TIDE PREDICTION FOR THE DOWNSTREAM BOUNDARY CONDITION OF THE CHAO-PHRAYA RIVER MODEL USING HARMONIC ANALYSIS Supatchaya Chuanpongpanch, Phatchaasak Ala, Manfed Koch 3, Kenj Tanaka 4 and Tawatcha Tngsanchal ABSTRACT Chao-Phaya ve basn coves Thaland's land aea of,5 sq.km and 37 km of length of Chao- Phaya ve. It stats fom Nakhon Sawan whee the fou upsteam sub-basns meet to Gulf of Thaland n Samut Pakan. About 85% of the total unoff occus n the months of July to Decembe. Theefoe, ths peod s used fo model calbaton of HEC-RAS model whch s used to smulate the flow n the channel of Chao-Phaya ve to povde flood pedcton nfomaton fo an ealy flood wanng system wth unsteady state upsteam and downsteam bounday condtons. The downsteam bounday of the model s located at Fot Chula gagng staton at the ve mouth just at the sea n the Gulf of Thaland. The wate level at Fot Chula s nfluenced by the upsteam of ve dschage and the tdal wave fom the sea. Theefoe, Hamonc Analyss method s appled at Fot Chula gagng staton fo pedcton of wate level at ths gagng staton. The esults of Hamonc Analyss ae found to be vey satsfactoy wth 87% effcency ndex.. INTRODUCTION The Chao-Phaya ve flow model has ts upsteam bounday at Nakhon Sawan (staton C.) whch s the meetng pont of fou nothen sub-basn, located about 37km upsteam of the Chao-Phaya ve mouth at the sea. The downsteam bounday of the model s located at Fot Chula gagng staton at the ve mouth just at the sea n the Gulf of Thaland. The wate level at Fot Chula s nfluenced by the upsteam of ve dschage and the tdal wave fom the sea. Theefoe, Hamonc Analyss method s appled at Fot Chula gagng staton fo pedcton of wate level at ths gagng staton.. METHODOLOGY Wate level ecods n coastal wateways, exhbt tdal chaactestcs of snusodal oscllaton contanng ethe two man cycles pe day (semdunal tdes), one cycle pe day (dunal tdes), o a combnaton of the two (mxed tdes). The undelyng pncple of tde analyss s that, no matte Ph.D student, Dsaste Peventon Reseach Insttute, Gaduate School of Engneeng, Kyoto Unvesty, Japan (chuanpongpanch.supatchaya.46a@st.kyoto-u.ac.jp) Reseach Cente of Sustanable Wate and Dsaste Mtgaton Management, Nakhon Pathom Rajabhat Unvesty, Thaland, (alap@npu.ac.th ) 3 Pofesso, Depatment of Geotechnology, Unvesty of Kassel, Gemany, (kochm@un-kassel.de) 4 Assocate Pofesso, Wate Resouces Reseach Cente, Dsaste Peventon Reseach Insttute, Kyoto Unvesty, Japan, (tanaka.kenj.6u@kyoto-u.ac.jp)
how complex they may appea, tdal oscllatons can be boken down nto a collecton of smple snusods (snusods usually epesented by the cosne functon fom tgonomety). Each cosne wave wll have the same peod of oscllaton as the celestal focng that gves se to t. As t tuns out, thee ae qute a few of these. The pupose of tde analyss s to detemne the ampltude and phase (the so-called tdal hamonc constants) of the ndvdual cosne waves, each of whch epesents a tdal consttuent dentfed by ts peod n mean sola hous o, altenately, ts speed n adans pe mean sola hou (speed = 36 /T whee T = peod). Fndng the tdal hamonc constants at a place allows one to pedct tdes at that place. Tdal consttuent ampltudes ae usually gven n metes, and phase s usually expessed n degees. Puttng these pats togethe, the patal tde coespondng to a sngle tdal consttuent s epesented by the followng equaton, h ( t ) = R cos( ω t φ ) () In equaton, h(t) s the heght of the patal tde calculated fo tme t, and R s the consttuent ampltude (equal to one-half the consttuent ange). The actual tde obseved at a patcula locaton s the esultant of the combnaton of all of the gavtatonally nduced consttuent tdes that ae pesent thee. Fom studes of celestal moton we know that each tdal cycle follows a smple ecung (hamonc) patten wth a fxed peod. The paametes that vay fom place to place ae the ampltude and tme lag (phase) of each consttuent. Thus, the esultant of the gavtatonally nduced consttuent tdes can be detemned by equaton, N πt η ( t) = a + a sn + δ = T () wheeη (t) s the tdal wate level ecoded as a functon of tme t at any staton, a s the mean sea level, N s the total numbe of consttuents, a, δ and T ae the ampltude, phase and peod of the th consttuent. The values of a, a, δ can be detemned fo each coespondng value of T usng the data nfomaton that ae obtaned fom tdal ecods. The paametes ae evaluated fom a dscete houly η (j) fo to M as follows; a M = ( j) M η (3) a M M πj πj = η ( )sn + ( )cos j η j (4) M T M T whee M s the numbe of wate level data, η. M πj η cos T δ = tan (5) M πj η sn T
