title: Modelling temporal dynamics of discharge and nutrient loading from a mixed land use catchment, and interactions with a eutrophic, temperate lake under climate change

authors: Me, Wang

abstract: Understanding anthropogenic–induced changes in catchment water discharge and nutrient loads is critical for eutrophication assessment and sustainable management of receiving environments. Anthropogenic activities have increased nutrient export from terrestrial systems to lakes, where they may lead to eutrophication. Impacts of excess nutrients may be exacerbated by a warming climate. A variety of catchment models has been developed to gain insight into the temporal and spatial variations in discharge, and suspended sediment and nutrient transport in response to climate forcing and rainfall–runoff. These models can be used to predict the effects of different land management strategies and climate change on discharge and losses of particulate and dissolved constituents of the discharge. The integration of individual components of the modelling framework, including climate, catchment and aquatic ecosystem models, enables simulation and prediction of present and future states of freshwater ecosystems, including their spatial and temporal dynamics. 
    The study area for this thesis is the Lake Rotorua catchment (~410 km²; Bay of Plenty, North Island, New Zealand). Commencement in 1991 of spray irrigation of treated wastewater (10 mm d⁻¹) from Rotorua city in the Whakarewarewa Forest was envisaged as a solution to eutrophication of Lake Rotorua (surface area ~80 km2) where treated wastewater (to secondary treatment level) had previously been discharged. The Waipa Stream draining the irrigated area (~2 km²) discharges to the Puarenga Stream, ultimately entering Lake Rotorua. The Puarenga Stream is the second–largest surface inflow to Lake Rotorua and drains a catchment of 77 km². Land use in the Puarenga Stream catchment is mostly plantation forest within which there are 16 blocks for spray irrigation of wastewater. The catchment has an area of pastoral farmland (8 km²) that is typically fertilised with nitrogen (N) and phosphorus (P), as well as being irrigated with cowshed washdown which also contributed N and P. 
    The overarching aim of this study was to utilize advanced modelling technologies to simulate the discharge and sediment and nutrient loads from a mixed land use catchment of Puarenga Stream, part of which is spray–irrigated with wastewater in Waipa Stream catchment, and to model and understand the impacts and effects of different management regimes on the receiving waterbody; a temperate eutrophic lake (Rotorua). To achieve this, the study encompassed three main areas of research: 1) a process–based catchment model (Soil and Water Assessment Tool) application in the Puarenga catchment of Lake Rotorua under different hydrologic conditions, testing the influence of parameter sensitivity; 2) improvements to the catchment model (SWAT) to represent high–frequency (daily and hourly) variability of nutrient discharges and to simulate different land and wastewater irrigation management strategies; and 3) an application of the improved catchment model (from (2) above) combined with the lake model (DYRESM–CAEDYM) to predict the response of Lake Rotorua to future climate in 2090 and catchment nutrient discharge.
    The objective of the first research component (Chapter 2) was to examine the applicability of SWAT2009 model (version rev488) to the Puarenga catchment. The research included quantifying model performance and parameter sensitivity during different hydrologic conditions. A Sequential Uncertainty Fitting (SUFI–2) procedure was used to auto–calibrate unknown parameter values in the SWAT2009 model for years 2004–2008. Model validation was performed using: 1) monthly instantaneous measurements of suspended sediment (SS), total phosphorus (TP) and total nitrogen (TN) concentrations (1994–1997); and 2) daily discharge–weighted mean concentrations calculated from high–frequency event–based samples for concentrations of SS (nine events), TP and TN (both 