Co ombining pre g machin ediction ne learni of tidal ing with

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Co ombiningg machinne learniing withh computtational hydrody h ynamics for Co ombiningg machinne learniing withh computtational hydrody h ynamics for preediction tidal surge innundation n at estu poorts IUTAM of Symposium on Storm Surge Modelling anduarine Forecasting preediction of tidal surge innundation n at estu uarine poorts a a b Jonn French Robert Mawdsley Takustatus Fujiy yama mal Achuth hanbb a*,prediction: a, T b, Kam Storm surge present and future challenges Jonn French *, Robert Mawdsley , T Taku Fujiy yama , Kam mal Achuthhan a

Coastal C and Estuarine Research Unnit, UCL Departm ment of Geographhy, University Co ollege London, Go ower Street, Londdon, WC1E 6BT, UK a,b, hy, c Gow Coastal CUCL and Estuat rine Research Unnit, UCLand Departm ment of Geograph UniversityCol Co ollege London, Go ower Street,Londo Londdon, WC1E6BT, 6BT,UK U Department of Civil Environm mental Geom matic Engineering g, University lege London, wer Street, on, WC1E UUK b UCL U Departmentt of Civil Environm mental and Geom matic Engineeringg, University College London, Gow wer Street, Londoon, WC1E 6BT, UK U

ab

Jiachun Li *, Bingchuan Nie

a

Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China. b School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China. c Absttract School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China.

Absttract

Accurrate forecasts of extreme storm suurge water levels are vital for operrators of major po orts. Existing reg gional tide-surge m models perform well w at Accur rate coast forecasts of extreme stormres suurge water levels areforecasts vital for oper of for major po Existing reg gional m models well w in at the op pen but the ir low spatial lessrators reliable ports sorts. located in estua ries. Intide-surge Decembeer 2013, perform a tidal su urge olution makes their Abstract the op pen coast but the low spatial resolution eir forecasts reliable for ports smmingham located in in estua In Decembe er on 2013, tidal su in makes thears period of 760 ye the North N Sea with an irestimated return partially less floooded the Port of Im the eries. Humber estuaryy, the aUK east turge coast. estimated return of weeks 760 yeears the North Nage toSea with inf anfrastructure partially floo Portchain of Im mmingham in the edHumber estuary on the UK easttgcoast. Dama critical causeedperiod several vvital the supply ns and highlighte a need for addiy, itional forecasting tools of disruption to oded Insup the review, the most pessimistic ofwe the globe in Artifi history addressed we present caused by storm surges. Dama agecurrent to critical infal frastructure causeed weeks vvitalare supply chain nswhen and(ANNs) highlighte agenerate need impacts forbetter addiritional forecasting tools disruption to ficial to pplement nationa surge warnings. . Inseveral thisevents paper, eofshow that Neural Netw works cadn severe short-term forecgasts of previous decades, great progresses inImmingh storm we surge have made. As a result, people developed a number of numerical toDuring sup pplement nationa al warnings. In this paper, eam show ficial Neural works (ANNs) cate n have generate better short-term forec of extrem me water levels aat surge estuarine ports... Using asmodeling athat test Artifi case, , anbeen ANN is Netw conf figured to simulat the tidal surger residual using an nasts input software such as SPLASH, SLOSH etc. implemented operational byatmospheric virtue of powerful supercomputers the help extrem water levels aat estuarine ports. Using Immingh as aroutine test case, , an ANNforecast is conf to simulat surge residualwith using an nomical inputof vecto ormethat includes ob bservations of su.rge atand distant tideeam gauges in NW S Scotland, wind and afigured pressure, pte the tidal and the predicted astrono meteorological satellites and sensors as time-series, verification However, storm surge as and killer from theapressure, is still human being and vecto or includes obbservations ofsur surge rge at distant tide e gauges inwith NWth S Scotland, wind a tide, atmospheric psea andthreatening thedition predicted tide at a that Immingham. T The forecast combined ctools. he astronomical provides boundary condi for aastrono local lomical highexerting enormous impacts on human due to economic population increase fastAlthou urbanization. Tocondi mitigate the storm tide at a Immingham. T The forecast sur rge time-series, combined cextent with th he astronomical provides augh boundary dition for effects a of local l ANN highresolu ution 2D hydrody ynamic model tha atsociety predicts flood e andgrowth, damag ge potential acros sstide, theand port. the forecastin ng horizon theeof surge hazards, research on (IRDR) asand an damag ICSU program is or put on agenda. challenging issues concerned resolu ution ynamic model thamingham atdisaster predictsrisk flood ean accuracy ge potential acros ss port. Althou ugh the forecastin ng model horizon of at thefar ef such ANN is lim mited, 62Dtohydrody 24integrated hour r forecasts at Imm achieve eextent com mparable to bet tterthe than theThe UKmost national tide-surgge and lessas abrupt variation in TC’s track and intensity, comprehensive study on the consequences of storm surge and the effects of climate change on risk is lim mited, 6 to 24 hour r forecasts at Imm mingham achieve e an accuracy com mparable to or bet tter than the UK national tide-surg ge model and at far f less comp putational cost. U Use of a local ratther than a largeer regional hydroodynamic model means that potential inundation can be simulated d very estimation are emphasized. In addition, it is of paramount importance for coastal developing countries to set up forecast and warning system and comp putational cost. U Use of a local rat ther than a large er regional hydro odynamic model ntial inundation can be simulated d very means that pote rapidlly at high spatiall resolution. Valiidation against th he 2013 surge shoows that the hyb brid ANN-hydrod dynamic model ggenerates realisticc flood reduce affected areas. rapidl ly that atvulnerability high lofresolution. Valiidation against th he 2013 surge shoows that the hyb brid ANN-hydrod dynamic model ggenerates realisticc flood exten nts can spatial inform m port resilience p planning. exten nts that can inform m port resilience planning. p

