Coupling of Coastal Zone Color Scanner Data to a Physical-Biological Model

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 95, NO. C11, PAGES 20,201-20,212, NOVEMBER 15, 1990 Coupling of Coastal Zone Color Scanner Data to a Physical-Biological Model of the Southeastern U.S. Continental Shelf Ecosystem 3. Nutrient and Phytoplankton Fluxes and CZCS Data Assimilation JoJI ISHIZAKA1 Department of Oceanography, Texas A&M University, College Station Phytoplankton and nutrient fluxes across the 40- and 75-m isobaths at a nominal depth of 17 m were calculated from the distributions obtained with a physical-biological model of the southeastern U.S. continental shelf ecosystem. These flux estimates represent integrated values over a 200-km region of the southeastern U.S. continental shelf and cover the period of April The phytoplankton and nutrient fluxes showed considerable variability with time; however, the fluxes across the 40-m isobath were primarily onshore while the fluxes across the 75-m isobath were primarily offshore. The fluctuations in the nutrient flux were associated with the passage of Gulf Stream frontal eddy events. The effect of frontal eddy events on the phytoplankton fluxes was less apparent. Comparison of the time average of the two fluxes over one month with similar estimates for the fluxes at m (Hofmann, 1988) showed a clear pattern of strong upwelling between the 40- and 75-m isobaths and an associated increase in phytoplankton concentration in the upper water column. In general, the pattern of the flux estimates was insensitive to the values chosen for the biological model parameters. The chlorophyll distributions obtained from nine Coastal Zone Color Scanner (CZCS) images from April 1980 were assimilated into the physical-biological model to improve the phytoplankton flux estimates. Three techniques were tested for CZCS data assimilation into physical-biological models, all of which gave stable model results. In general, the accuracy of the simulated chlorophyll fields was improved by assimilation of the CZCS data; however, the simulated fields rapidly converged to the fields obtained with no CZCS data assimilation after a few days. The time change of the phytoplankton carbon fluxes from the model with CZCS data assimilation were very similar to the fluxes obtained from the model with no CZCS data assimilation. However, the magnitude of the phytoplankton fluxes was less than the one obtained with no data assimilation because of the overestimation of the chlorophyll concentrations by the original model. The assimilation of CZCS chlorophyll into the physical-biological model significantly improved the predictive capability of the model for phytoplankton distributions and associated phytoplankton fluxes. However, it is difficult to determine if the accuracy of other components of the model, such as the nutrient fields, is also improved by the assimilation of CZCS data. 1. INTRODUCTION Walsh et al. [1981a, b] suggested that a significant portion of the organic carbon produced on continental shelves is exported and eventually buried on the continental slope. However, Walsh [1988] showed that carbon export from continental shelves varies with time and space and that carbon export is the result of complex physical and biological processes. For example, a carbon budget constructed for the broad Bering Sea continental shelf shows that the large benthic community consumes most of phytoplankton carbon produced in the inner continental shelf while the production at the outer continental shelf is mostly exported. In the Mid-Atlantic Bight, the Ekman flow produced by wind events resulted in different fates for the material transported in the upper and lower portions of the water column. Walsh et al. [1981b] speculated that the fate of ephemeral carbon production on the southeastern U.S. continental shelf is offshore export. Hofmann [1988] constructed a physical-biological model of the southeastern U.S. continental shelf ecosystem and used the simulated distributions obtained from the model to 1Now at the National Research Institute for Pollution and Resources, Tsukuba, Ibaraki, Japan. Copyright 1990 by the American Geophysical Union. Paper number 90JC /90/90JC estimate phytoplankton carbon and nitrate fluxes across the 40- and 75-m isobaths during April 1980 for a 200 km portion of this region. Holmann [1988] concluded that there was significant offshore phytoplankton flux during spring that was primarily associated with Gulf Stream frontal eddy upwelling. However, the flux of phytoplankton carbon was primarily onshore during summer months when Gulf Stream bottom intrusions are the major nutrient source for this region. These conclusions were based on flux estimates that are representative of a nominal depth of m and did not include information from other depths. Ishizaka [this issue (a)] constructed a similar physicalbiological model of the southeastern U.S. continental shelf ecosystem for a nominal depth of 17 m for the April 1980 period. In this last of the series of three papers, phytoplankton carbon and nutrient nitrogen fluxes across the 40- and 75-m isobaths are calculated from this model for 17 m, and the results are compared with those given by Holmann [1988]. The combination of the results of the two studies makes possible the construction of an overview of the fate of the average material flux along a portion of the outer southeastern U.S. continental shelf. Ishizaka [this issue (a)] compared the simulated chlorophyll fields obtained with the physical-biological model with nine Coastal Zone Color Scanner (CZCS)-derived chlorophyll distributions from the southeastern U.S. continental shelf and found good agreement between the two. Ishizaka [this issue (a)] also demonstrated how the correlation be- 20,201

