## 1. Introduction

[2] Mass transport is a core factor in the analysis and prediction of environmental quality, for example, as a control on time scales of environmental system resilience. Apart from quantifying key elements of environmental system response, models of fate and transport are central to contaminant data analysis, risk assessment, and prognostic modeling, to name but a few. Diffuse environmental pollution is ubiquitous [e.g., *Carey et al*. 2013; *Islam and Tanaka*, 2004; *Novotny*, 1999, 2007; *Posen et al*., 2011]; thus techniques for environmental protection and remediation rely on the accuracy of models that predict outcomes of alternative strategies for remediation. It is no surprise then that modeling approaches are heavily embedded in analysis of transport processes. For example, a search within the 5500 papers published in *Water Resources Research* from 2000 to the present revealed that two-thirds include “model” in the title, abstract, or keywords. Nearly one in five papers includes both “model” and “transport” in these search categories.

[3] J.-Y. Parlange has made a vast array of contributions to environmental mass transport. Here, we focus on solute and sediment transport leaving, for example, his extensive work on water flow to be described by *Assouline* [2013]. Later, we explore his contributions to mass transport in overland flow (including sediment transport and transfers to flow from the surface soil) and in the near subsurface. Additionally, we briefly examine his contributions to thermodynamics of soil solutions. Our objectives are, first, to provide a guide to his body of work in this domain and, second, to give a flavor of his approach, which is both theoretical and physically based. Table 1 is intended to satisfy the first objective. The second objective is addressed in the following sections.

Topic | Section in Paper | Papers | Brief Description |
---|---|---|---|

Laboratory scale columns: Experiments, theory and analysis | 2 | Parlange and Starr [1975] | Showed that breakthrough curves from finite columns can be predicted by the solution for a semi-infinite column for Pe > 4. |

Starr and Parlange [1975] | Developed an approximate analytical approach for determining solute dispersion coefficient and (nonlinear) reaction rate. | ||

Starr and Parlange [1976a] | Presents an optimized method for determining the overall spatially-dependent transformation kinetics in a soil column experiment. The method was used to analyze a denitrification experiment. | ||

Starr and Parlange [1976b] | Experiments and modeling of stable and unstable displacement experiments. | ||

Starr et al. [1976] | Experiments describing cation exchange of radioactive tracers in soil column experiments, along with a simplified analysis. | ||

Starr and Parlange [1977] | Presented, modeled, and analyzed experimental data on tailing in breakthrough curves due to flow variations in the inlet porous plate of a soil column. | ||

Parlange and Starr [1978] | Analytical approximations for the 1-D transport equation, taking account of zero- and first-order kinetics. | ||

Starr et al. [1979] | Developed theory for determination of the effective diffusion coefficient for a solute undergoing sorption in a capillary tube and porous medium. The theory was validated using laboratory experimental data. | ||

Starr and Parlange [1979] | Presented and analyzed (using a simplified analytical model) soil column data on the snow-plow effect, which occurs when a high-concentration influent displaces a low-concentration initial solution in a porous medium. | ||

Starr and Parlange [1980] | Discussion on determining dispersion coefficients. | ||

Starr et al. [1980] | Reports extensive experiments and modeling of nitrogen transformations in soil. | ||

Parlange et al. [1982] | Developed approximations for the 1-D transport equation for a solute undergoing zero-order kinetics. | ||

Starr et al. [1982] | Presents experimental data and an analytical approximation for the precursor effect, which occurs during cation exchange experiments when a low-concentration influent solution displaces a high-concentration initial solution in a soil. | ||

Barry et al. [1983b] | Numerical modeling and model-based analysis of the snow-plow effect. | ||

Parlange et al. [1984] | Analytical approximation for the 1-D transport equation for arbitrary degradation kinetics. | ||

Parlange et al. [1985] | Discussion of the effect of the exit condition applied in modeling solute transport in a soil column. | ||

Barry et al. [1986] | Solves the 1-D transport equation via an interpolation method. | ||

Barry et al. [1987a] | Moment analysis of solute transport through layered media | ||

Barry et al. [1987b] | Numerical modeling and model-based analysis of the precursor effect. | ||

Parlange et al. [1992] | General relationship between resident and flux concentrations within and at the exit of a soil column. Zero- and first-order kinetics considered, as well as non-reactive tracers. | ||

Barry et al. [1993] | Analytical approximation for 1-D solute transport with an arbitrary degradation reaction. | ||

Xiong et al. [2005] | Experiments on competitive sorption of metal cations in recycled wastewater to soil. | ||

Field scale transport | 3 | Starr et al. [1978] | Field study (two experiments) on vertical transport of water and chloride across soil layers. |

Dayananda et al. [1980] | Downward movement of a solute with water, with the latter modeled based on the field capacity. | ||

Rose et al. [1980] | Solute transport in a field profile—range of models, including water movement. | ||

Barry et al. [1983a] | General theory of 1-D vertical transport of water and solute, neglecting variability of hydraulic conductivity. | ||

Barry et al. [1985] | Modeling of transport of chloride and nitrate in a field soil with multiple fertilizer applications. | ||

Starr et al. [1986] | 3-D experiments on water and solute movement in the field, demonstrating formation of fingers. | ||

Parlange et al. [1990]. | Application of Miller scaling [Miller and Miller, 1956] to prediction of finger characteristics, with validation. | ||

Nijssen et al. [1991] | Test of a 1-D preferential flow and transport model using data from experiments on undisturbed soil cores. | ||

