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Understanding the CO₂cycle in the North Pacific Ocean using inverse box models Matear, Richard J. 1993

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UNDERSTANDING THE CO 2 CYCLE IN THE NORTH PACIFIC OCEAN USINGINVERSE BOX MODELSByRichard James MatearB.Eng., (Geophysics) University of SaskatchewanM.Sc., University of British ColumbiaA THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTSFOR THE DEGREE OF DOCTOR OF PHILOSOPHYINTHE FACULTY OF GRADUATE STUDIES(DEPARTMENT OF OCEANOGRAPHY)We accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLOMBIAJune 1993© Richard James Matear, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature) Department of  OCeavlOy rcephyThe University of British ColumbiaVancouver, CanadaDateDE-6 (2/88)ABSTRACTTracer transports across 35°N were computed using the hydrographic data from asynoptic section (INDOPAC) and from the Levitus annual mean section. The tracertransports calculated from the INDOPAC section were better able to close the tracerbudgets in the North Pacific than the Levitus section. The transport calculations showedthat highly resolved hydrographic data are necessary to accurately determine the tracertransports, and pointed out the sensitivity of the calculation to errors in the Ekmantransports and air-sea exchanges of fresh water.The inverse box model was applied to data generated from the Hamburg LSGOC-biogeochemical model. For this data, the mixing transports of the tracers were importantfor closing the tracer budgets. Applying the inverse box model to the temperature, salinity,total CO2, alkalinity, phosphate, oxygen, POC, calcite, and 14C fields produced poor results.With the addition of velocity shear information, the inverse box model extracted thecorrect velocity fields and produced air-sea exchanges and detrital rain rates consistentwith the known values from the Hamburg model.A model of the nutrient and carbon cycles in the North Pacific north of 24°N isformulated, and water flow rates, eddy mixing coefficients, particle fluxes and air-seaexchange rates of fresh water, heat, CO 2 and 02 are calculated. The model incorporatesgeostrophy, wind-driven Ekman transports and budget equations for a suite of seventracers. Geostrophic transports are based on two highly resolved synoptic sections acrossthe North Pacific at 24°N (Roemmich et al., 1991) and 47°N (Talley et al., 1991). Tracerdistributions are obtained from historical station data. Budgets of mass, heat, salt, oxygen,phosphate, silicate, CO2 and alkalinity are satisfied simultaneously in the North Pacific.The water transports in the model are in agreement with other transport calculations for thePacific. The calculated heat transport showed that the subtropical North Pacific transfersheat into the atmosphere while the subarctic ocean gains heat. The net heat lost by theNorth Pacific ocean was 0.12 ± 0.08 PW. The North Pacific Ocean was calculated to be asink of 0.1 ± 0.1 Gt C yr -1 of atmospheric carbon. The calculated maximum values of newproduction for the subarctic and subtropical regions are 42 g C m-2 yr-1 and 12 g C m-2 yr-1respectively. The influence of the dissolved organic matter on the nutrient and carboncycles is investigated using the data reported by Suzuki et al., (1985). The model showedthat the dissolved organic matter had little influence on the carbon and nutrient cycles.More data for the dissolved organic matter should be collected to verify this result.TABLE OF CONTENTSABSTRACT ^  iiLIST OF TABLES  viiiLIST OF FIGURES ^  xiLIST OF SYMBOLS AND ABBREVIATIONS ^  xviiACKNOWLEDGEMENT ^  xixCHAPTER 1. INTRODUCTION  11.1 INVERSE BOX MODELS^  21.2 OCEAN CARBON CYCLE  7CHAPTER 2. TRACER TRANSPORTS ACROSS 35 °N IN THE PACIFICOCEAN ^  142.1 INTRODUCTION ^  142.2 SECTIONS  162.2.1 INDOPAC Section ^  172.2.2 TRANSPAC Section  262.2.3 Levitus Section ^  262.3 COMPUTATION OF THE TRANSPORTS ^  272.4 MASS TRANSPORT ^  302.5 TRACER TRANSPORTS  362.5.1 Heat and Salt ^  402.5.2 Nutrient Tracers, DIC and Alkalinity ^  422.5.3 Corrections to the Tracer Transports due to BeringStrait Flow, Korean Strait Flow and FreshwaterExchanges ^  442.5.4 Tracer Budgets for the Pacific Ocean north of 35°N ^ 462.6 DISCUSSION AND CONCLUSION^  51CHAPTER 3. VALIDATING AN INVERSE BOX MODEL USING DATAGENERATED FROM THE HAMBURG CARBON MODEL^ 543.1 INTRODUCTION^  543.2 HAMBURG MODEL  553.2.1 Model Description ^  553.2.1.a. Physical Model  563.2.1.b Biotic model ^  583.2.2 Tracer Transports  593.3 INVERSE BOX MODEL ^  633.3.1 Model Topology  633.3.2 Model Constraints ^  643.3.3 Inversions ^  663.4 INVERSE SOLUTIONS  713.4.1 Tracer Studies ^  713.4.2 Reference Model  723.4.3 Model Sensitivity ^  853.4.4 Effects of Model Geometry ^  90V3.5 DISCUSSION AND CONCLUSION ^  92CHAPTER 4. DEVELOPING THE INVERSE BOX MODEL OF THE NORTHPACIFIC ^  944.1 DATA  944.1.1 Geostrophic Velocity Sections ^  954.1.2 Tracer Data ^  994.2 MODEL GEOMETRY  1154.3 MODEL CONSTRAINTS ^  1234.3.1 Horizontal water transports ^  1244.3.2 Eddy transports ^  1264.3.3 Biological processes  1274.3.4 Air-sea exchanges ^  1304.4 INVERSE SOLUTIONS  1324.5 TOLERANCES OF BALANCE EQUATIONS ^  135CHAPTER 5. MODEL RESULTS FOR THE NORTH PACIFIC OCEAN ^ 1385.1 EVALUATING AND UNDERSTANDING THE MODEL ^ 1385.1.1 Feasiblilty Studies ^  1395.1.2 Tracer Studies  1435.1.3 Sensitivity to Model Layering ^  1455.2 MODEL RESULTS ^  1465.2.1 Meridional Transports ^  1515.2.2 Freshwater transport  1535.2.3 Heat Transport ^  1545.2.4 Air-sea exchange of CO2 ^  160^5.2.5 02 gas exchange rates   1625.2.6 Mixing terms ^  1635.2.7 New production  1685.2.8 Particle fluxes ^  1735.3 MODEL INCLUDING DISSOLVED ORGANIC MATTER ^ 179CHAPTER 6. CONCLUSION ^  187APPENDIX A. THE NUMERICAL DIFFUSION OF THE IMPLICIT UPWINDADVECTION SCHEME USED IN THE LSGOC MODEL ^ 193BIBLIOGRAPHY ^  195LIST OF TABLESTable 2.1:^The tracer transports through the 35°N section for a) salt and heat, b)alkalinity and DIC, c) phosphate and nitrate and d) oxygen and silicate.These transports are determined with the assumption that there is no netmass transport through the section. Positive values indicate transport intothe North Pacific. The errors in the transports are determined from theintegrated layer transports multiplied by the variability of the tracers withinthose layers plus the estimated errors arising from the choice of referencelevel. ^  41Table 2.2:^The transport of phosphate and silicate across the 35°N using thehydrography from the Levitus seasonal data (FMA) and the tracermeasurements of INDOPAC. ^  43Table 2.3: The corrections to the tracer transports, the value in the "Difference"column should be added to the tracer transport given in Table 2.1 to obtainthe tracer budgets. *In the table the heat transport assumes the watertransport through the Bering Strait is replace by water with an averagetemperature of 5°C. ^  45Table 2.4:^Tracer budgets for the North Pacific Ocean north of 35°N for the twosections. A positive value indicates input into the North Pacific. ^ 47Table 3.1: Mean Advection transport into the North Pacific (positive value). Thefirst column gives the transports through 25°N into the North Pacific, thisgrid has no outflow into the Arctic Ocean. The second column gives the nettransports into the North Pacific between 22.5°N and the Bering Strait. ^ 62Table 3.2:^The molecular ratios for organic matter (R's) and shell material(S's).  73Table 3.3:^Summary of the various inverse box models used ^ 73Table 3.4:^The inverse results for the 4-region 6-layer models given in Table3.3. The maximum acceptable errors are 3.215 times greater than the errorsused to weight the LSI inversions. ^  86Table 3.5:^Inverse solutions obtained from experiments that change thedefinitions of the boxes. The numbers under the model heading give thenumber of regions and layers in the respective model. ^ 91Table 4.1:^The list of cruises used to determine nutrient concentrations. ^ 101Table 4.2:^The regions used for comparing the data from the different cruises. . . ^ 105Table 4.3:^The ocean layering used in the model    116Table 4.4: The processes that contribute to the biological source/sink terms for thevarious tracers. ^  127Table 4.5:^The processes that contribute to the air-sea source/sink terms for thevarious tracers ^  130Table 4.6:^Summary of model constraints ^  133Table 4.7:^A priori bounds on the model parameters ^  134Table 5.1:^The acceptable ranges for the air-sea exchanges determined from the^models used in the feasibility study.   140Table 5.2:^The maximum particle flux rate from the surface layer for the modelsused in the feasibility studies. ^  141Table 5.3:^The Ekman transport at 24°N and 47°N calculated from theHellerman and Rosenstein (1983) monthly windstress measurements. ^ 142Table 5.4:^A compilation of meridional layer fluxes across 24°N. ^ 154Table 5.5:^Select production data for the North Pacific^  170Table 5.6:^A variety of productivity measurements from Station P (50°N and145°W).  171Table 5.7:^Sediment trap measurements of CaCO3 fluxes in the North Pacific^ 177Table 5.8:^Sediment trap measurements of opal flux for the North Pacific. ^ 178xLIST OF FIGURESFigure 2.1:^Location of stations for the trans-Pacific sections. The long ticksabove the line at 35°N indicate the locations of the TRANSPAC stations; thelong ticks below, the deep stations; and the short ticks the 1200-m stations,both for INDOPAC.  ^16Figure 2.2: Tracer properties of the INDOPAC section along 35°N for (a)temperature (°C, (b) salinity (pss), (c) phosphate (Iimol/kg), (d) nitrate(p.mol/kg), (e) oxygen (innol/kg) , (f) silicate (p.mol/kg), (g) DIC (.tmol/kg),and (h) alkalinity (4E0(0^  18Figure 2.3: A comparison of the alkalinity and DIC measurements of theINDOPAC cruise (•), and the TRANSPAC cruise (0), at (a) 35°N and164°E, and (b) 35°N and 170°W. ^  28Figure 2.4: Layer transports for the INDOPAC section at the following referencelevels, 2500 m (shaded), 1750 m (solid line), 2000 m (dotted line), and 3000m (dashed line). A positive value indicated a northwardtransport. ^  31Figure 2.5:^Geostrophic velocities calculated from a reference level at 2500 m incm s -1 for (a) INDOPAC, (b) TRANSPAC, and (c) Levitus sections, thedotted areas denote a southward velocity. ^  32Figure 2.6:^The integrated mass transport along 35°N for the Levitus section(solid), the INDOPAC section (dashed) and the TRANSPAC section(dotted). A positive value indicates a northward transport^ 35Figure 2.7:^The integrated layer transport for the three section, with each sectionshifted by 3 Sv for clarity. The left plot is the INDOPAC section with zeroat -3 Sv, the middle plot is the Levitus section and the right plot is theTRANSPAC section. The Figure show: a) the transport for the entiresection, b) the transport for the western part of the section (139°E to 170°E)and c) the transport for the eastern part of the section (170°E to 240°E). Apositive value indicates a northward transport. ^  37Figure 3.1: The Hamburg model grid where the * denotes the points where the u and vare determined, and + denotes the location of the tracer concentrations and w. Inthe figure, the regions used in the 4-region inverse model are denoted by thehighlighted areas and are labelled. ^  60Figure 3.2:^The circulation field for the reference model where (a) shows thevolume transports (Sv) across the box faces, and (b) shows the mixingtransports as k * area / distance in Sv. ^  75Figure 3.3:^The integrated northward transport of (a) freshwater, (b) heat, and (c)CO2 . The curve in (a) shows the freshwater exchanges calculated byBaumgartner and Reichel (1975), and in (b) and (c) the curve denotes thevalues from the LSGOC model. In three plots the circles denote the valuesdetermined by the LSI inversion of the model and the error bars arecorresponding the maximum and minimum values determined from the LPinversions. ^  77Figure 3.4:^The acceptable ranges for the horizontal mixing coefficients for (a)region 1, and (b) region 2, if only one line is present then the lower range iszero. The dashed line is the calculated numerical diffusivity of the upwindadvection scheme used in the LSGOC-biogeochemical model. ^ 80Figure 3.5:^The acceptable ranges for the vertical mixing coefficients for (a)region 1, and (b) region 2, if only one line is present then the lower range iszero. The dashed line is the calculated numerical diffusivity of the upwindadvection scheme used in the LSGOC-biogeochemical model. ^ 81Figure 3.6:^The acceptable ranges of the particle fluxes of organic and shellmaterial, the minimum value is zero. The organic carbon flux for region 1and 2 is shown in (a) and (b) respectively, and the flux of shell matterial forregion 1 and 2 is shown in (c) and (d) respectively^  82Figure 3.7: Map of the new production from the LSGOC-biogeochemical modeltaken from Bacastow and Maier Reimer (1990). ^  84Figure 3.8:^The volume transports, (a), and mixing transports, (b), in Sv of amodel forced only by the tracer fields. ^  88Figure 4.1:^Map showing the hydrographic sections used in the model (TPS24and TPS47). ^  96Figure 4.2:^Geostrophic velocities (cm s -1 ) of the transpacific sections, shadedareas denote southward velocities, (a) TPS24, and (b) TPS47^ 98Figure 4.3: Station maps (a-c) of data from the IOS, GEOSECS, NOAA82,INDOPAC, and Japanese datasets, refer to Table 4.1 to identify the differentdatasets. ^  102Figure 4.4:^Station map of data in the NODC archive from 1970 and onward. .   103Figure 4.5: Comparison plots of alkalinity and DIC for the six selected regions inTable 4.2; use Table 4.1 to identify the different datasets. ^ 106Figure 4.6: Zonal variation of silicate at (a) 24°N and (b) 47°N, and phosphate at(c) 24°N and (d) 47°N, all units are in mol kg -1 ^  111Figure 4.7:^Average meridional section of (a) silicate and (b) phosphate inumol kg-1^  117Figure 4.8:^The meridional section showing the division of the model intolayers.  111Figure 4.9:^Map of potential density at 100 m with the division of the model intoregions.  120Figure 4.10: The zonal sections showing the layering used in the model, (a)24°N, and (b) 47°N. ^  113Figure 4.11: The ApCO2 maps of the North Pacific (Tans et al., 1990), the unitsare in .tAtm, with negative regions (lined) denoting areas of the ocean thatsinks of atmospheric CO2 , (a) winter (Jan.-Apr.) and (b) summer (Jul.-Oct.).The dots denote the regions where data are available. ^ 131Figure 5.1:^The integrated meridional transports calculated from the least squaressolution in Sv. ^  147MTVFigure 5.2:^Maps of air-sea exchanges for a) freshwater (Sv), b) heat (PW), c)CO2 (Kmol s -1 ) and d) 02 (Kmol s -1 ) from the least squares solution^ 149Figure 5.3: The mixing coefficients from the least squares solution, the isopycnalcoefficients are in 104 m2 s-1 and the diapycnal coefficients are in cm 2 s1 ^  150Figure 5.4:^The acceptable bounds on integrated meridional transports in Sv. ^ 152Figure 5.5:^Maps of the bounds on the air-sea exchanges for a) freshwater (Sv),^b) heat (PW), c) CO 2 (Kmol s -1 ) and d) 02 (Kmol s -1)    155Figure 5.6: The meridional freshwater transport calculated from the modelcompared to the estimates of Baumgartner and Riechel (1975)^ 156Figure 5.7: The annual mean meridional heat transport in the Pacific Ocean. (a)The values calculated by Talley (1984) for the heat fluxes of Clark andWeare et al., (solid, dash and dot) and Ebsensen and Kushnir (dot-dash).The heat transport at 60°N is assumed to be zero. The solid curve is basedon Clark's heat fluxes. The long dashes are based on heat fluxes of Weareet al.: The middle dotted curve deletes heat fluxes in the Bering Sea andSea of Okhotsk. (b) The heat fluxes calculated from the model along withthe direct estimates of heat by Roemmich and McCallister (1989) (RM),McBean (1991) (M), and Bryden et al., (1989) (B), and for comparison themiddle dotted line from (a) has been redrawn. ^  158Figure 5.8:^The bounds on the mixing coefficients, the units of the isopycnal anddiapycnal coefficients are 104 m2 s' and cm2 s -1 respectively. ^ 164X VFigure 5.9:^Profiles of the maximum bounds on the isopycnal mixing coefficientfor a) subtropical region (solid line) and subarctic region (dashed line). ^ 165Figure 5.10: Profiles of the maximum bounds on the diapycnal mixing coefficientfor the subtropical region (solid) and subarctic region (dash). ^ 166Figure 5.11: Maps of the maximum particle fluxes from the surface layer of themodel for a) organic carbon, b) inorganic carbon, and c) opal. The topnumber is in Kmol s -1 and the bottom number is in mol ni2 yr-1^  169Figure 5.12: Profiles of the particle fluxes of (a) organic carbon, (b) inorganiccarbon and (c) opal material. The solid lines denote the subtropical regionand the dashed lines denotes the subarctic region. ^  174Figure 5.13: Illustration of an oceanic DOC profile indicating the "new" DOC,additional DOC found by the HTCO method of Sugimura and Suzuki,(1988), and the "old" DOC, that found by older methods (redrawn fromBacastow and Maier-Reimer, 1991). ^  181Figure 5.14: DON concentration versus the nitrate from Toggweiler (1989)^ 184Figure 5.15: The vertical profiles of DON at 24° and 47°N. ^ 186XVILIST OF SYMBOLS AND ABBREVIATIONSAABW^Antarctic Bottom WaterAAIW^Antarctic Intermediate waterCaCO3^Calcium CarbonateCO2^Carbon dioxideCO3 -2^Carbonate ionDIC^Dissolved inorganic carbonDOC^Dissolved organic carbonDOM^Dissolved organic matterDON^Dissolved organic nitrogenHCO3 -^Bicarbonate ionH2O^WaterK i^First apparent dissociation constant for carbonic acidK2^Second apparent dissociation constant for carbonic acidkh^isopycnal mixing coefficentkv^diapycnal mixing coefficentKw^Ionization constant for waterLP^Linear ProgrammingLSG^Large Scale GeostrophicLSGOC^Large Scale Geostrophic Ocean CirculationLSI^Least Squares with inequality constraintsNPBW^North Pacific Bottom WaterNPIW^North Pacific Intermediate WaterNODC^National Oceanographic Data Center02^OxygenpCO2^Partial pressure of carbon dioxidePOC^particulate organic carbonPW^1015 WattsS^SalinityT^TemperatureTCO2^Total Dissolved inorganic carboncc^Solubility of carbon dioxide in waterii 10 611ACKNOWLEDGEMENTI would like to thank my committee members for their inspiration and guidanceduring the work on this thesis. I would especially like to express my gratitude to Dr. K.Holmen for our interesting discussion on applying inverse models to geochemical cycles,and for providing me with the opportunity to spend six months in Stockholm Sweden.Both of which were instrumental in shaping the research presented in this thesis. To Dr.C. S. Wong I wish to acknowledge the patience and encouragement he provided whendiscussing my doctorial research.To my wife Rhonda, I immensely appreciate the sacrifices she made and the moralsupport she has provided.This research was supported by a Joint Venture Agreement between the Institute ofOcean Sciences, Department of Fisheries and Oceans, and the Department ofOceanography at the University of British Columbia.AIXCHAPTER 1. INTRODUCTIONSince the start of the industrial age, the concentration of CO2 in the atmosphere hasincreased dramatically (Bacastow and Keeling, 1981). This increased CO 2 concentrationin the atmosphere is expected to lead to significant global climatic changes during thecoming decades (Dickinson, 1986; Ramanathan, 1988; Washington and Meehl, 1989).After 35 years of measurements of CO2 in the atmosphere and oceans, the global CO2budget is still surprisingly uncertain. An improved understanding of the CO 2 cycle isessential to predict the future rate of CO2 increase in the atmosphere and the futureclimatic changes, as well as to plan for a strategy to reduce CO2 emissions.The three most important reserves in the global carbon cycle are the atmosphere,the terrestrial ecosystem and the oceans. At present, the combustion of fossil fuelsoutputs 5.3 Gt/yr^g/yr) of carbon into the atmosphere (Tans et al., 1990). This is amajor contributor to the rise in atmospheric CO 2 concentrations. The measured rise inCO2 was about 57% ( 3 Gt/yr) of the fossil fuel input for 1981-87. The excess CO2 mustbe removed from the atmosphere by the ocean and by the terrestrial ecosystem.The effect of the terrestrial ecosystem on the atmospheric CO 2 concentration is notwell understood. Houghton (1986), Bolin (1986) and Wong (1978) consider that theterrestrial ecosystem is a source of CO2 due to a deforestation. Contrary to this, Tans etal., (1990) believe that it is a significant sink of carbon due to unknown processes.Chapter 1. Introduction^ 2Estimates of the uptake of CO2 by the ocean have been made using "box" modelsand 3-dimensional ocean circulation models (Siegenthaler, 1983; Maier-Reimer andHasselmann, 1987; Bacastow and Maier-Reimer, 1990; Toggweiler et al., 1989a and1989b; Bolin, 1986). From these models, the uptake of CO2 ranges between 26 - 44% (1.3 - 2.3 Gt/yr) of the fossil fuel output. This shows that the ocean is an important sinkof atmospheric CO2 , but its absolute magnitude is poorly determined. Betterunderstanding of the role of the ocean in the CO2 cycle is necessary to balance the CO2budget and to allow one to better assess the importance of the terrestrial ecosystem.The research in this thesis is based on the study of the CO2 cycle of the NorthPacific Ocean through the use of inverse box models. From previous work it is not clearif the North Pacific Ocean is a sink of carbon (Tans et al., 1990) or a source (Broecker etal., 1986). The goal of this work is to improve the understanding of the carbon cycle inthe North Pacific and to assess the role of this ocean basin in modulating the CO 2 in theatmosphere. This requires that one quantify the processes that transport carbon in theocean. Related to these questions, I will address the effectiveness of the box model inextracting information about the CO 2 cycle by making use of data generated by a generalcirculation model (GCM) of Bacastow and Maier-Reimer (1990).1.1 INVERSE BOX MODELSThe box model is a classical method used for developing a quantitative picture ofthe role of an ocean in transporting heat, salt, carbon  and other tracers. The studies ofChapter I. Introduction^ 3Wunsch and Minster (1982) and Bolin et al., (1983) provide the foundation forformulating this problem as an inverse problem. In these studies, the conservationconstraints are applied to a set of boxes for the observed distribution of physical andbiochemical tracers. This process generates a set of equations by which inverse methodsare used to extract a solution, giving values for rates of the processes which govern thetracer distributions. The work of Wunsch and Minster and Bolin et al., has been followedby other studies that use the inverse methodology with various tracers to quantify theadvective, biological and air-sea processes affecting the tracer distributions (Bolin et al.,1987; Schlitzer, 1988 and 1989; Wunsch 1984; Garcon and Minster, 1989; Metzl etal., 1989; Metzl et al., 1990, plus others not mentioned). In the studies referenced,questions concerning the problems of including different tracers, of including differentprocesses, of considering different model regions, of considering the seasonal scale, andof choosing the spatial scale (the box sizes) in the inverse models are addressed. Forexample, Rintoul (1988) looked at the compatibility of heat and nutrient transports in theSouth Atlantic. Garcon and Minster (1987) addressed the question of introducing heattransport in the Bolin et al., (1983) model. Schlitzer (1988, 1989) looked at the carboncycle in the North Atlantic and Bolin et al., (1987) for the whole Atlantic Ocean. Metzlet al., (1990) looked at the processes that must be included in inverse methods when oneuses biogeochemical tracers; the application was made in the Indian Ocean. The commoningredient of all these models is the desire to quantify the advective and biologicalprocesses from tracer distributions through the use of the inverse methodology. TheChapter I. Introduction^ 4models differ in the processes that are considered unknown, the tracer fields used, and theadditional equations generated from dynamical principles (e.g. geostrophy).From the past studies, it is useful to emphasize some of the important philosophicaldifferences in applying these models to tracer data. The main differences are 1) the dataused to calculate the mean circulation field, 2) how the geostrophic constraint is applied,3) how the tracer transports are determined, and 4) the algorithm employed to solve theinverse problem.The two different types of hydrographic data employed in the box models for thecomputation of geostrophic velocities are synoptic sections (Rintoul and Wunsch, 1991;Memery and Wunsch, 1990), and Levitus annual mean temperature and salinity data(Schlitzer, 1988, 1989). The advantage of using the Levitus data set is the flexibility indefining the boxes of the model (sampling of 1° in latitude and longitude). The drawbackto using the Levitus data set is the question of whether this data set is adequate forcalculating the mass and tracer transports. This question will be further explored inchapter 2.Setting aside the question of the "best" data to use in calculating the geostrophictransports, important differences exist among the various models in how the geostrophictransports are applied in the model. In Bolin et al., (1987) much effort is spent ondetermining the weighting to be used for the geostrophic constraints. Such a question cannever be satisfactorily answered, and in Matear (1989) I also devote much effort to thequestion of weighting the equations. The conclusion reached in Matear (1989) and inBolin et al., (1987) is that a simple weighting be employed that reflects the relative Chapter 1. Introduction^ 5information content of the equations. In part, the question of weighting constraints can becircumvented by assigning acceptable errors to the constraints and by using the linearprogramming routine to solve the problem. This will be discussed further in chapter 3.The problem of weighting of the geostrophic constraints arose in the Bolin et al., (1987)work; by demanding that geostrophy be exactly satisfied, the errors in the conservation ofthe tracers were greatly increased. In Bolin et al., (1987), only one reference velocitywas determined for each horizontal section used to defined the boxes; in part, thedifficulties experienced may have been resolved by determining more reference levelvelocities. Just such an approach was used by Rintoul and Wunsch (1991), in theirapplication of geostrophy. They allowed an unknown reference level velocity for eachstation pair in the section defining the boxes. Such an approach generates a largeunderdetermined system of equations (number of unknowns greatly exceeds the number ofconstraints). In order to solve such a system, one typically invokes the additionalconstraint that the square of the magnitude of the unknowns be minimized. The problemin such an approach is that the individual velocities are poorly resolved by the tracer data,and thus the added degrees of freedom introduced by having many reference levelvelocities are not justified. The results of Rintoul and Wunsch (1991) showed that, exceptfor the areas of significant topography, the reference level velocities were nearly constant.Schlitzer (1988, 1989) realized that the tracer fields did not provide adequate informationto resolve the small scale reference velocities (e.g. reference velocity for each station pair)and so allowed only several reference velocities for each section defining the boxes (lengthscale of 1000 km). By doing it this way he  ensured that the model was still Chapter 1. Introduction^ 6overdetermined (more equations than unknowns). This is the approach I take in applyingmy inverse model to the North Pacific data.How the tracer transports are calculated varies significantly with the differentstudies. In Bolin et al., (1983), Garcon and Minster (1988), and Metzl et al., (1990), theadvective transport is determined as the average transport through the box face times theaverage concentration between the two adjacent boxes. In the work of Schlitzer (1988 and1989) and Rintoul and Wunsch (1991), the advective transport is calculated from thetracer concentrations along the section. The other major difference in the tracer transportsis whether turbulent mixing transports are considered in the model. In the studies withreference level velocities determined at each station pair, the mixing terms are omitted.In the work of Schlitzer (1989) and Bolin et al., (1987), the turbulent mixing terms areparameterized by an apparent eddy diffusion term times the tracer gradient normal to thebox face. The two approaches are either to determine many reference level velocities andomit mixing or to limit the number of reference velocities but include mixing transports.It is unclear which approach is better. I will use the latter approach because, by ensuringthat the problem is overdetermined, it is possible to determine the unknown parametersmost consistent with the constraints. If too many unknown parameters were to beconsidered, the inverse model would be unable to resolve all the unknowns. Therefore, itseems logical to try and restrict the number of unknowns to a number that can be resolvedby the model. The inclusion of the mixing transports is in recognition of the fact that themodel will not resolve the small-scale transports.Chapter I. Introduction^ 7The choice of the algorithm in many ways reflects what one expects to answer bythe model. At this point I will only present and briefly discuss the two most commonalgorithms employed in the cited references above, the least squares with inequalityconstraints (LSI) and linear programming (LP) algorithms. In the LSI routine, oneessentially determines the "best" solution to the observed tracer properties. The solutionobtained in such a way may have more meaning physically and may be more easilycompared to other observations than the LP solutions. In the LP routine, one determinesthe maximum or minimum value of a given quantity that is consistent with the observedproperty distribution and constraints. I will employ both algorithms to extract informationfrom the model.The one common ingredient missing from all the cited references is the applicationof the inverse models to the North Pacific. With the extensive studies of JGOFS andWOCE, it is an ideal time to look at the situation in the North Pacific. Such a researcheffort can provide tools to use the data that will be generated by these experiments tofurther advance our understanding of the carbon and nutrient cycles.1.2 OCEAN CARBON CYCLECarbon is present in the ocean in the form of dissolved inorganic carbon (DIC),organic compounds (particulate organic carbon and dissolved organic carbon) and calciumcarbonate (CaCO 3). The DIC in the ocean accounts for about 97% of the carbon in theocean (Post et al., 1990). The ocean contains about 50 times more carbon than the Chapter I. Introduction^ 8atmosphere (Post et al., 1990). The main reason for the abundance of carbon in theocean is its chemical reactivity with water. The average surface water in the oceancontains only 0.5% of the DIC in the form of dissolved CO2 gas the remaining DIC iscomposed of bicarbonate ions, HCO3 (=90%) and carbonate ions, CO3 ' (..