Hydrological forecast is crucial for reservoir dispatching, flood control, power generation, irrigation and other tasks, and is an important basis for relevant departments and managers to make decisions. Therefore, it is particularly important to make accurate hydrological forecasts. In order to improve the accuracy and reliability of hydrological forecasts, especially medium- and long-term hydrological forecasts, people have proposed many methods for medium- and long-term hydrological forecasts from different directions and combined with corresponding subject knowledge. These methods can be roughly divided into two categories: traditional methods and new methods. The former mainly include cause analysis and hydrological statistics methods, while the latter mainly include methods such as artificial neural networks, gray system analysis, and fuzzy mathematical models. The details are as follows: 1.1 Cause analysis
① Predicting later hydrological conditions from the early atmospheric circulation situation
Atmospheric precipitation is the main water source of river runoff, and precipitation is closely related to atmospheric circulation. connect. The occurrence of droughts and floods in a river basin or region is linked to atmospheric circulation. Therefore, analyzing and studying the relationship between atmospheric circulation and hydrological elements has always been a subject of in-depth discussion by hydrometeorologists. Atmospheric circulation has global characteristics, so the northern hemisphere 500 hPa monthly average situation map is mainly used as a basis, which may reflect the main circulation index and circulation characteristic quantities. Based on the historical data of hydrological situation and circulation, summarize the pattern of circulation characteristics in the early period of drought and flood, and use the early circulation characteristics as a qualitative prediction of the hydrological situation in the later period; or find areas with significant relationship with the forecast object on the monthly average situation map and time periods, select factors with clear physical meanings and significant statistical contributions, use stepwise regression or other multivariate analysis methods to establish equations with the forecast objects, and make quantitative forecasts accordingly.
② Forecast based on the previous sea temperature distribution characteristics
The abnormal distribution of sea temperature has the characteristics of wide range, large thickness, and long duration. It is often a precursor to abnormal atmospheric circulation. It can provide information for long-term hydrological forecast. After summarizing the sea temperature distribution pattern before droughts and floods based on historical data, we can make qualitative predictions of later hydrological conditions based on the early sea temperature distribution characteristics; or consider the continuity in time and space, select a number of key sea areas and key periods. The sea temperature at the location is used as a forecast factor, and a regression equation is established with the forecast object to perform quantitative forecast.
③ Use certain information on solar activity for forecasting
Mainly use the relative number of sunspots to reflect the intensity of solar activity, and analyze sunspots based on the phase or sunspot number in the 11-year cycle The corresponding relationship between changes in numbers and changes in river water volume can be used to quantitatively predict possible droughts and floods that may occur in the later period. For example, Liu Qingren focused on sunspot activity, aimed at long-term and ultra-long-term hydrological forecasting, and used mathematical statistical analysis methods to analyze the characteristics of the impact of sunspots and El Ni?o events on the hydrology of the Songhua River Basin and the basic rules for the occurrence of floods and droughts. It reveals the pattern of rainfall changes between high and dry periods according to the magnetic cycle.
1.2 Hydrological statistical method
Hydrological statistical method is to carry out probability prediction through statistical analysis of hydrological data. It can be divided into two major categories: one is to analyze the statistical law of changes in hydrological elements over time, and then use this law to make forecasts, such as historical evolution method, time series analysis method, etc.; the other is to use multiple regression analysis method, Establish a forecast plan and conduct forecasts. Currently, the widely used hydrological statistical forecasting methods mainly include multiple regression analysis and time series.
① Multiple regression analysis
Regression analysis is one of the earliest and most widely used methods in medium and long-term flow forecasting. Its history of application in runoff can be traced back to early rainfall and runoff. The correlation graph method has rapidly become popular with the development of computer technology since the 1960s. Regression analysis is still an important means in the actual work of traffic forecasting. Commonly used methods include stepwise regression, cluster analysis, principal component analysis, etc.
The main advantage of regression analysis is that it is simple and easy to implement. The main problems are how to reasonably select the number of factors to solve the conflict between the fitting effect and the prediction effect; since the prediction value is the average of each factor data, it is difficult to predict hydrological phenomena with maximum or minimum values.
