a. Image preprocessing

Parallax is corrected by applying a uniform adjustment to the image. The navigation of the image is shifted ∼12 km (with the exact number depending on the instrument’s zenith angle) toward the satellite to compensate for the parallax of features at a height of 10 km. Of course, the height of the 85–92-GHz signal only averages 10 km, and can vary about that height, but the error caused by this difference is on the order of only a few kilometers, and is therefore minor compared to other sources of error. After correcting for parallax, the brightness temperature image is interpolated to a regular grid (evenly spaced latitude and longitude coordinates) for input into the centering algorithm.

b. First-guess position

An initial estimate of the rotational center is a necessary input to the algorithm because the algorithm must operate on a limited-size domain and because a first-guess position can serve as a useful reference point to check the validity of the algorithm result. Operationally, the ARCHER algorithm obtains its first-guess position from the most recent forecast track provided by the National Hurricane Center (NHC) for TCs in the North Atlantic and east Pacific basins, and by the Joint Typhoon Warning Center (JTWC) for TCs in other basins. However, in the calibration and validation of the ARCHER algorithm the first-guess position is set at a controlled offset distance from the NHC best-track position (section 3).

c. Large-scale method: Spiral centering

The purpose of this component is to present an objective, computational algorithm to substitute for, and hopefully improve on, the longstanding practice of subjectively fitting a spiral pattern to a satellite image of a TC. Although spiral centering is traditionally performed on visible and infrared images of tropical cyclones (Dvorak 1973; Olander and Velden 2007), the curved rainband structure observed in 85–92-GHz PMW imagery is also well suited to this method, even at the typically lower spatial resolution afforded by these frequencies. Numerically, matching a digital image of brightness temperatures with a spiral pattern is accomplished by calculating the cross product between the image gradient and a spiral-shaped unit vector field. This is substantially different from previous approaches of isolating and identifying the spiral paths of banding structures. Instead, the algorithm uses gradients throughout the image that have been shaped by the overall spiral wind field of the TC. A spiral pattern of unit vectors represented in Cartesian coordinates (x, y) and centered at the origin is represented as

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where α is the angle of inclination in radians; and ±, ∓ indicate the rotation of the spiral, either inward-counterclockwise in the Northern Hemisphere or inward-clockwise in the Southern Hemisphere, respectively. In a good match between the spiral pattern and a collocated image, the image gradients are strongly orthogonal to the spiral unit vectors. In practice, this formula applies well not only to the alignment of spiral bands and the eyewall inner edge, but also to the finer-scale shearing patterns caused by contrasting features elongated in the direction of the local wind. In fact, our experience from using this approach has shown that this finescale directional pattern in the image is probably a more important guide to the rotational wind field than the direction of the large-scale banding structures.

The spiral centering is performed by application of a two-step process: 1) a large-domain, coarse spiral score (CSS) function, and 2) a relatively smaller-domain fine spiral score (FSS) function. The reason for having two functions operate rather than one is that a large-domain function is effective at determining a rough estimate of the rotational center even with a very poor first-guess estimate of position, whereas a smaller domain function has more accuracy if it is provided with a good initial position estimate (supplied by the coarse step).

The formula for the coarse spiral score is the following:

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where

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and

• (c_SS, c₀) are coefficients (15, 20) to scale the result to a range of 0–50,

• (ϕ, θ) are (longitude, latitude) in the spiral score field,

• N is the number of points in the sample disk,

• i indicates a single a point inside the sample disk,

• disk is the domain of N grid points in a disk centered on the initial guess position (the “sample disk”),

• I is the microwave horizontal polarization brightness temperature image (and the log function on I de-emphasizes the extreme gradients),

• S is the log-5 spiral vector field,

• α is the inclination of the spiral vector field in radians (zero indicates a circular vector field and a log-5 field is inclined 5°, or 0.087 radians, outward from a circular vector field),

• ± means “+” in the Northern Hemisphere and “−” in the Southern Hemisphere, and ∓ means the opposite,

• (x̂, ŷ) are the unit vectors for north and east, respectively, and

• (x_i, y_i) are offset distances in the (x̂, ŷ) directions, respectively, where x_i is normalized to be approximately equal in spacing to y_i.

