Stoichiometric interpretations of C:N:P ratios in organic waste materials

Maria Lourdes San Diego-McGlone¹, Stephen V. Smith², Vivian F. Nicolas¹

¹Marine Science Institute, University of the Philippines, Diliman, Quezon City 1101, Philippines

Introduction

In pollution monitoring activities for water bodies, BOD is a commonly determined variable and is an important water quality indicator and descriptor of effluent content. Thus, many reports contain BOD values. Rapid assessment techniques such as provided by Economopoulos (1993), engineering tables to design or evaluate waste treatment facilities (e.g., Tchobanoglous and Burton, 1991), and most waste-stream monitoring programs are based on BOD as the main, often the sole, calibration variable for waste loading. Many such monitoring studies do not include other variables that may also be of environmental importance, e.g., N, P, TOC, and COD. Definitions of all the variables used in the study are given in Table 1.

The present exercise has been an attempt to determine generalized stoichiometric C:N:P ratios in organic waste materials from studies in which multiple variables have been measured. If general trends can indeed be found, then one can convert frequently available BOD data into estimates for N, P, or C. For ecosystems that are affected by anthropogenic activities, this information is important for assessing impacts of wastes on inventory and C, N, P balance and for inferring assimilative capacities of the environment for waste inputs. We have encountered the need for such general loading indices in the construction of mass balance budgets for coastal ecosystems for which sparse data on material loading are available (following the budgeting guidelines laid out for the LOICZ project, by Gordon et al., 1996).

A study by Strain et al. (1995) of nutrient loading and oxygen demand associated with multiple uses of a tidal inlet in Nova Scotia underscores the potential utility of such information. That inlet receives wastes from aquaculture, fish processing, a pulp mill, and a municipal sewage treatment plant. The authors made the assumption that oxygen demand and the C, N, and P content of these wastes could be related to the familiar Redfield Ratio, which characterizes the composition of phytoplankton. It would be useful to know how reliable the Redfield Ratio or some alternative general ratio is in the evaluation of organic waste loading to the environment.

Materials and Methods

Data on organic wastes were derived from 72 references in the primary literature (see References marked with *). Waste was classified into categories adapted from Economopoulos (1993). These are: Category 1, for animal agriculture and livestock production; Category 2, for food, tanneries, leather, wood and paper manufacturing; Category 3, for industrial chemicals; and Category 4, for sanitary services. Since stoichiometric proportionalities are most readily visualized on a molar basis, reported estimates of BOD, COD, TN, TP, TOC, TKN, NH₄-N, NO₃+NO₂-N, and PO₄-P from organic wastes were converted to molar units prior to the statistical analysis.    To download an excel spreadsheet containing these data, click here.  To download an excel spreadsheet that will allow you to estimate the nutrient load to coastal ecosytems associated with effluent, click here.

Statistical Procedure

We make the assumption that any two variables X and Y, representing chemical entities of interest, are proportional to one another. This may be called the "stoichiometric assumption." It is implicit that there is neither curvature in a scatter diagram of X versus Y nor residual amounts of either X or Y as the other value (Y or X) approaches 0. That is,

    Y = k₂X                             (1)  

The value k₂ can be calculated as the simple ratio of the mean of Y divided by the mean of X. This is equivalent to a regression equation in which the intercept (k₁) is forced through the origin. The slope (k₂) is simply the ratio of the mean value of Y to the mean value of X.

In the available data, the units for X and Y are mixed (e.g., concentration, flux). Moreover, the dilution factors for the materials vary by orders of magnitude. The result of these two characteristics is that the data are very non-normally distributed. This implies that solving the regression equation (whether or not k₁ is forced through the origin) will greatly bias the estimated proportionality constant towardss large numbers. The problem of data that are not normally distributed can be overcome by use of log-transformed data. This latter situation suggests an equation of the following form might be appropriate:

                                Y = aX^b                                         (2)

In order to preserve the simple proportionality of the "stoichiometric assumption," b is set equal to 1, and the equation is log-transformed:

                                log(Y) = log(a) + log(X)                  (3)

Equations (1) and (2) demonstrate that k₂ and a are algebraically equivalent, if b = 1. The statistical derivation of k₂ and a will give quite different results, however. Because the desire is not to weight the proportionality constant excessively by large numbers, equation (3) is the preferred equation to derive the proportionality constant. For n data points, the proportionality constant can therefore be simply estimated from the following relationship, which follows from a least-squares-fit of the parameter a:

                                                                                     (4)

This is equivalent to:

              (4a)

and

_i= a_est x_I                         (4b)

The next requirement is evaluating the goodness of fit of the data to equation (4). This is the equivalent of r², except that the simple calculation of r² is not directly applicable. The desired statistic (that is, the coefficient of determination, CD) is the ratio of the explained sum of squares to the total sum of squares of the log transformed Y values. The total sum of squares for log(Y) (SSTO) can be evaluated:

                                                                                     (6)

SSTO can be broken into the components SSR (the sum of squares explained by the proportionality constant) and SSE (the error sum of squares):

            (7)

SSE is calculated as the deviation of the log(Y) values from the proportionality constant, where log() is the estimated value. Thus

             8)

It follows from equations (7) and (8) that

                                                                                                      (9)

The proportion of the variance in log(Y) that is explained by the regression equation is given by the ratio SSR/SSTO. This value (CD) is analogous to r².

