A multi-source precipitation fusion probability estimation method and system

Abstract

This invention provides a multi-source precipitation fusion probability estimation method and system, relating to the fields of hydrological and meteorological data fusion, uncertainty quantification in Earth system science, and probability forecasting. The method includes: acquiring multi-source gridded precipitation characteristic data of a target area; inputting the multi-source gridded precipitation characteristic data into a trained estimation model to obtain mean parameters and discrete parameters; constructing a composite Poisson-Gamma distribution based on the mean parameters, the discrete parameters, and preset or learned power parameters from the estimation model, and generating a precipitation set using a Monte Carlo sampling method to obtain the precipitation probability distribution result. This achieves end-to-end precipitation probability estimation and can further generate distribution curves, zero precipitation probability, arbitrary quantile estimates, interval widths, confidence intervals, and a complete set of uncertainty indicators, meeting the needs of hydrological and meteorological applications for probability input products.

Description

Technical Field

[0001] This invention belongs to the field of hydrological and meteorological data fusion, uncertainty quantification and probability forecasting technology in Earth system science, and specifically relates to a multi-source precipitation fusion probability estimation method and system. Background Technology

[0002] Precipitation is a key variable driving the global hydrological cycle and climate system, and its accurate spatiotemporal estimation is crucial for responding to extreme weather events, managing water resources, and understanding the impacts of climate change. In recent years, multi-source data from remote sensing, numerical models, and ground observations have facilitated the development of high-resolution and globally covered precipitation products. Multi-source precipitation data fusion has become a mainstream technical direction in current operational and research fields, aiming to comprehensively utilize the advantages of various source data to generate a gridded precipitation product that is spatially continuous, temporally consistent, and more accurate than any single data source.

[0003] Currently, existing precipitation data fusion methods can be broadly categorized into the following two types:

[0004] Deterministic regression or interpolation methods, such as linear weighted regression, least squares, Kriging, and machine learning regression (e.g., random forests, neural networks), output point estimates but rarely provide reliable uncertainty. These methods often perform poorly on zero-precipitation and long-tailed extreme precipitation events because the objective function based on mean squared error or absolute error cannot reflect the mixed distribution characteristics.

[0005] Post-processing probabilistic fusion methods, such as Bayesian model averaging, ensemble or perturbation methods, and ex post-correction based on quantile regression, first obtain point estimates and then construct uncertainties based on residual assumptions (normal, log-normal, or empirical distribution). These methods are separate from fusion and fail to achieve end-to-end probabilistic estimation.

[0006] With the increasing frequency of extreme weather events and the growing demand for more refined hydrological and meteorological risk management, traditional deterministic precipitation estimation is no longer sufficient to meet the risk quantification requirements of applications such as flood warning, drought monitoring, and water resource allocation. Probabilistic precipitation fusion can provide uncertainty information such as precipitation probability and confidence intervals, offering a more complete scientific basis for risk decision-making. Although probabilistic fusion is a developing trend, existing methods still face several fundamental challenges that restrict their widespread application in practical operations and their physical interpretability:

[0007] 1. Mismatch between probability models and precipitation physical statistical characteristics: Most methods implicitly or explicitly assume that errors follow a Gaussian distribution or its variants. However, precipitation data has three typical characteristics: non-negativity (precipitation ≥ 0), zero-value accumulation (no precipitation in a large number of time steps), and positive skewness distribution (precipitation intensity is right-skewed). The Gaussian distribution assumption is difficult to characterize these features, resulting in non-zero predicted negative precipitation probabilities and severely distorted probability estimates for zero values and extremely heavy precipitation. Although some studies have used truncated Gaussian or mixture models (such as zero-inflated models) for improvement, the models are complex, parameter estimation is difficult, and the relationship between precipitation values and variances is decoupled.

[0008] 2. Fragmented process and low computational efficiency. The current mainstream probability fusion paradigm is "first deterministic fusion, then uncertainty quantification". For example, first train a neural network to output a deterministic value, and then train another model (such as a Gaussian process) to fit the distribution of the residuals. This fragmented process weakens the internal physical connection between uncertainty estimation and the fusion process, becoming a post hoc correction measure.

[0009] 3. Separation or fuzzy processing of precipitation occurrence and intensity. The generation of precipitation involves two basic problems: occurrence probability and intensity distribution. Many models fail to explicitly and uniformly model these two aspects. For example, models that directly regress precipitation amounts cannot accurately output the probability of precipitation being 0: while the simple classification-regression two-step method (first determine whether there is rain, and then estimate the rainfall amount) ignores the correlation between occurrence and intensity, and classification errors will be transmitted downstream.

[0010] In recent years, the compound Poisson-Gamma distribution has been widely used to model positive-valued data with a large number of zeros and right-skewed long tails, which is similar to the statistical characteristics of precipitation data. When the power parameter of this distribution is greater than 1 < p < 2, a compound Poisson-Gamma distribution is formed: where the Poisson process describes the frequency of event occurrence, and the Gamma distribution describes the average intensity of each event. This mathematical correspondence provides a solid physical statistical basis for precipitation modeling: the Poisson part naturally刻画了 the random occurrence characteristics of precipitation, and the Gamma part describes the positive skewness distribution of precipitation intensity.

[0011] However, existing studies mostly use this distribution for probability prediction or statistical fitting of univariate time series, and have not yet involved the deep fusion of multi-source spatial data. How to construct a deep learning model that can take the negative log-likelihood of the compound Poisson-Gamma distribution as the training objective and directly learn and output the two key parameters (mean parameter and dispersion parameter) that刻画 the precipitation probability distribution from multi-source, high-dimensional, and unstructured spatial inputs to achieve true end-to-end probability fusion remains an unsolved frontier technical problem.

