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  • View in gallery

    An example of the wind speed relationship from the parametric model in Eq. (2) with three different “b” parameters used; Vm.p = 50 m s−1, Rm.p = 75 km, and the center position latitude is 15°.

  • View in gallery

    A flow diagram that outlines the steps of the CYGNSS TC surface wind speed structure and intensity product algorithms.

  • View in gallery

    (a) HWRF wind speed field for Vongfong at 0300 UTC 9 Oct 2014, (b) simulated CYGNSS wind speed observations for (a), and (c) the parametric model algorithm fit for this test case.

  • View in gallery

    (a) HWRF wind speed field for Soulik at 0300 UTC 11 Jul 2013, (b) simulated CYGNSS wind speed observations for (a) with the NE quadrant (cornered off by red lines) currently being considered, and (c) the parametric model algorithm fit for this NE quadrant test case from which the NE quadrant wind radii are solved.

  • View in gallery

    Histograms of error, normalized to percentages, before QC is applied in all parametric and scaled-parametric metrics. Error is defined here as true − estimated.

  • View in gallery

    The additional error on average to expect from storm center offsets (here, only in latitude) for (a) VMAX and (b) RMAX.

  • View in gallery

    The additional error on average to expect from storm center offsets (here, only in latitude) for wind radii. This analysis is based on the cases available in the NE quadrant.

  • View in gallery

    (a) The RMSD between the HWRF- and CYGNSS-derived VMAX depending on the QC filter threshold used. The QC keeps test cases that have a number of observations within 100 km from the storm center above the sample number threshold plotted on the x axis. (b) As in (a), but for RMAX. (c) The fraction of the original test case estimates left that are used to derive the RMSD in (a) and (b).

  • View in gallery

    (a) The RMSD between the HWRF- and CYGNSS-derived wind radii depending on the QC applied. The QC keeps test cases that have a number of observations outside 100 km from the storm center (but within the estimate of R34) above the sample number threshold plotted on the x axis. (b) The fraction of the original test case estimates left that are used to derive the RMSD in (a).

  • View in gallery

    Histograms of error, normalized to percentages, in all parametric, scaled-parametric, and QCed scaled-parametric metrics. Error is defined here as true − estimated.

  • View in gallery

    Cumulative density function of number of s/c used to estimate VMAX and RMAX (solid black line) and wind radii (dashed blue line) for all test cases after QC has been applied.

  • View in gallery

    Histograms, normalized to show percentages, of the QCed scaled-parametric VMAX and RMAX depending on the HWRF VMAX threshold attained. Weaker storms (VMAX < 33 m s−1) are plotted in solid light blue. Stronger storms (VMAX ≥ 33 m s−1) are plotted in dashed dark red.

  • View in gallery

    Histograms, normalized to show percentages, of the QCed scaled-parametric metrics depending on the test case basin. Storms from the Atlantic and east Pacific basins are plotted in solid light green. Storms from the western Pacific basin are plotted in dashed dark blue.

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Determining Tropical Cyclone Surface Wind Speed Structure and Intensity with the CYGNSS Satellite Constellation

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  • 1 Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, Michigan
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Abstract

The Cyclone Global Navigation Satellite System (CYGNSS) consists of a constellation of eight microsatellites that provide observations of surface wind speed in all precipitating conditions. A method for estimating tropical cyclone (TC) metrics—maximum surface wind speed VMAX, radius of maximum surface wind speed RMAX, and wind radii (R64, R50, and R34)—from CYGNSS observations is developed and tested using simulated CYGNSS observations with realistic measurement errors. Using two inputs, 1) CYGNSS observations and 2) the storm center location, estimates of TC metrics are possible through the use of a parametric wind model algorithm that effectively interpolates between the available observations as a constraint on the assumed wind speed distribution. This methodology has a promising performance as evaluated from the simulations presented. In particular, after quality-control filters based on sampling properties are applied to the population of test cases, the standard deviation of retrieval error for VMAX is 4.3 m s−1 (where 1 m s−1 = 1.94 kt), for RMAX is 17.4 km, for R64 is 16.8 km, for R50 is 21.6 km, and for R34 is 41.3 km (where 1 km = 0.54 n mi). These TC data products will be available for the 2017 Atlantic Ocean hurricane season using on-orbit CYGNSS observations, but near-real-time operations are the subject of future work. Future work will also include calibration and validation of the algorithm once real CYGNSS data are available.

Current affiliation: Jet Propulsion Laboratory, Pasadena, California.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Mary Morris, mary.g.morris@jpl.nasa.gov

Abstract

The Cyclone Global Navigation Satellite System (CYGNSS) consists of a constellation of eight microsatellites that provide observations of surface wind speed in all precipitating conditions. A method for estimating tropical cyclone (TC) metrics—maximum surface wind speed VMAX, radius of maximum surface wind speed RMAX, and wind radii (R64, R50, and R34)—from CYGNSS observations is developed and tested using simulated CYGNSS observations with realistic measurement errors. Using two inputs, 1) CYGNSS observations and 2) the storm center location, estimates of TC metrics are possible through the use of a parametric wind model algorithm that effectively interpolates between the available observations as a constraint on the assumed wind speed distribution. This methodology has a promising performance as evaluated from the simulations presented. In particular, after quality-control filters based on sampling properties are applied to the population of test cases, the standard deviation of retrieval error for VMAX is 4.3 m s−1 (where 1 m s−1 = 1.94 kt), for RMAX is 17.4 km, for R64 is 16.8 km, for R50 is 21.6 km, and for R34 is 41.3 km (where 1 km = 0.54 n mi). These TC data products will be available for the 2017 Atlantic Ocean hurricane season using on-orbit CYGNSS observations, but near-real-time operations are the subject of future work. Future work will also include calibration and validation of the algorithm once real CYGNSS data are available.

