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AGU Jean Clary v5 .pdf


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Is it possible to estimate spectral kinetic energy fluxes
from high frequency radars?
Jean Clary, Cedric Chavanne and Louis-Philippe Nadeau
Jean.Clary@uqar.ca, Cedric_Chavanne@uqar.ca, Louis-Philippe_Nadeau@uqar.ca

I/ BACKROUND

IV/ ERRORS DUE TO GEOMETRY

III/ METHODS

The KE spectral flux is
defined as in [1,2,3,4] :

Barotropic KE budget is
checked. We compute the
KE
spectral
fluxes
of
barotropic
current,
and
average them between t1
and t2.
Figure 1 : (Top) Times series of barotropic KE (black),
baroclinic KE (blue) and of available potential energy (red).
(Bottom) Barotropic potential vorticity at t1 and t2.

V-1) Mapping total currents

We add white noise to synthetic radial currents, then we map them
with 2Dvar.
#10 -6
4

2Dvar - without noise

Virtual HFR

2Dvar - with 30% noise

1
0
-1
-2

-1

BT potential vorticity (s

2

)

3

-3
-4

a)

b)

#10 -15
2
10 -8

10 -8

30%

-2
-3

-12

-4
ref
UWLS
WLS
OI
2dvar

-5

K # KE(m2 :s!2 )

-1

10 -10

10 -10

-2
A min scale
30% noise

10 -12
reference
No noise
Noise 15% (hanning)
Noise 30% (hanning)
Noise 30% (no window)
noise level

10 -14

-6
10 -16

-7
10 0

10 -1

Wavelength/(2:Rd )

10 1

10 0

0

15%

K # F luxes(m:s!3 )

K # KE(m2 :s!2 )

0

10 -1

Wavelength/(2:Rd )

Figure 3 : KE spectra (left) and spectral fluxes (right) using local methods (UWLS,
WLS, OI) and a global method (2Dvar). Domain is doubly periodic.

10

1

10

0

-4

-6
min scale
no noise !

10

-1

Wavelength/(2:Rd )

10

1

10

0

L3 0

K # F luxes(m:s!3 )

#10 -15
1

10 1

-3

10

-4

-12

A max scale at 30Rd

10 -14

10 -16
10 1

A max scale at 10Rd
Reference
Domain size 30Rd (no window)
Domain size 30Rd (hanning)
Domain size 10Rd (hanning)

10 0

10 -1

Wavelength/(2:Rd )

-5
-6
-7
-8

10 1

10 0

10 -1

Wavelength/(2:Rd )

Figure 2 : KE spectra (left) and spectral fluxes (right) are shown for
non periodic domains. Reference (red) is estimated over the full doubly
periodic domain. Spectra and spectral fluxes are multiplied by the
wavenumber in order to highlight small horizontal scales. For domain
size 10Rd, maximal unaffected scale is around 3.5*Rd

VI/ CONCLUSIONS

Figure 4 : Barotropic potential vorticity field from mapped currents (a) without
noise, and (b) with 30% noise in amplitude (SNR~10).

10 -16

-2

10 -10

V-2) Random noise

We simulate HFRs measurements from QG model outputs (figures 3,
4 and 5). HFRs measure radial component of total currents on a
polar grid centered on the radar. We place 4 HFRs, two at the
bottom and two at the top (black bullets, figure 4a). Radial and
mapping resolutions are three times coarser than model resolution.
Unweigthed least squares (UWLS) and weigthed least square (WLS)
have uniform correlation function within the search radius. Optimal
interpolation (OI) has an exponential correlation function [5]. 2Dvar
[6,7] is a non local method : interpolation results at a given point
depend on all measurements. UWLS is the most often used method.
2Dvar is better than local methods (figure 3) for estimating KE
spectral fluxes.

