Ecological parameter reductions, environmental regimes, and characteristic process diagram of carbon dioxide fluxes in coastal salt marshes

Study wetlands and datasets

Four salt marshes located in Waquoit Bay and adjacent estuaries at Cape Cod, MA, USA were used as the case study sites: (1) Sage Lot Pond (SL), (2) Eel Pond (EP), (3) Great Pond (GP), and (4) Hamblin Pond (HP) (Fig. 1). The marshes represent a moderate gradient in nitrogen loading and a wide range of human population density^{31, 32}. On the basis of nitrogen loading influx, SL is in relatively pristine condition (~ 5 kg/ha/year), whereas HP (~ 29 kg/ha/year), EP (~ 63 kg/ha/year), and GP (~ 126 kg/ha/year) represent a medium to high nitrogen loading^{31, 33}. The vegetation community of the marshes is mostly dominated by Spartina alterniflora (a C₄ plant) in the low marsh zone.

A comprehensive detail on the collections and processing of gas fluxes and environmental variables for the four salt marshes were presented in Abdul-Aziz et al.⁷. Closed chamber-based measurements of the net ecosystem exchange (NEE) of CO₂ were made using a cavity ring-down spectrometer (CRDS) gas-analyzer (Model G2301, Picarro, Inc., Santa Clara, CA; frequency: 1 Hz; precision: 0.4 ppm) for different days during the extended growing season (May to October) in 2013 at the low marsh zones of the four salt marshes. The spectrometer analyzer was connected to the transparent, closed acrylic chamber (60 cm × 60 cm × 60 cm) through tubes. We calculated the molar concentrations of CO₂ in the chamber using the ideal gas law. The instantaneous molar concentrations of CO₂ were then linearly regressed with time (s). The regression slopes (i.e., rates of changes in CO₂ concentrations) were normalized by the chamber area (60 cm × 60 cm = 3,600 cm² = 0.36 m²) to compute the corresponding fluxes of CO₂ (i.e., changes in CO₂ concentrations per unit area and per unit time in μmol/m²/s) between the wetland soil and the atmosphere inside the chamber for each sampling period (typically ~ 5 min)^{6, 7}. To avoid impacts of any experimental error, a coefficient of determination (R²) of 0.90 was set as the minimum threshold for the regression to qualify the computed CO₂ fluxes as accurate and acceptable for analyses^{6, 7}.

The employed enclosed chamber-based technique of measuring CO₂ fluxes is a widely-used method in the carbon research domain^34,35,36,37. The technique provides an effective way to measure surface-atmospheric gas fluxes. As demonstrated above, the method first involves the calculation of the gradient of molar concentrations of CO₂ in time, which is then divided by the chamber area to compute the vertical CO₂ fluxes. Since the measurement chamber is small (e.g., 60 cm × 60 cm × 60 cm for our equipment) and enclosed, the vertical fluxes of CO₂ between soil and atmosphere (and not the divergence of CO₂ fluxes) drives the changes in CO₂ concentrations with time inside the chamber. Therefore, the chamber area-normalized rates of changes in CO₂ molar concentrations represent the vertical CO₂ gas fluxes between the soil and atmosphere inside the chamber.

The associated instantaneous environmental variables such as the photosynthetically active radiation (PAR), air temperature (AT), soil temperature (ST), and porewater salinity (SS) were concurrently measured⁷. The corresponding observations of atmospheric pressure (P_a) were collected from the nearby NOAA National Estuarine Research Reserve System (NOAA–NERRS) monitoring station located at Carriage House, MA³⁸. The filtered daytime net uptake fluxes of CO₂ (NEE_CO2,uptake) represented the measurements made between 8 a.m. and 4.30 p.m. (Eastern Standard Time, EST), with the corresponding PAR higher than 1.5 µmole/m²/s. AT was used to calculate the fluxes of NEE_CO2,uptake using the ideal gas law⁷; AT was, therefore, excluded as an environmental driver from further analyses. Instead, soil temperature (ST) was considered to represent the impact of temperature on NEE_CO2,uptake. The dataset included 137 observational panels from the four study wetlands for 25 sampling days (Table S1, Figure S1 and S2 in Supplemental notes).