The magntude of tdal consttuents shown n Table usually does not vay apdly wth lattude o longtude and, f no po nfomaton s avalable fom the ste unde study, t s faly safe to assume that the same consttuents wll domnate the tdal behavo at the new locaton as at othe known statons n the same geogaphcal aea. In the numecal tests below, selecton of fst magntude consttuents was smple, snce conventonal hamonc analyss esults fo the test ste wee aleady avalable. 3. RESULTS Table Pncpal tdal consttuents (Defant, 96) Name Symbol Peod (h) Lun-sola dunal K 3.9346 Pncpal luna dunal O 5.894 Pncpal luna M.46 Pncpal sola S. Lage luna ellptc N.658 Lun-sola semdunal K.9673 Lage luna evectonal ν.658 Vaatonal µ.879 Smalle sola ellptc L.98 Lage sola ellptc T.64 Luna ellptc second ode N.955 Smalle luna evectonal λ.6 Pncpal sola dunal P 4.658 Lage luna ellptc Q 6.8677 Smalle luna ellptc M 4.837 Small luna ellptc J 3.99 Luna fotnghtly M f 37.8689 Luna monthly M m 649.896 Sola semannual S sa 439.4 The numbe of consttuents and the tdal length ecods ae detemned to acheve the best tdal foecastng fo 7 days ahead n a yea 6. The numbe of hamonc analyss consttuents N vaes fom 4 to 8 consttuents and the ecod length vaes fom 7 to 8 days. Then, the compason of Root Mean Squae Eo (RMSE) of Hamonc Analyss fo vaous ecod length and numbe of consttuents s shown n fgue. The esult of 4 consttuents (N=4) fo 35 days ecod length showed the smallest RMSE and hghest EI, of.78m and 96%, espectvely. Theefoe, hamonc analyss of wate level n the Gulf of Thaland s based on the fou man tdal consttuents that ae: ) Pncpal luna M wth a peod of.46 hous. ) Pncpal sola S wth a peod of. hous. 3) Lun-sola declnatonal K wth a peod of 3.9346 hous. 4) Lage luna declnatonal O wth a peod of 5.894 hous.
Fgue RMSE compason of Hamonc Analyss Fgue Tde foecastng esult Fnally, Hamonc Analyss s appled fo tde pedcton fo pepang the downsteam bounday condtons of the ve flow model at Fot Chula ve gagng staton. The esults fo 7 days ahead foecastng s found to be satsfactoy wth 87% Effcency Index as shown n fgue. A longe peod ahead of pedcton o foecastng shows nceasng eo of foecast especally at the peaks and toughs of the tdal fluctuaton. 4. SUMMARY The downsteam bounday of the Chao-Phaya ve flow model s located at Fot Chula gagng staton at the ve mouth just at the sea n the Gulf of Thaland. The wate level at Fot Chula s nfluenced by the upsteam of ve dschage and the tdal wave fom the sea. Theefoe, Hamonc Analyss method s appled at Fot Chula gagng staton fo pedcton of wate level at ths gagng staton. The esults of hamonc analyss show an accuacy pefomance of 87% Effcency Index fo wate level foecastng at Fot Chula gagng staton based on the fou man tdal consttuents wth nput of 35 days.
ACKNOWLEDGEMENTS The authos ae gateful to Wate Resouces Reseach Cente (WRRC) of Kyoto Unvesty and Reseach Cente of Sustanable Wate Resouces and Dsaste Mtgaton Management (RCSWM) of Nakhon Pathom Rajabhat Unvesty fo coopeaton n developng an ealy flood wanng system; to Global Cente of Educaton (GCOE) and Reseach on Human Secuty Engneeng fo Asan Megactes (HSE) of Kyoto Unvesty fo feld tp fnancal suppotng; to Asan Insttute of Technology (AIT) fo the Hamonc Analyss pogam and data suppotng; and also to Royal Igaton Depatment (RID) and Tha Meteoologcal Depatment (TMD) fo data suppotng. REFERENCES Defant, A. (96). Physcal oceanogaphy, Volume, Pegamon Pess, New Yok. Weesakul, S. and Thammasttong, S. (). "Opeatonal Flood Foecastng fo Chao Paya Rve Delta", Poceedng of the Intenatonal Confeence the Chao Paya Delta : Hstocal Development, Dynamcs and Challenges of Thaland's Rce Bowl, p. 67-7. Vgna Insttute of Mane Scence (). TIDE ANALYSIS. Souce: http://web.vms.edu/physcal/eseach/tctutoal/tdeanalyss.htm?sv=www, Reteved: Septembe 3,.