title: Temporal moments of a tracer pulse in a perfectly parallel flow system

authors: Bardsley, W. Earl

subjects: stratified aquifier

abstract: Perfectly parallel groundwater transport models partition water flow into isolated one-dimensional stream tubes which maintain total spatial correlation of all properties in the direction of flow. The case is considered of the temporal moments of a conservative tracer pulse released simultaneously into N stream tubes with arbitrarily different advective–dispersive transport and steady flow speeds in each of the stream tubes. No assumptions are made about the form of the individual stream tube arrival-time distributions or about the nature of the between-stream tube variation of hydraulic conductivity and flow speeds. The tracer arrival-time distribution g(t,x) is an N-component finite-mixture distribution, with the mean and variance of each component distribution increasing in proportion to tracer travel distance x. By utilising moment relations of finite mixture distributions, it is shown (to r=4) that the rth central moment of g(t,x) is an rth order polynomial function of x or φ, where φ is mean arrival time. In particular, the variance of g(t,x) is a positive quadratic function of x or φ. This generalises the well-known quadratic variance increase for purely advective flow in parallel flow systems and allows a simple means of regression estimation of the large-distance coefficient of variation of g(t,x). The polynomial central moment relation extends to the purely advective transport case which arises as a large-distance limit of advective–dispersive transport in parallel flow models. The associated limit g(t,x) distributions are of N-modal form and maintain constant shapes independent of travel distance. The finite-mixture framework for moment evaluation is also a potentially useful device for forecasting g(t,x) distributions, which may include multimodal forms. A synthetic example illustrates g(t,x) forecasting using a mixture of normal distributions.

text: Temporal moments of a tracer pulse in a perfectly parallel flow system Perfectly parallel groundwater transport models partition water flow into isolated one-dimensional stream tubes which maintain total spatial correlation of all properties in the direction of flow. The case is considered of the temporal moments of a conservative tracer pulse released simultaneously into N stream tubes with arbitrarily different advective–dispersive transport and steady flow speeds in each of the stream tubes. No assumptions are made about the form of the individual stream tube arrival-time distributions or about the nature of the between-stream tube variation of hydraulic conductivity and flow speeds. The tracer arrival-time distribution g(t,x) is an N-component finite-mixture distribution, with the mean and variance of each component distribution increasing in proportion to tracer travel distance x. By utilising moment relations of finite mixture distributions, it is shown (to r=4) that the rth central moment of g(t,x) is an rth order polynomial function of x or φ, where φ is mean arrival time. In particular, the variance of g(t,x) is a positive quadratic function of x or φ. This generalises the well-known quadratic variance increase for purely advective flow in parallel flow systems and allows a simple means of regression estimation of the large-distance coefficient of variation of g(t,x). The polynomial central moment relation extends to the purely advective transport case which arises as a large-distance limit of advective–dispersive transport in parallel flow models. The associated limit g(t,x) distributions are of N-modal form and maintain constant shapes independent of travel distance. The finite-mixture framework for moment evaluation is also a potentially useful device for forecasting g(t,x) distributions, which may include multimodal forms. A synthetic example illustrates g(t,x) forecasting using a mixture of normal distributions.

year: 2003-06

title: Conceptualising leadership in early childhood education in Aotearoa New Zealand

authors: Thornton, Kate

subjects: education

abstract: The New Zealand Teachers Council Te Pouherenga Kaiako o Aotearoa is pleased to publish this occasional paper focused on leadership in early childhood education in Aotearoa New Zealand. The project that led to this publication grew out of a desire of the Council’s Early Childhood Education Advisory Group to promote some action on leadership development specifically for ECE. Whereas there is a well-developed leadership strategy for the school sector there is no equivalent support for teachers in ECE. Yet it is well established in the literature that an effective professional learning community is most likely to result from leadership that has learning as the central focus. Thus the absence of a cohesive leadership strategy was seen as a significant risk to professional initiatives supporting quality teaching in ECE.

text: Conceptualising leadership in early childhood education in Aotearoa New Zealand The New Zealand Teachers Council Te Pouherenga Kaiako o Aotearoa is pleased to publish this occasional paper focused on leadership in early childhood education in Aotearoa New Zealand. The project that led to this publication grew out of a desire of the Council’s Early Childhood Education Advisory Group to promote some action on leadership development specifically for ECE. Whereas there is a well-developed leadership strategy for the school sector there is no equivalent support for teachers in ECE. Yet it is well established in the literature that an effective professional learning community is most likely to result from leadership that has learning as the central focus. Thus the absence of a cohesive leadership strategy was seen as a significant risk to professional initiatives supporting quality teaching in ECE.

year: 2009

title: Te Pae Mahutonga and the measurement of community capital in regional Aotearoa New Zealand

authors: Ryks, John

abstract: Regionally, iwi and hapū have limited influence over structural changes such as population decline, proximity to labour markets and ageing, and to some extent economic cycles. However, there is still considerable value in thinking about how relevant indicators might point to the regeneration and overall well-being of Māori communities. In this paper we present an exploratory framework that links Durie’s Te Pae Mahutonga model of Māori well-being to the measurement of community capital. We use Te Pae Mahutonga as the basis for developing a number of key indicators for understanding Māori well-being in the regions and apply the framework and indicators to three regional settlements in Aotearoa New Zealand: Pōkeno, Huntly and Ōpōtiki.

text: Te Pae Mahutonga and the measurement of community capital in regional Aotearoa New Zealand Regionally, iwi and hapū have limited influence over structural changes such as population decline, proximity to labour markets and ageing, and to some extent economic cycles. However, there is still considerable value in thinking about how relevant indicators might point to the regeneration and overall well-being of Māori communities. In this paper we present an exploratory framework that links Durie’s Te Pae Mahutonga model of Māori well-being to the measurement of community capital. We use Te Pae Mahutonga as the basis for developing a number of key indicators for understanding Māori well-being in the regions and apply the framework and indicators to three regional settlements in Aotearoa New Zealand: Pōkeno, Huntly and Ōpōtiki.

year: 2018