This function essentially computes a score that reflects the average alignment of the image boundaries with a spiral centered at a given point (ϕ, θ). This alignment is expressed in terms of the cross product of the image gradient and its collocated element of the spiral field. The vector norm function (‖·‖) is necessary to give equal prominence to gradients directed either radially inward or outward. We use a log-5 spiral, which is less than the inclination generally associated with TC spiral patterns, because the gradients associated with horizontal shear throughout the image are generally more circular than the patterns of spiral bands. (However, the algorithm is not very sensitive to the particular value of the spiral inclination.) In practice, scores from this function are calculated at a spacing of several grid cells over a predetermined domain of points, and a successful result produces a contoured bull’s-eye pattern focused on or near the rotational center (Fig. 1).

Next, the formula for the fine spiral score is

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The components are the same as those defined in Eq. (2), except for the vector magnitude of the cross product (|·|), which can be positive or negative. The difference in weights between the two parts of Eq. (3) ensures that the inner boundary of the convective eyewall receives more weight than the outer boundary. The constant 0.62 was determined empirically to be the optimum weight for this split approach. As with the CSS, we determine the field of scores by calculating the results over a spacing of several grid points, and a successful result produces a contoured bull’s-eye pattern focused at or near the rotational center.

d. Small-scale method: Ring centering

The purpose of this method is to computationally determine the presence of an eyewall as it appears in the TC image, and thus locate the rotational center within the eye. The result is a field of values called the ring score (RS). The underlying method is simple, but more computationally expensive than the spiral method because it iterates over both the spatial domain and over a range of possible radii. The approach is to find the highest average dot product between the image gradients and a set of radially oriented unit vectors encircling a given ring pattern (a presumed eyewall inner edge). When iterated over a domain of points and a range of radii r, the maximum of this formula should occur at the eye center:

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where

• RSR is ring score radius, the ring score for each possible radius,

• (ϕ, θ) are (longitude, latitude) in the ring score field,

• c_RSR is a constant (value of 250) to scale the result to a range of 0–100,

• r is the length of the radius being evaluated (units: degrees),

• N is the number of points in the sample ring,

• i is the index for a point on the sample ring,

• I^1/3 is the microwave horizontal polarization brightness temperature image to the power of ⅓ (to deemphasize the higher gradients),

• r̂ is the unit vector pointed radially outward from the center of the ring to a point of index i on the ring, and

• max[RSR(ϕ, θ, r), r] is the maximum of the three-dimensional field RSR over the dimension r.

The purpose of the weight r^0.1 is to slightly favor the scores corresponding to larger radii, because larger eyes are more irregular and may not match the points on a perfect circle quite as well.

Of course not every TC image contains a well-defined eye. In such events, the ring score is normally quite low. This means that unless the corresponding spiral score is very high, the ARCHER algorithm will default to the first-guess position rather than use the position with the maximum score. This process is discussed further in the next subsection.

e. Optimized combination of spiral and ring centering

By design, the spiral-centering score field and the ring-centering score field combine into a weighted sum that takes advantage of the two methods’ complementary strengths. Specifically, the ring centering yields highly precise results for a well-defined eye, and the spiral-centering method is important both when an eye is not evident and when the ring-centering method finds one or more false eyes (i.e., inner-core, rain-free moat regions caused by convective downdrafts or environmental dry air intrusions). In the latter case, the spiral method provides a critically important additional weight to the feature nearest the rotational center.

One extra component in the combined scores is a distance penalty field that turns spiral score fields into “guided” spiral scores [Eqs. (5) and (6)]. The distance penalty is a field that varies with the square of the distance from the initial guess. Therefore it is minor near the first-guess position and dominant at the edges of the analysis domain. This acts as a check to insure that no matter how unusual the image, the final result will not stray unreasonably far from the first-guess position.

The scores are combined in a multistep algorithm as follows:

1) Step 1: Guided coarse spiral (GCS)

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where (ϕ₀, θ₀) is the initial guess position and dist²(ϕ, θ, ϕ₀, θ₀) is the square of the distance between the initial guess position and the point (ϕ, θ) on the domain. The score field for GCS then sets the stage for the next step in the algorithm.