[0012] Furthermore, the probability density function of this distribution contains infinite series terms without analytical solutions, making it unsuitable for large-scale computation as the loss function in deep learning backpropagation. Therefore, there is an urgent need for an end-to-end probabilistic multi-source precipitation fusion method that can directly employ the composite Poisson-Gamma distribution as the objective function within a deep learning framework. Summary of the Invention

[0013] To address the three major problems in existing technologies—mismatch between probabilistic models and precipitation statistical characteristics, separation between deterministic fusion and uncertainty quantification, and disconnect between precipitation occurrence and intensity modeling—which lead to difficulties in achieving end-to-end probabilistic precipitation estimation, this invention provides a multi-source precipitation fusion probabilistic estimation method and system. This method enables end-to-end precipitation probability estimation and can further generate distribution curves, zero precipitation probability, arbitrary quantile estimates, interval widths, confidence intervals, and a complete set of uncertainty indicators, meeting the needs of hydrological and meteorological applications for probabilistic input products.

[0014] To achieve the above objectives, the specific technical solution of the present invention is as follows:

[0015] In a first aspect, the present invention provides a multi-source precipitation fusion probability estimation method, characterized in that it includes:

[0016] Acquire multi-source gridded precipitation characteristic data for the target area;

[0017] The multi-source gridded precipitation characteristic data are input into the trained estimation model to obtain mean parameters and discrete parameters;

[0018] Based on the mean parameter, the discrete parameter, and the preset or learned power parameter from the estimation model, a composite Poisson-Gamma distribution is constructed, and a precipitation set is generated using the Monte Carlo sampling method to obtain the precipitation probability distribution result.

[0019] The estimation model is trained in the following manner:

[0020] Construct a deep learning-based fusion model, wherein the output layer of the fusion model contains at least two output nodes, which are used to output the mean parameter and discrete parameter of the composite Poisson-Gamma distribution, respectively.

[0021] Construct a loss function based on a composite Poisson-Gamma distribution, wherein the loss function includes a regularization term for the discrete parameters;

[0022] Using the acquired training set, with the goal of minimizing the loss function, the fusion model is trained using a staged training strategy to obtain the estimated model.

[0023] Furthermore, the phased training strategy includes:

[0024] In the first training phase, the coefficient of the regularization term is set to a first preset value;

[0025] In the second training phase, the coefficient of the regularization term is set to a second preset value, wherein the second preset value is greater than the first preset value;

[0026] In the third training phase, the coefficient of the regularization term is set to a third preset value, wherein the third preset value is greater than the second preset value.

[0027] Furthermore, the loss function includes a power parameter;

[0028] The power parameter is a preset value or a learnable value, and its value range is set between 1 and 2.

[0029] Furthermore, the loss function is set in the following manner:

[0030] For each sample in the training set, if the precipitation of the sample is zero, the loss function is set to a probability mass function based on the Poisson distribution; otherwise, it is set to a probability mass function based on the gamma distribution.

[0031] Furthermore, the precipitation probability distribution results include at least the zero precipitation probability, arbitrary quantile estimates, interval width, and confidence interval.

[0032] Furthermore, the fusion model includes any one of convolutional neural networks, residual neural networks, or Transformer networks; the output layer of the fusion model uses the Softplus activation function or the ReLU activation function.

[0033] Furthermore, during the training process of the estimation model, different learning rates are used for the mean parameter and the discrete parameter, wherein the learning rate for the mean parameter is greater than the learning rate for the discrete parameter.

[0034] Secondly, the present invention provides a multi-source precipitation fusion probability estimation system, comprising:

[0035] The data acquisition module is used to acquire multi-source gridded precipitation characteristic data of the target area;

[0036] The data input module is used to input the multi-source gridded precipitation characteristic data into the trained estimation model to obtain mean parameters and discrete parameters;

[0037] The data output module is used to construct a composite Poisson-Gamma distribution based on the mean parameter, the discrete parameter, and a preset or learned power parameter from the estimation model, and to generate a precipitation set using the Monte Carlo sampling method to obtain the precipitation probability distribution result.

[0038] Thirdly, the present invention provides a computer device including a memory and a processor, wherein the memory stores program instructions that are executed by the processor, and the processor invokes the program instructions to execute the multi-source precipitation fusion probability estimation method described in the first aspect.

[0039] Fourthly, the present invention provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the multi-source precipitation fusion probability estimation method described in the first aspect.

[0040] Compared with the prior art, the advantages of the present invention are:

[0041] This invention provides a multi-source precipitation fusion probability estimation method. Based on the acquired multi-source gridded precipitation characteristic data of the target area, the data is input into the estimation model. By directly learning the composite Poisson-Gamma distribution parameters (mean and discrete parameters) in the estimation model, the mean and discrete parameters are obtained, realizing the joint modeling of precipitation occurrence probability and precipitation intensity. This directly outputs the complete probability distribution of precipitation, achieving end-to-end probabilistic precipitation estimation. Based on the mean, discrete, and power parameters, a composite Poisson-Gamma distribution is constructed, and a Monte Carlo sampling method is used to generate a precipitation set. The output precipitation probability distribution results, including zero precipitation probability, arbitrary quantile estimation, interval width, and confidence interval, are used to quantify the uncertainty of precipitation fusion and meet the needs of hydrological and meteorological applications for probabilistic input products. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a schematic diagram of the structure of the deep learning-based fusion model provided in an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram illustrating the principle of the loss function based on the composite Poisson-Gamma distribution provided in an embodiment of the present invention;

[0045] Figure 3 This is a schematic diagram illustrating the evaluation based on the estimation model provided in an embodiment of the present invention;

[0046] Figure 4 This is a schematic diagram of the Brill's skill score (BSS) values, which compare the predicted values ​​obtained based on the estimation model with the climatological probability at different thresholds, provided in an embodiment of the present invention.

[0047] Figure 5 This is a graph showing the calculation results of indicators predicted by the estimation model in different precipitation intervals, provided by an embodiment of the present invention.

