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Article

The Increased Likelihood in the 21st Century for a Tropical Cyclone to Rapidly Intensify When Crossing a Warm Ocean Feature—A Simple Model’s Prediction

Forrestal Campus, Princeton University, Princeton, NJ 08544, USA
Atmosphere 2021, 12(10), 1285; https://doi.org/10.3390/atmos12101285
Submission received: 19 August 2021 / Revised: 26 September 2021 / Accepted: 30 September 2021 / Published: 2 October 2021
(This article belongs to the Special Issue Tropical Ocean-Atmosphere Interaction and Climate Change)

Abstract

:
A warm ocean feature (WOF) is a blob of the ocean’s surface where the sea-surface temperature (SST) is anomalously warmer than its adjacent ambient SST. Examples are warm coastal seas in summer, western boundary currents, and warm eddies. Several studies have suggested that a WOF may cause a crossing tropical cyclone (TC) to undergo rapid intensification (RI). However, testing the “WOF-induced RI” hypothesis is difficult due to many other contributing factors that can cause RI. The author develops a simple analytical model with ocean feedback to estimate TC rapid intensity change across a WOF. It shows that WOF-induced RI is unlikely in the present climate when the ambient SST is ≲29.5 °C and the WOF anomaly is ≲+1 °C. This conclusion agrees well with the result of a recent numerical ensemble experiment. However, the simple model also indicates that RI is very sensitive to the WOF anomaly, much more so than the ambient SST. Thus, as coastal seas and western boundary currents are warming more rapidly than the adjacent open oceans, the model suggests a potentially increased likelihood in the 21st century of WOF-induced RIs across coastal seas and western boundary currents. Particularly vulnerable are China’s and Japan’s coasts, where WOF-induced RI events may become more common.

1. Introduction

A tropical cyclone (TC) is said to undergo rapid intensification (RI) when its maximum 10-m wind increases by more than 15.4 m/s in 1 day [1]. RI may be due to TC internal dynamics, environmental factors, and a combination [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Often, storms that have undergone RI develop into major storms (Category 3 and above) [17,18]. They are therefore of interest to researchers and forecasters.
By supplying heat and moisture to the atmosphere, ocean, and coupled ocean feedback play a significant role in TC intensity change [19,20,21]. Some studies suggested that RI may be triggered when a TC crosses a warm ocean feature (WOF) [12,22,23,24,25,26,27,28,29]. The WOF may be a warm eddy, a western boundary current, or a summertime coastal shelf sea. It has an anomalously warmer sea-surface temperature (SST) than the ambient sea. We define WOF-induced RI when the RI triggered as a TC crosses a WOF. In practice, however, isolating and identifying WOF-induced RI is challenging due to the simultaneous existence of other factors cited above. Oey and Huang [30] designed numerical ensemble experiments to eliminate other potential RI-causing environmental factors and isolate the WOF-induced intensity change. They conducted twin experiments and showed statistically indistinguishable RI occurrences between the experiments with and without the WOF. They then used a strip-down version of the analytical model presented here to support their numerical findings.
In this manuscript, we extend and provide complete details of the analytical model. The analytical model includes ocean feedback and estimates the WOF-induced intensity change and RI. The model shows that ocean feedback decreases intensity change, necessitating a warmer WOF anomaly for a TC to develop RI. We provide observations and conclude that WOF-induced RI is unlikely under the present background and WOF SSTs in the tropics and subtropics. However, WOFs can potentially play an increasingly significant role in triggering RIs as these SSTs, particularly the WOF SST, continue to rise in a warming climate.

2. The Model

2.1. The Problem

A tropical cyclone (TC) translates westward along the negative x-axis at a constant speed Uh. Across x = 0, the SST (T) changes by δTW due to a WOF:
T = T 0 x 0 , = T 0 + δ T w x < 0 ,
where T0 is the ambient or background sea-surface temperature before the WOF (Figure 1). (For convenience, the variables are defined both in the text and in the Appendix A). The TC crosses onto the WOF where δTW > 0. We focus on the redpoint shortly after the crossing under the direct path of the storm’s core or eyewall, where SST changes, and ocean feedback can most influence intensity [19,31,32]. The goal is to calculate the change in the maximum wind (δVm) and estimate the (δTW, T0)-combination where a WOF-induced RI is possible. The analysis is independent of where the redpoint is, provided it is in the WOF and the direct path of the storm’s core.

2.2. Intensity Change Due to the WOF: The WOF-Induced RI

The TC experiences a warmer SST as it crosses x = 0. The warmer SST increases the wind, which we can estimate using the maximum potential intensity (MPI) theory [19]. We use the empirical form given by DeMaria and Kaplan [33]:
Vm = A + B eC(T-30).
Here, Vm (m/s) is the maximum wind, the SST T is in °C, and A, B, and C are empirical coefficients. DeMaria and Kaplan [33] limit the applicability of Equation (2) to T ≤ 30 °C. However, later extensions using higher-resolution data suggest no such limit [6,34,35]. The change in the maximum wind, δVm, due to a change in SST, δT, i.e., the WOF-induced intensity change, is:
δ V m = s   δ T + s   C   δ T 2 / 2 + 0 ( δ T 3 ) ;   s ( T ) = ( V m / T ) | 0 ,  
where (..)|0 means evaluation at the ambient state T0, and s is the slope of Vm in the T-space. Partial derivatives are a reminder that (A, B, C) may not depend on T alone. We assume the increased intensity occurs within one day of the storm crossing x = 0 and define WOF-induced RI when δVm ≥ 15.4 m/s. The vast majority (85%) of RI events occur in storms that translate faster than ~3 m/s [36]. The assumption is reasonable since the time for the TC core to cross a WOF of typical size 100–200 km [30] is one day or less. By definition, V0 ≲ Vm, where V0 is the maximum wind of the TC approaching the WOF. We will see that δV0 ≲ δVm (see Section 2.3.6 below). Therefore, the above RI criterion “δVm ≥ 15.4 m/s” is more easily satisfied than the conventional RI criterion “δV0 ≥ 15.4 m/s”. In other words, if the model predicts RI to be unlikely in the present climate, as will be shown to be the case, using the conventional criterion leads to the same conclusion.

2.3. Ocean Feedback

The increased δVm in the WOF (the red point) increases ocean mixing and upwelling [37,38], hence SST cooling, δT0 < 0, which reduces δVm. The reduced δVm modifies the amount of cooling, which further changes the δVm, in a coupled manner.

