A hydrological prediction-oriented basin adaptive PAS precipitation prediction scoring method

Abstract

The application discloses a hydrological prediction-oriented basin adaptive PAS precipitation prediction scoring method, which takes a sub-basin as an evaluation unit, obtains a predicted area rainfall, an actual area rainfall and a historical rainy day area rainfall sequence; constructs a standard hydrological sensitivity function with a lower limit of a rainstorm grade of the area rainfall, and forms a comprehensive hydrological sensitivity function in combination with an empirical quantile of the actual area rainfall in a corresponding sub-basin historical sample; then, a stable term and a stable proportion are constructed based on a median of the historical rainy day area rainfall, so as to reduce the influence of abnormal amplification of relative error under light rain and zero rainfall conditions; finally, hydrological PAS scores are calculated according to under-prediction or over-prediction, and an additional penalty is set for under-prediction of heavy precipitation. The method can output sub-basin scores, regional comprehensive scores and heavy precipitation missing report diagnosis results, and is used for precipitation prediction product testing, model comparison, correction effect evaluation and hydrological scheduling review.

Description

Technical Field

[0001] This invention relates to the fields of meteorological and hydrological forecast verification, watershed rainfall evaluation, precipitation forecast product verification, and reservoir operation support technology, and in particular to a watershed adaptive PAS precipitation forecast scoring method for hydrological forecasting. Background Technology

[0002] Areal rainfall forecasts are crucial inputs for watershed flood forecasting, reservoir operation, flood control consultations, and water resources management. Existing methods for verifying precipitation forecasts typically include root mean square error (RMSE), mean absolute error (MAE), correlation coefficient, TS score, BIAS score, and PAS-type scores. These indicators can describe forecast quality based on error magnitude, correlation degree, or hit rate. However, in operational hydrology, the same absolute error corresponds to different runoff generation, runoff concentration, and dispatch risks under light rain, heavy rain, and torrential rain conditions, and a single error or relative error score cannot directly express these differences.

[0003] When traditional PAS scoring is used for proportionality error verification, it tends to amplify relative errors under conditions where the actual rainfall is close to zero or under light rainfall conditions, resulting in severe penalties for even small differences in rainfall. Furthermore, it may be insufficient to reflect the impact of missed forecasts on flood forecasting and reservoir management when forecasts for heavy rainfall events are underestimated. If fixed rainfall level segments or artificial penalty coefficients are used, the scoring results may exhibit abrupt changes, and repeated parameter adjustments are required when using the system across different watersheds.

[0004] Significant differences exist in the area, topography, climatology, and historical extreme areal rainfall across different sub-basins. The hydrological meaning of the same daily areal rainfall may differ between large and small watersheds, and its historical percentile may also differ between humid and relatively arid watersheds. Therefore, a continuous scoring method is needed that can simultaneously utilize areal rainfall classification standards and historical precipitation distributions within sub-basins, making precipitation forecast verification results more suitable for use in hydrological model input evaluation and operational scheduling. Summary of the Invention

[0005] The purpose of this invention is to overcome the above-mentioned shortcomings and provide a basin-adaptive PAS precipitation forecast scoring method for hydrological forecasting. This method aims to solve the problems of unstable relative error under light rain conditions, insufficient penalty for heavy precipitation deviation, insufficient characterization of the risk of missed heavy precipitation, and insufficient applicability to different sub-basins in existing PAS and precipitation verification methods.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a watershed adaptive PAS precipitation forecast scoring method for hydrological forecasting, the method comprising the following steps: S1. Obtain the forecast areal rainfall of the i-th sub-basin during the evaluation period. F i Real-time rainfall O iAnd the historical daily isal rainfall sequence of the sub-basin, wherein the historical daily isal rainfall sequence includes at least historical samples of isal rainfall on rainy days; S2, based on actual rainfall. O i Constructing a standard hydrological sensitivity function based on the lower limit of 30mm for surface rainfall in heavy rain. ,in ; S3. Construct a watershed relative intensity function based on the historical daily rainfall sequence. ,in Real-time rainfall O i The empirical quantile in the historical sample of the i-th sub-basin; S4. By integrating the standard hydrological sensitivity function and the watershed relative intensity function, a comprehensive hydrological sensitivity function is obtained. ; S5. Based on the median of historical rainy day rainfall in the i-th sub-basin. Constructing a stability term using integrated hydrological sensitivity functions And calculate the stable ratio ; S6, when F i < O i When, calculate the hydrological PAS score of the i-th sub-basin according to the underestimation forecast scoring function; when F i ≥ O i At that time, the hydrological PAS score of the i-th sub-basin is calculated according to the overestimation forecast scoring function; S7. Output the hydrological PAS score of the i-th sub-basin, and integrate the scores of multiple sub-basins according to the area weight, the inflow contribution weight or the scheduling importance weight to obtain the regional PAS comprehensive score and corresponding diagnostic information.

