Estimates of tropical cyclone geometry parameters based on best-track data

Abstract

Parametric wind profiles are commonly applied in a number of engineering applications for the generation of tropical cyclone (TC) wind and pressure fields. Nevertheless, existing formulations for computing wind fields often lack the required accuracy when the TC geometry is not known. This may affect the accuracy of the computed impacts generated by these winds. In this paper, empirical stochastic relationships are derived to describe two important parameters affecting the TC geometry: radius of maximum winds (RMW) and the radius of gale-force winds ($\mathrm{\Delta }$AR35). These relationships are formulated using best-track data (BTD) for all seven ocean basins (Atlantic; S, NW, and NE Pacific; and N, SW, and SE Indian oceans). This makes it possible to (a) estimate RMW and $\mathrm{\Delta }$AR35 when these properties are not known and (b) generate improved parametric wind fields for all oceanic basins. Validation results show how the proposed relationships allow the TC geometry to be represented with higher accuracy than when using relationships available from literature. Outer wind speeds can be reproduced well by the commonly used Holland wind profile when calibrated using information either from best-track data or from the proposed relationships. The scripts to compute the TC geometry and the outer wind speed are freely available via the following URL: https://bit.ly/2k9py1J (last access: October 2019).

1 Introduction

Tropical cyclones (TCs) are among the most destructive natural hazards worldwide. TCs can cause hazardous weather conditions including extreme rainfall and wind speeds, leading to coastal hazards, such as extreme storm surge levels and wave conditions. The impacts of TCs are different in developed and developing countries. Generally, the worst effects in the developed world are direct economic losses. In the United States (US) alone, the mean annual damage due to TCs was estimated by Willoughby (2012) as USD 11.0 billion (year 2015). In the developing world, TCs result in immense social costs in terms of destruction and mortality. For example, between 1960 and 2004 more than half a million inhabitants of Bangladesh died as a consequence of TCs, primarily due to storm surges (Shultz et al., 2005). Peduzzi et al. (2012) showed that over the next 20 years the number of people exposed to TC risk will increase despite governmental efforts and implementation of adaptation measures. Additionally, TCs can also have devastating effects on nature, geomorphology, agriculture and freshwater supply. Thus, due to the extensive costs in lives, property and other damage, the ability to effectively model these storms is essential.

Numerical models can be applied to quantify the effects of TCs (e.g., Bloemendaal et al., 2018; Giardino et al., 2018; Vousdoukas et al., 2018). In hindcasting studies, this is generally done by using surface winds derived through data assimilation techniques (e.g., HRD Real-time Hurricane Wind Analysis System or H${}^{*}$WIND; e.g., Powell et al. 1998). However, in multi-hazard risk assessments, the spatial distribution of surface winds is generally not known. Therefore, wind fields based on best-track data (BTD) or synthetic tracks are generated using parametric wind profiles. Several (horizontal) parametric wind profiles (e.g., Fujita, 1952; Willoughby et al., 2006; Chavas et al., 2015) exist in literature, with the original Holland wind profile (Holland, 1980; hereafter H80) being the most widely used due to its relative simplicity. However, without calibration, parametric wind profiles are often unable to accurately reproduce the spatial distribution of winds in TCs (e.g., Willoughby and Rahn, 2004). This potentially leads to an under- or overestimation of wind speeds and associated coastal hazards. Calibration of TC formulations is possible by applying additional relationships, supported by the use of suitable data. In particular, information on the wind radii of cyclones can constrain the decay of wind speeds away from the eye wall and can be included in the most recent version of the Holland wind profile formulation (Holland et al., 2010; hereafter H10).

