Uncertainty analysis of Acoustic-Doppler Current Profilers ... · ADCP and flow characteristics...

Uncertainty analysis of Acoustic-Doppler Current Profilers (ADCP)

gaugings

Marian MusteIIHR-Hydroscience & Engineering

The University of Iowa, U.S.A.

The 4th WMO/IAHR/IAHS Stream Gauging Training Course, Lyon, France

September 4, 2018

Uncertainty analysis (UA): rigorous methodology for uncertainty assessment using statistical and engineering concepts

Over the last 60 years, considerable efforts have been put forth by professional societies to develop and implement UAs

Currently, GUM (1993) AIAA (1999) ASME (2005)

are the most recent internationally recognized UA methodologies

Critical review of UA methodologies/standards

Critical review of UA methodologies/standards

WMO’s Commission for Hydrology recommends adoption for hydrometry of the “Guide to Expression of Uncertainty in Measurement” (GUM, 1993)

• GUM methodology: rigorous, based on advanced statistical and engineering concepts• GUM approach: general, scientific, with recognition for the need for further adaptation for specific areas• GUM circulation: adopted as is by various scientific & research communities, e.g., NIST TN 1297 (1994),

NF ENV 13005 (1999), ISO 5168 (2005), UKAS (2007), ISO/TS 25377 (2007) = HUG, ISO 748 (2007), ISO 101088 (2007), (AIAA, 1995), (ASME, 1998)

• GUM outcomes: uncertainty estimation with specified confidence level and indication of the relativecontributions of the elemental uncertainty sources to the final result

!! THE CIVIL ENGINEERING COMMUNITY STILL LACKS A UA FRAMEWORK !!

The most recent UA guideline for hydrometry(https://library.wmo.int/opac)

The following examples follow strictly this guide

Synthesis of GUM (1993) Methodology

Step 3: most complex and

expensive(effort and $)

(the other steps can be executed by software)

Evaluate the standard uncertainty, u(xi) of each input estimate xi

Each input estimate and its associated standard uncertainty are obtained from a distribution of possible values of the input quantity (probability distribution may be frequency based, that is, based on a series of observations) or it may be a priori distribution.

Type A evaluation of standard uncertainty is obtained from the statistical analysis of a series of observations determined from the current measurements

Type B evaluations are founded on other means (prior information, expert knowledge, engineering judgment)

Step 3

GUM (1993) Methodology: step-by-step

Type A evaluation of standard uncertainty, u(xi), is based on the standarddeviation of a set of n repeated measurements

where

The standard uncertainty of a sets of measurements for the input estimate xi(standard deviation of the mean) is

[ ]2232221 )()()()(1)( nxxxxxxxxnsxu −++−+−+−==

∑==n

i ix

nx

1

1

)(1)( xun

xu =

Step 3


Type B evaluation is based on scientific judgment using previous measurement data, experience with or general knowledge of the behavior and properties of relevant materials and instruments, manufacturer’s specifications, data provided in calibration and other certificates, and uncertainties assigned to reference data taken from handbooks.

Identify the max and min values of x to determine and

Determine the standard deviation for the input from

with selected or declared expected dispersion of the deviation, d, and associated probability distribution, p(x)

( ) ( ) ( )dxxpxdxux

x

2

∫∆′

∆′−

=

Based on prior information

xx 'max ∆= xx'

min ∆−=

Step 3


The most commonprobability distributions, p(x), associated with the hydrometric uncertainties are: rectangular, normal, triangular, and bimodal

Distribution Standard uncertainty of a measured value xi Rectangular 3)( ii axu =

ai = estimated semi-range of the uncertainty Normal kUxu i =)(

U = expanded uncertainty; k = coverage factor Triangular 6)( ii axu =

Bimodal ii axu =)(

Step 3


Add uncertainty components for each input variable:

The various sources of uncertainties for a variable, irrespective of their provenance and type (A or B), are compounded using the root-sum-square (RSS) combination using:

∑=

=n

kiki xuxu

1

22 )()(

where u(xik) is the k-th elemental error associated with the variable xi.

Step 3


Results are reported as:

)(ykuyUyY c±=±=

Reports should include the uncertainty budget containing, at minimum: probability distribution type for uncertainties, standard uncertainties for all sources, sensitivity coefficients, degrees of freedom, etc.

Synthesis of GUM (1993) Methodology

UA Implementation

Ideally, UA should be implemented in multiple stages of the measurement process, i.e., from design to reporting.

