NASA/TM-2013-104606, Vol. 31

Technical Report Series on Global Modeling and

Data Assimilation, Volume 31

Max J. Suarez, Editor

Global Surface Ocean Carbon Estimates in a Model 

Forced by MERRA

Watson W. Gregg, Nancy W. Casey, and Cécile S. Rousseaux 

National Aeronautics and

Space Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771

March 2013
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NASA/TM-2013-104606, Vol. 31

Technical Report Series on Global Modeling and Data Assimilation, 

Volume 31

Max J. Suarez, Editor

Global Surface Ocean Carbon Estimates in a Model 

Forced by MERRA

Watson W. Gregg

NASA Goddard Space Flight Center, Greenbelt, Maryland

Nancy W. Casey

Science Systems and Applications, Inc., Lanham, Maryland

Cécile S. Rousseaux

Universities Space Research Association (GESTAR)

NASA Goddard Space Flight Center, Greenbelt, Maryland

National Aeronautics and

Space Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771

March 2013
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and Universities Space Research Association with the National Aeronautics and Space 

Administration. The United States Government has a non-exclusive, irrevocable, worldwide 

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1

Abstract

MERRA products were used to force an established ocean biogeochemical model to estimate 

surface carbon inventories and fluxes in the global oceans. The results were compared to public 

archives of in situ carbon data and estimates. The model exhibited skill for ocean dissolved 

inorganic carbon (DIC), partial pressure of ocean CO2 (pCO2) and air-sea fluxes (FCO2). The 

MERRA-forced model produced global mean differences of 0.02% (approximately 0.3 μM) for 

DIC, -0.3% (about -1.2 μatm; model lower) for pCO2, and -2.3% (-0.003 mol C m-2y-1) for 

FCO2 compared to in situ estimates. Basin-scale distributions were significantly correlated with 

observations for all three variables (r=0.97, 0.76, and 0.73, P<0.05, respectively for DIC, pCO2, 

and FCO2). All major oceanographic basins were represented as sources to the atmosphere or 

sinks in agreement with in situ estimates. However, there were substantial basin-scale and local 

departures. 
2
3

Table of Contents

List of Figures........................................................................................................................ 4

1 Introduction................................................................................................................... 5

2 Methods........................................................................................................................ 6

2.1 Global Three-Dimensional Circulation Model.............................................................................................. 6

2.2 Data Sets ...................................................................................................................................................................... 9

2.2.1 Forcing Data Sets..........................................................................................................................................................9

2.2.2 Methodological Approach ........................................................................................................................................9

3 Results......................................................................................................................... 10

4 Discussion.................................................................................................................... 13

5 References................................................................................................................... 13

6 Appendix A .................................................................................................................. 18

6.1 NASA Ocean Biogeochemical Model - Equations......................................................................................18

6.2 NASA Ocean Biogeochemical Model - Description...................................................................................19

7 Appendix B: Acknowledgements.................................................................................. 28
4

List of Figures

Figure 1: Interactions among the main components of NOBM, nominal outputs, and forcing fields. IOP 

indicates inherent optical properties. Forcing variables are shown in the gray boxes. MERRA forcing

variables are in bold. Surface pressure and precipitable water effects on surface irradiance play a 

small role in the inorganic carbon results and are ignored in this effort. ....................................8

Figure 2: Pathways and interactions among the components of the biogeochemical processes model, 

illustrating the interactions with the carbon cycle, comprising dissolved inorganic carbon (DIC), 

dissolved organic carbon and exchanges with the atmosphere as a function of the ocean and 

atmosphere partial pressures of CO2 (pCO2). The biological pump is represented by phytoplankton, 

herbivores, nutrients, and detritus. ................................................................................9

Figure 3: Annual surface alkalinity distributions and statistics from the model and data. The model-data 

basin correlation is statistically significant at P<0.05, as indicated by an asterisk. .......................10

Figure 4: Delineation of the 12 major oceanographic basins. ....................................................10

Figure 5: Annual surface dissolved inorganic carbon (DIC) distributions and statistics from the model 

(blue) and data (green). The model-data basin correlation is statistically significant at P<0.05, as 

indicated by an asterisk. Southern, tropical, and northern basins are delineated on the bar graph. 

Error bars indicate the standard deviation. ......................................................................12

Figure 6: Annual partial pressure CO2 (pCO2; 

Figure 7: Annual CO

uatm) distributions and statistics from the model (blue) and 

data (green). The model-data basin correlation is statistically significant at P<0.05, as indicated by an 

asterisk. Southern, tropical, and northern basins are delineated on the bar graph. Error bars indicate 

the standard deviation. .............................................................................................13

2 flux (FCO2) distributions and statistics from the model (blue) and data (green). The 

model-data basin correlation is statistically significant at P<0.05, as indicated by the asterisk. 

Southern, tropical, and northern basins are delineated on the bar graph. A positive flux indicates a 

source to the atmosphere. Error bars indicate the standard deviation. .....................................14
5

1 Introduction

 The Modern-Era Retrospective analysis for Research and Applications (MERRA) project 

represents a next generation of reanalysis products. Utilizing data from NASA Earth observing 

satellites, MERRA is intended to improve upon the widely recognized set of existing reanalysis 

products, primarily by including a more realistic representation of the hydrological cycle 

(Rienecker et al., 2011). A comprehensive approach using advanced data assimilation 

methodologies and modern Earth remote sensing observations, along with state of the art 

atmospheric and hydrological models, MERRA is expected to fully support climate-related 

modeling efforts.

