Predctng Wave Transformaton durng Extreme Weather Condtons Josephus LOPEZ 1, Karlo Marko NARIO 1, Patrck Joshua ROMARES 1, Maro DE LEON, Ryuchro NISHI 3, Hosotan KAZUNORI 4 1 Bachelor of Scence n Cvl Engneerng Graduate, Dept. of Cvl Eng., De La Salle Unversty (401Taft Avenue, Manla, 1004, Phlppnes) E-mal:josephus_lopez@yahoo.com Assocate Professor, Dept. of Cvl Eng., De La Salle Unversty (401Taft Avenue, Manla, 1004, Phlppnes) 3 Professor, Coastal Engneerng Laboratory, aculty of sheres, Kagoshma Unversty (Shmoarata 4-50-0, Kagoshma 890-0056, Japan) 4 Assocate Professor, Department of Electroncs and Control, Tsuyama Natonal College of Technology (Tsuyama Cty, Okayama 708-8509, Japan) Wave transformaton descrbes the propagaton of waves and water surface dsplacement from offshore to onshore. The magntude of wave generaton and wave set-up are dependent on a number of factors such as wnd speed, water depth and tde level. Ths paper has nvestgated the characterstcs of wave transformaton n Manla bay along Roxas boulevard durng extreme condtons specfcally on typhoon events. Records of typhoon that struck Manla bay area for the past 40 years were used to generate the wave heght and water dsplacement profles through a numercal smulaton model developed by Kraus and Larson (1991). Parameters such as water depth, wnd speed and tde level were the nput data n the smulaton. Sx transects were establshed up to a depth of 0m to descrbe the cross-shore profle fronted by breakwater structure and open sea. Results show that the wave heght and water surface dsplacement are sgnfcantly hgher n transects whch are not exposed to any breakwater structure. A wave generated by a typhoon wth a wnd speed of 4 mps smlar to that of typhoon Narsng n 1973 would defntely overtop the exstng seawall stuated along Roxas boulevard. Key Words : wave transformaton, extreme weather condton 1. INTRODUCTION Coastal regons n the Phlppnes are prone to floodng when typhoons wth hgh wnd speed generate waves of sgnfcant heght causng abrupt elevaton of seawater surface leadng to nundaton of coastal communtes. In 011 and 01, typhoons Gener and Pedrng characterzed by ntense ran wth precptaton of 100.3 mm and 89.4 mm coupled wth wnd speed at 13 and 15m/s respectvely flooded Roxas boulevard. The stretch of the road was submerged n knee-deep floodwaters non-passable for lght vehcles and wth tons of garbage and debrs accumulated at the boardwalk area. Ths scenaro led the researchers from De La Salle Unversty (DLSU) Department of Cvl Engneerng to conduct a feld survey n Manla bay to nvestgate the transformaton of wave as t propagates towards the coast along Roxas boulevard. Specfcally, the study ams to; (1) generate the cross-shore profle (bathymetrc map and actual topographc profle) n Manla bay along Roxas Boulevard, and use t to determne the effects of the profle of the seabed to the transformaton of wave, () determne wave clmate data (wave heght and wave perod) and utlze t as an nput parameter for wave transformaton, (3) perform smulaton of wave heght and water dsplacement as t propagates from offshore to onshore.. MATERIALS AND METHODS (1) Secondary data A 40-year record of tde, wnd speed and drecton of typhoons were gathered from the Natonal Mappng and Resource Informaton Authorty (NAMRIA) and Phlppne Atmospherc and Geophyscal Astronomcal Servces Admnstraton (PAGASA). The selecton of data on typhoon was based on the 011 and 01 ncdent that caused ntense floodng at Roxas boulevard and the strongest typhoon that ht Manla n 1973. Data on sgnfcant wave heght was obtaned wth the use of the Beau-
