FRED T. MACKENZIE: Research Models: TOTEM

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Model Methodology:

MODEL STRUCTURE AND ANALYSIS

TOTEM is a process-driven model of the global biogeochemical cycles of the
life-essential elements carbon, nitrogen, phosphorus, and sulfur. The model describes
the biogeochemical and physical transport behavior of these elements in the four
domains of the Earth’s surface: land, atmosphere, coastal ocean, and open ocean
(Mackenzie and others, 1993; Ver, Mackenzie, and Lerman, 1994; Mackenzie, Lerman,
and Ver, 1998; Mackenzie, Ver, and Lerman, 1998; Ver, Mackenzie, and Lerman,
1999). As defined in the model, the global surface environment is comprised of thirteen
reservoirs (fig. 1): the atmosphere; six terrestrial reservoirs (living biota, humus, inorganic
soil, continental soilwater, shallow groundwater, and lakes); three coastal-zone
reservoirs (organic matter, water, and sediments); and three open ocean reservoirs
(organic matter, surface water, and deep water). The rivers are not defined as a reservoir
because the residence time of water in rivers with respect to recharge by atmospheric
precipitation is very short, about 20 days (Berner and Berner, 1996). The initial masses in
the year 1700 of C, N, P, and S in the global reservoirs defined above are given in table
1A. In addition, other initial conditions (mass transfer fluxes and flux constants), flux
equations, and kinetic parameters, are given in table 1B–C and app. A. Detailed
calculations involving derivation of these equations and estimates are provided in Ver
(1998).

An essential feature of the model is the coupling between the C-N-P-S cycles at
every biologically mediated transfer process, such as photosynthesis, autorespiration,
decay, and burial. This provision for the diverse, process-based biogeochemical interactions
between the four element cycles in the four environmental domains distinguishes
TOTEM from most other models. The coupled-cycles approach is critical to modeling
the responses of biogeochemical systems to global change because an anthropogenic or
natural source of one of these elements, such as fossil fuel burning or humus respiration,
is often a source of all three other elements.

The coupling of the individual cycles is achieved in the model by the average
C:N:S:P ratios associated with oceanic and terrestrial photosynthesis (Redfield ratios,
Redfield, Ketchum, and Richards, 1963), autorespiration on land and in ocean waters,
humus formation, and sedimentation of organic matter in the coastal zone and open
ocean. We make a simplifying assumption that these biologically mediated coupling
processes are generic and apply over many different species and environments within
the terrestrial or oceanic domains, and occur with the same global mean elemental ratios
that do not change with time, on the decadal to century time scale. We recognize that the
wide range of C:N:S:P values for terrestrial plants, phytoplankton, humus, and organic
sediments found in the literature reflects the variations owing to differences in climatic
conditions, ecosystem type, and the possibly transient conditions to which land and
aquatic primary producers are adapted at any given time. For example, estimates for the
Redfield C:N:S:P ratio for higher land plants vary from 510:4:0.8:1 (Delwiche and
Likens, 1977) to 882:9:0.6:1 (Deevy, 1973) and 2057:17:3:1 (Likens, Bormann, and
Johnson, 1981). In TOTEM, we adopt the C:N:S:P ratio for land plants of 510:4:0.8:1
(Delwiche and Likens, 1977), for oceanic plankton of 106:16:1.7:1 (Redfield, Ketchum,
and Richards, 1963), for humus of 140:6.6:1.2:1 (Likens, Bormann, and Johnson, 1981),
and the C:N:P ratio for organic matter in marine sediments of 250:20:1 (Ingall and Van
Cappellen, 1990).

All the transfer processes between the model reservoirs are represented by linear or
nonlinear equations describing reaction mechanisms and physical transport processes.
Many details of the model have been reported elsewhere (Mackenzie and others, 1993;
Ver, Mackenzie, and Lerman, 1994; Mackenzie, Lerman, and Ver, 1998; Mackenzie,
Ver, and Lerman, 1998; Ver, 1998). In the following sections, we describe only those
model relationships and parameters that are particularly relevant to terrestrial and
oceanic processes that redistribute anthropogenic CO2.