The radius of maximum winds (RMW), which describes the distance from the center to the strongest axially symmetric wind in the core of the cyclone, is one of the most important parameters to define a parametric wind profile. Moreover, the RMW plays an important role in the assessment of hazards induced by TCs since the storm surge level increases as a function of the RMW (Loder et al., 2009). Several relationships exist in literature to estimate the RMW (e.g., Willoughby et al., 2006; Vickery and Wadhera, 2008; Knaff et al., 2015). However, these relationships are derived for either the Atlantic or eastern Pacific Ocean (i.e., US coast) and are therefore not necessarily valid for other ocean basins. Each ocean basin has its own climatological properties and, for example, there seems to be an observational relationship between (mean) storm size, in terms of precipitation area (Lin et al., 2015) or wind speeds (Chavas et al., 2016), and the relative sea surface temperature (SST). The reason that most relationships are derived for the US coast is because of the high-quality data available (i.e., aircraft reconnaissance data). Relationships that estimate wind radii at different wind speeds are scarcer. Knaff et al. (2007) explicitly describe the TC surface winds using a modified Rankine vortex, which also makes it possible to compute different wind radii corresponding to different wind speeds (i.e., 34, 50, 64, 100 kn). However, these results are derived from BTD of the Atlantic, northeast Pacific and northwest Pacific oceans.

In the last decades, a large amount of higher-quality data have become available, which can be used to improve and validate the relationships and parametric wind profiles found in literature. In addition to the RMW, the wind radii of 35 (or 34), 50, 65 (or 64) and 100 kn (hereafter referred to as R35, R50, R65, R100) for the four geographical quadrants around the cyclone are currently recorded (see also Fig. 1a). There are numerous sources that can provide information on the spatial distribution of surface winds ranging from in situ observations (e.g., surface reports and buoy observations) to scatterometry (e.g., QuikSCAT; see Chavas and Vigh, 2014). Some methods are more reliable than others, but a posteriori it is not clear which sources were used for individual wind radii estimates in the best-track data (BTD). However, the currently operationally available satellite-based wind radii estimates are characterized by higher accuracy than in the past (Sampson et al., 2017).

2 Data

2.1 Best-track data (BTD)

Two data sources were used to describe the RMW and R35: data from the North Atlantic and Northeast and North Central Pacific database from the National Hurricane Center (NHC) and the dataset from the Joint Typhoon Warning Center (JTWC). The second dataset includes data from different ocean basins (northwest Pacific Ocean, the South Pacific Ocean and Indian Ocean). Note that the estimation of wind radii is rather subjective and strongly dependent on data availability as well as different climatology and analysis methods (e.g., aircraft observations versus the Dvorak method). In this paper, all the available data were used and potential shortcomings in the data are disregarded in order to fit new empirical stochastic relationships with the largest possible dataset and for every ocean basin separately. This approach, with its advantages and disadvantages, is discussed in Sect. 5.1. Some of the historical records do not contain values for either the RMW or R35, and therefore these records are discarded. Although these BTD are used as the ground truth, the errors in the best-track wind radii are estimated to be as high as 10 %–40 % (e.g., Knaff and Sampson, 2015). The accuracy of a single record depends on the quality and quantity of the available observational data. For example, if in situ observations were available in proximity to the TC or if a complete scatterometer passed over the TC, the accuracy may increase. However, information on the accuracy is not available per single data entry.

The archives from the NHC and JTWC contain 6-hourly storm positions and maximum intensity estimates of tropical and subtropical systems. For this analysis, all data points with a wind speed of 20 m s${}^{-\mathrm{1}}$ or higher were included in the study since the focus is on tropical storms. Moreover, it is expected that parametric wind profiles cannot capture subtropical systems. Also, data points with an RMW larger than 100 km were excluded from the analysis because, generally, those points refer to tropical depressions, with large spatial coverage, which are outside the scope of this study. Moreover, the averaged value of R35 ($\stackrel{\mathrm{‾}}{R\mathrm{35}}$) over the four quadrants, similarly to Carrasco et al. (2014), was used. Only data entries with an estimate of R35 for all four quadrants were used. Therefore, all data entries additionally have an estimate for both RMW and $\stackrel{\mathrm{‾}}{R\mathrm{35}}$, and using all the 6-hourly storm positions and maximum intensity estimates in the calibration and validation assumes statistical independence.

