Precipitation runoff simulation method based on multi-station multivariable weather generator

Abstract

The invention discloses a rainfall runoff simulation method based on a multi-station multivariable weather generator, which adopts a multivariable first-order autoregression model to generate rainfall and air temperature sequences, and can effectively simulate interannual change characteristics of the rainfall and air temperature sequences. The multi-variable multi-site weather generator can generate a hydro-meteorological element simulation field with correlation among sites, variables and time sequences, can effectively reflect all-around characteristics of a hydro-meteorological process, and improves a runoff simulation effect; by introducing an Empirical Copula post-processing method, under the condition that the simulation result of a weather generator is poor, the space-time correlation of a meteorological element simulation field is further improved, and more reliable input data is provided for a hydrological model.

Description

Technical Field

[0001] The present invention relates to the technical field of processing methods for the purpose of simulation, and in particular to a precipitation runoff simulation method based on a multi-site multivariable weather generator. Background Art

[0002] At present, the main methods for simulating precipitation and runoff include mathematical statistics and mathematical physics modeling. The former establishes the relationship between precipitation and runoff by statistically analyzing historical meteorological data; the latter simulates the hydrological response of the basin by describing processes such as precipitation, evapotranspiration, and soil moisture based on the physical principles of the hydrological model.

[0003] As a tool for simulating weather variables, weather generators have been widely used in stochastic simulation of hydrological and meteorological processes. Based on the climate characteristics of a certain region, weather generators use statistical or random process theory methods to simulate and generate meteorological element sequences of any time length that can reflect the statistical characteristics of the observed sequence. Weather generators can provide ensemble inputs of multiple random simulations of multiple meteorological elements such as precipitation and temperature for precipitation-runoff simulation, which can better quantify the uncertainty of meteorological element inputs.

[0004] The hydro-meteorological process is continuous in both time and space, and there is physical correlation between various meteorological elements. These characteristics directly affect the subsequent hydrological simulation and must be accurately reflected in the simulation process. Taking precipitation as an example, if the precipitation data of each sub-basin is independent of each other, the runoff generated in each sub-basin will lose spatial correlation, resulting in misestimation of the total runoff and extreme values ​​of the outlet section of the basin. At the same time, the temperature determines the form of precipitation (rainfall or snowfall) and determines the time and amount of snow melting in the basin in winter. The physical correlation between precipitation and temperature has a significant impact on northern rivers dominated by snowfall. In addition, the continuity of precipitation in the time dimension (such as continuous dry periods or continuous wet periods, etc.) and the low-frequency variation characteristics of meteorological elements (such as interannual variation characteristics) are also important hydro-meteorological characteristics, which must be accurately measured in the simulation process. The traditional stochastic simulation method of hydro-meteorological processes cannot effectively reflect the full range of characteristics of hydro-meteorological processes at the regional / basin scale. Using it as the input of the hydrological model will lead to distortion of basin runoff simulation. Summary of the invention

[0005] Purpose of the invention: The present invention provides a precipitation runoff simulation method based on a multi-site multivariable weather generator, which generates a simulation field of hydrological and meteorological elements with correlations between sites, variables, and time series and reflects interannual variation characteristics to drive a 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 the present invention comprises the following steps:

[0007] Step 1: Collect daily precipitation, maximum and minimum temperatures, and flow data at the outlet of the basin at stations within the basin;

[0008] Step 2: Stochastic simulation of annual meteorological elements: The daily observation data are processed into an annual observation meteorological variable sequence, and the regional average annual precipitation, maximum and minimum temperature sequences are generated using an annual 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 that are close to the MAR1 regional average annual precipitation, maximum and minimum temperature simulation values ​​from the observation sequence according to the probability weight, and extract the regional average daily-scale precipitation, maximum and minimum temperature sequences corresponding to these 100 years to construct a daily-scale multi-station multivariable weather generator;

[0010] Step 4: Random simulation of daily-scale meteorological elements: Use a two-state first-order Markov chain and KNN model to construct a daily-scale weather generator to simulate the daily weather sequence consisting of R weather variables at L stations in a certain area;

[0011] Step 5, GR4J (Genie Rural a 4Parametres Journalier) hydrological model input data preprocessing: preprocessing the meteorological element data simulated by the above weather generator as 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 in the basin.