[0007] Preferably, the historical daily isal rainfall sequence includes one or more of the following: historical real-time daily isal rainfall sequence, historical reanalysis daily isal rainfall sequence, historical grid fusion daily isal rainfall sequence, radar estimated daily isal rainfall sequence, or watershed isal rainfall sequence formed by interpolation of station data.

[0008] Preferably, the relative intensity function of the watershed is: ,in For the first Historical sample size of each sub-basin For the first time in history Rainfall per sample area, This is an indicator function.

[0009] Preferably, the historical median rainfall on rainy days is... It is used to provide a stable scale under light rain or zero rainfall conditions, and to adapt to heavy precipitation conditions. Increase it, and decrease its stabilizing effect.

[0010] Preferably, the underestimation forecast scoring function is: ,in F i < O i And 0 ≤ r i <1.

[0011] Preferably, the over-prediction scoring function is: ,in F i ≥ O i And r i ≥ 1.

[0012] Preferably, when O i When smaller, Approaching 0, Approaching This suppresses the score variation of light rain or zero rainfall error.

[0013] Preferably, when O i When the rainfall reaches the level of heavy rain or torrential rain and is at a historically high level in this basin... Approaching 1, Approaching 0 makes the scoring function automatically more stringent for biases related to heavy precipitation.

[0014] Preferably, when F i < O i At that time, the under-prediction scoring function includes Additional penalties are used to increase the severity of point deductions for cases of unreported heavy rainfall.

[0015] Preferably, the regional PAS comprehensive score is: , where w i It contributes weight to the sub-basin area weight or inflow.

[0016] Beneficial effects of this invention: (1) The present invention uses the lower limit of the areal rainfall level as the continuous sensitivity anchor point, so that the scoring function has a clear business basis and reduces the subjectivity caused by manually setting the penalty coefficient; (2) This invention introduces the historical areal rainfall quantile of sub-basins, so that the same actual areal rainfall can be interpreted in combination with the historical precipitation background of different basins, thereby enhancing the consistency of cross-sub-basin evaluation; (3) This invention uses the median of the average rainfall on historical rainy days to construct a stable term, which can reduce the impact of the instability of the traditional relative error on the score under zero rainfall and light rain conditions; (4) The scoring function of this invention changes continuously with the comprehensive hydrological sensitivity, and does not use hard threshold segmentation for light rain, moderate rain, heavy rain and rainstorm, which can reduce the sudden change of the score at the level boundary; (5) This invention sets additional penalties for underestimation of heavy precipitation, so that the scoring results can reflect the attention to the risk of underreporting in flood forecasting, reservoir operation and flood control consultation; (6) The regional comprehensive score of the present invention can adopt area weight, inflow contribution weight or scheduling importance weight, and is applicable to forecast verification at the scale of single sub-basin, multi-sub-basin and basin group.

[0017] (7) This invention solves the problems of the existing PAS precipitation verification method having a large relative error under light rain conditions, insufficient penalty for heavy precipitation deviation, insufficient characterization of the risk of missed heavy precipitation, and insufficient applicability to different sub-basins. This invention constructs a standard hydrological sensitivity function, a basin relative intensity function, a comprehensive hydrological sensitivity function, and a stable ratio, so that the scoring function is continuously adjusted with the actual surface rainfall and its relative intensity in the historical samples of the basin. Attached Figure Description

