# Presentation: 417830

## TC Dressing: Next-generation GPCE

**Jim Hansen**
- NRL MRY, code 7504
- (831) 656-4741
- _[Jim.Hansen@nrlmry.navy.mil](mailto:Jim.Hansen@nrlmry.navy.mil)_
- Jim Goerss
- Buck Sampson

**Notes:**
I’m a new NRL employee who was lured to Monterey from academia.

This is a proposal about using forecasting as a tool to better understand the underlying system (the atmosphere, in this case), and represents the continuation of 6.1-ish work that I did last year at NRL MRY during my sabbatical

## Outline

- A spectrum of approaches to predict track error
- GPCE
- GPCE-AX
- TC Dressing
- Small ensemble size limits the utility of TC Dressing.
- Provide skewness-like information by extending GPCE-AX with probability of left/right/fast/slow (P-LRFS).

## Goerss Prediction Consensus Error (GPCE)

- Produces state-dependent, isotropic track error estimates.
- Multivariate linear regression
- Predictors include
- Ensemble spread
- Initial intensity
- Predicted longitudinal displacement
- Displays 70% probability isopleth
- Reliable, and sharp relative to climatology

## GPCE

- GUNA

- Consensus

- Verification

## GPCE Along/Across (GPCE-AX)

- Produces state-dependent, anisotropic track error estimates (ellipses).
- Eigenvectors are across-track/along-track directions
- Includes bias correction
- Multivariate linear regression
- Predictors include
- Across/along ensemble spread
- Initial intensity
- Initial longitude
- Predicted longitudinal displacement
- Displays 70% probability isopleth
- Reliable, and sharp relative to GPCE

## GPCE-AX

- GUNA

- Consensus

- Verification

## GPCE

- GPCE-AX

- GUNA

- Consensus

- Verification

## TC Dressing

- Each TC track forecast in an ensemble is dressed with a Gaussian “kernel”.
- The sum of the ensemble of Gaussian PDFs defines the total forecast PDF.
- Gaussian parameters (weight, spread) are tuned to optimize a probabilistic cost function.
- Climatology is included as a kernel whose spread is fixed but whose weight can vary.

## Dressed ensemble example

-         Total PDF
-         Individual PDFs
-         Forecast TC location

## Dressed ensemble example

-         Total PDF
-         Individual PDFs
-         Forecast TC location

- Weight

## Dressed ensemble example

-         Total PDF
-         Individual PDFs
-         Forecast TC location

- Spread

## Ensemble dress example

- TC Dressing is using only ensemble track information as predictors for spread and weight.

-         Total PDF
-         Individual PDFs
-         Forecast TC location

- Spread

- Weight

## TC Dress

- GUNA

- Consensus

- Verification

## GPCE

- GPCE-AX
- TC Dress

- GUNA

- Consensus

- Verification

## GPCE

- GPCE-AX
- TC Dress

- GUNA

- Consensus

- Verification

## GPCE

- GPCE-AX
- TC Dress

- GUNA

- Consensus

- Verification

## Ensemble size for TC Dressing?

- Ensemble size

- Ensemble size

- Variance changes by 300%

- Variance changes by 10%

- 30 ensemble members

- 1024 ensemble members

## Reliability and sharpness

- GUNA, 2 predictors, trained using 2002-2005, tested using 2006

| Lead | GPCE
70% reliability | GPCE-AX 70% reliability | Fractional difference between 70% areas | Sample
size |
| --- | --- | --- | --- | --- |
| 12hr | 0.80 | 0.77 | 0.31 | 193 |
| 24hr | 0.77 | 0.76 | 0.13 | 173 |
| 36hr | 0.81 | 0.73 | 0.19 | 157 |
| 48hr | 0.82 | 0.77 | 0.10 | 136 |
| 72hr | 0.82 | 0.80 | 0.11 | 98 |
| 96hr | 0.79 | 0.65 | 0.10 | 68 |
| 120hr | 0.84 | 0.70 | 0.12 | 50 |

## Probability of left/right/fast/slow (P-LRFS)

- Logistic regression
- Use 70% as a warning threshold.
- Simple tests indicate utility.
- Not clear how to communicate.

- Predictor

- Predictand

- 0

- 1

## Slide 20

## Slide 21

## Slide 22

## Slide 23

## Slide 24

## Conclusions

- TC Dressing is limited by small ensemble size.
- GPCE-AX outperforms GPCE.
- P-LRFS provides value for hedging (skewness-like information).

## Why does the uncertainty look the way it does?

## Ensemble track

- Landfall location

- Actual track

**Notes:**
Here is an example of how we can use ensemble information to tell us not only about uncertainty, but also about *why* the uncertainty looks the way it does.

This is an example of an ensemble forecast of tropical cyclone tracks.  The black dots show the track of the storm over three days.  The green lines show the ensemble forecast tracks from the forecast launched at the time when the storm was the furthest to the SE.  The magenta dots indicate the locations at which each of those ensemble members made landfall.

As you can see there is a lot of uncertainty in where the storm will make landfall.  A forecaster might be thankful that they had this information, but they are also going to want to know *why* all that uncertainty is there.

This information can be provided.

## Ensemble mean 500mb at 6hrs

- Sensitivity of latitude of landfall to
- 500mb heights at hour 6 of forecast

**Notes:**
The plot on the left is the ensemble mean 500mb height at hour 6 of the forecast (the location of the second black dot on the previous slide).  The big red blob is high pressure sitting over Japan.  The blue blob over the Philippines is the storm itself.

The picture on the right is the sensitivity of the latitude of landfall (happening around day 3) to the 500mb height field at hour 6.

The colors are sensitivities, not 500mb heights themselves!

Blue colors means there is a negative correlation between landfall latitude and the 500mb heights.  That means as the 500mb heights get smaller, the latitude of landfall gets bigger.

Red colors means there is a positive correlation between landfall latitude and 500mb heights.  That means as the 500mb heights get smaller the latitude of landfall also gets smaller.

What this plot tells us is that *if* the 500mb heights associated with the forecast high at hour 6 of the forecast are smaller than expected, then the latitude of landfall is expected to be large.  On the other hand, if the 500mb heights associated with the forecast high at hour 6 of the forecats is larger than expected, then the latitude of landfal is expected to be low.

The positive (red) sensitivities in the right plot indicate that if the storm is stronger at hour 6 than is expected by the mean (lower heights), then the latitude of landfall is also expect to be low.

The idea of this guidance product is that it provides the forecaster at a glance what the forecast problem of the day is.

## Slide 29

## Dan Gombos, MIT

- Typhoon Sepat

- Ensemble track

- Landfall location

- Actual track

- Ensemble mean 500mb at 6hrs

- Sensitivity of latitude of landfall to
- 500mb heights at hour 6 of forecast

**Notes:**
The combination of these three types of images 

O The ensemble associated with the event/parameter of interest
O The ensemble mean field of interest
O The sensitivity of the event to the field

could be sent to forecasters over MetCast or ATCF. 

## Northern Edge 2008: High seas

## Slide 33

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## Slide 37