A statistical post-processing correction method for meteorological and hydrological ensemble forecasts

Abstract

The present invention discloses a statistical post-processing correction method for meteorological and hydrological ensemble forecasts. The method of the present invention comprises the following steps: S1, collecting measured meteorological and hydrological elements and original ensemble forecasts, and ensuring the consistency of the temporal and spatial scales of the two; S2, taking each ensemble member in the original ensemble forecast as an independent forecast, and establishing the coupling distribution with the measured one by one; S3, inferring the posterior probability of the coupling distribution, establishing a correction model in the normal space, and using the inverse data conversion method to obtain the corrected forecast of a single ensemble member in the real space; S4, quantifying the correction performance of the ensemble members one by one, correcting the bridge through the Bayesian model averaging method, and weighting and outputting the final corrected ensemble forecast. The present invention provides a new technical means for meteorological and hydrological ensemble forecasts and statistical post-processing correction methods thereof, which can effectively improve the accuracy and reliability of the corrected meteorological and hydrological ensemble forecasts.

Description

Technical Field

[0001] The present invention relates to the field of meteorological and hydrological forecasting, and in particular to a statistical post-processing correction method for meteorological and hydrological ensemble forecasting. Background Art

[0002] Meteorological and hydrological forecast refers to the qualitative or quantitative forecast of meteorological and hydrological elements (such as precipitation, evaporation, temperature, air pressure, humidity, wind speed, sunshine, runoff, etc.) in a certain area in the future based on previous or current meteorological and hydrological information. It has important scientific value and social significance for flood control and drought relief, water resources allocation, and ecological civilization construction. Traditional meteorological and hydrological forecasts mainly use deterministic forecasts / single value forecasts, which have the disadvantages of large forecast uncertainty and cannot be quantified. The current solution is mainly to use ensemble forecasts.

[0003] Ensemble forecast is a set of forecasts for the same forecast time that contains a large number of equally weighted ensemble members. Ensemble members are components of the ensemble forecast and are generated by different numerical weather forecast models or different initial conditions of the same model. Ensemble forecasts provide the probability of occurrence of meteorological and hydrological elements and the corresponding numerical range. They can give deterministic forecasts in the form of ensemble member means and quantiles, and can also measure the uncertainty of forecasts in the form of probability distribution. They are the current research focus and hotspot in the field of meteorological and hydrological forecasts.

[0004] At present, global climate models are the main way to produce meteorological and hydrological ensemble forecasts. However, due to the uncertainty of forecast structure generalization, parameterization scheme, boundary conditions, etc., global climate models often lead to large forecast system deviations, obvious under-discrete or over-discrete phenomena, and cannot be directly used by end users. Therefore, it is an urgent problem to develop a statistical post-processing correction method that can calibrate the original ensemble forecast system deviation, retain forecast skills, and generate ensemble members that maintain the spatiotemporal dependency structure between variables. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention proposes a statistical post-processing correction method for meteorological and hydrological ensemble forecasts based on Bayesian theory and Markov Chain Monte Carlo method, which can not only calibrate the original ensemble forecast system deviation and retain the forecast skill, but also generate ensemble members that maintain the spatiotemporal dependency structure between variables, providing an important and feasible reference basis and technical means for meteorological and hydrological ensemble forecasts and their statistical post-processing correction methods, and can effectively improve the accuracy and reliability of the corrected meteorological and hydrological ensemble forecasts.

[0006] The technical solution adopted by the present invention is:

[0007] A statistical post-processing correction method for meteorological and hydrological ensemble forecasts comprises the following steps:

[0008] S1. Basic data collection and processing: Collect the measured sequences of meteorological and hydrological elements at stations or grid points in the basin, obtain the original ensemble forecast sequences of the same stations or grid points, and ensure the consistency of the temporal and spatial scales of the two;

[0009] S2. Establishing the coupled distribution for the ensemble members: taking the results of each ensemble member in the original ensemble forecast as an independent forecast sequence, using the data conversion method to synchronously map the forecast sequence in the real space and the measured sequence into the normal space, and establishing the coupled distribution of the two one by one;

[0010] S3. Establish a correction model for ensemble members: Estimate the posterior probability of the coupling distribution according to the parameter inference method, then establish a correction model in the normal space, and use the inverse data conversion method to obtain the correction forecast of a single ensemble member in the real space;

[0011] S4. Establish a weighted fusion mechanism: quantify the correction performance of the ensemble members one by one, correct the bridge through the Bayesian model averaging method, and give weighted output to the final corrected ensemble forecast.

