What Power Dissipation Measures — climatlas research

The substitution

A surface integral, indexed by a point

The rate at which a tropical cyclone dissipates kinetic energy against the sea surface is an integral over the whole storm:

PD = ∫∫ ρ C_D |V|³ dA dt ρ air density, C_D the drag coefficient, |V| the surface wind, integrated over the storm's area and its life

Emanuel (2005) introduced the power dissipation index, PDI = ∫ V_max³ dt, as a tractable stand-in, and it became the standard currency for arguments about tropical cyclones and climate. The substitution is exact under one condition: that

∫∫ |V|³ dA = κ V_max³ with κ the same for every storm, everywhere, always i.e. the wind field is self-similar and its area scale is fixed

Nobody ever believed that literally. What has been missing is the measurement: you cannot test it without a wind field for every fix in every basin, and until the size layer there was not one. There is now — tropical fixes from storms, radii analysed by the forecast agencies, no reanalysis anywhere in the sample.

The dissipation area

One number that holds the whole question

Rearranging the definition gives a quantity with units of area:

A_D ≡ PD / (ρ C_D V_max³) the area over which the peak wind would have to act to dissipate the power the storm actually dissipates

If PDI is a faithful index, A_D is a constant. It is not. Across the sample its median is km² — an equivalent radius of about km — and it spans a factor of between its 10th and 90th percentiles. More importantly, it is not random: it varies systematically with the two things a point index cannot see.

Finding 1

Dissipation follows the square of intensity, not the cube

The dissipation area falls as storms intensify

Three independent integrations of the same analysed radii. The 2-D field is this site's radii-constrained wind model; M13 is the quadrant/annulus method of Misra et al. (2013) as used by Klotzbach et al. (2022); M10 is the symmetric modified-Rankine vortex of Maue (2010, §7.4). They disagree on magnitude by up to a third and agree completely on shape.

The 34-kt wind area grows by a factor of from tropical-storm to major-hurricane force: intense storms really are bigger. But the area normalised by V_max³ falls by a factor of over the same range, because the peak wind becomes an ever worse description of the field beneath it. Fitting A_D ∼ V^b with latitude and basin controlled:

The exponent is stable across every split that could carry an artifact — the two independent radii sources, the post-2004 era in which NHC best-tracks its radii after the season rather than estimating them live, and each basin separately:

Finding 2

Size grows with latitude, at every intensity

Dissipation area by latitude, within fixed intensity bands

Median A_D, km². Reading across a row holds intensity fixed.

This is the mechanism that links storm structure to a well-known climate signal. If the latitude at which storms reach their strength is migrating poleward — Kossin, Emanuel & Vecchi (2014) — then the integrated energy of a storm population rises even with no change in how many storms form or how strong they get. Frequency and intensity can both hold still while dissipation climbs, purely because the population moved.

Finding 3

Two routinely-analysed numbers do far better than one

If size is what PDI is missing, then adding the one size number every agency already publishes should recover most of it. Fitting log PD on log V_max and log R34 (the quadrant-mean 34-kt radius):

Skill at reproducing area-integrated dissipation

Variance of log PD explained, per fix and per season (global, 2002–2025)

PDI and ACE share a per-fix bar by construction: in log space any pure power of V_max is the same predictor, so they can differ only in calibration, never in explained variance. They come apart per season, where aggregation weights storms of different size and duration differently — and that is the whole of the difference between them.

Per basin, over every season with observed radii, the size-weighted index beats PDI everywhere — and plain ACE, long dismissed as physically arbitrary next to PDI's cubic motivation, quietly beats it in five basins of six:

Finding 4

Size carries more interannual variance than intensity

Seasonal dissipation factors exactly into the things it convolves — how many storms, how long they last, how strong they get, how big they are, and the covariance between the last two:

PD = N × duration × ⟨V³⟩ × ⟨A_D⟩ × (1 + cov)

Where interannual variance comes from

Covariance share of log-variance, global 2002–2025. ACE has no size term to give.