2 20,202 ISHIZAKA: COUPLING CZCS DATA TO MODEL--FLUXES AND DATA ASSIMILATION tween chlorophyll fields obtained from the CZCS and those from a physical-biological model change with variations in the values used for the model parameters. This study continues the analysis of application of CZCS data to modeling studies by demonstrating how these data can be assimilated into a physical-biological model to improve the accuracy of the estimates of the phytoplankton distributions and the associated phytoplankton carbon flux. Three procedures for upgrading the physical-biological model with the CZCS chlorophyll fields are tested. In this study, upgrading is defined as replacing the model phytoplankton fields with the corresponding CZCS chlorophyll fields. This requires that the other model components be adjusted so as to be in agreement with the new phytoplankton concentration estimates. Several numerical experiments and statistical tests were conducted to determine which of the three methods was best for upgrading the physical-biological model. This study is focused on a small portion (200 km along-shore) of the outer southeastern U.S. continental shelf. However, the results of the CZCS data assimilation experiments have relevance to the more general problem of the use of ocean color measurements with physical-biological models. The following section describes the phytoplankton carbon and nutrient nitrogen fluxes across the 40- and 75-m isobaths that were obtained from the simulated phytoplankton and nutrient nitrogen distributions. Comparisons of these flux estimates with those given by Hofmann [1988], and a discussion of the sensitivity of the flux estimates to the values of the biological parameters used in the model are also given in this section. Section 3 presents the three methods that were developed for the assimilation of the CZCS data into the physical-biological model. The effect of assimilation of the CZCS measurements on the phytoplankton and nutrient nitrogen flux calculations is described in section 4. Section 5 is a discussion of the results. 2. ACROSS-SHELF FLUXES AND SENSITIVITY The across-shelf fluxes of nutrient nitrogen and phytoplankton carbon (Figure 1) were calculated along the 40- and 75-m isobaths in a manner similar to that used by Hofmann [1988]: flux = Cudy (1) TLy onshore flux that occurred here on April 1, 6, and 15 may be where TLy is the total length of the isobath in the along-shelf (y) direction, C represents either the nutrient or phytoplankton concentration obtained from the Eulerian model [Ishizaka, this issue (a)], and u is the across-shelf velocity at the particular isobath. Since the distributions obtained from the model are at a depth of 17 m, the flux estimates are representative of only this one level. Negative and positive values indicate onshore and offshore fluxes, respectively. The phytoplankton carbon estimates were calculated from the phytoplankton nitrogen distributions obtained from the model by assuming a Redfield C :N ratio of 6.6 (mol C :mol N). The nutrient and phytoplankton fluxes showed considerable time variations; however, the fluxes at the 40-m isobath tended to be onshore while those at the 75-m isobath tended to be offshore. This pattern is consistent with frontal eddy a. Phytoplankton Carbon Flux 1.00 I rn,,...,,,,,-/ ',,,/, "/ 40-m April b. Nutrient Nitrogen Flux rn 0 '-' "" :/ ' / - -"'"'"/ ß wj' ß v.,,,,; œ,.,,, m T T T? T T, April Fig. 1. (a) Phytoplankton carbon fluxes and (b) nutrient nitrogen fluxes at a depth of 17 m on 40- and 75-m isobaths. Dotted and solid lines indicate the flux at the 40- and 75-m isobaths, respectively. Positive indicates an offshore flux; negative indicates an onshore flux. Arrows on the bottom panel indicate the times when a Gulf Stream frontal eddy passed through the model domain. upwelling that is most intense between the 40- and 75-m isobaths. Frontal eddy events are the major factor influencing the nutrient nitrogen flux at the 75-m isobath. Eight frontal eddy events passed through the model domain during April of 1980 [Ishizaka, this issue(b)] (arrows at the bottom of Figure 1). Strong offshore fluxes immediately following onshore fluxes were observed at the 75-m isobath on April 5, 10, 13, and 21 when frontal eddies (2, 3, 4, and 6 of Ishizaka [this issue (b)]) passed through the middle of the model domain. The influence of the frontal eddies on the nitrogen fluxes at the 40-m isobath was not as clear; however, the strong the result of eddy events; the increased nutrient introduced by the upwelling moved across the shelf to the inshore. The influence of frontal eddies on the phytoplankton fluxes across both the 40- and 75-m isobaths was less obvious, probably because of time lags associated with the growth of phytoplankton. These patterns of time change fluxes were similar to the ones observed at nominal depth of m [Hofmann, 1988]. The time-integrated nutrient and phytoplankton fluxes for the 26 days from April 1 to April 26 are shown in Table 1. Also, shown for comparison are the fluxes estimated for a depth of m [Hofmann, 1988]. In general, the 17-m nutrient nitrogen fluxes were slightly lower and the phytoplankton carbon fluxes were higher than the values estimated at 37 m. It is reasonable to expect less nutrient and more phytoplankton at a depth of 17 m. A schematic

