Data assimilation model study of the Santa Barbara Channel

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. C7, PAGES 15,727-15,741, JULY 15, 1999 Data assimilation model study of the Santa Barbara Channel circulation Chi-Shao Chen and Dong-Ping Wang Marine Sciences Research Center, State University of New York at Stony Brook Abstract. The seasonal circulation in the Santa Barbara Channel (SBC) consists of a cyclonic eddy in the western basin and a poleward current along the northern coast. In this study the ly mean circulation is simulated using a three-dimensional primitive-equation model with data assimilation included. The data are derived from the Santa Barbara Channel and Santa Maria Basin Coastal Circulation Study, covering an 8- period from January to August The 6-hourly moored temperature observations in the upper 100 rn water column are continuously assimilated into the model using a local correction method, although salinity and wind forcing are not explicitly included. Comparisons with the observations indicate that the model results generate realistic flow and temperature structures inside the SBC. The assimilation model faithfully reproduces the cyclonic eddy, but it fails to predict the currents at the exits of the channel. The issue of the data need is addressed through a sensitivity study. 1. Introduction The Santa Barbara Channel (SBC) is located at the northern edge of the Southern California Bight (SCB), bounded to the north by the southern central California coast and to the south by four of the Channel Islands: San Miguel, Santa Rosa, Santa Cruz, and Anacapa (Figure 1). The California coastline turns a sharp angle around Points Arguello and Conception. The southern end of the central California coast is directed north-south north of Point Arguello. The coastline turns southeastward south of Point Arguello and eastward east of Point Conception. The coastal Santa Ynez Mountains rise to > 1000 m. Copyright 1999 by the American Geophysical Union. Paper number 1999JC /99/1999JC the southeast with maximum wind speed south of Point Conception [Atkinson et al., 1986]. Wind speeds decreased sharply toward the coast. The maximum wind stress curl was 0.45 gpa m 'l (dyn cm -2 km-1). Wind stress curls had comparable strength over the Southern California Bight [Winant and Dotman, 1997] In 1992, an intensive observational program, the Santa Barbara Channel and Santa Maria Basin (SBC-SMB) Coastal Circulation Study, sponsored by the MMS, was initiated by the Scripps Institution of Oceanography to obtain better descriptions of the near-surface flow field. From October 1992 to January 1996, 10 current meter moorings were deployed along the 100 m isobath. (The mooring at the The SBC basin is 100 km long and 50 km wide and has a eastern end of the channel was placed at 200 m.) Eight were maximum water depth of 600 m. It is separated from the located inside the SBC, and two were placed in the SMB and Santa Monica Basin (SMB) in the east by a sill 200 m deep the SCB, respectively. Each current meter mooring contained and from the Arguello Canyon in the west by a sill 400 m two current meters at 5 and 45 m; temperature loggers at 1, deep. The passages between the Channel Islands are 40 m 25, 65, and 100 m; and a bottom pressure sensor. Six National deep. South of the Channel Islands, the Santa Rosa Ridge, Data Buoy Center (NDBC) weather buoys were located in the 200 to 400 m deep, separates the SCB from the Pacific Ocean. vicinity, two off Point Arguello, two in the channel, and two The Organization of Persistent Upwelling Structures in the SCB. The current meter and weather mooring locations (OPUS) study in spring and early summer of 1983 and the are marked in Figure 1. concurrent Santa Barbara Channel study, sponsored by the Harms [1996] and Harms and Winant [1998] provided a Minerals Management Service (MMS), were the first detailed description of the wind stress, current, surface comprehensive field studies of the SBC circulation [Brink and temperature, and surface pressure patterns in the SBC-SMB Muench, 1986; Largerloef and Bernstein, 1988]. These study area. They found that the seasonal mean near-surface studies found that the seasonal mean currents in the western currents in the SBC consisted of a poleward flow along the entrance of the channel consisted of a poleward (westward) northern shelf and a cyclonic circulation in the western basin. coastal flow in the north and an equatorward (eastward) return They suggested that the mean circulation pattern is influenced flow in the south. Considerable mesoscale wind structures by the local wind stress, the alongshore pressure gradient, and were observed off Point Conception. An aircraft survey at the large-scale meandering current Unfortunately, these 152 m above sea level showed that during upwellingforcings are not precisely known, and it would be difficult to favorable winds the air streamlines were from the northwest to create a realistic ocean circulation model [Oey, 1996]. An 15,727 alternative approach is to assimilate part of the observations into a model simulation to compensate for lack of the forcing information. In atmospheric and ocean model simulations, two basic data assimilation strategies have been adopted [e.g., $medstad and O'Brien, 1991; Ghil and Malanotte-Rizzoli,

