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

Abstract

Disclosed in the present invention is a precipitation runoff simulation method based on a multi-station multivariate weather generator. A multivariate first-order autoregressive model is used to generate precipitation and temperature series, effectively simulating interannual variation attributes of the precipitation and temperature series; the multivariate multi-station weather generator can generate a hydrometeorological element simulation field having inter-station, inter-variable, and inter-time-series correlations, effectively reflecting comprehensive features of hydrometeorological processes and improving the runoff simulation effect. If a simulation result of the weather generator is poor, introducing an Empirical Copula post-processing method further improves the spatiotemporal correlation of the meteorological element simulation field and provides more reliable input data for a hydrological model.

Description

A precipitation runoff simulation method based on a multi-site multi-variable weather generator TECHNICAL FIELD

[0001] The present application relates to the technical field of processing methods for simulation purposes, and in particular to a precipitation runoff simulation method based on a multi-site multi-variable weather generator. BACKGROUND

[0002] At present, precipitation runoff simulation methods mainly include mathematical statistics method and mathematical physics model method. The former establishes the relationship between precipitation and runoff by statistically analyzing historical meteorological data, and the latter simulates the hydrological response of a basin by describing the processes of precipitation, evapotranspiration, soil moisture, etc. based on the physical principles of hydrological models.

[0003] As a tool for simulating weather variables, weather generators have been widely used in the random simulation of hydro-meteorological processes. A weather generator mainly simulates meteorological element sequences of any length of time and reflecting the statistical characteristics of observation sequences according to the climate characteristics of a certain region, using statistical or random process theory methods. The weather generator can provide an ensemble input of multiple random simulations of multiple meteorological elements such as precipitation and air temperature for precipitation runoff simulation, which can better quantify the uncertainty of meteorological element input.

[0004] The hydro-meteorological process has continuity in time and space dimensions and physical correlation between meteorological elements, which directly affects 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 the incorrect estimation of the total amount and extreme value of runoff at the outlet section of the basin. At the same time, air temperature determines the form in which precipitation exists (rain or snow) and determines the time and amount of snowmelt in winter, and the physical correlation between precipitation and air temperature has a significant impact on northern rivers dominated by snow. In addition, the continuity of precipitation in the time dimension (such as consecutive dry periods or consecutive wet periods) and the low-frequency variation characteristics of meteorological elements (such as interannual variation characteristics) are also important hydro-meteorological characteristics that must be accurately measured in the simulation process. The traditional random simulation method of hydro-meteorological processes cannot effectively reflect the full range of characteristics of regional / basin-scale hydro-meteorological processes, and using it as the input of a hydrological model will lead to distorted runoff simulation of the basin. SUMMARY

[0005] The present application provides a precipitation runoff simulation method based on a multi-site multi-variable weather generator, which generates a hydro-meteorological element simulation field with inter-site, inter-variable, inter-temporal correlation and reflecting interannual variation characteristics to drive a hydrological model for runoff simulation, thereby improving the simulation accuracy of the hydrological model.

[0006] Technical scheme: the precipitation runoff simulation method based on the multi-site multivariate weather generator, comprising the following steps:

[0007] Step 1, collecting daily precipitation, maximum and minimum temperature and runoff data of the outlet section of the basin in the basin;

[0008] Step 2, annual scale meteorological element random simulation: the daily scale observation data is processed into annual scale observation meteorological variable sequence, and the annual scale weather generator based on multivariate first-order autoregressive model (MAR1) is used to generate regional average annual precipitation, maximum and minimum temperature sequence;

[0009] Step 3, giving the annual variation characteristics of the daily scale simulation sequence: for each year of the regional average annual precipitation, maximum and minimum temperature simulation sequence generated by MAR1, 100 years similar to the MAR1 regional average annual precipitation, maximum and minimum temperature simulation value are randomly extracted from the observation sequence according to the probability weight, and the corresponding regional average daily scale precipitation, maximum and minimum temperature sequence of the 100 years is extracted to construct the daily scale multi-site multivariate weather generator;

[0010] Step 4, daily scale meteorological element random simulation: a daily weather sequence composed of R weather variables of L sites in a region is simulated by using two-state first-order Markov chain and KNN model to construct daily weather generator;

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

[0012] Step 6, after selecting the error standard as the objective function, the model parameters of GR4J hydrological model are calibrated;

[0013] Step 7, using the calibrated GR4J model to simulate the daily runoff of the basin.