2.3.1. Assumptions

We assume an ocean with no horizontal variation. For example, the SST front at x = 0 is fixed and has no dynamics. Vertical mixing then predominantly controls the SST cooling under super-critically translating storms when Uh/c > 1, where c is the ocean’s mode-1 baroclinic phase speed [39]. In the tropical and subtropical oceans, c ≈ 2.5 ~ 3 m/s [40,41]. Thus, we require that Uh exceeds ~3 m/s. Then we may neglect the contribution to SST cooling from horizontal processes, such as upwelling and mixing due to breaking near-inertial internal waves [42]. For Uh ≥ 3 m/s and a typical TC core’s diameter of 100–200 km (e.g., ref. [43]), a point in the storm’s path remains influenced by the maximum wind stress curl for at most 8–18 hours. This time is less than the inertial time > 1 day (for latitudes < 28°) required for wind curl-driven upwelling to establish and contribute significantly to SST cooling [39,44]. It is also less than the time required for near-inertial internal waves to develop and contribute to mixing [45,46]. As mentioned before, global TC observations also show that most RI events occur in storms with Uh > 3 m/s [6,36], providing a further incentive to focus on these storms. The one-dimensional model underestimates cooling for slow storms with Uh ≲ 3 m/s. Additional SST cooling due to horizontal processes mentioned above can be more significant for slow storms. However, as will become apparent, any additional cooling can only weaken the TC intensity and not change our conclusions. The one-dimensional model then provides an upper-bound intensity change.

2.3.2. Two-Layer Ocean

We divide the ocean into two active layers of thicknesses, h1 and h2. Layer 1 consists of warm water of a uniform temperature T1 and density ρ1 from sea-surface z = 0 to z = −h1. Layer 2 consists of cooler water of uniform temperature T2 (< T1) and density ρ2 (> ρ1) from z = −h1 to z = −(h1 + h2) (a third layer below extending to the ocean bottom is assumed to be inactive). Suppose the wind adiabatically mixes the two layers into a single layer, the uniform density and temperature after mixing (subscript ’mix’) are weighted averages of layers 1 and 2:
ρmix = (ρ2 h2 + ρ1 h1)/(h1 + h2),     Tmix = (T2 h2 + T1 h1)/(h1 + h2),
expressing mass and heat conservations. The SST after mixing is:
Tmix = T1 + δT,    δT = −[h2/(h1 + h2)] ΔT,
where ΔT = T1 − T2 (> 0) is the differenced temperature of the two original layers. The corresponding differenced density Δρ = ρ1 − ρ2 (< 0):
Δρ/ρ0 = −α ΔT,
where ρ0 is the reference seawater density ≈ 1025 kg/m3, and α = (∂ρ/∂T)/ρ0 is the thermal expansion coefficient of seawater, ≈ 3×10−4 K−1 at the sea surface with SST ≈ 28 °C and salinity ≈35 psu.

2.3.3. Potential Energy

Wind work raises the potential energy (PE) of the fluid by mixing it. Equating the raised PE = PE|mix − PE|2layers to wind work yields a formula relating the wind to density (and temperature). Thus, since
PE 2 layers = h 1 0 ρ 1   g   zd z + h 1 h 2 h 1 ρ 2   g   zd z ,
and
PE mix = h 1 h 2 0 ρ mix g   zd z ,
we obtain
PE = −(g/2) ∆ρ h2 h1 = (g/2) α ρ0 ∆T h2 h1   (J/m2).

2.3.4. Wind Energy

The wind power on the ocean is ρaCdV3 in J/(m2∙s), the scalar product of the surface drag ρaCd|V|V and wind V, neglecting the ocean current. Here, ρa is the air density, Cd is the drag coefficient, and V = |V| the wind speed. Due to the TC’s size, the redpoint (Figure 1) experiences the wind and SST cooling hours or days before the storm arrives, depending on Uh. Oey et al. [37] observed this ahead-of-storm SST cooling in buoy measurements in the Caribbean Sea before the arrival of Hurricane Wilma (2005). Therefore the wind energy for mixing at the redpoint is:
WE = γ 0 P ρ a C d V 3 dt   ( J / m 2 ) .
Here, the mixing efficiency γ takes into account that only a fraction of the wind work goes into mixing, and P = L/Uh, where L ≈ storm’s radius. The integral is from t = 0 when the outer-most circle of weak TC wind influences the redpoint to t = P when the TC center arrives (one could formally transform the integral by setting x = −Uh t + L + xredpoint but thinking in “t” is more straightforward). We neglect the contribution from the generally even weaker, non-TC wind before the TC’s outer-most circle arrives. We also assume that after time t = P, SST cooling at the redpoint will not affect intensity. For t > P, the TC center has passed the redpoint. Thus, ignoring the short distance across the back half of the eye, ocean cooling in the TC’s wake has a minor further impact on intensity.

2.3.5. Wind-Induced SST Cooling

Set PE = WE, and use (5) to yield:
T mix =   T 1 { [ γ 0 P ρ a C d V 3 dt ] / [ ( g 2 ) α ρ 0   h 2 h 1 ] } [ h 2 h 2 + h 1 ] .
Piecewise continuous formulae of V are available [43] to evaluate the integral. To obtain simple formulae, we choose to model V as a simple rise and fall as the TC passes the point:
V = V0 sin[πt/(2P)],   V0 = maximum wind,
Thus, ignoring the rapid wind change with two maxima as the TC center passes. Because of integration, the exact form is not crucial. Using Equation (12) in Equation (11), we obtain:
T mix =   T 1 [ ( 4 3 π ) ( L U h ) ( ρ a ρ 0 ) ( γ C d V 0 3 ) ] / [ ( g 2 ) α   h   h 1 ] ,  
where h = h1 + h2. Equation (13) gives the cooled SST the arriving TC sees at a point ahead of the TC path, including the redpoint. The SST cooling (= Tmix − T1) is inversely related to Uh and h1. It shows that a slower storm sees a cooler SST than a faster one, and a thicker upper warm layer is less susceptible to cooling than a thinner one.

2.3.6. Coupling

Focusing on the redpoint, as the TC crosses into the WOF, we assume that its maximum wind V0 changes while its temporal functional form remains unchanged:
δV ≈ δV0 sin[πt/(2P)].
This is a good approximation since the redpoint is only a short distance into the WOF. We can then use Equation (11) to relate the change in SST due to a change in the wind. Taking δ of Equation (11) and evaluating the integral (or taking δ of Equation (13)):
δ T 0 = δ V 0 F T
F T = [ ( 8 π ) ( L U h ) ( ρ a ρ 0 ) ( C d V 0 2 ) ] / [ g α   h   h 1 ] .
The special notation δT0 (with subscript ‘o’) is used instead of δTmix, as a reminder that it is the ocean cooling caused by increased δV0 as the TC crosses into the WOF. At the redpoint, the total SST change is the sum of the warmer SST due to the WOF and cooling due to ocean mixing:
δTredpoint = δTW + δT0.
The V0 refers to the incoming TC that translates into the WOF. To close the model (i.e., to couple), one needs to relate δV0 to δVm, where δVm depends on SST from Equation (3). A reasonable assumption is that δV0/δVm is proportional to V0/Vm, and we set the proportionality to one for simplicity. The assumption is equivalent to letting V0 be proportional to Vm, such that their ratio is approximately invariant, as the data and analysis of [6,33,34,35] suggest. Thus:
δV0 = μ δVm, μ = V0/Vm ≤ 1.
The μ is ≲0.5 for V0 ≲ 50 m/s and tropical/subtropical SST ≳ 28 °C (Figure 2) (in Oey and Huang [30], we set δV0 = δVm, i.e., μ =1, which overestimates the cooling, although their conclusions remain unchanged).
Setting δT = δTredpoint and using Equations (15)–(18) in Equation (3) yields a quadratic equation for δVm. Both roots are positive, but the smaller root is physically plausible:
δ V m = [ μ 2 μ 2 2 4 μ 1 μ 3 ] / [ 2 μ 1 ]
μ 1 = sC ( μ F T ) 2 / 2 ,   μ 2 = 1 + ( 1 + C δ T W ) s μ F T ,   μ 3 = s δ T W ( 1 + C δ T W / 2 ) .
Taylor’s expansion in small FT shows that the solution tends to Equation (3) without ocean cooling as FT ~ 0.
Although Equation (19) will be used in the plots, we can more easily see the effect of ocean feedback by dropping the O(δT2) term in Equation (3). The solution is:
δ V m =   s ( T 0 ) δ T W / [ 1 +   s ( T 0 ) μ F T ] ,
where s(T0) is a reminder that it depends on the ambient SST T0.