2016The TheAuthor Authors. Publishedby by ElsevierB.V. B.V. 017 rs. Published y Elsevier ©©20 ©Selection 2017 Theand Authors. Published by Elsevier B.V. peer-review under responsibility of IUTAM Symposium on Storm Surge Modelling and Forecasting. 017 The Author rs. Published by y Elsevier B.V. © 20 Peer-review rresponsibility of organizing of ommittee the IUTAM posium Storm m Surge lling and Forecaasting. co Selection andunder peer-review under responsibility IUTAM of Symposium on Symp Storm Surgeon Modelling and Model Forecasting. Peer--review under rresponsibility of organizing co ommittee of the IUTAM Symp posium on Storm m Surge Modellling and Forecaasting. Keywords: Stormsurg surge, Tropical cyclone; Extratropical cyclone; SPLASH, SLOSH; Risk analysis;planni IRDR Keyw words: storm e; extreme water levels; Artificial Neural Network k; Telemac; ports; resilience ing Keyw words: storm surge; extreme water levels; Artificial Neural Networkk; Telemac; ports; resilience planniing

1. Introduction Storm surge, an extraordinary sea surface elevation induced by atmospheric disturbance (wind and atmospheric pressure), is regarded as a most catastrophic natural disaster. According to long term statistical analysis, total death 1 toll tothor. 1.5Tel.: million * Corresponding C amounted aut +44 200and 7679property 0580; fax:losses +44 20 exceeded 7679 05665. hundred billions USD globally since 1875 . They could * Corresponding C Tel.: +44 200k 7679 0580; fax: +44 20 7679 05665. E-mail E address:aut j.fthor. [email protected] E-mail E address: [email protected]

2210--9838 © 2017 Thhe Authors. Publisshed by Elsevier B.V. 22102017resp Thhe Authors. of Publis shed by Elsevier B.V. Peer-r-9838 review©under ponsibility orgganizing committee of the IUTAM M Symposium on Storm Surge Modelling and Foreccasting. Peer-r review under resp ponsibility of orgganizing committ ee +86-010-6256-0914 of the IUTAM M Symposium on Storm Surge Modelling and Foreccasting. * Corresponding author. Tel.: +86-010-8254-4203; fax: E-mail address: [email protected]