Current affiliation: Jet Propulsion Laboratory, Pasadena, California.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Mary Morris, mary.g.morris@jpl.nasa.gov

1. Introduction

a. Motivation

Tropical cyclones (TCs) and their precursor storms spend most—if not all—of their lifetimes over the ocean, which makes them harder to observe in situ. Since the advent of remote sensing, fewer TCs go unobserved (Vecchi and Knutson 2011), and our increased observation of these storms has led to improved understanding of TC processes. Additionally, the observations that are collected through remote sensing support the TC situational awareness and forecasting efforts at warning centers like the National Hurricane Center (NHC) (Rappaport et al. 2009).

Forecasters are required to estimate the present and predict the future intensity of TCs, typically defined as the maximum 1- or 10-min sustained wind speed at the 10-m observing level associated with the system (Harper et al. 2010; Office of the Federal Coordinator for Meteorological Services and Supporting Research 2017). Only 30% of the 6-hourly intensity estimates in the North Atlantic Ocean (Rappaport et al. 2009) are guided by aircraft reconnaissance, and next to no aircraft reconnaissance is performed elsewhere. Unfortunately, accurate intensity estimation remains challenging with and without aircraft reconnaissance. Intensity estimates in the postseason reanalysis records have uncertainties of approximately 5 m s−1 (Landsea and Franklin 2013; Torn and Snyder 2012). Often, the observational guidance that TC forecasters use is based entirely on remote sensing observations.

Observations of surface wind speed can inform estimates of the intensity of a system. In addition to intensity estimation, surface wind speed observations can also guide forecasters who are analyzing the maximum radial extent of 34-, 50-, and 64-kt (1 kt = 0.51 m s−1) surface winds from the center of a storm in geographic quadrants—commonly collectively referred to as wind radii. Wind radii give insight into the surface wind structure and therefore are useful for a variety of applications (Knaff et al. 2016).

b. Examples of previous efforts

Satellite remote sensing–based methods have been developed to estimate intensity in situations where aircraft reconnaissance is not available. One of these methods is the Dvorak technique: a method of estimating TC intensity through image pattern recognition. Two types of Dvorak techniques exist: subjective and objective.

The subjective Dvorak methods were first based on visible imagery from geostationary meteorological satellites (Dvorak 1975); infrared imagery is now included in the technique (Dvorak 1984). The subjective Dvorak technique has proven to be a useful tool for estimating intensity operationally. A discussion of known performance limitations and error characteristics can be found in Knaff et al. (2010).

To lessen subjectivity and increase automation, objective Dvorak methods have been developed (Velden et al. 2006), leading to the objective Dvorak technique (ODT) (Velden et al. 1998) and, more recently, the advanced Dvorak technique (ADT) (Olander and Velden 2007). Dvorak techniques rely on data from geostationary satellites and are not plagued by data gaps typically seen if relying on polar-orbiting satellites or aircraft reconnaissance alone.

Because of the usefulness of geostationary data availability, a variety of other methods for TC characterization—both intensity and wind structure estimation—have been developed for geostationary infrared imagery and data (e.g., Mueller et al. 2006; Kossin et al. 2007; Piñeros et al. 2008, 2011; Fetanat et al. 2013; Knaff et al. 2015; Dolling et al. 2016). A number of studies have developed methods that need an estimate of storm intensity in order to estimate wind structure from infrared data (Mueller et al. 2006; Kossin et al. 2007; Knaff et al. 2011, 2015). The deviation angle variance (DAV) technique developed by Piñeros et al. (2008, 2011) correlates intensity and structure with the gradient in infrared brightness temperature; the DAV-based wind radii methods presented in Dolling et al. (2016) use a multiple linear regression technique. Fetanat et al. (2013) take advantage of historical hurricane satellite data (HURSAT) to estimate intensity from feature analogs—or brightness temperature patterns—in satellite imagery and analogous storms. In addition to infrared data inputs, the methods developed in Knaff et al. (2011, 2015) take advantage of multiple satellite inputs to estimate the TC wind field, from which wind radii are estimated.

TC intensity estimation is also possible using passive microwave sounders, like AMSU. This method takes advantage of the correlation between a TC’s warm-core structure and its intensity. Warm-core anomalies are greatest during peak intensity. Using the retrieved vertical temperature structure from AMSU, estimates of the minimum surface level pressure and maximum sustained wind speed are possible through the hydrostatic approximation and assumptions of gradient wind balance (Kidder et al. 2000). Care has to be taken to account for the effect of clouds and precipitation on the AMSU radiances. While AMSU does not have adequate horizontal resolution to estimate realistic wind structure alone, estimates of the 34-, 50-, and 64-kt wind radii and maximum wind speed can be made using statistically based algorithms (Bessho et al. 2006; Demuth et al. 2006). The performance from this microwave-sounder-type method is comparable to the Dvorak technique, but since this method relies on polar-orbiting sounders, temporal sampling of the TC inner core is limited.