In this paper, TC geometry variables RMW and R35 were treated as stochastic variables. This means that, although physically not realistic, RMW could assume larger values than R35. In order to overcome this, a new variable was defined: the average difference in radius of 35 kn ($\mathrm{\Delta }$AR35; similar to Xu and Wang, 2015), or radius of gale-force winds, describing the difference between the RMW and the average radius of 35 kn (AR35); see Eq. (1). In practical applications, one would first retrieve the RMW based on data or estimate the RMW based on an empirical relationship. Secondly, the R35 would be calculated by adding up the RMW with the $\mathrm{\Delta }$AR35 (see also Fig. 1b). An additional advantage of introducing this new variable is that $\mathrm{\Delta }$AR35 contains considerably less scatter. This might imply a correlation between R35 and RMW, but is not further explored in this paper.

1

Observed maximum sustained wind speeds and definition of the different ocean basins (a). The observed radius of maximum winds (b) and observed radius of gale-force winds (c) for all the BTD.

[Figure omitted. See PDF]

2.4 Data conversion

Data were converted to the International System of Units (SI) units (wind speeds in meters per second from knots with a conversion of 1 kn $=$ 0.514 m s${}^{-\mathrm{1}}$ and wind radii in kilometers from nautical mile with a conversion of 1 nm $=$ 1.852 km). Throughout this study, a maximum sustained cyclone wind $v_{\max }$ has been determined at a 10 m elevation over open sea and 1 min average. The reason for this averaging is to be consistent with the JTWC and NHC, which also report the maximum sustained surface winds in terms of 1 min mean wind speed. Other nations, however, report maximum sustained surface winds averaged over a different time interval, which in some cases is 10 min. Also, numerical models often require 10 min averaged winds. For the conversion of 1 to 10 min averaged wind speed, a conversion factor equal to 0.93 can be used, based on WMO guidelines (Harper et al., 2010). However, in this study, conversions between 1 and 10 min wind speeds were not needed.

3 New empirical relationships

In this section, empirical relationships to estimate the radius of maximum winds (RMW; Sect. 3.1; see Fig. 2b) and the radius of gale-force winds ($\mathrm{\Delta }$AR35; Sect. 3.2; see Fig. 2c) were derived based on BTD from the calibration period (2000–2014).

3.1 Radius of maximum winds (RMW)

The Vickery and Wadhera (2008) relationship, derived for all major hurricanes ($\mathrm{\Delta }{p}_{\mathrm{c}}>\mathrm{30}$ hPa or $v_{\max }>\mathrm{35}$ m s${}^{-\mathrm{1}}$) in the Gulf of Mexico and Atlantic Ocean (hereafter VW08), is one of the several relationships in literature providing an estimate of the RMW. VW08, derived based on H${}^{*}$WIND data, relates RMW to pressure drop in the eye and latitude. While we acknowledge the existence of several other relationships to estimate the RMW, VW08 was used due to its relative simplicity. Figure 3 compares RMW data from the BTD during the calibration period with results from VW08 in the form of a scatter plot with the maximum sustained wind speed ($v_{\max }$) indicated by color intensity. The data show a large amount of scatter, for both lower and higher RMW values. However, there is a clear pattern visible that larger maximum sustained wind speeds result in a smaller RMW. This is in line with other observations (e.g., Willoughby and Rahn, 2004) or based upon idealized Sawyer–Eliassen models (e.g., Schubert and Hack, 1982; Willoughby et al., 1982) that TC eye walls generally contract during intensification. There is also a tendency in the dataset for TCs at higher latitudes to have larger eye diameters (e.g., Knaff et al., 2015; not shown here). The large negative bias of 17 km, computed as a difference between observed and computed RMW, is noteworthy, indicating that VW08 often underestimates the RMW, especially for lower maximum sustained wind speeds. Furthermore, the root-mean-square deviation (RMSD) of almost 29 km is also large compared to the observed mean. In particular, the scatter index (RMSD divided by the mean) and relative bias (bias divided by the mean) result in a scatter index of 53 % and a relative bias of $-\mathrm{32}$ %.

