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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 point altitudes.

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.

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 are an expression of geographic location 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.

McNeill considers one of the most appealing aspects of LST is its role in enabling people to embrace, analyse and understand better the complexity of natural phenomena, an essential capability in relation to environmental, ecosystem and climate impact analysis.

In 1925, R. A. Fisher published a paper Statistics Methods for Research Workers which reviewed the development of statistics up until that time. Fisher describes how the efforts in statistics of population were directed towards determining the average. No particular effort had been made to analyse the degree to which populations deviated from the average. Fisher made significant contributions to the practical application of statistics by establishing methodologies which became a standard approach to the determination of the significance of experimental results. This was based upon a knowledge of the shape of a population curve and the variance about the mean, or average. If the response of say, a crop, to some input fell outside what would be a reasonable expectation of the normal variation, then results could be judged to be significant (at different degrees of confidence). A convenient way, perhaps too convenient, to provide a shorthand description of a population became the declaration of the average and the observed coefficient of variance.

Fisher's work, and especially that relating to experimental design and the analysis of variance (ANOVA), became widely applied in the field of agricultural research and constituted an important contribution to the methods of experimental design. In agricultural experimentation, performance trials and genetic selection work, the convenience of such methods has, to some extent, encouraged work to become too focused on detecting the immediate interrelationships between the so-called explained variance attributable to the factors of interest to the researcher. Most other influences often became ignored or ended up in the residual data called "unexplained variance".

Fisher, although the designer of methods which have simplified experimental design and their analysis was completely aware of the limitations inherent in such an approach. Thus, he made the following observation:

"No aphorism is more frequently repeated in connection with field trials, than that we must ask Nature few questions, or, ideally one question at a time. The writer is convinced that this view is wholly mistaken.”

“Nature will best respond to a logical and carefully thought out questionnaire, indeed, if we ask her a single question, she will often refuse to answer until some other topic has been discussed”
(R. A. Fisher, 1926)

The inevitable result is that because of a refusal or inability to embrace complexity, by asking the "right questions", our advance of understanding is constrained.

The role of LST in embracing and understanding complexity relates to the nature of experimentation. A simple example would be a series of plots set out to compare the response of a crop to different fertilizer treatments. The typical response curves can be plotted by comparing the measure results that correlate input to crop yield.

Production response to potassium

Johnson, J., “Assessing soil fertility; the importance of soil analysis and it’s interpretation” Rothamsted Research, Harpenden, AL5 2JQ, UK
Such a response curve is shown on the right. The absolute values in the response curves varied according to the year of experimentation. The differences in yield are explained by a combination of fertilizer input, temperature and water regimes in the years concerned. The experiment measured fertilizer input and yield response only i.e. nature was asked a simple question.

The results of the experiment in terms of ANOVA contain an explained variance, that directly related to the experimental objective and a large unexplained variance largely connected to the water and temperature regimes which were not recorded as inputs.

Locational State Theory in the case at the outset of an experiment would follow a due diligence procedure to identify all known determinants of yield. This would require the identification of all of the possible LST variables associated with the geographic position of the experimental plots in terms of latitude, longitude, altitude and aspect. Those variables at the location influencing crop yield are, other fertilizers that complement potassium, possible micronutrients, water availability and temperature regime. The crop itself has the LST variable "age" will vary according to when, during the season, the crop was planted since the physiological responses to the environment of any plant are conditioned by the age or stage of maturity in the growth cycle. Clearly, if the experiment was only measuring the response of the crop to potassium, a large number of the substantive determinants of yield are missing and as a group are responsible for the main differences in response curve levels, as observed, in each year of 5 years of experimentation.

The collection of data on the water and temperature regimes and potassium would represent a more "complete dataset" which would improve the error and precision of results by reducing the unexplained variations between the years.

The role of LST at the experimental design stage is simply to provide a check list of the environmental variable properties that determine the measured output of the experiment. At the outset it is self-evident that this is not just potassium input since there are other macro-nutrients of importance such as phosphorus, nitrogen as well as water and temperature. Therefore with a view to a more in depth more complex analysis of relationships it would be advisable to include the additional LST variables. Naturally there is a question of resources available to include more variables but the costs of collection of additional environmental data can be marginal whereas the improved level of understanding of the quantitative relationships provides a more reliable basis for taking production decisions with economic and financial consequences.