14 events) at 1 h or 2 h frequency (2010–2012). Model error associated with quick–flow was underestimated (44% bias for SS, 70% bias for TP) compared with monthly measurements derived predominantly from base flow measurements (< 1% bias for SS, 24% bias for TP). The use of low–frequency base flow measurements for model calibration provided poor simulation results for “flashy” lower–order streams. The model results highlight the importance of using high–frequency, event–based monitoring data for calibration, to alleviate the potential for underestimation of storm–driven fluxes. A manual procedure (one–at–a–time sensitivity analysis) was used to quantify parameter sensitivity for the two hydrologically–separated regimes. Parameters relating to tuning of main channel processes (e.g., lateral flow slope length and travel time) were more sensitive for base flow estimates (particularly discharge and SS), while those relating to overland processes (e.g., Manning's n value for overland flow) were more sensitive for the quick flow estimates. Separating discharge and loads of sediments and nutrients into a base flow and a quick flow component provided important insights into uncertainties in parameter values. This research has important implications for performance of hydrological models applied to catchments with large fluctuations in stream flow, and in cases where models are used to examine scenarios that involve substantial changes to the existing flow regime. 
    The SWAT2009 model described in Chapter 2 did not have algorithms to simulate a complex irrigation operation. The objective of the second research chapter (Chapter 3) was therefore to develop a capability to simulate the irrigated sub–catchment and examine alternatives for managing the wastewater. A modified version of the SWAT2012 code (rev629) using hourly routing algorithms was adapted to the Waipa Stream sub–catchment within the Puarenga catchment. A similar configuration to Chapter 2 was applied for the modelling except that a finer temporal resolution of rainfall records was used in Chapter 3. Hourly records at Kaituna rain gauge, which is outside of the irrigated sub–catchment, were used to allocate weekly records at Red Stag gauge, which is within the irrigated sub–catchment, to hourly rainfall values. The modified SWAT2012 model was run at an hourly time step for a 10–year (2003–2012) period using the daily irrigation routine, then calibrated and validated by comparing weekly average predictions with measurements. The optimised values of parameters were different from those in Chapter 2. A range of statistical metrics indicated that the SWAT2012 model performed well using hourly routing with respect to 10–year (2003–2012) daily simulations that were averaged to the weekly measurements for comparison of discharge (r ≥ 0.81; p < 0.001) and TN load (r ≥ 0.73; p < 0.001), but it did not perform so well for simulations of both SS (0.43 ≤ r ≤ 0.54; p < 0.001) and TP load (0.45 ≤ r ≤ 0.54; p < 0.001) in both the calibration and validation periods. Hourly routing gave high temporal variability of TN load, although lower than the variability of SS and TP loads (i.e., SS > TP > TN variability). Simulations were run using daily outputs for an unirrigated scenario and for a range of other management options including changes in the area, frequency and amount of irrigation. Increasing the irrigation area decreased TP and TN loads in the simulation. The impact of changing irrigation frequency from daily to one day each week was small for annual TP load simulations. Annual TN load increased considerably under weekly irrigation. Compared with low–frequency, high–volume wastewater applications (once every seven days), the current strategy of daily wastewater irrigation minimises TN leaching and reduces saturation of the subsurface layer. Improvements to the SWAT2012 model and the use of hourly routing to capture high–frequency (daily and hourly) variability of nutrient discharges and simulations of different wastewater irrigation management regimes may assist with future strategies to mitigate P and N losses from the irrigated area by refining the area, timing, frequency and amount of irrigation.
