# Presentation: 417809

## Introducing EKDMOS

- Matt Peroutka
- Meteorological Development Lab
- National Weather Service, NOAA

- Bob Glahn
- Jerry Wiedenfeld
- John Wagner
- Greg Zylstra

## Ensemble Kernel Density MOS (EKDMOS)

- Probabilistic forecast guidance for:
- Temperature (T), dew point (Td), daytime maximum temperature (MaxT), nighttime minimum temperature (MinT).
- 13 probability levels (0.05, 0.10, 0.20, 0.25, 0.30, 0.40, 0.50, 0.60, 0.70, 0.75, 0.80, 0.90, 0.95).
- NDGD grids.
- Days 1-8 x 3-h (T/Td).  Days 1-16 x 24-h (MaxT/MinT).

## PDFs for a Single Event

## EKDMOS Method

- Use screening multiple regression with the NCEP's GEFS ensemble means,
- Estimate error variance directly from the regression,
- Apply equations to individual ensemble members and combine results with Kernel Density fitting
- Gausian kernel
- Standard deviation produced by the regression
- Apply a spread adjustment based on the spread of the ensemble members.

## EKDMOS Method

- Development

- Implementation

- Ensemble Means

- Observations

- Regression

- Predictive Equation

- Error Variance

- Ensemble Members

- Forecast

- Kernel
- Density
- Fitting

- Spread
- Adjustment

- Probability Distribution

## Regression Framework

- Regression estimates *Y* as a function of *X*, sample of size *n*.
- Lines at probability level α can be placed with t distribution
- Ŷh(new) = new value of *Y* found from a new value of *X*, *X*h
*MSE* = error sum of squares divided by degrees of freedom
*r* = multiple correlation coefficient
*s* = standard deviation of the predictand
- Summations are taken over the *n* sample cases

## Regression Equation and Prediction Intervals

## Kernel Density Fitting

- Forecasts are combined with Kernel Density Fitting, using a Gausian kernel and the standard deviation produced by the regression.

## EKDMOS Spread Adjustment

*x* = ratio of new width to old width

## Evaluation

- Tools
- Probability Integral Transform (PIT) Histograms
- Square Bias (SB)
- Cumulative Reliability Diagram (CRD)
- Continuous Ranked Probability Score (CRPS)
- Baseline for Comparison
- Raw Ensembles
- Operational Ensemble MOS

## Baseline Reliability

- Day2

- Day5

- Day7

- Raw Ens

- Raw Ens

- OpnlEnsMOS

- OpnlEnsMOS

## EKDMOS:  Dep. and Ind. Data

- Day2

- Day5

- Day7

- Dep

- Dep

- Ind

- Ind

## EKDMOS:  Ind. Dew Point, Daytime MaxT, Nighttime MinT

- Day2

- Day5

- Day7

- Dew Point

- MinT

- MaxT

## Baseline Reliability/Accuracy

## Visualization--Grids

- NDGD grid projections
- 13 probability levels available; only 3 shown here.

- 0.50

- 0.10

- 0.90

## Meteograms

- Uses 3 probability levels (0.10, 0.50, 0.90)
- Time series of forecast values
- Mullin Pass, Idaho (KMLP)

## "Wings of Uncertainty"

## "Wings of Uncertainty"

- Image is median of distribution.
- Length of wings shows degree of cold and warm uncertainty

## "Wings of Uncertainty"

- Image is median of distribution.
- Length of wings shows degree of cold and warm uncertainty
- Black stripes shown at 5 deg F intervals from 50% value
- Black wing tips show cold or warm skew in uncertainty

## Conclusions

- Developed method for making MOS forecasts from ensembles for quasi-normally distributed variables.
- Regression applied to NCEP ensemble means.
- KDE, normal kernel, mean and standard deviation from regression.
- Spread Adjustment.
- Reliable and Robust.
- Can be implemented in NDGD.
- (E.g., temperatures as probability levels on the CDF)

## Introducing EKDMOS