2 15,728 CH N AND WANG: DATA ASSIM ATION MODEL OF TH SBC CIRCULATION 35ON - 34øN ; ', ", ", ('"?', "1;;1-, ',,':::,..,,..,,,_.,,,;,,,, -...,.:,,,, I, ',',.-'-'..'c.. :',,., --.', -:: ow 120oW 119oW Figure 1. The Santa Barbara Channel. Moored current meter and meteorological instrument locations are marked. 1991]. The first approach incorporates complex assimilation changes are small and have a maximum in winter and a schemes, such as variational methods, into relatively simple m in late spring and early summer. Figure 3 shows dynamical models. The second approach, which is used in this the observed ly mean salinities. At PAIN the 5-m study, uses simple data assimilation schemes, such as salinity is 33.2 practical salinity unit (psu) in February, "blending" and "nudging," in sophisticated and realistic increases to 33.7 in June, and decreases afterward. Other dynamical models [Rutherford, 1972; Moore et al., 1987]. stations have similar seasonal variations, except for ANMI, We incorporate a blending data assimilation method, whose salinity is relatively constant, between 33.4 and described in Section 4.2, in a three-dimensional primitive- Salinity changes at 45 m are similar to those at 5 m. equation coastal ocean circulation model. Data are derived Figure 4 shows the observed seasonal mean currents at 5 from the moored temperature and salinity observations. The and 45 m. A weak cyclonic circulation in the western SBC is model simulation covers a period of 8 s, from January evident in winter. The cyclonic circulation intensifies in to August The model results are averaged to obtain the spring, and part of the equatorward flow exits at the eastern ly mean currents. These are analyzed and compared end. The equatorward flow weakens slightly in summer, the with the observations. The objectives of this study are (1) to poleward flow increasesignificantly, and the mean current at provide a four-dimensional description of the seasonal mean the eastern end reverses to poleward. East of the SBC, mean circulation, (2) to relate the mean circulation to density currents are weak throughout the year. North of Point distribution, and (3) to examine the sensitivity of the model Conception they are strong and equatorward in spring and results. diminish (and reverse to poleward at 45 m) in summer. 2. Data 3. Model Configuration Figure 2 shows the observed ly mean temperatures The basic model is based on a three-dimensional primitiveselected stations for the first 8 s of 1994 when the data equation coastal ocean general circulation model of [Fang coverage was relatively complete. The seasonal temperature [1993, 1997]. It is formulated in a constant z coordinate. The cycles are confined mostly to the upper 45 m. The near- model uses a centered difference scheme in the momentum surface (5 m) temperatures have the largest amplitudes. They equations and a flux-corrected transport scheme in the decrease gradually from January to April and rise rapidly temperature equation. The horizontal eddy viscosity and eddy afterward. The two westernmost stations, PAIN and SMIN, diffusivity are constant (50 m 2 s-i). The vertical eddy have relatively small seasonal amplitudes, and their minimum coefficients are computed from an embedded one-dimensional temperatures occur in May. Below 45 m, temperature mixed-layer model of the Mellor-Yamada level 2 turbulence

3 CHEN AND WANG' DATA ASSIMILATION MODEL OF THIE SBC CIRCULATION 15, o '... --'"* _... e--- i i i i i i i I GOOF - ' ' ' '& SMOF Figure 2. Monthly mean temperatures mooting locations' 5 m (open circle), 25 m (solid circle), 45 m (open triangle), 65 m (solid triangle), and 100 m (open square). closure [Chen eta/., 1988]. Chen and Wang [1990] used a compiled by Dynalysis of Princeton. The model's horizontal two-dimensional model version in a comprehensive resolution is 5 km, and the vertical resolution varies from 10 simulation of the Coastal Ocean Dynamics Experiment m in the upper 100 m to m below 100 m. The (CODE) off northern California. integration is based on a split-mode calculation, and the time The model domain is a rectangular box 175 km wide and intervals are 12 s for the external mode and 240 s for the 400 km long (Figure 5). The orientation of the California internal mode. coast is rotated 52 ø clockwise so that the coast is A modified Orlanski radiation condition is used at the approximately parallel to the model's latitudinal axis. The latitudinal open boundaries (y = 0 and 400 km). The radiation model's bottom topography is based on a bathymetric data set condition is applied to the momentum (the internal mode) and

