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  • View in gallery

    NSCAT 24-h global coverage, depicting about 14 polar orbits of the dual swath pattern (two 600-km-wide swaths, separated by a 400-km nadir gap). A complete orbit consists of an ascending branch (SE to NW) toward the North Pole and a descending branch (NE to SW) toward the South Pole. Successive orbits precess westward. The orbits from the first 12-h period are dark shaded, and the orbits from the second 12-h period are light shaded. Within-swath resolution for the NSCAT-2 surface wind retrievals is 25 km.

  • View in gallery

    Bin-weight distributions for (a) wind stress and (b) wind stress curl at 0.5° resolution, for the 9-month period 1 Oct 1996–29 Jun 1997, spanning the NSCAT mission lifetime. Color bars and contour levels have been selected to emphasize bin-weight anomalies.

  • View in gallery

    Wind stress curl calculation schematic for an arbitrary 2 × 2 bin quadrangle at 0.5° resolution. Small dots represent NSCAT wind retrieval locations. Wind stress component bin averages, 〈τx〉 and 〈τy〉, are assigned to the bin centers (circles). Meridional gradients, ∂〈τx〉/∂y, are computed across the western and eastern bins (squares). Zonal gradients, ∂〈τy〉/∂x, are computed across the northern and southern bins (triangles). The averages of these gradients are subtracted to form the wind stress curl (solid diamond). Surrounding wind stress curl locations are denoted by open diamonds.

  • View in gallery

    The global distribution of NSCAT 9-month-average wind stress curl at 0.5° resolution. Wind stress curl is computed orbit by orbit as described in Fig. 3, and averaged over the lifetime of the mission. Units for this and subsequent color bars for wind stress curl plots are ×10−8 N m−3.

  • View in gallery

    The global distribution of NSCAT 9-month-average wind stress curl as in Fig. 4 but using 1° bins.

  • View in gallery

    The global distribution of NSCAT 9-month-average wind stress curl as in Fig. 4 but using bins from a Gaussian grid consistent with a T62 spectral model truncation. Bin dimensions in longitude are 1.875°. In latitude, the bin dimensions vary between 1.8° and 1.9°.

  • View in gallery

    The global distributions of NSCAT 9-month-average wind stress components in the (a) zonal (τx), and (b) meridional (τy) directions. The 25-km NSCAT-2 wind retrievals are collected in 0.5° bins and averaged.

  • View in gallery

    NSCAT enhanced 9-month wind stress curl at 0.5° resolution. Global surface winds from the NCEP CDAS are blended with coincident NSCAT winds as described in the appendix of Milliff et al. (1999b). The surface winds from the NSCAT enhanced dataset for the period 1 Oct 1996–29 Jun 1997 have been binned and differenced as in Fig. 4 to create a comparable 9-month-average wind stress curl.

  • View in gallery

    Representations of the analytic storm experiments described in the text. For purposes of illustration, the (a) wind stress (maximum vector length = 1 N m−2) and (b) wind stress curl are depicted for a time when an analytic storm is centered in the North Pacific domain. The NSCAT sample locations are depicted for a typical descending orbit at the wind stress locations in (a) and the valid wind stress curl locations in (b). Forty-day time series for (c) analytic τx, (d) analytic τy, and (e) analytic wind stress curl are taken from the experimental sequence as it crossed the domain midpoint. NSCAT samples of the time series are marked by dots, and 3-hourly sampling is marked by vertical lines for each time series. Plus signs in (e) mark wind stress curl values derived from the real NSCAT data for the time period at 40°N, 180°.

  • View in gallery

    Comparisons of 9-month-average wind stress curls in the North Pacific study domain from (a) the analytic storm sequence sampled at every grid point, every 3 h; (b) the analytic storm sequence sampled by NSCAT swaths; and (c) the real NSCAT data.

  • View in gallery

    NCEP CDAS 9-month-average wind stress curl on the Gaussian grid consistent with T62 spectral truncation. This figure compares directly with Fig. 6 based on the NSCAT data.

  • View in gallery

    The global distributions of wind stress divergence from 9-month averages on a T62 grid from (a) the NSCAT record and (b) the NCEP CDAS. Units are ×10−8 N m−3.

  • View in gallery

    Wind stress curl averaged (off South America) in 0.5° bins for the first 83 days of the NSCAT mission (26 Sep–18 Dec 1996) as derived from (a) the NSCAT-2 model function with NWP nudging as in Fig. 4 (25-km resolution), (b) the NSCAT-1 model function with NWP nudging (50-km resolution), and (c) the NSCAT-1 model function without NWP nudging (50-km resolution). White areas in (b) and (c) occur where a minimum bin weight of 30 was not achieved.

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The Global Distribution of the Time-Average Wind Stress Curl from NSCAT

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Abstract

The time-average wind stress curl field for the global ocean is computed from the wind retrievals of the NASA Scatterometer (NSCAT) mission spanning the period 1 October 1996–29 June 1997. Particular attention is paid to large-amplitude, small-scale “patchiness” in the average wind stress curl over the major ocean basins, and to long and narrow wind stress curl features that occur along ocean eastern boundary regions. The 9-month-average wind stress curl field from NSCAT is examined at 0.5°, 1°, and on a Gaussian grid consistent with T62 truncation in a spectral forecast model. The latter field is compared with the average wind stress curl field from NCEP analyses for the same period. Artifacts in the NCEP average overlap the regions of boundary wind stress curl extrema in the high-resolution averages from NSCAT. The artifacts are attributed to the effects of spectral truncation and tall near-coastal topography in the NCEP forecast model. Possible explanations are discussed for the boundary wind stress curl features that are most pronounced in the NSCAT data with 0.5° resolution. Patchiness in the average wind stress curl fields from NSCAT is considered in the context of aliases introduced by the complex spatiotemporal sampling pattern, and given the intermittency and large gradients that characterize the true wind stress curl field over the ocean. Implications from this rather detailed study of a single broad-swath, active scatterometer system are timely in light of recent plans for international cooperation in providing more than a decade of near-mesoscale resolution of the global surface vector wind field.

Corresponding author address: Dr. Ralph F. Milliff, Colorado Research Associates (a division of NWRA), 3380 Mitchell Lane, Boulder, CO 80301.

Email: milliff@colorado-research.com

Abstract

The time-average wind stress curl field for the global ocean is computed from the wind retrievals of the NASA Scatterometer (NSCAT) mission spanning the period 1 October 1996–29 June 1997. Particular attention is paid to large-amplitude, small-scale “patchiness” in the average wind stress curl over the major ocean basins, and to long and narrow wind stress curl features that occur along ocean eastern boundary regions. The 9-month-average wind stress curl field from NSCAT is examined at 0.5°, 1°, and on a Gaussian grid consistent with T62 truncation in a spectral forecast model. The latter field is compared with the average wind stress curl field from NCEP analyses for the same period. Artifacts in the NCEP average overlap the regions of boundary wind stress curl extrema in the high-resolution averages from NSCAT. The artifacts are attributed to the effects of spectral truncation and tall near-coastal topography in the NCEP forecast model. Possible explanations are discussed for the boundary wind stress curl features that are most pronounced in the NSCAT data with 0.5° resolution. Patchiness in the average wind stress curl fields from NSCAT is considered in the context of aliases introduced by the complex spatiotemporal sampling pattern, and given the intermittency and large gradients that characterize the true wind stress curl field over the ocean. Implications from this rather detailed study of a single broad-swath, active scatterometer system are timely in light of recent plans for international cooperation in providing more than a decade of near-mesoscale resolution of the global surface vector wind field.

Corresponding author address: Dr. Ralph F. Milliff, Colorado Research Associates (a division of NWRA), 3380 Mitchell Lane, Boulder, CO 80301.

Email: milliff@colorado-research.com

1. Introduction

Wind stress curl is the principal source of relative vorticity in theories of the wind-driven general circulation of the World Ocean (e.g., see the first few chapters of Pedlosky 1996). Away from western boundaries, the Sverdrup balance can be used to derive a transport streamfunction at a point that is proportional to the line integral of the wind stress curl, along a line of latitude starting from the eastern boundary of an ocean basin and ending at the point in question. In the vertical, the integral effect of direct mechanical forcing of the upper ocean is an Ekman pumping that perturbs the oceanic thermocline. Thermocline perturbations stretch vortex tubes, changing the relative vorticity of parcels over the full depth of the fluid. Conservation of potential vorticity requires that changes in relative vorticity be compensated by changes in position within the planetary vorticity gradient (i.e., meridional translations). In this theoretical context, the wind-driven general circulation can be considered for the whole fluid system to be the response to wind stress curl perturbations at the surface, as the system adjusts toward re-equilibration. Thus, the long-term average wind stress curl field contributes to our intuition for the ocean general circulation.