2

Fitting coefficients for the lognormal RMW as described in Eq. (2).

[Figure omitted. See PDF]

3.2

Radius of gale-force winds ($\mathrm{\Delta }$AR35)

By applying a parametric wind profile, it is possible to derive the $\mathrm{\Delta }$AR35. Here, the H10 wind profile was applied, in which the $B$ parameter was computed based on H80 (Eq. 3a), and in which information on the wind radii of cyclones was used to constrain the decay of wind speeds away from the eye wall (Eq. 3b). When no additional information on the wind radii is provided, H10 reduces to the original H80 wind profile, which is often unable to accurately reproduce the spatial distribution of winds in TCs (e.g., Willoughby and Rahn, 2004). $$\begin{array}{}\text{3a}& {\displaystyle }& {\displaystyle }B={\displaystyle \frac{v_{\max }^{\mathrm{2}}{\mathit{\rho }}_{\mathrm{a}}e}{\mathrm{100}\left(\mathrm{\Delta }{p}_{\mathrm{c}}\right)}}\text{3b}& {\displaystyle }& {\displaystyle }x=\mathrm{0.5}+(r-\mathrm{RMW}){\displaystyle \frac{x_n-\mathrm{0.5}}{r_n-\mathrm{RMW}}}\end{array}$$ Here $B$ represents the Holland pressure profile parameter, ${\mathit{\rho }}_{\mathrm{a}}$ is the air density (assumed constant at 1.15 kg m${}^{-\mathrm{3}}$), $e$ is the base of natural logarithms, $\mathrm{\Delta }{p}_{\mathrm{c}}$ is the pressure drop in the core of the TC in hectopascals, $x$ is the exponent used to compute the wind profile in H80–H10 and $x_n$ represents the adjusted exponent to fit the peripheral observations at radius $r_n$.

Knaff et al. (2007) relationships (hereafter CLIPER, climatology and persistence models), derived for the NAO, NWPO and NEPO, are among the few in literature providing an estimate of the TC surface winds. Knaff et al. (2007) fitted a modified Rankine vortex on the BTD of NHC and JTWC, which also makes it possible to retrieve the $\mathrm{\Delta }$AR35. Figure 5 compares $\mathrm{\Delta }$AR35 from the BTD, derived from the calibration period, with results from CLIPER, in which $v_{\max }$ is indicated by color intensity in the scatter plot. The data show a large amount of scatter and bias with a computed scatter index of 67 % and a relative bias of $-\mathrm{18}$ %. However, there is a clear pattern showing that larger maximum sustained wind speeds result in a larger $\mathrm{\Delta }$AR35. There is also a tendency in the dataset for TCs at higher latitudes to have a larger $\mathrm{\Delta }$AR35 (not shown here).

Figure 5

Scatter plot describing BTD $\mathrm{\Delta }$AR35 ($x$ axis) versus computed $\mathrm{\Delta }$AR35 based on CLIPER ($y$ axis). Data points are colored-coded based on the maximum sustained wind speeds in the BTD. The dashed line represents a perfect fit between the BTD and the computed data based on CLIPER.

[Figure omitted. See PDF]

In order to improve the estimate of the $\mathrm{\Delta }$AR35, generic relations were derived as part of this study based on BTD from the calibration period from all ocean basins, as well as data from each individual basin separately. The method followed is similar to the one applied to estimate RMW. First, a representative parent distribution of the data was sought, secondly the parameters of the PDF were determined, and thirdly the parameters of the PDF were fitted for a range of $v_{\max }$ and latitude values. The same parent distributions were tested and the lognormal distribution was again chosen as most representative, which is in line with Chavas et al. (2016).

