A comparison of a two-dimensional variational analysis method and a median filter for NSCAT ambiguity removal

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C6, 3176, doi: /2002jc001307, 2003 A comparison of a two-dimensional variational analysis method and a median filter for NSCAT ambiguity removal J. M. Henderson, R. N. Hoffman, and S. M. Leidner Atmospheric and Environmental Research, Inc., Lexington, Massachusetts, USA R. Atlas, E. Brin, 1 and J. V. Ardizzone 1 Goddard Space Flight Center, Greenbelt, Maryland, USA Received 16 January 2002; revised 30 July 2002; accepted 30 August 2002; published 4 June [1] The ocean surface vector wind can be measured from space by scatterometers. For a set of measurements observed from several viewing directions and collocated in space and time, there will usually exist two, three, or four consistent wind vectors. These multiple wind solutions are known as ambiguities. Ambiguity removal procedures select one ambiguity at each location. We compare results of two different ambiguity removal algorithms, the operational median filter (MF) used by the Jet Propulsion Laboratory (JPL) and a two-dimensional variational analysis method (2d- VAR). We applied 2d-VAR to the entire NASA Scatterometer (NSCAT) mission, orbit by orbit, using European Centre for Medium-Range Weather Forecasts (ECMWF) 10- m wind analyses as background fields. We also applied 2d-VAR to a 51-day subset of the NSCAT mission using National Centers for Environmental Prediction (NCEP) 1000-hPa wind analyses as background fields. This second data set uses the same background fields as the MF data set. When both methods use the same NCEP background fields as a starting point for ambiguity removal, agreement is very good: Approximately only 3% of the wind vector cells (WVCs) have different ambiguity selections; however, most of the WVCs with changes occur in coherent patches. Since at least one of the selections is in error, this implies that errors due to ambiguity selection are not isolated, but are horizontally correlated. When we examine ambiguity selection differences at synoptic scales, we often find that the 2d-VAR selections are more meteorologically reasonable and more consistent with cloud imagery. INDEX TERMS: 3337 Meteorology and Atmospheric Dynamics: Numerical modeling and data assimilation; 3360 Meteorology and Atmospheric Dynamics: Remote sensing; 3394 Meteorology and Atmospheric Dynamics: Instruments and techniques; KEYWORDS: variational data assimilation, NSCAT scatterometer, wind ambiguity removal, improving NWP representation of marine cyclones Citation: Henderson, J. M., R. N. Hoffman, S. M. Leidner, R. Atlas, E. Brin, and J. V. Ardizzone, A comparison of a two-dimensional variational analysis method and a median filter for NSCAT ambiguity removal, J. Geophys. Res., 108(C6), 3176, doi: /2002jc001307, Introduction [2] The ocean surface vector wind can be retrieved from space with scatterometers. A scatterometer measures backscatter reported as normalized radar cross section (NRCS, and usually denoted s 0 ). The backscatter responds monotonically to the apparent roughness of the ocean s centimeter-scale waves which are usually in equilibrium with the surface wind field. The apparent surface roughness on centimeter length scales depends on viewing angle relative 1 Also at General Sciences Corporation, Beltsville, Maryland, USA. Copyright 2003 by the American Geophysical Union /03/2002JC to the wind direction because the wave crests and troughs tend to be perpendicular to the wind direction. For a set of measurements that are spatially collocated but from several viewing directions, there will usually exist two, three, or four consistent wind vectors. These alternative solutions to the wind retrieval problem are known as ambiguities. Ambiguity removal procedures select one ambiguity at each location. [3] An earlier study [Hoffman et al., 2003] (hereinafter referred to as HLH) refined an existing two-dimensional variational analysis method (hereinafter 2d-VAR) for application to ambiguity removal of NASA Scatterometer (NSCAT) data. This paper compares results from 2d-VAR to those from the median filter (MF) which was used on an operational basis by the Jet Propulsion Laboratory (JPL) to 7-1

2 7-2 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT process the NSCAT data. The comparisons reported here apply the methodology of HLH to the entire NSCAT mission, as well as to a 51-day subset. For the 51-day subset, the same background fields used by JPL are used by 2d-VAR. Verification of ambiguity selection is difficult because of the sparsity of independent ocean surface wind vector data. Cloud imagery is used in HLH. As an alternative, one can examine forecast impacts, since improved ambiguity selection should result in improved forecasts. Such a study was conducted as part of this research, but the results were inconclusive. We comment on these impact experiments in the conclusion. [4] Many ambiguity removal procedures have been put forth and are listed in HLH. The two methods contrasted here are based on very different approaches, yet the ambiguity selections agree most of the time. The 2d-VAR seeks a smooth gridded analysis consistently combining in situ data, the scatterometer data, a background field, and a dynamical constraint. Ambiguities closest in direction to the 2d-VAR analysis are selected. The 2d-VAR is summarized in section 3.1 and in detail by HLH. MF, on the other hand, iteratively scans the wind field to detect and correct errors in a provisional ambiguity selection. At each iteration, MF forms a median filtered version of the currently selected ambiguities and selects the ambiguity closest to the filtered field to create the new wind field. MF is summarized in section 3.2 and in more detail by Shaffer et al. [1991]. For best results, MF is initialized with ambiguities closest to a high-quality background field. In many cases when 2d-VAR and MF disagree, the 2d-VAR solutions are more meteorologically reasonable. This does not necessarily imply they are correct. However, meteorologically unreasonable MF solutions are very likely incorrect, and we know that patently unphysical wind fields can pass through a MF unchanged. [5] We have created data sets of NSCAT 2d-VAR ambiguity selections. These data sets are available from the authors. For one data set, we applied 2d-VAR to the entire NSCAT mission, orbit by orbit, using European Centre