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Lake water-level fluctuation forecasting using machine learning models: a systematic review

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Abstract

Lake water-level fluctuation is a complex and dynamic process, characterized by high stochasticity and nonlinearity, and difficult to model and forecast. In recent years, applications of machine learning (ML) models have yielded substantial progress in forecasting lake water-level fluctuations. This paper presents a comprehensive review of the applications of ML models for modeling water-level dynamics in lakes. Among the many existing ML models, seven popular ML model types are reviewed: (1) artificial neural network (ANN); (2) support vector machine (SVM); (3) artificial neuro-fuzzy inference system (ANFIS); (4) hybrid models, such as hybrid wavelet-artificial neural network (WA-ANN) model, hybrid wavelet-artificial neuro-fuzzy inference system (WA-ANFIS) model, and hybrid wavelet-support vector machine (WA-SVM) model; (5) evolutionary models, such as gene expression programming (GEP) and genetic programming (GP); (6) extreme learning machine (ELM); and (7) deep learning (DL). Model inputs, data split, model performance criteria, and model inter-comparison as well as the associated issues are discussed. The advantages and limitations of the established ML models are also discussed. Some specific directions for future research are also offered. This review provides a new vision for hydrologists and water resources planners for sustainable management of lakes.

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Abbreviations

ADP:

Absolute deviation percent

AI:

Artificial intelligence

AIC:

Akaike information criterion

ANFIS:

Adaptive neuro-fuzzy inference system

ANN:

Artificial neural network

AR:

Autoregressive

ARMA:

Autoregressive moving average

BNN:

Bayesian neural network

CC:

Correlation coefficient

DL:

Deep learning

ELM:

Extreme learning machine

ERM:

Empirical risk minimization

ESN:

Echo state network

FA:

Firefly algorithm

FFNN:

Feed-forward neural network

GAANN:

Genetic algorithm artificial neural network

GEP:

Gene expression programming

GMDH:

Group method of data handling

GP:

Genetic programming

KGE:

Kling–Gupta efficiency

LLNF:

Local linear neuro-fuzzy

LMI:

Legate and McCabe’s index

LSTM:

Long short-term memory

MA:

Moving average

MAE:

Mean absolute error

MAPE:

Mean absolute percentage error

ML:

Machine learning

MLPNN:

Multilayer perceptron neural network

MLPNN-FA:

Multilayer perceptron neural network coupled with firefly algorithm

MSE:

Mean squared error

MSRE:

Mean squared relative error

MS4E:

Higher order mean squared error

NMSE:

Normalized mean squared error

NRMSD:

Normalized root mean squared deviation

NSC:

Nash–Sutcliffe coefficient

NWN:

Neural wavelet network

PSO:

Particle swarm optimization

PSO-ANN:

Artificial neural networks based on particle swarm optimization

R 2 :

Coefficient of determination

RAE:

Relative absolute error

RBNN:

Radial basis neural network

RF:

Random forest

RL:

Residual

RMAE:

Relative mean absolute error

RMSE:

Root mean squared error

\( \overline{\mathrm{RMSE}} \) :

Relative root mean squared error

RNN:

Recurrent neural network

RRSE:

Root relative squared error

RT:

Random tree

SBC:

Schwarz Bayesian criterion

SCC:

Squared correlation coefficient

SD:

Standard deviation

SEP:

Standard error prediction

SI:

Scatter index

SRM:

Structural risk minimization

SS:

Skill score

SVM:

Support vector machine

SVM-FA:

Support vector machine coupled with firefly algorithm

SY:

Similarity

VAF:

Variance accounted for

WA:

Wavelet analysis

WA-ANFIS:

Hybrid wavelet-artificial neural fuzzy inference system

WA-ANN:

Hybrid wavelet-artificial neural network

WA-MLPNN:

Hybrid wavelet-multilayer perceptron neural network

WA-SVM:

Hybrid wavelet-support vector machine

WDDFF:

Wavelet data-driven forecasting framework

WI:

Willmott’s index of agreement

WL:

Water level

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Funding

This work was jointly funded by the National Key R&D Program of China (2018YFC0407203) and China Postdoctoral Science Foundation (2018M640499).

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Authors and Affiliations

  1. College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou, 225127, China

    Senlin Zhu & Qingfeng Ji

  2. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing, 210029, China

    Senlin Zhu & Jiangyu Dai

  3. Division of Construction Engineering and Management, Purdue University, West Lafayette, IN, 47907, USA

    Hongfang Lu

  4. Department of Hydrology and Water Management, Adam Mickiewicz University, Krygowskiego 10, 61-680, Poznan, Poland

    Mariusz Ptak

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  1. Senlin Zhu
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Zhu, S., Lu, H., Ptak, M. et al. Lake water-level fluctuation forecasting using machine learning models: a systematic review. Environ Sci Pollut Res 27, 44807–44819 (2020). https://doi.org/10.1007/s11356-020-10917-7

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