Evaluation of Nearshore QuikSCAT 4.1 and ERA-5 Wind Stress and Wind Stress Curl Fields over Eastern Boundary Currents
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remote sensing
Article
Evaluation of Nearshore QuikSCAT 4.1 and ERA-5 Wind Stress
and Wind Stress Curl Fields over Eastern Boundary Currents
P. Ted Strub * and Corinne James
College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, 104 CEOAS Administration
Building, Corvallis, OR 97331-5503, USA; corinne.james@oregonstate.edu
* Correspondence: ted.strub@oregonstate.edu
Abstract: Fields of coastal wind stress and wind stress curl in the 10–100 km next to the land control
the processes of upwelling and downwelling of nutrients and water properties that are vital to highly
productive coastal marine ecosystems. Here we ask the question: Do the present surface wind stress
products from a satellite-borne scatterometer (QuikSCAT) and an atmospheric reanalysis model
(ERA-5) systematically overestimate the magnitude of wind speed and stress in the 10–50 km next
to the coast? We compare QuikSCAT wind speed retrievals to the relatively unused wind speed
retrievals from satellite altimeters, which are able to approach closer to the coast than scatterometers
without land reflections, due to their smaller radar footprints. Altimeter data on tracks approaching
and crossing the coast indicate that the increases in coastal QuikSCAT wind speed values and ERA-5
coastal wind stress values are unrealistic. For analyses of wind speed and stress requiring high
accuracy, especially those involving wind stress curl, we suggest considering individual Level 2B
scatterometer wind retrievals as suspect at distances of 10 km and less from the coast, along with use
of the Poor Coastal Processing flag. We found that similar increases in wind stress values next to the
Citation: Strub, P.T.; James, C.
coast in gridded ERA-5 fields are not due to errors in the model physics or wind speeds. They are
Evaluation of Nearshore QuikSCAT
created during the interpolation of wind stress from the original model grid to a regular rectangular
4.1 and ERA-5 Wind Stress and Wind
Stress Curl Fields over Eastern
grid. We recommend that researchers who are analyzing wind stress and wind stress curl should
Boundary Currents. Remote Sens. calculate wind stress themselves from the gridded ERA-5 vector wind speed fields, rather than using
2022, 14, 2251. https://doi.org/ the interpolated model wind stress or curl fields.
10.3390/rs14092251
Keywords: coastal winds; scatterometry; reanalysis surface winds; wind stress curl
Academic Editors: Bryan Stiles,
Svetla Hristova-Veleva, Lucrezia
Ricciardulli, Larry O’Neill,
Zorana Jelenak and Joe Sapp
1. Introduction
Received: 31 March 2022 1.1. Motivation and Questions Asked
Accepted: 5 May 2022
Although scatterometers and atmospheric circulation models have improved our
Published: 7 May 2022
understanding of the spatial variability in surface winds over the open ocean, the deter-
Publisher’s Note: MDPI stays neutral mination of high-resolution spatial variability in the wind fields within several tens of
with regard to jurisdictional claims in kilometers of land is still problematic. This affects studies of the wind stress and wind
published maps and institutional affil- stress curl over narrow continental shelves, such as those found in eastern boundary up-
iations. welling systems. Here, we evaluate wind speed and wind stress in two such systems—the
Benguela Current System (BCS) along the southwest coast of Africa and the California
Current System (CCS) next to the U.S. West Coast. The wind data sets came from both a
well-described scatterometer (QuikSCAT) and a much-used global atmospheric reanalysis
Copyright: © 2022 by the authors.
product (ERA-5).
Licensee MDPI, Basel, Switzerland.
Our initial motivation for this evaluation came from the appearance of unexpected
This article is an open access article
distributed under the terms and
results in the seasonally changing fields of wind stress and wind stress curl next to the coast
conditions of the Creative Commons
in these two upwelling systems. Both systems are the sites of economically and ecologically
Attribution (CC BY) license (https:// important marine ecosystems, which respond to climatic changes in the surface forcing by
creativecommons.org/licenses/by/ winds [1,2]. Upwelling brings to the surface an increase in nutrients and other changes
4.0/). in water properies, including hypoxic and acidic conditions. Causes of upwelling within
Remote Sens. 2022, 14, 2251. https://doi.org/10.3390/rs14092251 https://www.mdpi.com/journal/remotesensing
Remote Sens. 2022, 14, 2251 2 of 26
the water column include both alongshore wind stress and the curl of the wind stress.
Equatorward alongshore wind stress adjacent to the coast causes the Ekman transport of
mass in the surface away from the coast, which is replaced by upwelled water next to the
coast. This upwelling is usually assumed to be distributed over a narrow coastal band,
with estimates of 5–30 km width [3,4]. At the same time, the greater roughness and friction
of the land, compared to the water, slows the wind as land is approached, creating a wider
band of wind stress curl (positive in the northern hemisphere and negative in the southern
hemisphere for equatorward winds blowing along the west coast of a continent). This
curl results in divergence of the surface Ekman transports, again resulting in upwelling
to provide the vertical convergence to balance the surface horizontal divergence. Coastal
upwelling caused by the alongshore wind stress is an order of magnitude greater than
that caused by the wind stress curl, but the curl acts over a region that may be an order of
magnitude greater in area than the band of coastal upwelling (as seen in the figures below),
making the net effects of both types of upwelling comparable. To evaluate the relative
magnitude of each type of forcing, accurate estimates of the wind stress and wind stress
curl are needed in the 10–100 km next to the coast (see [5] for further descriptions of the
importance of wind forcing in coastal regions).
In the mid- and lower-latitude regions of the two eastern boundary current systems
studied here (BCS and CCS), monthly averages of the wind stress are persistently upwelling-
favorable (equatorward) year-round, strongest in summer. Winds in the higher-latitude
regions of each system are upwelling-favorable in summer and downwelling-favorable
(poleward) in winter. The results of the initial gridding of winds around Southern Africa
and the U.S. West Coast (USWC) are shown in Figure 1, where wind stress vectors from
QuikSCAT (QS, subset to every 0.4◦ ) and ERA-5 (subset to every 0.5◦ ) are overlayed on
color displays for the curl of the wind stress (showing all 0.1◦ and 0.25◦ gridded data
points). The 10-year averages are presented for summer months (January and July for the
southern and northern hemispheres, respectively), during which the direction of the wind
stress is equatorward almost everywhere. The decreases in wind speed and wind stress
in the 100–200 km bands next to the coast create bands of negative (positive) wind stress
curl along the coasts of the BCS and CCS, respectively. However, also evident are narrow
regions (1–2 grid points) of wind stress curl with opposite signs immediately adjacent to
the coast, narrower for the QS data than the ERA-5 data, due to the size of the grid spacing.