These fundamental concepts invoke very large spatial scales in the horizontal O(103–104 km). For the development of these concepts it has been sufficient to consider the wind stress curl variability only on these large scales. However, the capabilities of present-day observing systems and ocean numerical models are reaching levels of sophistication that focus attention on the synoptic-scale variability of the wind stress curl as well [O(102–103 km); e.g., Bryan and Smith 1998; Granier and Schopp 1999; Milliff et al. 1999b; Smith et al. 2000]. The synoptic-scale wind stress curl field is composed of large-amplitude events associated with atmospheric storms, and a background variability that is less well known. Our intuition for temporal and spatial variability is more likely to be developed with respect to the surface winds rather than the wind stresses or wind stress curls. Wind stress amplitudes vary as the square of the winds, which augments the dynamic range and high-frequency variability. The wind stress curl field is a spatial gradient of the wind stress, which increases the relative amplitudes of high wavenumbers. So the synoptic-scale wind stress curl field is geometrically more variable in space and time than the surface winds with which we are more familiar. One purpose of this paper is to examine the extent to which the relative contributions to the long-term average wind stress curl by the background variability and the storm-scale events can be measured and distinguished.

It is apparent that there are effects on the ocean general circulation that are driven by synoptic-scale structures in the wind stress curl. In midlatitude coastal domains along eastern boundaries of the World Ocean, wind stress curl extrema are indicative of smaller-scale dynamics associated with coastal upwelling (e.g., Nelson 1977; Husby and Nelson 1982; Bakun and Nelson 1991). Equatorward surface winds, and the lateral shears adjacent to the land–sea boundary, intensify on seasonal and synoptic timescales. This forcing induces an offshore mass flux in the upper ocean that is compensated near the coast by vertical flux of nutrient-rich, colder waters from below the surface. Spatial scales for coastal upwelling centers are on the order of several local first-baroclinic mode radii of deformation; O(10–102 km). The coastal upwelling centers localize on particular features of the coastal bathymetry and near-coastal topography, for example, capes, points, etc. Coastal upwelling is associated with fog and marine clouds thereby influencing indirectly the ocean general circulation through effects on air–sea exchanges of heat and moisture, and solar and longwave radiation (Kiehl et al. 1998).

Milliff et al. (1996) demonstrated that persistent eastern boundary wind stress curl features induce changes in the time-mean structure of the midlatitude subtropical gyres. Eastern boundary wind stress curl features occur in narrow cross-shore and elongated alongshore structures that align with ocean eastern boundaries and can overlap coastal upwelling centers. In long-term wind stress curl maps based on satellite-derived surface winds (see below), the boundary wind stress curl features are most apparent off subtropical gyre regions of North and South America, and northern and southern Africa. We identify these structures with the features first described by Nelson (1977). The time-average alongshore extent of these features exceeds 10° in latitude. We will explore upper bounds for the cross-shore scales in these regions in this paper.

Features of the synoptic wind stress curl field over the ocean are becoming apparent due to a growing database of surface wind observations from spaceborne scatterometers. However, true mesoscale resolution [O(100–102 km)] for the globe has yet to be achieved. This paper examines in some detail the sampling effects of the National Aeronautics and Space Administration (NASA) Scatterometer (NSCAT) system on an estimate of the average wind stress curl field for the global ocean. NSCAT represents a prototype for spaceborne, broad-swath, active scatterometer systems, which are being coordinated internationally to provide for more than a decade of near-mesoscale resolution of the surface vector wind field over the ocean (e.g., SeaWINDS on QuikSCAT, SeaWlNDS on ADEOS-II, ASCAT on METOP, alphaSCAT on GCOM-B1; see Milliff et al. 1999a). It follows from what will be shown here that a single broad-swath system is not sufficient to provide unaliased wind stress curl fields adequate to force the most sophisticated ocean models. While ocean model responses to wind forcing from NSCAT data is not the subject of this paper, the interested reader is referred to several recent papers that document these effects (e.g., Chen et al. 1999a,b; Chu et al. 1999; Kelly et al. 1999;Milliff et al. 1999b; Verschell et al. 1999).

In this paper we examine the global wind stress curl field averaged over the lifetime of the NSCAT mission. The present-day scatterometer database for the globe, and the NSCAT contribution to that database, are reviewed in section 2. Methods for computing average global wind stress curl maps from NSCAT winds are described in section 3. In section 4, we present several estimates of the average wind stress curl field from these data. These are compared with estimates from surface wind analyses from the National Centers for Environmental Prediction (NCEP) for the same time period. Implications of the average wind stress curl fields are discussed in section 5, and a summary is provided in section 6.

2. Data

Active scatterometer instruments direct radar energy, of known frequency and polarization, toward the sea surface where the radar is scattered by surface roughness elements in the wind-generated waves on the scale of the incident radar energy (e.g., capillary waves in the case of NSCAT). The backscattered radar return, or so-called ocean normalized radar cross section σ0, is the fundamental observation detected by the satellite antennae. Several σ0 overlap each surface resolution element or wind vector cell (WVC), providing sufficient overspecification to permit wind retrievals accurate to within a few meters per second in wind speed, and within O(20°) in wind direction, across a broad range of environmental conditions (e.g., see NASA Scatterometer Project 1998). The accuracies vary depending upon instrument system characteristics of the radar, and the number of σ0 per wind retrieval, as well as upon environmental conditions such as rain, calms, and/or very high wind speeds. The wind retrieval is achieved by a functional fit to an empirically derived relation between σ0 and the vector wind (i.e., speed and direction) that is called a geophysical model function (e.g., Freilich and Dunbar 1993; Wentz and Smith 1999).

The concept of spaceborne scatterometry was proved by the short-lived SEASAT mission in 1978. It was not until late 1991 that another scatterometer instrument was flown in space aboard the European Space Agency ERS-1 platform (Attema 1991). The ERS-1 platform was succeeded in 1995 by an identical system, ERS-2, which operates to this day. The ERS-1,2 set is the longest unbroken surface wind record from scatterometer observations. However, the ERS-1,2 data coverage is suboptimal in that 1) the scatterometer instrument was/is turned off frequently to divert onboard power to a synthetic aperture radar instrument; 2) the data occur in single, narrow swaths (500 km wide) off one side of the polar-orbit ground track, leaving 2300-km-wide gaps between adjacent swaths; and 3) the radar frequency used (C band) is not sufficiently sensitive to surface wind direction variations at wind speeds less than about 5 m s−1 (Freilich 1997; H. Graber 1997, personal communication). The nominal resolution of the surface wind field retrieval for the ERS systems is 50 km within the swath (Attema 1991).

a. NSCAT data

NSCAT was launched aboard the ADEOS-I platform of the National Space Development Agency of Japan in August 1996. Surface winds were retrieved from NSCAT observations beginning 15 September 1996. The NSCAT data stream came to an unexpected end with the failure of ADEOS-I on 30 June 1997. NSCAT observations occur off both sides of the spacecraft (2 × 600 km swaths) with a 400-km gap at nadir, leaving a gap of about 1200 km between swaths at the equator (Naderi et al. 1991; Spencer and Graf 1997). For about 83 days, data records were produced with a preliminary geophysical model function during the early part of the NSCAT mission. These are the so-called NSCAT-1 data, and the within-swath resolution is 50 km. The model function was refined and the entire NSCAT record reprocessed to create the NSCAT-2 dataset. The within-swath resolution for vector winds from NSCAT-2 is 25 km. A broad sample of calibration studies and early science results based on NSCAT data follow the guest editorial by O’Brien (1999).

The surface winds from NSCAT data used in this paper are based on the NSCAT-2 model function retrievals (Wentz and Smith 1999; NASA Scatterometer Project 1998) as provided by the Physical Oceanography Distributed Active Archive Center at the Jet Propulsion Laboratory (see http://podaac-www.jpl.nasa.gov). The time period of interest spans the majority of the NSCAT record, from October 1996 through June 1997. The NSCAT sampling pattern derives from a near-polar orbit (inclined about 8.6°) with an orbital period of about 100 min. The global swath pattern for a 24-h period is shown in Fig. 1. The portions of the satellite track that incline from southeast to northwest are the ascending branches, and the portions inclined northeast to southwest are the descending branches of the orbits. Because of the rotation direction of the earth, the swath sampling precesses westward with time such that the earliest orbit in Fig. 1 is the ascending branch in the Atlantic basin and the descending counterpart in the extreme western Pacific and Indian Oceans. About 14 complete orbits are achieved per day, and a given orbit is repeated exactly every 41 days. Surface vector winds are retrieved for about 98% of the ice-free global ocean every 2 days.

