title: Forecasting Lake Waikaremoana Water Availability for Hydro Power

authors: Hopkirk, Carrie Louise

subjects: lake water balance

abstract: Lake Waikaremoana is a high-altitude, large-volume lake located within the rugged terrain of the Urewera National Park. At the lake outflow a rapid elevation change of nearly 450 metres in 8 kilometres facilitates the lake’s use as the upper intake portal for the Waikaremoana Hydro Power Scheme. At the time of this study, Genesis Energy operated the Waikaremoana Power Scheme in response to a water availability model based on daily lake level differencing from which daily generation capacity is predicted, allowing strategic bidding into the electricity market. However, when river flows are low this model is subject to error, as small changes in lake level sometimes cannot be determined accurately beyond background noise on daily timescales.

This project develops a method of estimating both current day and day-ahead water availability of Lake Waikaremoana, independent of lake levels using simple hydrological models, thereby improving operational efficiency of the Waikaremoana Power Scheme. The forecasting is developed specifically for the lower inflow conditions when the lake level differencing approach is most error prone.

It has long been recognised that a significant volume of Lake Waikaremoana water leaks through the ancient landslide dam which created the lake. Previous to this study, it was considered that an inaccurate estimation of this leakage rate combined with evaporative losses might contribute to the error within the existing water availability model. A modified catchment water balance and simple regression approach was applied to Lake Waikaremoana to estimate the lake water loss not accounted for by recorded outflows. Estimating this unrecorded loss translates to estimating the intercept of a linear regression relation, where the assumption is made that there is a linear relationship between the discharge of the Aniwaniwa Stream and the net lake water balance (excluding known outflows) under low inflow conditions. On the basis of the confidence intervals about the intercept, the balance term (constant background lake inflow minus leakage and evaporative loss) is estimated to within the range of 2.89 and -1.17 m³s-¹ suggesting that the unknown portion of leakage and evaporative losses are not significant contributors to model error. A useful consequence of the regression was that regression coefficients could be used as a means of upscaling to give net lake storage change for low-flow conditions. This enabled day-ahead water availability forecasts to be acquired from Aniwaniwa Stream discharge day-ahead forecasts.

Two forecasting methodologies are developed to forecast the Aniwaniwa Stream discharge: a finite mixture rainfall-runoff model, and a multiple linear regression method. The rainfall-runoff model is formulated initially as a many-parameter model which is then subjected to a lasso-based model simplification concurrent with model calibration. The simplified model forecasts next-day inflows by using a weighted linear combination of hydrograph forms which best match the previous observed discharges in the calibration set where the various weights are linear functions of recent rainfalls. An auto-recalibrating version of the rainfall-runoff model was also developed where model simplification and calibration is carried out for each forecast, with the greatest fitting weights most likely on the most recent discharges to allow for changing catchment conditions.

The rainfall-runoff model was calibrated under a range of lasso-based parameter elimination pressures to determine the number of parameters which gave the best validation fit as quantified by the Nash-Sutcliffe fit. The highest validation fit using the original rainfall-runoff model was 50.7%. Using the auto-recalibrating rainfall-runoff model a slightly better maximum validation fit of (52.3%) occurred at an elimination pressure giving 14 final parameters from an initial 300. However, a validation fit which is not much lower (46.8%) is achieved at a higher elimination pressure yielding just 6 final parameters, demonstrating a trade-off between model simplification and validation fit. As expected, the rainfall-runoff model was more successful at predicting low to medium flows because forecasting focus was on the lower flows. Higher discharges were consistently under-predicted. Validation fits of the rainfall-runoff model could probably be improved by increasing the range of possible hydrograph forms available for selection at the expense of model simplicity.

The multiple regression technique was applied to forecast ‘next-day’ Aniwaniwa inflows in a simpler way, in this case using just current daily rainfall and discharges as independent variables. The discharge forecasts derived from both techniques are then scaled using the regression equation mentioned earlier to give net storage change estimates into Lake Waikaremoana for low to medium inflows. The regression approach was the more successful for overall day-ahead Aniwaniwa flow forecasts. The final prediction for current day storage change is: ΔS = 0.399(AQ) + 0.59 [1] Where AQ is the observed daily total discharge of the Aniwaniwa Stream. Day-ahead Aniwaniwa Stream forecasts can be approximated by equation [2] then scaled to storage change using equation [1] AQ(Next-day) = 0.095(Train) + 0.558(TQ) + 0.611 [2] Where Train is current day total rainfall and TQ is current day total discharge. This single equation gave higher calibration fits than separate regressions based on season. Using only current rainfall and current discharge as independent variables, the Nash-Sutcliffe validation fits were as high as 66%.

