title: Constellations with range and IS-categories

authors: Gould, Victoria

abstract: Constellations are asymmetric generalisations of categories. Although they are not required to possess a notion of range, many natural examples do. These include commonly occurring constellations related to concrete categories (since they model surjective morphisms), and also others arising from quite different sources, including from well-studied classes of semigroups. We show how constellations with a well-behaved range operation are nothing but ordered categories with restrictions. We characterise abstractly those categories that are canonical extensions of constellations with range, as so-called IS-categories. Such categories contain distinguished subcategories of insertions (which are monomorphisms) and surjections (in general different to the epimorphisms) such that each morphism admits a unique factorisation into a surjection followed by an insertion. Most familiar concrete categories are IS-categories, and we show how some of the well-known properties of these categories arise from the fact that they are IS-categories. For appropriate choices of morphisms in each, the category of IS-categories is shown to be equivalent to the category of constellations with range.

text: Constellations with range and IS-categories Constellations are asymmetric generalisations of categories. Although they are not required to possess a notion of range, many natural examples do. These include commonly occurring constellations related to concrete categories (since they model surjective morphisms), and also others arising from quite different sources, including from well-studied classes of semigroups. We show how constellations with a well-behaved range operation are nothing but ordered categories with restrictions. We characterise abstractly those categories that are canonical extensions of constellations with range, as so-called IS-categories. Such categories contain distinguished subcategories of insertions (which are monomorphisms) and surjections (in general different to the epimorphisms) such that each morphism admits a unique factorisation into a surjection followed by an insertion. Most familiar concrete categories are IS-categories, and we show how some of the well-known properties of these categories arise from the fact that they are IS-categories. For appropriate choices of morphisms in each, the category of IS-categories is shown to be equivalent to the category of constellations with range.

year: 2022

title: Sediment transport, river morphology and bottom sediments of the lower Waikato River

authors: Fenton, J. A.

subjects: River sediments

abstract: Sand extraction from the bed of the lower Waikato River has occurred over the past three decades, primarily to meet the demands of the Auckland construction industry. The extraction has affected bed levels over large areas of the river. 

From analysis of the Waikato Catchment Board's periodic river channel cross sectional surveys degradation of river bed levels is seen to be occurring in the Puni to Huntly reach as a result sand extraction and river training, and in the Karapiro to Hamilton reach as a result of construction of the Karapiro dam. Noticeable degradation has occurred since 1964, and the rate has increased between the most recent bed level surveys, 1981 to 1987. The river level has lowered to an extent where further lowering will hinder the operation of water intake structures at the Huntly Power Station, and promote drainage of the Whangamarino wetlands. 

From the interpretation of echo sounding traces, aerial photographs and field observations it is seen that sand bar, dune and ripple bedforms exist in the lower Waikato River. Two distinct dune populations exist, a short steep group with a ripple index (λ/h) of about 24 and a long flat group with a ripple index of about 40. Sand bar bedforms, which have previously been loosely referred to as 'dunes', dominate the Huntly to Mercer reach and are related to a sinuous thalweg pattern. The bars also exist in two forms, with straight or strongly curved crests. A relationship between flow discharge and the rate of bar migration exists. However, at high flows(~> 600 m³/s) the bars become rounded and the crests undefineable. The river bed is devoid of detectable bedform (h < 0.1 m) immediately downstream of sand extraction sites. 

Using the relationship between bedload transport and discharge determined from bar migration in the present study, and a similar relationship developed previously (Finley, 1974), an estimate of medium term (for the period 1975 - 1989) bedload transport is 180 000 m³/yr. Several bedload transport functions were applied to the lower Waikato River. Colby's Relations (1964) was found to be the most applicable mathematical approach as it provided estimates of bedload transport comparable to those estimated from bar migration. The Karapiro dam has blocked the major supply of bedload, so the bedload transport rate can be expected to drop in future. 

The bottom sediments of the lower Waikato River are predominantly coarse poorly sorted pumiceous sands. There is no significant difference in textural statistics between the Mercer and Puni areas. The Puni area has a shallow pre-fluvial basal unit, thereby limiting the useful resource to 7- 9 m³/ m² of river bed. No pre-fluvial unit was found in the Mercer area. A sedimentation rate of 2.8 mm/yr since the Taupo eruption was inferred from stratigraphic data. 

From the results and interpretations in this study, continued sand extraction at the present rate at Mercer will promote further bed level lowering, and operations would be better concentrated in the tidally influenced areas around Puni. It is recommended that future cross sectional surveys should be conducted more regularly (2-3 yrs) and each survey should be completed over a shorter period (4-6 weeks), and regular future assessment of bedload transport should be made. A need exists for further research into the effects of sand extraction and management of the lower Waikato River.

text: Sediment transport, river morphology and bottom sediments of the lower Waikato River Sand extraction from the bed of the lower Waikato River has occurred over the past three decades, primarily to meet the demands of the Auckland construction industry. The extraction has affected bed levels over large areas of the river. 

