P a g e 1 1 2 3 4 5 6 7 8 9 10 11 12 Supplementary Material: Cross flows in the Taiwan Strait in winter L.-Y Oey 1,2 *, Y.-L. Chang 3, Y.-C. Lin 1, M.-C. Chang 1, S. Varlamov 4 and Y. Miyazawa 4 1: National Central University 2: Princeton University 3: National Taiwan Normal University 4: Japan Agency for Marine-Earth Science and Technology *lyo@princeton.edu
P a g e 2 13 Appendix 1 The Numerical Model 14 The Advanced Taiwan Ocean Prediction (ATOP) numerical model uses the mpi-version 15 (Message Passing Interface) of the Princeton Ocean Model [Blumberg and Mellor, 1987]; the 16 mpi-implementations were by Dr. Antoni Jordi from the Mediterranean Institute for Advanced 17 Studies, Spain. Details are given in Oey et al [2013]. The model covers the entire North Pacific 18 99E-74W and -15S-70N at 0.1 o 0.1 o horizontal resolution and with 41 terrain-following vertical 19 levels: 20 k = -[0,0.004,0.007,0.015,0.029,0.059,0.088,0.118,0.147,0.176,0.206,0.235,0.265,0.294, 21 0.324,0.353,0.382,0.412,0.441,0.471,0.5,0.529,0.559,0.588,0.618,0.647,0.676,0.706,0.735,0.765, 22 0.794,0.824,0.853,0.882,0.912,0.941,0.971,0.985,0.993,0.996,1]. 23 A fourth-order scheme is used to reduce the internal pressure-gradient errors [Berntsen 24 and Oey, 2010]. The ETOPO2v2 topography with 2-minute resolution is used. In the open 25 ocean where water depths exceed 1000 m, satellite sea-surface-height (SSH) anomalies from 26 AVISO (http://www.aviso.oceanobs.com/duacs/) are assimilated into the model using a 27 statistical optimal-interpolation scheme by Mellor and Ezer [1991] and Ezer and Mellor [1994] 28 [see also Yin and Oey, 2007]. Sea-surface temperatures (SST) are obtained from AVHRR 29 MCSST (AVHRR-Advanced Very High Resolution Radiometer, Multi-Channel Sea Surface 30 Temperature; http://gcmd.nasa.gov/records/gcmd_navoceano_mcsst.html), and are also
P a g e 3 31 assimilated by using the MCSST to adjust the model s SST with an e-folding time constant of 1 32 day -1 applied as a surface flux. There is no data assimilation on shallow shelves and in Taiwan 33 Strait. Effects of wind-generated waves are included as (i) mixing due to wave-breaking near the 34 surface [Craig and Banner, 1994; Mellor and Blumberg, 2004]; (ii) enhanced friction near the 35 bottom [Grant and Madsen 1979] using Nielson s [1992] formula for wave-induced velocity and 36 assuming the Toba s [1972] 3/2-Power Law; and (iii) Stokes drift [Stokes, 1847] following 37 Kenyon [1969], assuming the Pierson and Moskowitz s [1964] empirical spectrum for fully- 38 developed seas. 39 Since the publication of Oey et al [2013], tides are now also included in ATOP (see 40 below). The present work focuses on subtidal responses which are obtained by low-passing the 41 model results with tides using a 40-hour Lanczos filter. However, during the winter s 42 northeasterly monsoon period being studied, results from the low-passed results do not differ 43 significantly from those derived using daily averages of the original model in which tides are 44 included implicitly as bottom friction [e.g. Csanady, 1982], as also assumed in the analytical 45 model developed in Appendix 2; this conclusion is consistent with the experiences from other 46 Taiwan Strait models which do not include tides [e.g. Wu and Hsin, 2005; and Wu et al, 2007]. 47 The model is run continuously from 2012 January 1 through present (hindcast and 48 nowcast), plus a 7-day forecast [see http://mpipom.ihs.ncu.edu.tw/index.php]. Six-hourly winds