IIA. Transfer Processes And Flux Equations
IIA1. Terrestrial photosynthesis.—The exchange of CO2 between the terrestrial biota
and the atmosphere is one of the major fluxes in the global carbon cycle. How the
terrestrial photosynthetic flux will respond to natural and anthropogenic perturbations,
specifically to increasing atmospheric CO2 concentrations, is uncertain. The close link
between the atmospheric and terrestrial biotic reservoirs of C is confirmed by the
temporal and spatial variations of atmospheric CO2 concentration since the late 1950s
that reflect the seasonal oscillations between net photosynthesis during the Northern
Hemisphere summer and net respiration during the Northern Hemisphere winter.
Evidence of a positive effect by rising atmospheric CO2 on terrestrial photosynthetic
rates is apparently revealed in the observed increase in amplitude of the high-latitude
seasonal fluctuations in atmospheric CO2 (Keeling, Chin, and Whorf, 1996; Myneni and
others, 1997). Whether or not the terrestrial biota is, or will be in the future, a sink for
anthropogenic CO2 has significant implications to future climate change, terrestrial
productivity, and other Earth system processes.
The photosynthetic production of terrestrial organic matter by plants is represented
in TOTEM by the biochemical transformation of atmospheric C (C10; designations used
in TOTEM for the reservoirs, fluxes, and rate constants are given in table 1A-C) and
inorganic nutrients N, P, and S from the continental soilwater reservoir (NSw, PSw, and
SSw) to organic matter in the terrestrial phytomass reservoir (C1, N1, P1, and S1). The
terrestrial gross photosynthetic uptake flux of C (CF101
GPP, moles/yr) is given by the
following relationship:

GPP(t) = kC101 x C1(t) x Kphoto

where kC101 in units of 1/yr is a rate constant, C1 is the terrestrial biotic reservoir mass in
units of 1012 moles, and Kphoto is a dimensionless parameter that represents the depen-
dence of photosynthetic carbon uptake on other environmental parameters, as defined
below.

The gross photosynthetic uptake rates of N, P, and S (NFSw1, PFSw1, and SFSw1,
respectively) are calculated from GPP by applying the appropriate Redfield-type C:X
ratio (where X = N, P, or S) for terrestrial phytomass uptake (see app. A).
The first two terms on the right hand side of eq (1) describe the photosynthetic
uptake flux as a first-order kinetic process dependent on the mass of the terrestrial
phytomass, conforming to the intuitive idea that biota grows and respires in proportion
to its mass (Bacastow and Keeling, 1973). The rate constant kC101 is derived from the
assumed steady-state values for the year 1700 of the carbon mass in terrestrial phytomass
and the photosynthetic uptake flux (table 1C). The factor Kphoto represents the coupling
between the C, N, and P cycles through the dependence of GPP on atmospheric CO2, N,
and P concentrations in continental soilwater and temperature;

Kphoto = fC10 x fNsw x fPsw x fT (2)

Each of the four terms on the right hand side of eq (2) represents a number of generalized
ecological and physiological response relationships rather than empirical results from
single literature sources. The f terms, defined below, vary with time, making K a
time-dependent parameter.
Factor fC10 is the response function to changes in atmospheric CO2, calculated using
a Michaelis-Menten relationship (hyperbolic reaction kinetics);

Michaelis-Menten kinetic relationships are also used to describe the response functions
of photosynthetic rate to available inorganic nutrient N and P in the continental soilwater
reservoir;

The Redfield ratio of uptake is assumed to be preserved in the Michaelis-Menten
constants Rmax and k. With these definitions of the parameters, the photosynthetic rate
tends to a constant value, Rmax/(Flux at t = 0), as the nutrient concentration increases
indefinitely, and it decreases with declining nutrient concentrations (in the preceding
equations, reservoir masses and fluxes are in units of 1012 mol and 1012 mol/yr,
respectively, table 1A-B and app. A).
The functional dependence of GPP on temperature generally varies considerably
among plant taxa, soils, and local climatic conditions. Drawing from the observations of
a positive effect of elevated temperature on photosynthesis (Larcher, 1983; Harvey, 1989;
Lashof, 1989; Kohlmaier, Janecek, and Kindermann, 1990), the term fT is defined as;

