A multi-dimensional diagnostic method and system for quantifying the ability of precipitation estimates to represent long-term trends

Abstract

The application discloses a kind of quantitative precipitation estimation long-term trend characterization ability multidimensional diagnostic method and system, the method includes: obtaining ground precipitation observation data and multi-source precipitation estimation data in research area, and unified scale is obtained after matching processing precipitation data;Calculate the sequence data of three kinds of precipitation characteristic indexes of precipitation total amount, precipitation frequency and precipitation intensity according to time dimension;The change trend slope and relative change rate of the precipitation characteristic indexes at each site or grid point are calculated, and the trend change rate is obtained;Statistical significance test is carried out, and trend type is determined;Trend capture skill framework is constructed, and trend direction consistency, trend significance skill, trend amplitude consistency and trend spatial pattern consistency are calculated respectively;Trend capture index is calculated to comprehensively evaluate the reproduction ability of observation trend of precipitation estimation data;The application can comprehensively and systematically diagnose the trend characterization ability of precipitation estimation product.

Description

Technical Field

[0001] This invention relates to the field of precipitation diagnostic technology, specifically to a multidimensional diagnostic method and system for quantitatively estimating the long-term trend of precipitation. Background Technology

[0002] With global warming, long-term precipitation changes and their variability have become crucial for hydrological and climate research. Specifically, long-term precipitation variations not only affect regional water resources but also influence the frequency of floods, droughts, and other extreme hydro-meteorological events. To quantify these changes, changes in total precipitation are typically used to characterize regional trends of increased wetness or drought, while variations in precipitation frequency and intensity can lead to different hydro-climate responses. Therefore, accurately characterizing the various features of long-term precipitation is critical for understanding regional climate variability and the causes of long-term climate change.

[0003] Among current technologies, ground-based rainfall observation is one of the most direct methods for measuring precipitation and forms the basis for long-term precipitation trend analysis. However, due to the limited number and uneven distribution of rainfall observation stations globally, especially in areas with complex terrain and lack of observation, the spatial coverage of ground-based observations is limited. Therefore, this restricts the effectiveness of relying solely on ground-based observations to comprehensively characterize long-term precipitation variations at regional and global scales.

[0004] To address these challenges, gridded precipitation products have begun to be applied in hydroclimate research. For example, atmospheric reanalysis data provides continuous spatial coverage and long-term climate records, enabling long-term precipitation trend analysis. ER point products such as ERA5 and its ground reanalysis component ERA-LAND have been used for multi-regional, multi-period precipitation trend studies. Simultaneously, with the development of remote sensing technology, satellite inversion techniques have provided satellite precipitation estimation products covering large areas of continuous precipitation data, such as IMERG (Global Precipitation Estimation System) and GSMAP (Global Satellite Precipitation Measurement). These products can provide data support in areas lacking ground observations and are gradually being applied to long-term precipitation trend analysis and hydroclimate change research.

[0005] While atmospheric reanalysis and satellite precipitation products can provide broad-coverage long-term precipitation information, their ability to reproduce long-term trends in spatial distribution remains uncertain. This uncertainty mainly lies in the spatial distribution of precipitation trends; different regions, and even the same watershed, may simultaneously exhibit trends of increasing or decreasing precipitation. Furthermore, changes in precipitation amount, frequency, and intensity display complex spatial structures. Relying solely on regional averages or isolated statistical indicators is insufficient to fully describe long-term variation characteristics. Existing research largely focuses on trend direction and statistical significance, while trend magnitude, spatial distribution characteristics, and differences between various precipitation features have not been systematically evaluated. Summary of the Invention

[0006] Purpose of the invention: This invention provides a multidimensional diagnostic method and system for quantitatively representing the long-term trend of precipitation estimation, enabling multidimensional quantitative assessment of the ability to reproduce precipitation trends.

[0007] The multidimensional diagnostic method of the present invention includes: We acquired surface precipitation observation data and multi-source precipitation estimation data within the study area, and performed time-scale and spatial-scale matching processing to obtain precipitation data at a unified scale. Based on the matched precipitation data, the time-series data of three types of precipitation characteristic indicators—total precipitation, precipitation frequency, and precipitation intensity—are calculated. Based on the sequence data, calculate the slope and relative rate of change of the precipitation characteristic indicators at each station or grid point to obtain the trend rate of change. The trend change rate is subjected to a statistical significance test. The trend significance is determined according to a preset significance level, and the trend type is determined by combining the preset no-trend threshold. Based on the slope and type of the changing trend, a trend capture skill framework is constructed, and the consistency of trend direction, trend significance, trend amplitude, and trend spatial pattern are calculated respectively to quantitatively characterize the trend reproduction ability of precipitation estimation data in different dimensions. The trend capture index is calculated by weighting and combining the consistency of trend direction, trend significance, trend amplitude, and trend spatial pattern to comprehensively evaluate the ability of precipitation estimation data to reproduce observed trends.

