quantifying and controlling error in salt dilution flow measurements gabe sentlinger (ard), andre...

AR s

Quantifying and Controlling Error in Salt Dilution Flow Measurements

Gabe Sentlinger (ARD), Andre Zimmermann (nhc),Mark Richardson (UBC), John Fraser (ARD)

AR s Quantifying Uncertainty

-We want to identify sources of error/uncertainty and control for them. -Ensure calibration, repeatability, linearity of method.

TCFdtbgECtEc

MassQ

.)()(

TCF

TCF

dt

dt

bgECtEC

bgECtEC

M

M

Q

Q

.

.

)()(

)()(

Components of Error

Lower Range

Upper Range Notes

Mixing 0% >200%Can be eliminated with long mixing length

Salt Mass <1% 10%Can be nearly eliminated with careful procedures

CF.T <1% 10% Temperature Compensation

BG EC.T <1% >40% Depending on SNR and EC.T Drift

Sensor Resolution <1% >40% Baseline and SNR

Summary <4% >300%

EC.T Uncertainty

AR s Salt Dilution Tracer Method

AR s Salt Dilution Tracer Method

Criteria [Cl] mg/l [NaCl] (mg/l) Peak over BGTaste 200 330 687

Benthic 800 1319 2747

ISO9555-3

-Previous studies have suggested a multiplier over background (ie 50% - 500%).-We recommend a SNR approach instead.-For Inst. Resolution of 0.1 uS/cm and low BG noise, a rise of 10 uS/cm is a SNR of 100. This introduces only 1% uncertainty into measurement.-Avoid Overdosing!

(from Moore, 2005)

Goals:1-Quantify Uncertainty2-Reduce Uncertainty and/or Dosage

Area/Doses*mg/l 10 30 60 10 30 60

200 5 2 1 10 3 2500 13 4 2 26 9 4

1,000 25 8 4 52 17 92,000 50 17 8 104 35 174,000 100 33 17 208 69 35

NOTESA) Peak : Average Factor 15

Peak mg/l for Transit Time (mins) Peak EC.T over BG EC.T for Transit Time (mins)

AR s

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4

Dosage (kg/cms)

Pe

ak

ov

er

BG

EC

.T

60 mins

30 mins

10 mins

Peak over BG EC.T

-Typically we are aiming for a Peak over BG EC.T of 10-30 uS/cm, with at least a sensor resolution of 0.1uS/cm. If 1uS/cm resolution, then larger peak over BG EC.T is needed (larger dose). Larger dose needed for longer transit time. Inject large doses slooooowwwwwllllyyy.

AR s Duration of Injection not important

-Injection rate not important. Better to ensure it doesn’t sink to bottom and avoid WQ guideline problems at point of injection. Better to spread injection out.

-There is no significant difference between Pulse 1 (instantaneous) and Pulse 2 (slowly over 1min) or Pulse 1+Pulse 2 (sum of both masses).

90

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10/17/14 7:53 10/17/14 7:56 10/17/14 7:59 10/17/14 8:02 10/17/14 8:05 10/17/14 8:08 10/17/14 8:11 10/17/14 8:13

DateTime

EC

.T(u

S/c

m @

25

C)

EC

(u

S/c

m)

EC.T

FINAL EC.T

Baseline

Start Baseline

End Baseline

S

E

Pulse 1

Q=0.085 m3/sUnc. =±3.7%

Pulse 2

Q=0.083 m3/sUnc. =±3.5%

Pulse 1 + 2

Q=0.0846 m3/sUnc. =±3.3%

AR s Lowest Fruit: Mixing Error

0.0

20.0

40.0

60.0

80.0

100.0

120.0

1/13/13 10:12 1/13/13 10:13 1/13/13 10:14 1/13/13 10:16 1/13/13 10:17 1/13/13 10:19 1/13/13 10:20 1/13/13 10:22

Date:Time

De

lta

[N

aC

l] m

g/m

l

Left Bank

Thalweg

Right Bank

• Difficult to quantify missing error. Multiple probes, or injections, can help determine appropriate mixing reach for given Q

• This is a single pulse measured on left and right bank, and thalweg. Standard Deviation ±21%.

Left Bank Q = 0.245 cmsThalweg Q = 0.297 cmsRight Bank Q = 0.345 cmsAverage Q = 0.304 cmsSwoffer Q = 0.297 cms

(from Carnation Creek, B.C. Courtesy of Robin Pike, MOE)

AR s Instrument Accuracy/Resolution

– What is the limit of the instrument?– This is a Unidata 6536B with resolution of 0.01 uS/cm but

accuracy of 0.5% of the reading. We found quanta of 0.4-0.6 uS/cm (+/-0.35%)

60

62

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80

4/13/12 13:40 4/13/12 13:55 4/13/12 14:09 4/13/12 14:24 4/13/12 14:38 4/13/12 14:52 4/13/12 15:07 4/13/12 15:21 4/13/12 15:36Elapsed Time (s)

EC

.T@

25oC

(u

S/c

m)

EC

(u

S/c

m)

CCTBackground C (uS/cm/oC)Background CT (uS/cm)Alt_BaselineALT CT

1.3 kg/cms3.01 cms ± 11%

0.69 kg/cms3.68 cms ± 11%

0.29 kg/cms3.52 ± 16% 0.17 kg/cms

3.07 ± 104%

Unidata 6536BRes: 0.01 uS/cmAccuracy: 0.5%

step = 0.4-0.6 uS/cm = 0.7% = ± 0.35%

AR s Instrument Accuracy/Resolution

– Oakton Con110 has better accuracy and resolution at lower ranges, higher SNR, therefore less uncertainty in Q.

