Subseasonal daily precipitation pattern error correction prediction method and related device

Abstract

The application provides a sub-seasonal daily precipitation model error correction prediction method and related device, the method comprises the following steps: obtaining historical return data, prediction data and corresponding historical observation precipitation data; convert the precipitation data into a standard normal distribution and construct an observation cumulative distribution function model, and use a generalized Pareto distribution to fit extreme precipitation; convert the return data into a normal distribution to construct a model return cumulative distribution function model; the observation conversion sequence is a prior distribution, and the statistical relationship between the model return conversion sequence and the observation conversion sequence is used to construct a likelihood function; convert the current prediction data into a prediction sequence that conforms to the normal distribution; calculate the mean and variance of the posterior distribution by fusing the prior distribution and the likelihood function; inverse conversion back to the original precipitation space to obtain the corrected daily precipitation prediction result. The bottleneck that the traditional linear correction method is not suitable for non-normal precipitation variables is solved, and the defect that the static correction method cannot adapt to the dynamic evolution of sub-seasonal scale model error is overcome.

Description

Technical Field

[0001] This application relates to the field of precipitation prediction technology, specifically to a method and related apparatus for error correction prediction of daily precipitation patterns in the second season. Background Technology

[0002] Climate forecasts on a sub-seasonal timescale, spanning the next two weeks to two months, are a crucial link between weather forecasting and seasonal climate prediction. They can provide early warnings of extreme events and offer strong scientific and technological support for disaster prevention and mitigation. Precipitation forecasts play a vital role in areas such as water resource management and drought / flood control. However, current sub-seasonal forecasting capabilities still lag significantly behind short-term weather forecasts and medium- to long-term climate predictions.

[0003] In the field of subseasonal precipitation forecasting, both domestic and international methods primarily employ dynamical and statistical forecasting. However, both methods have limitations in their predictive capabilities. Specifically, mainstream subseasonal-to-seasonal (S2S) dynamical models, such as those from the European Centre for Medium-Range Weather Forecasts (ECMWF), typically maintain their precipitation forecasting skill for only about two weeks, and this skill declines rapidly with increasing forecast lead time, particularly regarding strong precipitation events. Furthermore, while statistical models or combined dynamical-statistical models offer some predictive ability for subseasonal precipitation trends, they exhibit significant biases in predicting the central location and intensity of strong precipitation events and are unsuitable for correcting predictions of non-normally distributed precipitation values. Overall, current subseasonal climate forecasting technologies are insufficient to meet the critical service needs of meteorological disaster prevention and mitigation. Summary of the Invention

[0004] This application provides a sub-seasonal daily precipitation model error correction prediction method and related apparatus, which can solve the technical bottleneck that traditional linear correction methods are difficult to apply to non-normal precipitation variables, and overcome the defect that static correction methods cannot adapt to the dynamic evolution of sub-seasonal scale model errors.

[0005] A first aspect of this application provides a method for error correction and prediction of sub-seasonal daily precipitation models, the method comprising: Acquire the return data of the subseasonal dynamic model in the historical period, the forecast data for the current period, and the observed precipitation data in the corresponding historical period, and perform spatial grid standardization on the observed precipitation data in the corresponding historical period to obtain standardized historical observed precipitation data. The standardized historical precipitation data were converted into an observation transformation sequence conforming to a standard normal distribution using the equipercentage method of the cumulative distribution function, and an observation cumulative distribution function model was constructed. Based on the observed cumulative distribution function model, the historical return data is converted into a pattern return transformation sequence that conforms to a standard normal distribution, and a pattern return cumulative distribution function model is constructed. The forecast data for the current time period is input into the cumulative distribution function model of the model return to obtain the current forecast transformation sequence that conforms to the standard normal distribution; Using the observed transition sequence as a prior distribution, a likelihood function is constructed based on the statistical relationship between the model return transition sequence and the observed transition sequence; By fusing the prior distribution and the likelihood function, and incorporating the current forecast transformation sequence, the parameters of the posterior distribution are calculated. The parameters of the posterior distribution are input into the inverse function of the observed cumulative distribution function model, and the inverse transformation is performed back to the original precipitation space to obtain the corrected daily precipitation prediction results.

[0006] In one possible implementation, the process of converting the standardized historical precipitation data into an observational transformation sequence conforming to a standard normal distribution using the equipercentage method of the cumulative distribution function includes: For each grid point and each target date, the historical observed precipitation sequence is arranged in ascending order, the cumulative probability value corresponding to each precipitation value is calculated, and the mapping relationship from observed precipitation value to cumulative probability is constructed. For extreme precipitation data exceeding a preset threshold, a generalized Pareto distribution model is used to fit the tail probability distribution, replacing the corresponding cumulative probability value in the original ordered statistics. The cumulative probability value is converted into a transformed value conforming to the standard normal distribution by using the inverse function of the standard normal distribution, thus obtaining the observation transformation sequence.

[0007] In one possible implementation, the expression for the cumulative distribution function model of the pattern reward is as follows:

[0008] In the formula, For extreme precipitation, For position parameters, For scale parameters, For shape parameters.

[0009] In one possible implementation, the step of constructing a likelihood function based on the statistical relationship between the mode return transition sequence and the observed transition sequence, using the observed transition sequence as a prior distribution, includes: The ensemble mean of the model return transformation sequence is subjected to linear regression analysis with the observed transformation sequence to obtain the intercept, slope and residual variance of the regression equation; Based on the residual variance and the set variance of the current forecast transformation sequence, a likelihood function is constructed to describe the probabilistic relationship between model forecasts and actual precipitation.

