# Presentation: 438971

## Predicting the influence of observations on 3-7 day forecasts

- Sharanya J. Majumdar (RSMAS Division of Meteorology and Physical Oceanography, University of Miami)
- Kathryn Sellwood (RSMAS), Dan Hodyss (NRL, ex-RSMAS),
- Yucheng Song (IMSG at EMC)
- Acknowledgments: Istvan Szunyogh, Craig Bishop, Zoltan Toth, Funding by NOAA THORPEX
- THORPEX PI Workshop, NCEP EMC, 17-19 January 2006

## Initial time

- 84 hrs

- 168 hrs

*Influence of WSR data (00 UTC 20 Jan. 2005) on 1**st**, 2**nd**, & 3**rd** generation storms*

## Used by NWS/NCEP for Winter Storm Reconnaissance, NCEP and UKMO for ATReC ‘03. Extended for hurricane prediction (NOAA Joint Hurricane Testbed) and coastal ocean prediction (Autonomous Ocean Sampling Network).

- ti

- to

- tv

- Ensemble
- Initialization time

- Observing time

- Verification time

- t

- 1-2 days

- 1-? days

- ETKF: Adaptive Sampling

## ETKF: Adaptive Sampling

- STEP 1: Error covariance matrix for ROUTINE obs network
- Pr(t)	= Pf - Pf HrT (Hr Pf HrT + Rr)-1 Hr Pf  and   Zr = Zf Tr
- STEP 2: Using SERIAL ASSIMILATION theory, covariance update for q’th possible ADAPTIVE observational network
- Pq(t)	= Pr - Pr HqT (Hq Pr HqT + Rq)-1 Hq Pr
- 		= Zr(t)ZrT(t) – Zr(t) Cq q (q + I)-1 CqT ZrT(t)
- 		= Pr - Sq
- Holds for any time t if linear dynamics are obeyed.
- Sq is reduction in error covariance due to adaptive obs.

## Signals and Signal Variance

- Signal   sq 	= zr – zq
- 			= Pr HqT (Hq Pr HqT + Rq)-1 (yq – Hq zr)
- 			= Kq (yq – Hq zr)
- Signal covariance
-   Sq = *E*(sq sqT)
- 	   = Kq *E*((yq – Hq zr) (yq – Hq zr)T) KqT
- 	   = Kq (Rq – Hq *E*(zr yqT)–*E*(yq zrT) HqT + Hq Pr HqT)KqT
- 	   = Kq (Hq Pr HqT + Rq) KqT  [new obs uncorrelated w/analysis]
- 	   = Pr HqT (Hq Pr HqT + Rq)-1 Hq Pr
- Hence, the ETKF predicts SIGNAL COVARIANCE, which is precisely equal to the reduction in analysis/forecast error covariance.

## Limitations of ETKF

- Spurious long-distance correlations due to small number of operational ensemble forecasts.
- Assumptions of linearity in Kalman Filter and propagation of signal covariance.
- Inconsistency: ETKF Pf differs from NCEP Pf.
- Model error: No treatment.

## Slide 7

## Linear relationship between ETKF 2-3 day Signal Variance Prediction and variance of NCEP signal realizations

## Goals of NOAA THORPEX Research

- Assess whether variance of 3-7 day forecast “signals” can be predicted by ETKF
- Classify ETKF’s skill in situations of
- High-impact weather, extremes of climate indices
- Degree of non-linearity
- Significant influence of observations on forecasts
- Identify time limits beyond which NCEP signal propagation and signal variance prediction ceases to be meaningful
- Understand NCEP signal & ETKF signal variance propagation

## Preliminary Results

- Computed ETKF signal variance and NCEP signals for WSR05
- Chose WSR because observations are usually collected in areas of high ensemble variance.
- 20 T126 NCEP ensemble forecasts (10 initialized at each of 00Z/12Z, 24/36 hours prior to targeted observing time)
- All cases on http://www.rsmas.miami.edu/personal/ksellwood/

## Good case: Zonal flow, Small spurious initial SigVar in Atlantic, “real” SigVar propagates.

- Good case: Zonal flow, Small spurious initial SigVar in Atlantic, “real” SigVar propagates.