[0008] The multidimensional diagnostic system of the present invention includes: The data matching module is used to acquire surface precipitation observation data and multi-source precipitation estimation data within the study area, and to perform time-scale and spatial-scale matching processing to obtain precipitation data at a unified scale. The feature calculation module is used to calculate the time-series data of three types of precipitation feature indicators: total precipitation, precipitation frequency, and precipitation intensity, based on the matched precipitation data. The trend analysis module is used to calculate the slope and relative rate of change of the precipitation characteristic indicators at each station or grid point based on the sequence data, to obtain the trend change rate; and to perform a statistical significance test on the trend change rate, and determine the trend type by combining it with a preset no-trend threshold. The dimensional assessment module is used to construct a trend capture skill framework based on the slope and type of the changing trend, and to calculate the consistency of trend direction, trend significance, trend amplitude, and trend spatial pattern, respectively, in order to quantitatively characterize the trend reproducibility of precipitation estimation data in different dimensions. The comprehensive evaluation module is used to weight and combine the consistency of trend direction, trend significance, trend amplitude, and trend spatial pattern to calculate the trend capture index, so as to comprehensively evaluate the ability of precipitation estimation data to reproduce the observed trend.

[0009] Compared with existing technologies, this invention has the following significant advantages: by constructing a multidimensional trend capture skill framework, it can achieve a comprehensive and multidimensional quantitative assessment of the long-term precipitation trend characterization capability of precipitation estimation products, comprehensively analyze the consistency between the products and ground observations in terms of trend direction, significance, change magnitude and spatial pattern, effectively overcome the limitations of traditional single-dimensional assessment, retain the spatial heterogeneity information of precipitation trends, and simultaneously consider the changes in multidimensional characteristics such as total precipitation, frequency and intensity. Attached Figure Description

[0010] Figure 1 This is a schematic diagram of a multidimensional diagnostic method for quantitative precipitation estimation and its ability to characterize long-term trends, provided by an embodiment of the present invention.

[0011] Figure 2 It is a spatial distribution map showing the trend of precipitation changes between observed data and estimated precipitation values;

[0012] Figure 3 This is a heatmap of TCI component scores corresponding to precipitation in the Yangtze River Basin and its sub-regions under different precipitation estimates.

[0013] Figure 4 It is a seasonal TCI radar map of the total amount, frequency and intensity of precipitation in the Yangtze River Basin, drawn from different precipitation estimation data, and the scores of each component. Detailed Implementation

[0014] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0015] The inventive aspect of this invention lies in the design of a Trend-Capturing SkillFramework (TCSF), which aims to quantify the ability of precipitation estimation data to reproduce observed precipitation trends and decomposes it into multiple dimensions for consideration, including Trend Direction Consistency (TDC), Trend Significance Skill (TSS), Trend Amplitude Consistency (TMF), and Trend Spatial Pattern Consistency (TPC).

[0016] Example 1

[0017] This embodiment provides a multidimensional diagnostic method for assessing the long-term trend of quantitative precipitation estimation. Specifically:

[0018] S1. Obtain surface precipitation observation data and multi-source precipitation estimation data within the study area, and perform time-scale and spatial-scale matching processing to obtain precipitation data at a unified scale.

[0019] Specifically, surface precipitation observation data can be obtained from the National Meteorological Administration or relevant research institutions, while multi-source precipitation estimation data can be derived from satellite remote sensing products or atmospheric reanalysis products. Daily surface precipitation observation data and multi-source precipitation data within the study area are acquired and matched on both temporal and spatial scales to obtain precipitation data at a unified scale.

[0020] S2. Based on the matched precipitation data, calculate the time-series data of three precipitation characteristic indicators: total precipitation, precipitation frequency, and precipitation intensity. For example, total precipitation can be calculated as the simple sum of all daily precipitation over a preset time period (e.g., one year). Precipitation frequency can be calculated as the cumulative daily precipitation over a preset time period (e.g., 1.0 mm). Precipitation frequency is the proportion of precipitation days to the total number of observed days, where a precipitation day is defined as a day with precipitation greater than or equal to 1.0 mm, used to characterize the probability of precipitation occurrence. Precipitation intensity can be calculated as the average of all daily precipitation over a preset time period, used to characterize the strength of the precipitation process.