From analysis of the Waikato Catchment Board's periodic river channel cross sectional surveys degradation of river bed levels is seen to be occurring in the Puni to Huntly reach as a result sand extraction and river training, and in the Karapiro to Hamilton reach as a result of construction of the Karapiro dam. Noticeable degradation has occurred since 1964, and the rate has increased between the most recent bed level surveys, 1981 to 1987. The river level has lowered to an extent where further lowering will hinder the operation of water intake structures at the Huntly Power Station, and promote drainage of the Whangamarino wetlands. 

From the interpretation of echo sounding traces, aerial photographs and field observations it is seen that sand bar, dune and ripple bedforms exist in the lower Waikato River. Two distinct dune populations exist, a short steep group with a ripple index (λ/h) of about 24 and a long flat group with a ripple index of about 40. Sand bar bedforms, which have previously been loosely referred to as 'dunes', dominate the Huntly to Mercer reach and are related to a sinuous thalweg pattern. The bars also exist in two forms, with straight or strongly curved crests. A relationship between flow discharge and the rate of bar migration exists. However, at high flows(~> 600 m³/s) the bars become rounded and the crests undefineable. The river bed is devoid of detectable bedform (h < 0.1 m) immediately downstream of sand extraction sites. 

Using the relationship between bedload transport and discharge determined from bar migration in the present study, and a similar relationship developed previously (Finley, 1974), an estimate of medium term (for the period 1975 - 1989) bedload transport is 180 000 m³/yr. Several bedload transport functions were applied to the lower Waikato River. Colby's Relations (1964) was found to be the most applicable mathematical approach as it provided estimates of bedload transport comparable to those estimated from bar migration. The Karapiro dam has blocked the major supply of bedload, so the bedload transport rate can be expected to drop in future. 

The bottom sediments of the lower Waikato River are predominantly coarse poorly sorted pumiceous sands. There is no significant difference in textural statistics between the Mercer and Puni areas. The Puni area has a shallow pre-fluvial basal unit, thereby limiting the useful resource to 7- 9 m³/ m² of river bed. No pre-fluvial unit was found in the Mercer area. A sedimentation rate of 2.8 mm/yr since the Taupo eruption was inferred from stratigraphic data. 

From the results and interpretations in this study, continued sand extraction at the present rate at Mercer will promote further bed level lowering, and operations would be better concentrated in the tidally influenced areas around Puni. It is recommended that future cross sectional surveys should be conducted more regularly (2-3 yrs) and each survey should be completed over a shorter period (4-6 weeks), and regular future assessment of bedload transport should be made. A need exists for further research into the effects of sand extraction and management of the lower Waikato River.

year: 1989

title: Recognition and indigenizing official statistics: Reflections from Aotearoa New Zealand and Australia

authors: Kukutai, Tahu

subjects: Indigenou

abstract: In First World colonised nations such as Aotearoa New Zealand and Australia, population statistics form the evidentiary base for how Indigenous peoples are known and `managed' through state policy approaches. Yet, population statistics are not a neutral counting. Decisions of what and how to count reflect particular assumptions about Indigenous identity, ways of life and wellbeing. More often than not, the requirements and priorities of government take precedence over the informational needs and priorities of Indigenous communities. Whereas National Statistics Offices (NSOs) once rendered Indigenous peoples invisible in official statistics through non-recognition, the more pressing problem in the 21st century is that of misrecognition. In seeking to move beyond statistical misrecognition, we propose a set of guiding principles for bringing government reporting frameworks and Indigenous concepts of identity and wellbeing into closer proximity. We argue that a principled approach to collecting, disseminating and analysing Indigenous data not only avoids misrecognising Indigenous peoples but enhances the functionality of official statistics for Indigenous peoples and NSOs alike.

text: Recognition and indigenizing official statistics: Reflections from Aotearoa New Zealand and Australia In First World colonised nations such as Aotearoa New Zealand and Australia, population statistics form the evidentiary base for how Indigenous peoples are known and `managed' through state policy approaches. Yet, population statistics are not a neutral counting. Decisions of what and how to count reflect particular assumptions about Indigenous identity, ways of life and wellbeing. More often than not, the requirements and priorities of government take precedence over the informational needs and priorities of Indigenous communities. Whereas National Statistics Offices (NSOs) once rendered Indigenous peoples invisible in official statistics through non-recognition, the more pressing problem in the 21st century is that of misrecognition. In seeking to move beyond statistical misrecognition, we propose a set of guiding principles for bringing government reporting frameworks and Indigenous concepts of identity and wellbeing into closer proximity. We argue that a principled approach to collecting, disseminating and analysing Indigenous data not only avoids misrecognising Indigenous peoples but enhances the functionality of official statistics for Indigenous peoples and NSOs alike.

year: 2015