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

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

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

[0017] Step 31: Use the MAR1 model to generate a length of T a Simulated series 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 With historical observations The Euclidean distance between:

[0019]

[0020] Where: represents the simulated year t a The vector of regional average annual weather variables, represents the historical observation value of the corresponding year;

[0021] Step 33: Sort the distances d from small to large, and set k to n is the sample length; a discrete kernel function is used to assign a probability weight K to the k nearest years. The weight is 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 , according to the probability weight K, from the k nearest historical observations Randomly select 100 The simulated year t is generated by extracting the regional average daily precipitation, maximum and minimum temperature data corresponding to the 100 years. a Daily precipitation, maximum and minimum temperature data are used as the data basis for constructing a daily-scale multi-station 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:

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

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

[0028] Furthermore, in step 4, a daily-scale weather generator is constructed using a two-state first-order Markov chain and a KNN model to simulate a daily weather sequence consisting of R weather variables at L stations in a certain area, which specifically includes the following steps:

[0029] Step 41: randomly extract the meteorological data of any day corresponding to the simulation start month from the simulation data generated by the annual-scale weather generator, and the precipitation dry and wet state corresponding to the data must be consistent with the first precipitation state simulated by the Markov chain;

[0030] Step 42: Use a first-order Markov chain to simulate the temporal distribution of the regional average daily precipitation dry-wet sequence of L stations. The occurrence of precipitation depends on whether there is precipitation on the previous day. It is assumed that a day with a daily precipitation greater than or equal to 0.1 mm is a wet day (S t =1 means precipitation occurs), less than 0.1 mm means dry day (S t =0 represents no precipitation). Considering the seasonal variation characteristics of the precipitation process, the calculation of Markov chain parameters and the simulation of the dry and wet states of daily precipitation are carried out on a monthly basis.

[0031] 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 , and thus calculate the four transition probabilities (p 00 , p 01 , p 10 , p 11 ), where p 00 is the probability that there is no precipitation on the previous day and no precipitation on the current day, p 01 The probability of precipitation on the current day if there was no precipitation on the previous day, and so on;

[0032] Step 44: convert the regional average daily weather variables generated by the annual weather generator The solution is aggregated to L sites in the area;

[0033] Step 45: evaluate the suitability of the weather variable sequence simulated by the multi-site multivariable weather generator in the study area. If the spatiotemporal correlation of meteorological elements and the correlation between variables are poor, adopt the Empirical Copula post-processing method to improve the spatiotemporal correlation of meteorological elements and the correlation between variables.

[0034] Further, in step 44, the regional average daily weather variables generated by the annual scale weather generator are The steps of solving the problem of L sites in the area are as follows:

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

[0036] Step 442: Filter out and and Adjacent pairs of days with the same dry and wet state (i.e., both are wet days), assuming there are Q adjacent pairs of days, each pair contains the regional average weather variable vector of the two days before and after, and Calculate the Q historical regional average weather variable vectors and simulation vectors The weighted Euclidean distance between them;

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

[0038]

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

[0040] Step 445: Find the weather variable vector X of the 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 simulation days.

[0042] Further, in step 442, the Q historical regional average weather variable vectors and the simulation vectors are calculated The weighted Euclidean distance between:

[0043]

[0044] Where: represents the average weather variable of the ith region corresponding to the simulated day t-1, represents the regional average weather variable for the first day of the qth historical adjacent day pair, represents the monthly climatological average value of the average weather variable in the ith region on day t-1 (the average value of the data for that month in all years), w i Represents weight, set weight w i It is the inverse of the standard deviation of the climate state of the average weather variable in the i-th region in the month corresponding to the t-1 day. Each variable in the weighted Euclidean distance is standardized to avoid the large influence of different variables on the calculation result of the Euclidean distance due to different dimensions and numerical magnitudes.