 Here we use MERRA products to force a global ocean biogeochemical model. We seek to 1) 

simulate the distributions and fluxes of carbon components in the global oceans with an explicit, 

prognostic description of the carbon cycle and 2) evaluate the realism of the model results. The 

simulation is accomplished using an established three-dimensional model of the global oceans

containing prognostic representations of biological and chemical constituents involved in the 

ocean carbon cycle. Evaluation is achieved through comparison with observations of surface 

carbon inventories and fluxes.
6

2 Methods

2.1 Global Three-Dimensional Circulation Model 

 Global ocean carbon dynamics are simulated by the NASA Ocean Biogeochemical Model 

(NOBM; Figure 1). A complete description of the model can be found in Appendix 1. It is a 

three-dimensional representation of coupled circulation/ biogeochemical/radiative processes in 

the global oceans (Gregg et al., 2003; Gregg and Casey, 2007). It spans the domain from –84o to 

72o latitude in increments of 1.25o longitude by 2/3o latitude, including only open ocean areas, 

where bottom depth>200m. The biogeochemical processes model contains 4 phytoplankton 

groups, 4 nutrient groups, a single herbivore group, and 3 detrital pools (Figure 2). The 

phytoplankton groups differ in maximum growth rates, sinking rates, nutrient requirements, and 

optical properties. The 4 nutrients are nitrate, regenerated ammonium, silica to regulate diatom 

growth, and iron. Three detrital pools provide for storage of organic material, sinking, and 

eventual remineralization. 

Figure 1. Interactions among the main components of NOBM, nominal outputs, and forcing fields. IOP indicates 

inherent optical properties. Forcing variables are shown in the gray boxes. MERRA forcing variables are in bold. 

Surface pressure and precipitable water effects on surface irradiance play a small role in the inorganic carbon results 

and are ignored in this effort.

 Carbon cycling involves dissolved organic carbon (DOC) and dissolved inorganic carbon 

(DIC; Figure 2). DOC has sources from phytoplankton, herbivores, and carbon detritus, and a 

sink to DIC. DIC has sources from phytoplankton, herbivores, carbon detritus, and DOC, and 

communicates with the atmosphere, which can be either a source or sink. The ecosystem sink 

for DIC is phytoplankton, through photosynthesis. This represents the biological pump portion 

of the carbon dynamics. The solubility pump portion is represented by the interactions among 

temperature, alkalinity (parameterized as a function of salinity), silica, and phosphate 

(parameterized as a function of nitrate). The alkalinity/salinity parameterization utilizes the 

spatial variability of salinity in the model adjusted to mean alkalinity 
7

 TA = TA S/

where TA is total alkalinity and S is salinity. The underscore represents global mean values. 

S

TA

is specified as 2310 μE kg-1 (Ocean Model Intercomparison Project (OCMIP; 

www.ipsl.jussieu.fr/OCMIP) and S as 34.8 PSU (global model mean). Since the model contains 

nitrate but not phosphate, we adjust nitrate by multiplying by 0.1. This is derived from the 

global mean ratio of nitrate to phosphate from the National Oceanographic Data Center 

(Conkright et al., 2002) for their top three standard levels. The calculations for the solubility 

pump follow the standards set by the Ocean Model Intercomparison Project (reference above). 

We employ a locally-developed lookup table valid over modern ranges of DIC, salinity, 

temperature, and nutrients for computational efficiency, at no cost to accuracy. Air-sea CO2

exchange uses the Wanninkhof (1992) formulation, as is common in global and regional ocean 

carbon models (e.g., McKinley et al., 2006).

Figure 2. Pathways and interactions among the components of the biogeochemical processes model, illustrating the 

interactions with the carbon cycle, comprising dissolved inorganic carbon (DIC), dissolved organic carbon and 

exchanges with the atmosphere as a function of the ocean and atmosphere partial pressures of CO2 (pCO2). The

biological pump is represented by phytoplankton, herbivores, nutrients, and detritus.

 We acknowledge that the parameterization of alkalinity using salinity is a simplification. 

However, the relationship in the modern oceans is robust, especially in tropical and subtropical 

oceans (Millero et al., 1998; Key et al., 2004; Lee et al., 2006) and has been recommended for 

international carbon model intercomparison efforts (www.ipsl.jussieu.fr/OCMIP). Furthermore, 

the salinity-parameterization of alkalinity used in the model compares favorably globally and 

over major oceanographic basins with in situ data sets for the modern oceans (Figure 3). The 

basins are shown in Figure 4. 

 NOBM undergoes spin-up for 200 years under climatological forcing from MERRA. Initial 

conditions for DIC are derived from the Global Data Analysis Project (GLODAP; Key et al., 

2004). We average DIC over oceanographic basins and depth and use these mean values for 

initial conditions. DOC initial conditions are set to 0 μM. Other initial conditions are described 

in Gregg and Casey (2007). The first ten years of the run show a net pCO2 difference ΔpCO2
8

(year 10-year 1) of -0.982 μatm, at the first hundred years the 10-year ΔpCO2 (year 100-year 91) 

is 0.413 μatm, and at 200 years, the 10-year ΔpCO2

Alkalinity

2200

2250

2300

2350

2400

2450

2500

2200 2250 2300 2350 2400 2450 2500

Data (uEq l-1)

Model (uEq l-1)

N Pacific

Eq Pacific

N Cen Pacific

Eq Indian

Antarctic

 N 

Indian

S Indian

N Atlantic

S Pacific

Eq Atlantic S Atlantic

N Cen Atlantic

(year 200-year 191) is 0.102 μatm.

Figure 3. Annual surface alkalinity distributions and statistics from the model and data. The model-data basin 

correlation is statistically significant at P<0.05, as indicated by an asterisk. 

Figure 4. Delineation of the 12 major oceanographic basins.
9

2.2 Data Sets

2.2.1 Forcing Data Sets

 Forcing data sets are shown in Figure 1. Monthly climatologies are used in all cases. All 

except soil dust (iron), ozone, clouds, and atmospheric CO2 are obtained from MERRA 

products. Ozone is from the Total Ozone Mapping Spectrometer and Ozone Monitoring 

Instrument, and soil dust deposition is from Ginoux et al. (2001). Cloud data (cover and liquid 

water path) are obtained from the International Satellite Cloud Climatology Project. 

