Multi-scale radar-microwave fusion rainfall field construction method based on multi-grid dynamic weighting

Abstract

The invention discloses a multi-scale radar-microwave fusion rainfall field construction method based on multi-grid dynamic weighting, and the method comprises the steps: respectively obtaining microwave link data, actual rainfall and meteorological radar data through a microwave base station and a rainfall station in a research region, and carrying out the preprocessing of the obtained data; selecting a sliding standard deviation method to distinguish sunny and rainy periods; utilizing a power-law model to perform inversion calculation on the rainfall process after the rain and sunny periods are distinguished; a radar rainfall field is used as an initial background field, a multi-grid layered adaptive weight is introduced, and the fusion weight of radar and microwave data is dynamically adjusted according to the grid resolution; carrying out the cross-scale superposition of microwave inversion data based on a multi-grid variational method, achieving the construction of a multi-scale radar-microwave fusion rainfall field, and generating a fused two-dimensional space rainfall field. According to the technical method, the space coverage advantage of the microwave rain measurement technology and the refinement advantage of radar monitoring can be effectively utilized, accurate reconstruction of rainfall field space distribution is achieved, and traditional radar monitoring is effectively supplemented.

Description

Technical Field

[0001] The present invention relates to a method for constructing a multi-scale radar-microwave fusion rainfall field based on multi-grid dynamic weighting, and belongs to the field of ground meteorological monitoring. Background Art

[0002] It is crucial to develop real-time, accurate, and high spatio-temporal resolution precipitation monitoring technologies, which can not only provide accurate data support for hydrological and meteorological research, but also play an invaluable role in decision-making early warning and flood prevention and control. Monitoring meteorological elements such as precipitation using microwave links in the wireless communication field is one of the newly developed atmospheric environment monitoring technologies in recent years. Obtaining high-precision, high spatio-temporal resolution precipitation dynamic monitoring data provides important data support for research in fields such as numerical weather prediction, data assimilation, atmospheric circulation, and development of atmospheric water resources. In the research on two-dimensional rainfall field reconstruction based on microwave links, traditional methods have long relied on interpolation algorithms such as Kriging interpolation and inverse distance weighting. Although these algorithms can construct a spatial distribution field using the path-integrated rainfall data of microwave links, their essence is to fill the spatial data gaps through mathematical surface fitting, and there are significant limitations: on the one hand, the spatial resolution of a single microwave link data source is limited by the hardware layout density and it is difficult to capture the fine structure of the rainfall field; on the other hand, the interpolation process lacks constraints on the physical evolution mechanism of rainfall and is prone to generating pseudo-features that violate meteorological principles in data-sparse regions.

[0003] In recent years, fusion algorithms have gradually become a research hotspot. By collaborating with the three-dimensional volume scan data of radar reflectivity, the high-precision point measurements of rain gauges, and the wide-area coverage ability of satellite remote sensing, a complementary framework for multi-source heterogeneous data is constructed, effectively making up for the limitations of a single monitoring method in spatio-temporal resolution and coverage range, and opening up a new path for improving the accuracy of rainfall field reconstruction.

[0004] However, there is still a gap between the practical effects of current fusion algorithms and the theoretical expectations. Many fusion algorithms are relatively mature in traditional engineering fields. For example, the super-resolution reconstruction algorithm in the field of image processing has successfully restored high-frequency details from low-resolution images through multi-scale feature fusion at fixed levels. However, when these mature technologies are directly transplanted into the reconstruction of multi-scale radar-microwave fusion rainfall fields, there are some key technical problems that need to be overcome, such as the contradiction between static grid division and the multi-scale dynamic evolution of rainfall, which to a certain extent restricts the accuracy of two-dimensional rainfall field construction. Summary of the Invention

[0005] Objective of the Invention: To overcome the deficiencies in the prior art, the present invention provides a multi-scale radar-microwave fusion rainfall field construction method based on multi-grid dynamic weighting. Using radar as the background field and superimposing rainfall data retrieved by microwave to perform fusion, it effectively utilizes the advantages of microwave rain measurement technology to accurately reconstruct the spatial distribution of the rainfall field and effectively supplement traditional radar monitoring.

