1. Introduction

At 2100 UTC 22 September 2005, the National Hurricane Center forecast discussion for Hurricane Rita stated “The minimum central pressure has remained around 913 mb… which is a very low pressure to have only 125 knots.” This statement reflects a relatively infrequent but important issue when the minimum central pressure in a tropical cyclone differs strongly from what would be “expected” from its maximum wind speed alone based on historical experience. This example emphasizes the confusion that arises when our two common measures of tropical cyclone intensity—the point maximum wind speed V_max, which is the official measure of the Saffir–Simpson hurricane wind scale, and the minimum central pressure P_min—depart from one another. This confusion begins with the attempt to characterize a storm’s strength scientifically but then extends to the translation of this characterization into potential implications for the general public.

Indeed, it has long been standard to convert between the tropical cyclone maximum wind speed and P_min using a simple empirical wind–pressure relation (Dvorak 1975, 1984; Atkinson and Holliday 1977; Koba et al. 1990; Knaff and Zehr 2007, hereafter KZ07; Courtney and Knaff 2009). This one-to-one relation assumes that P_min depends predominantly on V_max. KZ07 demonstrated that minimum pressure also depends secondarily on storm size and latitude, motivated by gradient wind balance. This latter result was explained physically by Chavas et al. (2017) by combining gradient wind balance with a theoretical wind structure model. Chavas et al. (2017) demonstrated that a simple linear model that depends on V_max and the product of outer size and the Coriolis parameter successfully predicted the central pressure deficit in simulations and observations. However, that work employed as its size metric a radius of 8 m s⁻¹, which is not routinely estimated operationally nor reanalyzed for retention in a long-term archive. As a result, the utility of this model has been limited. A predictive¹ model aligned with Chavas et al. (2017) that takes as input parameters that are routinely estimated in operations would be much more useful.

The potential utility of a precise and easy-to-use model for P_min has grown as recent work has directly connected P_min to risk. The variable P_min is a remarkably good predictor of the normalized economic damage that has been wrought by landfalling hurricanes in the continental United States (Bakkensen and Mendelsohn 2016; Klotzbach et al. 2020, 2022). Klotzbach et al. (2020) demonstrated that P_min is a substantially better predictor than V_max, particularly for hurricanes making landfall from Georgia to Maine where weaker but larger storms are more common. Klotzbach et al. (2022) demonstrated that P_min is also at least as good of a predictor as integrated measures of the near-surface wind field, including both integrated kinetic energy and integrated power dissipation, that inherently require data from the entire wind field to estimate. The explanation lies in the fact that P_min is itself an integrated measure of the wind field that accounts for both maximum wind speed and storm size (Chavas et al. 2017). The total wind field drives the wind, storm surge, and rainfall hazards that ultimately cause damage and loss of life (Irish and Resio 2010; Zhai and Jiang 2014). Hence, P_min appears to be an especially well-suited measure of the damage potential of a storm, and it carries ancillary practical benefits.

First, P_min is relatively easy to estimate, as it requires a relatively few observations within a small area near the storm center and, moreover, it varies relatively smoothly in space and time since it is by definition an integrated quantity (either in radius via gradient wind balance or in height via hydrostatic balance). In contrast, V_max is a local estimate at a single point of a quantity that is inherently noisy and hence is notoriously difficult to estimate from sparse observations (Uhlhorn and Nolan 2012). Second, P_min is already routinely estimated operationally; indeed, it was used in conjunction with the maximum wind speed as part of the Saffir–Simpson Scale prior to 2009 (Schott et al. 2012).

The practical benefits of a model for P_min extend beyond operations to climate and risk modeling. Climate models are better able to reproduce the historical distribution of minimum pressure than maximum wind speed (Knutson et al. 2015), suggesting that the former is a more stable and suitable metric for model evaluation and intercomparison (Zarzycki et al. 2021). For risk modeling, the pressure field is included as input in storm surge models (Gori et al. 2023). More generally, a model that can relate P_min, V_max, and size to one another should enable the use of all available data to more precisely constrain the properties of historical tropical cyclones and their relationships to hazards and potential impacts.

Here, our objective is to create a simple model to predict P_min that can be easily used in operations and practical applications. The spirit of this effort to make theory directly useful for the community follows from a similar effort for predicting R_max presented in Chavas and Knaff (2022) and Avenas et al. (2023). Section 2 describes the datasets used in our analysis. Section 3 develops the empirical model and its physical basis. Section 4 estimates model parameters from data and applies the model in a few notable contexts, including an operational setting using only routinely estimated parameters. Section 5 provides a brief summary and discussion.

