Can we obtain viable alternatives to Manning’s equation using genetic programming?

Abstract

Applied water research, like the one derived from open-channel hydraulics, traditionally links empirical formulas to observational data; for example Manning’s formula for open channel flow driven by gravity relates the discharge (Q), cross-sectional average velocity (V), the hydraulic radius (R), and the slope of the water surface (S) with a friction coefficient n, characteristic of the channel’s surface needed in the location of interest.  Here we use Genetic Programming (GP), a machine learning technique inspired by nature’s evolutionary rules, to derive empirical relationships based on synthetic datasets of the aforementioned parameters. Specifically, we evaluated if Manning’s formula could be retrieved from datasets with: a) 300 pentads of A, n, R, S, and Q (from Manning’s equation), b) from datasets containing an uncorrelated variable and the parameters from (a), and c) from a dataset containing the parameters from (b) but using values of Q containing noise. The cross-validated results show success retrieving the functional form from the synthetic data in the first two experiments, and a more complex solution of Q for the third experiment. The results encourage the application of GP on problems where traditional empirical relationships show high biases or are non-parsimonious. The results also show alternative flow equations that might be used in the absence of one or more predictors; however, these equations should be used with caution outside of the training intervals.