INTERNATIONAL JOURNAL OF CLIMATOLOGY
Int. J. Climatol. 31: 770–782 (2011)
Published online 23 March 2010 in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/joc.2123
Statistical analysis of observed and simulated hourly surface
wind in the vicinity of the Panama Canal
Fang-Yi Chenga,c and Konstantine P. Georgakakosa,b *
a
c
Hydrologic Research Center, 12780 High Bluff Drive, Suite 250, San Diego, CA 92130, USA
b Scripps Institution of Oceanography, UCSD, La Jolla, CA 92093, USA
Department of Atmospheric Sciences, National Central University, No. 300, Zhongda Road, Zhongli City, Taoyuan County 320, Taiwan
ABSTRACT: Surface wind patterns at the Panama Canal vicinity are identified on the basis of 6 years of observed hourly
surface wind data and with the use of high-resolution numerical model simulations. Statistical analysis of the observed
wind at various stations in the Panama Canal is presented, together with the analysis of simulated surface wind fields
that are obtained from the MM5 mesoscale meteorological model using surface wind assimilation and forced by North
American regional reanalysis data. The performance analysis indicates that the 2-km-resolution MM5 model surface wind
simulations have skill when compared with the observations at the measurement sites. The analysis of the wind fields for
the period 2002–2007 shows that the dry season (January to April) is more spatially and temporally coherent than the wet
season in the region. The simulated wind shows that the average wind speed reaches up to 7–8 m s−1 and the frequency of
exceeding 5 m s−1 reaches up to 0.7–0.8 in Lake Gatun, the entrance/exit of the Canal in the Caribbean and Pacific coasts,
and at high elevations. The dry season exhibits higher climatological wind speeds and exceedence frequencies than the wet
season but the wet season shows greater spatial variability. For both seasons, the morning hours have lower average winds
than the evening hours. The analysis underlines the significant influence of convection, sea breeze and local conditions
(elevation gradients and land surface cover) in the observed and simulated surface wind patterns.
The information presented herein, particularly as regards the Canal centerline results, may be useful for identifying the
effects of air pollution from sources aboard transiting cargo ships on large communities in the Canal vicinity (e.g. Panama
City). Information presented is also relevant to regional wind energy studies and fog formation analyses. Copyright  2010
Royal Meteorological Society
KEY WORDS
Panama Canal surface winds; MM5 wind assimilation; boundary layer winds
Received 14 May 2009; Revised 5 February 2010; Accepted 7 February 2010
1.
Introduction
The Panama Canal is important for the global economy
(Gibbs, 1978). Although there are many published surface wind analysis studies for regions around the world
(e.g. Klink and Willmott, 1989; Green et al., 1992; Kastendeuch and Kaufmann, 1997; Luo et al., 2008; Fichet
et al., 2010), no previous study focussed on the analysis
of the Panama Canal vicinity winds. There are, however,
a few recent studies that have addressed climatological
features of the tropical Panama Canal region for various
purposes that are relevant to surface wind analysis. These
are outlined in the following sections.
Wang and Georgakakos (2007) studied the spatially
distributed potential evapotranspiration in the Panama
Canal watershed using remotely sensed plant cover information and observed the MM5-modelled surface meteorological fields. They conclude that a significant portion
of the substantial spatial variability of potential evapotranspiration in the watershed may be explained by
* Correspondence to: Konstantine P. Georgakakos, Hydrologic Research Center, 12780 High Bluff Drive, Suite 250, San Diego, CA
92130, USA. E-mail: KGeorgakakos@hrc-lab.org
Copyright  2010 Royal Meteorological Society
mesoscale modelling information on the surface temperature, humidity and wind. Xie et al. (2008) in the context
of their North Atlantic cooling experiments outlined the
climatological seasonal large-scale wind patterns over
Central America. They identify the Inter Tropical Convergence Zone (ITCZ) as an important determinant of
the wind flow in the region. During the boreal winter
(January to April) when the ITCZ is south of the region,
the pressure gradient from the Caribbean to the Pacific is
strong and sustains strong northeasterly low-level winds
over Panama which are intensified through the mountainous terrain and converge with the southeast trades
at the ITCZ. In boreal summer, when the ITCZ moves
north through the region, weaker winds prevail over Central America and significant convection is prevalent. In a
biological study of insect flight across the Panama Canal
and Lake Gatun, Srygley and Dudley (2008) underscore
the importance of accurate local wind information for the
estimation of insect drift during flight with crosswind.
Although the causes and patterns of the climatological
regional flow are well understood for Central America
on large scales (e.g. Xie et al., 2008), the specific
patterns of wind speed and direction for the Panama
STATISTICAL ANALYSIS OF OBSERVED AND SIMULATED HOURLY SURFACE WIND
(a)
771
(b)
(c)
Figure 1. Panama Canal region: (a) observation stations (background colour is elevation height in metres); (b) Canal centerline delineated with
stars; (c) 2-km resolution land cover data on the grid used in the simulations (blue colour is for water, and the large water body near the
Caribbean Sea to the North is Gatun Lake). The Pacific Ocean is in the southeastern part of the figure. This figure is available in colour online
at wileyonlinelibrary.com/journal/joc
Canal region have not been presented in resolution
useful for applications such as air pollution, wind energy
production, fog formation and others. The present paper
provides a statistical climatological analysis of hourly
observed and mesoscale-model-simulated wind speed at
various sites near the Panama Canal for the period
2002–2007.
