A method for estimating rainfall in alpine regions based on bayesian optimization sm2rain algorithm

Abstract

The application discloses a high-cold region rainfall method based on a Bayesian optimization SM2RAIN algorithm, and the method comprises the following steps: determining a first batch of to-be-optimized parameters based on the SM2RAIN algorithm and a soil moisture balance equation; determining a second batch of to-be-optimized parameters by considering soil moisture inversion errors; iteratively optimizing the first batch of to-be-optimized parameters and the second batch of to-be-optimized parameters based on a Bayesian algorithm to determine an optimal parameter interval; constructing an estimation model according to the optimal parameter interval; and estimating rainfall information based on the estimation model. By using the application, the rainfall estimation accuracy can be improved. The application can be widely applied to the field of rainfall monitoring as a high-cold region rainfall method based on the Bayesian optimization SM2RAIN algorithm.

Description

Technical Field

[0001] The present invention relates to the field of rainfall monitoring, and in particular to a method for estimating rainfall in alpine areas based on a Bayesian optimization SM2RAIN algorithm. Background Art

[0002] Satellite remote sensing observations offer the advantage of spatial continuity and can provide rainfall information in areas without observation stations. The continuous advancement and improvement of rainfall remote sensing technology has provided a key tool for resolving global precipitation estimates. Satellite remote sensing rainfall products have gradually become an important data source for hydrology and meteorology. Current satellite remote sensing precipitation estimates utilize a top-down observation approach, inverting atmospheric signals scattered or emitted by hydrometeors. This observational approach enables the estimation of different types of precipitation, including snow, light rain, and hail. However, the indirect and instantaneous nature of satellite observations can introduce significant uncertainty into precipitation estimates. Summary of the Invention

[0003] In order to solve the above technical problems, the purpose of the present invention is to provide a rainfall estimation method in high-cold areas based on the Bayesian optimization SM2RAIN algorithm, which can improve the accuracy of rainfall estimation.

[0004] The first technical solution adopted by the present invention is: a method for estimating rainfall in cold regions based on the Bayesian optimization SM2RAIN algorithm, comprising the following steps:

[0005] Based on the SM2RAIN algorithm and the soil water balance equation, the first batch of parameters to be optimized are determined;

[0006] Considering the soil moisture inversion error, the second batch of parameters to be optimized are determined;

[0007] Based on the Bayesian algorithm, the first batch of parameters to be optimized and the second batch of parameters to be optimized are iteratively optimized to determine the optimal parameter range;

[0008] Construct an estimation model based on the optimal parameter interval;

[0009] Estimate rainfall information based on the estimation model.

[0010] Furthermore, it also includes:

[0011] Evaluate the estimation model according to the preset evaluation indicators;

[0012] The preset evaluation indicators include the Pearson correlation coefficient between the predicted precipitation and the measured precipitation, the Nash-Sutcliffe efficiency, the root mean square error, the positive deviation and the negative deviation.

[0013] Furthermore, the expression of the estimation model is as follows:

[0014] Zds(t) / dt = p(t) - r(t) - e(t) - g(t)

[0015] In the above formula, p(t) represents the precipitation, r(t) represents the runoff, e(t) represents the total amount of soil moisture evaporation transpiration loss, g(t) represents the drainage rate, and Z represents the soil depth.

[0016] Further, the related formula of the first batch of parameters to be optimized is as follows:

[0017]

[0018] In the above formula, s(t) [-] represents the surface soil humidity, as(t) b represents the drainage rate, and a and b represent two parameters of the nonlinear relationship between the drainage rate and the soil saturation, Z, a, and b are the first batch of parameters to be optimized.

[0019] Further, the related formula of the second batch of parameters to be optimized is as follows:

[0020] SWI (n) = SWI (n-1) + K n (s(t n )- SWI (n-1) )

[0021]

[0022]

[0023] In the above formula, SWI represents the filtered soil moisture, K n represents the soil moisture gain, T represents the characteristic time length, T base and T pot represent the second batch of parameters to be optimized.