    In Chapter 4 the primary objective was to combine the modified SWAT2012 model from Chapter 3 with the lake model (DYRESM–CAEDYM version 4.0) to simulate the trophic state of Lake Rotorua (mean depth 10.8 m), in response to nutrient load reductions from wastewater–irrigated forest and farmland in the Puarenga Stream catchment under present and future climates. Initial parameter values required for the setup of both models were based on the monitoring data that were measured close to the start date of the simulation period. A range of statistical metrics indicated that the SWAT2012 model performed well (r ≥ 0.88, p < 0.001) with respect to comparisons of monthly catchment discharge, TN and TP loads, and less so (r = 0.78, p < 0.01) for TN concentration, and not at all well for TP concentration (r = 0.17, p > 0.05) for the 4–year (2006–2010) simulation period. SWAT2012 model simulations were used for the Puarenga Stream input to the DYRESM–CAEDYM model of Lake Rotorua while other inflows used either measured data or values derived from other studies. Considering the 1.5–year lake residence time for Lake Rotorua, the DYRESM–CAEDYM model was validated using monthly data collected at two sites during 2008–2010. The DYRESM–CAEDYM model performed well (r ≥ 0.63; p < 0.01) for surface water TP and TN concentrations in both the calibration and validation periods, but not for bottom–water nutrient concentrations. Effects of land management practice were then examined by simulating four nutrient application scenarios relating to wastewater irrigation and farmland fertilisation within the Puarenga catchment. Under the scenario of removing nutrient applications from both wastewater irrigation and farmland fertilisation, nutrient load reductions were 39.5% for TP and 75.2% for TN in the Puarenga catchment but these had much lesser effect on nutrient concentrations in the lake, with reduction of 3.5% for TP, 5.7% for TN, and 4.1% for chlorophyll a (Chl a; as a proxy for phytoplankton biomass) in surface waters. Based on the Intergovernmental Panel on Climate Change Fifth Assessment report, for the projected future climate of 2090 under the RCP8.5 scenario (equivalent to a short–wave radiation increase of 8.5 W m-2), annual mean precipitation and solar radiation increase by 2.8% and 1.4%, respectively, humidity decreases by 0.6%, and air temperature increases by 2.7 °C. Downscaled climate projections for 2090 were derived from 22 general circulation models and used as input to SWAT and DYRESM–CAEDYM models of the catchment and lake, respectively. Simulations using a projected climate for 2090 had moderate impact on catchment nutrient loads (6% increase for TP, 7.6% decrease for TN), but concentrations in surface waters were predicted to increase by 45.9% for TP, 44.5% for TN, and 44.9% for Chl a from 2010 to 2090, suggesting that future climate change would increase eutrophication. Increased water temperatures would cause more frequent and longer periods of thermal stratification in polymictic lakes such as Rotorua, which would likely result in greater depletion of dissolved oxygen and possible anoxia of hypolimnetic waters. This overarching effect of climate change is likely to be through a physical response of the lake in the form of increased stratification and greater levels of internal nutrient loading.
    This thesis has demonstrated the effects of different hydrologic conditions on SWAT2009 model performance and parameter sensitivity using an application to a small, mixed land use catchment, Lake Rotorua, New Zealand. By using the hourly routing algorithms and modifying relevant model code to simulate complex catchment irrigation operations, the SWAT2012 model performance was improved, particularly for high–frequency simulation of SS, TP and TN loads to the receiving lake. Finally, the modified SWAT2012 model combined with the lake model (DYRESM–CAEDYM) predicted that future climate change should be factored into assessments of the future trophic state of Lake Rotorua.

