title: A goodness of fit measure related to r² for model performance assessment

authors: Bardsley, W. Earl

subjects: fit

abstract: Checking the predictive worth of an environmental model inevitably includes a goodness of fit metric to quantify the degree of matching to recorded data, thereby giving a measure of model performance. Considerable analysis and discussion have taken place over fit indices in hydrology, but a neglected aspect is the degree of communicability to other disciplines. It is suggested that a fit index is best communicated to colleagues via reference to models giving unbiased predictions, because unbiased environmental models are a desirable goal across disciplines. That is, broad recognition of a fit index is aided if it simplifies in the unbiased case to a familiar and logical expression. This does not hold for the Nash–Sutcliffe Efficiency E which reduces to the somewhat awkward unbiased expression E = 2 – 1/r², where r² is the coefficient of determination. A new goodness of fit index V is proposed for model validation as V =  r²/(2-E), which simplifies to the easily communicated V = r4 in the unbiased case. The index is defined over the range 0 ≤ V ≤ 1, and it happens that V < E for larger values of E. Some synthetic and recorded data sets are used to illustrate characteristics of V in comparison to E

text: A goodness of fit measure related to r² for model performance assessment Checking the predictive worth of an environmental model inevitably includes a goodness of fit metric to quantify the degree of matching to recorded data, thereby giving a measure of model performance. Considerable analysis and discussion have taken place over fit indices in hydrology, but a neglected aspect is the degree of communicability to other disciplines. It is suggested that a fit index is best communicated to colleagues via reference to models giving unbiased predictions, because unbiased environmental models are a desirable goal across disciplines. That is, broad recognition of a fit index is aided if it simplifies in the unbiased case to a familiar and logical expression. This does not hold for the Nash–Sutcliffe Efficiency E which reduces to the somewhat awkward unbiased expression E = 2 – 1/r², where r² is the coefficient of determination. A new goodness of fit index V is proposed for model validation as V =  r²/(2-E), which simplifies to the easily communicated V = r4 in the unbiased case. The index is defined over the range 0 ≤ V ≤ 1, and it happens that V < E for larger values of E. Some synthetic and recorded data sets are used to illustrate characteristics of V in comparison to E

year: 2013

title: Morphology and geochemistry of glauconite from the Te Kuiti Group, South Auckland region, New Zealand

authors: Compton, Martyn Stephen

abstract: The late Eocene - Oligocene Te Kuiti Group comprises calcareous mudstone, calcareous sandstone and skeletal or sandy limestone formed in marginal marine to fully marine shelf settings. Glauconite is ubiquitous in all sedimentary units in low concentration (5-10%), but at unconformities or near formation boundaries can attain concentrations > 75%.
Binocular microscope studies show· the following morphological form abundances: ovoidal(40-55%) > fragmentary(20-40%) > lobate(5-15%) > casts (0-5%) with trace quantities of tabular, capsule, and vermicular grains. The abundance of ovoidal and fragmentary glauconite suggests the glauconite is dominantly allogenic. Only the highly fragile cast and lobate grains are considered reliable indicators of authigenic glauconite.
Because distinction of morphological types using the binocular microscope is subjective, an alternative classification based on measured variables using image analysis was attempted. Seven measurements (area, formfactor, convexicity, length, fractal, aspect, and fibre) were made for each grain image. Seven glauconite morphological types were investigated: capsule, cauliflower, fragmentary, lobate, ovoidal, tabular, and vermicular. Measurement data were analysed using canonical variate analysis. The calculated discriminating vectors were then used to distinguish the seven morpological forms. Using two canonical variates 81.5% of the variability within the database was accounted for.
X-ray diffraction studies shows a predominance of poorly crystalline glauconite. Many difficulties were encountered when applying previous literature techniques for calculating the expandable content of glauconite. An alternative technique based on the relationship between %K₂0 and % expandables is favoured for the calculation of % expandables. A relationship between host sediment lithology and glauconite expandable content was found; siltstone = 20-32%. expandables in the glauconite, sandstone = 8-15% expandables in the glauconite.
Major element data were obtained with the electron microprobe for 327 individual glauconite grain centres of 70 samples from 45 sites and 7 formations in the Te Kuiti. Group. The. chemical data were analysed using canonical variate analysis and the seven formations were clearly distinguished. Because only a small glauconite sample size is required (4-5 grains) the technique has potential for determining the stratigraphic correlation of drill core samples and small hand specimens of Te Kuiti Group material containing glauconite.
The range composition of Te Kuiti Group glauconite calculated from EMP major element data using the "Clayform" program is:
(Si ₃.₄₀₋₃.₆₈ Al ₀.₃₂₋₀.₆₀) (Al ₀.₀₈₋₀.₄₁ Fe ₁.₀₀³⁺₋₁.₃₆ Fe ₀.₁₉²⁺₋₀.₂₆ Mg ₀.₄₀₋₀.₆₀) (Ca ₀.₀₂₋₀.₁₆ Na ₀.₀₀₋₀.₀₄ K₀.₄₉₋₀.₆₇) O₁₀(OH₂)
The Te Kuiti Group passes stratigraphically upward from terrigenous and mixed terrigenous-skeletal carbonate deposits to very pure limestones. Early post-depositional diagenetic processes probably released Mg from the carbonate lattice of accumulating skeletal grains. Some of the released Mg was incorporated into the glauconite lattice as evidenced by the increase in Mg content of glauconite stratigraphically upward, parallel with the increased carbonate content of the rocks.
Major and trace element data were obtained using X-ray fluorescence for 29 bulk glauconite concentrates from 21 sites and 5 formations. Notably there were anomalous Mg, Pb and Ni concentrations in glauconite from the Otorohanga - Waitomo -Te Kuiti area. This suggests the area existed as a small semi-enclosed embayment, with a significantly higher terrigenous input compared with adjacent depocentres.
A strong correlation between the La/Ce ratio of glauconite and paleontological and oxygen isotope-derived sea-water temperatures suggests glauconite La/Ce ratio may be a useful paleotemperature indicator. The data collected in this study show no single previously suggested process adequately decribes the development of glauconite. Rather, glauconite should be considered polygenetic.

