CN112801342A - Adaptive runoff forecasting method based on rainfall runoff similarity - Google Patents
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Abstract
The invention discloses a self-adaptive runoff forecasting method based on rainfall runoff similarity, which adopts a data mining technology to search a similar process in a historical rainfall runoff producing process and forecast the most probable process line of later runoff; the method comprises the following steps: s1, constructing historical rainfall and runoff samples; s2, identifying key characteristic indexes of rainfall and runoff; s3, dynamically evaluating rainfall and runoff similarity based on data mining; s4, predicting runoff rolling based on rainfall flood similarity; and S5, switching forecast modes in an adaptive mode. The method can overcome the problem of difficult parameter calibration of the physically-driven runoff forecasting model, and also can break through the problem of poor interpretability of the forecasting result of the conventional data-driven runoff forecasting model, and break through the bottlenecks of low runoff forecasting precision and short forecasting period to a certain extent, thereby having important significance in improving the fine management and lean dispatching level of the watershed reservoir group.
Description
Technical Field
The invention relates to a runoff forecasting technology, in particular to a self-adaptive runoff forecasting method based on rainfall runoff similarity.
Background
Runoff forecasting is a key basis for basin management decisions such as flood control and disaster reduction, water resource guarantee, power production and the like, and is also a leading-edge hotspot in research of the field of water resources under global change. The runoff forecasting models widely used at present are divided into a physical driving model and a data driving model, wherein the physical driving model emphasizes process deduction, the data driving model emphasizes result approximation, and the two models have essential difference on the basic principle.
The runoff forecasting model driven by physics uses a series of mathematical physical equations containing parameters to describe the complete process from runoff production, confluence and riverway evolution from the physical cause of runoff, the related research contents comprise complex systems of atmospheric weather, riverways, soil, underground water and the like, and the equation parameters have strict physical significance. To reduce the modeling difficulty, common physical driving models are regional and seasonal, for example: mishra et al establishes a model for water runoff to forecast the dry season of the Qingnile river and obtains good results. The plum et al apply the SWAT model to runoff simulation of the upstream of the river, and have good simulation effect under the drought, humid and semi-arid semi-humid climates. There are also studies of optimizing the parameters of the model using intelligent algorithms, such as: the particle swarm algorithm is applied to optimize the parameters of the Xinanjiang model, and the like, and the results show that the particle swarm algorithm obviously improves the calculation efficiency and the prediction precision compared with the simplex mixed acceleration algorithm, the simplex polygonal evolutionary algorithm and the like.
In recent years, with the rapid development of artificial intelligence and big data technology, a data-driven runoff forecasting model is gradually mature, and the model is a black box model aiming at establishing an optimal mathematical relationship between input data and output data, so that the model does not need to consider the physical cause of runoff, but needs long-term and massive watershed hydrological survey station data as support. For example: sajikuamar et al uses a multi-level forward network and regression network to forecast the monthly runoff. Avinash Agarwal, r.d.singh established a multi-layer BP network to simulate the rainfall-runoff process of the indian Narmada river. In fact, the time and magnitude of flood in a specific region have the characteristic of periodic variation, and the historical flood contains the information of the change of the local weather system and the underlying surface to a certain extent, so that when the historical flood series has a long time and a large number of times, a data mining technology is adopted to find out similar flood, and a processing scheme of the future flood is constructed by referring to the past prediction future reference, namely, the relevant characteristics of the future flood are predicted according to the information provided by the historical similar flood, or referring to the processing scheme of the historical similar flood, which has important significance for the flood control decision of the future flood.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a self-adaptive runoff forecasting method based on rainfall runoff similarity, which is characterized in that real-time rainfall forecasting information is accessed, runoff in a future week is forecast in a rolling mode, early rainfall runoff characteristics are identified on the basis, forecasting modes are automatically switched, and the function of self-adapting to different forecasting scenes is realized.
The technical scheme is as follows: the invention discloses a self-adaptive runoff forecasting method based on rainfall runoff similarity, which comprises the following steps of:
s1, constructing historical rainfall and runoff samples: collecting the flow data of the key section of the drainage basin where the forecast object is located, the rainfall site data and the grid point data, and performing time dimension reduction and space dimension reduction on the collected original data to obtain historical rainfall and runoff samples;
s2, identifying key characteristic indexes of rainfall and runoff: analyzing rainfall and runoff characteristics of a basin where the forecast section is located and establishing the forecast section and quantitative characteristic indexes of the rainfall and the runoff of the basin based on historical rainfall and runoff samples; comprehensively determining key characteristic indexes of rainfall and runoff from two aspects of physical cause and statistical analysis of the runoff;
s3, rainfall and runoff similarity dynamic evaluation based on data mining: establishing a key characteristic index sample set of historically measured rainfall, runoff and forecast rainfall by adopting a sliding window sampling mode, quantitatively representing rainfall similarity and runoff similarity of a current sample and a historical sample by methods such as an Euclidean distance method, and providing a rainfall-runoff comprehensive similarity index considering rainfall influence weight by considering rainfall and runoff numerical magnitude difference; searching the most similar multi-field historical rainfall runoff actual measurement process, and taking the most similar multi-field historical rainfall runoff actual measurement process as a basis for obtaining a final forecast result;
s4, runoff rolling prediction based on rainfall flood similarity: constructing a multi-factor nearest neighbor sampling regression model, predicting runoff of a flow area by using rainfall flood similarity, combining modern heuristic algorithms such as a genetic algorithm and the like to optimize a forecasting effect, and optimizing parameters such as nearest neighbor number, key feature vector dimension, rainfall influence weight and the like related to the model; in order to prolong the forecast period of the runoff forecast, rolling and accessing future rainfall forecast information, providing a plurality of rolling forecast modes to carry out rolling forecast on the runoff, wherein the forecast result comprises a most possible process line of the flow;
s5, forecasting mode self-adaptive switching: aiming at the production convergence characteristics of the basin at different stages of water rising and water falling, a rainfall and runoff input mode which is self-adaptively switched according to the real-time water and rain conditions is established, and the runoff forecasting precision is further improved.
