A method for quantifying the uncertainty of precipitation measurement by meteorological radar based on random statistics

Abstract

The present invention provides a method for quantifying the uncertainty of precipitation measurement by a meteorological radar based on random statistics, including: obtaining the cumulative rainfall of rain gauges and the original radar precipitation field on the geographical grid of the precipitation field, where the geographical grid of the precipitation field includes grids with rain gauges and grids without rain gauges; in the grids with rain gauges, obtaining the mean expectation and the mean square error matrix expectation of the radar precipitation measurement error; in the grids without rain gauges, obtaining the mean expectation and the mean square error matrix expectation of the radar precipitation measurement error; constructing an error value, and obtaining a precipitation field set according to the error value to complete the quantification of the uncertainty of precipitation measurement by the meteorological radar. The present invention utilizes the principle of random statistics, treats the uncertainty of precipitation measurement by the meteorological radar as a whole for quantification, and the generated precipitation field set can be directly used as the input of a hydrological model, facilitating the subsequent quantification of the uncertainty of the hydrological model. The calculation amount of the present invention is relatively small and is suitable for processing a large amount of data.

Description

Technical Field

[0001] The present invention belongs to the field of radar precipitation measurement, and particularly relates to a method for quantifying the uncertainty of meteorological radar precipitation measurement based on random statistics. Background Art

[0002] Precipitation measurement is an important input data for hydrological simulation. The uncertainty of precipitation measurement largely determines the accuracy of hydrological simulation and prediction. For example, in the relatively simple "precipitation-runoff" conceptual model, precipitation is the only driving data of the model. Therefore, the quality of precipitation measurement is the most important factor determining the simulation results. In more complex distributed hydrological models, the absolute value and spatio-temporal resolution of precipitation also have an important impact on the model results.

[0003] Traditional precipitation measurement is usually obtained by rain gauges and then used as input data for hydrological models after spatial interpolation. As a precise meteorological observation instrument, a meteorological radar can perform three-dimensional high-frequency scans of the atmosphere. Therefore, precipitation measurement based on meteorological radar (hereinafter referred to as "radar precipitation measurement") has the characteristics of wide coverage, high spatio-temporal resolution, etc. With the gradual popularization of meteorological radars, more and more radar precipitation measurement data have been applied.

[0004] However, radar precipitation measurement also has its drawbacks. Since meteorological radars use non-direct methods of remote sensing to observe precipitation, there are many uncertainties in the observation results. These uncertainties may come from the hardware system of the radar (such as antenna calibration errors), the signal processing system (such as the error in converting radar echo signals into rainfall amounts), etc. Although meteorological radars have made progress in both software and hardware in recent years, the uncertainty of radar precipitation measurement cannot be completely eliminated. Therefore, when applying radar precipitation measurement data, it is necessary to understand the gap between the precipitation measured by the radar and the true precipitation, that is, to quantify the uncertainty of radar precipitation measurement.

[0005] In the prior art, when quantifying the uncertainty of radar precipitation measurement, it starts from the meteorological radar itself, searches for every possible physical cause of error, and quantifies each error cause separately. The problem with this technical route is that due to the very complex structure of meteorological radars, it is difficult to judge all the error sources at once. Even if all the error sources can be judged, it is difficult to form a reproducible uncertainty quantification method due to limited knowledge and data in the early stage. Summary of the Invention

[0006] To solve the above technical problems, the present invention proposes a method for quantifying the uncertainty of meteorological radar precipitation measurement based on random statistics. When the radar precipitation measurement data is applied to hydrological simulation, it is not necessary to characterize the errors generated in each step. It is only necessary to regard the radar precipitation measurement as a whole and quantify the relative error between the final measurement result and the true value.

[0007] To achieve the above object, the present invention provides a method for quantifying the uncertainty of meteorological radar precipitation measurement based on random statistics, including:

[0008] Obtain the cumulative rainfall of rain gauges and the original radar precipitation field on the geographical grid of the precipitation field, where the geographical grid of the precipitation field includes grids with rain gauges and grids without rain gauges;

[0009] In the grids with rain gauges, analyze the original radar precipitation field based on the cumulative rainfall of the rain gauges to obtain the mean expectation and the mean square error matrix expectation of the radar precipitation measurement error in the grids with rain gauges;

[0010] In the grids without rain gauges, based on the Kriging method, obtain the mean expectation and the mean square error matrix expectation of the radar precipitation measurement error in the grids without rain gauges;

[0011] Based on the mean expectation and the mean square error matrix expectation of the grids with rain gauges, and the mean expectation and the mean square error matrix expectation of the grids without rain gauges, obtain the error value of the original radar precipitation field, and obtain the precipitation field set according to the error value, thereby completing the quantification of the uncertainty of meteorological radar precipitation measurement.

