Inversion, correction and evaluation method for ensemble forecast

Abstract

The invention discloses an inversion, correction and evaluation method for ensemble forecast, which comprises the following steps of: S1, data inversion: adopting an improved cubic convolution interpolation model to match space lattice point scales of the ensemble forecast and actually-measured data, and ensuring that the ensemble forecast and the actually-measured data have consistent temporal-spatial resolution; s2, forecasting correction: adopting an improved quantile mapping model, establishing a probability distribution relation between set members and actually measured data one by one, and correcting shape errors of forecasting distribution point by point to play a role in correcting deviation; and S3, skill evaluation: systematically constructing an ensemble forecast probability evaluation system, and quantitatively judging the skill improvement rate of the corrected ensemble forecast by adopting the deviation degree improvement rate, the accuracy improvement rate, the reliability improvement rate and the sharpness improvement rate of the corrected ensemble forecast compared with the original ensemble forecast. The method is sufficient in theoretical basis, can effectively invert, correct and evaluate the ensemble forecast, and has a wide application prospect.

Description

Technical Field

[0001] The present invention relates to the field of hydrological forecasting, and in particular to an inversion, correction and evaluation method for ensemble forecasting. Background Art

[0002] Ensemble forecasting is a forecasting method that gives the possible numerical range and confidence level of hydrological and meteorological elements (such as precipitation, runoff, and evaporation). Ensemble forecasting can not only give a single-value forecast using the average or quantile value of the ensemble members, but also quantify the uncertainty of the forecast using probability distribution. It is the focus and hotspot of current medium- and long-term forecasting.

[0003] At present, the global climate model is the main way to produce ensemble forecasts. Taking the ensemble precipitation forecast as an example, there are three main problems. First, the grid scale of the forecast product output by the global climate model does not fully match the spatial resolution of the measured grid, and interpolation inversion is required; second, due to the uncertainty factors of structural generalization, parameterization scheme, initial perturbation and boundary conditions, the global climate model often leads to large system deviations, obvious under-discrete or over-discrete phenomena, and deviation correction is required; third, the global climate model product is composed of multiple ensemble member forecasts, which are unconventional deterministic single-value forecasts. It is necessary to further develop a systematic evaluation method for probabilistic ensemble forecasts to comprehensively clarify and judge the improvement rate of the skill of correcting forecasts from multiple aspects. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the present invention proposes an inversion, correction and evaluation method for ensemble forecast, which can effectively invert, correct and evaluate ensemble forecast and has broad application prospects.

[0005] The technical solution adopted by the present invention is: An inversion, correction and evaluation method for ensemble forecasting includes the following steps: S1. Data inversion: An improved cubic convolution interpolation model is used to match the spatial grid scales of the ensemble forecast and the measured data to ensure that the ensemble forecast and the measured data have consistent temporal and spatial resolutions; S2. Forecast correction: Using the improved quantile mapping model, the probability distribution relationship between the ensemble members and the measured data is established one by one, and the shape error of the forecast distribution is corrected point by point, which plays a role in correcting the deviation; S3. Skill evaluation: The system constructs an ensemble forecast probability evaluation system, and uses the deviation improvement rate, accuracy improvement rate, reliability improvement rate, and sharpness improvement rate of the corrected ensemble forecast compared with the original ensemble forecast to quantitatively judge the skill improvement rate of the corrected ensemble forecast.

[0006] Furthermore, in step S1, The improved cubic convolution interpolation model is defined as follows: (1) Where: The original ensemble forecast is processed by the improved cubic convolution interpolation model at the spatial grid latitude , longitude is The predicted value at ; The original ensemble forecast is at the spatial grid latitude , longitude is The predicted values ​​of the 16 nearest spatial grid points; and It is an intermediate variable in the calculation process.

[0007] Furthermore, in step S2, The improved quantile mapping model is defined as follows: (2) Where: is the measured value; is the forecast value of the original ensemble forecast; is the forecast value for correcting the ensemble forecast; is the inverse of the empirical cumulative distribution function of the measured values; is the inverse of the empirical cumulative distribution function of the original ensemble forecast.

