a. TC wind structure model

Absolute angular momentum is widely applied to understand the physics of the TC wind field, as it is directly linked to the tangential wind speed (Anthes 1974; Montgomery et al. 2001; E04; Lilly and Emanuel 1985). Within the boundary layer, absolute angular momentum transported inward from some outer radius via radial inflow is gradually lost to surface frictional dissipation. That which remains is gradually converted from planetary to relative angular momentum, thereby generating the tangential wind field of the TC vortex. When reaching the radius of maximum wind speed (r_m), air ascends within the convective eyewall and then flows radially outward aloft near the tropopause. Therefore, a theoretical model describing the low-level circulation beyond r_m can be formulated by precisely quantifying how absolute angular momentum changes with radius based on the local dynamics or thermodynamics. Recent work achieves this in two distinct regions: the outer nonconvecting region (E04) and the inner convecting region (ER11).

C15 mathematically merged the ER11 [Eqs. (1) and (2)] and E04 [Eq. (5)] solutions to produce a model for the complete azimuthal wind profile. This merging yields a unique solution; the process is described in C15. Parameters required to solve the solutions are V_m and r_m for the inner region, V_a and r_a at the merge point connecting the inner and outer region, r_fit as a specified radius input, χ and f for the environmental conditions. Given the environmental parameters χ, f, and C_k/C_d, one only needs to know two storm parameters—the intensity V_m and any wind radius (e.g., r_m, r_34kt)—to specify the model solution.

C15 is the simplest model that generates a first-order prediction of the full wind field. C15 evaluated the model against real-world storms over the ocean, and the model has been applied in storm surge risk analysis (Xi et al. 2020; Lin et al. 2020; Xi and Lin 2022). In addition, it performs best among existing wind models in simulating peak storm surge from historical U.S. landfalls (S. Wang et al. 2022). Thus, the C15 wind field model is examined against the simulated wind field response to idealized landfalls in this paper. A novel version of C15 is applied in this work, where the wind profile within the eye (r < r_m) generated by the ER11 solution is replaced with a quadratic profile as was done in Klotzbach et al. (2022).

b. TC size

As described in section 1, TC size on the f plane typically expands toward an equilibrium potential size given approximately by the ratio of the potential intensity to the Coriolis parameter, $V_p/f$. The size of real-world TCs is typically significantly smaller than this length scale (Chavas and Lin 2016; Chavas and Reed 2019), though, and instead follows the Rhines scale because the latter is much smaller than $V_p/f$ at low latitudes (Chavas and Reed 2019; Lu and Chavas 2022). In contrast, at high latitudes, the potential size is much smaller than the Rhines scale, and hence, the effect of the Rhines scale becomes negligible, yielding a polar cap regime in aquaplanet experiments in which the domain is filled with TCs, analogous to that found on the f plane (Chavas and Reed 2019).

Here we propose an analogous regime contrast for landfall: the transition from ocean to land is a transition to a near-zero value of V_p (CC21) and thus a transition to a regime where $V_p/f$ is suddenly much smaller than the Rhines scale. As with the polar cap regime, the Rhines scale becomes secondary and the TC would be expected to shrink toward its potential size, which is near zero. We currently lack an explicit theory for the rate of change of size toward its potential size, though. Instead, we posit that these dynamics ought to depend on $V_p/f$, just as the dynamics of intensity change in nature depends fundamentally on the potential intensity (Tang and Emanuel 2012), including for idealized landfall (CC21). Landfall is a transient adjustment between two equilibrium states (CC20), and hence, size will not scale directly with $V_p/f$ or else the storm would shrink to zero size nearly instantaneously, which clearly does not happen even for an instantaneous transition to land (CC21). Thus, we propose the next simplest hypothesis: that size after landfall will scale with ${\upsilon }_m/f$, where υ_m is the maximum wind speed itself. Unlike V_p, which can change instantly, υ_m will change over finite time scale and its response may also be predictable theoretically or empirically (CC21). This approach ties storm size to intensity in the transient response in the same manner as it is done at equilibrium via $V_p/f$. We test this hypothesis below.

