Satellite precipitation product improvement method, device and system based on dual-time-scale minimum error

Abstract

The invention discloses a satellite precipitation product improvement method, device and system based on a dual-time scale minimum error, and the method comprises the steps: carrying out the improvement of a first satellite precipitation product, a second satellite precipitation product and an interpolation precipitation product according to the obtained first satellite precipitation product, second satellite precipitation product and interpolation precipitation product; sequentially adopting a dual tool variable algorithm, a least square fusion algorithm and an inverse error weighting algorithm to respectively calculate first fusion rainfall products under a daily scale and a monthly scale; and fusing the first fused precipitation products under the daily scale and the monthly scale to generate a second fused precipitation product. Ground observation data are not needed, daily scale and monthly scale rainfall errors can be minimized at the same time, the thought of data fusion is incorporated, the performance of satellite rainfall products is enhanced, and detailed data support can be provided for natural disaster monitoring and early warning and regional water resource management.

Description

Technical Field

[0001] The present invention belongs to the field of satellite remote sensing precipitation estimation, and in particular relates to a method, device and system for improving satellite precipitation products based on dual-time-scale minimum error. Background Art

[0002] Precipitation is a key component driving the global water cycle and maintaining natural ecosystems. Accurate precipitation data is crucial for deepening our understanding of hydrological processes and climate change. It is also an important factor affecting basin flood forecasting, regional drought monitoring, and crop yield estimation. Traditional rain gauges are the most direct and accurate way to measure precipitation at a point scale. However, the sparse and uneven distribution of rain gauge networks limits their ability to capture the spatiotemporal dynamics of precipitation, posing challenges to surface precipitation estimation in high-altitude mountainous areas, deserts, and other regions, and hindering the development of regional hydrological research.

[0003] Satellite remote sensing offers a transformative alternative for observing precipitation over large areas and at high resolution. The launch of the Global Precipitation Measurement (GPM) mission in 2014 marked significant progress in global precipitation observations, exemplified by the GPM Integrated Multi-Satellite Retrieval (IMERG) precipitation product series. While these satellite precipitation products have been widely used worldwide, numerous assessments have demonstrated that IMERG satellite-only precipitation products often exhibit significant errors, particularly at daily and sub-daily timescales. These errors are primarily attributed to a lack of calibration with ground-based observations.

[0004] To improve the accuracy of purely satellite-based precipitation estimates, some researchers have used interpolated precipitation from global rain gauges as a benchmark to eliminate systematic biases in satellite precipitation errors, such as the IMERG Final and GSMaP-G satellite precipitation products. However, bias corrections for these satellite precipitation products are performed only on daily or monthly timescales. In addition to bias correction, some researchers have employed data fusion techniques to reduce errors in precipitation estimates, enhancing the accuracy of satellite precipitation by leveraging the complementary information from multiple-source precipitation products. Despite this, challenges remain in fully leveraging the advantages of purely satellite remote sensing and interpolated data. Summary of the Invention

[0005] To address the above problems, the present invention proposes a method, device and system for improving satellite precipitation products based on dual-time-scale minimum error. This method, which does not require ground observation data, can simultaneously minimize precipitation errors on both daily and monthly scales. It incorporates the idea of ​​data fusion to enhance the performance of satellite remote sensing precipitation estimation, and can provide detailed data support for natural disaster monitoring and early warning and regional water resources management.

[0006] In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

[0007] In a first aspect, the present invention provides a method for improving satellite precipitation products based on dual-time-scale minimum error, comprising:

[0008] For the first satellite precipitation product, second satellite precipitation product and interpolated precipitation product, the dual instrumental variable algorithm, least squares fusion algorithm and inverse error weighting algorithm are used in sequence to calculate the first fused precipitation product at the daily and monthly scales respectively.

[0009] The first fused precipitation products at the daily scale and the monthly scale are fused to generate a second fused precipitation product.

[0010] In conjunction with the first aspect, optionally, the calculation method of the first fused precipitation product at the daily and monthly scales includes:

[0011] Perform spatial scale interpolation on the first satellite precipitation product, second satellite precipitation product, and interpolated precipitation product obtained at the daily scale to achieve spatial scale unification;

[0012] The interpolated precipitation products are accumulated to obtain the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product at the monthly scale;

[0013] The dual instrumental variable algorithm is used to estimate the error variance of the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product relative to the unknown true precipitation at the daily and monthly scales.