[0014] Further, in step 2, the regional average annual precipitation, maximum and minimum temperature sequence is generated: t = w + AX t-1 +e t ;

[0015] In the formula: X t And X t-1is a [3x1] matrix, representing the regional average annual precipitation, annual maximum and minimum temperature (annual mean) in the t and t-1 year, respectively, and 3 rows represent 3 variables of annual precipitation, maximum and minimum temperature, respectively; A and w are [3x3] autocorrelation coefficient matrix and [3x1] intercept matrix, respectively, e t is a [3x3] independent random residual matrix with mean 0 and covariance C; the parameters A, w and C in the MAR1 model are estimated by piecewise least squares fitting method, and the MAR1 model can effectively simulate the interannual variability characteristics of the annual precipitation, maximum and minimum temperature series under the premise of maintaining the correlation between variables.

[0016] Further, in step 3, the daily scale multi-site multi-variable weather generator specifically includes the following steps:

[0017] Step 31, using the MAR1 model to generate a simulated sequence of regional average annual precipitation, maximum and minimum temperature with a length of T a ;

[0018] Step 32, for the simulated annual t a , calculate the Euclidean distance between the simulated regional average annual scale weather variable vector in step 2 and the historical observation value :

[0019] In the formula: indicates the simulated regional average annual scale weather variable vector in the t a year, indicates the historical observation value in the corresponding year;

[0020] Step 33, sort the distance d from small to large, and set k as n is the sample length; use the discrete kernel function to assign probability weights K to the k nearest years, and the weight size is determined by the distance, that is, the smaller the distance, the easier to be drawn, and the formula is as follows:

[0021] Step 34, for any simulated year t a , according to the probability weight K, randomly select 100 years similar to from the k nearest historical observation values , and extract the regional average daily precipitation, maximum and minimum temperature data corresponding to the 100 years, to generate the daily scale precipitation, maximum and minimum temperature data of the simulated year t a , as the data basis for constructing the daily scale multi-site multi-variable weather generator;

[0022] Step 35, considering the randomness of sampling, the annual scale weather generator is run for 50 times.

[0023] Further, in step 4, the daily weather sequence is:

[0024] wherein, represents the ith variable corresponding to the first station and time t, T represents the length of the simulation sequence sample.

[0025] Further, in step 4, a two-state first-order Markov chain and a KNN model are used to construct a daily weather generator to simulate a daily weather sequence composed of R weather variables of L stations in a region, which includes the following steps:

[0026] Step 41, randomly extract the meteorological data of any day corresponding to the simulation starting month from the simulation data generated by the annual scale weather generator, and the dry and wet state of the precipitation corresponding to the data is consistent with the first precipitation state simulated by the Markov chain;

[0027] Step 42, use a first-order Markov chain to simulate the time distribution of the regional average daily precipitation dry and wet sequence of L stations, whether the precipitation occurs or not depends on whether the previous day has precipitation, assuming that the daily precipitation is greater than or equal to 0.1mm is a wet day (S t =1 represents the occurrence of precipitation), less than 0.1mm is a 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 daily precipitation dry and wet state are carried out monthly;

[0028] Step 43, use maximum likelihood method to estimate the precipitation transition probability p ab from the state a of the previous day to the state b of the current day, thereby calculating the four transition probabilities (p 00 , p 01 , p 10 , p 11 ) of the two-state Markov chain, wherein p 00 is the probability of no precipitation in the previous day and no precipitation in the current day, p 01 is the probability of no precipitation in the previous day and precipitation in the current day, and so on;

[0029] Step 44, distribute the regional average daily weather variables generated by the annual scale weather generator to the L stations in the region;

[0030] Step 45, evaluate the applicability of the multi-station multi-variable weather generator simulation weather variable sequence of the study area, if the spatial and temporal correlation of meteorological elements and the correlation between variables are poor, then use the Empirical Copula post-processing method to improve the spatial and temporal correlation of meteorological elements and the correlation between variables.

[0031] Further, in step 44, the regional average daily weather variables generated by the annual weather generator are disaggregated to the L sites within the region Disaggregating the L site-specific weather variables to the region includes the following steps:

[0032] Step 441, assuming and represent the simulated regional average weather variable vectors for day t-1 and day t, respectively, and both t-1 and t are wet days, find all adjacent day pairs in the window (set window period to 7 days) centered on day t (e.g., if t is January 15th, then the window includes all dates from January 12th to 18th for all years) in the historical observation records extracted by the annual weather generator, if no suitable day pair is found, expand the window period to 30 days;

[0033] Step 442, filter out all adjacent day pairs and with the same wetness status (i.e., both are wet days), assuming there are Q adjacent day pairs, each pair contains the regional average weather variable vectors for the two days, and compute the weighted Euclidean distance between the Q historical regional average weather variable vectors and the simulated vector ;

[0034] Step 443, sort the distances d q in ascending order, set k to compute the weights for the k nearest neighbors using a discrete kernel function:

[0035] Step 444, randomly select a value from the k nearest neighbors based on the weights and record the corresponding historical date;

[0036] Step 445, find the weather variable vector X l for the L sites in the region for the next day of the historical date as the simulated vector for day t;

[0037] Step 446, repeat the above steps for T simulated days.