This indicates an unexpected increase in wind speed as land is approached. Although
more prevalent in summer, these anomalous curl values next to the coast can be found
during all seasons. As described below, overestimates of scatterometer wind speed near
the coast can be caused by uncorrected reflections of the radar signal from land. For the
ERA-5 fields, errors in coastal winds could indicate errors in the physics of air–sea and
air–land interactions, decreases in the Marine Boundary Layer heights near the coast, etc.
The unexpected increase in wind speed next to the coast in both of these products motivates
the detailed evaluations presented in this paper.
The questions we ask are:
(1) Do actual wind speeds generally increase as land is approached within 10–50 km of
the coast in the two regions examined here?
(2) If the increase in wind speeds near the coast in the scatterometer data is an artifact, at
what distance from the coast should we consider the data suspect?
(3) If the scatterometer wind speeds are in error, can we identify the cause of the error?
(4) If the increase in the wind stress values near the coast in the ERA-5 data is an artifact,
what causes it and can we find a procedure to avoid it?Remote Sens. 2022, 14, x FOR PEER REVIEW 3 of 26
Remote Sens. 2022, 14, 2251 3 of 26
Figure 1. Cont.Remote
Remote Sens.
Sens. 2022,
2022, 14,14, x FOR PEER REVIEW
2251 4 4of of
26 26
1. (Previous page) 10-year averages (11/1999-11/2009) ◦ ) overlaid on wind stress curl (full 0.1◦ grid) for
Figure
Figure 1. (Previous page) 10-year averages (11/1999-11/2009)ofofQuikSCAT
QuikSCAT v4.1 wind
v4.1 wind stress vectors
stress (subset
vectors (subsetto to
0.40.4°) overlaid on wind stress curl (full 0.1° grid) for
summer along thethe
coasts of of
(a)(a)
southern Africa and (b)(b)
western North America. AllAll
L2B retrievals areare
used to to
create thethe ◦ gridded values. (This page) 10-year
0.10.1°
summer along coasts southern Africa and western North America. L2B retrievals used create gridded values. (This page) 10-year
averages (QuikSCAT period) of of
ERA-5 reanalysis wind stress vectors (subset to to ◦
0.50.5°)
) overlaid ononwind stress curl (full 0.25 ◦ grid) forfor
summer along thethe
coasts of of
averages (QuikSCAT period) ERA-5 reanalysis wind stress vectors (subset overlaid wind stress curl (full 0.25° grid) summer along coasts
(c)(c)
southern
southern Africa andand
Africa (d)(d)
western North
western NorthAmerica. From
America. Fromthe the
interpolated
interpolated ◦ ERA-5
0.250.25° ERA-5wind stress
wind grid.grid.
stress The The
insets show
insets expanded
show views
expanded of the
views ofreversal in sign
the reversal in of
sign
theofwind
the wind
stressstress curl to
curl next next
thetocoast.
the coast.Remote Sens. 2022, 14, 2251 5 of 26
1.2. Previous Work
The improved retrieval of QuikSCAT vector wind speeds in coastal regions (ver-
sion 4.1) is described in detail by [5]. Each location on Earth’s surface within the continuous
swath mapped by QuikSCAT’s rotating antennas was sampled from several angles as the
satellite moved along its orbit, and the returned power of the radar was estimated in the
form of a sigma-0 parameter for each look angle. From the muliple values of sigma-0,
the surface vector wind was estimated. The nominal radar footprints were ovals with
major/minor axes of approximately 35 km and 25 km, respectively. The returned power
within each oval was further divided into 8 km by 25 km “slices.” When the slices are
oriented parallel to the coast, they may sample within several kilometers of land. For
each returned slice of radar power, a previous methodology (version 3.1) used the known
and more complicated radar surface footprint pattern to calculate the fractional coverage
of the footprint over land (version 3.1 is also called the Land Contribution Ratio, LCR).
Observations were rejected if too much land (typically >1%) was found within the footprint.
Improving on this in version 4.0, the known albedo of the land was combined with the
LCR to estimate the portion of returned power for each slice that was coming from land to
the scatterometer. If this “expected contribution to sigma-0 from land” (ES) was greater
than 0.4%, the observation was rejected. Otherwise, the returned power was subtracted to
form a modified (LCRES) value of sigma-0, which was used with the other observations
of sigma-0 at the same location to form the estimate of vector wind speed. This increased
the number of retrieved wind estimates within 20 km of land by more than an order of
magnitude [5]. The retrieved vectors were used to form an “irregular” grid of vector winds
within each swath with a grid spacing of ~12.5 km (the grid points change from swath to
swath). These are the basic Level 2B LCRES vector wind data, version 4.0. The increased
proximity to land allows for the analysis of winds in large lakes and semi-enclosed regions
of the ocean, such as the Inland Sea along southern Chile [5,6].
An additional evaluation of remaining errors due to land was added in version 4.1
in the form of a “Poor Coastal Processing” (PCP) flag. Comparisons of the difference
between wind speed magnitudes from LCRES retrievals and collocated meteorological
buoy wind speeds indicate that the differences are large when the distance to land is 5 km
or less [5]. Thus, the PCP flag was set for (1) observations within 5 km of land. It was also
set for (2) observations that occur when the “pitch” of the satellite is too great. Finally,
the differences between each LCRES observation wind speed and the nearest neighbor
observations farther offshore were used to flag (3) regions with persistent errors, and these
were included in the PCP flags [5]. Below, we show the results obtained both with and
without the use of the PCP flags.
In [5], meteorological buoy wind speeds within 100 km of land were used to quantify
the differences between scatterometer and buoy estimates of wind speeds, as a function of
distance to the coast. Here, we employed the relatively rare use of wind speeds derived from
alongtrack altimeter sigma-0 values as they approach and cross the land. This methodology
was used by [3] along the Chilean coast (another region of persistent upwelling) to show
that there was an average decrease in the wind speed as land is approached. In [3],
results of the less accurate altimeter retrieval algorithms were corrected by using collocated
scatterometer retrievals over open water. Here, we did not quantify the difference between
the scatterometer and altimeter wind speed estimates. We only used the altimeter to verify
that wind speeds decreased as land was approached in our two systems, as found by [3]
off Chile.
2. Materials and Methods
We used the Jet Propulsion Laboratory’s (JPL’s) version 4.1 of the ten-year (1999–2009)
QuikSCAT Level 2B (L2B) swaths of vector wind retrievals (see “Data Availability State-
ment” below). Wind stress was calculated from the scatterometer ten-meter equivalent
wind speed using a drag coefficient that depends only on wind speed [7]. In order to
resolve the wind stress and wind stress curl as close to land as possible, our initial analysesRemote Sens. 2022, 14, 2251 6 of 26
(Figure 1) did not exclude the retrieved winds that were flagged as uncertain by the PCP
flag, although figures showing our detailed (1-km) analyses (below) used color coding to
identify the observations that would have been eliminated by the PCP flag. Ignoring this
flag is approximately equivalent to using version 4.0 of the data set for oceanic applications.