text: Modelling temporal dynamics of discharge and nutrient loading from a mixed land use catchment, and interactions with a eutrophic, temperate lake under climate change Understanding anthropogenic–induced changes in catchment water discharge and nutrient loads is critical for eutrophication assessment and sustainable management of receiving environments. Anthropogenic activities have increased nutrient export from terrestrial systems to lakes, where they may lead to eutrophication. Impacts of excess nutrients may be exacerbated by a warming climate. A variety of catchment models has been developed to gain insight into the temporal and spatial variations in discharge, and suspended sediment and nutrient transport in response to climate forcing and rainfall–runoff. These models can be used to predict the effects of different land management strategies and climate change on discharge and losses of particulate and dissolved constituents of the discharge. The integration of individual components of the modelling framework, including climate, catchment and aquatic ecosystem models, enables simulation and prediction of present and future states of freshwater ecosystems, including their spatial and temporal dynamics. 
    The study area for this thesis is the Lake Rotorua catchment (~410 km²; Bay of Plenty, North Island, New Zealand). Commencement in 1991 of spray irrigation of treated wastewater (10 mm d⁻¹) from Rotorua city in the Whakarewarewa Forest was envisaged as a solution to eutrophication of Lake Rotorua (surface area ~80 km2) where treated wastewater (to secondary treatment level) had previously been discharged. The Waipa Stream draining the irrigated area (~2 km²) discharges to the Puarenga Stream, ultimately entering Lake Rotorua. The Puarenga Stream is the second–largest surface inflow to Lake Rotorua and drains a catchment of 77 km². Land use in the Puarenga Stream catchment is mostly plantation forest within which there are 16 blocks for spray irrigation of wastewater. The catchment has an area of pastoral farmland (8 km²) that is typically fertilised with nitrogen (N) and phosphorus (P), as well as being irrigated with cowshed washdown which also contributed N and P. 
    The overarching aim of this study was to utilize advanced modelling technologies to simulate the discharge and sediment and nutrient loads from a mixed land use catchment of Puarenga Stream, part of which is spray–irrigated with wastewater in Waipa Stream catchment, and to model and understand the impacts and effects of different management regimes on the receiving waterbody; a temperate eutrophic lake (Rotorua). To achieve this, the study encompassed three main areas of research: 1) a process–based catchment model (Soil and Water Assessment Tool) application in the Puarenga catchment of Lake Rotorua under different hydrologic conditions, testing the influence of parameter sensitivity; 2) improvements to the catchment model (SWAT) to represent high–frequency (daily and hourly) variability of nutrient discharges and to simulate different land and wastewater irrigation management strategies; and 3) an application of the improved catchment model (from (2) above) combined with the lake model (DYRESM–CAEDYM) to predict the response of Lake Rotorua to future climate in 2090 and catchment nutrient discharge.
    The objective of the first research component (Chapter 2) was to examine the applicability of SWAT2009 model (version rev488) to the Puarenga catchment. The research included quantifying model performance and parameter sensitivity during different hydrologic conditions. A Sequential Uncertainty Fitting (SUFI–2) procedure was used to auto–calibrate unknown parameter values in the SWAT2009 model for years 2004–2008. Model validation was performed using: 1) monthly instantaneous measurements of suspended sediment (SS), total phosphorus (TP) and total nitrogen (TN) concentrations (1994–1997); and 2) daily discharge–weighted mean concentrations calculated from high–frequency event–based samples for concentrations of SS (nine events), TP and TN (both 14 events) at 1 h or 2 h frequency (2010–2012). Model error associated with quick–flow was underestimated (44% bias for SS, 70% bias for TP) compared with monthly measurements derived predominantly from base flow measurements (< 1% bias for SS, 24% bias for TP). The use of low–frequency base flow measurements for model calibration provided poor simulation results for “flashy” lower–order streams. The model results highlight the importance of using high–frequency, event–based monitoring data for calibration, to alleviate the potential for underestimation of storm–driven fluxes. A manual procedure (one–at–a–time sensitivity analysis) was used to quantify parameter sensitivity for the two hydrologically–separated regimes. Parameters relating to tuning of main channel processes (e.g., lateral flow slope length and travel time) were more sensitive for base flow estimates (particularly discharge and SS), while those relating to overland processes (e.g., Manning's n value for overland flow) were more sensitive for the quick flow estimates. Separating discharge and loads of sediments and nutrients into a base flow and a quick flow component provided important insights into uncertainties in parameter values. This research has important implications for performance of hydrological models applied to catchments with large fluctuations in stream flow, and in cases where models are used to examine scenarios that involve substantial changes to the existing flow regime. 