2. Data and methods

Our dataset combines flight-based data for P_min, final best track data for storm central latitude, maximum wind speed V_max, a quadrant-maximum radius of 34-kt wind (R_34kt; 1 kt ≈ 0.51 m s^–1), storm translation speed V_trans, and estimates of environmental pressure P_env from analysis and best track data. We use R_34kt because it is the outermost radius routinely estimated operationally. We analyze storms in both the North Atlantic and eastern North Pacific basins for the period 2004–22, where 2004 is the first year in which postseason best tracking of R_34kt was performed. All information is contained in the databases of the Automated Tropical Cyclone Forecast (ATCF) system (Sampson and Schrader 2000). These data are identical to that available in the extended best track (EBTRK, Demuth et al. 2006).

A combination of the NCEP Climate Forecast System (CFS; Saha et al. 2014) and Global Forecast System (GFS) analyses (GFS 2021) were used to estimate P_env. CFS analyses were used in 2004 and 2005, and GFS analyses were used thereafter. We use the profile of tangential wind in the analysis, specifically a radius of 8 m s⁻¹ (R_8ms), to inform us what radius represents the outer edge of the storm and to calculate P_env. The variable P_env was calculated at 900 km for R_8ms = 0–600 km, 1200 km for R_8ms = 600–900 km, 1500 km for R_8ms = 900–1200 km, 1800 km for R_8ms = 900–1200 km, and 2100 km for R_8ms = 1200–1500 km. In the final section, we also estimate the environmental pressure for operational relevance using the pressure of the outermost closed isobar (P_oci) extracted from the ATCF databases or EBTRK dataset.

Following Chavas and Knaff (2022), to develop our model, we filter our data to focus on a subset of high-quality cases over the open ocean within the tropical western Atlantic basin where aircraft reconnaissance is routine. Hence, we restrict our data to cases west of 50°W and south of 30°N and with ${\overline{R}}_{34\text{kt}}$ smaller than the distance from the storm center to the coastline. We only include cases with at least three nonzero quadrant values of R_34kt to ensure a reasonable estimate of the azimuthal-mean value, and where ${\overline{V}}_{\max }$ is at least 20 m s⁻¹ to avoid weak tropical storms and tropical depressions. A map of the final training dataset is displayed in Fig. 1a. As described below, we will also apply our model to additional subsets of data to explore its broader utility.

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(a) Map of the aircraft-based historical P_min dataset used in this study; the color denotes the magnitude of P_min (hPa). (b) Model prediction for ΔP [Eq. (5); y axis] vs observed ΔP (x axis) for all data shown in (a), with conditional median (red solid), interquartile range (red dashed), and 5%–95% range (red dotted).

Citation: Weather and Forecasting 40, 2; 10.1175/WAF-D-24-0031.1

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3. Model for pressure deficit ΔP

We develop a model for ΔP that is derived from gradient wind balance applied to a two-region, modified Rankine vortex model of the axisymmetric tropical cyclone wind field. The full derivation is presented in the appendix. Here, we focus on the core outcome from the theory. The term ΔP_hPa (hPa) depends linearly on three physical predictors: ${\overline{V}}_{\max }^2$, $(1/2)f{\overline{R}}_{34\text{kt}}$, and $(1/2)f{\overline{R}}_{34\text{kt}}/{\overline{V}}_{\max }$. The variable ${\overline{V}}_{\max }$ is the azimuthal-mean maximum wind speed in units of meters per second; ${\overline{R}}_{34\text{kt}}$ is the radius of 34-kt winds in units meters (1 n mi = 1852 m); and f is the Coriolis parameter at the storm-center latitude (ϕ) in units of per second [f = 2Ω sin(ϕ), Ω = 7.292 × 10⁻⁵ s⁻¹].