To create gridded fields of wind stress and wind stress curl for our research projects, our
processing consisted of: (1) applying a minimum of QC criteria to the raw vector wind
retrievals in each Level 2B swath to remove extreme values; (2) calculating vector wind
stress from the remaining vector wind retrievals; and (3) interpolating vector wind stress
retrievals from each swath’s variable grid (with ~12.5 km grid spacing) to a common grid
with 0.1◦ spacing. The interpolation used retrieved winds within 40 km of each grid point
to estimate a polynomial surface, which provides estimates of both the wind stress and the
gradients of the wind stress at each grid point, from which the curl of the wind stress was
calculated. If there were not 10 values of L2B vector wind retrievals within the 40 km radius,
data at the grid point were treated as missing. The regridding method was similar to that
used by JPL to produce gridded Level 3 fields, although we required fewer observations in
our 40 km radius than required by JPL. The re-gridded swath data were averaged to form
individual monthly means, long-term (10-year) climatological monthly mean fields and a
long-term annual mean. While gridding the data, as described above, the PCP flag may
or may not be used to eliminate the L2B retrievals. Figure 1 presents the fields gridded by
ignoring the PCP flags.
Rather than using the gridded data, most of the results presented below used several
forms of binning of the individual L2B retrievals to investigate whether they showed
evidence of increased wind speed as land was approached. In some cases, they were
“binned” into 7 km by 13 km rectangular regions—averaging all retrievals that fall within
a region. To compare scatterometer averages of wind speeds to altimeter wind speed
retrievals, rectangular areas were arranged along altimeter tracks that cross land in the
two eastern boundary upwelling systems. Figure 2 presents an example of the boxes along
altimeter Track/Pass 031 off South Africa. (Note: The continuous altimeter track is formally
divided into numbered “passes” that cross the coast at different locations. We informally
refer to these interchangeably as both Track XX and Pass XX, since, from a regional point of
view, each Pass is a separate Track). The data were averaged in bins set by the along-track
distance to the altimeter track’s land crossing. Following the same tracks, altimeter and
scatteromater retrievals were also binned according to the actual distance to the nearest
land. For the scatterometer, this produces irregularly shaped regions of points, located
within 6.5 km on either side of the altimeter track and within the specified ranges of distance
from the nearest land (see figures below).
ERA-5 daily reanalysis wind stress data have been retrieved from the Copernicus
web site (https://cds.climate.copernicus.eu/, accessed on 30 June 2021) for the period
1979–2020. Although the original model fields were calculated on a reduced Gaussian grid
(RGG), data provided by the Copernicus Climate Data Store (CDS) web interface were
interpolated by the Copernicus system to a rectangular latitude-longitude grid with regular
0.25◦ spacing. We obtained the 10-m vector wind speed and wind stress on this rectangular
grid, calculating wind stress curl from the wind stress values. We also downloaded a short
period of data (August–September 2005) on the original RGG grid from the ECMWF web
site (https://apps.ecmwf.int/data-catalogues/era5/?class=ea, accessed on 20 June 2021),
which we used to evaluate the effect of the gridding on the nearshore values of wind speed
and wind stress.Remote Sens. 2022, 14, x FOR PEER REVIEW 7 of 26
Remote Sens. 2022, 14, 2251 7 of 26
Figure2.
Figure Altimeter track
2. Altimeter track031
031along
alongthethesouthwest
southwestcorner of South
corner Africa,
of South showing
Africa, the locations
showing of
the locations of
the nominal grid points that define the altimeter track (not data points) and the coastal crossing
the nominal grid points that define the altimeter track (not data points) and the coastal crossing (blue
dots).dots).
(blue The rectangular areas within
The rectangular areas which
withinL2B scatterometer
which wind speedwind
L2B scatterometer retrievals
speedareretrievals
binned extend
are binned
6.5 km6.5
extend on either
km onside of the
either track
side and track
of the 7 km along
and 7the
kmtrack,
alongstarting 7 kmstarting
the track, from the7coastal
km fromcrossing.
the coastal
The box that
crossing. Thewould be touching
box that would bethe coastal crossing
touching is not
the coastal shown or
crossing used.
is not shown or used.
Wind speed magnitudes (not directions) were available from the reference altimeters,
ERA-5 daily reanalysis wind stress data have been retrieved from the Copernicus
TOPEX/Poseidon (T/P) and Jason-1/2/3. The instantaneous footprints of these altimeters
web
weresite (https://cds.climate.copernicus.eu/,
smaller than those of the scatterometers, accessed in 30asJune
characterized 6–7 2021)
km byfor theSince
[8,9]. periodthe1979–
2020. Although
altimeter moves the original
~7 km modeland
per second fields were1-Hz
we used calculated
data, the onfootprint
a reduced Gaussian
represents an grid
(RGG),
elongated area of approximately 7 km by 14 km. Under extremely high significant wave were
data provided by the Copernicus Climate Data Store (CDS) web interface
interpolated
conditions, thebyinstantaneous
the Copernicus system
footprint mayto reach
a rectangular latitude-longitude
10 km, creating a slightly larger grid with reg-
oblong
ular 0.25° spacing.
footprint. In [3], theyWe obtained
described the 10-mofvector
a footprint 6.9 kmwind
by 20speed
km forandthesewind stress which
altimeters, on this rec-
seems overly
tangular grid,large. Altimeter
calculating windretrievals
stress are
curlcentered
from the on wind
the nadir points
stress of theWe
values. altimeter,
also down-
loaded a short period of data (August–September 2005) on the original RGG griddata
which fall within 1 km of the nominal altimeter track. We used along-track altimeter from the
from the RADS (Radar Altimeter Data System) data set, made available
ECMWF web site (https://apps.ecmwf.int/data-catalogues/era5/?class=ea, accessed on 20 at the Delft Techni-
cal University’s web site (https://rads.tudelft.nl/rads/rads.shtml, accessed on 25 February
June 2021), which we used to evaluate the effect of the gridding on the nearshore values
2021). The relationship between wind speed and returned radar power is opposite for
of wind speed and wind stress.
the nadir altimeter reflections to that for the slanted scatterometer reflections: high
Wind
winds speed
create magnitudes
small waves that(not directions)
reflect were available
the scatterometer’s fromradar
slanted the reference
beam back altimeters,
to
TOPEX/Poseidon
the satellite, while(T/P) and waves
the same Jason-1/2/3.