[0012] Optionally, obtaining the original radar precipitation field includes:

[0013] Obtain the meteorological radar reflectivity image;

[0014] Convert the meteorological radar reflectivity image into the original radar precipitation field by the Marshall-Palmer method.

[0015] Optionally, the Marshall-Palmer method is:

[0016]

[0017] where Z is the radar reflectivity, R is the original radar precipitation field, and both A and b are dimensionless parameters.

[0018] Optionally, obtaining the mean expectation and the mean square error matrix expectation of the grids with rain gauges includes:

[0019] Analyze the original radar precipitation field based on the cumulative rainfall of the rain gauges to obtain the expectation of the radar precipitation measurement error in the grids with rain gauges;

[0020] Based on the expectation of the rain gauge grid, obtain the mean expectation of the rain gauge grid. Based on the mean expectation of the rain gauge grid, obtain the expected value of the mean square error matrix of the rain gauge grid.

[0021] Optionally, the expression for the expectation of the rain gauge grid is:

[0022]

[0023] where is the first expectation of the radar precipitation measurement error, the subscript t represents a certain time point, and the subscript x k is the geographical grid overlapping with the rain gauge position in the radar precipitation field.

[0024] Optionally, the expression for the mean expectation of the rain gauge grid is:

[0025]

[0026] where is the first mean expectation of the radar precipitation measurement error, Q is the number of time steps, is the weight of the undisturbed radar precipitation measurement value, is the autocorrelation coefficient;

[0027]

[0028] where τ is the time delay, is the rainfall measurement value of the radar grid at the xk position at time t, Q is the number of time steps with autocorrelation, is the average value within the Q time period.

[0029] Optionally, the expression for the expected value of the mean square error matrix of the rain gauge grid is:

[0030]

[0031] where is the mean expectation of the radar precipitation measurement error in the rain gauge grid, is the autocorrelation coefficient, is the weight of the undisturbed radar precipitation measurement value, is the expectation of the radar precipitation measurement error at a certain time point, and the subscripts k and l are two spatially adjacent points.

[0032] Optionally, obtaining the mean expectation and the expected value of the mean square error matrix of the rain gauge-free grid includes:

[0033] Denote the mean expectation and the mean variance matrix expectation of the adjacent grids with rain gauge grids without rain gauge grids as known data;

[0034] Based on the known data, using the Kriging method, predict the mean expectation and the mean variance matrix expectation of any grid in the grids without rain gauge grids;

[0035] Put the mean expectation and the mean variance matrix expectation of any grid into the known data. Based on the known data after putting, use the Kriging method to predict the mean expectation and the mean variance matrix expectation of any remaining grid in the grids without rain gauge grids, and so on, until the mean expectation and the mean variance matrix expectation of all grids without rain gauge grids are predicted.

[0036] Optionally, the precipitation field set is:

[0037]

[0038] where R t is the original radar precipitation field at time point t, and δ t,i is the error value of the original radar precipitation field.

[0039] Compared with the prior art, the present invention has the following advantages and technical effects:

[0040] (1) The present invention uses the principle of random statistics to quantify the uncertainty of meteorological radar precipitation measurement as a whole.

[0041] (2) The precipitation field set generated by the present invention can be directly used as the input of the hydrological model, which is convenient for the subsequent quantification of the uncertainty of the hydrological model.

[0042] (3) The present invention greatly simplifies the calculation process and the amount of calculation. The amount of calculation is relatively small, and it is suitable for processing a large amount of data. Description of the Drawings

[0043] The drawings forming a part of this application are used to provide a further understanding of this application. The schematic embodiments and descriptions of this application are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0044] Figure 1 is a schematic flow chart of a method for quantifying the uncertainty of meteorological radar precipitation measurement based on random statistics according to an embodiment of the present invention. Detailed Embodiments

[0045] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine the embodiments to detail this application.

[0046] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. And although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0047] Embodiment

[0048] As Figure 1 shown, the present invention provides a method for quantifying the uncertainty of meteorological radar precipitation measurement based on random statistics, including:

[0049] Obtain the cumulative rainfall of rain gauges and the original radar precipitation field on the geographical grid of the precipitation field, where the geographical grid of the precipitation field includes grids with rain gauges and grids without rain gauges;

[0050] In the grids with rain gauges, analyze the original radar precipitation field based on the cumulative rainfall of the rain gauges to obtain the mean expectation and the mean square error matrix expectation of the grids with rain gauges of the radar precipitation measurement error;

[0051] In the grids without rain gauges, based on the Kriging method, obtain the mean expectation and the mean square error matrix expectation of the grids without rain gauges of the radar precipitation measurement error;

[0052] Based on the mean expectation and the mean square error matrix expectation of the grids with rain gauges, and the mean expectation and the mean square error matrix expectation of the grids without rain gauges, obtain the error value of the original radar precipitation field, and obtain the precipitation field set according to the error value to complete the quantification of the uncertainty of meteorological radar precipitation measurement.