-- 10%). Thusthe atmosphere only sees a tiny fraction of the carbon present in sea water, enabling theocean to be a relativelty large reservoir of carbon. The partition of carbon between theatmosphere and the ocean and the distribution of DIC within the ocean is affected by theocean circulation, by the biological activity and by the air-sea exchange of CO 2 .The atmosphere-ocean exchange of carbon is related to the difference in partialpressure of CO2 between the atmosphere and ocean (ApCO2). The partial pressure ofcarbon dioxide (pCO2) in water depends on its solubility, a, and its concentration inwater:[CO2]pCO2 = ^aThe solubility of CO 2 increases as temperature or salinity decreases (Weiss, 1974). Thedissolving of CO2 in water is described by the following reaction, (the concentration ofcarbonic acid is very small and is ignored)CO2 + H2O •.► H+ + HCO3^ (1.2)Bicarbonate ion then dissociates into hydrate proton and carbonate ionK1 =[CO2][Hi [HCO3 ]Chapter I. Introduction^ 9HCO3 r H+ + CO32 .^ (1.3)These two reactions reach equilibrium in less than a few minutes (Broecker and Peng,1982) and this requires that the concentrations of the species in these reactions obey thelaws of chemical equilibria. The equilibria of these reactions is given by[H+] [CO3 2]K2 =-^[HCO31where K 1 and K2 are called the first and second apparent dissociation constants of carbonicacid, respectively. In writing these equilibria equations, the concentration of water (H20)is assumed constant. The hydrogen ion is also involved in the ionization of water:H2O •-• [H+] + [0111 .^ (1.6)The equilibrium of this reaction is given byKn, = [H+] [OH -]^ (1.7)where K, is called the ionization constant of water.Typically when studying the carbon cycle in the ocean one measures DIC andalkalinity. The DIC in water is given by(1.4)(1.5)Chapter 1. Introduction^ 1 0[DIC] = [CO2] + [HCO3] + [CO32] .^(1.8)Since the equilibrium constants K 1 , K2, and Kw vary with temperature, salinity andpressure, a water parcel undergoing a change of state will experience variations in CO 2 ,HCO3, CO2-2 , H+, and OH -. However, a change of state will not affect DIC becausecarbon will simply be redistributed among the three carbon species.The point at which all buffering species in seawater are neutralized by the addedacid is called the alkalinity. A simple equation for alkalinity is given byALK = [1-1CO31 + 2[CO32] + [011 - ] - [H+] + [B(OH)41 .^(1.9)A more rigorous treatment, as by Peng et al. (1987), should include the silicatephosphorus-containing ions. In the equation for alkalinity, the borate ion concentrationcan be computed from the [H+] ^the salinity (Peng et al., 1987).One now has a system of equations (1.1, 1.4, 1.5, 1.7 1.8, 1.9) to solve. If DICand alkalinity along with temperature and salinity are specified, all unknowns can becompletely determined. This system of nonlinear equations can be used to look at thevariability of the partial pressure of CO 2 in seawater as a function of temperature, salinity,DIC and alkalinity. For pCO 2 as a function of T and S under average surface conditions(DIC =2000 it mol kg -1 , ALK = 2300 iEq kg - '), pCO2 increases with increasing DIC andwith decreasing ALK with approximately the same sensitivity (Najjar, 1992). DIC andALK can be changed by the exchange of freshwater at the air-sea interface. Thefreshwater flux can produce large variations in DIC and ALK, however, these variationsChapter 1. Introduction^ 11produce nearly equal but opposite effects on the dissolved CO 2 resulting in negligibleimpact on the seawater pCO 2 .Sizeable variations in the surface water partial pressure of CO2 occur from place toplace in the ocean. The variation of the CO 2 partial pressure in the surface ocean stemsfrom the complex interplay between the seasonal temperature cycles, the mixing dynamicsof the upper ocean, and the biological cycles of the sea. The CO 2 transfer between the airand sea tends to eliminate these differences but the time constant to achieve equilibrium isabout 1 year (Broecker and Peng, 1982).The marine biological productivity in the surface waters is primarily controlled bythe availability of nutrients, particularly nitrogen and phosphorous, and is not significantlyinfluenced by changes in DIC. Biological activity in the well-lit upper layers of the ocean(the euphotic zone) converts DIC into CaCO3 and organic carbon. This material istransported to the deeper, dark layers of the water column (the aphotic zone) and to thesediments by particle settling. In the aphotic zone and in the sediments, chemical andbiological processes dissolve CaCO3 and remineralize organic carbon to DIC. Thisbiological cycling of carbon in the ocean is known as the biological pump because itmaintains vertical gradients in DIC and many other chemical species in the ocean (eg.phosphate). It can be separated into an organic matter pump and a calcium carbonatepump.The photosynthesis due to the uptake of nitrate transported into the euphotic zoneby the ocean circulation is known as new production (Dugdale and Goering, 1967). Thetotal phytoplankton production, or primary production, is usually significantly higher thanChapter 1. Introduction^ 12new production. The f-ratio is used to define the proportion of new production to primaryproduction. New production is very important when considering the organic matter pump.Over seasonal time scales, new production must balance the input of nutrients into theeuphotic zone as well as the export of organic matter. In the absence of new production,all the primary production would be recycled within the euphotic zone, and theatmospheric CO 2 would be much higher.Calcium carbonate (CaCO3) is a mineral solid that plays an important role in themarine carbon cycle. Some plants and animals living in the euphotic zone have CaCO 3skeletons which they precipitate from dissolved calcium and carbonate ions. The CaCO 3formed in this manner eventually sinks and is dissolved back into calcium and carbonateions in the deeper parts of the water column and in the sediments. Ocean circulationcloses the loop and transports these ions back to the surface waters. This cycling of theCaCO3 , known as the carbonate pump (Volk and Hoffert, 1985), creates a surfacedepletion and a deep enrichment of DIC and alkalinity. Since variations due to thecarbonate pump are twice as great on alkalinity as on DIC, an increase In the strength ofthe carbonate pump will increase atmospheric CO2 .To use tracer distributions to quantify the cycling of carbon in the ocean requiresthat this data provide information on the ocean circulation, biological processes and air-seaexchanges that affect the distribution of carbon in the ocean. All tracers will be affectedby the physical processes but only certain tracers will contain information on the lattertwo processes. Alkalinity and DIC are essential tracers to understanding the carbon cycle.The nutrient data - phosphate, nitrate, and oxygen tracers - provide additional information Chapter 1. Introduction^ 13on the organic matter pump. Temperature, salinity, and silicate tracers are useful toprovide additional constraints on the ocean circulation. By using several different tracers,one attempts to overcome the limitation that no one tracer can adequately describe all therelevant processes affecting the cycling of carbon in the ocean. However, in using severaldifferent tracers it important to realize that the different tracer fields may containredundant information.The work presented in this thesis divides into three parts. In the first part (chapter2), the question of the best hydrographic data to use to determine the horizontal tracertransports is studied by looking at the tracer transports across 35°N in the Pacific. Theresults of this study are reflected in how the inverse model is applied to the data from theNorth Pacific. In the second part (chapter 3), I apply the inverse model to a data setgenerated by the Hamburg biogeochemical model. The purpose of this study is to providea means with which to assess the ability of the inverse model to determine air-seaexchanges. In the third and final part (chapters 4-5), I use the tracer data from the NorthPacific to formulate an inverse model. The model is used to investigate the nutrient andcarbon cycle in the North Pacific as well as the circulation fields. The role of dissolvedorganic matter in the carbon and nutrient cycles is examined using a model which includesthe dissolved organic nutrient measurements of Suzuki et al., (1985).CHAPTER 2. TRACER TRANSPORTS ACROSS 35 °N IN THEPACIFIC OCEAN2.1 INTRODUCTIONThe use of inverse models has been one approach to estimate the uptake of CO 2 bythe ocean (Bolin et al., 1983; Bolin et al., 1987; Schlitzer 1988 and 1989). The air-seaexchanges calculated from these models need an accurate determination of the transport ofcarbon by the horizontal flow field. The situation arises because one utilizes theimbalances in the horizontal transport to estimate the air-sea exchange of CO2 . Toreliably determine the importance of the oceans as a sink of anthropogenic CO 2 , therefore,requires an accurate calculation of the horizontal transport which is orders of magnitudelarger than the air-sea exchange.In applying inverse models to the problem of estimating the air-sea exchange ofCO2 , it is typical to assume that the horizontal transport is geostrophic. The unknownreference level velocities are adjusted in a manner that conserves mass, carbon and othertracers. An initial specification of the horizontal transport is required because the tracerfields do not possess enough information to fully constrain the flow (Schlitzer, 1988).The initial mass transport is usually determined using geostrophic equations with eithersynoptic data or the Levitus Climatological data (Levitus, 1982). The choice of data used14Chapter 2. Tracer Transports across 35°N in the Pacific Ocean^ 15for this initial mass transport calculation depends on which type of data one considersmore appropriate for calculating the tracer budgets in an ocean basin. This question hasbeen debated but not satisfactorily resolved, with proponents of both approaches stillexisting. Memery and Wunsch (1990) argue that the use of the Levitus dataset in theNorth Atlantic inverse box model produced unrealistic meridional heat fluxes at mid-latitudes. They feel that these difficulties can only be resolved by either introducing largelateral mixing terms or by assuming the Ekman fluxes in serious error as done bySchlitzer (1988). Schlitzer (1988) maintains that even though the Levitus dataset may notrepresent the average ocean circulation it still describes the average circulation better thansynoptic sections and does a better job of balancing the long term nutrient budgets. Thedifficulty with these two statements is that they are based on the results of inverse modelswhich have the tendency to blur the inconsistencies present between the mass and tracerfields. Thus it makes it difficult to state clearly what data are more appropriate.In this chapter, the problem is simplified by considering only one section acrossthe North Pacific at latitude 35°N. This can be thought of as a one box model of theNorth Pacific. The annual mean tracer transports calculated from a synoptic section arethen compared to the annual mean tracer transports calculated from the annual meanLevitus section. The transport of heat, salt, dissolved inorganic carbon (DIC), alkalinity,phosphate, nitrate, oxygen and silicate through the two sections are used to compare thesections. The goal is to show clearly which approach is most consistent with the data.The simplified approach of dealing with only one section will provide insight into90 ° N70 ° N50 ° N30 ° N10 ° N100 ° E^120 ° E 140 ° E^160 ° E^180 ° W 160 ° W 140 ° W 120 ° W 100 ° W^80° wChapter 2. Tracer Transports across 35°N in the Pacific Ocean^ 16Figure 2.1: Location of stations for the trans-Pacific sections. The long ticks above theline at 35°N indicate the locations of the TRANSPAC stations; the long ticksbelow, the deep stations; and the short ticks the 1200-m stations, both forINDOPAC.problems that one will encounter in applying inverse models to nutrient data to quantifythe carbon cycle processes and the limitation of these models. The analysis will also beapplicable to attempts to determine the air-sea exchanges of CO 2 by using the transportthrough a section (Brewer et al, 1989).2.2 SECTIONSFor this chapter, three sections across 35°N are used, the Levitus annual meansection, the INDOPAC section and the TRANSPAC section (Fig 2.1). Additional tracerdata from the NODC archives is included to create mean tracer fields along 35°N. In thisChapter 2. Tracer Transports across 35°N in the Pacific Ocean^ 17study the INDOPAC section and Levitus section have comparable horizontal resolution ofabout 1 degree longitude.2.2.1 INDOPAC SectionThe INDOPAC section consists of data from INDOPAC Cruises 1 and 16 of Mar.-Apr. 1976 and July 1977 respectively (Scripps Institution of Oceanography, 1978;Kenyon 1983). The data from the July 1977 cruise are only used to augment the deepdata missing in the original section (depth deeper than 1000 m). The data were collectedat 98 stations of 1 degree spacing with alternating casts to 1000 m and casts to the oceanbottom. The tracer data collected included temperature, salinity, dissolved inorganiccarbon (DIC), alkalinity, oxygen, nitrate, phosphate and silicate. Because the last stationin the INDOPAC section was well east of the Japanese coast in water of depth of 2300 m,an additional station closer to the coast was added to the section from the NODC files(NODC cruise number 1847, station RY4761). The station in the Kuroshio, 80 km westof the last INDOPAC station preceded the INDOPAC station by only 4 days and providedadditional measurements of temperature, salinity, oxygen and phosphate. The tracerproperties of the INDOPAC section are shown in Figure 2.2. In general, the contours ofthe property fields are zonal with evidence of increased eddy activity in the westernboundary region. The eastern part of the section has slightly greater concentrations ofsilicate, phosphate, nitrate, and salinity than the western portion of the section.(a)135^ 155^ 175^ 195LONGITUDEFigure 2.2: Tracer properties of the INDOPAC section along 35°N for (a) temperature (°C, (b) salinity(pss), (c) phosphate (knol/kg), (d) nitrate (Amol/kg), (e) oxygen (kanol/kg) , (f) silicate (tnol/kg),(g) DIC (Amol/kg), and (h) alkalinity (SEq/kg).215^235l■ ■000 1,-VVITW\IvirdNup. 0 1.•10000ate00 034.134.2. 34.2^-34.134.3 34.3 34.434. O2000300040005000800034.34.6(b)135^155^175^ 195^215^235LONGITUDE0010 0 0200030004400050008000(c)(d)(e)(0......._...-----ir _______,___.---------------7 40° ^ 40__V---^----------„—J\------rb0 1°13 ■------__/— ' ^-..---,v----1000------\______,,c \,.^ 120----------- 140'*-------- 140 ---i'165 ----------■.165 -6°----------2000^ 170 -----_,-- ----------.,____170tP ------N__3000^0^----400050008000135 155 175 195 235LONGITUDE 215LONGITUDE195 215 235(g)135^ 155^ 175010002000E30004-)a,a)A400050006000(h)NV iChapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 262.2.2 TRANSPAC SectionThe TRANSPAC section data were collected during Oct. 1972 (Wong, unpublishedcruise report; Wong et al., 1974). The data consisted of casts to a maximum depth of5000 m at every 5 degrees longitude along 35°N. The tracers measured weretemperature, salinity, DIC, alkalinity, oxygen, nitrate, and silicate. As with theINDOPAC section, an additional station in the Kuroshio was added to the section from theNODC files (NODC cruise number 994, station RY4204). The Kuroshio station precededthe most westerly TRANSPAC station by 9 days and included additional measurements oftemperature, salinity, oxygen, phosphate, and silicate.2.2.3 Levitus SectionThe Levitus section consisted of the annual mean temperature and salinitymeasurements with 1 degree longitude spacing in the latitude band 34°N - 35°N compiledby Levitus (1982). For this section, the average concentration of oxygen, phosphate,nitrate and silicate were computed from the NODC files, which included INDOPAC andTRANSPAC data. To determine these average tracer fields between 34-35°N, aprocedure similar to what was done with the temperature and salinity in the Levitus annualChapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 27mean dataset was followed. The data was objectively mapped to a one degree spacing(Roemmich, 1983). Because the NODC files did not contain DIC and alkalinitymeasurements, the average annual mean fields for these tracers were obtained byaveraging the INDOPAC and TRANSPAC data. The DIC and alkalinity measurements ofthe TRANSPAC cruise were systematically less than the INDOPAC cruises (Fig. 2.3).An offset of 41 1.4Eq kg' and 42 smol kg-1 for alkalinity and DIC respectively were addedto the TRANSPAC measurements to correct for the systematic differences between thetwo cruises for the deep water measurements. The two cruises displayed very similarfeatures despite systematic differences.2.3 COMPUTATION OF THE TRANSPORTSInstead of the traditional station pair calculation of geostrophic shear, the approachprescribed by Roemmich (1983) was followed. Using an objective mapping routine(Roemmich, 1983), all tracer fields and the specific volume anomaly were interpolated toa constant 1 degree horizontal spacing and to the 33 depth levels used in the Levitusdataset. The shear in the geostrophic velocity was calculated from the gridded values ofthe specific value anomaly. By using the objective mapping approach, one makes use ofboth the vertical and horizontal features of the field to extrapolate to the ocean bottom.Such an approach does a better job of calculating the geostrophic shear where there arelarge changes in the depth of the ocean bottom between stations (Roemmich andMcCallister, 1989). -^000000NE oO.ca0• 0000000180000o_000NE o— 0_a0000000_00001800• •O ••o o • •O ••OO •o •o ••••o ••• •0^•oO •o ••••2000^2200DIC (uMol/kg)8,92000^2200DIC (uMol/kg)gibecu°^••o  •o 02400•0•O •Oo •OO ••O0 •00 •O••2400(a) . _^••0o_ 00^•o^• •O••0_0E 0—0,OCI 0o_0ar0o_io000°•••O ••OOO••••OO00••••••••2300^2400Alkalinity (uEq/kg)250022000000• •o-(b)000NE o— _ao^•0OO^••OO^••Oo •OO^•O000OOOO•2200^2300^2400^2500Alkalinity (uEq/kg)Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 28Figure 2.3: A comparison of the alkalinity and DIC measurements of the INDOPACcruise (•), and the TRANSPAC cruise (0), at (a) 35°N and 164°E, and (b) 35°Nand 170°W. Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 29For each section a reference level was chosen and the relative geostrophic transportwas calculated by integrating the geostrophic shear.zv(z) = gt^ax dz + vo = vg +voP where v° is the velocity at the reference level zo . The Ekman transport across 35°N wascalculated using Hellerman and Rosenstein (1983) annual mean wind stress values. TheEkman transports of the tracers were assumed to be confined to the upper 50 m of theocean (Gill 1982). The total mass transport across the section is given bypM + f pyrdA + pv0A = 0^(1.2)where M. is the total Ekman transport through the section, and the integral is over thearea of the section, A. By assuming no net mass transport across the section, the velocityat the specified reference level (v.) is determined. Only one reference level velocity isdetermined for the section and this is added to the relative geostrophic transport to obtainthe geostrophic transport. The tracer transport through the section is determined byX = pC(vg +vo) dA + fpCmedS^(1.3)where C is the tracer concentration and me is the Ekman transport along the section. Thefirst integral is over the entire section while the second integral is only for the upper 50 mof the section.Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 302.4 MASS TRANSPORTThe depth of the reference level (;) chosen for all sections was 2500 m. The2500 m depth corresponds to the depth of the silicate maximum and the 14C minimumwhich are considered to represent the oldest and slowest moving water (Bien et al., 1965).Although the choice of the reference level is somewhat arbitrary, it was clear in thetransport across the INDOPAC section that a reference level shallower than 2000 m wouldproduce a southward flow of water in the deepest layer (Fig 2.4). In the Pacific, theabyssal water can be traced back to water of North Atlantic origin (Reid and Lynn, 1971);there is no source of deep water in the North Pacific (Warren 1981). The maps ofMantyla and Reid (1983) indicate the northward spreading of the bottom water at 35°N.These observations all suggest that the deep water should be flowing northward at 35°N.The variation in transports between the 2000 m and 3000 m reference levels were used toestimate the transport errors generated by the choice of reference level. With a referencelevel of 2500 m the INDOPAC section had approximately 10 Sv of deep water flowingnorth (2500 m to the bottom). The geostrophic velocities for the three sections are shownin Figure 2.5 . The two synoptic sections show much greater eddy activity than theannual mean Levitus section.The integrated geostrophic transport from 139°E for the three section showedsignificant differences between the sections (Fig 2.6). However, Figure 2.6 showed thatbetween 139°E and 240°E the integrated transport of the INDOPAC section was verysimilar to the Levitus section suggesting that the Levitus dataset poorly represents the Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 31-1^0^10-20-30-50-75-100-125-150-200-250-300-400-500-2- 600-... "0_soo-CD 900-C) 1000-1100-1200-1300-1400-1500-1750-2000-2500-3000-3500-4000-4500-5000-bottom -10^1^3•^I0I "2 3Mass Transport (Sv)Figure 2.4: Layer transports for the INDOPAC section at the following referencelevels, 2500 m (shaded), 1750 m (solid line), 2000 m (dotted line), and 3000 m(dashed line). A positive value indicated a northward transport.western boundary current. A depth profile of the total transport across the section (Fig2.7a), further elucidates some of the differences between the three sections. This profilereveals that in the upper 2000 m, the INDOPAC and TRANSPAC section are remarkably(a)135^ 155^ 175^ 195^ 215^ 235LONGITUDEFigure 2.5: Geostrophic velocity with a reference level at 2500 m in cm s' for (a) INDOPAC, (b) TRANSPAC,and (c) Levitus sections.(b)135 175^ 195LONGITUDE(c)175^ 195LONGITUDE215^ 235r_B00.rnCco2a)61)Wee'—2Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 35140^150 160 170 180^190 200 210^220 230^24C60SO40111111j^I1^iIII^:I  1 IA•AI1 30.III .1 :i11■•Ar I.^f . " . : I 1I k I20101^ir^1!To.11I Er1 :.j/IIIIIr :^IetIIt^:!^1• T. pa &t : 11^111^01 11 • i s111!1^•1^•o^IIs••Itit.i st.F o.0 I/ r.v^i t4 el.T%t •1- , i-la -^•.^II y_.....smisi..-.,.;1,.•0IT 1 t i^i„,.,.^..,...,11.,„11,11^I.,..,t iis1.1..^r•-•V1N1111...41‘, ,i,,,,,,„ISt:••••:bi.,„^1 ^I^11^%1 1I^I..11V:::^:tto,^*.•0IiN1ituI%.••.:140^150 160 170^180^190^200 210^220 230^240Longitude EastFigure 2.6: The integrated mass transport along 35°N for the Levitus section (solid), theINDOPAC section (dashed) and the TRANSPAC section (dotted). A positivevalue indicates a northward transport.Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 36similar considering how different they appeared in the integrated transport plot. It is thedeep layers where the transports differ significantly between the two sections. Thisclearly reveals the problem of insufficient deep casts in the TRANSPAC section, with nostations having data deeper than 5000 m. Based on these findings, the transports obtainedfrom the TRANSPAC section will be disregarded and only the tracer data from thissection will be used. The similarity of these two sections in the upper ocean suggests thatthe synoptic section does represent the gross features of the annual circulation. The depthprofile of the Levitus section showed no similarity with the INDOPAC section.The integrated layer transports for the western part of the section (139 - 170°E)and eastern part of the section (170 - 240°E) (Fig. 2.7b and 2.7c) reinforces the idea thatthe TRANSPAC section poorly resolves the deep layer transports. The number of deepcasts for the TRANSPAC section is insufficient to determine the deep geostrophic shear.However, in the upper ocean the TRANSPAC section has similar features to theINDOPAC section. The Levitus transport in Figure 2.7c clearly shows differences in thewestern boundary flow. The western boundary flow is more reduced in the Levitussection than the INDOPAC section. Away from the western boundary, the Levitustransports are very similar to the INDOPAC section for the upper 2500 m of the ocean.2.5 TRACER TRANSPORTSIn the previous section, it was obvious that there were significant differencesbetween the mass transport of the INDOPAC section and the mass transport of the Levitus-4^-3 -2^-1 0^1^2^3^4^5^6^7_,.■.i....1,,,..,,,i.".t"...1,,,10-20-30-50-75-100-125-150200-250-300-400-500-E 6°°""..-.. 700_E. aoo-o.(I) 900-° 1000-1100-1200-1300-1400-1500-1750-2000-2500-3000-3500-4000-4500-5000--bottom . . .