title: An analysis of total correctness refinement models for partial relation semantics I

authors: Deutsch, Moshe

subjects: operation refinement

abstract: This is the first of a series of papers devoted to the thorough investigation of (total correctness) refinement based on an underlying partial relational model. In this paper we restrict attention to operation refinement. We explore four theories of refinement based on an underlying partial relation model for specifications, and we show that they are all equivalent. This, in particular, sheds some light on the relational completion operator (lifted-totalisation) due to Wookcock which underlines data refinement in, for example, the specification language Z. It further leads to two simple alternative models which are also equivalent to the others.

text: An analysis of total correctness refinement models for partial relation semantics I This is the first of a series of papers devoted to the thorough investigation of (total correctness) refinement based on an underlying partial relational model. In this paper we restrict attention to operation refinement. We explore four theories of refinement based on an underlying partial relation model for specifications, and we show that they are all equivalent. This, in particular, sheds some light on the relational completion operator (lifted-totalisation) due to Wookcock which underlines data refinement in, for example, the specification language Z. It further leads to two simple alternative models which are also equivalent to the others.

year: 2003

title: Rediscovering Arsenoacetic Acid

authors: Wilson, Peter Stanley

subjects: arsenoacetic acid

abstract: Arsonoacetic acid, H₂O₃As¹CH₂COOH, and arsenoacetic acid, punitively [AsVCH₂COOH]₂ have been synthesised according to historical literature methods, and have been characterised using modern techniques. Arsonoacetic acid was shown by an X-ray crystal structure analysis to be a molecular species with an extensive hydrogen bonding network in the crystal. Arsenoacetic acid proved to be more enigmatic. Electrospray mass spectra suggested it consisted of a mixtures of rings (RAs)n, n = 3-11, with n = 6 dominating. This was partly confirmed by a crystal structure of (AsCH₂COOH)₆ (as the pyridine solvate). On the other hand, ¹H and ¹³C NMR gave spectra that indicated only a single component for arsenoacetic acid. The formation of crystals of the high temperature phase of elemental sulfur, β-S8, at ambient temperature is also discussed.

text: Rediscovering Arsenoacetic Acid Arsonoacetic acid, H₂O₃As¹CH₂COOH, and arsenoacetic acid, punitively [AsVCH₂COOH]₂ have been synthesised according to historical literature methods, and have been characterised using modern techniques. Arsonoacetic acid was shown by an X-ray crystal structure analysis to be a molecular species with an extensive hydrogen bonding network in the crystal. Arsenoacetic acid proved to be more enigmatic. Electrospray mass spectra suggested it consisted of a mixtures of rings (RAs)n, n = 3-11, with n = 6 dominating. This was partly confirmed by a crystal structure of (AsCH₂COOH)₆ (as the pyridine solvate). On the other hand, ¹H and ¹³C NMR gave spectra that indicated only a single component for arsenoacetic acid. The formation of crystals of the high temperature phase of elemental sulfur, β-S8, at ambient temperature is also discussed.

year: 2009

title: The hydrodynamic evolution of the Maketū Estuary after the re-diversion of the Kaituna River