4 . 15,730 CH]EN AND WANG: DATA ASSIMILATION MODEL OF TI-[E SBC CIRCULATION a O - ANMI GOIN I GOOF I o ROIN ROOF I I I I I I I " SMIN SMOF Figure 3. Monthly mean salinities at mooring locations: 5 m (open circle), and 45 m (solid circle). transport (the external mode) equations, following Wang 4. Model Setup [1997]. At the longitudinal (offshore) open boundary (x = km) the velocity normal gradient and elevation are set to zero. This setu permits the Ekman transport to pass through 4.1. Statistical Interpolation the open boundary. It tends to generate an artificial barotropic flow near the open boundary, although this flow does not The observations are point measurements. To map them appear to affect circulation inside the channel. (This is onto the model grid, a statistical interpolation scheme of verified by testing model sensitivity to the location of the Bretherton et al. [1976] is used. The optimum interpolation offshore boundary.) At the coast a free slip condition is used. (OI) equation is

5 CHEN AND WANG: DATA ASSIMILATION MODEL OF SBC CIRC ATION 15,731 35øN 34ON - 35øN 35øN Winter pring Summer i 05 m (overshooting) south of the channel. To avoid this problem, regions inside and outside of the channel are treated differently. For the inner domain, all observations are used in the analysis (except for SMOF, which has limited temperature data) and for the outer domain only ANMI and PAIN are used. The boundary between the inner and the outer domain is indicated on Figure 5. Since interpolation is done separately for the inner and the outer domain, a common station at the transition is needed. At the eastern entrance, ANMI is located at the transition. At the western entrance, PAIN is copied to where SMOF is located. At each observation depth, temperature and salinity are interpolated horizontally over the entire model grid. The resulting profiles at each model grid point are linearly interpolated in the vertical over the entire water column. Since the deepest observations are at 100 m for temperature T and at 45 m for salinity & extrapolation is required for model depths > 1 O0 m. Harms [ 1996] suggested that the horizontal pressure gradients vanish below 250 m ("level of no motion"). We assume the water column is homogeneous (T = 8øC and $ = 33.9) below 250 m and extend the interpolation down to 250 m. We use a correlation scale R c = 20 km for the inner domain. The horizontal distances between two adjacent 34ON _ øw 120øW 119øW I Figure 4. Seasonal mean currents at 5 m (solid arrow) and 45 m (open arrow) for winter (January and February), spring (March, April, and May), and summer (June, July, and August). e = Z CkiAij. /j (1) k j=l i=1 I 25O 200 ;z'i/"! t \ 0.8,",4/ ",,.. where is a state variable. Subscripts i and j indicate observation stations (total number of stations is N), and k indicates model grid. The superscripts o and e stand for the observed and estimated values, respectively. The C / is a covariance matrix for between model grid k and observation i, and A O. -1 is the inverse of the covariance matrix of an observation pair i and j. The values inside the parentheses of (1) are normalized weighting coefficients. The covariance C / is def'med as a function of the separation distance Cki = exp - Rk -i (2) where Rk_ i is the distance between model grids k and i and R c is a correlation scale. Since the observations are concentrated inside the channel, statistical interpolation using the entire data set would create strong temperature anomalies I ' ' x x ' N..: - 6 "' '', : :./ ============= ' ' I... I ' : ' Figure 5. The model domain and weighting coefficients. Boundaries between the inner and outer domains are marked by a dashed line.