for Medium Range Weather Forecasts (ECMWF) 10-m wind analyses as background fields, but using no other data. For NSCAT ambiguity removal, an orbit is taken to be a revolution around the Earth starting near the South Pole. For a second data set, we applied 2d-VAR to a 51-day subset of the NSCAT mission using National Centers for Environmental Prediction (NCEP) 1000-hPa wind analyses as background fields. This second data set uses the same background fields as the operational JPL data set. In all cases reported here, the NSCAT ambiguities were retrieved on a 25-km resolution grid of wind vector cells (WVCs) using the NSCAT-2 model function. [6] The plan of this paper is the following: The data sets used and produced in this study are described in more detail in section 2. The ambiguity removal methods are described in section 3. Difference statistics for the 51-day comparison are presented in section 4. The synoptic features associated with these differences are then illustrated in section 5. Case studies are presented from orbit 907, including the overflight of Hurricane Lili on 19 October In section 6, the importance of using a correct background is demonstrated by the difference statistics for a 7-day period during which NCEP background fields often were not available. Finally, section 7 contains some concluding remarks. 2. Data Sets [7] We use the ambiguous winds from the version km Merged Geophysical Data Record (MGDR) NSCAT data set produced by JPL and distributed by JPL s Physical Oceanography Distributed Active Archive Center (PODAAC). The entire data set in this format extends from 15 September 1996 (orbit 414) to 29 June 1997 (orbit 4521). For processing the entire NSCAT mission, we use ECMWF 10-m gridded wind fields every 12 hours on a longitude-latitude grid. Background fields used for 2d-VAR and MF during the 51-day period of study from 15 September to 8 November 1996 are gridded NCEP 1000-hPa wind analyses available every 6 hours at resolution obtained from JPL. The output data set is the original MGDR data set but with the ambiguity selection flag changed to the ambiguity selected by 2d-VAR. The new information is also stored in a compact form as overlay matrices relative to the WVC coordinate system. In this supplemental data set (available upon request from the authors), the matrices, one for each row, record the 2d-VAR ambiguity selections which differ from the MF selections. 3. Ambiguity Removal Procedures 3.1. Variational Analysis Method [8] The variational analysis method was originally developed to produce analyzed wind vector fields from ambiguous SeaSat-A Satellite Scatterometer (SASS) wind observations [Hoffman, 1982, 1984]. This work was important for showing that directly minimizing a large, highly nonlinear objective function was feasible. The nonlinearity comes about because of the multiple ambiguities of wind direction in the scatterometer data. At that time, wind speed information was used in conjunction with the ambiguous winds, because, at nadir, SASS observed only wind speed. Also at that time, it was suggested that the s 0 observations themselves might be used directly. Since the work on SASS, 2d-VAR has been applied to ERS-1 s 0 data and to SSMI wind speed data. The use of ERS-1 s 0 observations in a 4d- VAR system was tested by Thépaut et al. [1993]. The wind speed observations of SSMI have also been processed using the 2d-VAR for the entire period of operational SSMI data [Atlas et al., 1991, 1993, 1996]. The resulting wind fields have proven useful in forcing ocean models in several studies [Busalacchi et al., 1993; Liu et al., 1996; Atlas et al., 1996; Rienecker et al., 1996] and in assessing the impact of satellite information on surface wind stress estimates [Ponte and Rosen, 1993]. In this study, we examine the use of 2d-VAR for NSCAT ambiguity removal. [9] The variational analysis generates a gridded surface wind analysis which minimizes an objective function, J ¼ J b þ J o ; measuring the misfit of the analysis to the background, the data, and certain a priori constraints. Here, J b ¼ l VWM J VMW þ l LAP J LAP þ l DIV J DIV þ l VOR J VOR þ l DYN J DYN ; ð1þ ð2þ

3 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT 7-3 Table 1. Summary of the 2d-VAR Objective Functional a Term Expression Description of Constraint Observation Function J AMB k {1 exp[ (V a V k ) 2 ]} ambiguous winds Background Constraints J VWM R (Va V b ) 2 vector wind magnitude J LAP R [r 2 (u a u b )] 2 + R [r 2 (v a v b )] 2 Laplacian of the wind components J DIV R [r 2 (c a c b )] 2 divergence J VOR R [r 2 (y a y b )] 2 vorticity J DYN R (@za b /@t) 2 vorticity tendency a Subscript a refers to analyzed values (e.g., V a is the analyzed wind vector), subscript b to background values, and subscript k to the kth ambiguity retrieved from scatterometer data. The subscripts of the J terms are defined by the description column, and c, y, and z are the velocity potential, streamfunction and relative vorticity, respectively. For clarity, scaling factors are not included in this table. Complete definitions and our implementation are detailed by HLH. and J o ¼ l AMB J AMB : The l s are weights controlling the amount of influence each constraint has on the final analysis. Table 1 contains a summary of the constraints used. The observation function used here is somewhat similar to the approach used by Stoffelen and Anderson [1997] for ERS-1 data. Note that while 2d-VAR can use in situ data (e.g., ship and buoy reports) and other remotely sensed wind data to further constrain the problem, only NSCAT data were used in this study to make the results more directly comparable to those of MF which use no other observed data. The effects of the a priori constraints are that (1) the analysis should be close to the background field; (2) the differences between the analyzed and background wind, vorticity, and divergence should be smooth; and (3) the estimated time rate of change of the vorticity of the analysis should be small. These constraints control the degree to which the background field is modified to fit the observations. [10] For this study, the configuration for 2d-VAR is the following: (1) Data contaminated by sea ice or land are removed. (2) The background analyses are linearly interpolated to the nominal time of the orbit (defined as the midpoint between orbit start and end times), and to the 1 1 analysis grid. (3) The lambda weights are fixed at l VWM ¼ 1; l