For the definition of storm outer size, multiple metrics have been applied to define r₀ in past work, including r₁₂ and r_34kt, where r₁₂ represents the radius of 12 m s⁻¹ wind and r_34kt represents the radius of 34 kt (1 kt ≈ 0.51 m s⁻¹) azimuthal wind speed. In practice, r_34kt is the outermost wind radius that is commonly estimated in operations (Knapp et al. 2010; NHC 2022) and can be linked directly to r_m via the structural model described above (Chavas and Knaff 2022). Thus, we choose to focus on r_34kt as our outer size metric on practical grounds, as the outer circulation tends to vary coherently (C15).

a. Idealized landfall simulations

As discussed in CC20 and CC21, spatiotemporal heterogeneity in surface properties are complicated in real-world landfalls, but landfall is fundamentally a transient response to a rapid change in surface wetness and roughness. Here we design simplified landfall experiments in an axisymmetric geometry with a uniform environment and uniform boundary forcing to test the response of a mature TC to modified surface roughness and wetness, individually and in combination. Idealized landfall experiments are performed using the Bryan Cloud Model (CM1v19.8) (Bryan and Fritsch 2002) in an axisymmetric geometry with the same setup as CC21. CM1 solves the fully compressible equations of motion in height coordinates on an f plane on a fully staggered Arakawa C-type grid. Model parameters are summarized in Table 1. This simple approach neglects all water–radiation and temperature–radiation feedbacks (Cronin and Chavas 2019). The simulation results are robust to varying the choice of model resolutions or mixing lengths (CC21). Note that the axisymmetric responses discussed here may be considered akin to a 3D storm in the limit of a very rapid translation speed from uniform ocean to uniform land; asymmetry features will be introduced when heterogeneous surface properties change over a finite time scale beneath the storm (Hlywiak and Nolan 2021, 2022). Detailed explanations and discussions about the model setup can be fully referred to CC21.

Table 1.

Parameter values of the CM1 CTRL simulation. Only the two boldface parameters C_d and ϵ are modified individually or simultaneously in idealized landfall experiments as described in Fig. 1.

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We first run a baseline experiment with the above model setup to generate the control experiment (CTRL). The 200-day baseline simulation allows a mature storm to reach a statistical steady state, from which we identify a stable 15-day period and then define the CTRL as the ensemble mean of five 10-day segments of the baseline experiment from this stable period whose start times are each one day apart. Using ensemble data helps to reduce noise and increases the robustness of the results. During this 10-day evolution, a quasi-stable storm is maintained. Then we perform different types of idealized landfall experiments by restarting each of the five CTRL ensemble members with surface wetness and/or roughness modified. Surface wetness is modified by decreasing surface evaporative fraction ϵ, which reduces the surface latent heat fluxes F_LH through the decreased surface mixing ratio fluxes F_qυ in CM1 (sfcphys.F). Surface roughness is modified by increasing the drag coefficient C_d, which alters the surface roughness length z₀ and then the friction velocity $u^{*}$ for the surface log layer in CM1. Readers are referred to CC20 for full details of the modifications in CM1 experiments. Finally, analogous to the CTRL, the five 10-day segments of each landfall experiment are averaged to reduce noise and yield a single mean response evolution.