[0048] Figure 6 It is the precipitation probability density function obtained based on the estimation model provided in the embodiments of the present invention;

[0049] Figure 7 This is a comparison chart of performance indicators under different L2 regularization indices provided in the embodiments of the present invention. Detailed Implementation

[0050] To enable those skilled in the art to clearly and completely understand the technical solution of the present invention, the present invention will be further described in detail below with reference to embodiments. Obviously, the embodiments described herein are only for explaining the present invention and are not intended to limit the scope of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0051] To address the three major problems in existing technologies—mismatch between probabilistic models and precipitation statistical characteristics, separation between deterministic fusion and uncertainty quantification, and disconnect between precipitation occurrence and intensity modeling—which make end-to-end probabilistic precipitation estimation difficult, this invention proposes a multi-source precipitation fusion probabilistic estimation method and system. By directly learning composite Poisson-Gamma distribution parameters (mean and discrete parameters) in a deep network, it achieves joint modeling of precipitation occurrence probability and precipitation intensity, thereby directly outputting a complete probability distribution of precipitation and realizing end-to-end probabilistic precipitation estimation. Based on the estimated probability distribution, it can further generate distribution curves, component water density, arbitrary quantile estimates, interval widths, confidence intervals, and a complete set of uncertainty indicators, meeting the needs of hydrological and meteorological applications for probabilistic input products.

[0052] This invention proposes a method and system for probabilistic estimation of multi-source precipitation fusion. To facilitate understanding of the technical solution, the following first describes the construction process of the estimation model, and then elaborates on the specific implementation of applying this model to the probabilistic estimation of multi-source precipitation fusion. Specifically, it may include the following steps:

[0053] S1. Multi-source data integration preparation: Collect multi-source, heterogeneous precipitation-related data within the target area and time period to form multi-source gridded precipitation characteristic data for training and subsequent actual inference, including satellite gridded precipitation, reanalysis model gridded precipitation, and ground interpolation gridded precipitation. Extract surrounding gridded precipitation data (such as satellite products) and auxiliary meteorological data centered on the stations. Specifically, these data should include hourly or daily precipitation observation data from high-quality automatic weather stations (or rain gauges) (i.e., station precipitation truth information, serving as the benchmark for model training and supervised verification), multi-source precipitation information (obtained through satellite remote sensing precipitation products that have not undergone ground station system bias correction, including near-real-time satellite precipitation products and multi-satellite integrated precipitation products, such as IMERG, GSMAP, etc.), geographic environmental information (such as longitude, latitude, elevation information, etc.), and meteorological auxiliary information (precipitation-related data, such as surface temperature, near-surface air pressure, surface dew point temperature, etc.).

[0054] Based on the characteristics of the input data for deep learning, different spatial ranges are selected. Centered on the station, multi-source precipitation information, geographical environment information, precipitation true value information and meteorological auxiliary information are extracted from the grid surrounding each station to construct samples and define training and validation sets.

[0055] All data undergoes rigorous spatiotemporal matching, unifying data from different resolutions to a predefined spatial grid (e.g., 0.1° × 0.1°) using bilinear interpolation or conservative resampling methods. Temporally, data is unified to the same timestamp (e.g., UTC at the top of the hour), and data quality control is implemented, including removing significant outliers from each source data set. The system performs temporal scaling, spatial alignment, missing value handling, and normalization preprocessing on all data.

[0056] S2. Constructing a deep learning-based fusion model: See [link / reference] Figure 1, design a deep learning model capable of processing spatio-temporal data as the fusion backbone. The entire model consists of an input feature layer, a network structure layer, and an output parameter layer. Specifically, use the training set in step S1 above as the input. The network structure layer uses a deep learning model as the core fusion backbone. Convolutional neural networks, residual neural networks, or Transformer networks, etc. can be used to support custom loss functions and have the ability to extract spatio-temporal features. Preferably, a residual neural network is used, which enhances the deep feature extraction ability and alleviates the gradient vanishing problem through a skip connection structure, making it more suitable for the deep fusion and parameter mapping tasks of multi-source, heterogeneous, and high-dimensional precipitation features in this invention; the network structure layer realizes the efficient fusion of multi-source heterogeneous precipitation features in each sample of the training set through residual block stacking and multi-scale feature extraction. The output parameter layer (i.e., the output layer) is designed as two parallel parameter prediction heads (i.e., the output layer of the fusion model contains at least two output nodes). Based on the final feature map extracted by the backbone network, the mean parameter and the discrete parameter are respectively mapped and generated through two independent fully connected layers. The mean parameter represents the predicted mean precipitation intensity, and the discrete parameter controls the dispersion degree of the prediction distribution, which is directly related to the uncertainty magnitude. To ensure its non-negativity, both output layers use activation functions (such as Softplus or ReLU).

[0057] The structure of this dual-output layer extracts multi-scale spatio-temporal features shared by the backbone network, and simultaneously constrains the optimization of the two parameters (i.e., the mean parameter and the discrete parameter) through a zero-value loss term and a positive-value loss term in the loss function in subsequent step S3, realizing the joint modeling of precipitation occurrence probability and precipitation intensity, and depicting the probability distribution and uncertainty.

[0058] S3. Construct a loss function based on the compound Poisson-Gamma distribution: In order to deeply integrate the probability modeling idea into the training process, this invention abandons the commonly used mean square error or mean absolute error loss functions and instead uses the compound Poisson-Gamma distribution as the likelihood function. Its probability density function is applicable to precipitation data with zero values (no precipitation) and continuous positive values (precipitation). Define the negative log-likelihood as the loss function. This loss function has a power parameter p (1 < p < 2), and the power parameter p is a preset value or can be learned. The power parameter p can control the balance between zero probability and the continuity of the positive value part. A regularization term is added to the loss function, specifically the L2 regularization term of the discrete parameter, thereby enhancing the stability and generalization ability of model training. In the actual training of deep learning, a simplified form of the negative log-likelihood loss function is used, which omits the constant term irrelevant to the model parameters and only retains the parts that can be optimized for the mean parameter and the discrete parameter.

[0059] For each sample in the training set (i.e., the site precipitation true value information), the loss function is calculated according to the following formula (1), and this loss function includes a simplified negative log-likelihood term and a regularization term:

[0060] (1)

[0061] In equation (1) above, L is the loss function; N is the number of samples; Let be the precipitation amount for the i-th sample; This is an indicator function. If the condition inside the parentheses is true, the function value is 1; if it is false, the function value is 0. For regularization terms; is the coefficient of the regularization term, representing the regularization strength.