[0024] Further, the step of determining the best parameter interval based on the Bayesian algorithm to iteratively optimize the parameters to be optimized includes:

[0025] According to the first batch of parameters to be optimized and the second batch of parameters to be optimized, a parameter set is constructed and an optimization problem is obtained;

[0026] Based on the Bayesian algorithm, the parameters in the parameter set are iteratively optimized, and according to the Bayesian iteration result, the parameters are positioned to the first interval;

[0027] Fine-tuning is performed in the first interval to determine the final parameter range of the Bayesian optimization and obtain the best parameter interval.

[0028] Further, the step of estimating the rainfall information based on the estimation model includes:

[0029] Soil moisture data is obtained based on passive microwave radiometer and input into the estimation model;

[0030] Soil moisture data is processed based on the estimation model and rainfall information is output.

[0031] Furthermore, the Bayesian optimization formula is expressed as follows:

[0032]

[0033] In the above formula, θ is the model parameter set, P(θ) represents the prior probability distribution of the unknown target function f, P(θ|D) represents the posterior probability distribution of the unknown target function f, P(D) is the probability density function of the observed data, and P(D|θ) is the conditional probability density function of the observed data with prior information.

[0034] The beneficial effects of the method of the present invention are as follows: the present invention optimizes the parameter estimation of the SM2RAIN algorithm under the Bayesian framework and proposes a more robust model SM2RAIN-BayesOpt model, which can effectively improve the accuracy of precipitation estimation and has important reference value for rainfall monitoring in high-altitude and cold areas where there is a lack of observation data. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flowchart of the steps of a rainfall method for high-cold areas based on the Bayesian optimization SM2RAIN algorithm of the present invention;

[0036] Figure 2 It is a flow chart of the SM2RAIN-BayesOpt model of a specific embodiment of the present invention. DETAILED DESCRIPTION

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are provided for ease of description only and do not limit the order of the steps. The order of execution of the steps in the embodiments can be adaptively adjusted based on the understanding of those skilled in the art.

[0038] Reference Figure 1 and Figure 2 The present invention provides a method for estimating rainfall in high-cold areas based on the Bayesian optimization SM2RAIN algorithm, the method comprising the following steps:

[0039] S1. Based on the SM2RAIN algorithm and the soil water balance equation, the first batch of parameters to be optimized (Z, a, b) are determined;

[0040] The SM2RAIN algorithm uses the soil water balance equation as its inversion basis, directly estimating the cumulative rainfall between the previous and next phases using information about soil moisture changes. The soil water balance equation at soil depth Z [mm] can be expressed as follows:

[0041] Zds(t) / dt=p(t)-r(t)-e(t)-g(t)

[0042] In the above formula, s(t)[-] is the surface soil moisture, t(d) is the time, p(t), r(t), e(t), and g(t) (mm / d) represent precipitation, runoff, total soil evapotranspiration, and drainage rate, respectively. Assuming that the contributions of evapotranspiration and surface runoff are negligible during a rainfall event, the drainage rate can be calculated using the relationship g(t) = as(t). b , a (mm / d) and b (-) are two parameters that represent the nonlinear relationship between drainage rate and soil saturation.

[0043] Rearranging the soil water balance equation yields:

[0044]

[0045] The rainfall is estimated using soil relative humidity or soil relative saturation and its temporal fluctuations. The first three parameters to be corrected are (Z, a, b)

[0046] S2, considering the soil moisture inversion error, determine the second batch of parameters to be optimized;

[0047] The error in satellite soil moisture inversion will cause high-frequency fluctuations in soil moisture. Therefore, the soil moisture product needs to be filtered before input into the SMA2RAIN model. The recursive formula of the soil moisture index filter is:

[0048] SWI (n) =SWI (n-1) +K n (s(t n )-SWI (n-1) )

[0049] In the above formula, SWI is the filtered soil moisture, K is t n The gain is given by:

[0050]

[0051] Assuming that parameter T changes with SWI, since drainage rate is proportional to soil moisture change, parameter T decreases with the increase of soil moisture. Considering the nonlinearity of seepage process, T is calculated by T base and T pot Two parameters are determined:

[0052]

[0053] So far, the five parameters that need to be determined for the SM2RAIN algorithm are (Z, a, b, T base , T pot ).