Briefly, we note the contrast with Chavas et al. (2017), which found a simpler multiple linear regression relationship for ΔP on ${\overline{V}}_{\max }$ and $(1/2)fR$, where R was taken as the radius of 8 m s⁻¹. These two parameters were taken directly from the wind structure theory of Chavas and Lin (2016) applied to gradient wind balance, and indeed, they show up here too. However, since the theory of Chavas and Lin (2016) has no analytic solution, Chavas et al. (2017) could not derive an analytic solution for P_min and hence could not define exactly how P_min should depend on those parameters [their Eq. (12)]. Instead, they merely found that a pure linear dependence worked well. The new model presented here [Eq. (4)] now gives that analytic dependence. This dependence corroborates the results of Chavas et al. (2017) as both parameters appear in our first two terms, too, but with a slight deviation associated with the third term in Eq. (4) that depends on the ratio of the two parameters. Note that while it might seem desirable to take the reciprocal of the third term, this will make the dependence on the term nonlinear, and indeed doing so results in a significantly degraded performance.

To estimate model coefficients [Eq. (4)], we first bin the dataset into increments of 10 m s⁻¹ for ${\overline{V}}_{\max }$, 50 km for ${\overline{R}}_{34\text{kt}}$, and 10⁻⁵ s⁻¹ for f (i.e., approximately 4° latitude) and calculate the median value of each of the three quantities within the bin, resulting in a single data point per joint $({\overline{V}}_{\max },{\overline{R}}_{34\text{kt}},f)$ bin. Binning minimizes the effects of variations in sample size across the phase space of these variables when estimating model parameters, and it also helps reduce noise within a given bin. No minimum sample size is imposed within each bin, so all bins with at least one valid data point are retained to ensure more extreme cases are included in the fitting. Multiple linear regression coefficients are calculated using the fitlm function in MATLAB. We use the entire dataset in order to produce the best estimate of the model coefficients from all available data. We estimate the 95% confidence interval of each model coefficient as the 2.5th and 97.5th percentiles from a 1000-member bootstrap with resampling of the raw dataset, each fit following the same procedure as above. We explicitly account for the number of degrees of freedom in model performance metrics by calculating the adjusted r-squared value reduced from the nominal value based on the number of degrees of freedom relative to the sample size, $r_{\text{adj}}^2=1-[(n-1)/(n-p)](\text{SSE}/\text{SST})$, where n is the sample size, p is the number of coefficients, SSE is the sum of squared error, and SST is the sum of squared total. The adjustment factor (n − 1)/(n − p) is very small (≈1.0017, i.e., a 0.17% reduction from nominal) since the number of coefficients p = 4 is much smaller than our sample size of approximately 1700, indicating that model overfitting is not a concern. This approach is analogous to removing an arbitrary subset of years for out-of-sample validation, and it carries the added benefit of allowing us to use the entire dataset to yield the best possible coefficient estimates. Nonetheless, we also test our model against multiple out-of-sample subsets described below that further demonstrate the generality of the model. To evaluate model performance, we apply the model described above to the full, raw dataset and quantify the statistics of the observed versus predicted ΔP or P_min.

We first present the final model and its performance. We then demonstrate the utility of each term in the model, including a comparison with a standard “wind–pressure” model in which ${\overline{V}}_{\max }$ is the only predictor. We then apply the model to a few specific out-of-sample applications that are of practical interest. Finally, we show how to use the model in an operational setting using only routinely estimated data and examine model performance for a few case studies of impactful storms in the recent historical record.

4. Results

a. Model results

Our final model is

$\mathrm{\Delta }{P}_{\text{hPa}}=-6.60-0.0127({\overline{V}}_{\max }^2)-5.506\left(\frac{1}{2}f{\overline{R}}_{34\text{kt}}\right)+109.013\left(\frac{\frac{1}{2}f{\overline{R}}_{34\text{kt}}}{{\overline{V}}_{\max }}\right),$(5)

with ΔP_hPa in units of hectopascals, ${\overline{V}}_{\max }$ in units of meters per second, ${\overline{R}}_{34\text{kt}}$ in units of meters, and f in units of per second. As described in section 2, the coefficient values are estimated by fitting the model to the dataset binned in fixed increments of ${\overline{V}}_{\max },{\overline{R}}_{\text{34kt}}$, and f to minimize the effect of sample size variability. The bootstrapped 95% confidence interval range on each coefficient is (−7.51, −5.02) for β₀, (−0.0134, −0.0123) for ${\beta }_{{\text{Vmax}}^2}$, (−5.961, −5.122) for β_fR, and (96.439, 127.265) for β_fRdV.

