CN117171971A - A downscaling correction method for high-precision surface modeling based on Bayesian optimization - Google Patents

Abstract

The invention discloses a Bayesian optimization-based high-precision curved surface modeling downscaling correction method, which comprises the following steps of: constructing a downscaling model, and taking precipitation reference data points as sample point elements; acquiring sample point data and an iteration initial value; calculating high-precision curved surface modeling by using sample point data and iteration initial values; performing error calculation to obtain an error value; acquiring a mean function and a covariance matrix in a Gaussian process; judging whether the maximum iteration times are reached, if so, acquiring a target curved surface corresponding to the high-precision curved surface modeling model parameter with the minimum error, and correcting the existing downscaling result; otherwise, calculating the next group of high-precision curved surface modeling model parameters based on the current mean function and the covariance matrix, calculating sample point data and a target curved surface corresponding to the iteration initial value, and acquiring an error value again. The method can be used for downscaling correction, has lower model uncertainty, can obviously improve downscaling precision, and further obtains a downscaling result with higher precision.

Description

A downscaling correction method for high-precision surface modeling based on Bayesian optimization

Technical field

The invention relates to the field of remote sensing technology, and in particular to a high-precision surface modeling downscaling correction method based on Bayesian optimization.

Background technique

Precipitation is an important part of the global water cycle and the basic driving factor of surface hydrological processes. Precipitation data are also important basic data for river basin hydrological analysis, water resources planning and management, flood and drought monitoring and other research. At present, the main means of obtaining precipitation data include meteorological stations, radar observations and satellite remote sensing. Limited by the inherent flaws of various methods and the constraints of external conditions, downscaling of remote sensing precipitation data has become an important means of obtaining high-resolution precipitation data. At present, precipitation downscaling is mainly divided into two types: statistical downscaling and dynamic downscaling. With the research and development in recent years, statistical downscaling methods with small computational complexity and flexible methods have become more widely used.

Statistical downscaling is based on the following assumption: the precipitation field is composed of a determined heterogeneous part and a random homogeneous part, where the heterogeneous part can be explained by environmental variables, and this statistical relationship does not change with changes in scale. ; The homogeneous part will not be disturbed by other factors, has stable properties and is not easy to be simulated by statistical models. By constructing the statistical relationship between environmental variables and precipitation, the heterogeneous part of the precipitation field can be effectively simulated, while the homogeneous part needs to be supplemented by residual correction.

Residual correction is an important step in statistical precipitation downscaling. In the past few decades, many interpolation methods have been used in the study of downscaling residual correction. For example, Chen, Zhao, Alexakis, Zheng Jie, Peng Jie, etc. used spline interpolation method to correct precipitation downscaling residuals; He, Immerzeel, Jia et al. used simple tension spline interpolation method in precipitation downscaling residual correction; Ma Jinhui et al. combined Thiessen polygon and tension spline interpolation in the downscaling residual correction process; Hu Shi et al. used a bilinear interpolation method in the study of precipitation downscaling in the Taihang Mountains; Du Fangzhou et al. used inverse distance weight interpolation The residual correction method was applied to Northeast China; Shengxia et al. used the ordinary Kruger interpolation method to study precipitation downscaling on the Tibetan Plateau. Although there are many methods used to correct precipitation downscaling residuals, the existing methods are either based on geostatistical theory, or based on neighborhood correlation assumptions, or based on elastic mechanics mechanisms, but do not start from the elements of the surface itself. The constraint effect of surface intrinsic factors on surface reconstruction is considered. Error problems and multi-scale problems in the residual correction process cannot be effectively eliminated.

High Accuracy Surface Modeling (HASM) is a new spatial interpolation method developed in recent years. It is based on surface theory and optimal control theory, takes global approximate data as the driving field, and locally high Accuracy data is an optimized control condition, which can effectively solve the error problem and multi-scale problem in residual correction. The HASM method has shown strong advantages in the construction of digital elevation models (DEM), simulation of soil attribute elements, and analysis of spatial and temporal changes in climate elements. At the same time, a large number of studies by Yue Tianxiang and others have also shown that the simulation of high-precision surface modeling methods The accuracy is improved by many orders of magnitude compared to classical interpolation methods. Recently, some scholars have begun to use HASM to participate in precipitation downscaling research. However, current research mainly improves the accuracy of downscaling results by fusing downscaling results and actual measurement sites, and has not attempted to eliminate the influence of homogeneous parts of precipitation.