scatterThe instantaneous
the altimeter’s nadirfootprints
radar signal of these altimeters
away from
were smaller Land
the satellite. than also
thosescatters
of the the
scatterometers, characterized
slanted scatterometer signal as 6–7tokm
back theby [8,9]. and
satellite Since the
altimeter
either absorbs or scatters the altimeter’s nadir beam away from the satellite. Thus, for an
moves ~7 km per second and we used 1-Hz data, the footprint represents
both scatterometers
elongated and altimeters,7 land
area of approximately km by contamination
14 km. Under produces overestimates
extremely of wind wave
high significant
speed. The the
conditions, magnitude of the land
instantaneous effectsmay
footprint is much
reachgreater
10 km,for the scatterometer,
creating since oblong
a slightly larger
footprint. In [3], they described a footprint of 6.9 km by 20 km for these altimeters, which
seems overly large. Altimeter retrievals are centered on the nadir points of the altimeter,
which fall within 1 km of the nominal altimeter track. We used along-track altimeter data
from the RADS (Radar Altimeter Data System) data set, made available at the Delft Tech-
nical University’s web site (https://rads.tudelft.nl/rads/rads.shtml, accessed on 25 Febru-
ary 2021). The relationship between wind speed and returned radar power is opposite for
the nadir altimeter reflections to that for the slanted scatterometer reflections: high windsRemote Sens. 2022, 14, 2251 8 of 26
land can sometimes reflect 10 times more power than the wind-roughened water. For
the altimeter, the decrease in the signal can only be of the same magnitude as the signal,
producing a weaker change in returned power for the same fraction of land than in the
scatterometer signal [10]. The decreased effect of land on the altimeter signal may combine
with the smaller footprint to allow it to retrieve wind speeds closer to the coast than for the
scatterometer. We stress that we did not rely on the altimeter wind speeds for absolute wind
speed values, but simply detected increases or decreases in wind speeds. Thus, we did not
attempt to calibrate the altimeter wind speeds against the scatterometer wind speeds or
other wind measurements, as performed by [3].
For both scatterometer, altimeter and ERA-5 data, observations were collected within
each spatial bin to form 3-month seasonal averages. The altimeter collected a 1-Hz estimate
of wind speed for approximately 7-km sections of track, within 1 km of the nominal
track. The 10-day repeats over 28 years would produce a maximum of approximately
250 observations in each 3-month season over the open ocean without any data losses.
Losses due to rain and other atmospheric effects, orbital problems, electrical problems,
etc., reduce this number over the open ocean, while other factors reduce the usable data as
land is approached. With one exception, there were at least 68 valid altimeter observations
in all of the 3-month averages in the closest bin to the altimeter’s coastal crossing, as
presented below. Far from the coast there are usually over 200 altimeter observations used
in each average. Estimates of the expected errors/uncertainty in the individual altimeter
wind speed retrievals varied from 0.8–0.9 m s−1 [3] to 0.9–1.3 m s−1 [9]. Using a value
of 1.3 m s−1 and dividing by the square root of the number of observations resulted in
maximum expected errors of 0.2 m s−1 or less for the seasonal averages of the altimeter
wind speeds for all but one track in Figure 3. In Figure 4, the number of observations in
all averages produced estimated uncertainties of 0.1 m s−1 or less. For the scatterometer
data, the expected errors in the individual observations was 0.7 m s−1 [10]. Thus, for
the averages within the bins, only 50 observations were needed to reduce the expected
errors to 0.1 m s−1 . Only when considering narrow 1-km bins within ~5 km of the coast
does the number of scatterometer observations fall below 50. However, it is suggested
that unidentified systematic errors of ~0.1 m s−1 may continue to persist in scatterometer
averages [10]. Thus, for both altimeter and scatterometer averages of the wind speeds, we
characterized the uncertainties as ~0.1–0.2 m s−1 .
Expected errors in the ERA-5 wind fields were characterized by comparisons to ASCAT
scatterometer winds by [11]. Global comparisons yielded rms differences of 1.5–2.0 m s−1 .
Our comparisons here used data only from the 10-year QuikSCAT period to allow direct
comparisons between ERA-5 and satellite results. With decorrelation scales of 3–5 days for
the winds, three-month averages of the daily winds contained approximately 700 or more
independent observations, resulting again in estimated uncertainties of less than 0.1 m s−1 .
For wind stress values of approximately 0.05–0.2 N m−2 over water, as found below, this
wind speed translated to errors in wind stress of order 0.002–0.003 N m−2 .Remote Sens. 2022, 14, x FOR PEER REVIEW 9 of 26
Remote Sens. 2022, 14, 2251 9 of 26
Figure
Figure 3. (Top)
3. (Top) Locations
Locations of the
of the six altimeter
six altimeter tracks
tracks for for
the the northern
northern andand southern
southern regions
regions offoff
south-
southwest
west Africa,with
Africa, along along28-year
with 28-year (1993–2020)
(1993–2020) averages
averages of of winter(Middle)
winter (Middle)andandsummer
summer (Bottom)
(Bottom) al-
altimeter-derived
timeter-derived wind wind speeds
speeds retrieved
retrieved along
along 7-km
7-km sections
secions of the
of the tracks.
tracks. TheThe x-axis
x-axis shows
shows thethe
along-
along-track distance to the coastal crossing. Values for the 0–7 km bin closest to
track distance to the coastal crossing. Values for the 0-7 km bin closest to the coast are not shown.the coast are
not shown.Remote
RemoteSens.
Sens.2022,
2022,14,
14,x2251
FOR PEER REVIEW 1010ofof26
26
Figure
Figure4.
4. As
As in Figure
Figure 3,3,except
exceptthe
thealtimeter
altimeter wind
wind speed
speed retrievals
retrievals are averaged
are averaged into 7-km
into 7-km bins
bins based
based
on theon the distance
distance to theto the nearest
nearest land. land.
3. Results
Expected errors in the ERA-5 wind fields were characterized by comparisons to
3.1. Altimeter
ASCAT and QuikSCAT
scatterometer winds Wind Speed
by [11]. Analyses
Global comparisons yielded rms differences of 1.5–
2.0 mMost s−1. Our comparisons here used data only
of our evaluations of the QS coastal wind from the 10-year
speeds used theQuikSCAT
data next toperiod to
southern
allow direct comparisons between ERA-5 and satellite results. With decorrelation
Africa’s west coast. To compare the altimeter retrievals of wind speed to those from the scales
of 3–5 days for we
scatterometer, theinitially
winds, three-month averages
retrieved altimeter windof the daily
speed winds
values contained
in 7-km approxi-
sections of the
mately
tracks,700 or more
ignoring theindependent observations,
closest section resulting
to the coastal again inGiven
land crossing. estimated uncertainties
the lower amount
of
ofless
datathan 0.1 m from
available s−1. For wind
the stressfor
altimeter values of approximately
a given 0.05–0.2toNthe
period, as compared m−2scatterometer,
over water,
as
wefound below,this
conducted thisfor
wind
the speed
28-yeartranslated
altimeter to errors1993–2020.
record, in wind stress of order 0.002–0.003
Climatological three-monthN
m −2.
seasonal averages of these wind speeds were compared to averages of the wind speed
magnitude from QuikSCAT, averaged in 7 km by 13-km rectangles centered on the same
3.tracks.
