Near-real-time precipitation fusion methods, devices and systems

Abstract

This invention discloses a near-real-time precipitation fusion method, apparatus, and system. The method includes acquiring independent near-real-time precipitation products; preprocessing each near-real-time precipitation product to achieve a uniform spatiotemporal resolution; estimating the error of each near-real-time precipitation product using the Triple Collocation method, and calculating the weight of each near-real-time precipitation product using the error with the aim of minimizing the error between the fused precipitation data and the actual precipitation data; performing a weighted summation of the near-real-time precipitation products to obtain initial fused precipitation data; and correcting the initial fused precipitation data using a cumulative probability density function matching method to obtain a near-real-time fused precipitation dataset. This invention can obtain a more accurate near-real-time fused precipitation dataset.

Description

Technical Field

[0001] This invention belongs to the field of multi-source precipitation product fusion technology, specifically relating to a near real-time precipitation fusion method, device and system. Background Technology

[0002] Precipitation is an important component of global climate change and water cycle research. Timely and accurate precipitation information plays a crucial role in many applications, such as decision-making and prevention of frequent floods and droughts.

[0003] Traditional rain gauges provide the most reliable precipitation data at specific point scales. However, these stations are spatially unevenly distributed, with most located at low altitudes, and the acquired precipitation data exhibits significant delays and spatiotemporal discontinuities, making them insufficient to characterize the spatiotemporal variability of precipitation, especially in marine areas and mountainous regions with complex terrain. With the significant development of spatial interpolation techniques, satellite remote sensing, and numerical weather models, many different types of gridded multi-source near-real-time precipitation products have been developed, such as NASA's GPM IMERG Early Run (IMERG-E), the ERA5 multi-year atmospheric reanalysis precipitation data released by the European Centre for Medium-Range Weather Forecasts, and the CPC globally unified observational precipitation data provided by the Climate Prediction Centre of the National Oceanic and Atmospheric Administration. These precipitation products have advantages such as free access, wide coverage, spatiotemporal continuity, and good timeliness, providing alternative data sources for continuous precipitation estimation, especially for data-deficient regions. However, numerous studies have shown that the accuracy of near-real-time precipitation products is relatively low, with various sources of precipitation error, including errors and biases in precipitation estimation, which are related to limitations in their data sources and inversion algorithms. In addition, different precipitation products have their own advantages and disadvantages.

[0004] To better depict the true characteristics of precipitation, it is necessary to fully utilize the advantages of multi-source near-real-time precipitation products. How to comprehensively consider the error characteristics and advantages of different precipitation products in order to improve the quality of near-real-time precipitation estimation is a technical problem that urgently needs to be solved in the field of multi-source precipitation product fusion. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a near-real-time precipitation fusion method, apparatus, and system. The method utilizes the Triple Collocation method to estimate errors and calculate weights for independent near-real-time precipitation products, resulting in initial fused precipitation data. The cumulative probability density function matching method is then used to correct the initial fused precipitation data, yielding a more accurate near-real-time fused precipitation dataset.

[0006] To achieve the above-mentioned technical objectives and effects, the present invention is implemented through the following technical solution:

[0007] In a first aspect, the present invention provides a near-real-time precipitation fusion method, comprising:

[0008] Obtain independent near-real-time precipitation products;

[0009] Preprocessing is performed on each near-real-time precipitation product to ensure that each near-real-time precipitation product has a uniform spatiotemporal resolution;

[0010] The Triple Collocation method is used to estimate the error of each near-real-time precipitation product in order to minimize the error between the fused precipitation data and the actual precipitation data. The weight of each near-real-time precipitation product is calculated using the error, and the weighted sum of each near-real-time precipitation product is obtained to obtain the initial fused precipitation data.

[0011] The initial fused precipitation data was corrected using the cumulative probability density function matching method to obtain a near-real-time fused precipitation dataset.

[0012] Optionally, the independent near-real-time precipitation products must simultaneously meet the following conditions:

[0013] Condition 1: The data sources for each near-real-time precipitation product are independent of each other;

[0014] Condition 2: Each near-real-time precipitation product includes a near-real-time daily precipitation dataset.

[0015] Optionally, the near-real-time precipitation product with uniform spatiotemporal resolution is obtained through the following method:

[0016] Based on the scope of the study area, the near-real-time precipitation products were read, cropped, and outlier interpolated. The spatiotemporal scale matching of the three precipitation products was performed using bilinear interpolation to ensure that the near-real-time precipitation products had a uniform and appropriate spatiotemporal resolution and were stored in a uniform data format.