Although many scholars have proven that high-precision surface modeling algorithms have great advantages in residual correction, a large number of structural parameters need to be set in the actual application process, among which there are 8 main parameters that need to be considered, namely lamdazhi, songchi , jizhiid, pinghuaid, caiyangid, hasmtime, banjing, luid (as shown in Table 1). Users need to set parameters appropriately according to simulation requirements. The settings of these parameters introduce uncertainty into high-precision surface modeling, and also affect the accuracy and stability of the results.

Table 1 Model structure parameters table

Optimizing the selection of high-precision surface modeling model parameters is of great significance to improving the robustness of high-precision surface modeling models and the accuracy of results. However, current research on high-precision surface modeling parameter uncertainty and parameter optimization is still very scarce, resulting in low accuracy of downscaling correction using high-precision surface modeling models.

Contents of the invention

In view of the above-mentioned deficiencies in the prior art, the present invention provides a high-precision surface modeling downscaling correction method based on Bayesian optimization, which solves the problem that the existing technology cannot effectively eliminate the problems in the residual correction process during the downscaling correction process. Error problems and multi-scale problems lead to low downscaling accuracy.

In order to achieve the above-mentioned object of the invention, the technical solutions adopted by the present invention are:

A high-precision surface modeling downscaling correction method based on Bayesian optimization is provided, which includes the following steps:

S1. Construct a downscaling model, use the precipitation reference data points as sample point elements, and calculate the precipitation residual values at different sample points in the target area;

S2. Extract precipitation residual values based on sample point elements to obtain sample point data, perform bilinear interpolation on the sample point data, and obtain the iteration initial value;

S3. Use random parameters to initialize the high-precision surface modeling model, and bring in the sample point data and the target surface corresponding to the iterative initial value calculation;

S4. Perform error calculation on the current target surface and sample point data to obtain the error value;

S5. Use the current high-precision surface modeling model parameters and error values as prior knowledge, calculate the posterior distribution through the Gaussian process, and obtain the mean function and covariance matrix in the Gaussian process;

S6. Determine whether the maximum number of iterations has been reached. If so, proceed to step S8; otherwise, proceed to step S7;

S7. Calculate the next set of high-precision surface modeling model parameters based on the current mean function and covariance matrix, update the high-precision surface modeling model parameters, and input the sample point data and the target surface corresponding to the iterative initial value calculation, and return to step S4;

S8. Obtain the target surface corresponding to the high-precision surface modeling model parameters with the smallest error, and combine the target surface with the existing downscaling results in the target area to obtain the corrected downscaling result.

Further, the specific method of step S1 is:

Construct a downscaling model and use the longitude, latitude, NDVI, slope, aspect and DEM of the target area as inputs to the downscaling model to obtain the corresponding output results of the downscaling model. According to the formula:

Obtain the precipitation residual value ΔP; where P _O is the CGDPA benchmark value of the target area, and the pixel center point of the CGDPA data is used as the sample point element; the resolutions of longitude, latitude, NDVI, slope, aspect and DEM are all 0.01 °.

Further, the specific method of step S2 is:

Select 70% of the sample point elements to extract precipitation residual values to obtain sample point data, and perform bilinear interpolation on the sample point data to obtain an iterative initial value with a resolution of 0.01°.

Further, the specific method for calculating the corresponding target surface in step S3 is:

According to the formula:

Obtain the corresponding target surface z ^* ; where A and B are both coefficient matrices of the high-precision surface modeling model; and/> are the right-hand terms of the equation, which are respectively obtained by finite difference of the first basic quantity and the second basic quantity of the residual surface of the high-precision surface modeling model in the n ^* -1 iteration process; st represents the constraint; S is the high-precision surface modeling The sampling matrix of the model, the jth element in the sampling matrix is the sampling result obtained at the jth sample point; k is the sampling vector of the high-precision surface modeling model, the jth element in the sampling vector is the jth sample Point data; l and u are the minimum and maximum values of the bounded function respectively; n ^* represents the number of iterations; z ⁰ is the initial value of the iteration, /> is the precipitation residual surface after z ⁰ iteration n ^* times.