[0014] Based on the error variances at the daily and monthly scales, the least squares fusion algorithm is used to obtain the initial fused precipitation products at the daily and monthly scales respectively;

[0015] Based on the initial fused precipitation products at the daily scale and the monthly scale, the inverse error weighted algorithm is used to obtain the first fused precipitation products at the daily scale and the monthly scale, respectively.

[0016] In combination with the first aspect, optionally, the applying of a dual instrumental variable algorithm to respectively estimate the error variances of the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product relative to the unknown true precipitation at daily and monthly scales specifically includes:

[0017] Assuming the same time scale of satellite precipitation products , interpolated precipitation products Unknown true precipitation There is a linear correlation, and the mathematical expression of the linear correlation is:

[0018] (1),

[0019] Where, and Represents satellite precipitation products Unknown true precipitation The ordinary least squares slope between and a constant, Represents satellite precipitation products Random error; and Represent the interpolated precipitation products Unknown true precipitation The ordinary least squares slope between and a constant, Represents the interpolated precipitation product Random error;

[0020] Based on the linear correlation, the satellite precipitation product is calculated and interpolated precipitation products The covariance of , the calculation formula of the covariance is:

[0021] (2),

[0022] Where, Satellite precipitation products and interpolated precipitation products The covariance of represents the covariance calculation function, Unknown true precipitation The standard deviation of

[0023] According to the zero cross-correlation assumption and the unknown true precipitation The zero error cross-correlation assumption and the zero error expectation assumption of , simplify formula (2) to the following formula:

[0024] (3);

[0025] Will and As satellite precipitation products and interpolated precipitation products The estimation of the lagged series of There is a linear correlation, that is and , where Unknown true precipitation The lagged series of Satellite precipitation products The random error of the lagged series, Interpolated precipitation product Random errors of the lagged series;

[0026] Satellite precipitation products lagged series, interpolated precipitation products The lagged series and the unknown true precipitation There are still zero cross-correlation assumptions, zero error cross-correlation assumptions, and zero error expectation assumptions. Therefore, satellite precipitation products , interpolated precipitation products The covariance between the two lagged series can be written as:

[0027] (4),

[0028] (5),

[0029] (6),

[0030] (7),

[0031] (8),

[0032] Where, Represents satellite precipitation products The variance of Represents the interpolated precipitation product The variance of Represents satellite precipitation products and interpolated precipitation products The covariance of Represents satellite precipitation products and its lagged series The covariance of Represents the interpolated precipitation product and its lagged series The covariance of Indicates unknown true precipitation The variance of the lagged series of Satellite precipitation products Relatively unknown true precipitation The error variance, Interpolated precipitation product Relatively unknown true precipitation The error variance, Unknown true precipitation variance;

[0033] Calculating satellite precipitation products and interpolated precipitation products The scaling ratio is calculated as follows:

[0034] (9),

[0035] Where, is the scaling ratio;

[0036] Combining formula (4) to formula (9), in the absence of real precipitation, the satellite precipitation product is solved and interpolated precipitation products Relatively unknown true precipitation The error variance is calculated as follows:

[0037] (10).

[0038] In combination with the first aspect, optionally, the obtaining of initial fused precipitation products at the daily scale and the monthly scale using a least squares fusion algorithm based on the error variance at the daily scale and the monthly scale, respectively, includes:

[0039] Calculation of satellite precipitation products using a fusion framework based on the least squares method and interpolated precipitation products The fusion weight is calculated as follows:

[0040] (11),

[0041] Where, Satellite precipitation products The fusion weight of Interpolated precipitation product The fusion weight of

[0042] The initial fused precipitation product is calculated based on the fusion weights. The calculation formula for the initial fused precipitation product is:

[0043] (12),

[0044] Where, is the initial fused precipitation product.

[0045] In combination with the first aspect, optionally, the obtaining of first fused precipitation products at the daily scale and the monthly scale by respectively applying an inverse error weighted algorithm based on the initial fused precipitation products at the daily scale and the monthly scale includes:

[0046] The inverse error weighting method is used to integrate the first initial fused precipitation product and the second initial fused precipitation product according to their errors, so as to obtain the first fused precipitation product at the daily scale and the first fused precipitation product at the monthly scale, respectively. The first initial fused precipitation product is obtained based on the first satellite precipitation product and the interpolated precipitation product, and the second initial fused precipitation product is obtained based on the second satellite precipitation product and the interpolated precipitation product.