3 ISHIZAKA' COUPLING CZCS DATA TO MODEL--FLUXES AND DATA ASSIMILATION 20,203 TABLE 1. Phytoplankton and Nutrient Flux Across the 40- and 75-m Isobaths Depth 17 m m 40-m isobath 75-m isobath 40-m isobath 75-m isobath Phytoplankton -196 mol C m d p,g C m -2 S p, mol C m -2 s p, mol C m -2 s p, mol N m -2 s p, mol N m -2 s mol C m d p,g C m -2 s p, mol C m -2 s p, mol C m -2 s p, mol N m -2 s p, mol N m -2 s -1 Nutrient mol N m d /zg N m -2 s /xmol N m -2 s /xmol N m -2 s mol N m d /xg N m -2 s /xmol N m -2 s /xmol N m -2 s -1 The fluxes were averaged over 200 km in the along-shelf direction. The fluxes at 17- and 37 to 45-m depth represent averages over 26 and 21 days, respectively. Fluxes at m are from Hofmann [1988]. comparison of the nutrient and phytoplankton fluxes from 17 and 37 m is given in Figure 2. The nutrient fluxes were at all locations onshore except at 17 m on the 75-m isobath. The highest nutrient flux occurred at the bottom on the 45-m isobath where nutrient was input by upwelling between the 75- and 40-m isobaths. The small offshore nutrient flux at m 75 m Phytoplankton Nitrogen. l '.i. ;J...::..,...::...,:},_/...:.. ::. fi.,: Nutrient,.;.. :,..,,:.. :,,, Nitrogen r ' 10 gmoi-n r.2 s-1 ' Fig. 2. Phytoplankton nitrogen (upper arrows) and nutrient nitrogen (lower arrows) fluxes at 17 m (this study) and 37-45m [Holmann, 1988] at the 40- and 75-m isobaths. Both fluxes are expressed as nitrogen. 75-m isobath approached zero when the maximum phytoplankton growth rate(/a m) was zero (Figure 3a) and when the phytoplankton loss rate (/5) reached values of 0.8 d -i which is the standard value of/a, m (Figure 3c). These results arise because the consumption of phytoplankton by zooplankton was greater than the primary production in the model domain when/a, m was close to zero or when/5 was large. Similar to the phytoplankton flux, the nutrient flux was also insensitive to the parameter values used for the biological model (Figure 4). Negative nitrogen fluxes occurred at m on the 75-m isobath indicates that some of the upwelled water is transported offshore. The onshore phytoplankton flux at the 40-m isobath indicates that the nutrients brought onshore by the upwelling stimulates phytoplankton growth that is then transported across the shelf to the midshelf area. Also, a the 75-m isobath when/a, m exceeded 1.6 d -1(Figure 4a), which portion of the upwelled nutrient is consumed by phytoplankton indicates that all of the nutrient upwelled between the 40- and but then exported offshore in the surface waters at the 75-m isobath. However, in considering Figure 2, it should be noted that the flux calculation does not conserve mass because of the divergent flow field used to force the model and because of the open boundaries of the model domain. The effect of the value chosen for the biological parameters on the phytoplankton fluxes was examined with the 75-m isobaths was depleted due to the rapid uptake by phytoplankton. The values chosen for the phytoplankton half saturation constant (Ks), Ivlev constant (A), zooplankton ingestion efficiency (e), and nutrient regeneration rate (F) had little effect on the both nutrient and phytoplankton fluxes. The sensitivity of the fluxes to parameter values in a small region (_+ 10%) around the standard values was also calcumodel (Figure 3). The fluxes showed marked differences only when the model chlorophyll fields were significantly lated from the results of three different follows: model cases as different from the CZCS chlorophyll fields. The sign of the flux was almost always not effected by the value of the biological parameters. The phytoplankton carbon flux at the p Os (s(+ 10%) - s(- 10%)) / s Op s(standard) / 0.2 (2) where p is the biological parameter and s is the phytoplankton or nutrient flux. The flux obtained from the model with a standard parameter value is given by s(standard). The flux obtained from the model with _+ 10% of the standard value of a biological parameter is denoted by s(- + 10%). The factor, 0.2, represents a 20% change in the parameter. Positive and negative changes in the sensitivity indicate that the flux increases or decreases with an increase in the parameter value, respectively. This sensitivity analysis illustrates the extent to which the flux changes with changes in the biological parameters. The sensitivity of the fluxes was generally smaller than 1.0 and not very sensitive to the changes in the value of the biological parameters (Table 2). Changes in the maximum zooplankton grazing rate (Rm) had the most effect on the phytoplankton fluxes, and changes in the maximum phytoplankton growth rate (/am) had the most effect on the nutrient fluxes. Both the phytoplankton and nutrient fluxes were

4 ß 20,204 ISHIZAKA: COUPLING CZCS DATA TO MODœL--FLUXœS AND DATA ASSIMILATION ß (day's) Rm (day' ) 25O (day'1) d -500 ß!,! m day '1) 5OO ,3. ß i ß i ß i ß i ß K, (FM) ß._ -250 a "-'-' 'a'"' ,,., g, -, ' ß ß i ß f X. (FM'l ) ß i ß i ß i Fig. 3. Changes in the phytoplankton carbon flux that result from changes in the biological parameters. The biological parameters that were changed are (a) phytoplankton maximum growth rate/a m, (b) zooplankton maximum ingestion rate Rm, (c) phytoplankton death rate /5, (d) zooplankton death rate m, (e) half saturation constant for phytoplankton growth Ks, (f) Ivlev constant A, (g) zooplankton ingestion efficiency e, and (h) regeneration fraction F. Vertical lines indicate the standard values of the parameters. r' h insensitive to the nutrient regeneration ratio (F). The sensitivity of the fluxes was of the same order as the sensitivity of the statistics computed for the chlorophyll distributions [Ishizaka, 1989], which is a reflection of the fact that the fluxes were calculated from the output of the same model. 3. ASSIMILATION OF CZCS DATA INTO THE PHYSICAL-BIOLOGICAL MODEL One of the important potential uses for CZCS data is to provide a means to upgrade physical-biological models. In this study, upgrading means an improvement in model capability through the assimilation of available CZCS chlorophyll distributions into the model solutions. The upgrading of a physical-biological model with observations may significantly improve the predictive capability of the model through the incorporation of realistic field distributions. Several numerical experiments were conducted to test the feasibility of the use of CZCS measurements for the upgrading of a physical-biological model. First, the model simulations were upgraded with the CZCS chlorophyll distribution observed on April 10. The correlation and root mean square error (RMSE) between the model distributions and subsequent CZCS images were examined [cf. Ishizaka, this issue (a)]. April 10 was chosen as a starting point in this analysis because there were no cloud-covered areas in the CZCS image from this day and

