Multi-step ahead prediction of lake water temperature using neural network and physically-based model

ABSTRACT

Deep learning (DL) is a powerful tool that has proven highly effective in many applications, but creating new deep learning models is becoming increasingly challenging. However, in some fields, such as fluid dynamics, theoretical models can help design powerful DL models. Based on the existing air2water (A2W) model, this paper proposes a hybrid neural network model, DL-A2W, which combines the long short-term memory (LSTM) neural network with the A2W model to predict lake water temperature. The DL-A2W model was established using the datasets of the UK Centre for Ecology & Hydrology, and the performance of the model was evaluated through three experiments. Compared with other models, the DL-A2W model has the lowest mean absolute error (MAE), mean absolute percent error (MAPE), root mean squared error (RMSE), and the highest Nash-Sutcliffe efficiency coefficient (NSC) at any given prediction step. The values of MAE, MAPE, RMSE and NSC of the DL-A2W model on the test set were 0.223–0.388, 1.946–3.296%, 0.375–0.647 and 0.985–0.995, respectively. The results show that the DL-A2W model has good generalization ability and portability, and can accurately perform multi-step ahead prediction of lake water temperature.

KEYWORDS:

• Air2water model
• deep learning
• lake water temperature
• multi-step ahead
• prediction

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data will be made available on reasonable request.

Notation

$a_i$	=	Scaling coefficient (–)
$f$	=	Activation function (–)
$k$	=	Number of ahead steps (–)
$L$	=	Sequence length (–)
$M$	=	Statistical index value (–)
$N$	=	Total sample size (–)
$t$	=	Time (d)
$t_{\mathrm{yr}}$	=	Duration of the year expressed in days (d)
$T_a$	=	Air temperature (°C)
$T_r$	=	Reference value for the deep lake water temperature (°C)
$T_w$	=	Lake water temperature (°C)