The cost of uniqueness in groundwater model calibration

Calibration of a groundwater model requires that hydraulic properties be estimated throughout a model domain. This generally constitutes an underdetermined inverse problem, for which a Solution can only be found when some kind of regularization device is included in the inversion process. Inclusion of regularization in the calibration process can be implicit, for example through the use of zones of constant parameter value, or explicit, for example through solution of a constrained minimization problem in which parameters are made to respect preferred values, or preferred relationships, to the degree necessary for a unique solution to be obtained. The cost of uniqueness is this: no matter which regularization methodology is employed, the inevitable consequence of its use is a loss of detail in the calibrated field. This, ill turn, can lead to erroneous predictions made by a model that is ostensibly well calibrated. Information made available as a by-product of the regularized inversion process allows the reasons for this loss of detail to be better understood. In particular, it is easily demonstrated that the estimated value for an hydraulic property at any point within a model domain is, in fact, a weighted average of the true hydraulic property over a much larger area. This averaging process causes loss of resolution in the estimated field. Where hydraulic conductivity is the hydraulic property being estimated, high averaging weights exist in areas that are strategically disposed with respect to measurement wells, while other areas may contribute very little to the estimated hydraulic conductivity at any point within the model domain, this possibly making the detection of hydraulic conductivity anomalies in these latter areas almost impossible. A study of the post-calibration parameter field covariance matrix allows further insights into the loss of system detail incurred through the calibration process to be gained. A comparison of pre- and post-calibration parameter covariance matrices shows that the latter often possess a much smaller spectral bandwidth than the former. It is also demonstrated that, as all inevitable consequence of the fact that a calibrated model cannot replicate every detail of the true system, model-to-measurement residuals can show a high degree of spatial correlation, a fact which must be taken into account when assessing these residuals either qualitatively, or quantitatively in the exploration of model predictive uncertainty. These principles are demonstrated using a synthetic case in which spatial parameter definition is based oil pilot points, and calibration is Implemented using both zones of piecewise constancy and constrained minimization regularization. (C) 2005 Elsevier Ltd. All rights reserved.

Marcelian charm in nursing practice: The unity of agape and eros as the foundation of an ethic of care

Abstract In the nursing literature, a number of qualities are associated with loving care. Reference is made to, among other things, humility, attentiveness, responsibility and duty, compassion, and tenderness. The author attempts to show that charm, in the Marcelian sense, also plays a central role. It is argued that the moral foundation of charm is a unity of agape and eros. An impartial giving of the self for others is clearly of fundamental importance in an ethic of care. Including charm in the discussion points to the fact that eros also plays a crucial role. Eros produces a passion for people and for life. It is a physical and spiritual energy that animates a person in all facets of her life, including her caring work.

Predictors of care-giver stress in families of preschool-aged children with developmental disabilities

Background This study examined the predictors, mediators and moderators of parent stress in families of preschool-aged children with developmental disability. Method One hundred and five mothers of preschool-aged children with developmental disability completed assessment measures addressing the key variables. Results Analyses demonstrated that the difficulty parents experienced in completing specific caregiving tasks, behaviour problems during these caregiving tasks, and level of child disability, respectively, were significant predictors of level of parent stress. In addition, parents’ cognitive appraisal of care-giving responsibilities had a mediating effect on the relationship between the child’s level of disability and parent stress. Mothers’ level of social support had a moderating effect on the relationship between key independent variables and level of parent stress. Conclusions Difficulty of care-giving tasks, difficult child behaviour during care-giving tasks, and level of child disability are the primary factors which contribute to parent stress. Implications of these findings for future research and clinical practice are outlined.