After a description of the target region, measurement
sites and data attributes in the next section, Section 3
presents a statistical analysis of the observed hourly
wind speeds at the stations of interest. Both diurnal
patterns and covariability are discussed and the need for
mesoscale modelling for effective interpolation in other
sites is highlighted. Section 4 introduces the modelling
set-up used for the application of the MM5 model with
high resolution to simulate winds in the region. It also
discusses the performance of the MM5 surface wind
simulations by comparing with the observed winds using
a variety of performance measures. Lastly, it presents
and discusses the main features of the MM5-simulated
winds in the region, including wind speeds near the Canal
Copyright  2010 Royal Meteorological Society
centerline. Concluding remarks are presented in Section
5, and the three appendices support the discussion and
mathematical formulations used in the main text.
2.
Study site and data description
The tropical Panama Canal region, comprising the
Panama Isthmus, is characterised by the close proximity to two oceans (Caribbean Sea/Atlantic Ocean and
Pacific Ocean), by the presence of a large lake near
the Caribbean Coast (Gatun Lake) and by complex orographic terrain with a highest elevation approximately
1000 m (Figure 1(a)). The region experiences seasonal
precipitation with lowest precipitation in March and highest precipitation in October to November, when the ITCZ
passes over the region. The Caribbean Sea coast receives
more than 3 m of annual rainfall, whereas the Pacific
Ocean coast receives approximately half of that amount.
The regional wind climatology is characterised by strong
winds in January to April and weaker winds during the
rest of the months as outlined by Xie et al. (2008).
Int. J. Climatol. 31: 770–782 (2011)
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F.-Y. CHENG AND K. P. GEORGAKAKOS
Table I. Names and locations of surface wind observation stations.
Identifier
Description
CZL
FAA
GAM
GAT
GTW
GAD
LMB
VTM
Station
Station
Station
Station
Station
Station
Station
Station
Corozal
Balboa FAA
Gamboa
Gatun
Gatun West
Gasparillal
Limon Bay
Vistamares
Latitude
Longitude
Elevation (m)
Years of record
08 : 58 : 51N
08 : 58 : 08N
09 : 06 : 44N
09 : 16 : 06N
09 : 15 : 47N
08 : 51 : 46N
09 : 21 : 20N
09 : 14 : 04N
79 : 34 : 30W
79 : 32 : 58W
79 : 41 : 38W
79 : 55 : 14W
79 : 55 : 45W
80 : 00 : 56W
79 : 54 : 53W
79 : 24 : 05W
9
10
31
30
33
346
3
969
January 2007 to December 2007
January 2002 to December 2007
January 2002 to December 2007
January 2002 to May 2006
June 2006 to December 2007
January 2002 to December 2007
January 2002 to December 2007
January 2002 to December 2007
Table I gives the station characteristics of all the
available observation sites within and near the Panama
Canal watershed, together with the record coverage
within the period with available historical data. Figure 1
shows the location of the surface meteorological stations
within the Canal region, the Canal centerline discussed
in this paper, and the regional land use information as
obtained from the US Geological Survey (USGS) 25category database. Substantial variability in land cover
is indicated, with the original tropical forest (evergreen
broadleaf, evergreen needleleaf and mixed forest) now
replaced in several regions of the Isthmus with the
aerodynamically very different shrubland, cropland and
savanna. A significant urban area is indicated in the
scale of the map in Figure 1(c) for the Panama City
location near and at the Pacific Ocean coast. Sharp
changes between forest and shrubland are indicated all
along the Canal route. Significant freshwater bodies are
the Gatun Lake and smaller Madden Lake to the north
(regulate flood waters from the northeastern mountainous
region).
It is noted that station GAT was replaced by station
GTW in June 2006 and, even though the new station
is in the proximity of the old station and at about
the same elevation, it measures higher wind speeds
on average because of different local land use and
land cover (M. Chandeck, ACP-Autoridad del Canal de
Panama, personal communication). The stations FAA,
CZL, GAM, GAT, GTW and LMB are near the Canal
with distances less than 5 km from the Canal centerline.
GAD and VTM are substantially farther from the Canal
than the aforementioned stations and at higher elevations
(Figure 1(a)). For this analysis, data from all stations
were available only for 2007.
3.
3.1.
Statistical analysis of observed wind speeds
Diurnal behaviour
Figure 2 shows the diurnal variation of the average hourly
wind vectors at the Panama Canal stations for the dry and
wet seasons of 2007. (The hours indicated are local hours
and Appendix A details the formulation used to compute
the average wind direction.) The dry season (Figure 2(a))
shows typical land surface diurnal wind-speed patterns
for the GTW, GAM, CZL, FAA and GAD stations, with
Copyright  2010 Royal Meteorological Society
wind-speed maxima at about 03 : 00 p.m., and lower wind
speeds during the night and early morning hours. For
the prevailing northerly winds during this season, station
LMB near the Caribbean Sea exhibits less pronounced
diurnal variation than the other stations as it is exposed
to maritime winds. Only the VTM station (located at
the highest measurement elevation on top of a 1000-m
mountain) exhibits a reverse pattern in wind speed with
a significant dip of more than 2 m s−1 during the midday hours, sustaining high winds throughout the evening,
night and morning hours.