[0047] In combination with the first aspect, optionally, the calculation formula of the first fused precipitation product at the daily scale or the monthly scale is:

[0048] (16),

[0049] (17),

[0050] (18),

[0051] Where, It is the first fused precipitation product at the daily or monthly scale. is the first initial fused precipitation product on a daily or monthly scale. is the second initial fused precipitation product on a daily or monthly scale. and The first initial fused precipitation product at the daily or monthly scale is and the second initial fused precipitation product The weight of .

[0052] In combination with the first aspect, optionally, the method for generating the second fused precipitation product includes:

[0053] The first fused precipitation product at the monthly scale is linearly scaled to the first fused precipitation product at the daily scale to generate the second fused precipitation product.

[0054] In combination with the first aspect, optionally, when performing spatial scale interpolation, the interpolation method used is a bilinear interpolation method.

[0055] In a second aspect, the present invention provides a device for improving satellite precipitation products based on dual-time-scale minimum error, comprising:

[0056] The first fusion module is used to calculate the first fused precipitation product at the daily and monthly scales using the dual instrumental variable algorithm, the least squares fusion algorithm, and the inverse error weighted algorithm based on the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product.

[0057] The second fusion module is used to fuse the first fused precipitation products at the daily scale and the monthly scale to generate a second fused precipitation product.

[0058] In a third aspect, the present invention provides a satellite precipitation product improvement system based on dual-time-scale minimum error, comprising a storage medium and a processor;

[0059] The storage medium is used to store instructions;

[0060] The processor is configured to operate according to the instructions to execute the method according to any one of the first aspects.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] The present invention proposes a method, device and system for improving satellite precipitation products based on dual-time-scale minimum error. Without requiring ground observation data, the method can simultaneously minimize precipitation errors on both daily and monthly scales. By incorporating the concept of data fusion, the performance of satellite remote sensing precipitation estimation is enhanced, providing detailed data support for natural disaster monitoring and early warning, as well as regional water resources management. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive work, among which:

[0064] Figure 1 A schematic flow chart of a method for improving satellite precipitation products based on dual-time-scale minimum error according to an embodiment of the present invention;

[0065] Figure 2 A histogram comparing the regional average correlation coefficients of the fused precipitation, satellite precipitation products, and daily interpolated precipitation obtained in one embodiment of the present invention with the precipitation observed at the rain gauge station on a daily scale;

[0066] Figure 3 A histogram comparing the regional average root mean square error of the fused precipitation, satellite precipitation products, and daily interpolated precipitation obtained in one embodiment of the present invention with the precipitation observed at the rain gauge on a daily scale;

[0067] Figure 4 A histogram comparing the regional average key success index of the daily scale of the fused precipitation, each satellite precipitation product, and daily interpolated precipitation obtained in one embodiment of the present invention with the precipitation observed at the rain gauge station;

[0068] Figure 5 This is a numerical diagram of the regional average correlation coefficient and root mean square error of the fused precipitation, satellite precipitation products, and daily interpolated precipitation obtained in one embodiment of the present invention and the precipitation observed at the rain gauge on a monthly scale. DETAILED DESCRIPTION

[0069] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0070] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features specified as "first" and "second" may explicitly or implicitly include at least one of such features. In addition, the technical solutions between the various embodiments can be combined with each other, but this must be based on the fact that ordinary technicians in this field can implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0071] Example 1

[0072] An embodiment of the present invention provides a method for improving satellite precipitation products based on dual-time-scale minimum error, comprising the following steps:

[0073] (1) For the first satellite precipitation product, the second satellite precipitation product and the interpolated precipitation product, the dual instrumental variable algorithm, the least squares fusion algorithm and the inverse error weighting algorithm are used in sequence to calculate the first fused precipitation product at the daily scale and the monthly scale respectively;

[0074] (2) Fusing the first fused precipitation products at the daily scale and the monthly scale to generate a second fused precipitation product.

[0075] The improved method for satellite precipitation products based on dual-time-scale minimum error in the embodiment of the present invention does not require ground observation data, can simultaneously minimize precipitation errors on both daily and monthly scales, incorporates the idea of ​​data fusion, enhances the performance of satellite remote sensing precipitation estimation, and can provide detailed data support for natural disaster monitoring and early warning and regional water resources management.