Results

Tables 2 and 3 present a summary of the stoichiometric ratios of various variables scaled to BOD, TN, and TP, respectively that passed the 95% confidence criteria. Figures 1 - 4 show stoichiometric ratios scaled to BOD, COD, TN & TP and TOC.  Stoichiometric ratios for the various categories of organic wastes, as well as for combined categories, are reported. The underlying advantages of working with combined categories are a lessened need to "assign" a particular kind of waste load to a specific category when estimating pollutant loading, and a greater number of samples within each grouped category (hence, more robust statistics for the stoichiometric calculations). Close agreement was seen for some of the ratios derived from different and combined categories indicating similarity in the C, N, and P components of organic wastes from various sources. 

Discussion

The data in Tables 2 and 3 lead to the following generalities. The COD:BOD molar ratio for most materials can be well approximated by the value of 2.6 (n = 53). There is more scatter for the other scalings relative to BOD, but the following general overall COD:TOC:TN:TP:BOD ratio is reconstructed: 2.6:1.7:0.5:0.042:1. This ratio can be used in general to scale from BOD loading to the other variables. The Redfield (O₂:C:N:P) ratio as applied by Strain et al. (1995) was based on the composition of plankton (Redfield, 1934) and is
-138:106:16:1. The waste load ratio we have derived, expressed in equivalent units, is -62:40:12:1. Waste load is therefore rich in the nutrients N and P, relative to the C content of plankton.

It also appears from the data that about 50% of the P in waste loads is PO₄ albeit with considerable scatter in the data; the remainder is assumed to be organic, although polyphosphate may be important in some instances. Typically about 40% of the N is NH₄, with NO₃ usually being very minor; the remainder of the N is organic.

Moreover, the organic matter (as represented by C) has a higher oxygen demand (COD:TOC = 62/40 = 1.55) than either the classical Redfield ratio based on plankton and seawater composition (Redfield, 1934; Redfield et al., 1963) (O₂:C:N:P = -138:106:16:1; COD:TOC = 138:106 = 1.30) or more recent formulations by Takahashi et al. (1985) (O₂:C:N:P = -175:122:16:1; COD:TOC = 175:122 = 1.43). While BOD is traditionally treated as an index of the organic matter which is readily oxidized on time scales of days, it is likely that most or all of the COD represents oxygen loading on the receiving systems over longer time scales. Terrestrial plant-derived organic matter in general tends to have a relatively high carbon content (e.g., Vitousek et al., 1988), so we assume that the relatively low TOC content and high inorganic nutrient content of waste material represent partial (up to 50%) oxidation of organic matter in the waste production process.

The study by Strain et al. (1995), cited in the Introduction, used the Redfield Ratio to approximate the composition of various forms of waste discharge into a tidal inlet. That approximation seems likely to overestimate oxygen utilization relative to nutrient loading and to underestimate oxygen utilization relative to organic carbon loading. The more important point to the present analysis is not to take issue in any substantive way with that study, but rather to recognize a need for conversion factors and to present a generic ratio that can be more rationally related to waste load composition than the Redfield Ratio. Moreover, the analysis here provides basis to partition the nutrient loading in untreated effluent between organic and inorganic nutrients. The effects of these two forms of N and P delivery would be very different to subsequent reactions within the ecosystem.

It needs to be stressed that this analysis is based on untreated effluents. Waste treatment to secondary levels will have an elevated ratio of TN and TP relative to BOD, COD, and TOC and a higher ratio of inorganic nutrients relative to total nutrients. These changes will represent organic oxidation of a portion of the waste load, without nutrient removal. The TN:TP ratio of waste streams not subjected to tertiary treatment should tend to be relatively constant. Tertiary treatment will obviously remove some N or P, or both. Because much waste produced by human activities enters the environment with little or no treatment, the waste composition ratios constructed here should have relatively wide applicability.

Conclusions

The results of this exercise are stoichiometric interpretations of O₂:C:N:P ratios associated with organic wastes from various categories. The relatively small differences among categories suggest that for many purposes a single ratio can be used. While any assessment of mass loading to an environment will obviously be more robust if direct measurements of the waste composition are available, it appears that quite a bit can be inferred about the composition of mass loading from BOD alone.

Acknowledgements

Dennis Swaney is gratefully acknowledged for his critical evaluation and suggested modifications of the statistical analysis employed here. We also thank WOTRO for providing the funds for this exercise. This analysis has been undertaken as part of the biogeochemical modelling being undertaken by the IGBP core project element, Land-Ocean Interactions in the Coastal Zone (LOICZ).

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