5 ,,, ISHIZAKA: COUPLING CZCS DATA TO MODEL--FLUXES AND DATA ASSIMILATION 20,205 loo e / ,. loo Pm (day '1) ß! Rm (day" ) b 50 - i.e o! ( -loo! ß i ß i ß $ (day' ) loo c m (day' ) -I- 0, so o 50 0 C) ø50-50 i ß i ß i ß Ks X ( M ' ) 100,, f e : : ' g -100,., ß i i ß ' i ß i ' r' h 1.00 Fig. 4. Same as Figure 3, except for the nutrient nitrogen flux. because CZCS data were available on April 11, 12, 15, and 16 which formed a good sequence for comparisons. The procedure for upgrading the model with the CZCS is as follows: (1) The model was started on March 15, similar to previous numerical experiments, and run until April 10. (2) The simulated phytoplankton field for this day was replaced with the CZCS chlorophyll distributions. (3) The nutrient (N), zooplankton (Z) and detritus (D) fields were also replaced with one of the methods described below so as to be consistent with the new phytoplankton fields. (4) The model was then restarted and subsequent simulated fields were compared with the appropriate CZCS distributions. Upgrading the model with CZCS information requires new estimates for the other biological fields: N, Z, and D. Three different methods were tested in this study (Figure 5). The first assumes constant values of 0.1/aM N for both N and Z, TABLE 2. Sensitivity of Phytoplankton and Nutrient Fluxes at the 40- and 75-m Isobaths Phytoplankton Nutrient Parameters 40 m 75 m 40 m 75 m P'm K s Rm A e & rn F The sensitivity was calculated from the difference in the fluxes obtained from the model with _+ 10% of the standard value for each parameter.

6 20,206 ISHIZAKA: COUPLING CZCS DATA TO MODEL--FLUXES AND DATA ASSIMILATION o 1.0 Ratio x x _ Constant x ß ModelJ -x '" Ratio / 0 x Constant [] Model 1 2'0 April 1980 Fig. 5. Time variations in the COR and RMSE. Heavy line indicates the nonupgraded model (None). Other lines indicate the results obtained from the model that was upgraded with the April 10 CZCS data. Those results that used a constant 0.1 /am nutrient and 0.1/aM N zooplankton are indicated by the white square (constant). Results obtained with the model nutrient and zooplankton distributions are indicated by the solid square (model). Results obtained with a ratio of nutrient and zooplankton are indicated by the cross (ratio). See text for details of the three methods. and D was calculated by the difference between the total nitrogen estimated from temperature and the total of the P-N-Z nitrogen. Second, the model distributions were used for N and Z, and D was calculated in a manner similar to the previous method. Third, a ratio between N:Z:D in the model distributions was assumed to hold, and the new N-Z-D concentrations were calculated from the difference between the total nitrogen estimated from temperature and phytoplankton concentration obtained from the CZCS. The three approaches for estimating the new N-P-D fields gave results that were not very different from each other (Figure 5), and the correlation and RMSE for the resultant distributions converged to the values of nonupgraded model results quickly. The results obtained with the CZCS upgrade for the following day are better than the results obtained with the nonupgraded model. However, the differences between the nonupgraded and upgraded model were very small after 2 days. One practical concern is that the replacement of the phytoplankton fields with the CZCS chlorophyll distributions may introduce computational mode in subsequent simulated fields. For this study, there were no apparent computational problems associated with assimilating CZCS data into the model. The model was stopped for the upgrade once and then restarted with an explicit finite different scheme. This procedure maintained coupling of the two time levels required for the leapfrog differencing scheme and did not create a large computational mode. The results of a series of numerical experiments in which b the model was initialized with the April 10 CZCS distributions and in which the N-Z-D distributions were obtained with the ratio of model concentrations (method 3) are shown in Figure 6. For comparison, the COR and RMSE for the CZCS data and model distributions obtained without biological processes and the upwelling terms and with a smaller horizontal eddy diffusion coefficient (106 cm 2 s -1) are also shown on Figure 6. The model results from the small horizontal eddy diffusion coefficient case were chosen for the comparison because the original diffusion coefficient (8 x 106 cm 2 s -1) resulted in smooth chlorophyll distributions which do not show the detailed chlorophyll structures that are generated by horizontal advection [Ishizaka, this issue(a)]. The model without biological processes reproduces the chlorophyll distributions detected by the CZCS fairly well. As seen by the Lagrangian particle tracing experiments presented by Ishizaka [this issue(b)], the high-chlorophyll plume in the southern model domain extended to the north and formed a high-chlorophyll band on April 15 and 16. The low-chlorophyll water in the northern portion of the model domain on April 10 was trapped between the shelf water and this band. On April 12, the high-chlorophyll patch was advected northward from the south and eventually formed another high-chlorophyll band on April 15. However, the chlorophyll distribution obtained from the model with biological processes and the