[0054] S3. Iteratively optimize the first batch of parameters to be optimized and the second batch of parameters to be optimized based on the Bayesian algorithm to determine the optimal parameter range;

[0055] S3.1. Construct a parameter set based on the first batch of parameters to be optimized and the second batch of parameters to be optimized and obtain the optimization problem;

[0056] Specifically, the parameter set θ is formed. Parameter estimation for complex models can be regarded as finding the optimal parameter set θ opt A nonlinear optimization problem that maximizes (or minimizes) the unknown objective function f.

[0057]

[0058] In the above formula, θ is the model parameter set, R d is the d-dimensional value space of the parameter.

[0059] S3.2. Iteratively optimize the parameters in the parameter set based on the Bayesian algorithm, and locate the parameters to the first interval according to the Bayesian iteration results;

[0060] Specifically, the Bayesian optimization process utilizes Bayes' theorem:

[0061]

[0062] where P(θ) and P(θ|D) are the prior and posterior probability distributions of f, respectively; P(D) is the probability density function of the observed data; and P(D|θ) is the conditional probability density function of the observed data with prior information.

[0063] The Bayesian algorithm is to find the best parameters in a bounded area. The initial parameter θ i Randomly select within the bounded region and then iterate the following two steps to obtain the optimal parameters: 1) Update the posterior distribution f(θ) based on the Gaussian process model. 2) Find the next evaluation point θ that maximizes the acquisition function α(θ) i+1 =maxθ∈α i (θ; D 1:t ). The acquisition function is composed of the observed t groups of data D 1:t The posterior distribution of . The Gaussian distribution is

[0064]

[0065] In the above formula, μ is the expectation and σ is the variance.

[0066] S3.3. Fine-tune in the first interval to determine the final parameter range of Bayesian optimization and obtain the optimal parameter interval.

[0067] Specifically, when using Bayesian optimization to optimize the parameters of the SM2RAIN algorithm, the optimal parameters are searched within a parameter interval. An overly wide parameter interval will result in multiple Bayesian iterations, consuming significant time and computing power. An overly narrow parameter interval will result in missing the optimal parameter interval, reducing model accuracy. To address this issue, this paper conducts parameter optimization in two steps. In the first step, a sufficiently wide interval is set to cover the range of possible parameter values. Based on the results of the Bayesian iteration, the parameters are positioned near the optimal interval. In the second step, fine-tuning is performed near the optimal interval to determine the final parameter range for the Bayesian optimization.

[0068] S4. Construct an estimation model based on the optimal parameter interval;

[0069] S5. Estimate rainfall information based on the estimation model.

[0070] As a further preferred embodiment of the present method, it further includes:

[0071] S6. Evaluate the estimation model according to the preset evaluation indicators;

[0072] Specifically, these include the Pearson's correlation coefficient (R), Nash-Sutcliffe efficiency index (NSE), root mean square error (RMSE), overestimated bias (BIAS), and underestimated bias (BIAS) between predicted and measured precipitation. The specific formulas are shown in Table 2. R, which ranges from -1 to 1, represents the correlation between the two datasets. NS, which ranges from -∞ to 1, represents the overall estimation performance; the closer it is to 1, the more reliable the model. RMSE represents the overall estimation error; the closer it is to 0, the better. +BIAS represents the percentage of observed values ​​overestimated by the model estimate, reflecting the impact of soil moisture fluctuations caused by non-rainfall factors; the closer it is to 0, the better. -BIAS represents the percentage of observed values ​​underestimated by the model estimate, reflecting the degree of underestimation of precipitation during peak precipitation periods; the closer it is to 0, the better.

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] In the above formula, Pobs represents the rainfall observation value, Pest represents the rainfall estimation value, cov represents the covariance factor, σ represents the standard deviation operator, ∑ represents the summation operator, and N represents the number of samples. Mean.

[0079] The key to the SM2RAIN-BayesOpt model algorithm lies in the upper limit of the parameter interval. While excessively large values ​​can ensure that the optimal parameters fall within the interval, they cause the Bayesian algorithm to calculate invalid prior information at the initial random points, resulting in slow convergence. To achieve rapid parameter optimization, this paper uses the minimum root mean square error as the criterion, adopts a wide interval selection strategy, and sets the number of optimization iterations to 200. Based on the results of 200 Bayesian iterations, the upper limit of the interval is narrowed to find the optimal parameter range.