Thus, over any given 2-day period, WVCs in the low- and midlatitude ocean are typically sampled 2 times (about 12 h apart) on the first day, and then not at all on the second day. Because sequential orbits overlap at high latitudes, a WVC there can be sampled 4 times on the first day, for example, twice in the morning (100-min interval), and then twice again in the evening by another pair of sequential orbits. The same high-latitude WVC might also not be sampled at all on the second day.

b. NCEP analyses

For comparison (section 4), we present wind stress curl from surface winds of the NCEP analyses, averaged over the same time period as the NSCAT data. The analysis fields are the products of the NCEP Climate Data Assimilation System (CDAS), which was the operational system developed for the NCEP–NCAR reanalysis (Kalnay et al. 1996). The CDAS surface winds are available 4 times each day (at 0000, 0600, 1200, and 1800 UTC) on a Gaussian grid consistent with T62 resolution (i.e., triangular truncation, admitting 62 zonal wavenumbers).

c. NSCAT enhanced winds

We will also discuss comparisons with an averaged wind stress curl field from so-called NSCAT enhanced winds. The enhanced winds derive from a blend of high-wavenumber, but intermittent, NSCAT data with low-wavenumber, but ubiquitous, surface winds from the NCEP CDAS. The enhanced-wind dataset is described in the appendix of Milliff et al. (1999b), and the details of the blending methodology are the subject of Chin et al. (1998).

The blending creates global fields of surface winds by retaining NSCAT wind retrievals in swath regions, and in the unsampled regions (nadir and interswath gaps) augmenting the low-wavenumber NCEP fields with a high-wavenumber component that is derived from monthly regional NSCAT statistics (i.e., statistics accumulated over 4° × 8° bins). Twelve hours are required to achieve uniform global coverage from any single satellite system of NSCAT class (see Fig. 1). But the NCEP analyses are available every 6 h. Therefore, overlapping 12-h composites of NSCAT data are used in the blending procedure to create NSCAT enhanced winds every 6 h. Thus, the blended wind fields come from completely independent sets of NSCAT observations and analyses every 12 h. This procedure minimizes aliasing due to gaps in space of the NSCAT data but cannot prevent aliasing due to gaps in time because of the relatively infrequent NSCAT sampling.

3. Methodology

The wind stress curl is given by
i1520-0469-58-2-109-e1
where τ(x, y) are the zonal and meridional components of the surface wind stress. The surface wind stress, for each component, is derived from a standard drag law relation as in (for the zonal component):
τxρacDU10u,
where ρa = 1.2 kg m−3 is a typical density for the atmosphere near the sea surface. We let U10 = u2 + υ2 be the wind speed at 10-m height above the surface, which corresponds to the reference height for the NSCAT-2 winds (for u eastward, and υ northward, velocity components). We use a bulk transfer form for the dimensionless drag coefficient cD that depends on U10 as in Large et al. (1994). So assuming a neutral stability profile from the surface to 10 m:
i1520-0469-58-2-109-e3
Note that the drag laws for (τx, τy) in (2) are nonlinear in the wind components (u, υ).

Equation (1) is discretized in a centered finite-difference form to approximate wind stress curl. The discrete grid for time-averaged wind stress results from the accumulation of NSCAT wind retrievals into spatial bins that tile the globe. For 25-km resolution in the surface winds from NSCAT, the highest resolution that is natural for surface wind stress curl is 50 km, given the spatial derivative operation in (1).

Since we are interested in the time-average wind stress curl field for the globe, it is easier to discretize in latitude and longitude rather than in kilometers. This introduces the possibility of uneven distributions of wind retrievals as a function of latitude because the number of kilometers per degree longitude decreases as the cosine of the latitude. But the NSCAT orbits must necessarily come closer together at higher latitudes to overlap near the Poles. We will see in Fig. 2 that these effects nearly compensate in terms of the number of wind retrievals per latitude–longitude bin over 9 months. However, the distribution in time of the wind retrievals per grid element is a complicated function, and this can introduce a bias in the average curl. We investigate this further in section 4.

The number of surface wind retrievals per bin defines a bin weight. The bin-weight distributions for 0.5° bins, for the 9-month NSCAT period, are depicted in Fig. 2a for wind stress, and in Fig. 2b for wind stress curl. The color scale has been selected to emphasize uneveness in the bin-weight distributions. The bin weights for wind stress curl (Fig. 2b) depend upon the algorithm to be described below for computing and accumulating curl for each orbit. The median wind stress bin weight at 0.5° resolution is about 1070 for the 273-day period from 1 October 1996 through 29 June 1997. This is roughly consistent with what we have already introduced about the NSCAT sampling in that 1) usually four 25-km resolution surface wind retrievals from the same swath occur in a single 0.5° bin at low and middle latitudes; 2) one descending and one ascending orbit cover the same bin in a given 24-h period (separated by about 12 h); 3) at high latitudes (>50°), the NSCAT swaths overlap from orbit to orbit, separated by about 100 min, so that some bins are sampled 4 times in a day; and 4) except at extremely high latitudes, often no data occur in a bin for the 24-h period following a 24-h period in which samples did occur within that bin.

The wind stress bin-weight distribution between 60°N and 60°S is nearly uniform; within about 7% of the median bin weight of 1070 (i.e., the pale reds and blues in Fig. 2a). However, a number of localized wind stress bin-weight anomalies are superimposed on the uniform background bin-weight distribution. The lowest wind stress bin weights associate with seasonal sea ice distributions at high latitudes, for example, around Antarctica (Remund and Long 1999; Drinkwater 1998), and in nearshore regions of the Arctic Seas (Yueh and Kwok 1998), in Hudson and Baffin Bays, and off the coast of Labrador. A large region of anomalously low bin weights for wind stress is centered on the NSCAT calibration ground station in White Sands, New Mexico. Early in the NSCAT mission, the wind observation mode was turned off to calibrate the NSCAT antennae when the NSCAT orbit (ascending and/or descending) was in the vicinity of the White Sands ground station.

Low bin-weight anomalies for wind stress, closer to the median bin weight (i.e., light blues), appear in patterns that resemble the swaths from particular NSCAT orbits. These are due to purposeful temporary interruptions in the wind observation mode of the NSCAT instrument. A prominent example is an NSCAT orbit that crosses the Hatayama ground station in Japan on a descending branch. The corresponding ascending branch for this orbit crosses South America and eastern North America. A low bin-weight anomaly for wind stress, which does not resemble an NSCAT orbit, arcs across the South Pacific from the equator at about 175°E, to the west coast of South America. This pattern is due to the very few observations that are lost as the space craft data recorder banks are switched prior to downlinks (M. H. Freilich 1998, personal communication). A moderately low bin-weight anomaly, southeast of the anomaly due to sea ice in the Labrador Sea region, remains unexplained.

The highest bin weights for wind stress occur in the high northern latitudes, away from the effects of seasonal sea ice distribution. These are the regions where sequential NSCAT orbits overlap most. They represent only a few percent of the 0.5° bins in the global domain. Over most of the global ocean, the wind stress bin-weight differences with respect to the nearest bin neighbors are not larger than about 5%.

Although sampled about the same number of times during the 9-month period, adjacent wind stress bins are not always sampled at the same times. According to (1), the discretized wind stress curl involves spatial gradients across adjacent bins in two directions such that a 2 × 2 bin arrangement forms the most natural and compact spatial stencil (Fig. 3). The following procedure was used to compute curl at the common bin corner in 2 × 2 quadrangles, only when all four adjacent bins contain simultaneous wind retrievals (Fig. 3 depicts the procedure for the case of 0.5° bins). Curl is calculated separately for each orbit and accumulated in four steps.

  1. For each wind vector retrieval assigned to a bin, decompose the wind into u, υ components, and compute the wind stress components according to (2) and (3).
  2. Average the wind stress components in each bin (usually from 1 to 4 retrievals per bin) and assign the average stress components to the latitude and longitude of the bin center (the circles in Fig. 3).
  3. Compute curl at the intersection (corner) of four adjacent wind stress bins (2 × 2; i.e., at the diamonds in Fig. 3) by averaging differences according to (1). That is, the zonal gradient of τy is the average of the zonal gradients in τy across the northern and southern bin pairs (the solid triangles in Fig. 3). Similarly, the meridional gradient of τx is the average of the meridional gradients of τx across the western and eastern bin pairs (the solid squares in Fig. 3). The wind stress curl (diamonds in Fig. 3) is the subtraction of the latter from the former.
  4. Finally, wind stress curl is accumulated and weighted by the number of valid curls over the 9-month period.
Note, that wind stress curl can only be computed when all four adjacent bins contain wind data from the same orbit. The NSCAT observations are not regularly spaced within the bins and this could have been accounted for in computing the bin-average stress values (at the circles in Fig. 3). However, the irregular distributions within bins vary enough from orbit to orbit over the course of the mission that the added complexity of distance-weighted averaging was not warranted in computing the long-term average wind stress curl. The median bin weight over the NSCAT record for wind stress curl is 250. Only 5% of the wind stress curl bin weights are smaller than 200 (Fig. 2b).