[0008] Furthermore, in step S3, The deviation improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: (3) Where: is the deviation improvement rate; for The measured value at the time; The first The members of the collection are The forecast value at the time; To correct the ensemble forecast The members of the collection are The forecast value at the time; For the The rate of improvement of the deviation degree of each set member; is the sequence length; is the number of set members; The accuracy improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: (4) Where: To improve the accuracy rate; for The measured value at the time; The first The members of the collection are The forecast value at the time; To correct the ensemble forecast The members of the collection are The forecast value at the time; for The cumulative distribution function of the measured value at time; The first The members of the collection are The cumulative distribution function value of the forecast value at time; To correct the ensemble forecast The members of the collection are The cumulative distribution function value of the forecast value at time; For the The accuracy improvement rate of each set member; is the sequence length; is the number of set members; The reliability improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: (5) Where: To improve the reliability rate; for The measured value at the time; The first The members of the collection are The cumulative distribution function value of the measured value at the time; To correct the ensemble forecast The members of the collection are The cumulative distribution function value of the measured value at the time; For the The reliability improvement rate of each set member; is the sequence length; is the number of set members; The sharpness improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: (6) Where: To improve the sharpness rate; The first The members of the collection are The 95% quantile value of the cumulative distribution function of the forecast value at the time; The first The members of the collection are The 5% quantile value of the cumulative distribution function of the forecast value at the time; To correct the ensemble forecast The members of the collection are The 95% quantile value of the cumulative distribution function of the forecast value at the time; To correct the ensemble forecast The members of the collection are The 5% quantile value of the cumulative distribution function of the forecast value at the time; For the The sharpness improvement rate of each set member; is the sequence length; is the number of set members.

[0009] The beneficial effects of the present invention are: The present invention proposes an inversion, correction and evaluation method for ensemble forecasting, which has sufficient theoretical basis and broad application prospects. It fully considers the deficiencies of existing technologies and methods, and proposes corresponding inversion, correction and evaluation solutions for three problems existing in the current global climate model. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 is a flow chart of an embodiment of the present invention. DETAILED DESCRIPTION

[0011] In order to make the technical solutions, advantages and effects of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings. The specific implementation methods and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0012] The monthly grid precipitation data set of my country (covering 3781 spatial grid points in my country) is used as the measured value, the ensemble precipitation of the four more advanced global climate models in the current medium- and long-term forecast is used as the original ensemble forecast, and the ensemble forecast processed by the present invention is used as the correction ensemble forecast, and the inversion, correction and evaluation process of the ensemble forecast is comprehensively analyzed and judged. Table 1 shows the data results of the measured values ​​and the forecast values ​​of the four global climate models, including the number of ensemble members, spatial resolution, temporal resolution, and forecast period. Due to the different data structures, this embodiment uniformly processes the spatial resolution of the data set to 0.5°×0.5°, the temporal resolution is unified to 1994-2015, and the forecast period is unified to 1-5 months. CMCC is the global climate model of the European Mediterranean Climate Change Center, DWD is the global climate model of the German Meteorological Office, UKMO is the global climate model of the UK Meteorological Office, and SEAS4 is the global climate model of the European Center for Medium-Term Weather Forecasts.

[0013] Considering the huge amount of data, the following is based on the first set member of SEAS4 with a forecast period of one month. The calculation process is explained using grid point simulation results as an example, and the results of ensemble member means of four global climate models and a forecast period of 1-5 months at 3781 grid points across the country are comprehensively displayed.

[0014] Table 1 Basic information of measured precipitation and global climate model datasets

[0015] like Figure 1 As shown, the present invention provides an inversion, correction and evaluation method for ensemble forecasting, comprising the following steps: S1. Data inversion: An improved cubic convolution interpolation model is used to match the spatial grid scale of the ensemble forecast with the measured data to ensure that the ensemble forecast and the measured data have consistent temporal and spatial resolution.

[0016] The improved cubic convolution interpolation model is defined as follows: (1) Where: The original ensemble forecast is processed by the improved cubic convolution interpolation model at the spatial grid latitude , longitude is The predicted value at ; The original ensemble forecast is at the spatial grid latitude , longitude is The predicted values ​​of the 16 nearest spatial grid points; and It is an intermediate variable in the calculation process.