The design of the idealized landfall experiments is summarized in Fig. 1. This set of experiments is designed to systematically understand how the TC wind field responds to each surface forcing with varying magnitudes, and how each individual forcing affects the wind field in comparison to applying both forcings simultaneously. Therefore, there are roughening-only experiments (XC_d, warm color boxes), drying-only experiments (Υϵ, gradient blue boxes), combined experiments (ΥϵXC_d, gray boxes). Finally, we include a special set of combined experiments (0V_pXC_d, gradient green boxes) where both surface sensible and latent heat fluxes are set to zero, which sets V_p to zero, while increasing the roughness. The leading value X indicates the multiplicative enhancement factor applied to surface drag coefficient C_d, while Υ is the multiplicative reduction factor applied to the surface evaporative fraction ϵ. The modification in C_d or/and ϵ systematically weakens the CTRL storm, which can be understood via the response of potential intensity, ${\tilde{V}}_p=V_{p,\text{EXP}}/V_{p,\text{CTRL}}$ [Eqs. (4)–(6) in CC21; Fig. 1].

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Two-dimensional experimental phase space of surface drying (decreasing ϵ moving left to right) and surface roughening (increasing C_d moving top to bottom). CTRL is an ocean-like surface with (C_d, ϵ) = (0.0015, 1). Values of the potential intensity response ${\tilde{V}}_p$ for CTRL, individual drying or roughening, and representative combined experiments are listed in parentheses; ${\tilde{V}}_p$ for any combination of forcing is the product of ${\tilde{V}}_p$ for each individual forcing. Representative experiments testing combined forcings are shaded gray and the subset testing the most extreme combinations of each forcing are underlined. Experiment set 0V_pXC_d, corresponding to the special case where surface heat fluxes are entirely removed (V_p = 0), are shaded green.

Citation: Journal of the Atmospheric Sciences 80, 4; 10.1175/JAS-D-22-0156.1

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The combined experiments are conducted in a way where individual drying and roughening are systematically paired with each other. To compare the role of each forcing under different combined-forcing scenarios, we select two subsets of combined-forcing experiments for deeper analysis: 1) 0.7ϵ2C_d, 0.7ϵ10C_d, 0.1ϵ2C_d, and 0.1ϵ10C_d (underlined in Fig. 1) represent the extreme combinations where each forcing takes its highest or lowest nonzero magnitude; 2) 0.5ϵ2C_d, 0.25ϵ4C_d, and 0.1ϵ8C_d represent cases where the individual forcing in a combined experiment have similar contributions to reducing V_p. Finally, the experiment set 0V_pXC_d demonstrates how the magnitude of C_d changes the wind field decay when V_p is uniformly reduced to zero across the experiments. This simplified setup could be more useful for practical application to the real-world landfalls since no final equilibrium V_p estimation is required (CC21).

b. Testing theory against simulations

The near-surface wind field drives inland TC hazards. Thus, the evolution of the 10-m wind field in different types of idealized landfall experiments is compared to the C15 model prediction. The transient response of the TC wind field in each idealized landfall experiment and the corresponding physical mechanisms were analyzed in CC20. CC20 found that in response to surface roughening, storm size (r_m and r_34kt) decrease rapidly along with υ_m as the entire wind field weakened and shrank. In contrast, in response to surface drying, υ_m decreased rapidly while size, including the broad outer circulation, remained relatively constant, due to the relatively slow response to the stabilization of the overturning circulation.

We focus principally on the first 24 h of the evolution, during which the wind field response to each landfall type is the strongest while the circulation remains sufficiently well defined to easily identify r_34kt (Fig. 2). A stable gale wind radius is often no longer observable 24 h after TC landfall in the real world (Jing and Lin 2019). We compare model versus simulation at τ = 1, 6, 12, and 24 h where τ denotes the time since the start of a given forcing experiment, and we display results whenever a value of r_34kt is still discernible. Though the C15 model is not a forecast model, here we aim to test to what extent the C15 model can reproduce the simulated wind field response given the time-dependent responses of intensity, size, and the change in C_d in our experiments. For the C15 prediction, the simulated υ_m(τ) and r_34kt(τ) response of each experiment are used to fit the structural model. We hold C_k fixed at its CTRL value (C_k = 0.0015) and set C_d to be its modified value for each experiment. Since latitude typically varies minimally for a landfalling TC over a 24-h period, the Coriolis parameter f is held fixed at its CTRL value (5 × 10⁻⁵ s⁻¹). The radiative-subsidence rate W_cool is set to 0.002 m s⁻¹, which is the median of the best-fit value for observed storms (C15). The wind field solution is not very sensitive to W_cool except for at large radii well beyond r_34kt (online supplementary Fig. 1). For TC size, we test the simple hypothesis

