In chemistry, "stoichiometry" is the study of the combination of elements in chemical reactions. Therefore we use the term "stoichiometric analysis" to describe this approach to budgetary analysis. It should be kept in mind that the discussion to follow is based on the D Ys for C, N, and P, as derived in the previous section on nutrient budgets. The following sections outline the use of stoichiometric analysis to make rough estimates of biogeochemical processes from the comparison among fluxes of carbon, nitrogen, and phosphorus. More detail can be found in Gordon et al. (1996) and references contained therein.
Organic metabolism and "net ecosystem metabolism"
Figure 1 illustrates generalized pathways of carbon, nitrogen and phosphorus cycling in response to organic metabolism. In general, pathways of organic production are shown in green, while respiratory pathways are shown in red. It is assumed, for this figure, that organic matter with the "Redfield CNP ratio" of 106:16:1 is involved in the reaction. This is probably an adequate description for plankton-based systems, but systems dominated by benthic organisms such as seagrasses, benthic algae, or mangroves may not be well-described by this ratio.
Important points to note on this diagram are as follows: First, organic matter production takes up these nutrients, while respiration liberates nutrients. LOICZ budgeting is largely designed to describe the role of ecosystem-level metabolism as a source or sink of P, N, and especially C, so the interest is largely in the difference between primary production and respiration. This difference is often called either "net ecosystem production" (NEP) or "net ecosystem metabolism" (NEM); the terms are equivalent.
Accepting the Redfield ratio as a representation of organic metabolism, we can write the following general reaction to describe the simplest aspects of organic metabolism. For simplicity in writing this equation, we use nitrate as the dominant form of nitrogen being supplied to support primary production, and we assume that all nitrogen released during respiration is immediately converted from ammonium to nitrate. For the moment, we ignore the processes of denitrification and nitrogen fixation.
In its simplest form, this reaction proceeds from left to right during organic production (p) and from right to left during respiration (r). The difference between these two (p-r) is a measure of NEM. If organic matter of a composition other than the Redfield CNP ratio of 106:16:1 is being produced or consumed, the algebra of the reaction is adjusted to maintain a charge balance.
A second point is that even in the simple representation of metabolism illustrated by Figure 1), the nitrogen cycle is more complicated than the phosphorus and carbon cycles because of the side reactions of "denitrification" and "nitrogen fixation." We will discuss these reactions in more detail below, but even this simple consideration of organic metabolism really needs to include these pathways. Denitrification converts nitrate (which is routinely measured) to nitrogen gas (which, in practice, is never measured), while nitrogen fixation converts nitrogen gas to organic nitrogen. Thus, these side reactions produce or consume the measured forms of nitrogen (sometimes called "fixed nitrogen") without altering the carbon and phosphorus. In some coastal ecosystems, these side reactions are quantitatively important (sometimes dominating) processes altering nonconservative nitrogen flux. Note that the additional process of "nitrification" is a side reaction which converts nitrogen from one form of inorganic nitrogen (ammonium, which is measured) to another (nitrate; also measured). This part of the N cycle is included for completeness.
Figure 1. Generalized diagram illustrating C, N, and P cycling through the organic metabolic pathways of primary production, respiration, nitrification, denitrification, and nitrogen fixation.
Thus, the nitrogen cycle is very much more complicated than simple uptake of nitrogen into organic matter or liberation from organic matter. We can take advantage of this complexity by stoichiometric analysis. By contrast and with respect to the above cycle for organic metabolism, carbon and phosphorus simply move back and forth between dissolved inorganic forms and organic matter.
Nonconservative phosphorus flux and net ecosystem metabolism
One implication of the nutrient cycling as illustrated in Figure 1 is that phosphorus and carbon tend to "track one another" through the metabolic cycle, whereas nitrogen does not follow this track. Let us assume that the nonconservative flux of dissolved inorganic phosphorus (D DIP) has been calculated from a budget. Phosphorus is essential for life, and in many marine systems, it can be assumed that net ecosystem metabolism (that is, the difference between primary production and respiration [p-r]) accounts for D DIP. In detail, it is well understood that this is a great simplification of the phosphorus cycle, and the phosphorus is involved in inorganic reactions involving sorptiondesorption and precipitationdissolution (see references in Gordon et al., 1996). Nevertheless, these side reactions for phosphorus seem to be generally less quantitatively important for phosphorus than for either nitrogen or carbon in terms of net nonconservative fluxes of these three elements in coastal marine ecosystems. It was therefore decided that, in general, D DIP was likely to be a useful general proxy for net ecosystem metabolism.