    The SWAT2009 model described in Chapter 2 did not have algorithms to simulate a complex irrigation operation. The objective of the second research chapter (Chapter 3) was therefore to develop a capability to simulate the irrigated sub–catchment and examine alternatives for managing the wastewater. A modified version of the SWAT2012 code (rev629) using hourly routing algorithms was adapted to the Waipa Stream sub–catchment within the Puarenga catchment. A similar configuration to Chapter 2 was applied for the modelling except that a finer temporal resolution of rainfall records was used in Chapter 3. Hourly records at Kaituna rain gauge, which is outside of the irrigated sub–catchment, were used to allocate weekly records at Red Stag gauge, which is within the irrigated sub–catchment, to hourly rainfall values. The modified SWAT2012 model was run at an hourly time step for a 10–year (2003–2012) period using the daily irrigation routine, then calibrated and validated by comparing weekly average predictions with measurements. The optimised values of parameters were different from those in Chapter 2. A range of statistical metrics indicated that the SWAT2012 model performed well using hourly routing with respect to 10–year (2003–2012) daily simulations that were averaged to the weekly measurements for comparison of discharge (r ≥ 0.81; p < 0.001) and TN load (r ≥ 0.73; p < 0.001), but it did not perform so well for simulations of both SS (0.43 ≤ r ≤ 0.54; p < 0.001) and TP load (0.45 ≤ r ≤ 0.54; p < 0.001) in both the calibration and validation periods. Hourly routing gave high temporal variability of TN load, although lower than the variability of SS and TP loads (i.e., SS > TP > TN variability). Simulations were run using daily outputs for an unirrigated scenario and for a range of other management options including changes in the area, frequency and amount of irrigation. Increasing the irrigation area decreased TP and TN loads in the simulation. The impact of changing irrigation frequency from daily to one day each week was small for annual TP load simulations. Annual TN load increased considerably under weekly irrigation. Compared with low–frequency, high–volume wastewater applications (once every seven days), the current strategy of daily wastewater irrigation minimises TN leaching and reduces saturation of the subsurface layer. Improvements to the SWAT2012 model and the use of hourly routing to capture high–frequency (daily and hourly) variability of nutrient discharges and simulations of different wastewater irrigation management regimes may assist with future strategies to mitigate P and N losses from the irrigated area by refining the area, timing, frequency and amount of irrigation.
    In Chapter 4 the primary objective was to combine the modified SWAT2012 model from Chapter 3 with the lake model (DYRESM–CAEDYM version 4.0) to simulate the trophic state of Lake Rotorua (mean depth 10.8 m), in response to nutrient load reductions from wastewater–irrigated forest and farmland in the Puarenga Stream catchment under present and future climates. Initial parameter values required for the setup of both models were based on the monitoring data that were measured close to the start date of the simulation period. A range of statistical metrics indicated that the SWAT2012 model performed well (r ≥ 0.88, p < 0.001) with respect to comparisons of monthly catchment discharge, TN and TP loads, and less so (r = 0.78, p < 0.01) for TN concentration, and not at all well for TP concentration (r = 0.17, p > 0.05) for the 4–year (2006–2010) simulation period. SWAT2012 model simulations were used for the Puarenga Stream input to the DYRESM–CAEDYM model of Lake Rotorua while other inflows used either measured data or values derived from other studies. Considering the 1.5–year lake residence time for Lake Rotorua, the DYRESM–CAEDYM model was validated using monthly data collected at two sites during 2008–2010. The DYRESM–CAEDYM model performed well (r ≥ 0.63; p < 0.01) for surface water TP and TN concentrations in both the calibration and validation periods, but not for bottom–water nutrient concentrations. Effects of land management practice were then examined by simulating four nutrient application scenarios relating to wastewater irrigation and farmland fertilisation within the Puarenga catchment. Under the scenario of removing nutrient applications from both wastewater irrigation and farmland fertilisation, nutrient load reductions were 39.5% for TP and 75.2% for TN in the Puarenga catchment but these had much lesser effect on nutrient concentrations in the lake, with reduction of 3.5% for TP, 5.7% for TN, and 4.1% for chlorophyll a (Chl a; as a proxy for phytoplankton biomass) in surface waters. Based on the Intergovernmental Panel on Climate Change Fifth Assessment report, for the projected future climate of 2090 under the RCP8.5 scenario (equivalent to a short–wave radiation increase of 8.5 W m-2), annual mean precipitation and solar radiation increase by 2.8% and 1.4%, respectively, humidity decreases by 0.6%, and air temperature increases by 2.7 °C. Downscaled climate projections for 2090 were derived from 22 general circulation models and used as input to SWAT and DYRESM–CAEDYM models of the catchment and lake, respectively. Simulations using a projected climate for 2090 had moderate impact on catchment nutrient loads (6% increase for TP, 7.6% decrease for TN), but concentrations in surface waters were predicted to increase by 45.9% for TP, 44.5% for TN, and 44.9% for Chl a from 2010 to 2090, suggesting that future climate change would increase eutrophication. Increased water temperatures would cause more frequent and longer periods of thermal stratification in polymictic lakes such as Rotorua, which would likely result in greater depletion of dissolved oxygen and possible anoxia of hypolimnetic waters. This overarching effect of climate change is likely to be through a physical response of the lake in the form of increased stratification and greater levels of internal nutrient loading.
    This thesis has demonstrated the effects of different hydrologic conditions on SWAT2009 model performance and parameter sensitivity using an application to a small, mixed land use catchment, Lake Rotorua, New Zealand. By using the hourly routing algorithms and modifying relevant model code to simulate complex catchment irrigation operations, the SWAT2012 model performance was improved, particularly for high–frequency simulation of SS, TP and TN loads to the receiving lake. Finally, the modified SWAT2012 model combined with the lake model (DYRESM–CAEDYM) predicted that future climate change should be factored into assessments of the future trophic state of Lake Rotorua.

