easTerN Us coNTiNeNTal shelf carBoN BUdgeT integrating Models , data assimilation , and analysis

New Brunswick, NJ, USA. Th is aticle as been pulished in O ceagraphy, Vlum e 1, N um er 1, a qurterly jornal of Th e o ceagraphy soiety. coyright 2008 by Th e o ceagraphy soiety. a ll rhts rerved. perm ision is gnted to cpy his aticle or se in teching nd rearch. replication, sstem m tic repruction, or coective redirbution of ny prtion of his aticle by phocopy m acine, repsting, or oher m eans is perm ited only w ith he aproval of Th e o ceagraphy soiety. send ll corrondence o: ifo@ tos.org or Th

with justifiable assumptions, and in more appropriate data selection has been recognized for some time (e.g., Walsh, 1972); it is re-emphasized by recent discussions of approaches for development of marine biogeochemical and ecosystem models (e.g., Doney, 1999;Doney et al., 2001;Flynn, 2005;Anderson, 2005). For an analytical measurement where no standards exist, it may be only through sensitivity studies with numerical models that the analyst can predict what the values of certain parameters are likely to be.
Modeling and data-intensive programs often have the same goals, but they bring different tools to bear. The box models and statistical techniques common to data analyses are part of the quantitative view of data. But using all the methods available (e.g., empirical and deterministic approaches) will ensure greater progress toward the common goal of understanding large ecological systems.
We combined the expertise of model- that resulted have proven to be as important in successfully addressing the project goal as any infrastructure (e.g., computers), data sets, and numerical model codes that we used. However, the fruitful scientific collaborations have come with a steep learning curve.
Integrating results from different disciplines and expertise included using measurements from satellites, field studies, historical data, and one-dimensional data assimilative modeling. Simplified   (DOE, 1970s and1980s).
Much of the DOE-sponsored work in the SAB is summarized in Atkinson et al. (1985), and some of the earliest studies using the Coastal Zone Color Scanner (CZCS) were conducted in collaboration with the DOE SAB program (Yoder et al., 1987;McClain et al., 1988). In the MAB, the Shelf Edge Exchange Processes (SEEP) experiments I and II (1983)(1984)(1985)(1986)(1987)(1988)(1989) and the Ocean Margins Program (OMP) experiment (1994)(1995)(1996) provided insight into biogeochemical processes, with major findings reported in special issues of Continental Shelf Research (1988, 8[5-7]) and Deep-Sea Research Part II (1994, 41[2-3];2002, 49[20]). Yoder et al. (2001) used the entire 7.5-year CZCS data set to examine phytoplankton variability of the MAB and the SAB and showed noticeable interannual variability during 1978-1986. From these past studies, we know that the circulation dynamics and the productivity and chlorophyll fields in the MAB and SAB differ significantly. In the SAB, the Gulf Stream flows along the outer edge of the shelf break (e.g., Lee and Atkinson, 1983), producing upwelling with subsurface bottom intrusions and frontal eddies that have a strong effect on nutrient and plankton production (Yoder, 1985). The episodic forcing of the SAB by Gulf Stream-induced upwelling results in biological production that occurs in short-lived events (McClain et al., 1984) rather than the more traditional spring/fall blooms that are observed in the MAB. In summer, when SAB shelf waters are stratified and the Gulf Stream tends to be nearer the shelf break, the intrusions extend across the entire shelf and produce subsurface blooms that are not discerned in oceancolor imagery. In winter, when shelf waters are well mixed, satellite-derived ocean-color distributions from the SAB show the episodic nature of the chlorophyll production in this region and suggest that it occurs in multiple sites along the outer SAB shelf.
In contrast to the SAB, the MAB has an outer shelf front and a slope sea that separate the shelf proper from the Gulf Stream. The influence of the Gulf Stream on the MAB is through warm-core eddies that move southward along the shelf break (Evans et al., 1986). The shelf circulation in both systems is influenced by estuarine and riverine inputs and wind. In the MAB, the coastal flow is to the south, with offshore flow at Cape Hatteras, where much of the flow is entrained into the Gulf Stream front.
Cross-shelf exchange occurs along the entire shelf edge through meandering of the shelf-break front (Lozier and Gawarkiewicz, 2001), and is at times modulated by warm-core-ring interactions (Ryan et al., 2001). Ocean-color distributions from the MAB show an annual April-May spring bloom , as well as extensive summer phytoplankton blooms adjacent to the MAB coast in some years. The differences between these two regions provide a strong basis for comparative studies between a continental shelf region that is strongly affected by oceanic forcing

Model-daTa fUsioN
Model-data fusion embraces a number of approaches for integrating discrete observations into a modeling framework, ranging from simple model-data comparisons to more formal data assimilation methodologies such as ...collaborations between analysts and modelers strengthened a program that is yielding results that likely would not have been achieved without them.