2210-9838 © 2017 The Authors. Published by Elsevier B.V. Selection and peer-review under responsibility of IUTAM Symposium on Storm Surge Modelling and Forecasting. 2210-9838 © 2017 The Authors. Published by Elsevier B.V. Selection and peer-review under responsibility of IUTAM Symposium on Storm Surge Modelling and Forecasting. 10.1016/j.piutam.2017.09.005

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1. Introduction Effective E preddiction of tidall storm surgess is important for the operaators of major ports since thheir infrastructure is necessarily locateed close to seaa level. Inund dation of port ffacilities can damage d critical elements off this infrastru ucture, nificantly disrrupt port operrations and caause downstreeam impacts on supply ch hains. The rissk of inundatiion by sign storrm surge is typpically estimaated from peak k water levels computed fro om extreme vaalue analysis oof historic records1,2. Sho ort-term foreccasts of indivvidual flood events are ddelivered by regional r oceaan models, foorced by tidaal and metteorological innputs, which predict the sp pace-time evoolution of thee surge component of wateer level3. How wever, extrreme value annalysis is senssitive to the assumptions a m made2, and prrovides no infformation on spatial variattion in floo od extent, deppth and duratioon in large po ort facilities. A Also, whilst regional r tide-ssurge models pperform well at the opeen coast, their low spatial reesolution (typiically 1 to 10 kkm) limits forrecast accuracy for ports loccated in estuarries. As A part of a N NERC Enviroonmental Risk ks to Infrastruucture Innovaation Programme project, w we are investigating metthods for the generation off better storm surge forecassts to inform resilience plaanning by opeerators of the major Norrth Sea ports aalong the UK east coast (Fig. 1a). Of parrticular importtance is the Po ort of Imminggham in the Hu umber estu uary. Imminghham is the laargest bulk cargo port in the UK and handles flow ws of coal annd biomass th hat are imp portant for pow wer generationn. The North Sea tidal surgge of Decemb ber 2013 was larger l at Immi mingham than that t of the historic storm m of 1953, witth an estimateed return periood of 760 yearrs (Fig. 1b). The T 2013 evennt partly flood ded the mage to port annd rail transpo ort infrastructuure and disrup pting operations for severall weeks. portt, causing dam

Fig. 1. (a) Locatiion of Port of Imm mingham, UK, an nd of observationn locations used in n the generation of o ANN input vecctors; (b) recurren nce intervals for extreme water leevels1 for selected d North Sea portss, including Januaary 1953 and December 2013 storm m surge events.

In I this paper, we present a hybrid apprroach to storm m surge foreccasting and modelling m that combines maachine learrning with com mputational hydrodynamic h c modelling. A data-driven n Artificial Neeural Networkk (ANN) is used u to

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forecast the surge component of water level at a port of interest based on the observed far-field tidal surge, regional meteorological observations and the predicted astronomical tide. The forecast surge is combined with the predicted tide to generate a total water level series with which to force a numerical hydrodynamic model of inundation within the port. The ANN-generated local water-level boundary condition allows simulation of inundation at a high spatial resolution without the need for a larger coastal shelf model. This hybrid surge forecasting and modelling system can be run almost in real-time as a cost-effective supplement to existing national storm surge warnings and forecasts. 2. Approach 2.1. Artificial Neural Network implementation An Artificial Neural Network (ANN) is a massively parallel computational architecture that is inspired by and shares some of the operational characteristics of biological neural networks within the human brain4. Of particular importance for our problem are networks designed for supervised training in which relationships between a data and a parameter domain are learned given sufficient training data. Specifically, we use a feed-forward network architecture (Fig. 2a) in combination with an error back-propagation algorithm5 to discern complex non-linear mappings between time-series for a set of metocean variables that contain useful information (the input vector or ‘layer’) and a target time-series of the surge component of water level at the location of interest (the ‘output layer’). The goal of the ANN6 is to generalize a relationship of the form

