Dissertations / Theses on the topic 'Northern Mathematical models'

Predicting species occurrence based upon landscape-scale characteristics is a fundamental goal of ecology and conservation biology. Accurately predicting the potential occurrence of a species is fundamental to management activities that involve large areas where sampling is difficult due to logistical or financial constraints. During the summers of 2001-2003 mist nets were used to capture bats in Whiskeytown National Recreation Area (WNRA), Lassen Volcanic National Park (LVNP), and Lassen National Forest (LNF) in northern California. I used logistic regression and Akaike's Information Criterion (AIQ to model species distributions. Models developed a priori were used to determine which variables best discriminated between capture sites and non-capture sites. Prediction models were mapped using Geographic Information Systems. In WNRA, for all bat species combined total edge was most parsimonious, whereas in LVNP elevation was best for all species. Elevation and tree size were important in predicting the occurrence of pallid bats (Antrozous pallidus), in LNF. Results of this study are important to wildlife managers within the study areas because the models can be used to minimize deleterious impacts on bats. Moreover, distribution maps are valuable to bat conservation efforts because they provide baseline data important for evaluating and predicting population responses to management activities.
Department of Biology

A model (VTCROPS) was developed to simulate the long-term effects of nitrogen (N) leaching to groundwater in the Northern Neck region of Virginia, and ultimately to the Chesapeake Bay. VTCROPS simulates N fate and transport in a soil-plant-atmosphere continuum in a vertical slice between two crop rows, enabling consideration of nonuniform fertilizer placement and root growth patterns. VTCROPS models atmospheric, soil and crop subsystems. Atmospheric conditions (rainfall, temperature, solar radiation) may be directly input by the user or generated using a stochastic climatic generator. The soil subsystem simulates runoff, infiltration, drainage and soil-water redistribution, N immobilization, nitrification, mineralization, denitrification and advective N transport. The crop subsystem simulates plant N uptake, and vegetative and reproductive growth in response to soil and climatic factors, explicitly for maize or wheat. VTCROPS simulates soybean in a crop rotation empirically accounting for leaf area and root growth. The model is capable of simulating long-term cropping sequences under minimum and conventional tillage practices for continuous maize or for rotations involving maize, wheat, soybean and fallow. Critical internal model parameters were calibrated through comparison of output to field data. The sensitivity of output to input variables was determined. Model output is most sensitive to the climatic variables. Model predicted crop performance variables — grain and total dry matter yields and N content — and soil N content were compared with available field data from two sites over a three year period for maize. Data from six sites over a one year period were tested for wheat. Predictions for maize and total N content were fairly accurate, with a tendency to greater error in dry years. Predictions for wheat were somewhat less accurate, but incomplete field data precluded determining the source of discrepancies. Long-term model predictions, for two year crop rotations with minimum and conventional tillage, were evaluated by comparing performance variables with literature values. Appropriate responses were obtained for N transformation processes. Mass conservation for soil-water and N were good. Maize performance variables were within the range of literature values, and were higher under minimum till. Wheat yields and N contents were somewhat higher than values reported in the literature. Nitrogen load is correlated to drainage and water use over the short run, and to rainfall and drainage over longer periods. Minimum tillage did not increase N load to groundwater. Over a year nitrogen load was strongly periodic, with most leaching taking place from January through April. More than 50% of the N load over a rotation was lost during an extended fallow period that followed soybeans. Nitrogen load increased with fertilizer rates, however, N leaching fraction was optimal around rates of 150 — 200 kg/ha. The model was applied to the Virginia counties of Richmond, Westmoreland, Lancaster, King George and Northumberland to assess the potential for long term N leaching to groundwater. Soil surveys indicated that 34 soil map units occurred within 123,000 hectares of cultivated land. In order to reduce the number of simulations, principal component analysis and cluster analysis were employed to subdivide the cultivated area into 10 land units based on different soil properties. Historical climatic data from the area was used to calibrate the stochastic climatic generator. Analyses were performed to determine long-term crop performance and N loads to ground and surface waters in the study area over a 26 year period (13 rotations). Two management systems were applied to the land units. The first management system consisted of a rotation of minimum tilled maize, conventionally tilled wheat, minimum tilled soybeans and a fallow period. The second management system had a similar cropping sequence, but all crops were conventionally tilled. In both cases, fertilizer was applied at a rate of 150 kg-N/ha/crop. With the exception of two land units, mean yield, water use and N uptake over the simulation was fairly uniform among the land units. Runoff and drainage were highly variable between land units and over time within units. Mineralization, denitrification and N load were highly variable both between land units and over time. Nitrogen load ranged from 66 to 131 kg/ha/rotation between land units. Long-term average N loads and N concentrations from the cultivated area and from the total area of the study region were estimated. For this analysis it was assumed that 80% of the cultivated area was under minimum till and 20% under conventional tillage. An area-weighted average of 5.4 million kg-N/ha/year or 29% of total N applied is discharged to groundwater with an average drainage concentration of 9.9 mg/L. The average N concentration from the study area (including uncultivated areas) to groundwater is estimated at 5.1 mg/L. Average N concentration to the Chesapeake Bay from all sources, after dilution with runoff is 4.5 mg/L which is lower than the drinking water standard for nitrate N of 10 mg/L. The possibility of using sewage sludge as a replacement for, or in consort with N fertilizer was investigated for a typical land unit, under a conventionally tilled maize-wheat- soybean-fallow rotation. Simulations were conducted with 100%, 50% and 0% sludge (C—N ratio of 12). With fertilizer N augmenting the sludge, the total N input (250 kg/ha) was the same for each treatment. Mean yields were similar for 50% and zero sludge, but lowered by 10% and 16%, respectively, for maize and wheat with 100% sludge. Discrepancies in yields were attributed to the fact that mineralization rates of sludge are not high enough to supply the crop N requirement during periods of peak uptake. Nitrate leaching was reduced by 41 and 25% with 100 and 50% sludge applications, respectively.
Ph. D.

