A precipitation-runoff simulation method based on multi-site multivariable weather generators

Abstract

This invention discloses a precipitation-runoff simulation method based on a multi-site, multivariate weather generator. It employs a multivariate first-order autoregressive model to generate precipitation and temperature sequences, effectively simulating the interannual variation characteristics of these sequences. The multivariate, multi-site weather generator can generate a simulated field of hydrometeorological elements with inter-site, inter-variable, and inter-temporal correlations, effectively reflecting the comprehensive characteristics of hydrometeorological processes and improving runoff simulation results. By introducing the Empirical Copula post-processing method, the spatiotemporal correlation of the meteorological element simulated field is further improved when the weather generator simulation results are poor, providing more reliable input data for the hydrological model.

Description

Technical Field

[0001] This invention relates to the field of processing methods for simulation purposes, and more particularly to a precipitation runoff simulation method based on a multi-site multivariable weather generator. Background Technology

[0002] Currently, precipitation-runoff simulation methods mainly include mathematical statistics and mathematical physics models. The former establishes the relationship between precipitation and runoff by statistically analyzing historical meteorological data; the latter simulates the hydrological response of a watershed by describing processes such as precipitation, evapotranspiration, and soil moisture, based on the physical principles of hydrological models.

[0003] Weather generators, as tools for simulating weather variables, are widely used in stochastic simulations of hydrological and meteorological processes. Based on the climatic characteristics of a specific region, weather generators employ statistical or stochastic process theory methods to simulate and generate meteorological element sequences of arbitrary length that reflect the statistical characteristics of the observation sequence. Weather generators can provide ensemble inputs of multiple meteorological elements, such as precipitation and temperature, for precipitation-runoff simulations, enabling better quantification of the uncertainty of meteorological element inputs.

[0004] Hydrometeorological processes exhibit continuity in both time and space, and various meteorological elements are physically correlated. These characteristics directly influence subsequent hydrological simulations and must be accurately reflected during the simulation process. Taking precipitation as an example, if precipitation data from different sub-basins are independent, the runoff generated in each sub-basin will lose spatial correlation, leading to misestimation of the total runoff and extreme values ​​at the basin outlet. Simultaneously, temperature determines the form of precipitation (rain or snow) and the timing and amount of snowmelt in the basin during winter. The physical correlation between precipitation and temperature significantly impacts northern rivers where snowfall is dominant. Furthermore, the temporal continuity of precipitation (e.g., consecutive dry or wet periods) and the low-frequency variation characteristics of meteorological elements (e.g., interannual variability) are also important hydrometeorological features that must be accurately measured during the simulation process. Traditional stochastic simulation methods for hydrometeorological processes cannot effectively reflect the comprehensive characteristics of regional / basin-scale hydrometeorological processes; using them as input to hydrological models leads to distortion in basin runoff simulations. Summary of the Invention

[0005] Purpose of the invention: This invention provides a precipitation runoff simulation method based on a multi-site multivariate weather generator, which generates a hydrological and meteorological element simulation field with inter-site, inter-variable, and time-series correlations and reflects interannual variation characteristics to drive the hydrological model for runoff simulation, thereby improving the simulation accuracy of the hydrological model.

[0006] Technical solution: The precipitation runoff simulation method based on a multi-site multivariable weather generator described in this invention includes the following steps:

[0007] Step 1: Collect daily precipitation, maximum and minimum temperatures, and water flow data at the watershed outlet section for stations within the watershed;

[0008] Step 2, Annual-scale stochastic simulation of meteorological elements: The daily-scale observation data is processed into an annual-scale observation meteorological variable series, and the regional average annual precipitation, maximum and minimum temperature series are generated using an annual-scale weather generator based on a multivariate first-order autoregressive model (MAR1).

[0009] Step 3: Assign interannual variation characteristics to the daily-scale simulation sequence: For each year of the regional average annual precipitation, maximum and minimum temperature simulation sequence generated by MAR1, the K-nearest neighbor (KNN) algorithm is used to randomly select 100 years from the observation sequence that are similar to the MAR1 regional average annual precipitation, maximum and minimum temperature simulation values ​​according to probability weights. The regional average daily-scale precipitation, maximum and minimum temperature sequences corresponding to these 100 years are extracted to construct a daily-scale multi-site multivariate weather generator.

[0010] Step 4: Daily-scale stochastic simulation of meteorological elements: A daily-scale weather generator is constructed using a two-state first-order Markov chain and a KNN model to simulate the daily weather sequence of R weather variables for L stations in a certain area.

[0011] Step 5: Preprocessing of GR4J (Genie Rural a 4Parametres Journalier) hydrological model input data: The meteorological element data simulated by the weather generator above is preprocessed and used as the hydrological model data input;

[0012] Step 6: After selecting the error standard as the objective function, calibrate the model parameters of the GR4J hydrological model;

[0013] Step 7: Use the calibrated GR4J model to simulate the daily runoff of the watershed.