fort scale whch translates wnd speed to wave heght (Table 1), whle wave perod was derved usng the Unted States Army Corps of Engneer s Coastal Engneerng Manual (USACE CEM, 00) wth reference to Saffr Smson Hurrcance scale for the wave heght and perod relatonshp. Table 1. Wave clmate characterstcs of typhoon events Typhoon Wnd speed(m/s) H T (s) Gener (01) 13 4.8 10.68 Narsng (1973) 4.4 35.84 Pedrng (011) 15 5.66 11.30 () eld data Sx transects spaced at 00m and at 00m nterval was the bass for depth measurement of the study area n the nearshore regon up to 10m depth (g. 1). Actual depth measurement was conducted wth the ad of an echo sounder whch measured the depths along the sx transects establshed n the study area. The Phlppne Coast Guard (PCG) asssted the researchers n the hydrographc survey through the deployment of ther tugboat and personnel. Transects 1-6 span lengths of km,1.8, 1.4, 1.6, and 1.6km respectvely. Locaton coordnates of transect 1 are 14 0 34 9.60 N and 10 0 58 45.44 E and transect 6 14 0 33 53.60 N and 10 0 59 1.1 E. g. 1 Study area n Manla bay along Roxas boulevard (Source: https://maps.google.com.ph) (3) Wave transformaton analyss The applcaton of a two-dmensonal wave model for wave transformaton analyss s a smplfed approach that provdes a fundamental assessment on the characterstcs of wave heght and water surface dsplacement propagatng from offshore to onshore. Although there are lmtatons and assumptons of a -D wave model, followng are the justfcatons of ts applcaton, (1) the mouth of Manla bay s narrow and lmts the ncdent wave angle as nearly as perpendcular to the shore (along Roxas boulevard, the study area), () there are no natural and artfcal structures whch cause sgnfcant wave dffracton effect to the study area, (3) as an approxmaton to the frst order of accuracy, the current wave transformaton model was proven to be stable for many cases ncludng for coral reef topography by Dally et al. (1985) even though wave refracton may have mnor effect. Regular wave condtons are appled as representatve wave condtons such as sgnfcant wave condtons. It s also assumed that the applcaton of a detaled 3-D wave transformaton model ncludng reflecton, dffracton, refracton, mult-drectonal spectrum, and wave and current nteracton may be proposed as a further research topc. a) Governng equatons for the wave model (Kraus and Larson, 1991) Wave characterstcs across the cross-shore profle are determned by four fundamental equatons, namely wave energy flux, dsperson, cross-shore momentum and snell s law. The water surface dsplacement (η) s a functon of wave heght (H), wave length (L), radaton stress (S xx ) and stll water depth (h). Whle wave heght (H) s a functon of wave energy flux () and wave group speed (C g ). Wave Energy lux Equaton The -D equaton for conservaton of energy flux ncorporatng energy dsspaton produced by wave breakng s; κ ( cos θ ) + ( sn θ ) ( s ) x y d (1a) The wave energy flux n represented by; EC g (1b) The wave energy densty s wrtten usng lnear-wave theory as; 1 E ρgh 8 (1c) The total water depth d s the sum of the stll water depth h and the change n mean water level η produced by waves and wnd: d h + η (1d) The stable wave condton refers to a state where energy dsspaton produced by wave breakng ceases, permttng waves to reform. The stable energy flux s expressed as; s EsCg (1e) where E s s the wave energy densty correspondng to a wave that has decayed to a stable form. The stable wave energy flux corresponds to a stable wave heght H s, whch s a functon of the water depth (Horkawa