year: 2017

title: Eliciting informative priors by modeling expert decision making

authors: Falconer, Julia Ruth

abstract: There are significant limitations to current methods for eliciting the prior beliefs of experts. To combat some of these limitations, this paper proposes an alternative approach that infers an expert’s prior beliefs about an uncertain event, A, from the expert’s past decisions. We show that an analyst can use past information on an expert’s decision-making task, contingent on an expert’s prior of A, to model the decision-making process and infer an approximation of the prior for A. This concept is illustrated by an application to recidivism. We conclude this work by highlighting important directions for future research. Funding: J. R. Falconer’s research is funded through the University of Waikato Doctoral Scholarship.

text: Eliciting informative priors by modeling expert decision making There are significant limitations to current methods for eliciting the prior beliefs of experts. To combat some of these limitations, this paper proposes an alternative approach that infers an expert’s prior beliefs about an uncertain event, A, from the expert’s past decisions. We show that an analyst can use past information on an expert’s decision-making task, contingent on an expert’s prior of A, to model the decision-making process and infer an approximation of the prior for A. This concept is illustrated by an application to recidivism. We conclude this work by highlighting important directions for future research. Funding: J. R. Falconer’s research is funded through the University of Waikato Doctoral Scholarship.

year: 2023

title: “I learned quite a lot of the Maths stuff now that I think of it”: Māori Medium Students reflecting on their Initial Teacher Education

authors: Hawera, Ngārewa

subjects: initial teacher education

abstract: Research involving preservice or initial teacher education (ITE) indicates that mathematics education is a vital component of study. Little is known however, of indigenous student views of their compulsory mathematics education courses for a teaching degree. This research contributes to that knowledge space as it explores Māori medium ITE students’ perceptions of mathematics education in Aotearoa New Zealand. A thematic and qualitative analysis of a focused group discussion provides insights into key factors that students reported as significant links between their university and practicum experiences (teaching practice in schools). Some suggestions for strengthening that programme were also expressed. Findings indicate that factors linked to teacher ‘cultural competencies’, including an ethic of care, respectful relationships, revision of content knowledge, language learning, assessment practices, exposure to different ideas and planning and pedagogy were important. Navigating student-mentor teacher tensions as well as clarifying the significance of ideas in texts were highlighted as areas for strengthening. Mathematics educators preparing students for indigenous primary school settings may find this study useful.

text: “I learned quite a lot of the Maths stuff now that I think of it”: Māori Medium Students reflecting on their Initial Teacher Education Research involving preservice or initial teacher education (ITE) indicates that mathematics education is a vital component of study. Little is known however, of indigenous student views of their compulsory mathematics education courses for a teaching degree. This research contributes to that knowledge space as it explores Māori medium ITE students’ perceptions of mathematics education in Aotearoa New Zealand. A thematic and qualitative analysis of a focused group discussion provides insights into key factors that students reported as significant links between their university and practicum experiences (teaching practice in schools). Some suggestions for strengthening that programme were also expressed. Findings indicate that factors linked to teacher ‘cultural competencies’, including an ethic of care, respectful relationships, revision of content knowledge, language learning, assessment practices, exposure to different ideas and planning and pedagogy were important. Navigating student-mentor teacher tensions as well as clarifying the significance of ideas in texts were highlighted as areas for strengthening. Mathematics educators preparing students for indigenous primary school settings may find this study useful.

year: 2017