[0053] Further, obtaining the original radar precipitation field includes:

[0054] Obtain the meteorological radar reflectivity image;

[0055] Convert the meteorological radar reflectivity image into the original radar precipitation field by the Marshall-Palmer method.

[0056] Further, the Marshall-Palmer method is:

[0057]

[0058] where Z is the radar reflectivity, R is the original radar precipitation field, and both A and b are dimensionless parameters.

[0059] Further, obtaining the mean expectation and the mean square error matrix expectation of the grids with rain gauges includes:

[0060] Analyze the original radar precipitation field based on the cumulative rainfall in the rain gauge to obtain the expectation of the radar precipitation measurement error in the grid containing the rain gauge;

[0061] Based on the expectation of the grid containing the rain gauge, obtain the mean expectation of the grid containing the rain gauge. Based on the mean expectation of the grid containing the rain gauge, obtain the expectation of the mean square deviation matrix of the grid containing the rain gauge.

[0062] Further, the expression for the expectation of the grid containing the rain gauge is:

[0063]

[0064] where, is the first expectation of the radar precipitation measurement error. The subscript t represents a certain time point, and the subscript x k is the geographical grid that overlaps with the position of the rain gauge in the radar precipitation field.

[0065] Further, the expression for the mean expectation of the grid containing the rain gauge is:

[0066]

[0067] where, is the first mean expectation of the radar precipitation measurement error. Q is the number of time steps, is the weight of the undisturbed radar precipitation measurement value, is the autocorrelation coefficient;

[0068]

[0069] where τ is the time delay, is the rainfall measurement value at the position xk of the radar grid at time t. Q is the number of time steps with autocorrelation, is the average value within the Q time period.

[0070] Further, the expression for the expectation of the mean square deviation matrix of the grid containing the rain gauge is:

[0071]

[0072] where, is the mean expectation of the radar precipitation measurement error in the grid with a rain gauge, is the autocorrelation coefficient, is the weight of the undisturbed radar precipitation measurement value, is the expectation of the radar precipitation measurement error at a certain time point. The subscripts k and l are two spatially adjacent points.

[0073] Further, obtaining the mean expectation and variance matrix expectation of the grids without rain gauges includes:

[0074] Denote the mean expectation and variance matrix expectation of the adjacent grids with rain gauges of the grids without rain gauges as known data;

[0075] Based on the known data, using the Kriging method, predict the mean expectation and variance matrix expectation of any grid in the grids without rain gauges;

[0076] Put the mean expectation and variance matrix expectation of the any grid into the known data, and based on the known data after putting, use the Kriging method to predict the mean expectation and variance matrix expectation of the remaining any grid in the grids without rain gauges, and so on, until the mean expectation and variance matrix expectation of all the grids without rain gauges are predicted.

[0077] For example: Suppose there are 9 grids in total of 3*3, and 6 of them have rain gauge observations. Then, for the first calculation of the mean and variance, it is based on the data of these 6 points. The result generated by the random sampling method is any one of the remaining 3 grids without data. After that, the number of grids with data becomes 7. Then use these seven points to generate the updated mean and variance, and generate any one of the remaining 2 grids without data through the random sampling method. In this way, 8 grids have data. Finally, fill the last grid in the same way. The essence of the Kriging method is actually to predict the data at any position in space through the existing data points. When doing Kriging interpolation, it is necessary to know the mean and variance of the existing data. In ordinary Kriging, this mean and variance will not change. However, in this embodiment, because this method is random sampling, the mean and variance are constantly changing. That is to say, every time a new data point is obtained, the mean and variance will be updated once.

[0078] In this embodiment, only need to regard the radar precipitation measurement as a whole and quantify the relative error between the final measurement result and the true value. The specific data process is as follows:

[0079] When calculating the cumulative data R of the original radar precipitation measurement:

[0080] Establish the mutual relationship between the meteorological radar echo signal and the precipitation, retrieve the meteorological radar reflectivity (generally the dBZ image per minute) from the database, and convert the reflectivity image into the rainfall intensity through the Marshall-Palmer equation.