and Kuo, 1966; Dally, 1980), H s Γd (1f) where Γ s a nondmensonal emprcal coeffcent. Dsperson Relaton The wave group speed C g s related to the phase speed of an ndvdual wave C through the factor n, whch s a functon of the water depth and the wavelength L (or wave perod T): where C g n nc 1 1 4πd + L 4πd snh L (1g) (1h) The phase or form speed of a wave s determned through the dsperson relaton, where C C o C o πd tanh L gt π (1) (1j) Cross-shore Momentum Equaton The dsplacement of the mean water surface (setup or setdown) produced by waves s determned from the momentum equaton, ds xx dx ρgd dη dx (1k) where S xx radaton stress n the drecton of the waves (N/m). The radaton stress component S xx s gven by lnear-wave theory for an arbtrary wave angle of ncdence as: S xx 1 8 ρgh n 1 ( cos θ + 1) (1l) Snell s Law or straght and parallel bottom contours, there s no longshore varaton n wave propertes, thus: d dx sn θ L 0 (1m) b) Numercal soluton scheme Explct fnte-dfference scheme s used as the numercal method to solve the governng equatons for determnng the wave heght as a functon of dstance across the shore. The numercal calculaton starts at the most seaward pont on the grd and proceeds onshore, where quanttes known at one grd pont are used to determne correspondng quanttes at the next grd pont closer to shore. In the dfference equatons, the ndex denotes the number of a specfc grd pont. The fundamental quantty n the mddle of a cell s the water depth, and these grd ponts wll be referred to as h-ponts (depth ponts). At the boundares of calculaton cells, the man quantty s the wave heght, and grd ponts located here are known as H-ponts (wave ponts). The ncdent wave heght, perod, and drecton must be avalable at the most seaward grd pont. rom knowledge of the wave propertes at the seaward-most grd pont (an H-pont), wave setdown at the seaward-most pont s determned from the analytc soluton frst presented by Longuet-Hggns and Stewart (196): η 4L πh 4πh snh L (1n) To contnue from one H-pont to the next, wave refracton s frst determned f the ncdent wave approaches at a nonzero angle to the bottom contours. The angle θ between wave crests and bottom contours at the next shoreward H-pont s gven by: L θ arcsn sn θ + 1 L + 1 (1o) The next step n the calculaton s to determne the change n energy flux expressed as, ( θ 0.5A ) cos 1 cos θ + 1 + + c 0.5A c + A c s (1p) where κδx Ac h + η + 1 (1q) n whch Δx s the length step or grd cell length (meters). The stable wave energy flux s determned from: s 8 ( C + C ) 1 g g + 1 ρg[ Γ( h + η + 1) ] (1r) After the energy flux has been calculated at a specfc pont, the correspondng wave heght s determned by:
H 1 ρgcg 8 (1s) Usng the above wave heght, the radaton stress s calculated and the mean water surface dsplacement s expressed n the dfference form: η η + 1 + 1 ( Sxx ) ( S ) + 1 xx ρg( h + η ) 3. RESULTS AND DISCUSSION + 1 (1t) (1) Cross-shore profle Output on cross-shore profle conducted durng the 013 feld survey s presented n g. whch were then supermposed wth the nautcal chart of NAMRIA (005). Transect 1 shows the profle wth the presence of an offshore breakwater n Manla bay. Transects 3, and 6 are the cross-shore profles wthout a breakwater structure. The observed change n the two cross-shore profles ndcate the extent and locaton of areas possble for eroson and deposton of sedments durng the 8-year perod. () Wave heght and water dsplacement profles The output of the numercal smulaton provdes a profle on the wave heght dstrbuton and water surface dsplacement responses n the cross-shore drecton of the study area exposed to breakwater structure and open sea. gures 3-5 show the profles of wave transformaton for typhoons Gener, Pedrng and Narsng. The scenaros presented by the curves were durng the hghest, lowest and average level of tdes n the hghest recorded wnd speed for the respectve typhoon along transects 1 and 3. The two transects are dentfed to be the sgnfcant transects because transect 1 consders the effect of breakwater structure, whle transect 3 consders an open sea area. The graphs of wave transformaton descrbe the wave heght and water dsplacement profles at mnmum, maxmum and average tde level durng the typhoon perod. All of