yanwu zhang and james g. bellingham monterey bay aquarium research institute
DESCRIPTION
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. A Science Goal in MB06 Experiment: Heat Budget in the ASAP Box. - PowerPoint PPT PresentationTRANSCRIPT
Copyright MBARI 2006
Estimating Ocean Heat Flux Using AUVsError 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
dSnVTC p )( FluxHeat
dxxx
tPL
L 2
2
)speed AUV
(Fluxestimate
Control volume
dxxtP
xtVxtTxtP
tL
L
L
2
2
)(Flux
)( )()(
at time length of line aOn
real
Length L
normal current velocity
2estimatereal FluxFlux E
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
v
RP(τ λ) is the autocovariance function of P(t x)
Copyright MBARI 2006
Current Velocity Measurements during MB06 Experiment
Copyright MBARI 2006
Current Velocityrsquos Temporal-Spatial Autocovariance Function
Copyright MBARI 2006
Current Velocityrsquos Fitted to
00)(
eeR
vv ee
)( VR
Copyright MBARI 2006
Derivation of Temporal and Spatial Scales of [temperature current velocity]
km 6 km 9 km 22
hours 7 hours 8 days 22
where
)( )(
)( )( )( )()(
theneduncorrelately approximat and consider weIf
)( )()( )()(
)( )()(
PvT
PvT
vT
vTP
vT
vTP
VT
P
P
PPvvTT eeeeee
RR
xtVxtVExtTxtTER
VT
xtVxtTxtVxtTER
xtVxtTxtP
Copyright MBARI 2006
Heat Flux Estimation Error as a Function of AUVsrsquo Speed and Number
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
A Science Goal in MB06 Experiment Heat Budget in the ASAP Box
Copyright MBARI 2006
Heat Flux Estimation Using AUVs
dSnVTC p )( FluxHeat
dxxx
tPL
L 2
2
)speed AUV
(Fluxestimate
Control volume
dxxtP
xtVxtTxtP
tL
L
L
2
2
)(Flux
)( )()(
at time length of line aOn
real
Length L
normal current velocity
2estimatereal FluxFlux E
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
v
RP(τ λ) is the autocovariance function of P(t x)
Copyright MBARI 2006
Current Velocity Measurements during MB06 Experiment
Copyright MBARI 2006
Current Velocityrsquos Temporal-Spatial Autocovariance Function
Copyright MBARI 2006
Current Velocityrsquos Fitted to
00)(
eeR
vv ee
)( VR
Copyright MBARI 2006
Derivation of Temporal and Spatial Scales of [temperature current velocity]
km 6 km 9 km 22
hours 7 hours 8 days 22
where
)( )(
)( )( )( )()(
theneduncorrelately approximat and consider weIf
)( )()( )()(
)( )()(
PvT
PvT
vT
vTP
vT
vTP
VT
P
P
PPvvTT eeeeee
RR
xtVxtVExtTxtTER
VT
xtVxtTxtVxtTER
xtVxtTxtP
Copyright MBARI 2006
Heat Flux Estimation Error as a Function of AUVsrsquo Speed and Number
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Heat Flux Estimation Using AUVs
dSnVTC p )( FluxHeat
dxxx
tPL
L 2
2
)speed AUV
(Fluxestimate
Control volume
dxxtP
xtVxtTxtP
tL
L
L
2
2
)(Flux
)( )()(
at time length of line aOn
real
Length L
normal current velocity
2estimatereal FluxFlux E
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
v
RP(τ λ) is the autocovariance function of P(t x)
Copyright MBARI 2006
Current Velocity Measurements during MB06 Experiment
Copyright MBARI 2006
Current Velocityrsquos Temporal-Spatial Autocovariance Function
Copyright MBARI 2006
Current Velocityrsquos Fitted to
00)(
eeR
vv ee
)( VR
Copyright MBARI 2006
Derivation of Temporal and Spatial Scales of [temperature current velocity]
km 6 km 9 km 22
hours 7 hours 8 days 22
where
)( )(
)( )( )( )()(
theneduncorrelately approximat and consider weIf
)( )()( )()(
)( )()(
PvT
PvT
vT
vTP
vT
vTP
VT
P
P
PPvvTT eeeeee
RR
xtVxtVExtTxtTER
VT
xtVxtTxtVxtTER
xtVxtTxtP
Copyright MBARI 2006
Heat Flux Estimation Error as a Function of AUVsrsquo Speed and Number
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
v
RP(τ λ) is the autocovariance function of P(t x)
Copyright MBARI 2006
Current Velocity Measurements during MB06 Experiment
Copyright MBARI 2006
Current Velocityrsquos Temporal-Spatial Autocovariance Function
Copyright MBARI 2006
Current Velocityrsquos Fitted to
00)(
eeR
vv ee
)( VR
Copyright MBARI 2006
Derivation of Temporal and Spatial Scales of [temperature current velocity]
km 6 km 9 km 22
hours 7 hours 8 days 22
where
)( )(
)( )( )( )()(
theneduncorrelately approximat and consider weIf