[0014] Furthermore, in step 2, the regional average annual precipitation, maximum and minimum temperature sequences are generated: X t =w+AX t-1 +e t ;

[0015] In the formula: X t and X t-1 It is a [3×1] matrix, representing the regional average annual precipitation, annual maximum and minimum temperatures (annual averages) for years t and t-1, respectively. The three rows represent the three variables: annual precipitation, maximum and minimum temperatures; A and w are the [3×3] autocorrelation coefficient matrix and the [3×1] intercept term matrix, respectively, and et It is a [3×3] independent random residual matrix with a mean of 0 and a covariance of C. The parameters A, w, and C in the MAR1 model are estimated by piecewise least squares fitting. The MAR1 model can effectively simulate the interannual variation characteristics of annual precipitation, maximum and minimum temperature sequences while maintaining the correlation between variables.

[0016] Furthermore, step 3, constructing a daily-scale multi-site multivariate weather generator, specifically includes the following steps:

[0017] Step 31: Use the MAR1 model to generate a model of length T. a The simulated sequence of regional average annual precipitation, maximum and minimum temperatures;

[0018] Step 32, for the simulated year t a Calculate the regional average annual scale weather variable vector simulated in step 2. Compared with historical observations Euclidean distance between them:

[0019]

[0020] In the formula: Indicates simulated year t a Regional average annual scale weather variable vector, This represents the historical observation value for the corresponding year;

[0021] Step 33: Sort the distances d from smallest to largest, and set k to... n is the sample length; a discrete kernel function is used to assign probability weights K to the k nearest neighbor years. The weights are determined by the distance; the smaller the distance, the easier it is to be selected. The formula is as follows:

[0022]

[0023] Step 34: For any simulated year t a Based on probability weight K, from the k nearest historical observations 100 items were randomly selected from the list. For similar years, extract the regional average daily precipitation, maximum and minimum temperature data corresponding to those 100 years to generate a simulated year t. a The daily-scale precipitation, maximum and minimum temperature data serve as the data foundation for constructing a daily-scale multi-site multivariable weather generator.

[0024] Step 35: Considering the randomness of sampling, the annual-scale weather generator is run 50 times.

[0025] Furthermore, in step 4, the daily weather sequence is as follows:

[0026] Xl ={x l 1,t ,x l 2,t ,…,x l R,t |t=1,2,…,T}

[0027] in, Let represent the i-th variable corresponding to the l-th station and time t, where T represents the sample length of the simulated sequence.

[0028] Furthermore, in step 4, a diurnal weather generator is constructed using a two-state first-order Markov chain and a KNN model to simulate daily weather sequences consisting of R weather variables for L stations in a certain region. This specifically includes the following steps:

[0029] Step 41: Randomly extract meteorological data for any day corresponding to the starting month of the simulation from the simulation data generated by the annual scale weather generator, and the precipitation wet and dry state corresponding to the data should be consistent with the first precipitation state of the Markov chain simulation.

[0030] Step 42: Use a first-order Markov chain to simulate the temporal distribution of the regional average daily precipitation wet and dry series for L stations. Whether precipitation occurs depends on whether precipitation occurred the previous day. Assume that a daily precipitation greater than or equal to 0.1 mm is a wet day (S). t =1 indicates precipitation has occurred, and less than 0.1 mm is a dry day (S). t =0 represents no precipitation. Considering the seasonal variation characteristics of precipitation processes, the calculation of Markov chain parameters and the simulation of daily precipitation wet and dry states are carried out on a monthly basis.

[0031] Step 43: Use the maximum likelihood method to estimate the precipitation transition probability p from state a of the previous day to state b of the current day. ab Therefore, the four transition probabilities (p) of the two-state Markov chain are calculated. 00 p 01 p 10 p 11 ), where p 00 p represents the probability that there will be no precipitation tomorrow if there was no precipitation the day before. 01 This represents the probability of rain the day before if there was no rain the previous day, and so on.

[0032] Step 44: Calculate the regional average daily weather variables generated by the annual-scale weather generator. Decompose the data to L stations within the region;

[0033] Step 45: Conduct an applicability assessment of the multi-site multivariate weather generator simulated weather variable sequences in the study area. If the spatiotemporal correlation and inter-variable correlation of meteorological elements are poor, the Empirical Copula post-processing method is adopted to improve the spatiotemporal correlation and inter-variable correlation of meteorological elements.

[0034] Furthermore, in step 44, the regional average daily weather variables generated by the annual-scale weather generator are... Decomposing the data to L stations within the region involves the following steps:

[0035] Step 441, Assumption and These represent the simulated regional average weather variable vectors for day t-1 and day t, respectively, where both day t-1 and day t are wet days. Find all adjacent day pairs in the historical observation records extracted by the annual scale weather generator within a window centered on day t (set the window period to 7 days). (For example, if day t is January 15, then the window includes the dates corresponding to January 12 to 18 of all years.) If no suitable day pair is found, expand the window period to 30 days.

