# Statistics for Environmental Engineers

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5

17.3

29.8

31.9

36.4

43.3

39.2

44.5

46.4 Nitrification. Nitrification occurs in long-term BOD tests, and must be corrected for. One method is to separately model the nitrification oxygen demand by measuring ammonia and nitrate concentrations with time. Assume that nitrification occurs as consecutive first-order reactions A ^ B ^ C, where A, B, and C represent ammonia-N, nitrite-N and nitrate-N concentrations, respectively. Use the following ammonia and nitrate data to estimate the two first- order rate coefficients 1 and 62) and the initial ammonia and nitrate concentrations (CA0 and CC0). Assume the initial nitrite concentration is zero.

 Time Ammonia-N, CA Nitrate-N, CC (days) (mg/L) (mg/L) 0 — 0.05 1 1.4 — 3 1.3 — 8 10 0.8 0.55 15 0.3 — 18 0.05 1.8 23 — 1.8

The models for CA and CC are:

Ca = Ca0 exp(-dlt)

and

Cc = Ca0

1    02 exp(—011) — 01 exp(-02/)

02 — 01

+ Cb0( 1

exp (—02?)) + Cc0.

# 47

## A Problem in Model Discrimination

KEY WORDS biological kinetics, least squares, mechanistic models, model building, model discrimination, Monod kinetics, posterior probability, posterior odds ratio, prior probability, residual sum of squares, Tiessier model.

When several rival models are tentatively considered, it is common to find more than one model that seems to fit the data. For some applications there is no need to select one model as the best because, over the range of interest, either model will serve the intended purpose. In other situations, knowing which model is best may throw light on fundamental questions about reaction mechanisms, catalysis, inhibition, and other phenomena under investigation.

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