The inland station of GAM on the Canal (see Figure 1
for station locations) exhibits the lowest average wind
speeds, whereas the station LMB on the Caribbean Coast
exhibits the highest average wind speeds during the dry
season. Stations CZL and FAA, which are located on the
Pacific side and close to each other, have similar average
records of hourly wind speed but exhibit substantial
differences in direction during daylight hours. Among the
stations, station GTW shows the second highest observed
hourly wind speed during the middle of the day. During
the night-time and early morning/late afternoon hours,
the VTM station exhibits average wind speeds that are
as strong as those at the LMB station. The station GAD
shows the third highest wind speed during these same
hours in the day.
The 2007 dry season results indicate that a nearly uniform northeasterly to northwesterly surface wind regime
prevailed. Stations GAD and FAA show a surface wind
direction change from northwesterly to northeasterly
around 10 : 00 a.m. and a change back to a northwesterly direction between 02 : 00 p.m. and 06 : 00 p.m. The
surface wind pattern is influenced by sea breezes from the
two oceans and Lake Gatun as they interact with the complex topography (e.g. see discussion in Oliveira et al.,
2003). To provide a more complete picture of the surface wind spatial patterns for this season, high-resolution
numerical modelling is necessary.
During the wet season (May to December) when strong
and persistent convection occurs over the region of the
Panama Canal, the average hourly surface wind speed is
substantially reduced (compared to the dry season) at all
observation station sites throughout the day (Figure 2(b)).
During the afternoon hours, again the LMB station has
the highest wind speed and the GAM station has the
lowest. GTW, VTM and GAD stations follow LMB in
Int. J. Climatol. 31: 770–782 (2011)
STATISTICAL ANALYSIS OF OBSERVED AND SIMULATED HOURLY SURFACE WIND
773
(b)
(a)
(m s–1)
(m s–1)
Figure 2. Diurnal pattern of average wind vector for Panama Canal stations for the (a) dry and (b) wet seasons of 2007. Table I gives the station
IDs. Time of day in the vertical axis is in local hours.
average wind-speed magnitude for these hours of the day.
Notable fact is that during this season the high elevation
VTM station and the second highest elevation station
(GAD) exhibit diurnal patterns with reduced wind speed
between 10 : 00 a.m. and late afternoon hours.
The wet season involves greater diurnal changes in
surface wind direction and greater inhomogeneity among
observation stations (Figure 2(b)). Station VTM maintains reasonably uniform wind direction (northeasterly)
throughout the day. In particular, VTM exhibits a more
easterly direction in the wet season than in the dry season. The patterns of LMB and GTW near the Caribbean
Coast are characteristically similar, with a near reversal
of surface wind at about 10 : 00 a.m. from southerly to
northwesterly and back to southeasterly at 11 : 00 p.m.
In addition, FAA and CZL, located near the coast of
Pacific Ocean, show a temporary wind reversal in the
early afternoon hours of the day for the wet season of
2007. For the wet season, the wind direction for the stations LMB, GTW, CZL and FAA along the Canal is
better aligned during the hours 04 : 00 p.m. to 08 : 00 p.m.
than any other time during the day, albeit substantially
Copyright  2010 Royal Meteorological Society
non-uniform. Undoubtedly, lower level convergence and
storm outflows as well as sea breezes influence the direction of the local surface wind as they interact with the
spatial topographic gradients. The complexity of the patterns discussed suggest that for this season too, highresolution numerical modelling is necessary to provide
better understanding of the surface wind patterns in the
Canal region.
3.2. Covariability
In addition to determining the mean behaviour of the
wind speed, it is also fruitful to consider the covariation
of the wind speed at different locations. To compute the
covariance or correlation of the wind between different
stations, it is important to first transform the data to
render constant sample variances. Appendix B discusses
the evidence for linear dependence of the wind-speed
variance on the wind-speed mean for the various station
sites. On the basis of this evidence, a logarithmic
transformation is applied to the data and the covariance
analysis is performed on the log-transformed wind data
(referred to as the log-wind).
Int. J. Climatol. 31: 770–782 (2011)
774
F.-Y. CHENG AND K. P. GEORGAKAKOS
Figure 3. Covariance between log-wind residuals of any two stations as a function of interstation distance (markers) for 2007. The continuous
line represents the fitted exponential covariance, , as a function of distance h (km). R ln 2 is the coefficient of determination (fraction of data
variance explained by the exponential model). The text identifies the five stations used.
The covariance and correlation (see mathematical formulation in Appendix C) were computed for all the
stations reported in 2007 for the Panama Canal region
by season. For the purpose of this analysis, distance is
computed by the differences in longitude and latitude,
and a projection onto a standard spheroid with 1° latitude difference representing a distance of 111.2 km at
the Panama latitude of 9° N, and with 1° longitude difference representing a distance of 109.8 km at the Panama
longitude of 80 ° W. Different projections are of course
possible.