The Q10 function, commonly used in plant ecology and physiology, is the factor by
which the rate of photosynthesis increases with a 10°C increase in temperature. T and
T1700 are the global temperatures at times t and in the year 1700, in units of °C. Although
it is recognized that there are data, however sparse, to support values of Q10 other than
2.0, the value of 2.0 is adopted as a working approximation in TOTEM (Ver, Mackenzie,
and Lerman, 1994; Ver, 1998). Because the focus of interest with respect to changing
temperature is the magnitude of change from the initial, steady-state condition, the
temperature difference, (delta)T = T - T1700, determines the change in the rate of photosynthesis.
For a temperature rise of (delta)T = 1°C, the calculated factor is fT = 1.07,
corresponding to a 7 percent increase in the rate.
The function Kphoto in eq (1) describes the response of gross primary production to
changes in atmospheric CO2 concentration, concentrations of the nutrients N and P in
soilwater, and global mean temperature. As such, K is analogous to the ‘‘biotic growth
factor,’’ (beta), used by other investigators to describe the response of carbon uptake by the
phytomass to changing CO2 concentrations. At the initial conditions of the C-N-P-S

global system in the year 1700, the function Kphoto is unity; subsequently, its value
changes fractionally with the changing mass of C in the atmosphere, masses of N and P in
soilwater, and global temperature. Keeling (1973a) first introduced a factor (beta), defined as
the ‘‘degree of CO2 fertilization,’’ to express a logarithmic dependence in productivity on
an increase in atmospheric CO2. Since then, other mathematical formulations, varying
from logarithmic relationships to the Michaelis-Menten formulation such as that used in
this paper, have been proposed (see reviews and summaries by Bacastow and Keeling,
1973; Friedlingstein and others, 1995; and Wullschleger, Post, and King, 1995). A
common feature of such formulations is the non-linear response of the rates of primary
production to changes in atmospheric CO2 concentration.
Generally, the studies that include  in global carbon models indicate that terrestrial
ecosystems can sequester large amounts of carbon through a CO2 fertilization effect on
photosynthesis, and that this process might indeed function as a negative feedback to
future increases in global atmospheric CO2 (Goudriaan and Ketner, 1984; Kohlmaier
and others, 1987; Raich and others, 1991; Sellers, Los, and Randall, 1996). In most
carbon cycle models, the biotic growth factors used to balance the global carbon budget
range in value from 0.2 to 0.5. A relatively high (beta) value of 0.5 was used by Goudriaan
and Ketner (1984; Goudriaan, 1989) to reproduce the measured atmospheric CO2 trend
over the period from 1958 to 1980. Bacastow and Keeling (1973) required a (beta) value in
the range of 0.4 to 0.5 to reproduce the atmospheric CO2 trend over the shorter period
from 1959 to 1969. Empirical (beta) values ranging from 0.5 to 0.75 were obtained from
experiments with a variety of single plants under greenhouse conditions and an
unlimited supply of CO2 at a concentration of 340 ppmv (Gates, 1985). At 680 ppmv, the
(beta) values decreased to 0.3 to 0.5. Reverse calculation of the logarithmic beta function of
Bacastow and Keeling (1973) using TOTEM results shows that during the 300 yrs of
TOTEM simulation, the (beta) factor varies from close to zero to 0.7, well within the range of
experimental and theoretical values.
It should be pointed out that currently there is no clear understanding of the
long-term effect of increasing CO2 on terrestrial photosynthetic uptake at the ecosystem
and global levels. In contrast, the short-term response of terrestrial gross photosynthetic
uptake to increasing atmospheric CO2 is well documented (Eamus and Jarvis, 1989;
Mousseau and Saugier, 1992; Allen Jr., and Amthor, 1995; Schimel, 1995; Wullschleger,
Post, and King, 1995; Melillo and others, 1996a). Experimental studies of crop and
non-cropland plants grown in doubled CO2 atmospheres have shown growth rates
ranging from 43 to 375 percent, with the median response falling within the range of
15 to 71 percent (Poorter, 1993; Ceulemans and Mousseau, 1994; Idso and Idso, 1994;
McGuire, Melillo, and Joyce, 1995). However, in their interpretation of results from
controlled-exposure experiments within the context of global C models, Wullschleger
and others (1995) concluded that the link between gross photosynthetic uptake and rising
atmospheric CO2 concentrations has been limited at best. Simple information needed in
the models, including TOTEM, to verify or refute even the most basic of assumptions,
specifically on the role of changing atmospheric CO2 on the gross photosynthetic uptake
flux, may not all be addressed in the experimental studies. In extrapolating experimental
results to the global carbon cycle, many more factors need to be considered, such as
extrapolation of single-plant responses to heterogeneous biomes; interactions with light,
soil moisture, and nutrient availability; ecological adaptations; and competitive interactions
between various species and life forms. Thus, it is not surprising that the CO2
fertilization effect on land plants has been interpreted in several different ways. Given the
sensitivity of modeling calculations, including those of TOTEM, to the choice and
functional relationships of the biotic growth factor, it is important to recognize that there
are fundamental uncertainties involved in using results from controlled-exposure experiments,
such as those cited above, to estimates of a global biotic growth factor.
Other climatological factors that have been observed to affect changes in Earth’s
processes were not considered in the present model analysis, such as changes in global
mean precipitation and soil moisture. To date, however, there is no observational record
showing that global precipitation has changed significantly in recent centuries, although
its variability might have increased (Bradley and others, 1987; Diaz, Bradley, and
Eischeid, 1989). In certain regions, such as North America, there are equivocal historical
data indicating an increase in precipitation during the 20th century (Dai, Fung, and Del
Genio, 1997).