[0017] Optionally, the weights of each near-real-time precipitation product are calculated using the following formula:

[0018]

[0019] in,

[0020]

[0021]

[0022]

[0023] In the formula, w1, w2, and w3 represent the weights of the 1st, 2nd, and 3rd precipitation products, respectively. C represents the variance of the error between the corresponding 1st, 2nd, and 3rd precipitation products and the actual precipitation, respectively. 1,1 Let C represent the autocovariance of the first precipitation product. 1,2 C represents the covariance of the first and second precipitation products. 1,3 C represents the covariance of the first and third precipitation products. 2,2 C represents the autocovariance of the second precipitation product. 2,3 C represents the covariance of the second and third precipitation products. 3,3 Let β1, β2, and β3 represent the slopes of the first, second, and third precipitation products relative to the actual precipitation, respectively. σ represents the covariance of the third precipitation product. t 2 This represents the standard deviation of actual precipitation.

[0024] Optionally, the expression for the initial fused precipitation data is:

[0025]

[0026] In the formula, P s This is the initial fused precipitation data; w i Let x represent the weight of the i-th near-real-time precipitation product estimate. i Let k represent the dataset of the i-th near real-time precipitation product, where k = 1, 2, 3.

[0027] Optionally, the expression for the near real-time fused precipitation dataset is:

[0028]

[0029] In the formula, P cr P represents the near-real-time fused precipitation dataset after cumulative probability density function matching correction. s This indicates the initial fused precipitation data; cdf represents the inverse cumulative distribution function of a baseline dataset, which is data from an observational precipitation product; s This represents the cumulative distribution function estimated based on the initial merged precipitation dataset.

[0030] Secondly, the present invention provides a near-real-time precipitation fusion device, comprising:

[0031] The acquisition module is configured to acquire mutually independent near-real-time precipitation products;

[0032] The preprocessing module is configured to preprocess each near-real-time precipitation product to give each near-real-time precipitation product a uniform spatiotemporal resolution.

[0033] The initial fused precipitation data acquisition module is configured to estimate the error of each near-real-time precipitation product using the Triple Collocation method, with the aim of minimizing the error between the fused precipitation data and the real precipitation data. The weight of each near-real-time precipitation product is calculated using the error, and the weighted sum of each near-real-time precipitation product is performed to obtain the initial fused precipitation data.

[0034] The correction module is configured to correct the initial fused precipitation data using a cumulative probability density function matching method to obtain a near-real-time fused precipitation dataset.

[0035] Optionally, the weights of each near-real-time precipitation product are calculated using the following formula:

[0036]

[0037] in,

[0038]

[0039]

[0040]

[0041] In the formula, w1, w2, and w3 represent the weights of the 1st, 2nd, and 3rd precipitation products, respectively. C represents the variance of the error between the corresponding 1st, 2nd, and 3rd precipitation products and the actual precipitation, respectively. 1,1 Let C represent the autocovariance of the first precipitation product. 1,2 C represents the covariance of the first and second precipitation products. 1,3 C represents the covariance of the first and third precipitation products. 2,2 C represents the autocovariance of the second precipitation product. 2,3 C represents the covariance of the second and third precipitation products. 3,3 Let β1, β2, and β3 represent the slopes of the first, second, and third precipitation products relative to the actual precipitation, respectively. σ represents the covariance of the third precipitation product. t 2 This represents the standard deviation of actual precipitation.

[0042] Optionally, the expression for the initial fused precipitation data is:

[0043]

[0044] In the formula, P s This is the initial fused precipitation data; w i Let x represent the weight of the i-th near-real-time precipitation product estimate. i Let k represent the dataset of the i-th near real-time precipitation product, where k = 1, 2, 3;

[0045] The expression for the near real-time fused precipitation dataset is:

[0046]

[0047] In the formula, P cr P represents the near-real-time fused precipitation dataset after cumulative probability density function matching correction. s This indicates the initial fused precipitation data; cdf represents the inverse cumulative distribution function of a baseline dataset, which is data from an observational precipitation product; s This represents the cumulative distribution function estimated based on the initial merged precipitation dataset.

[0048] Thirdly, the present invention provides a near real-time precipitation fusion system, including a storage medium and a processor;

[0049] The storage medium is used to store instructions;

[0050] The processor is configured to operate according to the instructions to perform the steps of the method according to any one of the first aspects.

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0052] This invention utilizes the Triple Collocation method to estimate errors and calculate weights for independent near-real-time precipitation products, resulting in initial merged precipitation data. Using observed precipitation products as benchmark data, a cumulative probability density function matching method is employed to correct biases in the initial merged precipitation data, yielding a more accurate near-real-time daily merged precipitation dataset. This invention eliminates the need for inputting actual ground-based precipitation data and compensates for the inherent weaknesses of different precipitation products, leveraging their strengths to obtain a more reliable precipitation dataset. This provides higher-precision near-real-time precipitation data input for global or regional flood disaster monitoring and early warning. Attached Figure Description

[0053] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0054] Figure 1 A flowchart of the near real-time precipitation fusion method provided by the present invention;

[0055] Figure 2 This is a flowchart of a near-real-time precipitation fusion method provided in one embodiment of the present invention;

[0056] Figure 3 This is a comparison chart of the accuracy statistics of the merged precipitation and original precipitation products estimated based on this invention. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the scope of protection of the invention.