[0017] According to S1, SEAS4 is interpolated to a position matching the measured data. The measured value at the 16 nearest spatial grid points is 2.7. The forecast value of the first ensemble member of SEAS4 with a forecast period of 1 month is , according to the improved cubic convolution interpolation model and formula (1), the original ensemble forecast is obtained to be 1.8.

[0018] S2. Forecast correction: Using the improved quantile mapping model, the probability distribution relationship between the ensemble members and the measured data is established one by one, and the shape error of the forecast distribution is corrected point by point to correct the deviation.

[0019] The improved quantile mapping model is defined as follows: (2) Where: is the measured value; is the forecast value of the original ensemble forecast; is the forecast value for correcting the ensemble forecast; is the inverse of the empirical cumulative distribution function of the measured values; is the inverse of the empirical cumulative distribution function of the original ensemble forecast.

[0020] According to S2, the measured value 2.7 and the original ensemble forecast 1.8 in S1 are processed by the improved quantile mapping model and formula (2) to obtain a corrected ensemble forecast of 2.4.

[0021] S3. Skill evaluation: The system constructs an ensemble forecast probability evaluation system, and uses the deviation improvement rate, accuracy improvement rate, reliability improvement rate, and sharpness improvement rate of the corrected ensemble forecast compared with the original ensemble forecast to quantitatively judge the skill improvement rate of the corrected ensemble forecast.

[0022] The deviation improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: (3) Where: is the deviation improvement rate; is the measured value at the time; is the forecast value of the ensemble member at time in the original ensemble forecast; is the forecast value of the ensemble member at time in the corrected ensemble forecast; For the The rate of improvement of the deviation degree of each set member; is the sequence length, here it is 22; is the number of set members, here it is 15; According to S3 and formula (3), the deviation improvement rate can be calculated: It is 8.5%.

[0023] The accuracy improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: (4) Where: To improve the accuracy rate; for The measured value at the time; The first The members of the collection are The forecast value at the time; To correct the ensemble forecast The members of the collection are The forecast value at the time; for The cumulative distribution function of the measured value at time; The first The members of the collection are The cumulative distribution function value of the forecast value at time; To correct the ensemble forecast The members of the collection are The cumulative distribution function value of the forecast value at time; For the The accuracy improvement rate of each set member; is the sequence length, here it is 22; is the number of set members, here it is 15; According to S3 and formula (4), the accuracy improvement rate can be calculated as It is 13.8%.

[0024] The reliability improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: (5) Where: To improve the reliability rate; for The measured value at the time; The first The members of the collection are The cumulative distribution function value of the measured value at the time; To correct the ensemble forecast The members of the collection are The cumulative distribution function value of the measured value at the time; For the The reliability improvement rate of each set member; is the sequence length, here it is 22; is the number of set members, here it is 15; According to S3 and formula (5), the reliability improvement rate can be calculated as It is 9.8%.

[0025] The sharpness improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: (6) Where: To improve the sharpness rate; The first The members of the collection are The 95% quantile value of the cumulative distribution function of the forecast value at the time; The first The members of the collection are The 5% quantile value of the cumulative distribution function of the forecast value at the time; To correct the ensemble forecast The members of the collection are The 95% quantile value of the cumulative distribution function of the forecast value at the time; To correct the ensemble forecast The members of the collection are The 5% quantile value of the cumulative distribution function of the forecast value at the time; For the The sharpness improvement rate of each set member; is the sequence length, here it is 22; is the number of set members, here it is 15;

[0026] According to S3 and formula (6), the sharpness improvement rate can be calculated as It is 6.1%.

