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Soil formation catenas: Catenas are the transition or change in soil structure and texture that occurs between soil formations at the top of a valleys and those further down at lower altitudes

Temperature: Moving through horizontal axes, the ambient temperature varies in a continuum.

Altitude: Changes in terrain altitude normally has continuum sequence although there can be discontinuities associated with steep inclines such as cliffs.

Terrain temperature models: Topographic models that represent three dimensional terrain characteristics, often demarcated by contour lines, also provide the three dimensional structures for temperature models. These are based on the fall in temperature associated with altitude. These models are used to correct point temperature readings, for example at the meteorological station, and to extrapolate or interpolate these across neighbouring terrain according to altitude.

The diagram below provides a simple layout for micro-bioclimatic zones for the Northern hemisphere. The diagram represents a transition from north at the top to close to the equator at the bottom. As the geographic location of a terrain elevation model is moved further south, the temperature conditions shift as indicated. For example zone E migrates from being the ambient condition at a lower altitudes further north and migrates to be the ambient condition at the higher altitudes further south.

Therefore the states associated with one locational component (elevation or altitude) will migrate as a function of changes in another locational component (latitude) showing the location-state transition.

McNeill, H. W., Contribution to systems engineering project Demeter, “An Earth Resources Satellite System”, Section: “3.1 Immediate Activities of a Managing Agency – 3.1.2 Truth Site Establishment & Ground Data gathering”, School of Engineering, Stanford University, Stanford, California. Final Report, June 1968

One of most interesting aspects of locational-state is its ability to manage continua data sets, that is, data transitions which are characterized by very small differences in property values between physically adjacent objects but showing significant differences in the property values between the two tail ends of a transition. This has a direct application in ecology as well as in the quantification of the environmental impacts of the elements on biomass production. This can translate into physical and economic estimates of the impact of weather on crop yields as well as pasture carrying capacity of grazing livestock. Continua include such data transitions as terrain altitude, ambient temperature, precipitation, humidity and evapotranspiration. In the paper, "The Role of Micro-Bio-Climatic Zoning & Genotypic Mapping" McNeill1 sets out the specification of the locational-state data set as four locational space-time co-ordinates associated with any number of associated state of target variables measured at each location.
The locational vectors are an expression of geographic location as well as well as location in time.

The locational vectors include:
  • X Latitude - a vertical axis locating the vertical axis of the x coordinate of a geographic position. The basis for estimate is an angle as positive (north) and negative (south) of the equator with the equator taking up the 0o.

  • Y Longitude - a horizontal axis locating the vertical axes (great circles with rotational axis around north-south) of the y coordinate of a geographic position. The basis for estimate is an angle as positive (East) and negative (West) of the Greenwich meridian (the 0 o datum line or great circle).
  • A Altitude - a vertical axis Z estimated at any XY co-ordinate. The basis for estimate is the number of metres a point lies above mean sea level.

  • T Time - This is the time at which an observation is made or the time allocated to a conceptual event measured in standard time. The basis for estimate is year, month, day, hour, minute, second or parts of a second depending upon the application.
Individual readings of states (object properties) occur within a cycle of some kind and all objects have a life cycle whose lengths based on longevity or in the case of agriculture, a production cycle. Therefore the state variables are determined by:
  • C Cycle - This is the period of any cycle or repetitive occurrence of relevance to the observations at a given geographic location (X, Y, Z). These might be annual cycles such as repetitive seasonal climatic phenomenon such as rainfall or temperature cycles. Although these might have a repetitive annual cycle their beginning, end and duration can be selected to suit the purposes of the objective of data collection and in particular designed to capture those segments of the cycle which determine target variable values. Relevant cycles are those which have a determinant influence on the state of target variables of interest. The basis for estimate is the date of initiation, duration and date of completion according to the T Time axis of year, month, day, hour, minute, second or parts of a second depending upon the application.

  • A Age - This is the time of existence of the phenomena whose target variables are being observed. In the case of biota, flora and fauna it refers to the age or generation or in the case of inanimate objects such as aircraft or buildings, this would relate to time of construction or hours of service. The basis for estimate is the date of birth or germination for biota or initiation/completion of abiota, recording time elapsed (age) with estimates of life expectancy in terms of biota and expected operational life in the case of abiota and according to the T Time axis of year, month, day, hour, minute, second or parts of a second depending upon the application.

The state variables, that is object properties, are all measured within the context of the locational variables set out above.

The significance of locational-state continua is that some of these do not require a survey method based on object-property data collection. For example, temperature models (see box above) only require a reduced number of point source temperature readings to interpolate temperatures at any given location. This is a knowledge-based acquisition of data based on knowledge of two fixed non-variant relationships:
  • the topographic characteristics of the terrain
  • the determinant relationship between temperature and altitude2

McNeill,H. W., "LST EWT relationships for biomass generation", SEEL, June, Portsmouth 1998

LST can introduce predictability, within limits, of unstable seasonal relationships between the water, temperature and fertility regimes and the production of plant biomass. The projection below shows the seasonal (annual) variation in rates of growth of biomass

An example of the relationship between biomass production and the EWT complex is shown on the right.