In order to overcome these problems, in addition to selecting the early flow at the forecast station, the early flow at the upstream station, precipitation in the catchment basin, soil moisture, snow cover, temperature, etc. as the most commonly used forecast factors, some = on the flow process are also used. Influencing factors that control long-term change patterns are used as predictors, including geophysical quantities such as solar radiation, sunspot number, earthquake fields, and geothermal fields; ocean physical quantities such as ocean surface temperature and ENSO index; and atmospheric physical quantities such as pressure height fields and atmospheric circulation indexes. . Because many of the above factors will help improve long-term forecast accuracy. There are many research results in this area. For example, some studies have shown that seismic fields, geothermal fields and annual flow are highly correlated; many research results have shown that ENSO events are related to river flow changes, and this relationship can be used for long-term flow forecasting.
② Time series analysis
Time series analysis is the application of observation records of hydrological elements to find their own evolution rules for forecasting. There are many time series models used in flow process forecasting. According to the number of time series included in the model, they can be divided into two categories: single-variable models and multi-variable models.
The most commonly used univariate model is the autoregressive moving average (ARMA) model and its derivatives. The autoregressive (AR) model is a special type of ARMA model and is widely used in annual and monthly runoff simulation and forecasting. For example, Lu Huayou used the third-order autoregressive model AR(3) to forecast the annual runoff of the Danjiangkou Reservoir. However, the ARMA model is based on the assumption that the time series is stationary, and flows with time scales smaller than the year (such as monthly and ten-day flows) usually have strong seasonality and are not stationary sequences. Therefore, it is generally inappropriate to use the ARMA model directly. . There are three main models for simulating and forecasting this seasonal sequence: first, using the seasonal ARIMA model (SARIMA for short); (2) using the seasonal ARMA model, that is, first removing the seasonal mean and variance in the original flow sequence, Then fit the ARMA model to the seasonal series; (3) Periodic ARMA model (PARMA model for short), including the PAP model. These three models are commonly used in medium and long-term flow forecasting. In recent years, research on the long memory characteristics of river flow processes has attracted attention. Stochastic processes with long memory characteristics can be better described by the fractional difference autoregressive moving average (ARFIMA) model. For example, Montanari et al. used the ARFIMA model to simulate and forecast the monthly flow process of the Nile River in Aswan; Ooms et al. used the PARMA model. Combined with the ARFIMA model, it was proposed to use the periodic long memory model (PARFIMA, Periodic ARFIMA) to fit the monthly flow process; Wang Wen used a variety of time series models including the ARFIMA model to calculate the daily average flow of the Tangnaihai Station in the upper reaches of the Yellow River in the next 10 days. forecast.
If the influence of external input factors is considered, a multivariable time series model can be constructed. The most commonly used are the autoregressive moving average (ARMAX) model or the transfer function noise (TFN) model containing external variables. For example, Awadallahl et al. used sea temperatures in different sea areas as external input variables to establish a TFN model to forecast the summer runoff of the Nile River. Since external influencing factors are taken into account and more forecast information is used, the forecast accuracy of the TFN model is generally higher than that of the univariate ARIMA model. For example, Thompstone et al. established a seasonal ARMA model, a periodic autoregressive (PAR) model, a TFN model considering precipitation and snow melt inputs, and a conceptual model to conduct forecast tests on the flow process in January/April. The results showed that the accuracy of the TFN model Better than other models. If the flow process is significantly disturbed by some external factors and exhibits abnormal fluctuations, the interference model can be used to simulate this interference, which can be regarded as a special type of TFN model. Based on the AR(1) model, Kuo et al. considered the influence of typhoon factors and established an interference model to simulate this interference. It can be regarded as a special type of TFN model. Kuo et al., based on the AR (1) model and considering the influence of typhoon factors, established an interference model to forecast and model the 10-day average flow of Tamsui River in Taiwan.