[0027] according to For the grid point example, a total of 25635180 spatial grid point data of the four global climate models in each ensemble member and each forecast period are fully calculated, and the deviation improvement rate, accuracy improvement rate, reliability improvement rate, and sharpness improvement rate are further statistically classified into three numerical categories: <-5, -5~5, and >5. When the value is >5, it means that the deviation, accuracy, reliability, and sharpness of the corrected ensemble forecast are improved compared with the original ensemble forecast. When the value is <-5, it means that the deviation, accuracy, reliability, and sharpness of the corrected ensemble forecast are not improved compared with the original ensemble forecast. When the value is -5~5, it means that the deviation, accuracy, reliability, and sharpness of the corrected ensemble forecast are not much different from those of the original ensemble forecast.

[0028] For the deviation improvement rate, the results are shown in Table 2:

[0029] Table 2 The percentage of the improvement in the deviation of the corrected ensemble forecast compared with the original ensemble forecast Unit: %

[0030] When the forecast period of the global climate model CMCC is extended from 1 month to 6 months, the proportions of increased deviations are 74.9%, 74.4%, 74.9%, 75.4% and 74.2% respectively; when the forecast period of the global climate model DWD is extended from 1 month to 6 months, the proportions of increased deviations are 77.7%, 76.0%, 76.1%, 77.9% and 78.8% respectively; when the forecast period of the global climate model UKMO is extended from 1 month to 6 months, the proportions of increased deviations are 76.5%, 78.3%, 79.0%, 78.7% and 80.0% respectively; when the forecast period of the global climate model SEAS4 is extended from 1 month to 6 months, the proportions of increased deviations are 76.5%, 74.9%, 77.1%, 78.0% and 75.8% respectively.

[0031] As for the accuracy improvement rate, the results are shown in Table 3: Table 3 The percentage of the accuracy improvement of the corrected ensemble forecast compared with the original ensemble forecast Unit: %

[0032] When the forecast period of the global climate model CMCC is extended from 1 month to 6 months, the accuracy is improved by 80.9%, 82.5%, 83.1%, 83.3% and 85.1% respectively; when the forecast period of the global climate model DWD is extended from 1 month to 6 months, the accuracy is improved by 76.3%, 78.4%, 81.7%, 80.5% and 78.8% respectively; when the forecast period of the global climate model UKMO is extended from 1 month to 6 months, the accuracy is improved by 81.2%, 81.4%, 84.1%, 86.7% and 85.8% respectively; when the forecast period of the global climate model SEAS4 is extended from 1 month to 6 months, the accuracy is improved by 76.3%, 79.6%, 78.2%, 77.0% and 78.5% respectively.

[0033] For the reliability improvement rate, the results are shown in Table 4: Table 4 The percentage of reliability improvement of the corrected ensemble forecast compared with the original ensemble forecast Unit: %

[0034] When the forecast period of the global climate model CMCC is extended from 1 month to 6 months, the reliability is improved by 77.7%, 80.5%, 81.6%, 80.9% and 81.4% respectively; when the forecast period of the global climate model DWD is extended from 1 month to 6 months, the reliability is improved by 74.0%, 76.5%, 78.4%, 80.4% and 81.5% respectively; when the forecast period of the global climate model UKMO is extended from 1 month to 6 months, the reliability is improved by 78.5%, 77.8%, 80.4%, 80.5% and 81.4% respectively; when the forecast period of the global climate model SEAS4 is extended from 1 month to 6 months, the reliability is improved by 67.4%, 68.0%, 68.5%, 66.7% and 67.8% respectively.

[0035] For the sharpness improvement rate, the results are shown in Table 5: Table 5 The percentage of the improvement in sharpness of the corrected ensemble forecast compared with the original ensemble forecast Unit: %

[0036] When the forecast period of the global climate model CMCC is extended from 1 month to 6 months, the proportions of improved sharpness are 48.1%, 52.4%, 58.4%, 59.6% and 60.2% respectively; when the forecast period of the global climate model DWD is extended from 1 month to 6 months, the proportions of improved sharpness are 52.5%, 61.8%, 56.8%, 59.3% and 58.2% respectively; when the forecast period of the global climate model UKMO is extended from 1 month to 6 months, the proportions of improved sharpness are 64.1%, 59.0%, 53.4%, 53.8% and 64.8% respectively; when the forecast period of the global climate model SEAS4 is extended from 1 month to 6 months, the proportions of improved sharpness are 51.2%, 53.7%, 51.0%, 51.5% and 53.1% respectively.