[0038] Further, in step 442, the weighted Euclidean distance between the Q historical regional average weather variable vectors and the simulated vector is computed as:

[0039] where represents the simulated i-th regional average weather variable for day t-1, represents the regional average weather variable for the first day of the q-th historical adjacent day pair, w represents the weight, and the weight w is set i w represents the weight, and the weight w is set i w represents the weight, and the weight w is set

[0040] Further, in step 45, the Empirical Copula post-processing method is adopted to improve the spatial and temporal correlation of meteorological elements and the correlation between variables, and specifically includes the following steps:

[0041] In step 451, for the precipitation, maximum and minimum temperature of the K stations, the Empirical Copula post-processing method is applied to the observation sample data of the three weather variables in each month (the number of data points in each month = the number of years x the number of days in the 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 the month, and the number of columns is Kx3), considering the influence of seasonality.

[0042] In step 452, according to the reference sample rank matrix, the simulation sample data of the corresponding month is reordered according to the rank, so that the rank matrix of the reordered simulation sample is completely consistent with the observation sample, so as to rebuild the station-to-station, variable-to-variable and time sequence correlation of the simulation sample data.

[0043] In step 453, the processed weather variable simulation data of each month is spliced in time sequence to obtain the Empirical Copula function post-processed simulation data.

[0044] Beneficial effects: Compared with the prior art, the present application has the following significant advantages: a multivariate first-order autoregressive model is used to generate precipitation and temperature sequences, which can effectively simulate the interannual variation characteristics (low-frequency oscillation characteristics) of the precipitation and temperature sequences; the multivariate multi-station weather generator can generate a hydro-meteorological element simulation field with station-to-station, variable-to-variable and time sequence correlation, which can effectively reflect the all-around characteristics of hydro-meteorological processes and improve the runoff simulation effect; by introducing the Empirical Copula post-processing method, the spatial and temporal correlation of the meteorological element simulation field is further improved in the case of poor simulation results of the weather generator, and more reliable input data is provided for the hydrological model. BRIEF DESCRIPTION OF DRAWINGS

[0045] FIG. 1 is a flowchart of a precipitation runoff simulation method based on the coupling of the multistation multivariate weather generator and the GR4J hydrological model.

[0046] Figure 2 is a schematic diagram of a multi-site multi-variable weather generator involved in the present application.

[0047] Figure 3 is a graph of runoff simulation results based on the multi-site multi-variable weather generator and the GR4J hydrological model simulation of the present application.

[0048] Figure 4 is a graph of simulation results of high and low flow in spring and summer-autumn based on the multi-site multi-variable weather generator and the GR4J hydrological model simulation of the present application. DETAILED DESCRIPTION

[0049] A precipitation runoff simulation method based on a multi-site multi-variable weather generator, comprising the following steps:

[0050] Step 1, collecting daily precipitation, maximum and minimum temperature data of sites in the basin, and flow data at the outlet section of the basin;

[0051] Step 2, annual scale meteorological element random simulation: processing daily scale observation data into annual scale observation meteorological variable sequence, generating regional average annual precipitation, maximum and minimum temperature sequence using an annual scale weather generator based on a multi-variable first-order autoregressive model (MAR1): X t = w + AX t-1 + e t ;

[0052] In the formula: X t and X t-1 are [3x1] matrices, respectively representing regional average annual precipitation, annual maximum and minimum temperature (annual average) in the t and t-1 years, and 3 rows respectively represent 3 variables of annual precipitation, maximum and minimum temperature; A and w are [3x3] autocorrelation coefficient matrix and [3x1] intercept matrix, respectively; e t is a [3x3] independent random residual matrix with mean 0 and covariance C; the parameters A, w, C in the MAR1 model are estimated using piecewise least squares fitting method. The MAR1 model can effectively simulate the interannual variation characteristics of the annual precipitation, maximum and minimum temperature sequence under the premise of maintaining the correlation between variables.