Similarly to RMW, the BTD from the calibration period were divided based on a moving window with a bin width of 10 m s${}^{-\mathrm{1}}$ for wind speed (0–10, 1–11, 2–12, etc.) and 10${}^{\circ }$ for latitude. This led to Eq. (4) in which exponential functions, dependent on the wind speed per oceanic basin, were used to describe the location parameter and the shape parameter. Additionally, the analysis of the data showed that $\mathrm{\Delta }$AR35 is dependent on the latitude, with TCs generally increasing in size at higher latitudes. Adding additional parameters (e.g., storm duration or intensity change of the wind speed) resulted in very limited skill improvement for the estimate of $\mathrm{\Delta }$AR35. This procedure was applied to both the combined JTWC and NHC BTD from the calibration period of all basins, and for each individual ocean basin. Table 2 contains the values for the fitting parameters for the $\mathrm{\Delta }$AR35 of Eq. (4). 4$$\begin{array}{rl}& {\mathit{\sigma }}_{\mathrm{\Delta }\mathrm{AR}\mathrm{35}}=A_{\mathrm{3}}+e^{v_{\max }\cdot B_{\mathrm{3}}}\cdot \left(\mathrm{1}+C_{\mathrm{3}}\left|\mathit{\theta }\right|\right)\\ & {\mathit{\mu }}_{\mathrm{\Delta }\mathrm{AR}\mathrm{35}}=A_{\mathrm{4}}\cdot {\left(v_{\max }-\mathrm{18}\right)}^{B_{\mathrm{4}}}\cdot \left(\mathrm{1}+C_{\mathrm{4}}\left|\mathit{\theta }\right|\right)\end{array}$$ Here ${\mathit{\mu }}_{\mathrm{\Delta }\mathrm{AR}\mathrm{35}}$ and ${\mathit{\sigma }}_{\mathrm{\Delta }\mathrm{AR}\mathrm{35}}$ represent, respectively, the location and shape parameter of the lognormal distribution for $\mathrm{\Delta }$AR35, and $A_{\mathrm{3}}$, $A_{\mathrm{4}}$, $B_{\mathrm{3}}$, $B_{\mathrm{4}}$, $C_{\mathrm{3}}$ and $C_{\mathrm{4}}$ are fitting coefficients.

Table 2

Fitting coefficients for the lognormal $\mathrm{\Delta }$AR35 as described in Eq. (4).

	Shape ($\mathit{\sigma }$)				Location ($\mathit{\mu }$)
Basin	$A_{\mathrm{3}}$	$B_{\mathrm{3}}$	$C_{\mathrm{3}}$		$A_{\mathrm{4}}$	$B_{\mathrm{4}}$	$C_{\mathrm{4}}$	Count
NIO	0.1215	$-\mathrm{0.0522}$	0.0329		30.93	0.531	$-\mathrm{0.012}$	480
SWIO	0.1312	$-\mathrm{0.0444}$	0.0023		30.21	0.415	0.022	1889
SEIO	0.1223	$-\mathrm{0.0454}$	0.0133		26.59	0.426	0.029	832
SPO	0.1205	$-\mathrm{0.0350}$	$-\mathrm{0.0052}$		23.88	0.431	0.038	1118
NWPO	0.1561	$-\mathrm{0.0417}$	0.0050		33.27	0.429	0.017	4836
NEPO	$-\mathrm{0.2513}$	$-\mathrm{0.0091}$	$-\mathrm{0.0051}$		18.11	0.486	0.030	2570
AO	0.1319	$-\mathrm{0.0421}$	0.0124		17.00	0.454	0.055	3075
All	0.1900	$-\mathrm{0.0446}$	0.0061		29.61	0.413	0.024	14 800

A scatter plot describing the $\mathrm{\Delta }$AR35 derived from BTD as a function of the $v_{\max }$ and latitude and computed according to Eq. (4) is shown in Fig. 6. The green line shows the median $\mathrm{\Delta }$AR35 based on the BTD, whereas the solid blue line represents the mean $\mathrm{\Delta }$AR35 obtained from Eq. (4). The black lines indicate the 5 % and 95 % exceedance values computed based on BTD. Finally, the 90 % prediction interval is shown using a filled red color. The figure shows how the median $\mathrm{\Delta }$AR35 increases as a function of $v_{\max }$ while the variance stays fairly constant. The new empirical equation for $\mathrm{\Delta }$AR35 is evaluated in the next section.

