# Daily Consecutive
Dry Day Probability

## Technical Details

### Homogeneous Extreme Precipitation
Subregions (by storm occurrence
dates)

New York State was divided into a
set of subregions using a Smirnov test-based clustering algorithm (DeGaetano 1998). Using this procedure, stations were grouped based on
geographic proximity and similarities among the timing of precipitation events
throughout the annual cycle. In
order to quantify station-to-station timing comparisons, the frequency of
return period amount exceedences was tallied for each week throughout the
annual cycle and used to construct a cumulative distribution function (CDF) for
each station. These ÔtemporalÕ
CDFs specify probabilities that a return period exceedence will not occur after
a particular week in the annual cycle.
Therefore, these empirical CDFs have near-zero probabilities for week 1
and a probability of 100% for week 52.
Each subregion formed from this clustering procedure (7 subregions in
New York) consisted of stations that have no statistical differences between
their empirical ÔtemporalÕ CDFs.

### Consecutive Dry Day Probability Computation and Interpolation

Using all stations within a
subregion, tallies were made of the number of times that a precipitation event
greater than or equal to various magnitudes (0.01Ó, 0.10Ó, 0.25Ó, 0.50Ó) was
preceded by dry periods ranging from 1 to 30 days in length. These tallies were accumulated for each
day in the annual cycle. The
conditional probabilities were computed for each dry period length (n) and day
(j) as,

, (8)

where *C*_{nj} is the number of dry periods of length *n* ending on day *j* over all stations in a subregion, and *T*_{j} is the total number of precipitation events with a
magnitude equal to or exceeding a certain amount that occurred on day *j* over all stations. *T*_{j} was always greater than zero and thus the ratio in
equation 8 was always defined.

To account for some of the
sampling variability, daily values are smoothed using a 15-day moving
average. Therefore, for instance,
values corresponding to julian day *j* represent
averages of values computed for days (*j*-7) through (*j*+7). Values corresponding to each dry period
length-day pair is the daily conditional probability of ending a dry period of
an equal or greater length, given the occurrence of a precipitation event
meeting or exceeding the user-specified magnitude.