authors: Razzaghi, Mojgan

abstract: The Maketū Estuary and lower Kaituna River located in the Bay of Plenty, Aotearoa, New Zealand have undergone anthropic disturbances since late 1800s, including land reclamation, river diversion and re-diversion, and modifications to the river channels and estuary tidal inlet. This has resulted in estuarine degradation, as is a common issue worldwide. Globally different approaches to estuary restoration have aimed at mitigating the adverse impacts of estuarine degradation.  However, there are still gaps in restoration frameworks and how the success of the scheme is evaluated that mean there is no ready-made solution to the issues at Maketū.
This thesis examines the important role of the hydrodynamic processes (including water quality) that govern the overall physical response of Maketū Estuary to two stages of partial re-diversion of the Kaituna River into the estuary. The assessment of this physical response highlighted the necessity of a proper framework in which restoration attempts, such as at Maketū are evaluated.
Field time series data were collected before and after two stages of river re-diversion, Stage 1 in 2020 and Stage 2 in 2021, each over a span of a month, to record the immediate response of the estuary to the added freshwater flows. Freshwater flow into the estuary was constrained to approximately 4 hours during flood tides when the water level In the Kaituna River was at least 40 mm higher than the upper Maketū Estuary. The control gates also operate as a flood control scheme, so they remain shut if there is flood risk causing all the flood volume to discharge directly to the sea through Te Tumu Cut river mouth. 
The field data were obtained using Aquadopp ADPs, RBR Maestros, RBR Concertos, and Solinst water level loggers at seven different sites throughout the estuary and the Kaituna River. A hydrographic survey of the estuary using RTK-GNSS was undertaken and combined with LiDAR to produce a bathymetric map of the estuary and Lower Kaituna River. Comparison of this map to previous compilations showed that the tidal inlet and lower estuary have not undergone major changes since the original river diversion in 1958, apart from an expansion in the area occupied by the flood tidal delta. However, the upper estuary has undergone both artificial and natural changes, including construction of artificial channels, causeways and reclamation, which have influenced the flow regime, circulation patterns and the flushing ability of the upper estuary. 
Based on field observations, the freshwater inflow to the estuary during Stage 1 was higher than Stage 2 even though Stage 1 was a partial re-diversion restricted to 400,000 m3 per flood tide, compared to the maximum 600,000 m3 for Stage 2. There was great spatial variability in the response of the estuary to the added freshwater flow despite the estuary’s small size and lack of inter-tidal vegetation. To better isolate the impact of freshwater flow and eliminate variables such as spring/neap tidal events, rainfall and wind, all of the data were averaged over a semi-diurnal tidal cycle of 12.4 hours. There was an increase in mean water level after both stages. Flow in the mid and upper estuary shifted towards ebb-dominance after Stage 1, but no further shift to ebb-dominance was observed after Stage 2. Mean bottom salinity increased in the upper estuary while it decreased everywhere else after Stage 1. Mean bottom salinity reduced uniformly throughout the estuary after Stage 2, most likely due to higher rainfall rate during the monitoring period, and not the added freshwater flow.
To better understand the mixing patterns within the estuary, Estuarine Richardson number (R_iE) was calculated at 3 main sites before and after both stages of re-diversion. R_iE increased after Stage 1, but not sufficiently to cause a shift in classification; therefore, the estuary remained partially-mixed. Current dynamics within the estuary varied depending on proximity to the tidal inlet, with sites close to the inlet showing a strong tidal signal, and the ones near the control gates showing a decreased tidal influence and an increased response to freshwater inflows during flood tide when the control gates were open. Surface currents were influenced by strong winds during storm events and dictated the mixing (stratification) in the mid and upper shallow estuary. However, it was difficult to assess the significance of these changes in relation to the community aspirations for the re-diversion and estuarine restoration as there were insufficient quantitative or qualitative targets defined.
To complement the field observations and better evaluate the impact of alternative restoration options, a 2D numerical model of the estuary was developed using Delft3D. After successfully being calibrated and validated, Delft3D-FLOW and PART were used to simulate different scenarios to assess the flow regime and flushing ability of the estuary. The scenarios included Stage 1 re-diversion, river inflow flow without control gates; and a pulsed flood flow using control gates that imitated natural flood events. Particle tracking was used determine the residence time across the estuary, and assess within which zones decay rate changed with tidal fluctuations, and which zones were sheltered from the tidal fluctuations. Model results showed that the pulsed flood scenario created the optimal conditions for sediment transport, increased flushing ability, and reduced salinity throughout the estuary. The model results also highlighted differences in how various zones in the estuary responded to the added freshwater flow, further emphasising the need to monitor them separately with an improved monitoring framework.
The results of this study have led to a better understanding of the impact of added freshwater flow on estuarine hydrodynamics and water quality: specifically how the river input moves the boundaries of fluvially or tidally dominated, and mixing zones. The most vulnerable zones in terms of the flushing ability under different scenarios of freshwater restoration were also identified. This study also highlighted the importance of setting tangible targets in the restoration scheme in alignment with the environmental uncertainties such as the average river flow and limitations due to flooding issues in the upper catchment.