Further, the specific method of step S4 is:

According to the formula:

Get the error value RMSE of the current target surface and sample point data; where n is the total number of sample points; Represents the value corresponding to the i-th sample point in the target surface z ^* ; s _i is the true value of the residual at the i-th sample point.

Further, in step S7, the specific method for calculating the next set of high-precision surface modeling model parameters based on the current mean function and covariance matrix is:

According to the formula:

Obtain the _next set of high-precision surface modeling model parameters _t (x) is the mean function; σ _t (x) is the covariance matrix.

The beneficial effects of the present invention are: this method can correct the downscaling model, reduce its uncertainty and improve the accuracy of the downscaling model, thereby obtaining a more accurate downscaling result.

Description of drawings

Figure 1 is a schematic flow chart of this method;

Figure 2 is a schematic diagram comparing annual and quarterly scale confidence intervals in the embodiment;

Figure 3 is a schematic diagram comparing monthly scale confidence intervals in the embodiment;

Figure 4 is a schematic diagram comparing mid-scale confidence intervals in the embodiment;

Figure 5(a) is a schematic diagram of precipitation distribution before annual precipitation residual correction in the embodiment;

Figure 5(b) is a schematic diagram of precipitation distribution after correction of annual precipitation residuals in the embodiment;

Figure 6(a) is a schematic diagram of the accuracy before annual downscaling residual correction in the embodiment;

Figure 6(b) is a schematic diagram of the accuracy after correction of annual downscaling residuals in the embodiment;

Figure 7(a) is a schematic diagram of accuracy before spring residual correction in the embodiment;

Figure 7(b) is a schematic diagram of the accuracy after spring residual correction in the embodiment;

Figure 7(c) is a schematic diagram of the accuracy before summer residual correction in the embodiment;

Figure 7(d) is a schematic diagram of the accuracy after summer residual correction in the embodiment;

Figure 7(e) is a schematic diagram of accuracy before autumn residual correction in the embodiment;

Figure 7(f) is a schematic diagram of the accuracy after autumn residual correction in the embodiment;

Figure 7(g) is a schematic diagram of the accuracy before winter residual correction in the embodiment;

Figure 7(h) is a schematic diagram of the accuracy after winter residual correction in the embodiment;

Figure 8(a) is a probability density histogram of precipitation in January in the embodiment;

Figure 8(b) is a probability density histogram of precipitation in February in the embodiment;

Figure 8(c) is a probability density histogram of precipitation in August in the embodiment;

Figure 8(d) is a probability density histogram of precipitation in November in the embodiment;

Figure 9(a) is a probability density histogram of precipitation in mid-April in the embodiment;

Figure 9(b) is a probability density histogram of precipitation in early August in the embodiment;

Figure 9(c) is a probability density histogram of precipitation in mid-September in the embodiment;

Figure 9(d) is a probability density histogram of precipitation in late October in the embodiment.

Detailed ways

The specific embodiments of the present invention are described below to facilitate those skilled in the art to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the technical field, as long as various changes These changes are obvious within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions and creations utilizing the concept of the invention are protected.