P a g e 4 49 are specified using the NCEP s GFS (Global Forecasting System). The initial fields (on January 50 1, 2012) are obtained from a 24-year, free-running (i.e. non-assimilated) model run that is forced 51 by six-hourly CCMP wind and other surface fluxes from NCEP. For the experiments with tides, 52 the tidal forcing is also initiated on January 1 2012. In addition to the basic case, described 53 above, other runs are also conducted each day to test the sensitivities of the forecasts to different 54 initial conditions and model physics. In Oey et al [2013], model results are validated against 55 satellite data and compared with observations and other model results available from the 56 literature. The simulation reproduces various known circulation features of the western North 57 Pacific Ocean [see reviews in Oey et al 2013, and also Chang and Oey, 2011, 2012]. In 58 particular, the model reproduces reasonably well (i) Kuroshio intrusion in the northern South 59 China Sea, and (ii) subtropical counter current and eddies. Both of these processes are 60 considered to be necessary in improved understanding of the regional circulation [Chang and 61 Oey, 2012, where other references are given]. 62 Tides are included by specifying the tidal constituents (M2, S2, K1, O1, N2, K2, P1, Q1) 63 along the open boundaries [e.g. Oey and Chen, 1992] at 15S and 70N. Tidal potential (g eq ) 64 accounting for all but the three shallow-water tides (M4, MS4 and MN4) is included in the 65 momentum equations: 66 Du/Dt + kf u = -g ( - eq ) +
P a g e 5 67 where eq = n n is the sum of the 22 equilibrium tidal constituents n s which depend on the 68 Love numbers and potential amplitudes (as well as on longitude and latitude) [Cartwright, 1978]. 69 Effects of the ocean loading tide (due to the deformation of the elastic earth) are neglected. 70 Figure A1 shows the M 2 -cotidal chart which agrees reasonably well with those in the literature 71 [e.g. Fang et al, 1999; Lefevre et al, 2000]. Note the appearance of small-scale features in the 72 phase contours in northern South China Sea, produced by internal tides. Such small-scale 73 features are not present in experiments without density stratification (not shown). In South 74 China Sea, comparison with tidegauge stations gives averaged RMS errors (0.06m, 11.4 o ) for 75 amplitude and phase respectively, comparable to those reported by Fang et al [1999] (0.03m, 76 18 o ). RMS errors including stations in East China Sea and Taiwan Strait where the amplitudes 77 are large (Fig.A1) are correspondingly larger. Averages of all the stations of the RMS difference 78 over a tidal cycle, computed from [Cummins and Oey, 1997]: 79 E = [(A o 2 + A m 2 )/2 - A o.a m.cos( o - m )] 1/2, 80 is 0.23 m, which is larger than, but comparable to Lefevre et al s [2000] value of 0.18m. 81 For the present study, the ATOP results from February 1 through May 15 2012 are used; 82 this period includes the time from March 15 to 31 when shipwreck debris traversed across the 83 strait. Since open-ocean forcing mainly from the Kuroshio is necessary to produce the along- 84 strait pressure gradient, we check how the modeled Kuroshio compares with observations. In
P a g e 6 85 situ Kuroshio observations are not available during the 2012 period. Since pressure gradient 86 from south to north of the island of Taiwan contributes to driving the Kuroshio transport [Yang, 87 2007], we compare the model Kuroshio transport against the observed transport across PCM-1 88 northeast of Taiwan reported by Johns et al [2001] for the period September 1994 to May 1996. 89 Table A1 shows excellent agreement between the model (21.09 Sv) and observed (21.96Sv) total 90 transports. The vertical distribution also compares well: modeled 0-200 m transport is 13.87 Sv 91 compared with the observed 13.76 Sv, and modeled 200-400 m transport is 6.75 Sv compared to 92 observed 6.24 Sv. The model shows a reversed (i.e. equatorward) transport below z = -800 m 93 while the observed does not; the cause for this discrepancy has not been identified. Nonetheless, 94 the close agreement of the modeled Kuroshio transport with observation suffices to demonstrate 95 that the open-ocean pressure-gradient forcing is reasonably realistic. 96
