Disaggregation of the CPC seasonal outlooks

The present format of the U.S. Climate Prediction Center (CPC) long-lead seasonal forecasts is examined with respect to its implications for monthly anomalies. The CPC outlooks consist of probability forecasts for the upcoming month, the three-month period beginning in that month, and twelve additional overlapping 3-month periods each beginning one month later. The point of departure for the analysis is the result that the conditional (on the forecast probability) means of monthly or seasonal temperature and precipitation are computable monotonic functions of those probabilities. Neglecting differences in numbers of days per month, the mean for each 3-month season is exactly the average of the means for the three constituent months. Thus there is a linear system of equations for specifying constituent monthly means in terms of the implied forecast seasonal means, that is underdetermined by only one dimension. These relationships place such strong constraints on self-consistency among the seasonal forecasts that use of this format poses fundamental difficulties unless the forecasting of monthly rather than (or in addition to) seasonal probabilities is scientifically feasible.