[0081]

[0082] Among them, Z is the radar reflectivity (dBZ), R is the precipitation field calculated from the original radar data (hereinafter referred to as the "original precipitation field"), and both A and b are dimensionless parameters.

[0083] At a certain time point, the original precipitation field is superimposed with the perturbation generated by the uncertainty of radar precipitation measurement to generate a precipitation field ensemble Φ. A certain sample in the ensemble can be expressed as follows.

[0084] Φ t,i = R t + δ t,i [2]

[0085] Where R t represents the undisturbed original precipitation field, which is fixed and deterministic at a certain time point R t ; δ t,i is the perturbation field generated by the random statistical method, representing the uncertainty of radar precipitation measurement; Φ t,i is the random precipitation field generated by superimposing the above deterministic and uncertain terms; the subscript t represents a certain time point, and i represents the i-th sample in the ensemble.

[0086] Taking the logarithm on both sides of the equation in formula [2], the following formula can be obtained.

[0087] log[Φ t,i = log[R t + δ' t,i [3]

[0088] Where δ' t,i is the perturbation field after taking the logarithm.

[0089] Precipitation generally follows a lognormal distribution. According to this characteristic, it is assumed that the measurement error δ of precipitation also follows a lognormal distribution. Then, after taking the logarithm of δ, δ' follows a normal distribution.

[0090] δ' t = N(μ t , C t ) [4]

[0091] Where N is the Gaussian distribution function, μ is the mean of the measurement error, and C is the mean square error matrix of the measurement error.

[0092] S1. Within a certain time scale (hourly or daily), calculate the cumulative rainfall G of the rain gauge and the cumulative data R of the original radar precipitation measurement, and obtain the rain gauge-radar data G / R pair on the same geographical location grid. Assuming that the cumulative precipitation observed by the rain gauge is the most reliable data at the point scale, the rain gauge data is therefore used as the true value for comparison with the measurement value obtained by the weather radar.

[0093]

[0094] is the expectation of the radar precipitation measurement error, where the subscript t represents a certain time point, and xk represents the grid in the radar precipitation field that overlaps with the rain gauge position.

[0095] S2. As can be seen from formulas [4] and [5], the mean expectation of the radar precipitation measurement error in the grid with a rain gauge can be obtained by the following formula:

[0096]

[0097] where Q is the number of time steps, is the weight of the undisturbed radar precipitation measurement value, and generally this value is assumed to be the grid value of the original radar image. is the autocorrelation coefficient and can be obtained by the following formula.

[0098]

[0099] where τ is the time delay, is the rainfall measurement value at the position x of the radar grid at time t k Q is the number of time steps with autocorrelation, is the average value within the Q time period. For example, the r obtained from formula [7] 0 is the autocorrelation coefficient of an observation with itself, and r 1 is the autocorrelation coefficient of two adjacent observations in time.

[0100] S3. The expectation of the mean square error matrix of the radar precipitation measurement error can be obtained by the following formula, assuming that spatial correlation only exists between the two nearest neighboring spatial position points x k and x 1 .

[0101]

[0102] The first term in the formula represents the mean square error matrix of the precipitation measurement error in space, and the second term represents the mean square error matrix of the precipitation measurement error in time within the Q time period.

[0103] S4. For grids in the radar precipitation field without rain gauge observation points, the precipitation measurement error is obtained by the sequential Gaussian simulation method. This algorithm starts from a randomly selected radar precipitation grid, and the mean and variance of the radar precipitation measurement error of this grid are obtained by Kriging from the surrounding grids with rain gauge observation points. Different from the general Kriging method, the Kriging mean and variance are obtained by simulation sampling through the probability distribution function formula [4] at this time. After the calculation of this grid is completed, it enters the next randomly selected radar precipitation grid without an assigned measurement error until all radar precipitation grids are assigned measurement errors.

[0104] S5. When the error values on all precipitation field grids are obtained, δ t,i is complete, and the precipitation field ensemble Φ t,i can be obtained through the following formula.

[0105]

[0106] The present invention uses the principle of statistics to characterize the uncertainty of radar precipitation measurement in the form of a precipitation field ensemble. There are multiple members in the ensemble, each member is different, but statistically has the same realization possibility. The advantages of using this method are: First, taking the radar precipitation measurement as a whole, it greatly simplifies the calculation process and the amount of calculation; Second, each member of the precipitation field can be used as the input data of the hydrological model, which can facilitate the subsequent quantitative characterization of the uncertainty of the hydrological model.