[0036] Step 442, Filter out and and There are Q pairs of adjacent days with the same wet / dry conditions (i.e., both are wet days), each pair containing a vector of regional average weather variables for the two consecutive days. and Calculate the average weather variable vector and simulated vector for Q historical regions. The weighted Euclidean distance between them;

[0037] Step 443: Set the distance d q Sort in ascending order, k is set to Weights are calculated for the k nearest neighbor distances using a discrete kernel function:

[0038]

[0039] Step 444: Randomly select a value from the k nearest neighbor distances based on the weights and record its corresponding historical date;

[0040] Step 445: Find the weather variable vector X for L stations in the region on the day following the historical date. l As the simulation vector for day t;

[0041] Step 446: Repeat the above steps for T simulated days.

[0042] Furthermore, in step 442, the average weather variable vectors of Q historical regions and the simulated vectors are calculated. Weighted Euclidean distance between:

[0043]

[0044] In the formula: This represents the average weather variable for the i-th region corresponding to day t-1 in the simulation. This represents the regional average weather variable for the first day in the q-th historical adjacent day pair. w represents the monthly climatological average of the average weather variable for the i-th region on day t-1 (the average of data for that month across all years). i Indicates the weight, and sets the weight w. i The reciprocal of the climatological standard deviation of the average weather variable for the i-th region on day t-1 of the month is used to standardize each variable in the weighted Euclidean distance, thus avoiding the significant impact of different variables on the calculation results of the Euclidean distance due to differences in their dimensions and numerical magnitudes.

[0045] Furthermore, in step 45, the Empirical Copula post-processing method is used to improve the spatiotemporal correlation and inter-variable correlation of meteorological elements, specifically including the following steps:

[0046] Step 451: For the three weather variables of precipitation, maximum and minimum temperature at K stations, considering the seasonal effects, apply the Empirical Copula post-processing method to calculate the rank matrix of the three weather variables for each month (number of data points per month = number of years × number of days in the month) as a reference sample rank matrix (the number of rows in the matrix is ​​the number of data points in the month, and the number of columns is K×3).

[0047] Step 452: Based on the reference sample rank matrix, reorder the simulated sample data of the corresponding month according to the rank, so that the rank matrix of the simulated sample after sorting is completely consistent with the observed sample, thereby reconstructing the inter-site, inter-variable, and temporal correlations of the simulated sample data.

[0048] Step 453: Concatenate the processed simulation data of each weather variable for each month in chronological order to obtain the simulation data processed by the Empirical Copula function.

[0049] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: The use of a multivariate first-order autoregressive model to generate precipitation and temperature series can effectively simulate the interannual variation characteristics (low-frequency oscillation characteristics) of precipitation and temperature series; the multivariate multi-site weather generator can generate a hydrological and meteorological element simulation field with inter-site, inter-variable, and inter-temporal correlations, which can effectively reflect the comprehensive characteristics of hydrological and meteorological processes and improve the runoff simulation effect; by introducing the EmpiricalCopula post-processing method, the spatiotemporal correlation of the meteorological element simulation field is further improved when the weather generator simulation results are poor, providing more reliable input data for the hydrological model. Attached Figure Description

[0050] Figure 1 This is a flowchart of the precipitation-runoff simulation method based on the coupling of a multi-site multivariable weather generator and the GR4J hydrological model, as described in this invention.

[0051] Figure 2 This is a schematic diagram of the multi-site, multivariable weather generator involved in the present invention.

[0052] Figure 3 This is a diagram showing the runoff simulation results based on a multi-site multivariable weather generator and the GR4J hydrological model, according to the present invention.

[0053] Figure 4 This is a diagram showing the simulation results of high and low flow rates in spring and summer / autumn based on a multi-site multivariate weather generator and the GR4J hydrological model. Detailed Implementation

[0054] A precipitation-runoff simulation method based on a multi-site, multivariable weather generator includes the following steps:

[0055] Step 1: Collect daily precipitation, maximum and minimum temperatures, and water flow data at the basin outlet section of stations within the basin;

[0056] Step 2, Annual-scale stochastic simulation of meteorological elements: Daily-scale observation data are processed into annual-scale meteorological variable sequences. An annual-scale weather generator based on a multivariate first-order autoregressive model (MAR1) is used to generate regional average annual precipitation, maximum, and minimum temperature sequences: X t =w+AX t-1 +e t ;

[0057] In the formula: X t and X t-1 It is a [3×1] matrix, representing the regional average annual precipitation, annual maximum and minimum temperature (annual average) for years t and t-1, respectively. The three rows represent the three variables: annual precipitation, maximum and minimum temperature; A and w are the [3×3] autocorrelation coefficient matrix and the [3×1] intercept term matrix, respectively.t It is a [3×3] independent random residual matrix with a mean of 0 and a covariance of C; the parameters A, w, and C in the MAR1 model are estimated using piecewise least squares fitting. The MAR1 model can effectively simulate the interannual variation characteristics of annual precipitation, maximum and minimum temperature sequences while maintaining the correlation between variables.