Also, as shown in Fig. 3 (open diamonds), the 2 × 2 bin quadrangles overlap such that wind stress bins are reused to compute adjacent wind stress curls. This means, for example, that wind stress curl estimates from completely independent sets of NSCAT observations are separated by 1° in what we refer to as the 0.5° resolution wind stress curl data. Three aspects of the method—1) within-bin averaging, 2) averaged spatial differences, and 3) overlapping wind stress curl quadrangles—involve spatial smoothings of the wind stress curl at the bin resolution.

While this procedure avoids artificial gradients in the wind stresses from nonsimultaneous wind retrievals, it does not prevent artificial gradients in the long-term average wind stress curl map that appear because the average wind stress curls at adjacent points can derive from different time sequences. However, on average, any two neighboring wind stress curl time sequences match over more than 95% of the 9-month time period.

The bin-weight distribution is not an issue in computing the average wind stress curl field for the NCEP and NSCAT enhanced comparison datasets. Since these fields arise from a forecast model simulation, there is uniform coverage in space and time.

a. Variable bin sizes

Wind stresses were accumulated, and wind stress curl was computed at resolutions of 0.5°, 1.0°, and on a Gaussian grid corresponding to a T62 spectral model truncation. The NSCAT bin-weight distributions for 1° and T62 resolutions, (not shown) are consistent with coarsened representations of the 0.5° distribution (Fig. 2a). For the T62 discretization, the bin dimension in longitude is fixed at 1.875°, and the latitudinal bin dimensions range from 1.8° to 1.9° according to a Gaussian grid equivalent supplied by NCEP for the T62 spectral truncation. For each of the coarser resolutions (1°, T62), the wind stresses are resorted, and the bin weights and wind stress curls are recomputed orbit by orbit and accumulated in time to create the 9-month average distributions in Figs. 4 and 5 to be described.

In the vicinity of the coast, the NSCAT-2 model function makes a conservative distinction between σ0 returns from ocean versus land. The resulting coastline, that separates WVC over the ocean from cells identified with land, errors on the side of excluding ocean WVC from the NSCAT-2 dataset (M. H. Freilich 1998, personal communication). We ascribed to a similar philosophy in deciding to include or exclude near-coastal bins from the calculation of the average wind stress curl. In computing wind stress curl for the 0.5° map, we exclude all coastal bins for which the wind stress curl bin weight is less than 100 (Fig. 3). This eliminates about 5% of the total, from regions near coasts and ice edges. The same threshold was applied at all resolutions (i.e., 0.5° to T62). The bin weights for wind stress curl do not depend upon the number of wind stress retrievals per bin (which goes up with larger bins) but rather upon the number of orbits that cover the same bin location. Whether or not an orbit covers a given location is nearly independent of the bin size in the bin-size ranges we consider here.

4. Results

Figure 4 is the global wind stress curl map at 0.5° resolution for the NSCAT period (1 October 1996–29 June 1997). It is somewhat difficult to place this figure in the context of existing wind stress curl climatologies (e.g., Trenberth et al. 1990; Hellerman and Rosenstein 1983). Not only does the average in Fig. 4 cover just 9 months, excluding almost an entire season, but also the 9 months that are averaged here compose the onset period for an El Niño–Southern Oscillation (ENSO) warm event. Nonetheless, the large-scale distribution of positive and negative wind stress curl in subpolar and subtropical regions is roughly consistent with classic notions alluded to in the introduction, and with climatologies from coarse resolution historical observations (e.g., Hellerman and Rosenstein 1983), or weather center analyses (e.g., Trenberth et al. 1990).

The largest differences with respect to the climatologies occur in the eastern Pacific where narrow (in latitude) bands of positive and negative wind stress curl straddle the equator over more than 40° of longitude. Zonal bands of alternating sign and succeedingly broader latitude ranges occur in the Tropics and subtropics of the Northern Hemisphere, poleward of the equatorial signal (Fig. 4). The same regions are all negative wind stress curls in the Trenberth et al. (1990) annual average. However, Trenberth et al. (1990) demonstrate substantial interannual variability in tropical and midlatitude Pacific wind stress curl over a period including the 1982/83 ENSO warm event.

The discrepancy in the Tropics might be due to any combination of increased resolution in the data that compose Fig. 4, the fact that Fig. 4 is a 9-month average and not a climatology, or the effects of the ENSO warm event. Several recent papers (e.g., Kelly et al. 1999; Milliff et al. 1999b; Verschell et al. 1999; and D. Chelton 1999, personal communication) have described improvements in the representation of the intertropical convergence zone in this region from the NSCAT winds relative to winds from the weather center analyses (e.g., the NCEP CDAS). Figure 4 is consistent with a visual average of the seasonal wind stress curl averages from NSCAT for the tropical Pacific presented in Kelly et al. (1999).

Features in Fig. 4 that are not consistent with the conventional picture for the climatology of wind stress curl are 1) small spatial-scale variability in the wind stress curl, which we will refer to as mesoscale patchiness; and 2) narrow boundary wind stress curl extrema along the eastern boundaries of subtropical ocean basins in the Northern and Southern hemispheres (hereinafter referred to as EBWSC for eastern-boundary wind stress curl). We discuss these anomalous features below and examine their persistence in coarser-resolution maps of the average wind stress curl from the same data.

The patchy character of the average wind stress curl field in Fig. 4 complicates more quantitative comparisons with climatologies; that is, difference maps are dominated by patchiness rather than large-scale signals. In analyses below we will focus on the mesoscale patchiness in the North Pacific region of Fig. 4 as a typical example of mesoscale patchiness elsewhere in open ocean regions. The 9-month-average wind stress curl in the subpolar North Pacific (Fig. 4) is dominated by positive wind stress curl (red), but there are large-amplitude, small-scale patches of negative wind stress curl (blue) throughout the region as well.

Figure 5 is the average wind stress curl at 1° resolution. Perhaps not surprisingly, the mesoscale patchiness in Fig. 4 has aggregated into larger scales on the order of 2° or 3°. As in Fig. 4, the patchiness overlies a gyre-scale pattern in wind stress curl that is consistent with the classic pattern.

A quantitative sense of the aggregation effects on mesoscale patchiness is obtained by comparing a modified measure of rms variability for the time-average wind stress curl fields at several bin resolutions (Table 1). The usual rms statistic for c is
i1520-0469-58-2-109-eq1
for the N × M ocean grid locations in the domain where a time-average wind stress curl cij has been computed. To focus more exclusively on the mesoscale patchiness, we use here a gradient RMS (GRMS) defined by
i1520-0469-58-2-109-eq2
where Δ is the appropriate bin-size dimension (e.g., 0.5°, 1°, etc.; in meters). Units for GRMS are N m−4. We compute GRMS for ocean points (i, j) between the latitudes 60°N and 60°S. At higher latitudes the wind stress curl calculation for a given orbit might not involve the average of several wind stress retrievals per bin. Also, the GRMS statistic is sensitive to small values of Δ. The zonally averaged distribution of GRMS with latitude becomes nonuniform in the excluded high-latitude regions. The GRMS provides a measure of bin-to-bin differences in wind stress curl (i.e., patchiness) depicted for several bin resolutions in Table 1. We note that the GRMS statistic does not uniquely quantify the mesoscale patchiness. Undoubtedly, one could devise spatial patterns, which are somewhat large-scale, that would result in somewhat large amplitudes in GRMS. But as we demonstrate below, GRMS and the character of the mesoscale patchiness are usefully correlated.

At 1° resolution, the subtropical gyre regions of the North Pacific and North Atlantic are of homogeneous sign in the average curl (Fig. 5), but shorter spatial scales are more evident than for the classic picture described in the introduction. The subpolar gyre regions, and the region of the Antarctic Circumpolar Current, contain adjacent patches of opposite-signed average wind stress curl, as they did in Fig. 4, albeit now at larger spatial scales. Large-scale, opposite-signed, curl features straddle the equator in the eastern Pacific as was noted for Fig. 4. The positive signed part in the Northern Hemisphere is reduced slightly in spatial extent in Fig. 5.