[0010] In one possible implementation, the step of fusing the prior distribution and the likelihood function, and incorporating the current forecast transformation sequence, to calculate the parameters of the posterior distribution includes: Obtain the normal distribution transformation value corresponding to the historical observed precipitation mean in the observed cumulative distribution function model; Based on the variance of the prior distribution, the regression parameters of the likelihood function, and the ensemble mean and variance of the current forecast transformation sequence, the mean and variance of the posterior distribution are calculated by fusion. The mean is used as the deterministic forecast result, and the variance is used to generate probabilistic forecast information.

[0011] In one possible implementation, the mean and variance of the posterior distribution are calculated by fusing the variance of the prior distribution, the regression parameters of the likelihood function, and the ensemble mean and variance of the current forecast transformation sequence. The calculation formulas for the mean and variance are as follows:

[0012]

[0013] In the formula, The mean of the posterior distribution. For the posterior distribution variance, The intercept of the linear regression equation is denoted as . The slope of the linear regression equation is denoted as . The residual variance of the linear regression equation. The variance of historical observed precipitation that has turned to a normal distribution. To predict precipitation variance for models that have transitioned to a normal distribution, To predict the average precipitation value for models that have transitioned to a normal distribution, This represents the transformed value of the historical observed precipitation mean after converting it to a normal distribution, corresponding to the same percentile.

[0014] In one possible implementation, the step of inputting the parameters of the posterior distribution into the inverse function of the observed cumulative distribution function model, and inversely transforming it back to the original precipitation space to obtain the corrected daily precipitation forecast results includes: The posterior mean is converted into a cumulative probability value using the cumulative distribution function of the standard normal distribution; The cumulative probability value is input into the inverse function of the observed cumulative distribution function model, and mapped back to the precipitation value in the original precipitation space to obtain the corrected daily precipitation prediction result.

[0015] This example has at least the following beneficial effects: 1. By first eliminating the influence of skewed precipitation distribution through normal transformation, and then dynamically integrating historical climate state and model forecast information through Bayesian fusion, the cascade processing method not only solves the technical bottleneck that traditional linear correction methods are difficult to apply to non-normal precipitation variables, but also overcomes the defect that static correction methods cannot adapt to the dynamic evolution of sub-seasonal model errors.

[0016] 2. The refined modeling of the tail of extreme precipitation through the generalized Pareto distribution significantly improves the prediction ability of heavy precipitation events. The fusion of prior distribution and likelihood function in the Bayesian framework achieves coordinated correction of model systematic bias and forecast uncertainty, effectively reducing the bias and uncertainty of sub-seasonal precipitation forecasts. It significantly improves the prediction accuracy of dynamic models for daily precipitation, especially heavy precipitation events, with a long lead time, providing scientific support for major decisions such as flood control and drought relief, water resource management, and disaster reduction and relief.

[0017] A second aspect of this application provides a sub-seasonal daily precipitation model error correction and prediction system, the system comprising: The first module is used to acquire the return data of the sub-seasonal dynamic model in the historical period, the forecast data of the current period, and the observed precipitation data in the corresponding historical period, and to perform spatial grid standardization on the observed precipitation data in the corresponding historical period to obtain standardized historical observed precipitation data. The second module is used to convert the standardized historical precipitation data into an observation transformation sequence that conforms to the standard normal distribution using the equipercentage method of the cumulative distribution function, and to construct an observation cumulative distribution function model. The third module is used to convert the historical return data into a pattern return transformation sequence that conforms to a standard normal distribution based on the observed cumulative distribution function model, and to construct the pattern return cumulative distribution function model. The fourth module is used to input the forecast data of the current time period into the cumulative distribution function model of the model return to obtain the current forecast transformation sequence that conforms to the standard normal distribution; The fifth module is used to construct a likelihood function based on the statistical relationship between the model return transition sequence and the observation transition sequence, using the observed transition sequence as a prior distribution. The sixth module is used to fuse the prior distribution and the likelihood function, and to incorporate the current forecast transformation sequence to calculate the parameters of the posterior distribution; The seventh module is used to input the parameters of the posterior distribution into the inverse function of the observed cumulative distribution function model, and inversely transform it back to the original precipitation space to obtain the corrected daily precipitation prediction results.

[0018] A third aspect of this application provides a terminal including a processor, an input device, an output device, and a memory, wherein the processor, input device, output device, and memory are interconnected, wherein the memory is used to store a computer program, the computer program including program instructions, and the processor is configured to invoke the program instructions to execute the steps of the sub-seasonal daily precipitation pattern error correction prediction method in the first aspect of this application.

[0019] A fourth aspect of this application provides a computer-readable storage medium storing a computer program for electronic data interchange, wherein the computer program causes a computer to perform some or all of the steps described in the sub-seasonal daily precipitation pattern error correction prediction method of the first aspect of this application.

[0020] A fifth aspect of this application provides a computer program product, wherein the computer program product includes a non-transitory computer-readable storage medium storing a computer program operable to cause a computer to perform some or all of the steps described in the sub-seasonal daily precipitation model error correction prediction method of the first aspect of this application. The computer program product may be a software installation package. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This application provides a schematic diagram of the overall process for a sub-seasonal daily precipitation model error correction and prediction method. Figure 2 This application provides an embodiment of a sub-seasonal daily precipitation model error correction prediction method, which uses CDF percentile conversion to normal distribution to obtain the PDF and CDF curves of single-point observation precipitation on a certain date and the posterior distribution. Figure 3 This application provides a Bayesian model for a single date in an embodiment of a sub-seasonal daily precipitation pattern error correction prediction method, which is used to calculate the likelihood function of a specific date. Figure 4 This application provides a Bayesian-based method for error correction and prediction of sub-seasonal daily precipitation models, which includes the prior distribution, posterior distribution, and model forecast distribution converted to a normal distribution for a single point on a specific date in the CMA-CPSv3 model. Figure 5 This application provides an embodiment of the error correction prediction method for the sub-seasonal daily precipitation model, and provides a test score map of the CMA-CPSv3 sub-seasonal model based on Bayesian ideas for the summer precipitation in China in 2024. Figure 6 This application provides a schematic diagram of the overall structure of a sub-seasonal daily precipitation model error correction prediction system. Figure 7 This application provides a schematic diagram of the structure of a terminal. Figure label: Module 1-1, Module 2-2, Module 3-3, Module 4-4, Module 5-5, Module 6-6, Module 7-7. Detailed Implementation