[0058] Step 3: Assign interannual variation characteristics to the daily-scale simulation sequence: For each year in the regional average annual precipitation, maximum and minimum temperature simulation sequence generated by MAR1, the KNN algorithm is used to randomly select 100 years (with repeatable sampling) from the observed sequence according to probability weights. These years are similar to the simulated values ​​of regional average annual precipitation, maximum and minimum temperature in MAR1. The corresponding regional average daily-scale precipitation, maximum and minimum temperature sequences for these 100 years are extracted to construct a daily-scale multi-site multivariate weather generator.

[0059] Step 3.1, use the MAR1 model to generate a model of length T. a The simulated sequence of regional average annual precipitation, maximum and minimum temperatures;

[0060] Step 3.2, for the simulated year t a Calculate the regional average annual scale weather variable vector simulated in step 2. Compared with historical observations Euclidean distance between them:

[0061]

[0062] In the formula: Indicates simulated year t a Regional average annual scale weather variable vector, This represents the historical observation value for the corresponding year;

[0063] Step 3.3: Sort the distances d from smallest to largest, and k is generally set to... n is the sample length; a discrete kernel function is used to assign probability weights K to the k nearest neighbor years. The weights are determined by the distance; the smaller the distance, the easier it is to be selected. The formula is as follows:

[0064]

[0065] Step 3.4, for any simulated year t a Based on probability weight K, from the k nearest historical observations 100 samples were randomly selected from the sample (with repeatable sampling) and For similar years, extract the regional average daily precipitation, maximum and minimum temperature data corresponding to those 100 years to generate a simulated year t. aThe daily-scale precipitation, maximum and minimum temperature data serve as the data foundation for constructing a daily-scale multi-site multivariable weather generator.

[0066] Step 3.5: Considering the randomness of sampling, the annual-scale weather generator is run 50 times;

[0067] Step 4, stochastic simulation of daily meteorological elements: a daily weather generator is constructed using a two-state first-order Markov chain and a KNN model to simulate the daily weather sequence of L stations in a certain area, consisting of R weather variables;

[0068] X l ={x l 1,t ,x l 2,t ,…,x l R,t |t=1,2,…,T}

[0069] in, Let represent the i-th variable corresponding to the l-th station and time t, where T represents the sample length of the simulated sequence.

[0070] Step 4.1: In order to start the algorithm and generate initial values ​​for all weather variables, randomly select meteorological data for any day corresponding to the simulation start month (e.g., January 1) from the simulation data generated by the annual scale weather generator, and the precipitation wet / dry state corresponding to this data should be consistent with the first precipitation state of the Markov chain simulation.

[0071] Step 4.2: Use a first-order Markov chain to simulate the temporal distribution of the regional average daily precipitation wet / dry sequence for L stations. Whether precipitation occurs depends on whether precipitation occurred the previous day. Assume a wet day (S) with a daily precipitation greater than or equal to 0.1 mm. t =1 indicates precipitation has occurred, and less than 0.1 mm is a dry day (S). t =0 represents no precipitation. Considering the seasonal variation characteristics of precipitation processes, the calculation of Markov chain parameters and the simulation of daily precipitation wet and dry states are carried out on a monthly basis.

[0072] Step 4.3: Use the maximum likelihood method to estimate the precipitation transition probability p from state a of the previous day to state b of the current day. ab Therefore, the four transition probabilities (p) of a two-state Markov chain can be calculated. 00 p 01 p 10 p 11 ), where p 00 p represents the probability that there will be no precipitation tomorrow if there was no precipitation the day before. 01 This represents the probability of rain the day before if there was no rain the previous day, and so on.

[0073] Step 4.4: The regional average daily weather variables generated by the annual-scale weather generator... Decompose the data to L stations within the region;

[0074] Step 4.4.1, assuming and These represent the simulated regional average weather variable vectors for days t-1 and t, respectively, where both t-1 and t are wet days. In the historical observation records extracted by the annual-scale weather generator, find all adjacent day pairs within a window centered on day t (set to a 7-day window period). (For example, if day t is January 15th, the window includes dates from January 12th to 18th of all years). If no suitable day pair is found, expand the window period to 30 days.

[0075] Step 4.4.2, filter out and and Adjacent day pairs with the same wet / dry conditions (i.e., both are wet days). Assume there are Q adjacent day pairs, each containing a vector of regional average weather variables for the two consecutive days. and Calculate the average weather variable vector and simulated vector for Q historical regions. Weighted Euclidean distance between:

[0076]

[0077] In the formula: This represents the average weather variable for the i-th region corresponding to day t-1 in the simulation. This represents the regional average weather variable for the first day in the q-th historical adjacent day pair. w represents the monthly climatological average of the average weather variable for the i-th region on day t-1 (the average of data for that month across all years). i The weight is represented by w. In this invention, the weight w is set. i The reciprocal of the climatological standard deviation of the average weather variable for the i-th region on day t-1 of the month is used to standardize each variable in the weighted Euclidean distance, so as to avoid the large influence of different variables on the calculation results of Euclidean distance due to differences in the units and numerical magnitudes.