[0037] The above specific calculations further demonstrate that the inversion, correction and evaluation methods of the present invention are significantly effective.

[0038] The above embodiments and the specific parameters therein are only for clearly describing the invention verification process, and are not intended to limit the patent protection scope of the present invention. The patent protection scope of the present invention shall still be based on its claims. Any equivalent structural changes made using the contents of the description and drawings of the present invention should also be included in the protection scope of the present invention.

Claims

1. An inversion, correction and evaluation method for ensemble forecasting, characterized by: The steps include: S1. Data inversion: An improved cubic convolution interpolation model is used to match the spatial grid scales of the ensemble forecast and the measured data to ensure that the ensemble forecast and the measured data have consistent temporal and spatial resolutions; S2. Forecast correction: Using the improved quantile mapping model, the probability distribution relationship between the ensemble members and the measured data is established one by one, and the shape error of the forecast distribution is corrected point by point, which plays a role in correcting the deviation; S3. Skill evaluation: The system constructs an ensemble forecast probability evaluation system, and uses the deviation improvement rate, accuracy improvement rate, reliability improvement rate, and sharpness improvement rate of the corrected ensemble forecast compared with the original ensemble forecast to quantitatively judge the skill improvement rate of the corrected ensemble forecast.

2. The inversion, correction and evaluation method for ensemble forecasting according to claim 1, characterized in that: In step S1, The improved cubic convolution interpolation model is defined as follows: （1） Where: The original ensemble forecast is processed by the improved cubic convolution interpolation model at the spatial grid latitude , longitude is The predicted value at ; The original ensemble forecast is at the spatial grid latitude , longitude is The predicted values ​​of the 16 nearest spatial grid points; and It is an intermediate variable in the calculation process.

3. The inversion, correction and evaluation method for ensemble forecasting according to claim 1, characterized in that: In step S2, The improved quantile mapping model is defined as follows: （2） Where: is the measured value; is the forecast value of the original ensemble forecast; is the forecast value for correcting the ensemble forecast; is the inverse of the empirical cumulative distribution function of the measured values; is the inverse of the empirical cumulative distribution function of the original ensemble forecast.

4. The inversion, correction and evaluation method for ensemble forecasting according to claim 1, characterized in that: In step S3, The deviation improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: （3） Where: is the deviation improvement rate; for The measured value at the time; The first The members of the collection are The forecast value at the time; To correct the ensemble forecast The members of the collection are The forecast value at the time; For the The rate of improvement of the deviation degree of each set member; is the sequence length; is the number of set members; The accuracy improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: （4） Where: To improve the accuracy rate; for The measured value at the time; The first The members of the collection are The forecast value at the time; To correct the ensemble forecast The members of the collection are The forecast value at the time; for The cumulative distribution function of the measured value at time; The first The members of the collection are The cumulative distribution function value of the forecast value at time; To correct the ensemble forecast The members of the collection are The cumulative distribution function value of the forecast value at time; For the The accuracy improvement rate of each set member; is the sequence length; is the number of set members; The reliability improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: （5） Where: To improve the reliability rate; for The measured value at the time; The first The members of the collection are The cumulative distribution function value of the measured value at the time; To correct the ensemble forecast The members of the collection are The cumulative distribution function value of the measured value at the time; For the The reliability improvement rate of each set member; is the sequence length; is the number of set members; The sharpness improvement rate is denoted as , the value range is , the larger the value, the higher the forecast skill. The calculation formula is as follows: （6） Where: To improve the sharpness rate; The first The members of the collection are The 95% quantile value of the cumulative distribution function of the forecast value at the time; The first The members of the collection are The 5% quantile value of the cumulative distribution function of the forecast value at the time; To correct the ensemble forecast The members of the collection are The 95% quantile value of the cumulative distribution function of the forecast value at the time; To correct the ensemble forecast The members of the collection are The 5% quantile value of the cumulative distribution function of the forecast value at the time; For the The sharpness improvement rate of each set member; is the sequence length; is the number of set members.

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