The negative covariance term is not a rounding error: because A_D falls as V_max rises, seasons that are intense are, other things equal, seasons of compact storms. That anticorrelation is a first-order term in the energy budget of a season, and it is precisely the thing no point index can represent.

Finding 5

ENSO moves everything except size

Variance explained by ENSO, by metric

r² against ONI, 2002–2025 (ASO for northern-hemisphere basins, DJF for southern)

The canonical relationship between ENSO and basin-wide activity was established with size-blind metrics. Measured as energy actually dissipated, it is roughly a third weaker — not because ENSO's grip on frequency and intensity is any less firm, but because the largest single term in the energy budget is one that ENSO does not appear to touch at all. Whatever sets the size of a season's storms, it is not the state of the equatorial Pacific.

Finding 6

The honest null: a century of record to detect it

Global season totals, observed radii

Each series as a fraction of its 2002–2025 mean

No metric here has a significant trend, and the size term is the noisiest of them all. That cuts both ways. It means no claim of a size-driven change in dissipation is presently supportable — and it means the term carrying the most variance is the one furthest from detection, so arguments resting on PDI trends are resting on the part of the problem that happens to be measurable rather than the part that matters most.

The long view

1959–2022, and exactly what it costs

Everything above uses analysed radii only, which buys homogeneity and costs four decades. The Xu et al. (2024) ERA5 reconstruction offers the other trade: additional fixes reaching back to 1959, generated by a random forest on ERA5 azimuthal-mean wind profiles and fed through a parametric wind model. It is worse data. The question is what it is still good for, and the answer is specific.

It reproduces the structure

Both scaling relationships survive in the reconstruction, independently:

The size–intensity relationship in the reconstruction is partly imposed: its radii come from a parametric wind profile driven by machine-learned V_max and R_max, so agreement on the V exponent says its wind model resembles the observed radii, not that ERA5 independently measured the scaling. The latitude coefficient is the more informative of the two, because latitude enters through the learned R_max rather than the profile.

It strengthens the ENSO null

The most valuable thing a longer record buys is power against a null hypothesis. The observed-era finding that ENSO does not touch storm size rested on 24 seasons. It now rests on , and it holds:

And it must not be used for trends

This is not a caution in principle; it is a measurement. Fit a trend through the merged record and it returns large, highly significant changes — in the opposite direction to the observations, in both size and latitude:

Mean storm size, 1959–2022, and where the data comes from

Shading is the share of each season's fixes with analysed radii

What this changes

Six connections

Method & caveats

What is in the sample, and what could go wrong

References

Emanuel, K. (2005). Increasing destructiveness of tropical cyclones over the past 30 years. Nature 436, 686–688. doi:10.1038/nature03906
Powell, M. D. & Reinhold, T. A. (2007). Tropical cyclone destructive potential by integrated kinetic energy. BAMS 88, 513–526. doi:10.1175/BAMS-88-4-513
Misra, V., DiNapoli, S. & Bastola, S. (2013). Dynamic downscaling of the twentieth-century reanalysis over the southeastern United States. Reg. Environ. Change. (quadrant IKE method)
Klotzbach, P. J., et al. (2022). Characterizing continental US hurricane risk: which intensity metric is best? JGR-Atmospheres 127. doi:10.1029/2022JD037030
Kossin, J. P., Emanuel, K. A. & Vecchi, G. A. (2014). The poleward migration of the location of tropical cyclone maximum intensity. Nature 509, 349–352. doi:10.1038/nature13278
Chavas, D. R., Lin, N. & Emanuel, K. (2015). A model for the complete radial structure of the tropical cyclone wind field. JAS 72, 3647–3662.
Maue, R. N. (2010). Warm Seclusion Extratropical Cyclones. PhD dissertation, Florida State University, §7.4. read it here
Demuth, J. L., DeMaria, M. & Knaff, J. A. (2006). Improvement of advanced microwave sounding unit tropical cyclone intensity and size estimation algorithms. JAM 45, 1573–1581. (Extended Best Track)