6 . _ 15,732 CHEN AND WANG: DATA ASSIMILATION MODEL OF TI-IE SBC CIRCULATION :, z,,, :;,. c,,:.¾..? -I I '-, ' '/.;. ' "._..,.:".:<< :':% -I 250 -'" ::... ' "--' - ' I ' ' ' _. _,,. ':.¾' '', t 11\,'5, ,,',,,"l ',, O O0-50 Figure 6. Seasonal mean model currents at (left) 5 m and (right) 45 m. observations are km. A 20-km length scale produces a 4.2. Spatial Data Assimilation smooth interpolation and still maintains the observed values at mooring locations. For the outer domain a larger correlation A standardata assimilation procedure is [Daley, 1993] scale of 50 km is used, which creates a 50-km-wide temperature front south of the Channel Islands half way i between ANMI and PAIN. East of the front the water has the same characteristics as ANMI, and west of the front it has the where T is the temperature analysis and Tff is the same characteristics as PAIN. predicted temperature model grid k, T/ø is the observed temperature

7 CH N AND WANG: DATA ASS V LATION MODEL OF T E SBC C RCULA ON 15, ,... winter "./ I... I Ill x- J,Z" spring I I i I 25o I., %';(,,? 'h '--'- ',, '-,%' 200 "x-'5 ;) % -I -I "'..._--,,.x.,, - d' \,,- (' 'x.. N 250 ',:..',.?" '- --: '----= 5, / '"i i' i "... N, k_///,,'! '"'k,",, '/// ,... F, -' 5O -1 O Figure 7. Seasonal mean model temperatures (left) 5 m and (right) 45 m. Contour interval is 0.5øC. at mooring station i, and a / is a predetermined statistical weighting coefficient matrix. The estimated value is corrected from the prediction by a weighted prediction error vector, the O:ki = exp - - i (4) differences between observations and predictions. In this R k e ]2 study a local correction scheme is used such that a correction is made only if the model grids are located near an, where R e is an error correlation scale and Rk_ i is the distance observation point. The weighting coefficient matrix is def'med between model grid k and observation position i. At each as a function of the separation distance observation point the prediction is replaced by the observed

8 15,734 CHEN AND WANG: DATA ASSIM ATION MODEL OF SBC CIRCULATION x (kin) x (kin) x (km) - 1 O O O0-50 -loo O Figure 8. Vertical sections at y = 200 km of seasonal mean model cross-channel U and along-channel V velocities and temperatures T. Contour intervals are 2 cm s 'x for velocity and 1 øc for temperature. value (100% weighting), whereas outside the radius of 4.3. Temporal Integration influence, no correction is made. The map of the weighting The model integration starts on day 7. The mode coefficients corresponding to an error correlation scale of 20 assimilation is updated every 6 hours, although using daily km is shown in Figure 5. (The phantom station at the western frequency gives essentially the same results. The error entrance is used only for interpolation and not for correlation scale is 20 km. The model results are not sensitive assimilation.) to R e for R e > 10 km and that R e = 20 km agrees best with The data assimilation uses the observations to augment the observations. Convective adjustment is checked at each incomplete forcing information. It can work satisfactorily if assimilation step. there are adequate observations. In this study the bulk of the observations is from the temperature logger data inside the channel. We focus therefore only on assimilating temperature 5. Model Results data in the inner domain. Temperature in the outer domain is not assimilated. The salinity data are very limited even in the inner domain, and so salinity everywhere is also treated as a 5.1. Seasonal Flow and Temperature Pattern Figure 6 shows seasonal mean currents at 5 and 45 m. We diagnostic variable. Salinity and outer-domain temperature are focus attention on the circulation inside the channel. In prescribed at each assimilation step from their respective winter the flow in the eastern basin is poleward along the interpolated values. It is noted that the salinity cannot be ignored. In SBC the salinity variations have major impact on the density, as discussed in Section 5.4. southern shelf, and it forms a cyclonic eddy in the western basin. In spring the poleward flow increases and is along the northern shelf, and the cyclonic eddy significantly intensifies.