[0021] S3. Based on the sequence data, calculate the slope and relative rate of change of the precipitation characteristic indicators at each station or grid point to obtain the trend change rate.

[0022] Specifically, Sen's slope estimation method is used to calculate the trend slope of the time series. β By adjusting the trend slope β After normalization by dividing by the time series mean, the percentage change per unit time is calculated as the relative change rate (% / year). Sen's slope is a non-parametric statistical trend estimation method with advantages such as insensitivity to outliers and strong robustness. Therefore, when processing precipitation time series data that may contain extreme precipitation events or measurement errors, it can provide more robust and reliable trend estimation results, effectively avoiding the interference of a few extreme values ​​on the overall trend judgment.

[0023] The formula for calculating the trend slope is: ;

[0024] in, β The slope represents the trend, x represents the data sequence, the subscripts i and j represent the data indices, and n represents the total length of the sequence data. β When >0, it indicates that the variable is on an upward trend; when β When <0, it indicates a downward trend.

[0025] To facilitate comparisons between different variables, all trend slopes are converted to relative rates of change, i.e., in time series terms. mean After normalization, the rate of change of the trend per unit time is obtained. For time series... The trend slope is estimated by the median of the slopes of all possible pairwise combinations.

[0026] Trend change rate The calculation formula is: .

[0027] S4. Perform a statistical significance test on the rate of change of the trend, determine the significance of the trend based on the preset significance level, and determine the trend type in combination with the preset no-trend threshold.

[0028] Specifically, the Mann-Kendall test is used to calculate the statistic S and the standardized statistic Z, and the trend significance level P is determined in combination with the cumulative distribution function of the normal distribution. If the absolute value of the relative rate of change is less than the preset no-trend threshold, the corresponding trend is defined as no trend. Otherwise, the trend type is classified into significant increase, insignificant increase, no trend, insignificant decrease, or significant decrease according to the positive or negative sign of the relative rate of change and the significance level P.

[0029] The statistic S is defined as: ; ;

[0030] Where x represents the data sequence, subscripts i and j represent data indices, and n represents the total length of the sequence data. This is a sign function used to describe the direction of change between adjacent samples in a time series.

[0031] By calculating the standardized statistic Z and combining it with the cumulative distribution function, the trend significance level P can be obtained, thereby testing and evaluating the statistical significance of the trend at the 0.1 level.

[0032] ;

[0033] ;

[0034] ;

[0035] in, This represents the variance of the statistic S. Let represent the number of observations in the i-th group, n represent the total length of the sequence data, Z represent the standardized statistic, and P represent the trend significance level. The cumulative distribution function used to calculate the normal distribution.

[0036] Meanwhile, this invention introduces a preset no-trend threshold. The preset no-trend threshold is a pre-defined numerical limit used to define the actual significance of a trend. Its purpose is to distinguish between statistically significant but actually minimally variable (noisy) trends and trends with actual climatic significance. For example, it can be set as a certain percentage of the annual relative rate of change; changes below this threshold are considered insignificant in practical applications. This threshold can be flexibly set according to the specific climate background of the study area, data accuracy requirements, or application scenario needs. For example, a smaller threshold can be set in areas sensitive to change, while it can be appropriately relaxed in areas with larger changes.

[0037] Based on this, if the absolute value of the relative rate of change is less than a preset no-trend threshold, the corresponding trend is defined as no-trend. This step aims to perform preliminary screening and classification of trends according to the preset no-trend threshold. Specifically, when the absolute value of the calculated relative rate of change is less than the preset no-trend threshold, the trend is classified as no-trend regardless of its statistical significance. This definition method avoids misjudging small fluctuations as meaningful long-term trends, thereby improving the robustness and practicality of trend assessment.

[0038] Otherwise, the trend type is classified as significantly increasing, not significantly increasing, no trend, not significantly decreasing, or significantly decreasing based on the sign of the relative rate of change and the significance level P. This classification mechanism provides a refined method for trend identification, comprehensively considering the direction of the trend (increasing or decreasing), statistical reliability (significance level P), and the actual magnitude of change (compared to the no-trend threshold). For example, when the relative rate of change is positive and the P value is less than the preset significance level, the trend is classified as significantly increasing; when the relative rate of change is negative and the P value is less than the preset significance level, the trend is classified as significantly decreasing. If the P value is greater than or equal to the preset significance level, it is classified as not significantly increasing or not significantly decreasing, depending on the sign of the relative rate of change. This multi-dimensional classification helps to more accurately understand the ability of precipitation estimation products to reproduce real climate trends.

