A method for precipitation error component decomposition without ground reference value

Abstract

The application discloses a precipitation error component decomposition method without ground reference value, relates to the technical field of hydrology and meteorology, and comprises the following steps: obtaining three independent precipitation products of a target region, and unifying the three independent precipitation products into 0.1° space and 1-hour time resolution; classifying variable fusion algorithm is used to split the three independent precipitation products into hit and false precipitation data; then, the generalized triangular cap method is used to calculate total root mean square error of the precipitation products, root mean square error of the hit precipitation data, and directly calculate root mean square error of the false precipitation data; finally, the error propagation law is used to derive root mean square error of the missed precipitation data, so that the error component of the regional precipitation product without ground observation data is fully decomposed and traced. The application is free of ground reference value dependence, can accurately depict the space-time characteristics of precipitation error, provides technical support for error correction and application of satellite and reanalysis precipitation products in a data-deficient region, and solves the problem that traditional methods depend on ground observation data and cannot split precipitation error components in a data-deficient region.

Description

Technical Field

[0001] This invention relates to the field of hydrological and meteorological experimental equipment technology, and in particular to a method for decomposing precipitation error components without the need for ground reference values. Background Technology

[0002] Satellite precipitation products and reanalysis precipitation products provide crucial data support for hydrological simulation, weather forecasting, and climate research in areas lacking surface precipitation data, such as oceans and remote mountainous regions. Before practical application, these precipitation products require refined error interpretation and component decomposition to clarify their error types, magnitudes, and sources, in order to maximize data effectiveness.

[0003] Traditional methods for interpreting precipitation errors heavily rely on surface precipitation observation data as a reference. By comparing the deviations between precipitation products and surface observation data, various error indices are calculated and error components are decomposed to trace the source of errors. However, due to the limitations of the distribution of surface observation stations, most areas of the world (especially oceans, deserts, and plateaus) lack reliable surface precipitation observation data. This makes it impossible for traditional methods to decompose the error components of precipitation products in these data-scarce areas, making it difficult to understand the error characteristics and sources of precipitation products in these regions. This severely limits the depth and breadth of the application of precipitation products.

[0004] To address the problem of interpreting precipitation errors in data-scarce regions, scholars both domestically and internationally have explored the application of the Triple Combination Analysis (TC) method and the generalized triangular hat method. These methods can estimate the total root mean square error (RMSE) of precipitation products without the need for ground reference values. However, they can only obtain the quantitative result of the total RMSE and cannot further decompose the total RMSE into the three core components: the RMSE of the hit precipitation data, the RMSE of the falsely reported precipitation data, and the RMSE of the missed precipitation data. This makes it difficult to achieve accurate error tracing and still cannot meet the need for refined interpretation of precipitation product errors in data-scarce regions.

[0005] Therefore, there is an urgent need to develop a method that can achieve full component decomposition and error source tracing of precipitation errors without ground reference values, to make up for the deficiencies of existing technologies, and to provide technical support for the effective application of precipitation products in areas with scarce data. Summary of the Invention

[0006] This invention provides a method for decomposing precipitation error components without ground reference values. By combining a categorical variable fusion algorithm with the generalized triangular hat method, the total root mean square error of precipitation products is decomposed into three error components in the absence of ground precipitation observation data: root mean square error of hit precipitation data, root mean square error of falsely reported precipitation data, and root mean square error of missed precipitation data. This enables error component decomposition and accurate error source tracing of precipitation products in areas with missing data.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] This invention provides a method for decomposing precipitation error components without the need for ground reference values, comprising:

[0009] S1: Obtain three independent precipitation products for the target area and unify the spatiotemporal resolution of the precipitation products;

[0010] S2: Using a categorical variable fusion algorithm, without needing ground precipitation data as a reference value, the precipitation product is split into two parts: hit precipitation data and false alarm precipitation data.

[0011] S3: Calculate the total root mean square error of the precipitation product, the root mean square error of the hit precipitation data, and the root mean square error of the false alarm precipitation data using the generalized triangular hat method.