[0078] Step 4.4.3, the distance d q Sort in ascending order, k is usually set to The weights of the k nearest neighbor distances are calculated using a discrete kernel function;

[0079]

[0080] Step 4.4.4: Randomly select a value from the k nearest neighbor distances based on the weights and record its corresponding historical date;

[0081] Step 4.4.5: Find the weather variable vector X for the L stations in the region on the day following the historical date. l As the simulation vector for day t;

[0082] Step 4.4.6: Repeat the above steps for T simulated days;

[0083] Step 4.5: Conduct an applicability assessment of the multi-site multivariate weather generator simulated weather variable sequences for the study area. If the spatiotemporal correlation and inter-variable correlation of meteorological elements are poor, the Empirical Copula post-processing method is adopted to improve the spatiotemporal correlation and inter-variable correlation of meteorological elements.

[0084] Step 4.5.1: For the three weather variables of precipitation, maximum and minimum temperature at K stations, considering the seasonal effects, the Empirical Copula post-processing method is applied to calculate the rank matrix of the three weather variables for each month (number of data points per month = number of years × number of days in the month) as a reference sample rank matrix (the number of rows in the matrix is ​​the number of data points in the month, and the number of columns is K×3).

[0085] Step 4.5.2: Based on the reference sample rank matrix, reorder the simulated sample data of the corresponding month according to the rank, so that the rank matrix of the simulated sample after sorting is completely consistent with the observed sample, thereby reconstructing the inter-site, inter-variable, and temporal correlations of the simulated sample data.

[0086] Step 4.5.3: The processed simulation data of each weather variable for each month are spliced ​​together in chronological order to obtain the simulation data processed by the Empirical Copula function.

[0087] Step 5, GR4J hydrological model input data preprocessing: The meteorological element data simulated by the weather generator above (area average precipitation calculation, evapotranspiration calculation, etc.) are preprocessed and used as hydrological model data input;

[0088] Step 6: After selecting the error standard as the objective function, calibrate the model parameters of the GR4J hydrological model.

[0089] Step 7: Simulate the daily runoff of the watershed using the calibrated GR4J model.

[0090] Taking the Ticino watershed in Switzerland as an example, the following process is implemented using the R language platform, with the method and steps explained in detail with accompanying figures.

[0091] A precipitation runoff simulation method based on a multi-site multivariable weather generator, such as Figure 1 As shown, it includes the following steps:

[0092] Step 1: Collect data from 35 meteorological stations in the Ticino watershed from January 1, 1981 to December 31, 2020 as basic meteorological data, preprocess the data, and calculate the regional average meteorological variable series.

[0093] The CAMELS-CH dataset collected in this example contains daily meteorological data such as measured precipitation, maximum, minimum, and average temperatures from meteorological stations within the watershed, as well as daily flow data from hydrological stations and latitude and longitude coordinates for each station. This dataset comes from the Central European Swiss Hydrometeorological Large Sample Dataset, data source: https: / / zenodo.org / records / 10354485.

[0094] Step 2, annual-scale meteorological element stochastic simulation: Run an annual-scale weather generator based on a multivariate first-order autoregressive model (MAR1) to generate regional average annual precipitation, maximum and minimum temperature sequences, and generate 50 annual-scale meteorological element simulation sequences with a length of 40 years.

[0095] The multivariate first-order autoregressive model is: X t =w+AX t-1 +e t (1)

[0096] In the formula: X t and X t-1 It is a [3×1] matrix, representing the regional average annual precipitation, annual maximum and minimum temperature (annual average) for years t and t-1, respectively. The three rows represent the three variables: annual precipitation, maximum and minimum temperature; A and w are the [3×3] autocorrelation coefficient matrix and the [3×1] intercept term matrix, respectively. t It is a [3×3] independent random residual matrix with a mean of 0 and a covariance of C; the parameters A, w, and C in the MAR1 model are estimated using the piecewise least squares fitting method.

[0097] Step 3: Assign interannual variation characteristics to the daily-scale simulation sequence: For each year of the regional average annual precipitation, maximum and minimum temperature simulation sequence generated by MAR1, the KNN algorithm is used to randomly select 100 years from the observation sequence that are similar to the MAR1 regional average annual precipitation, maximum and minimum temperature simulation values ​​according to probability weights. The regional average daily-scale precipitation, maximum and minimum temperature sequences corresponding to these 100 years are extracted to construct a daily-scale multi-site multivariate weather generator.

[0098] Step 3.1: For a 40-year annual meteorological element simulation series, apply the KNN algorithm to calculate the regional average annual weather variable vector for each year. Compared with historical observations The Euclidean distance between them;

[0099] The Euclidean distance is:

[0100] In the formula: Indicates simulated year t a Regional average annual scale weather variable vector, This represents the historical observation value for the corresponding year;

[0101] Step 3.2: Sort the distances d from smallest to largest, and use a discrete kernel function to assign probability weights K to the k nearest neighbor years. The weights are determined by the distances; the smaller the distance, the easier it is to be selected.