10 -14

0

10 -8

K # F luxes(m:s!3 )

h
i
R∞
d u dK
Π(K ) = − K Re uc∗u.∇
h

V/ ERRORS DUE TO RADAR SAMPLING

10

#10 -15

-1

II/ OBJECTIVES
We propose here a feasibility study in order to estimate errors
involved in computing KE spectral fluxes from HFR data due to :
1) geometry (domain size and non-periodicity)
2) HFR sampling (mapping total currents, measurement noise)

We create non periodic subdomains of size between 10 and 30
Rd to test size effects on spectral analysis using a 75%
overlapping. For spectral analysis of non periodic fields it is
necessary :
1) to remove mean and linear trend.
2) to apply a window. Hanning, Hamming, 0.2 cosine taper,
Blackman, Kaiser Bessel windows were tested.

Two layer QG model with a flat bottom and a rigid lid.
Doubly periodic f-plane domain (similar to [1,2,3,4]).
Freely decaying turbulence.
Model resolution : 1.95 km. Domain area : 2000 km * 2000 km .
Rossby deformation Radius (Rd) : 30 km.

K # KE(m2 :s!2 )

Understanding the complete pathways of oceanic energy from its
inputs to its sinks would be a milestone of physical oceanography.
So far, kinetic energy (KE) transfers for scales larger than 100 km
have been inferred from satellite altimeter observations [1].
However, estimates for scales smaller than 100 km are still lacking
due to the limited resolution of present-day altimeters. Regional
estimates at scales ranging from tens to a few kilometers could in
principle be obtained from high-frequency radars (HFRs) provided
that measurement limitations do not introduce strong biases. This
is tested here using synthetic HFRs data from a quasi-geostrophic
(QG) model. Our goal is thus to assess if new information about
how the KE is transferred in this range of spatial scales (1-100
km) can be gained from HFRs.

-

-8

-10
10

-1

Wavelength/(2:Rd )

Figure 5 : KE spectra (left) and KE spectral fluxes (right) obtained from mapped
currents. Domain becomes non periodic if noise is added on radial currents, wich
affects spectral fluxes at small scales. This effect is mitigated by windowing, but the
larger wavelengths are modified (like in figure 2).

• Maximum unaffected scale for sudomains of size
10Rd, is around 3.5*Rd.
• 2Dvar is the best mapping method for KE spectral
fluxes. Transition scale is always shifted when total
currents are mapped with local methods.
• Minimal unaffected scale for 30% noise is around
1.3*Rd (when a window is applied).
• The range of spatial scales where KE spectral fluxes
from HFR measurements can be accurately estimated
will be quite narrow, depending on domain size and
noise level
To be done :
• Errors due to missing data (random gaps, missing
areas, missing radars)
• Determine objectively maximal and minimal
unaffected scales. Any suggestion?
Bibliography :
[1] Scott, R. B., & Wang, F. (2005). Direct Evidence of an Oceanic Inverse Kinetic Energy
Cascade from Satellite Altimetry. Journal of Physical Oceanography, 35(9), 1650–1666.
[2] Scott, R. B., & Arbic, B. K. (2007). Spectral Energy Fluxes in Geostrophic Turbulence:
Implications for Ocean Energetics. Journal of Physical Oceanography, 37(3), 673–688.
[3] Arbic, B. K., Scott, R. B., Flierl, G. R., Morten, A. J., Richman, J. G., & Shriver, J. F.
(2012). Nonlinear Cascades of Surface Oceanic Geostrophic Kinetic Energy in the Frequency
Domain. Journal of Physical Oceanography, 42, 1577–1600.
[4] Arbic, B. K., Müller, M., Richman, J. G., Shriver, J. F., Morten, A. J., Scott, R. B., …
Penduff, T. (2014). Geostrophic Turbulence in the Frequency–Wavenumber Domain: EddyDriven Low-Frequency Variability*. Journal of Physical Oceanography, 44(8), 2050–2069.
[5] Kim, S. Y., Terrill, E. J., & Cornuelle, B. D. (2008). Mapping surface currents from HF
radar radial velocity measurements using optimal interpolation. Journal of Geophysical
Research, 113(C10), C10023.
[6] Yaremchuk, M., & Sentchev, A. (2009). Mapping radar-derived sea surface currents with
a variational method. Continental Shelf Research, 29(14), 1711–1722.
[7] Yaremchuk, M., & Sentchev, A. (2011). A combined EOF/variational approach for
mapping radar-derived sea surface currents. Continental Shelf Research, 31, 758-768


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