector in the global precipitation station observation grid data Its expression is as follows: where x i represents the longitude value of the i-th global precipitation station observation grid data, and p is the total length of the global precipitation station observation grid data in the longitude direction; Obtain the longitude vector within the longitude range of the selected spatial region Its expression is as follows: Where a represents the starting longitude of the selected spatial region, and b represents the ending longitude of the selected spatial region; According to the longitude vector and the longitude vector Obtain the longitude vector in the global precipitation station observation grid data within the longitude range of the selected spatial region Its expression is as follows: Obtain the latitude vector in the global precipitation station observation grid data Its expression is as follows: where y i represents the latitude value of the i-th global precipitation station observation grid data, q = p, which is the total length of the global precipitation station observation grid data in the latitude direction; Obtain the latitude vector within the longitude range of the selected spatial region Its expression is as follows: where a ′ represents the starting latitude of the selected spatial region, and b ′ represents the ending latitude of the selected spatial region; According to the latitude vector and the latitude vector obtain the latitude vector in the global precipitation station observation grid data within the longitude range of the selected spatial region whose expression is as follows: According to the longitude vector containing the longitude information set X, and the latitude vector containing the latitude information set Y, calculate the spatial distribution S of the global precipitation station observation grid data within the selected spatial region, and its expression is as follows: S = X×Y = {(x,y)|x∈X,y∈Y} Filter out the precipitation data within the selected spatial region according to the global precipitation station observation grid data and the spatial distribution S; Test the overall distributions of the return period precipitation data and the forecast period precipitation data. If there are differences between the overall distributions of the return period precipitation data and the forecast period precipitation data, it is determined that the precipitation consistency between the return period and the forecast period has changed; When it is determined that the precipitation consistency between the return period and the forecast period has changed, calculate the mean change and variance change of the return period precipitation data and the forecast period precipitation data based on the bootstrap method, and determine the type of precipitation consistency change between the return period and the forecast period according to the mean change and variance change.

2. The consistency test method for observed precipitation between the return period and the forecast period according to claim 1, wherein Use the two-sample Kolmogorov-Smirnov method to test the overall distributions of the return period precipitation data and the forecast period precipitation data, specifically including: Extract the return period precipitation sets for each grid point in the selected spatial region and the precipitation sets for the forecast period where n represents the number of samples in the return period precipitation set and m represents the number of samples in the precipitation set for the forecast period; Calculate the empirical cumulative distribution function of the payback period and the empirical cumulative distribution function of the forecast period The expressions are as follows: Calculate the maximum value KS of the distance between the empirical cumulative distribution function of the return period and the empirical cumulative distribution function of the forecast period when the precipitation values are the same nm , and its expression is as follows: Among them, represents the supremum of the distance set; When the maximum value of the distance between the return period empirical cumulative distribution function and the forecast period empirical cumulative distribution function exceeds the significance threshold corresponding to the sample size mn, it is determined that there are differences between the overall distributions of the return period precipitation data and the forecast period precipitation data.

3. The method for testing the consistency of observed precipitation between the return period and the forecast period according to claim 1, characterized in that Calculate the mean change of the return period precipitation data and the forecast period precipitation data based on the bootstrap method, specifically including: A-1: Precipitation set from the return period Randomly draw n samples with replacement from it, and calculate the mean of the n samples The expression is as follows: where g 1i is the precipitation data for the i-th return period; A-2: From the precipitation set in the forecast period Randomly draw m samples with replacement and calculate the mean of the m samples The expression is as follows: where g 2i is the precipitation data for the i-th forecast period; A-3: According to the mean value and the mean value calculate the mean value consistency test statistic t, and its expression is as follows: A-4: Repeat steps A-1 to A-3 to a preset number of times j, calculate j mean consistency test statistics, and form an empirical distribution T using the j mean consistency test statistics. Its expression is as follows: T = {t1, t2…t j} A-5: Calculate the rejection region of the mean consistency test according to the empirical distribution T; the expression of the rejection region of the mean consistency test is: Among them, α represents a restrictive index of the significance level of the input control parameter, which is a parameter that can be set; represents that the cumulative quantile of the empirical distribution T reaches the mean consistency test statistic at this time; If the mean consistency test statistic t falls within the rejection region of the mean consistency test, it is determined that the mean between the return period precipitation data and the forecast period precipitation data has changed.