-4 -3 -2^-1^0 I 2 3 4 5 6Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 37a)Mass Transport (Sv)Figure 2.7: The integrated layer transport for the three section, with each sectionshifted by 3 Sv for clarity. The left plot is the INDOPAC section with zero at -3Sv, the middle plot is the Levitus section and the right plot is the TRANSPACsection. The Figure show: a) the transport for the entire section, b) the transportfor the western part of the section (139°E to 170°E) and c) the transport for theeastern part of the section (170°E to 240°E). A positive value indicates anorthward transport.Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 38-4 -0 " "^10-20—30—50—75—100—125—150—200—250—300—400—500—.-‘ 6°°—-m.o. 700_f. 800—o.a) 900—'3 1000—1100—1200—1300—1400—1500—1750—2000—2500-3000—3500—4000—4500—b)^b)4^5^6Mass Transport (Sv)Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 39-7 -6^-5^-4^-3^-1^-0^' ' ' ' I ' " ' I ' • ' ' I '^10-20-30-50-75-100-125-,150-200-250-300-400-500-E 6°°-...... 70Q_-5 800-Q.0 900-° 1000-1100-1200-1300-1400-1500-1750-2000-2500-3000-3500-4000-4500-5000-bottom4Mass Transport (Sv)section. We will now investigate the ability of the two sections to close several differenttracer budgets. First, we will compare the salt and heat transport through the twosections. Second, we will compare the calculated transport of DIC, alkalinity, oxygen,phosphate, nitrate and silicate of the two sections. Finally, we will correct the tracerc)Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 40transports through the section to obtain the corresponding tracer budgets for the PacificOcean north of 35°N.2.5.1 Heat and SaltThe calculated salt transport for the synoptic and climatological section (Table 2.1)is comparable, with both appearing to be consistent with expected values needed to closethe freshwater budget (Baumgartner and Reichel, 1975). The freshwater inputs implied bythese salt transports will be calculated in the next section. The calculated heat transportusing the two sections is drastically different. The Levitus section gives an unrealisticallylarge southward transport of heat which is not in agreement with the heat transportdetermined from air-sea exchanges (Talley, 1984). Part of this discrepancy can beattributed to the underestimated flow in the west boundary which reduces the northwardtransport of heat across the section. The heat transport determined from the INDOPACsection is much more believable but it is in the lower range of the oceanic heat fluxestimated by Talley (1984).Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 41Table 2.1: The tracer transports through the 35°N section for a) salt and heat, b)alkalinity and DIC, c) phosphate and nitrate and d) oxygen and silicate. Thesetransports are determined with the assumption that there is no net mass transportthrough the section. Positive values indicate transport into the North Pacific. Theerrors in the transports are determined from the integrated layer transportsmultiplied by the variability of the tracers within those layers plus the estimatederrors arising from the choice of reference level.a)Salt (106 kg s') Heat (10 15 W)Transport Levitus INDOPAC Levitus INDOPACGeostrophic 160.2 163.7 4.446 4.920Ekman -151.5 -151.3 -5.139 -5.083Total 8.7 12.4 -0.693 -0.163±5.3 ±2.8 ±0.075 ±0.130b)Alkalinity (k mol s') DIC (k mol s')Transport Levitus INDOPAC Levitus INDOPACGeostrophic 12,178 11,056 12,175 10,042Ekman -9,9767 -9,9767 -8,789 -8,789Total 2,200 1,080 3,390 1,250±380 ±320 ±790 ±700Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 42C)Phosphate (k mol s') Nitrate (k mol s')TransportGeostrophicEkmanLevitus26.7-0.9INDOPAC15.9-0.9Levitus331.3-7.8INDOPAC36.7-7.8Total 25.8±6.015.0±5.0323.5±94.028.9±76.0Oxygen (k mol s-1) Silicate (k mol s')TransportGeostrophicEkmanLevitus-682-1,144INDOPAC-845-1,144Levitus1,847-26INDOPAC684-26Total -1,826±510-1,989±5401,821+197658+1582.5.2 Nutrient Tracers, DIC and AlkalinityThe difference in the heat transport for the two sections was amplified furtherwhen comparing the transport of nutrient tracers, DIC and alkalinity (Table 2.1b, c, andd). With the exception of oxygen, the Levitus section produced values 2-3 times greaterthan the INDOPAC section. It should be recalled that for the Levitus section the annualmean nutrient tracer fields were determined from the NODC archives, and the DIC andalkalinity fields were calculated from the average of the INDOPAC and TRANSPAC data.Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 43Table 2.2:^The transport of phosphate and silicate across the 35°N using thehydrography from the Levitus seasonal data (FMA) and the tracermeasurements of INDOPAC.Phosphate (K mol s')^Silicate (K mol s')Transport^Levitus (FMA)^Levitus (FMA)Geostrophic 35.9 2356Ekman^-1.7^-50Total 35.2 2,307^±6.0^+197Although the study was meant to evaluate the annual mean tracer transports, it wasinteresting to see if the use of seasonal Levitus hydrography (Feb., Mar., Apr.)corresponding to the time of the INDOPAC cruise (Mar.) applied to the INDOPAC tracerfields would produce more comparable transports with the INDOPAC section. For thephosphate and silicate transports, the use of the seasonal hydrography (Table 2.2) did notreduce the difference between the INDOPAC section and the Levitus section. To assessthe significance of the tracer transports given in Table 2.1, one must consider additionaltransports to obtain the corresponding tracers budgets for the North Pacific.Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 442.5.3 Corrections to the Tracer Transports due to Bering Strait Flow, Korean Strait Flowand Freshwater ExchangesIn the North Pacific, the northward movement of water through the Bering Strait,Korean Strait and freshwater exchanges produce significant changes to the tracertransports estimated from the 35°N section, using the assumption of zero net masstransport through the section. The necessity of including these transports arises becauseof the significant differences in tracer concentrations between the Bering Strait water, theKorean Strait water, the freshwater input, and the average water along the 35°N section.The freshwater exchange is considered to have no tracer concentration (air-sea exchangesof heat, CO2 , and 02 are treated separately). The Bering Strait is very shallow (50 m orless), as is the Korean Strait (200 m), and therefore they have significantly differentaverage tracer concentrations than the average concentrations in the 35°N section.By using the Bering Strait salt transport of Anderson et al. (1983), the KoreanStrait transport of Yoon (1982) and the average salinity in the Korean Strait, the salt andmass budgets are closed. By closing the budgets, one obtains a freshwater exchange and amass transport correction for each of the sections. The freshwater exchange is an estimateof the net input of freshwater into the Pacific Ocean north of 35°N. The mass transportcorrection for the section is introduced as a correction to theChapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 45Table 2.3: The corrections to the tracer transports, the value in the "Difference" columnshould be added to the tracer transport given in Table 2.1 to obtain the tracerbudgets. *In the table the heat transport assumes the water transport through theBering Strait is replace by water with an average temperature of 5°C.Tracer Bering StraitTransportKoreanStrait35°N SectionCorrectionTransportDifferenceAlkalinity (kmol s-1) -2,978 4,975 -3,086 -1,089DIC (kmol s-1 ) -2,835 4,457 -3,002 -1,380Oxygen (kmol s -1) -405 541 -152 -16Nitrate (kmol s -1) 0.0 13.6 -47 -33Phosphate (kmol s-1 ) 0.0 1 -3 -2Silicate (kmol s-1) -31 20 -182 -193Heat (1015W) -1.48 2.52 -0.94* 0.100reference level velocity necessary to produce the required mass transport. The followingvalues are used for this calculation along with the salt transports determined by thesection. The volume transport through the Bering Strait is 1.35 Sv northward with anaverage salinity of 31.963. The transport through the Korean Strait is 2.2 Sv northwardwith an average salinity of 34.2 . The average salinity of the 35°N section is 34.55 . Forthe Levitus section the freshwater input into the North Pacific is 0.33 Sv with a masstransport correction of 1.18 Sv out of the North Pacific. For the INDOPAC section, thefreshwater input is 0.44 Sv and the mass transport correction is 1.29 Sv out of the NorthPacific. The freshwater input calculated by Baumgartner and Reichel (1975) for theChapter 2. Tracer Transport across 35W in the Pacific Ocean^ 46Pacific Ocean north of 35°N was 0.42 Sv which is very comparable to the valuesdetermined for the two sections.By using the appropriate transport corrections for the two sections and the averagetracer concentrations in the Bering Sea and the Sea of Japan, the correction to the tracertransport through the section necessary to obtain the tracer budgets for the North Pacificnorth of 35°N is calculated (Table 2.3). The values given in the 'difference' columnshould be added to the net tracers transports through the 35°N section in order to obtainthe tracer budgets.2.5.4 Tracer Budgets for the Pacific Ocean north of 35°NThe tracer budgets for the various tracers clearly show that the synoptic sectiondoes a better job at balancing these budgets than the climatological data (Table 2.4). Forthe INDOPAC section, one succeeds in closing the budgets for all tracers except oxygen,phosphate and silicate. For the Levitus section, none of the tracer budgets are closed withthe imbalances being 3 times larger than the estimated errors in these budgets and, withthe exception of oxygen, more than double the INDOPAC imbalances.It is interesting to investigate further the tracer imbalances in the sections foroxygen, phosphate and silicate budgets. For oxygen, part of the imbalance can beattributed to air-sea exchanges. To balance the oxygen budget would require an air-seaexchanged of 2.0 Mmol s' into the ocean which is considerably greater than the 0.8Mmol s-1 that were calculate from Craig and Hayward (19R7) data, The difference could Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 47Table 2.4:^Tracer budgets for the North Pacific Ocean north of 35°N for the twosections. A positive value indicates input into the North Pacific.Tracer Levitus INDOPACHeat (10' 2W) -593 +130 -63 +75Salt (kg s -1) 0 ±5.3 0 +2.8Alkalinity (Kmol s') 1,111 +380 -9 +320DIC (Kmol s') 2,010 +790 -130 +700Oxygen (Kmol s') -1,846 +510 -2,006 +540Nitrate (Kmol s -') 291 +94 -4 +76Phosphate (Kmol s') 24 ±6 13 ±5Silicate (Kmol s -1) 1,628 +197 465 +158be explained by a flux of dissolved organic matter (DOM) out of the North Pacific. Byusing the air-sea exchange value calculated from Craig and Hayward (1987) data (0.8Mmol s-1) the estimated DOM value required to balance the oxygen budget is +1.2 +0.54 Mmol s' of oxygen. By using the following the constant molecular ratio fromTakahashi et al. (1985) (P:N:C:O = 1:16:103:-172) for the composition of DOM, theDOM transport of nitrate, phosphate, and carbon were calculated. Broecker et al., (1985)showed that the ratio of 02 utilization to phosphate production in the sea is equal to 175 +6, with no significant changes with depth or location. The estimated DOM transport of1.2 +0.54 Mmol s' necessary to close the oxygen budget would alter the nitrate budgetby -112 + 50 Kmol s -1 , the phosphate budget by -7 + 3.1 Kmol s' phosphate and theChapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 48carbon budget by -720 ± 400 Kmol s'. For the INDOPAC section, such a DOM fluxwould be sufficient to balance the phosphate and the nitrate budgets.By using the results of Sugimura and Suzuki (1988), the apparent oxygenutilization (AOU) of the INDOPAC section was calculated and used to obtain a dissolvedorganic carbon (DOC) field for the section. From the DOC field, the transport across35°N is 2.253 Mmol s' southward. With the Bering Strait and Korean Strait having anaverage DOC value of 300 Amol n13 and the 35°N section average DOC value being 110Amol ni3 , this translated into a correction to the carbon budget of -1.733 Mmol s'. Thecalculated correction is double the value necessary to close the oxygen budget. From thetracer budgets, one could argue that there is a significant DOM transport but the resultsare probably not sufficient to prove this idea. The AOU - DOC relationship formulatedby Sugimura and Suzuki (1988) defines an upper limit for the transport of DOM.Recent measurements of the DOC concentration by Martin and Fitzwater (1992)show no evidence of the AOU - DOC relationship. However, in the equatorial Pacificthey did observe strong gradients in DOC between surface water at the equator (130 AM)and 9°N (230 AM), and strong vertical gradients at 9°N between the surface water (230AM) and 250 m (150AM). It is the existence of these strong gradients in the DOC fieldwhich are important in the net transport of DOC out of the North Pacific because theycause significant differences in the DOC concentration between the Bering Strait andKorean Strait and the average value along the 35°N section.Without considering the transport DOM, the carbon budget calculated for theINDOPAC section implies that the North Pacific is a weak sink of atmncpherir CO2, 0.05 Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 49± 0.2 Gt C yf'. Contrary to this, the Levitus section shows the North Pacific to be asource of 0.76 ± 0.2 Gt C^Tans et al., (1990) calculated the air-sea flux of CO2 intothe North Pacific north of 15°N to be 0.44 Gt C^(Jan.-Apr.) and -0.33 Gt C y' (Jul.-Oct.) with an estimated annual mean of 0.06 Gt C y'. The potential source/sink of CO2between 15°N and 35°N is small (ApCO2 is close to zero Broecker et al., 1986; Takahashi1989). This enables one to compare the Tans et al., (1990) air-sea exchange estimateswith the values determined in this study from the carbon budget. The INDOPAC sectionestimate of air-sea flux of CO 2 agrees with the annual mean value of Tans et al., (1990).The large flux of CO2 out of the ocean calculated from the Levitus sections appearsunrealistic when compared to the estimates of Tans et al. If one includes the estimatetransport of carbon as DOM that was required to close the oxygen budget (720 Kmolof carbon), the air-sea flux of CO2 into the ocean is increased by 0.3 Gt y -1 . Even withthe additional transport of carbon as DOM, the Levitus section still shows the NorthPacific ocean to be a large source of CO2.The excess in the silicate budget of 465 Kmol s -1 for the INDOPAC section ismore difficult to explain. If this silicate is removed by sedimentation, the calculateddeposition on the sea floor would be 70 mg re c1 -1 (area of the ocean taken as 2 X1013m2). This value is significantly greater than the average detrital flux of biogenoussilica at 3800 m of 17 mg m -2 d1 from station P (of which about 1% is permanentlydeposited on the sea floor). What other processes may affect the silicate budget? Couldthe time lag between when the silicate is removed from the surface water and redissolvedback into the water be important? This process may be significant because most of the Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 50silicate removed from the surface water is dissolved slowly at the ocean bottomintroducing an apparent time lag. The variability of the surface silicate at station P in theNorth Pacific (50°N and 145°W) showed seasonal fluctuations of 20 Arno' kg' (C.S. Wongunpublished data). The estimated southward mass transport between 170 -240°E in theupper 100 m is about 10 Sv (7 from geostrophy and 3 Sv from Ekman transport). Thiswould produce a seasonal fluctuation of 200 Kmol s -1 in the transport of silicate in theupper ocean. This value is large and is nearly enough to close the silicate budget. Thisbrings about the question, on what time scale do we expect the tracer budgets to bebalanced?Two other effects must be considered in assessing these imbalances in the oxygen,phosphate and silicate budgets. First is the resolution of the data. The resolution of theINDOPAC section is such that it may have missed significant transport at the east, west,and bottom boundaries of the ocean (Roemmich and McCallister, 1989). The errorsintroduced by these effects are difficult to determine but cannot be discounted as anexplanation for the imbalances in the tracer budgets. Second, the calculation of the tracerbudgets are sensitive to the prescribed Ekman transport. The Ekman transport does notgreatly affect the salt and heat budgets because the vertical structure of salinity andtemperature (°K) is relatively constant (deviations of only a few percentages from themean value). However, for nutrient tracers, DIC and alkalinity, the tracer concentrationin the upper ocean is significantly different from the mean value for the water column.In the 35°N section a 1 Sv change in the Ekman transport would produce a changeof 144 Kmol s' in the silicate budget, 2 Kmol s' in the phosphate bilriut, 45 Krnol s' in Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 51the nitrate budget, 76 Kmol s' in the oxygen budget, 131 Kmol s -1 in the alkalinity budgetand a 300 Kmol s -1 in the carbon budget. A 1 Sv error in Ekman transport corresponds toa 0.1 GT of carbon error in the air-sea exchange for the North Pacific. This placeslimitations on trying to estimate the air-sea exchange of carbon from the synoptic sectiondue to uncertainties in the windstress. The calculation above shows that errors in themass field can translate into important uncertainties in the nutrient budgets.2.6 DISCUSSION AND CONCLUSIONIn this chapter, I have shown that the annual mean Levitus section and the synopticINDOPAC section produced significantly different mass and tracer transports. The resultsprovided strong evidence of the inadequacy of using the Levitus dataset in trying toevaluate tracer budgets. It was not unexpected to find that the Levitus' mass transportpoorly represented boundary transports (west, east, and bottom). However, it appears thatthese inadequacies are not attenuated but rather amplified in the nutrient tracer transportcalculations. In hindsight it is not surprising that a flow field determined from theaverage temperature and salinity fields does not represent the average geostrophic flowbecause of the non-linear nature of the equation of state. The clear structural similaritiesin the mass transport field between the INDOPAC and the TRANSPAC sections in theupper 2000 m of the ocean emphasize the idea that synoptic sections do represent thegeneral circulation in the ocean.Chapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 52The tracer budgets calculated from the synoptic section for the North Pacific arebetter able to close the tracer budgets than the Levitus section. However, the INDOPACsection tracer budgets reveal several interesting results. One, the DOM transport mayplay an important role in the nutrient budgets. It is accepted that this section does nothave high enough resolution to confidently resolve this problem. However, it is clear thatif the DOM has a definite vertical structure at any time of the year it will be a significantcomponent to the nutrient budget in the North Pacific. Two, one may need to considerthe time-scale that is applicable to the conservation of tracers in the North Pacific. Theimbalance caused by the non-steady-state nature of the tracer is postulated to be mostimportant for the silicate budget because of the significant time lag between when thesilicate is removed from the surface water as detrital rain and when it is re-dissolved backinto the water column at the ocean bottom. Three, variations in the Ekman transport havesignificant effect on the tracer budgets. Any errors in the Ekman transport will producelarge discrepancies in the nutrient budgets because of the large vertical gradients in thenutrient tracers. A similar argument holds for the freshwater exchange processes becausethey introduce only a small amount of nutrient tracers due to continental runoff, but maygenerate significant nutrient tracer transport because of alterations to the mass field. Thelimitations in trying to determine the air-sea exchange of carbon are closely associatedwith deviations in the Ekman transport and freshwater exchanges. Therefore, it isimportant that one has an accurate determination of the flow field before one tries todetermine the air-sea exchanges that affect the nutrient tracers. Small modifications to themass field may be acceptable dynamically but the implications on the nutrient budgets willChapter 2. Tracer Transport across 35°N in the Pacific Ocean^ 53be much more profound. This will be especially true for air-sea exchanges making itdifficult to obtain meaningful results. Such a question forces one to critically assess thebest approach to take to understand the CO 2 cycle and what type of data would be mostuseful in providing information on this cycle. A formal inverse inverse approachconsidering several tracers simultaneously would help reduce the errors in the tracerbudgets cause by uncertainties in the Ekman transport and air-sea exchanges.The study reinforces the need for highly resolved hydrographic sections in order toproperly calculate the geostrophic and tracer transports. The inability of either theINDOPAC or Levitus section to close the tracer budgets to within the prescibed errorsuggest that these sections omit significant volume transports at in the western boundaryand ocean bottom due to their limited resolution. As a consequence, the inverse modelformulated for the North Pacific (chapters 4 and 5) will not uses these sections but rather Iwill use the only two highly resolved hydrographic sections across the Pacific (at 24°Nand 47°N) to constrain the horizontal transports.CHAPTER 3. VALIDATING AN INVERSE BOX MODEL USINGDATA GENERATED FROM THE HAMBURG CARBON MODEL3.1 INTRODUCTIONThe box model is a classical method used in developing a quantitative picture of therole of an ocean basin in transferring heat, salt, carbon and other tracers. In this method,one applies conservation constraints to a set of boxes for the observed distribution of physicaland biochemical tracers. This process generates a set of equations by which an inversemethod is used to extract a solution for rates of the processes which govern the tracerdistribution. Additional equations can be generated by considering other constraints, such asgeostrophy, to further restrict the solution. To better understand the ability of the inverse boxmodel and provide guidance in attacking the problem of understanding the CO 2 cycle in theocean, the inverse box model was applied to data generated from a biogeochemical-oceancirculation model.In this chapter, the annual fields produced by the Hamburg Large Scale GeostrophicOcean Circulation (LSGOC)-biogeochemical model (Maier-Reimer and Bacastow, 1990) wereused as data for an inverse box model of the North Pacific. The goal was to investigate theability of the inverse model to determine the air-sea exchange of heat and carbon and the newproduction of organic and shell material. By performing inversions in this controlled settingone can test the ability of the inverse box model.Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model ^553.2 HAMBURG MODEL3.2.1 Model DescriptionThe global ocean circulation model used for validating the inverse box model was theHamburg Large Scale Geostrophic (LSG) ocean circulation model (Maier-Reimer andBacastow, 1990). The Hamburg LSG ocean circulation model has evolved from an originalconcept of Hasselmann (1982). The model was based on the observations that, for climatestudies with a large scale ocean circulation model, the relevant characteristic times scales arelarge compared with the periods of gravity modes and barotropic Rossby wave modes. Fromthese scaling conditions, the baroclinic velocity field can be determined from the density fieldthrough local geostrophy. The barotropic velocity field and surface elevation, for a givendensity field, are determined as the equilibrium barotropic response to the prescribed surfacewindstress forcing and bottom torque. In this model, the advection equations for temperatureand salinity are solved using an implicit upwind differencing scheme. Coupled to thisphysical model is a biochemical model that computes the distributions of nutrient tracers usingthe transport field and computed biochemical source and sink terms. A brief discussion ofthe physical and biotic parts of the model are discussed in the next two sections.Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^563.2.1.a. Physical ModelApplying the standard hydrostatic and Boussinesq approximations and neglectingvertical friction, the prognostic equations of the model are given by:1) the horizontal momentum equation1 Px^/-Au - 2vQ sing() +^— = — +Atiu1^cos4 Q 0^Q01P^.74v + 2u12 shuts + ---± = — + A A u ;I^R Q 0^Q 02) the equation for the evolution of potential temperature (0) and salinity (S) (neglectingdiffusion terms)u^vOr + R cos0 Ox + —R00 + wOz = q °u^vSi + R cos0 Sx + —RS0 + wSz = q s(the source q° and qs only occur in the surface layer);and 3) the evolution equation of the surface elevation g, given by the surface boundaryconditions,r, = w^at z=0.^ (3.5)The prognostic equations are complemented by the diagnostic relations consisting of:1) the continuity equation(3.1)(3.2)(3.3)(3.4)Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^571^uxw' + —R [(v cos0) + —] = 0;cosh2) the hydrostatic pressurezp = geo^1 ozixz'^;Qoand 3) the equation of stateQ = Q (S T,P)where T is the in-situ temperature.The velocity terms were solved for by separating horizontal velocities intobarotropic and baroclinic components. The equations of motions for both the baroclinic andbarotropic components are solved using a rigorous Euler-backward method. The advectionof temperature and salinity (3.3 and 3.4) is then computed using an upwind method whichis implicit in time,T' = T"a+AtE uit(Tir -^Axi^(3.9)where the summation is over all neighbouring points for which u i is directed towards the pointof computation. The apparent diffusivity of this upwind scheme is derived in Appendix Aand is equal to Ax^u I AtK = lug^( 1 +2 Ax(3.10)The implicit upwind scheme numerical diffusion is u 2 At greater than the explicit upwindscheme (Smolarkiewicz, 1983) (see Appendix A for more detailc)_(3.6)(3.7)(3.8)Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^583.2.1.b Biotic modelThe basic details of the biotic model are presented by Maier-Reimer and Bacastow(1990). Formally the model is characterized by a set of differential equationsaci +vac, +AiCi = E Bik ,^ (3.11)at^ax; kwhere C, denotes the components of the chemical cycle, v i is the three-dimensional velocityfrom the LSGOCM, A, denotes the intrinsic processes like radioactive decay, and B ik denotesthe source/sink of tracer i due to metabolic processes (ie. the formation/dissolution of shelland organic material). The advection of the tracers are calculated by the same implicitupstream scheme used for temperature and salinity in the physical model. The model tracersare total dissolved inorganic carbon (TCO2), alkalinity, phosphate, dissolved oxygen,particulate organic matter (POC), calcium carbonate of shell material, silicate, radiocarbonand "C (in the model 14C and "C concentrations have been normalized by their fractions inthe atmosphere).The biotic cycle of the model is driven by a phosphate-limited primary productivity.In the model, photosynthesis of organic matter is assumed to be restricted to the surfacelayer. In the layers below the surface, remineralization of the carbon flux is accompaniedby a reduction in oxygen concentration corresponding to its Redfield ratio. The followinggeneralized ratios are used in the LSGOC model for the changes associated with thephotosynthesis of organic matter and its subsequent remineralization: P: N: C: 02: Ca: =1:16:122:-172:30.5 . An additional flux of calcium carbonate from shell material is assumedChapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^59to sink from the surface layer. In this model, CaCO 3 is allowed to undergo dissolution at alldepths.The system is closed by the boundary conditions, which for all tracers except TCO 2 ,oxygen, '4C, and ' 3C, is vC =0 across all boundaries where vC denotes diffusive andadvective fluxes of any tracer concentration C. The carbon tracer exchange CO 2 with a wellmixed atmosphere of 280 ppm, using the calculated partial pressure of CO 2 in the surfaceboxes and the gas transfer rates determined by Merlivat et al., (1991). In the model, themass conservation is fulfilled for the number of carbon, phosphate, and oxygen atoms andfor alkalinity.The model was run on two staggered 5° x 5° global grids with 15 vertical levels (Fig.3.1). The use of the staggered grid separates the model into two grids which are linkedthrough the use of an explicit horizontal diffusion (200 m 2 s') in the advection equations forthe various tracers (Bacastow and Maier-Reimer, 1990). The vertical levels were defined asthe mid-point of each layer and the layers were defined by the following depths: 0, 50, 100,150, 200, 250, 300, 400, 525, 700, 900, 1500, 2500, 3500, 4500, and 6000 m. The outputfrom the model used in the inverse box model consists of the annual mean velocity and tracerfields averaged over 2 years after the model has been completely spun-up (4000 years witha one month time step).3.2.2 Tracer TransportsIn a time varying flow one can separate the velocity, v(t),  and the concentration, c(t),aUfl,LIONOrlAl 00n^At 0 09T^S 0091At 0 00co At 0 017 3 0 OZT a 009 3 0 0 -17 o o•X•k•X .......