BoX 1: circUl aTioN Model de scripTioN realistic simulation of the circulation on the MaB and saB continental shelves is fundamental to realizing the objectives of the Usecos program; thus, considerable effort has been directed at achieving acceptable simulations. The circulation model used is the regional ocean Modeling system (roMs) (shchepetkin and McWilliams, 2005;haidvogel et al., in press; http://myroms. org) configured for the same Northeast North america (NeNa) spatial domain of fennel et al. (2006). The model has 10-km horizontal resolution, 30 vertical levels, and is embedded within the hybrid coordinate ocean Model (hycoM, http://hycom.org) North atlantic data assimilative model (chassignet et al., 2007). The hycoM open boundary transports are augmented by barotropic tides from a global analysis (egbert and erofeeva, 2002). coastal freshwater inputs have annual mean values from a watershed analysis (seitzinger et al., 2005) modulated by average monthly variability observed at Us geological survey-gauged rivers. air-sea fluxes are calculated using bulk formulae (fairall et al., 2003) applied to daily reanalysis of air temperature, pressure, humidity, and winds. all tracer advection is by the multidimensional positive definite advection transport algorithm (MpdaTa) scheme, which is important for accurate representation of biogeochemical model constituents.
The embedding procedure imposes external, remotely forced mesoscale and seasonal variability, but achieving realistic mean circulation in shelf waters proved critical to correct biases in the temperature and salinity provided by the hycoM North atlantic model. a simple correction procedure-supplanting the hycoM temporal mean temperature and salinity with values from the hydrobase climatology (lozier et al., 1995)-was devised that substantially improved the simulation of buoyancy-driven southwestward mean flow throughout the gulf of Maine and MaB. improvements to the properties of slope water adjacent to the saB (which enters the NeNa domain from the intra-american seas) were also noted.
The simulations exhibit well-recognized features of the local and remotely forced circulation: low salinity on the MaB inner shelf, the tidal mixing front and residual circulation around georges Bank, gulf stream intrusions in the saB, and interactions of gulf stream warm rings with the New england slope. comparisons of the modeled circulation and tracer fields to observations show progress over the simulations of fennel et al. (2006), due principally to the introduction of tides and unbiased open boundary data. features that are the focus of ongoing study are exaggerated upwelling of anomalously cold water in the saB, intermittent overshoot of the gulf stream at cape hatteras, and a weak slope sea gyre. Model development is investigating whether higher spatial resolution is required to improve these aspects of the simulation. in press) and Taylor (Taylor, 2001) diagrams, which reveal spatial and/or seasonal timing/phase relationships.
Overall spatial distributions of climatological means from the model should match those from in situ and satellite data with little bias; the model should also capture the dynamic range over seasonal time scales, as well as regional was computed using a criterion of 0.5°c with respect to the surface. Monthly Mld was binned to a 0.1° grid; monthly salinity and oxygen anomaly were binned to a 0.5° grid. annual mean salinity was computed when a given grid box contained measurements for more than nine calendar months. White indicates no data.

Model evaluation Through historical data comparisons
We focused our historical data-mining efforts on temperature, salinity, and  , 2006). in our roMs implementation, we distinguish the two inorganic nitrogen species, nitrate and ammonium; include chlorophyll as a prognostic variable in addition to phytoplankton biomass; distinguish two size classes of detritus to allow for different settling rates; and include explicit doM dynamics described in detail in Box 4.
it is important to note that none of the biological models available in roMs explicitly represents diagenetic processes at present. however, the inclusion or at least the parameterization of diagenetic processes is important for coastal applications because a major fraction of nutrient remineralization occurs in the sediment. in our application of the fasham-type model to the east coast continental shelves (western North atlantic) we use a relatively simple representation of benthic remineralization processes where organic matter settling out of the bottommost grid box results in a corresponding influx of inorganic nutrients at the sediment/water interface (fennel et al., 2006). This formulation conserves mass by assuming immediate equilibrium between particle deposition and influx of dissolved constituents from the sediment. soetaert et al. (2000) showed that this intermediate complexity approach captures most of the dynamics inherent in benthic-pelagic coupling when compared to coupling with a diagenetic submodel, but is computationally much more efficient. This approach also allows for the straightforward inclusion of processes such as sediment denitrification (fennel et al., 2006) using the relationship between sediment oxygen consumption and denitrification derived by seitzinger and giblin (1996).