4. The method for testing the consistency of observed precipitation between the return period and the forecast period according to claim 3, characterized in that Calculate the variance change of the return period precipitation data and the forecast period precipitation data based on the bootstrap method, specifically including: B-1: Precipitation data set for the return period Randomly draw n samples with replacement from it, and calculate the variance of the n samples The expression is as follows: B-2: From the precipitation set in the forecast period Randomly draw m samples with replacement, and calculate the variance of the m samples The expression is as follows: where g 2i is the precipitation data for the i-th forecast period; B-3: According to the variance and the variance calculate the variance consistency test statistic u, and its expression is as follows: B-4: Repeat steps B-1 to B-3 to a preset number of times j, calculate j variance consistency test statistics, and form an empirical distribution U using the j variance consistency test statistics. Its expression is as follows: U = {u1, u2…u j} B-5: Calculate the rejection region of the variance consistency test according to the empirical distribution U; the expression of the rejection region of the variance consistency test is: Among them, represents the variance consistency test statistic when the cumulative quantile of the empirical distribution U reaches ; If the variance consistency test statistic u falls within the rejection region of the variance consistency test, it is determined that the variance between the return period precipitation data and the forecast period precipitation data has changed.

5. The method for testing the consistency of observed precipitation between the return period and the forecast period according to claim 1, characterized in that The global precipitation station observation grid data includes time, longitude data, latitude data, and observed precipitation data.

6. The method for testing the consistency of observed precipitation between the return period and the forecast period according to any one of claims 1 to 5, the method further includes respectively plotting the overall distribution of the precipitation data in the return period, the overall distribution of the precipitation data in the forecast period, the mean change, and the variance change on different spatial schematic diagrams.

7. The method for testing the consistency of observed precipitation between the return period and the forecast period according to any one of claims 1 to 5, characterized in that, The method further includes plotting a first Sankey diagram and a second Sankey diagram; the types of precipitation consistency changes between the return period and the forecast period include simultaneous changes in the mean and variance, a change in the mean and no change in the variance, no change in the mean and a change in the variance, and no changes in both the mean and variance; The first Sankey diagram is used to show the proportion of the number of grids with mean changes and variance changes in the spatial area where precipitation consistency changes occur; The second Sankey diagram is used to show the proportion of different types of precipitation consistency changes between the return period and the forecast period in the same grid in the spatial area where precipitation consistency changes occur.

8. The method for testing the consistency of observed precipitation between the return period and the forecast period according to claim 7, characterized in that, The first Sankey diagram and the second Sankey diagram are respectively plotted using the Sankey module of Pyecharts.

9. A consistency test system for observed precipitation in the return period and the forecast period, which is applied to the consistency test method for observed precipitation in the return period and the forecast period according to any one of claims 1-8, and is characterized in that, Including: A data acquisition module for acquiring global precipitation station observation grid data; Cropping the global precipitation station observation grid data in the spatial dimension to obtain the precipitation data of the spatial area for precipitation consistency testing, and dividing the obtained precipitation data of the spatial area for precipitation consistency testing into precipitation data in the return period and precipitation data in the forecast period; A consistency test module, including a consistency judgment unit and a consistency discrimination unit; The consistency judgment unit is used to test the overall distribution of the precipitation data in the return period and the overall distribution of the precipitation data in the forecast period. If there are differences between the overall distribution of the precipitation data in the return period and the overall distribution of the precipitation data in the forecast period, it is determined that the precipitation consistency between the return period and the forecast period has changed; The consistency discrimination unit is used to calculate the mean change and variance change of the precipitation data in the return period and the precipitation data in the forecast period based on the bootstrap method, and discriminate the types of precipitation consistency changes between the return period and the forecast period according to the mean change and variance change.

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