Results An example of the sampling geometry is presented in Figure 2. The seasonal winter
and summer
3.1. Altimeter and averages
QuikSCAT of wind
Windspeed along the six altimeter tracks available between
Speed Analyses
20–35◦ S appear in Figure 3. Average wind speed values were plotted as a function of the
Most of our evaluations of the QS coastal wind speeds used the data next to southern
alongtrack distance from the 7-km section to the track’s land crossing (the closest coastal
Africa’s west coast. To compare the altimeter retrievals of wind speed to those from the
data point is at 10.5 km). Due to the angles at which the tracks approached the coast, and
scatterometer, we initially retrieved altimeter wind speed values in 7-km sections of the
also to capes and bays in the coastline, the distance of the track section (the bin) between
tracks, ignoring the closest section to the coastal land crossing. Given the lower amount
7–13 km of the coastal crossing was closer to the coast than 7 km. Data in this first bin
of data available from the altimeter for a given period, as compared to the scatterometer,
were affected by radar footprints that extend over the coast, resulting in wind speeds that
we conducted this for the 28-year altimeter record, 1993–2020. Climatological three-month
increased in some of the bin averages that were closest to the coast. The coastline near
seasonal
the crossing averages of these
of Track windparticularly
235 was speeds were compared producing
convoluted, to averagesa of the wind
decrease andspeed
then
magnitude from QuikSCAT, averaged in 7 km by 13-km rectangles centered on the sameRemote Sens. 2022, 14, 2251 11 of 26
increase next to the coast, as discussed below. As discussed above, expected errors for all
averages presented in Figure 3, except along Track 235, were less 0.2 m s−1 . For Track 235,
the low number of data points for the inner two averages during both seasons produced
uncertainties in Figure 3 between 0.2 m s−1 and 0.5 m s−1 .
Figure 4 eliminated the problem caused by the slanted altimeter tracks by binning the
altimeter wind speeds according to the actual distance to the nearest land, as reported in the
along-track data records. Ignoring Track 235, only Track 209 showed an increase in wind
speed in the bin closest to the coast (using data between 7–13 km from land). As discussed
below, this may be due to a small island that does not appear on the map. The lowest
number of points in any of the most coastal averages was 162, resulting in a maximum
expected error of 0.1 m s−1 . The decrease in wind speed (remembering that the altimeter
estimates were approximate) between the last two data points (at ~17 and ~10 km from
land) ranged from 0.2 to 0.9 m s−1 for most tracks during the two seasons. We concluded
that, based on the altimeter data, the actual wind speed did not increase in general as the
coast was approached, agreeing with the results of [3] along the Chilean coast.
Results of the 10-year binned averages of winter and summer L2B scatterometer
wind speed magnitudes appear in Figure 5, where the average scatterometer wind speed
magnitudes from within the 7 km by 13 km rectangular areas oriented along the altimeter
tracks (as in Figure 2) were plotted as a function of the along-track distance between the
center of the rectangle and the coastal crossing of the altimeter track. As in the altimeter
plots, the center of the first coastal rectangle next to the coast for which data were plotted
was at 10.5 km from the crossing. Solid lines show averages of the points within the
rectangles, excluding those marked as suspect by the PCP flag. All but the two most
northern tracks showed an increase in wind speed next to the coast during summer (Track
057) or winter (Tracks 133, 209 and 031), with increases of 0.3 m s−1 to 0.5 m s−1 . This result
did not change when all of the retrievals within the rectangles were used (ignoring the PCP
flag), represented by the dotted lines. The fewest number of points in the closest bin to the
crossing was 231 (Track 133 in winter), producing an uncertainty of 0.05 m s−1 ).
Even more than the altimeter data along the tracks, averages of the wind speeds in
the rectangles suffered from retrievals that were much closer than 7 km from the coast.
In Figure 6, the scatterometer wind speeds were averaged according to their distances to
the nearest land (compare to the similar binning of altimeter data in Figure 4). Thus, all
L2B scatterometer data within 6.5 km of the altimeter track and between 7–13 km from the
nearest land were averaged into the closest point from land (the PCP flags had no effect on
these points and were not used). In these averages, the fewest number of points in any of
the averages closest to the coast was 1066, producing an uncertainty of 0.02 m s−1 , although
a nominal uncertainty of 0.1 m s−1 was still used. The influence of land still affected three
of the six tracks at the 1–2 grid points closest to land, more strongly during summer. We
note that, in Figure 1a, the region covered by the two most northern tracks did not show
the reversal in sign of the wind stress curl next to the coast, consistent with the fact that
the data along those tracks did not show an increase in wind speed next to the coast in
either Figure 5 or Figure 6. From these results, we concluded that QuikSCAT data retrieved
from within 7–13 km of land may display an artificial increase in wind speed. The actual
increase between the last two grid points next to land depends on the track location and
the season but is as large as approximately 0.5 m s−1 .Remote Sens. 2022, 14, x FOR PEER REVIEW 12 of 26
Remote Sens. 2022, 14, 2251 12 of 26
actual increase between the last two grid points next to land depends on the track location
and the season but is as large as approximately 0.5 m s .−1
Figure
Figure 5.
5. As
As in
in Figure 3, except
except showing
showingQuikSCAT
QuikSCATwindwindspeeds
speeds binned
binned into
into rectangular
rectangular boxes
boxes (7
(7 km
km bykm)
by 13 13 km) arranged
arranged alongalong the altimeter
the altimeter tracks
tracks as as in
shown shown
Figurein2.Figure 2. Solid
Solid Lines: Lines: Retrievals
Retrievals marked as
marked
suspect as
by suspect
the PCPby the
flag PCP
are flag areDotted
excluded. excluded. Dotted
Lines: Lines: All
All retrieved retrieved scatterometer
scatterometer L2 wind speedL2values
wind
speed values within each rectangle are averaged. The x-axis shows the alongtrack distance
within each rectangle are averaged. The x-axis shows the alongtrack distance from the box center from theto
box center to the nearest coastal crossing. Values for the box that would be touching the coast are
the nearest coastal crossing. Values for the box that would be touching the coast are not shown.
not shown.