2.3.7. Values of Parameters

We use the following values of the model parameters:
  • A = 15.69 (2758) m/s, B = 98.03 (74.03) m/s, and C = 0.1806 (0.1903) °C−1 for western North Pacific (North Atlantic), from Zeng et al. [6] (Xu et al. [35]), see Equation (2);
  • L = 200 km, the TC’s radial scale (roughly to ~18 m/s) [40];
  • ρa0 = 10−3, the ratio of air to seawater densities;
  • γ = 0.02, see below;
  • Cd = 2 × 10−3, the drag coefficient at high wind speeds [47];
  • g = 10 m/s2, the Earth’s gravity;
  • α = 3 × 10−4 K−1, seawater’s thermal expansion coefficient [39];
  • h1 and h2 are chosen to be from the surface to the 26 °C isotherm z = −z26, and from z = −z26 to the 20 °C isotherm z = −z20. The h1 ≈ h2 ≈ 100 m in the RI region (10~25 °N) in the tropical and subtropical western North Pacific (Figure 3).
Choosing γ:
Given Z26 and Z20 as a slowly-varying background ocean state, one can calculate the SST cooling δT(Z26, Z20, Uh, V0; γ) (Equation (13)) along a storm’s track with γ serving as a parameter. Here we use the EN4 data as the ocean state given as monthly analysis from 1900 to the present [48]. We calculate Uh and V0 at a track location using the average of the present and previous day’s values. We then choose γ to yield SST cooling that reasonably matches the observed and full ocean model’s cooling in two TCs: Typhoon Nuri (2008) and Typhoon Soudelor (2015). We previously conducted detailed analyses and SST cooling simulations for these typhoons using the Princeton ocean model (POM) [16,49,50]. We find that γ = 0.02 gives reasonably good agreements between δT and SST cooling from GHRSST observation and POM (Figure 4). The γ = 0.02 is within the range cited in the literature for strong boundary stirring at high buoyancy Reynolds number [51,52,53,54].

3. Results

We describe the modeled WOF-induced intensity change δVm, focusing first on the western North Pacific’s typhoons since these have the largest intensity changes. Then, however, we will comment on the North Atlantic’s hurricanes.

3.1. δVm with No Ocean Feedback

Figure 5 (color shading) shows δVm without ocean feedback as a function of δTW and T0. Mathematically, it is equivalent to the maximum possible increased intensity as the storm enters the WOF at an infinite translation speed Uh. There is then little time for ocean mixing by the wind to cool the sea surface. It is also the δVm when the TC crosses onto a shallow warm sea where the entire water column is well-mixed. The white line shows the corresponding δVm = 15.4 m/s separating the (δTW, T0) on the upper right where a WOF-induced RI is possible from the lower-left where RI is unlikely. Figure 5 uses V0 = 30 m/s as a representative example. Most observed RIs develop when the TC is in the tropical storm (TS) or Categories 1–2 stages [15,17,18,30,36]. However, the δVm = 15.4 m/s line in this plot and Figure 6, hence the inferences derived from it are independent of V0 since the line is for the asymptotic limit of zero ocean cooling. The present climatological SST (T0) in the RI region is 28–29.5 °C (Figure 3). The composite (1993–2015) mean eddy’s SST anomaly is +0.3 °C [55], but δTW in individual WOFs can reach +1 °C [15,16,24,27]. For reference, white dashed lines indicate the present climate’s (δTW, T0) = (1, 29) °C. As the majority (~85%) of RIs occur for Uh ≲ 7 m/s [6,36], the result suggests that RIs triggered by the WOF alone are unlikely to be frequent occurrences in the present climate. In other words, factors other than WOF alone more likely trigger the RIs observed in the present climate. See Section 3.3.

3.2. δVm with Ocean Feedback

In Equation (20), the “s × δTW” is the MPI estimate of the WOF-induced intensification. The “s × μFT” (> 0) is the coupling term that includes the contribution (FT) from ocean cooling caused by the mixing of surface and subsurface water by the translating storm. The formula shows that ocean cooling always reduces δVm. Since FT is inversely related to Uh and h1 (see Equation (16)), the ocean cools more for slower storms, a thinner upper warm layer, or both, which then reduces δVm. For very deep h1, FT ~ 0, and ocean feedback is negligible. Ocean feedback is also weak for very fast storms since there is little time for the wind to mix the upper ocean, and the feedback to the storm is negligible. In either case, the intensification is due to the WOF alone and becomes the upper-bound MPI estimate: δVm = s × δTW.
The blue dashed lines in Figure 5 show the δVm = 15.4 m/s contours obtained from the solution with ocean feedback for different Uh. (The plot is for the solution 19, although the quadratic correction is small: 5–10% less cooling). Ocean cooling at finite Uh shifts the 15.4 m/s line rightward and upward, meaning ocean feedback makes it even harder for WOF-induced RI to develop under the present climate.

3.3. Observed RIs in the Present Climate

Figure 5 plots the (δTW, T0) points of nine TCs whose RIs may be related to WOFs (source references in the caption). We only include Tropical Cyclone Bansi for comparison since the empirical MPI used is not for the South Indian Ocean. The magenta line shows the 15.4 m/s using Xu et al.’s [35] empirical MPI coefficients for the North Atlantic. We use it to assess the four Atlantic hurricanes (E, H, Mw, and O). The magenta line shifts slightly rightward and upward relative to the western North Pacific line (white) because the Atlantic’s slope ∂Vm/∂T is less steep (roughly 0.8:1). The 9-TCs’ mean (δTW, T0) are (0.87, 28.8) °C (red asterisk), and the mean Uh is 5.2 m/s. The plot shows that none of the TCs’ rapid intensifications was WOF-induced. Typhoon Soudelor is the only storm that crosses the white 15.4 m/s-line. However, ocean cooling at Uh = 5.5 m/s would also render a WOF-induced RI unlikely in Soudelor. Instead, Oey and Lin [16] argued that weakened environmental vertical wind shear < 4 m/s contributes to the storm’s RI [5]. They also suggested that weak vertical wind shears may have contributed to the RIs in Hurricane Opal [57] and Typhoon Maemi [16]. These results show that for WOF-induced RIs to develop, the WOF and ambient SST would have to be warmer than the present-day T0 ≈ 28–29.5 °C and δTW ≲ 1 °C. Thus, as stated before, RIs triggered by the WOF alone are unlikely to be frequent occurrences in the present climate. Oey and Huang [30] arrived at this same conclusion in numerical experiments designed to isolate the WOF-induced intensity change. They found that although WOF increases intensity, the intensification is insufficient to trigger more RIs. Consequently, the number of RIs is not statistically significantly different between ensemble simulations with and without the WOF included in the model.