[0039] S5. Based on the slope and type of the changing trend, a trend capture skill framework is constructed. The consistency of trend direction, trend significance, trend amplitude, and trend spatial pattern are calculated respectively to quantitatively characterize the trend reproduction ability of precipitation estimation data in different dimensions.

[0040] Specifically, Trend Direction Consistency (TDC) can be calculated as the proportion of stations or grid points whose precipitation estimates and surface observations are consistent in the trend direction out of the total number of stations or grid points. The formula for calculating Trend Direction Consistency is: ; ;

[0041] in, Represents the direction function. This represents the relative rate of change at the k-th station. and Let N represent the trend direction classification of ground observations and products at the Kth station, respectively, and N represent the total number of stations. This represents the threshold value, which is set here. =0.1; The indicator function takes a value of 1 when the condition is met, and 0 otherwise; TDC represents the consistency of trend direction. The value of TDC ranges from 0 to 1. The larger the value, the more consistent the product trend direction is with the ground.

[0042] Trend significance skill (TSS) can be calculated as the proportion of stations or grid points that correctly identify the significance (significant or insignificant) of ground observation trends in precipitation estimation data out of the total number of stations or grid points. The formula for calculating trend significance skill is: ;

[0043] in, This represents a trend type classification function. Let N represent the relative rate of change for the k-th station, and N represent the total number of stations. and These represent the trend types of ground observations and products at the Kth station, respectively, with TSS representing the trend significance skill. Indicates an indicator function, This indicates the Mann-Kendall trend significance test result. When the p-value obtained from the test is less than the set significance level (p<0.1 in this invention), the trend is considered to be statistically significant; otherwise, the trend is considered not significant.

[0044] Trend magnitude consistency (TMF) can be calculated as the average absolute or relative difference between precipitation estimates and surface observations in the magnitude of trend change. The formula for calculating trend magnitude consistency is: ; ;

[0045] Wherein, TMF represents the consistency of trend magnitude. This represents the difference in the trend variation between the precipitation estimate product and the ground observation data for the k-th station. and Let represent the relative rates of change of the precipitation estimation product and the surface observation data at the k-th station, respectively, and M represent the stations that meet specific conditions. This indicates the threshold, the small threshold set here. It is 0.02.

[0046] To ensure that the indicators are uniformly within the range of 0-1 and to facilitate comprehensive comparison with other indicators, a normalized form is adopted: ;

[0047] Trend spatial pattern consistency (TPC) can be calculated as the Pearson correlation coefficient between precipitation estimates and surface observations on a trend spatial distribution map. The formula for calculating trend spatial pattern consistency is: ;

[0048] Where TPC represents the consistency of the trend spatial pattern, and N represents the total number of stations. and These represent the spatial mean values ​​of product trends and ground trends, respectively. and ... β Perform additional normalization.

[0049] S6. A trend capture index is calculated by weighting and combining the consistency of trend direction, trend significance, trend magnitude, and trend spatial pattern to comprehensively evaluate the ability of precipitation estimation data to reproduce observed trends. For example, the trend capture index can be calculated as the weighted average of the above four dimensions, where the weight of each dimension can be preset according to its relative importance in the evaluation.

[0050] The formula for calculating the Trend Capture Index (TCI) is as follows: ;

[0051] in, The weights represent the trend capture index (TCL), trend direction consistency (TDC), trend magnitude consistency (TMF), trend significance level (TSS), and trend spatial pattern consistency (TPC). By weighting and combining these different indicators, a comprehensive evaluation of trend reproduction capability is achieved.

[0052] And the weights satisfy: ;

[0053] in, This represents the weight, where i = 1 to 4.

[0054] Different weights are assigned to reflect the relative importance of each dimension in trend assessment. This weighting scheme is based on empirical design to highlight the direction and magnitude of the trend, with TDC and TMF weighted at 0.3 and TSS and TPC weighted at 0.2. Therefore, TCI should primarily be interpreted as a relative indicator for comparing precipitation estimation results, rather than an absolute measure of performance.

[0055] This method effectively addresses the limitations of traditional assessment methods in precipitation trend analysis. By matching the temporal and spatial scales of precipitation estimation data, data consistency is ensured. Furthermore, three characteristic indicators—total precipitation, frequency, and intensity—are calculated, and their trends are assessed from multiple dimensions, including trend direction, significance, magnitude, and spatial pattern. This allows for a comprehensive and systematic quantification of the ability of precipitation estimation products to reproduce observed trends, revealing performance differences across different dimensions, and providing more accurate scientific evidence for climate change research and hydrological applications.