[0012] S4: Based on the error propagation law, the root mean square error of missed precipitation is derived from the total root mean square error, the root mean square error of the hit precipitation data, and the root mean square error of the false precipitation data.

[0013] Furthermore, the spatiotemporal resolution is uniformly set to 0.1° spatial resolution and 1 hour temporal resolution.

[0014] Furthermore, S2 specifically includes:

[0015] Based on the principle of categorical variable fusion algorithm, each precipitation product is converted into a binary time series of rainfall / no rainfall, with a rainfall occurrence flag incremented by 1 and a no rainfall occurrence flag decremented by 1. Three independent sets of rainfall / no rainfall categorical time series are defined as follows: , , Their covariance can be obtained by the following formula:

[0016] (1)

[0017] (2)

[0018] (3)

[0019] Where Q is the covariance of the binary time series with different rainfall / no rainfall conditions; P is the true value of the binary time series with rainfall / no rainfall conditions. A function of the statistical properties of P; To improve the accuracy of rainfall / no rainfall classification for different precipitation products;

[0020] Based on equations (1) to (3), the statistical measure v that is positively correlated with the accuracy of each rainfall / no rainfall classification can be calculated. The specific calculation formula is as follows:

[0021] (4)

[0022] (5)

[0023] (6)

[0024] Based on the obtained positive correlation statistic The three independent precipitation products were weighted and fused to obtain a high-precision precipitation / no-rainfall classification time series. The calculation process is shown below:

[0025] (7)

[0026] (8)

[0027] in, (i=1,2,3) represents the fusion weights for the i-th precipitation product. The optimal time series for classification based on rainfall / no rainfall;

[0028] Three independent time series classifications of rainfall / no rainfall , , Classification time series with optimal rainfall / no rainfall Grid-by-grid comparison over time:

[0029] If there exists a grid point at time t...

[0030] ,and If so, then the data is classified as hit precipitation data;

[0031] ,and If so, the data is classified as false precipitation data;

[0032] ,and If so, the data is classified as underreported precipitation data;

[0033] Since the missed precipitation was 0, the three types of precipitation products with independent errors were divided into two parts: hit precipitation data and false alarm precipitation data.

[0034] Furthermore, S3 specifically includes:

[0035] The generalized triangular hat method is used to calculate the total root mean square error (RMSE) of precipitation products and the root mean square error (RMSE) of hit precipitation data. For the three types of precipitation products / hit precipitation data, the time series of each product / hit precipitation data can be represented as follows:

[0036] (9)

[0037] In the formula, Let i be the time series of the i-th precipitation product / hit precipitation data. For precipitation products / hit precipitation data true values, It represents the error of the i-th precipitation product / hit precipitation data.

[0038] Choose one precipitation product / hit precipitation data as the reference value. The difference between other precipitation products / hit precipitation data can be expressed as:

[0039] (10)

[0040] In the formula, For any selected precipitation product / hit precipitation data, it can be used as a reference value. Error in the reference value precipitation product / hit precipitation data time series;

[0041] Constructing the difference matrix Y, we have:

[0042] (11)

[0043] In the formula, M represents the number of each precipitation product / hit precipitation data;

[0044] The covariance matrix of the difference sequence matrix Y can then be expressed as:

[0045] (12)

[0046] In the formula, S is the covariance matrix. For covariance operators, ,for and The variance (i=j) or covariance (i) between them j);

[0047] Introduce a The covariance matrix R, where R is a symmetric matrix:

[0048] (13)

[0049] In the formula, ,yes and The variance (i=j) or covariance (i) between them j), diagonal elements It is the unknown quantity to be determined;

[0050] At this point, we can construct an expression relating R and S:

[0051] (14)

[0052] In the formula, It is a submatrix of R with dimension 2. 2; A vector of dimension 2; yes The variance; , I is 2 A unit array of 2; A vector of dimension 2;