these parameters are referenced wth respect to the mean sea level. Results of the profle revealed that most of the typhoons generated typcal wave heght rangng from 0 to meters and water dsplacements at a heght of less than meters. Typhoon Gener s wave heght and water dsplacement peaked at a level of.3 meters. Typhoon Pedrng s wave heght and water dsplacement reached a level of.9 meters and meters, respectvely. Typhoon Narsng havng the greatest recorded wnd speed of 151. klometers per hour generated the hghest wave heght and water dsplacement, 3.3 meters and 4 meters respectvely. Wth the current seawall heght of 3. meters, a typhoon as strong as Narsng would defntely overtop and flood the stretch of Roxas boulevard. Table presents the summary of comparng the effects of the water depth and wnd speed on the behavor of wave and water level propagatng towards the coast. Gven a specfc wnd speed as the forcng mechansm to generate waves n Manla bay area, the expected result n terms of the profle of wave heght and water dsplacement at the establshed transects can be projected. In addton, tde level durng the occurrence of the typhoon wll have a sgnfcant effect on the transformaton of waves and water dsplacement. Wth the scale and magntude of the wnd speed and water depth clustered nto three groups namely, hgh, moderate and low, ths would serve as relevant and useful nformaton n the assessment of wave heghts and water dsplacements that may occur at the coastlne. rom Table, t can be observed that transect 1 produced the smallest wave heght n the smulaton. An average of 19.6 percent decrease n wave heght s attaned n transect 1 compared to transect. The prmary dfference of transect 1 from transect 3 s the presence of a breakwater structure. Ths supports the functonal use of breakwater n the attenuaton of wave heght as t propagates towards the shore. Another observaton from the tables s that hgh wave heght would not necessarly produce hgh water surface dsplacement. The profle of the sea bed or the depth of water s also a factor that contrbutes to the dsplacement of water. It can be observed that the lower the depth, the hgher the water dsplacement produced. An average ncrease n water dsplacement of 58 percent n transect 1 compared to transect 3 s generated. rom the layout and locaton of transects 1-6 as shown n g. 1, the level of susceptblty of transect to the generaton of hgh waves can also be assessed. It was establshed that transects 3 to 6 have hgher susceptblty compared to transects 1 and. The reason for ths s that transects 3 to 6 dd not have any breakwater structure. Though transect s not exposed to any breakwater structure, the level of susceptblty to the generaton of hgh wave s moderate due ts proxmty to the breakwater. The study s focused on the wave transformaton of Manla Bay n the presence of typhoon. Consderng the strength of typhoons Pedrng and Gener, the smulaton produced wave heghts and water levels (set-up) on the seawall just below the seawall cap. Wth ths result, t s possble that sgnfcant amount of water wll cross-over the seawall cap due to the mpact of wave and water on the face of the seawall. In addton, the tde level durng these storm events were over a meter hgh and f storm surge heght s
factored n, then t s more evdent of a flooded Roxas boulevard scenaro. The government agences, PAGASA and DPWH, had also reported on the floodng ncdents that were attrbuted to the mpact of wave, water and storm surge that breached the seawall where sgnfcant amount of seawater entered Roxas boulevard. Based on the results of the smulaton, the wave heght and the water surface dsplacement generated by typhoons Pedrng and Gener reached ts heght just below the seawall cap. Even f ths s the case, a greater possblty of water to cross-over the cap s lkely to happen due to the mpact of wave and water on the seawall whch wll defntely cause floodng along Roxas boulevard frontng Manla bay. g. 3 Wave transformaton profles durng Typhoon Gener (c) Along transect 6 g. Cross-shore profles (005 Bathymetrc Map and 013 Actual Survey Map) g. 4 Wave transformaton profles durng Typhoon Narsng
