Ecological Archives A020-015-A6

John C. Lehrter and Just Cebrian. 2010. Uncertainty propagation in an ecosystem nutrient budget. Ecological Applications 20:508–524.

Appendix F. Uncertainty assessment for net exchange (N-Ex).

N-Ex = ½ AMP ( + )

(F.1)

where AMP was the cumulative annual tidal amplitude and and were the means of import and export nutrient concentrations, respectively. Table F1 contains the parameter values, SE, and degrees of freedom for the values on the right side of Eq. F.1.

AMP, SEAMP, and dfAMP were derived from 8 months of hourly water surface elevation (WSE) measurements obtained at the mouth of the embayment from April to December 2003. These hourly measured WSEs were used in conjunction with hourly measurements at the nearby Pensacola Bay tide gauge (NOAA Station ID 8729840) to develop a linear regression model for predicting WSEs at the embayment when gauged data were not available (January to June, 2004). Based on the measured hourly WSEs in Pensacola Bay (X1, X2, X3, … Xi), the regression model was used to predict the hourly WSEs (Ŷ1, Ŷ2, Ŷ3 … Ŷi) at the embayment for the period January to June 2004. The standard error of each predicted hourly WSE (SEŶi) was calculated as:

(F.2)

where s2YX is the unexplained variance of the regression model used to predict Ŷi (i.e., residual mean square), n is the number of X and Y pairs used to develop the regression model, and Σ x2 is the sum of squares from the regression model (Sokal and Rohlf 1995).The df for Ŷi are equal to n–2 (5871). Measured WSE in the embayment were corrected to the NAVD88 datum by subtracting the regression intercept. SE and df for the corrected WSE were calculated with Eqs. 3 and 7, respectively.

The WSEs referenced to NAVD88 were used to determine the maximum and minimum WSE for each day during the study period. The daily amplitude was then calculated as the difference between the daily maximum and minimum WSE, i.e., Daily amplitude = max WSE – min WSE with:

(F.3)

and

(F.4)

AMP was then calculated as the sum of the daily amplitudes. Unfortunately, the Pensacola WSE gauge did not acquire data from 4 April 2004 to 21 June 2004. Thus,

(F.5)

where N are the number of days (286) with measured or predicted WSE values. The SE and df of AMP were:

(F.6)

(F.7)

and were calculated by Eq. 2 with df = n – 1.

The SEN-Ex and dfN-ex were calculated from Eqs. 3 and 7, respectively, based on the N-Ex formulation (Eq. F.1) where:

(F.8)

(F.9)

TABLE F1. Parameter values used in net exchange (N-Ex) calculations. AMP was the cumulative tidal amplitude for the study period. and were the mean concentrations in the incoming (Import) or outgoing (Export) tides. SE and df were the standard error and degrees of freedom, respectively.

Parameter

Constituent

Value

SE

df

AMP (m/y)

34.88

0.74

285

(mmoles/m3)

5.19

1.95

24.0

 

26.93

2.05

24.0

 

7.26

1.24

21.0

 

0.40

0.14

24.0

(mmoles/m3)

3.23

0.81

24.0

 

24.55

0.99

24.0

 

7.46

1.35

23.0

 

0.12

0.01

24.0

LITERATURE CITED

Sokal, R. M., and F. J. Rohlf. 1995. Biometry. Third Edition. W. H. Freeman and Company, New York, New York, USA.


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