[0058] The application principle of the present invention will be described in detail below with reference to the accompanying drawings.

[0059] Example 1

[0060] This invention provides a near-real-time precipitation fusion method, such as... Figure 1 As shown, this method uses three independent near-real-time precipitation products. Preprocessing of each near-real-time precipitation product, such as outlier interpolation and spatiotemporal scale matching, forms a dataset with uniform spatiotemporal resolution. The Triple Collocation method is used to estimate the error of each near-real-time precipitation product, and the weight of each product is calculated using the error to minimize the error between the fused precipitation data and the true value. A weighted sum is then performed on each near-real-time precipitation product to obtain the initial fused precipitation data. Based on the observed precipitation products, the initial fused precipitation data is corrected using a cumulative probability density function matching method to obtain the near-real-time fused precipitation dataset.

[0061] like Figure 1 As shown, the near-real-time precipitation fusion method includes the following steps:

[0062] (1) Obtain mutually independent near-real-time precipitation products;

[0063] (2) Preprocess each near-real-time precipitation product to ensure that each near-real-time precipitation product has a uniform spatiotemporal resolution.

[0064] (3) The error of each near real-time precipitation product is estimated by using the Triple Collocation method, with the aim of minimizing the error between the fused precipitation data and the real precipitation data. The weight of each near real-time precipitation product is calculated using the error, and the weighted sum of each near real-time precipitation product is obtained to obtain the initial fused precipitation data.

[0065] (4) The initial fused precipitation data is corrected using the cumulative probability density function matching method to obtain a near real-time fused precipitation dataset.

[0066] In one specific embodiment of the present invention, the mutually independent near-real-time precipitation products must simultaneously meet the following conditions:

[0067] Condition 1: The data sources for each near-real-time precipitation product are independent of each other;

[0068] Condition 2: Each near-real-time precipitation product includes a near-real-time daily precipitation dataset.

[0069] In practical applications, to meet the requirement of mutual independence, precipitation products with simple data sources and different data types can be selected, such as uncorrected precipitation products based on satellite observations, reanalysis precipitation products based on data assimilation, raster precipitation products generated by interpolation of ground measurement data, and precipitation products based on remote sensing soil water inversion. All four types of precipitation products have mutually independent precipitation datasets. However, currently only the first three types of precipitation products meet the condition of providing long-sequence near-real-time precipitation datasets. Therefore, the following three types of precipitation products are typically selected as mutually independent near-real-time precipitation products for analysis: uncorrected precipitation products based on satellite observations, reanalysis precipitation products based on data assimilation, and raster precipitation products generated by interpolation of ground measurement data.

[0070] In one specific embodiment of the present invention, to facilitate subsequent calculations, the near-real-time precipitation product with uniform spatiotemporal resolution is obtained through the following method:

[0071] Based on the scope of the study area, the near-real-time precipitation products were read, cropped, and outlier interpolated (e.g., by interpolating with neighboring values). The spatiotemporal scale matching of the three precipitation products was performed using bilinear interpolation to ensure that each near-real-time precipitation product had a uniform and appropriate spatiotemporal resolution and was stored in a uniform data format.

[0072] In one specific embodiment of the present invention, the weights of each near-real-time precipitation product are obtained through the following steps:

[0073] (1) Linearity assumption.

[0074] A fundamental assumption in collocation analysis is that independent precipitation products are linearly correlated with actual precipitation variables. This correlation can be represented by a linear model, namely:

[0075] x i =α i +β i t+ε i

[0076] In the formula: x i α is the estimated value of the i-th near-real-time precipitation product; t is the unknown actual precipitation variable; i and β i Let ε represent the ordinary least squares intercept and slope of the i-th near-real-time precipitation product, respectively; i Let be the observation error of the i-th near-real-time precipitation product. The covariance of any two near-real-time precipitation products (including different and identical precipitation products) can be defined by the following formula:

[0077]

[0078] In the formula, C i,j and Cov(x) i ,x j () represents the covariance between the i-th near-real-time precipitation product and the j-th near-real-time precipitation product; The standard deviation represents the actual precipitation signal.

[0079] Based on three mathematical assumptions—namely, the zero cross-correlation assumption based on mutually independent near-real-time precipitation products (including their independent errors), the zero error cross-correlation assumption based on the independence of errors from the true value, and the zero error expectation assumption—the above equation can be simplified to:

[0080]

[0081] (2) Error estimation.