text: Morphology and geochemistry of glauconite from the Te Kuiti Group, South Auckland region, New Zealand The late Eocene - Oligocene Te Kuiti Group comprises calcareous mudstone, calcareous sandstone and skeletal or sandy limestone formed in marginal marine to fully marine shelf settings. Glauconite is ubiquitous in all sedimentary units in low concentration (5-10%), but at unconformities or near formation boundaries can attain concentrations > 75%.
Binocular microscope studies show· the following morphological form abundances: ovoidal(40-55%) > fragmentary(20-40%) > lobate(5-15%) > casts (0-5%) with trace quantities of tabular, capsule, and vermicular grains. The abundance of ovoidal and fragmentary glauconite suggests the glauconite is dominantly allogenic. Only the highly fragile cast and lobate grains are considered reliable indicators of authigenic glauconite.
Because distinction of morphological types using the binocular microscope is subjective, an alternative classification based on measured variables using image analysis was attempted. Seven measurements (area, formfactor, convexicity, length, fractal, aspect, and fibre) were made for each grain image. Seven glauconite morphological types were investigated: capsule, cauliflower, fragmentary, lobate, ovoidal, tabular, and vermicular. Measurement data were analysed using canonical variate analysis. The calculated discriminating vectors were then used to distinguish the seven morpological forms. Using two canonical variates 81.5% of the variability within the database was accounted for.
X-ray diffraction studies shows a predominance of poorly crystalline glauconite. Many difficulties were encountered when applying previous literature techniques for calculating the expandable content of glauconite. An alternative technique based on the relationship between %K₂0 and % expandables is favoured for the calculation of % expandables. A relationship between host sediment lithology and glauconite expandable content was found; siltstone = 20-32%. expandables in the glauconite, sandstone = 8-15% expandables in the glauconite.
Major element data were obtained with the electron microprobe for 327 individual glauconite grain centres of 70 samples from 45 sites and 7 formations in the Te Kuiti. Group. The. chemical data were analysed using canonical variate analysis and the seven formations were clearly distinguished. Because only a small glauconite sample size is required (4-5 grains) the technique has potential for determining the stratigraphic correlation of drill core samples and small hand specimens of Te Kuiti Group material containing glauconite.
The range composition of Te Kuiti Group glauconite calculated from EMP major element data using the "Clayform" program is:
(Si ₃.₄₀₋₃.₆₈ Al ₀.₃₂₋₀.₆₀) (Al ₀.₀₈₋₀.₄₁ Fe ₁.₀₀³⁺₋₁.₃₆ Fe ₀.₁₉²⁺₋₀.₂₆ Mg ₀.₄₀₋₀.₆₀) (Ca ₀.₀₂₋₀.₁₆ Na ₀.₀₀₋₀.₀₄ K₀.₄₉₋₀.₆₇) O₁₀(OH₂)
The Te Kuiti Group passes stratigraphically upward from terrigenous and mixed terrigenous-skeletal carbonate deposits to very pure limestones. Early post-depositional diagenetic processes probably released Mg from the carbonate lattice of accumulating skeletal grains. Some of the released Mg was incorporated into the glauconite lattice as evidenced by the increase in Mg content of glauconite stratigraphically upward, parallel with the increased carbonate content of the rocks.
Major and trace element data were obtained using X-ray fluorescence for 29 bulk glauconite concentrates from 21 sites and 5 formations. Notably there were anomalous Mg, Pb and Ni concentrations in glauconite from the Otorohanga - Waitomo -Te Kuiti area. This suggests the area existed as a small semi-enclosed embayment, with a significantly higher terrigenous input compared with adjacent depocentres.
A strong correlation between the La/Ce ratio of glauconite and paleontological and oxygen isotope-derived sea-water temperatures suggests glauconite La/Ce ratio may be a useful paleotemperature indicator. The data collected in this study show no single previously suggested process adequately decribes the development of glauconite. Rather, glauconite should be considered polygenetic.