Model performance is shown in Fig. 1b, which displays predicted [Eq. (5)] versus observed ΔP for the raw dataset shown in Fig. 1a. Equation (5) explains 94.2% of the variance in ΔP_hPa, with an RMS error of 5.24 hPa (Table 1). The model is nearly unbiased across the full range of ΔP_hPa, as evident by the solid red line (binned median) in Fig. 1b closely following the black one-to-one line. This unbiased behavior extends to the most extreme data points with the largest pressure deficits (lower-left region of the figure).

Table 1.

Model performance for our final MLR model (top line in bold) and alternative versions to test the effect of modifications to the model formulation. See the text for details. Model performance plots analogous to Fig. 1 for each entry are provided in Fig. S01.

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The sign of the dependence on each parameter matches the theory. First and foremost, the model predicts larger pressure deficit (ΔP_hPa) at higher intensity (${\overline{V}}_{\max }^2$; positive dependence) and at larger size or higher latitude [$(1/2)f{\overline{R}}_{34\text{kt}}$; positive dependence], as has been shown in past work (KZ07; Chavas et al. 2017). The third term is more complex and is new. Given the positive coefficient, it yields a more intense storm (more negative pressure deficit) at higher ${\overline{V}}_{\max }$ or at smaller size or higher latitude (these both would make the term less positive). Hence, this term slightly enhances the dependence on ${\overline{V}}_{\max }$ (first term) but slightly reduces the dependence on $(1/2)f{\overline{R}}_{34\text{kt}}$ (second term). We show below that this new predictor has the smallest effect of the three predictors but still adds value to the model’s predictive power.

c. Applications to special subsets

1) High-latitude storms

We next apply our model to the data for high-latitude storms spanning 30°–50°N in our database (Fig. 2). At these higher latitudes, jet stream interactions and the onset of extratropical transition are much more likely, storms tend to expand, and North Atlantic storms often have significant interactions with land to the west. Hence, data in this region are associated with much larger uncertainty in both input parameter estimates ${\overline{V}}_{\max }$ and ${\overline{R}}_{34\text{kt}}$ and structural relationships among parameters. Nonetheless, the model performs reasonably well for this generally more complex subset of cases, explaining 87.8% of the variance with an RMS error of 6.0 hPa. The model provides a nearly unbiased estimate of ΔP for values down to −60 hPa. For the deepest storms, though, there is evidence of a systematic overestimation of ΔP. Overall, while the performance is clearly worse than when applied to lower latitude storms as expected, the model appears to extrapolate well to higher latitudes. For further context, the high-latitude case of Hurricane Sandy is explored in the case studies section of this paper.

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As in Fig. 1, but for ΔP predicted by our final model [Eq. (5)] for data between 30° and 50°N.

Citation: Weather and Forecasting 40, 2; 10.1175/WAF-D-24-0031.1

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2) Land proximity storms

Finally, we apply our model specifically to tropical cyclones that are relatively close to land and hence potentially of greater risk for coastal populations. Land introduces significant asymmetry in the surface wind field that would be expected to increase uncertainty, particularly in the estimation of ${\overline{R}}_{34\text{kt}}$. Results for our model application to all data within 200 km of a coastline up to 50°N are shown in Fig. 3. Model performance is again quite strong, explaining 93.3% of the variance with an RMS error of 6.10 hPa and is nearly unbiased over the full range of pressure deficits. The error spread increases for stronger storms with pressure deficits <−60 hPa relative to weaker storms in this subset as well as comparable storms in our full dataset. Overall, though, the model also applies well for storms that are close to land.

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As in Fig. 1, but for ΔP predicted by our final model [Eq. (5)] for data close to land, defined as within 200 km of a coastline.

Citation: Weather and Forecasting 40, 2; 10.1175/WAF-D-24-0031.1

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d. Practical application: extended best track and historical case studies

We next demonstrate how the model can be put into direct practical use to predict P_min using only operationally available data. We use data exclusively from the EBTRK database (2004–22), which provides all parameters that are estimated in near–real time and are later refined in postseason best tracking. Translation speed is again defined from the change in storm center latitude and longitude during the preceding 12 h. We apply the model to the North Atlantic only to give a more apples-to-apples comparison to our observation-based dataset that is weighted heavily toward the North Atlantic.