Atmospheric CO2 is taken from the Lamont-Doherty Earth Observatory (LDEO) data set 

(Takahashi et al., 2009), using a mean over the entire range of observations of 358.7 μatm. 

Although the ocean pCO2 observations are nominally normalized to the year 2000 (Takahashi et 

al., 2009), we keep the mean atmospheric value from the data to help represent the spatial 

variability at the time of measurement. Our emphasis is to understand how the simulated surface 

carbon components compare with in situ data sets, so using atmospheric values from these 

datasets facilitates the comparison.

Comparison Data Sets

 The main outputs of interest in this effort are dissolved inorganic carbon (DIC), partial pressure 

of CO2 (pCO2), and the flux of CO2 (FCO2, notation following Arrigo et al., 2010; Doney et al., 

2009), representing the exchange of carbon between the atmosphere and ocean (positive is 

defined upward, indicating a source to the atmosphere). DIC data sets are obtained from 

GLODAP (Key et al., 2004), which are mapped on a 1o horizontal grid with 33 standard depth 

levels (http://cdiac.ornl.gov/oceans/glodap/). pCO2 and FCO2 data sets are mapped on a 5o

longitude by 4o

(

latitude horizontal grid and are surface only. They are obtained from the 

Lamont-Doherty Earth Observatory (LDEO)

http://cdiac.ornl.gov/oceans/LDEO_Underway_Database/index.html; Takahashi et al., 2009).

2.2.2 Methodological Approach

 The global model NOBM is forced with the MERRA variables shown in bold in Figure 1. The 

model is spun up for 199 years using monthly climatologies of MERRA forcing. In the 200th

year of simulation, model results of surface ocean carbon are compared graphically and 

statistically with climatological in situ data sets and estimates from GLODAP (DIC) and LDEO 

(pCO2 and FCO2). Results are evaluated globally and regionally in 12 major oceanographic 

basins (Figure 4). Statistical comparisons include global and basin differences between model 

and data global and regional means, expressed as percent, and correlation analysis. Our 

emphasis is on large scale results, so our correlation analysis is performed across the basins 

(N=12, with 10 degrees of freedom). All analyses here are performed for annual mean results, 

and the data sets are converted to the NOBM spatial grid prior to comparison.
10

3 Results

 Surface DIC from NOBM compares favorably with in situ data (Figure 5). There is substantial 

geographical similarity, and basins follow similar patterns. The global difference is 0.02%, 

representing ΔDIC=0.3μM, with a correlation across basins of 0.97, which is statistically 

significant at P<0.05. The most notable differences are the tropical upwelling regions. 

Upwelling in the Equatorial Pacific is not apparent in the in situ data, while it is prominent in the 

model. The in situ data show a depression in DIC in the Equatorial Atlantic upwelling region, 

which is in contrast to an increase seen in the model. The basin mean, however, is in agreement 

(Figure 5). The model also has modestly lower DIC in most of the Antarctic. The largest basin 

difference is 1.2% in the Equatorial Indian and Pacific (ΔDIC=24.5μM and ΔDIC=23.3μM, 

respectively). The remaining basin differences are <1%.

Figure 5. Annual surface dissolved inorganic carbon (DIC) distributions and statistics from the model (blue) and 

data (green). The model-data basin correlation is statistically significant at P<0.05, as indicated by an asterisk. 

Southern, tropical, and northern basins are delineated on the bar graph. Error bars indicate the standard deviation.
11

 There is also considerable similarity between the model and in situ data in global pCO2

distributions (Figure 6). The global difference is -0.3% (model lower), which is a difference of -

1.2 μatm. The correlation across basins is statistically significant with r = 0.76. The model 

pCO2 distributions are in general agreement in the tropical Pacific upwelling, in contrast with 

DIC, and there is no depression in the tropical Atlantic in the pCO2 data. There is an east-west 

departure in the North and Equatorial Indian basins between the model and data, with lower 

values in the model in the west, and higher values in the east. There is much more spatial 

variability in the model, as seen in the maps and also the standard deviations (Figure 6). The 

largest basin difference is -8.9% in the South Atlantic (ΔpCO2=-32.3μatm) followed by the 

Equatorial Indian at 4.3% (ΔpCO2=16.1μatm). The remaining basin differences are <4%. The 

largest local discrepancies are in the eastern South Pacific and Atlantic, where the model exhibits 

two regions of depressed pCO2 relative to the data, representing about a 35% difference. 

Figure 6. Annual partial pressure CO2 (pCO2

 There are many areas of agreement in the flux of CO

μatm) distributions and statistics from the model (blue) and data 

(green). The model-data basin correlation is statistically significant at P<0.05, as indicated by an asterisk. Southern, 

tropical, and northern basins are delineated on the bar graph. Error bars indicate the standard deviation.

2 (FCO2) between the model and in situ 

estimates, but there are also many areas of disagreement and they are more pronounced than with 
12

DIC and pCO2 (Figure 7). The global difference is -2.3%, representing ΔFCO2=0.003 mol C m2

y-1. Like DIC and pCO2, the basin correlation is statistically significant (r=0.73, P<0.05). The 

sign of the flux (source or sink) is the same for model and in situ estimates in all the basins, but 

there are large differences in some basins, such as the South Atlantic and Pacific, North Indian, 

Equatorial Atlantic, and North Pacific. 