Further, in step S1, performing dimensionality reduction on the data from two dimensions of space and time specifically includes:
on a time scale, converting collected rainfall and runoff data into a forecast demand time period;
on a spatial scale, the drainage basin is divided into a plurality of areas by analyzing natural geographic features and rainfall spatial distribution rules of the drainage basin, rainfall site data in the areas are converted into subarea rainfall data, and rainfall monitoring data of a plurality of sites are subjected to dimensionality reduction; firstly, dividing a research area into a plurality of sub-areas according to the difference of convergence modes of different areas, wherein the rainfall of the sub-areas is calculated by the weighted average of the rainfall of the included stations, and the calculation formula is as follows:
wherein, PiIs the areal rainfall of subregion i; phiiIs the rainfall site set contained in the sub-area i; p is a radical ofjIs the rainfall site index contained in the sub-area; p is a radical ofkThe number of rainfall stations contained in the sub-area i;
is the station rainfall of the ith station of the subregion;
is that
The station rainfall is converted into the weight of the surface rainfall.
Further, in step S2, based on the historical rainfall and runoff sample data, analyzing the rainfall and runoff characteristics of the basin where the forecast section is located, and establishing the forecast section and quantitative characteristic indexes of the rainfall and runoff in the basin above the forecast section; according to physical cause and characteristic indexes of runoff of the drainage basin, comprehensively utilizing cause analysis, correlation analysis, regression analysis and multi-factor comprehensive analysis methods to identify forecast key characteristic indexes of different spatial positions of the drainage basin and at different forecast time scales and different forecast periods; and comprehensively utilizing physical cause analysis and mathematical statistics methods to determine the early-stage influence time lag of the key characteristic indexes, specifically comprising the following steps:
s21, comprehensively analyzing the rainfall to forecast section production convergence time of each area from rainfall and runoff physical causes, preliminarily determining the response time of the rainfall and runoff, and taking the response time as an important basis for determining the early-stage influence time delay of key indexes;
s22, analyzing the correlations of rainfall and runoff with different early-stage influence time lags and runoff in a prediction period by using a mathematical statistical method, and selecting early-stage influence time lags with larger correlations;
s23, setting and considering rainfall and runoff combinations of different early-stage influence time lags as key indexes for identifying similar runoff processes based on the preliminarily determined early-stage influence time lags, forecasting historical runoff processes of river basin sections by adopting a rainfall runoff similarity forecasting model, and finally determining the optimal early-stage influence time lags according to forecasting result precision evaluation.
In addition, different key characteristic indexes of rainfall and runoff are identified according to different forecasting scenes, a general runoff process can be divided into a water rising stage and a water returning stage, proper early-stage influence time lags are respectively identified, a runoff forecasting mode suitable for the water rising rule and the water returning rule is established, and the forecasting mode is automatically switched according to early-stage runoff and rainfall forecasting conditions.
Further, in step S3, a sliding window sampling manner is adopted to construct a key feature index sample set to enrich the number of historical rainfall and runoff samples; quantitatively representing the similarity of the current rainfall and runoff sample and the historical rainfall and runoff sample by adopting an Euclidean distance method; taking the magnitude difference of rainfall and runoff value into consideration, and providing a rainfall-runoff comprehensive similarity index of rainfall influence weight; the similarity of the real-time rainfall runoff sample and the historical rainfall runoff sample is described as a key index.
Wherein, the rainfall similarity index is:
wherein, PjRepresenting rainfall characteristic value vectors of historical rainfall and runoff samples, wherein the dimensionality of the rainfall characteristic value vectors is equal to the early-stage influence delay time of the considered rainfall, j represents the serial numbers of the historical rainfall and the runoff samples, j is more than or equal to 1 and less than or equal to N, and N represents the total number of the historical rainfall and the runoff samples; p*Representing the rainfall eigenvalue vector of the current rainfall and runoff sample, the dimension and P thereofjThe same; dpjIndicating a sequence number jThe rainfall similarity indexes of the historical rainfall and runoff samples and the current rainfall and runoff samples;
the runoff similarity index is as follows:
wherein Q isjRepresenting runoff characteristic value vectors of historical rainfall and runoff samples, wherein the dimensionality of the runoff characteristic value vectors is equal to the earlier-stage influence dead time of the considered runoff, j represents the serial numbers of the historical rainfall and the runoff samples, j is more than or equal to 1 and less than or equal to N, and N represents the total number of the historical rainfall and the runoff samples; q*Representing the current rainfall, runoff eigenvalue vector of the runoff sample, its dimension and QjThe same; dqjRepresenting the runoff similarity indexes of the historical rainfall and runoff samples with the sequence number j and the current rainfall and runoff samples;
index of rainfall-runoff comprehensive similarity, i.e. rainfall-runoff comprehensive Euclidean distance djThe calculation formula of (2) is as follows:
dj＝wpdpj+dqj；
wherein, wpIs the rainfall impact weight.