[0045] Furthermore, in step 45, adopting the Empirical Copula post-processing method to improve the spatiotemporal correlation of meteorological elements and the correlation between variables specifically includes the following steps:

[0046] Step 451: for the three weather variables of precipitation, maximum and minimum temperatures at the K stations, taking into account the seasonal influence, the Empirical Copula post-processing method is applied to the observed sample data of the three weather variables in each month (the number of data points in each month = the number of years × the number of days in the month) to calculate the rank matrix as the 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: re-rank the simulated sample data of the corresponding month according to the reference sample rank matrix, so that the rank matrix of the sorted simulated sample is completely consistent with the observed sample, thereby reconstructing the inter-site, inter-variable and time-series correlations of the simulated sample data;

[0048] Step 453: splice the processed simulated data of each weather variable in each month in chronological order to obtain simulated 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 multivariable 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 multivariable multi-site weather generator can generate a hydrological and meteorological element simulation field with correlations between sites, variables and time series, which can effectively reflect the all-round characteristics of the hydrological and meteorological process and improve the runoff simulation effect; by introducing the EmpiricalCopula post-processing method, when the simulation results of the weather generator are poor, the spatiotemporal correlation of the meteorological element simulation field can be further improved, providing more reliable input data for the hydrological model. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 The present invention is a flow chart of the precipitation runoff simulation method based on the coupling of a multi-site multivariable weather generator and a GR4J hydrological model.

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

[0052] Figure 3 This is a runoff simulation result diagram based on the multi-site multivariable weather generator and GR4J hydrological model simulation of the present invention.

[0053] Figure 4 This is a simulation result diagram of high and low flows in spring, summer and autumn based on the multi-site multivariable weather generator and the GR4J hydrological model of the present invention. DETAILED DESCRIPTION

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

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

[0056] Step 2, random simulation of annual meteorological elements: The daily observation data are processed into an annual observation meteorological variable sequence, and the regional average annual precipitation, maximum and minimum temperature sequences are generated using an annual weather generator based on a multivariate first-order autoregressive model (MAR1): X t =w+AX t-1 +e t ;

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

[0058] 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 (repeatable sampling) from the observation sequence according to the probability weight that are similar to the regional average annual precipitation, maximum and minimum temperature simulation values ​​of MAR1. The regional average daily-scale precipitation, maximum and minimum temperature sequences corresponding to these 100 years are extracted to construct a daily-scale multi-station multivariate weather generator;

[0059] Step 3.1, use the MAR1 model to generate a length of T a Simulated series 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 With historical observations The Euclidean distance between:

[0061]

[0062] Where: represents the simulated year t a The vector of regional average annual weather variables, represents the historical observation value of the corresponding year;

[0063] Step 3.3, sort the distances d from small to large, and k is generally set to n is the sample length; a discrete kernel function is used to assign a probability weight K to the k nearest years. The weight is 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 simulation year t a , according to the probability weight K, from the k nearest historical observations Randomly select 100 (repeatable sampling) and The simulated year t is generated by extracting the regional average daily precipitation, maximum and minimum temperature data corresponding to the 100 years. aDaily precipitation, maximum and minimum temperature data are used as the data basis for constructing a daily-scale multi-station multivariable weather generator;

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

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

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

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

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

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

[0072] Step 4.3: 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 , from which we can calculate the four transition probabilities (p 00 , p 01 , p 10 , p 11 ), where p 00 is the probability that there is no precipitation on the previous day and no precipitation on the current day, p 01 The probability of precipitation on the current day if there was no precipitation on the previous day, and so on;

[0073] Step 4.4: convert the regional average daily weather variables generated by the annual weather generator into The solution is aggregated to L sites in the area;

