title: An analysis of the effect of topography on rainfall in the Taieri catchment area, Otago

authors: Hutchinson, Peter

subjects: Taieri

abstract: In an area of 2500 square miles, consisting of the Taieri Catchment basin and adjoining areas, there are only 37 rain gauges for which there are records for more than four years. Since the topography is varied, it is difficult to estimate rainfall in ungauged parts of the catchment. This study examines the effects of four topographic factors, altitude, position, exposure and aspect on the variation in measured rainfall, explains these effects in climatological and meteorological terms, and provides the basis of a method for estimating the rainfall on ungauged areas.

text: An analysis of the effect of topography on rainfall in the Taieri catchment area, Otago In an area of 2500 square miles, consisting of the Taieri Catchment basin and adjoining areas, there are only 37 rain gauges for which there are records for more than four years. Since the topography is varied, it is difficult to estimate rainfall in ungauged parts of the catchment. This study examines the effects of four topographic factors, altitude, position, exposure and aspect on the variation in measured rainfall, explains these effects in climatological and meteorological terms, and provides the basis of a method for estimating the rainfall on ungauged areas.

year: 1968

title: Families of Orthogonal and Biorthogonal Polynomials on the N-Sphere

authors: Kalnins, Ernie G.

subjects: Science & Technology

abstract: The Laplace–Beltrami eigenvalue equation $H\Phi = \lambda \Phi $ on the n-sphere is studied, with an added vector potential term motivated by the differential equations for the polynomial Lauricella functions $F_A $. The operator H is self adjoint with respect to the natural inner product induced on the sphere and, in certain special coordinates, it admits a spectral decomposition with eigenspaces composed entirely of polynomials. The eigenvalues are degenerate but the degeneracy can be broken through use of the possible separable coordinate systems on the n-sphere. Then a basis for each eigenspace can be selected in terms of the simultaneous eigenfunctions of a family of commuting second-order differential operators that also commute with H. The results provide a multiplicity of n-variable orthogonal and biorthogonal families of polynomials that generalize classical results for one and two variable families of Jacobi polynomials on intervals, disks, and paraboloids.

text: Families of Orthogonal and Biorthogonal Polynomials on the N-Sphere The Laplace–Beltrami eigenvalue equation $H\Phi = \lambda \Phi $ on the n-sphere is studied, with an added vector potential term motivated by the differential equations for the polynomial Lauricella functions $F_A $. The operator H is self adjoint with respect to the natural inner product induced on the sphere and, in certain special coordinates, it admits a spectral decomposition with eigenspaces composed entirely of polynomials. The eigenvalues are degenerate but the degeneracy can be broken through use of the possible separable coordinate systems on the n-sphere. Then a basis for each eigenspace can be selected in terms of the simultaneous eigenfunctions of a family of commuting second-order differential operators that also commute with H. The results provide a multiplicity of n-variable orthogonal and biorthogonal families of polynomials that generalize classical results for one and two variable families of Jacobi polynomials on intervals, disks, and paraboloids.

year: 1991

title: The cultural and ecological health of the Tokaanu Stream

authors: Eastwood, Kevin

abstract: Freshwater ecosystems worldwide face increasing threats from human activities like land development and altered flow regimes. These pressures, along with climate change, jeopardize water quality and quantity. Despite these challenges, effective management can improve water quality and habitat, thus sustaining biodiversity and ecosystem services.
Lake Taupō, Aotearoa New Zealand’s largest freshwater lake, holds immense significance for the local iwi, Ngāti Tūwharetoa. The Tokaanu Stream is a tributary of Lake Taupō that was once considered a premier fly-fishing spot. However, the stream has been severely impacted by the Tongariro Power Scheme, which required it to be bisected and channelized to accommodate the Tokaanu tailrace. Coupled with land-use changes in the catchment, these alterations have caused the local hapū, Ngāti Kurauia, who have mana whenua over the lower stream, to raise concerns about its ecological and cultural degradation. To address this problem, I developed a cultural monitoring framework (CMF) in collaboration with Ngāti Kurauia, alongside conventional stream monitoring, at six sites in the lower Tokaanu Stream.
The bespoke CMF was developed through kōrero and wānanga (discussions and workshops) with Ngāti Kurauia. This participatory approach resulted in a CMF with 16 attributes covering vegetation, birdlife, water quality, pollution, engineering, and substrate. Regular assessments revealed a longitudinal decline in stream condition from the most upstream site (Site 1) to the most downstream (Site 6). The state of Site 3 was identified as the most desirable, whilst Site 5 was the most degraded.
Alongside the CMF, I assessed stream health using conventional scientific measures. This monitoring also showed a longitudinal decline in stream ecosystem health moving downstream. Water quality worsened, with indicator bacteria increasing from 45 to 190 CFU/100 ml and total ammoniacal nitrogen from 0.029 to 0.125 g/m3 over the 4 km segment. Deposited fine sediment cover was high, increasing from 69% cover at Site 1 to 83% at Site 6. Cellulose degradation rates (a functional indicator) were diminished at Sites 5 and 6 in both years, even with warming from geothermal springs. Macroinvertebrate communities, monitored in 2023 and 2024, initially showed a linear decline moving downstream in 2023. However, in-stream remediation in early 2024, undertaken by a private contractor, significantly improved macroinvertebrate indicators at impacted sites (Sites 4-6).
The challenges facing the Tokaanu Stream are complex, stemming from geothermal inputs, urbanisation, upstream agriculture, and channelization. Declining water quality may be linked to faulty sewage infrastructure in Tokaanu Village. The stream's diversion includes a tailrace spillway that prevents larger downstream flows, potentially reducing scouring events crucial for natural sediment dynamics. These changes have significant ecological and cultural ramifications for Ngāti Kurauia.
To better understand and address these issues, I argue for an additional downstream State of the Environment (SOE) monitoring site. The current site, near the upstream spring, fails to capture the full impact of catchment inputs, including diffuse pollution from Tokaanu Village and altered sediment dynamics from the diversion. An additional SOE site, coupled with the findings of my thesis, would provide crucial knowledge to support efforts in restoring the Tokaanu Stream's ecological health and the mana of Ngāti Kurauia.