$r_{34\text{kt}}(\tau )\sim \frac{{\upsilon }_m(\tau )}{f}$(6)

that was motivated in the previous section. Since we hold f constant, this hypothesis simplifies to

${\tilde{r}}_{34\text{kt}}(\tau )\sim {\tilde{\upsilon }}_m(\tau ).$(7)

As in CC21, we analyze results as responses relative to initial state. Hence, the intensity and size in each experiment are normalized by the CTRL value, i.e., ${\tilde{\upsilon }}_m={\upsilon }_{m,\text{EXP}}/{\upsilon }_{m,\text{CTRL}}$ and ${\tilde{r}}_{34\text{kt}}=r_{34\text{kt,EXP}}/r_{34\text{kt,CTRL}}$. That is, we examine whether the simulated transient response of intensity can predict the transient response of storm outer size during the decay evolution.

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The simulated 10-m wind field in response to different magnitudes of each type of idealized landfall (colored lines) at τ = 24 h. The initial CTRL wind field is shown by the thick black line in each plot.

Citation: Journal of the Atmospheric Sciences 80, 4; 10.1175/JAS-D-22-0156.1

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a. TC structure

We first examine to what extent the C15 model can reproduce the response of the storm wind field structure in our idealized landfall experiments, with intensity and size taken as their simulated values. Figure 3 shows the C15 model and its inner and outer component models against our CM1 CTRL simulation. The model inputs are the CM1 CTRL values of υ_m and r_34kt. We set f to 0.000 05 s⁻¹, W_cool = 0.002 m s⁻¹, and C_d is 0.0015. In this example, the model does very well predicting the simulated wind profile for nearly the entire circulation beyond r_m, but it underestimates r_m, which will be discussed below.

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The 10-m wind field of the CM1 simulated steady-state, mature storm (shaded CM1 CTRL), the ER11-predicted wind profile (yellow dashed), the E04-predicted wind profile (blue dashed), and the C15-predicted wind profile (red solid). f = 5 × 10⁻⁵ s⁻¹, χ = 1.5, where C_d = 0.0015 and W_cool = 0.002 m s⁻¹. υ_m = 76.1 m s⁻¹, r_m = 33 km, and r_34kt = 202 km in the CM1 CTRL simulation.

Citation: Journal of the Atmospheric Sciences 80, 4; 10.1175/JAS-D-22-0156.1

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Figure 4 compares the C15 prediction fit to (υ_m, r_34kt) against the model simulation for representative idealized landfall experiments 0.25ϵ, 4C_d, 0.25ϵ4C_d, and 0V_p4C_d at τ = 1, 6, 12, and 24 h. The wind field difference between C15 prediction and model simulation across all the experiments are shown in Fig. 5.

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The 10-m wind field of the representative landfall experiments (a) 0.25ϵ, (b) 4C_d, (c) 0.25ϵ4C_d, and (d) 0V_p4C_d at τ = 1, 6, 12, and 24 h. Colored curves are the simulated wind field (solid) and C15-predicted wind field (dashed).

Citation: Journal of the Atmospheric Sciences 80, 4; 10.1175/JAS-D-22-0156.1

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The wind field difference between C15 prediction and the idealized landfall simulation from r = 50 to 800 km across all the experiments of (a) surface drying experiments, (b) surface roughening experiments, (c) combined experiments, and (d) 0V_pXC_d experiments at τ = 1, 6, 12, and 24 h. Each τ is indicated by the same color as in Fig. 4.