[0102] Step 3.3: Randomly select 100 observation years similar to the simulated years from the observation data based on the probability weight K (repeated sampling is allowed);

[0103] The probability weights are:

[0104] In the formula, d is the Euclidean distance, and k is set to... n is the sample length;

[0105] Step 3.4: Extract the regional average daily precipitation, maximum temperature and minimum temperature series corresponding to these observation years, and construct a daily-scale multi-site multivariate stochastic weather generator model;

[0106] Step 3.5: Considering the randomness of sampling, the annual-scale weather generator is run 50 times;

[0107] Step 4, daily-scale meteorological element stochastic simulation: A daily-scale weather generator is constructed using a two-state first-order Markov chain and a KNN model to simulate the daily weather sequence of 35 stations in the Ticino watershed, consisting of 3 weather variables. In this embodiment, the precipitation threshold is set to 0.1 mm. If the precipitation on a day is greater than the precipitation threshold, it is a precipitation day; otherwise, it is a no-precipitation day. The daily dry and wet states are assigned, and the precipitation transition probability is estimated using the maximum likelihood method. The two-state dry and wet transition probability matrix is ​​calculated, and a two-state first-order Markov chain is constructed.

[0108] Step 4.1: Randomly select meteorological data for any day in the starting month of the simulation (e.g., January 1st), and ensure that the precipitation wet / dry state corresponding to the data is consistent with the first precipitation state obtained from the Markov chain simulation.

[0109] Step 4.2: A first-order Markov chain is used to simulate the temporal distribution of the regional average daily precipitation wet / dry sequence for 35 stations. Whether precipitation occurs depends on whether precipitation occurred the previous day. In this embodiment, a precipitation threshold of 0.1 mm is set; if the precipitation on a given day is greater than the threshold, it is a rainy day; otherwise, it is a dry day. Daily wet / dry states are assigned. Considering the seasonal variation characteristics of precipitation processes, the calculation of Markov chain parameters and the simulation of daily precipitation wet / dry states are performed monthly.

[0110] Step 4.3: Use the maximum likelihood method to estimate the precipitation transition probability p from state a of the previous day to state b of the current day. ab Therefore, the four transition probabilities (p) of the two-state Markov chain are calculated. 00 p 01 p 10 p 11 ), where p 00 p represents the probability that there will be no precipitation tomorrow if there was no precipitation the day before. 01 This represents the probability of rain the day before if there was no rain the previous day, and so on.

[0111] Step 4.4: The regional average daily weather variables generated by the annual-scale weather generator... Data was collected from 35 stations within the Ticino watershed;

[0112] Step 4.4.1: In the historical observation records extracted by the annual scale weather generator, find all adjacent day pairs with the same dry and wet conditions on the previous day and the current day in the window centered on day t (set the window period to 7 days). If no suitable day pairs are found, expand the window period to 30 days.

[0113] Step 4.4.2: Within the window period, select adjacent day pairs with the same state on day t and day t-1, and extract the corresponding regional average weather variable vectors. and

[0114] Step 4.4.3, calculate the weighted Euclidean distance between the historical regional average weather variable vector and the simulated vector for all adjacent day pairs: The Euclidean distance is:

[0115] Step 4.4.4, the distance d q Sort in ascending order, k is set to The weights of the k nearest neighbor distances are calculated using a discrete kernel function; the formula for calculating the weights using the discrete kernel function is as follows:

[0116] Step 4.4.5: Randomly select a value from the k nearest neighbor distances according to probability weights and record its corresponding historical date;

[0117] Step 4.4.6: Extract the weather variable vector X for L stations within the region on the day following the historical date. l This is used as the simulation vector for day t, and the above steps are repeated for T simulation days to generate a daily-scale meteorological element simulation sequence based on the weather generator.

[0118] Step 4.5: After assessing the applicability of the multi-site multivariate weather generator to simulate the weather variable series in the watershed, it was found that the spatiotemporal correlation and inter-variable correlation of the simulated meteorological elements were good. Therefore, there is no need to use the EmpiricalCopula post-processing method to improve the spatiotemporal correlation and inter-variable correlation of the meteorological elements.

[0119] Step 5: Calibration of GR4J hydrological model parameters. Only seven years of flow data at the watershed outlet section are available, from July 15, 2013 to July 15, 2019. The five years from July 15, 2013 to July 15, 2017 are designated as the calibration period, with the remaining two years used as the validation period. Model parameters are calibrated using observed rainfall, flow, and temperature data from the calibration period.