The lone parameter from our original analysis that was not already routinely estimated is the environmental pressure P_env, which is needed to translate the model’s prediction for ΔP back into P_min. In our prior analyses, we had estimated P_env from the pressure field in global model reanalysis, which is more precise but not operationally available. Here, we utilize the pressure of the outermost closed isobar (P_oci) and apply a simple constant offset

$P_{\text{env}}=P_{\text{oci}}+2\hspace{0.17em}\text{hPa}.$(6)

The value of 2 hPa was estimated directly from our model by finding the value that eliminates the mean bias in our prediction (an increase/decrease in P_env simply acts to increase/decrease P_min by the same amount). As shown below, this offset results in a near-zero conditional bias across all values of P_min, which indicates that using a simple constant for an offset is reasonable. Notably, this estimate of P_env agrees with recommendations in Courtney and Knaff (2009).

We predict P_min by calculating ΔP using Eq. (5) and P_env using Eq. (6). The results are shown in Fig. 4. The prediction compares quite well with the EBTRK data, explaining 94.7% of the variance with an RMS error of 5.18 hPa. The performance is very similar to that found above using the observation-based database. This is to be expected, as EBTRK should mostly be very similar to our database, with the exception of EBTRK being at a 6-hourly temporal resolution and for occasional times when aircraft reconnaissance was not available, which should be relatively infrequent by design given our focus on the western Atlantic.

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As in Fig. 1, but for the “operational” model prediction, with ΔP predicted by our final model [Eq. (5)] using only the EBTRK database for the period 2004–22 in the North Atlantic for all data and P_env estimated from P_oci using Eq. (6).

Citation: Weather and Forecasting 40, 2; 10.1175/WAF-D-24-0031.1

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These results indicate that one can make a good prediction for P_min if given high-quality operational estimates of ${\overline{V}}_{\max }$, ${\overline{R}}_{34\text{kt}}$, storm-center latitude, and pressure of the outermost closed isobar. This may be of direct value when remote sensing–based wind speed measurements are available but measurements of P_min are not.

Historical case studies

Last, we illustrate our model applied to case studies of five impactful historical hurricanes: Patricia (2015), Ike (2008), Rita (2005), Michael (2018), and Sandy (2012) in Fig. 5. The cases are presented roughly in order from least complex to most complex in terms of life cycle evolution. We again compare our model by calculating ΔP using Eq. (5) and P_env using Eq. (6) using extended best track data. Overall, our model does reasonably well to predict P_min across all five cases, but it is insightful to discuss both successes and notable biases across the cases.

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Model prediction for five case studies of recent impactful storms. Patricia (2015, EP): (a) map of track and P_min (color); (b) time series of best track P_min vs model prediction from best track operational inputs only; (c) maximum wind speed (${\overline{V}}_{\max }$) and mean radius of 34-kt wind (${\overline{R}}_{34\text{kt}}$). Identical analyses for (d)–(f) Ike (2008, AL); (g)–(i) Rita (2005, AL); (j)–(l) Michael (2018, AL); and (m)–(o) Sandy (2012, AL). Note the change in scale for ${\overline{R}}_{34\text{kt}}$ for Sandy in (o). The vertical gray line in each time series denotes the time of CONUS landfall. The gray band represents an error of ±5.18 hPa, which is the model RMSE error of Fig. 4. Date labels on the map correspond to 0000 UTC.

Citation: Weather and Forecasting 40, 2; 10.1175/WAF-D-24-0031.1

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Patricia (2015; Figs. 5a–c) was a category 5 storm in the eastern North Pacific that made landfall in Jalisco in western Mexico as a category 4 hurricane (Fig. 5a). Patricia was the most intense hurricane on record based on ${\overline{V}}_{\max }$ and exhibited the fastest rate of 24-h intensification on record (Kimberlain et al. 2016). Hence, it represents an excellent test case for extreme maximum wind speeds for our model. Our model does a remarkably good job of predicting the minimum pressure throughout its entire life cycle (Fig. 5b). The model exhibits a near-zero error during its initial period of intensification through 1200 UTC 22 October as well as at its peak intensity (lowest pressure) at 1200 UTC 23 October, with a modest high bias of approximately +5 hPa during the intervening 18 h of very rapid intensification. In this case, the evolution of P_min is driven almost entirely by ${\overline{V}}_{\max }$, as size (${\overline{R}}_{34\text{kt}}$) increases only very gradually with time (Fig. 5c). Additionally, Patricia remained at a relatively constant latitude, moving poleward by only 5° prior to landfall.