[0053] To obtain the root mean square error, we need to solve for the covariance matrix R; R has 3... (3+1) / 2 = 6 unknowns, but only 3 are known. (3-1) / 2 = 3 equations (the number of distinct elements in S), making it impossible to calculate the solution to formula (14); the remaining 3 free parameters need to be uniquely solved by defining an objective function that minimizes it. The defined objective function is expressed as:

[0054] (15)

[0055] In the formula, ;

[0056] To satisfy the condition det(R)>0, the constraint conditions of the objective function (15) can be expressed as:

[0057] (16)

[0058] To ensure that the initial value is within the constraints, the initial value for iteration is set as follows:

[0059] (17)

[0060] (18)

[0061] By minimizing the objective function (15) under constraint (16), the three free parameters can be obtained. The unique solution to ) is given; the other unknowns can be calculated using the following formula:

[0062] (19)

[0063] Calculate the mean square error of each precipitation product / hit precipitation data point by point:

[0064] (20)

[0065] In the formula, Let be the root mean square error of the i-th precipitation product / hit precipitation data; to distinguish, the total root mean square error of the precipitation product is denoted by . The root mean square error of the hit precipitation data is expressed as... ;

[0066] The root mean square error of false precipitation data is calculated by taking the square root of the cumulative sum of squares of the false precipitation amounts. The specific calculation formula is as follows:

[0067] (twenty one)

[0068] Where n is the number of false precipitation data points.

[0069] Furthermore, the specific expression of the error propagation law is as follows:

[0070] (twenty two)

[0071] In the formula, Let be the root mean square error of the i-th missed precipitation data point; based on this, the root mean square error of missed precipitation can be derived, and the specific calculation formula is as follows:

[0072] (twenty three)

[0073] At this point, the underreporting error is solved. .

[0074] Compared with the prior art, the technical solution disclosed in this invention has the following beneficial effects:

[0075] By introducing a categorical variable fusion algorithm, the three independent precipitation products are split into two parts: hit precipitation and false alarm precipitation, without the need for ground reference values. Then, the generalized triangular hat method is used to calculate the total root mean square error (RMSE) of the three precipitation products (unsplit data) and the RMSE of the split hit precipitation data, as well as the RMSE of the split false alarm precipitation data. Finally, the false alarm error is derived using the error propagation law. Thus, the method of this invention completes the decomposition of precipitation error components without the need for ground reference values, achieving precise characterization of error source tracing and its spatial distribution. This solves the problem that traditional error interpretation methods rely on ground precipitation data as a reference value, making it impossible to interpret the error components of precipitation products in areas with scarce ground precipitation data, thus hindering error source tracing. Attached Figure Description

[0076] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0077] Figure 1 This is a schematic diagram of the precipitation error component decomposition method without ground reference values ​​provided in an embodiment of the present invention;

[0078] Figure 2 A technical roadmap for a precipitation error component decomposition method without ground reference values ​​provided in embodiments of the present invention. Detailed Implementation

[0079] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0080] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0081] This invention provides a method for decomposing precipitation error components without ground reference values. By combining a categorical variable fusion algorithm with the generalized triangular hat method, the total root mean square error of precipitation products is decomposed into three error components in the absence of ground precipitation observation data: root mean square error of hit precipitation data, root mean square error of falsely reported precipitation data, and root mean square error of missed precipitation data. This enables error component decomposition and accurate error source tracing of precipitation products in areas with missing data.

[0082] like Figures 1-2 As shown, this embodiment of the invention provides a method for decomposing precipitation error components without the need for ground reference values, including:

[0083] S1: Obtain three independent precipitation products for the target area and unify the spatiotemporal resolution of the precipitation products; that is, data preprocessing.

[0084] S2: Using a categorical variable fusion algorithm, without needing ground precipitation data as a reference value, the precipitation product is split into two parts: hit precipitation data and false alarm precipitation data; that is, precipitation event classification.

[0085] S3: Calculate the total root mean square error of the precipitation product, the root mean square error of the hit precipitation data, and the root mean square error of the false alarm precipitation data using the generalized triangular hat method; that is, calculate the three types of errors.