Figure 7. Annual CO2 flux (FCO2

 There is much greater spatial variability in the model than the in situ estimates of air-sea flux, 

as indicated in the maps and the standard deviations of the basin means (Figure 7). Locally, 

there are major sinks represented in the model in the northeastern portions of the South Pacific 

and Atlantic that do not appear in the data estimates (Figure 7). The Antarctic exhibits regions of 

strong sources that are also not apparent in the data. The location of sources and sinks in the 

North and Equatorial Indian basins are switched in the model from the data, where the model 

shows a sink in the west and a source in the east, while the data show the reverse pattern.

) distributions and statistics from the model (blue) and data (green). The modeldata basin correlation is statistically significant at P<0.05, as indicated by the asterisk. Southern, tropical, and 

northern basins are delineated on the bar graph. A positive flux indicates a source to the atmosphere. Error bars 

indicate the standard deviation.
13

4 Discussion

 The MERRA-forced biogeochemical model (NOBM) produces global estimates of DIC, pCO2, 

and FCO2 to within a few percent of corresponding in situ data sets and estimates. The global 

mean difference is 0.02%, -0.3%, and -2.3% respectively for DIC, pCO2, and FCO2

 We acknowledge that the agreement for DIC is perhaps not surprising, since it was used for 

initial conditions. But it is noteworthy that the model is able to hold these large scale 

distributions over 200 years, and also exhibit substantial agreement with smaller scale 

distributions (Figure 5). We note that, in contrast to pCO

, and all show 

statistically positive correlation with data (P<0.05) across the 12 major oceanographic basins. 

Our emphasis here is global and basin scales representations of ocean carbon surface inventories 

and fluxes, as appropriate for a global model, and the results suggest that NOBM, forced by 

MERRA atmospheric and oceanic variables, possesses skill for simulating ocean carbon 

quantities at these large spatial scales.

2 and FCO2

 The global scale agreement of carbon estimates from the model with in situ sources is 

encouraging, and is the main emphasis here, but it is notable that at smaller scales the agreement 

is not as good. Basin and local discrepancies increase as one evaluates the carbon from DIC to 

pCO

, the spatial variability of

model DIC, as represented by the standard deviation, is similar to in situ data on global and basin 

scales. 

2 to FCO2. The increase in basin and local scales from pCO2 to FCO2 is a reflection of the 

fact that small discrepancies between model and data in DIC and pCO2 can produce important 

differences in FCO2. Thus FCO2 is sensitive to small errors in DIC and pCO2

 We note that use of atmospheric pCO

, and it can be a 

challenge to represent this well in models, especially at smaller scales and using a global model.

2 for year 2000 only modestly changes the results shown 

here. Specifically, the global mean difference is 0.3%, 2.2%, and 7.8% respectively for DIC, 

pCO2, and FCO2, and again all show statistically positive correlation with data (P<0.05) across 

the 12 major oceanographic basins. The differences represent a stronger flux into the oceans as 

expected from the higher atmospheric pCO2

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Fritz, J.J. and W.M. Balch, 1996. A light-limited continuous culture study of Emiliana huxleyi: 

Determination of coccolith detachment and its relevance to cell sinking. Journal of 

Experimental Marine Biology and Ecology 207: 127-147.

Fung, I.Y., S.K. Meyn, I. Tegen, S.C. Doney, J.G. John, and J.K.B. Bishop, 2000. Iron supply 

and demand in the upper ocean. Global Biogeochemical Cycles 14: 281-295.

Furnas, M.J., 1991. Net in situ growth rates of phytoplankton in an oligotrophic, tropical shelf 

ecosystem. Limnology and Oceanography 36: 13-29.

Gavis, J., R.R.L. Guillard, and B.L. Woodward, 1981. Cupric ion activity and the growth of 

phytoplankton clones isolated from different marine environments. Journal of Marine 

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2581–2589.

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maritime atmospheres. Limnology and Oceanography 35: 1657-1675.

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Gregg, W.W., P. Ginoux, P.S. Schopf, and N.W. Casey, 2003. Phytoplankton and Iron: 

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18

6 Appendix A

6.1 NASA Ocean Biogeochemical Model - Equations

The governing equations of the model are

Phytoplankton

(A1)

i = 1 => diatoms

i = 2 => chlorophytes

i = 3 => cyanobacteria

i = 4 => coccolithophores

Nutrients

(A2)

(A3)

(A4)

(A5)

NN

N

= nitrate

A

N

= ammonium

S

N

= silica

F

 

= dissolved iron

Herbivores

(A6)

Detritus

(A7)
19

(A8)

(A9)

DC

D

= carbon/nitrogen detritus

S

D

= silica detritus

F = iron detritus

Carbon

Φ δ∑μiPi + Φ ωH + λDDC – φDOC (A10)

(A11)

where the symbols and values are identified in Table 1. Bold denotes a vector quantity. All 

biological processes are assumed to cease in the presence of sea ice, in proportion to the fraction 

of sea ice cover, which is included as an external forcing field.

6.2 NASA Ocean Biogeochemical Model - Description

Circulation Model

The Ocean General Circulation Model (OGCM) is a reduced gravity representation of circulation 

fields (Schopf and Loughe, 1995). It is global in scale, extending from near the South Pole to 

72o N, in increments of 2/3o latitude and 1 1/4o

Radiative Model

longitude, comprising all regions where bottom 

depth > 200m. The model contains 14 vertical layers, in quasi-isopycnal coordinates, and is 

driven by wind stress, sea surface temperature, and shortwave radiation.

 Radiative transfer calculations provide the underwater irradiance fields necessary to drive 

growth of the phytoplankton groups, and interact with the heat budget. The Ocean-Atmosphere 

Radiative Model (OARM; Gregg, 2002) contains a treatment of the spectral and directional 

properties of radiative transfer in the oceans, and explicitly accounts for clouds. The 

atmospheric radiative model is based on the Gregg and Carder (1990) spectral model, extended 

to the spectral regions 200 nm to 4 μm. It requires external monthly climatologies of cloud 

properties (cloud cover and liquid water path), surface pressure, wind speeds, relative humidity, 

precipitable water, and ozone. Aerosols are considered to be strictly of marine origin and are 

computed as in Gregg and Carder (1990).
20

 Oceanic radiative properties are driven by water absorption and scattering, the optical 

properties of the phytoplankton groups, and chromophoric dissolved organic matter (CDOM). 