Knaff et al. (2016) developed methods for estimating wind radii using routinely available estimates of TC intensity, motion, and location. These inputs, together with estimates of TC size from IR imagery or model analyses, are used to create modified Rankine vortices—one for each wind threshold—from which wind radii are estimated.

Scatterometers are used to measure ocean vector winds and therefore have some utility in observing TC scenes. Some examples of spaceborne scatterometers include the Ku-band NASA Quick Scatterometer (QuikScat) (Ebuchi et al. 2002), its replacement Rapid Scatterometer (RapidScat) (Madsen and Long 2016), which was put onboard the International Space Station, and the ESA/EUMETSAT series of C-band Advanced Scatterometers (ASCATs) (Figa-Saldana et al. 2002). A more complete discussion of the limitations of scatterometer observations of TC scenes is contained in Brennan et al. (2009). Most notably, scatterometers lose sensitivity at high wind speeds and are often plagued by rain contamination. However, scatterometer observations are valuable for wind radii analyses, with good reliability for 34-kt radius estimation.

L-band radiometers also have applications in observing storms. Observations from the Soil Moisture Active Passive (SMAP) (Fore et al. 2016) and the Soil Moisture Ocean Salinity (SMOS) (Reul et al. 2012, 2016) missions are useful for TC applications because the low-frequency observations are uncontaminated by rain. However, the spatial resolution of these instruments limits their performance. For example, SMAP observations, with a resolution of 60 km, require additional scaling if intensity is to be estimated from them. Yueh et al. (2016) developed SMAP-based TC intensity estimation methods after relating the VMAX observed by the SMAP platform to the true VMAX. Unfortunately, polar-orbiting satellites like these have poor revisit times.

c. CYGNSS

The Cyclone Global Navigation Satellite System (CYGNSS) constellation of eight small satellites provides unique ocean surface wind speed observations in all precipitating conditions (Ruf et al. 2016). The retrieval uncertainty is anticipated to be 2 m s−1 for winds less than 20 m s−1 and 10% for winds greater than 20 m s−1. Like SMAP/SMOS, CYGNSS operates at a sufficiently low frequency to see through the high precipitation of a TC eyewall and observe the highest surface wind speeds of TCs. Each CYGNSS observatory has a four-channel bistatic radar receiver for measuring the GPS L1 (1.575 GHz) signal reflected from the surface of Earth. Unlike SMAP/SMOS, CYGNSS observations will be 25 × 25 km2. Its temporal sampling is also significantly more frequent. Using a constellation of eight satellites in low-inclination circular orbit allows for mean and median revisit times over the tropics of 7.2 and 2.8 h, respectively.

While CYGNSS observations will be useful for estimating TC intensity and wind structure, there are some challenges to overcome with this new observing system. The sampling patterns are not analogous to the continuous-swath observations typical of other spaceborne wind-sensing instruments (e.g., SMAP, SMOS, and ASCAT). CYGNSS observes winds along a series of narrow tracks through the storm; portions of the wind field between observation tracks are not directly sampled. If for example, a CYGNSS-based intensity estimation method involved simply finding the highest wind speed observed by CYGNSS through a storm, the intensity estimate might not have good performance if the gaps in sampling happened to coincide with the location of maximum winds.

If the CYGNSS mission successfully demonstrates the value of its data products, a transition to near-real-time operations is possible in the future, and the data products developed here could be available to operational agencies. However, it should be noted that there are currently no plans for real-time data processing.

d. Outline

The capabilities of CYGNSS have wide applicability to TC science and forecasting activities. In this paper, CYGNSS-based methods are developed for the estimation of a variety of metrics commonly used to describe TCs: intensity (based on VMAX), the radius of maximum winds RMAX, and wind radii (R34, R50, and R64, corresponding to the 34-, 50-, and 64-kt wind radii, respectively). Section 2 describes the datasets used to develop and evaluate the method. Section 3 describes the algorithm. Sections 4 and 5 characterize the performance of the CYGNSS-based estimates of intensity and wind structure and develop quality-control measures of its reliability. Section 6 discusses these results. Section 7 offers some conclusions and opportunities for future investigations.

2. Datasets

A large set of realistic simulated observations was created using the CYGNSS end-to-end simulator (E2ES) (O’Brien 2014) in order to develop and test the CYGNSS integrated kinetic energy (IKE) algorithm prior to launch. The E2ES generates simulated CYGNSS level 2 wind speed data products from a time-evolving input wind field. It properly accounts for both the spatial and temporal peculiarities of the CYGNSS measurement technique by forward propagating the orbital trajectories of every satellite in the GPS and CYGNSS constellations and computing the location of the specular reflection point on Earth’s surface as a function of time for every possible GPS/CYGNSS pair. Additionally, the E2ES properly accounts for the 25-km spatial resolution of the CYGNSS wind speed measurements by appropriately averaging the input wind field, and it accounts for its measurement uncertainty by corrupting the input “truth” winds with noise that is statistically representative of the expected precision of the level 2 wind speed retrieval algorithm (Clarizia and Ruf 2016).

