# Analysis

This section has some suggestions of how you can analyze your model output and what other software you might consider using to do so. This suite of analytical and graphical manipulation software has been drawn together through personal experiences using and developing the model software and so is only a suggestion, and some of which are limited by software licensing, but you can use these suggestions as a guideline for what type of software can be useful.For analysis and display of your simulation results you may require additional software. Useful applications include

- Microsoft Excel versatile calculation and graphing tools for quick viewing of your outputs.
- Sigmaplot advanced graphing solution.
- GS+ geostatistics software useful for interpolating spatial outputs and for developing Kriged surfaces.
- Genstat advanced analysis solution.
- UnFREEz animated GIF builder.
- AVIQuick AVI movie builder.
- IrfanView image viewer and manipulation.

## Suggested techniques

You can get descriptive statistics (Daily Mean, Monthly Means per month, Monthly Mean for all months, Annual Means per year, Annual Mean for all years, Standard Error, Median, Mode, Standard Deviation, Sample Variance, Kurtosis, Skewness, Range, Minimum, Maximum, Sum and Count) for your User Defined Output using the Output Selector.

If you want descriptive statistics for your other ascii output then you need to generate these manually, but that's easy enough in a spreadsheet package like Excel. In fact, because you know the format of the static text files and of your own User Defined Output, it's also quite easy to either write macros to produce the calculations for you, or set up the first spreadsheet and then use this as a template for subsequent output with the same format.

You may also be interested to explore any relationships between the output variables in your results. You can use correlation and regression analysis for this, however if you were to follow standard code of practise for experiments then it may be a good idea to consider which hypotheses you wish to test about your model before you run your simulation.

Analysis packages like Genstat, SAS, SPlus, etc, can be used to carry out more advanced statistical analyses although there are limits to what is possible when analyzing simulation results. Instead, it is usual to consider the statistical validity of your simulations in terms of your simulation structure, and to use resampling techniques (replication, Monte Carlo simulation, bootstrapping, etc.).

How do elements of your model change during the course of the simulation? You can see the variables plotted against simulation time for each simulation using the graph windows but how much confidence you will have in your results will depend on your simulation structure.

You can get mean temporal sequences by averaging across replicated time units, e.g., for 20 replicates, take the mean of the 20 values for each simulated day. Now replot these against the time units (e.g., 365 days) using graphing packages like Excel and Sigmaplot. Sufficient replication will give you a general result rather than a result specific to your simulation conditions, especially rainfall sequence.

Load your ascii grid files exported from the Grid windows into the Grid Viewer to see how the distributions of your spatial grid variables change over the course of your simulation. You can also export bitmap image sequence from the Grid windows which you can then animate using AVI or animated GIF software like AVIQuick and UnFREEz.

Single grids are very specific to a single day's conditions, and the simulation history leading to those conditions. Use the statistical capabilities of the Grid Viewer to generate a mean distribution grid for your grid sequence which will be more general to the simulation context.

You could generate your own animations from any of the graphical output windows. Use a screen capture utility (there's one on IrfanView) to grab window contents to a sequence of image files which you can then animate using AVI or animated GIF software like AVIQuick and UnFREEz. For example, this animation was made by capturing the Landscape Surface Plot while sliding the rotation control.

You can investigate the spatial distributions in your spatial graphical outputs using geostatistics and software like GS+. Unless you have an image analyzer to reliably recapture your binary data as ascii data, you will want to collect ascii outputs from your graphical displays then use geostatistical variogram analysis to fit a regression model of semivariance and use it to interpolate your data. Kriged surfaces are a popular form of interpolated output that can be a valuable way to illustrate spatial trends such as this distribution of cattle grazing. Note that these statistical methods can introduce large errors into your results depending on your assumptions about the spatial dependency in your data, and it should be noted that interpolation is an extrapolation, however when properly used they have proven useful ways to present spatial results.

When you introduce into your model water points and animals dependent on those sources of water you will see the generation of a degradation pattern called the piosphere effect.

In your model, how this spatial pattern is generated simply depends on the balance between spatially constrained forage consumption during the dry season and plant regrowth during the wet. Where impacts are concentrated depends on the few spatial foraging rules in your animal module and defined in the section on Ecological Architechture. The resulting pattern of impacts is an emergent property of the grazing ecosystem (Derry 2004) which you can characterize and analyze in a number of ways illustrated in this section about piospheres.