[0053] Step 3, giving the interannual variation characteristics of the daily scale simulation sequence: for each year of the regional average annual precipitation, maximum and minimum temperature simulation sequence generated by MAR1, 100 (repeatable sampling) years with similar MAR1 regional average annual precipitation, maximum and minimum temperature simulation values are randomly extracted from the observation sequence according to the probability weight using KNN algorithm. Extract the corresponding regional average daily scale precipitation, maximum and minimum temperature sequence of the 100 years to construct a daily scale multi-site multi-variable weather generator;

[0054] Step 3.1, generating a daily scale multi-site multi-variable weather generator with length T athe simulated regional average annual precipitation, maximum and minimum temperature series;

[0055] Step 3.2, for the simulation year t a , calculate the Euclidean distance between the simulated regional average annual scale weather variable vector and the historical observation value :

[0056] In the formula: represents the simulated regional average annual scale weather variable vector of year t a , and represents the historical observation value of the corresponding year.

[0057] Step 3.3, sort the distance d from small to large, and generally set k n is the sample length; use the discrete kernel function to assign probability weights K to the k nearest years, and the weight size is determined by the distance, the smaller the distance, the easier to be drawn, the formula is as follows:

[0058] Step 3.4, for any simulation year t a , according to the probability weight K, randomly draw 100 (repeatable sampling) years similar to from the k nearest historical observation values , and extract the regional average daily precipitation, maximum and minimum temperature data of the 100 years corresponding to a , to generate daily scale precipitation, maximum and minimum temperature data of simulation year t a as the data basis for constructing daily scale multi-site multi-variable weather generator;

[0059] Step 3.5, considering the randomness of sampling, run the annual scale weather generator for 50 times;

[0060] Step 4, daily scale meteorological element random simulation: use two-state first-order Markov chain and KNN model to construct daily scale weather generator to simulate daily weather sequence composed of R weather variables of L stations in a certain area;

[0061] where, represents the i-th variable corresponding to the l-th station and time t, and T represents the sample length of the simulation sequence.

[0062] Step 4.1, in order to start the algorithm and generate the initial value of all weather variables, randomly draw the meteorological data of any day (for example, January 1) corresponding to the simulation starting month from the simulation data generated by the annual scale weather generator, and the dry and wet state of the data corresponds to the first precipitation state simulated by the Markov chain.

[0063] Step 4.2, the time distribution of the regional average daily precipitation dry-wet sequence of L stations is simulated by using a first-order Markov chain, and the occurrence of precipitation depends on whether the previous day has precipitation. It is assumed that daily precipitation greater than or equal to 0.1 mm is a wet day (S t = 1 represents the occurrence of precipitation), and less than 0.1 mm is a dry day (S t = 0 represents no precipitation), considering the seasonal variation characteristics of the precipitation process, the calculation of the Markov chain parameters and the simulation of the daily precipitation dry-wet state are carried out monthly;

[0064] Step 4.3, the precipitation transition probability p ab from the previous day state a to the current day state b is estimated by using the maximum likelihood method, so that the four transition probabilities (p 00 , p 01 , p 10 , p 11 ) of the two-state Markov chain can be calculated, where p 00 is the probability of no precipitation the previous day and no precipitation the current day, p 01 is the probability of no precipitation the previous day and precipitation the current day, and so on;

[0065] Step 4.4, the regional average daily weather variables generated by the annual scale weather generator are disaggregated to the L stations within the region;

[0066] Step 4.4.1, it is assumed that and represent the simulated regional average weather variable vectors of t-1 day and t day, respectively, and both t-1 day and t day are wet days. In the historical observation records extracted by the annual scale weather generator, find all adjacent day pairs in the window centered on t day (set the window period to 7 days), if no suitable day pair is found, expand the window period to 30 days;

[0067] Step 4.4.2, filter out the adjacent day pairs (i.e. both wet days) with the same dry-wet state as and . Assuming there are Q adjacent day pairs, each pair contains the regional average weather variable vectors of the previous and subsequent two days, and calculate the weighted Euclidean distance between the Q historical regional average weather variable vectors and the simulated vector :

[0068] In the formula: represents the i-th regional average weather variable corresponding to the simulated t-1 day pair, the regional average weather variable of the first day of the qth historical adjacent day, the climatological average value of the ith regional average weather variable in the month corresponding to day t-1 (the average value of all years of data in this month), w i represents the weight. In the present application, the weight w i is the inverse of the climatological standard deviation of the ith regional average weather variable in the month corresponding to day t-1, so that each variable in the weighted Euclidean distance is standardized, avoiding the influence of different variables on the calculation results of the Euclidean distance due to the difference in dimension and numerical magnitude;

[0069] Step 4.4.3, arrange the distances d q in ascending order, and k is generally set to using a discrete kernel function to calculate the weight of the k nearest neighbors;

[0070] Step 4.4.4, randomly select a value from the k nearest neighbors based on the weight and record the corresponding historical date;

[0071] Step 4.4.5, find the weather variable vector X l as the simulation vector of day t;