Three irradiance paths are enabled: a downwelling direct path, a downwelling diffuse (scattered) 

path, and an upwelling diffuse path. All oceanic radiative calculations include the spectral nature 

of the irradiance. 

 Optical properties of coccolithophores and other phytoplankton groups were derived from 

laboratory studies. Their values and references can be found in Gregg (2002).

Phytoplankton

 The growth formulation includes dependence on total irradiance (ET), nitrogen as nitrate plus 

ammonium (NT), silica (Si – for diatoms only), iron (Fe), and temperature (T)

, (A12)

where i indicates the phytoplankton functional group index (in order, diatoms, chlorophytes, 

cyanobacteria, and coccolithophores), μ is the total specific growth rate (d-1

) of phytoplankton, 

μma x is the maximum growth rate at 20oC (Table 1). The term μ(ET) represents the growth rate 

as a function solely of the total irradiance (μmol quanta m-2s

-1

), 

, (A13)

where kE is the irradiance at which μ = 0.5μm and equals 0.5 Ik, where Ik is the light saturation 

parameter. The nutrient-dependent growth terms are

(A14)

(A15)

(A16)

(Gregg and Walsh, 1992)

(A17)

. (A18)

Temperature-dependent growth is from Eppley (1972)

(A19)
21

which produces a temperature-growth factor normalized to 20oC. The term G in Eq. A12 is an 

additional adjustment used for the cyanobacteria component that reduces their growth rate in 

cold water (<15oC)

. (A20)

Gi = 1 for the other three phytoplankton components (i=1,2,4) where 0.0294 is in units of per 

degree Celsius. When T>15o

C, G3

 The cyanobacteria component possesses a modest ability to fix nitrogen from the water 

column, as observed in Trichodesmium spp. (Carpenter & Romans 1991). The nitrogen fixation 

is expressed as additional growth occurring when nitrogen availability is <(k

reaches its maximum value of 1. This effect conforms to 

observations that cyanobacteria are scarce in cold waters (Agawin et al., 2000; 1998). 

N)3, 

, (A21)

where the index 3 indicates cyanobacteria. The biomass dependence represents a progressive 

community changeover from non-N-fixing cyanobacteria to N-fixing bacteria as the total 

population declines under nitrogen-stressed conditions. The total N-limited growth rate plus the 

additional growth derived from N-fixation is not allowed to exceed the growth rate where total 

nitrogen = (kN)3. 

 Photoadaptation is simulated by stipulating 3 states: 50, 150 and 200 (μmol quanta m

No accounting for denitrification is made in the model. 

-2

s

-1

 Mean irradiance is computed during daylight hours, and then the phytoplankton photoadaptive 

state is classified accordingly. This calculation is only performed once per day to simulate a 

delayed photoadaptation response. Light saturation constants for the three light levels are 

provided in Table 1.

). 

This is based on laboratory studies which typically divided experiments into low, medium, and 

high classes of light adaptation. Carbon:chlorophyll ratios (Φ) are kept constant at 50 g:g for 

mass conservation.

 Phytoplankton group physiological parameters μm, Ik, and kN,S,F are derived from carefully 

controlled, inter-comparative laboratory studies. We require that at least two of the groups are 

involved simultaneously in order to utilize the experimental results. For μm

 Light saturation parameters, I

mean values of the 

relative growth rates are derived from the results of Ben-Amotz and Gilboa (1980), Brand et al. 

(1986, 1983), Eppley et al. (1969), Falkowski et al. (1985), Furnas (1991), Gavis et al. (1981), 

Goldman and Glibert (1982), Humphrey (1979), Subba Rao (1981), and Sunda and Huntsman 

(1995).

k, are formulated for the three irradiance categories used to define 

photoadaptation. Mean values are summarized from the reports of Barlow and Alberte (1985), 

Bates and Platt (1984), Langdon (1987), Perry et al. (1981), Sakshaug and Andresen (1986), and 

Wyman and Fay (1986).
22

 The coccolithophore half-saturation constant for nitrogen (kN) was observed by Eppley (1969) 

to be one-half the value of diatoms. Cyanobacteria kN is set slightly lower than 

coccolithophores, assuming small particle size leads to improved nutrient uptake efficiency. 

Chlorophyte kN is set at one-third the departure between diatoms and coccolithophores. The 

diatom kN

 Phytoplankton vector sinking is treated as additional advection in the z-direction. Sinking rates 

are specified at 31

is arbitrarily set to 1 μM.

o

C and derived from Stokes Law using representative phytoplankton sizes 

from Ahn et al. (1992), Bricaud and Morel (1986), Bricaud et al. (1983; 1988), Dubinsky and 

Berman (1986), Kirk (1980); Mitchell and Kiefer (1988), Morel (1987), Morel and Bricaud 

(1981), and Sathyendranath et al. (1987), for the individual groups. The rates are adjusted by 

viscosity according to Stokes Law (Csanady, 1986), which is parameterized here by temperature

. (A22)

Coccolithophore sinking rates are allowed to vary as a function of growth rate from 0.3 to 1.4 m 

d-1 based on observations by Fritz and Balch (1996). A linear relationship is assumed

, (A23)

where ws is the sinking rate of coccolithophores (m d-1), μ(high) is the highest growth rate 

actually achieved for the previous day, and the subscript 4 represents coccolithophores.

