Variables Determination of AI-based Models

In the development of AI-based models, determining the adequate input and output variables is a key issue to achieve high performance models. In models of Q prediction, model variables are commonly selected based on a priori knowledge of river basin hydrology, which provides initial indications of potential inputs and outputs (Bowden et al., 2005; Maier & Dandy, 2000). The SF in tropical rivers can be characterized as the function of several influential variables, including RF, WL and the physical characteristics of the river (Firat, 2007).

In this research, the main objective is to predict Q of downstream area from the hourly WL and RF records of upstream station. Thus, the hourly records of WL and RF of upstream stations were employed as input variables (independent variables) while, those of SF data in downstream station was used as output variable (dependent variables). The Equation 3.1 presents the relationship between the Q and influential variables:

Q_{( )}= f(X( )) + e (3.1)

where, Q(t+Lt) represents ahead hourly stream flow; Lt represents the lag time between

upstream and downstream stations; X(t) is the input vector, which include the input

variables i.e. RF and/or WL; e is the random error.

Three scenarios in selecting the input variables of the AI-based models were considered. In the first scenario, only the RF records of upstream stations were employed as input variables. In the second scenario, only the WL records of upstream stations were

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employed as input variables while in the third scenario, both of RF and WL records of upstream stations were employed as input variables.

In these three scenarios, two input vectors were applied. In the first, the single antecedent record of upstream stations was used. In the second, the average of three antecedent records was used. Given six input vectors, every one of them includes deferent combinations of input and output variables.

The single antecedent record of Q in the downstream station is considered another input variable of AI-based model that needed to predicts the Q for a head period equal to the Lt between the upstream and downstream stations. The estimated Lt between the upstream and downstream stations determines the Lag intervals between the input and output variables for the six input vectors. Using these input vectors, six combinations of input and out variables has been generated as shown in Table 3.7.

Table 3.7: Input vectors of the AI-based models

Where, Rfu(t) represents a single records of hourly rainfall intensity at Ulu Yam station,

Rfu(ŧ) represents the average of three antecedent records of hourly rainfall intensity at Ulu

No. Input Vector X(t) Output

1 Rfu(t), Rfb(t), Rfk(t), Rfa(t), Q(t) Q(t+Lt)

2 Rfu(ŧ), Rfb(ŧ), Rfk(ŧ), Rfa(ŧ), Q(t) Q(t+Lt)

3 Wlu(t), Wlb(t), Wlk(t), Wla(t), Q (t) Q(t+Lt)

4 Wlu(ŧ), Wlb(ŧ), Wlk(ŧ), Wla(ŧ), Q (t) Q(t+Lt)

5 Wlu(t), Wlb(t), Wlk(t), Wla(t), Rfu(t), Rfb(t), Rfk(t), Rfa(t), Q(t) Q(t+Lt)

6 Wlu(ŧ), Wlb(ŧ), Wlk(ŧ), Wla(ŧ), Rfu(ŧ), Rfb(ŧ), Rfk(ŧ), Rfa(ŧ), Q(t) Q(t+Lt)

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Yam station, Wlu(t) represents a single records of water level at Ulu Yam station and Wlu(ŧ)

represents the average of three antecedent records of hourly rainfall at Ulu Yam station. Rfb(t) represents a single records of hourly rainfall intensity at Batang Kali station, Rfb(ŧ)

represents the average of three antecedent records of hourly rainfall intensity at Batang Kali station, Wlb(t) represents a single records of water level at Batang Kali station and

Wlb(ŧ) represents the average of three antecedent records of hourly rainfall at Batang Kali

station.

Rfk(t) represents a single records of hourly rainfall intensity at Kerling station, Rfk(ŧ)

represents the average of three antecedent records of hourly rainfall intensity at Kerling station, Wlk(t) represents a single records of water level at Kerling station and Wlk(ŧ)

represents the average of three antecedent records of hourly rainfall at Kerling station. Rfa(t) represents a single records of hourly rainfall intensity at Ampang Pecah station,

Rfa(ŧ) represents the average of three antecedent records of hourly rainfall intensity at

Ampang Pecah station, Wla(t) represents a single records of water level at Ampang Pecah

station and Wla(ŧ) represents the average of three antecedent records of hourly rainfall at

Ampang Pecah station.

Q(t) represents hourly stream flow at Rantau Panjang station and Q(t+Lt) represents ahead

hourly stream flow at Rantau Panjang station with prediction time equal to Lt.

3.6.2 Estimation of the Lag Intervals between the Input and Output Variables

In determining the input variables of AI-based models to predict Q, the antecedent records of WL and RF that significantly affect the predicted Q should be estimated to select the most accurate lag intervals between the input and output variables (Sudheer et al., 2002).

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These records could be accurately selected based on the results of Lt estimation between upstream and downstream stations as the hourly records of WL and RF at the upstream station represent the input variables of the AI-based model, whereas Q from the downstream station represent the output variables of the AI-based model.

The Lt between the upstream and downstream station was estimated by three approaches i.e. empirical formulas, CCA and NGA. The results of Lt are indicative of the potential lag intervals between the input and output variables for the AI-based models to predict real-time Q in the downstream area. Both of second and third approaches to estimate Lt, were employed in the selection of the lag intervals between the input and output variables of AI-based models, while, the first approach is performed only to provide an initial approximation of Lt between the upstream and downstream stations.