Where experimental plots or experimental stations are located on different soils with respect to texture as well as at different altitudes, LST has a role in terms of introducing supplemental algorithms to "normalize" multi-site results such as that illustrated. This is necessary because the overall annual temperature regime is governed by the altitude at any location and this is fixed by the terrain model. A rule of thumb, concerning this relationship is that ambient temperatures fall by around 0.6oC for every 100 metre gain in altitude. This provides a temperature correction map based on altitude alone (fixed) for any region. Also by measuring temperatures at specific points at known altitudes (references) it is possible to interpolate all of the other point location temperatures based on the relative difference in altitude.
Terrain altitude-based temperature corrections at 100 metre contours

McNeill, H. W., "Some principles of nature", DAI, MOFTER, Sarajevo, 2011
This can be extended, depending upon distance from oceans along extensive latitude transects but longitude transects are more limited, in terms of temperature interpolation related to distance or proximity to the equator and insolation intensity. Usually a distance of 150 kilometers should maintain the relative precision of interpolations to acceptable levels. In terms of crop growth and depending upon the type and specific genotype an annual temperature difference of 2.5oC can have a significant impact on yields.

By making better use of LST variables, the level of unexplained variance concerning states, which were previously categorized as "uncertain", fall into a category of "expected". Thus, with ongoing measurement of LST variables what was previously uncertain because of lack of monitoring, can vary but the significance of any variation is better understood and can be explained. In terms of decision analysis models, more complete sets of determinants add a vital flexibility in the rather than limiting decision analysis to design and the projection of scenarios. More complete LSTs open up the possibility of deploying the same model to arrange input values based on monitoring, in real, or close to real time, both the controlled inputs e.g. fertilizer and LST variables enabling, for example, the ability have the decision analysis model run as a continuous dynamic simulation of the growth of a crop providing a foundation for production forecasting.

LST is a relativistic concept in the sense that it can be used to map equivalences across the globe of locations with identical or very similar bioclimatic conditions enabling the successful transfer of plant genotypes from one location where the crop has good production to another where no such genotype exists but where the conditions for successful production are similar. This is an extension of the application of the application of agro-ecological zoning. As can be appreciated this is based on longer term stable conditions in the locations concerned. However, from season to season the appearances of equivalence in bioclimatic conditions involves dislocations of bioclimatic conditions. So, in a cooler season lower altitude conditions emulate the normal conditions of locations at a higher altitude according to the temperature vector. These examples refer to geographic locational aspects.

A more intriguing example concerning time travel is more interesting. A considerable amount of agricultural experimentation is of the form described in relation to the potassium crop yield response described. However by collecting the temperature and rainfall data for the years concerned the "experiment" can be repeated in virtual terms to apply a more complete data set so as to secure a more complete analysis describing the combination of fertilizer, temperature and water regimes on yields.

Globally there are millions of agricultural experiments of this type associated with yield responses to inputs and differences in production systems e.g. disease control, assessment of new genotypes, biological pest control, resistance to disease and many others. Most will not have referred to key LST variable or any pertinent functional relationships between the LST variable as determinants and the objects of the experiments. However, in probably the majority of cases the critical LST variable, such as temperature and rainfall exist. This presents the exciting prospect of being able to revisit the results based on such environmental data to "re-run" the experiments to secure more meaningful results.

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
Based on McNeill, H. W., "3D production function", TP, Food Research Institute, University of Stanford, 1968.

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 these 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. This is becoming of importance to food security and the management of the logistics concerning storage of strategic reserves of food.

The growth 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 determinants 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.

FAO’s Agro-Ecological Zoning (AEZ) methodology is the primary tool used for land resources assessment. It is based on the FAO Framework for Land Evaluation which has been in use since 1978 for assessing agricultural production potential and production capacity, actual and potential yields and yield gaps. The agro-ecological zones are defined as homogenous and contiguous areas with similar soil, land and climate characteristics.

Since the launch of AGENDA 2030 and the 17 Sustainable Development Goals, Hector McNeill has developed several cloud-based analytical tools to optimize project and policy planning in low income countries to reduce risk associated with food security by applying the Real Income Production, Accessibility and Consumption Model which is particularly pertinent to "demand analysis" in low income countries. The critical properties of the successful online tools is their use of OPEE to generate evidence-based project designs which contain thorough risk analysis. The overall approach is based on a Due Diligence Design Procedure (3DP) for process, project and investment optimization developed at SEEL-Systems Engineering Economics Lab.

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 is undergoing a major reconfiguration was a result of a change in programming and scripting systems caused by a rise in licensing fees of proprietary server side JavaScript system. This took operational costs beyond the ability of customers (practitioners in low income countries) to pay. All development is now open source and operational status will come back online in Q4, 2020.

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-ecological zoning (AEZ), a basic heuristic is that temperature falls by around 0.6o C for each 100 metres gain in altitude.