[0062] For any given sample, the probability mass function is based on a Poisson distribution when precipitation is 0, and based on a gamma distribution when precipitation is greater than 0. That is, the loss function is set as follows:

[0063] When the true value of precipitation is 0, its zero-value loss for:

[0064] (2)

[0065] When the true value of precipitation is non-zero, its positive value loss for:

[0066] (3)

[0067] In equations (2) and (3) above, The mean parameter, These are discrete parameters;

[0068] The total loss is the sum of all samples. and The sum of losses, plus a regularization term for the discrete parameters, improves the model's ability to model uncertainty. See also... Figure 2 The Poisson process, as a counting process for zero precipitation events, naturally characterizes the zero-value accumulation feature in precipitation data, corresponding to the zero-value loss term in the loss function. The gamma process, as a process for positive precipitation event intensity, accurately describes the right-skewed long-tailed distribution of precipitation intensity, corresponding to the positive value loss term in the loss function. The combination of these two forms a composite Poisson-Gamma distribution, achieving a unification of zero-point probability density and long-tailed continuous distribution. The simplified form of this loss function is mathematically equivalent to ignoring the normalization constant term c(y, φ, p) in the composite Poisson-Gamma distribution probability density function, which is independent of the model's mean parameter. This normalization constant term has no analytical solution and requires infinite series summation, resulting in high computational cost. Therefore, deleting this term significantly improves computational efficiency while ensuring the correctness of gradient calculation. For discrete parameters, the normalization constant term is related to the discrete parameters; this loss term is equivalently replaced by the L2 regularization term, thereby constraining the learning of discrete parameters and constraining the range of uncertainty estimation.

[0069] This invention constructs a negative log-likelihood loss function based on a composite Poisson-Gamma distribution. It simultaneously constrains the optimization of the mean and discrete parameters through zero-value and positive loss terms, and imposes truncation constraints on the values ​​of the mean parameter µ and the discrete parameter φ, limiting the output to a preset range to ensure numerical stability during training. Furthermore, an L2 regularization term for the discrete parameters is added to the loss function to improve training stability and generalization ability. This loss function drives the network to simultaneously learn the mean and discrete parameters during training, enabling the output probability distribution to match the mixed zero- and positive value structure and intensity distribution of the observed data. In other words, it simultaneously models the fused precipitation probability, fused precipitation intensity, and fused precipitation uncertainty, achieving end-to-end joint modeling of these three factors.

[0070] S4. Training the Fusion Model: Input the preprocessed training set into the model, optimize it using a custom loss function as the training objective, and train the fusion model using a staged training strategy to obtain the estimated model. During the model training process, the AdamW optimizer can be used to assist in stabilizing the training, and ReduceLROnPlateau can be used as the learning rate scheduler for stabilizing the training. Since the mean parameter and the discrete parameter have different ranges, different learning rates are used for the mean parameter and the discrete parameter, with the learning rate for the mean parameter being higher than that for the discrete parameter.

[0071] To address the issue that inherent biases in multi-source satellite precipitation products lead to excessively large discrete parameters in the early stages of model training, this invention employs a phased training strategy, gradually increasing the regularization term at different training phases, namely:

[0072] In the first training phase, the coefficient of the regularization term is set to the first preset value;

[0073] In the second training phase, the coefficient of the regularization term is set to a second preset value, which is greater than the first preset value.

[0074] In the third training phase, the coefficient of the regularization term is set to a third preset value, which is greater than the second preset value.

[0075] This strategy focuses on optimizing the mean parameter in the early stages of training to ensure the accuracy of precipitation intensity estimation. In the later stages of training, it gradually strengthens the constraints on the discrete parameters, so that the model can output a reasonably calibrated uncertainty estimate while maintaining the accuracy of point estimation. This avoids the probability distribution from becoming too dispersed due to excessively large discrete parameters, thus losing its practical value.

[0076] This invention constructs a fusion model with dual output layers, unifying the modeling of precipitation occurrence probability (zero value) and precipitation intensity distribution (positive value) within the same framework, rather than the separate processing used in traditional methods. One output layer outputs the mean parameter of a composite Poisson-Gamma distribution, reflecting the expected precipitation intensity; the other output layer outputs discrete parameters, controlling the dispersion of the composite Poisson-Gamma distribution and directly quantifying the uncertainty of the prediction. The two output layers share deep features extracted from the same backbone network, and through collaborative optimization using a joint loss function, the network automatically balances the fitting of precipitation occurrence events and intensity values ​​during the learning process, overcoming the errors of error propagation and model fragmentation in traditional two-step methods (classification followed by regression). Furthermore, the two output layers naturally adapt to the parameterized form of the composite Poisson-Gamma distribution, giving the model's output probability distribution a clear physical meaning: the Poisson part corresponds to the precipitation occurrence probability, and the gamma part corresponds to the precipitation intensity distribution. These two parts are organically coupled through the power parameter p, achieving an accurate characterization of the statistical properties of precipitation.

[0077] S5. Precipitation Probability Estimation for the Target Area: The standardized multi-source gridded precipitation characteristic data of the target area is input into the training estimation model to obtain the mean and discrete parameters of the station precipitation probability distribution under different spatiotemporal distributions. Based on the mean parameter, discrete parameter, and preset or learned power parameters from the estimation model, a composite Poisson-Gamma distribution is constructed, and a precipitation set is generated using the Monte Carlo sampling method to obtain the precipitation probability distribution results.