upwelling terms gave overestimations in the northern part of model domain on April This overestimation is probably caused by the error in the upwelling terms which introduces an excess amount of chlorophyll and nutrient into this region. The chlorophyll concentrations in the southern portion of the model domain on April 16 were underestimated with the model. This underestimation is also apparent in the simulated distributions obtained from the the model without biological processes and the upwelling terms. This probably indicates that the source of the error in this region is horizontal advection or the phytoplankton boundary condition rather than the upwelling terms. Next, a series of numerical experiments were performed to investigate the effect of upgrading only a part of the chlorophyll fields, as opposed to the entire field. This is necessary because CZCS observations are not available for cloud-covered areas and because the spatial discontinuity in the CZCS data may produce artificial waves in the biological fields. Again starting on April 10, only the northern or southern half of the phytoplankton field was replaced with the CZCS data. The other three biological fields were estimated with the ratio method (method 3) described previously. The COR and RMSE of the partially upgraded model was midway between those for the entire upgraded and nonupgraded cases, and the differences in the distributions relative to the original model disappeared within a few days (Figure 7). These results are consistent with the case in which the entire field was replaced by CZCS observations. The model was stable, and there was no computational instability caused by the partial upgrading although the upgrade did produce a discontinuity in the biological fields. In physical models, discontinuities in distributions are adjusted through the radiation of waves. For example, discontinuities of the free surface adjust through the radiation of surface gravity waves. In physical-biological models, discontinuities in the

7 ISHIZAKA: COUPLING CZCS DATA TO MODEL--FLUXES AND DATA ASSIMILATION 20,207 CZCS Expt. I Expt. 5 CHLOROPHYLL CHLOROPHYLL CHLOROPHYLL NO -t-nc +NI-E ZOOPLANKTON (pg.,- ) (pg.,- ) (pg-,- ) (pu-n) (,uu- N),, Fig. 6. CZCS-derived chlorophyll distributions (CZCS), simulated chlorophyll from the model without biological processes and the upwelling terms (experiment 1), and simulated chlorophyll, nutrient, and zooplankton distributions from the model with biological processes and the upwelling terms (experiment 5). The models were upgraded with CZCS data on April 10. The diffusion coefficient for experiment 1 was 106 cm 2 s -1. Dates of the distributions are (a) April 10, (b)april 11, (c) April 12, (d) April 14, (e) April 15, and (f) April 16. The contour intervals are 0.5 krg L -1, 0.5 /. M, and 0.1 /. M N for chlorophyll, nutrients, and zooplankton, respectively. The tick marks in the box are separated by 5 km. See Figure 1 of Ishizaka [this issue (b)] for the coordinates of the model region. biological fields are adjusted by a combination of advective, diffusive and biological effects [Okubo, 1980]. In this model, the advective speed is probably much higher than the propagation speed of the biological phenomena. Consequently, discontinuities in the simulated fields are moved primarily by advection. Diffusive and biological processes only slightly modify the discontinuity. The discontinuity remained near the region of the biological fields separating the upgraded and nonupgraded distributions. The effects of the discontinuity did not radiate into the upgraded

8 ß,,. 20,208 ISHIZAKA: COUPLING CZCS DATA TO MODELreFLUXES AND DATA ASSIMILATION CZCS Expt. I Expt. 5 CHLOROPHYLL CHLOROPHYLL CHLOROPHYLL NO3+ NO- + NH ZOOPLANKTON (pg-2-') (/ag-.-') (/ag- -' ) (/am-n) (/am-n).. :!?'"' -.,,. zj. ',l" ß ',:i.i- " ii :. " "... ß., ;.. f. i' ' '"' Fig. 6. (continued) and nonupgraded portions of the chlorophyll distributions. Since the COR and RMSE are calculated from chlorophyll concentrations at discrete model grid points, the discontinuity itself does not have an effect on the statistics used for the comparisons between the model and CZCS distributions. The values of these statistics are better than those obtained without upgrading the model unless the upgraded portion of the distribution is evident in the model fields. Discontinuities sometimes cause instabilities in circulation models because of the use of assumptions that are inconsistent with the physical dynamics of the model. In this study, the stability of the model distributions after a partial upgrade suggests that the procedures used for upgrading the model are, at least to first order, consistent with the biological dynamics of the model. Finally, to test whether the results obtained with the upgrade on April 10 are general or specific, the model was upgraded with CZCS data from the eight other CZCS chlorophyll distributions. The results were consistent with those for the April 10 partial and full upgrade (Figure 8). The

