Guidance on Intensity Guidance Kieran Bhatia, David Nolan, Mark DeMaria, Andrea Schumacher IHC Presentation This project is supported by the NOAA Joint Hurricane Testbed. 1

Project Outline Real-time guidance of intensity forecast error Applications of error predictions 2

Project Motivation Bhatia and Nolan (2013) showed that intensity forecast error is often related to the nature of the particular storm and surrounding atmospheric environment. Parameters representing initial condition error and atmospheric stability (“proxies”) are also linked to forecast error. These proxies and environmental conditions can serve as independent variables in a regression formula to predict intensity forecast error. 3

Data Sample Dataset DetailData Used Hurricane Seasons (Atlantic Basin) Forecast Hours (12-hour increments) Models EvaluatedLGEM, DSHP, HWFI, and GHMI PredictorsGFS output obtained from SHIPS text files and proxies Verification criteria Excludes “LO”, “EX”, and INVESTS. All models must have verification and all predictors for particular time to be included (homogeneous). Land and no land cases combined. 4

Dynamical Predictors Initial and forecast intensity Initial % GOES Cold Pixels GOES IR Brightness Temperature Forecast average and 0 hour: – hPa RH – 200 hPa divergence – 850 hPa vorticity – Potential intensity – Storm speed – Latitude – Longitude – Sin(shear direction) – Shear magnitude ( hPa) – Ocean heat content 5

Initial Condition Error and Atmospheric Stability Predictors: Standard deviation of ensemble forecast intensity Deviation of the intensity forecast from ensemble mean (absolute value for AE) Deviation of the track forecast from ensemble mean Forecasted intensity change (absolute value for AE) Previous 12-hour intensity change Previous 12-hour error Initial and forecasted distance to land 6

Methodology: Multiple Linear Regression Independent variables (x’s) are proxies and synoptic parameters Dependent variable (y) is absolute error (AE) or bias M is the number of predictors μ is an intercept included to account for model biases y = β 1 * x 1 + β 2 * x 2 + … + β M * x M + μ 7

Methodology: Multiple Linear Regression Dependent and independent variables are normalized Separate regressions performed for each forecast interval (12, 24, …, 120 hr), model, and training period Backward-stepping used: predictor is used in regression model if the probability that the regression coefficient is different from zero exceeds 95% (F statistic) Dependent and independent verification (cross- validated) 8

Predictor and Predictand Transformations AE is bounded by 0, which leads to a positively skewed distribution Box-Cox transformation applied to AE to make it approximately Gaussian before regression is applied To account for non-linear relationships between predictors and forecast error, low order polynomials and Gaussian functions are applied to the predictors and tested For example, 0-hour relative humidity (RH) is fitted using a Gaussian to account for peak error at medium RH values 9

Results ALL RESULTS FOR INDEPENDENT DATASET, CROSS VALIDATION USED FOR

R^2 of AE Predictions # of Cases HoursDSHPLGEMHWFIGHMI

R^2 of Bias Predictions # of Cases HoursDSHPLGEMHWFIGHMI

Percent Improvement Over AE Climatology Forecasts HoursDSHPLGEMHWFIGHMI

Percent Improvement Over Bias Climatology Forecasts HoursDSHPLGEMHWFIGHMI

Applications 15

Motivation If model error can be successfully anticipated in certain situations, can we bias-correct the models or weight an ensemble accordingly? Two first attempts to create unequally weighted ensembles can be derived from AE and bias predictions. 16

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Methodology For Unequally Weighted Ensemble Technique 1 – Bias-correct individual models using bias forecasts and use the mean of the bias-corrected models Technique 2 – Inverse-weight individual models using AE forecasts and use the inverse-weighted average as the ensemble mean – i.e. if LGEM is predicted to have 20 knots of AE and DSHP is predicted to have 10 knots of AE, trust DSHP’s forecast more 18

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Conclusions Predictor pool selected using results of Bhatia and Nolan (2013) and added proxies Inputted into a modified multiple linear regression model Multiple linear regression techniques are promising with independent results showing percent improvement over climatology ranging from 6%-18% for AE and 8%-30% for bias 20

Extra Slides 21

Future Work Testing more proxies Developing nonlinear relationships between predictors and forecast error Varying the length of training period Producing error predictions using probabilistic forecasts Neural networking and nonlinear regression methods may be considered 22

Sample Output File 23

Potential Output Product 1 24

Potential Output Product 2 25

Potential Output Product 3a 26

Potential Output Product 3b 27

COEFFICIENT FILE 28

R=0.75, Skill Score = 31% Absolute Error = X (Avg Lat) X (Prev 12 Hr Int Chng) X (Abs. Val. Of Forecasted Intensity Change) X (Dev From Ensemble Mean) 29

R=0.93, Skill Score = 64% Bias = 0.14 X (0 hr Int) X (Avg Div) X (Fcst Int) X (Dev From Ensemble Mean) 30

Probabilistic Forecasts of AE and Bias 31

Logistic Regression 32

Methodology: Probabilistic Forecasts AE and Bias were converted to binary and ternary variables AE: Binary threshold = 20 knots, Ternary thresholds= 10 knots and 20 knots Bias: Binary threshold = 0 knots, Ternary thresholds= -20 knots and 20 knots 33

Reliability Diagram Graphical device that shows the full joint distribution of the forecasts and observations Observed frequency of an event is plotted against the forecast probability of an event A perfect forecast system will result in forecasts with a probability of X% actually occurring X% of the time (diagonal line on the graph) 34

60-Hour LGEM AE Tercile Forecast 35

96-Hour DSHP BIAS Tercile Forecast 36

36-Hour GHMI AE Binary Forecast 37

84-Hour HWFI BIAS Binary Forecast 38

Example of Atmospheric Instability Proxy 39

Goerss and Sampson (2014) Results 40

“For the Atlantic basin, the percent variance of IVCN TC absolute intensity forecast error that could be explained for this independent sample ranged from 2-5% compared with 4-6% for the dependent sample” 41

Boutique Predictors: Gaussian Fit of Relative Humidity vs. AE 42

Boutique Predictors: 2 nd Order Polynomial Fit of Dist. To Land vs. Bias 43

Example of AE Transformation 44

Methodology: Nonlinear Fits of Predictors Several predictors exhibiting nonlinear relationships with error were empirically fit Functions tested: Gaussian, second order Gaussian, second order polynomial, and third order polynomial 0-Hour Latitude, 0-Hour distance to land, and 0-Hour Relative Humidity exhibited the strongest non-linear relationships 45

2014 RESULTS 46

Percent Improvement Over AE Climatology Forecasts # of CasesHoursLGEMDSHPHWFIGHMI

Percent Improvement Over Bias Climatology Forecasts # of CasesHoursLGEMDSHPHWFIGHMI