[0078] See Figure 3 After inputting multi-source gridded precipitation characteristic data into the estimation model, only one network forward propagation is needed to obtain the mean parameter and discrete parameters. Based on these two parameters, further analysis can be performed to obtain deterministic and uncertain indices. When analyzing the deterministic indices, the mean parameter μ is directly used as the point estimate of precipitation, and the conditional probability function is calculated. The correlation coefficient (CC), root mean square error (RMSE), mean absolute error (MAE), corrected Kling-Gupta efficiency (MKGE), and bias (BIAS) are used to quantitatively assess the certainty and probability of precipitation probability distribution results. This is used to determine whether precipitation will occur; a value greater than 0.5 indicates no precipitation, otherwise precipitation is considered to have occurred. To further verify the reliability and accuracy of this method, indicators such as correlation coefficient (CC), root mean square error (RMSE), mean absolute error (MAE), corrected Kling-Gupta efficiency (MKGE), and bias (BIAS) can be used to quantitatively evaluate the certainty and probability of precipitation probability distribution results. When calculating uncertainty indicators, the model can generate the precipitation distribution under given multi-source precipitation input conditions by using mean and discrete parameters. The generated precipitation distribution simultaneously satisfies three major characteristics: zero expansion (probability density at 0), continuous positive values, and heavy tails (probability still exists at high precipitation levels). A composite Poisson-Gamma distribution is constructed, and the precipitation set can be obtained through Monte Carlo sampling. The precipitation probability distribution curve is plotted, and the results of the precipitation probability distribution, such as water density, arbitrary quantile estimation, interval width, and confidence interval, are output. Furthermore, probabilistic evaluation indicators such as Brill skill score (BSS), average interval width (AIW), continuous graded probability score (CRPS), and predicted interval coverage (PICP) can be calculated to quantitatively evaluate the determinism and probabilistic nature of the precipitation probability distribution results. This invention realizes a complete mapping from end-to-end probabilistic model output to interpretable and applicable probabilistic precipitation products, providing a scientific basis for operational scenarios such as flood warning, drought monitoring, and water resource allocation.

[0079] Example 1

[0080] This embodiment uses China as the experimental region to demonstrate the complete process of the multi-source precipitation fusion probability estimation method. These datasets are publicly available datasets used to verify the effectiveness of the method; the invention is not limited to specific data sources. The specific steps are as follows:

[0081] 1. Data Preparation

[0082] The Chinese region was selected as the experimental area, and multi-source precipitation data covering the study area were collected. This data includes:

[0083] (1) At least one satellite remote sensing precipitation product.

[0084] (2) Meteorological auxiliary information related to precipitation processes, including but not limited to temperature, humidity, wind speed or meteorological elements in reanalysis products.

[0085] (3) Geographical environment information, including latitude and longitude, elevation, slope, climate zone code and underlying surface type, etc.

[0086] Meanwhile, daily precipitation observation data from approximately two thousand ground meteorological stations were collected as reference ground truth for the model training and validation phases. All input data underwent temporal scaling, spatial alignment, missing measurement processing, and normalization preprocessing to construct a sample set adapted to the deep learning model input. The data acquisition and processing procedures were consistent with step S1 above and will not be elaborated here.

[0087] 2. Model Building

[0088] The construction process and principle of the fusion model are consistent with step S2 above, and will not be repeated here. In this embodiment, a residual neural network is used as the core model. This network takes multi-source precipitation feature vectors as input, and its output layer is designed with two neurons, corresponding to the parameters of a composite Poisson-Gamma distribution: one neuron outputs the mean parameter of the distribution (representing the expected precipitation value), and the other neuron outputs the discrete parameter of the distribution (related to uncertainty). An activation function is used to ensure that the output value is within a reasonable range (i.e., both the mean parameter and the discrete parameter are non-negative).

[0089] 3. Construct the loss function

[0090] The construction process and principle of the loss function are the same as in step S3 above, and will not be repeated here. In this embodiment, the power parameter p is set to 1.5.

[0091] 4. Model Training and Optimization

[0092] The prepared sample set is divided into training, validation, and independent test sets according to time or space. In this case, 2000–2010 is used as the training set, 2013–2016 as the validation set, and 2017–2019 as the test set. The specific training process and principles of the model can be found in step S4 above. In this embodiment, the AdamW optimizer is used to assist in stable training, and ReduceLROnPlateau is used as the learning rate scheduler for stable training. The learning rate for the mean parameter is set to 1e-4, and the learning rate for the discrete parameters is set to 1e-5. To better balance the model's estimation of the mean and discrete parameters, the following training strategy is adopted:

[0093] For 0-10 epochs (training rounds), set the coefficient of the regularization term of the discrete parameters in the loss function to 0.1, so that the model learns the estimate of the mean first;

[0094] For 11–30 epochs, the coefficient of the regularization term for the discrete parameters in the loss function is set to 0.5, allowing the model to gradually improve its learning of discrete parameters while ensuring mean learning.

[0095] For 31–50 epochs, the coefficient of the regularization term for the discrete parameters in the loss function is set to 1.0, which improves the model's ability to fit and estimate the discrete parameters in the later stages.

[0096] 5. Precipitation fusion estimation and uncertainty quantification

[0097] To verify the technical effect of the present invention, the certainty and probability of the precipitation probability distribution results are quantitatively evaluated using indicators such as correlation coefficient (CC), root mean square error (RMSE), mean absolute error (MAE), critical success index (CSI), and continuous graded probability score (CRPS). Since the present invention directly outputs the probability of zero precipitation, the calculation of the critical success index (CSI) does not rely on the artificially set precipitation threshold (such as 0.1 mm) in traditional methods, thus avoiding the subjectivity of threshold selection. The multi-source gridded precipitation characteristic data of the target area or time period are input into the trained estimation model, which directly outputs the composite Poisson-gamma distribution parameters of the corresponding samples, namely the mean parameter and the discrete parameter. Based on these two distribution parameters, the following prediction results can be obtained: (1) the point estimation result of the mean of precipitation conditions; (2) the probability of zero precipitation events; (3) the complete precipitation probability distribution for uncertainty analysis. Uncertainty analysis can generate a probability set of precipitation (i.e., precipitation set) by Monte Carlo sampling (e.g., sampling 1000 times), and then calculate the quantile interval (e.g., 95% confidence interval) to quantify uncertainty.

[0098] See Figure 4 The study demonstrates the Brill's skill score (BSS) of the predicted values ​​obtained using this method at different thresholds compared with the climatological probability. The Brill's skill score (BSS) is positive at all thresholds, indicating that the probability prediction of this invention is better than the reference baseline (climatological probability) at all precipitation thresholds, demonstrating that the precipitation predicted by this method has high accuracy in uncertainty fusion estimation.

