Isoprobability Time Series

Three exceedance fractiles with the same probability (say 0.5) form an isoprobability time series of estimates (say, a time series of the medians marked by circles): each of the estimates has the same probability of being exceeded at 7:00 am on a particular day. A time series conveys the forecasted change over time in the estimates having a constant exceedance probability (a constant risk of being exceeded).

For any day, the exceedance fractiles with probabilities 0.75 and 0.25 (dots) define the 0.5 credible interval: the probability is 0.5 that the river stage at 7:00 am will fall inside this interval.

For any day, the exceedance fractiles with probabilities 0.95 and 0.05 (squares) define the 0.9 credible interval: the probability is 0.9 that the river stage at 7:00 am will fall inside this interval.

One way to understand the PRSF is to consider the medians and the credible intervals. The medians depict the central tendency of the river stages. The credible intervals convey the uncertainty about the medians. The wider a credible interval, the larger the uncertainty. The time series of the credible intervals show how the uncertainty changes with the forecast lead time.