Further, in step S4, a multi-factor nearest neighbor sampling regression model is constructed, rainfall runoff is predicted by using rainfall flood similarity, and a modern heuristic algorithm is combined to optimize forecasting effect as a target, and nearest neighbor number, key feature vector dimension and rainfall influence weight parameter related to the model are optimized;
calculating the similarity degree of the current rainfall and runoff sample and each historical rainfall and runoff sample based on the determined rainfall-runoff comprehensive similarity index, sorting and selecting the similarity samples based on the similarity index, and calculating the weight of each similarity sample in future runoff forecast to be;
wherein k is the number of similarity samples in the historical rainfall and runoff samples, wiI is more than or equal to 1 and less than or equal to k and is the weight of the ith similarity sample;
after the similarity samples and their weights are determined, the runoff forecasting result is represented by the following formula:
wherein,
forecast flow, Q, representing time period tt-1Represents the measured flow, Δ q, over a period of t-1*Representing the relative value of the flow variation according to the similarity forecast,
a prediction value representing the ith similar sample;
a multi-factor nearest neighbor sampling regression model (NNBR) is adopted to forecast runoff similarity, and parameters related to the model mainly comprise: nearest neighbor sampling number, dimension of characteristic vector, rainfall influence weight and the like. The nearest neighbor sampling number refers to the number of samples searched and sampled by the forecasting model in the historical process; the feature vector dimension is closely related to the influence of the key feature indexes on the runoff in time delay; the rainfall influence weight is used for balancing rainfall and runoff magnitude difference.
Selecting a Nash coefficient NS and an average relative error MARE as evaluation indexes based on hydrologic information forecasting specifications, establishing a forecasting result precision evaluation index system, and comprehensively evaluating forecasting effects of different forecasting periods; the method comprises the steps of (1) independently modeling and parameter rating each key characteristic index combination scheme by taking the optimal forecasting effect as a target and combining modern heuristic optimization algorithms such as a genetic algorithm and the like; the objective function with the maximum objective for the nash coefficient NS is:
the objective function targeting the minimum of the average relative error MARE is:
wherein n represents the length of the training period, n time periods,
showing the measured value of the runoff in the ith time period,
a runoff forecast value representing an ith time period,
represents the average of measured values of runoff over the training period.
Further, in step S4, in order to extend the forecast period, the present invention accesses rainfall forecast information, and proposes three rolling forecast methods to realize rolling forecast from time period to time period within the forecast period; the three rolling forecasting methods are as follows:
s41, not considering rainfall forecast and runoff forecast;
the rainfall and runoff similarity process is directly searched according to the information of the rainfall and runoff which are actually measured and occur, and the rainfall forecast is not considered in the mode, so that the rolling method is adopted when the length of the rainfall forecast is insufficient or the precision is poor; predicting the runoff process in the period of t-t + m as follows:
wherein,
indicating that a measured early rainfall event has occurred,
represents the pre-stage runoff process, Q ', which has occurred and is actually measured't，Q′t+1，…，Q′t+mRespectively representing runoff forecasting results of each time interval in a forecast period, n1Represents the length of the early rainfall lag, n2Representing the length of the runoff stagnation period in the early stage, and m represents the length of the forecast period;
s42, rolling and updating rainfall similarity by considering rainfall forecast information;
continuously adding predicted flow information as input rolling updating runoff similarity, and continuously forecasting runoff in the next time period; the rolling method is completely accessed to forecast rainfall, and the forecast result of the previous time period can influence the forecast result of the next time period; therefore, when the rainfall forecast length is enough and the precision is high, the rolling mode is adopted; predicting the runoff process in the period of t-t + m as follows:
forecasting runoff Q 'in t period'tIn accordance with the above-described concept of S41, rainfall information is inputted
And runoff information
However, forecast runoff Q 'of t +1 period't+1In time, a runoff forecast result Q 'of a period t needs to be obtained'tAnd forecast rainfall P 'at time period t'tAdding into the input of the model; and then the forecast rainfall P 'in the period of t + 1't+1And forecast runoff Q't+1Inputting a model, and forecasting runoff Q 'of the next period t + 2't+2(ii) a By analogy, the forecast of the next time period updates the early rainfall and runoff information at the same time, and the day-by-day rolling forecast in the forecast period is realized;
s43, rolling and updating rainfall similarity by considering rainfall forecast information, but not updating runoff similarity;
the forecasting model considers the updating of rainfall forecasting information, but only updates the rainfall similarity in a rolling manner considering the error of the forecasting runoff in the previous period, and the rolling manner has the characteristics of the two rolling manners of S41 and S42; predicting the runoff process in the period of t-t + m as follows:
forecasting runoff Q 'in t period'tThe method is the same as the method of S41 above, but for runoff Q 'at forecast t +1 period't+1In time, forecast rainfall P 'of period t'tAnd inputting the model, and inputting the flow unchanged, and so on, updating only the rainfall similarity sample and not updating the flow similarity sample in the runoff forecast of the next time period.
Further, in step S5, a forecasting pattern capable of adaptively switching according to the early hydrologic conditions is established for the difference of the flow converging mechanism of the basin where the forecasting object is located in different runoff development stages such as water rising and water falling. For example, during the flood phase, the soil can be saturated earlier by the early accumulation of rainfall, and during the subsequent development, the same magnitude of rainfall will result in a more significant runoff rising process. Considering the difference of influence time delay of early rainfall, a short rainfall time delay mode and a long rainfall time delay mode are provided, the short rainfall time delay mode is mainly suitable for a period with rare rainfall and small rainfall, and the autocorrelation of runoff in the period is high. The long-rainfall time-lag mode is more suitable for the periods with frequent rainfall and large rainfall, in particular to the flood stage of the flood season of the basin. And providing switching conditions among different forecasting modes according to comprehensive factors such as early runoff, early rainfall, forecast rainfall and the like, and automatically switching the forecasting modes to the corresponding forecasting modes when the switching conditions are met.