4. Discussion

Three of the four listed typhoons in Figure 5 are close to the white 15.4 m/s-line. Thus, they are close to a “tipping point or line”, meaning that slight increases in T0 or δTW or both may potentially foster more RIs. We use the simple model to project how WOF-induced RIs may evolve as the Earth’s climate warms. The SST trend is +0.1 °C per decade in the western North Pacific, but two times higher in the Philippines Sea (latitudes ≲ 20 °N) [58,59,60]. Similar warming trends occur in the Atlantic. At these rates and assuming that SST continues to rise [61], T0 would reach 30–31 °C near the end of the 21st century.
SSTs in coastal seas and western boundary currents show higher rates of warming trends [60,62]. Along the western North Pacific rim and US southern and eastern shelves, coastal SST trends reach +0.4 °C per decade in summer [62], approximately two times higher than the adjacent open seas. The value is consistent with a recent estimate of |∇SST| trends of more than +0.2 °C/100 km/decade) across China’s and Japan’s coastal shelves, the northern Gulf of Mexico, the US south-mid-Atlantic, as well as across the Kuroshio and the Gulf Stream [60]. At these rates, the corresponding δTW|Coast and δTW|WBC would reach 1.2–1.8 °C or more near the end of the 21st century. The trend of δTW|Eddy for mesoscale eddies is harder to estimate. In the western North Pacific, Martínez-Moreno et al. [60] show an increasing |∇SST| trend of +0.02 °C/(100 km/decade) for eddies north of 20 °N, but a decreasing trend of −0.04 °C/(100 km/decade) south of 20 °N. The trends in tropical and subtropical North Atlantic are similarly weakly decreasing. However, these values for δTW|Eddy are weaker with larger uncertainty than the trends of δTW|Coast or δTW|WBC.
Figure 6 (color shading) shows δVm as a function of Uh and h1 for T0 = 29.5 °C and δTW = 1 °C near their upper limits in the western North Pacific in the present climate. The white line shows the corresponding δVm = 15.4 m/s separating the (Uh, h1) space on the upper right where a WOF-induced RI is possible from the lower-left where RI is unlikely. Ocean cooling is inversely related to h1 or Uh (Equations (15) and (16)). There is more (less) cooling as the upper layer gets thinner (thicker), or the storm translates slower (faster), or both. As a result, the atmospheric response is a weaker (stronger) δVm (Equation (3)). The white dashed box encloses the RI region’s Z26 range (60–120 m; Figure 3) and the Uh range (3–7 m/s; [36]), where the majority of RI events occur. Thus, as discussed before, one sees that WOF-induced RIs in the present climate T0 ≲ 29.5 °C and δTW = 1 °C are unlikely.
Blue dashed lines show the sensitivity of intensity change to ambient SST at a fixed δTW = 1 °C. These 15.4 m/s lines shift left and down as the T0 increases, sweeping across the white dashed box. For example, for a future T0 = 30 °C, WOF-induced RIs can occur over the small northeast corner of the box Uh > 5.5 m/s and Z26 > 95 m. When T0 = 31 (32) °C, the likelihood for WOF-induced RIs substantially increases as the region where δVm > 15.4 m/s now occupies 60% (95%) of the box.
Black lines show the sensitivity of intensity change to WOF’s anomaly at a fixed T0 = 29.5 °C. Note that the dependency of δVm on h1 or Uh is unchanged, and one can always find T0 and δTW pair for which the blue dashed and black lines coincide. However, from Equation (20), ( δ V m δ T W ) / ( δ V m T 0 )   1 / ( δ T W C ) + 0 ( s μ F T ) , where C ≈ 0.18 °C−1 (see Section 2.2). Thus, δVm is ~5 times more sensitive to δTW than T0 (the sensitivity difference is somewhat reduced by ocean feedback (the O(sμFT) term) especially when h1 or Uh or both are small). Thus a 1 °C change in T0 takes only ~0.2 °C change in δTW to effect the same intensity change. For example, Figure 6 shows that a 0.3 °C (0.5 °C) change of δTW from 1 to 1.3 °C (1.5 °C) increases the likelihood for WOF-induced RIs as the region where δVm > 15.4 m/s sweeps across more than 60% (95%) of the box. The effect is the same as a 1.5 °C (2.5 °C) change in T0 from 29.5 to 31 (32) °C.
One may question the suitability of using the empirical MPI relationship (Equation (2)) based on present climate’s data to make future inferences. In the absence of data, it is, of course, impossible to address this with absolute certainty. However, we can make some reasonable deductions that the empirical relation will remain valid, at least into the 21st century. First, the theoretical MPI critically depends on the saturation mixing ratio, which varies exponentially with SST according to the Clausius–Clapeyron relationship [63,64]. Thus, the exponential form of the empirical MPI relationship is likely to remain valid in the future. Second, any numerical change in the empirical MPI is likely to be ‘slow’. Evidence of the slow change is that the exponent coefficient C remains stable despite the different periods and regions in the four cited studies. In the North Atlantic, C = 0.1813, 0.1813, and 0.1903 for the data from 1962–1992, 1981–2003, and 1988–2014, respectively [33,34,35], while C = 0.1806 for the 1981–2003 data for the western North Pacific [6]. Zeng et al. [34] made a similar argument when noting that the C they obtained was identical to DeMaria and Kaplan’s [33] using an earlier dataset. Finally, in the simple model, the most critical parameter is the slope s on the T-space. Based on the three analysis periods for the North Atlantic hurricanes [33,34,35], s appears to be increasing. The s = 10.12, 11.71, and 14.09 m/s °C−1 for the 1962–1992, 1981–2003, and 1988–2014 data. We do not know the statistical significance of this increase. However, as long as this parameter is non-decreasing with time, the model would not overpredict WOF-induced RIs.
Rapid intensifications may become more frequent and storms more powerful as the planet warms [65]. Our simple model also predicts this as the likelihood for RI increases with increased ambient SST. Moreover, the greater sensitivity of RI to WOF anomaly suggests more powerful landfalling TCs as storms cross warmer coastal seas and western boundary currents. The simple model indicates that Western North Pacific coastlines: China and Japan, are particularly vulnerable. Wada [12] already suggests such a possibility with Typhoon Manyi crossing the warm Kuroshio south of Japan.