Nutrients

 The diversity in the processes affecting the four nutrient groups requires elucidation in 4 

separate equations, unlike the phytoplankton. All are taken up by phytoplankton growth, with 

silica subject only to diatom uptake (note the subscript=1 in Eq. A4 denoting diatoms). For three 

of the nutrients, nitrate, silica, and dissolved iron, corresponding detrital pools remineralize to 

return nutrients previously uptaken by phytoplankton. There is no detrital pool for ammonium, 

which is excreted as a function of herbivore grazing, and as a function of higher order ingestion 

of herbivores, represented by the term n2H2 in Eqs. A3, A5, A6, A7, and A9. Dissolved iron 

also has an excretion pathway, but nitrate and silica do not. The nutrient to chlorophyll ratios, 

denoted b in Eqs. A2-A5, are derived from Redfield ratios (Table 1) and the carbon:chlorophyll 

(Φ) ratio is constant. 

(A24)

(A25)

. (A26)

 As in Gregg et al. (2003) dust deposition fields are derived from Ginoux et al. (2001). In this 

model, four dust size fractions are transported, corresponding to clay (smallest) and three increasing 

fractions of silt. The iron content is assumed to vary among the clay and silt fractions as follows: 

clay = 3.5% iron, silt = 1.2% iron (Fung et al., 2000). Iron solubility is assumed at 2% for all 
23

fractions, which is toward the low end of current estimates (Fung et al., 2000), but is the same as 

used by Moore et al. (2004). The bottom boundary condition is 0.6 nM (Archer and Johnson,

2000).

 Iron scavenging is implemented in this version of NOBM. It is set at 2.74x10-5 d-1 at low iron 

concentrations (<0.6nM; Moore et al., 2002) and 50 times this rate at higher concentrations. A 

smooth transition is enabled as in Moore et al. (2002).

(A27)

. (A28)

Herbivores

 Grazing uses an Ivlev formulation (McGillicuddy et al., 1995), 

. (A29)

RH is the maximum grazing rate at 20o C (γm) adjusted by temperature

. (A30)

The temperature-dependence for grazing is more linear than that for phytoplankton, reflecting 

the larger size of their overall community. The grazing represents the total loss of phytoplankton 

to herbivores, as indicated by the summation symbol, but is applied to the individual 

phytoplankton functional groups proportionately to their relative abundances. This enables 

herbivore grazing to self-adapt the prevailing phytoplankton community.

 The two loss terms in Eq. A6 represent the death of herbivores (η1H) and higher order 

heterotrophic losses (η2H2

). These formulations and parameters (Table 1) were taken from 

McGillicuddy et al. (1995).

Detritus

 Three detrital components represent the three major nutrient elements, carbon/nitrogen, silica, 

and iron (Eq. A6-A9). The nitrogen detritus is kept as carbon in the model, but since the C:N 

ratio is constant, it is simple to convert when needed. All are subject to advection, diffusion and 

sinking. Detrital sinking, like phytoplankton sinking, is dependent on viscosity parameterized 

here in terms of temperature, using the same formulation. Remineralization, κ, is also 

temperature-dependent, and uses the phytoplankton growth-dependence term R in Eq. A19. 

Silica contained in the diatom component of phytoplankton is assumed to pass through 

herbivores upon grazing directly into the silica detritus pool. No silica remains in the herbivore 

component at any time.
24

Carbon

 Dissolved organic carbon cycling is taken from Aumont et al. (2002), with conversions added 

for compatibility with NOBM units. In addition, all parameters are temperature-dependent, 

unlike Aumont et al. (2002), using the phytoplankton temperature dependence defined in Eq. 

A19. Following Aumont et al. (2002), excretion of DOC by the herbivore component is

, (A31)

where rH is the herbivore excretion rate at 20oC, and Ho is the half-saturation constant for 

excretion (Table 1). Ho is adjusted from units of μM carbon in Aumont et al. (2002) to mg m-3

chlorophyll to conform to the NOBM units for herbivores. Bacterial degradation of DOC is 

represented by 

, (A32)

where λDOC is the DOC remineralization rate and K1 and K2 are half-saturation constants for 

remineralization (Aumont et al., 2002; Table 1). Aumont et al. (2002) used phosphate, so here 

we substitute nitrate, since phosphate is not available in NOBM. Again parameters are allowed 

to vary as a function of temperature. In addition, the value for K1

 Dissolved inorganic carbon has a single sink, uptake by phytoplankton during photosynthesis, 

and sources deriving from respiration by phytoplankton Ω in the process of growth, herbivores Θ 

at all times, and bacteria φ in the process of degrading DOC. There is also an interaction with 

the atmosphere (AO

was increased by a factor of 

10 to convert to nitrate rather than phosphate. According to Conkright et al. (1994), nitrate 

contours generally follow phosphate but nitrate concentrations are approximately 10 times 

higher.

CO2) which can be a source or a sink depending upon the difference in partial 

pressures of CO2 in the ocean and atmosphere (ΔpCO2), and the ability for gas to transfer across 

the ocean surface interface. These complex processes are follow procedures described by the 

Ocean Carbon Model Intercomparison Project (Dutay et al., 2002; Doney et al., 2004; 

http://www.ipsl.jussieu.fr/OCMIP/).
25

Table 1. Notation, parameters, and variables for NOBM. Values are provided for the parameters and ranges are 

provided for the variables. When a parameter varies according to temperature, the value at a specified temperature 

is shown and identified. Nutrient/chlorophyll ratios are variable because of photadaptation-dependence, and only 

the range is shown, corresponding to low-, and high-light adaptation, and therefore also corresponding to 

C:chlorophyll ratios of 20 to 80 g g-1

. All time units are converted to s-1 before use in A(1) to A(11).