Analysis of the correlation results obtained for all
reporting stations in 2007 indicate that the linear association of the log-wind for the stations of interest is
complex with correlations that range from 0.2 to 0.55
at the distance of 60 km for the dry period (January
to April 2007) and from 0.15 to 0.35 when all the
months of 2007 are considered. For most distances, during the dry period there is stronger association than when
both the dry and the wet periods are taken together,
but the variability of the correlation in that case is
higher. Also, when all the months of 2007 are taken
together, the correlation for distances less than 15 km
is substantially higher than that corresponding to longer
distances. The complex pattern of topographic gradients and the variability of land surface characteristics
(tropical forest vs shrubland vs cropland vs lake water)
within the Panama Canal region (Figure 1(a)) are responsible for the large correlation variation at the same
distance.
The variability of the interstation covariance for a
given distance is substantially reduced if the covariance
Copyright  2010 Royal Meteorological Society
analysis is limited to the stations in the close vicinity
of the Canal (LMB, GTW, GAM, CLZ and FAA). The
markers of Figure 3 represent the covariance values for
a given interstation distance for the study stations in the
Canal vicinity (there are ten unique distances formed by
the five stations). The best fit of an exponential function is
also shown together with the coefficient of determination
(R ln 2 ). The function parameters were estimated by fitting
the log(covariance) versus distance relationship, and the
coefficient of determination is a measure of the goodness
of the fit. It is clear from these results that, along the
Canal, an exponential distance-dependent function is a
good model for the covariance function of the log-wind
speed residuals. So, even though on a regional basis it
is not possible to fit a single distance-dependent function
to the data, it is feasible to use such a simple function
for the station data along the Canal. The function is
(h) = α exp{−ch} where h is the distance between
stations in kilometres, and α = 0.19, c = 0.032, when
the wind speed is in metres per second.
4.
Statistical analysis of MM5 simulated wind
To provide a more complete description of the spatial
wind patterns over the Panama Canal region, the authors
used a mesoscale numerical model (MM5) with high
resolution. The present section describes the MM5 model
set-up and compares the statistical properties of the MM5
simulated data to those of the observed data at the
available station sites for the period of record. It then
presents and discusses the statistical characteristics of the
Int. J. Climatol. 31: 770–782 (2011)
STATISTICAL ANALYSIS OF OBSERVED AND SIMULATED HOURLY SURFACE WIND
(a)
775
(b)
(m s–1)
(m s–1)
Figure 4. Diurnal variation of the average wind vectors at observation sites in the Panama Canal region for the period 2002–2007 for (a) the dry
and (b) the wet seasons. (Black vectors are for the on-site observations and grey vectors are for the MM5 simulation with a 2-km resolution).
MM5-simulated wind fields for the dry and wet seasons
in the Panama Canal area.
4.1. Model set-up
Due to the scarcity of local wind observations, the
coarse resolution of ETA regional reanalysis data (32 km)
and the artificial error introduced by the interpolation
itself, simple data-based interpolations of wind speed
and direction, provide wind that is not in balance with
the mass field (e.g. atmospheric pressure) and thermodynamic characteristics (stability) of the local atmosphere.
The MM5 model with complex model physical processes
(e.g. Grell et al., 1995) acts as an assimilator to filter out
noises introduced by the interpolation and to enforce balance between wind field and other atmospheric fields (e.g.
surface pressure) through the model physical processes
(e.g. planetary boundary processes and land surface processes). As a first step in using the mesoscale model as
an interpolator of wind speed, and to facilitate the production of a 6-year run with hourly resolution, the MM5
ran with no precipitation physics (dry run).
A 2-km horizontal grid with horizontal dimensions
of 91 × 91 and with 24 vertical levels has been set
Copyright  2010 Royal Meteorological Society
up for the model application (Figure 1(c) shows the
simulation domain and the gridded land surface cover
used). Data from the North American regional reanalysis (NARR) (Mesinger et al., 2006) were used to provide boundary and initial conditions to the MM5 model
runs for the years 2002–2007. The NARR data have
a horizontal spatial resolution of 32 km, 29 pressure
levels and temporal resolution of 3 h (data reference:
http://dss.ucar.edu/pub/narr/). The objective analysis procedure in the MM5 model system is used to assimilate
the observed surface wind into the 2-km grid over the
Panama Canal region.
4.2. MM5 simulation performance
4.2.1. Wind vector comparison at different observation
sites
Figure 4(a) and (b) shows the diurnal variation of the
average wind vectors at different sites near the Panama
Canal for the dry and wet seasons, respectively, for the
period 2002–2007. Black is for station observations and
grey is for the MM5 simulations. The results show that,
in general, the MM5 simulations reproduce the shape of
the observed wind diurnal variation for all stations.
Int. J. Climatol. 31: 770–782 (2011)
776
F.-Y. CHENG AND K. P. GEORGAKAKOS
Figure 5. Sample autocorrelation functions for observations and MM5 closest grids to observation sites (10-m wind). Also shown are the percent
relative biases in MM5 simulation means and standard deviations. Observed autocorrelations are computed using the observed records shown in
Table I. Simulated autocorrelations use the MM5 simulation record 2002–2007.