A simple linear reduced-gravity ocean model is developed to simulate the North Water polynya located in northern Baffin Bay. The model is an extension of Pease (1987) latent-heat model for a coastal polynya. Both northerly surface wind forcing and coastal upwelling processes are taken into account in modelling the steady state and time-dependent water velocities, upper layer depth, and polynya width measured southward from its northern boundary. Also, both uniform and variable wind forcing are considered. In most of this thesis a semi-infinite domain model is used in which upwelling occurs along the eastern boundary (the Greenland coast). It is found that the steady state polynya width is a strong function of the air temperature, but a weak function of the wind speed. The model results show that in the upwelling region near the Greenland coast, the polynya width is larger than further offshore (distance $>$ 2 Rossby radii), where it is a constant (the limiting Pease width). For a variable wind forcing, the southern ice edge of the North Water has a form that is similar to that of the wind forcing. In a channel, upwelling occurs in the eastern part and downwelling in the western part. Thus the polynya is much wider near Greenland and narrower near the Canadian Islands.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993.
18 color maps in back pocket. Vita. Abstract. Includes bibliographical references (leaves 137-139). Also available via the Internet.

Halogen-driven ozone and nonmethane hydrocarbon losses in springtime Arctic boundary layer are investigated using a regional chemical transport model (CTM). Surface observation of O3 at Alert and Barrow and aircraft observations of O3 and hydrocarbons during the TOPSE experiment from February to May in 2000 are analyzed. We prescribe halogen radical distributions based on GOME BrO observations and calculated or observed other halogen radical to BrO ratios. GOME BrO shows an apparent anti-correlation with surface temperature over high BrO regions. At its peak, area of simulated near-surface O3 depletions (O3 LT 20ppbv) covers GT 50% of the north high latitudes. Model simulated O3 losses are in agreement with surface and aircraft O3 observations. Simulation of halogen distributions are constrained using aircraft hydrocarbon measurements. We find the currently chemical mechanism overestimate the Cl/BrO ratios. The model can reproduce the observed halogen loss of NMHCs using the empirical Cl/BrO ratios. We find that the hydrocarbon loss is not as sensitive to the prescribed boundary layer height of halogen as that of O3, therefore producing a more robust measure for evaluating satellite column measurement. Tropospheric tracer transport and chemical oxidation processes are examined on the basis of the observations at northern mid-high latitudes and over the tropical Pacific and the corresponding global 3D CTM (GEOS-CHEM) simulations. The correlation between propane and ethane/propane ratio is employed using a finite mixing model to examine the mixing in addition to the OH oxidations. At northern mid-high latitudes the model agrees with the observations before March. The model appears to overestimate the transport from lower to middle latitudes and the horizontal transport and mixing at high latitudes in May. Over the tropical Pacific the model reproduces the observed two-branch slope values reflecting an underestimate of continental convective transport at northern mid-latitudes and an overestimate of latitudinal transport into the tropics. Inverse modeling using the subsets of observed and simulated data is more reliable by reducing (systematic) biases introduced by systematic model transport model transport errors. On the basis of this subset we find the model underestimates the emissions of ethane and propane by 14 5%.