Figure 6

Scatter plot describing $\mathrm{\Delta }$AR35 (BTD and computed, $y$ axis) as a function of the maximum sustained wind speeds ($x$ axis; and the latitude; not shown). The blue line is the median of the proposed relationship derived for all basins at an arbitrarily chosen latitude of 10${}^{\circ }$. The green line is the median of the BTD. The red area shows the 90 % prediction interval based on the proposed relationship for the standard deviation. The 5 % and 95 % exceedance values from the BTD are presented as black solid lines. The gray dots are observation points in which more frequent observations are shown as darker points and less frequent observations as lighter points.

[Figure omitted. See PDF]

4 Validation

In this section, empirical relationships to estimate the RMW and $\mathrm{\Delta }$AR35 were validated based on BTD from the validation period (2015–2017) (Sect. 4.1). Moreover, the outer wind profile based on the Holland wind profile, in combination with observed wind radii, were further validated using the QSCAT-R database (Sect. 4.2).

4.1 Wind radii

A subset of the BTD (from 2015 to 2017) was used to validate the wind radii. Error statistics are summarized in Table 3. The values indicate that, for all basins combined, the RMSD between the BTD and the proposed relations for the RMW is 17 % lower than compared to VW08 (RMSD of 18 km compared to 21 km). In the NEPO basin, VW08 performs relatively better than at other basins. When comparing the performance of the proposed relations and VW08, it is important to note that the relation of VW08 was derived for storms with central pressures lower than 980 hPa, thereby explicitly focusing on the most severe TCs. When the data were filtered to include only data points with a pressure drop ($\mathrm{\Delta }{p}_{\mathrm{c}}$) larger than 30 hPa, the RMSD decreases and differences become much smaller (0 %–10 % decrease in RMSD). Moreover, the bias also decreases.

Table 3

Root-mean-square difference (RMSD; first number) and bias (second number) for RMW in kilometers for the validation period for both the proposed relationships as for VW08. Statistics are presented for all data points, as well for data points with a pressure drop ($\mathrm{\Delta }{p}_{\mathrm{c}}$) larger than 30 hPa.

Basin	Proposed	VW08	Proposed,	VW08,	Count	Count
	all	all	$\mathrm{\Delta }{p}_{\mathrm{c}}>\mathrm{30}$	$\mathrm{\Delta }{p}_{\mathrm{c}}>\mathrm{30}$	all	$\mathrm{\Delta }{p}_{\mathrm{c}}>\mathrm{30}$
NIO	$\mathrm{20.9}/-\mathrm{14.2}$	$\mathrm{25.3}/-\mathrm{17.7}$	$\mathrm{14.0}/-\mathrm{4.5}$	$\mathrm{14.1}/-\mathrm{2.5}$	146	46
SWIO	$\mathrm{16.8}/-\mathrm{7.0}$	$\mathrm{20.0}/-\mathrm{8.6}$	$\mathrm{10.4}/-\mathrm{0.2}$	$\mathrm{9.8}/\mathrm{0.3}$	365	166
SEIO	$\mathrm{17.9}/-\mathrm{10.7}$	$\mathrm{24.0}/-\mathrm{14.0}$	$\mathrm{9.6}/-\mathrm{1.6}$	$\mathrm{10.9}/\mathrm{4.9}$	107	34
SPO	$\mathrm{18.1}/-\mathrm{9.1}$	$\mathrm{22.1}/-\mathrm{10.1}$	$\mathrm{12.9}/-\mathrm{3.0}$	$\mathrm{12.7}/\mathrm{1.5}$	424	184
NWPO	$\mathrm{17.2}/-\mathrm{6.4}$	$\mathrm{22.4}/-\mathrm{5.5}$	$\mathrm{12.1}/-\mathrm{0.3}$	$\mathrm{14.7}/\mathrm{4.6}$	1389	742
NEPO	$\mathrm{16.9}/-\mathrm{8.4}$	$\mathrm{17.5}/-\mathrm{6.7}$	$\mathrm{13.1}/-\mathrm{4.8}$	$\mathrm{11.6}/-\mathrm{1.2}$	1031	311
AO	$\mathrm{21.0}/-\mathrm{8.7}$	$\mathrm{21.5}/-\mathrm{0.8}$	$\mathrm{17.2}/-\mathrm{4.1}$	$\mathrm{18.2}/\mathrm{8.1}$	641	291
All	$\mathrm{18.0}/-\mathrm{7.1}$	$\mathrm{21.0}/-\mathrm{6.5}$	$\mathrm{13.1}/-\mathrm{1.6}$	$\mathrm{14.2}/\mathrm{3.3}$	4103	1774