As shown in Figure 1, the high-precision surface modeling downscaling correction method based on Bayesian optimization includes the following steps:

S1. Construct a downscaling model, use the precipitation reference data points as sample point elements, and calculate the precipitation residual values at different sample points in the target area;

S2. Extract precipitation residual values based on sample point elements to obtain sample point data, perform bilinear interpolation on the sample point data, and obtain the iteration initial value;

S3. Use random parameters to initialize the high-precision surface modeling model, and bring in the sample point data and the target surface corresponding to the iterative initial value calculation;

S4. Perform error calculation on the current target surface and sample point data to obtain the error value;

S5. Use the current high-precision surface modeling model parameters and error values as prior knowledge, calculate the posterior distribution through the Gaussian process, and obtain the mean function and covariance matrix in the Gaussian process;

S6. Determine whether the maximum number of iterations has been reached. If so, proceed to step S8; otherwise, proceed to step S7;

S7. Calculate the next set of high-precision surface modeling model parameters based on the current mean function and covariance matrix, update the high-precision surface modeling model parameters, and input the sample point data and the target surface corresponding to the iterative initial value calculation, and return to step S4;

S8. Obtain the target surface corresponding to the high-precision surface modeling model parameters with the smallest error, and combine the target surface with the existing downscaling results in the target area to obtain the corrected downscaling result.

The specific method of step S1 is: construct a downscaling model, use the longitude, latitude, NDVI, slope, aspect and DEM of the target area as inputs to the downscaling model, and obtain the corresponding output results of the downscaling model. According to the formula:

Obtain the precipitation residual value ΔP; where P _O is the CGDPA benchmark value of the target area, and the pixel center point of the CGDPA data is used as the sample point element; the resolutions of longitude, latitude, NDVI, slope, aspect and DEM are all 0.01 °.

The specific method of step S2 is: select 70% of the sample point elements to extract precipitation residual values to obtain sample point data, and perform bilinear interpolation on the sample point data to obtain an iterative initial value with a resolution of 0.01°.

The specific method of calculating the corresponding target surface in step S3 is: according to the formula:

Obtain the corresponding target surface z ^* ; where A and B are both coefficient matrices of the high-precision surface modeling model; and/> are the right-hand terms of the equation, which are respectively obtained by finite difference of the first basic quantity and the second basic quantity of the residual surface of the high-precision surface modeling model in the n ^* -1 iteration process; st represents the constraint; S is the high-precision surface modeling The sampling matrix of the model, the jth element in the sampling matrix is the sampling result obtained at the jth sample point; k is the sampling vector of the high-precision surface modeling model, the jth element in the sampling vector is the jth sample Point data; l and u are the minimum and maximum values of the bounded function respectively; n ^* represents the number of iterations; z ⁰ is the initial value of the iteration, /> is the precipitation residual surface after z ⁰ iteration n ^* times.

The specific method of step S4 is: according to the formula:

Get the error value RMSE of the current target surface and sample point data; where n is the total number of sample points; Represents the value corresponding to the i-th sample point in the target surface z ^* ; s _i is the true value of the residual at the i-th sample point.

In step S7, the specific method for calculating the next set of high-precision surface modeling model parameters based on the current mean function and covariance matrix is: according to the formula:

Obtain the _next set of high-precision surface modeling model parameters _t (x) is the mean function; σ _t (x) is the covariance matrix.

In the specific implementation process, the essence of Bayesian optimization is a kind of Bayesian inference, which uses Bayes' theorem combined with updated prior knowledge to calculate the posterior distribution and make inferences and predictions based on the posterior distribution. The prior knowledge is obtained through assumptions. The prior knowledge of Bayesian optimization includes two contents. First, it is assumed that the function to be regressed obeys the Gaussian process, and it is assumed that the mean function of this Gaussian process is 0, and the covariance function is as formula (1) is shown, then the joint distribution result of the observation result f and the test result f _* is shown in formula (2):

Among them, α ₀ and l are the hyperparameters of the Gaussian kernel; x ₁ and x ₂ represent two different model parameter combination vectors on the continuous domain of the Gaussian process;

The conditional distribution properties according to the multidimensional Gaussian distribution are shown in formula (3):

Substituting formula (2) into formula (3), the posterior distribution can be calculated as shown in formula (4):

f _* |X,X _* ,f～N(m,Σ) (4)

In the formula, X is the model parameter combination vector of the observation data set, and f is the result of the observation data set. X _* is the test model parameter combination vector, and f _* is the output result of the proxy model. Where m is the mean function which can be calculated by formula (5), and Σ is the covariance matrix which can be calculated by formula (6):

m＝K(X*,X)K(X,X) ^-1 y (5)

Σ＝K(X*,X*)-K(X*,X)K(X,X) ^-1 K(X,X*) (6)

Using the mean function m and the covariance matrix Σ, the Gaussian process can be uniquely determined. The acquisition function constructed from the mean function m and the covariance matrix Σ will select the point with the greatest possibility of increasing the current maximum value as the next query point.