[0086] S4: Based on the error propagation law, the root mean square error of missed precipitation is derived from the total root mean square error, the root mean square error of the hit precipitation data, and the root mean square error of the false precipitation data. This enables the decomposition of error components and the source of error in precipitation products in areas without ground observation data, i.e., the omission error is derived.

[0087] Preferably, the spatiotemporal resolution is uniformly set to 0.1° spatial resolution and 1 hour temporal resolution.

[0088] Preferably, S2 specifically includes:

[0089] Based on the principle of categorical variable fusion algorithm, each precipitation product is converted into a binary time series of rainfall / no rainfall, with a rainfall occurrence flag incremented by 1 and a no rainfall occurrence flag decremented by 1. Three independent sets of rainfall / no rainfall categorical time series are defined as follows: , , Their covariance can be obtained by the following formula:

[0090] (1)

[0091] (2)

[0092] (3)

[0093] Where Q is the covariance of the binary time series with different rainfall / no rainfall conditions; P is the true value of the binary time series with rainfall / no rainfall conditions. A function of the statistical properties of P; To improve the accuracy of rainfall / no rainfall classification for different precipitation products;

[0094] Based on equations (1) to (3), the statistical measure v that is positively correlated with the accuracy of each rainfall / no rainfall classification can be calculated. The specific calculation formula is as follows:

[0095] (4)

[0096] (5)

[0097] (6)

[0098] Based on the obtained positive correlation statistic The three independent precipitation products were weighted and fused to obtain a high-precision precipitation / no-rainfall classification time series. The calculation process is shown below:

[0099] (7)

[0100] (8)

[0101] in, (i=1,2,3) represents the fusion weights for the i-th precipitation product. The optimal time series for classification based on rainfall / no rainfall;

[0102] Three independent time series classifications of rainfall / no rainfall , , Classification time series with optimal rainfall / no rainfall Grid-by-grid comparison over time:

[0103] If there exists a grid point at time t...

[0104] ,and If so, then the data is classified as hit precipitation data;

[0105] ,and If so, the data is classified as false precipitation data;

[0106] ,and If so, the data is classified as underreported precipitation data;

[0107] Since the missed precipitation was 0, the three types of precipitation products with independent errors were divided into two parts: hit precipitation data and false alarm precipitation data.

[0108] Preferably, S3 specifically includes:

[0109] The generalized triangular hat method is used to calculate the total root mean square error (RMSE) of precipitation products and the root mean square error (RMSE) of hit precipitation data. For the three types of precipitation products / hit precipitation data, the time series of each product / hit precipitation data can be represented as follows:

[0110] (9)

[0111] In the formula, Let i be the time series of the i-th precipitation product / hit precipitation data. For precipitation products / hit precipitation data true values, It represents the error of the i-th precipitation product / hit precipitation data.

[0112] Choose one precipitation product / hit precipitation data as the reference value. The difference between other precipitation products / hit precipitation data can be expressed as:

[0113] (10)

[0114] In the formula, For any selected precipitation product / hit precipitation data, it can be used as a reference value. Error in the reference value precipitation product / hit precipitation data time series;

[0115] Constructing the difference matrix Y, we have:

[0116] (11)

[0117] In the formula, M represents the number of each precipitation product / hit precipitation data;

[0118] The covariance matrix of the difference sequence matrix Y can then be expressed as:

[0119] (12)

[0120] In the formula, S is the covariance matrix. For covariance operators, ,for and The variance (i=j) or covariance (i) between them j);

[0121] Introduce a The covariance matrix R, where R is a symmetric matrix:

[0122] (13)

[0123] In the formula, ,yes and The variance (i=j) or covariance (i) between them j), diagonal elements It is the unknown quantity to be determined;

[0124] At this point, we can construct an expression relating R and S:

[0125] (14)

[0126] In the formula, It is a submatrix of R with dimension 2. 2; A vector of dimension 2; yes The variance; , I is 2 A unit array of 2; A vector of dimension 2;