text: The cultural and ecological health of the Tokaanu Stream Freshwater ecosystems worldwide face increasing threats from human activities like land development and altered flow regimes. These pressures, along with climate change, jeopardize water quality and quantity. Despite these challenges, effective management can improve water quality and habitat, thus sustaining biodiversity and ecosystem services.
Lake Taupō, Aotearoa New Zealand’s largest freshwater lake, holds immense significance for the local iwi, Ngāti Tūwharetoa. The Tokaanu Stream is a tributary of Lake Taupō that was once considered a premier fly-fishing spot. However, the stream has been severely impacted by the Tongariro Power Scheme, which required it to be bisected and channelized to accommodate the Tokaanu tailrace. Coupled with land-use changes in the catchment, these alterations have caused the local hapū, Ngāti Kurauia, who have mana whenua over the lower stream, to raise concerns about its ecological and cultural degradation. To address this problem, I developed a cultural monitoring framework (CMF) in collaboration with Ngāti Kurauia, alongside conventional stream monitoring, at six sites in the lower Tokaanu Stream.
The bespoke CMF was developed through kōrero and wānanga (discussions and workshops) with Ngāti Kurauia. This participatory approach resulted in a CMF with 16 attributes covering vegetation, birdlife, water quality, pollution, engineering, and substrate. Regular assessments revealed a longitudinal decline in stream condition from the most upstream site (Site 1) to the most downstream (Site 6). The state of Site 3 was identified as the most desirable, whilst Site 5 was the most degraded.
Alongside the CMF, I assessed stream health using conventional scientific measures. This monitoring also showed a longitudinal decline in stream ecosystem health moving downstream. Water quality worsened, with indicator bacteria increasing from 45 to 190 CFU/100 ml and total ammoniacal nitrogen from 0.029 to 0.125 g/m3 over the 4 km segment. Deposited fine sediment cover was high, increasing from 69% cover at Site 1 to 83% at Site 6. Cellulose degradation rates (a functional indicator) were diminished at Sites 5 and 6 in both years, even with warming from geothermal springs. Macroinvertebrate communities, monitored in 2023 and 2024, initially showed a linear decline moving downstream in 2023. However, in-stream remediation in early 2024, undertaken by a private contractor, significantly improved macroinvertebrate indicators at impacted sites (Sites 4-6).
The challenges facing the Tokaanu Stream are complex, stemming from geothermal inputs, urbanisation, upstream agriculture, and channelization. Declining water quality may be linked to faulty sewage infrastructure in Tokaanu Village. The stream's diversion includes a tailrace spillway that prevents larger downstream flows, potentially reducing scouring events crucial for natural sediment dynamics. These changes have significant ecological and cultural ramifications for Ngāti Kurauia.
To better understand and address these issues, I argue for an additional downstream State of the Environment (SOE) monitoring site. The current site, near the upstream spring, fails to capture the full impact of catchment inputs, including diffuse pollution from Tokaanu Village and altered sediment dynamics from the diversion. An additional SOE site, coupled with the findings of my thesis, would provide crucial knowledge to support efforts in restoring the Tokaanu Stream's ecological health and the mana of Ngāti Kurauia.

year: 2025