As the statistics on field observations in any year are collected the overall shape of the biomass production curves take shape. Based on this principle it is therefore possible to gain medium term predictability of the likely end of year biomass production that can be translated into crop yields according to the specific determinant relationships between thee factors and each crop type.

The fine grain detail and diurnal variations which together contribute to the final biomass estimates can be described on the basis of Fourier transforms but the actual shape of the annual curve will vary with the individual inputs from the elements of the EWT complex (Edaphic (soil fertility & texture), Water and Temperature regimes). The actual quantitative impacts of the values of the EWT complex tend to be cumulative and the only way to measure this is by field observation.

By combining for Fourier transform combination of sine waves as a basic model structure but adjusting the actual values according to actual climatic and field observations a fairly accurate determination of ongoing growth and the likely yields, excluding extraordinary events, can be estimated. This is useful in projecting likely overall availability of commodities and to estimate the likely movements in commodity prices.

The gorwth in human populations and the depletion of ecosystems resulting from environmental degradation threaten human wellbeing for many now and increasing numbers in the future. One of the important factors in using human, natural and financial resources to secure a sustainable future is knowledge on the derterminants of agricultural productivity and methods of measuring this and using this knowledge in an effective fashion. By linking up these technical factors with economic analysis it is possible to identify economic development pathways that support, rather than undermine, the livelihoods of those who rely directly on natural resources for their survival. The advancing applications of LST can contribute to bringing about better project design and a more effective and efficient allocation of resources. LST has a significant potential role to play in determining optimised strategies under conditions of predictive and unstable climatic change.

McNeill,H. W., "Fourier transitions and Locational States", SEEL, August, Portsmouth 2017

The image below shows a variation around the average values of variations of the datasets associated with diurnal (daily) variations in temperature. Similar relationships exist for water availability as an essential input to plant transpiration and ability to absorb nutrients from the soil.

McNeill,H. W., "Fourier transitions and Locational States", SEEL, August, Portsmouth 2017

As can be readily observed the graph above is a combination to two sine curves with a 365 days and a 1 day cycle. The mathematical construct used to generate this is a Fourier transform.

It is self-evident that values of any variables are determined by the specific locational-state of the object whose properties are being measured. In terms of capturing those elements of variance in data sets which remain currently as "unexplained variance", locational state theory has much to contribute to this aspect of statistical analysis. Location state analysis has the advantage of providing a relational model between variables that can help detect, and in some cases measure, finer deterministic relationships. In general, it appears to be a more practical basis for analysis than multi-factoral analysis.

The Plasma Database is the first application of a Locational-State Data Reference Model (LSDRM) as a representation of reality (diversity) based on a NoSQL operation (For further information visit: Plasma Systems). The Locational-State Data Reference Model (LSDRM) combines space time elements in a object oriented format. The database holds data on specific objects and their properties and the utility of the data relates to the specific algorithms applied to it. These are associated with each data set as the OOP methods contained in each object, together with the target properties.

Plasma was initially designed to provide a more realistic representation and analysis of dynamic (changing) data on biological (living) phenomena. For these types of application it has proven to be extremely promising. Subsequent advances in Locational State Theory (post 1990) demonstrated that the types of relationships observed, in a more explicit fashion, in the case of living organisms also apply to all phenomena. A challenge facing knowledge engineers has been the difficulty of extracting tacit information & knowledge. Plasma can run fusion operations that isolate tacit variable values by type and quantification. This is a major advance in useful knowledge engineering laying the foundation for targeting performance enhancement actions in any business operation involving human resources. Plasma has a wide application in all vertical and horizontal sectors from primary, intermediate, industrial, manufacturing & service activities.

Currently Plasma prototyping is based on Microsoft Server operating systems (server side), server side ECMAScript (JavaScript) extension, virtual client access, STScripts and Plasma primitives. All applied research continues to be managed at SEEL-Systems Engineering Economics Lab, Hampshire, Portsmouth, UK. The main testing and pre-release evaluation units are located in Portsmouth, UK and Leeds in the UK.

1  McNeill, H. W.,"The Role of Micro-Bio-Climatic Zoning & Genotypic Mapping" Agricultural Research, Development & Dissemination, SEEL, HPC July, 2009. ISBN: 978-0-907833-26-0
2   There are several formulae relating temperature to altitude associated with Agricultural Land Classification systems (ALC) and so-called Agro-ecologial zoning (AEZ), a basic heuristic is that temperature falls by around 0.6o C for each 100 metres gain in altitude.