In the formula, Φ(·) represents the normal distribution cumulative distribution function, where m _t is the mean value of the Gaussian distribution probability density function in the t-th iteration process, Σ _t is the variance of the Gaussian distribution probability density function in the t-th iteration process, f(x ⁺ ) is the known maximum value of the first t iterations. argmax obtains the parameter that maximizes Φ(·), and ε is a minimum positive number used to weigh exploration and development. X _t+1 is the determined next model parameter combination.

Specifically in this method, a set of high-precision surface modeling model parameters x={x ₁ , x ₂ ,..., x _n } can be calculated to obtain an output value f(x). The search space of high-precision surface modeling model parameters is S, and the expression of the data set D consisting of several sets of parameters and output values is D={(X,f)}={(x ₁ ,f(x ₁ )) ,(x ₂ ,f(x ₂ )),…,(x _n ,f(x _n ))}. In the Gaussian process, D={(X,f)}={(x ₁ ,f(x ₁ )),(x ₂ ,f(x ₂ )),…,(x _t ,f(x _t ) )} and M (M is the surrogate function, this method selects the Gaussian process as the surrogate function, and assumes that the mean function of the Gaussian process here is 0, and the covariance function is as shown in formula (1)) as prior knowledge, and combined The Gaussian process calculates the mean function m and the covariance matrix Σ. And obtain the posterior distribution as shown in formula (4). The acquisition function A constructed using the mean function m and the covariance matrix Σ is shown in formula (7). Calculate _the next valuable _{hyperparameter} combination ₁ ,f(x ₁ )),(x ₂ ,f(x ₂ )),…,(x _t+1 ,f(x _t+1 ))}, complete one iteration.

In one embodiment of the present invention, the uncertainty of the existing HASM method and this method (Bayes-HASM) is analyzed through a Monte Carlo algorithm, and the 95% confidence interval of the error level is used for quantitative measurement.

Figure 2 compares the confidence intervals of the original HASM and Bayes-HASM at the annual and seasonal scales, and it is found that Bayes-HASM can significantly reduce the uncertainty of the model at the annual and seasonal scales. On the whole, the confidence intervals of the Bayes-HASM error differences are all near the 0 value, while the confidence intervals of HASM fluctuate greatly. The most obvious decrease in uncertainty is in spring and winter. The confidence interval drops from ±0.8 to ±0.1. Uncertainties in summer, autumn and annual scales also decrease to varying degrees, mainly because there is less precipitation in spring and winter, and fluctuations in model parameters are more likely to affect the calculation results of the residuals.

Figure 3 shows the model uncertainty of monthly scale HASM and Bayes-HASM. Overall, the confidence interval of the Bayes-HASM error difference is around the 0 value, with a fluctuation range of less than ±0.1. The original HASM confidence interval fluctuates greatly, with a fluctuation range of more than ±0.5. It can be seen from Figure 3 that the uncertainty of Bayes-HASM in different months is reduced compared to HASM. The reduction in January, February, March, November and December is not significant, and the reduction in April to October is more obvious. It is most obvious in July and August. It shows that using Bayesian optimization on the monthly scale does play a role in reducing high-precision surface modeling errors and uncertainties, and the reduction in uncertainty is more obvious in months with greater precipitation.

Figure 4 compares the confidence intervals of error levels between HASM and Bayes-HASM in different ten-year periods. On the whole, both HASM and Bayes-HASM can limit the error to a relatively small range, but the confidence interval of the Bayes-HASM error difference is tightly around the 0 value. In comparison, the error difference of HASM is flat. There are relatively large fluctuations, indicating that the Bayesian optimization algorithm can effectively reduce the uncertainty of HASM on the ten-day scale. The greatest reduction is in mid-July and mid-August, and the confidence interval of ±0.6 can be stabilized to Around ±0.1, other ten days can also stabilize the confidence interval near the 0 value, which shows that Bayesian optimization can play the role of a stabilizer and can effectively eliminate the uncertainty introduced by HASM parameter selection.

