Capabilities of deep learning models on learning physical relationships: Case of rainfall-runoff modeling with LSTM

Kazuki Yokoo; Kei Ishida; Ali Ercan; Tongbi Tu; Takeyoshi Nagasato; Masato Kiyama; Motoki Amagasaki

doi:10.1016/j.scitotenv.2021.149876

Capabilities of deep learning models on learning physical relationships: Case of rainfall-runoff modeling with LSTM

Sci Total Environ. 2022 Jan 1:802:149876. doi: 10.1016/j.scitotenv.2021.149876. Epub 2021 Aug 25.

Authors

Kazuki Yokoo¹, Kei Ishida², Ali Ercan³, Tongbi Tu⁴, Takeyoshi Nagasato⁵, Masato Kiyama⁶, Motoki Amagasaki⁷

Affiliations

¹ Graduated School of Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan. Electronic address: 207d2121@st.kumamoto-u.ac.jp.
² International Research Organization for Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan; Center for Water Cycle, Marine Environment, and Disaster Management, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan. Electronic address: keiishida@kumamoto-u.ac.jp.
³ Department of Civil and Environmental Engineering, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA.. Electronic address: aercan@ucdavis.edu.
⁴ School of Civil Engineering, Sun Yat-Sen University, Guangzhou 510275, China. Electronic address: tutb@mail.sysu.edu.cn.
⁵ Graduated School of Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan. Electronic address: 217d8320@st.kumamoto-u.ac.jp.
⁶ Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan. Electronic address: masato@cs.kumamoto-u.ac.jp.
⁷ Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan. Electronic address: amagasaki@cs.kumamoto-u.ac.jp.

PMID: 34464810
DOI: 10.1016/j.scitotenv.2021.149876

Abstract

This study investigates the relationships which deep learning methods can identify between the input and output data. As a case study, rainfall-runoff modeling in a snow-dominated watershed by means of a long short-term memory (LSTM) network is selected. Daily precipitation and mean air temperature were used as model input to estimate daily flow discharge. After model training and verification, two experimental simulations were conducted with hypothetical inputs instead of observed meteorological data to clarify the response of the trained model to the inputs. The first numerical experiment showed that even without input precipitation, the trained model generated flow discharge, particularly winter low flow and high flow during the snow melting period. The effects of warmer and colder conditions on the flow discharge were also replicated by the trained model without precipitation. Additionally, the model reflected only 17-39% of the total precipitation mass during the snow accumulation period in the total annual flow discharge, revealing a strong lack of water mass conservation. The results of this study indicated that a deep learning method may not properly learn the explicit physical relationships between input and target variables, although they are still capable of maintaining strong goodness-of-fit results.

Keywords: Long short-term memory (LSTM) network; Physical relationship; Rainfall-runoff modeling.

MeSH terms

Deep Learning*
Seasons
Snow
Temperature