^..X•X+X X•.14 .. ... ....S o° 6S 0 °4gaga:^gaga:.S 0 0gS 0 0CS 00TN 0 0IN 0 0CN 0 09N 0 04N 006. . .hhh.. ......^....^iii^"..." i ii =L=1;1; ii:al:Mil:UM ii iiiii-ilili!:" 1 :Silil .....^..^ . ^;Tgaagg♦ • ♦ ♦♦ai 1:Ilg .... gagagga . . ..+X ........... X.x......... X•X•X ..... ..... 1•Xf'Igagag.. ........ =1ga:4,1:gaga:Vag::......... X .X.X.Iiiiiiii! ! .. iiii: 41'::::. trat:r-" .......^••^•.:44.•...--•.••.• • ^t,- ......... ......41: *: • • ' 1-1-;4 + • •I. + • ^!h.:.^ ♦•^..4Alimilipsilimmlilimisimatir: .m.=1:1gmlmggnm4g=1,14gg .. ---- -".. --. . . . .  ... . . . . . . .  .  . ..:+: . : . : . : . 1.:1.1.1-:11........ .... :vg•.--.--.•---x•• • • ^• • •.:gagaggagg .• 44:4 . . ti: . • *LX.M.X.V^L• . : ... X ............ ...... X* 4, 4x.hfX ^1^..... X•X XX.X ..........^.....TraIloquI^puR seam paitpptptti alp Aq paiouap arR ppm avanuT uot2a.117 alput pasn SUOI20.1 atp 'wag alp tti 'AA pue suopRp11001103 .103P..11 atp Jo uonraoi atp saiouap^puR`paummaiap an n puR n atp atatim siuiod atp salouap * alp atatim pus iapotu 2.mcimulf ata^ant2t3Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^61a of some quantity into a time-average part and a fluctuating part according to:v(t) = v + v (t),^c(t) =^+ c i(t).^(3.12)An overbar indicates an average over a chosen time (2 years in our case). The time-averagetracer flux (per unit area) is then given by= Te = C + 1777.^(3.13)where the first term to the right is the transport by the mean advection, Ti, and the secondterm gives the "turbulent" (eddy) flux. The horizontal transport by the mean advection intothe North Pacific was calculated from the annual mean velocity and tracer fields byintegrating (3.13) along a specified latitude (Table 3.1). The resulting calculation for theNorth Pacific produced some surprising results. One, the heat and salt transports aresignificantly different for the two grids even though they differ by only 2.5° latitude in theirdefinition of the North Pacific. Two, for tracers with no air-sea exchange (phosphate,silicate, alkalinity, and salt), the mean advective transport does not close the budgets of thesetracers in the North Pacific. These results imply that, in the model, the horizontal eddytransports play an important role in closing the tracer budgets. The implicit numericaldiffusion of the upwind scheme may also work to increase the horizontal eddy transport.Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model ^62Table 3.1: Mean Advection transport into the North Pacific (positive value). The firstcolumn gives the transports through 25°N into the North Pacific, this grid has nooutflow into the Arctic Ocean. The second column gives the net transports into theNorth Pacific between 22.5°N and the Bering Strait.Tracer^Transport 1^Transport 2Volume -0.099 Sv -0.07 SvTemperature^-0.10 x 10 15W^0.02 x 10 15WSalinity -1.69 x 106 kg s' 0.01 x 106 kg s'Phosphate^3.03 kmol s-1^2.93 kmol s -1Silicate 352.82 kmol s -1^406.44 kmol s -1Alkalinity^10.0 kmol s -1^132.35 kmol s -1Oxygen -17.9 kmol s' -62.56 kmol s -1DIC -15.6 kmol s -1^-24.26 kmol s -1DIC 14^-881.4 kmol s -1^-944.61 kmol s-1POC -59.8 kmol s -1^-53.52 kmol s -1calcite -0.01 kmol s -1^0.095 kmol s -1The horizontal eddy transports of the tracers can be calculated using the "known"annual exchanges air-sea exchanges of the various tracers from the LSG ocean circulationmodel. For tracers with no air-sea exchanges (salinity, phosphate, silicate and alkalinity) theeddy transports must equal to but of opposite sign to the values given in Table 3.1. For heat,to produce the LSGOC model air-sea exchange of 0.25 PW into the atmosphere requires thehorizontal eddy transport of heat to be approximately 0.25 PW into the North Pacific. Theeddy transport of heat is significantly greater than the mean advective transport of heat. TheLSGOC model air-sea exchange of CO2 is 780 Kmol s -1 into the North Pacific which impliesChapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^63an eddy transport of CO2 of approximately 780 Kmol s' out of the North Pacific. The eddytransport of CO2 is much greater than the calculated from the mean advective transport ofCO2 .One critical test for the inverse box model is to see whether it can recover thesehorizontal eddy transports from the mean tracer distributions to produce a consistent estimateof the air-sea exchanges.3.3 INVERSE BOX MODEL3.3.1 Model TopologyThe inverse box model is applied by dividing the ocean into boxes. For this study,the boxes consist of large regions bounded by two depth surfaces. It was necessary toconsider large regional areas in the inverse box model in order to ensure that tracer gradientsbetween the boxes were greater than the tracer variability. The ability of the model to extracta solution rapidly degrades as the number of regions is increased and forces one to use largeregions in the inverse model.The inversions were performed on the Hamburg model data from the North PacificOcean. For comparisons with studies with actual measured data, the boxes were defined toreflect the inverse box models that will be pursued with this measured data. The inversemodel was first configured using a 6 layer model with 4 regions of the North Pacific. TheNorth Pacific was divided into 4 regions by the latitude bands 7.5°, 22.5°, 47.5°, 62.5°, and Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model ^6477.5°N (Fig. 3.1), and 6 layers by the depth surfaces 0 m, 50 m, 200 m, 525 m, 900 m,3500 m, and 6000 m. For the model, two of these regions are necessary to handle the openboundaries at the north and south. With this box configuration, several sets of experimentswere performed to investigate the information content in the tracer fields.3.3.2 Model ConstraintsThe basic constraints of the inverse box model are the continuity of tracers andfreshwater within the defined boxes. The general continuity equations applied to a box forany given scalar tracer C are :vac = f (v.(11C) -V .(kVC))dv +Qbio + Qair-sea — Q decay = 0atf(V.u)dV + air-sea = 0(3.14)(3.15)The rate of change of the concentration C in any box with volume V, (au at), is affected bythe net flux of the tracer C due to horizontal and vertical advection, horizontal and verticalmixing, biological processes (Q 1.), air-sea exchanges (Q air_se„), and radioactive decay (Qdecay).In the model, all tracers are assumed to be steady state and the density of the water isconstant (to be consistent with the LSGOC model). In (3.14) and (3.15), the Q, i,se, term onlyaffects boxes in contact with the surface. The advective transport is calculated by multiplyingthe velocity through the box face by the average concentration of the two connected boxes(like Bolin et al., 1987).Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^65In (3.14) the eddy transports are parameterized by an eddy diffusion approach whichassumes that the turbulent flux is proportional to the mean tracer gradient. The definition ofthe eddy transport is obtained by separating the time average flow into a space-average termand a part fluctuating in space:= <17> +7, *, c = <c> +C*, (3.16)where < > denotes a space averaging and * the spatial fluctuation. The flux in (3) can nowbe written as :F= <vc> = <1;> <C> + <7)*C"> + <I-7F> . (3.17)The average flux consists of a transport by mean advection <ii> ; a transport by the spatialfluctuations of the time-average circulation, that is standing eddies v*; and a transport bytransient eddies v'. The eddy diffusion approach followed here assumes that the turbulentflux is proportional to the mean tracer gradient. The eddy transports are determine bymultiplying the mixing coefficient (k) on the box face by the difference in tracerconcentrations between the two boxes and dividing by the distance between the centre of thetwo connected boxes. This parameterization of the eddy transports is a critical ingredient ofthe box model and will be evaluated in this chapter.The biological source parameter, Qbio, in (3.14) represents the formation of soft andhard shells in the surface boxes and the subsequent remineralization of the particulate matterin the deeper layers of the model. In the inverse model, the sedimentation rate is zero; allparticulate matter formed in the surface boxes is redissolved in the underlying boxes(consistent with the LSGOC-biogeochemical model). For this problem, the molecular rating Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^66linking the biological source/sink for the various tracers are known, and in the inverse boxmodel, they are set equal to the values used in the LSGOC-biogeochemical model.In applying the box model, several additional inequality constraints were included toimprove the solutions. One, the model was forced to satisfy exactly the freshwater budgetin all the defined boxes. Two, in the defined regions, the model conserved all tracersexactly. This required that the total amount of tracer leaving a region plus any radioactivedecay be equal to the air-sea exchange. Three, the mixing transports are assumed to onlytransport tracers down-gradient (k> 0). With the inverse box model it is relatively easy toaugment the problem with additional constraints in order to further investigate the problem.3.3.3 InversionsThe formulated constraints (3.14) and (3.15) are applied to the defined boxes andavailable tracers to generate a set of equations. This set of equations can be represented bythe equationGx = b +e^ (3.18)where the coefficients matrix G contains tracer concentrations and gradients, x is the vectorof unknownsChapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^67x = (u i , vo wo khi , lc, 0bio, 0^)9 — (3.19)and the vector b is a zero. Due to errors in the approximations in the model, the constraintequations are not expected to be exactly satisfied but only to be within a specified tolerancesei. The estimation of the tolerances will be discussed in later in this section.To solve this system of equations, I relied on two different algorithms: the leastsquares algorithm with inequality constraints (LSI) and linear programming (LP). For detailson how these routines work, refer to Lawson and Hanson (1974) for the LSI routine andLuenberger (1984) for the LP routine. The implementation of these routines in NAG libraryis ideal for solving this problem using either algorithm. The only difference between the twoapproaches is the objective function that one wishes to minimize. In the LSI routine, onedetermines a solution x by minimizing in a least squares sense(I) = 11 Gx - b 112 (3.20)subject to^ b - E 5_ Gx^b + E^ (3.21)(3.22)A priori bounds x and x+ are applied to the unknowns to restrict their numerical values tophysically meaningful ranges, like allowing only positive mixing coefficients. To properlyapply this inversion algorithm it is essential that the set of equations (G x =b) be properlyweighted. The need for weighting the equations arises because each tracer possesses adifferent signal to noise ratio. A proper weighting of the equations must reflect theChapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^68significance of the tracer concentrations, and force the model to rely most heavily on the mostsignificant tracers. A simple row normalization only works if one can assume the informationcontent of all tracers in all boxes is equal.In an inverse problem, one typically weights the equation by dividing this equationby the error in b i , Ob i . The difficulty of attempting this for our problem is that the errors inb are functions of the unknown transport terms. An appropriate estimate of Sb was thoughtto be determined by only considering the error in b due to advective transports by using thefollowing equations:= Ex1 C1(3.23)51) 1 = E 5xi Ci + E OCi xiwhere x i represents the volume transport through the i ll' box face, C, represents theconcentration on the box face, and 5 denotes the errors in these terms. The first term onthe rhs of (3.23) was dropped because for flow that is forced to conserve mass, the sum ofthe h i 's for the box is zero and hence the error from this term will be small. The secondterm on the rhs of (3.23) was evaluated by using the standard deviation of the tracers in thedefined boxes to determine the tracer errors on the box faces (SC) and multiplying this valueby the known volume transports (x 1). It should be noted that to properly weight theequations, the exact determination of bb is not required but rather only the relative weightingof different equations. By using just the SC's to weight the problem, one produced nearlyidentical results to the weighting given by (3.23). Another quantity one can make use ofChapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model ^69when weighting the equations by the standard deviation in b is that the chi-squared error (X 2)should approximately equal the number of equations (N):X2 = I Gx — ba N (3.24)If the X2 is much less than N, the data are overfitted, and if X 2 is much greater than N, thenone is underfitting the data. If one wishes to produce reasonable results, then care should betaken to ensure that X2 is not significantly different from N. In this problem small variationsin the known velocities (less than +0.2%) were allowed in order to produce solutions withX2 's approximately equal to N.In the LP approach one finds a solution to x which minimizes(13 = E wi , (3.25)subject to the same set of inequality constraints given in (3.21) and (3.22). If there is asolution to the set of constraints, the solution is said to be feasible; it usually is not a uniquesolution but an infinite number of solutions may exist. Running the model repeatedly witha convenient set of chosen objective functions allows one to explore the whole range ofpossible solutions.The great utility of the LP routine is its ability to provide solutions to any objectivefunction that is made up of a linear combination of the unknown x. A common set ofobjective functions that are used in analysing the model are ones that minimize and maximizeeach individual unknown by setting one wi to 1 or -1 and all the other w i to zero. Byminimizing and maximizing such objective functions one obtains the maximum and minimumChapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^70values of the model parameters that satisfy the constraints. This reveals how well the modeldetermines the different model parameters.It is a common feature of LP solutions that to obtain a maximum or minimum valuefor the objective function many of the constraints are pushed to their lower and upper bounds.The dual solution reveals the sensitivity of the objective function to changes in the bounds ofa constraint (Luenberger, 1984). Those constraints that limit the value of the objectivefunction are represented in the dual solution by non-zero values. The larger value the moresensitive the object function is to the bounds on the respective constraint. The examinationof the dual solution reveals the importance of the constraint in determining the value of theobjective function.The solutions that are calculated with LP algorithm are extremal solutions in the sensethat they maximize or minimize a conveniently chosen linear objective function. As aconsequence, as mentioned above, many of the constraints are pushed to their upper andlower bounds in order to minimize the value of the objective function. Thus thecorresponding solution may exhibit certain features that may not be realistic. This is why theLSI routine is used to look at the "best" solution. The main goal of the LP routine is not toproduce one "best" solution but to explore the range of solutions that are possible given themodel's constraints. This approach demonstrates which oceanographic parameters are well-determined and which are not, and it indicates which constraints have the largest errors.The ranges determined for the various objective functions are dependent on the errorsprescribed to the tracer budgets. The determination of these errors is intimately related tothe weighting of the LSI problem. For LP solutions, the errors in the equations are Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^71determined using (3.23) but are increased by a constant factor equal to the maximum factordetermined from the LSI solution. One should observe that the weighting of the equationshas no effect on the LP solution because the objective function is linear. However, the errorsin the equations are derived in a manner analogous to the weighting of the equations in theLSI routine and thus have similar ambiguities. In addition to providing ranges for theunknowns, the LP routine also provides information on which equations are most importantin determining these ranges through the dual solution. This gives clear information on howone could reduce the acceptable ranges for the different unknowns in the inversion.3.4 INVERSE SOLUTIONS3.4.1 Tracer StudiesThe first set of experiments was performed to assess the information content of thevarious tracer fields. In these experiments, the horizontal velocity field was considered well-determined (prescribed error of less than 0.2%) and LSI inversion was used to solve thesystem of equations.If only the temperature (T) and salinity (S) fields are included in the inverse boxmodel, the resulting solution produces a poor estimate of the air-sea exchange of heat for theNorth Pacific ( 0 PW compared to the LSGOC model value of -0.25 PW). By including totalCO2 (TCO2), phosphate (P), and alkalinity (A) fields in the model, the model is betterconstrained and the solution begins to reflect the known air-sea exchange of heat (-0.17 PW). Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model ^72The addition of oxygen (0 2) and radiocarbon ("C) to the model does surprisingly little to thesolution, it only slightly increases the detrital rain rate of organic matter. The addition of thePOC and calcite fields to the model increases the air-sea exchange of CO 2 , 02 and "C by100, 240 and 30 kmol s' respectively, and increase the heat exchange to -.184 PW. Toinclude POC and calcite fields in the model required that (3.14) be modified for TCO2 ,alkalinity, phosphate, oxygen and "C to address the transports of these tracers as organic andshell material. To include the effect of organic and shell material on the tracer budgets, thefollowing terms were added to (3.14):+Ri R V • (i[POC])) - V • (k( V [POC]) )](3.26)+Si [(V • (T[CaCO3]) ) - V • (k(V [CaCO3]) )] .The R and S are determined from the Hamburg model's Redfield's ratios and are given inTable 3.2 for the various tracers. This will be called the reference model and will be usedfor comparison with other inverse box models.3.4.2 Reference ModelTable 3.3 summarizes the different models studied. The circulation and mixing fieldsobtained from the reference box model are shown in Figure 3.2. This model made use ofT, S, TCO2 , P, A, 02 14C, POC and calcite fields to constrain the model; in all subsequentmodels all these tracer fields are used. With the T, S, TCO 2 , P, A, 0, "C, POC, and calcitefields, the inverse box model was able to produce consistent estimates for the heat and CO2Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^73Table 3.2:^The molecular ratios for organic matter (R's) and shell material(S's).Tracer^Organic Matter (R)^Shell Material (S)TCO2^1.0^ 1.0Alkalinity 0.3525 2.0Phosphate^1/122 0Oxygen -1.409^014c 1.0 1.0Table 3.3:^Summary of the various inverse box models usedModel Model DefinitionI^Reference ModelII^Reference Model but allowing negative eddy diffusionIII^Model with an unknown barotropic flowIV^Model III with limits on the fresh water fluxes of 0 -2 Sv into the oceanV^Reference Model but allowing Redfield's ratios tovary by +20%VI^Model III but allowing Redfield's ratios to vary by+20%VII^Model IV but allowing Redfield's ratios to vary by+20%exchange of the North Pacific when compared to the known values from the LSGOC model(model I in Table 3.4). The consistent results support the use of the eddy diffusion term withChapter 3. Validating an inverse Box Model using data generated from the Hamburg Carbon Model^74a positive k as a means of parameterizing the eddy transport. In contrast, the LSI inversionof a model that allowed negative k's (model II in Table 3.4) greatly underestimated the heatand the CO2 exchange. Furthermore, by allowing just a small error in the known velocities,a model with positive k's satisfies the problem equally as well as the model which allowedfor negative k's. These results suggest that the use of an inverse box model with positive k'sis sufficient to produce useful results.The LP solutions obtained from the reference model with positive k's express theability of the inverse model to estimate the unknown detrital rain rates and air-sea exchanges(model I in Table 3.4). The errors used for the LP problem were 3.215 times the Sb's usedto weight the LSI problem. This value, 3.215, was equal to the maximum error in theequations obtained from the LSI solution. The transport of freshwater, heat and CO 2 by theinverse model is plotted with the corresponding values from the LSGOC-biogeochemicalmodel (Fig 3.3a-c). In general the acceptable ranges for these transports determined fromthe inverse model were in good agreement with the unknown values.The acceptable ranges for the mixing coefficients are shown in Figure 3.4 along withthe apparent numerical diffusivity of the upwind advection scheme used by the LSGOC-biogeochemical model (derived in Appendix A). The horizontal mixing terms are not well-determined but they are consistent with the apparent numerical diffusivities of the originalmodel. The inverse results suggest that kt, is enhanced in both the surface layers and thebottom layer. The inverse results for kz show an exponential-like increase in vertical mixingwith depth for both the inverse model results and the apparent diffusivities of the originalmodel. 0 will 7.3 .6 0.3 '11.9I-4.3^I I 2.o^I i.1.0Lo.91-3.0^I 10.9^I1 2.9 1 0 11-1.1^1 0.21-1.5 -1f 3.9 I0.60.40.61 5.0 I15.6^1200400600800a.cutoo°2000300040005000(a)Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^75to^20^30^40^50^60^70LATITUDE NORTHFigure 3.2: The circulation field for the reference model where (a) shows the volumetransports (Sv) across the box faces, and (b) shows the mixing transports as k * area/ distance in Sv.0200400600800Cras10002000300040005000(b)mmointrovic0.60.50.4.10.1^r11°111111F2.81111111111"0.6Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^7610^20^30^40^50^60^70LATITUDE NORTHlllllllllllllllllllllllllllllllllllllllllllllllllllllllllll(a)u_0.400.300.200.10u.-aa) 0.00c:(1146 -0.10-0.200^10^20^30^40^50^60Latitude NorthChapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^77Figure 3.3: The integrated northward transport of (a) freshwater, (b) heat, and (c) CO 2 .The curve in (a) shows the freshwater exchanges calculated by Baumgartner andReichel (1975), and in (b) and (c) the curve denotes the values from the LSGOCmodel. In three plots the circles denote the values determined by the LSI inversionof the model and the error bars are corresponding the maximum and minimum valuesdetermined from the LP inversions.(b)Fci.x=El:(411a)Iva)150)a)4E4Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^780.40.30.20.10.0-0.1-0.2-0.3-0.4-0.50 10^20^30^40Latitude Northso^60I^1^1^I^I I^1^1^[^I^I^I^I^1^II^I^I^1^i^1^f^1^1^I^i^1Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^79^800.0 ^700.0600.0500.0400.0300.0200.0100.0^0.0 ^-100.00 10^20^30^40^50^60^70Latitude North(c)Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^80(a)^ (b)0 ^0^ 5000-0^5000^10000^15000^20000Horizontal Diffusivity (m 2/s)0^5000^10000^15000^20000Horizontal Diffusivity (m 2 /8)Figure 3.4: The acceptable ranges for the horizontal mixing coefficients for (a) region 1,and (b) region 2, if only one line is present then the lower range is zero. The dashedline is the calculated numerical diffusivity of the upwind advection scheme used in theLSGOC-biogeochemical model.Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^81•0^5^10^15^20Vertical Diffusivity (cm 2/s)(b)0200400600-00010002000300040005000• •0^5^10^15^20Vertical Diffusivity (cm 2/s)Figure 3.5: The acceptable ranges for the vertical mixing coefficients for (a) region 1, and(b) region 2, if only one line is present then the lower range is zero. The dashed lineis the calculated numerical diffusivity of the upwind advection scheme used in theLSGOC-biogeochemical model.The range in acceptable values for the particle fluxes in the different layers revealedthat the individual values are not well-determined (Fig. 3.6). For example, both the uppertwo layers are capable of dissolving all the particulate matter produced in the surface layer.200*400-BOO-1800^1000-2000-3000-4000-5000-I •Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^82The area of regions 1 and 2 are 25 x 10 12 and 7 x 1012 m2 respectively. Like the originalmodel (Fig 3.7), the new production in the two regions is of similar magnitude (14 g m2 y-').From the inverse model the new production is estimated to be 17 ± 17 g m2 y-1.(a)0^700^1400^2100Organic Carbon Flux (Kmol/s)(b)0^ 350^700Organic Carbon Flux (Kmol/s)Figure 3.6: The acceptable ranges of the particle fluxes of organic and shell material, theminimum value is zero. The organic carbon flux for region 1 and 2 is shown in (a)and (b) respectively, and the flux of shell matterial for region 1 and 2 is shown in (c)and (d) respectively.(C)0 ^200-400-500-en_"..,0.41A1000-2000-3000-4000-5000-200-400-000-2000-3000-4000-5000-Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^83(d)0^200^400^600^600^ 0^ 50^100Shell Material Flux (Kmol/s) Shell Material Flux (Kmol/s)Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^84New Production (gC/sqm-yr)LongitudeFigure 3.7: Map of the new production from the LSGOC-biogeochemical model taken fromBacastow and Maier Reimer (1990).In the discussion of the LP solutions, the importance of the prescribed error cannotbe overlooked. Further investigation of the prescribed errors shows that, if the errors aredoubled, the effect on the unknown air-sea exchanges would be less than 10%, but the detritalrain-rates would nearly double, lc, would increase by 80% and kh would increase by 20%.The vertical structure of the k h and lc., would be unaffected by the increased errors.Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model ^853.4.3 Model SensitivityTo examine the sensitivity of the inverse model to the various model constraintsseveral different experiments were performed using different model constraints. The differentmodels are summarized in Table 3.3.To see how well the inverse box model performs when the horizontal velocityinformation is less well-determined, two experiments were tried. First, the inverse box modelwas formulated to allow the horizontal volume transports to vary by +100% from the knownvalues. The circulation and mixing fields from the LSI inversion (Fig. 3.8) showed thatwithout additional velocity information the circulation is grossly underestimated. For thisinverse box model one relies on the 14C tracers to force the model since all of the othertracers are compatible with the null solution. Second, the inverse box model was formulatedto only determine an unknown barotropic flow through each section in the model (model IIIin table 3.4). In this case the information in the tracer fields is very capable of determiningthe unknown barotropic flows. The volume transports calculated from this model were nearlyidentical to the circulation given in Figure 3.2, however, the k's, detrital rain rates and air-sea exchanges differed from the reference solution. Using the same errors as the referencemodel, the LP solutions were obtained to give the acceptable ranges for the air-sea exchangesand detrital rain rates. The detrital rain rates and heat exchange results were reasonablyconsistent with the reference model but the air-sea exchanges of CO2, 02, and 14C exhibiteda much larger range. Most of the increased ranges were attributed to the increased acceptablerange for the freshwater exchange. This shows that consid erahle uncertainty in the air-sea86Table 3.4:^The inverse results for the 4-region 6-layer models given in Table3.3. The maximum acceptable errors are 3.215 times greater than theerrors used to weight the LSI inversions.Model Inversion Detrital Rain RateOrganic^ShellMatter^Material(Kmol/s)^(Kmol/s)HeatPWAir-sea exchangeCO2^02Kmol/s^Kmol/s"CKmol/sI LSI' 835 53.3 -0.18 573 314 1915LP' 120 0 -0.4 392 -46 1230to to to to to to2667 671 -0.16 807 899 2587II LSI 1120 134 -0.08 365 9 1722LP 13 0 -0.4 -98 -792 81to to to to to to2881 804 0.1 735 923 3649III LSI 523 17.8 -0.24 852 735 2008LP 66 0 -0.56 40 -951 1112to to to to to to2950 724 -0.09 1503 1939 2879IV LP 66 0 -0.48 353 -353 1112to to to to to to2814 677 -0.09 1068 1342 2862V LSI 872 136.8 -0.18 558 295 1943LP 92 0 -0.4 392 -45 1226to to to to to to2820 935 -0.16 808 899 2587VI LSI 613 34.8 -0.23 843 689 2045LP 54 0 -0.56 -13 -1636 1108to to to to to to3395 1065 -0.03 1505 1941 3111VII LP 54 0 -0.5 338 -640 1108to to to to to to3186 962 -0.04 1110 1340 2934'Refer to section 3.3.3 for a discusion of the LSI and LP inversion routines.Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^87exchange unknowns can arise from uncertainties in the freshwater exchanges. If thefreshwater exchanges were constrained to be more consistent with the reference model byrestricting the freshwater exchange for the North Pacific to be between 0 and 0.2 Sv, theacceptable ranges in the unknown air-sea exchanges are greatly reduced (model IV in Table3.4).In the inversions already discussed, the molecular ratios linking the C:P:O in theformation and remineralization of organic matter were specified according to the values usedin the Hamburg model. To observe how well the inverse model can predict these ratios, aninversion was performed using a model which allowed the Redfield ratios tovary by +20% from their known values. If the horizontal volume transport was specified,the inverse box model returned the correct ratios. The acceptable ranges determined fromthe LP solution showed that the air-sea exchanges were unaffected by a variable molecularratio (model V in Table 3.4). The detrital rain rates calculated from this model experienceda slight increase in the acceptable ranges from that of the reference model. If the horizontalvolume transport was specified with an unknown barotropic component, the inverse boxmodel (model VI) was still capable of returning the correct ratios and producing the samecirculation field as the reference model. The acceptable ranges for heat, CO2 , and 14C werethe same as for the model with an unknown barotropic term (model III). The acceptableranges for the detrital rain rates and 02 exchange increased significantly over that of modelIII. By including the mass constraint as was done in model IV, the uncertainty in air-seaexchanges was greatly reduced (model VII in Table 3.4).6001000Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^88(a)020040020003000400050000.2 0.2 0.00.0-0.2 0.50.40.0 11-1.5 I 0.1ri.7 1 0.0.81-3.0 13.9 1 0.9[WM I0.9^110^20^30^40^50^60^70LATITUDE NORTHFigure 3.8: The volume transports, (a), and mixing transports, (b), in Sv of a model forcedonly by the tracer fields.0.3 0 .002004006000.800...Jca.wal10002000300040005000Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model ^89(b)10^20^30^40^50^60^70LATITUDE NORTHChapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^903.4.4 Effects of Model GeometryThe last set of experiments performed investigated the sensitivity of the solution to theconfiguration of the inverse box model. By including more layers in the 4-region model, itwas observed that the uncertainties in the unknowns change very little (Table 3.5). A 15-layer model, (same number of layers as Hamburg model), produced a slightly different LSIsolution but the uncertainties in the unknowns were very similar to the 6-layer model. Byreducing the number of layers, the effect on the solution was more profound, and it wasdecided that a 6-layer model was a good compromise between producing results consistentwith more layers and limiting the computations.The sensitivity of the solution to how the regions of the North Pacific were drawn wasinvestigated with several different models (Table 3.5). A 5-region model was formulated bydividing the 22.5°-47.5° region into 22.5°-32.5°-47.5°. The model was purposely configuredso that the mean advective fluxes in the inverse model did not reflect the values determinedfrom the Hamburg data. The results from this model appear to have shifted the air-seaexchanges heat, CO2, 14C from that of the 4-region model. To remove this ambiguityinversions performed on the real data will use the actual tracer concentrations along the boxinterface rather then the average tracer concentration from the two adjacent boxes. The rangein uncertainties for the unknowns given in Table 3.5 are generally increases as the numberof regions in the model is increased. By dividing the 5-region model into 10 regions by ameridional line at 175°W, the resulting model produced results more consistent with the 4- 91Table 3.5:^Inverse solutions obtained from experiments that change thedefinitions of the boxes. The numbers under the model heading give thenumber of regions and layers in the respective model.Model Inversion Detrital Rain RateOrganic^ShellMatter^Material((Kmol/s)^Kmol/s)HeatPWAir-sea exchangeCO2^02Kmol/s^Kmol/s14CKmol/s4x6 LSI' 835 53.3 -0.18 573 314 1915LP' 120 0 -0.40 392 -46 1230to to to to to to2667 671 -0.16 807 899 25874x15 LSI 536 71.6 -0.15 471 153 1851LP 0 0 -0.44 271 -187 660to to to to to to2306 877 -0.08 854 883 19605x6 LSI 678 53.6 -0.12 377.6 -173 1450.6LP 203 0 -0.2 164 -329 622to to to to to to1930 580 -0.01 571 -46 21255x15 LSI 589.3 109.3 -0.03 213 -208 1443LP 66 0 -0.2 149 -374 306to to to to to to1330 590 0.05 601 -34 188610x6 LSI 903 29.7 -0.26 855.9 -91 2348LP 0 0 -0.75 385 -553 859to to to to to to3229 1030 -0.04 1746 822 344015x6 LSI 870 37.8 -0.20 840 68.5 2173LP 0 0 -1.28 316 -508 -25to to to to to to3841 3841 -0.04 1890 1393 4023I Refer to section 3.3.3 for a discussion of the LSI and LP inverse routines.Chapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^92region model than the 5-region model. By dividing the 5-region model by meridional linesat 190°W and 155°W, a 15-region model was produced. The results from the 15-regionmodel were more consistent with the 4-region model than the 5-region model. The increasingrange in uncertainty observed for the 10- and 15-region model reflects limited informationin the tracer fields at these scales. The annual tracer fields provided by the Hamburg modelare only suitable for providing information at the scales equivalent to the regions in the 4- or5-region inverse box model. A similar scaling of the regions of the North Pacific will applyto the inversions performed on the real data.3.5 DISCUSSION AND CONCLUSIONThe annual mean velocity and tracer fields produced by the Hamburg LSGOC-biogeochemical model were used to evaluate an inverse box model. The tracer fields fromthe LSGOC model showed that the eddy transports played an important role in theconservation of the tracer in the North Pacific. It was satisfying to see that, given theimportance of the eddy transports in the data, the inverse box model performed so well. Byusing the known velocity fields, a simple diffusive mixing parameterization with positivemixing coefficients for the eddy transports, and several tracer fields - the inverse box modelproduced consistent estimates of the air-sea exchange of heat and CO2 . The inverse boxmodel did not require negative k's to produce reasonable results. Furthermore, a LSIinversion with negative k's did not significantly reduce the errors in the conservationChapter 3. Validating an Inverse Box Model using data generated from the Hamburg Carbon Model^93equations. These two results clearly suggest that it is not necessary to allow negative k's inthe inverse model to produce good results.An inverse model that uses only the tracer fields to predict the velocity field revealedthat, by themselves, the tracer fields are insufficient to determine the velocity field. Ifadditional information on the velocity field, like the velocity shear, can be included in themodel the inverse model is quite capable of extracting the missing velocity information fromthe tracers fields. With the addition of the velocity shear information, the inverse box modelproduced air-sea exchanges and detrital rain-rates comparable to the model where the velocityfields were well-determined. An inverse box model was formulated to allow the molecularratios of C:P:O to vary by ±20% from their known values in the formation/remineralizationof organic matter. The results of this model show that the air-sea exchanges are not sensitiveto the variable molecular ratios. The maximum detrital rain rate of organic matter for theinverse box model with variable molecular ratios is only 5 % greater than the model withconstant molecular ratios.A set of experiments to investigate the sensitivity of the inverse box model topologyshow that results did depend on the box configurations. In drawing the boxes, it is importantthat the mean advection transports through the box faces adequately reflect the data. Byincreasing the number of regions, a point is quickly reached where the concentrationdifferences between boxes becomes insignificant. This is most obvious in the LP inversionsby the large range in the acceptable values for the various unknowns. The penalty one paysfor including too many regions is a poorly determined solution.CHAPTER 4. DEVELOPING THE INVERSE BOX MODEL OF THENORTH PACIFICIn this chapter I will discuss how the inverse box model is formulated and appliedto the North Pacific Ocean. In the first section the data used by the inverse box modelwill be presented. The second section, discusses the division of the North Pacific Oceaninto boxes. The third section presents the model constraints and applies these constraintsto generate the model equations. The fourth section deals with the different algorithmsused to solve the set system of equations. The chapter will conclude with a discussion ofhow the data are used to prescribe the acceptable errors in the equations generated insection 3.4.1 DATAThe inverse model requires tracer concentrations and concentration gradients on the boxfaces and geostrophic velocity shears along the sections as inputs. The datasets used inthe model were obtained from many different sources. First, I will discuss thehydrographic sections used in determining the geostrophic transports. Second, I willsummarize all the tracer used in the model and discuss how the data were combined toproduce a dataset for the inverse box model.Chapter 4. Developing the inverse box model of the North Pacific^ 954.1.1 Geostrophic Velocity SectionsThe conclusion reached in chapter 2 pointed out the need to accurately determinethe mass transport field in order to obtain reliable estimates of the horizontal tracertransports and ultimately determine the air-sea exchanges. At the present time, two highdensity hydrographic sections have been obtained across the North Pacific at 24°N and47°N (Figure 4.1). The high density of sampling of these sections should ensure accurateestimates of the geostrophic velocities. By using this data to constrain the large scale flowfeatures, it is assumed that the volume transports computed are representative of the meanocean circulation through these two sections.The CTD/hydrographic transect across the centre of the subtropical North PacificOcean at 24°N was carried out by the R. V. Thomas Thompson in the spring of 1985(Roemmich et al., 1991). The cruise will be referred to as TPS24. The first station wasoccupied off San Diego, California on March 30 and the ship proceeded westward endingin the East China Sea on June 1. A total of 206 full-depth CTD/hydrographic cast werecompleted on the long crossing. All CTD/hydrographic casts used a modified Neil BrownInstrument System Mark III CTD and rosette package carrying 36 10-litre Niskin bottles.All samples were obtained and analyzed by the Scripps Physical and ChemicalOceanographic Data Facility, providing measurements of temperature, salinity, oxygen,silicate, nitrate, and phosphate. The estimated sampling errors and random measurementerrors in these measurements for salinity, oxygen, phosphate, nitrate and silicate wereChapter 4. Developing the inverse box model of the North Pacific^ 96z0zz•w z00 •z•C •z000---,..........._...ate_-....c. ,:=>•trZ) ...=,.<3411... "41‘11,1._z15,Q \ \ - ..,^ 1\(144ril r----1 4130'^110'I^170'^no'^tee w^130. W^110 W^90 W^70 . WLONGITUDEFigure 4.1: Map showing the hydrographic sections used in the model (TPS24 andTPS47).0.001 psu, 0.021 ml 1 .1 , 0.036 limo'^and 2.0 µM011 -1 respectively (from Table 2,Roemmich et al., 1991).Chapter 4. Developing the inverse box model of the North Pacific^ 97In August of 1985, 115 relatively closely spaced CTD/hydrographic stations wereoccupied by the R. V. Thomas Thompson along the nominal latitude of 47°N in thesubpolar North Pacific (Talley et al., 1991). The cruise is henceforth referred to asTPS47. The data from TPS47 were collected and processed by the Oceanographic DataFacility at Sripps Institue of Oceanography an a full data report on the cruise is given byTalley et al., (1988). All stations consisted of a CTD/rosette cast, with a Neil BrownMark III CTD and a rosette package of 36 10-litre Niskin bottles. Salinity, oxygen,nitrate, phosphate, and silicate were measured at every bottle. The temperature precisionfor a given station was 0.001°C. The precision of the salinity was 0.001 to 0.002 psu.The oxygen measurement were made by Winkler titration, with accuracies of 1% andstation precision of 0.01 ml 1'. The precision of the silicate, phosphate, and nitratemeasurements were 1 %, 2% and 2-3% respectively. The nutrient measurements fromboth these cruises are include in the NODC archive of nutrient data that is used in thenext section.The geostrophic velocities for both sections are determined from the objectivelymapped values of specific volume anomaly using the objective mapping routine presentedby Roemmich (1983). The geostrophic velocity relative to reference levels of 3000 m and4000 m for TPS24 and TPS47 respectively are shown in Figure 4.2a-b.(a)(b)Chapter 4. Developing the inverse box model of the North Pacc^ 98120^140^180^100^200^220^240LONGITUDE140^ 180^ 180^ 200^ 220^ 240LONGITUDEFigure 4.2:^eostrophic velocities (cm s -i) of the transpacific sections, shaded areasdenote southward velocities, (a) TPS24, and (b) TPS47. Chapter 4. Developing the inverse box model of the North Pacific^ 994.1.2 Tracer DataThe data that are essential for this research are tracer data. This data must provideinformation on the physical, biological and air-sea processes that affect the carbondistribution in the ocean. All tracers will be affected by the physical processes by onlycertain tracers will contain information on the latter two processes. Alkalinity (ALK) anddissolved inorganic carbon (DIC) are essential to understanding the carbon cycle. Thenutrient data - phosphate and oxygen tracers - provide additional information on thebiological processes affecting carbon distribution in the ocean. Temperature, salinity andsilicate tracers are also included to provide additional information on the physicalprocesses affecting the carbon distribution. This provides for seven tracers to describe thecarbon cycle. By using more than one tracer, one attempts to overcome the limitation thatno one tracer can adequately describe all the relevant processes affecting the carbon cyclein the ocean.The values of potential temperature, salinity, DIC, alkalinity, phosphate, oxygen,and silicate used in the model are taken from many sources. It is necessary to use allthese data sources to provide sufficient coverage of the North Pacific. This is especiallytrue for alkalinity and DIC. The following is a brief description of the data used in themodel and summarized in Table 4.1.1) IOS Data - Useful data collected by IOS ships consists of four cruises: theHudson 70, Transpac 72, Pan 75 and Hudson 81 plus data from station P. Additionaldata from the joint Canadian-Russian expeditions (GEMS) in the summer of 1991 are also Chapter 4. Developing the inverse box model of the North Pacific^ 100used. The stations occupied by these cruises are shown in Figure 4.3. At all of thesestations, temperature, salinity, alkalinity, DIC, and nutrient data were collected. The datacollected at station P provides additional information for assessing the annual andinterannual variability of the tracer concentrations in the North Pacific.2) The GEOSECS cruises provide an essential source of data for the North Pacific(Fig 4.3). At all of the stations, all the relevant tracer were collected. The GEOSECScruises will serve as the standard to which other cruises will be compared to ensure thatall the data form the different cruises are consistent. A correction of -15 /2M01 kg' hasbeen made to the DIC measurements as suggested by Takahashi et al., (1980).3) The NOAA 82 Discoverer Cruise provides an important source of data foralkalinity and DIC measurements from the western Pacific (Fig. 4.3).4) The INDOPAC cruises provide data from the western Pacific south of Japan andacross the Pacific. However, it was only the INDOPAC 1 cruise where DIC andalkalinity measurements were made (Fig. 4.3).5) The Japanese cruises are another source of data (Fig. 4.3). Only data collectedafter 1970 are used. The drawback to these cruises is that DIC was not measured.However, pH and alkalinity were measured which enables one to determine DIC fromthese measured values. Although this introduces possible errors in the DICChapter 4. Developing the inverse box model of the North Pacific^ 101Table 4.1:^The list of cruises used to determine nutrient concentrations.Number on Plot^Cruise^Source of Data0^FGGE IOS Cruise1 GEOSECS^GEOSECS Pacific data2^HUD70 IOS Cruise3 HUD81^IOS Cruise4^INDOPAC1^INDOPAC (Scripps Institute ofOceanography)5^INDOPAC2^,,6 INDOPAC3^.,7^INDOPAC7^,,8 INDOPAC89^INDOPAC1510 INDOPAC1611^JAPAN^Collection of Japanese cruises(1970-1989)12^NOAA82-Chen^Chen pH and alkalinity13 NOAA82-Feely^Feely alkalinity and DIC14^PAN75^IOS Cruise15 TRANSPAC72^IOS Cruise16^GEMS91^IOS-Russian CruiseIIIIIIThe NOAA82-Feely data comes from Feely et al., (1984) and the estimateduncertainties are ± 5/.tEqu kg -1 and +12Amol kg' for alkalinity and DICrespectively.Chapter 4. Developing the inverse box model of the North Pacific^ 102Figure 4.3: Station maps (a-c) of data from the IOS, GEOSECS, NOAA82, INDOPAC,and Japanese datasets, refer to Table 4.1 to identify the different &facets Chapter 4. Developing the inverse box model of the North Pacific^ 103Figure 4.4: Station map of data in the NODC archive from 1970 and onward.Chapter 4. Developing the inverse box model of the North Pacific^ 104measurements, the data from these cruises are essential in order to provide adequatecoverage of all areas of the North Pacific.6) The NODC dataset provides temperature, salinity and nutrient data from 1970and onward, but not alkalinity and DIC. The NODC dataset is extensive, providing goodcoverage of all the North Pacific (Fig. 4.4). The nutrient data from the TPS24 andTPS47 cruises are contained in this dataset. This dataset provides more reliablecalculations of the average nutrient distribution than can be made from the previous fivedatasets alone.The first step in using the data was to check the data for errors and systematicdifferences. To compare the alkalinity and DIC data, six different regions in the NorthPacific were selected and the results are shown in Figures (4.5). In these plots, Table 4.2can be used to identify the appropriate dataset. The comparisons of the different datasetsshowed that the alkalinity data from the HUD70, HUD81, PAN75 and TRANPAC72cruise are suspect and were omitted.In dealing with large data sets like the NODC archives, the data were processed in10-degree squares in an attempt to remove obvious error in the data. The approach wassimilar to what Levitus (1982) used in creating his annual mean temperature and salinityfields. The data were passed twice through a filter that removed outlying points morethan 5 standard deviations away from a mean curve calculated from a least squares cubicspline approximation to the data (de Boor, 1978). If more than 30% of a particular castwere considered "bad", the entire cast was omitted. Next, the remaining data were Chapter 4. Developing the inverse box model of the North Pacific^ 105Table 4.2:^The regions used for comparing the data from the differentcruises.Region Cruises1) 33°N - 165°E GEOSECS, INDOPAC1, NOAA-Chen, NOAA-FEELY,TRANS722) 34°N - 150°W HUD70, INDOPAC1, INDOPAC16, NOAA-Chen,TRANSPAC723) 32°N - 150°W GEOSECS, NOAA-Chen4) 34°N - 122°W HUD81, INDOPAC1, PAN755) 32°N - 139°E GEOSECS, INDOPAC2, INDOPAC16, JAPAN,TRANSPAC726) 22°N - 128°E INDOPAC3, GEMS7) 12°N - 140°E INDOPAC3, JAPAN8) 45°N - 166°E JAPAN, NOAA-Chen, NOAA-Feely, GEMSinterpolated to a one-degree horizontal spacing and vertical sampling as that of the Levitusdata (I used one more depth, 6000 m). This was done by first interpolating the pointsvertical to the Levitus depths and then using a gaussian weighting function to combine thedata from different stations.1114412 '41 1'11i^11%.* 4l ik i1 13 341 1316 11 16151300O411130o _OOOOiNt15OOo04 4.3 13 4415 113116 15 Ityt1 6 1 1a416 1113116 4144 113 44Eaa)aO0Oco_4415^18115 416^1 1?1 6 14131 4141516 151324^4Uri1112/1116^12/ 144 4132116^141^16^1182 116^124 14^15 ^1824115415^112415^1t2115^4^1415 17415111610OoO00_0E--- 0_4 14 140OO2200 2300^2400Alkalinity fuEq/kg)2500^1800 2000^2200DIC (uMol/kg)2400OOo00_Otn.0aa)a2 2 0 0^2 3 0 0^2 4 0 0Alkalinity (uEq/kg)2500000000E 0---- 0000000if)0001800 ^2000^2200DIC (uMol/kg)2400I11 tri 1111 11 11 112200 2500 1800 24002000 ^2200DIC (uMol/kg)2300 ^2400Alkalinity (uEq/kg)Cp4OO00O0E oaa)O0O0O00LU0OO1^111111^111T1111111 11 111^111111110 --00000 _0(s4E 0"••-•••• 00thaa)00OO0LUOO01 1111111111111^11111 111111^11 11 111 1'I111 111111111111^111111 111 111112000 ^2200DIC (uMoI/kg)24000OOOOOO(-4Ea)0O0OOO_0LUOOO_t^1800Eca.a)0 1'4OO_O121312 1312 131t2121312312 1312131130O_0 1t2313132OOO _OOO _OU)OOOcp2200 2300 ^2400Alkalinity (uEq/kg)13 1212500131313131313131313131313131313111211aa)0O1OOO25002300^2400Alkalinity (uEq/kg)OOOco -122001800^2000^2200^2400DIC (uMoI/kg)O0111212^I^112^121^1^1oOOo-121 121 1 2Oo _O1 1111121y1E 0O11OoO1110o _OE 0Oo _O(NI4-0aa)0OO _O2200 2300 ^2400Alkalinity (uEq/kg)1800 2000^2200DIC (uMol/kg)2500^4416'41^e4 161. 4 3^333^3 3 31 14 ^44^14^31333Oo_Ocr)000OO.O3^443 43333 443 343 4444 3^34 333Oo_O•Eca.a)O a)Chapter 4. Developing the inverse box model of the North Pacific^ 109The tracer concentration c(x0 ,y0 ,4) at the interpolation point was calculated as aweight average of all the stations "near" (x0,y 0)E W(Axi ,Ayi)c(xi,yoz)c(x 0,z) = ^ E W(Axi ,Ay)^ (4.1)where c(xi ,yi ,z„) is the tracer concentration of the original data linearly interpolated to thedepth zo andAxi2^Ay i2W(dx,,Ayi) = exp -+ --,)rx`^r;(4.2)is the gaussian weighting function. Data points with a distance greater than (2r„, 2ry)from the interpolation point were assigned a weighting of zero. Two passes of theinterpolation scheme were used. On the first pass, the r x and ry values of the gaussianweighting function were both 5 degrees. The goal of the first pass was to reduce thebiasing of the highly sampled Japanese and Californian coasts on the interior ocean. Thesecond pass of the gaussian weighting function used the data from the first pass with r xand ry equal to 10 degrees. The larger length scale produced a smoother interpolatedfield. The interpolated fields for all tracers were used as input into the inverse model. Ingeneral the zonal variations in the tracers are small as shown by the plots of theinterpolated silicate and phosphate distributions (Fig. 4.6). For a more detailed display ofthe nutrient distributions, one can refer to the atlas of the GEOSECS Pacific survey whichChapter 4. Developing the inverse box model of the North Pacific^ 110contains a comprehensive overview of the tracer fields in the Pacific (Craig et al., 1981).The averaged meridional distributions of interpolated silicate and phosphate distributionare shown in Figure 4.7. Silicate is especially suited to distinguish the high silicateconcentration of the North Pacific Deep Water (NPDW) from the lower silicateconcentration of the Antarctic Bottom Water (AABW) and Antarctic Intermediate Water(AAIW). The concentration differences between the Antarctic water and NPDW makessilicate an important tracer for studying large-scale deep circulation. The phosphatedistribution reveals a northward spreading of a high phosphate concentration in the bottomwater. The phosphate maximum at 1500 m is lying at a shallower than the silicatemaximum at 2500 m because organic matter is less resistant to decomposition than opalmaterial.(a)120^ 140^ 180^ 180^ 200LONGITUDEFigure 4.6: Zonal variation of silicate at (a) 24°N and (b) 47°N, and phosphate at (c) 24°N and (d) 47°N, allunits are in mol kg 1.220 2405A4-)04a)a140^ 180^ 180LONGITUDE200 220 240(c)10002000E3000....,ca.a)c:1400050008000120 140 160 200 220180LONGITUDE 240(d)E4.,a,a)0140^ 180 220180^ 200LONGITUDE240Chapter 4. Developing the inverse box model of the North Pacific^ 1154.2 MODEL GEOMETRYIn the model, the North Pacific is divided into a series of layers by depth andisopycnal surfaces and the ocean bottom (Figure 4.8 and Table 4.3). In the model, layer1 represents the euphotic zone and it is assumed that all the biological production isrestricted to this zone. Near the surface, the vertical resolution of the model is relativelyhigh; the layer thicknesses of the top two layers are about 100 - 200 m. The deep layersof the model are relatively thick (1000-2500 m). They represent the major water massesin the North Pacific below the thermocline: the Antarctic Intermediate Water (AAIW),layer 4; the North Pacific Deep Water (NPDW), layer 5; and the Antarctic Bottom Water(AABW), layer 6. These layers are divided into boxes by zonal sections at 24°N, 47°Nand 65°N (Fig. 4.9). The divisions of the model domain by the three sections producestwo regions in the model (Fig.4.9). Region one, the subtropical Pacific region, is thelargest region with a surface area of 2.48 x 1em2 . This region contains the Kuroshiosystem and splits the subtropical gyre. Region two, the subarctic Pacific region, is aboutone-third the size of region one (surface area of 7.4 x 10 12m2); it contains the Alaska gyre.The subarctic region is suspected to play a role in the formation of the North PacificIntermediate Water (NPIW). In this region, the model allows NPIW to come into directcontact with the euphotic layer. This is consistent with Riser and Swift (1989) whoobserved that the 26.8 potential density surface outcrops in the Sea of Okhotsk. Van Scoyet al., (1991) also argue that the NPIW outcrops in the Alaska Gyre in the winter time.Chapter 4. Developing the inverse box model of the North Pacific^ 116Table 4.3:^The ocean layering used in the model.Water Mass^Upper surface^Lower surfacePhotic Zone^0 m^100 mNear Surface Water^100 m o-e =26.8NPIW^("0=26.8 (or 100 m)^0-0=27.3AAIW go=27.3^0-0=27.7NPDW^o-e=27.7 0-0=27.8AABW 0-0=27.8^ocean bottomThe Arctic Ocean is connected to the North Pacific through the shallow Bering Sea andinflows from the surface layer into the Arctic are allowed.The model shown in Figures 4.8, 4.9, and 4.10 is a compromise between thedesire for higher vertical resolution and the necessity to keep the system solvable. Thevertical resolution is highest near the surface where the biological activity is occurring andwhere the particle fluxes vary the most. In the deep water, only the major water massesAAIW, NPDW, and AABW are resolved. In region II, the nutrient concentrations in thesurface water are high leading to high productivity and new production. Region I, ismore typical of oligotrophic water where nutrients are the limiting ingredient to biologicalproductivity.