Bottom topography sgnfcantly affects the behavor of the wave as t approaches the coast. The presence of any breakwater structure to arrest the propagaton of waves s sgnfcant n the dsspaton of wave energy whch ultmately reduces ts wave heght and the dsplacement of water surface approachng the coastlne. g. 5 Wave transformaton profles durng Typhoon Pedrng 4. CONCLUSION Establshed are the wave clmate and cross shore profle of the study area whch are consdered sgnfcant nput parameters n the wave transformaton analyss. Wth the data on the scale and magntude of wave heghts and water surface dsplacement, a sound engneerng coastal protecton structure can be desgned whch s effectve and effcent aganst coastal floodng. Wnd speed n greater scale and ncreased tde level would result to hgh proportons of wave heght and water dsplacement. REERENCES 1) Coastal Engneerng Manual (CEM), (00, 003). EM 1110--1100. Coastal and Hydraulcs Laboratory (CHL) Engneerng Research Development Center, Waterways Experment StatonUS Army Corps of Engneers (USACE). ) Dally, W.R. (1980). A Numercal Model for Beach Profle Evoluton, M.S. Thess, Department of Cvl Engneerng, Unversty of Delaware, Newark, DE. 3) Dally, W.R., Dean, R.G. and Dalrymple, R.A. (1985). Wave Heght Varaton Across Beaches of Arbtrary Profle, Journal of Geophyscal Research, Vol. 90, No. C6, pp. 11917-1197. 4) Gerrtsen,. (1980). Wave Attenuaton and Wave Setup on a Coral Reef. Proceedngs of the 17th Internatonal Coastal Engneerng Conference, pp. 444-461. 5) Horkawa, K. and Kuo, C. (1966). A Study on Wave Transformaton Insde the Surf Zone, Proceedngs of 10th Coastal Engneerng Conference, Amercan Socety of Cvl Engneers, pp.17-33. 6) Kraus, N. and Larson, M. (1991). NMLONG: Numercal Model for Smulatng Longshore Current.Report 1 Model Development and Tests. Dredgng Research Program, Techncal Report DRP-91-1, Prepared for Department of the Army, US Army Corps of Engneers, Washngton, D.C. 7) Longuet-Hggns, M.S. and Stewart, R.W. (196). Radaton Stress and Mass Transport n Gravty Waves, wth Applcatons to Surf Beats, Journal of lud Mechancs, Vol. 13, No. 4, pp. 481-504. 8) Longuet-Hggns, M.S. and Stewart, R.W. (1964). Radaton Stress n Water Waves: A Physcal Dscusson, wth Applcatons, Deep Sea Research, Vol. 75, No. 33, pp. 6778-6789. 9) Me, C.C. (1983). The Appled Dynamcs of Ocean Surface Waves, John Wley and Sons, New York. 10) Thornton, E.B. and Guza, R.T. (1983). Transformaton of Wave Heght Dstrbuton, Journal of Geophyscal Research, Vol. 88, No. C10, pp. 595-5938.Mles, J. W. : On the generaton of surface waves by shear flows, J. lud Mech., Vol. 3, Pt., pp. 185-04, 1957. Table. Summary of wave heght and water surface dsplacement record Wnd Intensty Depth Speed Range (mps) Transect 1 Transect 3 Transect 6 Wave Water Dsplacement Depth Wave Water Dsplacement Heght Heght Depth Wave Water Dsplacement Heght Hgh 4-0.76.03 3.67-1.55 1.7.9-1.41.54 3.7 8-0.59 1.49.67-1.87.03.11-1.73.09.11 Moderate 0-0.44 1.09 1.89-1.8 1.7 1.7-1.14 1.30 1.4 0-0.61 1.14 1.88-1.40 1.3 1.19-1.6 1.35 1. 0-0.70 1.17 1.87-1.49 1.35 1.18-1.35 1.40 1.1 16-0.71 0.9 1.4-1.55 1.13 0.68-1.41 1.15 0.71 15-1.47 1.44 1.6 -.31 1.44 0.53 -.17 1.48 0.55 13-1.08 0.97 0.98-1.9 1.1 0.47-1.78 1.4 0.49 Low 13-0.43 0.64 0.93-1.7 0.91 0.5-1.13 0.91 0.54 1-1.04 0.85 0.77-1.88 1.16 0.41-1.74 1.18 0.4 10-0.51 0.61 0.78-1.35 0.87 0.36-1.1 0.86 0.38 10-0.44 0.56 0.79-1.3 0.81 0.37-1.09 0.81 0.39 9-0.43 0.54 0.75-1.7 0.80 0.31-1.13 0.79 0.33