[0023] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] The terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0025] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0026] To better understand the sub-seasonal daily precipitation model error correction prediction method provided in this application, the following is a brief introduction to the scenarios in which this method is applied. Utilizing long-term model historical reports and observational data to identify model error distribution characteristics and establish a model error correction prediction model is crucial for improving the accuracy of sub-seasonal daily precipitation. However, current model error correction and multi-model ensemble methods mainly focus on synoptic-scale forecasts, seasonal predictions, and even climate change predictions. In sub-seasonal scale predictions where initial and boundary value signals are insignificant, the combined influence of initial conditions and boundary forcing, along with the dynamic changes in their dominant mechanisms with seasons and regions, makes traditional correction methods based on static historical relationships difficult to adapt to such dynamically evolving systematic errors, leading to unstable correction results. Furthermore, methods such as CDF-QM and Singular Value Decomposition (SVD) are essentially linear tools, making it difficult to fully capture the complex nonlinear interactions between precipitation and precursory factors such as circulation. Their predictive ability highly depends on the stability of the statistical relationship between previous forecast factors and forecast quantities; if the relationship is weak or changes, the prediction accuracy will decrease.

[0027] The sub-seasonal daily precipitation model error correction prediction method is applied to the sub-seasonal daily precipitation model error correction prediction system. Figure 1 A schematic diagram of the overall process for a sub-seasonal daily precipitation model error correction prediction method is shown. Figure 1 As shown, it includes: S1. Obtain the return data of the subseasonal dynamic model in the historical period, the forecast data of the current period, and the observed precipitation data in the corresponding historical period. Then, perform spatial grid standardization on the observed precipitation data in the corresponding historical period to obtain the standardized historical observed precipitation data.

[0028] S2. The standardized historical precipitation data are converted into an observation transformation sequence that conforms to the standard normal distribution using the equipercentage method of the cumulative distribution function, and an observation cumulative distribution function model is constructed.

[0029] Step S2 includes the following steps: S201. For each grid point and each target date, arrange the historical observed precipitation sequence in ascending order, calculate the cumulative probability value corresponding to each precipitation value, and construct the mapping relationship from observed precipitation value to cumulative probability.

[0030] First, the historical long-term precipitation sequences of the regional grid points are arranged in ascending order. The group interval is calculated by dividing the precipitation range (maximum precipitation minus minimum precipitation) by the step size. The cumulative probability density value of precipitation within each precipitation interval is then calculated to obtain the cumulative probability density curve of the entire precipitation sequence.

[0031] In the formula, This represents the probability of the i-th interval. represents the precipitation sequence, and n represents the length of the precipitation sequence.

[0032] S202. For extreme precipitation data exceeding the preset threshold, the tail probability distribution is fitted using a generalized Pareto distribution model, replacing the corresponding cumulative probability value in the original ordered statistics.

[0033] For extreme precipitation events at the 90th percentile or higher, the generalized Pareto distribution (GPD) model is used to fit their probability distribution.

[0034] The distribution function model for cumulative pattern returns is expressed as follows:

[0035] In the formula, For extreme precipitation, For position parameters, For scale parameters, For shape parameters.

[0036] S203. The cumulative probability value is converted into a transformed value that conforms to the standard normal distribution by using the inverse function of the standard normal distribution, thus obtaining the observation transformation sequence.

[0037] The cumulative probability pi obtained in the previous step can be transformed using the inverse function of the standard normal distribution (PPF) as follows:

[0038] In the formula, Zi is the quantile corresponding to the normal distribution after equal percentile transformation.

[0039] Figure 2 This diagram illustrates the PDF and CDF curves of observed precipitation at a single point on a specific date, based on the CDF percentile conversion to a normal distribution. Figure 2 As shown, (a) and (c) are the PDF and CDF distributions of the original precipitation distribution, and (b) and (d) are the PDF and CDF distributions of the normal distribution. The black solid line represents the result of the observed data, and the gray solid line represents the result of the posterior distribution.

[0040] S3. Based on the observed cumulative distribution function model, convert the historical return data into a pattern return transformation sequence that conforms to the standard normal distribution, and construct the pattern return cumulative distribution function model.

[0041] Step S3 includes the following sub-steps: S301. For each grid point and each target date, collect the return precipitation data of all members of the sub-seasonal dynamic model within the historical period to form the model return precipitation sequence.

[0042] Specifically, for each grid point within the target area, and for each reporting date (e.g., every day from April 1 to September 30) and each forecast lead time (e.g., the first to the 60th day in the future), the daily precipitation of all members (e.g., 10 members in the CMA-CPSv3 model) for the corresponding reporting date and forecast lead time in historical years (e.g., from 2008 to 2023) is extracted from the historical return data of the sub-seasonal dynamics model. This yields the model return precipitation sequence for that grid point on the target date, with the sequence length being the number of historical years multiplied by the number of members.

[0043] S302. Using the same cumulative distribution function percentile method as in step S2, the model return precipitation series is converted into a model return transformed series that conforms to the standard normal distribution, and the model return cumulative distribution function model is constructed simultaneously.

