A Convolutional Neural Network-Weighted Cellular Automaton Model for the Fast Prediction of Urban Pluvial Flooding Processes

Abstract

Deep learning models demonstrate impressive performance in rapidly predicting urban floods, but there are still limitations in enhancing physical connectivity and interpretability. This study proposed an innovative modeling approach that integrates convolutional neural networks with weighted cellular automaton (CNN-WCA) to achieve the precise and rapid prediction of urban pluvial flooding processes and enhance the physical connectivity and reliability of modeling results. The study began by generating a rainfall-inundation dataset using WCA and LISFLOOD-FP, and the CNN-WCA model was trained using outputs from LISFLOOD-FP and WCA. Subsequently, the pre-trained model was applied to simulate the flood caused by the 20 July 2021 rainstorm in Zhengzhou City. The predicted inundation spatial distribution and depth by CNN-WCA closely aligned with those of LISFLOOD-FP, with the mean absolute error concentrated within 5 mm, and the prediction time of CNN-WCA was only 0.8% that of LISFLOOD-FP. The CNN-WCA model displays a strong capacity for accurately predicting changes in inundation depths within the study area and at susceptible points for urban flooding, with the Nash-Sutcliffe efficiency values of most flood-prone points exceeding 0.97. Furthermore, the physical connectivity of the inundation distribution predicted by CNN-WCA is better than that of the distribution obtained with a CNN. The CNN-WCA model with additional physical constraints exhibits a reduction of around 34% in instances of physical discontinuity compared to CNN. Our results prove that the CNN model with multiple physical constraints has significant potential to rapidly and accurately simulate urban flooding processes and improve the reliability of prediction.

Keywords

Convolutional neural networks / Physical continuity / Rapid prediction / Urban pluvial flooding processes / Weighted cellular automata

References

[1] Aldridge, T., O. Gunawan, R.J. Moore, S.J. Cole, and D. Price. 2016. A surface water flooding impact library for flood risk assessment. In Proceedings of the 3rd European Conference on Flood Risk Management (FLOODrisk 2016), 17–21 October 2016, Lyon, France.

[2] Bates PD, Horritt MS, Fewtrell TJ. A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling. Journal of Hydrology, 2010, 387(1–2): 33-45

[3] Beijing Institute of Municipal Engineering Design and Research Water supply and drainage design manual, 2004 2 Beijing: China Architecture and Building Publisher (in Chinese)

[4] Cea L, Garrido M, Puertas J. Experimental validation of two-dimensional depth-averaged models for forecasting rainfall-runoff from precipitation data in urban areas. Journal of Hydrology, 2010, 382(1–4): 88-102

[5] Changnon SA, Westcott NE. Heavy rainstorms in Chicago: INCREASING frequency, altered impacts, and future implications. JAWRA Journal of the American Water Resources Association, 2007, 38(5): 1467-1475

[6] Couclelis H. Cellular worlds: A framework for modeling micro-macro dynamics. Environment and Planning A, 1985, 17(5): 585-596

[7] Disaster Investigation Group of the State Council of China. 2022. Investigation report of the “7-20” extreme rainstorm disaster in Zhengzhou City, Henan (in Chinese).

[8] Donnelly J, Daneshkhah A, Abolfathi S. Physics-informed neural networks as surrogate models of hydrodynamic simulators. Science of the Total Environment, 2024, 912: 168814

[9] Dottori, F., and E. Todini. 2010. A 2D flood inundation model based on cellular automata approach. In Proceeedings of the XVIII International Conference on Computational Methods in Water Resources, 21–24 June 2010, Barcelona, Spain.

[10] Farsal, W., S. Anter, and M. Ramdani. 2018. Deep learning. In Proceedings of the 12th International Conference on Intelligent Systems: Theories and Applications, 24–25 October 2018, New York, USA.

[11] Fraehr N, Wang QJ, Wu W, Nathan R. Supercharging hydrodynamic inundation models for instant flood insight. Nature Water, 2023, 1(10): 835-843

[12] Fraehr N, Wang QJ, Wu W, Nathan R. Assessment of surrogate models for flood inundation: the physics-guided LSG model vs. state-of-the-art machine learning models. Water Research, 2024, 252: 121202

[13] Ghimire B, Chen AS, Guidolin M, Keedwell EC, Djordjević S, Savić DA. Formulation of a fast 2D urban pluvial flood model using a cellular automata approach. Journal of Hydroinformatics, 2013, 15(3): 676-686

[14] Goutte C, Gaussier E. Losada DE, Fernández-Luna JM. A probabilistic interpretation of precision, recall and F-score, with implication for evaluation. Advances in information retrieval: 27th European Conference on IR Research, ECIR 2005, Santiago de Compostela, Spain, March 21–23, 2005, Proceedings, 2005, Berlin: Springer 345-359

[15] Gu J, Wang Z, Kuen J, Ma L, Shahroudy A, Shuai B, Liu T, Wang X, et al. Recent advances in convolutional neural networks. Pattern Recognition, 2018, 77: 354-377

[16] Guha S, Jana RK, Sanyal MK. Artificial neural network approaches for disaster management: a literature review. International Journal of Disaster Risk Reduction, 2022, 81: 103276