For the dry season (Figure 4(a)), the model wind direction in all stations but LMB maintains a more northeasterly direction than the observation data (simulated wind
veers to the right of the observed wind). For this season, over-prediction is observed at GAT, GAM and FAA
sites, and under-prediction at the LMB site, whereas wind
speed is well reproduced for the GAD and VTM sites.
Very good reproduction of the direction is shown for the
LMB and GAD sites, whereas the VTM station shows
a persistent direction bias throughout the day and night.
However, it is noted that the directional bias for the stations examined is 45° or less.
Figure 4(b) shows that the mesoscale model reproduces reliably the reduction of wind speed at all sites
during the wet season (as compared with the dry season). Apart for the mid-day hours at VTM, the simulated
wind tends to veer to the right of the observed wind in
this season too. Substantial over-prediction of wind speed
is indicated for GAT from noon to 07 : 00 p.m., but in
general the observed wind vector magnitudes are reasonably well reproduced by the MM5 simulation. Greatest
discrepancy between the observed and simulated wind
direction is noted at GAD for this season and for the
hours 09 : 00 a.m. to noon.
The aforementioned comparison between simulated
and observed wind indicates that the MM5 as applied
is capable of reproducing the magnitude and direction
of the surface wind in the Panama Canal region, with
the noted discrepancies attributed in part to the substantial difference in resolution between the model wind
estimates and supporting land cover characteristics, and
the point observations and local conditions. It is also
Copyright  2010 Royal Meteorological Society
noted that the improved accuracy during the wet season would require fine-tuning the moist dynamics and
microphysics of the MM5 model.
4.2.2. Correlation structure of wind speed
Figure 5 presents the sample autocorrelation function
of the observed and simulated 10-m wind speed at
the station locations in the Canal centerline vicinity.
The sample autocorrelation has been computed with all
available data at each site (Table I).
Among the near-Canal stations, the LMB station
exhibits the highest temporal persistence followed by
the GTW station. The MM5 reproduces the LMB high
temporal persistence compared with the rest of the stations but does not differentiate very much in correlation
behaviour among the other stations. The MM5 simulation
autocorrelation function follows an intermediate curve
among the curves of the autocorrelation functions of the
station observations (excepting LMB). The shape of the
autocorrelation functions of the observations is reasonably well preserved by the MM5 simulations. It is noted
that by 12 h, the autocorrelations of all the stations but
LMB is 0.3 or less, whereas for LMB it is still greater
than 0.5 (both for observations and simulations).
4.2.3. Statistical performance for stations in the close
vicinity of the Panama Canal
The results of a statistical performance evaluation of
the MM5 model hourly simulations of surface wind
along and very near the Canal centerline for the period
2002–2007 are summarised in Table II. The analysis was
Int. J. Climatol. 31: 770–782 (2011)
STATISTICAL ANALYSIS OF OBSERVED AND SIMULATED HOURLY SURFACE WIND
777
Table II. Performance statistics of hourly MM5 surface wind simulations at station locations for the period 2002–2007.
Dry season (January to April)
LMB
GTW
GAT
GAM
FAA
−1
Wet season (May to December)
Mean (%)
Standard
deviation (%)
RMSE (m s )/(%)
CC
Mean (%)
Standard
deviation (%)
RMSE (m s−1 )/(%)
CC
−37.977
−16.735
76.784
72.093
19.835
−43.512
−35.911
21.092
2.757
−21.104
3.309/(44)
2.197/(45)
1.875/(91)
1.901/(94)
1.440/(53)
0.595
0.229
0.341
0.259
0.260
−28.619
5.831
132.163
135.809
27.004
−39.544
−15.677
33.716
29.786
−0.566
2.348/(52)
1.734/(59)
1.776/(141)
1.770/(147)
1.357/(69)
0.34
0.20
0.17
0.07
0.194
done for stations LMB, GTW, GAT, GAM and FAA,
which have the longest records. Both GAT and its most
recent replacement GTW are included in the analysis
given the large differences in surface wind speed due to
the location change of the observation site in the middle
of 2006. The table shows results for the wet and the dry
seasons, separately.
The statistical indices included for each season are
(1) the percent relative bias of the simulated means;
(2) the percent relative bias of the simulated standard
deviations; (3) the root mean square error (RMSE) of
the simulations in metres per second and also expressed
as a percent of the root mean square of observations;
and (4) the cross correlation (CC) between observed and
simulated hourly wind speed. In this context, the percent
relative bias of a quantity W (mean or standard deviation)
is defined as: 100(Wm − Wo )/Wo , where subscript ‘m’ is
for the model and the subscript ‘o’ is for the observations.
Negative bias implies that the model estimates are
lower in magnitude than the observations. The RMSE
is presented both in metres per second and also in
normalised form in percent of the root mean square of
the hourly observations.