[0074] Step 4.4.1, assuming and Represent the vectors of regional average weather variables of simulated day t-1 and day t, respectively, and both days t-1 and t are wet days. In the historical observation records extracted by the annual weather generator, find all adjacent day pairs in the window (set the window period to 7 days) centered on day t (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 pairs are found, expand the window period to 30 days;

[0075] Step 4.4.2, filter out and and Adjacent pairs of days with the same dry and wet state (i.e., both are wet days). Assume that there are Q pairs of adjacent days, each pair contains the regional average weather variable vector of the two days before and after, and Calculate the Q historical regional average weather variable vectors and simulation vectors The weighted Euclidean distance between:

[0076]

[0077] Where: represents the average weather variable of the ith region corresponding to the simulated day t-1, represents the regional average weather variable for the first day of the qth historical adjacent day pair, represents the monthly climatological average value of the average weather variable in the i-th region on day t-1 (the average value of the data for that month in all years), w i In the present invention, the weight w is set i The reciprocal of the standard deviation of the climate state of the average weather variable of the i-th region in the month corresponding to the t-1 day is used to standardize each variable in the weighted Euclidean distance to avoid the large impact of different variables on the calculation results of the Euclidean distance due to different dimensions and numerical magnitudes;

[0078] Step 4.4.3, set the distance d q Arrange in ascending order, k is generally set to Use discrete kernel function to calculate the weights of k nearest neighbor distances;

[0079]

[0080] Step 4.4.4, randomly select a value from the k nearest neighbor distances based on the weight and record its corresponding historical date;

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

[0082] Step 4.4.6, repeat the above steps for T simulation days;

[0083] Step 4.5, evaluate the suitability of the weather variable sequence simulated by the multi-site multivariable weather generator in the study area. If the spatiotemporal correlation of meteorological elements and the correlation between variables are poor, the Empirical Copula post-processing method is used to improve the spatiotemporal correlation of meteorological elements and the correlation between variables;

[0084] Step 4.5.1, for the three weather variables of precipitation, maximum and minimum temperature at K stations, considering the influence of seasonality, apply the Empirical Copula post-processing method to calculate the rank matrix of the three weather variable observation sample data of each month (the number of data points in each month = the number of years × the number of days in the month) as the 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, according to the reference sample rank matrix, re-rank the simulated sample data of the corresponding month so that the rank matrix of the sorted simulated sample is completely consistent with the observed sample, so as to reconstruct the inter-site, inter-variable and time-series correlation of the simulated sample data;

[0086] Step 4.5.3, the processed simulated data of each weather variable in each month are spliced ​​in chronological order to obtain simulated data processed by the Empirical Copula function;

[0087] Step 5, GR4J hydrological model input data preprocessing: preprocess the meteorological element data simulated by the above weather generator (calculation of surface average precipitation, evapotranspiration, etc.) 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: Use the calibrated GR4J model to simulate the daily runoff in the basin.

[0090] Taking the Ticino River Basin in Switzerland as an example, the following process is implemented based on the R language platform, and the method steps are described in detail with the accompanying drawings.

[0091] A precipitation-runoff simulation method based on multi-station multivariable weather generator Figure 1 As shown, the following steps are included:

[0092] Step 1: collect data from 35 meteorological stations in the Ticino Basin from January 1, 1981 to December 31, 2020 as basic data of meteorological elements, preprocess the data, and calculate the regional average meteorological variable series;

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

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

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

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

[0097] Step 3, assigning the 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 that are close to the MAR1 regional average annual precipitation, maximum and minimum temperature simulation values ​​from the observation sequence according to the probability weight, and extract the regional average daily-scale precipitation, maximum and minimum temperature sequences corresponding to these 100 years to construct a daily-scale multi-station multivariable weather generator;

[0098] Step 3.1: For the 40-year-long annual-scale meteorological element simulation sequence, the KNN algorithm is applied to calculate the regional average annual-scale weather variable vector simulated for each year. With historical observations The Euclidean distance between