5. Conclusions

This study presents a simple analytical model with ocean feedback of tropical cyclones’ rapid intensity change induced by warm ocean features (WOF). The model indicates that WOF-induced rapid intensification (RI) is unlikely in the present climate. We provide evidence of this inference using observations from nine TCs that developed RIs. We show that the observed RIs have parameters below the model’s RI threshold. In other words, in the present climate, other environmental and internal dynamical factors likely contributed to the RIs observed in these TCs. The inference is in excellent agreement with the conclusion of a recent numerical study [30].
On the other hand, the simple model shows that WOF-induced RI is very sensitive to the WOF’s anomalous amplitude, five times more sensitive than the background SST. Thus, as coastal seas and western boundary currents continue to warm in the 21st century, the model suggests an increased likelihood for RIs near the coasts, China and Japan in particular. Future work may seek to show evidence of this prediction by analyzing landfalling TCs. This model prediction that WOF-induced RI by increased δTW|Coast or δTW|WBC

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The observational data presented in this study are available from the cited public links and references, IBTrACS (https://www.ncdc.noaa.gov/ibtracs/ accessed on 1 October 2021), and GHRSST (https://www.ghrsst.org/ accessed on 1 October 2021).

Acknowledgments

I thank the three reviewers for their inputs.

Conflicts of Interest

The author declares no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Appendix A. Symbols and Abbreviations

A, B, CCoefficients of the empirical MPI
cOcean’s mode-1 baroclinic phase speed
Cd Drag coefficient
FTFactor expressing the effect of TC-induced SST cooling (Equation (16)); the term “sμFT” couples TC’s δVm to ocean cooling
g Earth’s gravity
h1 & h2Depths of the ocean’s upper and lower layers, i.e. before mixing
L TC’s radius
P= L/Uh, time taken for the TC to traverse its radius (i.e. half its size)
PERaised potential energy, PE after mixing minus before mixing
PE|2layersOcean 2-layer system’s potential energy before mixing
PE|mixOcean 1-layer system’s potential energy after mixing
sslope of Vm on the T-space: ( V m / T ) | 0
ta general variable for time
Ta general variable for SST
T1 and T2Uniform temperatures of the ocean’s upper and lower layers before mixing
TmixUniform temperature after mixing
T0 Ambient (i.e. background) SST (Figure 1)
UhTC translation speed
V = |V| wind speed of the wind vector V
Vm MPI maximum wind
V0Maximum wind of the TC approaching the WOF
WEWind energy
x & zHorizontal and vertical axes, z = 0 at the sea surface
Z26 & Z20Depths of the ocean’s 26 °C and 20 °C isotherms
α thermal expansion coefficient of seawater ≈ 3×10−4 K−1 at SST ≈ 28 °C
ρa Air density
ρ0 Reference seawater density ≈ 1025 kg/m3
ρ1 and ρ2Uniform densities of ocean’s upper and lower layers before mixing
ρmixUniform seawater density after mixing
δT= Tmix − T1 (< 0), the SST cooling due to TC (Equation (13)); used also as the usual mathematical notation of “Change in T” (e.g., Equation (3))
δT0< 0, ocean cooling caused by increased δV0 as the TC crosses into the WOF
δTWThe WOF’s SST anomaly (> 0); i.e. total WOF’s SST = T0 + δTW (Figure 1)
ΔT= T1 − T2 (> 0), the temperature difference between upper and lower layers
Δρ = ρ1 − ρ2 (< 0), the density difference between upper and lower layers
δVm Change in MPI maximum wind (m/s) due to change in SST, see Equation (2)
δV0Change in TC’s maximum wind as it crosses over the WOF
γMixing efficiency (~ fraction of the wind work that goes into mixing)
μRatio of TC wind to MPI wind = V0/Vm ≤ 1
μ1, μ2, μ3Coefficient variables used in the model solution (19)
MPIMaximum Potential Intensity
POMPrinceton Ocean Model
RIRapid Intensification
SSTSea Surface Temperature
TCTropical Cyclone
TSTropical Storm
WOFWarm Ocean Feature