Table II highlights the tendency of the model to underestimate the average wind speed at the stations with high
wind speeds (LMB and GTW), and to overestimate the
average wind speed at the stations with lower wind speed
(GAT, GAM and FAA). The percent relative negative bias
(underestimation) in the mean wind speed for the dry
season is as low as −38%, whereas in the wet season
it is as low as −29%, both for the LMB station. Overestimation ranges from 19% to more than 100% (GAT
and GAM for the wet season) for the stations reporting lower wind speeds. Generally, the percent relative
biases in standard deviations follow the behaviour of the
analogous statistics for the means, except for the FAA station where the standard deviation of the observed winds
is underestimated by the model (−21% in the dry season and −1% in the wet season). The underestimation
in average standard deviation ranges from −1 to −44%,
whereas the overestimation ranges from 3 to 34%. Generally for the low-wind stations, GAT and GAM, and
for the FAA station during the wet season, the percent
relative bias for wind-speed standard deviations is lower
than that for the means. The reverse is true for the other
stations.
Copyright  2010 Royal Meteorological Society
The RMSE (m s−1 ) for hourly wind simulations is
highest for the highest wind-speed stations and, for those
stations, it is higher in the dry season than in the wet season. However, when normalised by the root mean square
of hourly wind speed, the percent relative RMSE is lower
for the high wind stations LMB and GTW than for the rest
of the stations, with the wet season exhibiting higher values than the dry season for all stations. CC of hourly surface wind speeds between the simulations and observations is higher in the dry than in the wet season, reaching
up to about 0.6 (for the LMB station). The very substantial difference between the model grid size and the point
observation leads to low CC values on an hourly scale.
In addition to the statistical performance indices evaluated in Table II, the authors also examined the bias
factor of the simulated hourly surface wind speeds for
the near-Canal stations. An hourly bias factor, Bh , is
defined using
from all reporting stations as fol data lows: Bh = Oi / Si , where the summation index i
is over all the stations (numerator) and corresponding
closest MM5 grid points (denominator). The symbol O
represents observed data and the symbol S represents
MM5-simulated data for a given hour. A value of 1 for
Bh represents no bias, whereas the factor can assume both
values, lower and higher than 1. From this hourly bias
factor, a daily average bias factor, Bd , may be obtained by
averaging the hourly bias factors within a day. If missing
data are present for a given hour we do not consider this
hour in the computation. Only hours with both observed
and simulated positive values for all stations and grid
points are considered.
The computed daily average bias factor ranges from
about 0.4 to about 2.7, remaining within the range
(0.5–1.5) for most of the time (mean of 0.98 and standard deviation of 0.27 with a near normal distribution).
There is less bias variability during the early part of the
year (dry season) than the later part of the year. The
results of the present performance analysis indicate that
the MM5 is able to reproduce the daily regional average
wind speed with low long-term average bias.
4.3. MM5 simulated wind fields
4.3.1. Spatial features of mean and exceedence
frequency fields of wind speed
Figure 6 presents the spatial field of the mean of the
10-m MM5 simulated wind speed (m s−1 ) for morning
Int. J. Climatol. 31: 770–782 (2011)
778
F.-Y. CHENG AND K. P. GEORGAKAKOS
Figure 6. Contours of MM5-estimated average wind speed for 06 : 00 a.m. (upper panels) and 06 : 00 p.m. local time (lower panels). Six-year
averages (2002–2007) of surface wind are shown for the dry (left panels) and the wet seasons (right panels). The colour bar is in metres per
second. The Panama Isthmus and Canal outline are shown with white line (see also Figure 1(a) for elevation information).
(06 : 00 a.m.) and evening (06 : 00 p.m.) hours for the
dry and wet seasons. The fields shown have been
computed with data from the 6-year period 2002–2007.
The morning hour average wind speeds are lower than the
evening hour average wind speeds and have lower spatial
variability as well. In addition, the dry season average
wind speeds are higher than the wet season average
wind speeds for the same hour of the day. The evening
hour average wind speeds for the wet season exhibit
the highest spatial variability (smaller scales of spatial
coherence) in agreement with the expected surface wind
behaviour of convection over complex terrain. For all
cases, higher wind speeds are indicated in areas of lower
surface roughness and in high elevations. In all cases
and especially during the evening hours, higher average
wind speed prevails within the Gatun Lake and the
entrance/exit regions of the Canal in the Caribbean and
Pacific coasts. Large spatial gradients of the wind speed
are also shown in the northern side of Gatun Lake (near
stations GAT and GTW, Figure 1(a)) and at both coasts
of the Isthmus. In Gatun Lake, the maximum dry (wet)
season average wind speed is 6–7 m s−1 (4–5 m s−1 ).
The sample exceedence frequencies of wind speeds
that are greater than 5 m s−1 are shown in the panels
of Figure 7 for morning and evening hours in the
dry and wet seasons of the period 2002–2007. The
value of 5 m s−1 is frequently used in considerations
of wind energy generation in the Canal. Maximum
values and larger spatial coherence of sample exceedence
Copyright  2010 Royal Meteorological Society
frequencies are for Lake Gatun, the coastal regions of the
Isthmus and the higher elevations. Maximum exceedence
frequency reaches values of 0.6–0.8 for the evening
hours of the dry season, whereas for the same hours in the
wet season it reaches values of 0.3–0.4. For a complete
set of results for other hours in the day the reader is
referred to Cheng and Georgakakos (2008).