The linear regression approach gives the most useful inflow estimates to Lake Waikaremoana for the current day, based on upscaling the Aniwaniwa Stream discharges for low to medium flows. Estimating the day-ahead lake inflows is then equated to estimating day-ahead Aniwaniwa discharges for conditions outside of high flows. For this day-ahead forecasting the regression technique proved better than the rainfall-runoff models. It is thus recommended that the multiple regression technique is applied at the Waikaremoana Power Scheme.

text: Forecasting Lake Waikaremoana Water Availability for Hydro Power Lake Waikaremoana is a high-altitude, large-volume lake located within the rugged terrain of the Urewera National Park. At the lake outflow a rapid elevation change of nearly 450 metres in 8 kilometres facilitates the lake’s use as the upper intake portal for the Waikaremoana Hydro Power Scheme. At the time of this study, Genesis Energy operated the Waikaremoana Power Scheme in response to a water availability model based on daily lake level differencing from which daily generation capacity is predicted, allowing strategic bidding into the electricity market. However, when river flows are low this model is subject to error, as small changes in lake level sometimes cannot be determined accurately beyond background noise on daily timescales.

This project develops a method of estimating both current day and day-ahead water availability of Lake Waikaremoana, independent of lake levels using simple hydrological models, thereby improving operational efficiency of the Waikaremoana Power Scheme. The forecasting is developed specifically for the lower inflow conditions when the lake level differencing approach is most error prone.

It has long been recognised that a significant volume of Lake Waikaremoana water leaks through the ancient landslide dam which created the lake. Previous to this study, it was considered that an inaccurate estimation of this leakage rate combined with evaporative losses might contribute to the error within the existing water availability model. A modified catchment water balance and simple regression approach was applied to Lake Waikaremoana to estimate the lake water loss not accounted for by recorded outflows. Estimating this unrecorded loss translates to estimating the intercept of a linear regression relation, where the assumption is made that there is a linear relationship between the discharge of the Aniwaniwa Stream and the net lake water balance (excluding known outflows) under low inflow conditions. On the basis of the confidence intervals about the intercept, the balance term (constant background lake inflow minus leakage and evaporative loss) is estimated to within the range of 2.89 and -1.17 m³s-¹ suggesting that the unknown portion of leakage and evaporative losses are not significant contributors to model error. A useful consequence of the regression was that regression coefficients could be used as a means of upscaling to give net lake storage change for low-flow conditions. This enabled day-ahead water availability forecasts to be acquired from Aniwaniwa Stream discharge day-ahead forecasts.

Two forecasting methodologies are developed to forecast the Aniwaniwa Stream discharge: a finite mixture rainfall-runoff model, and a multiple linear regression method. The rainfall-runoff model is formulated initially as a many-parameter model which is then subjected to a lasso-based model simplification concurrent with model calibration. The simplified model forecasts next-day inflows by using a weighted linear combination of hydrograph forms which best match the previous observed discharges in the calibration set where the various weights are linear functions of recent rainfalls. An auto-recalibrating version of the rainfall-runoff model was also developed where model simplification and calibration is carried out for each forecast, with the greatest fitting weights most likely on the most recent discharges to allow for changing catchment conditions.

The rainfall-runoff model was calibrated under a range of lasso-based parameter elimination pressures to determine the number of parameters which gave the best validation fit as quantified by the Nash-Sutcliffe fit. The highest validation fit using the original rainfall-runoff model was 50.7%. Using the auto-recalibrating rainfall-runoff model a slightly better maximum validation fit of (52.3%) occurred at an elimination pressure giving 14 final parameters from an initial 300. However, a validation fit which is not much lower (46.8%) is achieved at a higher elimination pressure yielding just 6 final parameters, demonstrating a trade-off between model simplification and validation fit. As expected, the rainfall-runoff model was more successful at predicting low to medium flows because forecasting focus was on the lower flows. Higher discharges were consistently under-predicted. Validation fits of the rainfall-runoff model could probably be improved by increasing the range of possible hydrograph forms available for selection at the expense of model simplicity.

The multiple regression technique was applied to forecast ‘next-day’ Aniwaniwa inflows in a simpler way, in this case using just current daily rainfall and discharges as independent variables. The discharge forecasts derived from both techniques are then scaled using the regression equation mentioned earlier to give net storage change estimates into Lake Waikaremoana for low to medium inflows. The regression approach was the more successful for overall day-ahead Aniwaniwa flow forecasts. The final prediction for current day storage change is: ΔS = 0.399(AQ) + 0.59 [1] Where AQ is the observed daily total discharge of the Aniwaniwa Stream. Day-ahead Aniwaniwa Stream forecasts can be approximated by equation [2] then scaled to storage change using equation [1] AQ(Next-day) = 0.095(Train) + 0.558(TQ) + 0.611 [2] Where Train is current day total rainfall and TQ is current day total discharge. This single equation gave higher calibration fits than separate regressions based on season. Using only current rainfall and current discharge as independent variables, the Nash-Sutcliffe validation fits were as high as 66%.