[0018] Figure 1 This is a flowchart of Embodiment 1 of the present invention; Figure 2 Figure showing the variation of RMSE, PAS, and HPAS of ECMWF precipitation forecasts in the L2-level sub-basin of the upper Yangtze River with forecast lead time; Figure 3 Scatter plots of PAS / HPAS and RMSE for the L2-level sub-basin of the upper Yangtze River at 24, 48 and 72 h time points; Figure 4 This is a spatial distribution map of the cumulative precipitation in the upper reaches of the Yangtze River over 24 hours as of July 9, 2023. in, Figure 4 In the middle, (a) observation; (b) ECMWF; Detailed Implementation The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0019] Example 1: As Figure 1 As shown, this invention discloses a watershed-adaptive PAS precipitation forecasting scoring method for hydrological forecasting, comprising the following steps: S1. Acquire and preprocess watershed rainfall data For each sub-basin to be evaluated, obtain the forecast areal rainfall for the evaluation period. F i and actual rainfall O iAnd obtain the historical daily rainfall sequence for this sub-basin. Historical data can be derived from station interpolation, grid-fused precipitation, radar-estimated precipitation, reanalysis precipitation, or operational real-time rainfall products. Missing data, outliers, and ineffective watershed samples are removed or quality-controlled, while historical rainy day samples are retained for stable-scale calculations.

[0020] Where i represents the sub-basin number, F i This represents the forecast areal rainfall for the i-th sub-basin. O i This represents the actual areal rainfall in the i-th sub-basin. This represents the historical daily isal rainfall sample for the i-th sub-basin. The number of historical samples N is preferably not less than the number of daily-scale samples over 5 years; in scenarios with limited data, historical samples from the same season, rolling window samples, or historical samples after assimilation and correction can also be used.

[0021] S2. Constructing a standard hydrological sensitivity function Based on the operational standard of 30 mm as the lower limit for heavy rainfall in the "Rainfall Grading of Rivers in China", a continuous standard hydrological sensitivity function is constructed. The function takes values ​​from 0 to 1, and its value increases with... O i Monotonically increasing; when O i When it is 30 mm, Equals 0.5; when O i When it is 60 mm, Approximately 0.8; when O i When it is 15 mm, It is approximately 0.2.

[0022] S3. Constructing the relative intensity function of the watershed This function represents the current real-time rainfall. O i The empirical quantile in the historical sample of the i-th sub-basin. When This indicates a sample where the current rainfall exceeds 90% of the historical rainfall for that sub-basin. This function can be used to identify relatively heavy precipitation events in sub-basins of different areas and climatic states.

[0023] S4. Forming a comprehensive hydrological sensitivity function The comprehensive hydrological sensitivity function is: in, Ensure that the scoring meets the operational standards for areal rainfall classification. This allows the scoring to be adapted to the historical heavy rainfall characteristics of the sub-basin. This combination ensures... And avoid over-penalizing the light rain error simply because the light rain quantile is higher in arid watersheds.

[0024] S5. Calculate the stability scale and stability ratio. For the i-th sub-basin, calculate based on the median of historical rainy day areal rainfall. And calculate the stability term. Then the stability ratio was calculated. When the actual rainfall is low, Smaller near It can avoid O i When the relative error is 0 or close to 0, it is unstable; when the actual rainfall reaches the level of heavy rain or torrential rain and is at a historical high level in this basin, Approaching 1, A score close to 0 indicates a score that is closer to the relative error assessment of heavy precipitation.

[0025] S6. Calculate the hydrological PAS score when the forecast deviation is small. when F i < O i At that time, it was considered that the forecast was too small, 0 ≤ r i <1. The sub-basin hydrological PAS score is calculated using the following formula: in, This causes the scoring curve to narrow as the overall hydrological sensitivity increases; An additional penalty is imposed for forecasts of insufficient heavy rainfall. O i Larger and F i Obviously too small, Higher, r i The score was low, and the rating dropped further.

[0026] S7. Calculate the hydrological PAS score when the forecast is too high. when F i ≥ O i At that time, it was believed that the forecast was too high, r i For values ​​≥ 1, the sub-basin hydrological PAS score is calculated using the following formula: This formula results in a lighter penalty for overestimating light rain, while the penalty for overestimating heavy rain and torrential rain increases accordingly. Increase and strengthen.

