The Effects of Seasonality and ENSO Cycle on the Heat Budget and Ekman Transport on the Waters off
the Western Coast of Peru
Alex K. Chen ([email protected])
Department of Geological Sciences, Brown University, Providence, Rhode Island, USA
Abstract: This paper investigates the effects of seasonality and the El Nino cycle on the Ekman wind
stresses and Ekman transports on the Peru Current to the west of Peru (as predicted by the MIT GCM
model), compares the derived Ekman vertical velocities with the observations obtained by results in
Halpern 2002, and then attempts to find whether or not the Ekman transport and heat budget of the
region can be explained by seasonal variations and the El Nino/La Nina cycle. It then calculates a
preliminary heat budget for the region, successfully closes the budget, and finds suggestive evidence of
how El Nino affects both the heat and volume budgets.
Introduction: The Peru Current right off to the west of Peru contains an upwelling zone that is affected
by factors such as season and ENSO cycle (Halpern 2002). During El Nino events, the thermocline
deepens, and vertical velocities in the Eastern Pacific Ocean are at their most negative (or when
downwelling dominates over upwelling).
Wind creates a stress on the oceans, which induces a depth-dependent distribution of Ekman velocities
that follow an Ekman spiral. When these Ekman velocities are vertically integrated throughout the entire
depth of the water column, we arrive at terms for the Ekman transports. These vertically-integrated
water columns basically move in a direction perpendicular to that of the wind stress.
Under the right conditions, these Ekman transports can create the preconditions for Ekman upwelling
(or vertical Ekman transport). Ekman upwelling is often induced when certain season-varying wind
regimes blow parallel to the coast, force surface water to flow away from the coast, and allow water
from above to be replaced with water from below. As cooler water from below is often rich in
unconsumed nutrients, upwelling zones are of significant economic importance, often due to their
highly productive fisheries.
Data: ECCO (Estimating the Circulation and Climate of the Ocean) is a project that combines the MIT
GCM with real-time observations in order to model and characterize the ocean at a horizontal resolution
of 1°x1°. The data for this paper comes from the 73rd iteration of the ECCO project (ECCO3.73 , from
http://fox-kemper.com/data/ ). This data was in netCDF format and processed by Matlab. All regional
analysis was done on the red region shown in Figure 1 below. The red region was chosen to overlap with
the green region used by Halpern 2002 in order to facilitate comparisons. Data points over land were
represented as non-numbers and automatically excluded from the analysis.
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Figure 1: Red is the Area of Selection for the ECCO Analysis. Green is the Area of Selection used by Halpern 2002.
Analysis from the ECCO model will also be compared with Halpern 2002 (whose region is shown in green
above), which uses a 0.5° x 0.5° empirical dataset from the European Remote-sensing Satellite (ERS-1).
Halpern 2002 uses this dataset order to analyze variations in the Peru Current Ekman velocities that
could be caused by seasonal variations and El Nino.
Theory: The predicted Ekman velocities and transports induced by wind stress are shown by the
equations below (Cushman-Roisin and Beckers 2011), where τy is the meridional wind stress, U is the
vertically-integrated induced zonal Ekman transport from τy, uE is the zonal Ekman velocity, τx is the zonal
wind stress, V the vertically-integrated meridional Ekman transport induced from τx,vE is the meridional
Ekman velocity, H is the vertical length of the Ekman layer, and w is the vertical Ekman velocity
predicted from the curl of the wind stresses. When w is positive, there is upwelling (or Ekman suction),
and when w is negative, there is downwelling (or Ekman pumping).
From these equations, we can note that when f is very small near the equator, each of the terms “blows
up” and tends towards infinity for non-zero values of wind stress. This is an important effect to consider
when analyzing variations close to the equator. In the Southern Hemisphere, Ekman transport forces
surface water to move 90 degrees to the left of where the wind stress is applied. Equation (1) above
shows that southerly winds off the Peru coastline will force surface water to flow away from the coast,
as the southerly winds produce positive τy, which is then divided by a negative f, which makes U
negative (and water move westward). This, in turn, creates a gap that allows deeper water to rise.
These Ekman transports can then be used to calculate the advective terms for the heat budget shown
below. The terms of the heat budget are shown in equation 4 below (Talley et al. 2011). We assume that
they are in units of Joules, so they are integrated across an area.
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Here, QT is the net rate of heat into the body of water, Qs is the heat input through solar shortwave
radiation, Qb is the rate of heat loss by longwave radiation, Qh is the sensible heat flux, Q e is the latent
heat flux, and Qv is the advective heat flux from both horizontal and vertical directions.