Has the advantages that: compared with the prior art, the invention has the following advantages:
(1) the problem of difficulty in parameter calibration of the physically-driven runoff forecasting model is solved. The physically-driven runoff forecasting model starts from the physical cause of flood, forecasting accuracy depends on the value of model parameters to a great extent, but when the natural geographical environment of a drainage basin or the production convergence condition is complex, the problem of difficult calibration of the model parameters is faced. The number of parameters involved in the similarity forecasting model is far less than that of the physical driving runoff forecasting model, and the parameter calibration is simpler;
(2) the problem of poor interpretability of the forecast result of the conventional data-driven runoff forecasting model is solved. Conventional data-driven runoff forecasting models, such as artificial neural networks, support vector machines and the like, are black box methods aiming at establishing an optimal mathematical relationship of input and output data, and cannot explain physical causes of rainfall and runoff. The forecasting results of the similarity forecasting model can be backtracked to the historical runoff process which really occurs through the similarity samples, so that the model can clearly explain each forecasting result. In addition, the forecasting result of the similarity forecasting model can also provide historical basis for scheduling decision. Searching a historically similar process according to the current rainfall and section flow information, thereby providing a scheduling strategy facing similar conditions and providing decision support for decision makers;
(3) the bottlenecks of low runoff forecasting precision and short forecasting period are broken through to a certain extent. Taking the Danba section of the dry flow of the great river as an example, a runoff forecasting model is established based on the similarity principle, the Nash coefficient of 3 days in a forecasting period is more than 0.8, the average relative error is less than 10%, and the accuracy of a forecasting result exceeds 90%; the Nash coefficient in the forecast period of 7 days is more than 0.6, the average relative error is less than 20%, and the accuracy of the forecast result exceeds 80%.
Detailed Description
The present invention will be described in detail with reference to specific examples.
The invention discloses a self-adaptive runoff forecasting method based on rainfall runoff similarity, which comprises the following steps of:
s1, collecting and processing data;
and collecting historical actual rainfall and runoff process information of a controlled rainfall station and a hydrological station in a water condition forecasting system of a basin where the forecast object is located, and constructing a historical rainfall and runoff sample library. For rainfall data, the measured rainfall data of the water condition forecasting system, the rolling rainfall forecast data from the meteorological department and the lattice rainfall data issued by the Chinese meteorological office need to be collected at the same time, the reliability of the data from the controlled rainfall station in the water condition forecasting system and the lattice rainfall data is analyzed, and a proper data source is selected to evaluate the rainfall similarity. For runoff data, when no hydraulic engineering exists at the upstream of the forecast object, the runoff data of a key hydrological station of main and branch flows above the forecast object is collected; when there is water conservancy project above the forecast object, it also needs to collect the flow data of the upstream reservoir in and out as the basis of the flood data in the backward-deducing section.
And (4) judging the rainfall and runoff data abnormal conditions in an auxiliary manner according to the runoff magnitude difference in the dry season and the flood season and the rainfall and runoff response relation. The rainfall data is checked by fully utilizing historical weather data issued by the China weather bureau, station network monitoring data and weather grid data; the monitoring data of upstream and downstream hydrological stations and the hydrological and flow data are fully utilized to check the radial data. For the time interval with less data abnormality, the original abnormal data can be covered by adopting modes such as interpolation and the like; for the time period with more abnormal data, the time period is marked and is not included in the rainfall and runoff historical samples, so that the forecast result deviation caused by the abnormal data is avoided.
S2, constructing rainfall and runoff samples;
on the time scale, the collected rainfall and runoff data needs to be converted into the time scale of forecast requirements. For a branch flow region with a small water collecting area, flood generally has the characteristic of steep rise and steep fall, the forecast period is not suitable to be too long, but the forecast scale is refined. For a main flow area with a large water collecting area, the duration of flood in a field is long, the flood information with a longer forecast period is mastered, the benefit and flood control risk of the reservoir are coordinated, and the flood rising and falling law with a longer forecast period can be predicted by selecting a thicker forecast scale.
On the spatial scale, the rainfall monitoring data of a plurality of stations are subjected to dimension reduction by converting rainfall station data into subarea rainfall data. Firstly, dividing a research area into a plurality of sub-areas according to the difference of convergence modes of different areas, wherein the rainfall of the sub-areas is calculated by the weighted average of the rainfall of the included stations, and the calculation formula is as follows:
wherein, PiIs the areal rainfall of subregion i; phiiIs the rainfall site set contained in the sub-area i; p is a radical ofjIs the rainfall site index contained in the sub-area; p is a radical ofkThe number of rainfall stations contained in the sub-area i;
is the station rainfall of the ith station of the subregion;
is that
The station rainfall is converted into the weight of the surface rainfall.
S3, establishing a forecasting model;
s31, identifying key characteristic indexes of rainfall and runoff;
based on historical rainfall and runoff sample data, analyzing rainfall and runoff characteristics of a basin where the forecast object is located, and establishing the forecast object and quantitative characteristic indexes of the rainfall and the runoff of the basin. The rainfall process can be divided into two phases: a developmental stage and an end stage. The characteristic indexes of the development stage mainly comprise early accumulated rainfall, time interval rainfall and the like; the characteristic indexes of the ending stage mainly comprise rainfall duration, total rainfall, rainfall level and the like. The runoff process can also be divided into a development phase and an end phase: the characteristic indexes of the development stage comprise time interval runoff, accumulated time interval runoff and the like; the characteristic indexes of the ending stage comprise peak type, peak flow, peak current time and the like.