[0056] Example 2

[0057] This embodiment proposes a multidimensional diagnostic system for quantitative precipitation estimation, capable of representing long-term trends, including:

[0058] The data matching module is used to acquire surface precipitation observation data and multi-source precipitation estimation data within the study area, and to perform time-scale and spatial-scale matching processing to obtain precipitation data at a unified scale.

[0059] The feature calculation module is used to calculate the time-series data of three types of precipitation feature indicators: total precipitation, precipitation frequency, and precipitation intensity, based on the matched precipitation data.

[0060] The trend analysis module is used to calculate the slope and relative rate of change of precipitation characteristic indicators at each station or grid point based on the sequence data, obtain the trend change rate, and perform a statistical significance test on the trend change rate, and determine the trend type by combining the preset no-trend threshold.

[0061] The dimensional assessment module is used to construct a trend capture skill framework based on the slope and type of the trend, and calculates the trend direction consistency (TDC), trend significance skill (TSS), trend amplitude consistency (TMF), and trend spatial pattern consistency (TPC) respectively, which are used to quantitatively characterize the trend reproducibility of precipitation estimation data in different dimensions.

[0062] The comprehensive evaluation module is used to weight and combine the Trend Direction Consistency (TDC), Trend Significance Skill (TSS), Trend Amplitude Consistency (TMF), and Trend Spatial Pattern Consistency (TPC) to calculate the Trend Capture Index (TCI), which is used to comprehensively evaluate the ability of precipitation estimation data to reproduce observed trends.

[0063] Through the above technical solution, this embodiment decomposes trend characteristics into four dimensions: trend direction, trend significance, trend amplitude, and trend spatial pattern, constructing a trend capture skill framework and realizing a systematic quantitative assessment of the ability of precipitation estimation products to reproduce multi-dimensional trend characteristics over long-term time scales. The data matching module unifies the temporal and spatial scales of ground observations and multi-source precipitation data, eliminating differences in spatiotemporal definitions between different data sources and laying a reliable data foundation for subsequent trend comparison analysis. The feature calculation module extracts three key indicators—total precipitation, frequency, and intensity—based on unified-scale data, avoiding the one-sidedness of single-indicator evaluation and reflecting the evolution of precipitation processes from different perspectives. The trend analysis module calculates the slope and relative rate of change of the trend, and combines statistical significance tests and no-trend threshold determination to effectively identify the evolution direction and significance of precipitation characteristics, transforming complex precipitation sequences into trend change rates with clear physical meaning. The dimensional assessment module, through a trend capture skill framework, accurately captures the performance differences of precipitation estimation products across four dimensions: Trend Direction Consistency (TDC), Trend Significance Skill (TSS), Trend Amplitude Consistency (TMF), and Trend Spatial Pattern Consistency (TPC). In particular, the Trend Spatial Pattern Consistency (TPC) effectively preserves the spatial heterogeneity information of precipitation trends. The comprehensive evaluation module calculates the Trend Capture Index (TCI) by weighting and combining the above dimensional indicators, transforming the multi-dimensional assessment results into a single comprehensive index. This enables a quantitative evaluation of the ability of precipitation estimation products to reproduce observed trends. This method effectively overcomes the limitations of existing technologies that rely solely on single statistical indicators, providing a comprehensive and accurate diagnosis of the trend representation capabilities of precipitation estimation products. It is particularly suitable for hydrological and climatic trend analysis under complex terrain and different seasonal conditions, providing a scientific basis for performance optimization of precipitation estimation products and climate change research.

[0064] Example 3

[0065] The following example will provide a more detailed explanation of the above technical solution:

[0066] Suppose we need to assess the ability of study area A to characterize long-term precipitation trends from 2000 to 2024.

[0067] S1. Obtain daily precipitation data from Chinese national ground stations during the calibration period as surface precipitation data. At the same time, select daily satellite precipitation data IMERG-Final and GSMAP-Gauge, as well as daily reanalysis data ERA5-Land, and use them as the research objects to carry out precipitation matching analysis.