[0082] In the Triple Collocation method, the covariance of every two precipitation products among the three near-real-time precipitation products can be estimated as follows:

[0083]

[0084]

[0085] Using the above equations, the variance of the error between the three precipitation products and the actual precipitation can be calculated as follows:

[0086]

[0087] In the formula, C represents the variance of the error between the corresponding 1st, 2nd, and 3rd precipitation products and the actual precipitation, respectively. 1,1 Let C represent the autocovariance of the first precipitation product. 1,2 C represents the covariance of the first and second precipitation products. 1,3 C represents the covariance of the first and third precipitation products. 2,2 C represents the autocovariance of the second precipitation product. 2,3 C represents the covariance of the second and third precipitation products. 3,3 Let β1, β2, and β3 represent the covariance of the third precipitation product, and β1, β2, and β3 represent the slopes of the first, second, and third precipitation products relative to the actual precipitation, respectively. This represents the standard deviation of actual precipitation.

[0088] (3) Weight estimation.

[0089] Based on the least squares framework, the weight of each near-real-time precipitation product is calculated using the least squares fusion method to obtain the initial fused precipitation data. The formula for calculating the initial fused precipitation data is as follows:

[0090]

[0091] In the formula, P s This is the initial merged precipitation result; w i This represents the weight of the estimated i-th precipitation product.

[0092] The relationship between the variance of the initial fused precipitation data and the error variance of the input precipitation product can be expressed as:

[0093]

[0094] In the formula, It is the variance of the initial fused precipitation data; Let represent the error variance of the i-th input precipitation product.

[0095] The weights are calculated by minimizing the variance of the initial fused precipitation data. Therefore, the equation above is differentiated based on the weights, as shown below:

[0096]

[0097] Therefore, the formula for calculating the weight of each precipitation product is derived as follows:

[0098]

[0099] In the formula, w1, w2, and w3 represent the weights of the 1st, 2nd, and 3rd precipitation products, respectively.

[0100] (4) Rainfall fusion.

[0101] In the absence of real precipitation variables, the initial fusion results of multi-source precipitation products are achieved by using weights and weighted summation of the original precipitation products.

[0102] In one specific embodiment of the present invention, cumulative probability density function matching can correct spurious drizzle and decaying peaks.

[0103] Cumulative probability density function matching is a type of distribution mapping method. The basic idea is to correct the bias in the initial merged precipitation dataset by matching its cumulative distribution frequency, considering a benchmark dataset, to provide more accurate results. Typically, a Gamma distribution with shape and scale parameters is used to fit two data series and estimate the quantiles of the initial merged precipitation. Then, a transformation method for the initial merged precipitation is found based on the benchmark dataset using quantile mapping. This transformation method can be expressed as:

[0104]

[0105] In the formula, P cr P represents the near-real-time fused precipitation dataset after cumulative probability density function matching correction. s This indicates the initial fused precipitation data; cdf represents the inverse cumulative distribution function of a baseline dataset, which is data from an observational precipitation product; s This represents the cumulative distribution function estimated based on the initial merged precipitation dataset.

[0106] The following is combined Figure 2 The present invention also provides a specific implementation method, which details the implementation process of the near-real-time precipitation fusion method in the embodiments of the present invention.

[0107] Step 1, selection of near-real-time precipitation products, specifically:

[0108] To ensure the independence of the three near-real-time precipitation products, three data sources were selected: IMERG-E (0.1° spatial resolution and 1-day timescale), ERA5 (0.25° spatial resolution and 1-hour timescale), and CPC (0.5° spatial resolution and 1-day timescale). These data were sourced from NASA, the European Centre for Medium-Range Weather Forecasts (ECMWF) Atmospheric Research Center, and the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Centre, respectively. The IMERG-E precipitation product was derived from remote sensing estimation and was not corrected for by observed data; the ERA5 precipitation product was derived from atmospheric forcing data and data assimilation estimation; and the CPC precipitation product was derived from global surface observation data. Therefore, these three precipitation products are essentially independent of each other.

[0109] Step two involves preprocessing the three near-real-time precipitation products, specifically as follows:

[0110] Based on the scope of the study area, the three precipitation products were read, cropped, and outlier imputed. Then, spatiotemporal scale matching processing was performed on the three precipitation products to give them a uniform and suitable spatiotemporal resolution, namely 0.25° spatial resolution and a 1-day time scale, and they were stored in a unified data format. Specifically, bilinear interpolation was used to resample the IMERG-E and CPC precipitation products (including bilinear interpolation and accumulation calculation), and the 1-hour data of the ERA5 precipitation product was accumulated to the 1-day time scale data, ultimately achieving a spatiotemporal resolution of 0.25° spatial resolution and a 1-day time scale for all three precipitation products.