References

  1. Kaplan, J.; DeMaria, M. Large-scale characteristics of rapidly intensifying tropical cyclones in the North Atlantic basin. Weather Forecast. 2003, 18, 1093–1108. [Google Scholar] [CrossRef] [Green Version]
  2. Montgomery, M.T.; Nguyen, S.V.; Smith, R.K.; Persing, J. Do tropical cyclones intensify by WISHE? Q. J. R. Meteorol. Soc. 2009, 135, 1697–1714. [Google Scholar] [CrossRef] [Green Version]
  3. Doyle, J.D.; Moskaitis, J.R.; Feldmeier, J.W.; Ferek, R.J.; Beaubien, M.; Bell, M.M.; Cecil, D.L.; Creasey, R.L.; Duran, P.; Elsberry, R.L.; et al. A view of tropical cyclones from above. BAMS 2017, 2113–2134. [Google Scholar] [CrossRef]
  4. Chen, X.; Zhang, J.A.; Marks, F.D. A thermodynamic pathway leading to rapid intensification of tropical cyclones in shear. Geophys. Res. Lett. 2019, 46, 9241–9251. [Google Scholar] [CrossRef]
  5. Paterson, L.A.; Hanstrum, B.N.; Davidson, N.E.; Weber, H.C. Influence of Environmental Vertical Wind Shear on the Intensity of Hurricane-Strength Tropical Cyclones in the Australian Region. Mon. Weather Rev. 2005, 133, 3644–3660. [Google Scholar] [CrossRef]
  6. Zeng, Z.; Wang, Y.; Wu, C.C. Environmental dynamical control of tropical cyclone intensity—An observational study. Mon. Wea. Rev. 2007, 135, 38–59. [Google Scholar] [CrossRef] [Green Version]
  7. Kaplan, J.; DeMaria, M.; Knaff, J.A. A revised tropical cyclone rapid intensification index for the Atlantic and eastern North Pacific basins. Weather Forecast. 2010, 25, 220–241. [Google Scholar] [CrossRef]
  8. Hendricks, E.A.; Peng, M.S.; Fu, B.; Li, T. Quantifying environmental control on tropical cyclone intensity change. Mon. Weather Rev. 2010, 138, 3243–3271. [Google Scholar] [CrossRef] [Green Version]
  9. Wu, L.; Su, H.; Fovell, R.G.; Wang, B.; Shen, J.T.; Kahn, B.H.; Hristova-Veleva, S.M.; Lambrigtsen, B.H.; Fetzer, E.J.; Jiang, J.H. Relationship of environmental relative humidity with North Atlantic tropical cyclone intensity and intensification rate. Geophys. Res. Lett. 2012, 39, L20809. [Google Scholar] [CrossRef] [Green Version]
  10. Soloviev, A.V.; Lukas, R.; Donelan, M.A.; Haus, B.K.; Ginis, I. The air-sea interface and surface stress under tropical cyclones. Sci. Rep. 2014, 4, 5306. [Google Scholar] [CrossRef]
  11. Soloviev, A.V.; Lukas, R.; Donelan, M.A.; Haus, B.K.; Ginis, I. Is the state of the air-sea interface a factor in rapid intensification and rapid decline of tropical cyclones? J. Geophys. Res. Oceans. 2017, 122, 10–174. [Google Scholar] [CrossRef]
  12. Wada, A. Unusually rapid intensification of Typhoon Man-yi in 2013 under preexisting warm-water conditions near the Kuroshio front south of Japan. J. Oceanogr. 2015, 71, 131–156. [Google Scholar] [CrossRef]
  13. Donelan, M.A. On the decrease of the oceanic drag coefficient in high winds. J. Geophys. Res. Oceans 2017, 123, 1485–1501. [Google Scholar] [CrossRef]
  14. Chen, X.; Wang, Y.; Zhao, K. Synoptic flow patterns and large-scale characteristics associated with rapidly intensifying tropical cyclones in the South China Sea. Mon. Weather Rev. 2015, 143, 64–87. [Google Scholar] [CrossRef]
  15. Zhang, L.; Oey, L. Young ocean waves favor the rapid intensification of tropical cyclones-a global observational analysis. Mon. Weather Rev. 2019, 147, 311–328. [Google Scholar] [CrossRef]
  16. Oey, L.; Lin, Y. The Influence of Environments on the Intensity Change of Typhoon Soudelor. Atmosphere 2021, 12, 162. [Google Scholar] [CrossRef]
  17. Kossin, J.P.; Olander, T.L.; Knapp, K.R. Trend analysis with a new global record of tropical cyclone intensity. J. Clim. 2013, 26, 9960–9976. [Google Scholar] [CrossRef]
  18. Lee, C.-Y.; Tippett, M.K.; Sobel, A.H.; Camargo, S.J. Rapid intensification and the bimodal distribution of tropical cyclone intensity. Nat. Commun. 2016, 7, 10625. [Google Scholar] [CrossRef] [PubMed]
  19. Emanuel, K.A. Thermodynamic control of hurricane intensity. Nature 1999, 401, 665–669. [Google Scholar] [CrossRef]
  20. Schade, L.R.; Emanuel, K.A. The ocean’s effect on the intensity of tropical cyclones: Results from a simple coupled atmosphere–ocean model. J. Atmos. Sci. 1999, 56, 642–651. [Google Scholar] [CrossRef] [Green Version]
  21. Emanuel, K.; DesAutels, C.; Holloway, C.; Korty, R. Environmental control of tropical cyclone intensity. J. Atmos. Sci. 2004, 61, 843–858. [Google Scholar] [CrossRef]
  22. Shay, L.K.; Goni, G.J.; Black, P.G. Effects of a warm oceanic feature on Hurricane Opal. Mon. Weather Rev. 2000, 128, 1366–1383. [Google Scholar] [CrossRef]
  23. Hong, X.; Chang, S.W.; Raman, S.; Shay, L.K.; Hodur, R. The interaction between Hurricane Opal (1995) and a warm core ring in the Gulf of Mexico. Mon. Wea. Rev. 2000, 128, 1347–1365. [Google Scholar] [CrossRef] [Green Version]
  24. Lin, I.I.; Wu, C.C.; Emanuel, K.; Lee, I.H.; Wu, C.R.; Pun, I.F. The interaction of Supertyphoon Maemi (2003) with a warm ocean eddy. Mon. Weather Rev. 2005, 133, 2635–2649. [Google Scholar] [CrossRef]
  25. Ali, M.M.; Jagadeesh, P.V.; Jain, S. Effects of eddies on Bay of Bengal cyclone intensity. Eos Trans. Am. Geophys. Union 2007, 88, 93–95. [Google Scholar] [CrossRef]
  26. Mainelli, M.; DeMaria, M.; Shay, L.K.; Goni, G. Application of oceanic heat content estimation to operational forecasting of recent Atlantic category 5 hurricanes. Weather Forecast. 2008, 23, 3–16. [Google Scholar] [CrossRef]
  27. Jaimes, B.; Shay, L.K.; Uhlhorn, E.W. Enthalpy and momentum fluxes during Hurricane Earl relative to underlying ocean features. Mon. Weather Rev. 2015, 143, 111–131. [Google Scholar] [CrossRef]
  28. Mawren, D.; Reason, C.J.C. Variability of upper-ocean characteristics and tropical cyclones in the South West Indian Ocean. J. Geophys. Res. Oceans 2017, 122, 2012–2028. [Google Scholar] [CrossRef]
  29. Potter, H.; DiMarco, S.F.; Knap, A.H. Tropical Cyclone Heat Potential and the Rapid Intensification of Hurricane Harvey in the Texas Bight. J. Geophys. Res. Oceans. 2019, 124, 2440–2451. [Google Scholar] [CrossRef]
  30. Oey, L.; Huang, S.M. Can a warm ocean feature caus a typhoon to intensify rapidly? Atmosphere 2021, 12, 797. [Google Scholar] [CrossRef]
  31. Riehl, H. Some relations between wind and thermal structure of steady state hurricanes. J. Atmos. Sci. 1963, 20, 276–287. [Google Scholar] [CrossRef] [Green Version]
  32. Gray, W.M. Global view of the origin of tropical disturbances and storms. Mon. Wea. Rev. 1968, 96, 669–700. [Google Scholar] [CrossRef]