Ym  f  X n 

(1)

where X is an n-dimensional input vector consisting of variables x1, ..., xi, ..., xn; and Y is vector consisting of the target variables of interest y1, . . . , yi, . . . , ym (in our case, m = 1 as we have only a single target, the surge residual at the port of interest). Each neuron (Fig. 2b) operates according to an activation function given, for the jth node, by

y j  f  X W j  b j 

(2)

where Wj is the vector of input weights and bj a bias weight for node j. There are various options for the choice of the activation function, f in (2). One of the more widely used is the log-sigmoid function, a bounded, monotonic, nondecreasing function that provides a smooth nonlinear output response. A supervised ANN makes use of a suitably large set of paired input and output data values to guide a training process that finds an optimal set of weights and biases. Selection of suitable inputs must be guided by fundamental understanding of the system being modelled but also involves considerable trial and error. Other studies have demonstrated the potential of ANN to predict and forecast tidal and surge water levels when driven by observations from nearby tide gauges and metocean data such as atmospheric pressure and wind stress(e.g. 7,8). In the case of the North Sea, surges typically evolve along a southerly track and it seems reasonable to expect that we should see useful information contained in prior observations at tide gauges in NW Scotland (Fig. 1a) as well as wind and pressure fields. Surge-tide interaction is important in the North Sea and so the predicted astronomical tide is also a relevant input variable. The predictive value of the far-field ‘external’ surge is demonstrated by Fig. 3, which shows that the observed tidal surge residuals at Stornoway, Kinlochbervie and Ullapool (Fig. 1a) exhibit a maximum correlation with the surge at Immingham at a lag of about -18 to -24 hours. Trial and error sensitivity analysis resulted in a final input vector that included the observed surge at Kinlochbervie, together with the wind stress and atmospheric pressure at Foula and (more locally) Donna Nook, and the predicted tide at Immingham. Preceding observations of the surge residual at Immingham were also included to capture the occurrence of larger negative surges that are often seen to precede the larger positive surges. Inputs were subject to a range of lags to generate 6, 12, 18 and 24-hour forecasts of the surge residual at Immingham. ANN models were implemented using routines in the Matlab Neural Network Toolbox (Matlab release R16a; www.mathworks.com). The input vector was normalized from 0 to 1 and divided into training, validation and test datasets in the ratio 70:15:15. A log-sigmoid function was used between the input and hidden layers and a linear

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funcction betweenn the hidden annd output layeers. We use a single hidden n layer with a number n of neuurons guided by b the sizee of the probleem (number off inputs and observations avvailable for training) and th he need to avooid over-fitting g.

Fig. 2. (a) Definition sketch of feed-foorward network architecture a with eerror back-propag gation; (b) config guration of weight hted inputs and bias for a node within tthe hidden layer.

Fig.. 3. Correlogramss showing the lagged correlation between tidal surgge residual for varrious tide gauges and Immingham m. Analysis is perfformed for each year of dataa available (post-11950s). Dots show w lag at which peeak correlation occcurs in each yearr. Of significancee here are the -18 to -24 hour lags for tide gaug ges in NW Scotlaand (Stornoway, Kinlochbervie, K Ulllapool).

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2.2. Hydrodynamiic model impllementation Hydrodynamic H c computationns of surge inu undation withiin the port werre performed using the opeen source Teleemac2D code c (www.oppen-telemac.oorg). Telemac--2D9 solves thhe depth-averaaged 2D shallo ow water equaations given by b    h  u . grad h   h div v u   0 t  

(3)

   u   Z 1  u . grad u    g  Fx  div  h vT grad u  h t x  

(4)

   v   Z 1  u . grad v    g  Fy  div hvvT grad v  t y h  

(5)

pth, Z the free surface elevat ation, and t tim me. Fx wherre u and v are the flow veloocity in x and y directions, h is water dep and Fy are source terms to repreesent boundarry friction, vT iis an eddy visscosity and g is the gravitatiional accelerattion. Equations E (3) - (5) are solveed using a finite element disscretization on n an unstructu ured triangularr mesh. The model m dom main covers thee entire frontaage of the portt and extends landward to include i the top pography of th the enclosing flood com mpartment. Thee minimum element e size is about 2 m, sufficient to resolve the laarger structurees within the port. Terrrain was modeelled using airrborne lidar data d (0.25 to 2 m horizontaal interval). Prreliminary Tellemac-2D run ns for the surge s of Decem mber 2013 aree presented heere. These werre run in parallel using 16 cores c on a singgle compute node. n 3. Results R 3.1. ANN perform mance Trial T and errorr experimentaation showed that a hiddenn layer size of o 30 neuronss was adequaate to give a good perfo formance, withhout excessivee training times or any eviddence of over fitting (Fig 4a). 4 The overaall fit is good d (e.g. Fig. 4b), althoughh there is a sligght bias towarrds under-preddiction at the upper u end of the surge sampple.