[0127] To obtain the root mean square error, we need to solve for the covariance matrix R; R has 3... (3+1) / 2 = 6 unknowns, but only 3 are known. (3-1) / 2 = 3 equations (the number of distinct elements in S), making it impossible to calculate the solution to formula (14); the remaining 3 free parameters need to be uniquely solved by defining an objective function that minimizes it. The defined objective function is expressed as:

[0128] (15)

[0129] In the formula, ;

[0130] To satisfy the condition det(R)>0, the constraint conditions of the objective function (15) can be expressed as:

[0131] (16)

[0132] To ensure that the initial value is within the constraints, the initial value for iteration is set as follows:

[0133] (17)

[0134] (18)

[0135] By minimizing the objective function (15) under constraint (16), the three free parameters can be obtained. The unique solution to ) is given; the other unknowns can be calculated using the following formula:

[0136] (19)

[0137] Calculate the mean square error of each precipitation product / hit precipitation data point by point:

[0138] (20)

[0139] In the formula, Let be the root mean square error of the i-th precipitation product / hit precipitation data; to distinguish, the total root mean square error of the precipitation product is denoted by . The root mean square error of the hit precipitation data is expressed as... ;

[0140] The root mean square error of false precipitation data is calculated by taking the square root of the cumulative sum of squares of the false precipitation amounts. The specific calculation formula is as follows:

[0141] (twenty one)

[0142] Where n is the number of false precipitation data points.

[0143] Preferably, the specific expression of the error propagation law is:

[0144] (twenty two)

[0145] In the formula, Let be the root mean square error of the i-th missed precipitation data point; based on this, the root mean square error of missed precipitation can be derived, and the specific calculation formula is as follows:

[0146] (twenty three)

[0147] At this point, the underreporting error is solved. .

[0148] The basic principles of the present invention have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in the present invention are merely examples and not limitations, and should not be considered as essential features of each embodiment of the present invention. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the present invention to the necessity of employing the aforementioned specific details.

[0149] The block diagrams of devices, apparatuses, devices, and systems involved in this invention are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0150] It should also be noted that in the apparatus, device, and method of the present invention, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered as equivalent solutions of the present invention.

[0151] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the invention. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of the invention. Therefore, the invention is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.

[0152] It should be understood that the qualifying terms "first", "second", "third", "fourth", "fifth" and "sixth" used in the description of the embodiments of the present invention are only used to more clearly illustrate the technical solutions and are not intended to limit the scope of protection of the present invention.

[0153] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of the invention to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations therein.

Claims

1. A method for decomposing precipitation error components without requiring ground reference values, characterized in that, include: S1: Obtain three independent precipitation products for the target area and unify the spatiotemporal resolution of the precipitation products; S2: Using a categorical variable fusion algorithm, without needing ground precipitation data as a reference value, the precipitation product is split into two parts: hit precipitation data and false alarm precipitation data. S3: Calculate the total root mean square error of the precipitation product, the root mean square error of the hit precipitation data, and the root mean square error of the false alarm precipitation data using the generalized triangular hat method. S4: Based on the error propagation law, the root mean square error of missed precipitation is derived from the total root mean square error, the root mean square error of the hit precipitation data, and the root mean square error of the false precipitation data.

2. The precipitation error component decomposition method without ground reference values ​​according to claim 1, characterized in that, The spatiotemporal resolution is uniformly set at 0.1° spatial resolution and 1 hour temporal resolution.