Simulated CYGNSS observations were generated using real-time wind field analyses and forecasts produced by the operational version of the Hurricane Weather Research and Forecasting (HWRF) Model (Tallapragada et al. 2013) for Atlantic and Pacific Ocean storms during 2010, 2011, 2013, and 2014. HWRF wind fields were generated for storms every 3 h throughout their life cycles; 0300, 0900, 1500, and 2100 UTC data are the 3-h forecast fields for the previous analysis time. From each 3-h snapshot from HWRF, CYGNSS observations were simulated.

After the simulation data were created, a number of quality-control (QC) metrics were applied in order to get the best population of test cases to effectively test the methods presented in this paper. For each test case, there had to be no land in the smallest HWRF domain, a maximum wind speed of at least 17.49 m s−1 was required, and the center position—provided by the best-track databases (Chu et al. 2002; Landsea and Franklin 2013)—had to be within 1° latitude and longitude of the center of the smallest HWRF domain.

Performance of the algorithm is characterized using comparisons with simulated truth values derived from the HWRF data. True VMAX is defined as the maximum surface wind speed in the smallest HWRF domain. True RMAX is determined from the average location of the winds falling above the 95th percentile in the smallest HWRF domain. The true wind radii are determined from the extent of certain strengths (34, 50, and 64 kt) of wind speed within the smallest HWRF domain. In addition to the previously mentioned QC, cases for which the true R34 was located at the edge of the smallest HWRF domain were also excluded. After all QC filters are applied, a total of 302 test cases remain for developing and testing the algorithm in this study (details of each case are given in Table A1 in appendix A). A wide variety of storms are included. There are 113 cases from the Atlantic and eastern Pacific. There are 189 cases from the western Pacific. The mean R34 across all cases is 248 km, with a standard deviation of 99 km. The highest intensity (74 m s−1) test cases are found in the Lekima (2013) and Vongfong (2014) storms.

3. Methodology

a. Parametric wind model

CYGNSS wind speed observation tracks often have large gaps between them—gaps that may be in areas of interest (e.g., the location of the maximum wind speed). To account for the areas that have been missed by CYGNSS, a method is developed that effectively interpolates between the available observations using a parametric model as a constraint on the assumed wind speed distribution.

The parametric wind model used has roots in the method developed in Emanuel and Rotunno (2011) and was used in a previous study by Morris and Ruf (2017). In Emanuel and Rotunno (2011), the parametric wind profile most applicable to the region inside of approximately 2.5RMAX is given by
e1
where is the radius of maximum winds, is the maximum wind speed, is the radial distance from the storm center, and is the Coriolis parameter. The Coriolis parameter is determined by the storm center location coordinates and is not an independent parameter to be estimated from the CYGNSS observations.
As discussed in Chavas et al. (2015), the outer wind radii tend to be underestimated by Eq. (1). To address this tendency, two additional parameters have been added to the model to regulate the rate of decay of the wind speed at large radii. The model is given by
e2
where the two additional parameters are and . Examples of the wind speed radial dependence specified by Eq. (2) are shown in Fig. 1.
Fig. 1.
Fig. 1.

An example of the wind speed relationship from the parametric model in Eq. (2) with three different “b” parameters used; Vm.p = 50 m s−1, Rm.p = 75 km, and the center position latitude is 15°.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

Of the four model parameters—, , , and can be solved from the other three by requiring that the maximum value of be equal to the parameter . The solution for is outlined in appendix B. This effectively reduces Eq. (2) to a three-parameter model. As shown in Fig. 1, the parameter allows for adjustment of the radial decay rate of the wind speed in the outer storm region. Larger values of correspond to a faster radial decay. The model is fit to the CYGNSS wind speed data by adjusting the three parameters, , , and , to minimize the sum-squared difference between the model and all CYGNSS observations within a specified region near the storm center.

b. Parametric retrieval algorithm

A flow diagram of the parametric model retrieval algorithm is shown in Fig. 2. First, depending on the basin in question, an initial RLimit—the maximum radial distance from the storm center over which to draw an initial set of CYGNSS observations from—is set. For the Atlantic and eastern Pacific storms, the initial RLimit = 200 km. For the western Pacific storms, the initial RLimit = 300 km, as these storms are generally larger (Chan and Chan 2012; Chavas and Emanuel 2010; Knaff et al. 2014; Sampson et al. 2016). The algorithm requires two sets of inputs: 1) CYGNSS observations and 2) the center position of the storm. The amount of CYGNSS observation input also depends on the type of metric being estimated. For the wind radii estimates, which are quadrant dependent, only observations within a particular quadrant are used. If no observations are available in a quadrant, wind radii are not estimated there. However, observations available across the entire storm are used for estimates of VMAX and RMAX.

Fig. 2.
Fig. 2.

A flow diagram that outlines the steps of the CYGNSS TC surface wind speed structure and intensity product algorithms.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

Once the initial set of CYGNSS wind speed data is gathered, it is input into the parametric wind model algorithm. In this algorithm, the free parameters , , and are solved using an iterative least squares estimator. The procedures behind the parametric wind model algorithm are outlined in appendix C. These estimates are used to create a best-fit parametric wind model to the available observations. An example of this process is shown in Fig. 3. In Fig. 3a, the HWRF wind field from which the CYGNSS observations are derived is shown. In Fig. 3b, the simulated CYGNSS observations are shown for this test case. In Fig. 3c, an example of the final best-fit parametric wind model over all quadrants is shown. The model effectively interpolates between the gaps in the track, which are shown in Fig. 3b. The parametric model is used to derive VMAX and RMAX.