IIA2. Land-use activities.

—Prior to the start of the Industrial Revolution about the year
1850, land-use activities were primarily those of wood-fuel combustion for food preparation,
heating, construction, biomass burning for metal and clay pottery production, and
forest clearing for agricultural land-use. At the present time, these activities include
the conversion of land for food production (grazing land, agricultural land), for urbanization
(building human settlements, roads, and other structures), for energy development
and supply (building dams, hydroelectric plants, and mining of fossil fuels), and
for resource exploitation (mining of metals, harvest of forest hardwood) (Mackenzie,
1998). The consequences of these actions for Earth’s natural resources and makeup
of the land are manifested by increased deforestation, reforestation, logging, shifting
cultivation, desertification and salinization, local flooding, loss of wetlands, and
changes in the chemical and biological properties of aquatic systems (Meyer and Turner,
1994). The effect of changing land-use activities on Earth’s processes is modeled in
TOTEM via three mechanisms: First, as a direct perturbation when CO2 derived
from land-use changes is emitted to the atmosphere, and inorganic nutrients are released
to the continental reservoirs; Second, as a negative feedback mechanism to rising
atmospheric CO2 concentrations; Third, as a major mechanism of material transfer from
land to the coastal zone owing to soil erosion, mineral dissolution, and surface water
runoff.
The first mechanism represents the enhanced conversion of organic phytomass and
soil humus to its inorganic components when humans change the makeup of the land.
For example, the conversion of forests to agricultural land releases CO2 to the atmosphere
through burning and decay and seasonal accumulation of C in crops. The release
of CO2 is accompanied by the release of N, P, and S in the same elemental ratios as those
in phytomass or soils. This mechanism represents an enhanced source of CO2 to the
atmosphere and of nutrients N, P, and S to the continental reservoirs.
The rate of CO2 emission to the atmosphere from land-use activities is an input
function in TOTEM. The sources of the data used are discussed in section IIB on initial
conditions and forcings. The fraction of the land-use emission flux originating from the
phytomass is designated as fLU and the fraction originating from the humus and
dead organic matter reservoir is (1  fLU). Results of a model sensitivity analysis show a
better fit of the historical atmospheric CO2 data when 75 percent of the land-use CO2
emissions is derived from the humus and 25 percent is derived from the phytomass (Ver,
1998).
The rates of release of nutrients N and S from the terrestrial phytomass to the
continental soilwater reservoir owing to land-use activities are calculated by applying the
appropriate C:N:S:P ratio for terrestrial biomass on the land-use flux of carbon, CF1LU
(parameters in the equations are defined in app. A; see also section IIB2):

Enhanced release rates from the humus reservoir to the continental soilwater are
similarly calculated using the C:N:S:P ratio for humus and the land-use flux of carbon
from humus, CF2LU:

The release of phosphorus from the terrestrial organic reservoirs takes into account
the poorly soluble nature of most of the phosphorus compounds occurring in soil and the
rapid immobilization of soluble inorganic phosphorus. Phosphorus quickly becomes
unavailable for plant uptake after it precipitates out as poorly soluble iron, aluminum,
and calcium phosphates or by occlusion with clay minerals (Brady and Weil, 1996).
Studies have shown that repeated application of fertilizer P to croplands saturates the
P-fixation capacity of the soil, thus contributing to an apparent long-term buildup of P in
the continental soilwater reservoir. In TOTEM, the process of partitioning of soil
phosphorus is represented by the parameter fPLU react, that is the fraction of phosphorus
remineralized in land-use that remains in the reactive inorganic form; the remaining
fraction (1  fPLU react) is immobilized. Results of sensitivity analysis (Ver, 1998) indicate
the best-fit values for fPLU react are:

The rates of release of P from the terrestrial phytomass and humus reservoirs to the continental
soilwater are calculated as (parameters in the equations are defined in app. A);

The negative feedback response to the land-use perturbation is a consequence of the
release of CO2, N, and S gases to the atmosphere and of the enhanced remobilization of
N, P, and S to the continental soilwater reservoir. The increased availability of nutrients
in continental soil-water, coupled with rising atmospheric CO2 and warming temperatures,
stimulates terrestrial productivity and storage of organic carbon in the terrestrial
biota, thus increasing the drawdown of atmospheric CO2. For example, when humus
material with an average molar C:N:P ratio of 140:10:1 is mineralized, the remobilized N
and P can ideally support growth of plant matter with an average C:N:P ratio of 510:4:1.
Consequently, an additional 370 moles of the required C can be sequestered from the
atmosphere through this recycling process. Of the 6 moles of excess N remaining in the
continental soilwater reservoir, about 5.5 moles are eventually lost from the terrestrial
realm to the atmosphere through denitrification and about 0.5 moles are transported to
the coastal zone by rivers.
Land-use activities affect the rates of transfer of materials from land to the coastal
zone when repeated tilling and loss of soil protective cover render the land more
susceptible to soil degradation, particularly soil erosion (Houghton, 1983; Schlesinger,
1997; Brady and Weil, 1996). Soil erosion and water runoff contribute to the increased
transport of particulate organic matter, and dissolved organic and inorganic C, N, P, and
S to the coastal zone and to continental reservoirs, such as lakes and river flood plains
(Mulholland and Elwood, 1982).
The effect of land-use activities on soil degradation and erosion is expressed in the
fractional change in the process rate, fLUR, and applied to the flux equation from soil to
rivers (app. A). In the model, we assume that the temporal variation of this perturbation
follows that of the effect of land-use activities on the emissions of CO2 to the atmosphere.
Thus the temporal trend in soil degradation and erosion can be simulated by the trend in
land-use CO2 emissions to the atmosphere (see section IIB2 on land-use activities). To
calculate the values for fLUR, we applied a mathematical transformation on the land-use
CO2 emissions function such that the endpoints of the soil degradation and erosion
perturbation function had a value of 0 at initial time 1700 and of 1 in the year 1995. The
application of this function to the rate of soil degradation and erosion gives rise to a
fractional increase in soil erosion with increasing human activities on land, followed by
enhanced delivery to the coastal zone of terrestrially derived materials via the rivers.
Using this relationship for soil degradation and erosion leads to about a doubling in the
fluxes of particulate organic C, N, and P to the coastal margin via rivers between the
years 1700 and 1995 in the standard TOTEM simulation. This result is in accord with
literature data suggesting that the present fluxes of organic carbon, N, and P are
approximately double pristine flux values (Meybeck, 1982; Milliman and Meade, 1983;
Wollast and Mackenzie, 1989).

IIA3. Ocean-atmosphere exchange.

—At the ocean-atmosphere interface, CO2 gas exchange
is assumed to occur instantaneously to achieve chemical equilibrium. The
atmosphere above the ocean surface and the coastal and surface ocean reservoirs are
considered in the model as well-mixed reservoirs, such that CO2 is uniformly distributed
within the entire reservoir. The seawater buffer mechanism allows a fractional change in
total CO2 in the surface-ocean mixed layer relative to that in the atmosphere. This
partitioning was first introduced by Bacastow and Keeling (1973) and is known as the
Revelle function, R(C10);

The Revelle function is also calculated as;

The value of the Revelle factor R0 is 9, and d is a constant equal to 4; incremental
changes in the Revelle function due to changes in the atmospheric CO2 concentration
are expressed by the last term on the right hand side of eq (12). Combining and
rearranging eqs (11) and (12) yield an equation of the form expressing the time rate of
change of the mass of carbon in the surface ocean reservoir as a function of the mass of
carbon in the atmosphere;

A similar derivation is obtained for the flux of CO2 across the atmosphere-coastal
ocean interface, with C4 replacing C7 in eq (13) (see app. A).