The linear regression approach gives the most useful inflow estimates to Lake Waikaremoana for the current day, based on upscaling the Aniwaniwa Stream discharges for low to medium flows. Estimating the day-ahead lake inflows is then equated to estimating day-ahead Aniwaniwa discharges for conditions outside of high flows. For this day-ahead forecasting the regression technique proved better than the rainfall-runoff models. It is thus recommended that the multiple regression technique is applied at the Waikaremoana Power Scheme.

year: 2011

title: Genetic diversity among populations of Antarctic springtails (Collembola) within the Mackay Glacier ecotone

authors: Beet, Clare Rose

abstract: Climate changes are likely to have major influences on the distribution and abundance of Antarctic terrestrial biota. To assess arthropod distribution and diversity within the Ross Sea region, we examined mitochondrial DNA (COI) sequences for three currently recognized species of springtail (Collembola) collected from sites in the vicinity, and to the north of, the Mackay Glacier (77°S). This area acts as a transition between two biogeographic regions (northern and southern Victoria Land). We found populations of highly divergent individuals (5%–11.3% intraspecific sequence divergence) for each of the three putative springtail species, suggesting the possibility of cryptic diversity. Based on molecular clock estimates, these divergent lineages are likely to have been isolated for 3–5 million years. It was during this time that the Western Antarctic Ice Sheet (WAIS) was likely to have completely collapsed, potentially facilitating springtail dispersal via rafting on running waters and open seaways. The reformation of the WAIS would have isolated newly established populations, with subsequent dispersal restricted by glaciers and ice-covered areas. Given the currently limited distributions for these genetically divergent populations, any future changes in species’ distributions can be easily tracked through the DNA barcoding of springtails from within the Mackay Glacier ecotone.

text: Genetic diversity among populations of Antarctic springtails (Collembola) within the Mackay Glacier ecotone Climate changes are likely to have major influences on the distribution and abundance of Antarctic terrestrial biota. To assess arthropod distribution and diversity within the Ross Sea region, we examined mitochondrial DNA (COI) sequences for three currently recognized species of springtail (Collembola) collected from sites in the vicinity, and to the north of, the Mackay Glacier (77°S). This area acts as a transition between two biogeographic regions (northern and southern Victoria Land). We found populations of highly divergent individuals (5%–11.3% intraspecific sequence divergence) for each of the three putative springtail species, suggesting the possibility of cryptic diversity. Based on molecular clock estimates, these divergent lineages are likely to have been isolated for 3–5 million years. It was during this time that the Western Antarctic Ice Sheet (WAIS) was likely to have completely collapsed, potentially facilitating springtail dispersal via rafting on running waters and open seaways. The reformation of the WAIS would have isolated newly established populations, with subsequent dispersal restricted by glaciers and ice-covered areas. Given the currently limited distributions for these genetically divergent populations, any future changes in species’ distributions can be easily tracked through the DNA barcoding of springtails from within the Mackay Glacier ecotone.

year: 2016

title: Decolonising legal research: Developing legal theory to articulate Māori and non-Māori legal research paradigms equitably

authors: Hasan-Stein, Linda

abstract: Māori and non-Māori legal research paradigms in Aotearoa New Zealand are separated by a considerable theoretical knowledge gap. Māori knowledge systems are generally not well known in a non-Māori context. In order to bridge this theoretical knowledge gap jurisprudential studies need to address this gap from Māori and non-Māori perspectives. Doing so enables the development of decolonised legal research paradigms which allow for the sharing of knowledge from positions of respect. In this work, a new theoretical interpretation of legal research paradigms in our jurisprudence is presented, relying on an interdisciplinary approach to support these interpretive strategies. 

Beginning with the understanding that knowledge is empowering for both Māori and non-Māori, I foreground the epistemological character of decolonising legal research that supports Linda Tuhiwai Smith’s call for research to be conceived differently and highlight the need for an integrated recognition of kaupapa Māori in the development of legal theory in Aotearoa New Zealand. Reimagining our laws as something more than ‘sovereignty’ is the first step in narrowing the current theoretical knowledge gap. I translate the broader language of colonialism into the more specific vocabulary of the criminal justice system, in order to make more visible the manner in which Eurocentrism permeates decolonising legal research and stifles the potential future social development of Māori. 