[0099] See Figure 5 The results demonstrate the performance of the proposed model across different precipitation intervals. Uncertainty indices are used to characterize the model's performance. The average coefficient of variation reflects the level of uncertainty estimation under different precipitation intensities, showing that the model has a higher level of uncertainty estimation in heavy precipitation intervals. Predicted Interval Coverage (PICP) reflects the actual proportion of true values ​​falling within the predicted interval, indicating that the model's constructed predicted intervals completely cover all actual precipitation observations. Continuous Graded Probability Score (CRPS) measures the quality of probabilistic predictions, and the model demonstrates good prediction quality across different precipitation intervals. While the average interval width (AIW) increases, the predicted interval coverage (PICP) remains high, proving that the model ensures complete coverage across all intensities by expanding the interval width.

[0100] This embodiment verifies that the multi-source precipitation fusion method proposed in this invention, which combines residual neural networks and a composite Poisson-Gamma distribution probability framework, achieves integrated precipitation fusion modeling of point estimation and uncertainty estimation. It avoids the statistical assumptions of normalization or logarithmic transformation of precipitation data in traditional methods, and improves the ability to characterize zero precipitation and extreme precipitation events. Figure 6 This demonstrates how the composite Poisson-Gamma distribution, unlike the previously assumed Gaussian distribution, characterizes the long-tailed skewness of precipitation and the water density of components.

[0101] Example 2

[0102] This embodiment is based on the method framework described in Embodiment 1, with the difference being a focused comparative analysis of the impact of different values ​​of the power parameter p in the composite Poisson-Gamma distribution on the deterministic accuracy and uncertainty estimation calibration of the final model. This demonstrates that the selection of parameter p is a key optimization step in the method of this invention and clarifies the optimal parameter range. It should be noted that the data fusion method of this invention does not depend on specific data or regions and can also be applied to the fusion of other data to model precipitation probability distributions. The specific steps are as follows:

[0103] 1. Data Acquisition and Model Building

[0104] The experimental data, model architecture, and training strategy are exactly the same as in Example 1. The only variable is the power parameter p in the loss function.

[0105] 2. Parameter settings and experimental design

[0106] Five different power parameter p values ​​were set for comparative experiments: p=1.1, p=1.3, p=1.5, p=1.7, and p=1.9. Keeping all other hyperparameters (network structure, coefficients of regularization terms, training epochs, etc.) consistent, five independent fusion models were trained (same as in Example 1, using a residual neural network model).

[0107] 3. Evaluation and Comparative Analysis

[0108] Using a unified independent test set, a comprehensive quantitative and qualitative evaluation of the results of the five models was conducted. The comparison dimensions included: the correlation coefficient (CC), root mean square error (RMSE), mean absolute error (MAE), bias (BIAS), modified Kling-Gupta efficiency (MKGE), critical success index (CSI), and coverage probability and average width for different confidence intervals between the five models' outputs and station observations. The mean values ​​of the discrete parameters for the five models were also determined. The calculation results of the evaluation indicators are shown in Table 1 below.

[0109] Table 1. Calculation results of evaluation indicators for different power parameters p

[0110] power parameter p CC RMSE MAE BIAS MKGE PICP_95 (95% coverage) AIW_95 (95% average width of the interval) CSI Discrete parameter mean 1.1 0.572964 7.951989 2.12608 -0.684856 0.30227 0.964821 6.435424 0.644689 1.956494 1.3 0.758686 6.137186 2.042334 0.301609 0.578285 0.977895 8.537077 0.615192 1.506313 1.5 0.752762 6.206322 2.133833 0.380008 0.54566 0.982269 9.74871 0.419174 1.4355 1.7 0.750859 6.224101 2.114417 0.333684 0.556238 0.982708 11.273083 0.396485 1.398168 1.9 0.73924 6.359701 2.184675 0.43354 0.544542 0.628755 15.390839 0.300792 1.964559

[0111] Table 1 above uses point estimation accuracy indicators to evaluate the accuracy of the assessment. Specifically, when the power parameter p = 1.3, the correlation coefficient (CC) reaches its maximum value, the root mean square error (RMSE) and the mean absolute error (MAE) reach their minimum values, the bias (BIAS) is the smallest and is a positive bias, and when the power parameter p is 1.5, the above indicators can all be in a stable value. Prediction quality was evaluated using probabilistic prediction metrics. Specifically, when the power parameter p was between 1.3 and 1.7, a relatively high 95% prediction interval coverage was achieved. Within this range (1.3-1.7), the average width of the 95% interval was smallest when p=1.3, indicating the narrowest interval (highest sharpness) while maintaining high coverage. The interval remained relatively narrow when p=1.5, but began to widen significantly after p=1.7. Therefore, based on these two metrics, the optimal range for the power parameter p was 1.3-1.5. Furthermore, the modified Kling-Gupta efficiency (MKGE) peaked when p=1.3, indicating optimal probabilistic prediction quality. The Critical Success Index (CSI) monotonically decreased with increasing power parameter p value, suggesting that higher power parameter p values ​​might sacrifice the accuracy of precipitation event classification.

[0112] In summary, the model performs best on most comprehensive indicators when the power parameter p is between 1.3 and 1.5. This is mainly because when p is close to 1, the composite Poisson-Gamma distribution tends to describe a situation with a large number of zero values ​​and a small number of extreme values; when p is close to 2, it is closer to the gamma distribution. Daily precipitation data has a large number of zero values ​​(no rainy days) and right-skewed continuous positive values. Experimental results show that p = 1.3–1.5 can best balance the "zero expansion" characteristic of daily precipitation data and the continuous distribution characteristics of the positive value part, thus enabling the model to learn a probabilistic representation that best fits the actual data generation mechanism.

[0113] This embodiment, through systematic comparative experiments, determined that, within the framework of the method described in this invention, the optimal range for the power parameter p of the composite Poisson-Gamma distribution is 1.3 to 1.5 for the daily precipitation fusion task in China. This is not a fixed value, but a high-performance range verified by experiments, providing key parameter configuration guidance for the practical application of this method, and further highlighting the technical advantages of combining probabilistic framework design with parameter optimization in this invention.