Ike (2008; Figs. 5d–f) was a category 4 storm in the North Atlantic that made multiple landfalls along the coasts of the Turks and Caicos Islands, Cuba, and finally Texas (Fig. 5d). Ike grew substantially in size throughout its life cycle while its intensity fluctuated (Fig. 5f) and hence is a good test case of a storm that exhibited significant variations in both intensity and size. Our model does an excellent job of predicting the evolution of P_min (Fig. 5e). The model had a high bias (too weak) of approximately +10 hPa from 1800 UTC 8 September to 0600 UTC 11 September, a period during which Ike was passing along the long axis of Cuba. Note that many of those data occurred when the storm center was just offshore but close enough that the inner core of the storm almost certainly was partially onshore resulting in strong interaction with land (Berg 2009); the complexity of this interaction likely explains the discrepancy during that period. Thereafter, an eyewall replacement cycle occurred on 10 September that corresponded with a period of significant expansion through 1200 UTC 11 September while the maximum wind speed remained steady. At 0000 UTC 11 September, the minimum pressure dropped and then increased very slowly to 950 hPa through 1200 UTC, whereas our model predicted a more gradual decrease in pressure during this period. Finally, through landfall at 0600 UTC 13 September, the observed minimum pressure remained relatively constant, hovering within 5 hPa of its final landfall pressure along Galveston Island, Texas, of 950 hPa. Our model, on the other hand, predicted a continued decrease in minimum pressure due to the slight intensification during 0000–0600 UTC 12 September combined with its gradual poleward movement. Given the storm’s very large size as it approached land, there is likely greater uncertainty in the estimate of ${\overline{R}}_{34\text{kt}}$ in the model, which may explain the discrepancy during this period.

Rita (2005; Figs. 5g–i) was a category 5 storm in the North Atlantic that followed a very similar track as Ike through the northern Caribbean and Gulf of Mexico, except shifted slightly northward such that it passed through the Straits of Florida to the north of Cuba rather than directly over Cuba (Fig. 5g). Rita also expanded steadily after interacting with Cuba. In contrast to Ike, during this expansion period, Rita intensified rapidly, from 0000 UTC 21 September through 0000 UTC 22 September (Fig. 5i). The final combination of extreme intensity and large size yielded the lowest Atlantic P_min on record for the Gulf of Mexico (895 hPa). Our model performed very well over most of Rita’s life cycle (Fig. 5h), including a near-zero bias through the period of intensification and expansion and at peak intensity from 0000 to 0600 UTC 22 September. Thereafter, our model briefly exhibited a moderate high bias from 1800 UTC 22 September through 0000 UTC 23 September and then performed well with a smaller bias of 5–10 hPa leading up to landfall. The landfall pressure of 937 hPa was the lowest on record in the Atlantic basin for an intensity of 100 kt (Knabb et al. 2006), owing to its large size. Note that Rita’s landfall intensity was slightly higher than Ike (100 vs 95 kt), but Rita was also slightly smaller than Ike. Rita’s landfall pressure was lower than Ike’s landfall pressure, whereas our model predicted the opposite. Hence, the model had a low bias for Ike and a high bias for Rita at landfall. Similar to Ike, Rita’s large size as it approached land likely created larger uncertainty in the value of ${\overline{R}}_{34\text{kt}}$. Overall, Rita and Ike demonstrate how, for larger storms, size contributes significantly to reducing the minimum pressure relative to what would be expected from the maximum wind speed alone. Rita and Ike made landfall at very similar latitudes (29.7°N for Rita and 29.3°N for Ike), so Coriolis played effectively no role in the differences between these two storms at landfall. As noted at the start of the introduction, these large hurricanes with low P_min relative to best track V_max can cause confusion when considering how to communicate the severity of a storm, which is especially problematic when approaching land.

Michael (2018; Figs. 5j–l) was a category 5 storm in the North Atlantic that made landfall in the Florida Panhandle at its peak intensity of 140 kt. The system moved north throughout its life cycle prior to landfall from its genesis location in the far western Caribbean (Fig. 5j). Michael was similar to Patricia in that it reached extreme intensities while its size remained relatively constant, but it did so by intensifying more gradually and uniformly over a 4-day period leading up to landfall (Fig. 5l). Our model did very well in predicting the continuous decrease in P_min with time, particularly over its first few days prior to 0000 UTC 9 October during which the model had a near-zero error (Fig. 5k). Our model then exhibited a moderate low bias (too intense) from −10 to 15 hPa during the final 2 days leading up to landfall, with the error returning to near zero just prior to landfall. At 1800 UTC 8 October, Michael passed very close to the western tip of Cuba and thereafter experienced a decay in its eyewall structure (Beven et al. 2019). This interaction with land may have induced uncertainties in wind radii estimates and changes in Michael’s structure that were not captured by our model.