IIA4. Ocean mixing

.—Carbon exchange between the surface mixed layer and the
deeper ocean is a function of the carbon concentration difference between the surface
and the deep ocean layers and the time needed to disperse an ocean surface perturbation
into the bulk oceans, . The carbon concentration difference results from changes in C
concentration owing to primary production, oxidation of sinking biogenic detrital matter
below the photic zone, and changes in the dissolved inorganic carbon concentration in
the surface layer induced by invasion of anthropogenic CO2. The exchange of carbon
between the mixed surface layer and the deep ocean is modeled using an equation
proposed by Revelle and Munk (1977);

where h7 = 100 m and h9 = 3900 m are the mean depths of water in the surface ocean
and deep ocean reservoirs, respectively, and 9
500 yrs. This equation enables the
exchange flux between the mixed layer and deep ocean to be responsive to both the
increase of CO2 in the mixed layer as well as the changing concentration of dissolved
inorganic carbon (DIC) in the deep layer. Results from models using more complex
mathematical representations of ocean mixing (Hudson, Gherini, and Goldstein, 1994;
Friedlingstein and others, 1995) do not differ substantially from TOTEM results.

IIB. Initial Conditions and Forcings

We begin analysis of the behavior of the carbon cycle under human perturbations
prior to the year 1700 with the Earth system in an assumed steady state. This initial state
is defined by the reservoir masses, transport fluxes for each element, and other reaction
and transport parameters (table 1A-C; fig. 1; app. A). A major difference between
TOTEM and other terrestrial ecological models and global circulation (climate) models
(GCMs) is in the treatment of the observed atmospheric CO2 concentrations. In most
models of global environmental change (for example, Bruno and Joos, 1997; Cao and
Woodward, 1998a; Sarmiento and others, 1998), the data on the atmospheric CO2
concentrations are used as a prescribed input function. In TOTEM, however, the time
course of change of atmospheric CO2 concentration is not an input function, but—
significantly to the results of our analysis—it is the output of model computations based on
its mechanisms and external forcings of the past 300 yrs.
The assumption of the Earth system in a steady-state condition defined by the
pre-industrial reservoir masses and fluxes establishes a base line in the model for the
analysis of the effects of human perturbations and environmental stresses. This assumption
is appropriate because the pre-industrial period, generally defined as the decadal to
century time interval prior to the mid-1800s, was in a quasi-steady state under a small but
sustained global human disturbance of the environment. For example, the estimated
rates of release of CO2 and CH4 to the atmosphere associated with pre-industrial human
activities of land use and wood-fuel combustion were almost constant over a period of
500 yrs prior to 1700. In the year 1200, the land-use CO2 emissions were estimated as
about 33 x 1012 moles C/yr, increasing only by 0.06 percent/yr to the year 1700
(Kammen and Marino, 1993). Fossil fuel emissions were negligible during this period
(Keeling, 1973b), the Earth was about to enter a period of recovery from the lower global
temperature of the Little Ice Age, and atmospheric CO2 levels were relatively low
(Barnola and others, 1995; Etheridge and others, 1996). Indeed, measurements from ice
cores show that the concentration of atmospheric CO2 over a period of about 1000 yrs
prior to 1800 and including the pre-industrial era varied by no more than 10 ppmv,
indicating that the global carbon cycle was approximately in a steady state (Raynaud and
Barnola, 1985; Siegenthaler and others, 1988).
In our analysis, the steady state of the system is perturbed by five forcings owing to
changes in human activities and in a climatic variable, affecting the major pathways of
the C, N, P, and S cycles (fig. 2, Smil, 1985; Charlson, Anderson, and McDuff, 1992;
Caraco, 1995; Galloway and others, 1995; Houghton and others, 1996; Marland and
others, 1998). Four of these forcings are due to human activities: (1) gaseous emissions
from fossil fuel burning (and other activities, such as the more recent activity of cement
production), (2) land-use activities, (3) application of N and P inorganic fertilizers to croplands,
and (4) disposal of municipal and industrial sewage. The fifth forcing is due to
a change in a global climatic variable, the mean temperature of the Earth’s surface. These
forcings are input functions in TOTEM. Here, we describe the data sources and discuss
briefly how these input functions are integrated into the TOTEM structure.