4.3.2. Spatial features of simulated wind vectors along
the Canal centerline
Figure 8(a) and (b) shows the vector plots of surface
wind near the Canal centerline averaged through 6 years
(2002–2007) of hourly MM5 simulations for the dry
and the wet seasons, respectively. The X-axis represents
the Canal centerline from Caribbean Sea to the Pacific
Ocean (Figure 1(b)). The Y -axis represents the hours
(local time) in a day. The dry season shows consistent
northerly wind along the Canal centerline. During the
night-time and early morning hours, northeasterly wind
prevails for the Gatun Lake area (near the Caribbean
Sea end of the Canal). During late morning and early
afternoon hours, northeasterly winds are estimated for
the Pacific Ocean Canal end as well. The highest wind
speeds occur at the two ends of the Canal and in Gatun
Lake.
For the wet season, relatively strong northwesterly
wind is simulated in the afternoon and evening hours
over the Gatun Lake area. This time period in the day
also exhibits higher wind speeds for the Canal centerline.
Int. J. Climatol. 31: 770–782 (2011)
STATISTICAL ANALYSIS OF OBSERVED AND SIMULATED HOURLY SURFACE WIND
779
Figure 7. Contours of MM5-estimated surface wind exceedence frequencies for 06 : 00 a.m. (upper panels) and 06 : 00 p.m. local time (lower
panels). Sample frequencies, computed for 2002–2007, are shown for the dry (left panels) and the wet seasons (right panels). The Panama
Isthmus and Canal outline are shown with white line (see also Figure 1(a) for elevation information).
(b)
(a)
–1
5 (m s )
–1
5 (m s )
Figure 8. Average MM5-simulated wind vector distribution along the Canal centerline for (a) the dry and (b) the wet seasons (2002–2007).
The reversal of the wind direction in the afternoon
is most pronounced for the Pacific Ocean end of the
Canal whereby the wind changes from northwesterly to
southeasterly, most likely as a result of the sea breeze.
Copyright  2010 Royal Meteorological Society
On the Pacific side of the Canal centerline, the wind
shows clear maxima in the afternoon for both wet and dry
seasons, with minima during the early morning hours. In
the Caribbean side of the Canal centerline, for the dry
Int. J. Climatol. 31: 770–782 (2011)
780
F.-Y. CHENG AND K. P. GEORGAKAKOS
is in accordance with the surface observations and it is a
manifestation of the land and sea breezes. Weaker overall
winds are simulated during the wet season throughout the
depth of the atmospheric layer considered, with wind profiles that exhibit wind-speed maxima (4.4 and 4.8 m s−1 )
within the 1000-m deep layer.
5.
Figure 9. Vertical profile of average wind vectors simulated by the
MM5 for the year 2007 at LMB near the Caribbean Sea for (a) the
dry and (b) the wet seasons. Contours are in metres per second and
elevation is in metres on the vertical axis.
season, the wind maintains high speeds throughout the
late afternoon, evening and early morning hours, with a
minimum during late morning hours. For the wet season
in the Caribbean side of the centerline, the wind shows
a distinct maximum in the late afternoon hours with
a minimum again during the late morning hours. The
significant reduction of average wind speeds during the
wet season becomes apparent by comparing the results
in Figure 8(a) and (b).
4.3.3. Vertical profile of wind speed near
the Caribbean Sea
Figure 9(a) and (b) shows the vertical profile of the average wind vector simulated by the MM5 at the LMB site
for the dry and wet seasons of 2007 (year with most sites
reporting), respectively, up to a height of 1000 m. Persistent northeasterly winds are simulated for the dry season
throughout the depth of the atmospheric layer considered, with strongest winds in the afternoon hours. For the
wet season, the LMB site exhibits simulated southeasterly offshore flow during night-time and northwesterly
onshore flow during daytime in the surface layer. This
Copyright  2010 Royal Meteorological Society
Concluding remarks
The present paper, for apparently the first time, identifies
surface wind patterns in the Panama Canal region with
high resolution. It describes a statistical analysis of the
observed surface wind at various stations in the vicinity of
the Panama Canal, together with an analysis of simulated
wind fields that are obtained from the MM5 model using
NARR data and surface wind assimilation. The observed
and simulated wind temporal resolution is 1 h, whereas
the simulated wind horizontal spatial resolution is 2 km.
Analysis of the wind fields yields the conclusion that
the dry season (January to April) is more spatially and
temporally coherent than the wet season with stronger
winds. Substantial variability of the observed fields during the wet season (May to December) was found, presumably due to the influence of convection, sea breezes
and local conditions (elevation gradients, land surface
cover) at the observation sites, underscoring the need for
numerical simulation with high resolution. Overall, the
simulated fields reproduce the observations adequately
(e.g. higher winds in dry than wet season, reproduction
of reversals of average wind among sites), with a tendency of the model winds to veer to the right of the
observed winds on average. The model underestimates
the average observed winds at high wind observation
sites by about 15% to about 40% and overestimates the
low-wind sites by about 19% to more than 100% (in
the wet season). The bias in reproducing the standard
deviation of the observed wind is moderate with a range
from about −40% (underestimation) to about 35% (overestimation). Overall bias of 6-year average daily average
wind is low (2%) over the period of interest, and the normalised RMSE is from 44% to more than 100% (for the
wet season of lower wind variability). The performance
statistics mentioned are affected significantly by the difference of scale between the model grid size (2 km on the
side) and the station observations (point measurements),
but they show that even at that scale the model has skill
in reproducing average features and patterns of the hourly
wind vector.
