Friday, November 4, 2011

Ex 6.6 - Global hydrological model

1. What modifications should be made to the conceptual model if a time scale of 1 year and a spatial scale of 1 km2 are chosen for the model? What processes can be excluded? simplified? described in more detail? 

The elevation aspect of the model can be excluded; it is important when there is flow between adjacent cells, but if we're just modeling a single area, it is irrelevant. The climatic data, on the other hand, could be made more precise, both temporally and spatially.

2. Compare dry year (halved precipitation) and wet year (doubled precipitation) dynamics within the model. Does the model produce reasonable estimates for the state variables? Does it tend to an equilibrium if such conditions prevail, or it shows a trend over several years? 

It does reach an equilibrium, and equilibrium levels of saturated water and unsaturated water are remarkably similar despite the four-fold difference in precipitation. What does change quite significantly is the amount of surface water (and snowpack):
Half precipitation
1x precipitation
Double precipitation
 The same patterns and equilibria hold when the simulation is run over three years.

3. Can you find a parameter in this model, modifying which you can produce a trend over several years that destabilizes the system?

First of all, I love these how-to-break-the-system questions.

Second, if we're given sufficient latitude with the parameters, the question becomes rather simple. Increasing transpiration potential by a factor of ten does little to the system; it remains stable at a very similar equilibrium; however, increasing the same parameter by a factor of 1000 sucks all the water right out of the system:

1000-fold increasing in transpiration potential

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