[0111] Step 3: Generate initial merged precipitation data based on the Triple Collocation method, specifically as follows:

[0112] First, calculate the error between each precipitation product and the unknown actual precipitation, which is:

[0113]

[0114] Then, with the aim of minimizing the error between the fused precipitation data and the actual precipitation data, the weight of each precipitation product is calculated as follows:

[0115]

[0116] Finally, the datasets of each precipitation product are multiplied by their respective weights and summed to obtain the initial merged precipitation data, which is...

[0117]

[0118] Step four involves bias correction of the initial fused precipitation data, specifically as follows:

[0119] Using the observed precipitation product (CPC) as the baseline data, a transformation function between the initial fused precipitation data and the observed precipitation product data is found using the cumulative probability density function matching method, thus obtaining the final fused precipitation data. The transformation function is:

[0120]

[0121] After the above steps, a near real-time fused precipitation dataset with a spatial resolution of 0.25° and a temporal resolution of 1 day can be obtained for the study area.

[0122] Step 5 involves performance evaluation of the acquired near-real-time fused precipitation dataset, specifically as follows:

[0123] First, precipitation data measured by ground meteorological stations in the study area were collected as a reference dataset for evaluating the near-real-time fused precipitation dataset.

[0124] Secondly, the accuracy of the near-real-time fused precipitation dataset was verified using three conventional statistical indicators: correlation coefficient (CC), relative bias (RB), and root mean square error (RMSE).

[0125] The formula for calculating the correlation coefficient is:

[0126]

[0127] The formula for calculating relative deviation is:

[0128]

[0129] The formula for calculating the root mean square error is:

[0130]

[0131] In the formula: S i It is a near real-time fused precipitation dataset, G i These are actual precipitation data measured at the weather station.

[0132] Finally, the accuracy statistics of the merged precipitation dataset and precipitation products for the study area were calculated. Performance evaluations of the merged precipitation dataset and three original precipitation products (IMERG-E, ERA5, CPC) were conducted using meteorological station observation precipitation data from China during the period of 2013 to 2015. The accuracy statistics of the merged precipitation dataset and individual precipitation products are shown below. Figure 3 As shown in the figure, the correlation coefficient (CC) and root mean square error (RMSE) of the merged precipitation are both better than the statistical results of the three precipitation products; the bias (RB) of the merged precipitation is basically consistent with the results of the observational precipitation product CPC, but significantly better than the results of the satellite precipitation product IMERG-E and the reanalysis precipitation product ERA5. These results demonstrate the effectiveness of the method.

[0133] Example 2

[0134] Based on the same inventive concept as in Embodiment 1, this embodiment of the invention provides a near-real-time precipitation fusion device, comprising:

[0135] The acquisition module is configured to acquire mutually independent near-real-time precipitation products;

[0136] The preprocessing module is configured to preprocess each near-real-time precipitation product to give each near-real-time precipitation product a uniform spatiotemporal resolution.

[0137] The initial fused precipitation data acquisition module is configured to use the Triple Collocation method to estimate the error of each near-real-time precipitation product, with the aim of minimizing the error between the fused precipitation data and the real precipitation data. The weight of each near-real-time precipitation product is calculated using the error, and the weighted sum of each near-real-time precipitation product is performed to obtain the initial fused precipitation data.

[0138] The correction module is configured to correct the initial fused precipitation data using a cumulative probability density function matching method to obtain a near-real-time fused precipitation dataset.

[0139] In one specific embodiment of the present invention, the mutually independent near-real-time precipitation products must simultaneously meet the following conditions:

[0140] Condition 1: The data sources for each near-real-time precipitation product are independent of each other;

[0141] Condition 2: Each near-real-time precipitation product includes a near-real-time daily precipitation dataset.

[0142] In practical applications, to meet the requirement of mutual independence, precipitation products with simple data sources and different data types can be selected, such as uncorrected precipitation products based on satellite observations, reanalysis precipitation products based on data assimilation, raster precipitation products generated by interpolation of ground measurement data, and precipitation products based on remote sensing soil water inversion. All four types of precipitation products have mutually independent precipitation datasets. However, currently only the first three types of precipitation products meet the condition of providing long-sequence near-real-time precipitation datasets. Therefore, the following three types of precipitation products are typically selected as mutually independent near-real-time precipitation products for analysis: uncorrected precipitation products based on satellite observations, reanalysis precipitation products based on data assimilation, and raster precipitation products generated by interpolation of ground measurement data.