2) Step 2: Guided fine spiral (GFS)

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This is the gridded result used to calculate the overall spiral component of the combined score. The domain for step 2 is the area of points that are within a certain range of the maximum value of the GCS. The area is also expanded by a small amount. (The parameter values for this process are provided in Table 1).

4) Step 4: Combined score

The combined score (CS) normally generates a gridded field that contours to a bull’s-eye pattern around the maximum value. For simplicity, the position of this maximum value is hereafter called the target position. The formula for this score is a weighted sum of the guided fine spiral (step 2) and the ring score (step 3). The maximum value of this gridded score field is then used to determine the target position and the final ARCHER position (demonstrated in Fig. 2):

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where the scalar value MCS is the maximum combined score, (ϕ_t, θ_t) is the target position, (ϕ_f , θ_f) is the final ARCHER position, (ϕ₀, θ₀) is the default first-guess position, and τ is the MCS threshold value for either applying the target position or defaulting to the first-guess position. This arrangement has two unresolved parameters: w_GFS and τ. These two parameters are the most naturally empirical of all the algorithm parameters, with w_GFS determining the relative importance of the spiral score and the ring score, and τ determining the optimal distinction between effective and ineffective performance. Thus the next section is devoted to optimizing these parameters empirically, with special attention to how these values vary according to TC intensity.

a. Calibration dataset: 2007–08 North Atlantic TC seasons

The calibration dataset is selected from microwave imagery of TCs during the 2007 and 2008 North Atlantic storm seasons (Table 2). Taken together, the data from these two years make up a representative sample of a wide variety of TC structures intensities. The “truth” position of the rotational center for each case is a cubic interpolation of the NHC best-track dataset. To insure that the truth dataset is as accurate as possible, only the best-track values ±3 h from an aircraft reconnaissance position fix are used. This is the most limiting constraint on the sample size. Additional criteria for the microwave observations are the following: the best-track position must lie inside the satellite swath (allowing for partial coverage cases if the coverage of the TC exceeds 50%); all storms are required to be south of 40°N latitude to serve as a coarse exclusion of extratropical transition cases; and all observed TCs must have a surface wind speed greater than or equal to 34 kt (1 kt ≃ 0.5 m s⁻¹) because organized rotation is rarely evident in PMW imagery below tropical storm classifications.

It is desirable to partition the data sample by cases showing the effects of “weak vertical shear” and “strong vertical shear” because the displacement between surface center of rotation and image–height center of rotation can lead to difficulties in the application of the algorithm. Just as importantly, vertical shear can adversely effect the organization of the TC and disrupt the conventional spiral-eye configuration that makes the algorithm successful. Such a disruption naturally complicates the process of center-fixing. Unfortunately, systematic effects of vertical shear on vortex tilt and rotational asymmetries are not well understood or documented to the point that any particular static environmental analysis can serve as an effective measure to adequately stratify the sample. For example, the period of time a shear regime has been acting on a vortex might be just as important as the strength of the shear or the TC intensity at the analysis time. Consequently, several attempts to use objective environmental vertical shear statistics to partition the data did not yield very effective results.

However, it can be shown that the zonal translation velocity of the TC, which is easily extracted from the best track, can serve as a useful proxy for distinguishing TCs that are well-suited to the ARCHER algorithm from those in which vortex tilt and asymmetric structure are more likely to pose problems. Figure 3 shows that algorithm error increases sharply where TC eastward translation speeds (V_x) exceed 5 kt. This increase in error is predominantly caused by recurvature during which stronger westerly wind shear regimes can often quickly transform an organized vortex into more distorted asymmetric and/or tilted structures. Consequently, the calibration and validation steps partition the observations into TCs in which V_x < 5 kt (group A, including all westward-moving storms) and V_x ≥ 5 kt (group B). Only group A TCs are used in the calibration, because our investigation finds that the ARCHER algorithm is effective in only a minority of group B cases. The validation of the ARCHER algorithm in group B cases is handled in a separate analysis.