From equation (1): If the system is a net producer of organic matter ([p-r] > 0), then DIP is taken up (D DIP < 0); if the system is a net consumer of organic matter, then D DIP > 0. Note that primary production (p) and respiration (r) taken individually will each be much larger than the quantity [p-r]. >From a LOICZ perspective, though, [p-r] (or net ecosystem metabolism, NEM) measures the net role of organic metabolism in the system as a source or sink for C. If we know D DIP and we can make an assumption as to the C:P ratio of the organic matter being produced or consumed, then we can make a rough, system-level estimate of [p-r]:
where (C/P)part is the C:P ratio of the reacting particulate material. In general, the Redfield C:P ratio (106:1) is probably an adequate representation of (C/P)part. In systems where a more specific estimate of this ratio is available (e.g., seagrass-dominated systems, where the ratio is likely to be ~300:1, or higher), a system-specific ratio can be used.
Note that only DIP is used in the calculation of [p-r]. Dissolved organic phosphorus (DOP) is also present in the aquatic environment and may be produced or consumed. Note, however, that the production or consumption of DOP is one of the possible sinks or sources accounting for D DIP.
One might argue that more direct measures of [p-r] would be D
DIC or D O2. A problem with such a use
of D DIC is that this variable includes several
processes other than organic C metabolism (notably both CO2 gas flux and CaCO3
precipitation, each discussed below). In the case of D O2,
there may be significant intermediate oxygen sources (i.e., alternative oxidation
pathways) such as sulfate reduction which are not reflected in an O2 budget.
For both CO2 and O2 gas exchange may be sufficiently large budgetary
terms to compromise "direct" budgeting to derive organic C metabolism. As a
result of these considerations, the recommendation of the LOICZ Modelling
Guidelines is to use D DIP and equation (1) where
possible as a proxy for net ecosystem metabolism. This analysis is important within the
context of LOICZ, because a major question for LOICZ and all other parts of IGBP
is the evaluation of the various components of the Earth system in the global carbon
Nitrogen metabolism and net nitrogen fixation minus denitrification
Again consider the nutrient cycling illustrated in Figure 1. Let us assume that a budget is available to define the nonconservative flux of nitrogenand preferably that this flux is available for NO3 + NO2, NH4 (these grouped together here as dissolved inorganic N, DIN), and dissolved organic N (DON). These components of N may be referred to as "dissolved fixed N," to distinguish them from dissolved gaseous N. Dissolved gaseous N, dominated by N2, is almost never measured in water, because the concentrations are both large and almost entirely controlled by the solubility of atmospheric N2 in water. We may refer to this D N of dissolved fixed N as the observed value, that is, D Nobs. Net organic metabolism, as discussed above, is an important pathway for nonconservative fluxes of dissolved nitrogen. Note that DON is organic matter, so the production and consumption of DON is related to NEM.
An equation similar to equation (2) can be written to describe the expected amount of nitrogen (D Nexp). taken up and released with the dissolved phosphorus flux:
In this equation D DON and D DOP are considered along with D DIN and D DIP in order to allow for possible conversions between organic and inorganic forms of these materials. It is preferred to have data on D DON and D DOP, but usually these data are not available. In such cases, it can only be assumed that the nonconservative fluxes of these dissolved organic materials are small.
More importantly, there is often a large difference between D Nobs and D Nexp, and this difference is an indicator of processes other than organic metabolism which alter fixed N. Nitrogen fixation and denitrification are likely to be important pathways for nonconservative nitrogen flux in many marine systems, so this difference is taken as a measure of net nitrogen fixation minus denitrification ([nfix-denit]):
In the LOICZ context, this estimate is important. Coastal sediments can be
important sites of denitrification, and some coastal environments are important sites of
nitrogen fixation. It thus appears that the coastal environment may be important in the
global nitrogen cycle, yet relatively few sites have been studied adequately to
characterize this role. This budgetary analysis will help build our understanding of the
role of the coastal zone as a source or sink for fixed nitrogen.
