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Transition path theory insights into hurricane rapid intensification

F. J. Beron-Vera, G. Bonner, M. J. Olascoaga, S. Dong, H. Lopez

Abstract

We explore hurricane and ocean reanalysis data to understand how rapid intensification (RI) of tropical cyclones is impacted by the upper ocean density structure, with an emphasis on barrier layer (BL) thickness and thermocline depth in the eastern Caribbean Sea and adjacent western tropical North Atlantic. This analysis leverages transition path theory (TPT), supported by basic statistical methods. In TPT, Markov chains are constructed by discretizing data series related to weather system intensity, changes in intensity, translational speed, and BL thickness and thermocline depth. These series are viewed as trajectories in abstract state spaces, following a memoryless stochastic process. RI imminence is rigorously framed using a newly derived TPT statistic, which gives the time distribution to first reach a target -- the RI state -- from a source -- for instance, the state determined by a certain BL range and system intensity -- conditional on connecting paths exhibiting minimal detours. Increased RI frequency is observed in the eastern Caribbean and nearby Atlantic, influenced by river runoff, primarily in tropical storms and category 2 hurricanes. RI frequently correlates with a well-developed BL; however, increased translational speed is necessary for RI. TPT shows a stronger connection between RI and thermocline depth than BL presence, with RI likelihood rising for hurricanes with a thin BL, especially category 1. Across all strength categories, a deep thermocline consistently elevates RI probability, a factor missed by basic statistical analysis. Furthermore, translational speed is crucial, with faster, stronger hurricanes more susceptible to RI, while slower systems are less so.

Transition path theory insights into hurricane rapid intensification

Abstract

We explore hurricane and ocean reanalysis data to understand how rapid intensification (RI) of tropical cyclones is impacted by the upper ocean density structure, with an emphasis on barrier layer (BL) thickness and thermocline depth in the eastern Caribbean Sea and adjacent western tropical North Atlantic. This analysis leverages transition path theory (TPT), supported by basic statistical methods. In TPT, Markov chains are constructed by discretizing data series related to weather system intensity, changes in intensity, translational speed, and BL thickness and thermocline depth. These series are viewed as trajectories in abstract state spaces, following a memoryless stochastic process. RI imminence is rigorously framed using a newly derived TPT statistic, which gives the time distribution to first reach a target -- the RI state -- from a source -- for instance, the state determined by a certain BL range and system intensity -- conditional on connecting paths exhibiting minimal detours. Increased RI frequency is observed in the eastern Caribbean and nearby Atlantic, influenced by river runoff, primarily in tropical storms and category 2 hurricanes. RI frequently correlates with a well-developed BL; however, increased translational speed is necessary for RI. TPT shows a stronger connection between RI and thermocline depth than BL presence, with RI likelihood rising for hurricanes with a thin BL, especially category 1. Across all strength categories, a deep thermocline consistently elevates RI probability, a factor missed by basic statistical analysis. Furthermore, translational speed is crucial, with faster, stronger hurricanes more susceptible to RI, while slower systems are less so.
Paper Structure (15 sections, 41 equations, 10 figures, 1 table)

This paper contains 15 sections, 41 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Data
  3. Main datasets
  4. Preliminary data preparation
  5. Results
  6. Straightforward statistical analysis
  7. Transition path theory analysis
  8. Summary and conclusions
  9. Transition Path Theory (TPT)
  10. Reduction of the dynamics into a Markov chain
  11. The main objects of TPT
  12. Remaining transition time
  13. Open systems and connectivity
  14. Application of TPT to the RI problem
  15. Computation of $C^{\mathbb{A} \mathbb{B}}(t)$

Figures (10)

  • Figure 1: (a) Fraction of weather systems exhibiting RI in the Atlantic Ocean (top) and propagated uncertainty (bottom). (b) Overlaid on BL thickness on 15 July 1999, a subset of system tracks considered in this study. (c) Histogram (left) and PDF (right) of along-track intensity (top) and translational speed (bottom). (d) Histogram of along-track BL thickness (top left) and thermocline depth (bottom left) and fraction of systems exhibiting RI for given BL thickness and sea surface salinity (top right) and thermocline depth (bottom right). (e) Fraction of systems exhibiting RI (left) and propagated error (right) as a function of speed and intensity with BL present. (f) Same as (e), but with BL absent.
  • Figure 2: (left panel) CDFs of conditional RI times in a three-day window for each weather system class from a Markov chain generated by trajectory data in (BLT, Intensity)-space. The value of the CDF on the vertical axis is the probability that conditional RI occurs on or before the corresponding time on the horizontal axis. (middle panel) As in the left panel, with a Markov chain generated by trajectory data in (ILD, Intensity)-space. (right panel) Similar to the left panel, but in (Speed, Intensity)-space. The shaded areas around the curves represent the uncertainty due to error propagation in estimating transition probabilities through counting, as explained in the text.
  • Figure 3: As in Fig. \ref{['fig:cdf-by-class-weighted']}, but for each BLT (left panel) and ILD (right panel) box values of the Markov chain constructed using trajectory data in (BLT, Intensity) and (ILD, Intensity)-space, respectively.
  • Figure 4: The probability of undergoing RI in the initial step (i.e., after 6 hours) conditional on the Markov chain starting in each box of (BLT, Intensity)-space (top-left panel) and (ILD, Intensity)-space (top-right panel). Uncertainties from error propagation in estimating transition probabilities are shown in the bottom panels.
  • Figure 5: Stationary distribution of the Markov chain in (BLT, Intensity)-space (top-left panel) and (ILD, Intensity)-space (top-right panel).
  • ...and 5 more figures