This is a suggestive but not conclusive result. To investigate this further, we examined
This is a suggestive
in more detail but notdata
the scatterometer conclusive
that wereresult.
foundTowithin
investigate this further,
the 7–13-km we exam-
rectangles closest
ined incoast
to the moreon detail thetracks
all six scatterometer
(which were dataaveraged
that weretofound
form within
the wind thespeed
7–13-km rectangles
nearest to land
closest to the
in Figure coast on
5). Figure all six the
7 shows tracks (which
spatial were averaged
distribution of thesetopoints.
form the wind
First, speed
black nearest
points were
to land in Figure 5). Figure 7 shows the spatial distribution of these
plotted for all wind speed retrievals that fell within the 7 × 13 km rectangles, ignoring points. First, black
the
points were
PCP flag. plotted
Some for all
of these winddot)
(black speed retrievals that
observations werefell within
closer than the7 7km× 13
or km rectangles,
farther than 13
ignoring
km fromthe land.PCP flag.blue
Next, Some of these
dots (black dot)
were plotted observations
for all points within were 6.5closer
km ofthan
the 7nominal
km or
farther thanbetween
track and 13 km from 7–13land. Next,the
km from blue dots were
nearest land,plotted for allon
as reported points within 6.5 km
the scaterometer of
data
the nominal track and between 7–13 km from the nearest land, as reported
record. These overlay many of the black dots within the rectangle and include many more on the scater-
ometer data record.
points outside of theThese overlay
rectangle, many
due of the
to the black dots
coastline within Finally,
geometry. the rectangle
orange and include
dots were
many
plotted over all of the above data points within the rectangle that have the PCP flagorange
more points outside of the rectangle, due to the coastline geometry. Finally, set, so
dots were
at 5 km orplotted over
closer to theall of the
coast, or above data points
if otherwise within
they were the rectangle
considered that have the PCP
suspect.
flag set, so at 5 km or closer to the coast, or if otherwise they were considered suspect.RemoteSens.
Remote Sens. 2022, 14, x2251
2022, 14, FOR PEER REVIEW 1313ofof26
26
Figure
Figure 6.
6. As
As in
in Figure
Figure 5 except showing
showing QuikSCAT
QuikSCATwind windspeeds
speedsbinned
binnedaccording
accordingtotothethe distance
distance of
of the individual wind retrievals to the nearest land. Bins are again divided into 7 km distances
the individual wind retrievals to the nearest land. Bins are again divided into 7 km distances (7–13, (7–
13, 14–20,
14–20, etc.).
etc.). TheThe blue
blue dots
dots in Figure
in Figure 7 show
7 show thethe retrievals
retrievals within
within 7–13
7–13 kmkm of any
of any landland
andand within
within 6.5
6.5 km of the altimeter track. Above data points closest to the coast are the averages of the
km of the altimeter track. Above data points closest to the coast are the averages of the blue dots blue dots
in
in Figure 7.
Figure 7.
In
In Figure
Figure 7, 7, ifif one
one imagines
imagines the the altimeter
altimeter track
track running
running through
through the the middle
middle of of the
the
northern and southern faces of the rectangles (perpendicular to
northern and southern faces of the rectangles (perpendicular to those faces), the reason for those faces), the reason
for
thethe convoluted
convoluted altimeter
altimeter wind
wind speed
speed ininFigure
Figure3 3forforTrack/Pass
Track/Pass 235 235 becomes
becomes clear. clear. The
The
track
trackwas
wassheltered
shelteredfrom from thethewinds
winds(coming
(comingfrom fromthe thesoutheast)
southeast)as asititentered
enteredthe thesouthern
southern
end
end ofof the
the bay
bay near
near 23.4°S
23.4◦ S (the
(the wind
wind speed
speed decreases),
decreases), thenthen itit moved
moved into into the
the bay
bay and
and
actually touched land at the northeast corner of the track (the
actually touched land at the northeast corner of the track (the wind speed increases). Along wind speed increases).
Along Trackthe
Track 209, 209,
longthetaillongoftail
blue of points
blue points
to thetosouth
the south
of theof rectangle
the rectangle waswas caused caused by
by the
the proximity
proximity to Dassen
to Dassen Island
Island in the
in the southeast.
southeast. In visible
In visible high-resolution
high-resolution satellite
satellite images,
images, one
one
can can
see see another
another small small island,
island, Vodeling
Vodeling Island,
Island, located
located aboutabout a kilometer
a kilometer from from
the the
coastcoast
just
just north
north of where
of where the Track
the Track 209 crosses
209 crosses the coast
the coast (position
(position shownshown by theby starthein star
Figure in Figure
7). The
7). The island
island was not was
in thenot data
in thebase
dataused
basetoused
draw to draw our coastlines.
our coastlines. If it not
If it was wasinnot theindata
the data
base
base used to estimate the distance to nearest land that was included
used to estimate the distance to nearest land that was included in the RADS altimeter data in the RADS altimeter
data records,
records, reflections
reflections fromfrom this island
this island may mayexplainexplain the continued
the continued increaseincrease in altimeter
in altimeter wind
wind
speedspeed
for thisfortrack
this next
tracktonextthe to theincoast
coast Figurein Figure
4, even4,when
eventhe when the altimeter
altimeter bin wasbin was
thought
thought
to be over to 7bekm
overfrom 7 km from
land. land. altimeter
A 7-km A 7-km altimeter
footprintfootprint
might bemight 7 km be from7 km thefrom the
nominal
coast butcoast
nominal still receive
but stillreflections from the from
receive reflections island.the island.Remote Sens.
Remote2022,
Sens.14, x FOR
2022, PEER REVIEW
14, 2251 14 of1426of 26
Figure 7. For each altimeter track, the closest 7 km × 13 km box used to average the scatterometer
Figure 7. For each altimeter track, the closest 7 km × 13 km box used to average the scatterometer
wind speeds in Figure 5 is shown. Shown also are all retrievals within 7–13 km of land and within
wind speeds in Figure 5 is shown. Shown also are all retrievals within 7–13 km of land and within
6.5 km of the altimeter track (blue). Within each box, retrievals flagged by the “Poor Coastal
6.5 km of the altimeter track (blue). Within each box, retrievals flagged by the “Poor Coastal Pro-
Processing” flag as ‘suspect’ are in orange. Retrievals closer than 7 km or farther from 13 km from
cessing” flag as ‘suspect’ are in orange. Retrievals closer than 7 km or farther from 13 km from land
land but not flagged are shown in black.
but not flagged are shown in black.
To examine the wind speeds in more detail, in Figure 8, the points within the rectan-
gular binds in Figure 7 were averaged into 1-km bins based on their distance to the nearest
land. The black circles represent the averages of all points within the 1 km subsets of the
data within the rectangles, each circle with a diameter of approximately 0.5 m s−1. The red
triangles are averages that exclude the points identified by the PCP flag as suspect. Even
in these narrow bins, the number of points assures that the uncertainties in the averages
−1Remote Sens. 2022, 14, 2251 15 of 26
To examine the wind speeds in more detail, in Figure 8, the points within the rectan-
gular binds in Figure 7 were averaged into 1-km bins based on their distance to the nearest
land. The black circles represent the averages of all points within the 1 km subsets of the
data within the rectangles, each circle with a diameter of approximately 0.5 m s−115
Remote Sens. 2022, 14, x FOR PEER REVIEW
. The red
of 26
triangles are averages that exclude the points identified by the PCP flag as suspect. Even in
these narrow bins, the number of points assures that the uncertainties in the averages at
distances of 6 km or more from land were less than 0.1 m s−1 . At 5 km and less from land,
land, uncertainties
uncertainties werewere larger
larger but but
still still
less less
thanthan
0.5 m0.5s−m1 .sThe
−1. The lower of the two horizontal
lower of the two horizontal lines
lines (separated
(separated by 1.0
by 1.0 m sm s) passes
− 1 −1 ) passes through
through thethe center
center of of
thethe circle,
circle, representing
representing thethe av-
average
erage
wind wind speed
speed in bin
in the the centered
bin centeredat 11atkm 11 from
km from the nearest
the nearest land.land.