We also included inorganic carbon and oxygen dynamics in our biogeochemical model for the MaB and saB. aside from physical transport (i.e., advection and mixing), the local concentration of dissolved inorganic carbon (dic) and oxygen is affected by gas exchange with the atmosphere at the sea surface and by sources and sinks caused by biological processes such as the photosynthetic synthesis of organic matter or its metabolic or microbial oxidation. We describe the sources and sinks due to biological processes based on stoichiometric ratios and parameterize gas exchange as suggested by Wanninkhof (1992). The gas exchange of oxygen depends on the temperature-and-salinity-dependent oxygen solubility (garcia and gordon, 1992) and the piston velocity. for the air-sea gas exchange of carbon dioxide, the situation is more complicated because gas exchange does not directly depend on the concentration of dic but rather on the small fraction of dic that is present as carbon dioxide (carbon dioxide does not just dissolve in seawater, but rather reacts with water to form carbonic acid, which subsequently dissociates into bicarbonate and carbonate; the sum of all three makes up dic). only the small fraction of dic that is present in the form of carbon dioxide determines the partial pressure, pco 2 , that enters the parameterization of gas exchange. calculating this fraction (and thus pco 2 ) requires knowledge of dic, the local alkalinity, temperature and salinity, and the iterative solution of a set of nonlinear equilibrium equations (Zeebe and Wolf-gladrow, 2001). processes not yet represented.

Model evaluation Through satellite data comparisons Satellite-Model Comparisons
We are also using a wide range of      . The light penetration was calculated using a par attenuation coefficient developed for the ecosystem model, which is a function of chlorophyll a concentration and salinity. Note the high chlorophyll a concentration on the entire shelf below 10 m, which resulted from nutrient inputs from a subsurface gulf stream intrusion, and significant (> 10%) light penetration to the ocean floor. a coastal Zone color scanner (cZcs) summer composite for 1981 (d) shows that ocean-color retrievals miss the high chlorophyll a that is associated with the subsurface bottom intrusions (thick white line shows transect location). Note that there are no satellite data in the transect region near the coast (black regions) due to sensor amplifier ringing off the bright coastline. In April, the model results are inversely

BoX 3: TargeT aNd Taylor diagr a Ms
Target (Jolliff et al., in press) and Taylor diagrams (Taylor, 2001) quantitatively compare and visualize statistics associated with multidimensional time series (e.g., ssT or surface chlorophyll in figure 7). Typically used to compare models and data, they might also contrast observations derived from different sources. These diagrams are based on computations of the square root of mean square differences (rMsd) between model and data. The rMsd is composed of two components, the bias representing the difference between the means of the two fields, and the centered-pattern rMsd (rMsd cp ) representing differences in variability.
The Target diagram (Jolliff et al., in press) exploits the fact that rMsd squared is equal to the sum of rMsd cp squared and the bias squared. Thus, if these two statistics are plotted on the x-and y-axes, respectively, the distance from the origin is equal to the total rMsd. Though rMsd cp is a positive quantity, on Target diagrams rMsd cp is given the sign of the difference between the standard deviation of the model and observed time series. Thus, negative values of rMsd cp indicate that the model underestimates the observed variability, while positive values indicate that the model variability is an overestimate. if these quantities are normalized by the standard deviation of the observations, it is possible to compare model-data fit of monthly averages for multiple subregions (figure 7a, c), or compare modeled and observed spatial patterns for given months ( figure 7B, d). in addition, when normalized in this manner, symbols falling within the total rMsd = 1 circle indicate the model provides a better estimate of productivity than the mean of the observations. an inner circle (figure 7a, B) representing the uncertainty associated with the observations can also be included in Target diagrams; when points lie within this inner-circle (the bull's-eye), model and data are by definition statistically indistinguishable from each other.
The rMsd cp can be further decomposed into contributions from phase differences between the two time series (or cross correlation) and differences in their standard deviations (oke et al., 2002). The Taylor diagram (Taylor, 2001) quantitatively compares these three statistics for a given distribution (e.g., ssT or chlorophyll; figure 8). The normalized standard deviation of the simulated distribution is the radial distance from the origin, the correlation of the two distributions is the angle from the x-axis, and the normalized centeredpattern root-mean-square difference is then the distance between the data symbol at location [1,0] on the x-axis and each model symbol (indicated by the dashed lines, in the same units as the coordinates). Bias information is thus not inherently depicted on a Taylor diagram, but is included here by using colored symbols (figure 8). as in the Target diagrams, Taylor diagrams can illustrate temporal (figure 8a, c) or spatial (figure 8B, d) variability in model-data fit.