According to the physical cause of runoff and the characteristic indexes, methods such as cause analysis, correlation analysis, regression analysis, multi-factor comprehensive analysis and the like are comprehensively utilized to carry out deep mining analysis on historical rainfall and runoff data, preliminarily identify different spatial positions (upstream, midstream or downstream) of a drainage basin, and forecast key characteristic indexes in different forecast time scales (year, month, ten days and day) and different forecast periods (flood season, dry flood transition period and the like). The invention comprehensively utilizes physical cause analysis and mathematical statistics methods to determine the early-stage influence time lag of key characteristic indexes:
a. comprehensively analyzing the production convergence time from rainfall and runoff physical causes of each area to a forecast section, preliminarily determining the response time of the rainfall and runoff, and taking the response time as an important basis for determining the early-stage influence time delay of a key characteristic index;
b. analyzing the correlations of rainfall and runoff with different early-stage influence time lags and runoff in a prediction period by using a mathematical statistical method, and selecting early-stage influence time lags with larger correlations;
c. based on the preliminarily determined early-stage influence time lag, setting rainfall and runoff combination considering different early-stage influence time lags as key indexes for identifying similar runoff processes, forecasting the historical runoff process of the drainage basin section by adopting a rainfall runoff similarity forecasting model, and finally determining the optimal early-stage influence time lag according to the precision evaluation of forecasting results.
For the key feature index x to be selected, assuming that the determined early-stage influence time lag is 3 time periods, the similarity prediction model needs to consider the following time lag combination:
a.xt-3，xt-2，xt-1；
b.xt-3，xt-2；
c.xt-3，xt-1；
d.xt-3；
s32, similarity forecasting model;
the rationale for similarity is: for a specific watershed, under certain geographic environmental conditions, the dominant weather system and rainfall type restricting rainfall will appear repeatedly, and the rainfall (or rainstorm) process and the runoff (or flood) process thereof under the similar weather system conditions will be similar. The formation of the rainfall runoff process is a gradual evolution process, and mainly comprises the formation of a weather system, the generation of the rainfall process, the evolution of the runoff process and other stages. Each stage has a specific change rule, and the stages are also related to each other. These rules in the rainfall runoff evolution process usually repeat in the historical rainfall runoff data according to the characteristics of similarity, so it can be known that the rainfall runoff and the process thereof generated under these similar conditions will also be similar.
According to the current rainfall and runoff samples, searching the most similar samples in the historical rainfall and runoff samples through Euclidean distances, wherein each historical rainfall and runoff sample corresponds to one forecast result, and distributing the weight of each sample forecast result according to the Euclidean distances of each rainfall and runoff sample to obtain the final forecast result. The formulas (3), (4) and (5) are respectively used for calculating the rainfall similarity, the runoff similarity and the rainfall-runoff comprehensive similarity index.
Wherein, PjRepresenting rainfall characteristic value vectors of historical rainfall and runoff samples, wherein the dimensionality of the rainfall characteristic value vectors is equal to the early-stage influence delay time of the considered rainfall, j represents the serial numbers of the historical rainfall and the runoff samples, j is more than or equal to 1 and less than or equal to N, and N represents the total number of the historical rainfall and the runoff samples; p*Representing the rainfall eigenvalue vector of the current rainfall and runoff sample, the dimension and P thereofjThe same; dpjAnd (4) representing the rainfall similarity indexes of the historical rainfall and runoff sample with the sequence number j and the current rainfall and runoff sample.
Wherein Q isjAnd representing the runoff characteristic value vector of the historical rainfall and the runoff sample, wherein the dimension of the vector is equal to the influence delay time of the earlier stage of the considered runoff. j represents the serial number of the historical rainfall and runoff sample, j is more than or equal to 1 and less than or equal to N, and N represents the total number of the historical rainfall and runoff samples; q*Representing the current rainfall, runoff eigenvalue vector of the runoff sample, its dimension and PpjThe same; dqjAnd representing the runoff similarity indexes of the historical rainfall and runoff sample with the sequence number j and the current rainfall and runoff sample.
dj＝wpdpj+dqj (5)；
Wherein, wpIs the rainfall impact weight.
Similarity indexes of the current rainfall and runoff samples and each historical rainfall and runoff sample can be calculated based on the determined rainfall-runoff comprehensive similarity weight, the similarity samples are selected based on the similarity index sorting, and the weight of each similarity sample in future runoff prediction is calculated (see formula (6) and formula (7));
wherein k is the number of similarity samples in the historical rainfall and runoff samples, wiAnd i is more than or equal to 1 and less than or equal to k, which is the weight of the ith similarity sample.
After determining the similarity samples and their weights, the runoff forecasting result can be represented by the following formula:
wherein,
forecast flow, Q, representing time period tt-1Represents the measured flow, Δ q, over a period of t-1*Representing the relative value of the flow variation according to the similarity forecast,
the predicted value for each similar sample is represented.
S33, parameter calibration;
adopting a multi-factor NNBR model to forecast runoff similarity, wherein parameters related to the forecasting model mainly comprise: nearest neighbor sampling number, dimension of characteristic vector, rainfall influence weight and the like. The nearest neighbor sampling number refers to the number of samples searched and sampled by the forecasting model in the historical process; the feature vector dimension is closely related to the influence of the key feature indexes on the runoff in time delay; the rainfall influence weight is used for balancing rainfall and runoff magnitude difference.
And selecting a Nash coefficient NS and an average relative error MARE as main evaluation indexes based on hydrologic information forecast specifications, establishing a forecast result precision evaluation index system, and comprehensively evaluating forecast effects of different forecast periods. And (3) combining modern heuristic optimization algorithms such as a genetic algorithm and the like to independently model and rate parameters of each key characteristic index combination scheme. The following equations (10), (11) are objective functions targeting NS Max and MARE Min, respectively:
wherein n represents the length of the training period, and the total time is n periods.
Showing the measured value of the runoff in the ith time period,
a runoff forecast value representing an ith time period,
represents the average of measured values of runoff over the training period.