The sertao of northeast Brazil is a semiarid region characterized by recurring droughts. The vastness of the area (650,000 km$ sp2)$ poses a challenge to the effective monitoring of the impacts of drought at a scale that would be useful to the inhabitants of the sertao. Remote sensing data provide a viable way of assessing the extent and nature of drought across the landscape.
The work present a more effective algorithm to estimate rainfall from both the cold and warm cloud types present. Using a decision-tree methodology, the analysis yields rainfall estimates over the 0-21 mm range. Because seasonal variations in rainfall produce differences in vegetation, soils and hydrologic responses, Principal Components Analysis was used to examine these land surface responses. Individual components and component pairings were useful in identifying variations in vegetation density, geobotanical differences and drainage characteristics. The presence of cloud cover was found to dampen the land surface information that could be extracted. Landsat Thematic Mapper (TM) imagery was then used to produce a moisture index which characterizes surface wetness in relation to other features present in a scene. The multispectral combination of TM bands 1, 4 and 6 allowed for the separation of the surface types present, in locational space. This space was defined by an open-ended triange made up of a vertical "water line", a horizontal line of equal vegetation density; and a negatively-slopping iso-moisture line. The stability of the moisture index was influenced by varying scale and seasonal conditions.
In the drought conditions that prevailed in 1991-1992, these methods provide important additions to existing drought monitoring approaches in the Brazilian northeast. Further calibration is required in order to extend their applicability to other geographical regions and time frames.

An accurate fire model is a useful tool in predicting the behavior of a prescribed fire. Simulation of fire requires an extensive amount of data and can be accomplished best using GIS applications. This paper demonstrates integrative procedures of using of ArcGIS™, ERDAS Imagine™, GPS, and FARSITE© to predict prescribed fire behavior on the Kaibab-Paiute Reservation. ArcGIS was used to create a database incorporating all variables into a common spatial reference system and format for the FARSITE model. ArcGIS Spatial Analyst was then used to select optimal burn sites for simulation. Our predictions will be implemented in future interagency efforts towards vegetative restoration on the reservation.

Pastoralism is the major economic activity in the Victoria River District (VRD), and is dependent on sustainable pasture use. Analysing grazing practices for sustainability requires knowledge of annual pasture production, but little quantitative data is available. A study was undertaken to develop the capacity for predicting native pasture growth in the VRD using systems modelling. Twenty one field sites were studied for two years using a standard methodology, and the Grass Production (GRASP) model was calibrated using this field data. End of growing season total standing dry matter (TSDM) was well predicted (mean = 2513kg/ha, r2(1:1) = 0.966, RMSE = 132kg/ha, and 98% of predictions within measurement variance). Developing generic parameters for common soil and pasture types allowed extrapolation of the model. Predictive skill declined when using generic parameters (r2(1:1) = -0.265, RMSE = 807kg/ha and 64% of predictions within measurement variance). However, observation and prediction means were very similar, indicating that generic parameters are suitable for broad scale applications, but site-specific parameters are necessary if a high degree of accuracy is required. Parameters controlling plant water uptake largely determine pasture growth in low rainfall years, while nitrogen uptake and dilution parameters limit growth in high rainfall years. Pasture growth is constrained by nitrogen supply in 91% of seasons in the northern VRD, and in 25% of seasons in the drier south. Example applications of the model were demonstrated. Current and expected future levels of pasture utilisation in the district were calculated, showing a current average of 16%, rising to an expected 20% in the next decade. These levels are within the safe utilisation rates recommended for the region. Economic analysis shows positive returns ($4.54 million per year) from pasture augmentation with introduced legumes if past problems with establishment and persistence can be overcome. Model performance would be improved by accounting for simultaneous wetting of the entire profile in cracking clay soils, calculating growth of perennial and annual pasture species separately, and simulating variation in nitrogen uptake and dilution between years. Incorporation of these processes must be balanced against the increased complexity of the model and the additional data required for calibration.
Thesis(PhD)-- School of Agriculture, Food and Wine, 2006