year: 1989

title: Indigenous knowledges in health policy in Aotearoa New Zealand and Saskatchewan Canada: A comparative study

authors: Green, Jane Alison

subjects: Indigenous

abstract: For more than two decades, components of Māori knowledges in the form of Māori words and concepts have been part of health policy in Aotearoa New Zealand. Health policy that engages Māori words and concepts resonates with Māori community values and aspirations and is thought to contribute to the revitalisation of Māori knowledges. Absent from the literature is an examination of this phenomenon; specifically, the socio-political factors that facilitate and limit the engagement of Māori knowledges with health policy. Of the four settler states, only in Aotearoa New Zealand are the knowledges of the Indigenous peoples engaged with health policy. In Saskatchewan, Canada, the First Nations and Métis peoples have engaged their knowledges with federal and provincially funded health programmes and services but not health policy. This study adopts a two-country comparative policy framework to investigate and theorise the historical and contemporary socio-political factors associated with the engagement of Indigenous knowledges in health policy in Aotearoa New Zealand and Saskatchewan, Canada. An adaption is made to the Kaupapa Māori approach so that the complexities of a two-country case study approach are addressed and engagement in health policy as a strategy for knowledge revitalisation is theorised. The study also takes a path less travelled which is to investigate the impact that engagement with health policy has upon the intangible or the ontological aspects of Māori knowledges. Māori describe their knowledges as comprised of tangible and intangible elements, both of which are important. Another adaption is made to the Kaupapa Māori theoretical approach which is to add speculative inquiry. The study argues that speculative inquiry in the form of contemplative, analytical, relational and viscerally aware practices are commonplace in Māori communities. Adding speculative inquiry to an already rich theoretical body that is Kaupapa Māori research provides an opening for other Kaupapa Māori researchers to expand non-empirical inquiry. The study concludes that government policies have had a decimating effect upon Māori, First Nations and Métis knowledges. Moreover, recent reports from commissions and inquiries indicate these knowledges and associated languages continue to decline for a number of reasons, including the impact of contemporary government policies. Health policy, this study asserts, is an uncertain site from which to revitalise Māori, First Nations and Métis knowledges.

text: Indigenous knowledges in health policy in Aotearoa New Zealand and Saskatchewan Canada: A comparative study For more than two decades, components of Māori knowledges in the form of Māori words and concepts have been part of health policy in Aotearoa New Zealand. Health policy that engages Māori words and concepts resonates with Māori community values and aspirations and is thought to contribute to the revitalisation of Māori knowledges. Absent from the literature is an examination of this phenomenon; specifically, the socio-political factors that facilitate and limit the engagement of Māori knowledges with health policy. Of the four settler states, only in Aotearoa New Zealand are the knowledges of the Indigenous peoples engaged with health policy. In Saskatchewan, Canada, the First Nations and Métis peoples have engaged their knowledges with federal and provincially funded health programmes and services but not health policy. This study adopts a two-country comparative policy framework to investigate and theorise the historical and contemporary socio-political factors associated with the engagement of Indigenous knowledges in health policy in Aotearoa New Zealand and Saskatchewan, Canada. An adaption is made to the Kaupapa Māori approach so that the complexities of a two-country case study approach are addressed and engagement in health policy as a strategy for knowledge revitalisation is theorised. The study also takes a path less travelled which is to investigate the impact that engagement with health policy has upon the intangible or the ontological aspects of Māori knowledges. Māori describe their knowledges as comprised of tangible and intangible elements, both of which are important. Another adaption is made to the Kaupapa Māori theoretical approach which is to add speculative inquiry. The study argues that speculative inquiry in the form of contemplative, analytical, relational and viscerally aware practices are commonplace in Māori communities. Adding speculative inquiry to an already rich theoretical body that is Kaupapa Māori research provides an opening for other Kaupapa Māori researchers to expand non-empirical inquiry. The study concludes that government policies have had a decimating effect upon Māori, First Nations and Métis knowledges. Moreover, recent reports from commissions and inquiries indicate these knowledges and associated languages continue to decline for a number of reasons, including the impact of contemporary government policies. Health policy, this study asserts, is an uncertain site from which to revitalise Māori, First Nations and Métis knowledges.

year: 2018