Figure
Figure 8. Scatterometer
8. Scatterometer wind wind speeds
speeds fromfrom
L2B L2B retrievals
retrievals within
within the 7 the
× 137km× bin
13 km bin nearest
nearest to the
to the coast
(the rectangles in Figure 7), averaged into 1-km bins based on the distance from the L2B vector
coast (the rectangles in Figure 7), averaged into 1-km bins based on the distance from the L2B vector wind
retrieval to the nearest
wind retrieval land. All
to the nearest seasons
land. are included.
All seasons BlackBlack
are included. circles are the
circles averages
are the of all
averages points
of all points
within the 1-km bin within the rectangle; red triangles exclude those identified by the
within the 1-km bin within the rectangle; red triangles exclude those identified by the PCP flagPCP flag as as
suspect, including all points within 5 km of land. The two horizontal lines are separated by 1 m/s,
suspect, including all points within 5 km of land. The two horizontal lines are separated by 1 m/s,
while the lower of the two lines passes through the wind speed value at 11 km from the nearest
while the lower of the two lines passes through the wind speed value at 11 km from the nearest land.
land.
With the exception of Track 235, there was sometimes an initial decrease in wind
speed as land was approached from offshore, then an increase in wind speed starting
somewhere between 8–10 km from land. The increase between 10–11 km and 6 km wasRemote Sens. 2022, 14, 2251 16 of 26
With the exception of Track 235, there was sometimes an initial decrease in wind speed
as land was approached from offshore, then an increase in wind speed starting somewhere
between 8–10 km from land. The increase between 10–11 km and 6 km was least for Tracks
159 and 031 (0.3–0.5 m s−1 ) and greatest for Tracks 209, 133 and 057 (~1.0 m s−1 or more).
In some cases, excluding points based on the PCP flag reduces the increase in wind speed
slightly (triangles move to the lower half of the circles for Tracks 031 and 209), but the
general trend remains. For Track 235, the steady decrease in wind speed as land was
approached appears to be most strongly controlled by the sheltering provided within the
bay from the wind that was predominantly from the southeast (Figure 7).
To further increase the data and the regions investigated, nine tracks next to the U.S.
west coast were added to the analysis in Figure 9. In this analysis, we excluded the tracks
between Track 145 and Track 119 because they either passed over islands in the Southern
California Bight or ended in regions of complex coastal geometry, such as Track 221 (not
shown), which terminated within Monterey Bay (36–37◦ N). Along these tracks, an increase
in altimeter wind speed approaching the coast only occurred at the grid point closest to
the coast on the most northern Track 171 (not shown), even when distance was measured
along-track to the nearest coastal crossing rather than to the nearest land. The QuikSCAT
wind speed averages in Figure 9, on the other hand, showed consistent increases in wind
speed at 8–10 km and closer to the land from the six northern tracks (in typical exposed
coastal conditions with strong summer and winter winds of opposite directions) and the
three southern tracks (in the sheltered Southern California Bight where northerly winds are
typically much weaker). This is true for the averages of all of the points and for averages of
just the “good” points represented by the red triangles. This indicates that the elimination
of “suspect” points by the PCP flag does not eliminate the overestimates of wind speeds
within 10 km of the coast.
The magnitude of the increase in wind speed between 10–11 km and 6 km from land
indicated by the scatterometer data varies between altimeter tracks, from ~0.3 m s−1 to
over 1.0 m s−1 . Where there was enough data, this increase continued to grow at 5 km and
less from land, providing support for the flagging of data inshore of 5 km by the PCP flag.
Our results were consistent with those of [5], who showed (their Figure 7) an increase in
the differences between wind speeds measured by LCRES retrievals and meteorological
buoys (LCRES-buoy) when the distance to land decreased from about 15 km to 7–8 km,
increasing from ~0.7 m s−1 to ~1.3 m s−1 . They noted that the positive biases in the
QuikSCAT wind speeds (compared to buoys) were only modestly greater at 10 km from
land than at 40 km. Our results agree approximately with this difference (~0.5 m s−1 ).
Considering the altimeter result that the actual wind speed was decreasing toward land,
both results indicated an overestimate in wind speed of approximately 0.5 to 1.0 m s−1
between about 10–11 km and 6 km from land, producing the change in sign of wind stress
curl that attracted our attention.
Based on these results, and particularly because we were interested in accurate mean
values of wind stress curl, in our research applications we discarded all Level 2B wind
retrievals at 10 km and less from land. We also discard retrievals with the PCP flag set, since
it included factors in addition to proximity to land. Figure 10 shows the 10-year averages
of QuikSCAT wind stress and wind stress curl for the same domains as in Figure 1a,b, but
with the removal of retrievals at distances of 10 km and less of land and the use of the PCP
flag. We also counted the closest 0.1◦ grid point to the coast as missing, since the gridding
procedure essentially extrapolated to this position, using data from 40 km farther offshore.
Elimination of the narrow regions next to the coast with a reversal in sign of the wind stress
curl was clear. The appearance was minor over these large regions but became important in
our analysis of the relative roles of wind stress versus wind stress curl in driving upwelling
in specific coastal regions.increases in wind speed at 8–10 km and closer to the land from the six northern tracks (in
typical exposed coastal conditions with strong summer and winter winds of opposite
directions) and the three southern tracks (in the sheltered Southern California Bight where
northerly winds are typically much weaker). This is true for the averages of all of the
points and for averages of just the “good” points represented by the red triangles. This
Remote Sens. 2022, 14, 2251 17 of 26
indicates that the elimination of “suspect” points by the PCP flag does not eliminate the
overestimates of wind speeds within 10 km of the coast.
Figure 9. As in Figure 8, scatterometer
Figure 9. scatterometer wind
wind speeds
speeds from
fromL2B
L2Bretrievals
retrievalswithin
withinthe nearest77×× 13 km
thenearest
bin to the
the coast,
coast, averaged
averaged into 1-km bins based on the distance
distance from the
the L2B
L2B vector
vector wind
wind retrieval
retrieval
Figure 7).
to the nearest land along each altimeter track (similar to Figure 7). Here we composite all retrievals
during all seasons from multiple tracks along two regions of the U.S. West Coast: the more energetic
region off northern California, Oregon and Washington; and the calmer region within the Southern
California Bight. Black circles, red triangles and horizontal lines are as in Figure 8.