[0027] S8, Output Sub-basin Score and Diagnostic Quantity Output for each sub-basin Scoring, Standard Hydrological Sensitivity relative intensity of the basin Comprehensive hydrological sensitivity Stable items Stable ratio r i The deviation direction, whether heavy rainfall was missed, and the scoring quality indicators.

[0028] S9, Calculate the overall score of the region When a regional comprehensive evaluation of multiple sub-basins is required, according to Calculate the regional PAS comprehensive score, where w i For sub-basin weights. i Weights such as sub-basin area and inflow contribution can be used.

[0029] S10, Generate Business Evaluation Products Based on evaluation requirements, sub-basin scores, regional comprehensive scores, heavy precipitation underreporting diagnoses, heavy precipitation overestimation diagnoses, historical quantile distributions, and score time series are generated for daily, event-by-event, forecast lead time, or forecast product-by-product analysis. These results can be used for ranking precipitation forecast products, comparing different models, verifying correction effectiveness, and reviewing reservoir operation.

[0030] In this embodiment, the alternative solutions are as follows: (1) The 30 mm in the standard hydrological sensitivity function can be replaced according to the lower limit of the areal rainfall level issued by the target country, region or industry, and the business source of the threshold should be recorded during implementation; (2) (O) can be used i p ) / ( O i p +P b p In the form of ) where P b As the lower limit for heavy rainfall, p is preferably 2, but it can also be 1.5 to 3 based on historical stability tests; (3) It can be constructed using full-historical samples, samples from the same season, samples from the flood season, or rolling climate state samples; (4) The median of the areal rainfall on historical rainy days can be used, or the low quantile of rainy days, the operational light rain scale, or a stable scale after quality control can be used. (5) The regional comprehensive weight can be area weight, flow contribution weight, flood control scheduling importance weight, risk exposure weight or equal weight, or it can be combined according to the specific hydrological forecast object; (6) The scoring objects can be extended to hourly, 3-hourly, daily, session-by-session, or areal rainfall assessments with different forecast lead times; (7) Output formats may include rating maps, sub-basin rating tables, product comprehensive rankings, pattern correction evaluation reports, or scheduling review reports.

[0031] Example 2: Comprehensive scoring of multi-sub-basin regions The implementation covered 25 sub-basins at Level L2 in the upper reaches of the Yangtze River. The forecast product was the ECMWF 24-hour cumulative precipitation forecast, and the actual product was the CMPA gridded precipitation. The evaluation included changes in the traditional PAS method (hereinafter referred to as PAS), the basin-adaptive hydrological PAS method (hereinafter referred to as HPAS), and RMSE under 1-9 day forecast leads, as well as the relationship between the traditional PAS method / HPAS and RMSE under 24-hour, 48-hour, and 72-hour lead leads. This embodiment first converted the gridded precipitation into areal rainfall for each sub-basin, then calculated PAS and HPAS at the sub-basin areal rainfall scale, and finally obtained a comprehensive regional score for the upper Yangtze River based on the sub-basin area weights. This process is consistent with the operational process of lumped or semi-distributed hydrological models that use sub-basin areal rainfall as input.

[0032] This embodiment uses the 24-hour cumulative precipitation sequence for the 2023 flood season. For a given forecast start date D and forecast period L, the ECMWF forecast for day L is registered with the 24-hour cumulative precipitation for the actual day D+L-1. For example, the 24-hour forecast starting on July 9, 2023 is compared with the actual isal rainfall on July 9, 2023; the 48-hour forecast is compared with the actual isal rainfall on July 10, 2023; and the 72-hour forecast is compared with the actual isal rainfall on July 11, 2023. The latitude and longitude grid uses a resolution of 0.25°, with the grid center longitude being lon = 90.0 + 0.25 × i and the latitude being lat = 37.0 - 0.25 × j. For each L2 sub-basin, it is first determined whether the grid center falls within the sub-basin boundary, and then the sub-basin isal rainfall is calculated by approximating the grid area weight using the latitude cosine.