[0076] In a specific implementation of the embodiment of the present invention, the calculation method of the first fused precipitation product at the daily and monthly scales includes:

[0077] Perform spatial scale interpolation on the first satellite precipitation product, second satellite precipitation product, and interpolated precipitation product obtained at the daily scale to unify the spatial resolution of precipitation products for subsequent calculations;

[0078] The interpolated precipitation products are accumulated to obtain the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product at the monthly scale;

[0079] The dual instrumental variable algorithm is used to estimate the daily and monthly error variances of the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product relative to the unknown true precipitation. The dual instrumental variable algorithm can estimate the error variances of the satellite precipitation product and the interpolated precipitation product without requiring station data and can be used for statistical analysis of precipitation product uncertainty in any region.

[0080] Based on the error variance at the daily and monthly scales, the least squares fusion algorithm is used to obtain the initial fused precipitation products at the daily and monthly scales respectively; the least squares method achieves data fusion of the two precipitation products by minimizing the error;

[0081] Based on the initial fused precipitation products at the daily and monthly scales, the inverse error weighted algorithm is used to obtain the first fused precipitation products at the daily and monthly scales respectively; the data integration of the two initial fused precipitation products is realized through the inverse error weighted algorithm, overcoming the difficulty of the IVd method in fusing data of only two precipitation products.

[0082] In a specific implementation of the embodiment of the present invention, the dual instrumental variable algorithm is applied based on the interpolated precipitation product to estimate the error variance of the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product relative to the unknown true precipitation at the daily scale and the monthly scale, specifically including:

[0083] Assuming the same time scale of satellite precipitation products , interpolated precipitation products Unknown true precipitation There is a linear correlation, and the mathematical expression of the linear correlation is:

[0084] (1);

[0085] Where, and Satellite precipitation products Unknown true precipitation The ordinary least squares slope between and a constant, Represents satellite precipitation products Random error; and Represent the interpolated precipitation products Unknown true precipitation The ordinary least squares slope between and a constant, Represents the interpolated precipitation product Random error;

[0086] Based on the linear correlation, the satellite precipitation product is calculated and interpolated precipitation products The covariance of , the calculation formula of the covariance is:

[0087] (2);

[0088] Where, Satellite precipitation products and interpolated precipitation products The covariance of represents the covariance calculation function, Unknown true precipitation The standard deviation of

[0089] According to the zero cross-correlation assumption and the unknown true precipitation The zero error cross-correlation assumption and the zero error expectation assumption can simplify formula (2) to the following formula:

[0090] (3);

[0091] Will and As satellite precipitation products and interpolated precipitation products The estimation of the lagged series of There is a linear correlation, that is and , where Unknown true precipitation The lagged series of Satellite precipitation products The random error of the lagged series, Interpolated precipitation product Random errors of the lagged series;

[0092] Satellite precipitation products lagged series, interpolated precipitation products The lagged series and the unknown true precipitation There are still zero cross-correlation assumptions, zero error cross-correlation assumptions, and zero error expectation assumptions. Therefore, satellite precipitation products , interpolated precipitation products The covariance between the two lagged series can be written as:

[0093] (4);

[0094] (5);

[0095] (6);

[0096] (7);

[0097] (8);

[0098] Where, Represents satellite precipitation products The variance of Represents the interpolated precipitation product The variance of Represents satellite precipitation products and interpolated precipitation products The covariance of Represents satellite precipitation products and its lagged series The covariance of Represents the interpolated precipitation product and its lagged series The covariance of Indicates unknown true precipitation The variance of the lagged series of Satellite precipitation products Relatively unknown true precipitation The error variance, Interpolated precipitation product Relatively unknown true precipitation The error variance, Unknown true precipitation variance;

[0099] Calculating satellite precipitation products and interpolated precipitation products The scaling ratio is calculated as follows:

[0100] (9);

[0101] Where, is the scaling ratio;

[0102] Combining formula (4) to formula (9), in the absence of real precipitation, the satellite precipitation product is solved and interpolated precipitation products Relatively unknown true precipitation The error variance is calculated as follows:

[0103] (10).

[0104] In the specific implementation process, satellite precipitation products are calculated based on precipitation product data at daily and monthly scales. and interpolated precipitation products Relatively unknown true precipitation Since the satellite precipitation product in the present invention includes a first satellite precipitation product and a second satellite precipitation product, the error variance of the first satellite precipitation product and the interpolated precipitation product relative to the unknown true precipitation can be calculated, as can the error variance of the second satellite precipitation product and the interpolated precipitation product relative to the unknown true precipitation.

