New thresholds for n-year storms

[kbrose]

Is it possible to re-create the analysis done in bulletin 70 (http://www.isws.illinois.edu/atmos/statecli/RF/download.htm) to determine what the new thresholds are for an n-year storm? Not necessarily to re-create all of the research (probably only interested in the Northeast "Climatic section" since that contains Chicago, and probably not all "durations"),

For reference, these are the current definitions:

       1-year   2-year  5-year  10-year 25-year 50-year 100-year
Duration                            
10-day  4.12    4.95    6.04    6.89    8.18    9.38    11.14
5-day   3.25    3.93    4.91    5.70    6.93    8.04    9.96
72-hr   2.93    3.55    4.44    5.18    6.32    7.41    8.78
48-hr   2.70    3.30    4.09    4.81    5.88    6.84    8.16
24-hr   2.51    3.04    3.80    4.47    5.51    6.46    7.58
18-hr   2.30    2.79    3.50    4.11    5.06    5.95    6.97
12-hr   2.18    2.64    3.31    3.89    4.79    5.62    6.59
6-hr    1.88    2.28    2.85    3.35    4.13    4.85    5.68
3-hr    1.60    1.94    2.43    2.86    3.53    4.14    4.85
2-hr    1.48    1.79    2.24    2.64    3.25    3.82    4.47
1-hr    1.18    1.43    1.79    2.10    2.59    3.04    3.56
30-min  0.93    1.12    1.41    1.65    2.04    2.39    2.80
15-min  0.68    0.82    1.03    1.21    1.49    1.75    2.05
10-min  0.55    0.67    0.84    0.98    1.21    1.42    1.67
5-min   0.30    0.36    0.46    0.54    0.66    0.78    0.91

And in plot form:

[kbrose]

From bulletin 70:

As in any statistical analysis, the individual ob- servations or data points should be independent of each other. With a partial-duration series, one must be careful that the observations used are not meteor- ologically dependent; that is, they must be from sepa- rate storm systems. In the present study, data for precipitation durations of 24 hours or less were ob- tained from individual precipitation events, defined as precipitation periods in which there was no pre- cipitation for at least 6 hours before and 6 hours after the precipitation event (Huff, 1967); then, only the maximum value for the particular duration (6 hours, 12 hours, etc.) within such a precipitation event was used. This ensures that the precipitation values are independent of each other and are derived from individual storms. For precipitation durations of 2 to 10 days, no time separation criteria were needed.

This seems incomplete to me. How would we handle aggregating daily values into 48 hour chunks (or worse, hourly data to 48 hour chunks)? Consider the following:

day, rainfall
1,   0
2,   1.5
3,   3.5
4,   2.5
5,   0
6,   0

If we combine days such that 1 and 2 are aggregated, we get a different max value than if we aggregate 2 and 3. If we aggregate both 1 and 2 _and_ 2 and 3, then we do not have independent values...

On the plus side, apart from this issue it looks like it should be fairly reproducible. We won't have quite as much historical data as the original analysis, but hopefully it'll be enough to come to some conclusions...

[sbeslow]

Just to clarify what this means -- if we are looking at 24 hours where there are no 6 hour gaps in rainfall, then there can only be 1 n-year storm in that range even if there is no overlap in two periods that cross the thresholds. Is this right?

[kbrose]

Correct, if you have 48 straight hours of rain, then that entire chunk can only be counted once towards an n-year storm for durations <= 24 hours.

Seems kind of arbitrary since we don't do the same for 48 hours or more, but maybe talking about storms of <= 24 hours is viewed as a different kind of thing from lots of rain over >= 48 hours.

Regardless, it's not the way I would have defined it. To me, taking the fraction

all consecutive windows of a given duration with rainfall above some threshold T
--------------------------------------------------------------------------------
         the total number of consecutive windows of the given duration

(the denominator is easily convertible into "years") is more in line with what I was thinking. Then you can use the recurrence interval to answer the question "for any window of time with a given duration, what's the probability that it will rain more than T inches?" I believe this question is un-answerable in the given formulation.