Symbol Parameter/Variable Value Units

General

K Diffusivity Variable m

2

s

∇

-1

3D Gradient operator none none

V 3D Vector velocity Variable m s

L

-1

Layer thickness Variable m

Phytoplankton

ws Sinking rate of phytoplankton at 31°C

Diatoms 0.75 m d-1

Chlorophytes 0.25 m d-1

Cyanobacteria 0.0085 m d-1

Coccolithophores 0.3-1.4 m d

μ

-1

Specific growth rate of phytoplankton maximum (μm) at 20°C:

Diatoms 2.00 d-1

Chlorophytes 1.68 d-1

Cyanobacteria 1.33 d-1

Coccolithophores 1.50 d

κ

-1

Senescence rate 0.05 d

k

-1

E Half-saturation for growth as function of quota 0.5Ik μmol quanta m-2

s

E

-1

T Total quanta (direct+diffuse) variable μmol quanta m-2

s

R

-1

Temperature dependence for growth 0.25-9.4 none

G Temperature-dependence for cyanobacteria growth 0.5-1.0 none

Ik Light Saturation

Light level: Low (50) Medium (150) High (200)

diatoms 90.0 93.0 184.0 μmol quanta m-2s

-1

chlorophytes 96.9 87.0 143.7 μmol quanta m-2s

-1

cyanobacteria 65.1 66.0 47.0 μmol quanta m-2 s

-1

coccolithophore 56.1 71.2 165.4 μmol quanta m-2s

Nutrients (N)

-1

bN,S,F Nutrient:chlorophyll ratio

Nitrogen 0.63 μM (μg l-1

)

-1

Silica 1.26 μM (μg l-1

)

-1

iron 0.03 μM (μg l-1

)

ε

-1

Nutrient excretion

Nitrate 0.0 d-1

Ammonium 0.10 d-1

Silica 0.0 d-1

Iron 0.10 d-1
26

kN Half-saturation constant nitrogen/carbon

Diatoms 1.0 μM

Chlorophytes 0.67 μM

Cyanobacteria 0.45 μM

Coccolithophores 0.50 μM

KS Half-saturation constant silica

Diatoms 0.2 μM

KF Half-saturation constant iron

Diatoms 0.12 nM

Chlorophytes 0.09 nM

Cyanobacteria 0.08 nM

coccolithophores 0.08 nM

θ Iron scavenging rate

Low iron (<0.06nM) 2.74x10 d -5 -1

High iron ( 1.37x10 d -3

A

-1

Fe Atmospheric deposition of iron 0.03-967.0 nmol m-2 d

C:N

-1

Carbon:nitrogen ratio 79.5 μg l-1 (μM )

C:S

-1

Carbon:silica ratio 79.5 μg l-1 (μM )

C:Fe

-1

Carbon:iron ratio 1800 μg l-1 (nM )

Herbivores (H)

-1

γ Grazing rate maximum (γm) at 20°C 1.2 d

Λ

-1

Ivlev constant 1.0 (μg l-1

)

η

-1

1, η2 Heterotrophic loss rates 0.1,0.5 d

R

-1

H Temperature-dependence for grazing 0.75-2.7 none

Detritus (D)

wd Sinking rate of detritus at 31oC

Carbon/nitrogen detritus 40.0 m d-1

Silica detritus 50.0 m d-1

Iron detritus 5.0 m d

α

-1

C,S,F Remineralization rate at 20o

C

Carbon/nitrate 0.01 d-1

Silica 0.05 d-1

iron 0.50 d

Φ

-1

Carbon:chlorophyll ratio Variable g g

Carbon (DOC, DIC)

-1

δ Phytoplankton DOC exudation fraction 0.05 none

rH Excretion rate of DOC by herbivores at 20°C 0.05 d

H

-1

Half-saturation constant for herbivore excretion of 

DOC

o 0.14 mg m

λ

-3

D Detrital breakdown rate at 20°C 0.05 d

λ

-1

DOC Remineralization rate of DOC to nitrate 0.005 d

ω

-1

Herbivore excretion function for DOC variable d

Ω

-1

Phytoplankton respiration fraction 0.05 none

Θ Herbivore respiration 0.05 d-1
27

Φ Bacterial degradation of DOC to DIC variable d

K

-1

First half-saturation constant for remineralization to 

nitrate

1 3.0 μM

K Second half-saturation constant for

remineralization to nitrate

2 15.0 μM

AOCO2 Atmospheric-oceanic CO2 Equilibration Variable μatm
28

7 Appendix B: Acknowledgements

 We thank the NASA/MERRA Project, Lamont-Doherty Earth Observatory, NOAA Carbon 

Dioxide Information Analysis Center, and the NOAA National Oceanographic Data Center for 

the data sets and public availability. This work was supported by the NASA MAP and CMS 

Programs.
31

Volume 27

December 2008

The GEOS-5 Data Assimilation System - Documentation of Versions 5.0.1, 

5.1.0, and 5.2.0.

M.M. Rienecker, M.J. Suarez, R. Todling, J. Bacmeister, L. Takacs,

H.-C. Liu, W. Gu, M. Sienkiewicz, R.D. Koster, R. Gelaro, I. Stajner,

and J.E. Nielsen

Volume 28

April 2012

The GEOS-5 Atmospheric General Circulation Model: Mean Climate and 

Development from MERRA to Fortuna

Andrea Molod, Lawrence Takacs, Max Suarez, Julio Bacmeister, InSun Song, and Andrew Eichmann

Volume 29

May 2012

Atmospheric Reanalyses – Recent Progress and Prospects for the Future.