In order to obtain volumes of our fluid elements, we used an estimated Ekman layer depth of 50 meters.
Each line of latitude corresponded to 110 km, and each line of longitude had a length of|110*sin(x)|km,
where x was the latitude in degrees.
Advective heat fluxes were calculated through taking the dot product of the sea-surface temperature
and Ekman-derived velocities at the three edges of the region we used. These fluxes were converted
into transport terms by multiplying these fluxes by the area transected by the fluxes at the edges of the
region considered. Meridional transports at the northern border were subtracted from the meridional
transports from the southern border in order to calculate the total meridional transports. The terms are
shown in the figure below (obtained by Talley Lecture Notes at http://wwwpord.ucsd.edu/~ltalley/sio210/transports/lecture_transports.pdf). The first two terms will be henceforth
referred to as the “horizontal advective heat flux”.
Non-advective heat fluxes were calculated by taking ECCO3 data of each of the fluxes and then
multiplying each flux by the area of each grid point (over all internal grid points) in order to get a total
value of power (in Watts) for the entire region. These are shown by equation 6 below.
Results:
In order to get vertical Ekman velocities of the region, we used equation 3 above in order to get the
vertical Ekman velocity from the curl of the wind stresses. These Ekman velocities are shown in the
figure below, and compared with the vertical velocities obtained by the observational results of Halpern
2002. We calculated the Ekman velocities for both the extended red region and the two ECCO grid
points that overlap most with the restricted green region used by Halpern 2002.
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Figures 2 (top) and 3 (bottom): both show vertical velocities. Figure 2 uses w obtained from the curl tau
in ECCO 3.73. Figure 3 uses empirical data from Halpern 2002.
Figure 2 is an especially interesting figure. First of all, it shows that variations in mean vertical velocity of
the entire region are reduced when it is averaged across the entire region. It also shows that there are
surprisingly significant phase differences in vertical Ekman velocities between the two neighboring 1°x1°
gridpoints centered at 76.5°W, 14.5°S and at 76.5°W, 15.5°S. In particular, there are times (like early
1993) where there is downwelling in one of the gridpoints and upwelling in the other gridpoint. If it is
already difficult to compare the vertical velocities between two adjacent gridpoints from the same
dataset, then it would be even more difficult to comparing the vertical velocities between the two
gridpoints and the Halpern 2002 dataset. It would be hard to even know which gridpoint to compare
with the Halpern 2002 dataset.
There are also only a few times when the three ECCO vertical Ekman velocities are in phase with each
other and in phase with the vertical velocity of the greater region (as in early 1996). At the rare times
when they are in phase with each other, what does that then say about the nature of the winds in the
broader region?
What’s especially interesting in particular is that none of the 3 analyzed regions in Figure 2 show any
significant downwelling from the 1997-1998 El Nino, which is shown in the analysis from Halpern 2002.
Downwelling would be an expected outcome of El Nino, since El Nino events deepen the thermocline of
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the Eastern Pacific. So then this really begs the question of why the ECCO model fails to capture this
phenomena. Is it a product of ECCO’s poor spatial resolution? And how precisely extensive is the
downwelling observed in Halpern 2002?
Our analysis shows that even regions adjacent to each other can experience different amounts of timelagged and phase effects in response to various forcings (like the seasons). In fact, simply averaging out
the ECCO vertical velocities in the two adjacent Halpern 2002 gridpoints would destroy much of the
signal of the variability in ECCO vertical velocity. This would make it especially difficult to predict a
consistent time-lag between an El Nino index and an arbitrary phase in the Ekman vertical velocity for
any particular region. Reasons like these are why El Nino continues to remain poorly understood.
The Heat Budget
Figure 4: The Heat Budget of the Peru Current
As Figure 4 shows, the majority of the heat transport (represented by the total heat budget above) in
the Peru Current region comes from the non-advective (mostly radiative) heat transport terms (latent,
sensible, shortwave, and longwave terms). The horizontal advective heat transport terms seem to be
roughly in phase with the non-advective heat transport terms – they seem to roughly bring heat into the
region at the same times as the non-advective terms. All are most positive during austral winter (the
middle of the year) and most negative during austral summer (on the boundaries of years). This is
especially surprising since the location studied is in the Southern Hemisphere, so one would expect
more non-advective heat transport in austral summer than in austral winter.