Fig. 3.
Fig. 3.

(a) HWRF wind speed field for Vongfong at 0300 UTC 9 Oct 2014, (b) simulated CYGNSS wind speed observations for (a), and (c) the parametric model algorithm fit for this test case.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

Figure 3c also highlights another aspect of the algorithm flow shown in Fig. 2. Initially, observations within 300 km of the storm center are used. However, after the initial run of the algorithm, if the estimate of R34.P (the parametric model estimate of R34) is different than 300 km, then the algorithm is repeated until RLimit and R34.P converge. In the test case shown in Fig. 3, fewer observations are used in the final iteration of the algorithm because the final value of RLimit after convergence is less than 300 km.

Once the best-fit parametric model solution is attained, the metrics of interest can be derived from it. The parametric VMAX is defined as the maximum of V(r) and the parametric RMAX is defined as that r where the parametric VMAX occurs. The parametric wind radii are defined by the radius at the wind strength in question in the parametric model.

c. Three- versus two-parameter model impacts

In Fig. 4, the parametric model algorithm process is examined for a particular northeast quadrant test case. In this example, however, the results from using the two-parameter model given by Eq. (1) are shown in addition to those from using the three-parameter model [Eq. (2)]. In this test case, the simulated CYGNSS observations suggest that the decay in wind speed is slower than the original two-parameter model would fit. The estimates of the outer wind radii are improved by use of a model with a more flexible radial decay.

Fig. 4.
Fig. 4.

(a) HWRF wind speed field for Soulik at 0300 UTC 11 Jul 2013, (b) simulated CYGNSS wind speed observations for (a) with the NE quadrant (cornered off by red lines) currently being considered, and (c) the parametric model algorithm fit for this NE quadrant test case from which the NE quadrant wind radii are solved.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

d. Parametric scaling

There are two main drivers for this algorithm design: measurement noise and variable coverage. The variable nature of coverage from the CYGNSS constellation means that sometimes the maximum winds are not sampled directly. The use of a parametric wind model helps to overcome these two factors. However, after the model is fit to the available observations, parametric scaling—developed below—is needed to determine the final metrics. For a number of reasons, estimates of the intensity, radius of maximum wind, and wind radii derived directly from the parametric model function V(r) are found to have characteristic scale and bias difference from the actual values. This is true whether the parametric model is derived only from CYGNSS observations or is fit to the complete grid of HWRF wind samples. To elaborate further on this, even if perfect noise-free observations existed, the lowest observations would balance the highest ones, creating a bias in estimates derived directly from the best-fit parametric model. Another bias-inducing factor to consider is that CYGNSS data, at 25-km resolution, spatially filter some TC features. Scaling factors derived here help to correct for the characteristic bias and scale differences caused by these spatial filter–related factors as well as overcome limitations from using a simple parametric model.

The scale and bias differences are compensated by scaling the values derived directly from the parametric model using a power series transformation. The coefficients in the power series are determined as follows: Best-fit parametric models are determined for all storm cases using the complete grid of HWRF wind samples. In each case, estimates of the intensity , radius of maximum wind , and wind radii (, , and ) are derived directly from the parametric model and compared with the true values determined from the actual HWRF winds. A power series is fit to the comparison that translates the direct parametric values to scaled values that are closest, in a least squares sense, to the true values. A first-order power series is found to be sufficient for scaling the intensity and the three wind radii estimates, and a third-order power series is found to be necessary for scaling the estimate of the radius of maximum wind. The scaling relationships have the form
e3a
e3b
e3c
e3d
e3e
The coefficients used in this study are given in Table 1. In summary, TC metrics are first derived directly from the best-fit parametric model. The metrics derived directly from the best-fit parametric model are more representative of the mean value of those metrics. So, for example, the wind radii derived from the parametric model represent something closer to a mean extent rather than the maximum extent (i.e., the operational metric). To estimate the maximum extent, Eqs. (3c)(3e) are applied. All metrics are corrected using Eqs. (3) and the coefficients in Table 1 to estimate the true TC metrics. These final estimates will henceforth be referred to as the scaled-parametric metrics.
Table 1.

Coefficients used for translation from the parametric metrics to the scaled-parametric metrics, assuming the form of Eq. (3).

Table 1.

4. Initial results

a. Performance without quality control

To illustrate the effect of applying the scaling factors described above, histograms of error are plotted in Fig. 5 for each of the TC metrics. These histograms include all storm cases, with no QC filters related to algorithm performance applied. Both the parametric and scaled-parametric metrics are plotted to show that the scaling alleviates some of the larger biases in the parametric estimates. For example, there is a clear overall bias in the parametric VMAX, but after the scaling correction is applied, the mean error is close to zero. The mean and standard deviation of each population of errors are reported in Table 2. For some metrics, the scaling factor improves performance much more than for others. The inner wind radii R50 and R64 have very small scaling factors; their performance improves by a small amount. The standard deviations reported in Table 2 show that RMAX is the only metric where the scaling factors affect the root-mean-square error (RMSE) by a significant amount. The RMSE can be further improved by applying QC filters. These filters are developed below.

Fig. 5.
Fig. 5.

Histograms of error, normalized to percentages, before QC is applied in all parametric and scaled-parametric metrics. Error is defined here as true − estimated.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

Table 2.