Finally, Sandy (2012; Figs. 5m–o) was a highly destructive storm in the North Atlantic that became the largest storm ever recorded in the basin as measured by ${\overline{R}}_{34\text{kt}}$. Sandy made multiple landfalls in Jamaica, Cuba, and finally New Jersey as a posttropical cyclone 2.5 h after completing extratropical transition (Fig. 5m). Sandy represents perhaps the most complex of test cases, with dramatic changes in intensity, size, and latitude throughout its life cycle (Fig. 5o), multiple sustained interactions with land, and substantial extratropical interactions. Our model does well in predicting P_min during its early stages in the southern Caribbean prior to crossing Cuba at 0600 UTC 25 October (Fig. 5n). From 1200 UTC 25 October through 1800 UTC 26 October, our model exhibited a moderate low bias (too intense) from −10 to −20 hPa, particularly as the storm center crossed Cuba and then subsequently moved along the axis of the Turks and Caicos and the Bahamas. This period of time was associated with a sharp leveling off and then a decrease in ${\overline{V}}_{\max }$ concurrent with a very rapid expansion in storm size. This expansion was driven by the strong interaction with an upper-level trough and later a warm frontal boundary, which resulted in the development of an unusual structure with an exceptionally large R_max, and the strongest winds found on the western semicircle (Blake et al. 2013). The model performed better from 0000 to 1200 UTC 27 October before the bias increased again to −15 hPa as Sandy moved back out over the open water while rapidly undergoing extratropical transition. Sandy was formally designated as an extratropical system on 2100 UTC 29 October as the storm approached the New Jersey coastline, and indeed our model exhibited a very large low bias (far too intense) during 29 October, predicting a minimum pressure below 900 hPa when the actual value was 940 hPa prior to landfall. Hence, Sandy demonstrates how our model may not be well suited for storms that have undergone substantial extratropical transition, for which the assumptions regarding the radial structure of the winds may break down. However, it is also worth noting that the estimation of the input parameter values (${\overline{V}}_{\max }$ and ${\overline{R}}_{34\text{kt}}$) is likely highly uncertain during this latter period given that Sandy was a large and highly asymmetric storm whose wind field significantly overlapped with the adjacent land.

Note that the biases in the above cases, particularly Ike and Michael, tend to be persistent for periods of 1–2 days when they occur. Such biases may be driven by a variety of factors. Estimating R_34kt for larger storms may be more uncertain given that aircraft observations extend only 200 km from the center, so estimates depend more strongly on scatterometry data and can only be updated when new data become available. Land interaction may induce low biases in size as noted above. Additionally, there is uncertainty in estimating the environmental pressure P_env from P_oci, as the closure of isobars depends on the synoptic-scale atmospheric flow on the periphery of the storm that tends to vary more slowly in time. Evaluating the relative role of uncertainties lies beyond the scope of this work. Future work might seek to develop more precise estimates of the environmental pressure, such as our method used above based on global analyses, that can be used both in an operational setting and in the best track archive.

5. Conclusions

A simple model to predict P_min in a tropical cyclone from routinely estimated data would be useful for operations and practical applications. This work has developed an empirical linear model for the pressure deficit that takes as input the maximum wind speed, the mean radius of 34-kt wind, and storm central latitude, as well as the environmental pressure. The specific model predictors, given by ${\overline{V}}_{\max }^2$, $(1/2)f{R}_{34\text{kt}}$, and the ratio of the latter to the former, are derived from gradient wind balance applied to a modified Rankine vortex. Rather than using the full analytic solution itself, which will bake in the approximating assumptions of the theory, we instead use a simple linear regression model on those three parameters and estimate the coefficients from historical data: aircraft-estimated central pressure, historical best track data for storm wind field parameters, and global analyses for environmental pressure. This choice enables us to exploit the unique benefits of both physical theory (predictors) and data (dependence on predictors). The model shows excellent skill, capturing 94.4% of the variance in the historical dataset and outperforming various other versions of the model. It is superior to a standard wind–pressure relationship (89.4% variance explained), which indicates that the inclusion of size and latitude information captures approximately half of the residual variance that is unexplained by this simpler model. Though the model was fit to data over the open ocean in the tropics in order to minimize the effects of observational uncertainties, it also appears to perform well at high latitudes and near coastlines. Finally, it performs very well when applied solely using data from the extended best track database (94.9% variance explained), which indicates it is viable in an operational setting using only routinely estimated data.