[0143] In one specific embodiment of the present invention, to facilitate subsequent calculations, the near-real-time precipitation product with uniform spatiotemporal resolution is obtained through the following method:

[0144] Based on the scope of the study area, the near-real-time precipitation products were read, cropped, and outlier interpolated (e.g., by interpolating with neighboring values). The spatiotemporal scale matching of the three precipitation products was performed using bilinear interpolation to ensure that each near-real-time precipitation product had a uniform and appropriate spatiotemporal resolution and was stored in a uniform data format.

[0145] In one specific embodiment of the present invention, the weights of each near-real-time precipitation product are obtained through the following steps:

[0146] (1) Linearity assumption.

[0147] A fundamental assumption in collocation analysis is that independent precipitation products are linearly correlated with actual precipitation variables. This correlation can be represented by a linear model, namely:

[0148] x i =α i +β i t+ε i

[0149] In the formula: x i α is the estimated value of the i-th near-real-time precipitation product; t is the unknown actual precipitation variable; i and β i Let ε represent the ordinary least squares intercept and slope of the i-th near-real-time precipitation product, respectively; i Let be the observation error of the i-th near-real-time precipitation product. The covariance of any two near-real-time precipitation products (including different and identical precipitation products) can be defined by the following formula:

[0150]

[0151] In the formula, C i,j and Cov(x) i ,x j () represents the covariance between the i-th near-real-time precipitation product and the j-th near-real-time precipitation product; The standard deviation represents the actual precipitation signal.

[0152] Based on three mathematical assumptions—namely, the zero cross-correlation assumption based on mutually independent near-real-time precipitation products (including their independent errors), the zero error cross-correlation assumption based on the independence of errors from the true value, and the zero error expectation assumption—the above equation can be simplified to:

[0153]

[0154] (2) Error estimation.

[0155] In the Triple Collocation method, the covariance of every two precipitation products among the three near-real-time precipitation products can be estimated as follows:

[0156]

[0157]

[0158] Using the above equations, the variance of the error between the three precipitation products and the actual precipitation can be calculated as follows:

[0159]

[0160] In the formula, C represents the variance of the error between the corresponding 1st, 2nd, and 3rd precipitation products and the actual precipitation, respectively. 1,1 Let C represent the autocovariance of the first precipitation product. 1,2 C represents the covariance of the first and second precipitation products. 1,3 C represents the covariance of the first and third precipitation products. 2,2 C represents the autocovariance of the second precipitation product. 2,3 C represents the covariance of the second and third precipitation products. 3,3 Let β1, β2, and β3 represent the covariance of the third precipitation product, and β1, β2, and β3 represent the slopes of the first, second, and third precipitation products relative to the actual precipitation, respectively. This represents the standard deviation of actual precipitation.

[0161] (3) Weight estimation.

[0162] Based on the least squares framework, the weight of each near-real-time precipitation product is calculated using the least squares fusion method to obtain the initial fused precipitation data. The formula for calculating the initial fused precipitation data is as follows:

[0163]

[0164] In the formula, P s This is the initial merged precipitation result; w i This represents the weight of the estimated i-th precipitation product.

[0165] The relationship between the variance of the initial fused precipitation data and the error variance of the input precipitation product can be expressed as:

[0166]

[0167] In the formula, It is the variance of the initial fused precipitation data; Let represent the error variance of the i-th input precipitation product.

[0168] The weights are calculated by minimizing the variance of the initial fused precipitation data. Therefore, the equation above is differentiated based on the weights, as shown below:

[0169]

[0170] Therefore, the formula for calculating the weight of each precipitation product is derived as follows:

[0171]

[0172] In the formula, w1, w2, and w3 represent the weights of the 1st, 2nd, and 3rd precipitation products, respectively.

[0173] (4) Rainfall fusion.

[0174] In the absence of real precipitation variables, the initial fusion results of multi-source precipitation products are achieved by using weights and weighted summation of the original precipitation products.

[0175] In one specific embodiment of the present invention, cumulative probability density function matching can correct spurious drizzle and decaying peaks.

[0176] Cumulative probability density function matching is a distribution mapping method. The basic idea is to correct the bias in the initial merged precipitation dataset by matching its cumulative distribution frequency, considering a benchmark dataset, to provide more accurate results. Typically, a Gamma distribution with shape and scale parameters is used to fit two data series and estimate the quantiles of the initial merged precipitation. Then, a transformation of the initial merged precipitation is found based on the quantile-mapped benchmark dataset. This transformation can be expressed as:

[0177]

[0178] In the formula, P cr P represents the near-real-time fused precipitation dataset after cumulative probability density function matching correction.s This indicates the initial fused precipitation data; cdf represents the inverse cumulative distribution function of a baseline dataset, which is data from an observational precipitation product; s This represents the cumulative distribution function estimated based on the initial merged precipitation dataset.