[0072] Step 4.4.6, repeat the above steps for T simulation days;

[0073] Step 4.5, evaluate the applicability of the multi-site and multi-variable weather generator simulation weather variable sequence in the study area. If the spatial and temporal correlation of meteorological elements and the correlation between variables are poor, the Empirical Copula post-processing method is used to improve the spatial and temporal correlation of meteorological elements and the correlation between variables;

[0074] Step 4.5.1, for the precipitation, maximum and minimum temperature of K stations, considering the influence of seasonality, the Empirical Copula post-processing method is applied to the observation sample data of 3 weather variables of each month (the number of data points in each month = the number of years x the number of days in the month) to calculate the rank matrix as the reference sample rank matrix (the number of rows is the number of data points in the month, and the number of columns is Kx3);

[0075] Step 4.5.2, according to the reference sample rank matrix, reorder the simulation sample data of the corresponding month according to the rank, so that the rank matrix of the reordered simulation sample is completely consistent with the observation sample, so as to rebuild the inter-site, inter-variable and time sequence correlation of the simulation sample data;

[0076] Step 4.5.3, splice the processed weather variable simulation data of each day of each month in chronological order to obtain the simulation data after Empirical Copula function post-processing;

[0077] Step 5, pre-processing of GR4J hydrological model input data: pre-processing of meteorological element data simulated by the above weather generator (surface mean precipitation calculation, evapotranspiration calculation, etc.) as hydrological model data input;

[0078] Step 6, select error criteria as objective function, then calibrate the model parameters of GR4J hydrological model.

[0079] Step 7, use the calibrated GR4J model to simulate the daily runoff of the basin.

[0080] Taking the Ticino basin in Switzerland as an example, the following processes are realized based on the R language platform, and the method steps are described in detail in combination with the drawings.

[0081] A precipitation runoff simulation method based on a multi-site multi-variable weather generator is shown in FIG. 1, which includes the following steps:

[0082] Step 1, collect data of 35 meteorological stations in the Ticino basin from January 1, 1981 to December 31, 2020 as basic meteorological element data, and pre-process the data to calculate the regional average meteorological variable sequence;

[0083] The CAMELS-CH data set collected in this example contains meteorological data such as daily precipitation, maximum temperature, minimum temperature, and average temperature of meteorological stations in the basin and daily flow data of each hydrological station, and the coordinates of each station. The data set comes from the Central European Switzerland hydro-meteorological large sample data set, and the data source is: https: / / zenodo.org / records / 10354485.

[0084] Step 2, annual scale meteorological element random simulation: run the annual scale weather generator based on the 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;

[0085] The multivariate first-order autoregressive model is: X t = w + AX t-1 + e t (1)

[0086] In the formula: X t and X t-1is a [3x1] matrix, representing the regional average annual precipitation, annual maximum and minimum temperature (annual mean) in the t and t-1 year, respectively, and 3 rows represent 3 variables of annual precipitation, maximum and minimum temperature, respectively; A and w are [3x3] autocorrelation coefficient matrix and [3x1] intercept term matrix, respectively. t is a [3x3] independent random residual matrix with mean 0 and covariance C; the parameters A, w, C in the MAR1 model are estimated by piecewise least squares fitting method.

[0087] Step 3, give the daily scale simulation sequence interannual variability characteristics: for each year of the regional average annual precipitation, maximum and minimum temperature simulation sequence generated by MAR1, use KNN algorithm to randomly extract 100 years similar to the MAR1 regional average annual precipitation, maximum and minimum temperature simulation value from the observation sequence according to the probability weight, extract the regional average daily scale precipitation, maximum and minimum temperature sequence corresponding to the 100 years, to construct the daily scale multi-site multi-variable weather generator;

[0088] Step 3.1, for the 40-year length of annual scale meteorological element simulation sequence, apply KNN algorithm to calculate the Euclidean distance between each year simulation of regional average annual scale weather variable vector and the historical observation value .

[0089] The Euclidean distance is:

[0090] In the formula: indicates the simulation year t a The regional average annual scale weather variable vector, indicates the historical observation value of the corresponding year.