text: The hydrodynamic evolution of the Maketū Estuary after the re-diversion of the Kaituna River The Maketū Estuary and lower Kaituna River located in the Bay of Plenty, Aotearoa, New Zealand have undergone anthropic disturbances since late 1800s, including land reclamation, river diversion and re-diversion, and modifications to the river channels and estuary tidal inlet. This has resulted in estuarine degradation, as is a common issue worldwide. Globally different approaches to estuary restoration have aimed at mitigating the adverse impacts of estuarine degradation.  However, there are still gaps in restoration frameworks and how the success of the scheme is evaluated that mean there is no ready-made solution to the issues at Maketū.
This thesis examines the important role of the hydrodynamic processes (including water quality) that govern the overall physical response of Maketū Estuary to two stages of partial re-diversion of the Kaituna River into the estuary. The assessment of this physical response highlighted the necessity of a proper framework in which restoration attempts, such as at Maketū are evaluated.
Field time series data were collected before and after two stages of river re-diversion, Stage 1 in 2020 and Stage 2 in 2021, each over a span of a month, to record the immediate response of the estuary to the added freshwater flows. Freshwater flow into the estuary was constrained to approximately 4 hours during flood tides when the water level In the Kaituna River was at least 40 mm higher than the upper Maketū Estuary. The control gates also operate as a flood control scheme, so they remain shut if there is flood risk causing all the flood volume to discharge directly to the sea through Te Tumu Cut river mouth. 
The field data were obtained using Aquadopp ADPs, RBR Maestros, RBR Concertos, and Solinst water level loggers at seven different sites throughout the estuary and the Kaituna River. A hydrographic survey of the estuary using RTK-GNSS was undertaken and combined with LiDAR to produce a bathymetric map of the estuary and Lower Kaituna River. Comparison of this map to previous compilations showed that the tidal inlet and lower estuary have not undergone major changes since the original river diversion in 1958, apart from an expansion in the area occupied by the flood tidal delta. However, the upper estuary has undergone both artificial and natural changes, including construction of artificial channels, causeways and reclamation, which have influenced the flow regime, circulation patterns and the flushing ability of the upper estuary. 
Based on field observations, the freshwater inflow to the estuary during Stage 1 was higher than Stage 2 even though Stage 1 was a partial re-diversion restricted to 400,000 m3 per flood tide, compared to the maximum 600,000 m3 for Stage 2. There was great spatial variability in the response of the estuary to the added freshwater flow despite the estuary’s small size and lack of inter-tidal vegetation. To better isolate the impact of freshwater flow and eliminate variables such as spring/neap tidal events, rainfall and wind, all of the data were averaged over a semi-diurnal tidal cycle of 12.4 hours. There was an increase in mean water level after both stages. Flow in the mid and upper estuary shifted towards ebb-dominance after Stage 1, but no further shift to ebb-dominance was observed after Stage 2. Mean bottom salinity increased in the upper estuary while it decreased everywhere else after Stage 1. Mean bottom salinity reduced uniformly throughout the estuary after Stage 2, most likely due to higher rainfall rate during the monitoring period, and not the added freshwater flow.
To better understand the mixing patterns within the estuary, Estuarine Richardson number (R_iE) was calculated at 3 main sites before and after both stages of re-diversion. R_iE increased after Stage 1, but not sufficiently to cause a shift in classification; therefore, the estuary remained partially-mixed. Current dynamics within the estuary varied depending on proximity to the tidal inlet, with sites close to the inlet showing a strong tidal signal, and the ones near the control gates showing a decreased tidal influence and an increased response to freshwater inflows during flood tide when the control gates were open. Surface currents were influenced by strong winds during storm events and dictated the mixing (stratification) in the mid and upper shallow estuary. However, it was difficult to assess the significance of these changes in relation to the community aspirations for the re-diversion and estuarine restoration as there were insufficient quantitative or qualitative targets defined.
To complement the field observations and better evaluate the impact of alternative restoration options, a 2D numerical model of the estuary was developed using Delft3D. After successfully being calibrated and validated, Delft3D-FLOW and PART were used to simulate different scenarios to assess the flow regime and flushing ability of the estuary. The scenarios included Stage 1 re-diversion, river inflow flow without control gates; and a pulsed flood flow using control gates that imitated natural flood events. Particle tracking was used determine the residence time across the estuary, and assess within which zones decay rate changed with tidal fluctuations, and which zones were sheltered from the tidal fluctuations. Model results showed that the pulsed flood scenario created the optimal conditions for sediment transport, increased flushing ability, and reduced salinity throughout the estuary. The model results also highlighted differences in how various zones in the estuary responded to the added freshwater flow, further emphasising the need to monitor them separately with an improved monitoring framework.
The results of this study have led to a better understanding of the impact of added freshwater flow on estuarine hydrodynamics and water quality: specifically how the river input moves the boundaries of fluvially or tidally dominated, and mixing zones. The most vulnerable zones in terms of the flushing ability under different scenarios of freshwater restoration were also identified. This study also highlighted the importance of setting tangible targets in the restoration scheme in alignment with the environmental uncertainties such as the average river flow and limitations due to flooding issues in the upper catchment.

year: 2023