Polovina et al.: Application of satellite altimetry to simulate transport dynamics of Panulirus marglnatus 



135 



able on CD-ROM from JPL. However, a considerable 

 time lag may be associated with releases of these 

 data. 



After the data were downloaded, a unix shell script 

 was used to process the individual cycle data. This 

 script uses various subroutines of the Generic Map- 

 ping Tools (GMT) software package (the GMT soft- 

 ware package is available from an anonymous ftp at 

 kiawe.soest.hawaii.edu in /pub/gmt). The GMT script 

 first smoothed and then interpolated the data using 

 a subroutine called "nearneighbor." This subroutine 

 placed the irregularly spaced track data onto a uni- 

 formly spaced latitude-longitude matrix, assigning 

 values to each latitude-longitude location (node). 

 Each node was assigned a weighted mean of all 

 data points within a user-specified search radius 

 (SR); i.e. a mean of all data within a geographic 

 circle about each node. The weighting factor was a 

 function of radial distance from the node such that 

 iv(r) =1/(1-1- (3r/SR)'^), hence wir) ranged nonlinearly 

 from 1 at the node (r=0) to 0.1 at SR units from the 

 node (r=SR). When all orbital passes of the satellite 

 cycle were complete, a SR value of 3 degrees could 

 adequately interpolate regions between passes, in- 

 dependent of the relative date of the pass within the 

 10-day cycle, resulting in a complete grid file. For 

 cycles with missing passes, the SR was able to be 

 increased accordingly The SR could also be speci- 

 fied as an absolute distance to ensure that the 

 smoothing region was circular and not ovoid. After 

 the deviation data were assembled on a grid, the 

 script then added these data to another grid of equal 

 dimensions containing the Levitus long-term mean 

 dynamic height at 1000 m, which we assumed was 

 representative of the mean dynamic topography for 

 1993-96. The Levitus data originated from the 1994 

 NODC World Ocean Atlas (CD-ROM data set), U.S. 

 Department of Commerce, NOAA, National Environ- 

 mental Satellite, Data, and Information Service 

 (NESDIS). The grid file of absolute altimetry values 

 (2) was then evaluated by the subroutine grid- 

 gradient, which calculates the east-west and north- 

 south gradients, dz/dx and dz/dy, where x and y and 

 z are all in centimeters. These gradients were used 

 for calculating the u and v components of the geo- 

 strophic current as follows: 



and 



u = -(glf) 

 v = {glf) 



dz^ 

 dy 



dz 



(1) 



dx 



Q = 7.29 X 10"^ radians per second (earth 



angular rotational velocity); and 

 (]) = latitude. 



These u and v values represent estimates at the sur- 

 face. They can also serve as estimates of geostrophic 

 current over the top 100-m mixed layer if integrals 

 over the mixed layer of the horizontal density gradi- 

 ents are negligible. For the region of interest in our 

 study, given the weak horizontal density gradients, 

 the error in using these surface estimates as mixed 

 layer estimates, according to calculations with the 

 Levitus density field, was less than 2 cm/s. This is 

 negligible given the time and space scales we were 

 considering. 



The ;/ and v values were then output to an ASCII 

 file at 0.5-degree resolution. A separate file for each 

 10-day period (« = 169 from Oct 92 to Jun 97) was 

 constructed for the entire Topex-Poseidon data set. 

 The GMT script optionally produced a contour map 

 of dynamic height with an overlay of geostrophic 

 current vectors for each cycle. The resultant maps 

 showed eddy and meander features that were likely 

 important in recruitment processes (Fig. 4). 



Several authors have found excellent agreement be- 

 tween currents estimated ft-om T-P data and ground- 

 truthing. Comparisons between the current estimated 

 from satellite-tracked drogued buoys and geostrophic 

 current estimated fi-om T-P data in the western Pacific 

 resulted in correlations of 0.924 for zonal velocity (u) 

 and 0.760 for meridional velocity (v) (Yu et al., 1995). 

 Comparisons between current speed from an acoustic 

 Doppler current profiler along T-P track lines in the 

 Hawaiian Archipelago agreed with estimates from T-P 

 to within a few cm/sec (Mitchum, 1996). Sea surface 

 height from T-P and a large set of island tide gauges, 

 including those in the Hawaiian Archipelago, yielded 

 a correlation of 0.66 (Mitchum, 1994). 



Movement model 



Individual larvae were tracked for a series of time 

 steps starting from a given location by iteratively 

 applying advective displacements due to water flow 

 with additional random displacements caused by dif- 

 fusion. The position of each larva was updated at 

 each time step as follows: 



where g = 980 cm per second 

 f = 2 Q sin (]); 



•^f+A/ =-^f +["(.v,,v,,n'^^ + f^/'OA<]/cos(y, 



(2) 



2. 



where t = time in days; 



