In 1997, I and Curt Richardson published a paper on using a piecewise linear regression model for estimating the phosphorus retention capacity in the Everglades. At the time, fitting a piecewise linear model is not a simple task. As I was up to date on Bayesian computation, I used the Gibbs sampler. It was an interesting exercise to derive the full set of conditional probability distribution function. The process is tedious but not hard. When applied to the Everglades data, we concluded that the Everglades' phosphorus retention capacity is about 1 gram of phosphorus per year per square meter (the median is 1.15), with a 90% credible interval of (0.61, 1.47) (Table 2 in Qian and Richardson, 1997). The posterior distribution of the retention capacity is skewed to the left. In subsequent papers, Curt Richardson name the result as "the 1 gram rule". The South Florida Water Management District (SFWMD) never believed our work and often claimed that the retention rate would be much higher.
Since then, SFWMD has constructed several Stormwater Treatment Areas (STAs) -- wetlands for removing phosphorus and has been monitoring the performances. The latest results (Chen, et al, 2015) showed that the retention capacity of these STAs is 1.1 +/- 0.5 grams per square meter per year.
I was satisfied that finally SFWMD agreed with my finding, even if the agreement took them nearly 20 years (and hundreds of millions of dollars).
Chen, H., Ivanoff, D., and Pietro, K. (2015) Long-term phosphorus removal in the Everglades stormwater treatment areas of South Florida in the United States. Ecological Engineering, 29:158-168.
Qian, S.S. and C.J. Richardson (1997) Estimating the long-term phosphorus accretion rate in the Everglades: a Bayesian approach with risk assessment. Water Resources Research, 33(7): 1681-1688.