Parlange et al. [1991] | Unsaturated flow in a hillslope modeled using a linearly interpolated hydraulic conduction function. | ||

Stagnitti et al. [1991] | Hillslope flow and transport model, accounting for pore-size distribution, surface runoff, evaporation, and precipitation. | ||

Steenhuis et al. [1991] | Downward, 1-D preferential flow and transport model and field application, accounting for hydraulic conductivity variability. | ||

Selker et al. [1992]. | Experimental validation of 2-D and 3-D flow instability theory, showing that fingers are frequent and persistent features of vadose zone flow. | ||

Stagnitti et al. [1995] | Pesticide transport and biodegradation model combined with preferential/matrix flow theory and comparison with experiments. | ||

Parlange et al. [1996] | Preferential flow and transport based on pore-group sizes. | ||

Griffioen et al. [1998] | Characterization and dimensional analysis of published experiments on two-region solute transport. | ||

Selker et al. [1996] | Overview of unstable and preferential flow, from the perspective of predicting chemical transport in the field. | ||

Stagnitti et al. [1998] | Series of experimental validations of flow and transport theory under different field conditions. | ||

Wallach and Parlange [1998] | Two-region model concept applied to solute transport in a crack in a porous rock matrix. | ||

Wallach et al. [1998] | Systematic analysis of preferential water flow and solute transport from single fractures to multipore group models. | ||

Steenhuis et al. [2000] | Simplified solute transport model for preferential flow, including two model validations. | ||

Wallach and Parlange [2000] | Solute transport model for fracture flow with matrix exchange. | ||

Stagnitti et al. [2001] | Solute transport in undisturbed soil columns analyzed using single- and two-region models. | ||

Parlange et al. [2002b] | Explored differences in theories of unstable flow in Hele-Shaw cells and porous media. | ||

Stagnitti et al. [2003] | Preferential water flow model, with solute transport characterized by leaching distribution index. | ||

Kim et al. [2005] | Generalized preferential flow model, with solute transport, tested with laboratory data. | ||

Soil erosion | 4 | Sander et al. [1996] | Analytical solutions for sediment individual size classes determined assuming the event is only time dependent. |

Lisle et al. [1998] | The Rose model generalized as stochastic Markov model considering soil particles alternating between rest and ejection states. | ||

Hairsine et al. [1999] | Solutions to the HR model in unsteady conditions provided. | ||

Parlange et al. [1999] | Analytical solutions of the HR model by exploiting short and long terms behavior determined. | ||

Heilig et al. [2001] | The HR model tested using laboratory flume experiment and evidence development of the shield layer. | ||

Siepel et al. [2002] | The HR model modified and tested taking different vegetative cover. | ||

Hogarth et al. [2004b] | Spatial and temporal solutions provided for dynamic change of the soil erosion due to the rainfall impact. | ||

Rose et al. [2007] | Impacts of ponding water depth and soil detachability on soil erosion tested and the HR theories validated using experimental data. | ||

Sander et al. [2007] | HR model theory tested successfully using published experimental data under net erosion and net deposition conditions. | ||

Walker et al. [2007] | Influence of infiltration on soil erosion processes investigated experimentally. | ||

Shaw et al. [2008] | The stochastic form of Rose model tested experimentally. | ||

Tromp-van Meerveld et al. [2008] | Effect of sediment settling velocity on soil erosion delivery investigated under different experimental conditions. | ||

Barry et al. [2010] | Exact solutions of the HR model (assuming a single grain size), which are valid for all space and time, presented using appropriate assumptions. | ||

Jomaa et al. [2010] | Dependency of the boundary and initial conditions on rain splash studied with laboratory flume experiments. | ||

Jomaa et al. [2012a] | Effects of rock fragments on soil erosion delivery investigated and proportionality between soil erosion and area exposed to raindrops tested. | ||

Jomaa et al. [2012b] | HR model adjusted taking the rock fragments cover into account and tested using experimental data. | ||

Jomaa et al. [2013] | Antecedent soil conditions' effects on soil erosion investigated and the HR model tested through multiple rainfall events. | ||

Solute exchange with surface water | 5 | Walter et al. [2001] | Integrated raindrop-driven transport of solutes from the mixing layer into surface runoff, diffusion-driven transport from deeper soil layers into the mixing layer, and infiltration. |

Gao et al. [2004] | Model of chemical transfer to overland flow, no parameter calibration needed. | ||

Gao et al. [2005] | Models combined sediment and chemical transport in overland flow, following the HR approach. | ||

Pathogen transport | 5 | Brush et al. [1999] | Described Cryptosporidium transport in overland flow and soil columns. |

Darnault et al. [2003] | Experiments on preferential flow-driven transport of Cryptosporidium parvum oocysts. | ||

Darnault et al. [2004] | Prediction of Cryptosporidium parvum oocyst transport in preferential flow. | ||

Yeghiazarian et al. [2006] | Stochastic Markov model of microorganism transport. | ||

Thermodynamics of salt solutions | 6 | Parlange [1973] | Analytical model for salt, liquid, and vapor phase water movement adjacent to a concentrated salt boundary. |

Burns et al. [2006a] | Thermodynamic potentials for saline solutions in variably saturated porous media. | ||

Burns et al. [2006b] | Effects of sodium chloride on retention and conduction of water in variably, saturated porous media. | ||

Burns et al. [2007] | Physically-based correction of the Buckingham-Darcy Law for flow of high strength salts in variably saturated porous media. |