b. Method

We approximate the real-time distribution of forecast error on the dataset by simulating 12 scenarios per image of a first-guess position displaced to varying offsets from the best-track position: 0.1°, 0.4°, and 0.7° in the four cardinal directions. Thus, the total number of cases (3972) in the calibration is the number of microwave images in the calibration dataset (331) times the number of scenarios per image (12). The statistics from these cases (such as RMS) are then combined into weighted averages to approximate the algorithm performance for the North Atlantic operational environment, which has a certain probability of small (0.1°), medium (0.4°), and large (0.7°) forecast (first guess) position errors. The weights have been determined according to the observed distribution of forecast position error in the North Atlantic operational environment (appendix A).

The guided fine spiral and ring score fields are calculated for each case, and the final positions determined for a range of spiral weights (w_GFS) and score threshold values (τ). The errors of the final ARCHER positions form the basis of the performance statistics. With a set of statistics for the algorithm over this range of weights and thresholds, we can then judge the performance in order to identify the optimal weight–threshold combination, based on the following criteria:

1. RMS: Minimum possible RMS position error between the algorithm centers and the truth (best track) values.

2. Number of excessive errors: For all the scenarios, no case should have an algorithm position error exceeding the largest first-guess error in the simulation (0.7°).

3. Target usage: When presented with a range of parameter values that produce similar accuracy statistics, the value with the fewest defaults to first-guess positions will be selected. This is desirable because some amount of uncertainty in the application of the best-track dataset is inevitable; therefore the algorithm error is somewhat overstated by the statistics.

Several iterations of experimentation showed that three groupings of cases based on TC maximum surface wind speed (V_max) required separate weight–threshold combinations: tropical storm (34 ≤ V_max < 65 kt), category 1 hurricane (65 ≤ V_max < 84 kt), and category 2–5 hurricane (V_max ≥ 84 kt). Counter to our expectations, the data organized itself in this “trimodal” pattern rather than any sort of continuous evolution with increasing V_max. The final results are organized in this fashion and the weight–threshold combinations optimized accordingly.

c. Results and discussion

Figure 4 presents the results of all the cases for group A TCs in the 2007–08 dataset. The results are organized to illustrate the optimal weight–threshold combination for each of the three V_max groupings. However, one important note is that the threshold value is displayed as the scaled threshold:

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This conversion keeps the plotted trends reasonably “flat” as the spiral weight varies. Otherwise, the thresholds of interest would increase linearly (and out of scale) with the spiral weights.

Each row addresses one of the three criteria for parameter evaluation, weighted by the relative frequency of 0.1°, 0.4°, and 0.7° displacements in the North Atlantic (Table A1, described below in appendix A). The first row is the RMS error of the ARCHER position (with respect to the best-track position). The second row of Fig. 4 identifies the number of excessive errors, indicated by the (weighted) number of cases in which the errors exceed the largest offset distance used in the simulations (this can be a fractional value lower than 1 because of the weighting scheme). The third row in this figure is the fraction of cases in which the algorithm position was applied, as opposed to defaulting to the first guess. Finally, the fourth row plots the distribution of distances between the best track and the ARCHER result. This distribution is not weighted because a nonweighted version is easier to read and interpret.

For each column, a magenta polygon outlines the area in weight–threshold space that achieves the best compromise between the three criteria: low RMS, few excessive errors, and a high fraction of applied targets. The values in these polygons show that one should expect the algorithm performance to be essentially the same throughout the range of weights and thresholds therein. However, a specific weight and threshold value must be used in the validation, and so a specific point is selected for each group (marked with a white circle), based on the robustness of this point in weight–threshold space. The values corresponding to these points are presented in Table 3.

a. Method

The validation method is similar to that of the calibration section. First-guess forecast position error is simulated with displacements from the best-track position in the four cardinal directions at 0.1°, 0.4°, 0.7°, and 1.0°. (Although 1.0° is not used to compute basinwide statistics, it is included here just to show algorithm performance in a more extreme condition.) The performance statistics for each of these simulated first-guess displacements are combined in weighted averages to estimate the overall performance in the North Atlantic and other TC basins. As with the algorithm calibration, performance statistics for a particular basin are estimated by weighting a statistic (such as RMS position error) for the relative occurrence of small (0.1°), medium (0.4°), and large (0.7°) offsets in the forecast position corresponding to the distribution of forecast error common to that basin. This approach of simulating first-guess error in a variety of ways was preferable to using the single real-time NHC forecast at the time of each image because it generated more robust results for the sensitivity to forecast error.