[0006] Technical Solution: To solve the above technical problems, a multi-scale radar-microwave fusion rainfall field construction method based on multi-grid dynamic weighting of the present invention includes the following steps:

[0007] Step S1: Obtain microwave link data, actual rainfall, and meteorological radar data respectively through microwave base stations and rain gauges within the study area, and preprocess the obtained data.

[0008] Step S2: Select the sliding standard deviation method to distinguish between clear and rainy periods.

[0009] Step S3: Use the power-law model to perform inversion calculations on the rainfall process after distinguishing between clear and rainy periods.

[0010] Step S4: Use the radar rainfall field as the initial background field, introduce multi-grid hierarchical adaptive weights, and dynamically adjust the fusion weights of radar and microwave data according to the grid resolution.

[0011] Step S5: Based on the multi-grid variational method, perform cross-scale superposition of microwave inversion data to construct a multi-scale radar-microwave fusion rainfall field and generate a fused two-dimensional spatial rainfall field.

[0012] Preferably, in step S1, the microwave link data includes signal attenuation data, position information, polarization mode, and signal frequency data. Data preprocessing includes processing and analyzing abnormal data of the collected microwave link, rain gauge, and meteorological radar data and short link availability analysis.

[0013] Preferably, step S3 includes the following steps:

[0014] Step S3.1: The power-law model adopted is the ITU-R rain attenuation inversion model proposed by the International Telecommunication Union, and the calculation formula is as follows:

[0015]

[0016] Among them, R is the rainfall intensity, with the unit of mm / h; A is the path integral attenuation of the link, with the unit of dB; D is the link length, with the unit of km. a and b are power-law coefficients related to the microwave polarization mode and frequency. For microwave links with different frequencies and polarization modes, their calculation methods are as follows:

[0017]

[0018] Step S3.2: Calculation and derivation of rain attenuation. Subtract the basic attenuation and wet antenna attenuation from the total attenuation to obtain the rain attenuation;

[0019] Step S3.3: Calculate the rainfall intensity on the corresponding microwave link according to the ITU-R rain attenuation inversion model.

[0020] Preferably, the step S4 includes the following steps:

[0021] Step S4.1: Convert the radar echo intensity data into the actual rainfall intensity according to the Z-R relationship. The calculation formula is as follows:

[0022] dBZ = 10×log 10 (Z)

[0023] Z = αR k

[0024] In the formula, Z is the radar reflectivity factor, and the unit is mm 6 / m 3 .

[0025] Step S4.2: Construct a 1-hour radar rainfall distribution map and realize the conversion of longitude and latitude information through the cubic spline interpolation algorithm to obtain the radar rainfall field for fusion;

[0026] Step S4.3: Determine that the grid resolution of the first layer is n×n (n∈N + ), the grid resolution of the second layer is (2×n)×(2×n), and so on. The grid resolution of the l-th layer is (2 l-1 ×n)×(2 l-1 ×n). Among them, l = 1, 2,..., L. Divide the radar rainfall field according to the corresponding resolution of each layer until L layers of grids are generated.

[0027] Step S4.4: Construct a hierarchical adaptive weight model and dynamically adjust the fusion weight of radar and microwave data according to the grid resolution. Define the weight ratio of radar and microwave data on each layer of grid:

[0028] ω (l) = λ (l) / μ (l)

[0029] Among them, λ (l) , μ (l) are the dynamic weight coefficients of radar and microwave respectively, and are adaptively adjusted hierarchically. The weight ratio of radar and microwave data is negatively correlated with the grid resolution:

[0030]

[0031] Among them, γ is the scale sensitivity factor, with a value range of 1.2 to 1.8. Δx (l) is the grid resolution of the l-th layer; ω0 is the reference weight ratio, defined as the initial weight ratio of the L-th layer grid; Δx radar is the original resolution of the radar data. At the same time, the weight coefficients are normalized:

[0032]

[0033] Ensure that λ (l) + μ (l) = 1 to achieve weight normalization. The core idea of dynamically adjusting the weights is to automatically calculate the fusion weights of radar and microwave at the current layer according to the grid resolution of the current layer, and then distribute the weights of the two according to the normalization formula, ensuring that the spatial coverage advantage of microwave link data is preferentially used to correct the systematic deviation of the radar in the coarse grid layer (large scale); in the fine grid layer (small scale), it relies on the high spatio-temporal resolution of the radar to capture rainfall details, and through the negative correlation between resolution and weight, the fusion logic of microwave controlling large scales and radar preserving details is realized.