The similarity sample weight is a dynamic parameter of the model, and the parameter can dynamically change according to a real-time rainfall runoff scene, namely after the rainfall-runoff comprehensive similarity index and the number of the similarity samples are determined, the similarity forecasting model can dynamically calculate the weight of each similarity sample in future runoff prediction. The invention also adopts a rolling forecasting mode to prolong the forecast period, and obtains the forecast result by dynamically identifying the similar process of each time period in the forecast period. And searching similarity samples again in each time interval according to the updated forecast information, and realizing dynamic identification of the similarity process.
S4, realizing rolling forecast;
three rolling forecasting modes are proposed:
not considering rainfall forecast and runoff forecast
And directly searching the rainfall and runoff similar process according to the occurred and actually measured rainfall and runoff information. This approach does not take into account the forecasted rainfall, so this rolling method is more suitable when the length of the forecasted rainfall is insufficient or the accuracy is poor. Taking the runoff process of the t-t + m period as an example:
wherein,
indicating that a measured early rainfall event has occurred,
represents the pre-stage runoff process, Q ', which has occurred and is actually measured't，Q′t+1，…，Q′t+mRespectively representing the runoff forecast results day by day in the forecast period, n1Represents the length of the early rainfall lag, n2The length of the runoff lag in the early stage is shown, and m represents the length of the forecast period. For example, runoff Q 'whether forecast t period'tIs also runoff Q 'of a period t + 1't+1All input the same early rainfall
And early runoff
② rainfall similarity is updated by rolling considering rainfall forecast information
Continuously adding predicted flow information as input to update the runoff similarity in a rolling manner, and continuously forecasting the runoff in the next time period. The rolling method is completely connected with the forecast rainfall, and the forecast result in the previous time period influences the forecast result in the next time period. This rolling approach is more suitable when the length of the forecast rainfall is sufficient and the accuracy is high. Taking the runoff process of the t-t + m period as an example:
forecasting runoff Q 'in t period'tThe method is consistent with the idea of the method, and the rainfall information is input
And runoff information
However, forecast runoff Q 'of t +1 period't+1In time, a runoff forecast result Q 'of a period t needs to be obtained'tAnd forecast rainfall P 'at time period t'tAdding into the input of the model; and then the forecast rainfall P 'in the period of t + 1't+1And forecast runoff Q't+1Inputting a model, and forecasting runoff Q 'of the next period t + 2't+2. By analogy, the rainfall and runoff information in the early stage are updated simultaneously in the forecast of the next time period, and the day-by-day rolling forecast in the forecast period is realized.
Rolling updating rainfall similarity by considering rainfall forecast information, but not updating runoff similarity
The forecasting model considers the updating of rainfall forecasting information and continuously updates the rainfall similarity in a rolling mode, and the rolling mode has the characteristics of the two rolling modes. Taking the runoff process of the t-t + m period as an example:
for example, forecast runoff Q 'of period t'tThe method is the same as the method (r), but the runoff Q 'in the forecast t +1 period't+1In time, forecast rainfall P 'of period t'tThe model is input, while the input of the flow is unchanged. By analogy, the runoff forecast in the next time period only updates rainfall information and does not update runoff information.
S5, an adaptive forecasting mode;
aiming at the difference of the flow convergence mechanism of the basin where the forecast object is located in different runoff development stages such as water rising and water falling, a forecasting mode capable of being adaptively switched according to early hydrological conditions is established. For example, during the flood phase, the soil can be saturated earlier by the early accumulation of rainfall, and during the subsequent development, the same magnitude of rainfall will result in a more significant runoff rising process. Considering the difference of influence time delay of early rainfall, a short rainfall time delay mode and a long rainfall time delay mode are provided, the short rainfall time delay mode is mainly suitable for a period with rare rainfall and small rainfall, and the autocorrelation of runoff in the period is high. The long-rainfall time-lag mode is more suitable for the periods with frequent rainfall and large rainfall, in particular to the flood stage of the flood season of the basin. And providing switching conditions among different forecasting modes according to comprehensive factors such as early runoff, early rainfall, forecast rainfall and the like, and automatically switching the forecasting modes to the corresponding forecasting modes when the switching conditions are met.
In a word, the adaptive runoff forecasting method based on rainfall runoff similarity adopts a data mining technology to search for a similar process in the historical rainfall runoff production process and forecast the most probable process line of later runoff. Collecting rainfall and runoff data of a critical section of a drainage basin, and performing space-time dimensionality reduction on the data on the premise of keeping a spatial distribution pattern of the rainfall and the runoff; determining key characteristic indexes of rainfall and runoff by comprehensively utilizing a rainfall runoff physical cause analysis and mathematical statistics method, weighing the difference of rainfall and runoff numerical magnitude, providing a rainfall-runoff comprehensive similarity index considering rainfall influence weight, and dynamically evaluating the rainfall and runoff similarity by combining a data mining method: constructing a multi-factor nearest neighbor sampling regression model, predicting runoff in a runoff area by using rainfall flood similarity, and providing three different runoff rolling forecasting modes to prolong the runoff forecasting forecast period; aiming at the production convergence characteristics of the basin at different stages such as water rising and water falling, a rainfall and runoff input mode capable of being adaptively switched according to the real-time water and rain conditions is established, and the runoff forecasting precision is further improved. The method can overcome the problem of difficult parameter calibration of the physically-driven runoff forecasting model, and can also break through the problem of poor interpretability of the forecasting result of the conventional data-driven runoff forecasting model, and break through the bottlenecks of low runoff forecasting precision and short forecasting period to a certain extent, thereby having important significance in improving the fine management and lean dispatching level of the watershed reservoir group.