Citation: Journal of the Atmospheric Sciences 80, 4; 10.1175/JAS-D-22-0156.1

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For surface drying only (Fig. 4a), C15 does well in reproducing much of the wind field beyond 2r_m out to large radii (r = 800 km) during the slow decay. The model generally underestimates the wind speed within the convective inner region (r ≤ 200 km) due to the low bias in r_m that persists and acts to shift the peak wind region slightly inward of the simulation. At τ = 24 h, the low bias near r_m becomes much smaller for stronger drying (0.3ϵ, 0.25ϵ, 0.1ϵ in Figs. 4a and 5a). Beyond r_34kt, the C15 prediction bias is less than 2 m s⁻¹ across all the drying experiments (Fig. 4a). For experiments that include surface roughening (i.e., roughening only, combined, and 0V_pXC_d), the C15 prediction performs well in reproducing the wind field evolution at all radii beyond r_m (Figs. 4b–d). The negative r_m bias at the initial time step decreases over the first 12 h and becomes a slightly positive r_m bias through 24 h (Figs. 4b–d and 5b–d). The wind field bias is generally less than 2 m s⁻¹ outside r_34kt across all the roughening and combined experiments (Figs. 5b,c) similar to drying-only experiments. In 0V_pXC_d experiments, the C15 prediction underestimates the outer wind field when υ_m is decreased toward 34 kt at τ = 24 h (Figs. 4d and 5d) with a bias larger than 2 m s⁻¹. For r < r_m, the wind profile gradually transitions from concave to convex, and as a result C15 underestimates the winds after 12 h. Though for hazard footprints, the wind profile within the eyewall is not critical since these locations must also experience the stronger winds from the eyewall immediately before and after. A model for the wind profile inside r_m during the landfall could be developed to better depict the entire wind field.

Overall, this simple theory-based model reproduces the wind field response to idealized landfalls given a small number of physical, observable input parameters. The outer circulation in drying-only experiments is well captured throughout the evolution. With moderate or stronger surface roughening, which is more like the real world, the C15 model well reproduces the simulated wind field beyond r_m before the storm dissipates and loses its structure.

In experiments with surface roughening, the mismatched wind profile within the eye during the later period might arise from the limitations of the C15 model itself: when the storm remains strong during the initial period, the concave inner wind profile within the eye is well described by a quadratic profile. During later stages, the storm is largely weakened by surface roughening, and its inner wind profile transforms from a concave shape to a convex shape more rapidly than in the drying-only experiments, as found in Hlywiak and Nolan (2021) as well. This behavior cannot be captured by a quadratic profile.

b. TC size

We next examine to what extent the transient response of size ${\tilde{r}}_{34\text{kt}}(\tau )$ scales with the transient response of intensity ${\tilde{\upsilon }}_m(\tau )$ in individual-forcing experiments (Fig. 6a), combined-forcing experiments (Fig. 6b), and 0V_pXC_d experiments (Fig. 6c) throughout the 48-h evolution. For cases with strong surface roughening (8C_d, 10C_d, 0.7ϵ10C_d, 0.1ϵ8C_d, 0.1ϵ10C_d, and 0V_p8C_d, 0V_p10C_d), simulated intensity quickly decreases below 34 kt after τ = 12 h, and thus, their corresponding long-term ${\tilde{r}}_{34\text{kt}}(\tau )\sim {\tilde{\upsilon }}_m(\tau )$ relationship is not shown in Fig. 6.

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The relationship between ${\tilde{\upsilon }}_m(\tau )$ and ${\tilde{r}}_{34\text{kt}}(\tau )$ during a 48-h evolution (asterisks mark every 2 h) for (a) individual forcing experiments, (b) combined experiments, and (c) 0V_pXC_d experiments. The subplot in (a) emphasizes on the relationship between ${\tilde{\upsilon }}_m(\tau )$ and ${\tilde{r}}_{34\text{kt}}(\tau )$ during the first 12-h period for all surface drying experiments. For 0V_pXC_d experiments with stronger surface roughening (0V_p8C_d, 0V_p10C_d), the relationship no longer exits after τ = 24 h due to the rapid decay.