[0179] The following is combined Figure 2 The present invention also provides a specific implementation method, which details the implementation process of the near-real-time precipitation fusion device in the embodiments of the present invention.

[0180] Step 1, selection of near-real-time precipitation products, specifically:

[0181] To ensure the independence of the three near-real-time precipitation products, three data sources were selected: IMERG-E (0.1° spatial resolution and 1-day timescale), ERA5 (0.25° spatial resolution and 1-hour timescale), and CPC (0.5° spatial resolution and 1-day timescale). These data were sourced from NASA, the European Centre for Medium-Range Weather Forecasts (ECMWF) Atmospheric Research Center, and the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Centre, respectively. The IMERG-E precipitation product was derived from remote sensing estimation and was not corrected for by observed data; the ERA5 precipitation product was derived from atmospheric forcing data and data assimilation estimation; and the CPC precipitation product was derived from global surface observation data. Therefore, these three precipitation products are essentially independent of each other.

[0182] Step two involves preprocessing the three near-real-time precipitation products, specifically as follows:

[0183] Based on the scope of the study area, the three precipitation products were read, cropped, and outlier imputed. Then, spatiotemporal scale matching processing was performed on the three precipitation products to give them a uniform and suitable spatiotemporal resolution, namely 0.25° spatial resolution and a 1-day time scale, and they were stored in a unified data format. Specifically, bilinear interpolation was used to resample the IMERG-E and CPC precipitation products (including bilinear interpolation and accumulation calculation), and the 1-hour data of the ERA5 precipitation product was accumulated to the 1-day time scale data, ultimately achieving a spatiotemporal resolution of 0.25° spatial resolution and a 1-day time scale for all three precipitation products.

[0184] Step 3: Generate initial merged precipitation data based on the Triple Collocation method, specifically as follows:

[0185] First, calculate the error between each precipitation product and the unknown actual precipitation, which is:

[0186]

[0187] Then, with the aim of minimizing the error between the fused precipitation data and the actual precipitation data, the weight of each precipitation product is calculated as follows:

[0188]

[0189] Finally, the datasets of each precipitation product are multiplied by their respective weights and summed to obtain the initial merged precipitation data, which is...

[0190]

[0191] Step four involves bias correction of the initial fused precipitation data, specifically as follows:

[0192] Using the observed precipitation product (CPC) as the baseline data, a transformation function between the initial fused precipitation data and the observed precipitation product data is found using the cumulative probability density function matching method, thus obtaining the final fused precipitation data. The transformation function is:

[0193]

[0194] After the above steps, a near real-time fused precipitation dataset with a spatial resolution of 0.25° and a temporal resolution of 1 day can be obtained for the study area.

[0195] Step 5 involves performance evaluation of the acquired near-real-time fused precipitation dataset, specifically as follows:

[0196] First, precipitation data measured by ground meteorological stations in the study area were collected as a reference dataset for evaluating the near-real-time fused precipitation dataset.

[0197] Secondly, the accuracy of the near-real-time fused precipitation dataset was verified using three conventional statistical indicators: correlation coefficient (CC), relative bias (RB), and root mean square error (RMSE).

[0198] The formula for calculating the correlation coefficient is:

[0199]

[0200] The formula for calculating relative deviation is:

[0201]

[0202] The formula for calculating the root mean square error is:

[0203]

[0204] In the formula: S i It is a near real-time fused precipitation dataset, G i These are actual precipitation data measured at the weather station.

[0205] Finally, the accuracy statistics of the merged precipitation dataset and precipitation products for the study area were calculated. Performance evaluations of the merged precipitation dataset and three original precipitation products (IMERG-E, ERA5, CPC) were conducted using meteorological station observation precipitation data from China during the period of 2013 to 2015. The accuracy statistics of the merged precipitation dataset and individual precipitation products are shown below. Figure 3 As shown in the figure, the correlation coefficient (CC) and root mean square error (RMSE) of the merged precipitation are both better than the statistical results of the three precipitation products; the bias (RB) of the merged precipitation is basically consistent with the results of the observational precipitation product CPC, but significantly better than the results of the satellite precipitation product IMERG-E and the reanalysis precipitation product ERA5. These results demonstrate the effectiveness of the method.

[0206] Implementation 3

[0207] This invention provides a near real-time precipitation fusion system, including a storage medium and a processor;

[0208] The storage medium is used to store instructions;

[0209] The processor is configured to operate according to the instructions to perform the steps of the method according to any one of Embodiment 1.