9 CH]EN AND WANG: DATA ASSIMILATION MODEL OF TI-IE SBC CIRCULATION 15, x (kin) x (kin) x (kin) - 1 O O O [ I i [ I [ I [ ] I.] [ i i I I i I [. [ [ I ',,',.,,..,',,: ::! --',::,,! ',,,_..-',,':' ', - '-',' ',', '. :I.,,, :,',' "'"i"... ; er?'-.... : ng, i,,'" -'"': e 0 ' j,,.i I I I -loo -200 ;, -loo -200 Figure 9. Vertical sections at y = 240 km of seasonal mean model cross-channel U and along-channel V velocities and temperatures T. Contour intervals are 2 cm s '] for velocity and 1 øc for temperature. (Note the scale change at 5 m in Figure 6.) In summer the inshore poleward flow extends westward beyond Point Conception, and there is little recirculation within the channel. The eastward branch of the cyclonic circulation is fed by strong inflows through the interisland passages. Figure 7 shows the corresponding seasonal mean temperatures. Temperatures inside the channel (at 5 m) are marked by a tongue of cold water intruding eastward along the channel axis. Temperature differences across the cold tongue are small in winter, 0.5øC, increase to 1.5øC in spring, and are > 2.5øC in summer. The cold water is brought into the channel by the eastward current on the southern shelf. At 45 m the cold eddy is still evident. Figure 8 shows vertical cross sections of seasonal megan velocity and temperature at y = 200 km. (The coordinates are indicated in Figure 5.) This section is at approximately the eastern extent of the cyclonic eddy. Inflow through the Sant.a Cruz-Santa Rosa passage is indicated by positive crosschannel U and along-channel V velocities at x = km, and inshore poleward flow is indicated by a positive V. There is little equatorward flow along the southern shelf. Figure 9 shows seasonal mean velocity and temperature cross sections at y = 240 km, which is across the center of the cyclonic eddy. A positive V and negative U along the northern shelf indicates the inshore poleward flow, and a negative V along the southern shelf indicates the equatorward flow. Where the poleward flow reaches a maximum in summer, the equatorward flow decreases from spring to summer. Below 100 m the flow is poleward. The temperature sections indicate a distinct dome-shaped structure in the upper 100 m, which corresponds to the cyclonic circulation Mass and Heat Budget The three-dimensional flow structure in the SBC is very complicated. To quantify the basic flow properties, it is useful to examine the cross-sectional mass flux distributions along the channel. We focus on the channel interior, from the eastern tip of Santa Cruz Island 02 = 170 km) to the western

10 15,736 CI-IEN AND WANG' DATA ASSIMILATION MODEL OF SBC CIRCULATION Table 1. Seasonal Mass Budget in the Santa Barbara Channel Winter Spring Summer Table 2. Seasonal Heat Budget in the Santa Barbara Channel Transact Winter Spring Summer Transact Layer 170 km km upper km lower < 0.01 < 0.01 < 0.01 Santa Cruz-Santa Rosa passage 200 km upper lower < 0.01 < 0.01 Santa Rosa-San Miguel passage Santa Cruz-Santa Rosa passage upper km Santa Rosa-San Miguel passage upper + 0.0! km upper Units in Sv øc = 4 x 1012 W. lower Units in Sv = 106 m 3 s 'l GOIN GOOF _ -20 ROIN i ROOF '1 I I I I I I I 4o I - t SMIN -20,,,,,,,, SMOF Figure 10. Comparison of ly mean principal axis velocities at 5 m between the model (solid line with circle) and the data (dashed line with triangle). The zero velocity line is marked by the dashed line.

11 ,. CHEN AND WANG: DATA ASSIMILATION MODEL OF Tt-IE SBC CIRCULATION 15, A _ -20 GOIN GOOF I 40- _ -20 ROIN t ROOF I I I I I I I o -2O SMIN SMOF Figure 11. Comparison of ly mean principal axis velocities at 45 m between the model (solid line with circle) and the data (dashed line with triangle). The zero velocity line is marked by the dashed line. end of San Miguel Island (v = 240 km). This domain is divided into eastern and western regions, separated at approximately the eastern extent (3' = 200 km) of the cyclonic circulation. Table 1 lists the mass transport at y = 170, 200, and 240 km. For each cross section the transport is further divided into upper (above 100 m) and lower layers. The two interisland passages, which are shallower than 45 m, are included in the upper western region. At the eastern entrance (v = 170 km), mass transports are always in the channel and are confined to the upper layer. They are 0.02 Sv in winter and increase to 0.08 Sv in spring and to 0.12 Sv in summer. Transports through the midsection (v = 200 km) are the same as in the eastern entrance, except in winter when there is a significant input (0.03 Sv) from the lower layer. Transports through the two passages are in the channel and are comparable to those through the eastern entrance. At the western entrance the upper layer transports are in the channel in winter and spring and out of the channel in summer. The transports in the lower layer are significantly larger than in the upper layer and are out of the channel. The heat (thermal) transports are listed in Table 2. In winter the heat transports are 0.32 poleward (in units of Sv øc = 4 x 10 2 W) at the eastern entrance, 0.43 at the midsection, and 0.39 at the western entrance. The total heat transports through the two interisland passages are 0.3. The heat transport divergence results in a net heat loss of-0.11 in the eastern region and a net gain of 0.34 in the western region. Changes of the total heat content are relatively small, about in the eastern region and in the western region. Since heat advection is not balanced by heat storage, the data assimilation adds 0.07 to the eastern region and removes 0.41 from the western region.

