## Thursday, November 29, 2012

### A simple and trivial consideration about rainfall return period in relation with a spatial analysis, and discharges

Statistics at station, i.e. evaluated at ground measurements stations do not reflect the statistics of the areal event. This is obvious. However, even today, I read a report where the guys:
1. estimated the return period of rainfall in several point
2. used the estimated depths to infer the spatially varying rainfall intensities
3. use these rainfalls as inputs of a rainfall-runoff model to obtain extreme discharges
In between there are a lot of technicalities, often useless. The point is, which is clear to the most, I hope, that, when moving from point 1 to point 2, one assumes that all the measured events are isochronous, which is not (otherwise we could not have let say 200 hundred return period events each year ia a space-wide area).  The above operation actually correspond to consider a precipitation with a higher return period than established (usually following some design criterion) and therefore maximise excessively the discharges.

What one should do is instead:
1. studying the spatial statistics of precipitation to enable a stochastic weather generator^1^2
2. run in continuos time her/his rainfall-runoff model for a long period, say 20 years if one wants to get some statistics a return period of 4 years,
3. analyse the results and extracting the statistics of the discharges (i.e. their return period), eventually extracting the extreme events
The validity of each component of the modelling chain should have been tested against available data (of the basin) independently.  Traditionally engineers do not like to simulate events at continuos time, and prefer to model events. This latter approach, however, has several drawbacks, and especially:
• one has to determine the initial conditions (which also introduce a bias in the return period) of the catchments (models that do not have this problem cannot be good models)
• fall back into the issue of determining a spatially distributed rainfall with a certain return period
Engineers usually also neglect the role of snow in producing discharges. This cannot be neglect, except than in particular climatic conditions. Using continuos time simulations also implies the use of some parameterisation of evapotranspiration (and therefore requires a model like JGrass-NewAGE).

^1 - Remarkably using a weather generator can also allows the inclusion of foreseen trends (either in precipitation characteristics, as depth, interstorm inter-arrival time, or evapotranspiration or radiation).

^2 -  Usually these models are site depedent. Therefore, waiting for a spatial stochastic weather generator, one should run several copies of the weather generator, each one for each sites where there can be information to drive it, and subsequently, using the spatial data, spatially interpolate at each time-step the desired quantity.