A Markov Environment-dependent Hurricane Intensity Model and Its Application in Operational Forecasting Renzhi Jing and Ning Lin Department of Civil and Environmental Engineering, Princeton University Introduction MeHiM Simulations MeHiM + Rapid Intensification Indicator

Motivation MeHiM Diagnostics Ø MeHiM is improved by adding a process of state correction when applied in Improve statistical modeling of TC intensity climatology 100 100 operational forecasting. At the time of RI (given by historical record), storm’s FMR FMR by considering TC intensity change as a temporally IBTrACS IBTrACS underlying state is manually transitioned to the extreme state during next 24 hours. 4.979 4.979 MeHiM MeHiM correlated sequence. OLS OLS 0.248 0.248 Research Objective PDF (%) Ø Develop a new statistical model, the Markov PDF (%) 0.012 0.012

Environment-dependent Hurricane Intensity Model 0.001 0.001 (MeHiM), to simulate tropical cyclone intensity evolution. 0 0 Ø Evaluate MeHiM’s performance. −150 −100 −50 0 50 100 150 −150 −100 −50 0 50 100 150 24−HR DV (kt) 24−HR DV (kt) Ø Evaluate MeHiM when appling to operational forecasting

by introducing a rapid intensification indicator. 9% 9% ↑ Histograms of 6-h and 24-h FMR non−RI Storms RI Storms IBTrACS intensity change probability MeHiM FMR IBTrACS MeHiM OLS 6% OLS 6% distribution in logarithmic scale. Data and Method Data are binned in 5-kt interval. PDF PDF 3% 3% ← PDFs of lifetime maximum Data intensity. Right: LMI distribution ↑ MeHiM (upper) vs. MeHIM with RI state correction (lower). Selected four RI storms • Best Track Data IBTrACS (1979-2014) 0% 0% of RI storms (dashed lines) and are (a, e) Paula (2010), (b, f) Harvey (1981), (c, g) Andrew (1992) and (d, h) Felix (2007). 0 50 100 150 200 0 50 100 150 200 • ECMWF ERA-Interim climate reanalysis. Environmental LMI (kt) LMI (kt) non-RI storms (solid lines). The black arrow indicates the occurrence of RI for each storm. variables: maximum potential intensity, wind shear and ↓ Performance on three recent hurricanes (Hurricane Harvey, Hurricane Irma and ← TC intensity distributions at landfall over different segments of the North Atlantic coastline; Hurricane Maria ) in the 2017 Atlantic hurricane. relative humidity. → Spatial intensity distribution with color showing maximum intensity (kt) in each 2°×2° grid. The Method intensities plotted are from (a) observation, (b) one simulation randomly selected from 100 MeHiM - Simulated intensity evolutions • Three regression models realizations, (c) median of 100 MeHiM realizations, (d) 80th percentile of 100 MeHiM realizations. from OLS (yellow), MeHiM (red), Ø Ordinary Least Squares (OLS): Linear regression MeHiM-RI (blue) are shown. ALL North-East USA 0.6 0.6 OLS median OLS median 15th-85th percentile 15th-85th percentile (a) (b) model for whole data. 0.4 IBTrACS 0.4 IBTrACS

PDF - The colored shading boundaries 0.2 0.2 60 60

Ø 0 0 Finite Mixture Regression (FMR): Separates data 0 50 100 150 0 50 100 150 represent the deciles of 100

South-East USA MEXICO 0.6 0.6 OLS median OLS median 40 40 15th-85th percentile 15th-85th percentile realizations while the solid into specified number of groups with unique IBTrACS IBTrACS 0.4 0.4 20 20 statistical properties and performs linear regression Fraction 0.2 0.2 colored lines are the mean of 0 0 0 50 100 150 0 50 100 150 0 0 Landfall Intensity (kts) Landfall Intensity (kts) −100 −50 0 −100 −50 0 ensemble average in each single ALL North-East USA ALL North-East USA for each group. 0.6 0.6 0.6 0.6 FMR median FMR median MeHiM median MeHiM median 15th-85th percentile 15th-85th percentile 15th-85th percentile 15th-85th percentile (c) (d) storm simulation. 0.4 IBTrACS 0.4 IBTrACS 0.4 IBTrACS 0.4 IBTrACS PDF Ø Markov environment-dependent Hurricane PDF 125 0.2 0.2 0.2 0.2 60 60

0 0 0 0 100 Intensity Model (MeHiM): storm’s intensity change 0 50 100 150 0 50 100 150 0 50 100 150 0 50 100 150 - The dashed lines indicate South-East USA MEXICO South-East USA MEXICO 75 0.6 0.6 0.6 0.6 FMR median FMR median MeHiM median MeHiM median 40 40 15th-85th percentile 15th-85th percentile 15th-85th percentile 15th-85th percentile 50 is assumed to be a Markov process with three 0.4 IBTrACS 0.4 IBTrACS 0.4 IBTrACS 0.4 IBTrACS observations that are over land, 25 Fraction Fraction 20 20 0.2 0.2 0.2 0.2 during which the land model is 0 0 0 0 0 unobserved discrete states. The three components in 0 50 100 150 0 50 100 150 0 50 100 150 0 50 100 150 0 0 Landfall Intensity (kts) Landfall Intensity (kts) Landfall Intensity (kts) Landfall Intensity (kts) −100 −50 0 −100 −50 0 the MeHiM, namely the initial model, state transition applied. model, and response model are all dependent on large-scale environment variables. Test of Ocean Feedback Parameter Conclusions

