Deconvolving Smooth Residence Time Distributions from Raw Solute Transport Data

Abstract

A residence time distribution (RTD) provides a complete model of longitudinal mixing effects that can be robustly derived from experimental solute transport data. Maximum entropy deconvolution has been shown to recover RTDs from preprocessed laboratory data. However, data preprocessing is time consuming and may introduce errors. Assuming data were recorded using sensors with a linear response, it should be possible to deconvolve raw data without preprocessing. This paper uses synthetically generated raw data to demonstrate that the quality of the deconvolved RTD remains satisfactory when preprocessing steps involving data cropping or calibration are skipped. Provided noise levels are relatively low, filtering steps may also be omitted. However, a rough subtraction of background concentration is recommended as a minimal preprocessing step. Deconvolved RTDs often include small-scale fluctuations that are inconsistent with a well-mixed fully turbulent system. These are believed to be associated with oversampling and/or unsuitable interpolation functions used in the maximum entropy deconvolution process. This paper describes a new interpolation function—linear interpolation with an automatic moving average (LAMA)—and demonstrates that, in combination with fewer sample points (e.g., 20), it enables smoother RTDs to be generated. The two improvements, to deconvolve raw data and to generate smoother RTDs, have been validated with experimental data. Raw solute transport traces collected from a river were deconvolved after background subtraction. The deconvolved RTDs compare favorably with those generated from the more traditional advection-dispersion equation (ADE) and aggregated dead zone (ADZ) models, but provide more detail of mixing processes. A laboratory manhole solute transport data set was deconvolved with and without preprocessing using 40 sample points and linear interpolation. The raw data were also deconvolved using 20 sample points and LAMA interpolation. The two sets of RTDs deconvolved from the raw data show the same mixing trends as those deconvolved from preprocessed data. However, those deconvolved with LAMA interpolation and 20 sample points are significantly smoother.