The EBWSC extrema are reduced in amplitude and spatial scale in Fig. 5. Strong negative average curls off the coasts of Peru and Chile in Fig. 4 are nearly absent from Fig. 5. The strong local positive average wind stress curls off the California and Baja California coasts are reduced significantly in alongshore extent. In the Atlantic, the positive signed EBWSC off north Africa in Fig. 4 are diminished in Fig. 5. A similar reduction is evident for negative signed EBWSC off southern Africa.

Because of the coarser resolution in Fig. 5 (1°), there is a wider band of near-coastal bins (not colored) that are excluded from the long-term average due to insufficient bin weights. This coarsening of the coastal boundary is perhaps one cause for the reduction in the signal of the EBWSC in Fig. 5. Another reason is that the EBWSC features are lost in the averages with offshore bins that are part of the aggregation from 0.5° to 1° resolution.

Figure 6 is the average wind stress curl map for NSCAT-2 on a grid that corresponds to the transform of a T62 spectral discretization. The spatial scale of the patchiness is further enlarged to length scales on the order of 5° or more. The GRMS variability has dropped more than 80% with respect to 0.5° resolution (Table 1). The positive wind stress curl signal in the Northern Hemisphere eastern equatorial Pacific is completely averaged out of Fig. 6. The negative counterpart on the Southern Hemisphere side of the equator survives the aggregations in Figs. 5 and 6 but is successively reduced in spatial extent.

In the next sections we put forward arguments that identify the mesoscale patchiness in Fig. 4, and therefore its aggregations in Figs. 5 and 6, with artifacts due to the space–time sampling of the highly intermittent wind stress curl process over the open ocean. Following that, we argue that the EBWSC feature is not an artifact of this kind but more plausibly is the first manifestation from global observations of a real physical feature of the atmospheric general circulation, with important implications for the oceanic general circulation.

a. Mesoscale patchiness

We begin our investigation of the source of the mesoscale patchiness in Fig. 4 by isolating, to the extent possible, the temporal and spatial effects that contribute to the intermittency of the wind stress curl.

The amplification of high wavenumbers in spatial differences is removed by examining the wind stress fields. Figures 7a,b depict the 9-month-average wind stress components τx, τy. These averages are computed from the orbital bin averages of wind stress components that are used to compute the 9-month-average wind stress curl in Fig 4. The subpolar and subtropical gyre regions are homogeneous with respect to sign in τx (Fig. 7a), but some small-scale structure is still evident within each region. The amplitudes for τy (Fig. 7b) are smaller than for τx, but the spatial variability is more patchy.

The fields in Fig. 7 can be compared directly with longer-term average fields from ship and buoy observations, from weather center analyses, and with 7-yr averages of the ERS-1,2 satellite data in the atlas of air–sea flux fields by Beranger et al. (1999). For both components, the large-scale spatial patterns are smoothest in stress fields derived from ship and buoy observations where the spatial resolution of the observations is lowest. There are regular patterns of small-scale variability, within a narrow wavenumber band, in the fields from weather center analyses (most evident in the European Centre for Medium-Range Weather Forecasts fields). These patterns are identified later in this paper (section 4b) as artifacts of the spectral models leading to the analysis fields. Small-scale variability is also evident in the fields from ERS-1,2, but the variability is more broadband than in the analysis fields. The variability in the fields from ERS-1,2 data most closely resembles that in Fig. 7. The stress component fields in Fig. 7 exhibit only subtle indicators of the ENSO event. The negative zonal wind stress extremum (τx) in the tropical Pacific is displaced toward the east in Fig. 7 relative to the average position in the ERS climatologies in Beranger et al. (1999; not shown here).

1) NSCAT enhanced analyses

A sense of the temporal effects of NSCAT sampling in creating the mesoscale patchiness in Fig. 4 can be gained by comparing with the time-average wind stress curl field from the NSCAT enhanced winds described in the section 2. Figure 8 shows this average at 0.5° resolution. The surface winds used to create Fig. 8 are uniformly available at 0.5° resolution, every 6 h, over the same time period examined in Fig. 4.

The wind stress curl field in Fig. 8 is less patchy than the counterpart in Fig. 4 in the sense that the subtropical gyre regions are single signed. However, a large-amplitude high-wavenumber variability is still evident as a granular texture that comprises the time-average large-scale wind stress curl patterns. The GRMS variability is lower by 45% with respect to Fig. 4, but this is substantially closer to the GRMS variability in Fig. 4 than was the case for the 1° bin discretization (Table 1). There are noticeable differences with respect to Fig. 4 in the large scales of the average wind stress curl features in the equatorial eastern Pacific and equatorial western Atlantic. The positive wind stress curl features that border the equator in the Northern Hemisphere are reduced in longitudinal extent in Fig. 8 relative to Fig. 4. Aspects of the EBWSC features in Fig. 8 are also different from the counterparts in Fig. 4, and they will be discussed in section 4b below.

2) Analytic wind stress curl

For a more definitive test of the effects of the NSCAT space–time sampling on the estimate of long-term average wind stress curl over the ocean, we developed a procedure using analytic wind stress curl fields with simple, known, long-term averages. Departures from known averages can then be attributed to artifacts of the sampling scheme. The experimental domain is a 20° longitude by 20° latitude region in the North Pacific (30°–50°N, 170°E–170°W) at 0.5° resolution. The domain spans the transition from the subtropical to subpolar gyre regions of the North Pacific. The experiments with analytic wind stresses and NSCAT sampling will be particularly informative if the departures from analytic long-term average wind stress curl exhibits mesoscale patchiness of the kind in Fig. 4.

Our analytic storm is modelled after wind stress curl features evident in the forcing dataset described in the appendix of Milliff et al. (1999b; e.g., see their plate 1). Wind stress curl patterns associated with Northern Hemisphere cyclones are characterized by intense, circular patches of large positive wind stress curl, with bands of weaker negative wind stress curl farther from the storm center. Figures 9a,b depict the analytic wind stress (Fig. 9a), and wind stress curl (Fig. 9b) for a prescribed storm located in the middle of the study domain. Typical NSCAT sampling overlays the wind stress field in Fig. 9a. Figures 9c–e depict continuous time series as well as the NSCAT sampling of analytic τx (Fig. 9c), τy (Fig. 9d), and the wind stress curl (Fig. 9e) for a 40 day period at the midpoint (40°N, 180°) of the study domain. The expanded 40 day timescale allows for easier identification of storm events, and it is very near the NSCAT repeat cycle time of 41 days.

The spatial patterns of the wind stress (Fig. 9a) and the derived wind stress curl (Fig. 9b) for analytic storms are radially symmetric in zonal and meridional extent, with a total diameter of about 1800 km, and a storm center diameter of about 600 km. These dimensions were fixed for each storm, as was the maximum wind stress amplitude for each component (⩽1 N m−2), and the zonal propagation speed of about 8° longitude per day. The storm frequency, and the latitude of zonal propagation, were selected randomly within realistic ranges (3–6 days and 30°–50°N, respectively), in order to generate a 9-month time series from which domain average wind stress curls could be computed and compared at 0.5° resolution.

The true mean wind stress curl from the random sequence of analytic storms spanning 9 months was computed for each point in the test domain every 3 h. This sampling is indicated in Figs. 9c–e by vertical bars on the 40 day time histories of τy, τx, and wind stress curl, respectively. The irregular NSCAT sampling is indicated by dots on these time histories as well. The 40-day time history for wind stress curl (Fig. 9e) also depicts wind stress curl computed from the real NSCAT observations at the same location, for the same dates (plus signs).

The 9-month-average wind stress curl for the analytic storms from perfect sampling of the study domain every 3 h is shown in Fig. 10a. Since the analytic storm propagation is constrained to be strictly zonal, and since each radially symmetric storm is sufficiently sampled as it propagates through the domain, the long-term average has no zonal variability. This is roughly consistent with notions of single-signed large-scale averages for subpolar (positive) and subtropical (negative) wind stress curl distributions in nature. However, in the analytic storm case, there was no preferred latitude or storm track region in the study domain.

Figure 10b depicts the 9-month average of the analytic storms using NSCAT sampling, and Fig. 10c is the 9-month average from the real NSCAT dataset for the study region (i.e., a blowup of the northwest Pacific in Fig. 4). The NSCAT sampling is not sufficient to capture the zonal independence in the 9-month average for the analytic storms. In fact, the artifacts of the NSCAT sampling (Fig. 10b) are similar in spatial-scale content to the mesoscale patchiness of Fig. 10c, but amplitudes of GRMS (Table 1) and wind stress curl extrema (Fig. 10) are significantly lower. Of course, the analytic storms are severe simplifications of the real case in several respects (e.g., spatial symmetry, time dependence, propagation direction, etc.), which could account for some or all of the reductions in these amplitudes. The strong suggestion remains that the mesoscale patchiness in the open ocean regions of Fig. 4 are artifacts of NSCAT sampling of large-amplitude wind stress curl events associated with atmospheric storms.

b. Eastern boundary wind stress curl

The EBWSC features in the 9-month-average wind stress curl (Fig. 4) are not patchy in the sense of the open ocean signals just diagnosed. The across-shore scale in the EBWSC is comparable to the scales of the open ocean mesoscale patchiness in Fig. 4, but coherence in the alongshore directions spans much longer length scales. The EBWSC signals are persistent in 3-month averages (i.e., seasonal averages, not shown) throughout the 9-month NSCAT record, with slight strengthenings possibly associated with the local upwelling season for each hemisphere (i.e., April–June for the Northern Hemisphere, and September–November for the Southern Hemisphere; see Bakun and Nelson 1991).