[0105] In a specific implementation of the embodiment of the present invention, the obtaining of initial fused precipitation products at the daily scale and the monthly scale using a least squares fusion algorithm based on the error variance at the daily scale and the monthly scale, respectively, includes:

[0106] Calculation of satellite precipitation products using a fusion framework based on the least squares method and interpolated precipitation products The fusion weight is calculated as follows:

[0107] ,

[0108] Where, Satellite precipitation products The fusion weight of Interpolated precipitation product The fusion weight of

[0109] The initial fused precipitation product is calculated based on the fusion weights. The calculation formula for the initial fused precipitation product is:

[0110] ,

[0111] Where, In a specific implementation, a first initial fused precipitation product can be obtained based on the first satellite precipitation product and the interpolated precipitation product, and a second initial fused precipitation product can be obtained based on the second satellite precipitation product and the interpolated precipitation product.

[0112] In a specific implementation of the embodiment of the present invention, the first fused precipitation products at the daily scale and the monthly scale are obtained by respectively applying an inverse error weighted algorithm based on the initial fused precipitation products at the daily scale and the monthly scale, including:

[0113] The inverse error weighting method is used to integrate the first initial fused precipitation product and the second initial fused precipitation product according to their errors, so as to obtain the first fused precipitation product at the daily scale and the first fused precipitation product at the monthly scale, respectively. The first initial fused precipitation product is obtained based on the first satellite precipitation product and the interpolated precipitation product, and the second initial fused precipitation product is obtained based on the second satellite precipitation product and the interpolated precipitation product.

[0114] In a specific implementation of the embodiment of the present invention, the calculation formula of the first fused precipitation product at the daily or monthly scale is:

[0115] (15);

[0116] (16);

[0117] (17);

[0118] Where, It is the first fused precipitation product on daily or monthly scale. is the first initial fused precipitation product, is the second initial fused precipitation product, and The first initial fused precipitation product and the second initial fused precipitation product The weight of .

[0119] In a specific implementation of the embodiment of the present invention, the method for generating the second fused precipitation product includes:

[0120] The first fused precipitation product at the monthly scale is linearly scaled to the first fused precipitation product at the daily scale to generate the second fused precipitation product. Based on this step, the daily and monthly fused precipitation products obtained by minimizing the error are integrated to minimize the error of the second fused precipitation product relative to the unknown true precipitation at both time scales.

[0121] In a specific implementation of the embodiment of the present invention, when performing spatial interpolation, the interpolation method used is a bilinear interpolation method.

[0122] The application principle of the present invention is described in detail below with reference to specific embodiments.

[0123] refer to Figure 1In an embodiment of the present invention, a method for improving satellite precipitation products based on dual-time-scale minimum error is disclosed, comprising the following steps: first, collecting and preprocessing two satellite precipitation products and an interpolated precipitation product to obtain precipitation data with uniform spatial resolution at daily and monthly scales; second, using the IVd (double instrumental variable) method to sequentially estimate the error variance of two pairs of input precipitation product groups (one satellite precipitation product and the interpolated precipitation product, the other satellite precipitation product and the interpolated precipitation product) relative to the unknown true precipitation at the daily scale; third, based on the error variance obtained in step 2, using the least squares method to minimize the error, respectively fuse the single satellite precipitation product and the interpolated precipitation product to obtain the initial fused precipitation products at two daily scales; fourth, using the inverse error weighting method to integrate the two initial fused precipitation products to generate a daily fused precipitation product; fifth, repeating the second to fourth calculation processes at the monthly scale to generate a monthly fused precipitation product; sixth, using the linear scaling method to distribute the monthly fused precipitation to the daily fused precipitation, thereby improving the accuracy of satellite remote sensing precipitation estimation through data fusion. For details of the specific process, see Figure 1 .

[0124] The technical solution of the present invention is further described in detail below through embodiments and in conjunction with the accompanying drawings:

[0125] Step 1: collect and preprocess two satellite precipitation products and one interpolated precipitation product;

[0126] This example collects two satellite precipitation products, GPM IMERG Early (IMERG-E) and GPM IMERG Late (IMERG-L), along with an interpolated precipitation product, from 2001 to 2019 over the Qinghai-Tibet Plateau. Bilinear interpolation is used to ensure that these three precipitation products have daily and monthly data at the same spatial resolution, facilitating subsequent calculations. This example uses a uniform spatial resolution of 0.1°.