The final model for the pressure deficit is given by Eq. (5). The pressure deficit prediction is then translated to a prediction for P_min via Eq. (3) by adding an estimate of the environmental pressure, which may be estimated operationally using the pressure of the outermost closed isobar via Eq. (6).

Overall, this simple and fast model can predict P_min from maximum wind speed, storm size, storm central latitude, and environmental pressure in practical applications. In operations, the model could give a preliminary estimate of P_min if other input predictors are available. Perhaps more importantly, P_min can potentially be forecast up to 5 days from the operational forecast time in the North Atlantic and eastern North Pacific given that the National Hurricane Center forecasts V_max and storm central position operationally out to 120 h and in 2024 will begin doing so for 34-kt wind radii as well. Currently, the National Hurricane Center does not operationally forecast P_min, but this simple tool would allow for a simple estimate of P_min, which would not entail additional work for the forecaster on duty. This information combined with a radius of maximum wind estimates using similar methods (Chavas and Knaff 2022; Avenas et al. 2023) could particularly be useful for storm surge model initial conditions.

In risk analysis, the model can help provide mutually consistent estimates of these three parameters that extend to other/future climate states where no observational data exist. In weather and climate modeling, the model could provide a new tool to evaluate the representation of TC intensity, size, and P_min jointly, as well as to understand how future changes in P_min reflect changes in intensity versus size. More broadly, given the strong correlation between P_min and historical economic damage, the model offers a full quantitative bridge from the wind field to hazards to damage that may be of use in the study of damage risk in both real-time forecasting and under climate change. Moreover, this model can help explain why larger storms can make it difficult to communicate the potential severity of a storm when P_min is substantially lower than expected for a given maximum wind speed (and the Saffir–Simpson hurricane wind scale category) based on a standard wind–pressure relationship.

We note that improved parameter estimation, particularly of R_34kt and of the environmental pressure, may both help improve model performance for individual cases. As this method relies on operational estimates of V_max, R_34kt, and P_env, any improvements in those estimates will help in predicting P_min. Our estimates of P_env can certainly be improved by more direct methods using global model analyses. Uncertainties associated with V_max and R_34kt are on the order of 5 m s⁻¹ and 26 km, respectively (Torn and Snyder 2012; Sampson et al. 2017; Combot et al. 2020), which will likely persist as a few observational platforms exist that accurately estimate R_34kt and V_max (Knaff et al. 2021). Additionally, recent work has shown that satellite-based Dvorak current intensity estimates could be used in lieu of maximum wind speed to predict the minimum pressure (Aizawa et al. 2024), which is a viable alternative in the absence of direct observations of the maximum wind speed.

Finally, we note that this model provides a physical explanation for how the TC minimum pressure is expected to change with global warming. On average, we expect tropical cyclones in a warmer world to become more intense (higher maximum wind speed; Knutson et al. 2020; Emanuel 1987, 2021) at a relatively constant outer size (Knutson et al. 2015; Schenkel et al. 2023; Stansfield and Reed 2021; Lu and Chavas 2022) and a relatively constant latitude with the exception of a slow expansion of the poleward edge of TC activity (Kossin et al. 2014). Environmental pressures would not be expected to change significantly. Taken together, our model would then predict lower central pressures, driven by the increase in maximum wind speed, consistent with modeling studies (Knutson et al. 1998; Kanada et al. 2013; Tran et al. 2022). Additionally, based on the simple modified Rankine vortex that underlies our model, the radial structure of the wind field would be expected to remain constant with the exception of a slight contraction of the radius of maximum wind at higher intensities, as is found in observations and modeling studies (Chavas and Lin 2016; Kanada et al. 2013; Tran et al. 2022; Chen et al. 2022). Hence, the physical basis of the model provides a pathway to link changes in different aspects of tropical cyclone structure and to more confidently extrapolate to other climate states for which we do not have direct observations.

Data availability statement.

Data and code for this work are publicly available via the Purdue University Research Repository (PURR) at https://doi.org/doi:10.4231/GSVZ-D752 (Chavas 2025).