[17] Guidolin M, Chen AS, Ghimire B, Keedwell EC, Djordjević S, Savić DA. A weighted cellular automata 2D inundation model for rapid flood analysis. Environmental Modelling & Software, 2016, 84: 378-394

[18] Guo Z, Leitão JP, Simões NE, Moosavi V. Data-driven flood emulation: speeding up urban flood predictions by deep convolutional neural networks. Journal of Flood Risk Management, 2020, 14(1): e12684

[19] Gupta HV, Kling H, Yilmaz KK, Martinez GF. Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. Journal of Hydrology, 2009, 377(1–2): 80-91

[20] Han Y, Wu Z, Guo Y, Hu Y. Comparative study on Chicago rainstorm pattern and urban disastrous precipitation. Yangtze River, 2022, 53(5): 35-40

[21] Itami RM. Simulating spatial dynamics: Cellular automata theory. Landscape and Urban Planning, 1994, 30(1–2): 27-47

[22] Kabir S, Patidar S, Xia X, Liang Q, Neal J, Pender G. A deep convolutional neural network model for rapid prediction of fluvial flood inundation. Journal of Hydrology, 2020, 590: 125481

[23] Keifer CJ, Chu HH. Synthetic storm pattern for drainage design. Journal of the Hydraulics Division, 1957, 83(4): 1332-1325

[24] Kiranyaz, S., T. Ince, R. Hamila, and M. Gabbouj. 2015. Convolutional neural networks for patient-specific ECG classification. In Proceedings of the 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 25–29 August 2015, Milan, Italy.

[25] Leandro J, Chen AS, Djordjević S, Savić DA. Comparison of 1D/1D and 1D/2D coupled (sewer/surface) hydraulic models for urban flood simulation. Journal of Hydraulic Engineering, 2009, 135(6): 495-504

[26] LeCun Y, Bengio Y. Arbib MA. Convolutional networks for images, speech, and time series. The handbook of brain theory and neural networks, 1998, Cambridge, MA: MIT Press 255-258

[27] LeCun Y, Bengio Y, Hinton G. Deep learning. Nature, 2015, 521(7553): 436-444

[28] Liao Y, Wang Z, Chen X, Lai C. Fast simulation and prediction of urban pluvial floods using a deep convolutional neural network model. Journal of Hydrology, 2023, 624: 129945

[29] Lin L, Wu Z, Liang Q. Urban flood susceptibility analysis using a GIS-based multi-criteria analysis framework. Natural Hazards, 2019, 97(2): 455-475

[30] Löwe R, Böhm J, Jensen DG, Leandro J, Rasmussen SH. U-FLOOD–Topographic deep learning for predicting urban pluvial flood water depth. Journal of Hydrology, 2021, 603: 126898

[31] Luan Q, Fu X, Song C, Wang H, Liu J, Wang Y. Runoff effect evaluation of LID through SWMM in typical mountainous, low-lying urban areas: a case study in China. Water, 2017, 9(6): 439

[32] Mishra C, Gupta D. Deep machine learning and neural networks: an overview. IAES International Journal of Artificial Intelligence, 2017, 6(2): 66

[33] Nandi S, Reddy MJ. An integrated approach to streamflow estimation and flood inundation mapping using VIC. RAPID and LISFLOOD-FP. Journal of Hydrology, 2022, 610: 127842

[34] Neal J, Keef C, Bates P, Beven K, Leedal D. Probabilistic flood risk mapping including spatial dependence. Hydrological Processes, 2013, 27(9): 1349-1363

[35] Neal J, Schumann G, Fewtrell T, Budimir M, Bates P, Mason D. Evaluating a new LISFLOOD-FP formulation with data from the summer 2007 floods in Tewkesbury, UK. Journal of Flood Risk Management, 2011, 4(2): 88-95

[36] Palla A, Colli M, Candela A, Aronica G, Lanza L. Pluvial flooding in urban areas: the role of surface drainage efficiency. Journal of Flood Risk Management, 2018, 11: S663-S676

[37] Reichstein M, Camps-Valls G, Stevens B, Jung M, Denzler J, Carvalhais N, Prabhat F. Deep learning and process understanding for data-driven Earth system science. Nature, 2019, 566(7743): 195-204

[38] Rosbjerg D, Madsen H. Initial design of urban drainage systems for extreme rainfall events using intensity-duration-area (IDA) curves and Chicago design storms (CDS). Hydrological Sciences Journal, 2019, 64(12): 1397-1403

[39] Roy S, Bose A, Singha N, Basak D, Chowdhury IR. Urban waterlogging risk as an undervalued environmental challenge: An integrated MCDA-GIS based modeling approach. Environmental Challenges, 2021, 4: 100194

[40] Saleh F, Ducharne A, Flipo N, Oudin L, Ledoux E. Impact of river bed morphology on discharge and water levels simulated by a 1D Saint-Venant hydraulic model at regional scale. Journal of Hydrology, 2013, 476: 169-177