[0127] Step 2: Use the dual instrumental variable algorithm to estimate the error variance of the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product relative to the unknown true precipitation at the daily and monthly scales. The details of this step are as follows:

[0128] Assuming the same time scale of satellite precipitation products , interpolated precipitation products Unknown true precipitation There is a linear correlation. The mathematical expression of the linear correlation is:

[0129] (1)

[0130] Where, and Satellite precipitation products Unknown true precipitation The ordinary least squares slope between and a constant, Represents satellite precipitation products Random error; and Represent the interpolated precipitation products Unknown true precipitation The ordinary least squares slope between and a constant, Represents the interpolated precipitation product Random error;

[0131] Based on the linear correlation, the satellite precipitation product is calculated and interpolated precipitation products The covariance of , the calculation formula of the covariance is:

[0132] (2)

[0133] Where, Satellite precipitation products and interpolated precipitation products The covariance of represents the covariance calculation function, Unknown true precipitation The standard deviation of

[0134] According to the zero cross-correlation assumption and the unknown true precipitation The zero error cross-correlation assumption and the zero error expectation assumption of , formula (2) is simplified to the following formula:

[0135] (3)

[0136] Two lagged series (e.g., lag-1 series, which means a lagged series determined by 1 day) are obtained from two precipitation products. For illustration, I and J are satellite precipitation products, respectively. and interpolated precipitation products The estimated lagged series of There is a linear correlation, that is and Similarly, satellite precipitation products , interpolated precipitation products The lagged series and the unknown true precipitation There are still zero cross-correlation assumptions, zero error cross-correlation assumptions, and zero error expectation assumptions. Therefore, satellite precipitation products , interpolated precipitation products The covariance between the two lagged series can be written as:

[0137] (4)

[0138] (5)

[0139] (6)

[0140] (7)

[0141] (8)

[0142] Where, Represents satellite precipitation products The variance of Represents the interpolated precipitation product The variance of Represents satellite precipitation products and interpolated precipitation products The covariance of Represents satellite precipitation products and its lagged series The covariance of Represents the interpolated precipitation product and its lagged series The covariance of Indicates unknown true precipitation The variance of the lagged series of Satellite precipitation products Relatively unknown true precipitation The error variance, Interpolated precipitation product Relatively unknown true precipitation The error variance, Unknown true precipitation The variance of .

[0143] Calculating satellite precipitation products and interpolated precipitation products The scaling ratio is calculated as follows:

[0144] (9)

[0145] Combining formula (4) to formula (9), in the absence of real precipitation, the satellite precipitation product is solved and interpolated precipitation products Relatively unknown true precipitation The error variance is calculated as follows:

[0146] (10)

[0147] Step 3: Based on the error variances at the daily and monthly scales, the least squares fusion algorithm is used to obtain the initial fused precipitation products at the daily and monthly scales respectively;

[0148] The fusion framework based on the least squares method first calculates the weights of the satellite precipitation product x and the interpolated precipitation product y, and then obtains the initial fused precipitation product. The calculation formula of the initial fused precipitation product is:

[0149] (11)

[0150] Where, Satellite precipitation products The fusion weight of Interpolated precipitation product The fusion weight of .

[0151] Combined with the zero cross-correlation assumption, satellite precipitation products and interpolated precipitation products The relationship between the error variances can be expressed as:

[0152] (12)

[0153] To minimize , using weights and Differentiate equation (12), that is:

[0154] (13)

[0155] According to equation (13), the fusion weight of the x and y precipitation products is:

[0156] (14)

[0157] Step 4: Based on the initial fused precipitation products at the daily and monthly scales, an inverse error weighted algorithm is used to obtain the first fused precipitation products at the daily and monthly scales;

[0158] After determining the fusion weights, the error of the initial fused precipitation product is calculated using equation (12): . Using the inverse error weighting method, based on the error of the first initial fused precipitation product and the error of the second initial fused precipitation product, the first initial fused precipitation product and the second initial fused precipitation product are integrated, and the first fused precipitation product at the daily scale and the monthly scale is obtained, wherein the first initial fused precipitation product is obtained based on the first satellite precipitation product and the interpolated precipitation product, and the second initial fused precipitation product is obtained based on the second satellite precipitation product and the interpolated precipitation product. The calculation formula of the first fused precipitation product at the daily scale or the monthly scale is:

[0159] (15)

[0160] (16)

[0161] (17)

[0162] In the formula, in the formula, It is the first fused precipitation product at the daily or monthly scale. is the first initial fused precipitation product on a daily or monthly scale. is the second initial fused precipitation product on a daily or monthly scale. and The first initial fused precipitation product at the daily or monthly scale is and the second initial fused precipitation product The weight of .