LAP ¼ 1; l DIV ¼ 4; l VOR ¼ 1; l DYN ¼ 16; l AMB ¼ 5: (4) The scaling factors applied to each of the lambda weights are taken from Hoffman [1984], S VWM ¼ ; S LAP ¼ ; S DIV ¼ 1; S VOR ¼ 1; S DYN ¼ 10 8 ; S AMB ¼ 1: [11] Only the first two ambiguities are used during a preliminary variational analysis and dual quality control (QC) is applied. Dual QC is a conceptual model of dual ambiguities based on experience. The geophysical model ð3þ ð4þ ð5þ function which relates the ocean surface wind vector to backscatter is relatively insensitive to reversals of wind direction at low incidence angle [Wentz and Smith, 1999]. There is more of this so-called upwind-downwind sensitivity for horizontally polarized measurements but NSCAT has only one antenna which makes such measurements. Therefore, for NSCAT, the wind directions of the two most likely or dual ambiguities are often opposed by 180. WVCs are suspect if this does not hold and are not included in the preliminary analysis. Specifically, if the first two ambiguities in a WVC are not at least 135 apart, the WVC is not used. Dual QC typically eliminates 20% of WVCs from the preliminary analysis. During the second and final variational analysis, all ambiguities are included. This second pass also allows for readjustment of the analysis in the few cases where the third or fourth ranked ambiguity is closest to the true wind. Note that a multipass MF could also make use of the dual QC strategy [e.g., Pak et al., 1998] Median Filter Procedure [12] Median filters have long been used to remove salt and pepper noise from images. The median of a set of numbers is that number in the set such that half of the members of the set are smaller and half are larger. In other words, it is the member of the set closest to the fiftieth percentile. An alternative definition of the median of an arbitrary set of objects is that object in the set which minimizes the sum of the distances between it and all other objects in the set. This definition is the basis of the MF-based ambiguity removal algorithm for NSCAT [Shaffer et al., 1991]. Note that this definition can be applied to vectors or directions, as well as to scalars. For scalars, distance is the absolute value of the difference. For directions, distance is the absolute value of the interior angle. For vectors, distance is the magnitude of the vector difference. [13] The vector MF is applied by JPL to the NSCAT data as follows: [14] 1. The background field closest in time to the ascending equator crossing time of the orbit is interpolated to the NSCAT WVCs, linearly in latitude and longitude, and the ambiguity with the smallest vector difference compared to the background field is selected. [15] 2. The field of selected ambiguities is median filtered making use of the WVC grid and a 7 7 stencil. That is, at each WVC, the vector median is calculated of the currently selected wind vectors in the stencil. [16] 3. If the median filtered field is equal to the current selected field, the process has converged. Otherwise, a new selected field is defined as the set of ambiguities closest to the median filtered field and the process returns to step Difference Statistics [17] There is generally very good agreement between the MF and 2d-VAR wind fields. Unless stated otherwise, the ambiguity selections at WVCs are considered to disagree, or to be a change, if the vector difference between the selected ambiguities is >2 m s 1. This criterion corresponds to small directional differences at high wind speeds, but relatively large directional differences at low wind speeds. For the 51- day subset, the MF and 2d-VAR (using the NCEP back-

4 7-4 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT Figure 1. Histogram of the number of WVCs with winds (shaded, scale on the left) and number of WVCs with changes (drawn with a solid line and filled with diagonals, number of changes above scale on the right) as a function of across-track cell number for the 51-day subset (15 September to 8 November 1996). The 2d-VAR uses the NCEP background analysis. Note that the scale on the right is exactly an order of magnitude smaller than the scale on the left. Thus, a solid horizontal line half the height of a shaded bar indicates a frequency of change of 5%. ground analysis) selected ambiguities differ in only 3.0% of the WVCs. This frequency rises only to 3.3% if we remove the above magnitude criterion. These number of differences are small compared to the total number of WVCs. However, in most of the WVCs the background is good and the ambiguity removal schemes both choose the ambiguity closest to the background. Overall, the MF and 2d-VAR selected ambiguities differ from the ambiguity closest to the NCEP background by 5.3% and 4.8%, respectively. Therefore, in the subset of WVCs where at least one of 2d-VAR or MF have chosen a different ambiguity, the differences between these two algorithms are large. [18] We now present summary statistics binned according to across-track cell number, wind speed, and geographic region for the 51-day subset. In the following three figures, both techniques use the same NCEP background fields. For this large number of orbits, there are approximately equal numbers of WVCs with winds for each cell number (Figure 1). The frequency of changes increases from 2.7% near the center of each of the two swaths to 4.1% near the outer edges of the swaths and at the edge of the nadir gap which occurs between cell numbers 24 and 25. [19] Figure 2 is similar to Figure 1 but shows the number of changes as a function of wind speed. The frequency of changes decreases from 9.6% to 0.9% with increasing wind speed. Note that this trend would be even greater if we had not eliminated WVCs with differences of <2 m s 1 between the selected ambiguities. The lower frequency of differences at high wind speeds implies that differences in ambiguity selection will be relatively rare for small mobile features with high wind speeds such as cyclones and fronts. [20] Figure 3 shows that there are more WVC comparisons in the Southern Hemisphere and that the frequency of changes decreases slightly from the Northern Hemisphere (3.4%) to the tropics (equatorward of 20 latitude) to the Southern Hemisphere (2.8%). This observation may be surprising because the large expanses of open ocean (and, hence, the many WVCs available for comparison) in the tropics and Southern Hemisphere have relatively few conventional observations. This