## Same observing time, improve 1-day forecast

- ETKF “summary map” of vertically averaged (u,v,T) signal variance in VR

- Vertically averaged NCEP GFS (u,v,T) variance

- Same observing time, improve 2-day forecast

- ETKF “summary map” of vertically averaged (u,v,T) signal variance in VR

- Vertically averaged NCEP GFS (u,v,T) variance

- Same observing time, improve 3-day forecast

- ETKF “summary map” of vertically averaged (u,v,T) signal variance in VR

- Vertically averaged NCEP GFS (u,v,T) variance

- Same observing time, improve 4-day forecast

- ETKF “summary map” of vertically averaged (u,v,T) signal variance in VR

- Vertically averaged NCEP GFS (u,v,T) variance

## Same observing time, improve 5-day forecast

- ETKF “summary map” of vertically averaged (u,v,T) signal variance in VR

- Vertically averaged NCEP GFS (u,v,T) variance

- Bad case: Blocking flow, Large spurious initial SigVar in Atlantic, minimal propagation of “real” SigVar.

- Same verification time, improve 5-day forecast

- ETKF “summary map” of vertically averaged (u,v,T) signal variance in VR

- Vertically averaged NCEP GFS (u,v,T) variance

- Same verification time, improve 4-day forecast

- ETKF “summary map” of vertically averaged (u,v,T) signal variance in VR

- Vertically averaged NCEP GFS (u,v,T) variance

- Same verification time, improve 3-day forecast

- ETKF “summary map” of vertically averaged (u,v,T) signal variance in VR

- Vertically averaged NCEP GFS (u,v,T) variance

- Same verification time, improve 2-day forecast

- ETKF “summary map” of vertically averaged (u,v,T) signal variance in VR

- Vertically averaged NCEP GFS (u,v,T) variance

- Same verification time, improve 1-day forecast

- ETKF “summary map” of vertically averaged (u,v,T) signal variance in VR

- Vertically averaged NCEP GFS (u,v,T) variance

## Grades based on >3-day propa-gation of ETKF signal variance

| F | D | C | B | A |
| --- | --- | --- | --- | --- |
| 2/19 | 2/7 | 2/5 | 2/10 | 1/20 |
| 2/25 | 3/9 | 2/6 |  | 2/2 |
| 3/12 |  | 2/20 |  | 2/12 |
| 3/13 |  | 2/23 |  | 2/13 |
| 3/14 |  | 3/2 |  | 2/21 |
|  |  | 3/16 |  |  |
|  |  | 3/17 |  |  |

## Preliminary Findings: ETKF

- ETKF target regions are generally found at the base of and slightly downstream of upper-level troughs.
- Little sensitivity of optimal observation location to verification variable, e.g. 250mb **u** vs surface variables.
- Blocking ridges and cut-off lows hurt ETKF predictions.
- ETKF signal variance at initial time is usually localized near the observations, but also appears in NW Atlantic.
- Spurious signal variance lingers and amplifies downstream, contaminating “real” signal variance in Atlantic.
- In cases where the “real” ETKF signal variance can be traced to NE America, it usually reaches the east coast by 3-4 days and Europe by 5-7 days.

## How to mitigate spurious correlations in ETKF?

- Can’t propagate localized covariance.
- Will try computing signal variance for some false deployments. Subtract (or normalize by) some part of this false signal variance from that produced from our desired observations.
- Also apply Zimin et al. (2002, 2006) wavepacket modulation to signal variance (and also NCEP signals)

## NCEP Signals

- Compute T126 L28 NCEP GFS “data denial” run by removing a small group of observations at one time, using the operational first guess field.
- Signal = Operational - Data Denial Run

## Trajectory Divergence

## NCEP Signals

- http://www.rsmas.miami.edu/personal/dhodyss/
- Signal generally propagates to western verification region (AK, Pac NW) and improves forecasts for which it is targeted during WSR.
- Blocking and bifurcations act to weaken signal propagation further east.  Significant forecast improvement in eastern USA was rare: zonal flow regime necessary?
- Rapid local growth of signals up/downstream

## Future Work

- Attempt to alleviate spurious correlations
- Evaluate ETKF’s ability to predict signal variance, and NCEP signals / forecast improvement
- Versus ensemble’s ability to predict forecast error variance
- Versus non-linearity measure (Hansen and Smith 2000)
- Versus flow regime parameters (PNA, NAO, blocking index)
- Versus high-impact or low-impact weather situation
- Test where ETKF signal variance / NCEP signals agree or disagree with dynamical basis proposed by Szunyogh et al. (2000, 2002)
- Extend NCEP data denial tests to hurricanes ...

## Hurricane Charley: Surface Pressure Signal produced by NOAA G-IV aircraft

## Contrasting Adaptive Sampling Techniques: Hurricane Katrina

- ETKF: NCEP ENSEMBLE

- VARIANCE SVs: NOGAPS

- [Courtesy Carolyn Reynolds, NRL]