[0068] Since the daily precipitation data from China's national ground stations are point-based observation data, and the spatial resolution of IMERG-Final, GSMAP-Gauge, and ERA5-Land data is all 0.1°, it is necessary to match gridded data with station data to achieve spatial consistency between different types of data. Using the ground station location as a reference, satellite precipitation and reanalysis data values ​​are extracted within the corresponding 0.1° grid, or gridded data are converted into station-scale data through neighboring grid interpolation. This ensures that each ground station corresponds to a unique IMERG-Final, GSMAP-Gauge, and ERA5-Land precipitation value, achieving a one-to-one spatial correspondence.

[0069] Because the daily data from China's national ground stations use Beijing time (UTC+8) to define the day boundary, while the IMERG-Final, GSMAP-Gauge, and ERA5-Land data are all recorded in Coordinated Universal Time (UTC), a time system conversion is required. The diurnal data in UTC time are reorganized according to Beijing time, i.e., the UTC time series is shifted (+8 hours), and the day boundary is redefined, thus obtaining diurnal precipitation data consistent with the time definition of the ground observation data.

[0070] S2. Based on the matched precipitation data, calculate the sequence data of precipitation characteristic indicators. For each station and each data source, calculate the total annual precipitation, precipitation frequency, and precipitation intensity (time dimension). Based on these sequence data, calculate the trend slope and relative rate of change of the precipitation characteristic indicators. For each time series, use the Sen's slope estimation method to calculate the trend slope of its total precipitation. β To facilitate comparisons between different variables, all trend slopes... β All converted to trend change rate The percentage change rate, or relative change rate, is obtained by normalizing the mean of the time series.

[0071] S3. Perform a statistical significance test and determine the trend type. Calculate the Mann-Kendall test statistic S and the standardized statistic Z, and determine the trend significance level P using the cumulative distribution function of the normal distribution. Preset a significance level (e.g., 0.1) and a no-trend threshold. If the absolute value of the trend change rate is less than the preset no-trend threshold, the corresponding trend is defined as no trend. Otherwise, based on the sign of the trend change rate and the significance level P, classify the trend type as significantly increasing, not significantly increasing, not significantly decreasing, or significantly decreasing.

[0072] S4. Based on the topographic features of study area A, it is divided into three sub-regions: plateau area, complex terrain area, and plain area. All stations or grid points are assigned to the corresponding sub-regions according to their spatial location. Pie charts and stacked bar charts show the proportion of meteorological stations in each trend category: the pie chart represents the entire study area, while the stacked bar chart shows the sub-regional distribution of the plateau area, complex terrain area, and plain area.

[0073] Figure 2 The spatial distribution map shows the precipitation change trends (% / year) of observed data (OBS) and estimated precipitation values. It can be seen that no trend indicates a change within ±0.1% / year; black dots indicate statistical significance at the 10% significance level. Pie charts and stacked bar charts show the distribution of meteorological stations in each trend category: the pie chart represents the entire study area, while the stacked bar chart shows the sub-regional distribution of the plateau, complex terrain, and plain areas.

[0074] Compared with OBS observation data, satellite precipitation products IMERG-Final and GSMAP-Gauge both reproduce the overall increasing trend of precipitation, but the proportion of stations with positive trends is significantly higher than that of OBS, especially in complex terrain areas and plains, where almost all stations show a positive trend, compared to approximately 75% in OBS. In contrast, the reanalysis product ERA5-Land shows a negative trend in most parts of the watershed, with the proportion of stations with negative trends reaching 66% in complex terrain areas, far higher than the 11% in OBS. These results indicate that there are significant differences in the spatial trend performance of different precipitation data. This invention can more accurately reflect the spatial distribution characteristics of OBS observations, helping to improve the accuracy of watershed precipitation trend assessment.

[0075] Figure 3 Heatmaps of TCI component scores for precipitation in the Yangtze River Basin and its sub-regions based on different precipitation estimates are provided. Each sub-map uses an independent color scale to facilitate comparison between different precipitation estimates.

[0076] S4. Trend slope at each station β Trend Direction Consistency (TDC), Trend Significance Skill (TSS), Trend Amplitude Consistency (TMF), and Trend Spatial Pattern Consistency (TPC) are calculated separately to quantitatively characterize the trend reproducibility of precipitation estimation data across different dimensions.

[0077] Although these components do not correspond to a unified physical quantity, they are all dimensionless and numerically bounded, facilitating meaningful comparisons and integration. The values ​​of trend direction consistency, trend significance skill, and trend amplitude consistency range from 0 to 1; while the value of trend spatial pattern consistency theoretically ranges from −1 to 1, but in this invention, it remains positive in all cases. This practical consistency within a bounded range helps to integrate them into a unified evaluation index.