Mean and standard deviation of the error plotted in Fig. 5 for each parametric and scaled-parametric metric.

Table 2.

b. Sensitivity to storm center location error

One of the required inputs to the TC metric estimator algorithm is the location of the storm center. During algorithm development, the best-track database is used for storm center information, and storm center data sources have yet to be finalized for on-orbit data processing. Potential sources of center information include the working best track, interpolation from the forecast track or an objective position location algorithm such as that from the Automated Rotational Center Hurricane Eye Retrieval (ARCHER) (Wimmers and Velden 2010).

Sensitivity experiments were performed to assess the impact of center location error on the metrics. In these experiments, the algorithm was executed multiple times using all available test cases, each time perturbing the center position latitude by an increasing amount. After performing some quality control (described in the following section), the error due to latitude offset was calculated by decomposing it from the overall error in the TC metric estimate. Specifically, the RMSE due to center location offset is given by
e4
where is the total RMSE for a certain offset , and is the RMSE with no latitude offset. The results are shown in Fig. 6 for VMAX and RMAX, the metrics that are derived using observations from all four quadrants, and in Fig. 7 for wind radii, the metrics derived in individual quadrants. For the wind radii, the northeast quadrant was used. The results are similar in other quadrants.
Fig. 6.
Fig. 6.

The additional error on average to expect from storm center offsets (here, only in latitude) for (a) VMAX and (b) RMAX.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

Fig. 7.
Fig. 7.

The additional error on average to expect from storm center offsets (here, only in latitude) for wind radii. This analysis is based on the cases available in the NE quadrant.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

The results show a consistent monotonic increase in error with increasing uncertainty in the storm center location for all TC metrics. For example, a storm center offset of 55 km introduces an RMSE in VMAX of 4.7 m s−1; in RMAX of 12 km; and in R64, R50, and R34 of 39, 43, and 48 km, respectively. In terms of relative error (relative to the mean value of each TC metric), these errors correspond to 12% for VMAX; 13% for RMAX; and 32%, 28%, and 19% for R64, R50, and R34.

c. Sensitivity to CYGNSS coverage

The spatial distribution of observations, or coverage, by CYGNSS of the TC wind field will affect the quality of its retrieval of the TC metrics. The sensitivity of the retrievals to coverage is illustrated in Figs. 8 and 9. Different sampling characteristics are considered and different regions are examined for different TC metrics. Figure 8 shows the sensitivity of VMAX (Fig. 8a) and RMAX (Fig. 8b) performance to the number of CYGNSS samples, or observations, within 100 km of the storm center. Other thresholds were examined, and 100 km provided the best sensitivity for VMAX and RMAX. In Fig. 8, the root-mean-square difference (RMSD) between the HWRF and CYGNSS values is shown for different populations of storm cases. The population used for the RMSD calculation is selected based on the coverage threshold attained (defined on the x axis), or the number of observations within 100 km of the storm center in a test case. The x axis in the figure is the threshold—the (minimum) number of observations required within 100 km. For example, at an x-axis value of 10, the population of test cases that went into the RMSD calculation at this point all had at least 10 CYGNSS observations within 100 km of the storm center. Cases with poor coverage near the center of the storm drive the RMSD up; these cases are included in the population at low sample number thresholds. As the threshold is increased, more and more undersampled cases are thrown out, and the performance improves. The key takeaway from these results is that an adequate number of CYGNSS observations are needed within the inner core in order to make a reliable estimate of inner-core metrics like VMAX and RMAX. Therefore, quality control can and will be derived from the coverage statistics in this region for the VMAX and RMAX metrics.

Fig. 8.
Fig. 8.

(a) The RMSD between the HWRF- and CYGNSS-derived VMAX depending on the QC filter threshold used. The QC keeps test cases that have a number of observations within 100 km from the storm center above the sample number threshold plotted on the x axis. (b) As in (a), but for RMAX. (c) The fraction of the original test case estimates left that are used to derive the RMSD in (a) and (b).

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

Fig. 9.
Fig. 9.

(a) The RMSD between the HWRF- and CYGNSS-derived wind radii depending on the QC applied. The QC keeps test cases that have a number of observations outside 100 km from the storm center (but within the estimate of R34) above the sample number threshold plotted on the x axis. (b) The fraction of the original test case estimates left that are used to derive the RMSD in (a).

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

Figure 9 shows the results of a similar sensitivity experiment for the wind radii. Here, a different sampling characteristic was found to be more indicative of the performance. The number of CYGNSS samples between 100 km and R34 was used. As above with VMAX and RMAX, as the minimum threshold for the number of samples increases, the performance of the wind radii estimates improves (see Fig. 9a). Of course, the more stringent the threshold is, the fewer cases remain (see Fig. 9b).

d. Quality-control test procedures

QC filters are derived using the results of the sensitivity experiments. The filters are intended to identify CYGNSS sampling conditions under which the TC metric estimates are of acceptable quality. However, the filters should not be so stringent that they eliminate too large a fraction of the possible storm cases. For estimates of VMAX and RMAX, a sampling threshold test is used given by
e5
where is the number of observations within 100 km of the storm center for a particular storm case, and is the filter threshold. For this study, we choose = 20 as a good balance between high algorithm performance and not filtering out too many storm cases. For estimates of wind radii, a different sampling test is used given by
e6
where is the number of observations between 100 km of the storm center and R34 for a particular quadrant, and is the filter threshold. For this study, we choose = 30. Higher values produce only marginal improvement in performance while eliminating a significant fraction of the storm cases.

