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.
Weekly Extreme Precipitation Probability Computation and Interpolation
Weekly probabilities of exceeding extreme precipitation return period amounts were computed for each of 7 subregions in New York by the following procedure. Weekly counts were made of the number of times the daily precipitation total equaled or exceeded the 1-, 2-, 5-, 10-, 25- and 50-yr return period amounts at any station within a subregion. Only independent exceedences were considered a valid occurrence. Therefore, multiple stations in a subregion observing a return period exceedence during the same precipitation event were only counted as one subregional exceedence. This eliminates the dependence of probability computation on the density of stations within a subregion, since the same precipitation event may influence a large area that encompasses many of the stations. Conditional weekly probabilities were calculated for each subregion from the independent exceedence tallies using the equation
, n=1, 52 (7)
where the conditional probability of return period exceedence during week n (Pn) is determined by the ratio of wn, the frequency of independent return period amount exceedences for a particular week ‘n’ and subregion, and the total number of independent exceedences observed throughout the entire annual cycle. Conditional probabilities were then converted to absolute probabilities by dividing Pn by the number of years in the recurrence interval. These values were then subjected to a 5-week smoothing to eliminate some of the sampling variability. The values for each return period-week pair in these products are associated with the absolute probability of experiencing a precipitation event of equal or greater magnitude than the corresponding return period amount.
The weekly probabilities computed by the methods above for daily exceedences were assumed identical for 24-, 18- and 12-hr accumulation periods. For shorter accumulation periods (6-, 3-, 2- and 1-hr) hourly data from stations across New York (Table 4) were used rather than empirical or regression-based estimates from daily precipitation totals (fixed observation times). The events of shorter duration were then compared to the corresponding return period amounts, and weekly probability computation proceeded in the same manner.