# Presentation: 669871

## The Credible-Interval Forecast

**“****An attractive concept for **
**adding probabilistic information **
**to digital forecasts”**

**Kennard “Chip” Kasper**
**WFO Key West, Florida**

## Why is it desirable to add probabilistic information to forecasts?

**To improve forecast quality **
**To improve forecast value**
**In essence, to provide users with information regarding forecast uncertainty so that they may make sound decisions**

## What is a “credible-interval” forecast?

**A “credible interval” is an interval of potential values of a variable together with a probability that the actual value of the variable will fall in the interval.  **
**Example:**
**   ****Interval of Temps****	****	****Probability**
**   ****{80, 81, 82, 83, 84},           {0.75}**

## Two types of credible intervals

**1.****	****Variable-width credible interval**
**      ****(Variable interval; fixed probability)**
**Fixed-width credible interval**
**      ****(Fixed interval; variable probability)**

## IFPS?

**The type of credible interval most appropriate for IFPS is the “fixed-width” type (fixed interval; variable probability)**
**Basically, we can make a fixed-width credible-interval forecast in IFPS by taking some weather element like MaxT and adding one additional element (ProbMaxT).**

## Here’s how:

**Define a fixed interval of temperature values for a given forecast MaxT**
**“****84” is in the grid, but let us define  “84” to be the 5-degree (F) fixed interval including {82, 83, 84, 85, 86} where “84” is the median value. **
** ****Introduce another element called ProbMaxT.  We will assign a probability to this grid.  The probability will represent a forecaster’s “degree of belief” that the observed MaxT will in fact fall in the defined interval for a given point, grid, or edit area.**

## Slide 7

## A forecaster would then edit a probability grid where probabilities are assigned to the intervals for various points, grids, or areas as appropriate.

**WITHIN A CREDIBLE-INTERVAL **
**FORECAST FRAMEWORK, EACH **
**TEMPERATURE VALUE IN THE  **
**IMAGE WOULD BE DEFINED AS **
**THE MEDIAN OF A FIXED INTERVAL OF, SAY FOR THIS EXAMPLE, 5 DEGREES F.**
**78**** :****	****{76, 77, ****78****, 79, 80}**
**83**** :****	****{81, 82, ****83****, 84, 85}**
**85**** :****	****{83, 84, ****85****, 86, 87}**
**81**** :****	****{79, 80, ****81****, 82, 83}**

**A forecaster would then edit a probability grid where probabilities are assigned to the intervals for various points, grids, or areas as appropriate.**

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## The credible interval concept also provides a means of describing the uncertainty inherent in forecasts of other meteorological variables.

## CAVEATS

**Effective implementation of a credible-interval forecast program would require education of  both forecasters and users regarding proper forecast formulation and use, respectively.**
**A survey of user needs should precede implementation in order to address the length of intervals and details with respect to how the forecasts should be presented (tables, text, graphics???)**

## “Cooke (1906) first provided the rationale for, and demonstrated the ability of, experienced forecasters to formulate, probabilistic

**“****Cooke (1906) first provided the rationale for, and demonstrated the ability of, experienced forecasters to formulate, probabilistic**
**weather forecasts almost three-quarters of a century ago.  **
**Unfortunately, 60 years elapsed before the “meteorological**
**establishment” recognized the merits of the arguments and evidence set forth by Cooke (and others in the interim) and decided to initiate an operational program of precipitation probability forecasting.  We hope that another 60 years will not pass before the meteorological and user communities realize at least some of the benefits that could be obtained from the implementation of a nationwide program of operational probabilistic temperature forecasting.”**
**Murphy, A.H. and R.L. Winkler, 1979:  Probabilistic              ****	****Temperature Forecasts:  The Case for an Operational ****	****Program.  Bull. Am. Meteorol. Soc., 60, 12-19.****  **

## Kennard.Kasper@noaa.gov

- Copyright, 2000 Kennard B. Kasper

- _[Kennard.Kasper@noaa.gov](mailto:Kennard.Kasper@noaa.gov)_
**WFO Key West, Florida**