[0163] Step 5: Linearly scale the first fused precipitation product at the monthly scale to the first fused precipitation product at the daily scale to generate the second fused precipitation product (i.e., use the linear scaling method to assign the first fused precipitation product at the monthly scale to the first fused precipitation product at the daily scale, and improve the accuracy of satellite remote sensing precipitation estimation through data fusion). The temporal and spatial resolution is 0.1° / 1 day.

[0164] This example also collects the GPM IMERG Final (IMERG-F) satellite precipitation product for the Qinghai-Tibet Plateau from 2001 to 2019. This product is generated by NASA using the GPCC interpolated precipitation product and performing bias correction on a monthly scale. In this example, the IMERG-F satellite precipitation product is used to demonstrate the effectiveness of the satellite precipitation product improvement method in this example. Using independent observation data from 119 rainfall stations and correlation coefficients, root mean square errors, and key success indices, the accuracy of IMERG-E, IMERG-L, CPC, fused precipitation, and IMERG-F was evaluated on daily and monthly scales. Figures 2 to 5The results show that the fused precipitation product not only outperforms the IMERG-E, IMERG-L, and CPC precipitation products, but also outperforms the official corrected IMERG-F satellite precipitation product. These results confirm the effectiveness of the satellite precipitation product improvement method in this example.

[0165] Example 2

[0166] An embodiment of the present invention provides a device for improving satellite precipitation products based on dual-time-scale minimum error, comprising:

[0167] The first fusion module is used to calculate the first fused precipitation product at the daily and monthly scales using the dual instrumental variable algorithm, the least squares fusion algorithm, and the inverse error weighted algorithm based on the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product.

[0168] The second fusion module is used to fuse the first fused precipitation products at the daily scale and the monthly scale to generate a second fused precipitation product.

[0169] The rest are the same as in Example 1.

[0170] Example 2

[0171] Based on the same inventive concept as that of Example 1, an embodiment of the present invention provides a satellite precipitation product improvement system based on dual-time-scale minimum error, including a storage medium and a processor;

[0172] The storage medium is used to store instructions;

[0173] The processor is configured to operate according to the instructions to perform the method according to any one of the embodiments 1.

[0174] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0175] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0176] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0177] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0178] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which are all protected by the present invention.

[0179] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for improving satellite precipitation products based on dual-time-scale minimum error, characterized in that: include: For the first satellite precipitation product, second satellite precipitation product and interpolated precipitation product, the dual instrumental variable algorithm, least squares fusion algorithm and inverse error weighting algorithm are used in sequence to calculate the first fused precipitation product at the daily and monthly scales respectively. The first fused precipitation products at the daily scale and the monthly scale are fused to generate a second fused precipitation product.

2. The method for improving satellite precipitation products based on dual-time-scale minimum error according to claim 1, characterized in that: The calculation method of the first fused precipitation product at the daily and monthly scales includes: Perform spatial scale interpolation on the first satellite precipitation product, second satellite precipitation product, and interpolated precipitation product obtained at the daily scale to achieve spatial scale unification; The interpolated precipitation products are accumulated to obtain the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product at the monthly scale; The dual instrumental variable algorithm is used to estimate the error variance of the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product relative to the unknown true precipitation at the daily and monthly scales. Based on the error variances at the daily and monthly scales, the least squares fusion algorithm is used to obtain the initial fused precipitation products at the daily and monthly scales respectively; Based on the initial fused precipitation products at the daily scale and the monthly scale, the inverse error weighted algorithm is used to obtain the first fused precipitation products at the daily scale and the monthly scale, respectively.