should result in less accurate background fields. However, there are two other factors operating here. First, wind speeds are generally higher in the Southern Hemisphere, and higher wind speeds are related to fewer changes as seen in Figure 2. Second, the variability of wind direction in the tropics is relatively small, so the background wind direction is a good estimate. As will be seen in section 6, even climatology is a satisfactory background in the tropics. [21] To demonstrate the sensitivity of our technique to the choice of background analysis, we examined the effect of using ECMWF 10-m wind analyses as the background for the same 51-day subset. In general, the frequency of changes using ECMWF background analyses is qualitatively similar to those using the NCEP background analyses, though with consistently higher percentages. While using the ECMWF background, the percentage of WVCs changed increases to 3.9% of all WVCs; the percentage rises to 4.3% if WVCs with differences of <2 m s 1 between the selected ambiguities are not eliminated. The detailed results for ambiguity removal using the two background analyses are summarized in Table 2. This table also summarizes differences between the ambiguity closest to the NCEP background and the ambiguity selected by MF or 2d-VAR. The general trends observed in Figures 1 3 are present in the last two comparisons of Table 2 (i.e., the last two columns) except that the position of the maximum of cross-track changes occurs near the center of each swath for the 2d-VAR-background comparison. This is possibly due to heavier weights given to the gridded fields near the edges of the NSCAT swaths. Figure 2. WVC histograms as a function of wind speed (m s 1 ). Otherwise, as in Figure 1.

5 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT 7-5 Figure 3. WVC histograms as a function of geographic region. Otherwise, as in Figure 1. [22] An increase in the percentage of WVCs changed when using ECMWF analyses as backgrounds was expected as we provided 2d-VAR with different a priori information than MF. Even subtle differences in the wind direction of two different background analyses are likely to cause some changes in ambiguity selection. An extreme example of the effect of different background fields will be presented in section Association of Differences With Synoptic Features [23] To provide further insight into the value of 2d-VAR, we now illustrate the spatial patterns of WVCs with different ambiguity selections. Figure 4 shows the magnitude of the difference between 2d-VAR and MF-selected winds for the descending NSCAT swaths for 6 November Changes tend to occur in clumps and are associated with synoptic and mesoscale features in the wind field. In the midlatitudes, repositioning of fronts often appears as long thin bands. An example can be seen just west of Scotland and east of Japan. Such bands can extend across adjacent NSCAT orbits, even though both techniques have been applied orbit by orbit. Selection of ambiguities that differ in direction by 180 leads to more rectangular regions of changes of large magnitude (e.g., reds and blues in the Southern Hemisphere). The tropics often have mottled regions of relatively small speed changes that may be caused by rain contamination (e.g., northeast of Australia). Archived images of precipitation rate derived from SSMI F10 confirm the presence of convective rain in this region. Methods of quality control for rain contamination based on the internal consistency among the backscatter measurements and with the geophysical model function have been advanced by Figa and Stoffelen [2000], by Mears et al. [2000], and by Huddleston and Stiles [2000]. [24] We now demonstrate the ability of 2d-VAR to select a meteorologically consistent wind field using examples from orbit 907. Figure 5a shows the vector magnitude of the difference between 2d-VAR and MF-selected winds from orbit 907 over part of the North Atlantic Ocean. The narrow band-like structure of the northern end of the region of changes suggests that the ambiguity selections differ over the placement of a front. The more rectangular nature of the southern end suggests that repositioning of a cyclonic circulation is involved. The GOES brightness temperature image (Figure 5b) at 1616 UTC 19 October 1996 shows two main circulation features. The first is a region of low brightness temperatures associated with transport of abundant tropical moisture into the midlatitudes in a region of deep southeasterly flow centered south of Cape Cod. Its western edge delineates the boundary between cloudy onshore flow ahead of a large cut-off upper level low pressure area and drier offshore flow (box A ). Though not apparent in the GOES image, a surface cyclone is positioned near the upper left corner of box A. The second feature is Hurricane Lili (box B ), a category 3 hurricane [Simpson, 1974], positioned near 25 N, 72 W. Hurricane Lili is described by Pasch and Avila [1999]. The region of dark blue in the vicinity of the storm is typical of the cold cloud tops associated with the deep convection in a robust tropical cyclone. Upper level clouds extending northeast from Lili indicate southwesterly flow at high altitudes Effect of Ambiguity Removal Technique: 2d-VAR Versus MF [25] Sufficient NSCAT coverage allows us to demonstrate the ability of 2d-VAR to select a spatially smooth and meteorologically consistent wind field in the vicinity of the extratropical low just off the mid-atlantic states. The surface wind field from NCEP s Global Data Assimilation System (GDAS) is presented in Figure 5c. An extensive area of Table 2. Ambiguity Selection Changes (%) for the 51-Day Subset a Category 2d-VAR - MF 2d-VAR E - MF MF - BG 2d-VAR - BG Overall Across-track min Across-track max Wind speed min Wind speed max Region min Region max a The columns identify the comparisons between 2d-VAR, MF, and selecting the ambiguity closest to the background (BG). Comparisons are made for WVCs with more than one ambiguity and which are not flagged as having suspect data. The backgrounds used are the NCEP backgrounds except in the one case where 2d-VAR used ECMWF backgrounds (2d- VAR E ). The first row is the value for all WVCs with winds. Subsequent rows give the minimum (min) and maximum (max) value for different ways of binning the data. The bins are those shown in Figure 1 for across-track position, in Figure 2 for wind speed, and in Figure 3 for geographic region.