Pastoralism is the major economic activity in the Victoria River District (VRD), and is dependent on sustainable pasture use. Analysing grazing practices for sustainability requires knowledge of annual pasture production, but little quantitative data is available. A study was undertaken to develop the capacity for predicting native pasture growth in the VRD using systems modelling. Twenty one field sites were studied for two years using a standard methodology, and the Grass Production (GRASP) model was calibrated using this field data. End of growing season total standing dry matter (TSDM) was well predicted (mean = 2513kg/ha, r2(1:1) = 0.966, RMSE = 132kg/ha, and 98% of predictions within measurement variance). Developing generic parameters for common soil and pasture types allowed extrapolation of the model. Predictive skill declined when using generic parameters (r2(1:1) = -0.265, RMSE = 807kg/ha and 64% of predictions within measurement variance). However, observation and prediction means were very similar, indicating that generic parameters are suitable for broad scale applications, but site-specific parameters are necessary if a high degree of accuracy is required. Parameters controlling plant water uptake largely determine pasture growth in low rainfall years, while nitrogen uptake and dilution parameters limit growth in high rainfall years. Pasture growth is constrained by nitrogen supply in 91% of seasons in the northern VRD, and in 25% of seasons in the drier south. Example applications of the model were demonstrated. Current and expected future levels of pasture utilisation in the district were calculated, showing a current average of 16%, rising to an expected 20% in the next decade. These levels are within the safe utilisation rates recommended for the region. Economic analysis shows positive returns ($4.54 million per year) from pasture augmentation with introduced legumes if past problems with establishment and persistence can be overcome. Model performance would be improved by accounting for simultaneous wetting of the entire profile in cracking clay soils, calculating growth of perennial and annual pasture species separately, and simulating variation in nitrogen uptake and dilution between years. Incorporation of these processes must be balanced against the increased complexity of the model and the additional data required for calibration.
Thesis(PhD)-- School of Agriculture, Food and Wine, 2006

