Uncertainty Uncertainty Workshop:Workshop:Sounding Sounding attributesattributes

Rob HareRob HareManager, Hydrographic SurveysManager, Hydrographic Surveys

Canadian Hydrographic Service, Pacific RegionCanadian Hydrographic Service, Pacific Region

CHC2004 May 24, 2004CHC2004 May 24, 2004

AbstractAbstract

A discussion of attributes on A discussion of attributes on soundingssoundings, sources of error and , sources of error and computation of sounding error. computation of sounding error. Plus a whole lot morePlus a whole lot more

An error prediction tool along with An error prediction tool along with the characteristics and capabilities the characteristics and capabilities of (a few) sounding systems will be of (a few) sounding systems will be reviewedreviewed..

Data Quality ElementsData Quality Elements CompletenessCompleteness Logical consistencyLogical consistency Positional accuracyPositional accuracy

Has Has horizontal and verticalhorizontal and vertical components components Sub-elements: Sub-elements: absolute accuracyabsolute accuracy, attribute , attribute

completeness, shape fidelity, time accuracy, completeness, shape fidelity, time accuracy, topologic consistencytopologic consistency

Temporal accuracyTemporal accuracy Thematic accuracyThematic accuracy

Estimation of Quality Estimation of Quality metricsmetrics

Direct and indirect methodsDirect and indirect methods Require absolute coordinate Require absolute coordinate

reference frame (e.g. WGS-84)reference frame (e.g. WGS-84) Most direct methods impracticalMost direct methods impractical

source inter-comparison is an exceptionsource inter-comparison is an exception Indirect methods require validationIndirect methods require validation

e.g. deductive error estimation (forward e.g. deductive error estimation (forward error prediction)error prediction)

Statistical estimatorsStatistical estimators

Measures of central tendencyMeasures of central tendency Sample meanSample mean Median, ModeMedian, Mode

Measures of dispersion (1-D and 2-D)Measures of dispersion (1-D and 2-D) Standard deviation (or variance), Standard deviation (or variance), RMSRMS CEP, MSEP,CEP, MSEP, drmsdrms

Total Propagated Error (TPE)Total Propagated Error (TPE) CAUTIONCAUTION - many hydrographic - many hydrographic

measurements are correlated (e.g. H&V measurements are correlated (e.g. H&V components of soundings)components of soundings)

Why estimate Why estimate error/uncertainty?error/uncertainty?

PreanalysisPreanalysis Will my system meet specifications?Will my system meet specifications? Do I purchase a new … C/B analysis?Do I purchase a new … C/B analysis?

Real-time QA Real-time QA Am I collecting enough data to meet specifications?Am I collecting enough data to meet specifications? Do I modify my sampling/processing strategy, discard outer Do I modify my sampling/processing strategy, discard outer

beams, increase overlap, take more sound speed profiles, beams, increase overlap, take more sound speed profiles, etc.?etc.?

Post-mission assessmentPost-mission assessment Did I meet specifications? Classification - what Order did I Did I meet specifications? Classification - what Order did I

achieve?achieve? Provide metadata for informed decision making/risk Provide metadata for informed decision making/risk

assessmentassessment Data attribution for integration/validation/comparison of Data attribution for integration/validation/comparison of

different data setsdifferent data sets Assessment of historic sourcesAssessment of historic sources

Initialization of CUBE estimator?Initialization of CUBE estimator? Create Source Classification or Reliability Diagrams or ZOCsCreate Source Classification or Reliability Diagrams or ZOCs

Part 1 - The VERTICALPart 1 - The VERTICAL

Absolute Vertical Absolute Vertical AccuracyAccuracy

Estimates of vertical precisionEstimates of vertical precision Errors common to all vertical Errors common to all vertical

measurementsmeasurements Errors common to GPS vertical Errors common to GPS vertical

measurementsmeasurements Depth soundingsDepth soundings

Shoal examinationsShoal examinations Drying heightsDrying heights Elevations and clearancesElevations and clearances

Depth soundingsDepth soundings

Leadline, sounding pole, rodLeadline, sounding pole, rod Single-beam echosounder - SBESSingle-beam echosounder - SBES

analogue soundersanalogue sounders digital soundersdigital sounders

Sweep (multi-transducer)Sweep (multi-transducer) Lidar Lidar Swath (multibeam echosounder - MBES)Swath (multibeam echosounder - MBES) Other – e.g. TIBS, wire or bar sweep, Other – e.g. TIBS, wire or bar sweep,

diverdiver

Sources of error - water Sources of error - water levelslevels

gauge measurement precisiongauge measurement precision method of filtering sea surface wavesmethod of filtering sea surface waves timing synchronisation of gauge and timing synchronisation of gauge and

measurement measurement vertical datum precision vertical datum precision spatial extrapolation to the location of the spatial extrapolation to the location of the

vertical measurement, or in the case of vertical measurement, or in the case of predictions,predictions,

quality of constituent set (length/quality of quality of constituent set (length/quality of observations)observations)

correction for environmental effectscorrection for environmental effects

Other sources of vertical Other sources of vertical errorerror

Draft and squat or settlementDraft and squat or settlement Antenna to transducer offset Antenna to transducer offset

