title: The application of equilibrium beach profile theory to coastal hazard identification in the Bay of Plenty

authors: Pickett, Vernon

abstract: The Bay of Plenty (BoP) is situated on the north-eastern coast of New Zealand. It is low wave energy sand rich environment that is susceptible to the effects of intense mid latitude depressions and ex tropical cyclones. These can produce strong winds and onshore directed swells that are frequently associated with episodes of significant beach erosion. Such conditions are often exacerbated during the La Nina phase of the El Nino Southern Oscillation (ENSO). 

The beaches in the BoP monitoring data set (48 sites) have been classified in this research using Dean's parameter to determine beach states according to the classification system of Wright and Short. Principally the beaches can be described from this analysis as Intermediate beaches with occasional Dissipative beach types, for example those located in the lee of headlands as at West End Ohope, and Reflective beach types, as for example those on the steeper opencoast beaches at Otamarakau. 

Intermediate beaches consist modally of Longshore Bar and Trough morphologies (LBT) with strong representations from the other more dynamic and responsive intermediate beach types including the Low Tide Terrace (LTT), Transverse Bar and Rip (TBR) and Rhythmic Bar and Beach (RBB). The analysis confirmed that considerable beach state variability (involving up to +56 to - 60 m³m⁻¹) can be expected from these beach types over relatively short time frames of days to months. The indications are that the Dean beach equilibrium model (1977) fitted the more dynamic intermediate beaches better than beaches located at the extremes of the Wright and Short (1983) spectrum.

The equilibrium beach profile (EBP) models and their derivations have been described prior to applying the Dean (1977) and Dean et al. (1993) two dimensional parametric models to the 48 profiles in the BoP dataset. The purpose of this assessment was to determine the equilibrium beach status of profiles for potential use in defining coastal hazard zones in the BoP. Both models require the definition of boundary conditions, the onshore limit being defined by mean sea level, while the offshore limit was defined by closure depth. This was determined from review of the geomorphic evidence, repeat profile analysis and calculation using wave data and the Hallermeier formulae (19878, 1981a).

The two EBP models were fitted by least squares regression (LSR) analysis to all beach profiles in the BoP dataset. In carrying this out both scale and shape factors were allowed freedom to vary so as to minimise the residual errors in the assessments. The results from this allowed statistical analyses to be carried out on both parameters to determine their most probable values. This confirmed the appropriateness of Dean's (1977) value of ⅔ for the shape factor (or exponent) based on linear wave theory and uniform wave energy dissipation per unit volume. 

The LSR analysis was repeated holding the shape factor at ⅔ while allowing the scale factor (A) to change. The results from this analysis were then compared to the mean sediment data obtained from the profile monitoring database. This confirmed Dean's relationship between sediment fall velocity (grain diameter) and the regression derived scale factor values based on a log-log transformation.

Dean's 1977 and 1991 equilibrium profile models were then applied to the BoP profile dataset to determine each profile's equilibrium status representing the beach's potential to either erode or accrete. This potentially forms the first element of inputs to any coastal hazard zone determination because it affects spatially the location of mean sea level as a baseline from which to measure erosion limits. This analysis was carried out using three different closure depths and the two models with or without piecewise variation of the scale factor. The best overall fit using LSR analysis confirmed the appropriateness of the Dean (1977) model with profile averaged scale factor derived from the related sediment sampling. 

As part of this work the Wang and Davis three sector profile model was also examined and applied to the BoP dataset. This model potentially better describes the nearshore 2-dimensional beach morphology because it incorporates the offshore bar so typical of Intermediate beaches in the BoP. However when scale and shape factors were held according to the data obtained from the earlier LSR analysis, the model fails to replicate the success achieved by its authors using Florida data. 

Sea Level Rise (SLR) forms a second component of any coastal hazard analysis. The derivation of the Bruun Rule was examined from a variety of theoretical perspectives and was confirmed using equilibrium beach profile theory. As a consequence the Bruun Rule was applied within an equilibrium model using a MATLAB routine to predict likely profile shifts for the 'business as usual' climate change scenario of the IPPCC. Large Scale Coastal Behaviour (LSCB) theory (Cowell et al., 2003; Stive, 2004) was then applied to four different locations to ascertain the potential counter effects of sedimentation utilising coastal sediment budgets and progradation rates.

