Data driven models

Another alternative for hydrological modelling is to apply data driven (also called black box) techniques on hydrological time series. Unlike process-based models, these models require very limited understanding of the hydrological system and mainly rely on the quality of the available data. Data driven models find the relation between inputs (river flow and/or rainfall time series) and output (runoff) without considering the underlying hydrological process. Figure 2.3 depicts the learning system in data driven method. These methods can be categorized in two main types of classical and computational intelligence approaches.

Input data Observed data Real system model Data driven model M in imi zin g the di ffe re nc e Forecasted output

18 2.4.1 Classical data driven approach

The classical data driven models are generally regression models. Autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA), seasonal ARIMA, autoregressive exogenous (ARX), threshold autoregressive (TAR) and multiple linear regression (MLR) are the most popular regression models (Wang, 2006). Among them, ARIMA has been the most frequently used method for river flow forecasting that is first introduced by Box and Jenkins (1970). ARIMA is an extended type of ARMA, which has two main components of autoregressive and moving average as following;

𝐴𝑅𝑀𝐴 (𝑝, 𝑞) = 𝑍𝑡 = �𝜑1𝑍𝑡−1+ ⋯ + 𝜑𝑝𝑍𝑡−𝑝� + �𝜀𝑡− 𝜃1𝜀𝑡−1− ⋯ − 𝜃𝑞𝜀𝑡−𝑞� (2.1)

where 𝑝 is the order of autoregressive, 𝑞 is the order of moving average, 𝑡 is the time step (e.g. 12 for monthly modelling), 𝜀_𝑡 is a white noise and 𝜑 and 𝜃 are the AR and MA coefficients, respectively. The past events are processed by AR component and the summation of forecasting error is presented by MA component.

These traditional techniques usually assume that a signal is stationary and can be described by a set of linear equations. Therefore, they are not reliable for achieving accurate river flow forecasting as river flow time series is highly nonlinear and nonstationary (Martins et al., 2011).

2.4.2 Computational intelligence approach

In the last two decades, computational intelligence (CI) approaches have been increasingly substituted regression models and applied in many hydrological forecasting. CI models are capable of recognizing complex non-linear relationships between input and output data sets. A number of different types of CI methods which are successfully applied in hydrological forecasting is as follows;

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- Artificial neural networks (multi-layered perceptron, radial basis function, recurrent, product unit)

- Fuzzy rule-based systems

- Adaptive neuro-fuzzy inference system - Support vector machines

- Chaos theory and dynamic systems - Hybrid wavelet models

- Genetic algorithm/programming

- Swarm intelligence optimization (ant colonies, fish schooling, bee algorithm)

Given the complexity of rainfall-runoff process, computational intelligence methods are generally very powerful tool for river flow forecasting. Although CI models do not provide detailed information on hydrological process (black box type models) and require high quality historical time series, they are highly reliable and accurate. Following is a summary of CI models’ advantages over physically-based and conceptual models for river flow forecasting application:

- Unlike physically-based models, CI models do not require a large number of hydrological and geological parameters for representing the catchment behaviour. CI models are able to achieve accurate forecasts by applying high quality river flow time series (long historical records) as the single input .

- CI based models are self-trained. The input-output relationship is formulated automatically based on historical data in a catchment. Therefore, understanding the complex interaction between hydrological and geological process is not necessary for developing the model.

- They are able to train the model with multiple effective inputs like meteorological parameters. Therefore, future climate changes could be considered in the CI modelling process.

- Contrary to conceptual, semi-distributed or even distributed physically-based models, no assumptions or estimations need to be taken for formulation and calibrating the catchment.

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- Developed CI models are also easily applicable to different case studies with different catchment characteristics as they extract all necessary information from time series analysis.

- These models can be cost-effective as in-field measurements or gauging station maintenance would be reduced.

- Computational intelligence are the most efficient models for infilling of missing rainfall and river flow data to be used in river flow forecasting or any other hydrological applications.

- These models are the best option for modelling ungauged catchments when there is no other feasible solution for modeling. They are able to simulate the catchment by using effective inputs such as upstream data or data from other catchments with similar characteristics (Dawson et al., 2006; Besaw et al., 2010).

Despite the numerous advantages of data driven approaches, they also have some limitations. The main drawbacks of CI methods could be categorized as followings;

- These models require high quality historical data as the simulation is based on the previous trends. Accurate river flow forecasting with short period of river flow recoding is not achievable unless there are some other effective inputs data with good quality are available.

- Unlike process-based methods, they do not provide insight into the underlying hydrological processes in the catchment.

In this study, a number of CI based approaches are developed for river flow forecasting, using artificial neural networks, adaptive Neuro-fuzzy inference system and hybrid wavelet-CI techniques. More details on these CI approaches, are given in Chapter three.