Since Linda Tuhiwai Smith’s call to decolonise research, significant progress has been made with regard to the inclusion of principles of tikanga Māori to guide legal research that includes Māori. However, transforming principles of tikanga Māori into our jurisprudential landscape is a complex task. It is increasingly recognised that understanding the key principles of tikanga Māori is not always sufficient and that a greater theoretical understanding of decolonising legal principles is needed. I will analyse theoretical features of research epistemologies with the goal of grasping the complex array of historically-specific practices through which particular dimensions of our socio-legal experience are produced. 

Finally, I will explore how an interdisciplinary approach enables us to link forms of subjectivity to forms of objectivity in a distinctively “cultural” way, by working through difference rather than against it, and by acknowledging as meaningful each law’s characteristic discursive formation. 

This work is written as an intervention in Eurocentrism, aimed at providing a fresh interpretation of decolonising legal research. On this level, the most important argumentative thread is the one that demonstrates how Eurocentrism can be read as a colonising tool, which deploys positions that marginalise Indigenous knowledge. By unpacking Eurocentrism’s complex meaning it is possible to refashion Eurocentrism to include the notions of “partnerships”, that value subjective experience over objective, and that, in reality, include “Indigenous cultural” qualities. 

This style of decolonising jurisprudence pushes strenuously for a legal paradigm shift towards a culturally safe space for all legal scholars, not just Māori; a shift that could encourage our legal theory to converge in a more holistic way. The most important argumentative threads are those centred on the inclusion of Indigenous arguments, and the emergent character of decolonising legal research categories such as whanaungatanga or relational accountability. This type of innovative legal interpretation offers the possibility for a new theoretical era for decolonising legal research.

text: Decolonising legal research: Developing legal theory to articulate Māori and non-Māori legal research paradigms equitably Māori and non-Māori legal research paradigms in Aotearoa New Zealand are separated by a considerable theoretical knowledge gap. Māori knowledge systems are generally not well known in a non-Māori context. In order to bridge this theoretical knowledge gap jurisprudential studies need to address this gap from Māori and non-Māori perspectives. Doing so enables the development of decolonised legal research paradigms which allow for the sharing of knowledge from positions of respect. In this work, a new theoretical interpretation of legal research paradigms in our jurisprudence is presented, relying on an interdisciplinary approach to support these interpretive strategies. 

Beginning with the understanding that knowledge is empowering for both Māori and non-Māori, I foreground the epistemological character of decolonising legal research that supports Linda Tuhiwai Smith’s call for research to be conceived differently and highlight the need for an integrated recognition of kaupapa Māori in the development of legal theory in Aotearoa New Zealand. Reimagining our laws as something more than ‘sovereignty’ is the first step in narrowing the current theoretical knowledge gap. I translate the broader language of colonialism into the more specific vocabulary of the criminal justice system, in order to make more visible the manner in which Eurocentrism permeates decolonising legal research and stifles the potential future social development of Māori. 

Since Linda Tuhiwai Smith’s call to decolonise research, significant progress has been made with regard to the inclusion of principles of tikanga Māori to guide legal research that includes Māori. However, transforming principles of tikanga Māori into our jurisprudential landscape is a complex task. It is increasingly recognised that understanding the key principles of tikanga Māori is not always sufficient and that a greater theoretical understanding of decolonising legal principles is needed. I will analyse theoretical features of research epistemologies with the goal of grasping the complex array of historically-specific practices through which particular dimensions of our socio-legal experience are produced. 

Finally, I will explore how an interdisciplinary approach enables us to link forms of subjectivity to forms of objectivity in a distinctively “cultural” way, by working through difference rather than against it, and by acknowledging as meaningful each law’s characteristic discursive formation. 

This work is written as an intervention in Eurocentrism, aimed at providing a fresh interpretation of decolonising legal research. On this level, the most important argumentative thread is the one that demonstrates how Eurocentrism can be read as a colonising tool, which deploys positions that marginalise Indigenous knowledge. By unpacking Eurocentrism’s complex meaning it is possible to refashion Eurocentrism to include the notions of “partnerships”, that value subjective experience over objective, and that, in reality, include “Indigenous cultural” qualities. 

This style of decolonising jurisprudence pushes strenuously for a legal paradigm shift towards a culturally safe space for all legal scholars, not just Māori; a shift that could encourage our legal theory to converge in a more holistic way. The most important argumentative threads are those centred on the inclusion of Indigenous arguments, and the emergent character of decolonising legal research categories such as whanaungatanga or relational accountability. This type of innovative legal interpretation offers the possibility for a new theoretical era for decolonising legal research.

year: 2026