A dynamical explanation for the existence of the EBWSC has yet to be confirmed. Hoskins and coworkers have put forward a description of a monsoon–desert relationship in the subtropics that is consistent with persistent EBWSC (Hoskins 1996; Rodwell and Hoskins 1996; Hoskins et al. 1999). In this scenario, the subsidence over the eastern portions of oceanic subtropical high pressure systems is described as a characteristic summertime response to downstream atmospheric convection associated with monsoon dynamics. The anticyclonic direction of the descending air is altered at the surface by the presence of the land–sea boundary (i.e., the ocean eastern boundary), inducing a signal in the wind stress curl. In their Fig. 1 (not shown here), Hoskins et al. (1999) use ECMWF reanalyses to demonstrate enhanced equatorward flow in both hemispheres along ocean eastern boundaries. The regions of strongest equatorward flows correspond well with the EBWSC signals in Fig. 4 (here). The importance of the monsoon–desert relationship has been challenged recently by Chen (1999, manuscript submitted to J. Atmos. Sci.) in the context of the maintenance of seasonal anticyclones over the subtropical oceans. Chen (1999, manuscript submitted to J. Atmos. Sci.) argues that the zonal asymmetries in monsoon heating in the Northern Hemisphere could not support the nearly symmetric distribution of the subtropical anticyclones over the Northern Hemisphere oceans.

The narrow cross-shore scale of the EBWSC is not in concert with the large scales implied by Hoskins and coworkers, or by Chen (1999, manuscript submitted to J. Atmos. Sci.). Neither does the persistence of the EBWSC features throughout the 9-month period conform to the arguments so far based on summertime heating. Instead, local dynamical explanations should be pursued for the forcing and persistence of the narrow EBWSC in the NSCAT data. The importance of synthetic analogues of the EBWSC (albeit somewhat wider in cross-shore scale) to the general circulation of the subtropical gyre on the Atlantic Ocean was demonstrated by Milliff et al. (1996). Given the existence of EBWSC features in the observations from NSCAT, it will be interesting to see if a comparable ocean model response ensues. This is the subject of ongoing research.

The EBWSC features in the NSCAT data occur in regions of known, large-amplitude artifacts in the weather center analyses derived from spectral atmospheric models. Figure 11 is the 9-month-average wind stress curl of the NCEP CDAS T62 analyses for the same time period as the NSCAT mission. This figure can be compared directly with the aggregation of the NSCAT data in Fig. 6. As we have already noted, the EBWSC features are best resolved at 0.5° resolution (Fig. 4) and all but absent at T62 (Fig. 6). In contrast, Fig. 11 exhibits large amplitude and relatively large spatial extents for boundary wind stress curl features, many of which correspond to the positions of EBWSC features in Fig. 4 (e.g., off the west coasts of North and South America, northern and southern Africa). The alongshore and across-shore scales of the boundary wind stress curl features in Fig. 11 are larger than the counterparts in Fig. 4.

At first, the presence of boundary wind stress curl features in Fig. 11 appears to contradict the notion that high-wavenumber surface winds from NSCAT are required to resolve these signals. But a more careful inspection of Fig. 11 demonstrates that distribution of near-boundary wind stress curl features differs in fundamental ways from the EBWSC feature in Fig. 4. The wind stress curl features in Fig. 11 are not confined to ocean eastern boundaries as they are in Fig. 4 but instead are evident in the average from NCEP analyses on western boundaries (e.g., see China, Japan, Australia, the Arabian Peninsula). Also, the sign of the boundary wind stress curl extrema in Fig. 11 can differ from the sign of EBWSC features from NSCAT data in Fig. 4 (e.g., see Cape Horn). Since the NSCAT enhanced winds are constructed from the NCEP CDAS, the EBWSC artifacts contaminate the 9-month average in Fig. 8 as well.

The near-coastal structures in wind stress curl in Fig. 11 have counterparts in the time-average wind stress divergence field that are more easily identified with an atmospheric model artifact. Wind stress divergence is given by
i1520-0469-58-2-109-eq3
Figure 12a is the wind stress divergence computed from the NSCAT data. Figure 12b is the comparable field computed from NCEP for the NSCAT period. Both Figs. 12a and 12b derive from T62 bin resolutions. A characteristic signature of spectral ringing or Gibbs phenomena (e.g., Hack 1992) is evident throughout the global domain in Fig. 12b. Features of this kind appear in derivative fields of surface winds from all the well-known weather centers that provide products based on a spectral atmospheric model (e.g., see Beranger et al. 1999). The Gibbs phenomena result from the spectral model inability to represent abrupt transitions in surface topography with a truncated set of spectral modes. Gibbs artifacts are largest in regions of greatest topographic gradients—most notably for our purposes, in locations of tall near-coastal topography (e.g., the Andes). Gibbs artifacts contaminate the nearshore regions of the EBWSC on spatial scales that match or exceed those of the EBWSC signals we can detect in the NSCAT data.

What is perhaps even more unfortunate is that the contamination due to spectral truncation that plagues surface winds in weather center analyses has also crept into the processing of the NSCAT-2 data. As described above, in processing the NSCAT data several σ0 are taken for each WVC to determine wind speed and direction according to an empirical geophysical model function. The model function, however, returns a set of usually four ambiguous wind speed and directions, in order from most to least likely. The ambiguities are usually similar in wind speed but can be very different in direction. Often, the two most likely ambiguities are in opposite directions (so-called upwind–downwind ambiguities). The most likely wind direction at any given WVC can be opposite or perpendicular to the most likely directions at surrounding WVC. In particular, this can happen when the ambiguous solutions of the model function are almost indistinguishable by their likelihoods.

The ambiguity removal step in the NSCAT data processing employs a median filter to select a wind direction at each WVC that is closest to the median of most likely directions in the surrounding 7 × 7 WVC neighborhood (Gonzales and Long 1999; Atlas et al. 1999). The median filter operation is an iterative process, and the iterations can be seeded in at least two ways. In what we refer to as the “not nudged” case, the seed at each WVC is the highest ranked ambiguity. In the “NWP nudged” case, the seed for a given WVC is guided by the direction nearest in space and time from a 2.5° resolution NCEP analysis of the 1000-hPa winds. The median filter seed at each WVC is either the first or second most likely ambiguity, whichever is closest to the nearest analysis direction.

The effect of the numerical weather product (NWP) nudging on the EBWSC is demonstrated in Figs. 13a–c for the signals off South America. Figures 13b,c are based on early NSCAT data products that are not the standard that is now available (i.e., from the NSCAT-1 model function at 50-km resolution for 83 days in the period 26 September–18 December 1996). The EBWSC signals cannot be compared directly with those in Fig. 4 because 1) the model functions and resolutions differ, and 2) the time period for the averages in Fig. 13 is a fraction of the time period in Fig. 4. Figure 13a is the average based on a subset of the NSCAT-2 record that matches the NSCAT-1 datasets. The early NSCAT products allow a consistent comparison of NWP nudged versus not nudged effects on the EBWSC signals since the same data were processed both ways. Figure 13b depicts the EBWSC off South America in the NWP nudged case, and Fig. 13c for the not nudged case. The NWP nudging has enlarged the representation of the EBWSC at this resolution, particularly off the Chilean coast. This is a region where the Gibbs effect in the NWP model is likely to be large, given tall topography adjacent to the flat sea surface. The alongshore scale of the EBWSC in the NSCAT-2 data (Fig. 13a) is more like the NWP nudged case (Fig. 13b).

It is important to note that the EBWSC signal off Peru is evident in the average wind stress curl in the not nudged case (Fig. 13c), although with reduced alongshore scale. Figures 4, 11, 12, and 13 demonstrate that the EBWSC signals occur in precisely the locations where the Gibbs artifacts from spectral model based analyses are largest. A broad-swath, spaceborne, active scatterometer instrument like NSCAT provides the clearest manifestation to date of the true EBWSC signal in the global context.