A Report from a Technical Workshop, April 2010

Michele M. Rienecker, Dick Dee, Jack Woollen, Gilbert P. Compo, 

Kazutoshi Onogi, Ron Gelaro, Michael G. Bosilovich, Arlindo da Silva, 

Steven Pawson, Siegfried Schubert, Max Suarez, Dale Barker, 

Hirotaka Kamahori, Robert Kistler, and Suranjana Saha

Volume 30

September 2012

The GEOS-ODAS, Description and Evaluation

Guillaume Vernieres, Michele M. Rienecker, Robin Kovach and 

Christian L. Keppenne
29

Previous Volumes in This Series

Volume 1

September 1994

Documentation of the Goddard Earth Observing System (GEOS) general 

circulation model - Version 1 

L.L. Takacs, A. Molod, and T. Wang

Volume 2

October 1994

Direct solution of the implicit formulation of fourth order horizontal 

diffusion for gridpoint models on the sphere 

Y. Li, S. Moorthi, and J.R. Bates

Volume 3

December 1994

An efficient thermal infrared radiation parameterization for use in general 

circulation models 

M.-D. Chou and M.J. Suarez 

Volume 4

January 1995

Documentation of the Goddard Earth Observing System (GEOS) Data 

Assimilation System - Version 1 

James Pfaendtner, Stephen Bloom, David Lamich, Michael Seablom, 

Meta Sienkiewicz, James Stobie, and Arlindo da Silva

Volume 5

April 1995

Documentation of the Aries-GEOS dynamical core: Version 2 

Max J. Suarez and Lawrence L. Takacs

Volume 6

April 1995

A Multiyear Assimilation with the GEOS-1 System: Overview and Results 

Siegfried Schubert, Chung-Kyu Park, Chung-Yu Wu, Wayne Higgins, 

Yelena Kondratyeva, Andrea Molod, Lawrence Takacs, Michael 

Seablom, and Richard Rood

Volume 7

September 1995

Proceedings of the Workshop on the GEOS-1 Five-Year Assimilation 

Siegfried D. Schubert and Richard B. Rood

Volume 8

March 1996

Documentation of the Tangent Linear Model and Its Adjoint of the 

Adiabatic Version of the NASA GEOS-1 C-Grid GCM: Version 5.2 

Weiyu Yang and I. Michael Navon

Volume 9

March 1996

Energy and Water Balance Calculations in the Mosaic LSM 

Randal D. Koster and Max J. Suarez

Volume 10

April 1996

Dynamical Aspects of Climate Simulations Using the GEOS General 

Circulation Model 

Lawrence L. Takacs and Max J. Suarez

Volume 11

May 1997

Documentation of the Tangent Linear and its Adjoint Models of the 

Relaxed Arakawa-Schubert Moisture Parameterization Package of the 

NASA GEOS-1 GCM (Version 5.2) 

Weiyu Yang, I. Michael Navon, and Ricardo Todling

Volume 12

August 1997

Comparison of Satellite Global Rainfall Algorithms 

Alfred T.C. Chang and Long S. Chiu

Volume 13

December 1997

Interannual Variability and Potential Predictability in Reanalysis Products 

Wie Ming and Siegfried D. Schubert
30

Volume 14

August 1998

A Comparison of GEOS Assimilated Data with FIFE Observations 

Michael G. Bosilovich and Siegfried D. Schubert

Volume 15

June 1999

A Solar Radiation Parameterization for Atmospheric Studies 

Ming-Dah Chou and Max J. Suarez

Volume 16

November 1999

Filtering Techniques on a Stretched Grid General Circulation Model 

Lawrence Takacs, William Sawyer, Max J. Suarez, and Michael S. 

Fox-Rabinowitz

Volume 17

July 2000

Atlas of Seasonal Means Simulated by the NSIPP-1 Atmospheric GCM 

Julio T. Bacmeister, Philip J. Pegion, Siegfried D. Schubert, and Max J. 

Suarez

Volume 18

December 2000

An Assessment of the Predictability of Northern Winter Seasonal Means 

with the NSIPP1 AGCM 

Philip J. Pegion, Siegfried D. Schubert, and Max J. Suarez

Volume 19

July 2001

A Thermal Infrared Radiation Parameterization for Atmospheric Studies 

Ming-Dah Chou, Max J. Suarez, Xin-Zhong, and Michael M.-H. Yan

Volume 20

August 2001

The Climate of the FVCCM-3 Model 

Yehui Chang, Siegfried D. Schubert, Shian-Jiann Lin, Sharon Nebuda, 

and Bo-Wen Shen

Volume 21

September 2001

Design and Implementation of a Parallel Multivariate Ensemble Kalman 

Filter for the Poseidon Ocean General Circulation Model 

Christian L. Keppenne and Michele M. Rienecker

Volume 22

August 2002

Coupled Ocean-Atmosphere Radiative Model for Global Ocean 

Biogeochemical Models 

Watson W. Gregg

Volume 23

November 2002

Prospects for Improved Forecasts of Weather and Short-term Climate 

Variability on Subseasonal (2-Week to 2-Month) Time Scales 

Siegfried D. Schubert, Randall Dole, Huang van den Dool, Max J. 

Suarez, and Duane Waliser

Volume 24

July 2003

Temperature Data Assimilation with Salinity Corrections: Validation for 

the NSIPP Ocean Data Assimilation System in the Tropical Pacific Ocean, 

1993–1998 

Alberto Troccoli, Michele M. Rienecker, Christian L. Keppenne, and 

Gregory C. Johnson

Volume 25

December 2003

Modeling, Simulation, and Forecasting of Subseasonal Variability 

Duane Waliser, Siegfried D. Schubert, Arun Kumar, Klaus 

Weickmann, and Randall Dole

Volume 26

April 2005

Documentation and Validation of the Goddard Earth Observing System 

(GEOS) Data Assimilation System – Version 4

Senior Authors: S. Bloom, A. da Silva and D. Dee

Contributing Authors: M. Bosilovich, J-D. Chern, S. Pawson, S. 

Schubert, M. Sienkiewicz, I. Stajner, W-W. Tan, and M-L. Wu