The long-term economic viability and ecological integrity of savanna rangelands is being undermined by increasingly dense woody thickets at the expense of palatable herbaceous cover. This process is known as shrub- or bush-encroachment. Bush encroachment is a subset of a broader ecological riddle underlying the coexistence of woody and herbaceous vegetation that has been the subject of many ecological models. The ecophysiological mechanisms and interactions between trees and grasses on which most assumptions of ecological models are premised have seldom been tested empirically. This document synthesises the results of greenhouse and field-based investigations of the underlying ecological mechanisms and ecophysiological interactions between encroaching Acacia mellifera trees and grasses in a semi-arid environment. In a greenhouse study, I determined the contribution of N2 fixation to the N-budget of Acacia mellifera under conditions of both varying N availability and competition from grass. Tree seedlings had longer shoots and greater total dry mass in the absence of grass. The leaf δ15N values were lower with grass than without grasses. Thus, trees were more reliant on N2 fixation in the presence of grasses. N2 fixation may enable the tree seedlings to survive competition with grass at critical and vulnerable developmental stages of germination and establishment. In a field removal experiment, I monitored the growth rates, water relations and mortalities of shrubs around which neighbouring woody plants were removed (target) and control shrubs over three years. Results showed target trees to have benefitted from removal of neighbours, which was manifested in significantly faster growth rates, less negative predawn water potential and a relatively small degree of canopy die-back. Nonetheless, neighbouring trees appeared to prevent the whole plant mortalities resulting from severe environmental stress. Growing in close proximity with neighbours could therefore yield positive and negative ecophysiological effects. In another greenhouse experiment, I tested the effects of the separation of moisture uptake with depth between tree seedlings and grasses on two common substrate types. I also examined the influence of repeated grass clipping on the persistence of soil moisture. Results indicated a three-tier rooting pattern with a top layer exclusively exploited by grasses, an intermediate layer occupied by both grass and tree roots and deeper layers exclusively tapped by trees. Tree seedling biomass was negatively affected by grass competition although the biomass of grass was enhanced in the presence of tree seedlings on sandy substrates only. The repeated clipping of grass benefitted tree seedlings on rocky substrate more than it did on sandy substrate. The effects of heavy grazing on soil moisture availability to woody shrubs and thus bush encroachment may be contingent on substrate type, being more acute on rocky terrains. Grass competition suppresses tree seedlings but the removal of grass by grazing weakens this suppressive effect, particularly on rocky substrates. The insufficiency of space and soil resources on rocky substrates may necessitate increased investment in root biomass by plants. It is not known why grasses have lower densities on rocky substrates than on sandy substrates, but the obstruction by rocks disadvantages grasses against tree seedlings, leaving grasses vulnerable to grazing pressure. This may allow the woody plants on rocky substrates to benefit more from grass removal than on sandy substrates. Root restriction by rock barriers and, perhaps, sparse soil volume further lead to small tree sizes on the rocky substrate. Small shrubs are less likely to compete intensively for resources and cause density-dependent mortality. Intraspecific competition may maintain shrub sizes within the threshold that can be supported by available resource pools. I conclude from my results that the two-layer hypothesis of niche separation between savanna vegetation is valid although there is an overlap in the grass and tree rooting depth/moisture uptake. An additional factor that affects the success of A. mellifera is the substrate.Trees are more dense on rocky substrates but grow larger on sand. I have further shown that A. mellifera trees fix nitrogen when competing with grasses but do not do so when grasses are absent. A mechanistic model of savanna dynamics will need to integrate water use patterns, substrate and nutrients to make effective predictions about encroachment patterns.
Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.

This study examined “problem solving skills in circle geometry concepts in Euclidean Geometry. This study was necessitated by learners’ inability to perform well with regards to Euclidean Geometry in general and Circle Geometry in particular. The use of naturalistic observation case study research (NOCSR) study was employed as the research design for the study. The intervention used for the study was the teaching of circle geometry with Polya problem solving instructional approach coupled with social constructivist instructional approach. A High School in the Northern Cape Province was used for the study. 61 mathematics learners (grade 11) in the school served as participants for the first year of the study, while 45 mathematics learners, also in grade 11, served as participants for the second year of the study. Data was collected for two consecutive years: 2018 and 2019. All learners who served as participants for the study did so willingly without been coerced in any way. Parental consent of all participants were also obtained. The following data were collected for each year of the research intervention: classroom teaching proceedings’ video recordings, photograph of learners class exercises (CE), field notes and the end-of-the- Intervention Test (EIT). Direct interpretations, categorical aggregation and a problem solving rubric were used for the analysis of data. Performance analysis and solution appraisal were also used to analyse some of the collected data. It emerged from the study that the research intervention evoked learners’ desire and interest to learn circle geometry. Also, the research intervention improved the study participants’ performance and problem solving skills in circle geometry concepts. Hence, it is recommended from this study that there is the need for South African schools to adopt the instructional approach for the intervention: Polya problem solving instructional approach coupled with social constructivist instructional approach, for the teaching and learning of Euclidean geometry concepts.
Mathematics Education

