A Bayesian approach for identifying drip emitter insertion head loss coefficients

The use of a Bayesian approach to identify the emitter insertion head loss coefficients required for the design of drip laterals is demonstrated. Total discharge and pressure measurements taken along commercially available 100m rolls of pressure compensating drip laterals laid on a 1% slope wooden platform were used. The Metropolise-Hastings Markov Chain Monte Carlo algorithm was used to sample the parameters from the posterior distributions. An average emitter discharge exponent parameter was estimated as 0.1, and only 2 out of the 6 laterals examined had an average emitter discharge below the range published by the manufacturer. Due to statistical variability inherent in the emitter properties along the laterals, as a result of the manufacturing process, the generated parameters for the downhill and uphill directions of the same lateral were slightly different. A representative parameter set of the lateral type examined were generated from the joint posterior distribution of the 4 statistically similar laterals (as judged by overlapping of their paired k-a hydraulic parameter space) using their combined data sets. It was observed that the range (0.95-1.17) of the emitter insertion head loss coefficient identified by the Bayesian approach was similar to that published by the manufacturer (0.95-1.12), demonstrating to the power of the methodology. Simulation of pressures along the laterals and the total discharges yielded an average absolute error of 6.1% in pressure and 3.1% in total discharge for the 4 statistically similar laterals, while the errors were over three times higher for the remaining laterals.