Representation errors, such as Gibbs phenomena, inherent in spectral model approximations, might be avoided in gridpoint or finite-difference approximations for the general circulation model equations (R. Atlas 1999, personal communication). However, the gain in representation accuracy in the gridpoint framework can be offset by dispersion errors and numerical diffusion that plague low-order finite-difference approximations. Analytical and computational effort is required to ameliorate these errors in gridpoint general circulation models (e.g., Lin and Rood 1996; Rasch and Williamson 1990).

5. Discussion

The sampling characteristics of polar-orbiting, swath-based systems have been quantified in a general way by Chelton and Schlax (1994). The authors identify the wavenumber and frequency resolution limitations of a given system such that nearly uniform distributions of expected error are obtained in space and time. Their analysis is based on global properties of the sampling scheme stemming from a Fourier transform. Averages of ERS and NSCAT winds have been based appropriately on the guidance in Chelton and Schlax (1994) (e.g., Kelly et al. 1999). However, one point of this paper is that long-term averages of the wind stress curl field pose more stringent requirements on the space–time sampling scheme. Schlax et al. (2000, manuscript submitted to J. Atmos. Oceanic Technol.) deal specifically with sampling characteristics for a variety of polar-orbiting scatterometer mission scenarios. Their focus is on the feasibility of global mesoscale resolution.

The results of the analytic storm analyses in the previous section indicate that given observations from a single polar-orbiting scatterometer system of the NSCAT class, temporal averaging over periods as long as 9 months cannot ameliorate aliases in the global wind stress curl field. The survival of mesoscale patchiness when spatial bins are enlarged (Figs. 5 and 6) suggests that spatial averaging alone will also not solve the problem. Moreover, enlarged spatial bins are shown to remove the EBWSC, a physical signal of interest that has heretofore only been represented in regional studies (e.g., Nelson 1977; Bakun and Nelson 1991).

Kriging, or objective analysis techniques, have also been used to create several-day composites of scatterometer winds for global and regional studies (e.g., Kelly and Caruso 1990; Bentamy et al. 1998; Liu et al. 1998). These methods involve the specification of temporal and spatial covariance structures that dictate the properties of the interpolation. The specified covariance structures are usually simplified (e.g., analytic, symmetric, etc.), and applied uniformly over the domain of interest to yield smooth results. Derivative fields, such as wind stress curl and divergence, are necessarily functions of the chosen covariance structures. Here again, the EBWSC features will be removed in the treatments of this kind.

Zeng and Levy (1995) have identified sampling artifacts in monthly mean surface winds calculated from ERS-1 data that are relevant to the present study. They suggest a space–time interpolation, using nearby observations to replace missing values of the field before averaging. Again however, the intermittency of wind stress curl in space and time, and the narrow across-shore structure of the EBWSC, defy this approach. Space–time interpolators are most appropriate when the observations bound well the missing data. The blending technique developed by Chin et al. (1998), and implemented with NSCAT data by Milliff et al. (1999b), represents an interpolation more sophisticated than the linear approach proposed by Zeng and Levy (1995). The 9-month-average wind stress curl based on this approach (Fig. 9) demonstrates the survival of mesoscale patchiness we suspect to be an artifact.

Ultimately, optimal surface wind field estimates will derive from four-dimensional variational (4D-VAR) data assimilation products based on, perhaps, gridpoint general circulation models (e.g., Li et al. 1994). Surface vector wind data from scatterometer observations will undoubtedly be key inputs to these products. Still, the intermittency of the true wind stress curl process will define stringent sampling requirements in order to gain the full benefit of 4D-VAR methods.

a. GRMS budgets

Indeed, the true intermittency of the wind stress curl field over the global ocean has yet to be quantified fully, but the NSCAT experience permits us to place bounds on some of the sources of intermittency. Time series of wind stress curl estimates in adjacent 0.5° bins in the North Pacific study region are not strongly correlated as sampled by NSCAT. Let us assume that a wind stress curl time series at a point is composed of two parts: 1) intermittent bursts with very large amplitudes associated with the development and propagation of atmospheric storms; and 2) a short timescale, small spatial-scale background variability that separates in spatial and temporal scale content from the storm-scale events. It is reasonable to further assume that 1) the storm-scale variability will be at least weakly correlated in time series of wind stress curl from adjacent 0.5° bins, and 2) the small-scale variability can be uncorrelated in this same sense. Then GRMS can be decomposed into four parts:1) the true signal of the large-amplitude storm-scale events, 2) the errors that come from undersampling the storm-scale events, 3) the true signal of the small-scale variability, and 4) the errors that come from undersampling that field as well. That is,
storm_truestorm_errorbkgrnd_truebkgrnd_error
where the second and fourth terms on the right-hand side are the errors that contribute to mesoscale patchiness in the time-average global distribution of the wind stress curl (Fig. 4).
We can attempt to bound estimates for the magnitudes of each of these terms from information that has been presented thus far at 0.5° resolution. For the left-hand side, GRMS ≈ 16 × 10−13 N m−4 from Fig. 4 and Table 1. From the analytic storm experiments, we gain an estimate of the lower bound on the errors from undersampling storm events. Since the analytic storms were designed to contain no small-scale background variability, the difference in GRMS between perfect sampling and the NSCAT sampling is a measure of the error (Table 2). This will be a lower-bound estimate in that the analytic storm was probably not as difficult to sample sufficiently as true storm variability would be. Thus,
storm_error−13−4
Estimates for the background variability components (signal and error) are more difficult. If we make the questionable assumption that the storm-scale wind stress curl variability is not badly aliased in 6-hourly NCEP CDAS, then an upper bound on the combined terms for small-scale signal and error comes from a difference between GRMS for NCEP (Fig. 7) and GRMS for the NSCAT enhanced case (Fig. 8). So,
bkgrnd_truebkgrnd_error−13−4
This is an upper-bound estimate for the background variability in that the entire difference (NSCAT enhanced minus NCEP) is being attributed to the background scale. Moreover, we are not able to separate signal and error in the background scale. It is probably the case that the NSCAT enhanced field contains additional variability on the storm scale as well.

The residual (e.g., ∼[16 − 4 − 7] × 10−13 N m−4) is on the order of 5 × 10−13 N m−4. This represents a rough estimate of the GRMS amplitude in the long-term average global wind stress curl from storm-scale events. (e.g., GRMSstorm_true). Thus, the signal and error in large-amplitude storm-scale events and the signal and error in background variability are comparable in terms of a gradient RMS measure in the long-term average. Recall, however that the estimate for the background variability is a rough upper bound, and that the estimate for the storm-scale error is a rough lower bound, suggesting that the storm-scale signal in GRMS could be larger. The North Pacific study region was selected because of its representative patchiness. It is in the vicinity of the North Pacific storm track region. The total GRMS from real NSCAT data exceeds the global value by more than 20% for this region (Tables 1 and 2).

A map (not shown) locating wind stress curl events, from NSCAT data, of amplitudes exceeding 1 × 10−5 N m−3 (i.e., 2 to 3 orders of magnitude larger than the values in Table 1) identifies clearly the Northern Hemisphere storm track regions (Atlantic and Pacific), the region of the Antarctic Circumpolar Current, and very high latitude regions presumably affected by ice-edge proximity. Within these regions, the wind stress curl RMS as a function of time can exceed 1 × 10−6 N m−3. Elsewhere (e.g., in the Tropics and subtropics, in regions of the EBWSC), the wind stress curl rms as a function of time is of order 1 × 10−7 N m−3 or smaller. This suggests uncertainty in the estimates of long-term average wind stress curl due to storm-scale events, and therefore in the budget balances just presented. These uncertainties can only be lowered with improved resolution of the large-amplitude storm events.

Spatial and temporal resolution of the storm-scale events will improve with SeaWINDS data from the QuikSCAT mission. The SeaWINDS swath width is 1800 km, and there is no nadir gap. The within-swath resolution is anticipated to be O(10 km). In late 2001, a second SeaWINDS instrument will fly on the ADEOS-II mission. The true wind stress curl variability could conceivably be resolved by multiple scatterometer missions flown along identical orbits but lagged in time. The time lag between platforms should be set to be less than the decorrelation time for wind stress curl associated with the smaller of 1) the time for development and propagation of large-amplitude storm systems at sea; or 2) the timescales of the background, small-scale variability that can obtain moderate amplitudes. The statistics of the wind stress curl variability could then be extended to interswath gaps by methods similar in spirit to Chin et al. (1998).

We have evidence that the resolution of large-amplitude events will affect the ocean response on large scales (e.g., Crawford and Large 1996; Lee et al. 1994). There is yet to be a demonstration that the smaller-scale variability in the wind stress curl field is rectified into a large-scale ocean response. But this might be due to the fact that unbiased synoptic-scale observations of this variability are not yet available.