5. Final results

Figure 10 shows the histograms of error for all TC metrics after the QC filters described above have been applied. The original histogram data shown in Fig. 5 are included for convenience. The means and standard deviations derived from the Fig. 10 cases are listed in Table 3. Overall, the QC filters remove the egregious outliers while retaining most of the higher-quality estimates. As a result, the RMSE in the metrics is improved. Additionally, the bias in the estimates remains small after QC filters are applied.

Fig. 10.
Fig. 10.

Histograms of error, normalized to percentages, in all parametric, scaled-parametric, and QCed scaled-parametric metrics. Error is defined here as true − estimated.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

Table 3.

Mean and standard deviation of the error plotted in Fig. 10 for each parametric and scaled-parametric metric as well as the QCed scaled-parametric metrics.

Table 3.

6. Discussion

The methods presented here enable CYGNSS-based estimates of VMAX, RMAX, and wind radii. The estimates require a sufficient number of observations in the appropriate regions of the storm; this requirement is met using appropriate quality-control filters. For example, data availability within the inner core best predicts the quality of the inner-core metrics, namely, VMAX and RMAX. Wind radii estimates require sufficient sampling in an annular region outside of the inner core of the storm, between 100 km and R34, and the sampling is quadrant dependent.

The results presented here assume that all eight microsatellites are available to sample the winds. If a failure were to occur, the number of observations available for retrievals might be affected. To illustrate the effect of losing spacecraft (s/c), Fig. 11 shows the cumulative density function (CDF) of the number of s/c used by all test cases after the quality-control filter is applied. For example, ~81% of the test cases use six or fewer s/c to estimate VMAX and RMAX, and ~92% use six or fewer to estimate the wind radii. Note that wind radii estimates are more likely to have fewer s/c involved than for estimates of VMAX and RMAX because the wind radii estimates are quadrant limited. The decrease in the CDF when fewer s/c are available gives an indication of the impact of losing one or more of them. For example, the decrease from CDF(6 s/c) to CDF(5 s/c) describes the fraction of test cases using six s/c for which estimates would not have been possible if one s/c were lost. If the decrease from CDF(N) to CDF(N − 1) is averaged over all N = 2–8, this gives an estimate of the fraction of all test cases for which estimates would not have been possible if one s/c were lost. For the CDF corresponding to VMAX and RMAX, the result is an average decrease by 14%. For the case of two s/c lost [i.e., a decrease from CDF(N) to CDF(N − 2)], the average decrease is 29%, and it is 44% for a loss of three s/c. For estimates of the wind radii, the corresponding decreases are comparable. Note that these are overall statistical impacts on s/c loss, and the impact on any individual test case would require a more detailed sensitivity analysis.

Fig. 11.
Fig. 11.

Cumulative density function of number of s/c used to estimate VMAX and RMAX (solid black line) and wind radii (dashed blue line) for all test cases after QC has been applied.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

Another potential factor in performance is the type and location of the storm. Figure 12 examines the impact that intensity has on the performance of the VMAX and RMAX estimates. Here, the test cases are separated into those that, according to HWRF, have an intensity estimate either below or above 33 m s−1—differentiating between tropical storm and hurricane strength. Figure 12a shows that the spread in error is slightly larger in the stronger storms. Figure 12b shows that the spread in RMAX error is larger for tropical storms. Both of these performance distinctions make sense considering that, in both instances, the spread is larger for the population with larger values of the metric in question.

Fig. 12.
Fig. 12.

Histograms, normalized to show percentages, of the QCed scaled-parametric VMAX and RMAX depending on the HWRF VMAX threshold attained. Weaker storms (VMAX < 33 m s−1) are plotted in solid light blue. Stronger storms (VMAX ≥ 33 m s−1) are plotted in dashed dark red.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

Figure 13 compares the performance of all TC metrics depending on the basin location of the storm. The error plotted is with QC filtering. Notably, the spread in VMAX error is larger in the western Pacific test cases, which makes sense as these cases tend to have higher intensity. Another interesting takeaway from Fig. 13 is shown in Fig. 13c; here, the bias in Atlantic and eastern Pacific RMAX error is more pronounced than that in the western Pacific. Basin-specific RMAX performance will be examined further postlaunch with CYGNSS data in order to determine whether different scaling factors are required for different basins. In summary, assuming that these simulations are close to the true or real data fields, Figs. 12 and 13 illustrate situations where one might expect better or worse performance.

Fig. 13.
Fig. 13.

Histograms, normalized to show percentages, of the QCed scaled-parametric metrics depending on the test case basin. Storms from the Atlantic and east Pacific basins are plotted in solid light green. Storms from the western Pacific basin are plotted in dashed dark blue.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0375.1

7. Conclusions

CYGNSS will allow for a unique opportunity to estimate certain metrics of tropical cyclones that are typically quite challenging to estimate with other platforms. Since CYGNSS observations consist of collections of tracks rather than complete swaths, new estimation methods have been developed that effectively interpolate between observations in order to produce the TC metric estimates.