3.2. ERA-5 Wind Stress and Wind Speed Analyses
Moving to the ERA-5 wind stress and wind stress curl fields in Figure 1c,d, our
analysis focused on the coastal region off northern California between 37–42◦ N. Off Cape
Mendocino (~40.4◦ N) and north of Cape Blanco (~43◦ N), the July average in Figure 1d
depicts negative wind stress curl adjacent to land, indicating an increase in the equatorward
winds next to the coast. In Figure 11, we formed averages of ERA-5 10-m wind speed
magnitudes and cross-transect wind stresses along transects that moved from ocean to land,
approximately perpendicular to the coastline (Figure 11, maps, not along altimeter tracks).
In Figure 11 line plots, it is evident for summer and winter (and for the other seasons, not
shown) that there was a universal decrease in wind speed over the ~50 km next to the coast,
continuing to decrease over land. Red arrows identify the two grid points over water and
closest to the coast near Cape Mendocino. This decrease in wind speed over the ocean next
to the coast was also found along all three transects in Figure 11, as well as along all other
transects that we examined crossing the coast between 30–50◦ N.4, x FOR PEER REVIEW
Remote Sens. 2022, 14, 2251 18 of 26
Figure 10. Edited 10-year averages of QuikSCAT wind stress vectors overlaid on wind stress curl for
Figure 10. Edited 10-year averages of QuikSCAT wind stress vectors overlaid on wind stress curl for summer along the coasts of (a) so
summer
western U.S, as in Figure 1a,b. along retrievals
L2B wind the coastsmarked
of (a) southern Africa
as suspect andPCP
by the (b) the
flagwestern U.S,within
or located as in Figure 1a,b.
10 km of landL2B
arewind
eliminated.
retrievals marked as suspect by the PCP flag or located within 10 km of land are eliminated.
However, cross-transect vector (i.e., signed) wind stress values in Figure 11 can be seen
to increase near Cape Mendocino at the same points (red arrows pointing at blue circles),
whether winds were from the north (negative wind stress in summer, June–August) or
from the south (positive wind stress during winter, December–February). The increase
in wind stress magnitude was even greater over land inshore of Cape Mendocino. The
increase near and over land was not the same for all transects, although the magnitude of
the wind stress was greater over land during some seasons for all transects.
The cause for increasing wind stress over land was due to the difference in “surface
roughness” between water (very low) and land (much greater). To examine the behavior of
the wind stress within the ERA-5 model, one month (August 2005) of data on the native
RGG grid of the model was examined. Figure 12 presents the “surface roughness” (used to
calculate wind stress) and cross-transect vector wind stress on the native RGG grid points
of the model, along with the same variables on the regular lat-lon grid, onto which all of
our ERA-5 data were interpolated.Remote Sens. 2022, 14, 2251Remote Sens. 2022, 14, x FOR PEER REVIEW 1919ofof2626
Figure 11. (Above,Figure
single
11.panel)
(Above,ERA-5 interpolated
single panel) grid pointsgrid
ERA-5 interpolated surrounding three transects
points surrounding crossing
three transects cross-
ing the coast of northern California. Colors identify the transects and correspond to the colors of
the coast of northern California. Colors identify the transects and correspond to the colors of lines
in the line plots. Red arrows point to two grid points over water just offshore of Cape Mendocino
(40.4◦ N). (Below, four panels) (Left) Averages of the ERA-5 10-meter wind speed magnitude at the
interpolated grid points shown in the map, as a function of the distance between the grid point and
the nearest land (negative is distance over land to nearest coastline). (Right) Cross-transect wind
stress at the same gridpoints. Three-month seasonal averages for the 10-year QuikSCAT period
are shown for equatorward winds in summer (top) and poleward winds in winter (bottom). Red
arrows point to data at the two grid points over water just offshore of Cape Mendocino (40.4◦ N).
The transects are identified by the latitude of their coastal crossing.Remote Sens. 2022, 14, 2251 20 of 26
The locations of the grid points on the map (Figure 12, left panel) can also be seen
relative to the coastline on the plots of roughness and wind stress (middle and right panels).
For clarity, we plotted only the more northern line of points at 41.4◦ N and the more southern
line of points at 40.4◦ N. On the plot of surface roughness, the values on the RGG grid points
(circles) over water were very low (appearing near zero), rising to much greater values
over land. On the interpolated grid (crosses), the roughness was also low over water away
from the coast. On the dark blue interpolated grid point over water but closest to land near
Cape Mendocino (red arrow), roughness showed an increase compared to farther offshore
over water. This is because that grid point lies between the RGG grid point located over
water and the next RGG point, located on land. The method of interpolation was bi-linear,
so the interpolated point did not appear exactly on the line between the RGG points. As
evident on the Figure 12 map, only along the transect that crosses Cape Mendocino did the
interpolated points over water next to the coast lie directly between land and ocean RGG
grid points. This is also seen in the line plots of monthly averaged (August) cross-transect
wind stress, where the circles and dotted lines over water showed a decrease in wind stress
as land was approached, then an increase over land. On the wind stress line plot, the
first dark blue circle over land inshore of Cape Mendocino was off-scale with a greater
(negative) wind stress magnitude. Interpolation between this point and the first RGG point
(dark blue circle) over water created the increased value of the interpolated wind stress
(red arrow) over water for that transect.
Figure 13 presents a map of the August 2005 average vector wind stress field, with blue
vectors on the RGG grid and orange vectors on the interpolated grid. Just offshore of Cape
Mendocino, in the black box, one finds two orange vectors next to the coast that are greater
than the next orange vectors offshore (the same grid points identified in Figures 11 and 12).
We see again that these two orange vectors lie between weaker blue vectors just to their
west over water and stronger blue vectors over land to their east. Interpolation from the
blue to orange vector locations caused the increased wind stress values next to the coast on
the rectangular interpolation grid.
Most ERA-5 data sets are provided on a regular rectangular lat-lon grid such as the
one shown here, interpolated from the model RGG grid, as described in Section 2. To obtain
wind stress fields that are not affected by the interpolation artifact described above, we
recommend using the interpolated vector wind speeds and then calculating the vector
wind stress from the wind speeds over water using a bulk algorithm such as [7]. This is the
approach adopted in our modeling of the eastern Pacific with the Regional Ocean Modeling
System (ROMS). The interpolation still affected the wind speeds at some near-land grid
points, but since the wind speeds were generally lower over land, it reduced the wind
speeds in a manner similar to the reduction by the land’s increased roughness. It will not
reverse the sign of the wind stress curl. As an example, Figure 14 shows the mean 10-year
July wind stress vectors over wind stress curl, as calculated within the ROMS system
from the interpolated ERA-5 vector wind speeds (interpolated to 1/12◦ ). A comparison to
Figure 1d indicates that the large regions of incorrect wind stress curl next to the coast in
Figure 1d is not present in Figure 14.You can also read
