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Spatial and temporal scales

The success of models predicting the distribution of benthic animals and plants depends strongly on the spatial and temporal scales chosen when designing sampling and modelling. This is because spatial patterns are strong at some scales and less so at others, and because the importance of processes affecting patterns vary among scales.

Two important aspects of scale need to be considered when designing sampling and modelling: extent and grain (resolution).

Extent

  • The temporal extent of a model is the time-span within which the samples are taken. If a model is based on samples collected at a particular season during one year, this is the temporal extent of the model.
  • The spatial extent of the model is the size of the area that needs to be modelled and mapped, and therefore sampled representatively.
     

Grain (resolution)

  • The temporal grain is the time represented by a single sample (usually extremely small and not in need for attention here).
  • The spatial grain is the resolution of the model and it corresponds to the grid-size of the desired map.
     


Extent

Temporal extent - models should ideally be based on data from several years
In most cases we need maps of vegetation that represent longer periods of time, otherwise they are of no use in planning. The only solution to this is to base models on samples from several times, usually years. This will improve the representativity of the data and increase the temporal extent of models. The temporal extent is usually not accounted for in a systematic way, but may be important source of error for some biological features.

In PREHAB we have used existing data, some of which have been sampled during several years while others have not. Therefore PREHAB cannot in a systematic way assess the size of uncertainties due to sampling during one year only. The general recommendation, however, is to plan sampling in a way that allow modelling and testing of models to represent several years! Considering the sometimes large temporal variability observed in the distribution and abundance of vegetation, we also identify lack of temporal extent of data and models as a potentially important source of error in models and maps of coastal vegetation.

Spatial extent - size of area to be mapped not crucial
In a spatial context, decisions about both grain and extent are likely to have substantial effects on the strength of models and reliability of maps. In general, increasing the spatial extent of models has the effect of increasing the range of conditions in which the distribution of vegetation is to be modelled, thus making the task more complex. This is because the spatial variability in vegetation may increase and that the importance of environmental factors changes.

As an example of this, a study on the Swedish coastline in the entire Baltic Sea showed that the success of models of vegetation decreased with XX%? from scales of 25 – 1500 km’s (Sandman et al, manus+avhandling) . On the other hand the decrease in performance was not proportional to the increase in spatial extent (most of the decrease was observed at distances smaller than 75 km) and highly dependent on the species to be modelled.

Within PREHAB, modelling of the distribution and abundance of vegetation was done in areas ranging from 40 to 9 000 km2. At these scales there was no evidence to suggest that the spatial extent - the size of the area - is a major determinant of the success of models prediciting distribution (Fig. 1) or abundance.

Figure 1. Performance of models for predicting vegetation does not decrease with the size of the modelled area. AUC is a measure of model performance. A general rule of thumb is that 0.8 (dashed line) is taken as a threshold for acceptable model performance.


Grain

Relevant spatial grain
It is important to realise that even if the area to be mapped is increased by, say a factor 10, it is generally not advisable to increase the spatial grain of models by a similar amount. This does not mean that maps always need to be excessively detailed, the resolution of the maps depend on the context (and with use of GIS maps can be shown at an arbitrary resolution), but in terms of modelling it is important to maintain a spatial grain that can resolve important patterns of vegetation and the dominating environmental factors.

For instance, if depth is a powerful predictor for the occurence of a reasonably wide-spread type of vegetation in coastal areas, a grain size of 1 km or even 100 m probably is much too coarse. If surveys are properly done, it is very likely that the species is found in all of these grid cells and furthermore it is also very likely that a wide range of depths occur, raising the question of which depth to use for prediction. Therefore, beyond a certain spatial grain, modelling is no longer informative. This is not the same as to say spatial grain should be minimised into excessively small units.

As an example of this, we can study the precision of models of total vegetation cover based on depth and abundance (Fig. 2). In this example it is clear that predictions at the finest resolution, 1x1 m, is less precise than at 10x10 m resolution. Analyses within PREHAB suggest that this is mainly a result of stronger explanatory power of these environmental factors at the coarser resolution rather than differences in precision of data.

Fig. 2. Illustration of changes in precision and predictive power as a consequence of spatial resolution. Excessive resolution (1x1 m) adds uncertainty to the empirical model.



PREHAB has not made a comprehensive evaluation of optimal spatial grain of models of vegetation distribution, but there are a number of theoretical and practical arguments to consider:

  1. Errors in positioning using GPS is on the order of ±5 m, a finer grain is not warranted.
  2. The number of grid cells to model increase by the power of two, given a certain grain and total area (Fig. 3). This means for example that if we use a grain of 10x10 m in a 10x10 km area, the number of cells where the occurrence of vegetation is to be predicted is roughly 1 million. In our experience, this is workable with normal computers. If on the other hand we would have used a grain of 1x1 m, we are approaching 100 million cells, which is considerably more difficult to handle. This is a practical consideration which may be worth considering in the early planning stages of a sampling and modelling.


Nevertheless, the necessary spatial extent of a map and therefore the model used to produce it, is usually determined by the applied context. If a map is needed for regional planning or status assessment, then modelling and mapping needs to be and can be done at this scale. If maps are needed at a national or Baltic wide scale, then the model can be done at that scale.


Figure 3. Number of grid cells to be predicted as a function of spatial extent and resolution. The number of grid cells to model/ predict increase by the power of two given a certain grain and total area.

 

 Author: Mats Lindegarth

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