[0099] The Euclidean distance is:

[0100] Where: represents the simulated year t a The vector of regional average annual weather variables, represents the historical observation value of the corresponding year;

[0101] Step 3.2, sort the distances d from small to large, and use the discrete kernel function to assign probability weights K to the k nearest 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 simulation year from the observation data based on the probability weight K (repeatable sampling);

[0103] The probability weights are:

[0104] Where 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 multi-station multivariate random weather generator model at the daily scale;

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

[0107] Step 4, random simulation of daily-scale 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 consisting of three weather variables at 35 stations in the Ticino Basin; in this embodiment, the precipitation threshold is set to 0.1 mm; if the precipitation on that day is greater than the precipitation threshold, it is a precipitation day, otherwise, it is a non-precipitation day, and the daily dry and wet states are assigned, and the precipitation transition probability is estimated using the maximum likelihood method and 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 the meteorological data of any day in the simulation start month (for example, January 1), and ensure that the precipitation dry and wet state corresponding to the data is consistent with the first precipitation state obtained by Markov chain simulation;

[0109] Step 4.2, using the first-order Markov chain to simulate the time distribution of the regional average daily precipitation dry and wet sequence of 35 stations, the occurrence of precipitation depends on whether there is precipitation on the previous day. In this embodiment, the precipitation threshold is set to 0.1mm; if the daily precipitation is greater than the precipitation threshold, it is a precipitation day, otherwise, it is a non-precipitation day, and the daily dry and wet state is assigned. Considering the seasonal variation characteristics of the precipitation process, the calculation of Markov chain parameters and the simulation of daily precipitation dry and wet states are performed on a monthly basis;

[0110] Step 4.3: 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 , and thus calculate the four transition probabilities (p 00 , p 01 , p 10 , p 11 ), where p 00 is the probability that there is no precipitation on the previous day and no precipitation on the current day, p 01 The probability of precipitation on the current day if there was no precipitation on the previous day, and so on;

[0111] Step 4.4: convert the regional average daily weather variables generated by the annual weather generator into The solution was clustered into 35 sites within the Ticino watershed;

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

[0113] Step 4.4.2: Filter out pairs of adjacent days with the same state on day t and day t-1 within the window period and extract the corresponding regional average weather variable vector 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, set the distance d q Sort in ascending order, k is set to The discrete kernel function is used to calculate the weights of the k nearest neighbor distances; the weight calculation formula of the discrete kernel function is:

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

[0117] Step 4.4.6: Extract the weather variable vector X of the L stations in the region on the next day of the historical date l , and use it as the simulation vector of the tth day, and repeat the above steps for T simulation days to generate a daily-scale meteorological element simulation sequence based on the weather generator;

[0118] Step 4.5: After evaluating the suitability of the weather variable sequence simulated by the multi-site multivariable weather generator in the basin, it was found that the temporal and spatial correlation of the simulated meteorological elements and the correlation between variables performed well, so there was no need to adopt the EmpiricalCopula post-processing method to improve the temporal and spatial correlation of the meteorological elements and the correlation between variables;

[0119] Step 5, GR4J hydrological model parameter calibration. The flow data at the outlet section of the basin only have 7 years of flow data from July 15, 2013 to July 15, 2019. The 5 years from July 15, 2013 to July 15, 2017 are divided into the calibration period, and the remaining 2 years of data are used as the verification period. The model parameters are calibrated using the observed rainfall, flow, temperature and other data during the calibration period;

[0120] Step 5.1, calculate the basin surface average of the observed meteorological series (precipitation, temperature);

[0121] Step 5.2, calculate the daily average potential evapotranspiration of the Ticino Basin using the Oudin formula combined with the basin average temperature;

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

[0123] Where PE is the potential evapotranspiration rate, R e is the extraterrestrial radiation, λ is the latent heat flux, ρ is the density of water, T a is the daily average temperature;

[0124] Step 5.3, combine the flow data of the watershed outlet section with the watershed surface average meteorological data calculated above as the GR4J model data input;

[0125] Step 5.4: divide July 15, 2013 to July 15, 2017 into the GR4J model parameter rate period.