[0120] Step 5.1: Calculate the average watershed area of ​​the observed meteorological sequence (precipitation, temperature);

[0121] Step 5.2: Calculate the daily average potential evapotranspiration of the Ticino basin using the Oudin formula combined with the basin's average surface temperature;

[0122] Oudin's formula is: If T a +5 > 0, Otherwise, PE = 0 (6)

[0123] In the formula, PE is the potential evapotranspiration rate, and R is the potential evapotranspiration rate. e For extraterrestrial radiation, λ is the latent heat flux, ρ is the density of water, and T is the total heat flux. a The average daily temperature;

[0124] Step 5.3: Combine the watershed outlet section flow data with the watershed surface average meteorological data calculated above as the data input for the GR4J model;

[0125] Step 5.4: Divide the period from July 15, 2013 to July 15, 2017 into the GR4J model parameter calibration period.

[0126] Step 5.5: Set the model warm-up period to one year (≥1 year), i.e., from July 15, 2013 to July 15, 2014;

[0127] Step 5.6: Select the Nash-Sutcliffe efficiency coefficient (NSE) as the parameter calibration error standard;

[0128] The Nash efficiency coefficient NSE is:

[0129] In the formula, Q o For the observed value, Q m These are simulated values. The average value is t, where t is the time period.

[0130] Step 5.7: After selecting the error standard as the objective function, the model parameters are calibrated using the Irstea algorithm proposed by C. Miche.

[0131] Step 6: Use the observed meteorological element sequence from July 16, 2017 to July 15, 2019, during the validation period, to drive the GR4J model to obtain the daily runoff simulation sequence;

[0132] Step 7: Drive the GR4J model with the simulated meteorological element sequence based on the weather generator during the validation period to obtain the runoff simulation sequence based on the weather generator-GR4J model. Compare this sequence with the runoff simulation sequence obtained in Step 6. The results are as follows: Figure 3 , Figure 4 As shown. The precipitation-runoff simulation method based on a multi-site multivariable weather generator proposed in this invention can effectively simulate the runoff variation trend in the Ticino watershed of Switzerland, while also providing the uncertainty range for runoff simulation.

Claims

1. A precipitation-runoff simulation method based on a multi-site, multivariable weather generator, characterized in that, Includes the following steps: Step 1: Collect daily precipitation, maximum and minimum temperatures, and water flow data at the watershed outlet section for stations within the watershed; Step 2, Annual-scale stochastic simulation of meteorological elements: The daily-scale observation data is processed into an annual-scale observation meteorological variable series, and the regional average annual precipitation, maximum and minimum temperature series are generated using an annual-scale weather generator based on the multivariate first-order autoregressive model MAR1. Step 3: Assign interannual variation characteristics to the daily-scale simulation sequence: For each year of the regional average annual precipitation, maximum and minimum temperature simulation sequence generated by MAR1, the KNN algorithm is used to randomly select several years from the observation sequence that are close to the regional average annual precipitation, maximum and minimum temperature simulation values ​​according to probability weights, and extract the regional average daily-scale precipitation, maximum and minimum temperature sequences corresponding to the years to construct a daily-scale multi-site multivariate weather generator. Step 4: Daily-scale stochastic simulation of meteorological elements: A daily-scale weather generator is constructed using a two-state first-order Markov chain and a KNN model to simulate daily weather sequences consisting of R weather variables for L stations in a certain region; specifically, the following steps are included: Step 41: Randomly extract meteorological data for any day corresponding to the starting month of the simulation from the simulation data generated by the annual scale weather generator, and the precipitation wet and dry state corresponding to the data should be consistent with the first precipitation state of the Markov chain simulation. Step 42: Use a first-order Markov chain to simulate the temporal distribution of the regional average daily precipitation wet / dry sequence for L stations. Whether precipitation occurs depends on whether precipitation occurred the previous day. Assume that a daily precipitation greater than or equal to 0.1 mm is a wet day, S t =1 indicates precipitation occurred; less than 0.1 mm is considered a dry day. S t =0 represents no precipitation. Considering the seasonal variation of precipitation processes, the calculation of Markov chain parameters and the simulation of daily precipitation wet and dry states are carried out on a monthly basis. Step 43: Use the maximum likelihood method to estimate the precipitation transition probability p from the previous day's state a to the current day's state b. ab Therefore, the four transition probabilities (p) of the two-state Markov chain are calculated. 00 p 01 p 10 p 11 ), where p 00 p represents the probability that there will be no precipitation tomorrow if there was no precipitation the day before. 01 This indicates the probability of rain the day before if there was no rain the previous day, and so on. Step 44: Calculate the regional average daily weather variables generated by the annual-scale weather generator. The data is distributed to L stations within the region; specifically, the following steps are included: Step 441, Assumption and These represent the regional average weather variable vectors for simulated days t-1 and t, respectively, where both t-1 and t are wet days. Find all adjacent day pairs centered on day t in the historical observation records extracted by the annual scale weather generator. Set the window period to 7 days. If no suitable day pair is found, expand the window period to 30 days. Step 442, Filter out and and There are Q pairs of adjacent days with the same wet / dry conditions. Each pair contains a vector of regional average weather variables for the two consecutive days. and Calculate the average weather variable vector and simulated vector for Q historical regions. The weighted Euclidean distance between them; Step 443: Set the distance d q Sort in ascending order, k is set to Weights are calculated for the k nearest neighbor distances using a discrete kernel function: Step 444: Randomly select a value from the k nearest neighbor distances based on the weights and record its corresponding historical date; Step 445: Find the weather variable vector X for L stations in the region on the day following the historical date. l As the simulation vector for day t; Step 446: Repeat the above steps for T simulated days; Step 45: Conduct an applicability assessment of the multi-site multivariate weather generator simulated weather variable series for the study area. If the spatiotemporal correlation and inter-variable correlation of meteorological elements are poor, the Empirical Copula post-processing method is adopted to improve the spatiotemporal correlation and inter-variable correlation of meteorological elements; specifically, the following steps are included: Step 451: For the three weather variables of precipitation, maximum and minimum temperature at K stations, considering the seasonal effects, the Empirical Copula post-processing method is applied to the observation sample data of the three weather variables in each month to calculate the rank matrix as a reference sample rank matrix. The number of rows in the matrix is ​​the number of data points in that month, and the number of columns is K×3. Step 452: Based on the reference sample rank matrix, reorder the simulated sample data of the corresponding month according to the rank, so that the rank matrix of the simulated sample after sorting is completely consistent with the observed sample, thereby reconstructing the inter-site, inter-variable, and temporal correlations of the simulated sample data. Step 453: Combine the processed simulated weather variable data for each month in chronological order to obtain the simulated data processed by the Empirical Copula function. Step 5: Preprocessing of input data for the GR4J hydrological model: The meteorological element data simulated by the weather generator above is preprocessed and used as input data for the hydrological model; Step 6: After selecting the error standard as the objective function, calibrate the model parameters of the GR4J hydrological model; Step 7: Use the calibrated GR4J model to simulate the daily runoff of the watershed.