[0080] Evaluation of the optimized rainfall estimation model: Taking the ground-measured rainfall at meteorological stations as a reference, the SM2RAIN-BayesOpt algorithm generally outperforms the SM2RAIN algorithm, mainly in terms of the improvement of the NS value.

[0081] Comparison of the accuracy of different rainfall products: Taking the observed rainfall at the station as the benchmark, the results of the SM2RAIN-BayesOpt model are compared. The +BIAS of the SM2RAIN-BayesOpt estimated rainfall has a significant advantage over the SM2RAIN-ASCAT rainfall product. At the same time, the +BIAS of the SM2RAIN-ASCAT rainfall product also has a significant advantage over ERA5. This shows that the high temporal and spatial resolution of SMAP soil moisture can improve the phenomenon of overestimation of rainfall by the SM2RAIN algorithm caused by soil moisture noise.

[0082] Performance of rainfall estimation algorithms under different land cover types: The performance of the SM2RAIN algorithm under different land cover types was analyzed by comparing the R, NS, RMSE, +BIAS, and -BIAS indicators of the SM2RAIN-BayesOpt model and the SM2RAIN-ASCAT rainfall product for alpine meadows, grasslands, deserts, and woodlands. The SM2RAIN-BayesOpt rainfall estimation results showed that grasslands (R mean = 0.703, NS mean = 0.48, RMSE mean = 2.062 mm / day) performed better than alpine meadows (R mean = 0.664, NS mean = 0.41, RMSE mean = 2.757 mm / day). Alpine meadows also performed better than deserts (R = 0.545, NS = 0.281, RMSE = 1.422 mm / day at the Ali station) and woodlands.

[0083] In view of the uncertainty of soil moisture input and parameter estimation of the SM2RAIN model, this paper proposes a rainfall estimation model SM2RAIN-BayesOpt based on Bayesian optimization, taking the SMAPLevel-4 soil moisture product as input. The Qinghai-Tibet Plateau, Heihe River Basin and Shandian River Basin are used as study areas to evaluate the rainfall estimation effect of the improved model in alpine areas. Compared with the SM2RAIN model, SM2RAIN-BayesOpt has higher optimization efficiency and can ensure that the model has a better fitting effect after parameter optimization. This study draws the following main conclusions: (1) The mean R and NS of the SM2RAIN-ASCAT rainfall product and the ground station rainfall are 0.571 and 0.254, respectively, and the accuracy is relatively low. After Bayesian optimization, the accuracy of SM2RAIN-BayesOpt rainfall is significantly improved, and its mean R and NS reach 0.669 and 0.425, respectively. This paper constructs a rainfall estimation model based on the Bayesian optimization algorithm, providing an effective method for rainfall estimation in alpine areas with insufficient data.

[0084] like Figure 2 As shown in FIG, a rainfall estimation system for high-altitude cold regions based on the Bayesian optimization SM2RAIN algorithm includes:

[0085] The optimization parameter determination module, based on the SM2RAIN algorithm and the soil moisture balance equation, determines the first batch of parameters to be optimized; considering the soil moisture inversion error, determines the second batch of parameters to be optimized;

[0086] Iterative optimization module, which iteratively optimizes the first batch of parameters to be optimized and the second batch of parameters to be optimized based on the Bayesian algorithm to determine the optimal parameter range;

[0087] Model building module, which builds an estimation model based on the optimal parameter interval;

[0088] an estimation module configured to estimate the rainfall information based on an estimation model.

[0089] In particular, the method further comprises:

[0090] an evaluation module configured to evaluate the estimation model according to a preset evaluation index.

[0091] The contents in the above method embodiments are applicable to the system embodiments, the system embodiments specifically implement the same functions as the above method embodiments, and achieve the same beneficial effects as the above method embodiments.

[0092] A high-cold region rainfall device based on a Bayesian optimization SM2RAIN algorithm:

[0093] at least one processor;

[0094] at least one memory configured to store at least one program;

[0095] When the at least one program is executed by the at least one processor, the at least one processor implements the high-cold region rainfall method based on the Bayesian optimization SM2RAIN algorithm.