The dataset is partitioned into group A and group B cases. Throughout the validation, the empirical difference between the best-track position and the “true” rotational center at the height and navigation of the image is a very important consideration in interpreting the results, and so this issue is analyzed as well.

b. Validation dataset: 2005 North Atlantic hurricane season

The very active 2005 hurricane season of the North Atlantic was chosen for the independent validation dataset, with 241 separate 85–92-GHz PMW observations. The constraints for data quality were the same as with the calibration dataset: all observations must be ±3 h from an aircraft reconnaissance position fix, the best-track position must be inside the satellite swath, TCs must be south of 40°N latitude, and TCs must have maximum surface wind speeds greater than 34 kt. Of these 241 observations, approximately 40% are tropical storms, 20% are category 1 hurricanes, and 40% are category 2–5 hurricanes.

c. Algorithm performance for group A TCs

To interpret the performance of the algorithm, the results are first partitioned into a matrix of histograms (Fig. 5) that breaks the cases down by TC intensity (rows) and first-guess displacement (columns). A few trends and features in Fig. 5 are immediately apparent. The consequence of the algorithm defaulting to the first guess is a peak in the histogram at 0.1°, 0.4°, 0.7°, or 1.0°. The number of defaults decreases with increasing TC intensity, with defaults predominant in tropical-storm-strength TCs and almost nonexistent with category 2–5 hurricanes. Each group of TC intensities (the top three rows) shows a different feature that dominates the distribution of error. For tropical storms, the likelihood of a default is high for all values of first-guess position displacement. For category 1 hurricanes, the number of defaults increases with first-guess displacement (increasing from left to right), showing that the ARCHER score for the target center is more likely to fall below the threshold as the accuracy of the first-guess decreases. For category 2–5 hurricanes, the peak of the error distribution is unchanged with the accuracy of the first guess, and the shape remains similar except that the tail of the histogram grows slightly as the accuracy of the first-guess decreases.

Another significant feature of the category 2–5 hurricane row of histograms is that the error peaks at 0.05° rather than 0, as one might expect in a grouping where a majority of cases have well-defined eyes. This suggests that a portion of the error in the ARCHER product is due to an “intrinsic error” in the correspondence between the PMW images and the best-track dataset, which causes a departure of the best-track positions from the true center indicated by the image. Several factors contribute to the difference between best-track center and the center of rotation at the level of the microwave retrieval in a given image: vortex tilt caused by vertical shear or vortex precession, residuals in parallax correction, satellite navigational error, and best-track error.

This knowledge is important to consider in applications that use the ARCHER result because most applications (such as intensity estimation) require the image-relative center rather than the center of rotation at the surface. Therefore, it is highly useful to quantify this type of intrinsic error between the best track and the image-relative center if at all possible. Appendix B provides an estimation of the intrinsic error and shows that it can be approximated as an additive component of the ARCHER product’s variance with respect to the best track. In the following analysis, this approximation is used to complement the standard RMS error (relative to the best track) with a corresponding image-relative RMS error value.

Table 4 presents these complementary statistics. Results are sorted in columns by first-guess displacement, and then by estimates for the values in a North Atlantic basin environment in the fifth column and all other basins in the sixth column. The statistic “percentage applied” (percentage of ARCHER target positions applied rather than defaulting) varies greatly by TC intensity. For tropical storms, only about 17% of the cases use the ARCHER target position; whereas, about 84% of category 1 cases and 99.9% of the category 2–5 cases use the ARCHER target position. The statistic “percentage worsened” (percentage of cases in which the final position was in error by greater than 0.71° for first-guess displacements of 0.1°–0.7° and greater than 1.1° for first-guess displacements of 1.0°) was very low: less than 1% in all relevant groupings. (The value was 1% for one grouping when the first-guess displacement is 1.0°, which is already a very rare circumstance operationally.)