[0044] The processing method in this step is completely consistent with the method for constructing the observation cumulative distribution function model in step S2, specifically including: Arrange the model-reported precipitation series in ascending order, calculate the cumulative probability value corresponding to each precipitation value, and construct a mapping relationship from model precipitation values ​​to cumulative probabilities. For the th in the series... precipitation value Its cumulative probability ,in The total length of the sequence. The sequence number is the result of sorting in ascending order.

[0045] For extreme precipitation data exceeding a preset threshold (e.g., precipitation exceeding the 90th percentile), a generalized Pareto distribution (GPD) model is used to fit the tail probability distribution, replacing the corresponding cumulative probability value in the original ordered statistics. The GPD distribution function is:

[0046] In the formula, This is an extreme precipitation value. The location parameter is a preset threshold, such as the 90th percentile. For scale parameters, These are shape parameters. The L-moment method is used to estimate them. and After fitting, for any pattern-reported precipitation value exceeding the threshold, its cumulative probability can be directly calculated using the GPD function, replacing the original ranking probability.

[0047] The cumulative probability value corresponding to each precipitation value Convert to standard normal distribution quantiles using the inverse function (PPF) of the standard normal distribution:

[0048] This yields the standard normal distribution transformation value corresponding to the precipitation reported by each model member, i.e., the model report transformation sequence.

[0049] Based on the correspondence established in the above process between the original model precipitation values ​​and the transformed normal quantiles (which can be stored through interpolation functions or parameterized forms), a cumulative distribution function model of model returns is constructed. This model can be used to subsequently convert any new model forecast precipitation values ​​into standard normal distribution quantiles.

[0050] S303. Based on the model return transformation sequence, calculate the ensemble average for each historical year and each forecast lead time, which serves as the input for subsequent linear regression analysis.

[0051] For each historical year and each forecast lead time, the model return transformation values ​​of all members under the same year and the same target date are averaged to obtain the set average transformation value of model returns for that year. This sequence, along with the corresponding observation transformation sequence, will be used in the linear regression analysis in step S5 to establish the statistical relationship between the model and the observations.

[0052] S4. Input the forecast data for the current period into the cumulative distribution function model of the pattern return to obtain the current forecast transformation sequence that conforms to the standard normal distribution.

[0053] Step S4 includes the following sub-steps: S401. For each grid point, each reporting date, and each forecast lead time, obtain the forecast data for the current period of the sub-seasonal dynamic model. This forecast data includes the daily precipitation forecast values ​​of multiple members.

[0054] Specifically, for each grid point within the target area, and for the current reporting start date (e.g., a day between April 1st and September 30th, 2024) and each forecast lead time (e.g., the 1st to the 60th day in the future), the daily precipitation forecast values ​​for all members (e.g., the CMA-CPSv3 model has 10 members) corresponding to the reporting start date and forecast lead time are extracted from the current forecast data of the sub-seasonal dynamical model. This yields the current forecast precipitation sequence for that grid point on the target date, with the sequence length equal to the number of model members. .

[0055] S402. Substitute the current forecast precipitation value of each member into the cumulative distribution function model of the model return constructed in step S3, obtain the cumulative probability value corresponding to the precipitation value by looking up a table or interpolation, and then convert it into the standard normal distribution quantile through the inverse function of the standard normal distribution.

[0056] For the Current forecast precipitation values ​​for each member First, find the cumulative probability value corresponding to the precipitation value in the cumulative distribution function model of the model return constructed in step S3. .like If the cumulative probability is exactly equal to a discrete point in the model, then the corresponding cumulative probability is read directly; if it is between two discrete points, then the cumulative probability is calculated using a linear interpolation method.

[0057] Then, the cumulative probability value Convert to standard normal distribution quantiles using the inverse function (PPF) of the standard normal distribution:

[0058] This yields the standard normal distribution transformation value corresponding to the current forecast precipitation value for each member, i.e., the current forecast transformation sequence. ,in The number of members in the pattern.

[0059] S403. Based on the current forecast transformation sequence, calculate its ensemble mean and ensemble variance, which will serve as input parameters for subsequent likelihood function construction and posterior distribution calculation.

[0060] ensemble mean The formula for calculating the overall trend reflected in the current forecast is as follows:

[0061] set variance The formula for calculating the degree of uncertainty in the current forecast is as follows:

[0062] In this example, the model forecast data for the current time period was successfully converted to standard normal space, and the central tendency and dispersion of the forecast were quantified.

[0063] S5. Using the observed transformation sequence as the prior distribution, construct the likelihood function based on the statistical relationship between the model return transformation sequence and the observed transformation sequence.

[0064] Step S5 includes the following steps: S501. Using the observed transformation sequence as the prior distribution, calculate the mean and variance of the observed transformation sequence.

[0065] Among them, the observation transformation sequence obtained in step S2 As a prior distribution This sequence describes the distribution characteristics of historical climatologies in standard normal space. For each grid point and each target date, the observational transformation sequence consists of transformation values ​​for historical years (e.g., 2008 to 2023), i.e. .

[0066] Based on this sequence, calculate the mean of the prior distribution. and variance :

[0067]

[0068] In the formula, This represents the total number of historical years. For the first Observational conversion values ​​for each historical year.

[0069] The prior distribution This represents the "climate background knowledge" of precipitation at this grid point on this target date in the absence of model forecast information. Its mean reflects the average conditions for the same period in history, while the variance characterizes the natural variability of the climate state. This prior information will be Bayesianly fused with model forecast information in subsequent steps.

[0070] S502. Perform linear regression analysis on the ensemble mean of the model return transformation sequence and the observed transformation sequence to obtain the intercept, slope and residual variance of the regression equation.