Theoretical formulation of dimensionless numbers through parametric reductions

Dimensional analysis using Buckingham pi ((Pi)) theorem were applied to formulate wetland ecological similitudes and derive dimensionless functional groups or (Pi) numbers^{18, 20}. According to the pi theorem, a combination of ({text{n}}) dimensional variables would lead to (({text{n}} – {text{r}})) dimensionless Π numbers (({text{r}} =) number of relevant fundamental dimensions). NEE_CO2,uptake, PAR, ST, SS, P_a, and the time-scale of measurement or estimation (t) were used for the dimensional analysis. PAR, ST, SS were the most dominant drivers of NEE_CO2,uptake, as identified in the study of Abdul-Aziz et al.⁷. Furthermore, P_a negatively correlates with net photosynthesis as stomatal conductance increases with decreasing pressure³⁹. The selected variables for the dimensional analysis included four fundamental dimensions (mass: M; length: L; temperature: K; time: T) (Table 1). Since the variables were in different unitary systems, they were converted to the SI units by using appropriate conversion factors (Table 1). As the temperature dimension (K) was only represented by ST, specific heat of wet soil (c_p = 1.48 kJ/kg/K) was further incorporated in the dimensional analysis to normalize ST. Following the pi theorem, a functional relationship ((f)) among the response (NEE_CO2,uptake) and the potential predictors was expressed as follows:

where the total number of variables, (n = 7); number of fundamental dimensions, (r = 4). Therefore, the total number of possible ({Pi }) numbers (= {text{n}} – {text{r}} = 3). The functional relation of Eq. (1) was then represented with (Phi) in terms of dimensionless numbers as follows:

Based on the pi theorem, four variables ((r = 4)) could be considered as “repeating variables” in each iteration to formulate a dimensionless number by involving any of the remaining variables. Although the repeating variables should include all relevant fundamental dimensions (M, L, K, and T in this study), they should not form a dimensionless number among themselves. For example, considering PAR, ST, SS, and t as the “repeating variables”, the first pi number (left( {Pi _{1} } right)) was expressed as follows:

where (a), (b), (c), and (d) were exponents. For (Pi _{1 }) to be dimensionless, the following equation was obtained using the principle of dimensional homogeneity (i.e., equal dimensions on both sides):

Therefore,

Equating the exponents of M, L, K, and T on both sides, we obtained the following matrix–vector form:

The system of linear equations was algebraically solved to compute the exponents as: (a = – 1), (b = 0), (c = 0), and (d = 0) (see Text S1 in Supplemental notes for detailed algebraic equations and solutions). Therefore, from Eq. (3), we obtained the first pi number as

Similarly, the other two ({Pi }) numbers were formulated as (see Text S1 in Supplemental notes)

The pi theorem also allowed the derivation of new (Pi) numbers by combining any two (or more) original (Pi) numbers through multiplication or division as follows:

Thus, the functional relationship of Eq. (2) could be represented in any of the following forms:

Therefore, dimensional analysis reduced the 7 original variables to 2–3 dimensionless numbers. Recalling the definition of similitude from the physical domain^{18, 20}, such parametric reductions for the daytime net uptake fluxes of CO₂ and the associated environmental drivers were termed as “wetland ecological similitudes” in this research. As apparent, (Pi _{1}) represented the dimensionless CO₂ flux number (i.e., response), whereas (Pi _{2}) to (Pi _{5}) represented the environmental driver numbers (i.e., predictors).

Various sets of dimensionless numbers were obtained by iteratively changing the “repeating variables” (Table S2; see Text S1 in Supplemental notes for full derivations). However, only the unique ({Pi }) numbers were considered for further analysis with empirical data. For example, (frac{{ SS^{2} cdot ST cdot c_{p} }}{{PAR^{2} }}) (iteration-1 or 4 in Table S2) and (frac{{SS cdot sqrt {ST cdot c_{p} } }}{PAR}) (iteration-3) were considered non-unique ({Pi }) numbers, because the latter could be obtained as a square root function of the former. Similarly, (frac{{P_{a} }}{{PAR cdot sqrt {ST cdot c_{p} } }}) (iteration-3) could be obtained from a square root and inversion of (frac{{PAR^{2} cdot ST cdot c_{p} }}{{P_{a}^{2} }}) (iteration-2 or 5), and were considered the same number. Based on the pi theorem, the response ({Pi }) number (i.e., dimensionless CO₂ flux number) were expressed as a general function ((psi)) of all unique dimensionless environmental numbers as follows:

Empirical analysis to determine the linkages among the derived numbers

The multivariate method of principal component analysis (PCA) was applied to the observational dataset from the salt marshes of Waquoit Bay to identify the important environmental driver number(s) that had dominant linkage(s) with the response pi number⁴⁰. PCA can resolve multicollinearity (mutual correlations) among the environmental driver numbers in a multivariate space, identifying the relatively unbiased information on their individual linkages with the response^{40, 41}. To incorporate any non-linearity in the data matrix, observed (i.e., calculated) values of all pi numbers were log₁₀-transformed, which were further standardized (centralized and scaled) as follows: (Z = left( {X – overline{X}} right)/s_{X}); (X) = log₁₀-transformed pi number, (overline{X}) = mean of (X), and (s_{X}) = standard deviation of (X).

Source: Ecology - nature.com