6 7-6 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT Figure 4. Magnitude of vector differences between MF and 2d-VAR ambiguity selections (m s 1 )for descending NSCAT passes of 6 November The 2d-VAR uses the NCEP background analysis. onshore flow exists between an elongated cyclonic circulation center positioned near the New Jersey coastline and higher pressure in the Canadian Maritimes. A trough of low pressure, as seen from the cyclonic wind shift, extends from the cyclone to the southeast and then south. (We defer discussion of Figure 5d until section 5.2.) Figure 6a (covering the region outlined by box A in Figure 5b) shows the NSCAT coverage east of the Virginia and North Carolina coastlines and along the cloud edge. Note that all ambiguities are plotted to show the spatial pattern of the retrieved winds. For reference, ambiguities closest to the NCEP background field used to initialize both the MF and 2d-VAR are shown in Figure 6b. [26] The wind field selected by MF (Figure 6c) places a 180 wind shift line oriented northwest to southeast (near 37.0 N, 74.0 W to 34.0 N, 72.0 W) well to the west of the cloud edge. There is no indication of any closed circulation in the wind field, except a small center near 32.5 N, 71.5 W in a region of light winds. [27] The ambiguities chosen by 2d-VAR using the same NCEP background (Figure 6d), however, show a welldefined and meteorologically consistent closed circulation near 36.5 N, 72.5 W, with southeasterly winds of 25 m s 1 east and northeast of the low. The trough axis and wind shift line are positioned farther to the northeast relative to the NCEP analysis and closer to the cloud edge. As in the NCEP analysis, the circulation pattern in the wind field retains its northwest-southeast elongation. [28] The 2d-VAR analysis (shown in black in Figure 5c), to which each NSCAT ambiguity s wind direction is compared as part of the 2d-VAR selection procedure, reflects the incorporation of the NSCAT wind data. The wind field in the vicinity of the northern end of the trough has been increased. At the resolution of the figure, however, there is only a hint of the closed offshore circulation that is seen in the 2d-VAR-selected ambiguities. [29] In support of the 2d-VAR-selected wind field, the mean sea-level pressure (MSLP) field from the NCEP Eta model analysis valid at 1800 UTC 19 October (Figure 7), as well as time series of MSLP analyses from ECMWF operations and the NCEP reanalysis (not shown), suggest a small-scale, and weak, transient low positioned near Figure 5. (opposite) Overview plots of the case presented. (a) Magnitude of vector differences between MF and 2d-VAR ambiguity selections for the descending portion of orbit 907 from 19 October 1996 over part of the North Atlantic Ocean. The 2d-VAR uses the NCEP background analysis. Color scale is as in Figure 4. (b) GOES-8 brightness temperature (shaded, K) at 1616 UTC 19 October 1996 and NSCAT WVC locations (black dots) from approximately 1619 UTC 19 October The boxes labeled A and B define regions presented in later figures. (c) NCEP GDAS background wind analysis (red) and 2d-VAR analysis using the NCEP background (black), valid at 1601 UTC. The resolution of all gridded fields is 1 1. Here, and in figures which follow, the wind vectors are shown in standard notation with one (half) barb representing 5 m s 1 (2.5 m s 1 ). The two analyses have been overplotted to highlight regions where NSCAT data have significantly changed the wind direction in the 2d-VAR analysis. (d) As in Figure 5c but showing ECMWF background wind analysis (red) and 2d-VAR analysis using the ECMWF background (black).

7 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT 7-7

8 7-8 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT Figure 6. NSCAT ambiguities in region A identified in Figure 5b. GOES brightness image color scale is as in Figure 5b. (a) All NSCAT ambiguities, (b) ambiguities closest to the NCEP background, (c) ambiguities selected by MF, and (d) ambiguities selected by 2d-VAR.