Figure 5(a) and Figure 5(b) compare the spatial distribution of annual precipitation before and after residual correction. Figure 5(a) shows the spatial distribution of annual precipitation before residual correction. Its southern spatial feature is that the precipitation flows from the south to the south. It decreases toward the north, showing an obvious strip distribution. There is no obvious spatial feature in the north, different precipitation amounts are mixed, and the distribution is relatively scattered. Figure 5(b) shows the spatial distribution of annual precipitation after residual correction. It not only reflects the spatial distribution characteristics of precipitation in the southern Luanhe River Basin, with precipitation decreasing from south to north, but also clearly shows the precipitation pattern in the northern Luanhe River Basin. Circular decreasing spatial distribution characteristics. In summary, it can be inferred that residual correction can more accurately reflect the spatial distribution characteristics of precipitation in the southern Luanhe River Basin, and can also effectively capture the precipitation characteristics in the north that cannot be well described by the downscaling model.

Figure 6(a) and Figure 6(b) compare the accuracy evaluation indicators before and after the annual precipitation downscaling residual correction. By comparing the scatter distribution, it is found that the deviation of the scatter points from the 1:1 line is smaller after the residual correction. Compared with before residual correction, there has been a significant improvement; by comparing the accuracy evaluation indicators, it is found that all indicators have been greatly improved. R increased from 0.66 to 0.97, an increase of 0.31, and the IA indicator increased from 0.78 to 0.98, an increase of 0.2. , RMSE dropped from 54.71mm to 18.03mm, a drop of 36.68mm, BIAS dropped from 0.70% to -1.2%, and the accuracy was slightly reduced. In summary, it can be proved that Bayes-HASM has greatly improved the accuracy of annual precipitation downscaling.

Figure 7(a) to Figure 7(h) show the comparison of accuracy indicators before and after correction of seasonal precipitation downscaling residuals. By comparing the scatter distribution before and after correction of downscaling residuals in the four quarters, it is found that after residual correction, the scatter distribution The deviation degree of the points from the 1:1 line has been greatly reduced, and the scattered points are concentrated near the 1:1 line; comparing the changes in the accuracy index before and after the residual correction, it is found that the accuracy index has been significantly improved after the residual correction , among which R increased by 0.18, IA increased by 0.11, RMSE decreased by 5mm, BIAS improved by 4.35%, summer R increased by 0.27, IA increased by 0.18, RMSE decreased by 39.07mm, BIAS improved by 4.17%, and R increased by 4.17% in autumn. R increased by 0.10, IA increased by 0.13, RMSE decreased by 4.27mm, and BIAS improved by 8.64%. In winter, R increased by 0.15, IA increased by 0.10, RMSE decreased by 0.68mm, and BIAS improved by 16.86%. In summary, it can be proved that Bayes-HASM can significantly improve the accuracy of seasonal precipitation downscaling.

Table 2 compares the accuracy evaluation indicators before and after monthly precipitation downscaling residual correction. Comparing the accuracy indicators before and after residual correction, it is found that the accuracy indicators have been greatly improved after residual correction in all months. R exceeded 0.89 in all months, among which R increased significantly by more than 0.3 in 1, 2, 3, 6, 8, 10 and November; IA indicators in all months also exceeded 0.94, among which 1, 2, 6, 8, 10 and The IA indicator increased significantly by more than 0.3 in November; the RMSE dropped significantly in April, May, June, July, August and November, exceeding 4mm; the improvement in BIAS was obvious, but it got slightly worse in April and September. In summary, it can be proved that Bayes-HASM significantly improves the accuracy of monthly precipitation downscaling.