[0210] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A near real-time precipitation fusion method, characterized by, The method comprises the following steps: obtaining independent near real-time precipitation products; preprocessing each near real-time precipitation product to make each near real-time precipitation product have a unified spatio-temporal resolution; using a Triple Collocation method to estimate the error of each near real-time precipitation product, calculating the weight of each near real-time precipitation product by using the error for the purpose of minimizing the error of the fused precipitation data and the real precipitation data, and performing weighted summation on each near real-time precipitation product to obtain initial fused precipitation data; using a cumulative probability density function matching method to correct the initial fused precipitation data to obtain a near real-time fused precipitation data set; the calculation formula of the weight of each near real-time precipitation product is: wherein, wherein w1, w2, w3 represent the weights of the 1st, 2nd, 3rd precipitation products respectively, respectively represent the error variances of the corresponding 1st, 2nd, 3rd precipitation products and the real precipitation, C 1,1 represents the autocovariance of the 1st precipitation product, C 1,2 represents the covariances of the 1st, 2nd precipitation products, C 1,3 represents the covariances of the 1st, 3rd precipitation products, C 2,2 represents the autocovariance of the 2nd precipitation product, C 2,3 represents the covariances of the 2nd, 3rd precipitation products, C 3,3 represents the autocovariance of the 3rd precipitation product, β1, β2, β3 represent the slopes of the 1st, 2nd, 3rd precipitation products and the real precipitation respectively, standard deviation of the true precipitation; the expression of the initial fused precipitation data is: where P s is the initial blended precipitation data; w i represents the weight of the i-th near real-time precipitation product estimate, x i represents the data set of the i-th near real-time precipitation product, k = 1, 2, 3; the expression of the near real-time fused precipitation data set is: where P cr represents the cumulative probability density function matched to the near real-time fused precipitation dataset, P s represents the initial fused precipitation data; represents the inverse cumulative distribution function of the reference dataset, which is data in the observed precipitation product; cdf s represents the cumulative distribution function estimated from the initial fused precipitation dataset.

2. The near real-time precipitation fusion method of claim 1, wherein: each near real-time precipitation product must meet the following conditions: condition 1: the data sources of each near real-time precipitation product are independent of each other; condition 2: each near real-time precipitation product includes a near real-time daily precipitation data set.

3. The near real-time precipitation fusion method of claim 1, wherein: The near real-time precipitation product with a unified spatio-temporal resolution is obtained by the following method: According to the range of the research area, each near real-time precipitation product is read, cropped, and outlier interpolated, and a bilinear interpolation method is used for spatio-temporal scale matching processing of the three precipitation products, so that each near real-time precipitation product has a unified and suitable spatio-temporal resolution, and is stored in a unified data format.

4. A near real-time precipitation fusion apparatus, characterized by, The method comprises the following steps: an acquisition module configured to obtain independent near real-time precipitation products; a preprocessing module configured to preprocess each near real-time precipitation product to make each near real-time precipitation product have a unified spatio-temporal resolution; an initial fused precipitation data obtaining module configured to use a Triple Collocation method to estimate the error of each near real-time precipitation product, calculate the weight of each near real-time precipitation product by using the error for the purpose of minimizing the error of the fused precipitation data and the real precipitation data, and perform weighted summation on each near real-time precipitation product to obtain initial fused precipitation data; a correction module configured to use a cumulative probability density function matching method to correct the initial fused precipitation data to obtain a near real-time fused precipitation data set; the calculation formula of the weight of each near real-time precipitation product is: wherein, where w1, w2, w3 represent the weights of the 1st, 2nd, 3rd precipitation products respectively, respectively represent the error variances of the 1st, 2nd, 3rd precipitation products and the real precipitation, C 1,1 represents the autocovariance of the 1st precipitation product, C 1,2 represents the covariances of the 1st and 2nd precipitation products, C 1,3 represents the covariances of the 1st and 3rd precipitation products, C 2,2 represents the autocovariance of the 2nd precipitation product, C 2,3 represents the covariances of the 2nd and 3rd precipitation products, C 3,3 represents the autocovariance of the 3rd precipitation product, β1, β2, β3 represent the slopes of the 1st, 2nd, 3rd precipitation products and the real precipitation respectively, represents the standard deviation of the real precipitation; the expression of the initial fused precipitation data is: where P s is the initial blended precipitation data; w i represents the weight of the i-th near real-time precipitation product estimate, x i represents the data set of the i-th near real-time precipitation product, k = 1, 2, 3; the expression of the near real-time fused precipitation data set is: where P cr represents the cumulative probability density function matched to the near real-time fused precipitation dataset, P s represents the initial fused precipitation data; represents the inverse cumulative distribution function of the reference dataset, which is data in the observed precipitation product; cdf s represents the cumulative distribution function estimated from the initial fused precipitation dataset.

5. A near real-time precipitation fusion system characterized by: The method comprises the following steps: a storage medium and a processor; the storage medium is used to store instructions; the processor is used to operate according to the instructions to perform the steps of the method according to any one of claims 1-3.

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