[0034] A multi-scale radar-microwave fusion rainfall field construction method based on multi-grid dynamic weighting proposed by the present invention has the following beneficial effects compared with the prior art:

[0035] 1. By fusing the radar rainfall field and microwave-inverted rainfall data, the present invention realizes the complementary advantages of radar and microwave data by using multi-grid variational technology, and greatly improves the spatial resolution and accuracy of rainfall field construction.

[0036] 2. By processing data at different time scales, the present invention can realize the construction of rainfall fields at different time scales, meeting various application requirements from real-time monitoring to historical analysis.

[0037] 3. By combining microwave link signal attenuation data with traditional rain gauge and meteorological radar data, the potential of various data resources is maximally exploited, overcoming the limitations of a single data source.

[0038] 4. By introducing multi-grid hierarchical adaptive weights and dynamically adjusting the fusion weights of radar and microwave data according to the grid resolution, the present invention overcomes the limitations of traditional multi-grids using fixed hierarchical divisions and being unable to adapt to the multi-scale dynamic changes of rainfall systems; it overcomes the defects of global fixed grids leading to waste of computing resources or insufficient resolution in key areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is the technical roadmap of the present invention;

[0040] Figure 2 is the identification diagram of clear and rainy periods based on the sliding standard deviation method in the present invention;

[0041] Figure 3 It is the rainfall inversion map of the present invention. Specific implementation manners

[0042] The technical solution of the present invention will be described in detail below in conjunction with embodiments, but the protection scope of the present invention is not limited to the described embodiments.

[0043] The target basin of this case study is located in Zigui County, Yichang City, Hubei Province. It is located in the mid-latitudes and belongs to the subtropical continental monsoon climate. The annual rainfall is between 950 and 1590 mm, with an average annual rainfall of 1439 mm. The rainfall varies greatly between years. The rainfall within a year is of a single-peak type, mainly from May to August. There are 18 rain gauges and 100 microwave transceiver sites in the basin, forming a ground rainfall observation network.

[0044] In this case, as Figure 1 shown, a multi-scale radar-microwave fusion rainfall field construction method based on multi-grid dynamic weighting specifically includes the following steps:

[0045] Step S1: Obtain microwave link data, actual rainfall, and meteorological radar data through microwave base stations and rain gauges in the study area, and preprocess the obtained data.

[0046] The microwave link data includes signal attenuation, position information, polarization mode, and signal frequency data of 50 microwave links in the basin.

[0047] The data preprocessing includes abnormal data processing, analysis, and short-link availability analysis of the data collected from 50 microwave links, 18 rain gauges, and 1 X-band meteorological radar.

[0048] Step S2: Select the sliding standard deviation method to distinguish between rainy and non-rainy periods.

[0049] The sliding standard deviation method is a commonly used method in the fields of signal processing and time series data analysis. By setting a window of a fixed size to move on the time series data, the standard deviation of the data within the window is calculated. Finally, the different states of the signal can be identified through the difference in the standard deviation between the rainy period and the non-rainy period.

[0050] Assume that A(t) is the total path integral attenuation of a certain link at time t. Then A(t) can be decomposed into the sum of the basic attenuation A B (t) and the attenuation A R (t) caused by rainfall events:

[0051]

[0052] For a sliding time window W with a duration s>0 t= [t - s, t], and the test statistic for sunny - rainy period discrimination is as follows:

[0053]

[0054] where is the arithmetic mean of all microwave real - time attenuation data A(k) with length N within the W t window, is the standard deviation within the sliding window W t .

[0055] By examining the differences during sunny - rainy periods and setting thresholds, the decision rule is applied to the entire microwave data set to distinguish between rainy periods and non - rainy periods, and the discrimination results are as follows:

[0056]

[0057] Step S3: Use the power - law model to perform inversion calculations on the rainfall process after sunny - rainy period discrimination, including the following steps:

[0058] Step S3.1: The power - law model adopted is the ITU - R rain attenuation inversion model proposed by the International Telecommunication Union, and the calculation formula is as follows:

[0059]