UA Implementation

CAUTIONARY COMMENTS UA methods assumes that blunders in the raw data (outliers) are removed and known

biases are corrected before the analysis. Measures of uncertainties are not intended to account for such omissions.

Each INDIVIDUAL measurement has it OWN uncertainty; transfer of uncertainty assessments from one case to another should be done after thorough scrutiny

UA results should be classified using criteria that captures the main features of the facility (site)

measurement instrument operations (operator & measurement environment)

data acquisition and processing data reduction

Software for UA: QMSys GUM

(www.qsyst.com)

Muste, Kim, Merwade (2012)

3D velocities

Discharge

Fixed or moving boats

UA Implementation: ADCP case studies

• Acoustic Doppler Current Profiler (ADCP)

ADCP (cross section)

UA Implementation: ADCP case studies

Stream discharge = sum of discharge in small cells Stream discharge = velocity-area method

Moving-boat (ADCP transects) Fixed ADCP (section-by-section, SxS)

Measurable Area

Unmeasurable Near-bank Areas

Unmeasurable Top Area

Unmeasurable Bottom Area

Lee et al., (2013)

Methods for ADCP gauging

UA Implementation: Case study #1 – ADCP transects

Data Reduction Equation for in-bin discharge (Teledyne/RDI’s ADCP)

( )fff vuV ,=

( )bbb vuV ,=

x

y

E

( )( ) dtdzkVVQT tz

tz

bfm

U

L

∫ ∫ ⋅×=0

)(

)(

Steps 1,2

Gonzalez-Castro, Muste (2007)


Steps 1,2


Data Reduction Equation for in-bin discharge


Using BT

[ ]zthprFFFFCFFFFFfQ abDbDbDbDSDDDDm ji δδθ ,,,,,,,,,,,,,,, 11114321,1 =+With If , the functional relationship for Q depends on 16 variables:

WATER VELOCITY WITH RESPECT TO ADCP

( ) ( ) ( )( )( )34432121 cscsin2seccossin+csccos241 vvPvvvvPRvvRua −++++−= θθθ

( ) ( )( )432134 secsin-csccos241 vvvvPvvPva +++−= θθ

BOAT VELOCITY WITH RESPECT TO CHANNEL BED

( ) ( ) ( )( )( )34432121 cscsin2seccossin+csccos241

bbbbbbbbb vvPvvvvPRvvRu −++++−−= θθθ

( ) ( )( )432134 secsin-csccos241

bbbbbbb vvvvPvvPv +++−−= θθ

( ) ( )( )1, 1 11,i jm a b b a j j i ii j

Q u v u v z z t t+ + ++

= − − −

SD F

CFv2

=

Steps 1,2 Data Reduction Equation for in-bin discharge


Steps 1,2 Data Reduction Equation for top & bottom discharges

BTM Q

MID Q

TOP Q 3 Z

1 Z

Z

DEPTH CELL Da

ADCP TRANSDUCER FACE

D total

POW ER FIT

SCALAR

TRIPLE (m2/s2)

PRODUCT

ADCP

MEASURED DISCHARGE

TOP LAYER (ESTIMATED)

BOTTOM LAYER (ESTIMATED)

DISCHARGE (m3/s)

ACTUAL PROFILE

ADCP VELOCITIES

D

2 Z CONSTANT

POW ER 3-POINT SLOPE

POW ER

CONSTANT POW ER IN LOW 0.2 D total

D avg

D ADCP

D top B D

D LG

( )( ) ( )( )11

11

11

12

23

++=

+++

−

−−−=

∑bb

m

jjabbaii

bba

b ZZ

vuvuttZZDQ

i

( ) ( )

( )111

11

12

1

++

=+

+

−

−−=

∑bb

m

jjabbaii

ba

t ZZ

vuvuttZDQ

i


Steps 1,2 Data Reduction Equation for total discharge

Measurable Area

Unmeasurable Near-bank Areas

Unmeasurable Top Area

Unmeasurable Bottom Area

etQ

mQ

elQ erQ

ebQ

erelebetemmt QQQQQQQ +++++=

;lllel ZLKVQ = rrrer ZLKVQ =where

Step 3


Source Depends upon Can be estimated from

1 Spatial resolution ADCP, mode, settings, boat speed End-to-end calibration 2

2 Doppler noise ADCP characteristics Instrument comparison

3 Velocity ambiguity Mode, settings End-to-end calibration 4 Side-lobe interference Beam angle, settings, bathymetry End-to-end calibration 5 Temporal resolution Settings End-to-end calibration 6 Sound speed Water properties UA of Celerity(Salinity, Temperature) 7 Beam angle ADCP Manufacturer’s specifications 8 Boat speed Site, flow, boat operation End-to-end calibration

