Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department


Major Professor

Mark C. Rains, Ph.D.

Co-Major Professor

Alexandre M. Tartakovsky, Ph.D.

Committee Member

Joseph D. Hughes, Ph.D.

Committee Member

Jeffrey A. Cunningham, Ph.D.

Committee Member

Andres E. Tejada-Martinez, Ph.D.

Committee Member

Patricia Spellman, Ph.D.


Analytical solutions, Bidirectional flow, Numerical models, Residence time, Superposition approximation, Surface and groundwater quality


My research has focused on the effects of surface-water flow on the quality of groundwater and surfacewater systems. For the first part of my research (Chapter 2 ), I s tudied the effects of s urface flow system changes in the water-conservation areas and canals in southeast Florida on the quality of groundwater in the surficial aquifer system.

For the second part of my research, by developing analytical models using the superposition method, I investigated the effects of bidirectional surface-water flow on the conservative contaminant concentrations (Chapter 4) and mean residence time (Chapter 5) in streams and rivers as well as other surface water bodies. Additionally, a supplemental chapter (Chapter 3) was added to this dissertation to validate the analytical transport model by comparing the analytical solution from this research with the numerical solutions from a numerical transport model developed in this study and the OTIS model by the USGS.

The surface flow s ystem i n s outheast F lorida h as b een c hanged i n water-conservation a reas a nd by constructing canals with control structures to prevent flooding and seawater intrusion after the 1950s. These changes may have altered groundwater quality of a surficial aquifer under the surface flow system, and also have modified s urface-water quality because of t he c ontrol s tructures c ausing bidirectional surface-water flow. The bidirectional surface-water flow is very common in flat areas like in Florida and other parts of the world. However, surface-water systems with the bidirectional flow have rarely been investigated by an analytical method due to the difficulty of applying spatially-varying initial conditions that change each time a flow reversal o ccurs. To better understand the effects of s urface flow system changes and bidirectional flow on groundwater and surface-water quality, my research has been conducted as follows.

In Chapter 2, the effects of surface-water flow system changes caused by constructing the water-conservation areas and canals in southeast Florida on groundwater quality was investigated with numerical modeling. Numerical simulation results indicate that the time for low TDS groundwater under the Atlantic Coastal Ridge to reach equilibrium with high TDS surface water in the water-conservation areas and Everglades National Park are approximately seventy and sixty years, respectively. The high TDS groundwater would be restricted to the water-conservation areas and the Park due to its slow eastward movement caused by small hydraulic gradients in Rocky Glades and its mixing with the low TDS groundwater under the high-recharge area of the Ridge. The flow or physical boundary conditions such as high recharge rates or low hydraulic conductivity layers may affect how the spatial distribution of groundwater quality in an aquifer will change when a groundwater flow system reaches equilibrium with an associated surface water flow system.

In Chapter 3, we propose an analytical model for computing tracer concentration resulting from a continuous release of the conservative tracer during a forward cycle of bidirectional surface-water flow by solving the one-dimensional advection-dispersion equation (ADE) in bidirectional surface-water flow field using the superposition method. In this study, the analytical solution is obtained for a single flow reversal and compared to numerical solutions. We found the analytical solution is in good agreement with the numerical solutions (Root Mean Square Error of 0.0021), showing consistency between two numerical methods and the analytical solution.

In Chapter 4, this study proposes a general method for computing contaminant concentrations resulting from an instantaneous source by solving the ADE analytically for bidirectional surface-water flow problems with initial and boundary conditions using the superposition method. Additionally, we propose a Lagrangian approach utilizing a change of variables technique to validate the analytical solutions obtained from the superposition method by comparing them to the solutions from the Lagrangian approach. It also investigates the effects of bidirectional surface-water flow on contaminant transport processes in streams and rivers, as well as in other surface water bodies.

In this study, we propose two analytical transport models for analyzing concentration profiles and breakthrough curves for equivalent unidirectional flow with a constant dispersion coefficient and bidirectional flow with velocity-dependent dispersion coefficients. The results of this study indicate the concentration profiles for bidirectional flow do not match the profiles for equivalent unidirectional flow except during even flow cycles. The peak of the concentration profile for the bidirectional flow model is slightly lower than the peak of the equivalent unidirectional model.

The bidirectional flow transport models predict multiple concentration peaks for concentration histories as shown in breakthrough curves; however, the equivalent unidirectional model predicts only one concentration peak. The effects of forward and reverse flows (positive and negative velocities, respectively) for bidirectional surface-water flow on a breakthrough curve are different before and after a transition period during which stream concentrations increase first and then decrease after a peak concentration within a flow cycle. Before the transition period, the forward flow will increase concentrations, and the reverse flow will decrease them; however, after the transition period, vice-versa. All the transition periods occur during forward flow periods (even flow cycles) when flow velocities are positive. As the evaluation locations move toward the outlet, the transition period occurs later.

The bidirectional surface-water flow will cause the spatial and temporal concentration distributions of a conservative contaminant in a control segment to change significantly, as shown in concentration profile mismatches and multiple peak concentrations, such that the concentration distribution obtained by using an analytical model with the assumption of equivalent unidirectional surface-water flow cannot replace the concentration distribution from a bidirectional flow transport model in a bidirectional surface-water flow system. Therefore, the spatial and temporal concentration distributions predicted by analytical and numerical simulations with the assumption of equivalent unidirectional surface-water flow may overestimate the peak of concentration profiles and underestimate the peaks of breakthrough curves resulting from an instantaneous release of a point source in streams and rivers. Also, an analytical model with velocity-dependent dispersion coefficients should be used for estimating the spatial and temporal concentration distribution of a conservative contaminant in a control segment more accurately.

In Chapter 5, a quasi-analytical model is proposed to estimate the mean residence time for tracer particles to spend inside a control segment of interest. For many environmental studies, estimating the mean residence time of a conservative contaminant in a given water body is essential for predicting the time spent by the contaminant transported in the surface water. In this chapter, the mean residence time is calculated using the analytical solutions proposed in Chapter 4 to evaluate how the mean residence time will vary for bidirectional surface-water flow compared with the solutions for equivalent unidirectional surface-water flow in streams and rivers. The results of this study suggest the unidirectional model results in an approximately 15% error in the estimated mean residence time as compared to the bidirectional model.