This study examined “problem solving skills in circle geometry concepts in Euclidean Geometry. This study was necessitated by learners’ inability to perform well with regards to Euclidean Geometry in general and Circle Geometry in particular. The use of naturalistic observation case study research (NOCSR) study was employed as the research design for the study. The intervention used for the study was the teaching of circle geometry with Polya problem solving instructional approach coupled with social constructivist instructional approach. A High School in the Northern Cape Province was used for the study. 61 mathematics learners (grade 11) in the school served as participants for the first year of the study, while 45 mathematics learners, also in grade 11, served as participants for the second year of the study. Data was collected for two consecutive years: 2018 and 2019. All learners who served as participants for the study did so willingly without been coerced in any way. Parental consent of all participants were also obtained. The following data were collected for each year of the research intervention: classroom teaching proceedings’ video recordings, photograph of learners class exercises (CE), field notes and the end-of-the- Intervention Test (EIT). Direct interpretations, categorical aggregation and a problem solving rubric were used for the analysis of data. Performance analysis and solution appraisal were also used to analyse some of the collected data. It emerged from the study that the research intervention evoked learners’ desire and interest to learn circle geometry. Also, the research intervention improved the study participants’ performance and problem solving skills in circle geometry concepts. Hence, it is recommended from this study that there is the need for South African schools to adopt the instructional approach for the intervention: Polya problem solving instructional approach coupled with social constructivist instructional approach, for the teaching and learning of Euclidean geometry concepts.
Mathematics Education
M. Sc. (Mathematics Education)

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2016.
The Jacomynspan Ni-Cu sulphide mineralisation is hosted within a 100m thick steeply dipping tabular, differentiated, sill of mafic to ultramafic composition intruded into country gneissic rocks of the Namaqualand Metamorphic complex. This sill is predominantly composed of tremolite schist (metamorphosed pyroxenite) containing lenticular bodies of harzburgite. The harzburgite generally hosts net-textured mineralisation with up to 50% by volume of the rock. Massive sulphide veins and stringers are occasionally present within the harzburgite. The sulphide minerals are a typical magmatic assemblage of pyrrhotite, chalcopyrite and pentlandite. The sill covers an approximate strike length of about 5km but only a small portion covering 1km x 1km was selected for this study. Physical property studies carried out on the drill core (magnetic susceptibility and conductivity) indicate that the country gneissic rocks are not conductive and neither are they magnetically susceptible. However, the mineralized sill has elevated values of both magnetic susceptibility and relative conductivity compared to its host making it a suitable target for both magnetic and electromagnetic inversion. Drilling done so far on the study area has shown that the well-mineralised harzburgite (hosted within the poorly mineralised ultramafic sill) is not a continuous body but occurs in ‘pockets’. There is therefore need to use the available geophysical and geological datasets to derive a model of these well mineralised pods. This study is therefore intended to assess the feasibility of using electromagnetic (EM) methods together with other geophysical methods and geology in obtaining a model of the harzburgite pods hosted within the less conductive poorly mineralised ultramafic sill in order to guide further drilling. Geosoft’s VOXI Earth Modelling software was used to model the high resolution airborne magnetic data for this study. Cooper’s Mag2dc (www.wits.ac.za) and Stettler’s Magmodintrp software (personal communication, 2015) was also used during modelling of the magnetic data to compliment the modelling from VOXI. The mineralised ultramafic sill was clearly mapped in both the 3D model representation from Mag2dc modelling and VOXI’s 3D unconstrained smooth model inversion for the study area. Based on the physical properties studies carried out on the study area, EM data (both ground and downhole EM) were modelled using Maxwell software. The poorly mineralised tremolite schist was clearly modelled. In order to better constrain the targets, an assumption was made that at late decay times the currents would be focused in the centre of the large EM plate probably giving an indication of the most conductive part of the intrusion. Smaller ‘Resultant EM plates’ of dimensions, 300mx300m that coincide with the centre of the large EM plates (with a conductance above 100S) were constructed in iv Maxwell software and integrated with the DXF file of the Micromine geology model of the well mineralised harzburgite clearly mapping the well-mineralised harzburgite and showing its possible extensions. 2D inversion modelling was conducted on all audio-frequency magnetotelluric (AMT) data for this study area. The modelling results clearly mapped the mineralised intrusion.