[0096] The contents in the above method embodiments are applicable to the device embodiments, the device embodiments specifically implement the same functions as the above method embodiments, and achieve the same beneficial effects as the above method embodiments.

[0097] A storage medium having processor-executable instructions stored therein, wherein the processor-executable instructions, when executed by a processor, are configured to implement the high-cold region rainfall method based on the Bayesian optimization SM2RAIN algorithm.

[0098] The contents in the above method embodiments are applicable to the storage medium embodiments, the storage medium embodiments specifically implement the same functions as the above method embodiments, and achieve the same beneficial effects as the above method embodiments.

[0099] The above is a specific description of the preferred embodiments of the application, but the application is not limited to the above embodiments, and those skilled in the art can make various equivalent modifications or replacements without departing from the spirit of the application, and these equivalent modifications or replacements are all included in the scope defined by the claims of the present application.

Claims

1. A method for estimating rainfall in cold regions based on the Bayesian optimization SM2RAIN algorithm, characterized in that: The following steps are involved: Based on the SM2RAIN algorithm and the soil water balance equation, the first batch of parameters to be optimized are determined; Considering the soil moisture inversion error, the second batch of parameters to be optimized are determined; Based on the Bayesian algorithm, the first batch of parameters to be optimized and the second batch of parameters to be optimized are iteratively optimized to determine the optimal parameter range; Construct an estimation model based on the optimal parameter interval; Estimating rainfall information based on the estimation model; The expression of the estimation model is as follows: Zds(t) / dt=p(t)-r(t)-e(t)-g(t) In the above formula, p(t) represents precipitation, r(t) represents runoff, e(t) represents the total amount of soil water loss by evaporation and transpiration, g(t) represents drainage rate, and Z represents soil depth; The relevant formulas for the first batch of parameters to be optimized are as follows: In the above formula, s(t)[-] represents the surface soil moisture, as(t) b represents the drainage rate, a and b represent two parameters of the nonlinear relationship between drainage rate and soil saturation, Z, a, and b are the first batch of parameters to be optimized; The relevant formulas for the second batch of parameters to be optimized are as follows: SWI (n) <SWI (n-1) +K n (st n )-SWI (n-1) ) In the above formula, SWI represents the filtered soil moisture, K n represents soil moisture gain, T represents the characteristic time length, T base and T pot Represents the second batch of parameters to be optimized, and n represents the nth observation data in the time series.

2. The method for estimating rainfall in cold regions based on the Bayesian optimization SM2RAIN algorithm according to claim 1, characterized in that: Also includes: Evaluate the estimation model according to the preset evaluation indicators; The preset evaluation indicators include the Pearson correlation coefficient between the predicted precipitation and the measured precipitation, the Nash-Sutcliffe efficiency, the root mean square error, the positive deviation and the negative deviation.

3. The method for estimating rainfall in cold regions based on the Bayesian optimization SM2RAIN algorithm according to claim 1, characterized in that: The step of iteratively optimizing the parameters to be optimized based on the Bayesian algorithm and determining the optimal parameter range specifically includes: Construct a parameter set based on the first batch of parameters to be optimized and the second batch of parameters to be optimized and obtain an optimization problem; Iteratively optimize the parameters in the parameter set based on the Bayesian algorithm, and locate the parameters to the first interval according to the Bayesian iteration results; Fine-tune in the first interval to determine the final parameter range of Bayesian optimization and obtain the optimal parameter interval.

4. The method for estimating rainfall in cold regions based on the Bayesian optimization SM2RAIN algorithm according to claim 3, characterized in that: The step of estimating rainfall information based on the estimation model specifically includes: Soil moisture data is obtained based on passive microwave radiometer and input into the estimation model; Soil moisture data is processed based on the estimation model and rainfall information is output.

5. The method for estimating rainfall in cold regions based on the Bayesian optimization SM2RAIN algorithm according to claim 4, characterized in that: The Bayesian optimization formula is expressed as follows: In the above formula, θ is the model parameter set, P(θ) represents the prior probability distribution of the unknown target function f, P(θ|D) represents the posterior probability distribution of the unknown target function f, P(D) is the probability density function of the observed data, and P(D|θ) is the conditional probability density function of the observed data with prior information.

Images