(a)5000600010^ 20^ 90^ 40^ 50^ 80^ 70LATITUDE NORTHFigure 4.7: Average meridional section of (a) silicate and (b) phosphate in Amol kg 1.(b)10^20^90^ 40^50^60^70LATITUDE NORTHphotic zone110^20^90^ 40^50^60^70LATITUDE NORTHFigure 4.8: The meridional section showing the division of the model into layers.Chapter 4. Developing the inverse box model of the North Pacific^ 120Figure 4.9: Map of potential density at 100 m with the division of the model intoregions.( )^ photic zonesoon4400050008000200^ 220^ 240120^140^ 1130^ 180LONGITUDEFigure 4.10: The zonal sections showing the layering used in the model, (a) 24°N, and (b) 47°N.140^ 180 180LONGITUDEphotic zone/Chapter 4. Developing the inverse box model of the North Pacific^ 1234.3 MODEL CONSTRAINTSThe three basic principles applied in the model are: 1) continuity of mass within theboxes of the model, 2) continuity of tracers within the boxes of the model and 3)geostrophic flow through the sections. The continuity of equations for tracers and massare given in the following two equationsp Vat = f[V.(11Cp)—V.(kVCp)lciV+ Q bio + Qair-sea = 0^(4.3)'Cl'( P 17) ÷ V "Qfrestwater = 0^ (4.4)The tracer continuity equation states that the concentration of a tracer C within a volumeV changes with time if the total (net) tracer transport does not balance internal sourcesand sinks (the Q's) of that tracer. The tracer transports are composed of advective partswhich represent the tracer transport due to the 3-dimensional mean flow field (u, v, andw), and an eddy mixing term which describe the tracer transports due to temporal andspatial fluctuations of the flow fields and tracer concentrations. The usual approach ofparameterizing these eddy transports as the product of the concentration gradient andapparent mixing coefficient is used in this model. By integrating both equations aroundthe volume defined by a box and assuming steady-state, one can write the equations as asum of transports through the surfaces of the box.Chapter 4. Developing the inverse box model of the North PacificE (u i (C p)i A) - E (Ici^A + Q.. 0+o —air-sea =a(p),ax .E (p 17) . A, + Qfreshwamr = 0124(4.5)(4.6)The summation, i, includes all horizontal (isopycnal) and vertical (diapycnal) surfaces ofthe box. The parameter A, refers to the surface area of the surface, u i is the averagevelocity through the surface, (C) i and (aC/ax) are the concentration and concentrationgradient on the surface. The concentration gradient is evaluated perpendicular to thesurface. The values and 0',freshwater are the net air-sea exchange of tracers andfreshwater through the ocean surface, and Qbk, are net biological source/sink of tracersinside the box.4.3.1 Horizontal water transportsThe horizontal water flows through the box surfaces are assumed to begeostrophic; ie., the horizontal velocities satisfy the thermal wind equation:vg(z) =^. ax1^dz + v0f z. (4.7)v° is the unknown reference velocity at the reference level (z 0). The Ekman transports areadded to the surface layer of each section. The Ekman transports are calculated from theintegral equationChapter 4. Developing the inverse box model of the North Pacc^ 1251M = f— (ty, ,-Tx) •rt dSewhere n is the unit vector normal to the vertical box face into the box; r. and ry are windstress in the x and y direction respectively; and f is the coriolis parameter. The annualwind stresses from Hellerman and Rosenstein (1983) are used to calculate the Ekmantransport. The total horizontal transport through the horizontal surface j, isXH E^pv, dS + E p voi A jk + E Mekk^A it(4.9)Except for surface layers, the Ekman transport is zero (M e =0). The total horizontaltracer transport through a surface j isJH = E Ck pvg, as 4- E Ck p vok Ajk + EA a (4.10)The first two terms represent the transport due to geostrophic flow and the third term isthe contribution from the Ekman transport. The summation k is over all the parts in thesection and Aik denotes the corresponding area of that box face. The TPS24 and TPS47sections are used to calculate the geostrophic velocities. Because it was believed that thetracer data which are used in the model did not contain information to resolve theindividual station pairs reference velocities, no attempt was made to determine theseindividual velocities. Instead the sections are divided into four subsections and thesereference velocities are determined. The inverse results of Rintoul and Wunsch (1991)(4.8)Chapter 4. Developing the inverse box model of the North Pacific^ 126show how ill-conditioned the determination of the individual reference velocities are and,except in regions of large changes in bottom topography, their modelling results producenearly constant velocities.The total tracer transport into a box by horizontal and vertical advection is givenby^ Ja = E^+ x wi0C),Ai^(4.11)where the summation j is over all horizontal surfaces and the summation i is over allvertical surfaces. The parameter A ; denotes the surface area of the box face.4.3.2 Eddy transportsIt has already been mentioned that the eddy transports in the model areparameterized by a diffusion term. In the model, the diffusive transport is broken downinto diapycnal and isopycnal terms. The transport of mixing isa(pC)^a(pC)J.^h=Eic^J4+EK,^ax;^az, (4.12)where the summation j is over all isopycnal surfaces and the summation i is over allvertical surfaces. The parameter A denotes the surface area of the box faces. Thegradients on the surface are calculated from the average concentrations in the twoconnected boxes divided by the distance from the centre of the two boxes. In the model,the mixing terms are forced to be positive (in chapter 3 it was shown that it wasChapter 4. Developing the inverse box model of the North Pacific^ 127Table 4.4: The processes that contribute to the biological source/sink terms forthe various tracers.Tracer^ ProcessMassHeatSaltOxygen (Q0)Phosphate (Qp)Silicate (Qs)Carbon (Qc)Alkalinity (QA)photosynthesis and remineralization of organic tissueformation and remineralization of organic tissueopal formation and dissolutionformation and remineralization of organic tissue andCaCO3formation and dissolution of CaCO 3 ** Alkalinity is also slightly affected by the biological source/sink of nitrate.unnecessary to have negative K's), making the coefficient physically meaningful (Olbers etal., 1985).4.3.3 Biological processesThe biological source parameter, Qbi,„ in equation (4.3) is the net source (sink ifnegative) for the various tracers due to biological processes. This parameter for thedifferent tracers is the result of various processes (Table 4.4). The biological uptake ofdissolved nutrients, and the formation of organic tissue and calcareous and opaline shellsChapter 4. Developing the inverse box model of the North Pacific^ 128in the surface water represents a sink for nutrients and carbon and a source for oxygen.The subsequent remineralization of the particulate matter in the deeper ocean leads to arelease of nutrients and carbon (sources) and the utilization of oxygen (sink). The use ofthe tracer pair, DIC and alkalinity, allows for the distinction between formation(dissolution) or organic matter and CaCO3 . Only the formation (dissolution) of CaCO3contributes to the alkalinity source term.In the model, organic tissue and calcareous and opaline shells are formed in thesurface boxes. This particulate matter formed in the surface box is assumed to becompletely remineralized or dissolved in underlying deeper boxes of that same region.This assumption is reasonable because advective transport of particulate matter from onemodel region to another, as well as nutrient input from the continents and nutrient lossdue to sedimentation, are small compared with the advective transport of the dissolvednutrients and uncertainties in the nutrient conservation equations.The biological source terms for phosphate, nitrate, carbon and oxygen in the oceanare related. This is because of the relatively constant composition of organic matter. Inthe formation of organic tissue by photosynthesis, the uptake of phosphate is accompaniedby a proportional uptake of nitrate and carbon and a release of oxygen. Theseproportionality factors were originally determined by Redfield and are called Redfield'sratios. The inverse model uses the values from Takahashi et al ., (1985) of P:N:C:02 =1:16:103:-172. These differ slightly from Redfield's original values P:N:C: 02 =1 : 16:106:-138. Broecker et al ., (1985) showed that the P:0 2 = 1:-172 is applicable toIIL 1^ icunLs u^11Chapter 4. Developing the inverse box model of the North Pacific^ 129Q, — Rap Qp = 0 ± eQc (4.13)Qc — Rao Q„ = 0 ± eQc^ (4.14)are used to allow the Redfield ratios to vary from the values of Takahashi by a givenpercentage, E.In addition to Redfield ratios, alkalinity of the ocean is not only affected by theformation/dissolution of CaCO3 but by the following equation:QA =2xCcarb - 16Qp^(4.15)where QA and Qp are the biological source terms for alkalinity and phosphate respectively.The formation of CaCO3 reduces the amount of dissolved inorganic carbon (Cad, isnegative) and the ocean alkalinity. The formation of organic material alters the alkalinityby the uptake of nitrate.In the ocean, one could restrict the formation of CaCO 3 to boxes above thelysocline and the dissolution to boxes below the 100% carbonate saturation level.However, in the North Pacific Ocean the situation is simplified because the 100%carbonate saturation level is so shallow, 500 m in the equatorial regions to shallower than200 m in the high latitudes (Feely and Chen, 1982). In the model, CaCO 3 will form onlyin the surface boxes and will experience dissolution in all subsequent deeper boxes.Chapter 4. Developing the inverse box model of the North Pacific^ 130Table 4.5:^The processes that contribute to the air-sea source/sink terms forthe various tracersTracer^ ProcessMassHeatSaltOxygenPhosphateNitrateSilicateCarbonAlkalinityprecipitation, evaporation and river runoffair - sea heat fluxgas exchange with the atmospheregas exchange with the atmosphere4.3.4 Air-sea exchangesThe air-sea processes that contribute to various tracer concentrations are given inTable 4.5. These processes only affect boxes that are exposed to the atmosphere. It isknown that in order for CO2 to enter the ocean, pCO2 in the ocean must be less than thepCO2 in the atmosphere. This information will be incorporated into the model toprescribe the direction of air-sea flux of CO 2 using the data from Tans et al., (1990). Themaps of the summer and winter zpCO 2 are shown in Figure 4.11. From this data one can(a)160' E120° E 120°11 so' irWLONGITIUDE70' N5e N10 ° N1208 E 160 ° EI •160 ° w^120° W^80°LONGITIUDE70 ° N60 ° N10' NChapter 4. Developing the inverse box model of the North Pacific^ 131(b)Figure 4.11: The zpCO 2 maps of the North Pacific (Tans et al., 1990), the units are ingAtm, with negative regions (lined) denoting areas of the ocean that sinks ofatmospheric CO 2 , (a) winter (Jan.-Apr.) and (b) summer (Jul.-Oct.). The dotsdenote the regions where data are available.Chapter 4. Developing the inverse box model of the North Pacific^ 132see that in winter the subarctic Pacific is generally a source of atmosphere CO 2 and thesubtropical Pacific is generally a sink of CO 2 . In the summer, the situation is reversed,the subarctic is now a weak sink and the subtropics is a source. The net annual effectdetermined from these maps are that the subtropics behaves like a sink of CO 2 and thesubarctic behaves like a source. The strong source of CO2 in the high latitudes of thePacific is somewhat surprising. Given the large seasonal fluctuation in the direction of theCO2 in the subarctic Pacific and the limited data in the high latitudes, the sign of this fluxwas left undetermined. However, in the subtropics, the CO2 flux is more definite and inthe model this region is assumed to be a sink of CO2 .4.4 INVERSE SOLUTIONSFrom equations 4.5 and 4.6 one develops a set of equations that links theconcentration data (C and the gradient of C) to the unknown reference velocities, mixingcoefficients, biological parameters and air-sea exchanges. Mass and tracer balances forheat, salt, DIC, alkalinity, phosphate, oxygen and silicate are formulated for the individualboxes and for the two regions of the model. These continuity equations make up thelargest part of the set of model constraints, but other constraints are added to exert morecontrol on the model (Table 4.6).Chapter 4. Developing the inverse box model of the North Pacific^ 133Table 4.6:^Summary of model constraints Constraint^NumberMass, heat, salt, phosphate, oxygen, silicate,^112E CO2, alkalinity continuity for the individualboxes and regions of the modelRedfield constraints for phosphate and oxygen^20Geostrophic constraints^ 12Total^ 144The model constraints represent a set of linear equationsGx = b +c (4.16)where the coefficients matrix G contains tracer concentrations and gradients, x is thevector of unknownsx = (vo , up wp 0 0vj , —biol —air-seal Qfreshwater) (4.17)and the vector b contains the relative geostrophic components of the tracer fluxes acrosssurfaces of the boxes. Due to errors in the data and approximations in the model, theconstraint equations are not expected to be exactly satisfied but only to be within aspecified tolerance^The estimation of the tolerances will be discussed in section 4.5.A priori bounds x and x + are applied to the unknowns to restrict their numerical values tophysically meaningful ranges:(4.18)Chapter 4. Developing the inverse box model of the North Pacific^ 134Table 4.7:^A priori bounds on the model parametersParameter LowerBoundUpper BoundReference velocities (vo) cm s-1 -5.0 5.0Isopycnal mixing coefficients,kh, m2 s-10 30,000Diapycnal mixing coefficients,kv , cm2 s-10 10Air-sea exchange of CO2 in thesubtropics0 00Water outflow through the 0 2.0Bering Sea, SvKorean Strait, northward flow, 2.0 4.0SvTable 4.7 summarizes these constraints. The outflow through the Bering Sea is based onthe estimate of Coachman and Aagaard (1988) of 0.8 Sv annual mean transport with ±0.6Sv in seasonal variability. The flow through the Korean Straits (Tsushima Straits) wasbased on estimates of Bingham (1991), Yi (1966) and Nitani (1972). The advantage ofthis routine is that it can determine if feasible solutions exist and produce a realisticsolution to the problem. This provides one with a clear visualization of the solutionsbeing forced by the model. In this research, the LSI routine was extensively used to studydifferent models and to assess how well the model was working. By studying thesolutions from such models, one can see what information the data is providing to themodel.Chapter 4. Developing the inverse box model of the North Pacific^ 135To solve these system of equations (4.18) and (4.19), I relied on two differentalgorithms: the least squares algorithm with inequality constraints (LSI) (Lawson andHanson; 1974) and linear programming (LP) (Luenberger; 1984). Refer to §3.3.3 for amore detailed discussion of these two inverse methods.4.5 TOLERANCES OF BALANCE EQUATIONSThe continuity equations (4.3) for the various tracers are not expected to besatisfied exactly but only to within certain tolerances E. These tolerances reflect errors inthe tracer data as well as simplifications in the model. In the present model, I assumedthat the flow is geostrophic (with Ekman transport added to the surface layers) and thatthe reference velocities, v., vary only on large scales. Also, I assumed that the tracertransport through box surfaces can be decomposed into advective, diffusive and particletransports and that the diffusive transport can be parameterized by mixing coefficients.Though this approach is a standard method and frequently used, it is important to keep inmind that it is only an approximation to the correct tracer transports.The effect of the approximations in (4.3) on the tracer budgets create part of the errorin (4.16); however, these errors are difficult to assess quantitatively. An additionaldifficulty in determining the errors E in (4.16) are that the errors in b are functions of theunknown transport terms. An appropriate estimate of these errors, 45b, was thought to bedetermined by only considering the error in b due to advective transports by using thefollowing equations:Chapter 4. Developing the inverse box model of the North Pacific^ 136= E viA i(4.19)Ob i = E SVA 1 Ci + Ewhere vi represents the average velocity through the box face, A i the area of the boxface and C, the concentration on the box face, and S denotes the errors in these terms.The first term on the rhs of (4.19) was dropped because for flow that is forced toconserve mass, the sum of Sv A i for all boxes will be zero and hence the error from thisterm will be small. The second term on the rhs of (4.19) was evaluated by using thestandard deviation of the tracers in the defined boxes to determine the tracer errors on thebox faces (SC) and by multiplying this value by the rms volume transports of the relativegeostrophic transports (x i , the x i approximately equalled 5.1 Sv). The tracers errorsprescribed in (4.19) were 1.25 times greater than the temporal variability of the tracerdata from Station P. Large fluctuations in some of the station P measurements resulted inthe decision to use the values calculated from the boxes. It is felt that these valuesrepresent an upper limit of the errors expected in the tracers.In the model, the mass continuity constraints are considered to be almost perfectlysatisfied (±0.001 Sv). This approach was taken because large mass imbalances degradethe information content of the tracer continuity by introducing tracer imbalances. If largemass imbalances are allowed, one is in effect introducing artificial sources and sinks intothe tracer's balances and corrupting these equations. Being aware that geostrophictransports across the surfaces of the boxes might be inconsistent with the principle ofperfect man balance, small errors in the thermal wind equations are allowed in the modelChapter 4. Developing the inverse box model of the North Pacific^ 137(± 1 %). The model also forces the tracer continuity in the two regions to be nearly-perfectly satisfied. The logic for this comes from the fact that the steady-state assumptionis assumed to be a valid approximation; then at least for the large regions of the model,this condition should be satisfied. Without this tightening of the regional constraints, themodel would be allowing the equivalent of artificial air-sea exchanges to add and removetracers from the model.CHAPTER 5. MODEL RESULTS FOR THE NORTH PACIFIC OCEANIn this chapter I will look at inverse solutions to models formulated for the NorthPacific. The chapter is separated into three sections. In the first section, I attempt tounderstand and evaluate the model. The second section is devoted to discussing theresults obtained from the inverse box model. In the third section, I aim to investigate theeffect of dissolved organic matter on the tracer budgets by including the "new" DOMconcentrations in the model in a simple way.5.1 EVALUATING AND UNDERSTANDING THE MODELIn this section I will evaluate the model to better understand how it works and toprovide insight into the problem. In the discussion to follow, I will first look at thefeasibility of several slightly different models, focusing on the change in the solutionsobtained. Second, a study of the importance of the various tracers will be performed inorder to evaluate the differences in the information content of the various tracers. Third,I will evaluate the model's sensitivity to the choice of layering and reference level.138Chapter 5. Model results for the North Pacific Ocean^ 1395.1.1 Feasiblilty StudiesOne powerful tool of inverse modelling is its flexibility. It is relatively easy tochange the constraints of the model to investigate the effects on the solution. Theflexibility of inverse models is exploited in the follOwing analysis with four differentinverse models. These models investigate the feasibility of the constraints and changes inthe solutions of air-sea exchanges of freshwater, heat, CO 2 and 02 and detrital rain ratesof organic carbon, inorganic carbon and opal material.The first model formulated satisfied the Ekman and Geostrophic transports to+1%, had positive unbounded mixing terms and satisfied the Redfield ratios for theformation/dissolution of organic matter exactly. The model had a feasible solution,showing that significant deviations in the Ekman or Geostrophic transports are notnecessary for a feasible solution. The model's acceptable ranges for the unknown air-seaexchanges and maximum detrital rain rates are summarized in Table 5.1 and 5.2.To further explore the feasibility of the constraints, a second model was formulatedfrom the first model by including an upper limit on the diapycnal and isopycnal mixingterms of 10 cm2 s' and 30,000 m2 st respectively. The acceptable ranges for the air-seaexchanges are sensitive to the bounds on the mixing terms and the ranges in theseunknowns are better constrained in the second model (Table 5.1). The maximum detritalrain rates are considerably more sensitive to the a priori bounds on the mixing terms thanthe air-sea exchanges (Table 5.2). In the second model, the maximum detrital rain rates apter 5. Model results for the North Pacific OceanTable 5.1:^The acceptable ranges for the air-sea exchanges determined from the models used in the feasibility study.Air Sea exchange Region Model IMIN^MAXModel IIMIN^MAXModel IIIMIN^MAXModel IV(referencemodel)MIN^MAXFresh water 1 0.04 0.53 0.07 0.33 0.0 0.42 0.0 0.42(Sv) 2 -0.45 -0.02 -0.3 -0.05 -0.39 0.03 -0.40 0.03Heat (PW) 1 -0.3 0.3 0.03 0.21 -0.04 0.31 -0.04 0.312 -0.53 -0.11 -0.35 -0.17 -0.39 -0.02 -0.40 0.0CO2 (Kmol s') 1 -170.5 122.1 -132 62 -178 104 -178 1052 0 432.8 152 422 0.0 435 0.0 43502 (Kmol s -1 ) 1 218 1749 272 996 -46 1139 -46 11492 -1488 189 -925 85 -1434 253 -1446 253Chapter 5. Model results for the North Pacific Ocean^ 141Table 5.2:^The maximum particle flux rate from the surface layer for themodels used in the feasibility studies.Particle Flux(Kmol s1)Region Model I Model II Model III Model IV(referencemodel)Organic Carbon 12802.7592.5452.5303.6594.6627.3730.3771.4CaCO3 1 355.3 201.4 264.4 275.82 331.8 233.7 298.6 310.2Opal 1 667.8 413.5 458.7 458.82 134.9 84.5 157.4 157.7are up to 50% less than the first model. The differences in the first two models for themaximum detrital rain rates provide some indication of the linkage between the unknowndetrital rain rates and the unknown mixing terms. The second model shows that withgood hydrographic data one does not need to have unreasonably large mixing terms orviolate the Ekman transport significantly in order to obtain a feasible solution, as was thecase with the Levitus dataset in the North Atlantic (Memery and Wunsch, 1990)In the first two models, one assumes that the Ekman transport was well determinedbut it must be recognized that the Ekman transports in the North Pacific exhibit significantseasonal variability (Table 5.3). Furthermore, there is doubt about the accuracy of thesemeasurements. To account for these effects of seasonal variability and errors in thewindstress data, a third model was formulated that allowed the Ekman velocities to varyChapter 5. Model results for the North Pacific Ocean^ 142Table 5.3:^The Ekman transport at 24°N and 47°N calculated from theHellerman and Rosenstein (1983) monthly windstress measurements.Section^Minimum (Sv)^Maximum (Sv)^Annual Mean (Sv)24°N 4.6 (Jan.)