[0107] The above is only the preferred specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for quantifying the uncertainty of precipitation measurement by meteorological radar based on random statistics, characterized in that, it includes: Obtain the cumulative rainfall of rain gauges and the original radar precipitation field on the geographical grid of the precipitation field, wherein the geographical grid of the precipitation field includes grids with rain gauges and grids without rain gauges; In the grids with rain gauges, analyze the original radar precipitation field based on the cumulative rainfall of the rain gauges, and obtain the mean expectation and the mean square error matrix expectation of the grids with rain gauges for the radar precipitation measurement error; In the grids without rain gauges, based on the Kriging method, obtain the mean expectation and the mean square error matrix expectation of the grids without rain gauges for the radar precipitation measurement error; Based on the mean expectation and the mean square error matrix expectation of the grids with rain gauges, and the mean expectation and the mean square error matrix expectation of the grids without rain gauges, obtain the error value of the original radar precipitation field, and obtain the precipitation field set according to the error value, and complete the quantification of the uncertainty of precipitation measurement by meteorological radar.

2. The method for quantifying the uncertainty of precipitation measurement by meteorological radar based on random statistics according to claim 1, characterized in that, Obtaining the original radar precipitation field includes: Obtain the meteorological radar reflectivity image; Convert the meteorological radar reflectivity image into the original radar precipitation field by the Marshall-Palmer method.

3. The method for quantifying the uncertainty of precipitation measurement by meteorological radar based on random statistics according to claim 2, characterized in that, The Marshall-Palmer method is: where Z is the radar reflectivity, R is the original radar precipitation field, and both A and b are dimensionless parameters.

4. The method for quantifying the uncertainty of precipitation measurement by meteorological radar based on random statistics according to claim 1, characterized in that, Obtaining the mean expectation and the mean square error matrix expectation of the grids with rain gauges includes: Analyze the original radar precipitation field based on the cumulative rainfall of the rain gauges, and obtain the expectation of the radar precipitation measurement error in the grids with rain gauges; Based on the expectation of the grids with rain gauges, obtain the mean expectation of the grids with rain gauges, and based on the mean expectation of the grids with rain gauges, obtain the mean square error matrix expectation of the grids with rain gauges.

5. The method for quantifying the uncertainty of precipitation measurement by meteorological radar based on random statistics according to claim 4, characterized in that, The expression of the expectation of the grids with rain gauges is: Among them, is the first expectation of the radar precipitation measurement error, with the subscript t representing a certain time point and the subscript x k being the geographical grid in the radar precipitation field that overlaps with the location of the rain gauge, G being the cumulative rainfall of the rain gauge, and R being the cumulative data of the original radar precipitation measurement.

6. The method for quantifying the uncertainty of precipitation measurement by meteorological radar based on random statistics according to claim 4, characterized in that, The expression of the mean expectation of the grids with rain gauges is: wherein, is the first mean expectation of the radar precipitation measurement error, Q is the number of time steps, is the weight of the undisturbed radar precipitation measurement value, is the autocorrelation coefficient; where τ is the time delay, is the rainfall measurement value of the radar grid at position xk at time t, Q is the number of time steps with autocorrelation, is the average value within the Q time period.

7. The method for quantifying the uncertainty of precipitation measurement by meteorological radar based on random statistics according to claim 6, characterized in that, The expression of the mean square error matrix expectation of the grids with rain gauges is: Among them, is the mean expectation of the radar precipitation measurement error in the grid with rain gauges, is the autocorrelation coefficient, is the weight of the undisturbed radar precipitation measurement value, is the expectation of the radar precipitation measurement error at a certain time point, and the subscripts k and 1 are two spatially adjacent points.

8. The method for quantifying the uncertainty of precipitation measurement by meteorological radar based on random statistics according to claim 1, characterized in that, Obtaining the mean expectation and the mean square error matrix expectation of the grids without rain gauges includes: Denote the mean expectation and the mean variance matrix expectation of the adjacent rain gauge grids without the rain gauge grid as known data; Based on the known data, use the Kriging method to predict the mean expectation and the mean variance matrix expectation of any grid in the rain gauge grids without the rain gauge grid; Put the mean expectation and the mean variance matrix expectation of the any grid into the known data, and based on the known data after putting, use the Kriging method to predict the mean expectation and the mean variance matrix expectation of the remaining any grid in the rain gauge grids without the rain gauge grid, and so on, until the mean expectation and the mean variance matrix expectation of all the rain gauge grids without the rain gauge grid are predicted.

9. The method for quantifying the uncertainty of meteorological radar precipitation measurement based on random statistics according to claim 1, wherein, the precipitation field set is: Among them, R t is the original radar precipitation field at time point t, and δ t,i is the error value of the original radar precipitation field.

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