P a g e 7 97 Appendix 2. Analytical Model of Wind and Pressure-Driven Responses in Taiwan Strait 98 Steady linearized momentum equations for a homogeneous fluid are: 99 -fv = -g / x + 2 u/ z 2 = -fv g + 2 u/ z 2 (A2.1a) 100 +fu = -g / y + 2 v/ z 2 = fu g + 2 v/ z 2 (A2.1b) 101 where (x, y) points cross-strait (along-strait) approximately southeastward (northeastward), = 102 (constant) eddy viscosity and 103 (u g, v g ) = u g = (g/f).(- / y, / x) (A2.2) 104 is the depth-independent geostrophic velocity. 105 To estimate u g, integrate the first forms of (A2.1) from bottom (z = -H, assumed constant) 106 to surface (z = 0): 107 -fv A.H = -gh / x + ox - b x (A2.3a) 108 +fu A.H = -gh / y + oy - b y (A2.3b) 109 where (u A,v A ) is the depth-averaged velocity given by, 110 (u A,v A ) = -H 0 (u,v).dz/h, the depth-averaged velocity, (A2.4)
P a g e 8 111 o = ( ox, oy ) is the kinematic wind stress vector, and b = kinematic bottom stress vector which is 112 parameterized using u A as: 113 b = rh.u A, r = constant friction coefficient in s -1 (A2.5) 114 Because of the strait, v A >> u A 0, and assuming also that oy >> ox 0 (i.e. wind is 115 predominantly along the strait), (A2.3) and (A2.5) give: 116 -fv A = -g / x (A2.6a) 117 rv A = -g / y + oy /H (A2.6b) 118 Thus cross-strait (x) momentum is geostrophic, and along-strait balance is frictionally-dominated, 119 i.e. / t << r -1. The v A can then be computed from (A2.6b) given oy and / y which is 120 assumed to be quasi-steady, externally imposed. Then (A2.6a) gives / x, and from (A2.2): 121 v g = v A = (g/f). / x, also: u g = -(g/f). / y (A2.7) 122 The surface Ekman solution [e.g. Gill, 1982] 123 (u E, v E ) = (u, v) (u g, v g ) (A2.8) 124 is then computed from (A2.1) for a given wind stress 125 u/ z = o = (0, oy ) at z = 0 (A2.9)
P a g e 9 126 for regions away from the coasts and H >> (2 /f) 1/2 : 127 {u E, v E } = 2 1/2 e.[ oy /(f E )].{cos( + /4), sin( + /4)} (A2.10) 128 where 129 = z/ E and E = (2 /f) 1/2 (A2.11) 130 Lin et al s [2005; their fig.10] observations at 4 ADCP moorings across the strait show 131 approximately coherent responses to northeasterly wind, in the middle of the strait as well for 132 stations near the coasts. This suggests that over most of the strait, the assumption that the coasts 133 are far (hence the local Ekman solution A2.10) is approximately valid. 134 The total velocity is then: 135 u = -(g/f). / y + 2 1/2 e.[ oy /(f E )].cos( + /4) (A2.12a) 136 v = -(g/r). / y + oy /(Hr) + 2 1/2 e.[ oy /(f E )].sin( + /4) (A2.12b) 137 The surface velocity (u o, v o ) is: 138 u o = -(g/f). / y + oy /(f E ) (A2.13a) 139 v o = -(g/r). / y + oy /(f E ).[1 + f E /(Hr)] (A2.13b)
P a g e 10 140 i.e., a simple superposition of the Ekman transport oy /f depth-averaged over the surface Ekman 141 layer E and the geostrophic velocity u g (for u o ) and the depth-averaged along-strait velocity v A 142 (for v o ). 143 The friction coefficient r may be estimated by modifying the Island Rule [Godfrey, 144 1989] by adding two closed-circuit integrals [Pedlosky et al. 1997]. One counter-clockwise 145 circuit goes around Taiwan [the island; Yang, 2007]. The other one, also counter-clockwise, 146 starts from SE Taiwan eastward along the latitude 22 o N to the America, then northward to 25 o N 147 along the American continent, then back (westward) along 25 o N to NE Taiwan, and finally 148 southward along the eastern coast of Taiwan to complete the circuit. The friction along the 149 Taiwan s western coast is then balanced by the integrals of the zonal wind stress along the 22 o N 150 and 25 o N latitudes. Taking the 22-year (1988-2009) mean wind from the CCMP dataset, the 151 resulting r Island 3 10-5 s -1, which despite the various assumptions made in Island Rule [see 152 Pedlosky et al. 1997] is remarkably close to the more exact value, derived next. 153 The r is estimated more directly by regressing v A against oy see (A2.6b). The result 154 is shown in Fig.A2 which gives, 155 r 1.66 10-5 s -1. (A2.14) 156 The zero-intercept of the best-fit line with the y-axis gives -(g/r) / y 0.28 m s -1, hence:
P a g e 11 157 / y -4.5 10-7 (A2.15) 158 i.e. a sea-level drop of approximately 0.18 m from south to north over the along-strait distance of 159 about 400 km. Note that for the study period of predominantly northeasterly winds, the 160 magnitude of this sea-level drop is, by definition (since it is determined when oy = 0), a 161 minimum. Physically, the northeasterly winds always produce a steeper sea-level tilt than 162 (A2.15). Also, the magnitude is approximately 2~3 times larger than the amplitude of the 163 fluctuating along-strait sea-level tilt which we show in the main text is dominated by SSH-EOF2 164 (Fig.8c). Together (i.e. A2.15 plus SSH-EOF2), they contribute to more than the 50~70% 165 increased sea-level tilt sometimes seen in the modeled SSH-field following the weakening of 166 northeasterly wind events (e.g. Mar 15 in Fig.2). 167 The above values of r and / y may be compared against Wu and Hsin s [2005] (their 168 equation 4 after converting to MKS and using an averaged strait s width of 175 km) r WH 169 1.65 10-5 s -1 and ( / y) WH -3.8 10-7 in good agreements with ours. The values are also 170 estimated using 24-year unassimilated experiment, which gives r 22yr 1.39 10-5 s -1 and 171 ( / y) 22yr -3.2 10-7. The 3 different estimates are within 5~11% of each other. 172 Set v o = 0 in (A2.13b) to find the critical v oy which balances the pressure gradient : 173 v oy = (fg E /r). / y/[1 + f E /(Hr)] (A2.15)
P a g e 12 174 From the numerical model, the averaged eddy viscosity near the surface ranges from 10-3 ~ 10-175 2 m 2 s -1, and the corresponding E 15 m (for f 6 10-5 s -1 ). Then, 176 v oy -1.2 10-4 m 2 s -2 (A2.16) 177 which corresponds to a wind speed of approximately 10 m s -1 using the drag formula in Oey et al. 178 [2013]. The along-strait flow is equatorward for northeasterly wind stress that is stronger (i.e. 179 more negative oy ) than v oy. For northeasterly wind stress that is weaker than this critical value, 180 a flow reversal from equatorward to poleward is predicted. This appears to be the case (see main 181 text). 182 Similarly, the critical wind stress u oy weaker than which the cross-strait u o reverses from 183 being negative (i.e. from Taiwan to mainland China) under a strong northeasterly to being 184 positive when the wind weakens may be derived from (A2.13a) (by setting u o = 0): 185 u oy = g E. / y -0.68 10-4 m 2 s -2 (A2.17) 186 This is approximately half the v oy in (A2.16), and the corresponding wind speed is 7 m s -1. 187 Therefore, for a given sea-level tilt, because of bottom friction, the along-strait surface current 188 can reverse more readily (i.e. under a stronger v oy ) than the corresponding cross-strait current
P a g e 13 189 which reverses when the wind further weakens (to u oy ). For northeasterly wind stresses (< 0) 190 that lie between these two critical values: 191 u oy > oy > v oy (A2.18) 192 193 the currents are further analyzed in the main text.
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P a g e 18 262 263 264 265 266 Table A1 Comparison of mean model volume transport in depth layers for Kuroshio and Johns et al. s [2001] corresponding values (the authors Table 5) at the PCM-1 transect northeast of Taiwan. Values in parentheses in 150-200 row is the summed transport from 0 to 200m, and those in 350-400 row is the summed transport from 200 to 400 m. Kuroshio Volume transport (Sv) at PCM-1 Depth layer (m) Observation Model 0-50 4.27 3.44 50-100 3.79 3.97 100-150 3.15 3.49 150-200 2.55 (13.76) 2.97 (13.87) 200-250 2.08 2.39 250-300 1.69 1.87 300-350 1.37 1.43 350-400 1.10 (6.24) 1.06 (6.75) 400-450 0.82 0.76 450-500 0.52 0.53 500-550 0.25 0.34 550-600 0.14 0.21 600-650 0.10 0.11 650-700 0.06 0.04 700-750 0.03-0.01 750-800 0.02-0.06 >800 0.03-1.43 Total 21.96 21.09 267 268
P a g e 19 269 270 271 272 Fig.A1 The M 2 co-tidal chart analyzed from the ATOP hindcast. Shade and solid contours are amplitudes: interval = 0.2 m; dotted contours are phases: interval = 30 degrees.
P a g e 20 273 274 275 276 277 278 Fig.A2 Plot of the Taiwan Strait s area-averaged (23-25 o N) and depth-averaged along-strait velocity v A (the y in m s -1 ) versus the corresponding windstress oy (the x in m 2 s -2 ). The thick line is the linear best-fit with a slope (rh) -1 = 1.212 10 3 (m/s) -1 ; hence r 1.66 10-5 s -1 for averaged (Taiwan Strait s) depth H 50m. Seven-day mean v A from ATOP analysis is used for the period Feb/01-May/15/2012. 279 280