Claims (7)
1. A self-adaptive runoff forecasting method based on rainfall runoff similarity is characterized by comprising the following steps:
s1, constructing historical rainfall and runoff samples: collecting the flow data of the key section of the drainage basin where the forecast object is located, the rainfall site data and the grid point data, and performing time dimension reduction and space dimension reduction on the collected original data to obtain historical rainfall and runoff samples;
s2, identifying key characteristic indexes of rainfall and runoff: based on historical rainfall and runoff samples, comprehensively determining key characteristic indexes of the rainfall and runoff from two aspects of physical cause and statistical analysis;
s3, rainfall and runoff similarity dynamic evaluation based on data mining: measuring sample similarity by adopting an Euclidean distance method, and providing a rainfall-runoff comprehensive similarity index considering rainfall influence weight by considering rainfall and runoff numerical magnitude difference;
s4, runoff rolling prediction based on rainfall flood similarity: constructing a multi-factor nearest neighbor sampling regression model, predicting runoff in a runoff area by using rainfall flood similarity, and providing three different runoff rolling forecasting modes to prolong the runoff forecasting forecast period;
s5, forecasting mode self-adaptive switching: aiming at the production convergence characteristics of the basin at different stages of water rising and water falling, a rainfall and runoff input mode which is self-adaptively switched according to the real-time water and rain conditions is established, and the runoff forecasting precision is further improved.
2. The adaptive runoff forecasting method based on rainfall runoff similarity according to claim 1, wherein in the step S1, the dimensionality reduction of the data from two dimensions of space and time is specifically as follows:
on a time scale, converting collected rainfall and runoff data into a forecast demand time period;
on a spatial scale, converting rainfall station data into subarea rainfall data, and performing dimension reduction on rainfall monitoring data of a plurality of stations; firstly, dividing a research area into a plurality of sub-areas according to the difference of convergence modes of different areas, wherein the rainfall of the sub-areas is calculated by the weighted average of the rainfall of the included stations, and the calculation formula is as follows:
wherein, PiIs the areal rainfall of subregion i; phiiIs the rainfall site set contained in the sub-area i; p is a radical ofjIs the rainfall site index contained in the sub-area; p is a radical ofkThe number of rainfall stations contained in the sub-area i;
is the station rainfall of the ith station of the subregion;
is that
The station rainfall is converted into the weight of the surface rainfall.
3. The adaptive runoff forecasting method based on the rainfall runoff similarity according to claim 1, wherein in the step S2, based on historical rainfall and runoff sample data, the rainfall and runoff characteristics of the basin where the forecast section is located are analyzed, and the forecast section and quantitative characteristic indexes of the rainfall and runoff of the basin above the forecast section are established; according to physical cause and characteristic indexes of runoff of the drainage basin, comprehensively utilizing cause analysis, correlation analysis, regression analysis and multi-factor comprehensive analysis methods to identify forecast key characteristic indexes of different spatial positions of the drainage basin and at different forecast time scales and different forecast periods; and comprehensively utilizing physical cause analysis and mathematical statistics methods to determine the early-stage influence time lag of the key characteristic indexes, specifically comprising the following steps:
s21, comprehensively analyzing the rainfall to forecast section production convergence time of each area from rainfall and runoff physical causes, preliminarily determining the response time of the rainfall and runoff, and taking the response time as an important basis for determining the early-stage influence time delay of key indexes;
s22, analyzing the correlations of rainfall and runoff with different early-stage influence time lags and runoff in a prediction period by using a mathematical statistical method, and selecting early-stage influence time lags with larger correlations;
s23, setting and considering rainfall and runoff combinations of different early-stage influence time lags as key indexes for identifying similar runoff processes based on the preliminarily determined early-stage influence time lags, forecasting historical runoff processes of river basin sections by adopting a rainfall runoff similarity forecasting model, and finally determining the optimal early-stage influence time lags according to forecasting result precision evaluation.
4. The adaptive runoff forecasting method based on rainfall runoff similarity according to claim 1, wherein in step S3, a sliding window sampling mode is adopted to construct a key characteristic index sample set to enrich the number of historical rainfall and runoff samples; quantitatively representing the similarity of the current rainfall and runoff sample and the historical rainfall and runoff sample by adopting an Euclidean distance method; and (3) taking the magnitude difference of rainfall and runoff values into consideration, and providing a rainfall-runoff comprehensive similarity index of rainfall influence weight:
wherein, PjRepresenting the rainfall characteristic value vector of the historical rainfall and runoff sample, wherein the dimensionality of the vector is equal to the influence delay time of the early rainfall considered, j represents the serial number of the historical rainfall and runoff sample, j is more than or equal to 1 and less than or equal to N, and N represents the historical rainfall and the rainfall runoff sampleThe total number; p*Representing the rainfall eigenvalue vector of the current rainfall and runoff sample, the dimension and P thereofjThe same; dpjRepresenting the rainfall similarity indexes of historical rainfall and runoff samples with the sequence number j and current rainfall and runoff samples;
wherein Q isjRepresenting runoff characteristic value vectors of historical rainfall and runoff samples, wherein the dimensionality of the runoff characteristic value vectors is equal to the earlier-stage influence dead time of the considered runoff, j represents the serial numbers of the historical rainfall and the runoff samples, j is more than or equal to 1 and less than or equal to N, and N represents the total number of the historical rainfall and the runoff samples; q*Representing the current rainfall, runoff eigenvalue vector of the runoff sample, its dimension and QjThe same; dqjRepresenting the runoff similarity indexes of the historical rainfall and runoff samples with the sequence number j and the current rainfall and runoff samples;
rainfall-runoff comprehensive Euclidean distance djThe calculation formula of (2) is as follows:
dj＝wpdpj+dqj；
wherein, wpIs the rainfall impact weight.