[0114] Example 3

[0115] This embodiment is based on the method framework described in Embodiment 1, with the difference being a focused comparative analysis of the impact of different regularization strategies for discrete parameters in the composite Poisson-Gamma distribution on the deterministic accuracy and uncertainty estimation calibration of the final model. This demonstrates that the selection of the regularization strength for discrete parameters is a key optimization step in the method of this invention. The regularization strength reflects, to some extent, the model's trade-off between uncertainty indices and the mean, and also serves as a substitute for the normalization constant term in the probability density function of the composite Poisson-Gamma distribution, which has no analytical solution. It should be noted that the data fusion method of this invention does not depend on specific data or regions and can also be applied to the fusion of other data to model precipitation probability distributions. The specific steps are as follows:

[0116] 1. Data Acquisition and Model Building

[0117] The experimental data and model architecture are exactly the same as in Example 1; the only variable is the training strategy.

[0118] 2. Parameter settings and experimental design

[0119] Five different training strategies were set up for comparative experiments: keeping all other hyperparameters (network structure, choice of power parameter p, training epochs, etc.) consistent, five independent fusion models were trained respectively (same as in Example 1, using a residual neural network model).

[0120] The five different training strategies are as follows:

[0121] 1) During the training process, no regularization method is added to the discrete parameters in 0-50 epochs, that is, no regularization term is added;

[0122] 2) Add low-intensity regularization during training. The L2 regularization intensity is 0.05 in 0-10 epochs, that is, the coefficient of the regularization term in the above formula (2) is set to 0.05; the L2 regularization intensity is 0.1 in 11-30 epochs; and the L2 regularization intensity is 0.2 in 31-50 epochs.

[0123] 3) Add medium-strength regularization during training: L2 regularization strength is 0.1 in 0-10 epochs; L2 regularization strength is 0.2 in 11-30 epochs; and L2 regularization strength is 0.5 in 31-50 epochs.

[0124] 4) Add high-intensity regularization during training: L2 regularization strength is 0.2 in 0-10 epochs; L2 regularization strength is 0.5 in 11-30 epochs; and L2 regularization strength is 1.0 in 31-50 epochs.

[0125] 5) Add extremely high-intensity regularization during training: L2 regularization strength is 0.5 in 0-10 epochs; L2 regularization strength is 1.0 in 11-30 epochs; and L2 regularization strength is 2.0 in 31-50 epochs.

[0126] 3. Evaluation and Comparative Analysis

[0127] Using a unified independent test set, a comprehensive quantitative and qualitative evaluation of the results of the five models was conducted. The five training strategies were compared, and the results of the fused precipitation index were compared with a power parameter p of 1.5. (See [reference needed]). Figure 7 The chart shows a comparison of model performance metrics under different L2 regularization intensities. The comparison reveals that: as regularization intensity increases, the correlation coefficient (CC) gradually increases and tends to stabilize, indicating a strong linear correlation between model predictions and actual precipitation; regularization significantly reduces the root mean square error (RMSE), indicating a slight improvement or stabilization in point estimation accuracy; regularization reduces the mean absolute error (MAE), and while MAE increases slightly with increasing regularization intensity, the difference is not significant, indicating that regularization has no significant negative impact on the mean absolute error. Bias decreases, indicating that regularization helps reduce systematic bias; the continuous graded probability score (CRPS) reaches its optimum at extremely high regularization, indicating that appropriate regularization helps improve probabilistic prediction accuracy; as regularization intensity increases, the average value of discrete parameters (mean Φ) gradually increases, indicating that regularization effectively improves the model's ability to estimate uncertainty.

[0128] This embodiment, through systematic comparative experiments, determines that, within the framework of the present invention, the regularization strength of discrete parameters reflects the model's ability to balance point estimation accuracy and probability distribution calibration for diurnal precipitation fusion tasks. Experimental results demonstrate that the L2 regularization introduced in this invention not only solves the problem of the composite Poisson-Gamma distribution being difficult to optimize directly due to the incalculable normalization constant, but also achieves effective control over the precipitation probability distribution by adjusting the regularization strength. This results in fusion results that possess both accurate deterministic estimation and reliable probabilistic information, fully demonstrating the innovative advantages of this method in probabilistic precipitation estimation. This invention uses a composite Poisson-Gamma distribution for probabilistic precipitation modeling. The regularization term of the discrete parameters, to a certain extent, compensates for the drawback of the pure composite Poisson-Gamma distribution, where the normalization parameter is an infinite series, making it unsuitable for deep learning computation. By adjusting the regularization strength, the model achieves a balance between overall point value accuracy and ensemble member uncertainty.

[0129] In summary, the method of this invention constructs a deep learning-based fusion model with dual output layers, deeply integrating the loss function of the composite Poisson-Gamma distribution into the network training process. This achieves end-to-end mapping from multi-source heterogeneous inputs to the complete probability distribution function, thereby providing high-quality, interpretable probabilistic input products for applications such as refined flood forecasting, water resource probabilistic prediction, and meteorological disaster risk assessment. Furthermore, by ignoring the normalization constant term and introducing L2 regularization constraints on discrete parameters when constructing the loss function, the originally non-differentiable mathematical model is reconstructed in an engineering manner, making it usable in backpropagation. This overcomes the aforementioned technical obstacles and has significant theoretical and engineering value.

[0130] By driving the network to learn from input data through a custom-defined differentiable loss function and jointly optimizing the mean and discrete parameters, a unified modeling of precipitation probability and intensity is achieved. Compared with existing methods, this method can output a complete fused precipitation probability distribution end-to-end, including the zero precipitation probability, arbitrary quantile estimates, and confidence intervals, reducing the dependence of probability estimates on post-correction. This method significantly improves the uncertainty quantification capability of precipitation fusion and has the advantages of computational efficiency, clear principle, strong adaptability, and physically consistent results, providing high-quality probabilistic input products for hydrological forecasting and meteorological risk assessment.