3. The precipitation error component decomposition method without ground reference values ​​according to claim 1, characterized in that, S2 specifically includes: Based on the principle of categorical variable fusion algorithm, each precipitation product is converted into a binary time series of rainfall / no rainfall, with a rainfall occurrence flag incremented by 1 and a no rainfall occurrence flag decremented by 1. Three independent sets of rainfall / no rainfall categorical time series are defined as follows: , , Their covariance can be obtained using the following formula: (1) (2) (3) Where Q is the covariance of the binary time series with different rainfall / no rainfall conditions; P is the true value of the binary time series with rainfall / no rainfall conditions. A function of the statistical properties of P; To improve the accuracy of rainfall / no-rain classification for different precipitation products; Based on equations (1) to (3), the statistical measure v that is positively correlated with the accuracy of each rainfall / no rainfall classification can be calculated. The specific calculation formula is as follows: (4) (5) (6) Based on the obtained positive correlation statistic The three independent precipitation products were weighted and fused to obtain a high-precision precipitation / no-rainfall classification time series. The calculation process is shown below: (7) (8) in, (i=1,2,3) represents the fusion weights for the i-th precipitation product. The optimal time series for classification based on rainfall / no rainfall; Three independent time series classifications of rainfall / no rainfall , , Classification time series with optimal rainfall / no rainfall Grid-by-grid comparison over time: If there exists a grid point at time t... ,and If so, then the data is classified as hit precipitation data; ,and If so, the data is classified as false precipitation data; ,and If so, the data is classified as underreported precipitation data; Since the missed precipitation was 0, the three types of precipitation products with independent errors were divided into two parts: hit precipitation data and false alarm precipitation data.

4. The precipitation error component decomposition method without ground reference values ​​according to claim 1, characterized in that, S3 specifically includes: The generalized triangular hat method is used to calculate the total root mean square error (RMSE) of precipitation products and the root mean square error (RMSE) of hit precipitation data. For the three types of precipitation products / hit precipitation data, the time series of each product / hit precipitation data can be represented as follows: (9) In the formula, Let i be the time series of the i-th precipitation product / hit precipitation data. For precipitation products / hit precipitation data true values, It represents the error of the i-th precipitation product / hit precipitation data; Choose one precipitation product / hit precipitation data as the reference value. The difference between other precipitation products / hit precipitation data can be expressed as: (10) In the formula, For any selected precipitation product / hit precipitation data, Error in the reference value precipitation product / hit precipitation data time series; Constructing the difference matrix Y, we have: (11) In the formula, M represents the number of each precipitation product / hit precipitation data; The covariance matrix of the difference sequence matrix Y can then be expressed as: (12) In the formula, S is the covariance matrix. For covariance operators, ,for and The variance (i=j) or covariance (i) between them j); Introduce a The covariance matrix R, where R is a symmetric matrix: (13) In the formula, ,yes and The variance (i=j) or covariance (i) between them j), diagonal elements It is the unknown quantity to be determined; At this point, we can construct an expression relating R and S: (14) In the formula, It is a submatrix of R with dimension 2. 2; A vector of dimension 2; yes The variance; , I is 2 A unit array of 2; A vector of dimension 2; To obtain the root mean square error, we need to solve for the covariance matrix R; R has 3... (3+1) / 2 = 6 unknowns, but only 3 are known. (3-1) / 2 = 3 equations (the number of distinct elements in S), making it impossible to calculate the solution to formula (14); the remaining 3 free parameters need to be uniquely solved by defining an objective function that minimizes it. The defined objective function is expressed as: (15) In the formula, ; To satisfy the condition det(R)>0, the constraint conditions of the objective function (15) can be expressed as: (16) To ensure that the initial value is within the constraints, the initial value for iteration is set as follows: (17) (18) By minimizing the objective function (15) under constraint (16), the three free parameters can be obtained. The unique solution to ) is given; the other unknowns can be calculated using the following formula: (19) Calculate the mean square error of each precipitation product / hit precipitation data point by point: (20) In the formula, Let be the root mean square error of the i-th precipitation product / hit precipitation data; to distinguish, the total root mean square error of the precipitation product is denoted by . The root mean square error of the hit precipitation data is expressed as... ; The root mean square error of false precipitation data is calculated by taking the square root of the cumulative sum of squares of the false precipitation amounts. The specific calculation formula is as follows: (21) Where n is the number of false precipitation data points.

5. The precipitation error component decomposition method without ground reference values ​​according to claim 1, characterized in that, The specific expression of the error propagation law is as follows: (22) In the formula, Let be the root mean square error of the i-th missed precipitation data point; based on this, the root mean square error of missed precipitation can be derived, and the specific calculation formula is as follows: (23) At this point, the underreporting error is solved. .

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