5. The adaptive runoff forecasting method based on rainfall runoff similarity according to claim 1, wherein in step S4, a multi-factor nearest neighbor sampling regression model is constructed, rainfall runoff is predicted by utilizing rainfall runoff similarity, and a modern heuristic algorithm is combined to optimize forecasting effect as a target, and nearest neighbor number, key feature vector dimension and rainfall influence weight parameter related to the model are optimized;
calculating the similarity degree of the current rainfall and runoff sample and each historical rainfall and runoff sample based on the determined rainfall-runoff comprehensive similarity index, sorting and selecting the similarity samples based on the similarity index, and calculating the weight of each similarity sample in future runoff forecast to be;
wherein k is the number of similarity samples in the historical rainfall and runoff samples, wiI is more than or equal to 1 and less than or equal to k and is the weight of the ith similarity sample;
after the similarity samples and their weights are determined, the runoff forecasting result is represented by the following formula:
wherein,
forecast flow, Q, representing time period tt-1Represents the measured flow, Δ q, over a period of t-1*Representing the relative value of the flow variation according to the similarity forecast,
a prediction value representing the ith similar sample;
adopting a multi-factor NNBR model to forecast runoff similarity, wherein parameters related to the forecasting model mainly comprise: nearest neighbor sampling number, dimension of the characteristic vector and rainfall influence weight, wherein the nearest neighbor sampling number refers to the number of samples searched and sampled by the forecasting model in the historical process;
selecting a Nash coefficient NS and an average relative error MARE as evaluation indexes, establishing a forecast result precision evaluation index system, and comprehensively evaluating forecast effects of different forecast periods; combining a modern heuristic optimization algorithm, and independently modeling and parameter rating each key characteristic index combination scheme; the objective function with the maximum objective for the nash coefficient NS is:
the objective function targeting the minimum of the average relative error MARE is:
wherein n represents the length of the training period, n time periods,
showing the measured value of the runoff in the ith time period,
a runoff forecast value representing an ith time period,
represents the average of measured values of runoff over the training period.
6. The adaptive runoff forecasting method based on the rainfall runoff similarity according to claim 1, wherein the three rolling forecasting methods in the step S4 are as follows:
s41, not considering rainfall forecast and runoff forecast;
the rainfall and runoff similarity process is directly searched according to the information of the rainfall and runoff which are actually measured and occur, and the rainfall forecast is not considered in the mode, so that the rolling method is adopted when the length of the rainfall forecast is insufficient or the precision is poor; predicting the runoff process in the period of t-t + m as follows:
wherein,
indicating that a measured early rainfall event has occurred,
represents the pre-stage runoff process, Q ', which has occurred and is actually measured't，Q′t+1，…，Q′t+mRespectively representing the runoff forecast results from time period to time period in the forecast period, b1Representing the length of the delay of early rainfall, b2Representing the length of the runoff stagnation period in the early stage, wherein n represents the length of the forecast period;
s42, rolling and updating rainfall similarity by considering rainfall forecast information;
continuously adding predicted flow information as input rolling updating runoff similarity, and continuously forecasting runoff in the next time period; the rolling method is completely accessed to forecast rainfall, and the forecast result of the previous time period can influence the forecast result of the next time period; therefore, when the rainfall forecast length is enough and the precision is high, the rolling mode is adopted; predicting the runoff process in the period of t-t + m as follows:
forecasting runoff Q 'in t period'tIn accordance with the above-described concept of S41, rainfall information is inputted
And runoff information
However, forecast runoff Q 'of t +1 period't+1In time, a runoff forecast result Q 'of a period t needs to be obtained'tAnd forecast rainfall P 'at time period t'tAdding into the input of the model; and then the forecast rainfall P 'in the period of t + 1't+1And forecast runoff Q't+1Inputting a model, and forecasting runoff Q 'of the next period t + 2't+2(ii) a By analogy, the forecast of the next time period updates the early rainfall and runoff information at the same time, and the day-by-day rolling forecast in the forecast period is realized;
s43, rolling and updating rainfall similarity by considering rainfall forecast information, but not updating runoff similarity;
the forecasting model considers the updating of rainfall forecasting information, but only updates the rainfall similarity in a rolling manner considering the error of the forecasting runoff in the previous period, and the rolling manner has the characteristics of the two rolling manners of S41 and S42; predicting the runoff process in the period of t-t + m as follows:
forecasting runoff Q 'in t period'tThe method is the same as the method of S41 above, but for runoff Q 'at forecast t +1 period't+1In time, forecast rainfall P 'of period t'tInput model, and input of flow is unchanged, and so on, the nextAnd only the rainfall similarity sample is updated in the runoff forecast of the time period, and the flow similarity sample is not updated.
7. The adaptive runoff forecasting method based on rainfall runoff similarity according to claim 1, wherein in step S5, a forecasting mode capable of being adaptively switched according to early hydrological conditions is established for the difference of the runoff converging mechanism of the basin where the forecasting object is located in different runoff development stages of rising and falling water; in the stage of rising water, the accumulated rainfall in the early stage can earlier saturate the soil, and in the subsequent development process, the rainfall with the same magnitude can cause a more obvious runoff rising process; considering the difference of influence time delay of early rainfall, a short rainfall time delay mode and a long rainfall time delay mode are provided, wherein the short rainfall time delay mode is used for a period with rare rainfall and small rainfall; the long-rainfall time-lag mode is used for the period of frequent rainfall and large rainfall; and providing switching conditions among different forecasting modes according to comprehensive factors of runoff in the early period, rainfall in the early period and rainfall forecast, and automatically switching the forecasting model to the corresponding forecasting mode when the switching conditions are met.
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