12 15,738 CH]EN AND WANG: DATA ASSIMILATION MODEL OF TttlE SBC CIRCULATION X (Km) X (km) X (km) - 1 O O O i, I. i [ [ [ I [ [ ol [ i ].t I ] ol [ ] i [ I -100,,",._'",; '.i::: -200 :: / I SpringH /,., I [ [,.4_. [ I,, I, ], oj I, j.i,] [ [ [ I o.,,, i ii ',,!ii -1 O0 i'i'i,' -200 o I, I I -oo -200 Figure 12. Vertical sections at y = 240 km of seasonal mean model cross-channel U and along-channel V velocities and temperatures T from a diagnostic model calculation. Contour intervals are 2 cm s ' for velocity and 1 øc for temperature. The heat source resulting from the data assimilation is 5.3. Comparison with the Observations converted into an equivalent surface heat flux. In the eastern region the corresponding surface heat fluxes are 254, -217, The ly mean model currents are compared with the and -108 Wm -2 in winter, spring, and summer, respectively, observations. For convenience, the observed and model using a surface area of 1.1 x 109 m 2. In the western region the currents are rotated to their principal axes. Figure 10 shows equivalent surface heat fluxes are -654,-1070, and comparisons at 5 m for six moorings inside the channel. Wm -2 in winter, spring, and summer, respectively, using a Stations outside the channel, including PAIN, ANMI, and surface area of 2.5x109 m 2. The observed heat loss over the BARB, are ignored as they are impacted directly by the northern California shelf during the CODE study ranges from prescribed temperature distribution in the outer domain. The -28 to -118 Wm -2 [Beardsley, 1986]. The amount of heat three stations on the northern shelf, SMIN, ROIN, and GOIN, removed by the data assimilation is too large and does not trace the inshore poleward current. The model currents at represent true forcing. Since heat loss in the western region is ROIN and GOIN are comparable with the observed seasonal mostly associated with the transport in the lower layer (Table amplitude variation. The model currents at SMIN are too 2), we testhe effect of changing reference temperature (at small, suggesting that the predicted poleward current leaves 250 m) on heat budget. By using a warmereference coast too soon. The three stations on the southern shelf, temperature of 9øC the net heat loss is reduced by 10%. SMOF, ROOF, and GOOF, trace the equatorward current.

13 CH]EN AND WANG: DATA ASSIMILATION MODEL OF THE SBC CIRCI ATION 15, O 2O e" "'e"' 20 o -20,, td Figure 13. Horizontal velocity shears between KOIN and KOOF (model, open circle; observation, solid circle) for (a) the base case, (b) the diagnostic case, (c) the constant salinity case, and (d) the deep reference level case. The zero velocity line is marked by a dashed line. The model currents at ROOF agree well with the interpolated value. This setup co Tesponds to a diagnostic observations; sudden increase of the equatorward flow in calculation. In the second case, salinity is fixed at a constant spring is well reproduced. The model currents at GOOF are value of 33.4 (the mean of all SBC observations) to examine too small, indicating that the equatorward flow turns away the effect of incorporating horizontal salinity gradients. In the from the southern shelf too early. In summary, the model third case the reference level is moved to 1000 m to evaluate results capture the strength of the cyclonic eddy but the effect of including deep (>250 m) horizontal temperature underestimate its east-west extent. gradients. (The temperature structure below 100 m is obtained Figure 11 shows comparisons of currents at 45 m. The by interpolation between 100 m and the reference depth; see model currents on the southern shelf agree with the Section 4.1.) observations. The strong surfac equatorward flow (in spring) Figure 12 shows seasonal mean velocity and temperature at GOOF is barely noticeable at 45 m. The model currents on cross sections obtained from the diagnostic calculation at y = the northern shelf severely underestimate the observed 240 km. The interpolated isotherms are flat, lacking the poleward flow in summer. Auad et al. [1999] suggested that distinct doming structure obtained from the data assimilation the core of the inshore poleward flow is at about 100 m depth calculation (Figure 8). Because temperature moorings are [see also Hickey, 1993]. Since the observations are restricted located on the edge of the cold eddy, statistical interpolation to the upper 100 m, perhaps they do not resolve the cannot be expected to yield realistic temperature structures. subsurface temperature structure. Smaller horizontal temperature gradients in the diagnostic model consequently lead to weaker cyclonic circulation Sensitivity Study Figure 13 compares the velocity differences between ROIN Three modifications of the base case are tested to highlight and ROOF (at 5 m) between the base case and the three test the velocity response to different data assimilation cases. ROIN minus ROOF measures the strength of the applications. In the first test case the data assimilation is cyclonic eddy. The base case faithfully reproduces the mined off, and temperature and salinity are updated using the amplitude and the seasonal cycle of the cyclonic eddy. The