Traffic process time series forecast models can also be divided into linear models and nonlinear models according to whether the model has a linear structure. The previously mentioned ARMA, TFA and other models can be regarded as linear models. In recent years, research on nonlinear models of hydrological systems has attracted more and more attention, and accordingly, the number of application examples of nonlinear models has also increased. The threshold autoregressive model (TAR) is a nonlinear time series model commonly used in medium and long-term flow process forecasting. The commonly used PARMA and PAR models mentioned earlier can actually be regarded as a special type of TAR model. They use seasons as thresholds to establish linear models for different seasons. If the influence of external factors is considered, TAR can be extended to a threshold regression model, which can be described as a tree structure and is also called a model tree model by some researchers. This method has been applied to real-time rainfall and runoff forecasting examples. It will also be of great application value in long-term forecasting. 2.1 Artificial Neural Network
Artificial neural network (ANN) is an intelligent bionic model constructed based on the connection theory. It is a nonlinear dynamic system composed of a large number of neurons and has parallel distributed processing, self-organization, and self-adaptation. , self-learning and fault tolerance and other characteristics. Since the 1990s, the application of artificial neural networks in hydrological forecasting has gradually increased. It is a nonlinear forecasting method that has attracted the most attention in the past 20 years and has been widely used in real-time medium and long-term hydrological forecasting. The most commonly used ANN type for runoff forecasting is the multilayer perceptron (MLP) neural network (also known as BP network) using the error back propagation (BP) algorithm, which is widely used in annual and monthly runoff or average flow forecasts. Birikundavyi et al. used the MLP network to conduct traffic forecasting for the next 1 to 7 days; Zealand et al. used the MLP network to conduct traffic forecasting for the next 1 to 4 periods; Markus, Jain, Kisi, etc. used the MLP network model to conduct monthly traffic forecasting research. Radial vector function (RBF) neural network is also used by many researchers for monthly average flow forecast. In addition, in order to better fit the nonlinear characteristics of the flow process, modular neural networks can be used for mid- and long-term flow forecasting.
The most important thing when using the ANN model for forecasting is to determine which data will be used as input, what type of neural network to use and the corresponding grid structure. Regarding how to determine the ANN input variables, there are two issues that need to be considered: First, when the training data length is short and cannot cover the entire possible range of the sequence, that is, when it cannot cover the uncertainty information in hydrological prediction, how to improve the ANN's probability of Ability to predict extreme situations. To solve this problem, when Cigizoglu used the MLP model to forecast monthly average flow, he first used the AR model to generate a simulation sequence to increase the amount of training data and improve the forecast accuracy. The second is how to solve the meteorological input data of the ANN model when making multi-step forecasts. The ideal choice is to use meteorological forecast data, but some researchers also use historical meteorological data as input to the ANN model for multi-step forecasting.
2.2 Gray System Theory
In 1982, Deng Julong founded the gray system theory and believed that the water resource system can be treated as a gray system. The most commonly used mathematical model to describe the gray system model is GM (1, 1), G stands for Gray (gray), M stands for Model (model), and GM (1, 1) refers to a linear ordinary differential equation of 1 order and 1 variable. Model. It has many application examples in runoff forecasting and disaster prediction. Xia Jun proposed using gray correlation pattern recognition method for mid- and long-term runoff prediction. Since then, some researchers have applied this type of model to annual and monthly runoff prediction.
Due to its model characteristics, gray system theory is more suitable for problems with exponential growth trends. For other changing trends, sometimes the fitting gray level is larger, making it difficult to improve the accuracy. Moreover, the gray system theoretical system is not yet perfect and is in the development stage. Its application in medium and long-term hydrological forecasting is experimental and exploratory.
2.3 Fuzzy mathematics theory
There are two types of prediction methods using fuzzy mathematics in the field of hydrology. One is the fuzzy pattern recognition prediction method, and the other is the fuzzy logic method.
The basic idea of ??the fuzzy pattern recognition prediction method is: based on fuzzy clustering of historical sample patterns, calculate the category feature value of the state to be measured, and then calculate the category feature value of the state to be measured, and then use the regression between the forecast value and the category feature value to Equation for forecasting. This method organically combines hydrological analysis, statistical analysis, and fuzzy set analysis, providing a new way to improve the accuracy of mid- and long-term forecast characteristics.
Fuzzy logic method can describe the causal relationship between variables that is not very clear. According to the fuzzy logic relationship between variables, a fuzzy logic model (or fuzzy expert system) can be established for flow forecasting. For example, Zhu, Mahabir, etc. use fuzzy logic models for long-term flow forecasting.