Storm erosion presents a third coastal hazard component predictable using EBP theory. The model chosen for this was EDUNE (Kriebel, 1989), a two dimensional parametric model based around the concepts described in Kriebel and Dean (1985) and Kriebel (1989). A design storm was developed from regional climate and weather information and applied to all profiles in the dataset to determine erosion limits. This was then applied cumulatively with the other two erosion drivers (profile disequilibrium and SLR) as shown to predict a suitable coastal setback line (or coastal hazard zone) from mean sea level as a protection measure for development occurring along this sandy coastline.

text: The application of equilibrium beach profile theory to coastal hazard identification in the Bay of Plenty The Bay of Plenty (BoP) is situated on the north-eastern coast of New Zealand. It is low wave energy sand rich environment that is susceptible to the effects of intense mid latitude depressions and ex tropical cyclones. These can produce strong winds and onshore directed swells that are frequently associated with episodes of significant beach erosion. Such conditions are often exacerbated during the La Nina phase of the El Nino Southern Oscillation (ENSO). 

The beaches in the BoP monitoring data set (48 sites) have been classified in this research using Dean's parameter to determine beach states according to the classification system of Wright and Short. Principally the beaches can be described from this analysis as Intermediate beaches with occasional Dissipative beach types, for example those located in the lee of headlands as at West End Ohope, and Reflective beach types, as for example those on the steeper opencoast beaches at Otamarakau. 

Intermediate beaches consist modally of Longshore Bar and Trough morphologies (LBT) with strong representations from the other more dynamic and responsive intermediate beach types including the Low Tide Terrace (LTT), Transverse Bar and Rip (TBR) and Rhythmic Bar and Beach (RBB). The analysis confirmed that considerable beach state variability (involving up to +56 to - 60 m³m⁻¹) can be expected from these beach types over relatively short time frames of days to months. The indications are that the Dean beach equilibrium model (1977) fitted the more dynamic intermediate beaches better than beaches located at the extremes of the Wright and Short (1983) spectrum.

The equilibrium beach profile (EBP) models and their derivations have been described prior to applying the Dean (1977) and Dean et al. (1993) two dimensional parametric models to the 48 profiles in the BoP dataset. The purpose of this assessment was to determine the equilibrium beach status of profiles for potential use in defining coastal hazard zones in the BoP. Both models require the definition of boundary conditions, the onshore limit being defined by mean sea level, while the offshore limit was defined by closure depth. This was determined from review of the geomorphic evidence, repeat profile analysis and calculation using wave data and the Hallermeier formulae (19878, 1981a).

The two EBP models were fitted by least squares regression (LSR) analysis to all beach profiles in the BoP dataset. In carrying this out both scale and shape factors were allowed freedom to vary so as to minimise the residual errors in the assessments. The results from this allowed statistical analyses to be carried out on both parameters to determine their most probable values. This confirmed the appropriateness of Dean's (1977) value of ⅔ for the shape factor (or exponent) based on linear wave theory and uniform wave energy dissipation per unit volume. 

The LSR analysis was repeated holding the shape factor at ⅔ while allowing the scale factor (A) to change. The results from this analysis were then compared to the mean sediment data obtained from the profile monitoring database. This confirmed Dean's relationship between sediment fall velocity (grain diameter) and the regression derived scale factor values based on a log-log transformation.

Dean's 1977 and 1991 equilibrium profile models were then applied to the BoP profile dataset to determine each profile's equilibrium status representing the beach's potential to either erode or accrete. This potentially forms the first element of inputs to any coastal hazard zone determination because it affects spatially the location of mean sea level as a baseline from which to measure erosion limits. This analysis was carried out using three different closure depths and the two models with or without piecewise variation of the scale factor. The best overall fit using LSR analysis confirmed the appropriateness of the Dean (1977) model with profile averaged scale factor derived from the related sediment sampling. 

As part of this work the Wang and Davis three sector profile model was also examined and applied to the BoP dataset. This model potentially better describes the nearshore 2-dimensional beach morphology because it incorporates the offshore bar so typical of Intermediate beaches in the BoP. However when scale and shape factors were held according to the data obtained from the earlier LSR analysis, the model fails to replicate the success achieved by its authors using Florida data. 