Fig. 4. Illustrative AN NN training (a) annd performance (b) ( for a 12 hour ssurge residual forrecast. This simullation uses traininng data for 2010 and a hidden layer oof 30 neurons.

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It I is interestingg to compare the performan nce of a simp le ANN with the forecast accuracy a of thhe UK nationaal CS3 num merical tide-suurge model. Only O 6-hour archived a foreccasts for the CS3 C model weere available in numerical form. Theese also show good perform mance, with leess bias but a slightly weak ker overall co orrelation thann the ANN (F Fig 5.) Tab ble 1 shows a comparison of 6, 12, 18 and a 24 ANN forecasts witth the 6-hour CS3 model fforecasts. Herre it is evid dent that overrall model performance is actually a slightlly better with the ANN in terms t of root--mean square errors (RM MSE) and corrrelations betw ween predicteed and observved surge. Th he two approaches yield rrather more similar resu ults for 2013 ((which had a relatively r high h surge variannce) than in 20 010 (which had d fewer large surge events).

Fig.. 5. CS3 numericaal tide-surge mod del performance ((6-hour forecast) at Immingham fo or a) 2010; and b)) 2013.

A key test of the surge foreecast is its ability to resolvve the magnitu ude and timin ng of the largeest events. Heere we focu us on the Deccember 2013 surge, s which caused c damagge at Immingh ham. Fig. 6 shows time-seriies for the obsserved Deccember 2013 ssurge at Immiingham, togetther with the 66-hour CS3 model m and the comparable 66-hour ANN model m foreecasts. Both m models resolvve the event well w in terms of both timin ng and magnitude, although gh the CS3 fo orecast actu ually over-preedicts a little on o this occasio on. This show ws the skill of a relatively siimple ANN m model at forecasting a major m event to aan accuracy comparable to that of a moree complex num merical tide-surge model.

Table 1. Summarry comparison off RMSE and correelation (r) for AN NN and CS3 (Natiional Storm Tide Warning Servicee) ssurge residual forrecasts at the Portt of Immingham ffor select forecasting time window ws and two differeent years. CS3 model

ANN model Data year

6 hr

12 hr

18 hr

24 hr

6 hr

010 RMSE (m) 20

0.057

0.0 063

0.067

0.068

0.091

0.937

0.9 912

0.910

0.907

0.823

0.064

0.0 070

0.077

0.080

0.097

0.950

0.9 941

0.928

0.921

0.849

r 20 013 RMSE (m) r

3.2. Simulated inundation of port facilities Only O an approoximate floodd extent map, together with th qualitative evidence obtaained from diiscussions with the portt operators, exxists with whhich to validatte the Telemaac-2D simulattions of surge inundation. H However, an initial test simulation off the Decembber 2013 surgee (forced by im imposition of an ANN-geneerated forecasst of the total water

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level at the port eentrance) corrresponds very y well to the iindicative actu ual flood exteent polygon (FFig. 7a). The peak ( mean n sea-level), oof which abou ut 1.6 wateer level duringg this event reeached 5.22 m above Ordnnance Datum (roughly m was w attributablle to the instantaneous surg ge at high watter. Maximum m flood depths exceeded 1 m in a numb ber of locattions, and largger areas of the t port were flooded to ovver 0.5 m. Ex xisting assessm ments of floodd risk and dam mage poteential are typically based on o GIS-based extrapolationn of single-vaalued extreme water levels associated with w a giveen return periiod. Fig. 7b shows s how th his approach over-estimatees overall flo ood extent annd predicts grreater inun ndation depthss. Given the sensitivity s of infrastructuree damage and d port operatiion to depth oof inundation, this migh ht trigger cosstly adaptive measures m (e.g g. movement of equipmentt or shipping containers) in some parts of a facillity when effoort might be beetter expended d elsewhere.