Model refinement Through onedimensional data assimilation
Another approach taken to incorporate discrete observations into the NENA framework and to quantitatively assess model skill is the variational adjoint method (Friedrichs et al., 2006(Friedrichs et al., , 2007. Due to our incomplete knowledge, biogeochemical models are often by necessity highly empirical, have many nonmechanistic formulations, and include numerous parameters that are difficult to measure with current oceanographic instrumentation. Data assimilation techniques such as the variational adjoint method (Hofmann and Friedrichs, 2001) provide an approach for objectively estimating the best-fit set of model parameters and their associated uncertainties (Fennel et al., 2001). These methods can be used to compute sensitivities and correlations between parameters and assess predictive abilities of a given model (Friedrichs et al., 2006), and are thus a crucial component of successful marine biogeochemical modeling studies.
We are currently making use of an existing one-dimensional data assimilative ecosystem-modeling framework that has been recently developed to quantitatively compare the performance of 12 models characterized by varying levels of ecosystem complexity (Friedrichs et al., 2007). figure 9. (a) comparison of surface chlorophyll time series on the outer New Jersey shelf from: seaWifs, Northeast North america (NeNa) model, the forward one-dimensional model, and the data assimilative one-dimensional model. also shown are depth-time contour plots of (B) NeNa and (c) post-assimilation chlorophyll concentrations. prior to assimilation of ocean-color data, the model significantly overestimated chlorophyll concentrations in the spring. These were reduced to reasonable values by adjusting the maximum growth rate, the initial slope of the photosynthesis versus irradiance curve, and the mortality rate of phytoplankton; however, these parameter changes did not improve the fit for the short-lived fall bloom (year day 306-316), which may reveal missing complexity in the ecosystem dynamics.

eValUaTioN of Model pro ce sse s
In addition to using historical data sets to evaluate distributions of various concentrations predicted by our models, we also evaluated process mechanisms.
For example, it is known that DOM represents the largest pool of organic carbon on the MAB shelf and may thus play a significant role in carbon cycling and transport. Furthermore, under nutrient-depleted conditions, nitrogen and carbon primary production are partially decoupled; the DOM produced is carbon-rich and thus may represent a significant source of organic carbon (Williams, 1995), which can be exported to the open ocean (Bauer and Druffel, 1998;Vlahos et al., 2002). To investigate this aspect of shelf carbon cycling, we  Because a large portion of organic carbon is stored in dissolved organic matter (doM), the transport of doM may be an important pathway for carbon. as a first step toward addressing this question, we added two semilabile doM components (dissolved organic nitrogen [doN] and dissolved organic carbon [doc]) to the biogeochemical model. Note that the model does not include the biologically inert "refractory" doM fraction that dominates doM in deep waters and is thought, except in areas influenced by rivers (druffel et al., 1992), to act as a conservative tracer and be relatively uniform with depth (hansell and carlson, 1998; carlson, 2002). The source and sink terms of doM are phytoplankton exudation, "sloppy feeding" of zooplankton, poM solubilization, and doM remineralization. The sources and sinks of doM are thus directly related to primary production, grazing, and detritus pool concentration. exudation of semilabile doc by phytoplankton includes two processes: nutrient-based and carbon-excess-based release. The nutrient-based release reflects the exudation of semilabile doc and doN by healthy phytoplankton. This term is proportional to primary production. The carbon-excess-based release represents carbohydrate over-production by nutrient-stressed cells. This process is responsible for the mucilage events that are often observed during summer in eutrophic coastal areas. The carbon excess uptake can be seen as an "overflow" of photosynthesis under nutrient limitation. We described this process as the difference between nutrient-saturated (and light-limited) and nutrient-limited (and light-limited) primary production (andersen and Williams, 1998;ianson and allen, 2002).
as a result, in nutrient-depleted conditions, the nitrogen primary production and carbon primary production are partially decoupled and carbonrich doM is produced; c-to-N ratios for doM range between 10 and 25 (hopkinson and Vallino, 2005;søndergaard et al., 2000;Biddanda and Benner, 1997;Benner et al., 1992). Values vary from 9.95 for fresh material (hopkinson and Vallino, 2005) to 19-25 for high molecular weight doM (i.e., mainly the semilabile fraction [Biddanda and Benner, 1997]). The accumulation and subsequent transport of carbon-rich doM may thus present an efficient mechanism for export of organic carbon from productive shelf systems to the open ocean. Thomas et al. (2002) (Henrichs and Reeburgh, 1987).