The simulated wind shows that there are highest
average wind speeds and exceedence frequencies (for
a 5-m s−1 wind threshold) in Lake Gatun and the
entrance/exit of the Canal in the Caribbean and Pacific
coasts. The dry season exhibits higher climatological
wind speeds and exceedence frequencies than the wet
season. Maximum climatological wind speeds for the
dry season were 6–7 m s−1 with exceedence frequencies of 0.6–0.8. The wet season exhibits highest spatial
variability of average winds and exceedence frequencies.
Int. J. Climatol. 31: 770–782 (2011)
STATISTICAL ANALYSIS OF OBSERVED AND SIMULATED HOURLY SURFACE WIND
Substantial diurnal variation is exhibited by the simulated
wind in accordance with the observed wind behaviour,
with higher winds during the afternoon hours. Analysis
of the MM5-simulated winds in the atmospheric layer
extending from the surface to 1000 m indicates higher
variability of the vertical wind profile during the wet season with more persistent and stronger winds throughout
the depth of the layer for the dry season. The influence
of the sea breeze and of the interaction of convection
with the complex terrain on the average winds was made
apparent by the analysis.
The wet season remains a challenge for the MM5
model simulations due to the pervasive effects of convection on smaller temporal and spatial scales, and the
interaction with the complex topography of the Panama
Canal region. It is expected that the higher spatial resolution and refined microphysical parameterisations are
necessary for improving substantially the simulations of
the surface wind in the Canal region for that season.
Acknowledgements
The authors wish to thank the editor and two anonymous
reviewers for their substantial contribution towards an
improved manuscript. They also gratefully acknowledge
the contribution of Jorge Espinoza, Michael Hart, Maritza
Chandeck and Urho Gonzal of the ACP with data and
information pertaining to conditions in the vicinity of the
Panama Canal.
Appendix A
A measure of direction i for hour i in the day is
computed based on average u and v components of the
wind as follows:



|W | sin(θj ) 
i = tan−1 (1)

W | cos(θj ) 
where tan−1 { } signifies the inverse tangent function, |W |
signifies the wind speed and the summation in brackets
extends to all the data available for hour i in a day. Note
that |W | sin(θj ) is the j th u component of the wind for
hour i, and |W | cos(θj ) is the corresponding v component
of the wind. The wind direction of the j th measurement
of the ith hour is denoted by θj .
Appendix B
As the mean of wind speed increases, the variance
of wind speed increases producing a heteroscedastic
random process that requires transformation of the wind
speed data for reliable wind covariance analysis among
different stations (e.g. Gibescu et al., 2006). Figure B1
shows the correspondence between mean and standard
deviation for all the stations at each season in 2007
and the corresponding linear fits. Heteroscedasticity is
Copyright  2010 Royal Meteorological Society
781
evident in Figure B1 with significant linear relationships
between standard deviation and mean for both seasons
but with seasonal differences (i.e. the nature of the
heteroscedasticity depends on season). Although the
means of the dry season have a larger range than those of
the wet season, the standard deviations in the wet season
are greater than those in the dry season for the same mean
wind speed that is greater than 4 m s−1 .
With this evidence of heteroscedasticity, statistical
analysis of the wind-speed data from different stations
is facilitated by the use of a wind data transformation
to render a constant sample variance, so that covariance
analysis may be performed. Various such variance stabilising transformations are possible (Bickel and Doksum,
1977; Wilks, 1995). In this case, the strong linear relationship shown in Figure B1 suggests a logarithmic transformation (using the natural logarithm). Thus, covariance
analysis is performed on the log-wind data.
Appendix C
W (x, y, m, d, k) denotes the log-wind speed at station
location (x, y) and month m, day d and hour of
day k. Then, we may decompose this log-wind speed
into a mean value for the hour of day of month m,
M(x, y, m, k), and a residual or random component,
ε(x, y, m, d, k), about the mean value:
W (x, y, m, d, k) = M(x, y, m, k) + ε(x, y, m, d, k)
(2)
The M(x, y, m, k) diurnal variation is similar to that
discussed for the wind diurnal variation in Figure 2 and
will not be highlighted here. More importantly, however,
we may use the residuals in Equation (2) to study the
covariability of the wind at different sites. A useful
measure of this covariability is the correlation C12 of
the residuals between two locations (x1 , y1 ) and (x2 , y2 ):
C12 =
1 [ε(x1 , y1 , m, d, k)ε(x2 , y2 , m, d, k)]
N
V1 V2
(3)
with Vi representing the standard deviation of the residual
time series for all m, d, and k. N is the number of all the
data in the time series and the summation extends over
all m, d and k. A second useful measure of covariability
is the covariance 12 of the log-wind speed at station 1
and station 2:
[ε(x1 , y1 , m, d, k)ε(x2 , y2 , m, d, k)]
=
(4)
12
N
where all the symbols have been defined earlier.
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