Citation: Journal of the Atmospheric Sciences 80, 4; 10.1175/JAS-D-22-0156.1

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For roughening experiments (Fig. 6a, warm colors), ${\tilde{r}}_{34\text{kt}}$ scales very closely with ${\tilde{\upsilon }}_m$ throughout the 48 h period, and it does so consistently across all experiments. For τ = 24–48 h, ${\tilde{\upsilon }}_m$ gradually equilibrates while ${\tilde{r}}_{34\text{kt}}$ continues to decrease slowly. Thus, there is a slight deviation away from the scaling toward the end of the evolution.

For drying experiments (Fig. 6a, blue colors), ${\tilde{r}}_{34\text{kt}}$ scales reasonably closely with ${\tilde{\upsilon }}_m$ by the end of the 48 h period. However, during the first 12 h, the storm intensity principally weakens while its outer size shrinks very slowly (Fig. 6a, subplot) as found in CC20. After that, size shrinks steadily with the decreasing intensity, scaling closely with one another from τ = 12–36 h. During the final 12 h, size continues to gradually shrink as the intensity begins to equilibrate. Thus, ${\tilde{r}}_{34\text{kt}}$ scales more closely with ${\tilde{\upsilon }}_m$ by τ = 48 h, at which time ${\tilde{r}}_{34\text{kt}}$ is approximately 10%–15% larger than ${\tilde{\upsilon }}_m$ across all the drying experiments. The trajectories through (${\tilde{\upsilon }}_m$, ${\tilde{r}}_{34\text{kt}}$) space is consistent across all experiments similar to the roughening experiments.

For the combined experiments (Fig. 6b) and the 0V_pXC_d experiments (Fig. 6c), the storm size response ${\tilde{r}}_{34\text{kt}}(\tau )$ also generally scales with the intensity response ${\tilde{\upsilon }}_m(\tau )$ throughout the evolution, especially with at least moderate roughening. For experiments with relatively weaker roughening than drying (0.5ϵ2C_d, and 0.1ϵ2C_d in Fig. 6b, 0V_p2C_d and 0V_p4C_d in Fig. 6c), ${\tilde{\upsilon }}_m(\tau )$ and ${\tilde{r}}_{34\text{kt}}(\tau )$ are less linearly related while exhibiting both characteristics of surface drying (initially faster weakening than shrinking) and roughening experiments (weakening and shrinking scale together). Specifically, during the initial period (τ = 0–6 h), ${\tilde{r}}_{34\text{kt}}(\tau )$ decreases sharply and nearly linearly with ${\tilde{\upsilon }}_m(\tau )$ across all the experiments, as seen in pure roughening. For τ = 6–12 h, the storm weakens while size remains relatively steady. After τ = 12 h, size steadily decreases again as the storm weakens, as seen in pure drying. For τ out to 48 h, the trajectories return toward a close scaling between intensity and size responses similar to roughening, particularly in the presence of at least moderate roughening.

The hypotheses proposed in Eqs. (9) and (10) are tested against our representative combined simulations (Fig. 7). First we compare the predicted responses ${\tilde{r}}^{*}(\tau )$ and ${\tilde{\upsilon }}^{*}(\tau )$ to the corresponding simulated responses, ${\tilde{r}}_{34\text{kt}}(\tau )$ and ${\tilde{\upsilon }}_m(\tau )$, of the combined experiments (Fig. 7, red pentagrams and dots) at τ = 0, 6, 12, 24, 36, and 48 h. Overall, the predicted size–intensity relationship ${\tilde{r}}^{*}(\tau )\sim {\tilde{\upsilon }}^{*}(\tau )$ closely follows the simulated relationship ${\tilde{r}}_{34\text{kt}}(\tau )\sim {\tilde{\upsilon }}_m(\tau )$ throughout the evolution across all the combined experiments. The relationship is again strongest in the presence of at least moderate roughening. In experiments with stronger surface drying and weaker surface roughening (Figs. 7c,e–g), the prediction (red pentagrams) deviates from the simulation (red dots) from τ = 12 to 36 h, with ${\tilde{\upsilon }}^{*}(\tau )$ decreasing to smaller values than the simulated ${\tilde{\upsilon }}_m(\tau )$.