[0033]

[0034] The regional comprehensive score uses the area weights of 25 sub-basins at the L2 level. Weight w i The ratio of the area of ​​the i-th sub-basin to the total area of ​​the 25 sub-basins satisfies Σw i ≈1. The specific weights are as follows:

[0035] Based on the above S1-S7 process, the PAS, HPAS, and RMSE of ECMWF precipitation forecasts in the L2 sub-basin of the upper Yangtze River were calculated. Figure 2 The changes of three types of indicators with forecast lead time are shown.

[0036] Depend on Figure 2It is evident that as the lead time increases from 1 day to 9 days, the PAS of ECMWF decreases from 0.47 to 0.37, the HPAS decreases from 0.77 to 0.57, and the RMSE increases from 4 mm to 8 mm. This result indicates that as the forecast lead time increases, the closeness between the predicted precipitation and the actual areal rainfall decreases, and the absolute error increases. Meanwhile, the HPAS maintains a higher score than the PAS, reflecting the moderating effect of the stability term and the hydrological sensitivity function on small-scale areal rainfall errors.

[0037] This embodiment further selects daily samples with forecast leads of 24 h, 48 h, and 72 h, and plots PAS-RMSE and HPAS-RMSE scatter plots respectively. The color of the scatter plots represents the actual rainfall in the upper reaches of the Yangtze River on the corresponding date. This diagnosis is used to illustrate whether HPAS can form a consistent judgment with the absolute error index.

[0038]

[0039] Depend on Figure 3 It is evident that the HPAS and RMSE of ECMWF show a significant negative correlation at 24 h, 48 h, and 72 h lead times, with correlation coefficients of -0.59, -0.60, and -0.60, respectively. The correlation between PAS and RMSE is relatively weak, with correlation coefficients of 0.25, 0.21, and 0.03, respectively. These results indicate that HPAS and RMSE can corroborate each other at the areal rainfall scale, while traditional PAS is difficult to stably reflect areal rainfall errors.

[0040] To illustrate the application of this method in a single precipitation event, a precipitation event in the upper reaches of the Yangtze River on July 9, 2023, was selected as a typical case. The spatial distribution of precipitation on that day was uneven, with a distinct local center of heavy precipitation, making it suitable for testing the response of the scoring method to deviations in the location of heavy precipitation centers and the degree of proximity of areal rainfall. This case uses an L2-level sub-basin area-weighted comprehensive score. The 24-hour forecast corresponding to ECMWF has a PAS of 0.61 and an HPAS of 0.79. From... Figure 4 It can be seen that the ECMWF has a certain ability to depict the main precipitation areas and heavy precipitation belts in the eastern part of the upper reaches of the Yangtze River. There are differences between the forecast and the actual situation in details of the rain belt in the Yalong River, Minjiang River basins, and Hengjiang River. The areal rainfall forecast in a hydrological sense is usable and is considered a relatively good forecast. PAS and HPAS reflect the degree of closeness between the forecast and the actual areal rainfall from a continuous scoring perspective. Comparing the scores of the two, HPAS is more in line with the intuitive understanding of operational personnel.

[0041] Example 3: Daily Rainfall Forecast Scoring for a Single Sub-basin Select a reservoir's inflow control sub-basin, obtain the historical 10-year daily isal rainfall series, and calculate based on rainy day samples. For a given evaluation day, read the forecast areal rainfall.F i and actual rainfall O i First calculate Then, based on historical experience, a distribution query is performed. and calculate Then calculate and .like F i < O i Then calculate according to the underestimation forecast scoring function. ;like F i ≥ O i Then, the overestimation score function is used for calculation. Finally, the daily hydrological PAS score and deviation direction diagnosis for this sub-basin were obtained.

[0042] For example, when a large river basin O i When the value is 60 mm and it is located at the 97th percentile of the historical record of this watershed, Approximately 0.8, The value is approximately 0.955, indicating that the process has high hydrological sensitivity in this watershed. If the forecast is significantly underestimated, the curve narrowing term and additional penalty term in the underestimation forecast scoring function will jointly reduce the score, thus reflecting the operational risk of missed heavy precipitation reports.

[0043] Example 4: Application for Verification of Precipitation Forecast Products This invention is applied to the verification of daily isal rainfall in different numerical weather prediction models, ensemble forecast members, correction products, or fused precipitation forecast products. Calculations are performed for each forecast product, each forecast lead time, and each sub-basin. and regional comprehensive score, and combined with , Diagnostic methods are used to determine the direction of deviation. The results can be used for product ranking, assessment of heavy rainfall forecasting capabilities, review of missed reporting risks, verification of correction algorithm effectiveness, and decision support in reservoir scheduling consultations.