[0012] Further, in step S1:

[0013] The collected meteorological and hydrological element measured series and original ensemble forecast series of stations or grid points in the basin include: historical measured data of meteorological and hydrological elements such as precipitation, evaporation, temperature, runoff, corresponding historical forecast data of original ensemble forecast, and original ensemble forecast data to be corrected by statistical post-processing;

[0014] If the time scales of the measured sequence and the forecast sequence are not uniform, data expansion, interpolation, reduction, etc. are used to match them to ensure the consistency of the length of the time series of the two;

[0015] If the spatial scales of the measured sequence and the forecast sequence are not uniform, bilinear interpolation, inverse distance weighted method, Kriging interpolation and other methods are used to match them to ensure the consistency of their spatial position and resolution;

[0016] Further, in step S2:

[0017] The data conversion method needs to be selected according to the difference in the characteristics of meteorological and hydrological element variables. If the meteorological and hydrological elements are precipitation and runoff sequences, the data conversion adopts the two-parameter log-sinh method. If it is other meteorological and hydrological elements, the data conversion adopts the single-parameter Yeo-Johnson method, which is defined as:

[0018]

[0019] In the formula, y and are the measured sequences in the real space and normal space respectively, and α, β, and λ are the conversion parameters.

[0020] The coupling distribution of the measured sequence and the forecast sequence is a binary joint normal distribution is the forecast sequence in the normal space, μ is the mean, ∑ is the covariance matrix, σ is the standard deviation, r is the Pearson correlation coefficient between the two,

[0021] Further, in step S3:

[0022] The parameter inference method needs to be selected according to the difference in the length of the meteorological and hydrological element sequence. If the element sequence length is sufficient and the amount of data reaches hundreds, the maximum likelihood estimation is used for parameter estimation. If the element sequence length is insufficient, Gibbs sampling and maximum a posteriori estimation are used for parameter estimation. Gibbs sampling is a parameter estimation method based on the Markov chain Monte Carlo method. The parameter inference of the posterior probability in the coupled distribution is:

[0023]

[0024] Where θ = (α1, α2, β1, β2, λ1, λ2, μ1, μ2, σ1, σ2, r) is the set of parameters to be estimated, P(θ) is the prior distribution of θ, is the likelihood function, is the maximum likelihood estimation parameter scheme, is the maximum a posteriori estimation parameter scheme, is the historical data set, T is the length of the data set. The prior distribution is:

[0025]

[0026] The likelihood function is:

[0027]

[0028] Where c1 and c2 are the lower limits of the thresholds of x and y, and for and The lower threshold of for The Jacobian determinant when converted to y is defined as:

[0029]

[0030] Based on the coupled distribution parameters, the conditional probability distribution of the measured sequence under a certain forecast sequence is theoretically derived. This distribution is the correction model for a single ensemble member in the normal space. The confidence and the corresponding numerical interval are deduced according to the quantile mapping (sufficient element sequence length) or Gibbs sampling (insufficient element sequence length), and the correction forecast of a single ensemble member in the real space is obtained by inverse data conversion. The correction model is:

[0031]

[0032] In the formula, is the parameter scheme derived from the coupled distribution. The inverse data conversion method is defined as:

[0033]

[0034] Further, in step S4:

[0035] The correction performance of the quantitative set members is to use Wasserstein distance to quantify the similarity between the corrected prediction sequence of each set member and the measured sequence, and to form a distance matrix W = [W1, W2, ..., W K ] is used as the prior distribution for the subsequent steps, and the Wasserstein distance is defined as:

[0036]

[0037] Where, M={M1,M2,...,M K} is the forecast sequence of the correction set members, K is the number of set members, Y is the measured sequence, Ω is the joint distribution of the two, and D(p,q) is the cost function, which is defined as

[0038] The Bayesian model averaging method is widely used. It is a fusion method that calculates the weights of independent forecast sequences based on the posterior probability, uses the weights to linearly combine and output the final corrected ensemble forecast. The posterior probability is:

[0039]

[0040] In the formula, p(M k |y D ) is the given historical data y D Next M k is the probability of the optimal correction model, p(y|M k ,y D ) is a given y D and M k The probability density function of the predicted variable y is given by: solve.

[0041] The beneficial effects of the present invention are:

[0042] The statistical post-processing correction method for meteorological and hydrological ensemble forecasts proposed in the present invention has sufficient theoretical basis, reliable practical application, and fully takes into account the shortcomings of existing technologies and methods. It can provide important and feasible reference basis and technical means for meteorological and hydrological ensemble forecasts and their statistical post-processing correction methods, and can effectively improve the accuracy and reliability of the corrected meteorological and hydrological ensemble forecasts. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The present invention is a flowchart of a statistical post-processing correction method for meteorological and hydrological ensemble forecasts according to an embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to make the technical solutions, advantages and effects of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings. The specific implementation methods and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0045] like Figure 1 As shown, the statistical post-processing correction method for meteorological and hydrological ensemble forecast provided by the embodiment of the present invention includes the following steps:

[0046] S1. Basic data collection and processing: Collect the measured sequences of meteorological and hydrological elements at stations or grid points in the basin, obtain the original ensemble forecast sequences of the same stations or grid points, and ensure the consistency of the temporal and spatial scales of the two;

[0047] The collected station or grid meteorological and hydrological element measured series and original ensemble forecast series include: historical measured data of meteorological and hydrological elements such as precipitation, evaporation, temperature, runoff, corresponding historical forecast data of original ensemble forecast, and original ensemble forecast data to be corrected by statistical post-processing;

[0048] If the time scales of the measured series and the forecast series are not consistent, data expansion, interpolation, reduction, etc. are used to match them to ensure the consistency of the time series length;

[0049] If the spatial scales of the measured sequence and the forecast sequence are not uniform, bilinear interpolation, inverse distance weighted method, Kriging interpolation and other methods are used to match them to ensure the consistency of spatial position and resolution;

[0050] S2. Establishing the coupled distribution for the ensemble members: taking the results of each ensemble member in the original ensemble forecast as an independent forecast sequence, using the data conversion method to synchronously map the forecast sequence in the real space and the measured sequence into the normal space, and establishing the coupled distribution of the two one by one;

[0051] The data conversion method needs to be selected according to the difference in the characteristics of meteorological and hydrological element variables. If the meteorological and hydrological elements are precipitation and runoff sequences, the data conversion adopts the two-parameter log-sinh method. If it is other meteorological and hydrological elements, the data conversion adopts the single-parameter Yeo-Johnson method, which is defined as:

[0052]

[0053] In the formula, y and are the measured sequences in the real space and normal space respectively, and α, β, and λ are the conversion parameters.

[0054] The coupling distribution of the measured sequence and the forecast sequence is a binary joint normal distribution is the forecast sequence in the normal space, μ is the mean, Σ is the covariance matrix, σ is the standard deviation, r is the Pearson correlation coefficient between the two,

[0055] S3. Establish a correction model for ensemble members: Estimate the posterior probability of the coupling distribution according to the parameter inference method, then establish a correction model in the normal space, and use the inverse data conversion method to obtain the correction forecast of a single ensemble member in the real space;

[0056] The parameter inference method needs to be selected according to the difference in the length of the meteorological and hydrological element sequence. If the element sequence length is sufficient (the amount of data reaches hundreds), the maximum likelihood estimation is used for parameter estimation. If the element sequence length is insufficient, Gibbs sampling and maximum a posteriori estimation are used for parameter estimation. Gibbs sampling is a widely used parameter estimation method based on the Markov chain Monte Carlo method. The parameter inference of the posterior probability in the coupled distribution is:

[0057]

[0058] Where θ = (α1, α2, β1, β2, λ1, λ2, μ1, μ2, σ1, σ2, r) is the set of parameters to be estimated, P(θ) is the prior distribution of θ, is the likelihood function, is the maximum likelihood estimation parameter scheme, is the maximum a posteriori estimation parameter scheme, is the historical data set, T is the length of the data set. The prior distribution is:

[0059]

[0060] The likelihood function is:

[0061]

[0062] Where c1 and c2 are the lower limits of the thresholds of x and y, and for and The lower threshold of for The Jacobian determinant when converted to y is defined as:

[0063]

[0064] Based on the coupled distribution parameters, the conditional probability distribution of the measured sequence under a certain forecast sequence is theoretically derived. This distribution is the correction model for a single ensemble member in the normal space. The confidence and the corresponding numerical interval are deduced according to the quantile mapping (sufficient element sequence length) or Gibbs sampling (insufficient element sequence length), and the correction forecast of a single ensemble member in the real space is obtained by inverse data conversion. The correction model is:

[0065]

[0066] In the formula, is the parameter scheme derived from the coupled distribution. The inverse data conversion method is defined as:

[0067]

[0068] S4. Establish a weighted fusion mechanism: quantify the correction performance of the ensemble members one by one, correct the bridge through the Bayesian model averaging method, and give weighted output to the final corrected ensemble forecast.

[0069] The Wasserstein distance is used to quantify the similarity between the corrected forecast sequence and the measured sequence of each set member, and the distance matrix W = [W1, W2, ..., W K ] is used as the prior distribution for the subsequent steps, and the Wasserstein distance is defined as:

[0070]

[0071] Where, M={M1,M2,...,M K} is the forecast sequence of the correction set members, K is the number of set members, Y is the measured sequence, Ω is the joint distribution of the two, and D(p,q) is the cost function, which is defined as

[0072] The Bayesian model averaging method is widely used. It is a fusion method that calculates the weights of independent forecast sequences based on the posterior probability, uses the weights to linearly combine and output the final corrected ensemble forecast. The posterior probability is:

[0073]

[0074] In the formula, p(M k |y D ) is the given historical data y D Next M k is the probability of the optimal correction model, p(y|M k ,y D ) is a given y D and M k The probability density function of the predicted variable y is given by: solve.

[0075] The above embodiments and the specific parameters therein are only for clearly describing the invention verification process, and are not intended to limit the patent protection scope of the present invention. The patent protection scope of the present invention shall still be based on its claims. Any equivalent structural changes made using the contents of the description and drawings of the present invention should also be included in the protection scope of the present invention.

Claims

1. A statistical post-processing correction method for meteorological and hydrological ensemble forecasts, characterized by: It includes the following steps: S1. Basic data collection and processing: Collect the measured sequences of meteorological and hydrological elements at stations or grid points in the basin, obtain the original ensemble forecast sequences of the same stations or grid points, and ensure the consistency of the temporal and spatial scales of the two; S2. Establishing the coupled distribution for the ensemble members: taking the results of each ensemble member in the original ensemble forecast as an independent forecast sequence, using the data conversion method to synchronously map the forecast sequence in the real space and the measured sequence into the normal space, and establishing the coupled distribution of the two one by one; S3. Establish a correction model for ensemble members: Estimate the posterior probability of the coupling distribution according to the parameter inference method, then establish a correction model in the normal space, and use the inverse data conversion method to obtain the correction forecast of a single ensemble member in the real space; S4. Establish a weighted fusion mechanism: quantify the correction performance of the ensemble members one by one, correct the bridge through the Bayesian model averaging method, and weight the output of the final corrected ensemble forecast; In step S3, the parameter inference method needs to be selected according to the difference in the length of the meteorological and hydrological element sequences. If the element sequence length is sufficient and the data volume reaches hundreds, the maximum likelihood estimation is used for parameter estimation. If the element sequence length is insufficient, Gibbs sampling and maximum a posteriori estimation are used for parameter estimation. On the basis of obtaining the coupled distribution parameters, the conditional probability distribution of the measured sequence under a certain forecast sequence is theoretically derived. This distribution is the correction model for a single ensemble member in the normal space. The confidence and the corresponding numerical interval are deduced according to the quantile mapping or Gibbs sampling, and the inverse data transformation is used to obtain the corrected forecast of a single ensemble member in the real space.