[0060] where R is the rainfall intensity, with the unit of mm / h; A is the path integral attenuation of the link, with the unit of dB; D is the link length, with the unit of km. a and b are power - law coefficients related to microwave polarization and frequency. For microwave links with different frequencies and polarization modes, their calculation methods are as follows:

[0061]

[0062] Based on the relationship between rainfall intensity and microwave rain - induced attenuation, the International Telecommunication Union gives references for the values of a and b in horizontal and vertical polarization modes, as shown in Table 1:

[0063] Table 1

[0064]

[0065] In this embodiment, the microwave link frequency is 24 GHz. Therefore, the average of the reference values of 23 GHz and 25 GHz in Table 2 is taken, that is, a H = 0.126, a V = 0.1205, b H = 0.9965, b V = 1.0255.

[0066] Step S3.2: Derivation of rain attenuation calculation. Subtract the basic attenuation and wet antenna attenuation from the total attenuation to obtain the rain attenuation;

[0067] This process not only considers the basic attenuation but also the influence of wet antenna attenuation. To accurately extract the rain attenuation and reduce this adverse effect, the attenuation during rainfall is corrected for the wet antenna. Select the minimum attenuation during the rain period as the reference, and the value range of the wet antenna attenuation is between the maximum attenuation during the dry period and the reference value during the rain period. Subtract this part of the attenuation from the total attenuation to obtain a more accurate rain attenuation for subsequent rainfall inversion.

[0068] Step S3.3: Calculate the rainfall intensity R1 on the corresponding microwave link according to the ITU-R rain attenuation inversion model.

[0069] To comprehensively and accurately evaluate the actual effect of rainfall inversion on the microwave link, five indicators are selected to quantitatively evaluate the difference between the inverted rainfall and the measured rainfall process. The specific calculation methods of the indicators are as follows:

[0070] Correlation Coefficient (CC):

[0071]

[0072] Mean Absolute Error (MAE):

[0073]

[0074] Root Mean Square Error (RMSE):

[0075]

[0076] Relative Error (RE):

[0077]

[0078] Nash-Sutcliffe Efficiency (NSE):

[0079]

[0080] Due to space limitations, the inversion indicators of two links are shown, such as the calculated values of the five indicators for Link 311 and Link 715, as shown in Table 2:

[0081] Table 2

[0082]

[0083] Step S4: Using the radar rainfall field as the initial background field, introduce a multi-grid hierarchical adaptive weight, and dynamically adjust the fusion weight of radar and microwave data according to the grid resolution, including the following steps:

[0084] Step S4.1: Convert the radar echo intensity data into actual rainfall intensity according to the Z-R relationship, and its calculation formula is as follows:

[0085] dBZ = 10×log 10 (Z)

[0086] Z = αR k

[0087] where Z is the radar reflectivity factor, with the unit of mm 6 / m 3 , and α and k are empirical coefficients determined according to the data information of the study area.

[0088] Step S4.2: Construct a 1-hour radar rainfall distribution map and realize the conversion of equi-longitude and equi-latitude information through the cubic spline interpolation algorithm to obtain the radar rainfall field R2 for fusion;

[0089] Step S4.3: Determine that the grid resolution of the first layer is n×n (n∈N + ), the grid resolution of the second layer is (2×n)×(2×n), and so on. The grid resolution of the l-th layer is (2 l-1 ×n)×(2 l-1 ×n). Among them, l = 1, 2,..., L. Divide the radar rainfall field according to the corresponding resolution of each layer until L layers of grids are generated.

[0090] In this embodiment, considering factors such as the area of the study area, the resolution of radar data, and the real-time rolling calculation efficiency, n = 8 and L = 6 are selected.

[0091] Step S4.4: Construct a hierarchical adaptive weight model to dynamically adjust the fusion weight of radar and microwave data according to the grid resolution. Define the weight ratio of radar and microwave data on each layer of grid:

[0092] ω (l) = λ (l) / μ (l)

[0093] where λ (l) , μ (l) are the dynamic weight coefficients of radar and microwave respectively, and are adaptively adjusted hierarchically. When the grid is coarser, the microwave data constraint is dominant (μ (l) is dominant); when the grid is finer, the high-resolution characteristics of the radar are strengthened (λ (l) is dominant). The weight ratio of radar and microwave data is negatively correlated with the grid resolution:

[0094]

[0095] Among them, γ is the scale-sensitive factor, and its value ranges from 1.2 to 1.8. Δx (l) is the grid resolution of the l-th layer; ω0 is the reference weight ratio, defined as the initial weight ratio of the grid of the L-th layer; Δx radar is the original resolution of the radar data. At the same time, the weight coefficients are normalized:

[0096]

[0097] Ensure that λ (l) + μ (l) = 1 to achieve weight normalization.