^16.8 (Nov)^12.047°N^-2.0 (Jun-Jul)^-10.3 (Dec)^-5.8by +25% from their annual mean values. With the exception of the increased variance ofthe Ekman transports, model three is identical to model two. The acceptable range in theair-sea exchanges for model three (Table 5.1) are greater than model two, the heat fluxesrange increased by approximately 0.1PW, the CO2 flux by about 100 Kmol s-1 , and theoxygen flux by about 500 Kmol s -1 . By increasing the uncertainty in the Ekman transport,the ranges in the air-sea exchanges are still reasonably well-constrained. The maximumdetrital rain rates are also greater than model two (Table 5.2). The organic carbon rainrate increased by 300 Kmol s -1 and 150 Kmol s -1 for regions one and two respectively.The increase in the inorganic carbon and opal rain rates from model two is approximately60 KmolThe fourth model formulated was based on model three but allowed the Redfieldratios between phosphate, carbon and oxygen in the formation/dissolution of organicmatter to vary by ±20% from the values given by Takahashi et al., (1985). Theacceptable ranges from this model for the air-sea exchanges were nearly identical withmodel three (Table 5.1). Allowing variable Redfield ratios are not important inetermuung the air-sea exchanges. ine maximum rain rates or et^matenal rrom theChapter 5. Model results for the North Pacific Ocean^ 143euphotic layer (Table 5.2) are increased from model three. The organic carbon rain rateincreased by 130 Kmol s' for both regions and the inorganic rain rates increased by 10Kmol s-1 for region one. The opal rain rate did not change from model three. The fourthmodel formulation will henceforth be referred to as the reference model and will be usedto further investigate the problem. The reference model makes use of the criticalinformation in the geostrophic shear to constrain the horizontal transports. However, themodel does allows some uncertainty in the Ekman transports to account for the seasonalvariability in Ekman transports and variability in the Redfield's ratios to reflectuncertainty in the actual values of these ratios.5.1.2 Tracer StudiesBefore discussing the results of the reference model it will be helpful to have anidea of the importance of various tracers in the solution of the reference model. Toinvestigate the effectiveness of various tracer fields, three models were formulated using asubset of the inorganic tracers. The following is a discussion of the solutions obtainedfrom these models.The first model only conserved mass, heat, and salt and the acceptable ranges forall unknowns in the solution are poorly determined. The acceptable ranges for thefreshwater and heat flux into the North Pacific Ocean are -0.07 to 0.88 Sv and -.8 to .88PW respectively. In part, the large amount of heat gained by the North Pacific can beattributed to the large freshwater flux into the North Pacific. The increased freshwaterChapter 5. Model results for the North Pacific Ocean^ 144flux causes an increased volume transport out of the North Pacific, and associated withthis volume transport is an accompanying heat flux. Therefore, an increase in 0.1 Sv inthe freshwater flux into the ocean produces an approximate 0.11 PW increase in the heatflux into the ocean. It is interesting to observe that the lower limit for the heat gained bythe ocean is more consistent with the heat estimates made by Roemmich and McCallister(1989) of -0.75 PW and by Bryden et al., (1991) of -0.76 PW. Both of these estimateswere made using only the TPS24 cruise temperature and salinity data.The second model conserves mass, heat, salt and silicate. With the addition ofsilicate to the model, the change in acceptable ranges for freshwater and heat exchangesbetween the ocean and atmosphere is slightly reduced. The freshwater flux into the NorthPacific is -0.06 to 0.71 Sv and the heat flux is -0.60 to 0.27 PW. For this model, themaximum rain rate of opal from the euphotic zone is 304 Kmol s -1 (10.6 g Sim-2 yr-1) and530 Kmol s-1 (62.4 g Si m2 yr-1) for regions one and two respectively. The maximumrain rates of opal material are about double the values obtained using all of the tracers.The third model formulated conserved heat, salt, mass, phosphate, oxygen, DIC,and alkalinity. The acceptable ranges from this model for freshwater flux and heat fluxinto the North Pacific are -0.04 to 0.45 Sv and -0.18 to 0.34 PW. The lower range forthe heat flux into the North Pacific is consistent with the model of all the tracers. For thismodel the maximum rain rate of organic carbon from the euphotic zone is 1250 Kmol s -1and 860 Kmol s 1 for regions one and two respectively. The maximum rain rate ofinorganic carbon is 350 Kmol s-1 (6.8 g C M-2 yr-1) and 370 Kmol s -1 (21.1 g C m2 yr 1)for regions onP and two respectively. Both the rain rate of organic carbon and inorganic Chapter 5. Model results for the North Pacific Ocean^ 145are much greater in region one than for the model with all the tracers, while in region twothe rain rates of organic and inorganic carbon have increased slightly.5.1.3 Sensitivity to Model Layering and Choice of Reference LevelIn developing the model several different layerings of the ocean were considered.In general, the effect of the model layering did produce different LSI solutions, howeverthe acceptable ranges for the unknown air-sea exchanges and maximum detrital rain rateswere very similar. The only exception to this was if the euphotic zone was defined to be50 m or shallower. In this case, incompatibilities developed between the phosphate andcarbon tracers and the silicate tracer. This was taken as an indication that the euphoticzone must be deeper than 50 m. Measurements compiled by Longhurst and Harrison(1989) place the euphotic depth at 75 m and 95 m for the Station P and the VERTEXlocation respectively. From Longhurst and Harrison (1989) analysis it is observed thatmost primary productivity occurs in the upper 100 m.The reference levels used in the 24° and 47°N sections were varied between 1000m and the ocean bottom. Again the LSI solution was sensitive to the prescribed referencelevel, and the fit to the data for these models varied significantly. The reference levelswere chosen such that the chi-squared error of the LSI model was the smallest. Theacceptable ranges for the air-sea exchanges and maximum detrital rain rates were not veryChapter 5. Model results for the North Pacific Ocean^ 146sensitive to the prescribed reference level. They all produced results similar to thereference model.5.2 MODEL RESULTSTo help visualize and assess the standard model, I will first present the LSIsolution of the model. This solution was obtained by minimizing the errors in theconservation equations in a least squares sense while being consistent with the inequalityconstraints on the conservation equations and the bounds on the unknowns. The equationsin the model are weighted by the same errors used for the LP model. The solutioncalculated from this model was not unique but the minimum objective function was. Thismeans that I have selected one solution produced by the model. This limitation does notaffect the meridional transports but the effect on the mixing coefficients and detrital rainrates are more obvious and will be discussed below.The meridional transport shown in Figure 5.1 is consistent with the general idea ofmeridional circulation in the North Pacific. In the bottom layer, AABW enters the NorthPacific (NP); in layer 5, NPDW leaves the NP; and in layer 4, AAIW enters the NP.The NPDW is formed by the mixing of AABW and AAIW in both regions one and two.In the upper layers, the flow pattern is more confusing, reflecting the more zonalcirculation in these layers. Two interesting features in the surface layer are theconvergent flow in the subtropics and the upwelling of NPIW into the euphotic layer inphotic zone 7.4 19.9Chapter 5. Model results for the North Pacific Ocean 147Near surface layer10^20^30^40^50^60^70LATITUDE NORTHFigure 5.1: The integrated meridional transports calculated from the least squaressolution in Sv.Chapter 5. Model results for the North Pacific Ocean^ 148the subarctic. In this model, the flow of water through the Japanese Sea into region twois 2.35 Sv. The outflow of water through the Bering Sea is at its lower bound of 0 Sv.The air-sea exchanges are summarized in Figure 5.2a-d. The freshwater fluxes for thismodel are small but the direction of the fluxes is consistent with the estimates ofBaumgartner and Riechel (1975). The subarctic ocean gains freshwater while thesubtropical ocean losses freshwater. The solution shows that heat leaves the ocean in thesubtropics and enters the ocean in the subarctic. The values are in reasonable agreementwith the bulk formula estimates of the annual mean air-sea heat fluxes calculated by Clarkand Weare et al., (Talley 1984). The net loss of heat by the North Pacific ocean at24°Nis 0.1 PW. In the subarctic ocean there is a small outgassing of CO2 into the ocean(0.005 Gt C yr') but the North Pacific ocean is a net sink of atmospheric CO 2 (0.07 Gt Cyr -1). Oxygen outgasses into the atmosphere in the subtropics but enters the surface waterof the subarctic. The flux of oxygen into the subarctic ocean is cause by the divergencein the horizontal and vertical oxygen transport of ocean in the surface layer.The mixing coefficients calculated from the least squares inversion are in generalsmall (Fig. 5.3). The notable exceptions are the large horizontal mixing terms in thesurface layer of the subarctic Pacific and the large diapcynal mixing terms in the bottomlayer of the subtropics region, and between layers 3 and 1 in the subarctic region. Boththe horizontal mixing term for the Bering Sea and the mixing term between layers 1 and 3are at their upper-bound limit. The relatively small values for the mixing terms arereflected in the equally small values for detrital rain rates. The total rain rates from the70 ° N -----ze.C-I180' W1 1 4 0 ° W^LOU' W(d)4F1-62.1 150 0Chapter 5. Model results for the North Pacific Ocean^ 149Figure 5.2: Maps of air-sea exchanges for a) freshwater (Sv), b) heat (PW), c) CO2(Kmol s') and d) 0 2 (Kmol sA) from the least squares solution.Chapter 5. Model results for the North Pacific Ocean0200150400600BOOa,a.,A1000200030004000500010^20^30^40^50^60^70LATITUDE NORTHFigure 5.3: The mixing coefficients from the least squares solution, the isopycnalcoefficients are in 104 m2 s' and the diapycnal coefficients are in cm' s'.Chapter 5. Model results for the North Pacific Ocean^ 151surface layer for organic carbon, inorganic carbon and opal in the North Pacific are 97,49 and 74 Kmol s -1 respectively. The algorithm used to solve the least squares problemhas a tendency to place poorly constrained unknowns at their a priori bounds. Thistendency is reflected in the mixing and detrital rain rates by the fact that most of theseunknowns are at the a priori bounds and implying that the model has difficultydetermining these unknowns.5.2.1 Meridional TransportsSchlitzer (1988) showed that the specification of the geostrophic fluxes across asection does not determine the integrated layer transports through the section completely.The upper and lower bounds of the integrated layer transports depend on bottomtopography, layer thickness along the section, bounds on the reference velocities and thetracer constraints. The upper and lower bounds of the zonally-integrated layer transportsand diapycnal water fluxes have been calculated by using the linear programming routinewith the appropriate objective functions. The results of these calculations are summarizedin Figure 5.4. Typically the average of these ranges is comparable to the least squaressolution in Figure 5.1. The meridional circulation pattern in the deep ocean is thesamefor all possible solutions. AABW flows northward through the bottom layer of 24°Ninto the subtropical region where it mixes with AAIW and produces the NPDW whichleaves the North Pacific through layer 5. The model does not show any deep waterformation in the North Pacific.1521.6—1.4... 1.2600-V^AAIWtoot)-^6.2—5.2... 2.31-8.4... 4.5Chapter 5. Model results for the North Pacific Oceanphotic zone' 3.2... 8.0200- Near surface layer1-12.0. ,-3.4400NPIVV6001-5.0... 0.3^1—12.5... 2.9^1^1 12.3.. 10.2I-2.2... 2.4 ^1 —7.0... 15.9—14.4. 8.3—2.2... 3.1^1—2 8 2.4 3.0... 11.0^1 L-3.6... 6.1^12000-3000- NPDW—12.1. .-7.3 —5 2^.34000-AABW50003.2... 7.27.210^20^30^40LATITUDE NORTH50 60 70Figure 5.4: The acceptable bounds on integrated meridional transports in Sv.Chapter 5. Model results for the North Pacific Ocean^ 153The meridional water transports of the model and the results of other studies arecompared in Table 5.4. The deep water transports across the 24°N section agree wellwith Bryden et al., (1991) estimates. The northward transport of AABW determine bythe inverse model also agrees with the transports of 8.4 Sv estimated by Johnson (1992) at10°N.In the upper layers the meridional circulation pattern is more confusing reflectingthe more zonal circulation pattern of the upper ocean in the North Pacific. From themodel the Kuroshio transport through 24°N is 25+5 Sv.5.2.2 Freshwater transportThe minimal and maximal freshwater fluxes into the surface layer of the model areshown in Figure 5.5a. The freshwater input in the subarctic ocean is nearly balanced by afreshwater flux into the atmosphere in the subtropics. For comparison with freshwaterflux estimates of Baumgartner and Riechel (1975), I have plotted their northward transportof freshwater along with the range of values determined by the model (Fig. 5.6). At 47°Nthe agreement between the two measurements is good but at 24°N the two measurementsshow a distinct difference in magnitude. McBean (1989) points out that care must beexercised in interpreting the freshwater estimates, such as Baumgartner and RiechelChapter 5. Model results for the North Pacific Ocean^ 154Table 5.4:^A compilation of meridional layer fluxes across 24°N.Section 1: 24°NWater MassAAIWNPDWAABWBryden'4.3-8.44.9Roemmich2-10.010.0this study3.0 ... 11.9-12.1 ... -7.33.2 ... 7.2illydrographic data from cruise TPS24 and the fluxes calculated by Bryden et al.,(1991).2Hydrographic data from cruise TPS24 and the fluxes calculated by Roemmich andMcCallister (1989).(1975), due to the inherent difficulties in calculating the evaporation and precipitationvalues over the open ocean.5.2.3 Heat TransportThe bounds on the air-sea exchange of heat are shown in Figure 5.5b. The air-seaexchanges of heat calculated from the model show that the subtropics can act as aimportant source of heat for the atmosphere. The heat flux into the atmosphere in thesubtropical Pacific is in part balanced by a heat gain by the subarctic Pacific.140° E 180° W 140° W too' w10 ° N100 ° E70' N '^(b)50 ° N1-0.40... 0.00 30°140 ° E 180 ° W 140 ° W 100 ° W1-0.40... 0.03^170 ° N50 ° N30 ° N70 ° N—46.4... 111679-if-1---'50°1-1445.6... 253.6130 ° N(d)140 ° E^180° W 140° W^100° WChapter 5. Model results for the North Pacific Ocean^ 155Figure 5.5: Maps of the bounds on the air-sea exchanges for a) freshwater (Sv), b) heat(PW), c) CO2 (Kmol s') and d) 0 2 (Kmol s').Chapter 5. Model results for the North Pacific Ocean 1560.1S'0, 0.0tO -0.10-u)cEt! -0.2i—tt -0.3its.c -0.42u. -0.5-0tti3 -0.6.cO -0.7Z-0.870 65 60 55 50 45 40 35 30 25 20 15 10 5 0Latitude NorthFigure 5.6: The meridional freshwater transport calculated from the model compared tothe estimates of Baumgartner and Riechel (1975).Chapter 5. Model results for the North Pacific Ocean^ 157The meridional northward heat transport in the Pacific computed by Talley (1984) usingEsbensen and Kushnir (1981), and Clarke and Weare et al., (1981) heat fluxmeasurements demonstrates even uncertainty in the sign of the northward heat transport inthe Pacific (Fig 5.7a). The two curves for Clarke and Weare et al., show the differenceif the data poor regions of the Bering Sea and Sea of Okhotsk are neglected. The need toneglect these regions arises from the idea that the data are seasonally biased and shows asignificant and unexpectedly large annual heat gain by these regions. The meridional heattransports determined by the model are plotted along with the heat transports calculatedfrom Clarke and Weare et al., by Talley (1984) (Fig 5.7b). The direct estimates of heattransport estimates of Bryden et al., (1989), Roemmich and McCallister (1989), andMcBean (1991) are also included in this Figure. At 47°N, the model results are consistentwith the other measurements but the model does allow significantly more equatorial heattransport. The heat transport measurements at 24°N show considerably greater variability.Bryden et al., (1989) calculated a northward heat flux of 0.76 PW, which is in betteragreement with the values of EK in Figure 5.7a. My model estimate also shows anorthward heat flux of about 0.2 PW, slightly greater than the measure from C WE. Thecomparison with Bryden et al., (1989) measurement is of interest because both estimateswere obtained using the TPS24 section but using different calculations. Bryden et al.,(1989) used a traditional station pair calculation using the temperature data from the40•40• 20•80•N 60•1.00.50-0.5-1 0-1.5-2.0-2.5-3.00•^20' 60•SChapter 5. Model results for the North Pacific Ocean^ 158Figure 5.7: The annual mean meridional heat transport in the Pacific Ocean. (a) Thevalues calculated by Talley (1984) for the heat fluxes of Clark and Weare et al.,(solid, dash and dot) and Ebsensen and Kushnir (dot-dash). The heat transport at60°N is assumed to be zero. The solid curve is based on Clark's heat fluxes. Thelong dashes are based on heat fluxes of Weare et al.: The middle dotted curvedeletes heat fluxes in the Bering Sea and Sea of Okhotsk. (b) The heat fluxescalculated from the model along with the direct estimates of heat by Roemmich andMcCallister (1989) (RM), McBean (1991) (M), and Bryden et al., (1989) (B), andfor comparison the middle dotted line from (a) has been redrawn.(b)Chapter 5. Model results for the North Pacific Ocean^ 159to0.8fa_^0.6ro 0.4Cl)c 0.2F.3.i—ris'^0.0a)x -0.2'2co -0.4.ct -0.6oz-0.8..1 .0^*11111/ »111111111/1111111/111t1/1111,t/i1,13111I1.11111 /11/1111111111, 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0Latitude NorthChapter 5. Model results for the North Pacific Ocean^ 160synoptic section for the heat transport; I averaged many different datasets to obtain theaverage temperature in the six layers along the section. In my calculation I employ adiffusive transport to parameterize the eddy transports. In the model run that onlyconserved mass temperature and salinity, the maximum northward heat transport is muchlarger (0.8 PW), negating the discrepancy between the two estimates. This suggests thatthe differences in the way we calculate the heat transport are not that significant. Thesmaller northward heat transport determined by the reference model is a direct result ofthe model trying to satisfy the conservation of phosphate, oxygen, DIC, alkalinity andsilicate.5.2.4 Air-sea exchange of CO2The model results for the bounds on the carbon input into the North Pacific areshown in Figure 5.5c. In the subtropics, the ocean can take up 0 to 0.2 Gt C yr'. Thesign of the subarctic CO 2 air-sea exchange is uncertain but the exchange is not large (-0.07 to 0.04 Gt C yr'). As alluded to in the discussion of the ApCO 2 maps, the ApCO2data is questionable and incomplete in the subarctic Pacific making it difficult to drawconclusion from this data. The CO 2 fluxes calculated at station P showed that this pointwas a weak sink of atmospheric CO2 of 0.7 mol tn -2 yr' (Wong and Chan, 1991) or 0.06Gt C yr' for the entire subarctic region of the model. The estimate of the CO 2 flux ofWong and Chan for the entire subarctic region is comparable to the model results. Wongand Chan data showed that the orean at Station F could 13P- z w.vk neutrrl se ‘r^ fChapter 5. Model results for the North Pacific Ocean^ 161CO2 in July and August and predominantly a CO 2 sink in other months. Wong and Chanbelieve the temporal variation in the gas exchange of CO 2 in the eastern subarctic Pacificwater around Station P may differ from that of other oceanic areas in the high northernlatitudes. In the Bering Sea and the northwest subarctic Pacific the summer depression ofpCO2 in the surface water may exceed 100 /atm (Kelly and Hood, 1971; Gordon et al.,1973; Wong, unpublished data). The strong summer sink of CO 2 in the Alaska gyre andBering Sea is demonstrated in the pCO 2 maps of Tans et al., (1990) that are redrawn inFigure 4.11. The net degassing of CO 2 from the North Pacific of 5 mol m 2 y 1 ( 1.9 Gt Cyr-1 for the subarctic region of the inverse model) was calculated by Thomas et al., (1988)using the seasonal programme data of Takahashi et al., (1986). The critical factorobserved by Thomas et al., (1988) in the calculation of the air-sea flux of CO2 was theneed to use seasonally-sampled 4002 data in deriving the annual fluxes.In the subtropical region, the inverse model calculated a maximum of 0.2 Gt C yr -1enters the Ocean. For the entire North Pacific region of the model, the bounds on the air-sea exchange of CO 2 are between 0-0.2Gt C yr'. Tans et al., (1990) calculated that theNorth Pacific (>15°N; 110°E to 90°W) takes up 0.06 Gt C yr-1 . Although my maximumacceptable uptake of CO 2 is slightly larger than Tans et al., estimate, it clearly shows thatthe North Pacific Ocean is not a significant sink of atmospheric CO 2 . The results of thebudget methods used in this model do show that this technique is able to make reasonableestimates of CO2 uptake in large regions (+0.1GT C yr 1). Recall from chapter two thatthe estimated air-sea exchange from the INDOPAC section was 0.05 ± .2 Gt C yr i forthe North Pacific north of 35°N, which is very consistent with the inverse model.Chapter 5. Model results for the North Pacific Ocean^ 1625.2.5 02 gas exchange ratesThe calculated bounds on the 02 gas exchange rates between the ocean andatmosphere are shown in Figure 5.5d. In general, the subarctic Pacific can act as a largesink of atmospheric 02 while in the subtropics, the North Pacific is an even bigger sourcefor atmospheric 02. The bounds on the 02 gas exchange rate for the North Pacific regionof the model are -467 to 497 Kmol s-1 . An obvious difference between the air-seaexchange of 02 and CO2 is the much larger ranges for the 02 exchanges. The acceptableranges for 02 are more than four times greater than the CO2 ranges. This demonstratesthe difficulty the model has in determining the gas exchange rates of 02.At Station P in the northeast subarctic Pacific Ocean, Thomas et al., (1990)calculated a net 02 degassing of 5.6 mol M-2 yr' from monthly average gas transfercoefficients and 02 concentrations. Thomas et al., concluded from this data that themeasured flux was uncertain due to undersampling and the uncertainty and naturalvariability of 02. The one-dimensional modelling results of Thomas et al., (1989) suggestthat this degassing is the 02 produced by biological activity in the mixed layer. However,the modelling was not able to provide a robust estimate of the annual air-sea exchange of02. Their modelling results suggest that episodic events modify the 02 content by up to 4mol m" in the mixed layer but that gas exchange later draws this content back towards asmooth evolution curve. This suggests that highly sampled 02 data are necessary toresolve the gas exchange between the ocean and atmosphere. The inverse model resultsshow that the subarctic region is a sink, 6.3 to -1. 1 mol m-2 yr- 1 of atmospheric 0,,Chapter 5. Model results for the North Pacific Ocean^ 163opposite in sign to the Thomas et al., (1989) measurements from Station P. The input of02 into the subarctic region of the model is the result of a divergence in the 02 horizontaltransport in this region.5.2.6 Mixing termsFigure 5.8 shows the minimal and maximal values of the isopycnal and diapycnalmixing coefficients in the model solutions. The lower bounds in all the mixingcoefficients are limited only by the a priori bound of zero. The upper bounds on themagnitude of the mixing coefficients are reasonable with the exception of the bottom layerat 24°N and the Bering Sea. The model does a reasonable job of resolving the isopycnalmixing terms. Profiles of the isopycnal mixing coefficients maximum bounds display amaximum value in the surface layer and a nearly constant or decreasing value with depth(except for the bottom layer of region one) (Fig. 5.9).The upper bounds of the diapcynal mixing coefficients appear to be resolved by themodel with the exception of the deep water and in the outcropping of layer 3 with 1 wherethe values attain their a priori bound of 10 cm 2 Profiles of the maximum diapycnalPhotic zone 0.0... 6.3^IChapter 5. Model results for the North Pacific OceanNear surface layera600-.-1+.)aal^AdUnV10001 0.0... 2.9 16410^20^30^40^50^60^70LATITUDE NORTHFigure 5.8: The bounds on the mixing coefficients, the units of the isopycnal anddiapycnal coefficients are 104 m2 s -1 and cm' s -1 respectively.Chapter 5. Model results for the North Pacific Ocean^ 1650 ^200-400-600-800-t000-2000-3000-4000-5000-0^5000^10000^15000^20000Horizontal Diffusivity (rn 2 /s)Figure 5.9: Profiles of the maximum bounds on the isopycnal mixing coefficient for a)subtropical region (solid line) and subarctic region (dashed line).400-600-2000-.,,1IIII■166Chapter 5. Model results for the North Pacific Ocean3000-4000-5000-o^5^ 10Vertical Diffusivity (cm 2/s)Figure 5.10: Profiles of the maximum bounds on the diapycnal mixing coefficient for thesubtropical region (solid) and subarctic region (dash).200-Chapter 5. Model results for the North Pacific Ocean^ 167mixing coefficient show an increase in value with depth (Fig. 5.10). In region one theincrease in mixing is quite gradual, however in region two, the diapycnal values increaserapidly in the upper two layers and then remain relatively constant.The model's ability to determine the isopycnal and diapycnal mixing coefficientsseems to depend on the relative size of the tracer fluxes induced by mixing compared withthe advective tracer fluxes and thus depends on the size of the horizontal and verticaltracer gradient. The vertical and horizontal gradients in the upper ocean are large enoughthat varying the mixing coefficients has a significant effect on the tracer budgets, andconsequently those mixing coefficients are well-determined. However in the deeperwater, the vertical gradients are small and larger diapycnal mixing coefficients arenecessary to produce significant differences in the tracer budgets. This explains why onesees a narrow range of diapycnal mixing coefficients in the upper ocean and a much largerrange in the deeper layers. This same argument can be employed to explain the largecoefficients of the isopycnal mixing in the Bering Sea and in the bottom water and thelarge diapycnal mixing coefficient in the outcropping of NPIW with the euphotic layer.The relatively small areas through which mixing occurs for these coefficients demands thatmuch larger mixing coefficients are required in order for these transports to significantlyaffect the tracer budgets.The solutions with the smallest and largest overall diapycnal and isopycnal mixinghave also been calculated (4) = E kv, E kh). The results of minimizing the diapycnalcoefficients are that the mass, heat, salt, nutrient and carbon balances can be achievedwith no diapycnal mixing and small particle fluxes. The solution with the maximum Chapter 5. Model results for the North Pacific Ocean^ 168diapycnal mixing coefficients also produces a solution with large particle fluxes. Thelinkage between the particle fluxes and diapycnal mixing is a reflection of the increase innutrient concentrations with depth. This allows the downward transport of nutrients byparticle fluxes to be compensated by the upward transport of nutrients by diapycnalmixing. By minimizing the isopycnal mixing coefficients, one generates a solution thatrequires very little mixing; only the surface layer has non-zero isopycnal mixingcoefficients. This solution also has almost no particle fluxes. The solution thatmaximizes the isopycnal mixing coefficients generates a solution that has large particlefluxes.5.2.7 New productionNew production in the model has been studied by calculating the solutions thatminimize and maximize the amount of organic carbon leaving the surface layer as detritalrain. Figure 5.11a shows the maximal values of new production in the model domain.The minimum values are zero for new production which is a reflection of the model'sinability to constrain the lower bounds of the mixing terms. The maximum values of newproduction for the subarctic and subtropical North Pacific are 730 Kmol s -1 (42 g C m'y -1)and 771 Kmol s -1 (12 g C m -2 yr-1) respectively. This geographic pattern of the maximumnew production is consistent with measurements of primary production (Koblentz-Mishkeet al., 1970 and Berger et al., 1989). For comparison with the model output, estimates ofthe primary and new productions are shown in Tablc 5.5. Bcfore100' w(a)Chapter 5. Model results for the North Pacific Ocean70' N -^50' N —30'N -1140° Ei i 140' Wlee w42.0.12.01771.4169Figure 5.11: Maps of the maximum particle fluxes from the surface layer of the modelfor a) organic carbon, b) inorganic carbon, and c) opal. The top number is inKmol s-1 and the bottom number is in mol rn -2 yr-1 .Chapter 5. Model results for the North Pacific Ocean^ 170Table 5.5:^Select production data for the North Pacific.Location^Primary^New^f-ratio^ReferenceProduction^ProductiongC rri2 y1^gC in2 y'Subtropic Ocean^26 1.6^0.06^Eppley and(Oligotrophic) Peterson (1979) 1 '2Subtropics to^51^6.6^0.13^Eppley andSubpolar Peterson (1979) 1 '2Subpolar^73^13.1^0.18^Eppley andPeterson (1979) 1 '2Inshore^124^37.2^0.30^Eppley andPeterson (1979) 1 '2Open Ocean^55^7.7^0.14^Eppley andPacific Peterson (1979) 1 '2N.E. Pacific^130^18^0.14^Martin et al. 1987(oligotrophic 3water)N.E. Pacific^250^42^0.17^Martin et al.Coastal Regions 1987 3N.E. Pacific^121.4^13-17^0.11-.014^Knauer et al.,(oligotrophic 1990 3water)Subarctic North^219 - 365^ Miller (1988) 4PacificBering Sea 100*^—1^Codispoti et al,1986'primary productivity data from Platt and Subbaa Rao (1975) and an empiricalrelationship between primary productivity and new productivity.'primary productivity derived from the Koblentz-Mishke et al., (1970).3sediment trap data from the VERTEX experiment.4productivity measurements from the SUPER experiment*one spring bloomChapter 5. Model results for the North Pacific Ocean^ 171Table 5.6:^A variety of productivity measurements from Station P (50°N and145°W).McAllister (1969)Wheeler and Kokkinakis(1990)Wong (unpublished)Maximum primary productionMinimum primary productionPeak productionf-ratio, June 1987f-ratio, September 1987f-ratio, October 1987f-ratio, May 1988f-ratio, August 1988primary production,August 1987annual mean particle flux,200 mannual mean particle flux,1000 mannual mean particle flux,3800 m136 g C m -2 yr-112 g C m-2 yr-1July0.38+0.060.52+0.270.39+0.110.41+0.120.25±0.05200 to 310 g C m -2yr-15.6 g C m -2 yr-12.7 g C m -2 yr 11.3 g C m -2 yr-1comparing the model results of new production with the estimates given in the Table 5.5,it will be useful to first discuss these measurements in more detail. The global estimatesof primary production have increased since about 1980 and new production even more.For example, several authors have suggested that the annual average f-ratio (newproduction/primary production) for oligotrophic central oceans may be higher than the0.06 value for the oligotrophic central gyres proposed by Eppley and Perterson (1979).Chapter 5. Model results for the North Pacific Ocean^ 172Recent estimates from station P for the f-ratio in the summer and early fall (Table 5.6)produce much larger values than the f-ratio of 0.18 proposed by Eppley and Peterson forthe subpolar ocean. These larger values for the f-ratio in part reflect the time of the yearthe measurements were made. During the year when the productivity is greater than theaverage annual mean value one expects the corresponding f-ratio to also be greater thanthe annual mean value. Production studies in the VERTEX program in the northeastPacific by Martin et al. (1987) and Knauer et al. (1990) have much higher values ofprimary production and new production (Table 5.5) than earlier estimates by Eppley andPeterson (1979). In view of the present discrepancy in the literature, the values ofprimary production and new production require further study.The average of the upper and lower bounds of new production from the model aregreater than the values proposed by Eppley and Peterson but are less than newer estimatesfrom oligotrophic water of the northeast Pacific. Modelling the 02 cycle at Station P,Thomas et al., calculated the new production to be 30 to 88 g C M-2 yr' (C/0=172/106).Wong (unpublished) calculated at Station P the primary productivity to 200 - 310 g C M-2yr' for August 1987. Using the f-ratio calculated by Wheeler and Kolchnakis (1990) forAugust 1988, the estimated new production from Wong data is 50 - 70 g C m2 yr'.From the values presented above it is clear that large differences exist in the estimates ofprimary and new production. In part, the difficulty in comparing measurements arisesfrom the measurements different spatial and temporal sampling. The inverse modelresults for new production in the subarctic and subtropic Pacific are, in general, consistentChapter 5. Model results for the North Pacific Ocean^ 173with various measurements; they are greater than the Eppley and Petersons estimates butless than some of the newer estimates from Station P and the VERTEX experiments.5.2.8 Particle fluxesThe minimum and maximum particle fluxes of organic carbon, CaCO 3 and opalthrough each layer have been determined. For all the particle fluxes, the minimum valueis zero. Figure 5.12 shows profiles of the maximum detrital rain rate of particulateorganic carbon (Fig. 5.12a), CaCO 3 (Fig. 5.12b) and opal (Fig. 5.12c). Flux densitiescan be derived by dividing the rain rates by the surface area of the two regions; thesurface areas of region one and two are 2.48 x 10" m 2 and 7.4 x 10 12 m2 respectively.The particle flux of organic carbon at 100 m is equal to the value of newproduction discussed in the previous section. The model results show a decreasing valueof particle flux with depth; region two particle flux decreases faster with depth than regionone. To get an idea of the values of the molecular ratios linking the particle flux of C,Pand 0 that were being generated by the model, I looked at the solutions that maximizedthe particle flux of: 1) organic carbon, 2) phosphate, and 3) oxygen utilization. One, forthe solution that maximized the particle flux of organic carbon, the -0 2/P ratio equalled170. The value shows good agreement with the value suggested by Takahashi et al.,(1985) and Broecker et al., (1985). Two, the solution for the maximum particle flux ofphosphate produced a C/0 2 ratio of -1.36. Three, the solution that maximized the oxygenutilization flux had a C/P ratio of 125. The three values determined in this manner are,Chapter 5. Model results for the North Pacific Ocean(a) (b)174200-400-600-800-4-)A.