14 15,740 CI-[EN AND WANG: DATA ASSIM/LATION MODEL OF THE SBC CIRCULATION m 0,4-0, a_ tc Month Month Figure 14. (a) Temperature and (b) salinity differences between ANMI and PAIN for 5m (circle), 45 m (triangle), and 100 m (square). (c) The pressure difference in the base case (circle), and the constant salinity case (triangle), and (d) the deep reference level case (circle). diagnostic model predicts a velocity shear about half that of' the base case, the constant salinity case misses the velocity increase in spring and summer, and the 1000 m reference level case produces a velocity shear too large in summer. The differences in the model response may be understood in terms of the along-channel pressure forcing. We calculate the surface pressure with respect to a reference level according to Psurface = Preference_level + lreference_level gp dz (5) where g is gravity constant and p is density. Figure 14 shows temperature and salinity differences at 5, 45, and 100 m between ANMI and PAIN and the corresponding surface pressure differences. The temperature differences between ANMI and PAIN are IøC in winter and 5øC in summer (at 5 m). Salinity at ANMI is higher than at PAIN in winter but lower in summer. The salinity effect tends to compensate the temperatureffect in winter but enhances the density contrast in summer. This leads to a significant seasonal cycle in the surface pressure gradient. With a constant salinity the seasonal signal diminishes (test case 2), and for a deeper reference level the small density difference below 250 m is greatly exaggerated in summer (test case 3) Discussion In this study the data assimilation model generates realistic temperature and flow fields inside the SBC. The diagnostic calculation, using identical data information content, gives far less satisfactory results. This is because the data assimilation model is constrained by the equations of motion to produce dynamically consistent temperature and flow fields. The data assimilation model thus can be used as a sophisticated fourdimensional analysis tool, which likely will be superior to a statistical interpolation. The analyzed flow and temperature fields are useful for many practical applications. For example, the particle trajectories and the mass and material transports can be calculated from the model flow field. By assimilating a comprehensive real data set as opposed to the more common practice of using model "data" this study unveils a challenging data issue [Malanotte-Rizzoli and Young, 1992]. Current meter moorings are typically localized, and extrapolations outside the mooring array are bound to be erroneous. In this study the permanent front near San Miguel is bogus, and the relatively uniform temperature in the SMB also are unrealistic. This problem represents probably the most severe drawback in present approach, but there is no obvious technique to circumvent the difficulty of having too few data.