9 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT 7-9 Figure 7. NCEP Eta model MSLP field, overlaid by ship and buoy observations, valid at 1800 UTC 19 October N, 72.5 W within the larger northwest-southeast oriented trough. (By transient, we mean that this feature did not become the dominant circulation and that it moved steadily to the northeast within the larger trough). Also, the cyclonic curvature in the MSLP trough in these analyses agrees better with the cyclonic curvature of the 2d-VAR wind field. Note that the Eta model has higher resolution than the NCEP background field and does not incorporate NSCAT winds into its analyses. Thus, the model provides independent higher-resolution verification for the mesoscale information added by 2d-VAR. [30] Surface observations from various platforms, including ships and buoys, agree with the placement farther north of the northwest-to-southeast oriented trough in the Eta model and 2d-VAR versus MF. However, the surface observations are not dense enough to validate the existence of a closed offshore circulation embedded in the trough. Note that the observations and Eta analysis are valid approximately 105 min after the 2d-VAR analysis. This likely contributes to the Eta model s placement of the low center farther north than even the 2d-VAR position Effect of Background Field: NCEP Versus ECMWF [31] Using Hurricane Lili, we now show the effect of the choice of background field in 2d-VAR. At 1616 UTC 19 October, the storm was positioned at the southern end of the western Atlantic trough in Figure 5b. Lili, however, in both the NCEP 1000-hPa wind analysis (red wind field in Figure 5c) and the ECMWF 10-m wind analysis (red wind field in Figure 5d), is represented as an open trough, with no conclusive evidence of a closed cyclonic circulation. The trough axis in the NCEP (ECMWF) analysis extends from near 26 N, 73 W (25 N, 75 W) to 30 N, 71 W (30 N, 70 W). Thus the southern end of the trough near Lili is approximately 2 of longitude farther west in the ECMWF analysis. [32] Figure 8a shows that NSCAT data are available for the western half of Hurricane Lili according to the GOES brightness temperature image at 1616 UTC 19 October. The field of MF-selected ambiguities using the NCEP analysis as the background (Figure 8b) shows unrealistic discontinuities in the wind direction around Lili. In contrast, the 2d- VAR-selected ambiguities also using the NCEP analysis as the background (Figure 8c) depict a physically realistic cyclonic circulation centered around the warmest (yellow) pixel, which is likely the center of Lili. Just to the northwest of the center of Lili, isolated locations where the wind field shows discontinuities in the wind direction are WVCs with only two retrieved ambiguities (see Figure 8a). The difference in ambiguity selections between MF (in Figure 8b) and 2d-VAR (in Figure 8c) is a result of the choice of ambiguity removal scheme, since both methods used the NCEP analysis as the background.

10 7-10 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT Figure 8. As in Figure 6, but for region B. (a) All NSCAT ambiguities, (b) ambiguities selected by MF, (c) ambiguities selected by 2d-VAR using the NCEP background analysis, and (d) ambiguities selected by 2d-VAR using the ECMWF background analysis.

11 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT 7-11 Figure 9. Histogram of the number of WVCs with winds and number of WVCs with changes as a function of across-track cell number for batch 37. The 2d-VAR uses the ECMWF background analysis. Otherwise, as in Figure 1. [33] The sensitivity to the background analysis is illustrated in Figure 8d. The 2d-VAR-selected ambiguities using the ECMWF background result in strong easterly and southeasterly surface winds through most of the deep convection of Lili. This is a consequence of the ECMWF s placement of the southern end of the trough at least 2 farther west than in the NCEP background field. 6. Effect of an Incorrect Background [34] We now present results for NSCAT batch 37 (orbits 3852 to 3950, May 1997), which has an anomalously high number of changes. MF ambiguity selections are of poorer quality than for other periods because the NCEP analyses were often not available, in which case a wind climatology was used to initialize the MF. We compare these MF ambiguity selections to 2d-VAR ambiguity selections which used ECMWF analyses as background fields. The trends with respect to cell and wind speed for this period are similar to other periods, but all frequencies of changes are larger. Figure 9 shows that the rate at which MF and 2d-VAR select different ambiguities varies from 6.6% to 8.4% or approximately 4% higher than in Figure 1. Similarly, Figure 10 shows a decrease in the rate of changes with increasing wind speed similar to Figure 2, but, in this case, the decrease with increasing wind speed is slower and the frequency remains at or above 5% for winds > 9 m s 1. On the other hand, Figure 11 is considerably different from Figure 3. The number of changes in the Southern Hemisphere increases from 2.7% to 9.1%, but in the tropics there is only a small impact. Apparently, climatology is sufficiently good in the tropics where the day-to-day variability of wind direction is small. 7. Conclusions [35] NSCAT winds are generally of high accuracy if ambiguity removal is successful [Freilich and Dunbar, 1999; Atlas et al., 1999]. For most WVCs, this condition is met [Gonzales and Long, 1999]. We have compared results of two different ambiguity removal algorithms: the operational MF as implemented by JPL and our own 2d-VAR. Agreement is very good over a 51-day subset of the NSCAT mission when both methods use the same NCEP background fields. Only in approximately 3% of the WVCs do MF and 2d-VAR select different ambiguities. When 2d-VAR uses the ECMWF backgrounds, the frequency of changes increases to approximately 4%. These values are to be compared to the approximately 5% frequency of changes for MF or 2d-VAR when each is compared to the ambiguity closest to the background. The quality of the background affects the ability of the ambiguity removal to select the proper wind field. For example, in batch 37, NCEP analyses were often unavailable to JPL and a climatological wind field was used as the background for the MF. This more than doubles the frequency of changes in the extratropics and presumably results in a much higher occurrence of an incorrect ambiguity being chosen (compare Figures 3 and 11). [36] When using a good background, the ambiguity selection error rate is low, approximately 5% according to HLH and Gonzales and Long [1999]. A good background is critical to resolve the inherent 180 ambiguity of the NSCAT winds. Ambiguity selection is most difficult in Figure 10. Histogram of the number of WVCs with winds and number of WVCs with changes as a function of wind speed for batch 37. The 2d-VAR uses the ECMWF background analysis. Otherwise, as in Figure 1.