Comparing the accuracy changes of downscaled residual correction in 12 months, the improvement in January and November is the most significant, mainly because there is less precipitation in the Luanhe River Basin in January and November, and there are fewer effective rainfall samples, so the downscaled model is easy to overfit; and in winter Most of the precipitation in the Luanhe River Basin is snow. Due to the limitations of the sensor, there will be a large deviation in the IMERG and CGDPA data, resulting in poor accuracy before residual correction. From this, it can be inferred that the homogeneous part of the winter precipitation field accounts for a higher proportion, and the residual correction It can effectively eliminate the influence of the homogeneous part of the precipitation field.

Table 2 Comparison of accuracy before and after monthly scale residual correction

Figure 8(a) to Figure 8(d) compare the histograms of months with greater improvement in residual correction accuracy. It can be clearly seen from the whole that the histogram of the residual-corrected precipitation data is more similar to the CGDPA data, and can accurately reflect the real precipitation probability density curve of the Luanhe River Basin. Comparing the probability density histograms of CGDPA, before residual correction and after residual correction in January, February and November, it was found that there was less precipitation in these months, and the monthly cumulative precipitation of almost all pixels was less than 1 mm, making the effective precipitation With fewer samples, the fitting effect of the model is poor. However, after correction of the Bayes-HASM residual, the precipitation can reach a probability density curve similar to the CGDPA data. Comparing the probability density histograms of CGDPA, before residual correction and after residual correction in August, it was found that the precipitation in August was larger. Affected by extreme precipitation such as heavy rains, the homogeneous part of the precipitation field accounted for a larger proportion. At the same time, it was affected by The global model cannot effectively simulate the influence of details, and the model results are poor before residual correction. However, the downscaling accuracy is significantly improved after Bayes-HASM residual correction. In summary, it is proved that this method can effectively compensate for the poor model fitting effect caused by small precipitation and few effective precipitation samples, and can also effectively eliminate the influence of the homogeneous part of the precipitation field.

Table 3 compares the accuracy evaluation indicators before and after decadal precipitation downscaling residual correction. Among them, the cumulative precipitation of all pixels in mid-to-late February, early May, early November, and late December is less than 0.5mm. It is determined that It is invalid precipitation 2 and deleted from the table. By comparing the accuracy evaluation indicators before and after residual correction, it is found that the accuracy evaluation indicators have been significantly improved after residual correction. Among them, R increased by 0.41 on average, IA increased by 0.34 on average, RMSE decreased by 5.52mm on average, and BIAS improved on average. 256.12. Through longitudinal comparison of different days, it is found that the improvement of downscaling accuracy by residual correction shows obvious time differences. Although the accuracy is significantly improved in spring and summer, the improvement is more obvious in autumn and winter, mainly because of the precipitation in autumn and winter. Less, the homogeneous part of precipitation accounts for a higher proportion, which is difficult to be simulated by the downscaling model, and the effect of residual correction is better.

Table 3 Comparison of accuracy before and after decadal scale residual correction

On the ten-day scale, Bayes-HASM also performs very well. The months with larger improvements include early to mid-to-late January, mid-February, mid-April, early August, mid-September, early October, and mid-November. and mid-December. The significant increases in January, February, November and December are mainly caused by low precipitation in the Luanhe River Basin in autumn and winter, insufficient effective precipitation samples, and low model simulation accuracy. Bayes-HASM can effectively make up for the problems caused by model accuracy. Downscaling bias. In addition, there was a significant increase in mid-April, early August, mid-September and late October. By looking at the precipitation probability density histograms in Figure 9(a) to Figure 9(d), we found that these ten-day IMERG and CGDPA data There is a large deviation between the downscaled model results calculated from environmental factors and IMERG data and the real rainfall. At the same time, the residual-corrected results are extremely similar to the CGDPA data, which proves that this method is effective. Eliminate precipitation downscaling residuals caused by data bias.