[0091] Step 3.2, sort the distance d from small to large, and assign probability weight K to the k nearest neighbors with discrete kernel function, the weight size is determined by the distance, the smaller the distance, the easier to be drawn;

[0092] Step 3.3, based on the probability weight K, randomly extract 100 observation years similar to the simulation year (repeat sampling) from the observation data;

[0093] The probability weight is:

[0094] In the formula, d is the Euclidean distance, k is set to n is the sample length;

[0095] Step 3.4, extract the regional average daily scale precipitation, maximum and minimum temperature sequence corresponding to these observation years, to construct the daily scale multi-site multi-variable random weather generator model;

[0096] Step 3.5, considering the randomness of sampling, the annual-scale weather generator is run 50 times;

[0097] Step 4, daily-scale weather variables stochastic simulation: daily weather series composed of 3 weather variables at 35 stations in Ticino basin are simulated by daily-scale weather generator using two-state first-order Markov chain and KNN model; in this embodiment, the precipitation threshold is set to 0.1 mm; if the daily precipitation is greater than the precipitation threshold, it is a rainy day, otherwise, it is a non-rainy day, and the daily dry-wet state is assigned, the precipitation transition probability is estimated by maximum likelihood method and the two-state dry-wet transition probability matrix is calculated to construct the two-state first-order Markov chain;

[0098] Step 4.1, randomly select the meteorological data of any day in the simulated starting month (for example, January 1), and ensure that the dry-wet state corresponding to the data is consistent with the first precipitation state simulated by the Markov chain;

[0099] Step 4.2, the time distribution of the regional average daily precipitation dry-wet sequence of 35 stations is simulated by using the first-order Markov chain, and whether the precipitation occurs depends on whether the precipitation occurs the previous day. In this embodiment, the precipitation threshold is set to 0.1 mm; if the daily precipitation is greater than the precipitation threshold, it is a rainy day, otherwise, it is a non-rainy day, and the daily dry-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-wet state are carried out monthly;

[0100] Step 4.3, the precipitation transition probability p ab from the state a of the previous day to the state b of the current day is estimated by maximum likelihood method 00 , p 01 , p 10 , p 11 , where p 00 is the probability of no precipitation the previous day and no precipitation the current day, p 01 is the probability of no precipitation the previous day and precipitation the current day, and so on;

[0101] Step 4.4, the regional average daily weather variables generated by the annual-scale weather generator are disaggregated to 35 stations in Ticino basin;

[0102] Step 4.4.1, find all adjacent day pairs with the same dry-wet state in the window (set the window period to 7 days) centered at day t in the historical observation records extracted by the annual-scale weather generator, if no suitable day pair is found, expand the window period to 30 days;

[0103] ​Step 4.4.2, screen out the adjacent day pairs with the same state in the window period and extract the corresponding regional average weather variable vector And

[0104] Step 4.4.3, calculate the weighted Euclidean distance between the historical regional average weather variable vector of all adjacent day pairs and the simulation vector: the Euclidean distance is:

[0105] Step 4.4.4, sort the distance d q in ascending order, and set k to Weighted calculation of the k nearest distances using discrete kernel function; the weighted calculation formula of the discrete kernel function is:

[0106] Step 4.4.5, randomly extract a value from the k nearest distances according to the probability weight and record the corresponding historical date;

[0107] Step 4.4.6, extract the weather variable vector X l of the next day of the L stations in the region on this historical date as the simulation vector of the tthday, and repeat the above steps for T simulation days to generate a daily scale meteorological element simulation sequence based on the weather generator;

[0108] Step 4.5, after the applicability evaluation of the multi-site multi-variable weather generator simulation weather variable sequence of the basin, it is found that the spatial and temporal correlation and variable correlation of the simulated meteorological elements are good, so there is no need to take the Empirical Copula post-processing method to improve the spatial and temporal correlation and variable correlation of the meteorological elements;

[0109] 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. Divide the 5 years from July 15, 2013 to July 15, 2017 into the calibration period, and the remaining 2 years of data as the verification period. Use the observed rainfall, flow, temperature and other data in the calibration period to calibrate the model parameters;

[0110] Step 5.1, calculate the observed meteorological sequence (precipitation, temperature) basin average value;

[0111] Step 5.2, calculate the Ticino basin daily surface average potential evapotranspiration using the Oudin formula combined with the basin surface average temperature;

[0112] The Oudin formula is: if T a +5>0, otherwise PE=0 (6)

[0113] where PE is the potential evapotranspiration rate, R e is the extraterrestrial radiation, λ is the latent heat flux, and p is the density of water, T a is the daily average air temperature;

[0114] Step 5.3, combine the flow data of the outlet section of the watershed with the calculated average meteorological data of the watershed surface as the data input of the GR4J model;

[0115] Step 5.4, divide July 15, 2013 to July 15, 2017 as the parameter calibration period of the GR4J model,

[0116] Step 5.5, set the model warm-up period to be one year (≥1 year), i.e., from July 15, 2013 to July 15, 2014;

[0117] Step 5.6, select the Nash efficiency coefficient (Nash-Sutcliffe efficiency coefficient, NSE) as the parameter calibration error standard;

[0118] The Nash efficiency coefficient NSE is:

[0119] where Q o is the observed value, Q m is the simulated value, is the average value of the observed value, and t is the time period;

[0120] Step 5.7, after selecting the error standard as the objective function, the model parameters are calibrated by combining the Irstea algorithm proposed by C. Miche;

[0121] Step 6, the observed meteorological element sequence in the verification period from July 16, 2017 to July 15, 2019 is used to drive the GR4J model to obtain the daily runoff simulation sequence;

[0122] Step 7, the GR4J model is driven by the simulated meteorological element sequence based on the weather generator in the verification period to obtain the runoff simulation sequence based on the weather generator-GR4J model, and the runoff simulation sequence obtained in step 6 is compared, and the results are shown in Figures 3 and 4. The precipitation runoff simulation method based on the multi-site multi-variable weather generator proposed in the application can better simulate the runoff change trend of the Ticino watershed in Switzerland, and can also provide the uncertainty interval of runoff simulation.

Claims

1. A method for simulating precipitation runoff based on a multi-site multivariate weather generator, characterized by, Comprising the following steps: Step 1, collect daily precipitation, maximum and minimum temperature of stations in the basin and runoff data of outlet section in the basin; Step 2, annual scale weather generator: the daily scale observation data is processed into annual scale observation weather variable sequence, and a weather generator based on a multivariate first-order autoregressive model MAR1 is used to generate regional average annual precipitation, maximum and minimum temperature sequence; Step 3, giving annual variation characteristics of daily scale simulation sequence: for each year of the regional average annual precipitation, maximum and minimum temperature simulation sequence generated by MAR1, a KNN algorithm is used to randomly extract several years similar to the regional average annual precipitation, maximum and minimum temperature simulation value from the observation sequence according to the probability weight, and the regional average daily scale precipitation, maximum and minimum temperature sequence corresponding to the year is extracted to construct a daily scale multi-station multi-variable weather generator; Step 4, random simulation of daily scale meteorological elements: a daily scale weather generator is constructed by using a two-state first-order Markov chain and a KNN model to simulate daily weather sequence composed of R weather variables of L stations in a region; Step 5, pre-processing of GR4J hydrological model input data: the meteorological element data simulated by the above weather generator is pre-processed as hydrological model data input; Step 6, after selecting error standard as objective function, the GR4J hydrological model is calibrated; Step 7, the calibrated GR4J model is used to simulate daily runoff of the basin.

2. The multi-site, multi-variable weather generator based precipitation runoff simulation method of claim 1, wherein, 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 [3x1] matrix, representing the regional average annual precipitation, annual maximum and minimum temperature (annual mean) in the t and t-1 years, respectively, and 3 rows represent 3 variables of annual precipitation, maximum and minimum temperature, respectively; A and w are a [3x3] autocorrelation coefficient matrix and a [3x1] intercept term matrix, respectively, e t is a [3x3] independent random residual matrix with mean 0 and covariance C; the parameters A, w, and C in the MAR1 model are estimated by piecewise least squares fitting method, and the MAR1 model can effectively simulate the interannual variability characteristics of the annual precipitation, maximum and minimum temperature series while maintaining the correlation between variables.

3. The multi-site, multi-variable weather generator based precipitation runoff simulation method of claim 1, wherein, In step 3, the daily scale multi-station multi-variable weather generator comprises the following steps: Step 31, generate a sequence of regional average annual precipitation, maximum and minimum temperature simulations of length T using the MAR1 model a Step 31, generate a sequence of regional average annual precipitation, maximum and minimum temperature simulations of length T using the MAR1 model Step 32, for simulation year t a The vector of simulated regional average annual weather variables from step 2 with historical observations Euclidean distance between: In the formulae: representing the simulated year t a a region-averaged annual-scale weather variable vector, Indicates the historical observation value of the corresponding year; Step 33, sort the distances d from small to large, set k to n is the sample length; k nearest years are assigned probability weights K using a discrete kernel function, with the size of the weights determined by distance, with smaller distances more likely to be drawn, as follows: Step 34, for any simulated year t a , the probability weight K from the k nearest historical observations The 100 samples were randomly selected from the 1000 samples In the same year, the average daily precipitation, maximum and minimum temperature data of the region corresponding to the 100 years are extracted to generate the simulation year t a The daily scale precipitation, maximum and minimum temperature data of the simulation year t are generated as the data basis for constructing the daily scale multi-site multi-variable weather generator. Step 35, considering the randomness of sampling, the annual scale weather generator is run 50 times.

