# Presentation: 028988

##  A new method for moderating spurious ensemble correlations

**Craig H. Bishop, Daniel Hodyss **
** ****Naval Research Laboratory**
**Monterey, California**

## Initial Error Covariance Challenge

**Initial Error Covariance Challenge**

- True error correlation structure is flow dependent

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

## Initial Error Covariance Challenge

**Initial Error Covariance Challenge**

- Ensembles give flow dependent ***noisy*** correlations

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

## Initial Error Covariance Challenge

**Initial Error Covariance Challenge**

- Today’s fixed moderation functions limit adaptivity

- Current ensemble DA techniques
- reduce noise by multiplying ensemble
- correlation function by fixed
- moderation function (green line).
- Resulting correlations (blue line) are too thin when true correlation is broad and too noisy when true correlation is
- thin.

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- km

- Unstable flow error correlations

- Fixed moderation

- Fixed moderation

## Initial Error Covariance Challenge

- SENCORP moderation functions ***adapt***

- Smoothed ENsemble Correlations Raised to a Power (SENCORP) moderation functions provide flow adaptive moderations functions.

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- km

- Unstable flow error correlations

- km

- Unstable flow error correlations

- SENCORP moderation

- SENCORP moderation

**Initial Error Covariance Challenge**

## Single variable. Varying error correlation length scales.

- Dotted line denotes optimal analysis error

## The Error Propagation Challenge

**The Error Propagation Challenge**

- True time dependent error correlation function

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- 4D DA requires accurate error correlations of variables separated in time

- t=0

- t=0

## The Error Propagation Challenge

**The Error Propagation Challenge**

- True time dependent error correlation function

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- 4D DA requires accurate error correlations of variables separated in time

- t=0

- t=0

- t=1

- t=1

## The Error Propagation Challenge

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- Current ensemble moderation functions poorly represent 4D** **error correlations.

- t=0

- t=0

**The Error Propagation Challenge**

## The Error Propagation Challenge

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- Current ensemble moderation functions poorly represent 4D** **error correlations.

- t=0

- t=0

- t=1

- t=1

**The Error Propagation Challenge**

## The Error Propagation Challenge

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- Current ensemble moderation functions poorly represent 4D** **error correlations.
- SENCORP moderation functions do better.

- t=0

- t=0

**The Error Propagation Challenge**

## The Error Propagation Challenge

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- Current ensemble moderation functions poorly represent 4D** **error correlations.
- SENCORP moderation functions do better.

- t=0

- t=0

- t=1

- t=1

**The Error Propagation Challenge**

## The model error challenge

**The model error challenge**

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- Our models are approximate.
- Microphysical and sub-grid scale turbulence associated with storms are particularly difficult to approximate.
- 4D DA will fail to generate a time series of states consistent with observations if model error is not represented.

- t=0

- t=0

## The model error challenge

**The model error challenge**

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- Our models are approximate.
- Microphysical and sub-grid scale turbulence associated with storms are particularly difficult to approximate.
- 4D DA will fail to generate a time series of states consistent with observations if model error is not represented.

- t=0

- t=0

- t=1

- t=1

## The model error challenge

**The model error challenge**

-  SENCORP makes perturbed model ensembles useable in 4D DA

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- Our models are approximate.
- Microphysical and sub-grid scale turbulence associated with storms are particularly difficult to approximate.
- 4D DA will fail to generate a time series of states consistent with observations if model error is not represented.
- Perturbed model ensembles describe model error.
- SENCORP makes perturbed model ensembles useable in 4D DA

- t=0

- t=0

## The model error challenge

**The model error challenge**

-  SENCORP makes perturbed model ensembles useable in 4D DA

- Stable flow error correlations

- km

- km

- Unstable flow error correlations

- Our models are approximate.
- Microphysical and sub-grid scale turbulence associated with storms are particularly difficult to approximate.
- 4D DA will fail to generate a time series of states consistent with observations if model error is not represented.
- Perturbed model ensembles describe model error
- SENCORP makes perturbed model ensembles useable in 4D DA

- t=0

- t=0

- t=1

- t=1

## Propagating Large Scale Error

- Dotted line denotes optimal analysis error

## Propagating Small Scale Error

- Dotted line denotes optimal analysis error