Trends in image-relative RMS are best explained visually (Fig. 6). The RMS of the ARCHER target positions (left plot) is encouragingly small (∼0.05°) for category 1 and category 2–5 hurricanes when the first-guess displacement is small (0.1°). The RMS for these two groups increases at roughly the same rate with increasing first-guess displacement. This increase with displacement is of the same order of magnitude as the RMS at the lowest first-guess displacement, showing that the sensitivity of the ARCHER algorithm to the first-guess displacement is significant but does not reduce the overall performance appreciably, because first-guess displacements of 0.4° and greater are considerably less common. However, the ARCHER target RMS for tropical-storm-strength TCs is significantly higher. The RMS at 0.1° does not even exceed accuracy of the default displacement. However, Table 4 shows that the tropical storm ARCHER target RMS for the North Atlantic basin (0.171°) and other basins (0.173°) is lower on the whole than if the default value were used every time.

The right side of Fig. 6 shows that the percentage of defaults in the ARCHER algorithm is still significant for tropical storm and category 1 hurricanes. However, it is important to note that the frequency of occurrence of these cases decreases sharply as the displacement increases, and so these errors at displacements of 0.4 and 0.7 have only a small impact on the general algorithm performance.

Table 4 (V_max ≥ 34, All) provides the aggregate results for the ARCHER algorithm in the right two columns. Overall, the image-relative RMS of the applied ARCHER targets is 0.064° (7.1 km) for the North Atlantic basin and 0.067° (7.4 km) for all other basins. When including the cases in which ARCHER must default to the first-guess, the ARCHER image-relative RMS is 0.146° (16.2 km) for the North Atlantic basin and 0.165° (18.3 km) for all other basins. However, when considering only category 1–5 hurricanes (fourth grouping in Table 4), the overall performance is considerably better, with an image-relative RMS of 0.080° (8.8 km) in the North Atlantic and 0.087° (9.7 km) in the other basins.

d. Algorithm performance for group B TCs

The 2005 North Atlantic observations of group B TCs (eastward translation speed V_x ≥ 5 kt) verified by aircraft reconnaissance do not provide a large enough sample to perform a statistically significant validation (45, 8, and 45 cases for tropical storm, category 1, and category 2–5 hurricanes, respectively). Instead, we use a combined dataset from the 2005, 2007, and 2008 seasons to validate the ARCHER algorithm for these cases. This does not violate the independence of the calibration and validation datasets, because the group B cases for 2007–08 were not included in the calibration.

Figure 7 shows a histogram matrix corresponding to the group B validation; note that the x axes have changed in scale. In this figure, both the category 1 and category 2–5 hurricane rows show peaks in their distributions at 0.15°–0.20°, which is greater than the position of the peaks for group A storms. This suggests two possible factors: 1) a larger intrinsic error, or 2) a systematic error in resolving the center of group B storms caused by possible effects from high-shear–tilt in extratropical transition events to be expected in this grouping. Our examination of all group B images for category 2–5 storms shows that both factors are likely in effect.

Throughout the group B sample we also observe a common, alternative mode of convective organization primarily responsible for the algorithm’s systematic error here, which we will refer to as the “hook” pattern. This systematic pattern appears to contribute significantly the histogram peaks at 0.15°–0.20°. Figure 8 shows a typical example of a hook pattern. In this image, convection is dominant in the north, curving cyclonically inward toward the best-track center of rotation. However, the guided fine spiral algorithm finds a center of the curvature to the south, indicated by low-level gradients and the other banding structure. Furthermore, the absence of any clear eye leads to a weak ring score field. Thus the guided fine spiral score field dominates in the combined result and the final position falls farther away from the best track than does the first guess. This may appear to be easily remedied by weighting the spiral score less, or setting the threshold higher, but each of these options tend to increase the error in other cases—for example, by choosing the wrong eye pattern or unnecessarily defaulting to the first guess.