4. The multi-site, multi-variable weather generator based precipitation runoff simulation method of claim 1, wherein, In Step 4, the daily weather sequence was: wherein Indicates 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 multi-site, multi-variable weather generator based precipitation runoff simulation method of claim 1, wherein, In step 4, the daily scale weather generator is constructed by using a two-state first-order Markov chain and a KNN model to simulate daily weather sequence composed of R weather variables of L stations in a region, which comprises the following steps: Step 41, randomly extract meteorological data of any day corresponding to the simulation starting month from the simulation data generated by the annual scale weather generator, and the dry and wet state of the data is consistent with the first precipitation state simulated by the Markov chain; Step 42, simulate the time distribution of the regional average daily precipitation dry-wet sequence of L sites by using the first-order Markov chain, whether the precipitation occurs or not depends on whether the previous day has precipitation, assuming that the daily precipitation greater than or equal to 0.1 mm is a wet day, S t = 1 represents that the precipitation occurs, and less than 0.1 mm is a dry day, S t = 0 represents that the precipitation does not occur, considering the seasonal variation characteristics of the precipitation process, the calculation of the Markov chain parameters and the simulation of the daily precipitation dry-wet state are performed monthly; Step 43, estimate the precipitation transition probabilities p from the previous day's state a to the current day's state b using maximum likelihood ab , p 00 , p 01 , p 10 , p 11 ), where p 00 is the probability of no precipitation the previous day and no precipitation the current day, p 01 is the probability of no precipitation the previous day and precipitation the current day, and so on. Step 44, regional average daily weather variables generated by the annual-scale weather generator Solve the set to the L stations in the region; Step 45, the applicability of the multi-station multi-variable weather generator simulation weather variable sequence of the study area is evaluated, if the spatio-temporal correlation of meteorological elements and the correlation between variables are poor, the Empirical Copula post-processing method is adopted to improve the spatio-temporal correlation of meteorological elements and the correlation between variables.

6. The multi-site, multi-variable weather generator based precipitation runoff simulation method of claim 5, wherein, In step 44, the regional average daily weather variables generated by the annual weather generator are disaggregated to L sites within the region Disaggregating the L regional average daily weather variables to the L sites within the region includes the following steps: Step 441, assuming and Respectively represent the regional average weather variable vectors of the simulated t-1 day and t day, and t-1 and t day are both wet days, find all adjacent day pairs in the window with t day as the center in the historical observation record extracted by the annual scale weather generator, set the window period to 7 days, if no suitable day pair is searched, expand the window period to 30 days; Step 442, screening out and and Adjacent day pairs with the same wetness state, assuming there are Q adjacent day pairs, each of which contains the area-averaged weather variable vector of the two days, Xk = (Xk, Xk+1), k = 1, 2,..., Q, and computing Q historical regional average weather variable vectors and simulated vectors The weighted Euclidean distance between them; Step 443, distance d q arranged in ascending order, k is set to The k-nearest neighbor distances are weighted using a discrete kernel function: Step 444, a value is randomly extracted from the k nearest distances based on the weight and the corresponding historical date is recorded; Step 445, 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 of the tth day; Step 446, repeat the above steps for T simulation days.

7. The multi-site, multi-variable weather generator based precipitation runoff simulation method of claim 6, wherein, In step 442, the average weather variable vectors of Q historical regions and the simulated vectors are calculated. Weighted Euclidean distance between: In the formulae: representing the i-th regional average weather variable corresponding to day t-1 of the simulation, a representative historical average weather variable for the first day of the qth historical adjacent day pair, w represents the weight, and the weight w is set i w represents the weight, and the weight w is set i The inverse of the climate standard deviation of the i-th regional average weather variable in the month corresponding to t-1 day is used to normalize each variable in the weighted Euclidean distance, so as to avoid the influence of different variables on the calculation result of the Euclidean distance due to the difference in the dimension and the magnitude of the numerical value.

8. The multi-site, multi-variable weather generator based precipitation runoff simulation method of claim 5, wherein, In step 45, the Empirical Copula post-processing method is adopted to improve the temporal and spatial correlation of meteorological elements and the correlation between variables, which specifically includes the following steps: Step 451, for the precipitation, maximum and minimum temperature of K stations, considering the influence of seasonality, the rank matrix of the three weather variables observation sample data of each month is calculated by applying the Empirical Copula post-processing method, as the reference sample rank matrix, the number of rows of the matrix is the number of data points in the month, and the number of columns is K*3; Step 452, according to the reference sample rank matrix, the simulation sample data of the corresponding month is reordered according to the rank, so that the rank matrix of the sorted simulation sample is completely consistent with the observation sample, so as to rebuild the station-to-station, variable-to-variable and time sequence correlation of the simulation sample data; Step 453, splice the processed simulation data of each weather variable of each month in time sequence to obtain the simulation data processed by the Empirical Copula function.

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