Net sulfate reduction, net CaCO3 precipitation, and CO2 gas flux
The chemistry of carbon dioxide in seawater is more complex than implied by Figure 1. There are two aspects to this complexity which require discussion here. The first point of discussion becomes the description of the CO2 system in seawater. Because several forms of dissolved inorganic carbon exist in aqueous solution (carbonic acid, bicarbonate, carbonate), two variables (besides temperature and salinity) are required to describe the CO2 chemical system in seawater. Two common variables to describe the CO2 content of seawater are total dissolved inorganic carbon (DIC) and total alkalinity (TA). Note that it is possible in principle to measure any two of the following variables to describe the CO2 system: DIC, TA, pH, and CO2 partial pressure (pCO2). Of these, DIC and TA are the most useful for instruction about the system.
In the second place, various classes of processes can alter the CO2 content of seawater. Figure 2 illustrates those major classes of processes and shows how those processes alter both total dissolved inorganic carbon and total alkalinity.
More detail on these processes is given by Gordon et al. (1996) and references cited therein. That discussion is simplified here. Note that, according to the following equation, the precipitation of one mole of CaCO3 lowers DIC by one mole and lowers TA by two equivalents; CaCO3 dissolution reverses these fluxes.
Various other versions of this equation result in the same shift of total alkalinity from CaCO3 reactions, so in some environments (e.g., coral reefs) D TA is a measure of net CaCO3 reactions.
Sulfate reduction (an anaerobic respiration pathway) alters TA by one equivalent for each mole of organic matter oxidized, because of the liberation of H2S (which will be either re-oxidized back to SO4-2, for no net TA shift; or bound into metal sulfides, for a net shift). We write this equation with a "simple form" of organic matter (CH2O), deliberately ignoring the nitrogen reactions:
Figure 2. Diagram illustrating how the dissolved inorganic content and the total alkalinity of seawater are each altered by the processes of: CaCO3 precipitation and dissolution; sulfate reduction; net organic production and respiration; and gas exchange across the air-sea interface.
In different environments, shifts in total alkalinity have been used as records of each of these classes of processes. In general, systems dominated by carbonate sediments probably show alkalinity responses primarily due to CaCO3 as shown on the figure. Sulfate reduction undoubtedly occurs in the sediments of these systems; however, in the absence of iron to react with the free sulfide, that sulfide probably back-reacts to sulfate with little net shift in alkalinity. In systems with terrigenous material (hence available iron) most net changes in alkalinity are likely to be due to sulfate reduction. There is a minor shift in alkalinity in response to uptake or liberation of both nitrate and ammonium in aquatic environments, but these non-carbonate shifts in alkalinity can be corrected out of the data.
Net production minus aerobic respiration also alters the dissolved inorganic carbon content of water but do not significantly alter alkalinity (equation 1, allowing for the slight and correctable shifts associated with nitrogen fluxes; see footnote #1). Finally, gas exchange, a purely physical process driven by the CO2 partial pressure difference between water and the overlying atmosphere, also alters DIC without affecting TA. Because both gas exchange and metabolism affect the dissolved inorganic carbon content of seawater, the nonconservative flux of dissolved inorganic carbon is not an unambiguous record of net ecosystem metabolism. This is the reason that D DIP, rather than D DIC, is recommended as a record of net organic metabolism.
Where direct measurements exist that allow the calculation of D DIC, comparisons between observed and calculated DIC can provide useful checks between the two results - one measured directly and the second derived from the stoichiometry. Large discrepancies indicate the need for further analysis or measurements to account and resolve the two independent estimates. It must be remembered that although close agreement between the two provides support the conclusion that the results are robust, they cannot be considered perfect. The modelling approach described here recommends as many possible independent estimates as possible from real measured data.
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