[0098] Step S5: Based on the multi-grid variational method, cross-scale superposition of microwave inversion data is carried out to realize the construction of a multi-scale radar-microwave fusion rainfall field, and a fused two-dimensional spatial rainfall field is generated. It includes the following steps:

[0099] Step S5.1: On the grid of the l-th layer, define the fusion objective function:

[0100]

[0101] Among them, R (l) is the fusion rainfall field of the l-th layer to be solved, R2 is the radar background field, is the path integral rainfall of the microwave inversion data at level l, Φ(·) is the microwave link path integral operator (linear projection matrix), α (l) is the smoothing coefficient, α (l) = 0.1·2 -l , weak smoothing for the coarse layer and strong smoothing for the fine layer, is the gradient operator.

[0102] Step S5.2: Coarse grid solution. Downsample the radar background field to the coarsest resolution, and average the microwave data according to the path coverage area. Simplify the objective function and ignore the spatial smoothing term α (1) = 0, focusing on the microwave constraint:

[0103]

[0104] Use the conjugate gradient method to solve, and the convergence condition is Obtain R (1) ;

[0105] Step S5.3: Cross-level residual transfer. Use the interpolation method to interpolate the solution R of the coarse grid to the next layer: (1) Interpolate to the next layer:

[0106] R(2) = I 1→2 (R (1) ) + δR (2)

[0107] where I 1→2 is a bilinear interpolation operator, and δR (2) is the fine grid correction. Meanwhile, calculate the residual of the microwave data at the current layer:

[0108]

[0109] Step S5.4: Fine grid optimization. Adjust the smoothing weight according to the radar reflectivity gradient direction:

[0110]

[0111] In the formula, Z is the radar reflectivity factor, with the unit of mm 6 / m 3 , and the L-BFGS algorithm is used to accelerate the convergence. x is the horizontal axis of the grid, y is the vertical axis of the grid, i = 1, 2,..., l, j = 1, 2,..., l, and iterate until δR (2) is obtained.

[0112] Step S5.5: Multi-scale superposition and result generation: According to the methods in steps 5.2 - 5.4, obtain the correction amounts of each layer, interpolate the correction amounts of each layer to the original resolution layer by layer and accumulate them to obtain the final fused rainfall field R f :

[0113]

[0114] where I l→L is the interpolation operator from level l to the highest level L.

[0115] The above are only the preferred embodiments of the present invention. It should be noted that: for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for constructing a multi-scale radar-microwave fusion rainfall field based on multi-grid dynamic weighting, characterized in that It includes the following steps: Step S1: Obtain microwave link data, actual rainfall, and meteorological radar data through microwave base stations and rain gauges in the study area, and preprocess the acquired data; Step S2: Select the sliding standard deviation method to distinguish between clear and rainy periods; Step S3: Use the power-law model to perform inversion calculations on the rainfall process after distinguishing between clear and rainy periods; Step S4: Use the radar rainfall field as the initial background field, introduce multi-grid hierarchical adaptive weights, and dynamically adjust the fusion weights of radar and microwave data according to the grid resolution; Step S5: Based on the multi-grid variational method, perform cross-scale superposition of microwave inversion data to realize the construction of a multi-scale radar-microwave fusion rainfall field and generate a fused two-dimensional spatial rainfall field.

2. A multi-scale radar-microwave fusion rainfall field construction method based on multi-grid dynamic weighting according to claim 1, characterized in that, In the above Step S1, the microwave link data includes signal attenuation data, position information, polarization mode, and signal frequency data. The data preprocessing includes abnormal data processing, analysis, and short-link availability analysis of the collected microwave link, rain gauge, and meteorological radar data.