This study uses a mission simulator that reproduces realistic sampling patterns to be expected with CYGNSS. Sampling patterns are important to consider, as the quality of the TC metric estimates can depend strongly on them. Given good coverage, the methodology presented here enables VMAX, RMAX, and wind radii estimates to be made from two inputs: 1) CYGNSS observations and 2) the storm center location. Quadrant-specific inputs are used for wind radii estimates. Observations across all quadrants are used to estimate VMAX and RMAX. Future work includes determining if quadrant-dependent (or possibly other more complicated) methods could be used to account for asymmetries in order to improve VMAX and RMAX methods.

Development of the methods and applications described in this paper, as well as related areas of research (e.g., center fixing), are ongoing. Future work also includes calibration and validation of the TC metric estimates made from actual on-orbit CYGNSS data. Calibration might, for example, include retuning of the scaled-parametric relationships described in section 3d or revision of the QC filter thresholds. Validation will follow from comparisons with coincident ground truth sources such as airborne reconnaissance underflights. If skillful, CYGNSS-based wind radii estimates could be included in the objective best-track methodology used at JTWC and NHC (Sampson et al. 2017); the small-biased CYGNSS-based method presented here—as determined from simulated observations—could be complementary to the other methods, which are typically high biased. Finally, while these methods were developed with CYGNSS in mind, it is possible that this methodology could also be applied to other types of observations, in particular those for which gaps in spatial sampling also exist.

Acknowledgments

The authors thank Chris Landsea, John Knaff, and one anonymous reviewer for their in-depth reviews and helpful suggestions that have helped to improve this paper. The authors acknowledge the hard work of several CYGNSS science team members who supported this work. The HWRF dataset was gathered by Faozi Said and Golf Seubson Soisuvarn. The simulated CYGNSS observations were developed based on the work by Andrew O’Brien and Aaron Ridley. This work was supported in part by NASA Science Mission Directorate Contract NNL13AQ00C.

APPENDIX A

Summary of Storms Used

Table A1 provides a summary of all the storms used in this study.

Table A1.

A summary of all of the storms used in this study, with the storm name, the number of cases for that particular storm, the maximum wind speed VMAX, the storm center latitude and longitude at the point in time corresponding to the VMAX case, and the year for each storm.

Table A1.

APPENDIX B

Derivation of Solution for Parameter in Eq. (2)

The solution for parameter starts with Eq. (2), previously described in section 3a:
eb1
To solve for the parameter , which forces the maximum value of Eq. (B1) to be equal to parameter , the derivative of Eq. (B1) with respect to is found given by
eb2
After setting , solving for gives
eb3
where, for convenience and ease of reading, we define
eb4
eb5
and
eb6
The negative root in Eq. (B3), which we define as , gives physical results and will be used for the remainder of the solution. Next, is used to substitute in for both and in Eq. (B1), and is set equal to , which gives a solution for in terms of , , and as
eb7
where, for ease of readability, we define
eb8
eb9
eb10
eb11

APPENDIX C

Parametric Wind Model Algorithm Procedures

The parametric wind model algorithm is embedded in the outlined procedures in Fig. 2. The algorithm consists of two main parts, with the ultimate goal of solving for the three free parameters in Eq. (2): , , and . To start, first guesses for and are determined, assuming = 1 and = 2, as the original model suggests. Second, a series of iterative steps take place in order to minimize the difference between the parametric wind model estimate of wind speed and the L2 wind speed observations. In brief, after a first guess for parameters is made, the model parameters are solved using an iterative, least squares fit of the model to the CYGNSS observations.

The iterative routine consists of a number of steps:

  1. Calculate , which is the estimate of the radial profile of winds according to the parametric wind model, at all observation points, using the current estimate of , , , and with Eq. (2). Location is defined by , a vector of radial distances corresponding to the location of CYGNSS observations with respect to the center of the storm.

  2. Calculate , where is the vector consisting of the L2 surface wind speed observations collected at certain radial points defined by .

  3. Populate the Jacobian matrix for all free parameters, defined here as
    eq1
    where N is the number of CYGNSS observations, or points in . The derivatives are approximated numerically by perturbing the parametric model by small amounts, separately, for each free parameter.
  4. Perform the generalized matrix inversion, defined as , where is a regularization matrix, used for numerical stability, defined as
    eq2
    with the amount of regularization dependent on the value of the relaxation parameter .
  5. Update the estimate of the free parameters with
    eq3
    where the state vector is filled with the estimates of the free variables as defined by
    eq4
    with a corresponding change vector,
    eq5
  6. Calculate , with the constraint that = the maximum value of the parametric wind model. See details in appendix B.

  7. Update using the latest parametric wind model estimate.

  8. Check to make sure parameters are positive, and force them positive if necessary.

  9. Iterate steps 1–8 until the problem has converged.

The entire iterative routine outlined above in steps 1–9 is potentially repeated as well. The population of CYGNSS observations that are used in the parametric wind model fit are the samples lying within a distance RLimit of the storm center. The RLimit is initially set to 200 km for North Atlantic and eastern Pacific storms and 300 km for western Pacific storms. After the first iteration, the estimate of R34, given the parametric model R34.P is compared with RLimit. If they are not sufficiently close, currently defined as being within 10 km, then RLimit is set equal to R34.P, a new population of observations is selected, and the processes outlined above are repeated. Eventually (in practice, within just a few iterations), the values of R34.P and RLimit converge, and the parametric model estimation is complete. Results from the last iteration are used for the products.

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