Correction to: The generalized Ekman model for the tropical cyclone boundary layer revisited,Quarterly Journal of the Royal Meteorological Society

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Correction to: The generalized Ekman model for the tropical cyclone boundary layer revisited
Quarterly Journal of the Royal Meteorological Society ( IF 8.9 ) Pub Date : 2021-03-04 , DOI: 10.1002/qj.3999

In the published version of the recent article by Smith and Montgomery (2020), there was a coding error in plotting the vertical velocity field shown in Figures 2e,f. Most of the differences are small except for the area of subsidence in part 2e, which is not present in the corrected figure. The coding error led also to minor errors in plotting the nonlinear and total acceleration terms in Figures 4c–f,i–l and 5c–j. The corrected figures and captions are shown below.

QJ-3999-FIG-0001-c — **FIGURE 2**
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Isotachs of (a), (b) radial velocity u, (c), (d) tangential velocity v and (e), (f) vertical velocity w in the r − z plane obtained by solving Equations (3) and (4) with the two tangential wind profiles shown in Figure 1. Left columns are for the wind profile with x = 1.6, right columns with x = 2.3. Contour intervals: for u, 2 m·s⁻¹ for negative values (blue contours) and 0.05 m·s⁻¹ for positive values (thin red contours); for v, 5 m·s⁻¹ for values <50 m·s⁻¹ (red contours) and 0.5 m·s⁻¹ for values >50 m·s⁻¹ (thin blue contours); for w > 0; 0.02 m·s⁻¹ for the broad profile or 0.05 m·s⁻¹ for the narrow profile (red contours); for w < 0, 0.01 m·s⁻¹ for the narrow profile (thin blue contours). (g), (h) show the corresponding radial variation of boundary‐layer scale depth, δ(r) (km) [Colour figure can be viewed at wileyonlinelibrary.com]

QJ-3999-FIG-0002-c — **FIGURE 4**
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Isopleths in the r–z plane of (a, b) linear radial acceleration −ξv′ in Equation (1), (c, d) nonlinear radial acceleration *u∂u*/∂r + *w∂u*/∂z − v′²/r, with the nonlinear term calculated from the linear solution to Equations (7) and (8), (e, f) total radial acceleration (linear + nonlinear) *u∂u*/∂r + *w∂u*/∂z − v′²/r − ξv′, (g, h) linear tangential acceleration ξ_au in Equation (2), and (i, j) nonlinear tangential acceleration *u∂v′*/∂r + *w∂v′*/∂z + *uv′*/r with the nonlinear term calculated from the linear solution to Equations (7) and (8), (k, l) total tangential acceleration (linear + nonlinear) *u∂v*′/∂r + *w∂v*′/∂z + uv′/r + ξ_au. The left column is for the tangential wind profile in Figure 1 with x = 1.6, and the right column for x = 2.3. Contour intervals for radial terms are 10 m· s⁻¹·hr⁻¹ (thick contours), 2 m·s⁻¹·hr⁻¹ (thin contours); for tangential terms are 2 m·s⁻¹·hr⁻¹ (thick contours), 0.5 m·s⁻¹·hr⁻¹ (thin contours). Positive values are red, solid, and negative values blue, dashed [Colour figure can be viewed at wileyonlinelibrary.com]

QJ-3999-FIG-0003-c — **FIGURE 5**
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(a–f) Isopleths in the r–z plane of the contributions to the nonlinear (left) radial and (right) tangential acceleration terms and the sum of these contribution in the calculation with K = 50 m²·s⁻¹. All terms are calculated from the linear solution. (a) Radial advection contribution including the perturbation centripetal acceleration, *u∂u*/∂r − v′²/r; (c) vertical advection contribution *w∂u*/∂z to (e) the nonlinear radial acceleration *u∂u*/∂r + *w∂u*/∂z − v′²/r; (d) radial advection contribution *u∂v′*/∂r + *uv′*/r; (e) vertical advection contribution *w∂v′*/∂z to (f) the nonlinear tangential acceleration *u∂v′*/∂r + *w∂v′*/∂z + *uv′*/r. (g) shows nonlinear radial acceleration and (h) nonlinear tangential acceleration based on the linear solution with K = 20 m²·s⁻¹. (i) shows nonlinear radial acceleration and (j) nonlinear tangential acceleration based on the linear solution with K = 90 m²·s⁻¹. Contour intervals: 10 m·s⁻¹·h⁻¹ (thick contours), 2 m·s⁻¹·h⁻¹ (thin contours). Positive values are red, solid and negative values blue, dashed [Colour figure can be viewed at wileyonlinelibrary.com]

In addition, the specification of the coefficients a₁ and a₂ in Equation 14 were incorrect. The corrected equation is as follows:

a_{1} = \frac{v (v + 1)}{2 v^{2} + 3 v + 2}, a_{2} = \frac{v}{2 v^{2} + 3 v + 2}

(14)

The incorrect specification was used for plotting parts c and d in Figure A1, which affected the magnitudes of the coefficients shown. The corrected figure is shown below.

QJ-3999-FIG-0004-c — **FIGURE A1**
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Radial variation of (a) v, (b) I², (c) a₁ and a₂. Curves for x = 1.6 are in red, for x = 2.3 in blue [Colour figure can be viewed at wileyonlinelibrary.com]

The overall conclusions of the article are not affected by the errors.

中文翻译：

更正为：重新讨论了热带气旋边界层的广义Ekman模型

在Smith和Montgomery（2020）最近发表的文章的出版版本中，在绘制图2e，f所示的垂直速度场时存在编码错误。除了第2e部分中的沉降面积（校正后的数字中未显示）以外，大多数差异很小。在图4c–f，i–l和5c–j中绘制非线性和总加速度项时，编码错误还导致较小的错误。校正后的数字和标题如下所示。