9 Sampling time Flow temporal large scales Instrument comparison

10 Near-transducer ADCP and flow characteristics Customized experiments

11 Reference boat velocity Sediment concentration, flow 4 Manufacturer’s Specifications

12 Depth ADCP and bed characteristics Instrument comparison

13 Cell positioning ADCP, setting, water properties √

14 Rotation ADCP, setup, site Manufacturer’s Specifications

15 Timing ADCP, speed of sound, gating time Manufacturer’s Specifications

16 Edge Discharge model and measurements Manufacturer’s Specifications

17 Vertical profile model Distribution model, turbulence Field and Laboratory Experiments

18 Discharge model Discharge model Highly resolved data 19 Finite summation ADCP settings, boat velocity √ 20 Site conditions & operation Site, boat operation Concurrently measured data

fVADCP9

UA Implementation: Case study #1 – ADCP transectsIdentification of the sources of uncertainties


Step 3 Sampling time (duration) uncertainty (source #9)

Difference in velocity:- 21.9% for one ping- less than 3% for over 3 min(reference velocity: long-term averaged ADCP velocities at fixed location)

Collection time span (min)0 2 4 6 8

Perc

enta

ge e

rror

(%)

0.00

0.05

0.10

0.15

0.20

0.25

Site and flow specific f (mean velocity, turbulence intensity)

Step 3 Near-transducer uncertainty (source #10)

Muste, Kim, Gonzalez-Castro (2010)


Instrument, deployment, and flow specific f (mean velocity)


Step 3 Vertical velocity model (source #17)

Difference in the velocity:- 1% power law- 1.7% logarithmic law- 4.3% for 1/6 power law(reference velocity: long-term averaged ADCP velocities at fixed location)

Velocity (ft/s)

Dep

th(ft

)

0.1 0.2 0.3 0.4 0.5

0

5

10

15

20

Vta ln(h) + ba hba h(1/6)

( )

Velocity (ft/s)D

epth

(ft)

0.2 0.3 0.4 0.5 0.6

0

5

10

15

20

Vta ln(h) + ba hba h(1/6)

( )

Site and flow specific f (turbulence intensity, bed roughness)

V

e

l

o

c

i

t

y

(

f

t

/

s

)

D

e

p

t

h

(

f

t

)

0

.

1

0

.

2

0

.

3

0

.

4

0

.

5

0

5

1

0

1

5

2

0

V

t

a

l

n

(

h

)

+

b

a

h

b

a

h

(

1

/

6

)

F

I

X

E

D

P

O

I

N

T

(

4

5

)

V

e

l

o

c

i

t

y

(

f

t

/

s

)

D

e

p

t

h

(

f

t

)

0

.

2

0

.

3

0

.

4

0

.

5

0

.

6

0

5

1

0

1

5

2

0

V

t

a

l

n

(

h

)

+

b

a

h

b

a

h

(

1

/

6

)

F

I

X

E

D

P

O

I

N

T

(

4

7

)


Difference in discharge:- 0.5% mid section- 0.49% mean section(reference discharge using the long-term averaged ADCP velocities acquired at fixed locations)

b) a) c )

1−j

ijQ ,

1−j 1+j

( )jj

jjj Vh

DDQ ⋅⋅

+= +

21

1−j

2211 jj

jjj

j

VVD

hhQ

+⋅⋅

+= −−

jD 1+jDjD

∑=i

ijj QQ ,

jD

ijijjij VhDQ ,,, ⋅⋅=

1, +ijQ

j j j

Step 3 Discharge algorithm (source #18)

Site specific f (cross-section shape and aspect ratio)

b)

a)

c)

1

-

j

i

j

Q

,

1

-

j

1

+

j

(

)

j

j

j

j

j

V

h

D

D

Q

×

×

+

=

+

2

1

1

-

j

2

2

1

1

j

j

j

j

j

j

V

V

D

h

h

Q

+

×

×

+

=

-

-

j

D

1

+

j

D

j

D

å

=

i

i

j

j

Q

Q

,

j

D

i

j

i

j

j

i

j

V

h

D

Q

,

,

,

×

×

=

1

,

+

i

j

Q

j

j

j

Step 3


Source Depends upon Can be estimated from

1 Spatial resolution ADCP, mode, settings, boat speed End-to-end calibration 2

2 Doppler noise ADCP characteristics Instrument comparison

3 Velocity ambiguity Mode, settings End-to-end calibration 4 Side-lobe interference Beam angle, settings, bathymetry End-to-end calibration 5 Temporal resolution Settings End-to-end calibration 6 Sound speed Water properties UA of Celerity(Salinity, Temperature) 7 Beam angle ADCP Manufacturer’s specifications 8 Boat speed Site, flow, boat operation End-to-end calibration