9 ISHIZAKA' COUPLING CZCS DATA TO MODEL--FLUXES AND DATA ASSIMILATION 20, ] Noah Full [] ß o,outh x NOne ß x ß / Full b o April 1980 Fig. 7. Time variations in the COR and RMSE when the model was updated with a part of the CZCS data. Crosses indicate the results from the model in which the entire domain was updated with CZCS data (full). Open squares indicate the results from the model in which only the northern half of the domain was upgraded with CZCS data (north). Solid squares indicate the results from the model in which only the southern half of the domain was upgraded with CZCS data (south). correlations and RMSE were improved for several days following the input of the CZCS data and then converged to the values obtained for the original model. None of initializations seriously increased the error of the calculations even though some of the CZCS images were irregularly covered by clouds. 4. EFFECT OF ASSIMILATION OF CZCS DATA ON THE ESTIMATE OF ACROSS-SHELF FLUXES As a comparison, the across-shelf phytoplankton and nutrient fluxes were calculated from the model distributions after assimilation of the CZCS data into the model (Figure 9). The basic patterns of the fluxes did not change from those estimated from the model without data assimilation (cf. Figure 1). The time variation of the phytoplankton flux was very similar to the one without data assimilation except that the magnitude of the flux was smaller. This result is consistent with the overestimation of the CZCS chlorophyll concentration by the model [Ishizaka, this issue(a)]. Assimilation of the CZCS measurements into the model resulted in a lower phytoplankton concentration and a smaller magnitude for the phytoplankton flux. There are some discontinuities in the phytoplankton flux following the assimilation of the CZCS data (cf. April 10). These discontinuities are caused by the sudden change in chlorophyll concentration associated with the upgrade. The pattern of the nutrient flux also did not change much from the previous flux estimates; however, the magnitude of the peaks in the nutrient flux became larger. Because chlorophyll concentrations were usually overestimated by the O O None April 1980 bl Fig. 8. Time variations in the COR and RMSE when the model was updated with CZCS data from the nine available dates in April model [Ishizaka, this issue(a)], the assimilation of the CZCS chlorophyll data results in a reduction of phytoplankton concentrations. This results in an increase of the nutrient nitrogen and consequently an increase of the nutrient flux. The time-integrated phytoplankton fluxes across the 40- and 75-m isobaths for the upgraded model results are shown a. Phytoplankton Carbon Flux m o.oo. /x_,.. I /,v...,-,,...,-,-,; ß I 40-m April b. Nutrient Nitrogen Flux o.10 3 v ß i - ' % 75-m,T... T,,T,,:. 2 4 ( ( April Fig. 9. Same as Figure 1, except that the model was upgraded with the CZCS chlorophyll distributions. White arrows on the top panel indicate the times of the model update.

10 20,210 ISHIZAKA: COUPLING CZCS DATA TO MODELreFLUXES AND DATA ASSIMILATION TABLE 3. Phytoplankton and Nutrient Flux Across the 40- and 75-m Isobaths 40-m isobath 75-m isobath 40-m isobath 75-m isobath Depth 17 m Phytoplankton -124 mol C m d gmol C m -2 s mol C m d /xmol C m -2 s -1 Nutrient mol N m d gmol N m-2 s mol N m d /xmol N m -2 s -1 The fluxes were averaged over 200 km in the along-shelf direction and over 26 days. These results are from a numerical experiment in which the simulaiton was upgraded with nine CZCS chlorophyll distributions. 1 0 x o. m-[]- a-= 0.8 I.... x o n' 0' None x in Table 3. The phytoplankton carbon fluxes were smaller for both the 40- and 75-m isobaths. The negative fluxes previously obtained were the result of the overestimation of the phytoplankton biomass by the nonupgraded model. The nutrient nitrogen flux at the 40-m isobath was approximately twice that obtained with the nonupgraded model. The fluxes at the 75-m isobath were slightly smaller. 5. DISCUSSION Phytoplankton and nutrient fluxes were calculated from the distributions obtained with the 17-m horizontal plane physical-biological model. Both the phytoplankton and nutrient flux were offshore at the 75-m isobath and were onshore at the 40-m isobath. The direction of these fluxes is consistent with the hypothesis that most of the upwelling occurs on the outer shelf between the 40- and 75-m isobaths. Combined with the flux estimates made at 37 m [Hofmann, 1988], the fluxes give an indication of the fate of upwelled water on the southeastern U.S. continental shelf. Most of the upwelled water is advected onshore across the 40-m isobath. The nutrients are consumed by the phytoplankton, and phytoplankton concentrations increase. At 17 m, some of the upwelled water is advected offshore across the 75-m isobath and nutrients in the water are depleted by the phytoplankton. The sensitivity analyses of the phytoplankton and nutrient fluxes illustrate the robustness of flux estimates of this study. The direction of the flux did not change, in general, with changes in the values of the biological parameters. The magnitude of the flux also did not change significantly, except for parameter sets that were unrealistic. As discussed by Ishizaka [this issue(a)], most of the error in the simulated chlorophyll distributions may result from the estimate of the upwelling term. The omission of phytophagous fish and larger gelatinous zooplankton may also result in error in the simulated phytoplankton biomass. The effect of these factors, which were not investigated with the sensitivity analysis, should be studied. Assuming that the upgraded model provides more accurate estimates of the phytoplankton carbon flux, the error associated with the magnitude of the estimates obtained from the non-upgraded model can be obtained by comparing Figures 1 and 9. The difference in the magnitude of the two carbon flux estimates is approximately 50%; those from the b : April 1980 Fig. 10. Same as Figure 8, except that the model does not include biological processes and the upwelling terms. upgraded model are one-half those from the nonupgraded model. Hence the error in the flux calculation obtained from the nonupgraded model should be approximately 50% of the carbon flux estimates. The two horizontal physical-biological models developed for the southeastern U.S. continental shelf do not have sufficient resolution or dynamics to calculate accurately the nutrient and phytoplankton fluxes throughout the entire water column. However, it is possible to use the results from these models to obtain an order of magnitude estimate for the carbon flux from the