(GPS)(GPS) Datum separation model (GPS)Datum separation model (GPS) Sounding measurementSounding measurement HeaveHeave Sound speedSound speed

Traditional sounding Traditional sounding reductionreduction

Dynamic draft

ChartedDepth, D

Chart datumMeasuredDepth, d

Tide, WL

θr

D = d + draft – WLd = r cos (θ+R) cos P

r = rangeΘ = beam angleR = Roll angleP = Pitch angle

RTK GPS sounding RTK GPS sounding reductionreduction

Dynamic draft

ChartedDepth, D

Chart datum

MeasuredDepth, d

Tide, WL

θr

Ellipsoid

GPS RTK, Z

Separation Model, M

AntennaHeight, K

D = d + K – Z – M

K = Δx sinP + Δy cosP sinR + Δz cosP cosR

Vertical error Vertical error propagationpropagation

SBES error sourcesSBES error sources

depth measurementdepth measurement algorithm, frequency, beamwidth, pulse algorithm, frequency, beamwidth, pulse

lengthlength sound speed correction methodsound speed correction method draft (and squat if applied)draft (and squat if applied) heave (measured)heave (measured) tidestides manual trace reading, resolution, manual trace reading, resolution,

recording and reduction methodrecording and reduction method

Lidar error sourcesLidar error sources

Depth measurementDepth measurement Refraction correction (calibration)Refraction correction (calibration) Sea-surface modellingSea-surface modelling Tides Tides Footprint spreadingFootprint spreading

MBES error sourcesMBES error sources Range and beam angle Range and beam angle

measurementmeasurement detection method (amplitude or phase)detection method (amplitude or phase)

Refraction correctionRefraction correction Dynamic draft Dynamic draft

includes squat, settlement, change of includes squat, settlement, change of trimtrim

Heave (measured and induced)Heave (measured and induced) Tides or water levelsTides or water levels Roll, pitch, headingRoll, pitch, heading Calibration (patch test) offsetsCalibration (patch test) offsets

Roll, pitch, heading, sensor latencyRoll, pitch, heading, sensor latency Positioning systemPositioning system

Patch test - Heading offsetPatch test - Heading offset

Patch test - Roll offsetPatch test - Roll offset Patch test - Pitch and latencyPatch test - Pitch and latency

Alignment errorsAlignment errors

MBES coordinate MBES coordinate systemssystems

Positioning system antenna

VRU, attitude sensor,sometimes HRP sensor

Transducerx

z

y

Direction of vessel travel

PortStarboard

Pitch angle

Roll angle

Yaw

Gyro

Y

Bow

Stern

XLL

LL

y

(range = 1/2 of 2-way travel time)Beam angle

Draft

d

z

r

(cross-track distance)

(measured depth)

Sample error mapping equationsSample error mapping equations

1dP r

2 2 2 cos cos

2dr P2 2 2 sin cos

3dr P

P2 2 2 cos sin

Map of sources of depthMap of sources of depthmeasurement errormeasurement error

d

Pv

R R v

r

v v

P P

pitch stabilization

non-orthogonally-steered beams

Rv m

m

m s

m

p s

d d dd4 1 2 3

, d r m

v m v m

Mapping reduced depth errorMapping reduced depth error

D

D WL

dynamic draughtdH

load squat draughtH H

R P offsets

Measured depth

Depth reduced for vessel

Reduced depth

(transducer to VRU)

(t)

im

Mapping depth errorsMapping depth errors

Confidence levelsConfidence levels For a normal distribution, the probabilities of For a normal distribution, the probabilities of

univariate random errors of a single univariate random errors of a single measurement falling within a certain level of measurement falling within a certain level of error (number of standard deviations, error (number of standard deviations, ) are ) are

given in the following table.given in the following table.