[0044] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A basin-adaptive PAS precipitation forecast scoring method for hydrological forecasting, characterized in that, The method includes the following steps: S1. Obtain the forecast areal rainfall of the i-th sub-basin during the evaluation period. F i Real-time rainfall O i And the historical daily isal rainfall sequence of the sub-basin, wherein the historical daily isal rainfall sequence includes at least historical samples of isal rainfall on rainy days; S2, based on actual rainfall. O i Constructing a standard hydrological sensitivity function based on the lower limit of 30mm for surface rainfall in heavy rain. ,in ; S3. Construct a watershed relative intensity function based on the historical daily rainfall sequence. ,in Real-time rainfall O i The empirical quantile in the historical sample of the i-th sub-basin; S4. By integrating the standard hydrological sensitivity function and the watershed relative intensity function, a comprehensive hydrological sensitivity function is obtained. ; S5. Based on the median of historical rainy day rainfall in the i-th sub-basin. Constructing a stability term using integrated hydrological sensitivity functions And calculate the stable ratio ; S6, when F i < O i When, calculate the hydrological PAS score of the i-th sub-basin according to the underestimation forecast scoring function; when F i ≥ O i At that time, the hydrological PAS score of the i-th sub-basin is calculated according to the overestimation forecast scoring function; S7. Output the hydrological PAS score of the i-th sub-basin, and integrate the scores of multiple sub-basins according to the area weight, the inflow contribution weight or the scheduling importance weight to obtain the regional PAS comprehensive score and corresponding diagnostic information.

2. The watershed-adaptive PAS precipitation forecast scoring method for hydrological forecasting as described in claim 1, characterized in that: The historical daily isal rainfall sequence includes one or more of the following: historical real-time daily isal rainfall sequence, historical reanalysis daily isal rainfall sequence, historical grid fusion daily isal rainfall sequence, radar-estimated daily isal rainfall sequence, or watershed isal rainfall sequence formed by interpolation of station data.

3. The watershed-adaptive PAS precipitation forecast scoring method for hydrological forecasting as described in claim 1, characterized in that: The relative intensity function of the watershed is: ,in For the first Historical sample size of each sub-basin For the first time in history Rainfall per sample area, This is an indicator function.

4. The watershed-adaptive PAS precipitation forecast scoring method for hydrological forecasting as described in claim 1, characterized in that: The historical median rainfall on rainy days It is used to provide a stable scale under light rain or zero rainfall conditions, and to adapt to heavy precipitation conditions. Increase it, and decrease its stabilizing effect.

5. The watershed-adaptive PAS precipitation forecast scoring method for hydrological forecasting as described in claim 1, characterized in that: The underestimation forecast scoring function is: ,in F i < O i And 0 ≤ r i <1.

6. The watershed-adaptive PAS precipitation forecast scoring method for hydrological forecasting according to claim 1, characterized in that: The over-optimized forecast scoring function is: ,in F i ≥ O i And r i ≥ 1.

7. The watershed-adaptive PAS precipitation forecast scoring method for hydrological forecasting as described in claim 1, characterized in that: when O i When smaller, Approaching 0, Approaching This suppresses the score variation of light rain or zero rainfall error.

8. A basin-adaptive PAS precipitation forecasting scoring method for hydrological forecasting according to claim 7, characterized in that: when O i When the rainfall reaches the level of heavy rain or torrential rain and is at a historically high level in this basin... Approaching 1, Approaching 0 makes the scoring function automatically more stringent for biases related to heavy precipitation.

9. A basin-adaptive PAS precipitation forecasting scoring method for hydrological forecasting according to claim 1, characterized in that: when F i < O i At that time, the under-prediction scoring function includes Additional penalties are used to increase the severity of point deductions for cases of unreported heavy rainfall.

10. A basin-adaptive PAS precipitation forecasting scoring method for hydrological forecasting according to claim 1, characterized in that: The overall PAS score for the region is: , where w i It contributes weight to the sub-basin area weight or inflow.

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