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The relationship between simulated ${\tilde{\upsilon }}_m(\tau )$ and ${\tilde{r}}_{34\text{kt}}(\tau )$ for different combined experiments and their corresponding deconstructed individual forcing experiments at τ = 0, 6, 12, 24, 36, and 48 h, as long as ${\tilde{r}}_{34\text{kt}}(\tau )$ still exist in the experiment. The predicted ${\tilde{\upsilon }}^{*}(\tau )$ and ${\tilde{r}}^{*}(\tau )$ relationship [Eqs. (8)–(10)] of each combined experiment are marked by pentagrams at the same τ as the simulated results. Here (a) 0.7ϵ2C_d, (b) 0.7ϵ10C_d, (c) 0.1ϵ2C_d, and (d) 0.1ϵ10C_d are representative combined experiments where each individual forcing takes its highest or lowest nonzero magnitude. (e) 0.5ϵ2C_d, (f) 0.25ϵ4C_d, and (g) 0.1ϵ8C_d are representative combined experiments where the magnitude of individual forcing in a combined experiment yields similar contribution to the intensity response.

Citation: Journal of the Atmospheric Sciences 80, 4; 10.1175/JAS-D-22-0156.1

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Finally, we identify the dominant forcing for driving the responses in ${\tilde{\upsilon }}_m(\tau )$ and ${\tilde{r}}_{34\text{kt}}(\tau )$ in our combined experiments by comparing the combined experiments to individual-forcing experiments. Overall, the outer size responses in the combined experiment and the analogous roughening-only experiment with identical C_d are similar from τ = 0 to 12 h, during which size and intensity change most strongly, before deviating thereafter (Fig. 7, red and gray dots). This consistency suggests that the size response is primarily dominated by surface roughening, regardless of its magnitude or the concurrent magnitude of drying. This is consistent with the findings of CC20 that size does not feel the effects of surface drying in the first 12 h, whereas size responds immediately to surface roughening. However, for experiments with relatively weaker surface roughening (0.7ϵ2C_d, 0.5ϵ2C_d, 0.1ϵ2C_d, and 0.25ϵ4C_d as shown in Figs. 7a,c,e,f), surface drying imposes an impact on the intensity–size relationship primarily during an early stage (τ = 6–12 h) and final stage (τ > 36 h). In early stage, ${\tilde{\upsilon }}_m(\tau )$ decreases more than the ${\tilde{r}}_{34\text{kt}}(\tau )$ in these combined experiments compared to the roughening-only experiments. In the final stage after the storm has already weakened considerably, ${\tilde{\upsilon }}_m(\tau )$ and ${\tilde{r}}_{34\text{kt}}(\tau )$ in combined experiments decreases more than the corresponding roughening-only experiments before reaching the equilibrium.

To summarize, r_34kt(τ) scales quite closely with υ_m(τ) for mature storms in response to idealized landfall, especially for a rougher land surface. For drying-only and weaker-roughening cases, the theory fits a bit less well due to slower shrinking than weakening during the first 24 h before shrinking accelerates. These findings provide some evidence for our hypothesis that the equilibrium size length scale on the f plane becomes important for the dynamics of the transition to land. Testing the role of β lies beyond the scope of this work. The above results suggest that a viable simple prediction of the storm outer size for any combination of surface drying and roughening magnitudes can be made if given an estimate of the intensity response [Eq. (10)]. In the real world, C_d of the land surface is typically much more than 4 times higher than the ocean surface [C_d is calculated from Eq. (13) in Hersbach (2010) using the ERA5 surface roughness length data]. Thus, with such strong roughening, the theoretical r_34kt(τ) prediction may be directly applicable to real-world landfalls too.