Sea Level Rise (SLR) forms a second component of any coastal hazard analysis. The derivation of the Bruun Rule was examined from a variety of theoretical perspectives and was confirmed using equilibrium beach profile theory. As a consequence the Bruun Rule was applied within an equilibrium model using a MATLAB routine to predict likely profile shifts for the 'business as usual' climate change scenario of the IPPCC. Large Scale Coastal Behaviour (LSCB) theory (Cowell et al., 2003; Stive, 2004) was then applied to four different locations to ascertain the potential counter effects of sedimentation utilising coastal sediment budgets and progradation rates.

Storm erosion presents a third coastal hazard component predictable using EBP theory. The model chosen for this was EDUNE (Kriebel, 1989), a two dimensional parametric model based around the concepts described in Kriebel and Dean (1985) and Kriebel (1989). A design storm was developed from regional climate and weather information and applied to all profiles in the dataset to determine erosion limits. This was then applied cumulatively with the other two erosion drivers (profile disequilibrium and SLR) as shown to predict a suitable coastal setback line (or coastal hazard zone) from mean sea level as a protection measure for development occurring along this sandy coastline.

year: 2004

title: Experiences with a weighted decision tree learner

authors: Cleary, John G.

subjects: computer science

abstract: Machine learning algorithms for inferring decision trees typically choose a single “best” tree to describe the training data. Recent research has shown that classification performance can be significantly improved by voting predictions of multiple, independently produced decision trees. This paper describes an algorithm, OB1, that makes a weighted sum over many possible models. We describe one instance of OB1, that includes all possible decision trees as well as naïve Bayesian models. OB1 is compared with a number of other decision tree and instance based learning algorithms on some of the data sets from the UCI repository. Both an information gain and an accuracy measure are used for the comparison. On the information gain measure OB1 performs significantly better than all the other algorithms. On the accuracy measure it is significantly better than all the algorithms except naïve Bayes which performs comparably to OB1.

text: Experiences with a weighted decision tree learner Machine learning algorithms for inferring decision trees typically choose a single “best” tree to describe the training data. Recent research has shown that classification performance can be significantly improved by voting predictions of multiple, independently produced decision trees. This paper describes an algorithm, OB1, that makes a weighted sum over many possible models. We describe one instance of OB1, that includes all possible decision trees as well as naïve Bayesian models. OB1 is compared with a number of other decision tree and instance based learning algorithms on some of the data sets from the UCI repository. Both an information gain and an accuracy measure are used for the comparison. On the information gain measure OB1 performs significantly better than all the other algorithms. On the accuracy measure it is significantly better than all the algorithms except naïve Bayes which performs comparably to OB1.

year: 1998-05

title: The experience of homemaking in unaffordable and precarious housing

authors: Barrett, Patrick

abstract: Housing is the platform on which people build their lives. The experience of homemaking in unaffordable and precarious housing (Barrett, P., Cram, F. & James, B, 2024) is a new monograph from the Affordable Housing for Generations programme. Across 110 pages, 10 housing researchers share experiences from different groups of people in Aotearoa, burdened by the insecurity of unaffordable housing. The findings show how institutional, social and market dynamics impacting on life circumstances can cause people to be in precarious housing situations. Yet people continue to love homemaking and being contributors to their communities. Reinforcing the pivotal nature of housing in supporting all peoples’ health and wellbeing, this research demonstrates how much more can be achieved through improving access to stable, affordable housing and by understanding what is at the heart of a home.

text: The experience of homemaking in unaffordable and precarious housing Housing is the platform on which people build their lives. The experience of homemaking in unaffordable and precarious housing (Barrett, P., Cram, F. & James, B, 2024) is a new monograph from the Affordable Housing for Generations programme. Across 110 pages, 10 housing researchers share experiences from different groups of people in Aotearoa, burdened by the insecurity of unaffordable housing. The findings show how institutional, social and market dynamics impacting on life circumstances can cause people to be in precarious housing situations. Yet people continue to love homemaking and being contributors to their communities. Reinforcing the pivotal nature of housing in supporting all peoples’ health and wellbeing, this research demonstrates how much more can be achieved through improving access to stable, affordable housing and by understanding what is at the heart of a home.

year: 2024