)( )()( )()(
)( )()(
PvT
PvT
vT
vTP
vT
vTP
VT
P
P
PPvvTT eeeeee
RR
xtVxtVExtTxtTER
VT
xtVxtTxtVxtTER
xtVxtTxtP
Copyright MBARI 2006
Heat Flux Estimation Error as a Function of AUVsrsquo Speed and Number
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Current Velocity Measurements during MB06 Experiment
Copyright MBARI 2006
Current Velocityrsquos Temporal-Spatial Autocovariance Function
Copyright MBARI 2006
Current Velocityrsquos Fitted to
00)(
eeR
vv ee
)( VR
Copyright MBARI 2006
Derivation of Temporal and Spatial Scales of [temperature current velocity]
km 6 km 9 km 22
hours 7 hours 8 days 22
where
)( )(
)( )( )( )()(
theneduncorrelately approximat and consider weIf
)( )()( )()(
)( )()(
PvT
PvT
vT
vTP
vT
vTP
VT
P
P
PPvvTT eeeeee
RR
xtVxtVExtTxtTER
VT
xtVxtTxtVxtTER
xtVxtTxtP
Copyright MBARI 2006
Heat Flux Estimation Error as a Function of AUVsrsquo Speed and Number
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Current Velocityrsquos Temporal-Spatial Autocovariance Function
Copyright MBARI 2006
Current Velocityrsquos Fitted to
00)(
eeR
vv ee
)( VR
Copyright MBARI 2006
Derivation of Temporal and Spatial Scales of [temperature current velocity]
km 6 km 9 km 22
hours 7 hours 8 days 22
where
)( )(
)( )( )( )()(
theneduncorrelately approximat and consider weIf
)( )()( )()(
)( )()(
PvT
PvT
vT
vTP
vT
vTP
VT
P
P
PPvvTT eeeeee
RR
xtVxtVExtTxtTER
VT
xtVxtTxtVxtTER
xtVxtTxtP
Copyright MBARI 2006
Heat Flux Estimation Error as a Function of AUVsrsquo Speed and Number
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Current Velocityrsquos Fitted to
00)(
eeR
vv ee
)( VR
Copyright MBARI 2006
Derivation of Temporal and Spatial Scales of [temperature current velocity]
km 6 km 9 km 22
hours 7 hours 8 days 22
where
)( )(
)( )( )( )()(
theneduncorrelately approximat and consider weIf
)( )()( )()(
)( )()(
PvT
PvT
vT
vTP
vT
vTP
VT
P
P
PPvvTT eeeeee
RR
xtVxtVExtTxtTER
VT
xtVxtTxtVxtTER
xtVxtTxtP
Copyright MBARI 2006
Heat Flux Estimation Error as a Function of AUVsrsquo Speed and Number
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Derivation of Temporal and Spatial Scales of [temperature current velocity]
km 6 km 9 km 22
hours 7 hours 8 days 22
where
)( )(
)( )( )( )()(
theneduncorrelately approximat and consider weIf
)( )()( )()(
)( )()(
PvT
PvT
vT
vTP
vT
vTP
VT
P
P
PPvvTT eeeeee
RR
xtVxtVExtTxtTER
VT
xtVxtTxtVxtTER
xtVxtTxtP
Copyright MBARI 2006
Heat Flux Estimation Error as a Function of AUVsrsquo Speed and Number
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Heat Flux Estimation Error as a Function of AUVsrsquo Speed and Number
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Heat Flux Estimation Performance Using Spray Gliders and Dorado AUVs
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
bull Extend the analysis from a line to a surface Estimate heat flux into the ASAP box during the MB06 Experiment
bull Acknowledgments ndash Prof Steven Ramp of Naval Postgraduate School for the bottom-
mounted ADCP stations data
ndash Prof Timothy Cowles and Dr Stephen Pierce of Oregon State University for RV Thompson ADCP data
ndash Prof Russ Davis of Scripps for discussions on heat flux calculation
ndash Packard Foundation and ONR for projects funding
Next-Step Work
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Formulation and Calculation of Heat Flux Estimation Error
21212
2112
21
2
one_AUV
) (2) () 0(
)( )(
2
2
2
2
2
2
2
2
dxdxxxv
xRxx
v
xxRxxR
dxxv
xtPdxxtPE
L
L
L
L
L
L
L
L
PPP
vOne AUV
2
v
2
v
2
2
two_AUVs
4
4
4
4
4
4
4
4
4
4
4
4
2
2
)4
2
( )4
( )4
2
( )4
(
)4
2
( )4
2
( )(
L
L
L
L
L
L
L
L
L
L
L
L
L
L
dxL
xv
xtPdx
LxtPdx
Lx
v
xtPdx
LxtPE
dxL
xv
xtPdx
Lx
v
xtPdxxtPE
Two half-speed AUVs
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Temporal Autocovariance Function of [temperature middot 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 Temperatureby 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 Temperatureby Measurements at MBARI Moorings M1 and M2
Copyright MBARI 2006
Temporal Autocovariance Function of Temperatureby Measurements at MBARI Moorings M1 and M2