# Presentation: 782224

## The CPC Consolidation Forecast

**David Unger**
**Dan Collins, Ed O’ Lenic, **
**Huug van den Dool **
***NOAA/NWS/NCEP/Climate Prediction Center***

## Overview

**A regression procedure designed for ensembles.**
-    **Derive a relationship between the BEST member of an N-member ensemble and the observation:**
-       Y = a0 + a1fb + ε

## Ensemble Regression 

**Weights represent the probability of a given member being the best**.
**If weights are known, coefficients can be calculated from the ensemble set**.
-  (*No need to explicitly identify the best member*)

## Ensemble Regression

## Example ForecastCFS 1-month Lead Forecast  Nino 3.4 SST, May, 1992

- April Data  June-August Mean SST’s
- A series of forecasts
-  Start with the ensemble mean
-  Gradually increase the ensemble spread
- K = The fraction of the original model spread

## Slide 6

## Slide 7

## Slide 8

## Slide 9

## Slide 10

## Slide 11

## Slide 12

## Slide 13

## Slide 14

## Slide 15

## Slide 16

## Slide 17

## Slide 18

## Slide 19

## Slide 20

## Slide 21

## Slide 22

## Slide 23

## Slide 24

## Slide 25

## Slide 26

## Slide 27

## Multi Model Consolidation

**At least 25 years of “hindcast” data**
**Standardize each model (means and standard deviations)**
**Remove trend from models and observations**
**Weight the various models**
**Perform regression**
**Add trends onto the results**

## Nino 3.4 Consolidation

**CFS, CCA, CA, MKV**
**   **(Statistical and Dynamic models mixed**)**
**Lead -2 and Lead -1 are a mix of observations and the one and two-month forecast from the CFS**

## Skill  May Initial TimeCalibrated CFS Vs. Consolidation

## U.S. Temperature and Precipitation Consolidation

**CFS**
**Canonical Correlation Analysis (CCA)**
**Screening Multiple Linear Regression(SMLR)**
**OCN  - Trends****. **

## SON Consolidation Forecast

## Performance

| .046 | .076 | .191 | -.147 | 63% |
| --- | --- | --- | --- | --- |
| .067 | .076 | .162 | -.334 | 59% |
| .063 | .100 | .215 | -.268 | 73% |
| .074 | .100 | .199 | -.203 | 62% |
| .023 | .040 | .098 | -.858 | 38% |

**CCA+SMLR**

**CFS**

**CFS+CCA+SMLR, Wts.**

**All – Equal Wts.**

**Official**

**HSS**

**CRPSS  **

**RPSS - 3**

**% Cover**

**Bias (C)**

## Future Work

**Add more tools and models**
**Improve weighting method**
**Trends are too strong**
**Improve method of mixing statistical and dynamical tools**

## END

## Recursive Regression

- Y = a0 + a1fi
-     _***a***_**+**** **= (1-α) _***a***_** **+ α _*Stats(F,Y)*_
-   _*Stats(F,Y)*_ represents error statistic based on the most recent case
-  α = .05
** ****a****+**** **= .95 **a **+ .05 _*Stats(F,Y)*_

## SST Consolidation

- CFS – 42 members       (29%)
- Constructed Analog
-         (CA) – 12 members  (18%)
- CCA – 1 member          (17%)
- MKV – 1 member          (36%)

## Advantages

**Ideally suited for dynamic models.**
**Uses information from the individual members (Variable confidence, Clusters in solutions, etc.)**
***                          ******Disadvantages***
**Statistical forecasts are not true Solutions  **
**Trends are double counted when they accelerate**
**Weighting is not optimum (Bayesian seems appropriate)    **