Table 4 shows the error statistics related to the estimation of $\mathrm{\Delta }$AR35. In particular, the RMSD between the proposed relations and the BTD for all basins combined is 25 % lower compared to CLIPER (RMSD of 74 km compared to 94 km) and there is a negative bias ranging between 9 and 37 km. Remarkably, the deviations of the $\mathrm{\Delta }$AR35 based on BTD in the NIO and SEIO from CLIPER are significantly smaller compared to the differences for the AO for which CLIPER was derived. When the H10 wind profile is applied without additional information to compute the decay of wind speeds away from the eye wall (H80), the $\mathrm{\Delta }$AR35 is strongly overestimated (overall bias of 177 km).

Table 4

Root-mean-square difference (RMSD; first number) and bias (second number) for $\mathrm{\Delta }$AR35 in kilometers for the validation period for the proposed relationships, CLIPER (Knaff et al., 2015) and the H80 wind profile.

Basin	Proposed	CLIPER	H80	Count
NIO	$\mathrm{48.0}/-\mathrm{17.5}$	$\mathrm{51.0}/\mathrm{3.3}$	$\mathrm{275.2}/\mathrm{221.9}$	146
SWIO	$\mathrm{68.9}/-\mathrm{31.4}$	$\mathrm{123.1}/-\mathrm{95.3}$	$\mathrm{248.4}/\mathrm{190.9}$	365
SEIO	$\mathrm{37.2}/-\mathrm{9.0}$	$\mathrm{69.0}/-\mathrm{58.3}$	$\mathrm{238.8}/\mathrm{187.7}$	107
SPO	$\mathrm{59.6}/-\mathrm{16.3}$	$\mathrm{104}/-\mathrm{74.7}$	$\mathrm{267.2}/\mathrm{214.1}$	424
NWPO	$\mathrm{83.8}/-\mathrm{37.3}$	$\mathrm{95.0}/-\mathrm{25.6}$	$\mathrm{294.2}/\mathrm{198.8}$	1389
NEPO	$\mathrm{47.4}/-\mathrm{10.3}$	$\mathrm{86.4}/\mathrm{68.7}$	$\mathrm{125.4}/\mathrm{59.3}$	1031
AO	$\mathrm{90.0}/-\mathrm{26.0}$	$\mathrm{116.8}/\mathrm{7.1}$	$\mathrm{552.7}/\mathrm{252.4}$	641
All	$\mathrm{74.1}/-\mathrm{23.3}$	$\mathrm{94.2}/-\mathrm{13.9}$	$\mathrm{316.8}/\mathrm{177.0}$	4103

4.2 Outer wind speeds

The QSCAT-R database was used to validate the computed (outer) azimuthal wind speeds while using the H10 wind profile in combination with several sources to constrain the decay of wind speeds. QuikSCAT includes 690 unique tropical cyclones and is known to provide reliable results for outer wind speeds of lower intensity. Figure 7 displays the error profile, representing the difference between modeled wind speed and measured data based on QuikSCAT, as a function of the normalized radius. This means that for all validated TCs the radius on the $x$ axis is divided by the RMW. A horizontal line equal to zero indicates no difference between modeled and measured wind speed data, while the solid colored lines represent the median difference. The filled area indicates the interquartile range (IQR).