Table 5 provides the numerical results of the validation for group B TCs. Statistics from this table show that for group B, the ARCHER target position is used less often for tropical storms and category 1 hurricanes than it is used for group A cases of corresponding intensities. Although the target position is used in more than 50% of the cases of the category 1 grouping, the percentage of cases in which the algorithm error exceeds the 0.71° threshold (% worsened) is substantial: ∼10%. Judging by inspection of the whole dataset, the largest displacements between best-track and the ARCHER target positions occur during convective hook patterns, whereas cases with coherent eyewalls are still resolved accurately.

a. Geostationary longwave infrared

It is desirable to investigate the possibility of ARCHER working effectively on geostationary infrared (IR) imagery, because the temporal availability is much greater than that of PMW. TCs often share similar structural characteristics viewed in the IR as with the 85–92-GHz PMW imagery: curved gradients throughout the areas of convective banding, and an eye with a local brightness temperature maximum. The image values also vary in the same direction: convection causes lower brightness temperatures and subsidence causes higher brightness temperatures. The two main differences are that infrared gradients tend to be less sharp but more widespread (because IR gradients generally follow contours in cloud height rather than edges of convection–precipitation) and the eye is more often obscured. Fortunately, the ARCHER algorithm can operate well in these environments because weak gradients can have a significant effect on the spiral scores, and also, the combination of spiral scores and ring scores give the algorithm a measure of resilience to obstructions in the eye.

Figure 9 shows the performance of the ARCHER algorithm on Geostationary Operational Environmental Satellite (GOES-12) IR image during an intensifying stage of Hurricane Katrina (2005) in the Gulf of Mexico. In this scenario, the first-guess position is located 0.7° (77 km) to the west. The guided fine spiral score is affected only by the gradients of the eyewall and the minor gradients caused by rotation in the surrounding cloud cap. The ring score is at a maximum in the center of the eye, and is not adversely affected by the clouds in the southwest portion of the eye. The final result is in excellent agreement with the best-track position (within 0.05°, or 5 km).

The ARCHER performance is also good when applied to major hurricanes with no discernable eye patterns. In Fig. 10, the first-guess position is 0.7° (77 km) to the west of the best-track position, yet the spiral score is still guided to the correct center. The strong spiral score in this scenario clearly dominates the combined score, leading to a center estimate that is 0.16° (18 km) away from the best-track center.

b. The 37-GHz brightness temperature

The imagery from 37-GHz microwave radiometers, particularly at the high resolution of the AMSR-E instrument, has a number feature-tracking characteristics found in both 85–92-GHz imagery and IR imagery. This channel is sensitive primarily to microwave emission by water droplets, so the image shows the distribution of low-level precipitation in the TC. Accordingly, the image is unobstructed by high clouds as in the 85–92-GHz imagery. However, the 37-GHz image also shows a wider distribution of convective events than the 85–92-GHz image and the convective bands are similar in appearance to those in an IR image. To apply ARCHER to the horizontal polarization of 37-GHz imagery, two simple changes are necessary because the gradients are generally of the opposite sign: first, reversing the weights on positive and negative gradient cross products of the guided fine spiral score [Eq. (3)]; and, second, reversing the sign in the ring score summation term [Eq. (4)]. These changes would not be necessary on 37-GHz polarization corrected temperature (PCT) imagery, but we apply the algorithm to the horizontal polarization instead because of its better texture.

Figures 11 and 12 show the ARCHER algorithm applied to two AMSR-E 37-GHz horizontal polarization images of Hurricane Katrina (2005) in the Gulf of Mexico. The first-guess position is located 0.7° (77 km) west of the best-track position. Both cases show ample distributions of spiral-oriented edges in the convective bands to guide the spiral scores to the rotational center. The eye is also evident in both images even though it is not apparent in the corresponding IR images. This leads the algorithm toward an accurate ring score center as well. In the final result, the ARCHER positions are accurate to 0.11° (11 km) in Fig. 11 and 0.05° (5 km) in Fig. 12. Part of the reason for such close agreement is likely the fewer opportunities for intrinsic error because it represents an estimate that is much closer to the surface than that of the 85–92-GHz retrieval.