The vertical heat transport is effectively negligible. Interestingly, there seems to be a significant
depression in horizontal advective heat transport in early 1997, which was known to be a significant El
Nino year. This implies that the effects of the 1997-1998 El Nino were captured in the horizontal Ekman
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transports of ECCO, even if not in the vertical Ekman velocities. There is also an interesting depression in
non-advective heat transport in 2003 for some reason, which could be a model-related issue.
Figure 5: Cumulative Heat and Volume Budgets of the Peru Current integrated over time
Interestingly, we can see how the 1997-1998 El Nino affects the regional heat budget in Figure 5. The
1997-1998 El Nino seemed to temporarily reduce both the horizontal advective heat transport and the
cumulative total heat budget. The horizontal advective heat transport also seemed to slightly decline
from 2002-2003, which was another El Nino season. 2003 was also the year when there was a
mysterious sudden decline in non-advective heat transport (which could be model-related). Somehow,
the cumulative horizontal advective heat transport stepped in to fill in the gap caused by the sudden
decline in non-advective heat transport in 2003, so the cumulative total heat budget remained strikingly
constant.
Interestingly, the SST in the Peru Current region was unusually high in 1997 (see Figure 6), which could
have resulted in the temporary net advection of excess heat out of the region in 1997 (there are also
brief depressions in the cumulative total volume budget during those periods as well, which may or may
not be related to temperature). While Halpern 2002 also shows that 1997 was also associated with an
unusually high amount of downwelling (figure 3), the ECCO model does not show vertical heat transport
as a significant contribution to the heat budget even during this period (as seen from Figure 4). None of
our results provide a hint as to the cause of
this high SST.
Figure 6: Sea Surface Temperatures of the Peru Current obtained from Halpern 2002
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Figure 7: Cumulative Volume Transport of the Peru Current
Finally, we can examine the cumulative volume Ekman transports of the Peru Current. Figure 7 shows
that there were small depressions in the volume transports after 1997 and late 2002, both which
reflected depressions in horizontal advective heat transport that followed the El Nino in 1997 and in
2002. Otherwise, the cumulative volume Ekman transport seems to roughly mirror the cumulative
advective heat transport. While this transport seems to monotonically increase, we have not yet studied
how evaporation would affect this volume budget (which could presumably close it). This would be a
next step.
Discussion and Conclusion: Talley et al. 2011 says that the advective heat flux typically ranges from 1%
to 20% of the value of the incoming solar radiation (which averages out to 1366*111000*111000 = 1.68
* 1013 Watts per unit grid cell). Our results are surprisingly similar to Talley’s ballpark estimate.
The ECCO dataset has a notoriously coarse resolution, so it is generally poor at capturing fine-scale
features, especially fine-scale variations in wind stress along the coastline, which are often necessary for
showing upwelling zones (which means that the ECCO model often underestimates the extent of
upwelling). While the sea-surface temperatures in the ECCO come from empirical satellite observations,
many of the velocities are inferred from the MIT GCM model, and not particularly well-constrained.
While this analysis could potentially be improved by using inferred wind stresses from the SCOW dataset,
it probably would not help in closing our budgets.
Ultimately, the results from this paper illustrate the immense difficulty in making convincing conclusions
from oceanography datasets, especially given the extreme sensitivity of the time-evolution of certain
variables to various boundary conditions (like adjacent gridpoints). At the same time, the paper obtains
a closed budget for the heat budget of the Peru Current region, which means that the basic heat fluxes
discussed in Talley 2011 are perfectly sufficient enough to close off the budget in the MIT GCM region.
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Furthermore, it provides highly suggestive evidence that the El Nino of 1997-1998 and 2002-2003 have
affected both the heat and volume Ekman transports of the Peru Current, even though it failed to
replicate the findings of Halpern 2002 in finding a relationship between El Nino and the vertical Ekman
velocity.
Acknowledgments: The author would like to thank Baylor Fox-Kemper for providing the ECCO wind
stress data and some support. The author would also like to thank the users on both Stack Exchange and
Quora (particularly Achilleas Vortselas and Edwin Khoo) for answering his relentless Matlab questions in
a very timely manner. This work was supported by a University Fellowship from Brown University. The
state estimates were provided by the ECCO Consortium for Estimating the Circulation and Climate of the
Ocean funded by the National Oceanographic Partnership Program (NOPP).
References:
Halpern, D. (2002), Offshore Ekman transport and Ekman pumping off Peru during the 1997–1998 El
Nino, Geophysical Research Letters,29,5, 1075.
Cushman-Roisin and Beckers (2011). Introduction to geophysical fluid dynamics
Talley, L. et al. (2011). Descriptive Physical Oceanography, 6th edition
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