Table 5

Root-mean-square difference (RMSD) and bias (m s${}^{-\mathrm{1}}$) between modeled and measured azimuthally averaged wind speeds based on QSCAT-R data. The data analyzed in the table refer to all TCs with wind speeds between 40 and 5 m s${}^{-\mathrm{1}}$ and a normalized radius between 3 and 16. Statistics are shown for median values (50 %) and the IQR range (25 %–75 %). With “H10: observed” the authors refer to the Holland et al. (2010) wind profile in combination with the RMW and AR35 from the BTD.

[Figure omitted. See PDF]

6 Conclusions

In this paper, new empirical relationships are derived which estimate tropical cyclone (TC) geometry with simple and generic equations and with higher accuracy with respect to other well-known empirical relationships available from literature. Those new relationships are valid for any ocean basin (Atlantic; S, NW, and NE Pacific; N, SE, and SW Indian oceans). Moreover, the new relationships include a stochastic description for both the radius of maximum winds (RMW) and the radius of gale-force winds ($\mathrm{\Delta }$AR35). This allows the quantification of the prediction interval around the median estimates, making the estimation more useful.

According to the derived relationships, the RMW is described as a function of the maximum sustained wind speeds and latitude. The radius of gale-force winds is estimated using a newly introduced $\mathrm{\Delta }$AR35 parameter (average difference between radius of 35 kn and radius of maximum wind), and is also dependent on the maximum sustained winds and latitude. Both parameters are fit through simple exponential functions. Compared to best-track data, the proposed relationships improve the estimation of RMW and $\mathrm{\Delta }$AR35 by reducing the root-mean-square difference (RMSD) up to 25 %. Larger improvements were found in particular for non-US TCs since most of the existing relationships are based on data from the Atlantic Ocean, northeastern Pacific Ocean and/or northwestern Pacific Ocean.

The new relationships, in combination with the Holland wind profile, were validated using a subset of the BTD and (outer) azimuthal wind speeds from the QSCAT-R database. The results showed that (outer) azimuthal wind speeds of the TC can be reproduced with the H10 wind profile when using either the BTD (“observed”) for RMW and $\mathrm{\Delta }$AR35 or the relationships derived in this paper. When no additional information on wind radii was used to calibrate the H10 wind profile, which is generally done when the radius of gale-force wind is not known, surface wind speeds were overestimated.

The derived empirical relationships can be used in a variety of applications. For example, a better estimate of TC pressure and surface wind speeds for Monte Carlo analysis with synthetic tracks for risk assessments with numerical models can result in a more accurate description of wave and surge conditions resulting from the TC. As a result, this can lead to a better quantification of coastal hazards, and consequent risks and damages. Similarly, an improved assessment of those hazards can help the design of appropriate adaptation measures. Other fields of application may vary from improved design parameters for offshore structures to navigation. The application of the new empirical relationships will be presented as part of a separate paper currently under preparation.

Code and data availability

The best-track data (BTD) are freely available and collected from the National Hurricane Center (NHC) and the Joint Typhoon Warning Center (JTWC). Upon request this combined dataset can be shared with other researchers. Moreover, the QSCAT-R (open) database (10.5065/D6J67DZ4) (Chavas and Vigh, 2014), with data for the period 1999–2008, was used to validate the computed outer winds. The MATLAB script to compute the tropical cyclone geometry is freely available via the following URL: https://bit.ly/2k9py1J (last access: October 2019).

Author contributions

KN and MvO analyzed the data and developed the MATLAB code for computing (stochastic) tropical cyclone geometry. AG and DV provided the idea and wrote the paper.

Competing interests

The authors declare that they have no conflict of interest.

Acknowledgements

The authors thank the Deltares research program “Hydro- and morphodynamics during extreme events” and “Enabling Technologies”, which provided financing to write this paper. Final thanks are due to Stuart Pearson for proofreading a previous version of the article and providing valuable comments, which have led to an improved paper.

Financial support

This research has been supported by the Deltares research programs (Extreme hydro and morphodynamic events and Enabling Technologies).

Review statement

This paper was edited by Gregor C. Leckebusch and reviewed by two anonymous referees.