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

[0127] Step 5.6, select Nash-Sutcliffeefficiency coefficient (NSE) as the parameter calibration error standard;

[0128] The Nash efficiency coefficient NSE is:

[0129] In the formula, Q o is the observed value, Q m is the analog value, is the average value of the observations, and t is the time period;

[0130] Step 5.7, after selecting the error standard as the objective function, the model parameters are calibrated in combination with the Irstea algorithm proposed by C. Miche;

[0131] Step 6, using 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, the GR4J model is driven by the simulated meteorological element sequence based on the weather generator during the verification period to obtain the runoff simulation sequence based on the weather generator-GR4J model, which is compared with the runoff simulation sequence obtained in step 6. The results are as follows: Figure 3 , Figure 4 The precipitation-runoff simulation method based on multi-station multivariable weather generator proposed in the present invention can better simulate the runoff variation trend of the Ticino Basin in Switzerland and provide the uncertainty interval of runoff simulation.

Claims

1. A precipitation runoff simulation method based on a multi-site multivariable weather generator, characterized in that: The steps include: Step 1: Collect daily precipitation, maximum and minimum temperatures, and flow data at the outlet of the basin at stations within the basin; Step 2, random simulation of annual-scale meteorological elements: the daily-scale observation data are processed into an annual-scale observational meteorological variable sequence, and the regional average annual precipitation, maximum and minimum temperature sequences 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 a number of years with similar regional average annual precipitation, maximum and minimum temperature simulation values ​​from the observation sequence according to the probability weight, and extract the regional average daily-scale precipitation, maximum and minimum temperature sequences corresponding to the year to construct a daily-scale multi-station multivariable weather generator; Step 4: Random simulation of daily-scale meteorological elements: Use a two-state first-order Markov chain and KNN model to construct a daily-scale weather generator to simulate the daily weather sequence consisting of R weather variables at L stations in a certain area; Step 5, GR4J hydrological model input data preprocessing: preprocess the meteorological element data simulated by the above weather generator as hydrological model data input; 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 in the basin.

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

3. The precipitation runoff simulation method based on a multi-site multivariable weather generator as claimed in claim 1, characterized in that: In step 3, constructing a daily-scale multi-site multivariable weather generator specifically includes the following steps: Step 31: Use the MAR1 model to generate a length of T a Simulated series 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 With historical observations The Euclidean distance between: Where: represents the simulated year t a The vector of regional average annual weather variables, represents the historical observation value of the corresponding year; Step 33: Sort the distances d from small to large, and set k to n is the sample length; a discrete kernel function is used to assign a probability weight K to the k nearest years. The weight is 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 , according to the probability weight K, from the k nearest historical observations Randomly select 100 The simulated year t is generated by extracting the regional average daily precipitation, maximum and minimum temperature data corresponding to the 100 years. a Daily precipitation, maximum and minimum temperature data are used as the data basis for constructing a daily-scale multi-station 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 claimed in claim 1, characterized in that: In step 4, the daily weather sequence is: in, represents the i-th variable corresponding to the l-th station and time t, and T represents the sample length of the simulation sequence.