EM1002 depth error estimates (95%)(view looking aft, EA mode)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-250 -200 -150 -100 -50 0 50 100 150 200 250

Cross-track distance (m)

Dep

th e

rro

r (m

)

Sounder Heave Roll Pitch

Refraction Total depth measurement Dynamic draft Water level

Total reduced depth (EA mode) IHO Special Order IHO Order 1

Depth error estimatesDepth error estimates

Additional vertical Additional vertical correctionscorrections

sounding datum sounding datum adjustmentsadjustments

metric conversionmetric conversion may include generation of may include generation of

metric contoursmetric contours sound speed correctionssound speed corrections

Potential limitationsPotential limitations

heave estimation (manual)heave estimation (manual) phase lag or latencyphase lag or latency sound speed changessound speed changes manual trace readingmanual trace reading vertical display resolutionvertical display resolution stepped vertical datum zonesstepped vertical datum zones shoal biasingshoal biasing datum separation modelsdatum separation models

Part 2 - The Part 2 - The HORIZONTALHORIZONTAL

Absolute Horizontal Absolute Horizontal AccuracyAccuracy

Estimates of horizontal precisionEstimates of horizontal precision Field sheet processesField sheet processes SoundingsSoundings

Shoal examinationsShoal examinations Other data typesOther data types

Heights, elevations, clearancesHeights, elevations, clearances Navigational AidsNavigational Aids ShorelineShoreline Bathymetric contoursBathymetric contours

Cartographic processes (including digitizing)Cartographic processes (including digitizing)

Sounding Position Sounding Position EquationsEquations

sx r R r P R cos sin( ) sin sin cos( )

sy r R r P R sin sin( ) cos sin cos( )

meas sy ay ty M( )/

meas sx ax tx N( )/ cos

ax x P y R P R z R P R sin cos (cos cos sin sin sin ) (cos sin sin sin cos )

tx tSOG P sin cos ty tSOG P cos cos

ay x P y R P R z R P R cos cos (sin cos cos sin sin ) (sin sin cos sin cos )

Estimates of precisionEstimates of precision

Rigorous - error ellipsesRigorous - error ellipses HDOPHDOP MSEPMSEP CEPCEP CSECSE drms drms badrms 22

22yxMSEP

Errors in Multibeam Errors in Multibeam soundingssoundings

GPS or POS/MV position errorGPS or POS/MV position error transducer - antenna offsets transducer - antenna offsets sounder measurement errorsounder measurement error

range, beam angle, detection methodrange, beam angle, detection method refraction correction errorrefraction correction error

transducer shape, orientation, roll-modulationtransducer shape, orientation, roll-modulation roll, pitch and roll, pitch and headingheading error error latency between systems latency between systems

GPS, sounder, VRUGPS, sounder, VRU

Sample position error mappingSample position error mappingequationsequations

1sp P r2 1 2 2 ( (cos cos ) )

2sp r P2 2 1 2 2 ( (cos cos ) )

Sounding position error mapSounding position error mapp

Pv

R R v

r

v v

m

pitch stabilizationR

non-orthogonally-steered beams

PPrm

vm

sm

m

s

p s

ps ps ps ps4321

vm

vm

m

Mapping total position errorMapping total position error

p

drms pp p

speed latency P offsets P R

s at

Mapping position errorsMapping position errors

Confidence levelsConfidence levels

EM1002 position error estimates (2MSEP)(view looking aft, EA mode)

0

2

4

6

8

10

12

-250 -200 -150 -100 -50 0 50 100 150 200 250

Cross-track distance (m)

Po

siti

on

err

or

(m)

Positioning System Sounding Refraction Roll Pitch Heading Sounding position IHO Special Order IHO Order 1

Position error estimatesPosition error estimates

Field Sheet processesField Sheet processes Horizontal datumHorizontal datum Manual processesManual processes

Materials and constructionMaterials and construction Horizontal controlHorizontal control Station plottingStation plotting

Data typesData types SoundingsSoundings

Shoal examinations, drying heightsShoal examinations, drying heights ContoursContours

Navigational aidsNavigational aids Shoreline (natural and man-made)Shoreline (natural and man-made) Seafloor samplesSeafloor samples Topography, elevations, clearancesTopography, elevations, clearances

These are scale-dependent errors

Soundings - sources of Soundings - sources of errorerror

Positioning system/methodPositioning system/method Sounding system Sounding system

including offsets in space and timeincluding offsets in space and time

PlottingPlotting InkingInking DigitizingDigitizing

Mytyaysm /)( cos/)( Nxtxaxsm

Positioning Positioning systems/methodssystems/methods

Manual/OpticalManual/Optical Sextant (eccentric circle LOP)Sextant (eccentric circle LOP) Subtense (eccentric circle LOP)Subtense (eccentric circle LOP) Range poles (straight-line LOP)Range poles (straight-line LOP) Azimuth (straight-line LOP)Azimuth (straight-line LOP)