  33. DeMaria, M.; Kaplan, J. Sea surface temperature and the maximum intensity of Atlantic tropical cyclones. J. Clim. 1994, 7, 1325–1334. [Google Scholar] [CrossRef] [Green Version]
  34. Zeng, Z.; Chen, L.; Wang, Y. An observational study of environmental dynamical control of tropical cyclone intensity in the Atlantic. Mon. Weather Rev. 2008, 136, 3307–3322. [Google Scholar] [CrossRef]
  35. Xu, J.; Wang, Y.; Tan, Z. The relationship between sea surface temperature and maximum intensification rate of tropical cyclones in the North Atlantic. J. Atmos. Sci. 2016, 73, 4979–4988. [Google Scholar] [CrossRef]
  36. Zhang, L.; Oey, L. An observational analysis of ocean surface waves in tropical cyclones in the western North Pacific Ocean. J. Geophys. Res. Oceans 2019, 124, 184–195. [Google Scholar] [CrossRef]
  37. Oey, L.Y.; Ezer, T.; Wang, D.P.; Fan, S.J.; Yin, X.Q. Loop current warming by Hurricane Wilma. Geophys. Res. Lett. 2006, 33, L08613. [Google Scholar] [CrossRef] [Green Version]
  38. Oey, L.Y.; Ezer, T.; Wang, D.P.; Yin, X.Q.; Fan, S.J. Hurricane-induced motions and interaction with ocean currents. Cont. Shelf Res. 2007, 27, 1249–1263. [Google Scholar] [CrossRef]
  39. Price, J.F. Upper Ocean Response to a Hurricane. J. Phys. Oceanogr. 1981, 11, 153–175. [Google Scholar] [CrossRef] [Green Version]
  40. Chelton, D.B.; de Szoeke, R.A.; Schlax, M.G.; El Naggar, K.; Siwertz, N. Geographical variability of the first-baroclinic Rossby radius of deformation. J. Phys. Oceanogr. 1998, 28, 433–460. [Google Scholar] [CrossRef]
  41. Xu, F.H.; Oey, L.Y. Seasonal SSH variability of the Northern South China Sea. J. Phys. Oceanogr. 2015, 45, 1595–1609. [Google Scholar] [CrossRef]
  42. Gill, A.E. Atmosphere-Ocean Dynamics; Academic Press: Cambridge, MA, USA, 1982; p. 662. [Google Scholar]
  43. Holland, G.J.; Belanger, J.I.; Fritz, A. A revised model for radial profiles of hurricane winds. Mon. Weather Rev. 2010, 138, 4393–4401. [Google Scholar] [CrossRef]
  44. Chiang, T.L.; Wu, C.R.; Oey, L.Y. Typhoon Kai-Tak: A perfect ocean’s storm. J. Phys. Oceanogr. 2011, 41, 221–233. [Google Scholar] [CrossRef]
  45. Kunze, E. Near-inertial wave propagation in geostrophic shear. J. Phys. Oceanogr. 1985, 15, 544–565. [Google Scholar] [CrossRef]
  46. Oey, L.Y.; Inoue, M.; Lai, R.; Lin, X.H.; Welsh, S.E.; Rouse, L.J., Jr. Stalling of near-inertial waves in a cyclone. Geophys. Res. Lett. 2008, 35, L12604. [Google Scholar] [CrossRef] [Green Version]
  47. Powell, M.D.; Vickery, P.J.; Reinhold, T.A. Reduced drag coefficient for high wind speeds in tropical cyclones. Nature 2003, 422, 279–283. [Google Scholar] [CrossRef] [PubMed]
  48. Good, S.A.; Martin, M.J.; Rayner, N.A. EN4: Quality controlled ocean temperature and salinity profiles and monthly objective analyses with uncertainty estimates. J. Geophys. Res. Oceans 2013, 118, 6704–6716. [Google Scholar] [CrossRef]
  49. Sun, J.; Oey, L.Y. The influence of ocean on Typhoon Nuri (2008). Mon. Weather Rev. 2015, 143, 4493–4513. [Google Scholar] [CrossRef]
  50. Sun, J.; Oey, L.Y.; Chang, R.; Xu, F.; Huang, S.M. Ocean response to typhoon Nuri (2008) in western Pacific and South China Sea. Ocean. Dyn. 2015, 65, 735–749. [Google Scholar] [CrossRef]
  51. Etemad-Shahidi, A.; Imberger, J. Anatomy of turbulence in a narrow and strongly stratified estuary. J. Geophys. Res. 2002, 107, 3070. [Google Scholar] [CrossRef]
  52. Bouffard, D.; Boegman, L.A. Diapycnal diffusivity model for stratified environmental flows. Dyn. Atmos Oceans 2013, 61, 14–34. [Google Scholar] [CrossRef]
  53. Monismith, S.G.; Koseff, J.R.; White, B.L. Mixing efficiency in the presence of stratification: When is it constant? Geophys. Res. Lett. 2018, 45, 5627–5634. [Google Scholar] [CrossRef]
  54. Smyth, W.D. Marginal instability and the efficiency of ocean mixing. J. Phys. Oceanogr. 2020, 50, 2141–2150. [Google Scholar] [CrossRef]
  55. Sayol, J.M. On the Complexity of Upper Ocean Mesoscale Dynamics. Ph.D Thesis, IMEDEA(CSIC-UIB), Majorca, Spain, 2016; p. 178. [Google Scholar]
  56. Balaguru, K.; Foltz, G.R.; Leung, L.R.; Hagos, S.M.; Judi, D.R. On the use of ocean dynamic temperature for hurricane intensity forecasting. Weather Forecast. 2018, 33, 411–418. [Google Scholar] [CrossRef]
  57. Bozart, L.E.; Velden, C.S.; Bracken, W.D.; Molinari, J.; Black, P.G. Environmental influences on the rapid intensification of Hurricane Opal (1995) over the Gulf of Mexico. Mon. Weather Rev. 2000, 128, 322–352. [Google Scholar] [CrossRef]
  58. Oliver, E.C.J. Mean warming not variability drives marine heatwave trends. Clim. Dyn. 2019, 53, 1653–1659. [Google Scholar] [CrossRef]
  59. Seager, R.; Cane, M.; Henderson, N.; Lee, D.E.; Abernathey, R.; Zhang, Z. Strengthening tropical Pacific zonal sea surface temperature gradient consistent with rising greenhouse gases. Nat. Clim. Chang. 2019, 9, 517–522. [Google Scholar] [CrossRef]
  60. Martinez-Moreno, J.; Hogg, A.; England, M.H.; Constantinou, N.C.; Kiss, A.E.; Morrison, A.K. Global changes in oceanic mesoscale currents over the satellite altimetry record. Nat. Clim. Chang. 2021, 11, 397–403. [Google Scholar] [CrossRef]
  61. Flato, G.; Marotzke, J.; Abiodun, B.; Braconnot, P.; Chou, S.C.; Collins, W.; Cox, P.; Driouech, F.; Emori, S.; Eyring, V.; et al. Evaluation of climate models. In IPCC Report Chapter 9; Cambridge University Press: Cambridge, UK; New York, NY, USA, 2013. [Google Scholar]
  62. Lima, F.P.; Wethey, D.S. Three decades of high-resolution coastal sea surface temperatures reveal more than warming. Nat. Commun. 2012, 3, 704. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  63. Emanuel, K.A. The theory of hurricanes. Annu. Rev. Fluid Mech. 1991, 23, 179–196. [Google Scholar] [CrossRef]
  64. Lighthill, J. Ocean spray and the thermodynamics of tropical cyclones. J. Engr. Math. 1999, 35, 11–42. [Google Scholar] [CrossRef]
  65. Kossin, J.P.; Knapp, K.R.; Olander, T.L.; Velden, C.S. Global increase in major tropical cyclone exceedance probability over the past four decades. Proc. Natl. Acad. Sci. USA 2020, 117, 11975–11980. [Google Scholar] [CrossRef] [PubMed]
Figure 1. A tropical cyclone (TC) translates westward at a constant Uh across x = 0 onto a warm ocean feature (WOF) where SST increases by δTW. The circles depict the TC wind from weak, e.g., 18 m/s in the outer circle of radius L to the maximum in the inner-most ‘core’. As the storm approaches, wind at the redpoint strengthens from weak to the maximum over a time ~L/Uh shortly after the storm crosses into the WOF. The goal is to calculate the increased wind δVm due to the coupled response of the WOF and ocean cooling.