Claims (6)

1. A Bayesian optimization-based high-precision curved surface modeling downscaling correction method is characterized by comprising the following steps of:

s1, constructing a downscaling model, and calculating precipitation residual values at different sample points of a target area by taking precipitation reference data points as sample point elements;

s2, extracting precipitation residual values based on sample point elements to obtain sample point data, and carrying out bilinear interpolation on the sample point data to obtain an iteration initial value;

s3, initializing a high-precision curved surface modeling model by using random parameters, and carrying in sample point data and iterative initial value calculation corresponding target curved surfaces;

s4, performing error calculation on the current target curved surface and sample point data to obtain an error value;

s5, taking the current high-precision curved surface modeling model parameters and error values as priori knowledge, and calculating posterior distribution through a Gaussian process to obtain a mean function and a covariance matrix in the Gaussian process;

s6, judging whether the maximum iteration times are reached, if so, entering a step S8; otherwise, entering step S7;

s7, calculating the next group of high-precision curved surface modeling model parameters based on the current mean function and the covariance matrix, updating the high-precision curved surface modeling model parameters, inputting sample point data and a target curved surface corresponding to iterative initial value calculation, and returning to the step S4;

s8, obtaining a target curved surface corresponding to the high-precision curved surface modeling model parameter with the minimum error, and combining the target curved surface with the existing downscaling result of the target area to obtain a corrected downscaling result.

2. The high-precision curved surface modeling downscaling correction method based on Bayesian optimization according to claim 1, wherein the specific method of the step S1 is as follows:

constructing a downscaling model, taking longitude, latitude, NDVI, gradient, slope direction and DEM of a target area as inputs of the downscaling model, and obtaining an output result corresponding to the downscaling modelAccording to the formula:

obtaining a precipitation residual value delta P; wherein P is _O The CGDPA standard value is used as a target area, and a pixel center point of CGDPA data is used as a sample point element; the resolution of longitude, latitude, NDVI, grade, slope direction and DEM are all 0.01 °.

3. The high-precision curved surface modeling downscaling correction method based on Bayesian optimization according to claim 1, wherein the specific method of the step S2 is as follows:

and extracting precipitation residual values from 70% of sample point elements to obtain sample point data, and performing bilinear interpolation on the sample point data to obtain an iteration initial value with the resolution of 0.01 degrees.

4. The high-precision curved surface modeling downscaling correction method based on Bayesian optimization according to claim 1, wherein the specific method for calculating the corresponding target curved surface in the step S3 is as follows:

according to the formula:

acquiring a corresponding target curved surface z ^* The method comprises the steps of carrying out a first treatment on the surface of the Wherein A and B are coefficient matrixes of a high-precision curved surface modeling model;andas the right-hand end terms of the equation, respectively by the nth ^* -obtaining a first basic quantity and a second basic quantity of a residual curve of the high-precision curve modeling model in the 1-time iteration process through finite difference; s.t. represents constraints; s is a sampling matrix of a high-precision curved surface modeling model, and the sampling matrix isThe j-th element is a sampling result obtained at the j-th sample point; k is a sampling vector of the high-precision curved surface modeling model, and a j element in the sampling vector is j sample point data; l and u are the minima and maxima of the bounded function, respectively; n is n ^* Representing the iteration number; z ⁰ For the initial iteration value, ++>Is z ⁰ Iteration n ^* And (5) a residual curve of precipitation after the second time.

5. The high-precision curved surface modeling downscaling correction method based on Bayesian optimization according to claim 4, wherein the specific method of the step S4 is as follows:

according to the formula:

obtaining an error value RMSE of current target curved surface and sample point data; wherein n is the total number of sample points;representing the target surface z ^* The value corresponding to the i-th sample point; s is(s) _i Is the residual true value at the i-th sample point.

6. The bayesian-optimization-based high-precision surface modeling downscaling correction method according to claim 5, wherein the specific method for calculating the next set of high-precision surface modeling model parameters based on the current mean function and the covariance matrix in the step S7 is as follows:

according to the formula:

obtaining a next group of high-precision curved surface modeling modulesParameter X _t+1 The method comprises the steps of carrying out a first treatment on the surface of the Wherein ε is a positive number; phi (·) represents a standard normal distribution cumulative distribution function; argmax represents the parameter to obtain the maximum value of Φ (); mu (mu) _t (x) Is a mean function; sigma (sigma) _t (x) Is a covariance matrix.