5. The precipitation runoff simulation method based on a multi-site multivariable weather generator as claimed in claim 1, characterized in that: In step 4, a daily-scale weather generator is constructed using a two-state first-order Markov chain and a KNN model to simulate a daily weather sequence consisting of R weather variables at L stations in a certain area. The specific steps include: Step 41, randomly extracting meteorological data of any day corresponding to the simulation start month from the simulation data generated by the annual-scale weather generator, and the precipitation dry and wet state corresponding to the data must be consistent with the first precipitation state simulated by the Markov chain; Step 42: Use a first-order Markov chain to simulate the time distribution of the regional average daily precipitation dry-wet sequence of L stations. The occurrence of precipitation depends on whether there is precipitation on the previous day. Assume that a day with a daily precipitation greater than or equal to 0.1 mm is a wet day. S t =1 means precipitation occurs, less than 0.1mm means dry day, S t =0 means no precipitation occurs. Considering the seasonal variation characteristics of the precipitation process, the calculation of Markov chain parameters and the simulation of the dry and wet state of daily precipitation 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 , and thus calculate the four transition probabilities (p 00 , p 01 , p 10 , p 11 ), where p 00 is the probability of no precipitation on the previous day and no precipitation on the current day, p 01 The probability of precipitation on the current day if there was no precipitation on the previous day, and so on; Step 44: convert the regional average daily weather variables generated by the annual weather generator The solution is aggregated to L sites in the area; Step 45: evaluate the suitability of the weather variable sequence simulated by the multi-site multivariable weather generator in the study area. If the spatiotemporal correlation of meteorological elements and the correlation between variables are poor, adopt the Empirical Copula post-processing method to improve the spatiotemporal correlation of meteorological elements and the correlation between variables.

6. The precipitation runoff simulation method based on a multi-site multivariable weather generator as claimed in claim 5, characterized in that: In step 44, the regional average daily weather variables generated by the annual weather generator are The steps of solving the problem of L sites in the area are as follows: Step 441: Assumption and Represent the vectors of regional average weather variables of simulated day t-1 and day t, respectively. Both day t-1 and day t are wet days. Find all adjacent day pairs in the window 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 pairs are found, expand the window period to 30 days. Step 442: Filter out and and Adjacent day pairs with the same dry and wet state, assuming there are Q adjacent day pairs, each pair contains the regional average weather variable vector of the two days before and after, and Calculate the Q historical regional average weather variable vectors and simulation vectors The weighted Euclidean distance between them; Step 443: Set the distance d q Sort in ascending order, k is set to The k nearest neighbor distances are weighted using a discrete kernel function: Step 444: randomly select a value from the k nearest neighbor distances based on the weight and record its corresponding historical date; Step 445: Find the weather variable vector X of the 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 simulation days.

7. The precipitation runoff simulation method based on a multi-site multivariable weather generator as claimed in claim 6, characterized in that: In step 442, the Q historical regional average weather variable vectors and the simulation vectors are calculated. The weighted Euclidean distance between: Where: represents the average weather variable of the ith region corresponding to the simulated day t-1, represents the regional average weather variable for the first day of the qth historical adjacent day pair, represents the monthly climatological average of the average weather variable in the i-th region on day t-1, w i Represents weight, set weight w i It is the inverse of the standard deviation of the climate state of the average weather variable in the i-th region in the month corresponding to the t-1 day. Each variable in the weighted Euclidean distance is standardized to avoid the large influence of different variables on the calculation result of the Euclidean distance due to different dimensions and numerical magnitudes.

8. The precipitation runoff simulation method based on a multi-site multivariable weather generator as claimed in claim 5, characterized in that: In step 45, the Empirical Copula post-processing method is used to improve the spatiotemporal correlation of meteorological elements and the correlation between variables, which specifically includes the following steps: Step 451: for the three weather variables of precipitation, maximum and minimum temperatures at the K stations, considering the seasonal influence, apply the Empirical Copula post-processing method to the observation sample data of the three weather variables in each month to calculate the rank matrix as the reference sample rank matrix, the number of rows of the matrix is ​​the number of data points in that month, and the number of columns is K×3; Step 452: re-rank the simulated sample data of the corresponding month according to the reference sample rank matrix, so that the rank matrix of the sorted simulated sample is completely consistent with the observed sample, thereby reconstructing the inter-site, inter-variable and time-series correlations of the simulated sample data; Step 453: splice the processed simulated data of each weather variable in each month in chronological order to obtain simulated data processed by the Empirical Copula function.

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