Fig. 6. Observed (redd line) surge residdual and the 6-hou ur CS3 numericall model (black do ots) and 18 hour ANN A model (bluee line) forecasts for f the December D 2013 evvent at Imminghaam.

Fig. 7 (a) Illustrativee Telemac2D simuulation of maxim mum inundation deepths within the port p for the Decem mber 2013 surge;; (b) simple GIS ‘bath tub’’ model in which flood extent is esstimated by extraapolation of the m maximum water leevel reached durin ng the surge. Notte that the estuary y and dock have been masked in both b images to hiighlight the inund dation of normally y dry areas.

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4. Discussion and conclusions Numerical tide-surge models are necessarily implemented for large areas of coastal shelf, but limited bathymetric resolution, and a relatively coarse mesh resolution, restricts their ability to resolve the propagation of surges within estuaries, where many large ports are located. Our hybrid ANN-computational forecast model demonstrates the ability of an ANN to transfer surge forecast information from a small set of metocean forcing variables, including the observed far-field surge, directly to an estuarine port. While the ANN does not offer the longer-range (24 to 42 hour) forecasting capability of a full numerical tide-surge model, it can be used to provide forecasts within a 12 to 24 hour window that are of comparable or better accuracy. ANN-generated water level series can then be used as a boundary condition for a local computational hydrodynamic simulation of flood extent, depth, and duration for a forecast event within the port facility. The use of a smaller model domain and focus on a single surge event means that this simulation can be run at a very high spatial resolution. Simulation times of 15 - 20 minutes (or less) are well within the capability of a single multi-core compute node and can be completed ‘on demand’ if a predicted surge water level exceeds a port-specific threshold. Work is currently ongoing to further refine the ANN through the extension of the sensitivity analysis to include different combinations of input variables. A key aim here is to eliminate as a far as possible the slight tendency of the initial ANN implementation to under-predict peak water levels. Refinements to the Telemac-2D model include improvements to the mesh to include a more complete representation of structures in conjunction with an improved treatment of buildings and defensive structures and experiments with more sophisticated turbulence and friction parameterizations. We are also progressing towards an operational version of the forecasting system that is able to receive live data feeds and can therefore be used directly by the port operator. Acknowledgements This work has been funded by the Natural Environment Research Council (NERC) under the Environmental Risks to Infrastructure Innovation Programmed (grant NE/N01295X/1). The authors gratefully acknowledge the active support of Associated British Ports plc (Port of Immingham), ABPmer Ltd for the provision of tidal and meteorological datasets, the Environment Agency for provision of airborne lidar data under an Open Government License, and the National Oceanography Centre (Liverpool) for providing archived CS3 model forecasts. References 1. Batstone C, Lawless M, Tawn J, Horsburgh K, Blackman D, McMillan A, Worth D, Leager S, Hunt T. A UK best-practice approach for extreme sea-level analysis along complex topographic coastlines. Coast Eng 2013; 71:28-39. 2. Lopeman C, Geodatis G, Franco G. Extreme storm surge hazard estimation in lower Manhattan. Nat. Hazards 2015; 78:355-91. 3. Flowerdew J, Horsburgh K, Wilson C, Mylne K. Development and evaluation of an ensemble forecasting system for coastal storm surges. Quart J Roy Meteorol Soc 2010; 136: 1444-56. 4. Haykin S. Neural networks: A comprehensive foundation. 2nd. New York: Prentice-Hall; 1998. 5. Rumelhart DE, Hinton GE, Williams RJ. Learning representations by back-propagating errors. Nature 1986; 323:533-6. 6. ASCE Task Committee. Artificial neural networks in hydrology. I: preliminary concepts. J Hydrologic Eng 2000; 5:115-23. 7. Sztorbryn. M. Forecast of storm surge by means of artificial neural network. Neth J Sea Res 2003; 49:317-22. 8. Nitsure SP, Londhe SN, Khare KC. Prediction of sea water levels using wind information and soft computing techniques. Appl. Ocean Eng 2014; 46:344-51. 9. Hervouet J-M. Hydrodynamics of free surface flows: modelling with the finite element method. Chichester: John Wiley & Sons; 2007.