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Food Department, Ministry of Agriculture and Forestry of Finland, Helsinki, Finland
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Better Border Biosecurity (B3), Plant and Food Research, Christchurch, New Zealand
David Teulon

North American Plant Protection Organization (NAPPO), Raleigh, NC, USA
Stephanie Bloem

Comite Regional de Sanidad Vegetal del Cono Sur (COSAVE), Dirección de Protección Vegetal, del Servicio Nacional y Sanidad Vegetal y Semillas, Asuncion, Paraguay
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Organismo Internacional Regional de Sanidad Agropecuaria (OIRSA), San Salvador, El Salvador
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Asia and Pacific Plant Protection Commission (APPPC), Bangkok, Thailand
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Pacific Plant Protection Organization (PPPO), Pacific Community Land Resources Division, Suva, Fiji
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Near East Plant Protection Organization (NEPPO), Rabat, Morocco
Mekki Chouibani

African-Union Interafrican Phytosanitary Council (IAPSC), Yaoundé, Cameroon
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European Food Safety Authority (EFSA), Parma, Italy
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French Agency for Food, Environmental and Occupational Health and Safety (ANSES), Plant Health Laboratory, Angers, France
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Research Institute for Agriculture, Fisheries and Food (ILVO), Merelbeke, Belgium
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Netherlands Food and Consumer Product Safety Authority (NVWA), Wageningen, the Netherlands
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Julius Kühn Institute (JKI), Braunschweig, Germany
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National Institute for Agricultural and Food Research and Technology (INIA), Madrid, Spain
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National Institute for Agriculture and Veterinary Research (INIAV), Oeiras, Portugal
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Plant Biosecurity Research Initiative (PBRI), Hort Innovation, Melbourne, Victoria, Australia
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Plant Health Australia (PHA), Deakin, Canberra, Australian Capital Territory, Australia
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International Plant Protection Convention (IPPC), Food and Agriculture Organization of the United Nations, Rome, Italy
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Centre for Agriculture and Bioscience International (CABI), Nairobi, Kenya
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French National Institute for Agricultural Research (INRA), INRA-Montpellier-CBGP, Montferrier-sur-Lez, France
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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 density31, 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 loading31, 33. The vegetation community of the marshes is mostly dominated by Spartina alterniflora (a C4 plant) in the low marsh zone.
Figure 1

Locations of the case study salt marshes along the southern shore of Cape Cod in the Waquoit Bay and adjacent estuaries, MA. Nitrogen loading rates of the Sage Lot Pond, Hamblin Pond, Eel Pond, and Great Pond were 5, 29, 63, and 126 kg/ha/year, respectively.

Full size image

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 analyses6, 7.
The employed enclosed chamber-based technique of measuring CO2 fluxes is a widely-used method in the carbon research domain34,35,36,37. 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 (Pa) 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 (NEECO2,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 NEECO2,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 NEECO2,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) numbers18, 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). NEECO2,uptake, PAR, ST, SS, Pa, and the time-scale of measurement or estimation (t) were used for the dimensional analysis. PAR, ST, SS were the most dominant drivers of NEECO2,uptake, as identified in the study of Abdul-Aziz et al.7. Furthermore, Pa 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 (cp = 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 (NEECO2,uptake) and the potential predictors was expressed as follows:

$$fleft( {NEE_{CO2,uptake} , PAR, ST, SS,{ }P_{a} ,{ }c_{p} , t} right) = 0$$
(1)

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:

$$Phi left( {Pi _{1} ,Pi _{2} , Pi _{3} } right) = 0$$
(2)

Table 1 List of variables, units and dimensions used for the dimensional analysis.
Full size table

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:

$$Pi _{1} = PAR^{a} cdot ST^{b} cdot SS^{c} cdot t^{d} cdot NEE_{CO2,uptake}$$
(3)

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):

$$M^{0} cdot L^{0} cdot T^{0} cdot K^{0} = left( {frac{M}{{L^{2} T}}} right)^{{text{a}}} cdot left( K right)^{b} cdot left( {frac{M}{{L^{3} }}} right)^{c} cdot left( T right)^{d} cdot frac{M}{{L^{2} T}}$$
(4)

Therefore,

$$M^{0} cdot L^{0} cdot T^{0} cdot K^{0} = M^{{{text{a}} + {text{c}} + 1}} cdot L^{{ – 2{text{a}} – 3c – 2}} cdot T^{ – a + d – 1} cdot K^{b}$$
(5)

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

$$left[ {begin{array}{*{20}c} 1 & 0 & 1 & 0 \ { – 2} & 0 & { – 3} & 0 \ { – 1} & 0 & 0 & 1 \ 0 & 1 & 0 & 0 \ end{array} } right] left[ {begin{array}{*{20}c} a \ b \ c \ d \ end{array} } right] = left[ {begin{array}{*{20}c} { – 1} \ 2 \ 1 \ 0 \ end{array} } right]$$
(6)

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

$$Pi _{1} = frac{{NEE_{CO2,uptake} }}{PAR}$$
(7)

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

$$Pi_{2} = frac{{SS cdot P_{a} }}{{PAR^{2} }}$$
(8)

$$Pi_{3} = frac{{ST cdot c_{p} cdot SS^{2} }}{{PAR^{2} }}$$
(9)

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:

$$Pi _{4} =Pi _{2} timesPi _{3} = frac{{ST cdot c_{p } cdot SS^{3} cdot P_{a} }}{{PAR^{4} }}$$
(10)

$$Pi _{5} = frac{{Pi _{3} }}{{Pi _{2} }} = frac{{ST cdot c_{p} cdot SS}}{{P_{a} }}$$
(11)

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

$$Phi left( {Pi _{1} ,Pi _{4} } right) = 0$$
(12)

$$Phi left( {Pi _{1} ,Pi _{5} } right) = 0$$
(13)

Therefore, dimensional analysis reduced the 7 original variables to 2–3 dimensionless numbers. Recalling the definition of similitude from the physical domain18, 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:

$$frac{{NEE_{CO2,uptake} }}{PAR} = psi left[ {left( {frac{{SS cdot P_{a} }}{{PAR^{2} }}} right),left( {frac{{ST cdot c_{p} cdot SS^{2} }}{{PAR^{2} }}} right),left( {frac{{ST cdot c_{p } cdot SS^{3} cdot P_{a} }}{{PAR^{4} }}} right),left( {frac{{ST cdot c_{p} cdot SS}}{{P_{a} }}} right),left( {frac{{PAR^{2} cdot ST cdot c_{p} }}{{P_{a}^{2} }}} right),left( {frac{{SS cdot P_{a}^{3} }}{{PAR^{4} cdot ST cdot c_{p} }}} right)} right]$$
(14)

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 response40, 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). More