welling include upwarping of density surfaces 

 within a geostrophic current (Stommel and 

 Wooster, 1965) and cross-isobar onshore flow at 

 the bottom due to bottom friction (Hsueh and 

 O'Brien, 1971). However, these are more likely 

 to be important in narrower, more intense flows 

 than normally occur in the area covered by this 

 report. 



Our present understanding of surface wind 

 transport is based on Ekman's (1905) theory. 

 Under Ekman's assumptions of steady state 

 motion, uniform wind, and infinite homogeneous 

 ocean, the mass transport per unit width of ocean 

 surface is directed 90 degrees to the right (in the 

 Northern Hemisphere) of the direction toward 

 which the wind is blowing and is related to the 

 magnitude of the wind stress by the expression 



M 



/ 



(1) 



where M is the mass transport resulting from a 

 wind stress, r, and / is the Coriolis parameter. 

 This mass transport has come to be called the 

 Ekman transport. The layer in which appreciable 

 transport occurs is often referred to as the Ekmun 

 layer and extends from the surface to depths not 

 exceeding 50 to 100 m. The bottom of the Ekman 

 layer is sometimes identified with the bottom of 

 the homogeneous wind-mixed zone. 



Smith (1967) has shown that Yoshida's (1955) 

 expression for the offshore transport in the early 

 stage of coastal upwelling reduces to the Ekman 

 transport expression if the stress is assumed 

 constant. This leads to the conclusion that the 

 Ekman theory gives a valid description of wind- 

 driven offshore flow in the early nonequilibrium 

 phase of upwelling as well as in the later steady- 

 state phase. 



The approach taken in generating the indices 

 presented in this report has been to estimate the 

 monthly mean wind stress on the sea surface at 

 points near the coast, from this to compute the 

 Ekman transport, and finally to resolve the com- 

 ponent of Ekman transport perpendicular to the 

 coast. The magnitude of the offshore component 

 is considered an indication of the amount of water 

 upwelled through the bottom of the Ekman layer 

 to replace that driven offshore (Fig. 1). Negative 

 values indicate onshore transport or convergence 

 at the coast. Since accumulation of surface wa- 

 ters tends to cause downward displacement of 

 the density structure in the coastal area, this sit- 



uation is sometimes referred to as downirelling. 



The basic input data is the wind field over the 

 ocean. However, the distribution of sea-surface 

 wind observations in the near coastal regions of 

 the northeastern Pacific is uneven, both spatially 

 and temporally. The number available for a given 

 area during a given month is often insufficient to 

 form a good estimate of the monthly mean stress 

 on the sea surface. In order to construct a consis- 

 tent series, use is made of the relationship in mid- 

 latitude regions of wind to atmospheric pressure. 

 Incorporating atmospheric pressure data in- 

 creases the coverage in data-sparse areas and 

 allows an understanding of the behavior of large- 

 scale pressure systems to aid in providing contin- 

 uity to the analysis of scattered observations. 

 Therefore, winds derived from analyzed atmo- 

 spheric pressure fields are used in the produc- 

 tion of these indices. 



Calculations 



The computed values are based on monthly 

 mean pressure fields prepared by Fleet Numeri- 

 cal Weather Central (FNWC). These data are 

 available on a 63 by 63 point square grid which is 

 superimposed on a polar stereographic projection 

 of the Northern Hemisphere (Hughes, 1966). The 

 mesh length is 200 nautical miles at lat. 60 °N and 

 decreases southward to about 144 nautical miles 

 at lat. 20 °N. The data were transferred to a 

 3-degree mesh length geographical (spherical 

 coordinates) grid (Fig. 2) using Bessel's central 

 difference formula. 



First derivatives of the surface pressure at 

 each grid point were estimated by taking the dif- 

 ference in pressure between the grid points to 

 either side and dividing by the 6-degree angular 

 mesh length. For example, the derivatives of the 

 pressure at point "0" in Figure 3(a) would be ap- 

 proximated as 



dP_ 



P, 



2h 



dp 



2h 



12) 



where 6 and A denote the northward and east- 

 ward angular coordinates, h is the 3-degree an- 

 gular mesh length in radians and P, denotes the 

 pressure at point "1", etc. The geostrophic wind 

 was computed according to 



I dP I dP 



fn„ R 36 



fp R cos 6 d\ 



(3) 