2. The precipitation-runoff simulation method based on a multi-site, multivariable weather generator as described in claim 1, characterized in that, In step 2, the regional average annual precipitation, maximum and minimum temperature sequences are generated: X t =w+AX t-1 +e t ; In the formula: X t and X t-1 It is a [3×1] matrix, representing the regional average annual precipitation, annual maximum and minimum temperatures (annual averages) for years t and t-1, respectively. The three rows represent the three variables: annual precipitation, maximum and minimum temperatures; A and w are the [3×3] autocorrelation coefficient matrix and the [3×1] intercept term matrix, respectively, and e t It is a [3×3] independent random residual matrix with a mean of 0 and a covariance of C. The parameters A, w, and C in the MAR1 model are estimated by piecewise least squares fitting. The MAR1 model effectively simulates the interannual variation characteristics of annual precipitation, maximum and minimum temperature sequences while maintaining the correlation between variables.

3. The precipitation-runoff simulation method based on a multi-site, multivariable weather generator as described in claim 1, characterized in that, Step 3, constructing a daily-scale multi-site multivariate weather generator, specifically includes the following steps: Step 31: Use the MAR1 model to generate a model of length T. a The simulated sequence of regional average annual precipitation, maximum and minimum temperatures; Step 32, for the simulated year t a Calculate the regional average annual scale weather variable vector simulated in step 2. Compared with historical observations Euclidean distance between them: In the formula: Indicates the simulated year t a Regional average annual scale weather variable vector, This represents the historical observation value for the corresponding year; Step 33: Sort the distances d from smallest to largest, and set k to... n is the sample length; a discrete kernel function is used to assign probability weights K to the k nearest neighbor years. The weights are determined by the distance; the smaller the distance, the easier it is to be selected. The formula is as follows: Step 34: For any simulated year t a Based on probability weight K, from the k nearest historical observations 100 items were randomly selected from the list. For similar years, extract the regional average daily precipitation, maximum and minimum temperature data corresponding to those 100 years to generate a simulated year t. a The daily-scale precipitation, maximum and minimum temperature data serve as the data foundation for constructing a daily-scale multi-site multivariable weather generator. Step 35: Considering the randomness of sampling, the annual-scale weather generator is run 50 times.

4. The precipitation-runoff simulation method based on a multi-site, multivariable weather generator as described in claim 1, characterized in that, In step 4, the daily weather sequence is as follows: in, Let represent the i-th variable corresponding to the l-th station and time t, where T represents the sample length of the simulated sequence.

5. The precipitation-runoff simulation method based on a multi-site, multivariable weather generator as described in claim 1, characterized in that, In step 442, the average weather variable vectors of Q historical regions and the simulated vectors are calculated. Weighted Euclidean distance between: In the formula: This represents the average weather variable for the i-th region corresponding to day t-1 in the simulation. This represents the regional average weather variable for the first day of the q-th historical adjacent day pair. w represents the monthly climatological average of the i-th regional average weather variable on day t-1. i Indicates the weight, and sets the weight w. i The reciprocal of the climatological standard deviation of the average weather variable for the i-th region on day t-1 of the month is used to standardize each variable in the weighted Euclidean distance, thus avoiding the significant impact of different variables on the calculation results of the Euclidean distance due to differences in their dimensions and numerical magnitudes.

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