continental shelf across the 40- and 75-m isobaths. Assuming that the flux estimates obtained from this study (Table 3) and those obtained from Holmann [1988] (Table 1) represent the average carbon flux for the upper and lower portions of the water column, relative to a middepth of 27 m on the 40-m isobath and 31 m on the 75-m isobath, the depth-integrated carbon exports are 1331 and 1727 g C m -1 d -] for the 75- and 40-m isobaths, respectively. The estimated depth-integrated fluxes are 961 and 1219 g C m -] d -, if the fluxes are calculated assuming a linear increase from zero at the surface to the flux value at 17 m and a linear decrease from the flux value at m to zero at the bottom. For middepth, a linear decrease was assumed between the flux value at 17 m and that at m. Yoder et al. [1983] estimated an average primary production for the southeastern U.S. continental shelf during spring of 1 g C m -2 d -1. This can be used to obtain an estimate of the total primary production of 2 x 104 g C m - d -1 for the region between the 40- and 75-m isobaths, assuming a mean distance between the two isobaths of 20 km. The total export across the 45- and 75-m isobaths based on the model-derived flux estimates ( g C m -1 d -1) is about 5-10% of the total primary production between these isobaths. The offshor export ( g C m -1 d -1) is only 6-9% ofthe total primary production. These percentages are only 1/5 -- 1/10 of the annual carbon budgets estimated for the Bering Sea, Mid-Atlantic Bight, and Gulf of Mexico [Walsh, 1988]. Using a three-dimensional physical-biological model, Walsh et al.

11 ISHIZAKA: COUPLING CZCS DATA TO MODELreFLUXES AND DATA ASSIMILATION 20,211 [1987] found that approximately 14% of the spring bloom primary production was exported from the Mid-Atlantic Bight. Additional modeling studies [Walsh et al., 1988] found that carbon export for the Mid-Atlantic Bight ranged from 8 to 38% of the average new production. These percentages are similar but still higher than the shelf carbon export estimated from this study. This would appear to contradict the speculation by Walsh et al. [1981b] that the fate of ephemeral carbon production on the southeastern U.S. continental shelf is offshore export. As shown by Walsh [1988], carbon flux on continental shelves is a complicated process which varies considerably with time and space. This variability may be one explanation of the low estimate of primary production export from the southeastern U.S. continental shelf. There are many physical and biological processes that can affect the estimate of carbon flux on the southeastern U.S. continental shelf. For example, on the basis of the same CZCS data used in this study, McClain et al. [1984] concluded that there was a significant offshore flux of inshore water during April This discrepancy is caused primarily by the integration of processes over varying time and space scales. Furthermore, Hanson et al. [1988] recently found that the bacterioplankton production was very different between April 1984 and 1985 and depended to a large extent on the physical dynamics at the southeastern U.S. continental shelf. Thus a model restricted to an along-shelf distance of 200 km and to the time of April 1980 may underestimate or overestimate the carbon export from the continental shelf. Also, the low vertical resolution of the flux calculations used for this estimate and the use of independent estimates obtained from two different physical-biological models may cause a significant bias in the estimate of the total carbon export from the shelf. A quantitative analysis of fate of phytoplankton carbon in this region requires additional field observations and modeling studies. In this study, three different methods for estimating the nutrient, zooplankton, and detritus fields from the CZCS chlorophyll fields and the model results were tested. The results are not significantly different each other. This is an indication that horizontal advection is the main mechanism controlling the phytoplankton distributions in this region and that biological processes are a secondary mechanism that maintains the phytoplankton biomass [lshizaka, this issue(a)]. However, for regions where the biological effects are much stronger, the particular choice for an assimilation method may result in more difference in the results obtained with a physical-biological model. The results of numerical experiments designed to investigate the upgrading procedures used in this study are both encouraging and discouraging. The stability of the model was very good and upgrading of the model with CZCS data improved the accuracy of the simulated phytoplankton distributions. Furthermore, even when the model was upgraded with CZCS data that had irregular cloud covered regions, the model results were significantly improved. However, the correlation and error converged to the nonupgraded model results after only a few days, thereby, implying that it is necessary to update the model frequently, every 1-2 days, in order to keep the error of the simulated distributions small. One question is then obviously, why do the correlation and error converge to the results of the nonupgraded model so quickly? The model was run without biological processes and the upwelling terms, but with the chlorophyll fields upgraded with the CZCS data as described for the previous experiments (Figure 10). The results obtained were very close to the results of previous experiments, with the correlation and errors of the two converging within a few days. However, the convergence was not as strict as seen for the previous experiments which indicates that the upwelling and associated biological processes may have some effect on the convergence. Consistent with the results given by Ishizaka [this issue(a)], generally the COR was lower and the RMSE was