[0071] For each grid point and each target date, the average transformation value of the pattern return set for each historical year calculated in step S303 is used. ( ) as the dependent variable, with the corresponding observed transformation sequence As the independent variable, construct a univariate linear regression model:

[0072] In the formula, The regression intercept reflects the systematic bias of the model; The regression slope reflects the model's sensitivity to changes in actual precipitation. For the first The annual regression residuals represent the random error portion that the model cannot explain.

[0073] The regression coefficients are estimated using the least squares method, and the calculation formula is as follows:

[0074]

[0075] In the formula, This is the mean of the average transformation value sequence of the pattern return set.

[0076] Regression Residual Variance It is used to measure the fluctuations that cannot be explained by the regression model, and its calculation formula is as follows:

[0077] Among them, residual variance reflects the degree of conditional fluctuation of the model return set mean under known actual precipitation conditions, and is an important parameter for characterizing the uncertainty of the model itself.

[0078] S503. Based on the residual variance and the ensemble variance of the current forecast transformation sequence, construct a likelihood function to describe the probabilistic relationship between model forecasts and actual precipitation.

[0079] Among them, based on the regression analysis results of step S502, given the actual precipitation When the conditional distribution of the average value of the pattern's return set is given by:

[0080] In the formula, The average value of the set of returns for the representative pattern.

[0081] For the current forecast, it is assumed that the forecast values ​​of its members are normally distributed around the ensemble mean, and the degree of dispersion is determined by the ensemble variance. Depiction, that is:

[0082] In the formula, The current forecast transition value representing a single member. The ensemble mean of the current forecasts .

[0083] Considering that the regression error of the model return and the ensemble dispersion of the current forecast originate from independent error sources (the former characterizes the historical stability of the model system performance, while the latter characterizes the ensemble dispersion of the current forecast), they can be superimposed to obtain the given true precipitation. Current forecast members Conditional distribution:

[0084] The distribution is the likelihood function constructed in this invention.

[0085] Specifically, the mean term This reflects the model's expected response to actual precipitation. and Estimated from historical return data, it reflects the systematic bias and sensitivity of the pattern; Furthermore, the variance term It takes into account the uncertainty of historical regression of the pattern ( ) and the discrete uncertainty of the current forecast set ( This allows for a complete characterization of forecast uncertainty.

[0086] in, Figure 3 This diagram illustrates the likelihood function for a single date in a Bayesian model.

[0087] S6. By fusing the prior distribution and the likelihood function, and incorporating the current forecast transformation sequence, the parameters of the posterior distribution are calculated.

[0088] Step S6 includes the following steps: S601. Obtain the normal distribution transformation value corresponding to the historical observed precipitation mean in the observed cumulative distribution function model.

[0089] For a given grid point and each target date, the arithmetic mean of all observed precipitation over the historical period is first calculated. :

[0090] In the formula, For the first The original observed precipitation (in mm) for each historical year on the target date. This represents the total number of historical years.

[0091] Furthermore, this historical average precipitation Input the observation cumulative distribution function model constructed in step S2. Use this model to find... The corresponding cumulative probability value :

[0092] In the formula, To observe the cumulative distribution function, the raw precipitation values ​​are mapped to... Cumulative probability of the interval.

[0093] like If the cumulative probability is exactly equal to a discrete point in the model, it is directly read; if it is between two discrete points, the cumulative probability is calculated using linear interpolation. For extreme cases (such as historical average precipitation exceeding the threshold used when building the model), the generalized Pareto distribution model established in step S202 is called for extrapolation calculation.

[0094] Finally, the cumulative probability value Convert to standard normal distribution quantiles using the inverse function (PPF) of the standard normal distribution:

[0095] Should This refers to the corresponding position of the historical observed precipitation mean in the standard normal space. It will serve as an important input parameter in the posterior fusion formula, used to constrain the mean of the posterior distribution to converge towards the climatological mean.

[0096] S602. Based on the variance of the prior distribution, the regression parameters of the likelihood function, and the ensemble mean and variance of the current forecast transformation sequence, the mean and variance of the posterior distribution are calculated by fusion.

[0097] The mean is used as the deterministic forecast result, while the variance is used to generate probabilistic forecast information.

[0098] Specifically, according to Bayesian theory, the posterior distribution With prior distribution and likelihood function The product is proportional. The prior distribution follows a normal distribution. The likelihood function follows a normal distribution. Under the condition that, the posterior distribution is also a normal distribution, that is The mean and variance are calculated using the following formulas: The reciprocal of the posterior variance (i.e., the precision) is:

[0099] The ratio of the posterior mean to the posterior variance is:

[0100] In the formula, The mean of the posterior distribution. For the posterior distribution variance, The intercept of the linear regression equation is denoted as . The slope of the linear regression equation is denoted as . The residual variance of the linear regression equation. The variance of historical observed precipitation that has turned to a normal distribution. To predict precipitation variance for models that have transitioned to a normal distribution, To predict the average precipitation value for models that have transitioned to a normal distribution, To find the corresponding percentile value of the historical observed precipitation mean under a normal distribution, we can solve the above two equations simultaneously to obtain the two core parameters of the posterior distribution. and .

[0101] In this example, the posterior mean It is the prior mean vs. the model-implied true precipitation estimate The weighted average is calculated by weighting each factor by its respective precision (the reciprocal of its variance). Posterior variance. It is less than either the prior variance or the likelihood variance, reflecting the reduction in uncertainty brought about by information fusion.

[0102] in, Figure 4 The diagram illustrates the prior distribution, posterior distribution, and model forecast distribution converted to a normal distribution for a single point on a specific date in the CMA-CPSv3 model based on Bayesian principles. The black dashed line represents the equal percentile value corresponding to the observed precipitation in 2024 after conversion; the black solid line represents the posterior distribution result; the gray dashed line represents the prior distribution; and the gray solid line represents the converted model forecast distribution.