IIB1. Emissions of gaseous C, N, and S from fossil fuel burning and other activities

.—The annual global CO2 emissions from fossil fuel burning and cement production for the
period 1860 to 1995 are based on the estimates by Marland and others (1998). Global
emissions of gaseous nitrogen-oxides (NOx) and sulfur-oxides (SOx) are based on
estimates for the period 1860 to 1994 and extrapolated to 1995 (Dignon and Hameed,
1989; Dignon, 1992; Hameed and Dignon, 1992; Brown, Renner, and Flavin, 1997). On
the decadal to century time scale, the anthropogenic emissions of C, N, and S gases are
treated as external inputs to the atmosphere in our model. Fossil fuel CO2 is injected into
the atmosphere according to its emissions history and becomes part of the well-mixed
atmospheric C reservoir. The prescribed boundary conditions for fossil fuel emissions
are described by the function CFF(t) in units of 1012 moles C/yr (section IIA, fig. 2,
app. A).
The fate of anthropogenic N and S in the atmosphere, however, is controlled by the
very short lifetimes of these gases and their conversion products in the atmosphere. The
nitrogen component does not mix with the large N2 reservoir but is deposited onto the
terrestrial and coastal ocean reservoirs by wet and dry deposition and sedimentation of
large particles. This flux is superimposed on the natural fluxes of N out of the atmosphere
(fig. 1, app. A). Anthropogenic sulfur gases emitted to the atmosphere are also rapidly
deposited onto terrestrial and oceanic surfaces. The partitioning of the deposition of the
anthropogenic N and S products from the atmosphere on terrestrial and oceanic surfaces
is based on the studies of long-range transport of these compounds (Logan, 1983;
Bischoff, Paterson, and Mackenzie, 1984; Levy and others, 1990). In TOTEM, the
fraction of anthropogenic N deposited onto the coastal ocean zone is fNFF = 0.4, and that
of anthropogenic S is fSFF = 0.5. The remaining fractions of anthropogenic N (1 - fNFF)
and S (1 - fSFF) are deposited directly on the land surface.

IIB2. Land-use activities.

—The primary effect of land-use activities on the terrestrial
organic reservoirs is prescribed by the time course of net C emissions to the atmosphere,
CLU(t) (app. A). Kammen and Marino (1993) estimated the C emissions for the period
1700 to 1850 based on historical data for the pre-industrial, non-fossil fuel CO2
emissions. Estimates by Houghton (1983; 1991a,b) for the more recent (1850-1990)
land-use activities are reported as net CO2 emissions, including the drawdown or release
of CO2 from such processes as conversion of forest to agricultural land, abandonment of
agricultural land, harvest, and regrowth. Emission estimates for the period from 1990 to
1995 were extrapolated linearly from that of 1990 (Houghton, 1991b). The non-fossil fuel
emission estimates used in TOTEM for the period 1800 to 1930 are consistent with those
deduced from a deconvolution of high-precision ice core data from the Law Dome site in
Antarctica (Bruno and Joos, 1997) and from atmospheric 13C and 14C data (Joos and
Bruno, 1998). The parameters describing the effects of land-use activities in TOTEM
were discussed in section IIA2.

IIB3. N and P inorganic fertilizer application.