higher for the model with biological processes and upwelling terms. This indicates that the fast convergence is at least partially caused by the error in the advective fields, the boundary conditions, and the difference in the spatial scales between the CZCS and simulated phytoplankton fields. However, the upwelling terms and biological parameters may also contribute to the quick convergence. Phytoplankton and nutrient fluxes were calculated from the simulated distributions obtained from the numerical experiments in which CZCS data were assimilated into the model. The fluxes estimated from these distributions gave nutrient fluxes that were doubled, relative to those obtained from the nonupgraded model distributions, and lower phytoplankton fluxes. The phytoplankton flux is calculated from the phytoplankton biomass; therefore assimilation of information that improves the phytoplankton biomass estimate should increase the accuracy of the phytoplankton flux calculation. However, the consequence of this is that the nutrient concentration increased with the reduction of the phytoplankton biomass and consequently overestimates the nutrient flux. The nutrient flux estimated after the inclusion of CZCS data in the model is probably less accurate than the estimate obtained from the nonupgraded model because errors in the model may accumulate in the nutrient component. This implies that data assimilation may not necessarily improve the accuracy of the entire model and may actually reduce the accuracy of individual model components. Thus caution is warranted when assimilating data into models, particularly models that contain many interlinked components, such as ecosystem models. However, data assimilation does hold promise for improving the accuracy of certain model components. Hurlburr [ 1986] considered methods for updating an eddyresolving primitive equation circulation model with sea surface altimeter data. This study also discussed procedures for obtaining subsurface pressure distributions from the combination of altimeter data and model results. For this horizontal plane model, biological components other than chlorophyll were estimated from a combination of the CZCS chlorophyll data and the model results. In order to assimilate the ocean color data into a three-dimensional physicalbiological model, further constraints need to be developed that will allow estimation of the subsurface phytoplankton fields and other biological parameters. Acknowledgments. I thank E. E. Hofmann and C. R. McClain for their continuous advising throughout this study and for various comments on the three manuscripts. E. E. Hofmann kindly provided me with her computer programs. I also thank three anonymous reviewers for their helpful comments. This work is partial fulfillment of the requirements for the degree of doctor of philosophy in the Department of Oceanography at Texas A&M University. This research was supported by grant UPN /2714-IRP-120 from the NASA Ocean Processes Branch, NASA grant NAGW-852.

12 20,212 ISHIZAKA: COUPLING CZCS DATA TO MODEL--FLUXES AND DATA ASSIMILATION REFERENCES Hanson, R. B., L. R. Pomeroy, J. O. Blanton, B. A. Biddanda, S. Wainwright, S.S. Bishop, J. A. Yoder, and L. P. Atkinson, Climatological and hydrographic influences on nearshore food webs off the southeastern United States: Bacterioplankton dynamics, Cont. Shelf Res., 8, , Hofmann, E. E., Plankton dynamics on the outer southeastern U.S. continental shelf, part III, A coupled physical-biological model, J. Mar. Res., 46, , Hurlburt, H. E., Dynamic transfer of simulated altimeter data into subsurface information by a numerical ocean model, J. Geophys. Res., 91, , Ishizaka, J., Coupling of Coastal Zone Color Scanner data to a physical-biological model of the southeastern U.S. continental shelf ecosystem, Ph.D. dissertation, 175 pp., Tex. A&M Univ., College Station, Ishizaka, J., Coupling of Coastal Zone Color Scanner data to a physical-biological model of the southeastern U.S. continental shelf ecosystem, 2, An Eulerian model, J. Geophys. Res., this issue (a). Ishizaka, J., Coupling of Coastal Zone Color Scanner data to a physical-biological model of the southeastern U.S. continental shelf ecosystem, 1, CZCS data description and Lagrangian particle tracing experiments, J. Geophys. Res., this issue (b). McClain, C. R., L. J. Pietrafesa, and J. A. Yoder, Observations of Gulf Stream-induced and wind-driven upwelling in the Georgia Bight using ocean color and infrared imagery, J. Geophys. Res., 89, , (Correction, J. Geophys. Res., 90, 12,015-12,018, 1985.) Okubo, A., Diffusion and Ecological Problems: Mathematical Models, 254 pp., Springer-Verlag, New York, Walsh, J. J., On the Nature of Continental Shelves, 520 pp., Academic, San Diego, Calif., Walsh, J. J., G. T. Rowe, R. L., Iverson, and C. P. McRoy, Biological export of shelf carbon is a sink of the global CO2 cycle, Nature, 291, , 1981a. Walsh, J. J., E. T. Premuzic, and T. E. Whitledge, Fate of nutrient enrichment on continental shelves as indicated by the C/N content of bottom sediments, in Ecohydrodynamics, edited by J. C. J. Nihoul, pp , Elsevier, New York, 1981b. Walsh, J. J., D. A. Dieterie, and W. E. Esaias, Satellite detection of phytoplankton export from the Mid-Atlantic Bight during the 1979 spring bloom, Deep Sea Res., 34, , Walsh, J. J., D. A. Dieterie, and M. A. Meyers, A simulation analysis of the fate of phytoplankton within the Mid-Atlantic Bight, Cont. Shelf Res., 8, , Yoder, J. A., L. P. Atkinson, S.S. Bishop, E. E. Hofmann, and T.N. Lee, Effect of upwelling on phytoplankton productivity of the outer southeastern United States continental shelf, Cont. Shelf Res., 1, , J. Ishizaka, National Research Institute for Pollution and Resources, Tsukuba, Ibaraki, 305 Japan. (Received July 27, 1989; revised April 18, 1990; accepted April 27, 1990.)