[0103] S7. Input the parameters of the posterior distribution into the inverse function of the observed cumulative distribution function model, and inversely transform back to the original precipitation space to obtain the corrected daily precipitation prediction results.

[0104] Step S7 includes the following steps: S701. Convert the posterior mean into a cumulative probability value using the cumulative distribution function of the standard normal distribution.

[0105] For each grid point and each target date, the posterior mean is calculated. Substituting the cumulative distribution function of the standard normal distribution Calculate its corresponding cumulative probability value :

[0106] In practical calculations, numerical integration or table lookup methods can be used to achieve this cumulative probability value. This reflects the percentile position of the revised precipitation forecast in the climate distribution: This indicates that the predicted value is at the climatic median level. This indicates that the predicted value is higher than the climate average. This indicates that the value is below the average climate level.

[0107] For applications that require generating probabilistic prediction information, the posterior variance can also be used. Taking this into account, a complete posterior probability density function can be generated. For example, it can be based on the posterior distribution. Multiple quantile points are randomly sampled and converted into cumulative probability values ​​to obtain the confidence interval or probability density curve for the probability forecast. However, in this step, the focus is on deterministic forecasting, with particular emphasis on the post-evaluation mean. The conversion.

[0108] S702. Input the cumulative probability value into the inverse function of the observed cumulative distribution function model, map it back to the precipitation value in the original precipitation space, and obtain the corrected daily precipitation prediction results.

[0109] This step will accumulate probability values. By observing the inverse function of the cumulative distribution function model This maps back to the original precipitation (unit: mm) with physical meaning, completing the final output of the entire correction process.

[0110] For each grid point and each target date, the cumulative probability value obtained in step S701 is... Input the inverse function of the observation cumulative distribution function model constructed in step S2, and calculate the corresponding precipitation:

[0111] In the formula, To observe the inverse function of the cumulative distribution function, The cumulative probability of the interval is mapped back to the precipitation value in the original precipitation space. The construction of this inverse function corresponds to the forward mapping in step S2: like The corresponding quantiles are located in the non-extreme precipitation range (i.e.) If the cumulative probability mapping of the observed precipitation series is not found, the corresponding precipitation amount is then determined by interpolation. Specifically, the cumulative probability closest to the value in the "precipitation value-cumulative probability" mapping table constructed in step S201 can be searched. The final precipitation value is obtained by linear interpolation from the two points:

[0112] In the formula, and Cumulative probability in the mapping table and The corresponding precipitation value, and satisfying .

[0113] like If the region falls within the extreme precipitation range, then the inverse function of the generalized Pareto distribution model established in step S202 is used for calculation. For a given cumulative probability... First, convert it into a conditional probability that exceeds the threshold:

[0114] Then, the increase in precipitation exceeding the threshold is calculated using the inverse GPD function:

[0115] The final precipitation is the threshold plus the increment:

[0116] In the formula, The location parameters of the GPD model (i.e., extreme precipitation thresholds, such as the precipitation corresponding to the 90th percentile). and These are the scale parameter and the shape parameter, respectively.

[0117] Through the aforementioned inverse transformation process, this example restores the posterior information obtained after Bayesian fusion into a precipitation prediction value with a clear physical meaning. This prediction value retains the distribution characteristics of historical climate states (through observation of the CDF model) while also incorporating the dynamic information from the current model forecast (through the posterior mean). The introduction of GPD tail modeling maintains statistical continuity and physical plausibility in extreme precipitation ranges.

[0118] Final output This refers to the corrected daily precipitation forecast results for the target grid points, target reporting dates, and target forecast lead times. By repeating all the above steps (S1 to S7), complete forecast coverage of all grid points, all reporting dates (e.g., April 1 to September 30), and all forecast lead times (e.g., the first day to the 60th day in the future) within the target area can be achieved, generating a complete set of sub-seasonal scale daily precipitation correction forecast products.

[0119] This example provides a method for error correction and prediction of sub-seasonal daily precipitation models. First, historical return data, current forecast data, and corresponding historical observed precipitation data from the sub-seasonal dynamical model are acquired and spatially standardized using a grid. Then, the equipercentile method of the cumulative distribution function is used to convert the historical observed precipitation data into an observation transformation sequence conforming to a standard normal distribution, and an observation cumulative distribution function model is constructed. Simultaneously, a generalized Pareto distribution is introduced for tail fitting of extreme precipitation events to improve the modeling accuracy of heavy precipitation events. Finally, based on the observation cumulative distribution function model, the historical return data is converted into a model return transformation sequence. A cumulative distribution function model of model returns is constructed. Then, using the observed transformation sequence as the prior distribution, a likelihood function is constructed through linear regression analysis of the statistical relationship between the model return transformation sequence and the observed transformation sequence. Next, the current forecast data is transformed into a current forecast transformation sequence conforming to a standard normal distribution using the cumulative distribution function model of model returns. The prior distribution and likelihood function are then fused, and the mean and variance of the posterior distribution are calculated by incorporating the current forecast transformation sequence. Finally, the posterior parameters are inversely transformed back to the original precipitation space using the inverse function of the observed cumulative distribution function model to obtain the corrected daily precipitation forecast results, including the following beneficial effects: 1. By first eliminating the influence of skewed precipitation distribution through normal transformation, and then dynamically integrating historical climate state and model forecast information through Bayesian fusion, the cascade processing method not only solves the technical bottleneck that traditional linear correction methods are difficult to apply to non-normal precipitation variables, but also overcomes the defect that static correction methods cannot adapt to the dynamic evolution of sub-seasonal model errors.