Electronic positioning systems (EPS)Electronic positioning systems (EPS) Range-bearing (hybrid - circle and line) Range-bearing (hybrid - circle and line) Two-range or range-range (later multi-range) - concentric Two-range or range-range (later multi-range) - concentric

circle LOPcircle LOP Hyperbolic (2 and later multi-hyperbola) LOPHyperbolic (2 and later multi-hyperbola) LOP Transit satellite (Doppler) - spherical LOPTransit satellite (Doppler) - spherical LOP GPS (spherical LOP)GPS (spherical LOP)

DGPSDGPS OTFOTF

Plotting, Inking, Plotting, Inking, Digitizing errorsDigitizing errors

PlottingPlotting 3-arm protractor3-arm protractor latticeslattices collector registrationcollector registration fixes and ‘tweeners’fixes and ‘tweeners’

InkingInking on collectoron collector on field sheeton field sheet registrationregistration

DigitizingDigitizing digitizer resolutiondigitizer resolution registration (rms of fit on HCP) - transformation usedregistration (rms of fit on HCP) - transformation used datum shiftdatum shift projectionprojection

These are scale-dependent errors

Systematic error sources Systematic error sources (safety biasing)(safety biasing)

GeneralizationGeneralization Line smoothingLine smoothing SymbolizationSymbolization Feature displacementFeature displacement

soundingssoundings bottom samples (more for clarity than bottom samples (more for clarity than

safety)safety)

Drafting Drafting (from final compilation (from final compilation

manuscript)manuscript) Control pointsControl points Linework (shoreline)Linework (shoreline) SoundingsSoundings SymbolsSymbols ContoursContours Bottom samplesBottom samples

DigitizingDigitizing

Registration/rectification methodRegistration/rectification method Digitizer precision, resolutionDigitizer precision, resolution Optical centre recognitionOptical centre recognition Line-following abilityLine-following ability QC tolerances (chart specifications)QC tolerances (chart specifications)

Sources, products and points of digitization

Manually-compiled

source

Digitally-collected

source

digitizeconvert

Digitalsource

manualcompilation

manualdrafting

printing

digitalcompilation

Digitalchart/ENC

Digitalchart/ENC

Paperchart

QER

QER

QER

digitizeconvert

digitizeconvert

Field sheet processes

Cartographic processes

QER QERQER

Data inter-comparisons:Data inter-comparisons:validating error prediction validating error prediction

assumptionsassumptions MethodsMethods

compare same data set at different process stagescompare same data set at different process stages difference DTM (soundings)difference DTM (soundings) inter-comparison of point features (shoal examinations, inter-comparison of point features (shoal examinations,

drying heights)drying heights) linework comparisons (HWL, LWL, contours)linework comparisons (HWL, LWL, contours) validate inference methods (expected vs. actual)validate inference methods (expected vs. actual)

LimitationsLimitations small statistical samplesmall statistical sample is it the same feature?is it the same feature? separation of depth from position errorseparation of depth from position error

22

21 mm

Quality ImplementationsQuality Implementations Data collection - ASCII, Simrad, Hypack, NMEAData collection - ASCII, Simrad, Hypack, NMEA Data processing - HIPS (Quality flag, coverage, Data processing - HIPS (Quality flag, coverage,

standard deviation), CUBE (stochastic surface, standard deviation), CUBE (stochastic surface, etc.)etc.)

Data storage - Caris ASCII, GSF, SDS, …Data storage - Caris ASCII, GSF, SDS, … Paper Charts - Source Classification/Reliability Paper Charts - Source Classification/Reliability

Diagrams, Explanations in Sailing Diagrams, Explanations in Sailing Directions/PilotsDirections/Pilots

ENC - S-57 objects and meta-objects ENC - S-57 objects and meta-objects (M_QUAL, M_ACCY, CATZOC, CATQUA, QUASOU, (M_QUAL, M_ACCY, CATZOC, CATQUA, QUASOU,

TECSOU, POSACC)TECSOU, POSACC) Raster Charts?Raster Charts?

SummarySummary Depth and position errors can be estimated Depth and position errors can be estimated

using forward error predictionusing forward error prediction These estimates can be validated by inter-These estimates can be validated by inter-

comparison of data setscomparison of data sets Estimates can be used:Estimates can be used:

To make decisions regarding equipment To make decisions regarding equipment selection and purchaseselection and purchase

To determine if specifications can be/have been To determine if specifications can be/have been metmet

To adapt your sampling strategyTo adapt your sampling strategy As an input to statistical processing algorithmsAs an input to statistical processing algorithms

These are but two of many These are but two of many Quality/Uncertainty MeasuresQuality/Uncertainty Measures