A concise representation of hysteretic soil hydraulic properties is given based on a combination of M. T. van Genuchten's (1980) parametric K-O-h model and P.S. Scott et al.'s (1983) empirical hysteresis model modified to account for air entrapment. The resulting model yields compact closed-form expressions for the hysteretic water retention curve O(h) and soil water capacity C(h), as well as for the hydraulic conductivity function K(h). Depending on the degree of simplification involved, the model entails a total of 6-9 parameters which can be calibrated from direct measurements of O(h) and saturated conductivity or by an inverse solution approach from transient flow experiments. Comparison of modelpredicted and measured K-O-h relations for eight soils revealed one case in which model predictions were very poor. Model accuracy was judged to be acceptably good in the other cases. Mualem's modified (Y. Mualem, 1984) dependent domain model was found to be more accurate for soils with very narrow pore size distributions. Use of a simplified version of the proposed model with two parameters eliminated provided overall accuracy very similar to that of the more complex model. Numerical simulations of flow during transient infiltration and drainage using the proposed model and a variant of Y. Mualem's (1984) modified dependent domain model did not differ greatly and agreed reasonably well with experimental water content distributions, even when scanning curves were not described very accurately. By contrast, simulations without consideration of hysteresis produced highly unacceptable results. It is concluded that the proposed model provides a convenient and simple means of incorporating hysteretic effects into numerical flow models to provide significant improvement in prediction accuracy with little additional effort and with minimal data requirements. though these models may not be the easiest to use. Recently, Scott et al. [1983] introduced a simple empirical hysteresis model and showed that this model predicts scanning curves and hysteretic flow processes for different soils quite well. daynes [1984] evaluated four different hysteresis models and found that the different models gave generally equivalent results. In the event of approximately equivalent accuracy, ease of incorporating the hysteresis model into a numerical flow analysis will be a primary consideration. Although models with demonstrated effectiveness in modeling hysteretic flow are available and the importance of hysteresis has been shown many times in laboratory studies, hysteresis is usually ignored in studie•' of field-scale flow and transport problems. As Royer and Vachaud [1975] noted, one rationale for disregarding hysteresis is that spatial variability of hydraulic properties may overwhelm local hysteretic effects. While this is a feasible argument, certain evidence to the contrary has been observed. Stauffer and Dracos [1984] argue that the observed fast response of groundwater to infiltration in watersheds can be explained by hysteresis in the...

A parametric model is developed to describe relative permeability‐saturation‐fluid pressure functional relationships in two‐ or three‐fluid phase porous media systems subject to monotonic saturation paths. All functions are obtained as simple closed‐form expressions convenient for implementation in numerical multiphase flow models. Model calibration requires only relatively simple determinations of saturation‐pressure relations in two‐phase systems. A scaling procedure is employed to simplify the description of two‐phase saturation‐capillary head relations for arbitrary fluid pairs and experimental results for two porous media are presented to demonstrate its applicability. Extension of two‐phase relations to three‐ phase systems is obtained under the assumption that fluid wettability follows the sequence water > nonaqueous phase liquid > air. Expressions for fluid relative permeabilities are derived from the scaled saturation‐capillary head function using a flow channel distribution model to estimate effective mean fluid‐conducting pore dimensions. Constraints on model application are discussed.

Transformations between volume‐averaged pore fluid concentrations and flux‐averaged concentrations are presented which show that both modes of concentration obey convective‐dispersive transport equations of identical mathematical form for nonreactive solutes. The pertinent boundary conditions for the two modes, however, do not transform identically. Solutions of the convection‐dispersion equation for a semi‐infinite system during steady flow subject to a first‐type inlet boundary condition is shown to yield flux concentrations, while solutions subject to a third‐type boundary condition yield volume‐averaged concentrations. These solutions may be applied with reasonable impunity to finite as well as semi‐infinite media if back mixing at the exit is precluded. Implications of the distinction between resident and flux concentrations to laboratory and field studies of solute transport are discussed. It is suggested that perceived limitations of the convection‐dispersion model for media with large variations in pore water velocities may in certain cases be attributable to a failure to distinguish between volume‐averaged and flux‐averaged concentrations.

In these companion papers, a general theoretical model is presented for the description of functional relationships between relative permeability k, fluid saturation S, and pressure P in two‐or three‐phase (e.g., air‐water or air‐oil‐water) porous media systems subject to arbitrary saturation paths. A parametric description of hysteretic S‐P relations is developed in paper 1 which includes effects of air and oil phase occlusion or “entrapment” during imbibition. Entrapped nonwetting fluid saturations at a given point along a saturation path are linearly interpolated between endpoints of primary imbibition scanning curves using maximum trapped saturations estimated by extension of the method of Land (1968). Arbitrary order scanning curves are predicted using an empirical interpolation scheme coupled with a scaling procedure which simplifies computations and minimizes the parametric complexity of the model. All model parameters are defined in terms of measurements which may be obtained from two‐phase systems (air‐water, air‐oil, oil‐water). Extension to three‐phase systems is based on the assumption that fluid entrapment processes in three phase systems are similar to those in two‐phase systems and that wettability decreases in the order: water to oil to air.