[0131] The implementation of the various embodiments of this invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of this invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, this invention provides a multi-source precipitation fusion probability estimation system, which is used to execute the multi-source precipitation fusion probability estimation method described in the above embodiments. The system includes:

[0132] The data acquisition module is used to acquire multi-source gridded precipitation characteristic data of the target area;

[0133] The data input module is used to input multi-source gridded precipitation characteristic data into the estimation model to obtain mean parameters and discrete parameters;

[0134] The data output module is used to construct a composite Poisson-Gamma distribution based on the mean parameter, discrete parameters, and preset or learned power parameters from the estimation model, and to generate a precipitation set using the Monte Carlo sampling method to obtain the precipitation probability distribution results.

[0135] It should be noted that the system embodiments provided by the present invention are used not only to implement the methods in the above method embodiments, but also to implement the methods in other method embodiments provided by the present invention. The only difference is that corresponding functional modules are set. The principle is basically the same as that of the above system embodiments provided by the present invention. As long as those skilled in the art can improve the equipment in the above system embodiments based on the above system embodiments, refer to the specific technical solutions in other method embodiments, obtain the corresponding technical means and the technical solutions composed of these technical means by combining technical features, and improve the equipment in the above system embodiments under the premise of ensuring the practicality of the technical solutions, the corresponding system-like embodiments can be obtained to implement the methods in other method-like embodiments.

[0136] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides a computer device, including a memory and a processor. The memory stores program instructions that are executed by the processor, and the processor calls the program instructions to execute a multi-source precipitation fusion probability estimation method.

[0137] In embodiments of the present invention, the memory can be non-volatile memory, such as a hard disk drive (HDD) or a solid-state drive (SSD), or it can be volatile memory, such as random-access memory (RAM). Memory is any other medium capable of carrying or storing desired program code having an instruction or data structure form and accessible by a computer, but is not limited thereto. The memory in embodiments of the present invention can also be a circuit or any other device capable of implementing a storage function for storing program instructions and / or data.

[0138] In this embodiment of the invention, the processor may be a general-purpose processor, a digital signal processor, an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components, capable of implementing or executing the methods, steps, and logic block diagrams disclosed in this embodiment of the invention. The general-purpose processor may be a microprocessor or any conventional processor. The steps of the methods disclosed in this embodiment of the invention can be directly manifested as being executed by a hardware processor, or executed by a combination of hardware and software modules within the processor.

[0139] Based on the same inventive concept as the foregoing embodiments, this embodiment of the invention also provides a non-transitory computer-readable storage medium that stores computer instructions that cause a computer to execute a multi-source precipitation fusion probability estimation method.

[0140] The above detailed embodiments describe the implementation of the present invention; however, the present invention is not limited to the specific details described in the above embodiments. Within the scope of the claims and technical concept of the present invention, various simple modifications and changes can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.

Claims

1. A multi-source precipitation fusion probability estimation method, characterized in that, include: Acquire multi-source gridded precipitation characteristic data for the target area; The multi-source gridded precipitation characteristic data are input into the trained estimation model to obtain mean parameters and discrete parameters; Based on the mean parameter, the discrete parameter, and the preset or learned power parameter from the estimation model, a composite Poisson-Gamma distribution is constructed, and a precipitation set is generated using the Monte Carlo sampling method to obtain the precipitation probability distribution result. The estimation model is trained in the following manner: Construct a deep learning-based fusion model, wherein the output layer of the fusion model contains at least two output nodes, which are used to output the mean parameter and discrete parameter of the composite Poisson-Gamma distribution, respectively. Construct a loss function based on a composite Poisson-Gamma distribution, wherein the loss function includes a regularization term for the discrete parameters; Using the acquired training set, with the goal of minimizing the loss function, the fusion model is trained using a staged training strategy to obtain the estimated model.

2. The multi-source precipitation fusion probability estimation method according to claim 1, characterized in that, The phased training strategy includes: In the first training phase, the coefficient of the regularization term is set to a first preset value; In the second training phase, the coefficient of the regularization term is set to a second preset value, wherein the second preset value is greater than the first preset value; In the third training phase, the coefficient of the regularization term is set to a third preset value, wherein the third preset value is greater than the second preset value.

3. The multi-source precipitation fusion probability estimation method according to claim 1, characterized in that, The loss function includes a power parameter; The power parameter is a preset value or a learnable value, and its value range is set between 1 and 2.

4. The multi-source precipitation fusion probability estimation method according to claim 1 or 3, characterized in that, The loss function is set in the following manner: For each sample in the training set, if the precipitation of the sample is zero, the loss function is set to a probability mass function based on the Poisson distribution; otherwise, it is set to a probability mass function based on the gamma distribution.

5. The multi-source precipitation fusion probability estimation method according to claim 1, characterized in that, The precipitation probability distribution results include at least the zero precipitation probability, arbitrary quantile estimates, interval width, and confidence interval.

6. The multi-source precipitation fusion probability estimation method according to claim 1, characterized in that, The fusion model includes any one of convolutional neural networks, residual neural networks, or Transformer networks; the output layer of the fusion model uses the Softplus activation function or the ReLU activation function.

7. The multi-source precipitation fusion probability estimation method according to claim 1, characterized in that, During the training of the estimation model, different learning rates are used for the mean parameter and the discrete parameter, wherein the learning rate for the mean parameter is greater than the learning rate for the discrete parameter.

8. A multi-source precipitation fusion probability estimation system, characterized in that, include: The data acquisition module is used to acquire multi-source gridded precipitation characteristic data of the target area; The data input module is used to input the multi-source gridded precipitation characteristic data into the trained estimation model to obtain mean parameters and discrete parameters; The data output module is used to construct a composite Poisson-Gamma distribution based on the mean parameter, the discrete parameter, and a preset or learned power parameter from the estimation model, and to generate a precipitation set using the Monte Carlo sampling method to obtain the precipitation probability distribution result.

9. A computer device, characterized in that, The system includes a memory and a processor, the memory storing program instructions that are executed by the processor, the processor invoking the program instructions to execute the multi-source precipitation fusion probability estimation method according to any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to execute the multi-source precipitation fusion probability estimation method according to any one of claims 1 to 7.

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