Transcript Estimating Ocean Heat Flux Using AUVs: Error Analysis, Sampling Design, and Preliminary Results from the MB06 Experiment Yanwu Zhang and James G.

Estimating Ocean Heat Flux Using AUVs:
Error Analysis, Sampling Design,
and Preliminary Results from the MB06 Experiment
Yanwu Zhang and James G. Bellingham
Monterey Bay Aquarium Research Institute
Copyright MBARI 2006
A Science Goal in MB06 Experiment: Heat Budget in the ASAP Box
Copyright MBARI 2006
Heat Flux Estimation Using AUVs
Control volume
Length L
normal current velocity
 
Heat Flux    C p T (V  n ) dS
On a line of length L, at timet :
P(t , x)  T (t , x) V (t , x)
Flux real 

Flux estimate

L
2
 L2
P(t , x) dx

L
2
x
 L P(t 
, x) dx
2
AUV speed
  E Flux real  Flux estimate 2

Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
v


  E 




L
2
L
2


L
2
x2  x1
x2


R (0, x1 x2 )  RP (
, x1 x2 )  2 RP ( , x1 x2 ) dx1 dx2
L  P
 
v
v

2


2
 
x
P(t , x) dx  L P(t  , x) dx 
L


v
 
2
2

L
2
L
2
RP(τ, λ) is the autocovariance function of P(t, x)
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Current Velocity Measurements during MB06 Experiment
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Current Velocity’s Temporal-Spatial Autocovariance Function
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Current Velocity’s RV ( ,  ) Fitted to e
R( ,  )  e





v
v
e



0
0
e
Copyright MBARI 2006
Derivation of Temporal and Spatial Scales of
[temperature · current velocity]
P(t , x)  T (t , x) V (t , x)
RP ( ,  )  ET (t , x) V (t , x)T (t   , x   ) V (t   , x   )
If we considerT andV approximately uncorrelated, then
RP ( ,  )  E T (t , x) T (t   , x   ) E V (t , x) V (t   , x   )
 RT ( ,  ) RV ( ,  )
  

  e  T e T


    
  v v
 e e

  

P
P

e
e


T  v
T v
where P 
, P 
T  v
T  v
 T  2.2 days, v  8 hours  P  7 hours
T  22 km,v  9 km
 P  6 km
Copyright MBARI 2006
Heat Flux Estimation Error as a Function of AUVs’ Speed and Number
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
Next-Step Work
• Extend the analysis from a line to a surface. Estimate heat flux
into the ASAP box during the MB06 Experiment.
• Acknowledgments:
– Prof. Steven Ramp of Naval Postgraduate School for the bottommounted ADCP stations data.
– Prof. Timothy Cowles and Dr. Stephen Pierce of Oregon State University
for R/V Thompson ADCP data.
– Prof. Russ Davis of Scripps for discussions on heat flux calculation.
– Packard Foundation and ONR for projects funding.
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
v
One AUV


 one_AUV  E 


L
2
L
2


L
2
x2  x1
x2


R
(
0
,
x

x
)

R
(
,
x

x
)

2
R
(
,
x

x
)
1
2
P
1
2
P
1
2  dx1 dx2
L  P
 
v
v

2


2
 
x
P(t , x) dx  L P(t  , x) dx 
L


v
 
2
2

L
2
L
2
v
2
Two half-speed AUVs
v
2
 two_AUVs
2
L
L
 L

 4
 
2x
L
2x
L
 2
4
 E  L P(t , x) dx   L P(t  , x  ) dx  L P(t  , x  ) dx 
 


v
4
v
4
4
  2
 4
 
2
L
L
L
 L




L
2x
L
L
2x
L


4
4
4
4
 E  L P(t , x  ) dx  L P(t  , x  ) dx   L P(t , x  ) dx  L P(t  , x  ) dx 

  



4
v
4
4
v
4
4
4
  4
  4
 







Copyright MBARI 2006
Temporal Autocovariance Function of [temperature · current velocity]
by Co-Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Temporal Autocovariance Function of Current Velocity
by Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Temporal Autocovariance Function of Temperature
by Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006