3. The method for improving satellite precipitation products based on dual-time-scale minimum error according to claim 2, characterized in that: The dual instrumental variable algorithm is used to estimate the error variances of the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product relative to the unknown true precipitation at the daily and monthly scales, respectively. Specifically, the method includes: Assuming the same time scale of satellite precipitation products , interpolated precipitation products Unknown true precipitation There is a linear correlation, and the mathematical expression of the linear correlation is: （1）， Where, and Satellite precipitation products Unknown true precipitation The ordinary least squares slope between and a constant, Represents satellite precipitation products Random error; and Represent the interpolated precipitation products Unknown true precipitation The ordinary least squares slope between and a constant, Represents the interpolated precipitation product Random error; Based on the linear correlation, the satellite precipitation product is calculated and interpolated precipitation products The covariance of , the calculation formula of the covariance is: （2）， Where, Satellite precipitation products and interpolated precipitation products The covariance of represents the covariance calculation function, Unknown true precipitation The standard deviation of According to the zero cross-correlation assumption and the unknown true precipitation The zero error cross-correlation assumption and the zero error expectation assumption of , formula (2) is simplified to the following formula: （3）； Will and As satellite precipitation products and interpolated precipitation products The estimation of the lagged series of There is a linear correlation, that is and , where Unknown true precipitation The lagged series of Satellite precipitation products The random error of the lagged series, Interpolated precipitation product Random errors of the lagged series; Satellite precipitation products lagged series, interpolated precipitation products The lagged series and the unknown true precipitation There are still zero cross-correlation assumptions, zero error cross-correlation assumptions, and zero error expectation assumptions. Therefore, satellite precipitation products , interpolated precipitation products The covariance between the two lagged series can be written as: （4）， （5）， （6）， （7）， （8）， Where, Represents satellite precipitation products The variance of Represents the interpolated precipitation product The variance of Represents satellite precipitation products and interpolated precipitation products The covariance of Represents satellite precipitation products and its lagged series The covariance of Represents the interpolated precipitation product and its lagged series The covariance of Indicates unknown true precipitation The variance of the lagged series, Satellite precipitation products Relatively unknown true precipitation The error variance, Interpolated precipitation product Relatively unknown true precipitation The error variance, Unknown true precipitation variance; Calculating satellite precipitation products and interpolated precipitation products The scaling ratio is calculated as follows: （9）， Where, is the scaling ratio; Combining formula (4) to formula (9), in the absence of real precipitation, the satellite precipitation product is solved and interpolated precipitation products Relatively unknown true precipitation The error variance is calculated as follows: （10）。 4. The method for improving satellite precipitation products based on dual-time-scale minimum error according to claim 3, characterized in that: The least squares fusion algorithm is used to obtain the initial fused precipitation products at the daily scale and the monthly scale based on the error variance at the daily scale and the monthly scale, respectively, including: Calculation of satellite precipitation products using a fusion framework based on the least squares method and interpolated precipitation products The fusion weight is calculated as follows: （11）， Where, Satellite precipitation products The fusion weight of Interpolated precipitation product The fusion weight of The initial fused precipitation product is calculated based on the fusion weights. The calculation formula for the initial fused precipitation product is: （12）， Where, is the initial fused precipitation product.

5. The method for improving satellite precipitation products based on dual-time-scale minimum error according to claim 2 or 4, characterized in that: The first fused precipitation products at the daily scale and the monthly scale are obtained by respectively applying an inverse error weighted algorithm based on the initial fused precipitation products at the daily scale and the monthly scale, including: The inverse error weighting method is used to integrate the first initial fused precipitation product and the second initial fused precipitation product according to their errors, so as to obtain the first fused precipitation product at the daily scale and the first fused precipitation product at the monthly scale, respectively. The first initial fused precipitation product is obtained based on the first satellite precipitation product and the interpolated precipitation product, and the second initial fused precipitation product is obtained based on the second satellite precipitation product and the interpolated precipitation product.

6. The method for improving satellite precipitation products based on dual-time-scale minimum error according to claim 5, characterized in that: The calculation formula for the first fused precipitation product on a daily or monthly scale is: （16）， （17）， （18）， Where, It is the first fused precipitation product at the daily or monthly scale. is the first initial fused precipitation product on a daily or monthly scale. is the second initial fused precipitation product on a daily or monthly scale. and The first initial fused precipitation product at the daily or monthly scale is and the second initial fused precipitation product The weight of .

7. The method for improving satellite precipitation products based on dual-time-scale minimum error according to claim 2, characterized in that: The method for generating the second fused precipitation product includes: The first fused precipitation product at the monthly scale is linearly scaled to the first fused precipitation product at the daily scale to generate the second fused precipitation product.

8. The method for improving satellite precipitation products based on dual-time-scale minimum error according to claim 2, characterized in that: When performing spatial scale interpolation, the interpolation method used is the bilinear interpolation method.

9. A satellite precipitation product improvement device based on dual time scale minimum error, characterized in that: include: The first fusion module is used to calculate the first fused precipitation product at the daily and monthly scales using the dual instrumental variable algorithm, the least squares fusion algorithm, and the inverse error weighted algorithm based on the first satellite precipitation product, the second satellite precipitation product, and the interpolated precipitation product. The second fusion module is used to fuse the first fused precipitation products at the daily scale and the monthly scale to generate a second fused precipitation product.

10. A satellite precipitation product improvement system based on dual time scale minimum error, characterized by: including storage media and processors; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the method according to any one of claims 1-8.

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