[0078] S5. The Trend Capture Index (TCI) is calculated by weighting and combining the consistency of trend direction, trend significance, trend amplitude, and trend spatial pattern. The TCI comprehensively evaluates the ability of products P1 and P2 to reproduce observed trends. By weighting and combining different dimensional indicators, a comprehensive evaluation of trend reproduction ability is achieved. The weights of different indicators can be adjusted according to evaluation needs to reflect the differences in importance of each dimension. The weights for trend direction consistency and trend amplitude consistency are set to 0.3, and the weights for trend significance and trend spatial pattern consistency are set to 0.2. Therefore, the TCI should primarily be interpreted as a relative indicator for comparing precipitation estimation results, rather than an absolute measure of performance.

[0079] Figure 3 It can be seen that ERA5-Land generally has high TSS values ​​across all regions of the watershed, but relatively low TDC values, especially in areas with complex topography. This indicates a mismatch between statistical significance and consistency with trend direction, resulting in its lowest precipitation TCI. GSMAP-Gauge shows low TMF and TSS values, particularly in areas with complex topography. Even when a trend is detected, its magnitude and statistical significance are difficult to match with OBS observations. In contrast, IMERG-Final shows no significant deficiencies in any of the four indicators, indicating that its errors are not concentrated on any particular trend, thus demonstrating relatively robust overall performance.

[0080] Figure 4 Seasonal TCI radar maps of total precipitation, frequency, and intensity in the Yangtze River Basin, plotted for different precipitation estimates, along with scores for each component. Rows represent total precipitation, frequency, and intensity, respectively, while columns correspond to spring (March to May), summer (June to August), autumn (September to November), and winter (December to February of the following year). Figure 4 The calculation methods of TCI and its components in China and Figure 3 Completely consistent with this, the analysis focus is expanded from the spatial dimension to the temporal dimension, dividing the precipitation series into seasonal scales and extracting precipitation data subsets corresponding to each season. Subsequently, within each season, based on three characteristics—total precipitation, precipitation frequency, and precipitation intensity—according to... Figure 3The same calculation process is used to calculate the TCI and its four components, thereby obtaining the index score results under different seasons and different precipitation characteristics.

[0081] from Figure 4 As can be seen, winter presents the greatest challenge for trend reproduction in terms of seasonality, with TCI values ​​generally being low. IMERG-Final shows a clear advantage in summer and winter, mainly due to improved TPC in summer and improved TDC in winter, while TMF also contributes significantly; its performance in spring and autumn is comparable to GSMAP-Gauge. GSMAP-Gauge has the lowest TCI across all seasons, and its limiting index varies with the seasons, indicating that the trend amplitude and significance are inconsistent with OBS. ERA5-Land shows a balanced TCSF in spring, but outperforms satellite products in trend direction, precipitation, and frequency in winter, exhibiting a seasonal advantage. Overall, this invention improves the spatial and seasonal consistency of trend capture through correction, significantly optimizing the reproduction capabilities of precipitation, frequency, and intensity.

[0082] The results above demonstrate that this invention can effectively distinguish the ability of different precipitation estimation products to reproduce observed trends. It can quantitatively evaluate the trend performance of precipitation estimation products from multiple dimensions, including trend direction, trend amplitude, statistical significance, and spatial pattern, and can reveal the systematic differences between different products under different topographical regions and seasonal conditions. This indicates that the trend capture skill framework constructed by this invention has good applicability and stability, and can provide a reliable basis for the selection and application of precipitation estimation products in trend analysis, climate change research, and hydrological applications.

Claims

1. A multidimensional diagnostic method for quantitative precipitation estimation with long-term trend characterization capability, characterized in that, include: We acquired surface precipitation observation data and multi-source precipitation estimation data within the study area, and performed time-scale and spatial-scale matching processing to obtain precipitation data at a unified scale. Based on the matched precipitation data, the time-series data of three types of precipitation characteristic indicators—total precipitation, precipitation frequency, and precipitation intensity—are calculated. Based on the sequence data, calculate the slope and relative rate of change of the precipitation characteristic indicators at each station or grid point to obtain the trend rate of change. The trend change rate is subjected to a statistical significance test. The trend significance is determined according to a preset significance level, and the trend type is determined by combining the preset no-trend threshold. Based on the slope and type of the changing trend, a trend capture skill framework is constructed, and the consistency of trend direction, trend significance, trend amplitude, and trend spatial pattern are calculated respectively to quantitatively characterize the trend reproduction ability of precipitation estimation data in different dimensions. The trend capture index is calculated by weighting and combining the consistency of trend direction, trend significance, trend amplitude, and trend spatial pattern to comprehensively evaluate the ability of precipitation estimation data to reproduce observed trends.