2. The statistical post-processing correction method for meteorological and hydrological ensemble forecast according to claim 1 is characterized by: In step S1: The collected meteorological and hydrological element measured sequences and original ensemble forecast sequences of stations or grid points in the basin include: historical measured data of meteorological and hydrological elements, historical forecast data of corresponding original ensemble forecasts, and original ensemble forecast data to be corrected after statistical post-processing; If the time scales of the measured sequence and the forecast sequence are not uniform, data expansion, interpolation, and reduction are used to match them to ensure the consistency of the length of the time series of the two; If the spatial scales of the measured sequence and the forecast sequence are not uniform, bilinear interpolation, inverse distance weighted method, and Kriging interpolation are used for matching to ensure the consistency of their spatial positions and resolutions.

3. The statistical post-processing correction method for meteorological and hydrological ensemble forecast according to claim 1 is characterized by: In step S2: The data conversion method needs to be selected according to the difference in the characteristics of meteorological and hydrological element variables. If the meteorological and hydrological elements are precipitation and runoff sequences, the data conversion adopts the two-parameter log-sinh method. If it is other meteorological and hydrological elements, the data conversion adopts the single-parameter Yeo-Johnson method, which is defined as: In the formula, y and are the measured sequences in the real space and normal space, respectively, α, β, and λ are the transformation parameters; The coupling distribution of the measured sequence and the forecast sequence is a binary joint normal distribution is the forecast sequence in the normal space, μ is the mean, ∑ is the covariance matrix, σ is the standard deviation, r is the Pearson correlation coefficient between the two, 4. The statistical post-processing correction method for meteorological and hydrological ensemble forecast according to claim 3 is characterized by: Gibbs sampling is a widely used parameter estimation method based on the Markov Chain Monte Carlo method; the parameter inference of the posterior probability in the coupled distribution is: Where θ = (α1, α2, β1, β2, λ1, λ2, μ1, μ2, σ1, σ2, r) is the set of parameters to be estimated, P(θ) is the prior distribution of θ, is the likelihood function, is the maximum likelihood estimation parameter scheme, is the maximum a posteriori estimation parameter scheme, is the historical data set, T is the length of the data set; the prior distribution is: The likelihood function is: Where c1 and c2 are the lower limits of the thresholds of x and y, and for and The lower threshold of for The Jacobian determinant when converted to y is defined as: The calibration model is: In the formula, is a parameter scheme for coupling distribution derivation; the inverse data conversion method is defined as:

5. The statistical post-processing correction method for meteorological and hydrological ensemble forecast according to claim 1, characterized in that: In step S4: The correction performance of the quantitative set members is to use Wasserstein distance to quantify the similarity between the corrected prediction sequence of each set member and the measured sequence, and to form a distance matrix W = [W1, W2, ..., W K ] as the prior distribution for subsequent steps, The Wasserstein distance is defined as: Where, M={M1,M2,...,M K } is the forecast sequence of the correction set members, K is the number of set members, Y is the measured sequence, Ω is the joint distribution of the two, and D(p,q) is the cost function, which is defined as The Bayesian model averaging method is a fusion method that calculates the weights of independent forecast sequences based on the posterior probability, uses the weights to linearly combine and output the final corrected ensemble forecast. The posterior probability is: In the formula, p(M k |y D ) is the given historical data y D Next M k is the probability of the optimal correction model, p(y|M k ,y D ) is a given y D and M k The probability density function of the predicted variable y is: solve.

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