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 ‘temporal’ 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 ‘temporal’ CDFs.
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 (0.01”, 0.10”, 0.25”, 0.50”) 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,
where Cnj is the number of dry periods of length n ending on day j over all stations in a subregion, and Tj 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. Tj 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.