12 7-12 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT Figure 11. Histogram of the number of WVCs with winds and number of WVCs with changes as a function of geographic region for batch 37. The 2d-VAR uses the ECMWF background analysis. Otherwise, as in Figure 1. regions where the background flow crosses the steamlines implied by the two most likely ambiguities. Indeed, we see that WVCs with changes occur in patches. Since at least one of the selections is in error, this implies that errors due to ambiguity selection are not isolated but are horizontally correlated. Such errors present a challenge to existing data assimilation systems. Since any error in the background field may degrade ambiguity selection, and since smaller scales are less accurate than larger scales in the background, ambiguity removal may be enhanced by using a smoother background. Techniques based on planetary boundary layer models to convert winds to pressure fields, that are then spatially filtered and converted back to winds have recently been developed for ambiguity removal [Kim, 2000]. These techniques may eliminate or greatly limit the need for background fields. [37] Both 2d-VAR and MF are mathematical techniques, but they have different objectives. The 2d-VAR produces analysis increments which are smooth, while MF removes random noise while preserving sharp features. The 2d-VAR includes more a priori meteorological information in terms of using the background as a constraint and using the dynamical balance of the vorticity equation. When we examine ambiguity selection differences on synoptic scales, we often find that the 2d-VAR selections are more meteorologically reasonable and more consistent with cloud imagery. HLH validated somewhat different configurations of both MF and 2d-VAR using cloud imagery for 29 cases of significant ambiguity selection differences. They concluded that the MF results were clearly superior in only two cases, but that the 2d-VAR results were superior in seven cases. Together, HLH and this study suggest that the 2d- VAR selections tend to be superior than MF selections. [38] Since incorrect selections may have a deleterious effect on data assimilation system analyses and forecasts of particular synoptic events, even small improvements in ambiguity selection may have significant associated forecast improvements. Thus Atlas and Hoffman [2000] reported that using s 0 data in 2d-VAR to select ERS-1 ambiguities could significantly improve forecast skill relative to using a version of the wind retrieval and ambiguity selection method of Offiler [1992]. However, in experiments with the NASA Data Assimilation Office (DAO) modeling system, we find essentially no effect on global forecast skill scores when changing from MF to 2d-VAR-selected NSCAT winds. These experiments parallel the experiments reported by Atlas et al. [2001] which used version 2 of the Goddard Earth Observing System data assimilation system (GEOS-2 DAS), including asynoptic treatment of the scatterometer winds. These findings are consistent with the small number of different ambiguity selections between 2d-VAR and MF and the effectiveness of the DAO QC system at removing NSCAT ambiguity selection errors [Atlas et al., 1999]. In addition, the number of different ambiguity selections between 2d-VAR and MF is especially small for high wind speeds implying little potential for difference when forecasting mature storms and associated fronts. [39] In a related set of experiments at ECMWF, we find that while NSCAT data are useful in forecasting tropical cyclones in a 4d-VAR system, the impact on global forecast skill scores is also effectively zero [Leidner et al., 2003]. In such cases, where the impact of the entire data set is marginal, the impact of improvements in ambiguity removal might be expected to be negligible. However, evidence from the ECMWF NSCAT experiments and more recent experiments with SeaWinds suggest that, with a higher resolution version of the model, NSCAT might have had a larger impact. In fact, now at ECMWF, the model resolution is finer (40 km), and SeaWinds data are used operationally. Good results were obtained once the experimental Sea- Winds rainflags were used in the QC procedure. We anticipate even greater impacts with refined rainflags and ambiguity removal procedures. Candidate methods are currently under investigation by several groups, including the authors. Two-dimensional variational algorithms such as 2d-VAR will be a useful testbed for evaluating and refining some of these methods before implementation in operational data assimilation systems. [40] Acknowledgments. Data used in the research reported here were provided by the Jet Propulsion Laboratory (JPL) Physical Oceanography Distributed Active Archive Center (PO.DAAC), the National Center for Environmental Prediction (NCEP), and the European Centre for Medium- Range Weather Forecasts (ECMWF). General Sciences Corporation is a subsidiary of Science Applications International Corporation. This research was supported by the NASA scatterometer projects. References Atlas, R., and R. N. Hoffman, The use of satellite surface wind data to improve weather analysis and forecasting, in Satellites, Oceanography and Society, Elsevier Oceanogr. Ser., vol. 63, edited by D. Halpern, pp , Elsevier, New York, Atlas, R., S. C. Bloom, R. N. Hoffman, J. V. Ardizzone, and G. Brin, Space-based surface wind vectors to aid understanding of air-sea interactions, Eos Trans. AGU, 72, , Atlas, R., R. N. Hoffman, and S. C. Bloom, Surface wind velocity over the oceans, in Atlas of Satellite Observations Related to Global Change, edited by R. J. Gurney, J. L. Foster, and C. L. Parkinson, pp , Cambridge Univ. Press, New York, 1993.