2. The multidimensional diagnostic method according to claim 1, characterized in that, Among the precipitation characteristic indicators: total precipitation is the cumulative value of daily precipitation within a preset time period; precipitation frequency is the proportion of precipitation days to the total number of observed days.

3. The multidimensional diagnostic method according to claim 1, characterized in that, The method for calculating the trend slope and relative rate of change is as follows: The trend slope of the time series is calculated using Sen's slope estimation. β By the slope of the trend β Divide by the time series mean for normalization, and calculate the percentage change per unit time, which is used as the relative change rate.

4. The multidimensional diagnostic method according to claim 1, characterized in that, The method for statistically significant testing of the trend change rate further includes: calculating the statistic S and standardized statistic Z using the Mann-Kendall test, and determining the trend significance level P by combining the cumulative distribution function of the normal distribution; if the absolute value of the relative change rate is less than the preset no-trend threshold, the corresponding trend is defined as no trend; otherwise, the trend type is classified as significantly increasing, not significantly increasing, no trend, not significantly decreasing, or significantly decreasing according to the positive or negative sign of the relative change rate and the significance level P.

5. The multidimensional diagnostic method according to claim 1, characterized in that, The formula for calculating the consistency of the trend direction is: ； ； in, Represents the direction function. This represents the relative rate of change at the k-th station. and These represent the trend direction classifications of ground observations and products at the Kth station, respectively, where N represents the total number of stations, and TDC represents the consistency of trend direction. Indicates the threshold. This indicates an indicator function.

6. The multidimensional diagnostic method according to claim 1, characterized in that, The formula for calculating the consistency of the trend amplitude is: ； ； Wherein, TMF represents the consistency of trend magnitude. This represents the difference in the trend variation between the precipitation estimate product and the ground observation data for the k-th station. and Let represent the relative rates of change of the precipitation estimation product and the surface observation data at the k-th station, respectively, and M represent the stations that meet specific conditions. This represents the threshold.

7. The multidimensional diagnostic method according to claim 1, characterized in that, The formula for calculating the trend significance skill is as follows: ； ； in, This represents a trend type classification function. Let N represent the relative rate of change for the k-th station, and N represent the total number of stations. and These represent the trend types of ground observations and products at the Kth station, respectively, with TSS representing the trend significance skill. Indicates an indicator function, This indicates the results of the Mann-Kendall trend significance test.

8. The multidimensional diagnostic method according to claim 1, characterized in that, The formula for calculating the consistency of the trend spatial pattern is: ； Where TPC represents the consistency of the trend spatial pattern, and N represents the total number of stations. and These represent the spatial mean values ​​of product trends and ground trends, respectively. and represents the relative rate of change of the precipitation estimation product and the ground observation data at the k-th station, respectively.

9. The multidimensional diagnostic method according to claim 1, characterized in that, The formula for calculating the trend capture index is as follows: ； in, The terms represent weights, TCL represents the trend capture index, TDC represents trend direction consistency, TMF represents trend amplitude consistency, TSS represents trend significance skill, and TPC represents trend spatial pattern consistency.

10. A multidimensional diagnostic system for quantitative precipitation estimation with long-term trend characterization capability, characterized in that, include: The data matching module is used to acquire surface precipitation observation data and multi-source precipitation estimation data within the study area, and to perform time-scale and spatial-scale matching processing to obtain precipitation data at a unified scale. The feature calculation module is used to calculate the time-series data of three types of precipitation feature indicators: total precipitation, precipitation frequency, and precipitation intensity, based on the matched precipitation data. The trend analysis module is used to calculate the slope and relative rate of change of the precipitation characteristic indicators at each station or grid point based on the sequence data, and obtain the trend change rate. The statistical significance of the trend change rate is then tested, and the trend type is determined by combining the preset no-trend threshold. The dimensional assessment module is used to construct a trend capture skill framework based on the slope and type of the changing trend, and to calculate the consistency of trend direction, trend significance, trend amplitude, and trend spatial pattern, respectively, in order to quantitatively characterize the trend reproducibility of precipitation estimation data in different dimensions. The comprehensive evaluation module is used to weight and combine the consistency of trend direction, trend significance, trend amplitude, and trend spatial pattern to calculate the trend capture index, so as to comprehensively evaluate the ability of precipitation estimation data to reproduce the observed trend.

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