15 CHEN AND WANG: DATA ASSIMILATION MODEL OF TI-IE SBC CIRCULATION 15,741 We test a hypothetical situation in which all interisland Beardsley, R. C., The surface heat flux over the northern California passages are closed. We are interested to find out how the shelf during spring and summer, 1982 (abstract), Eos Trans. AGU, 67 (44), Fall Meet. Suppl., 1032, frontal location may affect model results. The model is renm Bretherton F. P., R. E. Davis, and C. B. Fandry, A technique for for the summer condition when the temperature front is objective analysis and design of oceanographic experiment strong. The results indicate that the poleward flow is not applied to MODE-73, Deep Sea Res., 23, , affected but the equatorward flow is greatly reduced. The Brink, K. H., and R. D. Muench, Circulation in the Point Conception -Santa Barbara Channel region, J. Geophys. Res., 91, , temperature gradients also become much weaker on the southern shelf. This suggests that within the constraint of Chen, D., and D.-P. Wang, Simulating the time-variable coastal assumed outside temperature structure the warm inflow upwelling during CODE 2, J. Mar. Res., 48, , through the interisland passages is important in keeping a Chen, D., S. G. Horrigan, and D.-P. Wang, The late summer vertical vigorous cyclonic circulation. On the other hand, factors not nutrient mixing in Long Island Sound, J. Mar. Res., 46, , considered in the model, such as wind forcing may also be Daley, R., Atmospheric Data Analysis, Cambridge Univ. Press, 455 able to keep a strong equatorward flow. pp., New York, Wind forcing is not explicitly included in this study. This Ghil, M., and P. Malanotte-Rizzoli, Data assimilation in meteorology may sound peculiar considering that wind forcing is and oceanography, Adv. Geophys., 33, , Harms, S., Circulation induced by winds and pressure gradients in ultimately responsible for the east-westemperature gradient the Santa Barbara Channel, Ph.D. thesis, 138 pp., Scripps Inst. of along the SBC. However, not explicitly including wind Oceanogr., Univ. of Calif., San Diego, La Jolla, forcing does not imply the model should fail to capture the Harms, S., and C. D. Winant, Characteristic pattern of the circulation wind-driven currents. The seasonal mean currents are in the Santa Barbara Channel, J. Geophys. Res., 103, baroclinic and therefore are closely related to the density 3065,1998. Hickey, B., Circulation over the Santa Monica-San Pedro Basin and structure. The effect of wind forcing is felt through the shelf, Prog. Oceanogr., 30, , adjustment in density field, which is assimilated by the model. Largerleof, G. S. E., and R. L. Bernstein, Empirical orthogonal The only important missing wind-driven component is the function analysis of advanced very high resolution radiometer surface Ekman current, which nonetheless is poorly resolved surface temperature pattern in Santa Barbara Channel, J. Geophys. Res., 93, , by the 5-m current. Including wind forcing may allow the Malanotte-Rizzoli, P., and R. E. Young, How useful are localized model to predict temperature and velocity structures in clusters of traditional oceanographic measurements for data regions where the observations are lacking. This could assimilation, Dyn. Atmos. Oceans, 17, 23-61, improve the overall performance, although success is not Moore, A.M., N. S. Cooper, and D. L. T. Anderson, Initialization and data assimilation in models of the Indian ocean, J. Phys. necessarily guaranteed. Oceanogr., 17, , Oey, L.-Y., Flow around a coastal bend, a model of the Santa Barbara eddy, J. Geophys. Res., 101, 16,667-16,682, Acknowledgments. This study was supported by the Pacific Outer Continental Shelf (OCS) Region of the Minerals Management Rutherford, I. D., Data assimilation by statistical interpolation of forecast error fields, J. Atmos. Sci., 29, , Service (MMS). Dave Browne is the MMS contract officer. Clinton Smedstad, O. M., and J. O'Brien, Variational data assimilation and Winant organized the SBC-SMB Coastal Circulation Study and parameter estimation in an equatorial Pacific Ocean model, Prog. furnished the current meter data for this study. Leo Oey provided Oceanogr., 26, , valuable inputs to the model study. We also acknowledge the critical Wang, D.-P., Model of frontogenesis: Subduction and upwelling, J. comments from two anonymous reviewers. Chen was on educational Mar. Res., 51, , leave from the Taiwan (ROC) Navy during the course of this study. Wang, D.-P., Effects of small-scale wind on coastal upwelling with application to Point Conception, J. Geophys. Res., 102, 15,555-15,566, References Winant, C. D., and C. E. Dorman, Seasonal patterns of surface wind stress and heat flux over the Southern California Bight. J. Geophys. Res., 102, , Atkinson, L. P., K. H. Brink, R. E. Davis, B. H. Jones, T. Palusziewicz, and D. Stuart, Mesoscale hydrographic variability in the vicinity of Point Conception and Arguello during April- May 1983: The OPUS 1983 experiment, J. Geophys. Res., 91, 12,899-12,918, Auad, G., M. C. Hendershott, and C. D. Winant, Mass and heat balances in the Santa Barbara Channel: estimation, description, and forcing. Prog. Oceanogr., in press, C.-S. Chen, and D.-P. Wang, Marine Sciences Research Center, State University of New York, Stony Brook, NY (wang pro.msrc.sunysb.edu.) (Received March 24, 1998; revised March 15, 1999; accepted March 24, 1999.)