All our results taken together suggest the potential to predict the complete wind field evolution to idealized landfall if given the intensity response. We explore this avenue next.

c. A model for the wind field in idealized landfalls

Finally, we combine the findings for modeling structure and size in this work to predict the responses of the near-surface wind field and compare them against our subsets of combined-forcing landfall experiments.

We model the wind field using the C15 model with inputs as described above, which requires the temporal evolution of intensity and size. To first focus on evaluating our predictions for size and structure, here we take the simulated intensity evolution υ_m(τ) to serve as a “perfect” intensity model. We predict the outer size response ${\tilde{r}}_{34\text{kt}}(\tau )$ by assuming it scales directly with ${\tilde{\upsilon }}_m(\tau )$ as in Eq. (7). Theory is compared to the simulation for each experiment at τ = 6 h (Figs. 8a,c) and 24 h (Figs. 8b,d). For the latter, experiments 0.1ϵ8C_d, 0.7ϵ10C_d, 0V_p6C_d, 0V_p8C_d, and 0V_p10C_d are excluded at τ = 24 h since their corresponding intensity quickly decreases below 34 kt (Figs. 8b,d).

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Comparison of the simulated wind field of combined-forcing landfall experiments (solid) and the corresponding theoretical prediction (dashed) at (a),(c) τ = 6 h and (b),(d) τ = 24 h. The theoretical prediction applies the simulated intensity response υ_m(τ) and the corresponding size prediction r_34kt(τ) [Eq. (7)] in the C15 model. Experiments with stronger surface modifications decay too fast to produce the input υ_m and r_34kt for C15 model at τ = 24 h; thus, those experiments (0.1ϵ8C_d, 0.7ϵ10C_d and 0V_p6C_d, 0V_p8C_d, 0V_p10C_d) are not shown in (b) and (d).

Citation: Journal of the Atmospheric Sciences 80, 4; 10.1175/JAS-D-22-0156.1

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Overall, the wind field model prediction performs reasonably well in capturing the simulated wind field response across all experiments. The prediction of r_m itself is imperfect, especially for experiments with weak surface roughening (Fig. 8), since the model begins with the low bias in r_m from CTRL. For weak roughening (Figs. 8b,d), as υ_m decreases toward 34 kt, the model more strongly underestimates the simulated r_m. For strong roughening, though, (Figs. 8a,c) this inner-core bias tends to decrease with time.

Here we have used the simulated intensity evolution directly, but this evolution could also be predicted via a statistical model such as Jing and Lin (2019), a numerical weather prediction model forecast, or a theory-based model such as that proposed in CC21. We also tested this simple wind field model using the intensity model of CC21 ${\upsilon }_{\text{th}}^{*}(\tau )$ introduced in CC21 [Eqs. (14) and (15) therein] and its corresponding size estimation $r_{\text{th}}^{*}$ via Eq. (10) (supplementary Fig. 2). This approach also works reasonably well, though it still requires specification of the boundary layer depth parameter, which is poorly constrained as described in CC21. Hence, we have focused here on taking the intensity evolution as known in order to focus on evaluating our predictions for size and structure. In practice, an intensity model would be required to make a true prediction.

To summarize, given the TC intensity and r_34kt prior to landfall and knowledge of the idealized land surface conditions, one can predict the first-order postlandfall wind field evolution. Notably, in contrast to the intensity decay model of CC21, which depends on a poorly understood boundary layer height parameter, the size and structure results presented here do not depend on any free parameters and hence are expected to apply generally. This simple model may serve as a foundation for a model to predict the wind field response to landfall that further incorporates the many additional complexities associated with real-world landfalls.