13 HENDERSON ET AL.: COMPARING AMBIGUITY REMOVAL METHODS FOR NSCAT 7-13 Atlas, R., R. N. Hoffman, S. C. Bloom, J. C. Jusem, and J. Ardizzone, A multiyear global surface wind velocity data set using SSM/I wind observations, Bull. Am. Meteorol. Soc., 77, , Atlas, R., S. C. Bloom, R. N. Hoffman, E. Brin, J. Ardizzone, J. Terry, D. Bungato, and J. C. Jusem, Geophysical validation of NSCAT winds using atmospheric data and analyses, J. Geophys. Res., 104, 11,405 11,424, Atlas, R., et al., The effects of marine winds from scatterometer data on weather analysis and forecasting, Bull. Am. Meteorol. Soc., 82, , Busalacchi, A. J., R. M. Atlas, and E. C. Hackert, Comparison of Special Sensor Microwave Imager vector wind stress with model-derived and subjective products for the tropical Pacific, J. Geophys. Res., 98, , Figa, J., and A. Stoffelen, On the assimilation of Ku-band scatterometer winds for weather analysis and forecasting, IEEE Trans. Geosci. Remote Sens., 38, , Freilich, M. H., and R. S. Dunbar, The accuracy of the NSCAT 1 vector winds: Comparisons with National Data Buoy Center buoys, J. Geophys. Res., 104, 11,231 11,246, Gonzales, A. E., and D. G. Long, An assessment of NSCAT ambiguity removal, J. Geophys. Res., 104, 11,449 11,457, Hoffman, R., SASS wind ambiguity removal by direct minimization, Mon. Weather Rev., 110, , Hoffman, R. N., SASS wind ambiguity removal by direct minimization: II. Use of smoothness and dynamical constraints, Mon. Weather Rev., 112, , Hoffman, R. N., S. M. Leidner, J. M. Henderson, R. Atlas, J. V. Ardizzone, and S. C. Bloom, A two-dimensional variational analysis method for NSCAT ambiguity removal: Methodology, sensitivity, and tuning, J. Atmos. Oceanic Technol., 20, , Huddleston, J. N., and B. W. Stiles, A multidimensional histogram rainflagging technique for SeaWinds on QuikSCAT, paper presented at International Geoscience and Remote Sensing Symposium (IGARSS), Inst. of Electr. and Electr. Eng., Honolulu, Hawaii, Kim, Y.-J., A physical-model-based, field-wise and self-contained algorithm for removing directional ambiguities of ocean surface winds retrieved from scatterometer measurements, Geophys. Res. Lett., 27, , Leidner, S. M., L. Isaksen, and R. N. Hoffman, Impact of NSCAT winds on tropical cyclones in the ECMWF 4D-Var assimilation system, Mon. Weather Rev., 131, 3 26, Liu, W. T., W. Tang, and R. Atlas, Responses of the tropical Pacific to wind forcing as observed by spaceborne sensors and simulated by an ocean general circulation model, J. Geophys. Res., 101, 16,345 16,359, Mears, C., D. Smith, and F. Wentz, Detecting rain with QuikSCAT, paper presented at International Geoscience and Remote Sensing Symposium (IGARSS), Inst. of Electr. and Electr. Eng., Honolulu, Hawaii, Offiler, D., Wind retrieval and ambiguity removal, EPIPVS Project Note 9, Met Office, Bracknell, UK, Pak, K. S., Y.-J. Kim, P. S. Callahan, R. S. Dunbar, S. V. Hsiao, and A. Zhang, A multi-pass median filter technique to remove ambiguities in retrieved wind fields from spaceborne scatterometer data, paper presented at International Geoscience and Remote Sensing Symposium (IGARSS), Inst. of Electr. and Electr. Eng., Seattle, Wash., Pasch, R. J., and L. A. Avila, Atlantic hurricanes of 1996, Mon. Weather Rev., 127, , Ponte, R. M., and R. D. Rosen, Determining torques over the ocean and their role in the planetary momentum budget, J. Geophys. Res., 98, , Rienecker, M. M., R. Atlas, S. D. Schubert, and C. A. Willett, A comparison of surface wind products over the North Pacific Ocean, J. Geophys. Res., 101, , Shaffer, S. J., R. S. Dunbar, S. V. Hsiao, and D. G. Long, A median-filterbased ambiguity removal algorithm for NSCAT, IEEE Trans. Geosci. Remote Sens., 29, , Simpson, R. H., The hurricane disaster potential scale, Weatherwise, 27, , Stoffelen, A., and D. Anderson, Ambiguity removal and assimilation of scatterometer data, Q. J. R. Meteorol. Soc., 123, , Thépaut, J.-N., R. N. Hoffman, and P. Courtier, Interactions of dynamics and observations in a four-dimensional variational assimilation, Mon. Weather Rev., 121, , Wentz, F. J., and D. K. Smith, A model function for the ocean-normalized radar cross section at 14 GHz derived from NSCAT observations, J. Geophys. Res., 104, 11,499 11,514, J. V. Ardizzone, R. Atlas, and E. Brin, NASA Goddard Space Flight Center, Mail code 910.3, Greenbelt, MD 20771, USA. ( jardizzone@ dao.gsfc.nasa.gov; ratlas@dao.gsfc.nasa.gov; ebrin@dao.gsfc.nasa.gov) J. M. Henderson, R. N. Hoffman, and S. M. Leidner, Atmospheric and Environmental Research, Inc., 131 Hartwell Avenue, Lexington, MA 02421, USA. ( jhenders@aer.com; rhoffman@aer.com; mleidner@aer.com)