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Title: Modelling tracer breakthrough curves to determine stream reaeration and hydrodynamic properties
Author: Semuwemba, James
ISNI:       0000 0004 2745 060X
Awarding Body: Queen's University Belfast
Current Institution: Queen's University Belfast
Date of Award: 2012
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This study investigates and applies robust modelling techniques for analysis of tracer concentration versus time curves (so-called breakthrough curves; BTCs) for the direct (gas) tracer technique in an attempt to quantify more accurately both the reaeration coefficient (K2) and other hydrodynamic parameters with associated uncertainties. Three issues related to the Peak, Modified Peak and Area methods (the standard methods in literature) used to compute K2 from tracer BTCs have been addressed. (a) The three methods rely on the presumption that transport is prescribed by the Advection-Dispersion Model (ADM), which is not always true for natural rivers, thus estimated K2 might be in error (the magnitude of which is not yet known). (b) Although K2 is computed, important hydrodynamic parameters characterising advection, dispersion and transient storage, which determine rates of spreading of solutes and pollutants are not. (c) Uncertainty in K2 has not been quantified, yet this is a critical requirement for stochastic water quality modelling. This study addresses these issues. To address issue (a), the three standard methods are appraised using 800 tracer BTCs simulated for hypothetical rivers both with and without transient storage. The former was achieved using the Transient Storage Model (TSM) and the latter using the ADM. The error in K2 computed with each method was quantified. To address issue (b), a global inverse modelling routine is introduced and tested using perfect and noisy synthetic BTCs. The inversion routine is used to compute both K2 and hydrodynamic parameters for two reaches of the River Lagan in Northern Ireland using real data from 33 tracer tests. In order to address issue (c), both the Linear Approximation method and the Metropolis Hastings (MH) algorithm (a Markov Chain Monte Carlo sampler) are used to compute linear and nonlinear parameter uncertainties, respectively. The MH algorithm, thought to be applied here for the first time in tracer studies, gives posterior distributions both for K2 and key hydrodynamic parameters. A Gelman statistic indicated that the MH algorithm converges to stationary posterior distributions both for synthetic and real data. This study shows, for BTCs described by the TSM (as evidenced by "tailing" of most tracer BTCs in natural rivers), none of the three standard methods gives reliable values of K» Errors in K2 reach 80% for noise-free data; .noise in data exacerbates the errors and leads to inconsistencies in K2 from these methods. For perfect synthetic BTCs, the global inversion routine returned the true hydrodynamic parameters and K2, although this proved impossible for noisy BTCs; but the posterior distributions encompass the true parameter values, highlighting the importance of estimating parameter uncertainty. For the River Lagan, the modelling revealed that transport in the reaches is influenced by transient storage due to stagnant zones, the cross section area of which accounts for 18-60% of that of the main channel. Posterior distributions show non-uniqueness mainly for the exchange coefficient and area of storage zones for some tests. For tests where all parameters are unique, parameter values are comparable with those in literature. More importantly values of the cross section area of the main channel are comparable with those measured physically. Values of K2 at 20°C (K2(20)= 6 - 45 d-I) are comparable with those in literature for similar rivers and show a positive trend with volumetric flow and mean velocity. Linear uncertainty (13-31% of K2(20)) is not equal to the nonlinear uncertainty (16-44% of K2(20)) implying fallibility of the Linear Approximation method despite it requiring minimal computational resources. The uncertainty analysis of dissolved oxygen predictions using a QUAL2Kw model demonstrates the relevance of an accurate K2 and its uncertainty to water quality modelling. It justifies the case for routine use of robust modelling methods to compute K2 and its uncertainty.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available