9 Sampling time Flow temporal large scales Instrument comparison

10 Near-transducer ADCP and flow characteristics Customized experiments

11 Reference boat velocity Sediment concentration, flow 4 Manufacturer’s Specifications

12 Depth ADCP and bed characteristics Instrument comparison

13 Cell positioning ADCP, setting, water properties √

14 Rotation ADCP, setup, site Manufacturer’s Specifications

15 Timing ADCP, speed of sound, gating time Manufacturer’s Specifications

16 Edge Discharge model and measurements Manufacturer’s Specifications

17 Vertical profile model Distribution model, turbulence Field and Laboratory Experiments

18 Discharge model Discharge model Highly resolved data 19 Finite summation ADCP settings, boat velocity √ 20 Site conditions & operation Site, boat operation Concurrently measured data

fVADCP9

UA Implementation: Case study #1 – ADCP transectsNo full-fledged analysis available yet!

Instrument: Acoustic-Doppler Current Profiler (RDI StreamPro)

# Cells: 30 Min Cell Size: 2 cmMax Cell Size: 20 cmMax Range: 6mResolution: 0.1 cm/sec

UA Implementation: Case study #2 – ADCP SxS

Left edge

Steel pole

Right edge

1st vertical

23rd

Measurement site: Small stream (Clear Creek, Iowa, USA) Velocity profiles acquired at fixed positions (0.25 m apart)

Streampro SxS Pro software screen shotCross-section location

Measurement process: SxS approach in steady flow

)2

()2

()2

( 2223232322

2

111211

bbdv

bbdvbbdvQ

n

nnnnm

−××+

−××+

−××= ∑

=

−+

(IV.1)

REmLEt QQQQ ++= (IV.2)

1113535.0 vdbQLE = (IV.3)

232323 )(3535.0 vdbbQ RBRE −= (IV.4)

Data reduction equation (DRE) for discharge calculation

Layout of the StreamPro measurements


Steps 1,2

(IV.1)

(IV.2)

(IV.3)

(IV.4)

1

1

1

3535

.

0

v

d

b

Q

LE

=

23

23

23

)

(

3535

.

0

v

d

b

b

Q

RB

RE

-

=

)

2

(

)

2

(

)

2

(

22

23

23

23

22

2

1

1

1

2

1

1

b

b

d

v

b

b

d

v

b

b

d

v

Q

n

n

n

n

n

m

-

´

´

+

÷

ø

ö

ç

è

æ

-

´

´

+

-

´

´

=

å

=

-

+

RE

m

LE

t

Q

Q

Q

Q

+

+

=

Identification & grouping uncertainty sources around DRE variables


Step 3

Velocity calibration (lab and field)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.03.0

2.5

2.0

1.5

1.0

0.5

0.0 LAB TEST

Dis

tanc

e fro

m th

e su

rface

(ft)

Total velocity(ft/s)

StreamPro_1 StreamPro_2 FlowTracker

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.01.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

Dis

tanc

e fro

m th

e su

rface

(ft)

Total Velocity(ft/s)

StreamPro_1 before Flowtracker StreamPro_2 before Flowtracker StreamPro_1 after Flowtracker StreamPro_2 after_Flowtracker FlowTracker

Field Test

+/-4.55 % uncertainty in depth-averaged velocity

5.24 % uncertainty in depth-averaged velocity


Step 3

Laboratory tests Field tests

Sampling duration (mean velocity)

Moving average for velocities in individual bins

Moving average for depth-averaged velocity (bulk flow velocity 2 ft/s)

0.23%


Step 3

Number of verticals


Step 3

Obvious display of the effect of site condition on the uncertainty (narrow & shallow stream with considerable flow through the edges)

Edge discharge

cfsQQQQQQQQ LRLRLRLLE 996.082.33318.218.236.136.1 =++++++=

cfsvbdQLE 4.13535.0 1 ==

Option 1

Option 2 -

cfsvbdQLE 98.121

1 ==

Q1.36L Q1.36R Q2.18L Q2.18R

Q3L Q3R Q3.82L

Reference edge discharge:

Estimated edge discharge :1.24 % uncertainty

0.54 % uncertainty


Step 3

Summary Assessment of uncertainty sourcesSource Type Standard uncertainty, u(xi) Estimation source