Observations DV &&& DV &&& DV &&& DV &&& DV &&& (one-step DV) t=1 t=2 t=3 t=4 t=5 Ø A Markov environment-dependent hurricane intensity model (MeHiM) is developed to $ = 1 − 0.87,-. / ≡ 0.01Γ-2.3ℎ 6 8 8-: , 5 7 9 simulate the climatology of hurricane intensity given surrounding large-scale environment. Ø MeHiM shows great improvement over previous statistical models (such as OLS and FMR) Hidden States Markov Chain Ocean feedback parameter depends on upper in simulating TC intensity climatology, such as DV distribution and LMI distribution. thermal stratification, mixed layer depth, storm’s Ø A ocean feedback parameter is tested and shown to be statistically significant in • Simplified Land Model translation speed, storm’s maximum potential developing hurricane intensity model. A separate filling rate land model is added to intensity and storm’s current wind speed. Ø MeHiM’s shows great potential in operational real-time forecasting when combined with a simulate storm’s behavior over land. RI indicator, which calls for an index that can accurately represent the occurrence of RI. • Model Evaluation ← Comparisons of MeHiM simulated intensity References [7]Knaff, J.A., C.R. Sampson, and M. DeMaria, 2005: An Operational Statistical Typhoon Intensity Prediction Scheme for the Western North Pacific. Wea. Forecasting, 20, 688-699. with (upper) and without (lower) ocean [1]DeMaria, M., and J. Kaplan, 1999: An updated statistical hurricane intensity prediction scheme (SHIPS) for the [8]Knapp, K. R., M. C. Kruk, D. H. Levinson, H. J. Diamond, and C. J. Neumann, 2010: The International Best Track Archive for Monte Carlo simulations are performed , where Atlantic and eastern north Pacific basins. Wea. Forecasting, 14, 326-337. Climate Stewardship (IBTrACS): Unifying tropical cyclone best track data. Bull. Amer. Meteor. Soc., 91, 363-376. parameter. Selected storms are (a, c) Tropical [2]Emanuel, K. A., 2000: A statistical analysis of tropical cyclone intensity. Mon. Weather Rev., 128, 1139-1152. [9]Lee, C., M.K. Tippett, A.H. Sobel, and S.J. Camargo, 2016: Rapid Intensification and the Bimodal Distribution of Tropical [3]Emanuel, K. A., S. Ravela, E. Vivant, C. Risi, 2006: A Statistical Deterministic Approach to Hurricane Risk Cyclone Intensity. Nature Communications 7 (February): 10625. doi:10.1038/ncomms10625. MeHiM is run freely to simulate historical storms Assessment. Bull. Amer. Meteor. Soc., 87, 299–314. [10] Lin, N., R. Jing, Y. Wang, E. Yonekura, J. Fan, and L. Xue, 2017: A Statistical Investigation of the Dependence of Tropical storm Larry (2003) and (b, d) Hurricane Felix [4]Hall, T., and E. Yonekura, 2013: North-American tropical cyclone landfall and SST: A statistical model study. J. Cyclone Intensity Change on the Surrounding Environment. Mon. Wea. Rev, 145, 2813–2831, doi:10.1175/MWR-D-16- Climate, 26, 8422-8439. 0368.1. using historical tracks and environment taken from [5]Kaplan, J., and M. DeMaria, 1995: A Simple Empirical Model for Predicting the Decay of Tropical Cyclone Winds [11] Murakami, H., and Coauthors, 2015: Simulation and Prediction of Category 4 and 5 Hurricanes in the High-Resolution (1995). after Landfall. J. Appl. Meteor.,34, 2499–2512. GFDL HiFLOR Coupled Climate Model*. http://dx.doi.org/10.1175/JCLI-D-15-0216.1, 28, 9058–9079, doi:10.1175/JCLI-D-15- [6] Schade, L. R., and K. A. Emanuel, 1999: The Ocean’s Effect on the Intensity of Tropical Cyclones: Results from a 0216.1. reanalysis datasets. Simple Coupled Atmosphere–Ocean Model. http://dx.doi.org/10.1175/1520- [12] Walsh, K., 2015: Fine resolution simulations of the effect of climate change on tropical cyclones in the South Pacific. Clim 0469(1999)056<0642:TOSEOT>2.0.CO;2, 56, 642–651, doi:10.1175/1520-0469(1999)056<0642:TOSEOT>2.0.CO;2. Dyn, 45, 2619–2631, doi:10.1007/s00382-015-2497-1.