The numerical feasibility of determining water retention and hydraulic conductivity functions simultaneously from one-step pressure outflow experiments on soil cores by a parameter estimation method is evaluated. Soil hydraulic properties are assumed to be represented by van Genuchten's closed-form expressions involving three unknown parameters: residual moisture content 6, and coefficients a and n. These parameters are evaluated by nonlinear least-squares fitting of predicted to observed cumulative outflow with time. Numerical experiments were performed for two hypothetical soils to evaluate limitations of the method imposed by constraints of uniqueness and sensitivity to error. Results indicate that an accurate solution of the parameter identification problem may be obtained when (i) input data include cumulative outflow volumes with time corresponding to at least half of the final outflow and additionally the final outflow volume; (ii) final cumulative outflow corresponds to a sufficiently large fraction (e.g., >0.5) of the total water between saturated and residual water contents; (iii) experimental error in outflow measurements is low; and (iv) initial parameter estimates are reasonably close to their true values.

The inverse problem of determining unsaturated soil hydraulic properties from one‐dimensional, transient infiltration and redistribution events is analyzed. Hydraulic properties are assumed to be described by an extension of van Genuchten's (1980) model which allows for hysteresis in the retention function and air entrapment. Unknown parameters in the model are estimated from observed water contents and heads during transient flow by numerical inversion of the unsaturated flow equation. The inverse problem is formulated as a weighted least squares problem and solved using an efficient Levenberg‐Marquardt algorithm. The flow event consists of ponded infiltration followed by gravity drainage with evaporation at the soil surface. Sensitivity analyses indicate that observations during ponded infiltration should be made near the position of the wetting front. The location of observation points during the drying stage is less critical than during the infiltration stage, but for the relatively high imposed evaporative flux sensitivity of pressure head is highest near the soil surface. Large differences in sensitivity are observed among the various model parameters. Unknown evaporative fluxes are approximated in the inverse solution as an equivalent first‐type boundary condition requiring only periodic measurements of surface water content during the drying stage. Little error is incurred provided accurate measurements are possible. Corruption of input data with random error is shown to have a larger effect on the predicted conductivity function than on the retention function and more effect on the wetting branch of the hysteretic retention function than on the drying. When measurements are subject to error and the assumed parametric model for water retention and conductivity relations is not exact, it may no longer be possible to detect hysteresis in the retention function.

This paper presents a discussion of the physical and mathematical significance of various boundary conditions applicable to one‐dimensional solute transport through relatively short laboratory soil columns. Based on mass balance considerations, it is shown that a first‐type or concentration‐type condition at the inlet boundary incorrectly predicts the volume‐averaged or resident concentration inside both semi‐infinite and finite systems. A third‐type or flux‐type inlet boundary condition preserves mass in semi‐infinite systems, but underpredicts effluent concentrations from finite columns unless a local transformation is used to convert volume‐averaged concentrations into flux‐averaged concentrations. This transformation leads to an expression for the effluent concentration that is identical to the solution for the semi‐infinite system using a concentration‐type boundary condition. For column Peclet numbers greater than about five, the resulting analytical expression for the effluent curve is shown to be nearly identical to the analytical solution for a finite system based on a flux‐type inlet boundary condition and a zero‐concentration gradient at the exit boundary. Both solutions correctly preserve mass in the system; other solutions of the convective‐dispersive transport equation are shown to be inappropriate for analyzing column effluent data.

Background Chronic obstructive pulmonary disease (COPD) is highly prevalent and significantly affects the daily functioning of patients. Self-management strategies, including increasing physical activity, can help people with COPD have better health and a better quality of life. Digital mobile health (mHealth) techniques have the potential to aid the delivery of self-management interventions for COPD. We developed an mHealth intervention (Self-Management supported by Assistive, Rehabilitative, and Telehealth technologies-COPD [SMART-COPD]), delivered via a smartphone app and an activity tracker, to help people with COPD maintain (or increase) physical activity after undertaking pulmonary rehabilitation (PR). Objective This study aimed to determine the feasibility and acceptability of using the SMART-COPD intervention for the self-management of physical activity and to explore the feasibility of conducting a future randomized controlled trial (RCT) to investigate its effectiveness. Methods We conducted a randomized feasibility study. A total of 30 participants with COPD were randomly allocated to receive the SMART-COPD intervention (n=19) or control (n=11). Participants used SMART-COPD throughout PR and for 8 weeks afterward (ie, maintenance) to set physical activity goals and monitor their progress. Questionnaire-based and physical activity–based outcome measures were taken at baseline, the end of PR, and the end of maintenance. Participants, and health care professionals involved in PR delivery, were interviewed about their experiences with the technology. Results Overall, 47% (14/30) of participants withdrew from the study. Difficulty in using the technology was a common reason for withdrawal. Participants who completed the study had better baseline health and more prior experience with digital technology, compared with participants who withdrew. Participants who completed the study were generally positive about the technology and found it easy to use. Some participants felt their health had benefitted from using the technology and that it assisted them in achieving physical activity goals. Activity tracking and self-reporting were both found to be problematic as outcome measures of physical activity for this study. There was dissatisfaction among some control group members regarding their allocation. Conclusions mHealth shows promise in helping people with COPD self-manage their physical activity levels. mHealth interventions for COPD self-management may be more acceptable to people with prior experience of using digital technology and may be more beneficial if used at an earlier stage of COPD. Simplicity and usability were more important for engagement with the SMART-COPD intervention than personalization; therefore, the intervention should be simplified for future use. Future evaluation will require consideration of individual factors and their effect on mHealth efficacy and use; within-subject comparison of step count values; and an opportunity for control group participants to use the intervention if an RCT were to be carried out. Sample size calculations for a future evaluation would need to consider the high dropout rates.