We estimated the burial efficiency for particulate organic nitrogen (PON) using a C to N ratio of buried organic matter of 9.3; values of 9-10 have been found for shelf and estuarine surface sediments and slightly lower values in deeper waters (Gelinas et al., 2001). The model gave burial rates of POC in the sediments ( Figure 10B) that agree well with estimates by Thomas et al. (2002) of 0.1-0.2 mol C m -2 yr -1 in the slope off BoX 5: deVelopMeNT of e Mpirical algoriThMs for cd oM aNd d o c as part of a limited Usecos field program focused on the chesapeake Bay region, samples were collected at multiple depths for measurement of pigments, dissolved organic carbon (doc), particulate organic carbon (poc), absorption of chromophoric dissolved organic matter (cdoM), and particles. These samples have provided data sets critical for development of satellite-derived doc and poc algorithms and for evaluation of the biogeochemical model results (figures 4 and 5).
in order to develop empirical algorithms for cdoM and doc, we collected field measurements to correlate a cdoM (cdoM absorption coefficient) to in situ radiometry (reflectance band ratios) and then correlated doc to reflectance band ratios through the a cdoM to doc relationships. results from our current fieldwork in the continental margin of the southern MaB and the mouth of the chesapeake Bay demonstrate that we can retrieve a cdoM from seaWifs and Modis observations through empirical relationships similar to those described by other researchers (d'sa and Miller, 2003;Johannessen et al., 2003). our a cdoM algorithm takes an exponential decay form with the remote-sensing reflectance band ratios (488/551 nm for Modis and 490/555 nm for seaWifs) plotted on the ordinate and a cdoM on the abscissa; author Mannino, M.e. russ, and s.B. hooker are preparing a paper on satellite-derived distributions of doc and cdoM in the Us Middle atlantic Bight. Because cdoM contributes to light absorption across the visible spectrum, several band ratio solutions are possible to avoid the atmospheric correction problems associated with the 412-nm, ocean-color satellite band in coastal waters (e.g., negative water-leaving radiances). furthermore, comparisons of cdoM absorption at other relevant wavelengths (e.g., 443 nm) are possible, for example, with the garversiegel-Maritorena inversion model (gsM-01; Maritorena et al., 2002). Uncertainties for a cdoM derived from Modis-aqua are on average 20-25% and < 10% for doc (Mannino manuscript noted above). seasonal variability in cdoM absorption and doc is quite evident along the continental margin, with the estuarine plumes and nearshore regions as most dynamic (Box 5 figure). our results show that at least two seasonal algorithms (fall-winter-spring and summer) are required to retrieve doc from Modis and seaWifs due to seasonal variability in the cdoM-to-doc relationship caused by the accumulation of primarily nonchromophoric doc from net ecosystem production (Nep) and the concomitant loss of cdoM through sunlight-induced photooxidation between late spring and early fall.
satellite ocean-color data and field measurements are helping us to evaluate results from our biogeochemical model. for example, the increase in doc distributions observed from ocean-color satellite data can be compared with model results on the seasonal accumulation of semilabile doc from net ecosystem productivity (figure 5c and Box 5 figure, part B). The satellite ocean-color data are also helping us to evaluate how well the model represents the inputs and fate of doc to the continental shelf from estuarine and riverine systems. Box 5 figure. (a) satellite-derived distributions of a cdoM (355 nm, m -1 ) and (B) dissolved organic carbon (doc) (µM c). from spring to summer, a cdoM decreases due to photooxidation and possibly from reduced inputs of terrigenous doM as a result of reduced river discharge. from summer to fall, storm events will vertically mix the water column and introduce chromophoric dissolved organic matter (cdoM) from depth into surface waters. Much higher doc values are observed in summer compared to early spring due to ecosystem productivity that promotes the accumulation of semilabile doc. our estimate of the doc reservoir within the 10-100-m isobaths for the continental shelf region shown in figure 1 is on the order of 1.2 Tg c. source data for the images shown are from Nasa's seaWifs and Modis-aqua sensors. The focus on a single model forces the team to resolve issues and reconcile differences of opinion (i.e., a disciplined approach, rather than simply going in different directions, as can happen with a focus on more than one model). refereNce s