[0120] 2. The refined modeling of the tail of extreme precipitation through the generalized Pareto distribution significantly improves the prediction ability of heavy precipitation events. The fusion of prior distribution and likelihood function in the Bayesian framework achieves coordinated correction of model systematic bias and forecast uncertainty, effectively reducing the bias and uncertainty of sub-seasonal precipitation forecasts. It significantly improves the prediction accuracy of dynamic models for daily precipitation, especially heavy precipitation events, with a long lead time, providing scientific support for major decisions such as flood control and drought relief, water resource management, and disaster reduction and relief.

[0121] In this example, Figure 5 The diagram shows a test score for the Bayesian-based CMA-CPSv3 subseasonal model of precipitation in China during the summer of 2024. Figure 5 As shown, RMSE and FAR represent the root mean square error and false alarm rate, respectively; a smaller score indicates a higher forecast skill. ACC, ETS, TS, and POD represent the spatial correlation coefficient, fairness skill score, risk score, and hit rate, respectively; a larger score indicates a higher forecast skill. CPSv3 represents the model's direct output raw results, CPSv3-CDF represents the result corrected by the model's cumulative probability density distribution percentile mapping (CDF-QM), and CPSv3-Bayes represents the result of the model's error correction method based on Bayesian principles. ETS, TS, POD, and FAR are calculated to have forecast skills of 0.1, 1.0, 5.0, 10, and 20 mm of precipitation, respectively.

[0122] For those consistent with the above, please refer to Figure 6 , Figure 6 This application provides a schematic diagram of the structure of a sub-seasonal daily precipitation model error correction prediction system, as illustrated in this embodiment. Figure 6 As shown, the system includes: The first module 1 is used to acquire the return data of the sub-seasonal dynamic model in the historical period, the forecast data of the current period, and the observed precipitation data in the corresponding historical period, and to perform spatial grid standardization on the observed precipitation data in the corresponding historical period to obtain the standardized historical observed precipitation data. The second module 2 is used to convert standardized historical precipitation data into an observation transformation sequence that conforms to the standard normal distribution using the equipercentage method of the cumulative distribution function, and to construct an observation cumulative distribution function model. The third module 3 is used to convert historical return data into a pattern return transformation sequence that conforms to a standard normal distribution based on the observed cumulative distribution function model, and to construct the pattern return cumulative distribution function model. Module 4 is used to input the forecast data of the current period into the cumulative distribution function model of the pattern return, and obtain the current forecast transformation sequence that conforms to the standard normal distribution; Module 5 is used to construct a likelihood function based on the statistical relationship between the model return transition sequence and the observed transition sequence, using the observed transition sequence as the prior distribution. Module 6 is used to fuse the prior distribution and the likelihood function, and to incorporate the current forecast transformation sequence to calculate the parameters of the posterior distribution; Module 7 is used to input the parameters of the posterior distribution into the inverse function of the observed cumulative distribution function model, and inversely transform it back to the original precipitation space to obtain the corrected daily precipitation prediction results.

[0123] For examples consistent with the above embodiments, please refer to... Figure 7 , Figure 7 This is a schematic diagram of the structure of a terminal provided in an embodiment of this application, such as... Figure 7 As shown, it includes a processor, input devices, output devices, and a memory, which are interconnected. The memory is used to store a computer program, which includes program instructions. The processor is configured to invoke the program instructions. The program includes instructions for performing the following steps. The system acquires the return data of the subseasonal dynamic model in historical periods, the forecast data for the current period, and the observed precipitation data in the corresponding historical periods. It then performs spatial grid standardization on the observed precipitation data in the corresponding historical periods to obtain standardized historical observed precipitation data. The standardized historical precipitation data were converted into an observational transformation sequence conforming to the standard normal distribution using the equipercentage method of the cumulative distribution function, and an observational cumulative distribution function model was constructed. Based on the observed cumulative distribution function model, historical return data are transformed into a pattern return transformation sequence that conforms to the standard normal distribution, and a pattern return cumulative distribution function model is constructed. Using the observed transition sequence as the prior distribution, a likelihood function is constructed based on the statistical relationship between the model return transition sequence and the observed transition sequence; Input the forecast data for the current period into the cumulative distribution function model of the pattern return, and obtain the current forecast transformation sequence that conforms to the standard normal distribution; By integrating the prior distribution and the likelihood function, and incorporating the current forecast transformation sequence, the parameters of the posterior distribution are calculated. The parameters of the posterior distribution are input into the inverse function of the observed cumulative distribution function model, and the inverse transformation is performed back to the original precipitation space to obtain the corrected daily precipitation prediction results.

[0124] The above mainly describes the solutions of the embodiments of this application from the perspective of the method execution process. It is understood that, in order to achieve the above functions, the terminal includes the corresponding hardware structure and / or software modules for executing each function. Those skilled in the art should readily recognize that, in conjunction with the units and algorithm steps of the various examples described in the embodiments provided herein, this application can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed in hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0125] This application embodiment can divide the terminal into functional units according to the above method example. For example, each function can be divided into a separate functional unit, or two or more functions can be integrated into one processing unit. The integrated unit can be implemented in hardware or as a software functional unit. It should be noted that the unit division in this application embodiment is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods.

[0126] This application also provides a computer storage medium storing a computer program for electronic data interchange, which causes a computer to perform some or all of the steps of any of the sub-seasonal daily precipitation pattern error correction prediction methods described in the above method embodiments.

[0127] This application also provides a computer program product, which includes a non-transitory computer-readable storage medium storing a computer program that causes a computer to perform some or all of the steps of any of the sub-seasonal daily precipitation pattern error correction prediction methods described in the above method embodiments.

[0128] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0129] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0130] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical or other forms.

[0131] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0132] Furthermore, the functional units in the various embodiments of the application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software program module.