•a)A1000-2000-3000-4000-5000- ;200-400-600-800-4....)a,a)A1000--200°-3000-;4000-^rr5000- r/,,,,I10^200^400^600^800^1000Organic Carbon Flux (Kmol/s)0^100^200^300^900Inorganic Carbon Flux (Kmol/s)Figure 5.12: Profiles of the particle fluxes of (a) organic carbon, (b) inorganic carbonand (c) opal material. The solid lines denote the subtropical region and the dashedlines denotes the subarctic region.Chapter 5. Model results for the North Pacific Ocean(c)0200400600800...,ai0)rz100020003000400050001^1^•^I^1^•^1^•0^100 200 300 400 500 600Opal Flux (Kmol/s)175Chapter 5. Model results for the North Pacific Ocean^ 176internally consistent and produced molecular ratios linking organic matter of P:C:0 2 =1:125:-170. The objective functions for this study were chosen to produce interestingsolutions without requiring the desired unknowns in the ratio to be extremized. In thisway the model is free to determine the selected unknowns in the desired ratio.The maximum values for CaCO3 fluxes gave particle fluxes of 6.0 and 15.8 g Cm-2 yr-1 from the surface layers of the subtropics and subarctic respectively. The fluxdensities in the subarctic region are double the subtropical region. A comparison ofparticle fluxes of CaCO 3 with organic carbon showed that CaCO3 was more resistant todissolution than organic carbon. Table 5.7 presents a brief summary of CaCO 3 fluxesfrom sediment traps in the North Pacific. The sediment traps data from Noriki andTsunogai (1986) do show indications that the CaCO3 fluxes are greater in the subarcticPacific than in the subtropics. The maximum particle fluxes in the model are significantlyhigher than the sediment trap data suggesting the values are poorly determined by themodel. The slow redissolution of CaCO 3 with depth shown by the three sediment traps atStation P, is evident in the model results by the small change in the particle fluxes withdepth.The maximum values from the inverse model for the opal fluxes produced fluxdensities in the subarctic of 54 g Si m -2 yr-1 which are nearly an order of magnitudegreater than 5.5 g Si m' yr -1 determined for the subtropics. Selected sediment trap datafor the North Pacific (Table 5.8) does show that the opal flux varies by nearly an order ofmagnitude between the subtropics and subarctic North Pacific. This agrees with the CaCO3 Flux(g C in-2 yri)3.71.4ReferenceMartin and Knauer 1983Noriki and Tsunogai,1986^2.3^Noriki and Tsunogai,19861.0^Noriki and Tsunogai,19860.3^Noriki and Tsunogai,1986Wong unpublishedII^It3.82.82.1Chapter 5. Model results for the North Pacific Ocean^ 177Table 5.7:^Sediment trap measurements of CaCO3 fluxes in the North Pacific.LocationSubtropical NortheastPacific (50m)Subarctic Pacific (1000m)Subarctic Pacific (1000 m)Subtropical Eastern Pacific(500 m)Subtropical Eastern Pacific(500 m)Subarctic Pacific (200 m)Subarctic Pacific (1000 m)Subarctic Pacific (3800 m)model maximum results but the model maximum opal fluxes are considerably greater thanthe sediment trap data. The comparison with sediment traps data is limited usefulnessbecause of the very limited spatial and temporal sampling of the sediment trap data.Although the particle fluxes from the surface layer for the subarctic are high,measurements from the Antarctic have given particle fluxes of 87.6 g Si m" yr' (Norikiand Tsunogai, 1986).Unlike CaCO3 , seawater is everywhere undersaturated with respect to opal. Thesolubility of opal decrease by about 30% for a fall in temperature from 25 to 5°C, thoughOpal Flux(g Si m2 yr')2.71.80.4ReferenceNoriki and Tsunogai, 1986Noriki and Tsunogai, 1986Noriki and Tsunogai, 19860.04^Noriki and Tsunogai, 19867.4^Wong unpublished10.3 I^II7.0Chapter 5. Model results for the North Pacific Ocean^ 178Table 5.8:^Sediment trap measurements of opal flux for the North Pacific.LocationSubarctic Pacific (1000m)Subarctic Pacific (2100 m)Subtropical Eastern Pacific(500 m)Subtropical Eastern Pacific(500 m)Subarctic Pacific (200 m)Subarctic Pacific (1000 m)Subarctic Pacific (3800 m)this is offset somewhat in the deep ocean because the high pressure acts to increase theopal solubility (Bearman, 1989). Inspection of samples from sediment data suggest aconsiderable amount of opal is dissolved at the ocean bottom (Bearman 1989). In orderfor this to occur the opal reaching the sea bed must be rapidly transport in large fast-sinking particles. The model results, like the sediment trap data at station P, do show thata significant amount of opal is dissolved at the ocean bottom, allowing up to 3.7 g Si m2yr' to redissolve in the bottom layer.The model results for the particle fluxes and new production suggest a correlationbetween the particle fluxes and the mixing coefficients. The sensitivity of the newproduction rates to the change in mixing processes suggests that these mixing coefficientscould be better determined by including data for new production and particle fluxes in theChapter 5. Model results for the North Pacific Ocean^ 179model. The potential value of productivity data for the determination of isopycnal anddiapycnal mixing coefficients was carried out using a simple experiment. New productionrates and particle fluxes of organic carbon are incorporated into the model to estimate theimprovement in the mixing coefficients. For this purpose, the minimal and maximalmixing coefficients have been recalculated for a model that constrained the new productionto be 600+300 Kmol s-1 for both regions. With the new constraints on new production,the acceptable bounds on the diapycnal mixing coefficients in the upper 4 layers aretypically reduced by 30% and isopycnal mixing coefficients in the upper 4 layers aretypically reduced by 10%. In the deeper ocean mixing coefficients are unaffected.5.3 MODEL INCLUDING DISSOLVED ORGANIC MATTERIn addition to the inorganic components of phosphate, nitrate, and carbon, recentmeasurements have shown that significant amounts of dissolved organic nitrate (DON) anddissolved organic carbon (DOC) compounds are found in seawater (Sugimura and Suzuki,1988, and Suzuki et al., 1985) (Fig. 5.13). The new method of Sugimura and Suzuki(1988) of high temperature catalytic oxidation (HTCO) of dissolved organic carbon (DOC)extracted up to four times more organic carbon from the near-surface water oceanicwaters and two times more carbon from deep waters than the existing wet-chemicaloxidation methods. Sugimura and Suzuki claimed that much of the new DOC is high-molecular-mass material (Mr > 20,000). The additional DOC extracted by the Sugimuraand Suzuki method appears to have high surface concentrations and large gradients withinChapter 5. Model results for the North Pacific Ocean^ 180the ocean's main thermocline. These qualities suggest that the new DOC must beproduced and broken down by open ocean plankton communities within a decade or two.Throughput of such a large amount of carbon would make the new DOC one of the mostactive carbon reservoirs on the planet. The new higher concentrations of DON and DOCare suspected to play a role in the oceanic nutrient and carbon cycles (Williams andDruffel, 1988).At present the measurement techniques are controversial and the distribution ofdissolved organic compounds in the ocean are not well determined. Recently three papershave been published that re-examine the results of Sugimura and Suzuki. Martin andFitzwater (1992) used the HTCO method to analyze vertical profiles of seawater from59.5°N in the North Atlantic, from the Drake Passage and from the equatorial Pacific.They find very little differences between stations for the DOC concentrations in the deepwater in spite of large differences in 14C age and dissolved oxygen at the three locations.This result suggests that the bacterial consumption of DOC in the ocean's interior does notaccount for much of the observed consumption of oxygen. Martin and Fitzwater do,however, find a very strong DOC gradient in surface water between the equator (130 AM)and 9°N (230 AM) in the equatorial Pacific. Overall, Martin and Fitzwater report thattheir HTCO measurements produced excellent agreement with Suzuki's when the samewater is analyzed.New DOC High molecular wt.Short-livedLabile, eaten by microbesResistant to ultraviolet andchemical oxidations; oxidizableby high temperature catalysisOld DOC Low molecular wt.Long-livedResistant to microbial degradationOxidizable by ultraviolet light andchemical oxidants1000a_a)2000Chapter 5. Model results for the North Pacific OceanDOC (MM/kg)100^200Figure 5.13: Illustration of an oceanic DOC profile indicating the "new" DOC,additional DOC found by the HTCO method of Sugimura and Suzuki, (1988), andthe "old" DOC, that found by older methods (redrawn from Bacastow and Maier-Reimer, 1991).181300Chapter 5. Model results for the North Pacific Ocean^ 182Ogawa and Ogura (1992) compared the HTCO method with the wet chemicaloxidation method and found the HTCO extracted only about one-third more carbon thanthe wet chemistry method. Using the process of ultrafiltration, Ogawa and Ogura foundlittle DOC with molecular masses above 10,000. Contrary to Sugimura and Suzuki, theseauthors suggest that there might be no chemically refractory, high-M,. DOC in seawater.Benner et al. (1992) attempt to characterize the Mr > 1000 fraction using the sameultra filtration technique as Ogawa and Ogura. They find that a third of the surface-waterDOC falls in this size fraction, a result that agrees very well with Ogawa and Ogura's.Although they disagree with many of Sugimura and Suzuki's results, Benner et al.,"concur that the high-Mr in the upper ocean are reactive and support much of theheterotrophic activity in the surface ocean".The one consistent conclusion drawn from these new measurements is that theAOU is not linearly correlated with DOC. In these new reported measurements only twodirect comparisons can be made. Both Martin and Fitzwater (1992) and Benner et al.,(1992) measured water from the Hawaii Ocean Time Series station. Martin and Fitzwaterreport 152 AM for the surface water whereas Benner et al., report only 82 AM.Similarly, large difference exists for the water at the 02 minimum (86 compared to 38AM) and for deep water (112 compared to 41 AM). In part some of the differences in themeasurements can be attributed to whether one subtracts a system blank or not. Benner etal., subtract a system blank of 22 p,M from their raw data; Martin and Fitzwater do notsubtract any blank. The same differences for both the surface and deep water samples (70AM) between Benner et al., and Martin and Fitzwater suggest that system blanks may be Chapter 5. Model results for the North Pacific Ocean^ 183at the heart of the disagreement. Studies by Benner and Stom (reference from Toggweiler1992) showed that the observed blanks ranged from 10 to 50 /AM for the differentcatalysts.The most intriguing aspects of Sugimura and Suzuki's and of Martin andFitzwater's data are the large vertical and horizontal DOC gradients revealed in the upperocean. These gradients cannot be maintained unless large amounts of DOC productionand remineralization are taking place. This reflects Toggweiler's (1992) conclusion thatthe actual size of the DOC pool is less interesting than the role DOC may be playing inthe carbon cycle and marine ecosystems.To address the question of the importance of the dissolved organic nutrients in thenutrient budgets of the ocean, a model was developed that implemented the data fromSugimura and Suzuki (1988) and Suzuki et al., (1985) in a simple way. Toggweiler(1989) showed that a more appropriate correlation for DOM was obtained by plottingDON versus nitrate concentration rather then the AOU versus DOC plot of Sugimura andSuzuki (1988). The plot of DON versus nitrate for the Northwest Pacific is shown inFigure 5.14 (Toggweiler, 1989). The least squares linear fit to this data (r 2 =0.96) is184Chapter 5. Model results for the North Pacific OceanDON (prnol/ I )10^20 30^40 ‘ 50,^surfacewater10int. Water •..—..20 ..=.1-.....041. 30 — slope= —0.8 _cu4....0CUa.—:•—• • 4000m4•40 —^• / —// 0 2 minimum501^1 I^1 IFigure 5.14: DON concentration versus the nitrate from Toggweiler (1989).Chapter 5. Model results for the North Pacific Ocean^ 185given by (Najjar et al., 1992)[DON] = 40.4pmofficg - 0.806[NO3].^ (5.1)By using the [NO3] in the North Pacific, the corresponding DON concentrations( [DON] ) is calculated using the linear equation above. The vertical profiles of DON at24°N and 47°N are shown in Figure 5.15. The addition of the DON to the model requiresthat the tracer budgets of phosphate, DIC, alkalinity and oxygen be modified to includethe DOM. This is accomplished by assuming a constant molecular ratio of P:N:C:02 =1:16:102:-172 for the individual constituents of the DOM.With the inclusion of the DOM as described above, to the model with the inorganictracers one is able to obtain a feasible solution. The inverse solutions obtained from thismodel are nearly identical with the solutions without DOM. The ranges in acceptablevalues for the horizontal transport of DON into the subtropics and subarctic are -0.62 to7.8 Kmol s -1 and -8.9 to 0.16 Kmol s -1 respectively. The highly productive subarcticregion is capable of exporting a small amount of DOM into the subtropics. The smallrange of acceptable values for the horizontal transport of DON for the two regionsemphasizes the modest role played by the horizontal transport of DOM in the carbon andnutrient cycles. This is contrary to Rintoul and Wunsch's (1991) budget studies in theNorth Atlantic which required a southward transport of DON of 119 ± 35 Kmol s-1 across36°N.200-400-600-800-4a.a)a)1000-2000-3000-4000-5000-Chapter 5. Model results for the North Pacific Ocean^ 1861 '1^l'I•I'I'l•0^5 10 15 20 25 30 35 40Dissolved Organic Nitrate (umol/kg)200-400-600-BOO-1000-2000-3000-4000-5000-0^5 10 15 20 25 30 35 40Dissolved Organic Nitrate (umol/kg)Figure 5.15: The vertical profiles of DON at 24° and 47°N.CHAPTER 6. CONCLUSIONThe work presented in this thesis was based on the analysis of tracer fields to inferinformation about the ocean carbon cycle. This work will be summarized in three parts:1) the study of the tracer transports through the 35°N sections;2) the assessment of the performance of the inverse box models whenapplied to the model data generated by the Hamburg model; and3) the factors influencing the carbon, nutrient, heat, and salt content of theNorth Pacific Ocean.In the first part of the thesis (chapter 2), the tracer transports across 35°N werecomputed using the hydrographic data from a synoptic section (INDOPAC) and from theLevitus annual mean section. The computations from the two sections producedsignificant differences in the mass and tracer transports. The study suggested that theLevitus section was inadequate for calculating tracer transports. The tracer transportscalculated from the INDOPAC section were better able to close the tracer budgets of theNorth Pacific than the Levitus section. The transports calculation performed in thischapter pointed out the need to use highly resolved hydrographic data to accuratelydetermine the tracer transports. The calculations reveal the sensitivity of the tracertransports to the estimated Ekman transports and air-sea exchanges of freshwater. Thebudget calculations from the INDOPAC sections suggested that dissolved organic matter(DOM) may play a significant role in the budgets of the nutrient tracers. The limitedresolution of the INDOPAC section made it difficult to confidently assert this conclusion.187Chapter 6. Conclusion^ 188In the second part of the thesis (chapter 3), the inverse box model was applied todata generated from the Hamburg LSGOC-biogeochemical model. In this model, themixing transport of tracers played an important role in closing the tracer budgets.Applying the inverse box model to the temperature, salinity, total CO 2 , alkalinity,phosphate, oxygen, POC, calcite, and 14C fields produced poor results. With the additionof velocity shear information, the inverse box model extracted the correct velocity fieldsand produced air-sea exchanges and detrital rain rates comparable to the known valuesfrom the Hamburg model. This provides some confidence that the inverse box model iscapable of extracting information about the carbon cycle from the tracer fields.In the third part of the thesis (chapters 4-5), inverse box models were formulatedfor the nutrient and carbon budgets of the North Pacific Ocean, and water flow rates,eddy mixing coefficients, particle fluxes and air-sea exchange rates of freshwater, heat,CO2 and 02 were calculated. The model incorporates geostrophy, wind-driven Ekmantransports and budget equations for a suite of seven tracers (temperature, salinity,phosphate, DIC, oxygen, alkalinity, and silicate). As suggested in chapter 2, two highlysampled hydrographic sections across the Pacific at 24°N and 47°N are used to calculatethe geostrophic transports. Historical station data are used and the budgets of mass, heat,salt, phosphate, oxygen, silicate, carbon and alkalinity are simultaneously satisfied in theNorth Pacific Ocean.Feasibility studies using the inverse model showed that feasible solutions existedfor a model that satisfied geostrophy, Ekman transport, and the prescribed Redfield ratios.A reference model was formulated by relaxing constraints on the Ekman transports andChapter 6. Conclusion^ 189Redfield ratios; this model satisfied the Ekman transports to within +25% and theprescribed Redfield ratios to within +20%. Tracer studies with the reference modelshowed that the unknowns are much better constrained when all 7 tracers are included inthe model than by using only a subset of the tracers. Investigation showed the inversesolutions to be insensitive to the model layering and to the prescribed reference level usedin the calculating the geostrophic transports.From the reference inverse box model, the acceptable maximum and minimumbounds for the advective transports, mixing coefficients, air-sea exchanges and particlefluxes were determined. These bounds were determined using the LP algorithm and thecalculated errors in the conservation equations.The deep water transports of the model showed that 3.2 - 7.2 Sv of AABW and3.0 - 11.9 Sv of AAIW enters the North Pacific at 24°N, and 7.3 - 12.1 Sv of NPDWleaves the North Pacific. The estimated transport by the Kuroshi through 24°N was 25 ±5 Sv. In the upper ocean the flow pattern is much more confusing, reflecting the morezonal flow pattern of the North Pacific.The northward transports of freshwater and heat by the model into the NorthPacific were 0.05 ± .06 Sv and 0.12 ± 0.08 PW respectively. The model showed thatthe North Pacific Ocean was not a significant source of heat for the atmosphere. Themodel determined the North Pacific to be a sink of atmospheric CO2 . It was calculatedthat 0.1 ± 0.1 Gt C yr' enters the North Pacific, predominently between 24°N and 47°N.The model was unable to resolve the direction of the air-sea exchange of oxygen in theNorth Pacific, the calculated uptake of oxygen by the ocean was 467 to 497 KmolChapter 6. Conclusion^ 190The inverse model produced horizontal mixing terms that were greatest in thesurface layer and decreased with depth. The vertical mixing coefficients were smallest inthe surface layer and increased with depth. The inverse model showed a close connectionbetween the unknown mixing coefficients and the particle fluxes of organic and inorganiccarbon, and opal. By specifying the new production in the two regions of the model to be600 ± 300 Kmol s -1 , the variance in the vertical and horizontal mixing coefficients arereduced by 30% and 10% respectively.The new production determined in the subarctic region (21 ± 21 g C m -2 yr') was3.5 times greater than the subtropical region (6 ± 6 g C M-2 yr'). The model was notable to resolve the lower limit of new production.The minimum bounds for all particle fluxes of organic and inorganic carbon andopal was zero. The decreases in particle fluxes with depth were consistent with sedimenttrap data. The maximum particle fluxes of CaCO 3 were 16.5 and 43.5 mg C m -2 yr' forthe subtropics and subarctic regions respectively. The maximum particle fluxes of opalshowed the subarctic region capable of producing nearly an order of magnitude larger fluxthan the subtropical region, 148 to 15 mg Si m2 yr-1 respectively.The large ranges in the acceptable values for the air-sea exchange of heat, CO 2 and02, and of the particle fluxes of organic carbon, CaCO 3 and opal material reflect the factthat these processes transport significantly less tracers than horizontal advection. Ideally,the determination of the air-sea exchanges and the biological processes can be thought ofas small residual terms necessary to offset the tracer budget imbalances caused by themuch larger horizontal transports. Two points should be emphasized as a consequence ofChapter 6. Conclusion^ 191this situation. One, the horizontal advective transports of the tracers must be veryaccurately determined in order to extract useful estimates of the air-sea exchanges and thebiological processes. Two, additional information to constrain the air-sea exchanges orbiological processes will play an important role in the model solutions. In the future, asthe measurements of biological productivity and air-sea exchanges of CO 2 increase, thisinformation can easily be incorporated into the inverse model to demand more realisticsolutions.The role of dissolved organic matter (DOM) in the carbon and nutrient budgets inthe North Pacific was investigated. The model used dissolved organic nitrogen (DON)data determined from the nitrate using the linear relationship of DON to nitrate derivedfrom Suzuki et al., (1985) data. For this model, the inclusion of DOM played a smallpart in the carbon and nutrient budgets. The subarctic region lost 4.4 ± 4.5 Kmol s' ofnitrogen and the subtropical region gained 3.6 ± 4.2 Kmol s -1 of nitrogen. The net effectfor the North Pacific was nearly zero. This contradicts the results from the tracertransports across 35°N. The results of the inverse model are much more believeablebecause these results do close the tracer budgets in the North Pacific. The differentresults obtained from the tracer transports across 35°N are attributed to the inadequancy ofthis section in calculating the tracer transports as was discussed in chapter 2.In conclusion I would like to emphasize that further work should be done toinvestigate the role of DOM in the carbon and nutrient budgets. At present there isinsufficient data available to directly include the fields of DON or dissolved organiccarbon in the inverse model. It is expected that this problem will be rectified in the futureChapter 6. Conclusion^ 192as more laboratories develop the ability to reproduce the measurements of Sugimura etal., (1988) and Suzuki et al., (1985). It is also apparent that the inverse box modelapproach should be applied to data that will be acquired by WOCE cruises.193APPENDIX A. THE NUMERICAL DIFFUSION OF THE IMPLICITUPWIND ADVECTION SCHEME USED IN THE LSGOC MODELIn one dimension, with u assumed positive and constant the implicit upwind advectionscheme used in the LSGOC-biogeochemical model is given by (Bacastow and Maier-Reimer,1990)+ At ril l11 =^Ax^Its(A.1)In order to satisfy the continuity of mass in one dimension u must be constant. Thenumerical diffusion of this scheme is obtained by expanding T'1 and Tni_ I in (A.1) around thepoint Tni using Taylor series expansions. For clarity the is and n's are dropped to give theexpanded equationpx - At 2 T _ u Ax2 Txxx +,,,^At T^utTt + x = TTtt + /1 "T xx 6^6(A.2)The 2nd order and higher time derivatives are removed by subtracting various differentiatedequations of (A.2) from (A.2) to giveTfuT_uAx^-uAt)T^maa 2 + 3UZit^2u 24,t 22 xx —6 ^ Ax^Ax 2^) T +x (A.3)The first term on the RHS of (A.3) is a diffusion term with a diffusivity coefficient given by194K = u -4—x (l+u—At ) .2^Az(A.4)For comparison, the numerical diffusion of the explicit advection scheme is (Smolarkiewicz,1983)K = u -L-^Ax11(1 -u—At ) .2 (A.5)The numerical diffusion of the implicit upwind advection scheme is (u 2 At) greater than thenumerical diffusion of the explicit scheme.To estimate the apparent diffusivities of the model from (A.4), for comparison withthe inverse model results I used the rms velocities of the LSGOC model along each of the boxfaces defined in the inverse box model.By considering the implicit upwind advection equation in three dimensions additionalcross derivatives terms are generated. In three dimensions with the (u,v,w) assumed positive(for simplicity) the expanded equation would beuAx ^ 7,^vAy vAtTt +u7;+v7;+w7;^-^+ --(A+^+2^Ax^2^Ay YYwdz wat)T +(1+—Az(uvAt)T„y + (uwAt)T,, + (vwAt)Ty, +. . . (A.6)This equation is presented to show that additional numerical diffusion is generated in threedimensions from the cross derivative terms. In my evaluation of the numerical diffusion, Iwill neglect these terms and evaluate (A.4).195BIBLIOGRAPHYAnderson L.G., D.W. Dryssen, E.P. Jones, and M.G. Lowings, 1983: Inputs and Outputsof salt, freshwater, alkalinity and silica in the Arctic Ocean. Deep Sea Res., 30, 87-94.Bacastow, R., and E. Maier-Reimer, 1991: Dissolved organic carbon in modelingoceanic new production, Global Biogeochemical Cycles, 5, 71 -85.Bacastow, R., and E. Maier-Reimer, 1990; Ocean circulation model of the carboncycle, Climate Dynamics, 4, 95 -125.Bacastow, R., and C. 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