[41] Sampson CC, Smith AM, Bates PD, Neal JC, Alfieri L, Freer JE. A high-resolution global flood hazard model. Water Resources Research, 2015, 51(9): 7358-7381

[42] Savić DA, Djordjević S, Keedwell EC, Guidolin M, Chen AS, Ghimire B. Formulation of a fast 2D urban pluvial flood model using a cellular automata approach. Journal of Hydroinformatics, 2013, 15(3): 676-686

[43] Schumann GJP, Stampoulis D, Smith AM, Sampson CC, Andreadis KM, Neal JC, Bates PD. Rethinking flood hazard at the global scale. Geophysical Research Letters, 2016, 43(19): 10249-10256

[44] Sidek LM, Jaafar AS, Majid WHAWA, Basri H, Marufuzzaman M, Fared MM, Moon WCh. High-resolution hydrological-hydraulic modeling of urban floods using InfoWorks ICM. Sustainability, 2021, 13(18): 10259

[45] Situ Z, Wang Q, Teng S, Feng W, Chen G, Zhou Q, Fu G. Improving urban flood prediction using LSTM-DeepLabv3+ and Bayesian optimization with spatiotemporal feature fusion. Journal of Hydrology, 2024, 630: 130743

[46] Trong NG, Quang PN, Cuong NV, Le HA, Nguyen HL, Tien Bui D. Spatial prediction of fluvial flood in high-frequency tropical cyclone area using TensorFlow 1D-convolution neural networks and geospatial data. Remote Sensing, 2023, 15(22): 5429

[47] Wang H, Hu Y, Guo Y, Wu Z, Yan D. Urban flood forecasting based on the coupling of numerical weather model and stormwater model: a case study of Zhengzhou City. Journal of Hydrology: Regional Studies, 2022, 39: 100985

[48] Wang H-W, Lin G-F, Hsu C-T, Wu S-J, Tfwala SS. Long-term temporal flood predictions made using convolutional neural networks. Water, 2022, 14(24): 4134

[49] Weesakul, U., W. Chaowiwat, M. Mudassar Rehan, and S. Weesakul. 2017. Modification of a design storm pattern for urban drainage systems considering the impact of climate change. Engineering & Applied Science Research 44(3). https://doi.org/10.14456/easr.2017.24.

[50] Willmott CJ, Matsuura K. Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Climate Research, 2005, 30(1): 79-82

[51] Wing OEJ, Bates PD, Smith AM, Sampson CC, Johnson KA, Fargione J, Morefield P. Estimates of present and future flood risk in the conterminous United States. Environmental Research Letters, 2018, 13(3): 034023

[52] Wolfram S. Cellular automata as models of complexity. Nature, 1984, 311(5985): 419-424

[53] Xu G, Ren T, Chen Y, Che W. A one-dimensional CNN-LSTM model for epileptic seizure recognition using EEG signal analysis. Frontiers in Neuroscience, 2020, 14: 578126

[54] Yan X, Xu K, Feng W, Chen J. A rapid prediction model of urban flood inundation in a high-risk area coupling machine learning and numerical simulation approaches. International Journal of Disaster Risk Science, 2021, 12(6): 903-918

[55] Youssef AM, Pradhan B, Dikshit A, Al-Katheri MM, Matar SS, Mahdi AM. Landslide susceptibility mapping using CNN-1D and 2D deep learning algorithms: comparison of their performance at Asir Region, KSA. Bulletin of Engineering Geology and the Environment, 2022, 81(4): 165

[56] Yu H, Zhao Y, Fu Y, Li L. Spatiotemporal variance assessment of urban rainstorm waterlogging affected by impervious surface expansion: a case study of Guangzhou. China Sustainability, 2018, 10(10): 3761

[57] Zhang W, Liu Y, Tang W, Chen S, Xie W. Rapid spatio-temporal prediction of coastal urban floods based on deep learning approaches. Urban Climate, 2023, 52: 101716

[58] Zhang Z, Tian J, Huang W, Yin L, Zheng W, Liu S. A haze prediction method based on one-dimensional convolutional neural network. Atmosphere, 2021, 12(10): 1327

[59] Zhang Q, Wu Z, Zhang H, Dalla Fontana G, Tarolli P. Identifying dominant factors of waterlogging events in metropolitan coastal cities: the case study of Guangzhou. China. Journal of Environmental Management, 2020, 271: 110951

[60] Zhao G, Pang B, Xu Z, Peng D, Zuo D. Urban flood susceptibility assessment based on convolutional neural networks. Journal of Hydrology, 2020, 590: 125235

[61] Zhao G, Xu Z, Pang B, Tu T, Xu L, Du L. An enhanced inundation method for urban flood hazard mapping at the large catchment scale. Journal of Hydrology, 2019, 571: 873-882

[62] Zheng X, Duan C, Chen Y, Li R, Wu Z. Disaster loss calculation method of urban flood bimodal data fusion based on remote sensing and text. Journal of Hydrology: Regional Studies, 2023, 47: 101410

[63] Zounemat-Kermani M, Batelaan O, Fadaee M, Hinkelmann R. Ensemble machine learning paradigms in hydrology: A review. Journal of Hydrology, 2021, 598: 126266