Figure 1. A tropical cyclone (TC) translates westward at a constant Uh across x = 0 onto a warm ocean feature (WOF) where SST increases by δTW. The circles depict the TC wind from weak, e.g., 18 m/s in the outer circle of radius L to the maximum in the inner-most ‘core’. As the storm approaches, wind at the redpoint strengthens from weak to the maximum over a time ~L/Uh shortly after the storm crosses into the WOF. The goal is to calculate the increased wind δVm due to the coupled response of the WOF and ocean cooling.
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Figure 2. Plot of μ = V0/Vm.
Figure 2. Plot of μ = V0/Vm.
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Figure 3. Top: mean Z26 (= h1) and Z20-Z26 (= h2, contours) (m) from the EN4 reanalysis [46]. Bottom: RI locations as red dots [15] from IBTrACS (https://www.ncdc.noaa.gov/ibtracs/ accessed on 1 October 2021) and SST contours 26, 28, 29, and 30 °C (blue, black, magenta, and orange). Only a few 30°C contours exist close to the Philippines’ eastern coast. The period is 1992–2015 June–September.
Figure 3. Top: mean Z26 (= h1) and Z20-Z26 (= h2, contours) (m) from the EN4 reanalysis [46]. Bottom: RI locations as red dots [15] from IBTrACS (https://www.ncdc.noaa.gov/ibtracs/ accessed on 1 October 2021) and SST contours 26, 28, 29, and 30 °C (blue, black, magenta, and orange). Only a few 30°C contours exist close to the Philippines’ eastern coast. The period is 1992–2015 June–September.
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Figure 4. Comparisons of the analytical SST cooling (with γ = 0.02) with GHRSST (Group for High resolution Sea Surface Temperature, https://www.ghrsst.org/ accessed on 1 October 2021) and three-dimensional POM simulated cooling along the daily track of Typhoons Nuri [49,50] and Soudelor [16]. Note that due to interpolation GHRSST tends to underestimate TC-induced SST cooling [49]. For Nuri, the discrepancy on Day 3 is due to the storm crossing the warm Kuroshio in the Luzon Strait, which the simple model poorly represents.
Figure 4. Comparisons of the analytical SST cooling (with γ = 0.02) with GHRSST (Group for High resolution Sea Surface Temperature, https://www.ghrsst.org/ accessed on 1 October 2021) and three-dimensional POM simulated cooling along the daily track of Typhoons Nuri [49,50] and Soudelor [16]. Note that due to interpolation GHRSST tends to underestimate TC-induced SST cooling [49]. For Nuri, the discrepancy on Day 3 is due to the storm crossing the warm Kuroshio in the Luzon Strait, which the simple model poorly represents.
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Figure 5. Color shading: western North Pacific’s δVm for Uh = ∞ (i.e., no ocean feedback) as TC encounters a WOF with δTW warmer than the ambient T0; white line is δVm = 15.4 m/s. Blue dashed lines are 15.4 m/s with ocean feedback for various Uh. White dashed lines mark T0 = 29 °C and δTW = 1 °C. Letters are observed RI TCs: Bansi (2015; pre-RI intensity (pRIi) Cat.2) [28], Earl (2010; pRIi Cat.1) [27], Harvey (2017; pRIi TS) [29], Maemi (2003; pRIi Cat.1) and Maon (2004; pRIi Cat.1) [24], Manyi (2013; pRIi TS) [12], Matthew (2016; pRIi Cat.1) [56], Opal (1995; pRIi Cat.1) [22], and Soudelor (2015; pRIi TS) [16]. The red asterisk is their mean. The Uh ranges from 3 (Mn) to 8.5 m/s (O). The magenta line is δVm = 15.4 m/s for the N Atlantic (no ocean feedback). The model uses γ = 0.02, h1 = h2 = 100 m and V0 = 30 m/s.
Figure 5. Color shading: western North Pacific’s δVm for Uh = ∞ (i.e., no ocean feedback) as TC encounters a WOF with δTW warmer than the ambient T0; white line is δVm = 15.4 m/s. Blue dashed lines are 15.4 m/s with ocean feedback for various Uh. White dashed lines mark T0 = 29 °C and δTW = 1 °C. Letters are observed RI TCs: Bansi (2015; pre-RI intensity (pRIi) Cat.2) [28], Earl (2010; pRIi Cat.1) [27], Harvey (2017; pRIi TS) [29], Maemi (2003; pRIi Cat.1) and Maon (2004; pRIi Cat.1) [24], Manyi (2013; pRIi TS) [12], Matthew (2016; pRIi Cat.1) [56], Opal (1995; pRIi Cat.1) [22], and Soudelor (2015; pRIi TS) [16]. The red asterisk is their mean. The Uh ranges from 3 (Mn) to 8.5 m/s (O). The magenta line is δVm = 15.4 m/s for the N Atlantic (no ocean feedback). The model uses γ = 0.02, h1 = h2 = 100 m and V0 = 30 m/s.
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Figure 6. Western North Pacific’s δVm as a function of Uh and h1 for (T0, δTW) = (29.5, 1) °C (shading and white 15.4 m/s-line). Other lines are 15.4 m/s for blue dashed: T0 = 29, 30, 31, 32, 33 °C at fixed δTW = 1 °C; black: δTW = 0.92, 1.1, 1.3, 1.5, 1.8 °C at fixed T0 = 29.5 °C; yellow: (T0, δTW) = (30, 1.3) °C. The white dashed box shows the 3 ≤ Uh ≤ 7 m/s and 60 ≤ h1 ≤ 120 m region where RI events are frequently observed. The model uses γ = 0.02 and V0 = 30 m/s. Add 3 °C to T0 to apply the plot to the Atlantic hurricanes, i.e., 29.5 °C becomes 32.5 °C, 30 °C becomes 33 °C, etc.
Figure 6. Western North Pacific’s δVm as a function of Uh and h1 for (T0, δTW) = (29.5, 1) °C (shading and white 15.4 m/s-line). Other lines are 15.4 m/s for blue dashed: T0 = 29, 30, 31, 32, 33 °C at fixed δTW = 1 °C; black: δTW = 0.92, 1.1, 1.3, 1.5, 1.8 °C at fixed T0 = 29.5 °C; yellow: (T0, δTW) = (30, 1.3) °C. The white dashed box shows the 3 ≤ Uh ≤ 7 m/s and 60 ≤ h1 ≤ 120 m region where RI events are frequently observed. The model uses γ = 0.02 and V0 = 30 m/s. Add 3 °C to T0 to apply the plot to the Atlantic hurricanes, i.e., 29.5 °C becomes 32.5 °C, 30 °C becomes 33 °C, etc.
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Oey, L. The Increased Likelihood in the 21st Century for a Tropical Cyclone to Rapidly Intensify When Crossing a Warm Ocean Feature—A Simple Model’s Prediction. Atmosphere 2021, 12, 1285. https://doi.org/10.3390/atmos12101285

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Oey L. The Increased Likelihood in the 21st Century for a Tropical Cyclone to Rapidly Intensify When Crossing a Warm Ocean Feature—A Simple Model’s Prediction. Atmosphere. 2021; 12(10):1285. https://doi.org/10.3390/atmos12101285

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Oey, Leo. 2021. "The Increased Likelihood in the 21st Century for a Tropical Cyclone to Rapidly Intensify When Crossing a Warm Ocean Feature—A Simple Model’s Prediction" Atmosphere 12, no. 10: 1285. https://doi.org/10.3390/atmos12101285

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