3. A method for constructing a multi-scale radar-microwave fusion rainfall field based on multi-grid dynamic weighting according to claim 1, characterized in that, The following steps are included in the above Step S3: Step S3.1: The power-law model adopted is the ITU-R rain attenuation inversion model proposed by the International Telecommunication Union, and the calculation formula is as follows: where, R is the rainfall intensity, with the unit of mm / h; A is the path integral attenuation of the link, with the unit of dB; D is the link length, with the unit of km, and a and b are power-law coefficients related to the microwave polarization mode and frequency. For microwave links with different frequencies and polarization modes, the calculation method is as follows: Step S3.2: Calculate the rain-induced attenuation. Subtract the basic attenuation and wet antenna attenuation from the total attenuation to obtain the rain-induced attenuation; Step S3.3: Calculate the rainfall intensity on the corresponding microwave link according to the ITU-R rain attenuation inversion model.

4. A multi-scale radar-microwave fusion rainfall field construction method based on multi-grid dynamic weighting according to claim 1, characterized in that, The specific implementation steps of the above Step S4 include: Step S4.1: Convert the radar echo intensity data into actual rainfall intensity according to the Z-R relationship, and the calculation formula is as follows: dBZ = 10×log 10 (Z) Z = αR k where Z is the radar reflectivity factor with the unit of mm 6 / m 3 , and α and k are empirical coefficients; Step S4.2: Construct a 1-hour radar rainfall distribution map and realize the conversion of longitude and latitude information through the cubic spline interpolation algorithm to obtain the radar rainfall field R2 for fusion; Step S4.3: Determine that the resolution of the first-layer grid is n×n, where n ∈ N + , N + is a positive integer, the resolution of the second-layer grid is (2×n)×(2×n), and so on. The resolution of the l-th layer grid is (2 l-1 ×n)×(2 l-1 ×n), where l = 1, 2, …, L. Divide the radar rainfall field according to the corresponding resolution of each layer until L layers of grids are generated; Step S4.4: Construct a hierarchical adaptive weight model, dynamically adjust the fusion weights of radar and microwave data according to the grid resolution, and define the weight ratio of radar and microwave data on each layer of the grid: ω (l) = λ (l) / μ (l) Among them, λ (l) , μ (l) are the dynamic weight coefficients of the radar and the microwave respectively, and are adaptively adjusted hierarchically: Among them, γ is the scale sensitivity factor, with a value range of 1.2 to 1.8, and Δx (l) is the grid resolution of the l-th layer; ω0 is the reference weight ratio, defined as the initial weight ratio of the L-th layer grid; Δx radar is the original resolution of the radar data, and at the same time, the weight coefficient is normalized as follows: Ensure that λ (l) + μ (l) = 1.

5. A multi-scale radar-microwave fusion rainfall field construction method based on multi-grid dynamic weighting according to claim 1, characterized in that, The above Step S5 includes: Through the cross-scale coupling of the variational objective function, fuse the link inversion data with the radar rainfall field to generate a fused two-dimensional spatial rainfall field, which specifically includes the following steps: Step S5.1: On the grid of the l-th layer, define the fusion objective function: R2 is the radar background field, is the path-integrated rainfall of the microwave inversion data at level l, Φ(·) is the microwave link path-integral operator, α (l) is the smoothing coefficient, α (l) = 0.1·2 -l , is the gradient operator; Step S5.2: Conduct coarse grid solution: Downsample the radar background field to the coarsest resolution, average the microwave data according to the path coverage area, simplify the objective function, and ignore the spatial smoothing term α (1) = 0, focusing microwave constraint: The conjugate gradient method is used for solution, and the convergence condition is obtain R (1) ; Step S5.3: Cross-level residual transfer: Interpolate the solution R of the coarse grid to the next level using interpolation method (1) Interpolate to the next level: where I 1→2 is a bilinear interpolation operator, and δR (2) is the fine grid correction amount; Step S5.4: Fine-grid optimization: Adjust the smoothing weight according to the radar reflectivity gradient direction: Where Z is the radar reflectivity factor, with the unit of mm 6 / m 3 , and the L-BFGS algorithm is used to accelerate convergence. x is the horizontal axis of the grid, y is the vertical axis of the grid, i = 1, 2, …, l, j = 1, 2, …, l, iterate until obtain δR (2) ; Step S5.5: Multi-scale superposition and result generation: Interpolate the correction amounts of each layer to the original resolution layer by layer and accumulate them to obtain the final fused rainfall field: where I l→L is an interpolation operator from level l to the highest level L.

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