Environmental data analysis

1. Environmental data analysis Вонр. проф. д-р Александар Маркоски Технички факултет – Битола 2008 год. Enviromatics 2008 - Environmental data analysis

2. Introduction • Applications of data analysis methods are helpful to form a base for environmentalmodelling and simulation as well as for decision making and environmentalimpact assessment. • Disturbances of data analysis are caused by smallsets of representative regular sampled data which are available. The power ofexternal and internal driving forces on environmental indicators influences thequality of data to be obtained. The a-priori process information onenvironmentalindicators is low. • Re-sampling of data can be done by interpolation or approximationmethods to place data on a regular time and space grid. Interpolation methodsdeliver equidistant data while functional relationships result from approximations. Enviromatics 2008 - Environmental data analysis

3. Scales of operation of environmental data • Nominal scale: Pie charts, no arithmetic operation possible, sometimes codedby numbers. • Ordinal scale: Ranking of events or representations, classification of environmentalindicators (e.g. EU water quality classes, soil classes), ordinal comparisonsare possible: Class I > Class II, estimation of median and quartiles. • Interval scale: Ordinal scale with equal intervals (e.g. temperature), statementson distances and differences between data are allowable. No “natural” origin(zero point) exists. • Ratio scale: It is an interval scale with a “natural” origin and allows statementson ratios (e.g. concentrations). • Scale transformations from one data scale to another serve as unifications ofvariables. The information content and the scale level shall not be changed. Ifthere is no empiric equivalence scale, the data are valuated as “comparable”. Enviromatics 2008 - Environmental data analysis

4. Re-sampling of environmental data • How to handle missing environmental data? Mostly, series of measurements ofenvironmental data are time series of data recorded at discrete points in timewith variable intervals. The goal should be mapping of time series on a regulartime grid. • Re-sampling generally requires a data interpolation or, in the case ofnoisy information, a data approximation. The goal of the application of interpolationand approximation methods on incomplete time series is to fill the intervalsbetween two grid points so that series of measurements with small intervals arekept. • If data series contain missing values, then the following procedures areusefully: 1. Filling of gaps with the help of interpolation. 2. Generating of values with the help of approximation functions. 3. Filling of gaps with values of reference curves (analytical or stochasticallyfunctions). Enviromatics 2008 - Environmental data analysis

5. Procedure of environmental data processing Enviromatics 2008 - Environmental data analysis

6. Filling missing data • In the case of missing data the gaps should be filled in by “artificial” data. Missingdata can be estimated by interpolation methods, approximation proceduresor data from reference relationships. • In each case, the data should be placed ona regular time grid with constant observation (sampling) intervals. Only suchdata should be used for statistics, modelling,simulation and optimisation. • Otherwise,misinterpretations and incorrect simulation results will be getting. Suchresults are not suitable for environmental management. Enviromatics 2008 - Environmental data analysis

7. Types of environmental data series Enviromatics 2008 - Environmental data analysis

8. Types of data series • Type 1: Average is time dependent, dispersion is approximately time constant. • Type 2: Average is approximately time constant, dispersion is time dependent. • Type 3: Average and dispersion are time dependent. Enviromatics 2008 - Environmental data analysis

9. Interpolating environmentaldata Enviromatics 2008 - Environmental data analysis

10. Interpolation of two-weekly water quality data Enviromatics 2008 - Environmental data analysis

11. Comparison of the goodness of different interpolation methods Enviromatics 2008 - Environmental data analysis

12. Approximation of environmental data • Approximation of ecological signals means that given or estimated functionsexist which are able to reproduce sampled environmental data. It can be seenfrom figure 4 where the following polynomial was computed: NO3-N(t) = 1,8987 – 0,0754 t + 0,0028 t² - 0,00003 t³ Enviromatics 2008 - Environmental data analysis

13. Trend estimation of environmental data • Linear trend y(t) = a0 (t) + a1 (t) x(t). • Quadratic trends y(t) = a0 (t) + a1 (t) x(t) + a2 (t) x2 (t). • Polynomial trend: y(t) = a0 (t) + a1 (t) x(t) + a2 (t) x2 (t) + ..... + an (t) xn (t). • Exponential trend: x(t) = x(0) e - kt + E. Enviromatics 2008 - Environmental data analysis

14. Environmental data analysis The End Enviromatics 2008 - Environmental data analysis