Given the quality and information content of the NSCAT data, and the prospects for multiple, internationally coordinated, broad-swath scatterometer missions, we can anticipate new insights into atmosphere–ocean dynamics on scales from the synoptic to the climatic associated with more accurate estimates of the global wind stress curl field.

6. Summary

The wind stress curl at the air–sea interface is fundamental in establishing and maintaining the ocean general circulation. Wind stress curl is geometrically more variable in space and time than the surface wind for which we have a better intuition. As such, synoptic sampling on a global basis, of the wind stress curl field, presents a particularly stringent challenge. Owing to a premature failure of the space craft, the NSCAT mission provides only a first glimpse of the sampling capabilities of a single spaceborne, broad-swath scatterometer instrument in this regard. Nonetheless, a careful examination of these capabilities with respect to wind stress curl is timely in that SeaWINDS on QuikSCAT begins what is planned to be more than a decade of surface wind sampling by multiple, coordinated, international scatterometer missions (i.e., SeaWINDS on ADEOS-II, ASCAT on METOP, alphaSCAT on GCOM-B1; Milliff et al. 1999a).

The 9-month record of NSCAT-2 surface wind retrievals were binned and differenced to form estimates of the wind stress curl on an orbit by orbit basis. These estimates were then averaged in time to form global distributions of the wind stress curl using three bin resolutions: 0.5°, 1°, and a Gaussian grid corresponding to a T62 spectral truncation. Gyre-scale features of the 9-month averages from NSCAT are in rough agreement with climatological estimates based on in situ observations (Hellerman and Rosenstein 1983) and/or weather center analyses (Trenberth et al. 1990). The awkward length of record (9 months as opposed to a full annual cycle), and the climatic setting of the NSCAT data (i.e., the onset of the 1997/98 ENSO warm event), preclude more quantitative comparisons with the climatologies.

However, the 9-month-average distribution differs from climatologies in at least two important ways: 1) a mesoscale patchiness overlies the gyre-scale structures evident in the climatologies, and 2) narrow alongshore eastern boundary wind stress curl features are resolved at 0.5° resolution. The mesoscale patchiness is shown to be an artifact of the space–time sampling in the NSCAT data, with temporal sampling deficiencies perhaps most severe. Improved spatial and temporal resolutions will be obtained from coordinated, multiple-scatterometer missions in the coming decade.

The EBWSC features have been documented before by Nelson and coworkers in high-resolution regional studies. The EBWSC features are not contaminated by mesoscale patchiness, presumably because they are fixed in space. The initiation and maintenance of the EBWSC features has yet to be quantified dynamically. The EBWSC features occur in regions of large artifacts in the weather center analyses based on special forecast model output (i.e., Gibbs phenomena). Wind retrieval methods that rely upon weather center analyses (e.g., seeding the median filter based on NWP estimates) run the risk of enlarging artificially the EBWSC scales. Nonetheless, broad-swath scatterometry is perhaps the only means by which accurate synoptic estimates of the wind stress curl in these regions might be obtained on a global basis. The response of sophisticated ocean models to the observations of the EBWSC has yet to be quantified.

Acknowledgments

Drs. T. M. Chin, P. R. Gent, W. G. Large, and A. M. Moore commented usefully on earlier versions of this work. Dr. Robert Atlas provided a constructive review. In particular, we thank Dr. M. H. Freilich for sharing his insights and advice throughout the course of our research. We are grateful for continuing support from the NASA Ocean Vector Winds Science Team program.

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Fig. 1.
Fig. 1.

NSCAT 24-h global coverage, depicting about 14 polar orbits of the dual swath pattern (two 600-km-wide swaths, separated by a 400-km nadir gap). A complete orbit consists of an ascending branch (SE to NW) toward the North Pole and a descending branch (NE to SW) toward the South Pole. Successive orbits precess westward. The orbits from the first 12-h period are dark shaded, and the orbits from the second 12-h period are light shaded. Within-swath resolution for the NSCAT-2 surface wind retrievals is 25 km.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 2.
Fig. 2.

Bin-weight distributions for (a) wind stress and (b) wind stress curl at 0.5° resolution, for the 9-month period 1 Oct 1996–29 Jun 1997, spanning the NSCAT mission lifetime. Color bars and contour levels have been selected to emphasize bin-weight anomalies.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 3.
Fig. 3.

Wind stress curl calculation schematic for an arbitrary 2 × 2 bin quadrangle at 0.5° resolution. Small dots represent NSCAT wind retrieval locations. Wind stress component bin averages, 〈τx〉 and 〈τy〉, are assigned to the bin centers (circles). Meridional gradients, ∂〈τx〉/∂y, are computed across the western and eastern bins (squares). Zonal gradients, ∂〈τy〉/∂x, are computed across the northern and southern bins (triangles). The averages of these gradients are subtracted to form the wind stress curl (solid diamond). Surrounding wind stress curl locations are denoted by open diamonds.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 4.
Fig. 4.

The global distribution of NSCAT 9-month-average wind stress curl at 0.5° resolution. Wind stress curl is computed orbit by orbit as described in Fig. 3, and averaged over the lifetime of the mission. Units for this and subsequent color bars for wind stress curl plots are ×10−8 N m−3.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 5.
Fig. 5.

The global distribution of NSCAT 9-month-average wind stress curl as in Fig. 4 but using 1° bins.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 6.
Fig. 6.

The global distribution of NSCAT 9-month-average wind stress curl as in Fig. 4 but using bins from a Gaussian grid consistent with a T62 spectral model truncation. Bin dimensions in longitude are 1.875°. In latitude, the bin dimensions vary between 1.8° and 1.9°.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 7.
Fig. 7.

The global distributions of NSCAT 9-month-average wind stress components in the (a) zonal (τx), and (b) meridional (τy) directions. The 25-km NSCAT-2 wind retrievals are collected in 0.5° bins and averaged.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 8.
Fig. 8.

NSCAT enhanced 9-month wind stress curl at 0.5° resolution. Global surface winds from the NCEP CDAS are blended with coincident NSCAT winds as described in the appendix of Milliff et al. (1999b). The surface winds from the NSCAT enhanced dataset for the period 1 Oct 1996–29 Jun 1997 have been binned and differenced as in Fig. 4 to create a comparable 9-month-average wind stress curl.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 9.
Fig. 9.

Representations of the analytic storm experiments described in the text. For purposes of illustration, the (a) wind stress (maximum vector length = 1 N m−2) and (b) wind stress curl are depicted for a time when an analytic storm is centered in the North Pacific domain. The NSCAT sample locations are depicted for a typical descending orbit at the wind stress locations in (a) and the valid wind stress curl locations in (b). Forty-day time series for (c) analytic τx, (d) analytic τy, and (e) analytic wind stress curl are taken from the experimental sequence as it crossed the domain midpoint. NSCAT samples of the time series are marked by dots, and 3-hourly sampling is marked by vertical lines for each time series. Plus signs in (e) mark wind stress curl values derived from the real NSCAT data for the time period at 40°N, 180°.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 10.
Fig. 10.

Comparisons of 9-month-average wind stress curls in the North Pacific study domain from (a) the analytic storm sequence sampled at every grid point, every 3 h; (b) the analytic storm sequence sampled by NSCAT swaths; and (c) the real NSCAT data.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 11.
Fig. 11.

NCEP CDAS 9-month-average wind stress curl on the Gaussian grid consistent with T62 spectral truncation. This figure compares directly with Fig. 6 based on the NSCAT data.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 12.
Fig. 12.

The global distributions of wind stress divergence from 9-month averages on a T62 grid from (a) the NSCAT record and (b) the NCEP CDAS. Units are ×10−8 N m−3.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Fig. 13.
Fig. 13.

Wind stress curl averaged (off South America) in 0.5° bins for the first 83 days of the NSCAT mission (26 Sep–18 Dec 1996) as derived from (a) the NSCAT-2 model function with NWP nudging as in Fig. 4 (25-km resolution), (b) the NSCAT-1 model function with NWP nudging (50-km resolution), and (c) the NSCAT-1 model function without NWP nudging (50-km resolution). White areas in (b) and (c) occur where a minimum bin weight of 30 was not achieved.

Citation: Journal of the Atmospheric Sciences 58, 2; 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2

Table 1.

GRMS variabilities for several bin sizes. Global domains (60°N–60°S), GRMS variabilities ×10−13 N m−4.

Table 1.
Table 2.

GRMS variabilities for NSCAT and perfect sampling. North Pacific domain (20° × 20°), GRMS variabilities ×10−13 N m−4.

Table 2.
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