—The time course of this agricultural perturbation is based on data for the global
consumption of inorganic fertilizer N and P
from the United Nations Food and Agricultural Organization (United Nations FAO,
various years) for the years 1950 to 1995. For data pre-dating the FAO collection
(1917-1949), we used the estimates by Smil (1991). No provision for organic fertilizer
application is included in the present version of the model. In TOTEM, fertilizer
application is an external input to the N and P biogeochemical cycles because the
residence times of N and P in their source reservoirs of atmosphere and crustal rocks,
respectively, are much longer than the decadal to century time scales we consider. Only
the fraction of applied fertilizer that is not assimilated by crops is considered as a forcing
in the model. Although it is recognized that the partitioning of fertilizer N and P
following its application to agricultural soils is very specific to the agricultural site, soil,
and plant crop, we maintain the simplifying assumption of a global average condition
that is consistent with the definition of the global reservoirs in the model. The partitioning
used in TOTEM is based on estimates by Smil (1991): 45 percent of applied nitrogen
fertilizer is converted to crop biomass, and the remaining 55 percent is the perturbation
on the cycle. Of this fraction, at least 25 percent is transported to the coastal zone with
surface runoff, 20 percent is volatilized to the atmosphere, and 10 percent is either stored
in the soil or leached into the continental soilwater or groundwater reservoirs.
The partitioning of the fertilizer P in TOTEM differs somewhat from the partitioning
of N: more of the applied phosphorus fertilizer (about 70 percent of the total)
constitutes the perturbation after its partial assimilation by crops. Of this fertilizer P, most
(about 50 percent of the total) is quickly rendered unavailable for plant uptake by
precipitating out as insoluble iron, aluminum, and calcium phosphates or by occlusion
with clay minerals. About equal amounts are transported with surface runoff (10 percent)
and leached into the continental soilwater (10 percent) (Smil, 1991). Unlike N, there is no
gaseous loss of fertilizer P. The unreactive P fraction is returned to the inorganic soil
reservoir where it may be either weathered back into the dissolved phase or transported
in solid form to the coastal zone or continental environment. The potential for the
unlimited increase in storage of P in the inorganic soil reservoir is counteracted by the
first-order dependence of the weathering and runoff export fluxes to the size of the soil
reservoir. The effect of temperature change on the weathering flux is small because the
change in temperature over the past 300 yrs was only about 1°C.

IIB4. Sewage disposal.

—In TOTEM, we assume that the global average sewage load is
discharged into the coastal zone without undergoing any sewage treatment process.
Following the analysis of Billen (1993) and Caraco (1995), we calculate the loading of
municipal sewage into the coastal zone, in units of moles of organic C and total N and
P/yr, using a globally averaged C, N, and P content of sewage and an average per capita
rate of discharge applied to the global population (United Nations Population Division,
1995). Detergent phosphates are assumed to originate from urban industrialized regions
(Caraco, 1995), where very little P is removed by wastewater treatment (Esser and
Kohlmaier, 1991). Thus detergent-P is ultimately discharged into the coastal zone in the
inorganic phosphate form. We calculate the global loading of detergent P into the coastal
waters using an average per capita consumption rate applied to the urban industrialized
population (United Nations Population Division, 1995).
The cumulative amounts of organic C and total N and P added by sewage
discharges to the coastal zone, as defined in the model pathways (fig. 1), have been small
relative to the other perturbations so far. However, continuing growth of the human
population that produces sewage and detergents at the same rates as at present may result
in a stronger fertilization of the coastal zone in the future. Conversely, different pathways
of discharge of untreated sewage and other products of human perturbations on land
may lead to consequences that are outside the present analysis of TOTEM. For example,
discharges of municipal sewage and detergent may go into riverine systems where
increased organic matter production and adsorption onto suspended and bedload
sediments may occur, and where both detrital and newly formed organic matter may be
stored for at least decades to centuries, in part delaying their transport to the coastal zone
and in part contributing to the conversion of organic C and N into inorganic forms in the
storage areas.

IIB5. Temperature.

—The mean global temperature history of the Earth for the period
1700 to 1995 was derived from data given in UCAR/OIES (1991), by Nicholls and
others (1996), and by Houghton and others (1996). For the terrestrial realm, temperature
and availability of water are two of the most important climatic variables. At present,
large variations in mean annual temperature (or mean temperature of the growing
season) and water balance, as reflected in net precipitation, characterize the continental
environment. In this model, the response of the global ecosystem to changes in
temperature is through the biologically mediated processes of photosynthesis, plant and
soil respiration, and denitrification on land, and the inorganic process of rock weathering.
Because the temperature change between 1700 to the late 1990s was only about 1°C,
the response of Earth system processes to this perturbation was small (see discussion of
eq (6) in section IIA1).

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