Sources associated with the mean velocity in verticals,

Instrument accuracy B 0.0016ft/s (0.0005 m/s) RDI

Instrument calibration ALab

(vs. Flowtracker)Field

(vs. Flowtracker) Field/laboratory tests

± 4.55% ±5.24%Sampling time B 0.23% Field tests

Near transducer B Not evaluated -

Vertical velocity model B Variable (see Section IV.1.4.2.1.5) ISO 1088(2007) Table F.1

Flow angle correction BVariable (see Section IV.1.4.2.1.6)

(Not active)Huang (2012)

Operational conditions A ± 0.021 ft/s (0.006 m) Field testsSources associated with the depth in verticals, d

Instrument accuracy B 0.005ft RDI

Instrument calibration A

Lab(vs. wading rod)

Field(vs. wading rod)

Field/laboratory tests± 0.032ft(0.001 m)

± 0.059ft(0.002m)

Operational conditions A 0.006ft (0.002m) Field testsSources associated with the distance between verticals, b

Instrument accuracy B 0.003ft (0.0009 m) Scale resolutionOperational conditions A 0.05ft (0.015m) WMO(2011)

Sources associated with the estimation of discharge, QtDischarge model B 0.50% Muste et al. (2004)

Number of verticals B 0% Field tests

Edge discharge model B 2.48% (Option1) and 1.08% (Option2) Field tests

Flow unsteadiness B Not active -

Operational conditions B Not active -


Step 3

Uncertainty propagation to result (QMSys)


Steps 4-5

Final UA results

Discharge Method Estimated Q(cfs)

Expanded uncertainty

(cfs)

Expanded uncertainty (%)

Qm QMsys SxS 20.036 ± 0.862 ± 4.30

Qm WinRiver II (traverse) 19.412 - -

Qt Qmsys SxS(Option 1) 40.33 ± 2.33 ± 5.79

Qt QMsys SxS(Option 2) 39.738 ± 1.494 ± 3.76

Qt WinRiver II (traverse) 40.228 - -

Uncertainty budget for Qm (from QMSys) Uncertainty budget for Qt (Option1, from QMSys)


& decision-making hintsStep 6

UA is doable using available frameworks (as opposed to standards specific to individual instruments)

UA protocols converge toward common ground (compared with 50 years ago); e.g., Joint Committee for Guides in Metrology works toward unifying and grouping standards rather than expanding them (the ISO approach)

Visible agencies, such as WMO, propose the adoption of the “Guide to Expression of Uncertainty in Measurement” (GUM, 1993) for measurements and modeling of hydrologic processes.

Automation of laborious UA calculations in generic software promises smooth progress toward the extension of UA usage

Lessons learned

Resistance to UA adoption

The case specific vs. generalized UA requires conceptualization and extensive effort. Fortunately, the digital and open communication make the task of centralizing information easier than ever before

Many UA efforts undergoing in various water- related areas. There is, however, little communication among the disciplines.

Multiple approaches used for hydroscience (e.g., Monte Carlo simulations, First-order second-moment, Point estimate method, Logic tree analysis) but specialized fora (ASCE, ISO –Hydrometry, etc) have not agreed on a common methodology

Challenges remain

UA in a new (hot-off the press) book

Experimental Hydraulics

The first comprehensive book on hydraulic experimentation (from design to data reporting, from lab to field, from simple to complex experimentation):

1. Experimental Hydraulics, volume 1: Fundamentals and Methods; edited by M. Muste, D. Lyn, D. Admiraal, R. Ettema, V. Nikora, M.H. Garcia HB; ISBN: 978-1-138-03816-5; Price: UK£ 115.00/US$149.95; 500 pages

2. Experimental Hydraulics, volume 2: Instrumentation and Measurement Techniques; edited by J. Aberle, C. Rennie, D. Admiraal, M. Muste, HB; ISBN: 978-1-138-03815-8; Price: UK£ 115.00/US$149.95; 450 pages

Thank you

Questions?

Questions?

Questions?

66

Slide Number 1Critical review of UA methodologies/standardsCritical review of UA methodologies/standardsSynthesis of GUM (1993) MethodologyGUM (1993) Methodology: step-by-stepGUM (1993) Methodology: step-by-stepGUM (1993) Methodology: step-by-stepGUM (1993) Methodology: step-by-stepGUM (1993) Methodology: step-by-stepSynthesis of GUM (1993) MethodologySlide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Thank you

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Uncertainty analysis of Acoustic-Doppler Current Profilers ... · ADCP and flow characteristics...

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