[0133] If the integrated unit is implemented as a software program module and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0134] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage device, which may include: a flash drive, a read-only memory, a random access memory, a magnetic disk, or an optical disk, etc.

[0135] The embodiments of this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for error correction and prediction of sub-seasonal daily precipitation models, characterized in that, include: Acquire the return data of the subseasonal dynamic model in the historical period, the forecast data for the current period, and the observed precipitation data in the corresponding historical period, and perform spatial grid standardization on the observed precipitation data in the corresponding historical period to obtain standardized historical observed precipitation data. The standardized historical precipitation data were converted into an observation transformation sequence conforming to a standard normal distribution using the equipercentage method of the cumulative distribution function, and an observation cumulative distribution function model was constructed. Based on the observed cumulative distribution function model, the return data within the historical period is transformed into a pattern return transformation sequence conforming to a standard normal distribution, and a pattern return cumulative distribution function model is constructed; the expression formula of the pattern return cumulative distribution function model is as follows: In the formula, For extreme precipitation, For position parameters, For scale parameters, For shape parameters; The forecast data for the current time period is input into the cumulative distribution function model of the model return to obtain the current forecast transformation sequence that conforms to the standard normal distribution; Using the observed transition sequence as a prior distribution, a likelihood function is constructed based on the statistical relationship between the model return transition sequence and the observed transition sequence; By fusing the prior distribution and the likelihood function, and incorporating the current forecast transformation sequence, the parameters of the posterior distribution are calculated, including: Obtain the normal distribution transformation value corresponding to the historical observed precipitation mean in the observed cumulative distribution function model; Based on the variance of the prior distribution, the regression parameters of the likelihood function, and the ensemble mean and variance of the current forecast transformation sequence, the mean and variance of the posterior distribution are calculated. The mean is used as the deterministic forecast result, and the variance is used to generate probabilistic forecast information. The calculation formulas for the mean and variance are as follows: In the formula, Let be the mean of the posterior distribution. Let V be the variance of the posterior distribution. The intercept of the linear regression equation is denoted as . Let be the slope of the linear regression equation. The residual variance of the linear regression equation. The variance of historical observed precipitation that has transitioned to a normal distribution. To predict precipitation variance for models that have transitioned to a normal distribution, The model predicts the average precipitation value to be normalized. This represents the transformed value of the historical observed precipitation mean after converting it to a normal distribution, corresponding to the same percentile. The parameters of the posterior distribution are input into the inverse function of the observed cumulative distribution function model, and the inverse transformation is performed back to the original precipitation space to obtain the corrected daily precipitation prediction results.

2. The method for error correction and prediction of sub-seasonal daily precipitation models according to claim 1, characterized in that, The step of constructing a likelihood function based on the statistical relationship between the model return transition sequence and the observed transition sequence, using the observed transition sequence as a prior distribution, includes: The ensemble mean of the model return transformation sequence is subjected to linear regression analysis with the observed transformation sequence to obtain the intercept, slope and residual variance of the linear regression equation; Based on the residual variance and the set variance of the current forecast transformation sequence, a likelihood function is constructed to describe the probabilistic relationship between model forecasts and actual precipitation.

3. The method for error correction and prediction of sub-seasonal daily precipitation models according to claim 1, characterized in that, The step of inputting the parameters of the posterior distribution into the inverse function of the observed cumulative distribution function model, and inversely transforming it back to the original precipitation space to obtain the corrected daily precipitation forecast results includes: The mean of the posterior distribution is converted into a cumulative probability value using the cumulative distribution function of the standard normal distribution; The cumulative probability value, transformed by the cumulative distribution function of the standard normal distribution, is input into the inverse function of the observed cumulative distribution function model, and mapped back to the precipitation value in the original precipitation space to obtain the corrected daily precipitation prediction result.

4. A sub-seasonal daily precipitation model error correction and prediction system, used to implement the sub-seasonal daily precipitation model error correction and prediction method as described in any one of claims 1-3, characterized in that, include: The first module is used to acquire the return data of the sub-seasonal dynamic model in the historical period, the forecast data of the current period, and the observed precipitation data in the corresponding historical period, and to perform spatial grid standardization on the observed precipitation data in the corresponding historical period to obtain standardized historical observed precipitation data. The second module is used to convert the standardized historical precipitation data into an observation transformation sequence that conforms to the standard normal distribution using the equipercentage method of the cumulative distribution function, and to construct an observation cumulative distribution function model. The third module is used to convert the return data within the historical period into a pattern return transformation sequence that conforms to a standard normal distribution based on the observed cumulative distribution function model, and to construct the pattern return cumulative distribution function model. The fourth module is used to input the forecast data of the current time period into the cumulative distribution function model of the model return to obtain the current forecast transformation sequence that conforms to the standard normal distribution; The fifth module is used to construct a likelihood function based on the statistical relationship between the model return transition sequence and the observation transition sequence, using the observed transition sequence as a prior distribution. The sixth module is used to fuse the prior distribution and the likelihood function, and to incorporate the current forecast transformation sequence to calculate the parameters of the posterior distribution; The seventh module is used to input the parameters of the posterior distribution into the inverse function of the observed cumulative distribution function model, and inversely transform it back to the original precipitation space to obtain the corrected daily precipitation prediction results.

5. A terminal, characterized in that, The system includes a processor, an input device, an output device, and a memory, which are interconnected. The memory stores a computer program, which includes program instructions. The processor is configured to invoke the program instructions to execute the sub-seasonal daily precipitation model error correction prediction method as described in any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, the computer program including program instructions that, when executed by a processor, cause the processor to perform the sub-seasonal daily precipitation model error correction prediction method as described in any one of claims 1-3.

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