A Fractal Analysis of Rainfall Time Series

Fractal Rainfall

"Two-year series of 1-min rainfall intensities observed by rain gages at six different points are analyzed to obtain information about the fractal behavior of the rainfall distribution in time. First, the rainfall time series are investigated using a monodimensional fractal approach (simple scaling) by calculating the box and correlation dimensions, respectively. The results indicate scaling but with different dimensions for different time aggregation periods. The time periods where changes in dimension occur can be related to average rainfall event durations and average dry period lengths. Also, the dimension is shown to be a decreasing function of the rainfall intensity level. This suggests a multidimensional fractal behavior (multiscaling), and to test this hypothesis, the probability distribution/multiple scaling method was applied to the time series. The results confirm that the investigated rainfall time series display a multidimensional fractal behavior, at least within a significant part of the studied timescales, which indicates that the rainfall process can be described by a multiplicative cascade process."

The above comes from a study done by Jonas Olsson, Janusz Niemczynowicz and Ronny Berndtsson. with the Department of Water Resources Engineering, Lund Institute of Technology, Lund University, Lund, Sweden.  It was reported on in the WaterSISWEB site just as above - nothing else.

Can anyone tell me what this means and why it might be important?  John Fleck?  Is this up your alley?   I understand that fractals are patterns that exist at various scales so I'm guessing this report is saying that rainfall patterns are similar over various scales... of time?  Distance?  Intensities?

When I first read it I was sure it was an attempt by the Three Swedes to prove the 23 Enigma!  But I think now it's more sophisticated than that.  Now I'm thinking it's design is to expose the 6 degrees of separation from any of the 23 enigmas!  A mind-bender any way you look at it.

GMD 4 Rain - Pumping - Water Table Relationship

I continue to be struck by the simplicity of the water use patterns inside our groundwater management district.  The graph included (click on it to enlarge) shows 3 graphed data sets from roughly 1980 through 2002 - average in-season rainfall; reported groundwater pumped; and water level change.  (We used only the data from the late 1980s forward for reported water use - when our reporting process was enhanced significantly.)

When the rains come, the pumpage drops and the water table change is mitigated.  And of course, the opposite is true as well.  A really good example of inversely related data sets.  Now, if we could only get it to rain more...

One of these days I'm going to update this graph because it's so instructional.  You should note also the three trend lines included on the graph.  While the in-season rainfall and the water level change trend lines are relatively flat, the reported pumped water trend line is decidedly downsloping. 

Why, you ask, should the water level change line NOT be upward sloping if less water is getting pumped?  It's because consumptive use drives the water level changes.  While pumped water is actually declining due largely to irrigation efficiency improvements, the consumptive use of the reduced water pumped has held more or less steady.  To affect the water level change trend line, we need to reduce consumptive water use - or, make it rain more.

The extremes of weather in Kansas

If Aguanomics can post a picture of a pretty lake in droughty California, I can post a picture of a desert in rain-filled NW Kansas!  This radical rainfall difference being experienced between parts of California and SE Texas and NW Kansas is indicative of the extreme variability of precipitation in the Western US.  But if the truth be known, it is actually more the norm - at least for NW Kansas. 

In 2002 Thomas County received an average of just 12.69 inches of annual rainfall.  One of the stations had a low of 9.72 inches for the entire year.  This year, we are to date at a County average of 27.49 inches - with 4 months yet to go.  In case you don't know, the long-term average is 18 inches for Colby - which is rarely ever received.  Feast or famine is our rainfall lot it seems.  All we can do is enjoy it while it lasts, because the drier times are somewhere out there.

All the extra rain does have it's disadvantages.  I just took my schnauzer to the vet for a swollen hind foot today.  Seems the cheatgrass is particularly bad this year with all the moisture, and she had some of it worked into her foot and it managed to get infected.  $63.00 this darned rain cost me.  I actually have no cheatgrass in my yard, but without having to water much at all this summer, I have been taking the dog for walks with all my spare time!   Actually, I'm loving every minute of it!