70

75

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85

90

95

100

4/13/12 13:40 4/13/12 13:55 4/13/12 14:09 4/13/12 14:24 4/13/12 14:38 4/13/12 14:52 4/13/12 15:07 4/13/12 15:21 4/13/12 15:36Elapsed Time (s)

EC

.T@

25oC

(u

S/c

m)

EC

(u

S/c

m)

CCTBackground C (uS/cm/oC)Background CT (uS/cm)Alt_BaselineALT CT

1.33 kg/cms3.03 cms ± 4%

0.69 kg/cms2.90 cms ± 6%

0.29 kg/cms2.88 ± 6%

0.16 kg/cms2.96 ± 13%

Oakton CON110AutoRangingRes: 0.05% FullScale Accuracy: 1% FS + 1 digit0-20 uS/cm: 0.01 uS/cm, ±0.2 uS/cm20-200uS/cm: 0.1 uS/cm, ±2 uS/cm

step = 0.1 uS/cm

AR s

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

0 1000 2000 3000 4000 5000 6000 7000

Elapsed Time (s)

CT(u

S/c

m/o

C)

C (

uS

/cm

)

Measured

Modeled

Initial study examined SNR

– Difficult to assess true error without knowing Q.– Built an Instrument Model to model SNR. Random noise and Sensor

Resolution. Random noise is not divided between real and sensor. Modeled is simple chi-squared function.

– Noise in SNR includes quantization noise.– When Noise < Resolution, bias is likely, depending on background EC.T– Max Error is worst out of 20 simulations (α≈0.05)

0.0

5.0

10.0

15.0

20.0

25.0

0 1000 2000 3000 4000 5000 6000 7000

Elapsed Time (s)

CT(

uS

/cm

/oC

)

C (

uS

/cm

)

Measured

Modeled

Noise = 5, Res = 10, SNR = ~2, MaxE≈15% Noise = 1, Res = 1, SNR≈40, MaxE≈1.5%

Noise < Resolution = Bad

AR s

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0 1000 2000 3000 4000 5000 6000 7000

Elapsed Time (s)

CT(u

S/c

m/o

C)

C (

uS

/cm

)

Measured

Modeled

– Best Instrument for SD is• High Resolution and Quanta (0.1 uS/cm or better for EC.T <200uS/cm)• Repeatable, Linear, Stable (these are different than accuracy).• Absolute calibration not necessary if insitu CF.T derivation carried out

for each site.• Benefit of absolute calibration is that it gives expected CF.T values for

QA/QC.

-5.0

0.0

5.0

10.0

15.0

20.0

0 1000 2000 3000 4000 5000 6000 7000

Elapsed Time (s)

CT(u

S/c

m/o

C)

C (

uS

/cm

)

Measured

Modeled

Noise = 5, Res = 1, SNR ≈ 4, MaxE ≈ 13%

Noise > Resolution = Good

Noise = 1, Res = .1, SNR ≈ 90, MaxE ≈ 3%

Noise > Resolution = Good

Initial study examined SNR

AR s

Need for fast, accurate, reproducible method

– Reduce the amount of salt required for a given flow/ reduce uncertainty associated with salt dilution measurement.

– Establish SOP to ensure data quality and traceability, quantify uncertainty, and protect sensitive habitat.

Showing 95% Confidence (2s) results

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

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15%

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17%

18%

19%

20%

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Salt Injection Concentration (kg/cms)

%U

nce

rta

inty

in

Q (

alp

ha

= 0

.05)

Inst.Err:0.01 uS/cm and Trans.Time: 10 mins






Inst.Err:1 uS/cm and Trans.Time: 10 mins



AQUARIUS RESEARCH & DEVELOPMENT INC.

AUTOSALT

Nov 2, 2014

Uncertainty as a function of Instrument Accuracy and Transit Time

Notes:1) This plot shows the relationship between instrument error and required salt slug injection concentration.2) The "Inst.Err." value is the uncertainty in the measurement, which is a function of the signal stability, the instrument resolution, and instrument accuracy.3) The current acceptable range of uncertainty and Injection concentration excludes instrument error of 1 uS/cm and transit time greater than 10 mins.4) The target range is primarily from an Instrument Error of 0.01 uS/cm. This resolution is not available on most commercial sensors when the baseline conductivity is greater than 20 uS/cm.5) Assumes complete mixing, stable background conductivity, and insignificant error from Concentration Factor and Salt Mass measurement. Uncertainty in background conductivity included.

Acceptable Range

Target Range

C:\Users\gsentlin\AQUARIUS_R&D\BUSINESS\Research&Development\Conferences\AWRA_Virginia\CF.T Calcs\[Raffuse_SD-CM_Apr 13 2012_InstrumentNoiseModel_v0.9.xls]Notes

AR s

– I generally use 10 points pre and 10 points post. I use SE of entire 20 point sample. This takes into account changing BG or incomplete trace.

– EC.T Unc. is larger of SE and ½ Sensor Resolution

Uncertainty in Area under Pulse

n

sSE TBGEC

TBGEC.

.

RSEUncTEC TBGEC 21,max. .

– Determine Standard Error (SE) of mean for pre- and post-.

– Assume SE is representative of signal and background error

n

sSE TBGEC

TBGEC.

.

AR s Uncertainty in Area under Pulse

– Noise = EC.TUnc*Trans.Time– Signal=Area under curve

=AverageEC.T*Trans.Time

– SNR=AverageEC.T/ECTUnc.– AreaUnc. = 1/SNR– Example:– Area under curve =1228

sec.uS/cm– Noise = 89.2 sec.uS/cm– SNR= 1228/89

=13.8 or 7.3% or 14.6% uncertainty at α=0.05

– *In most figures, ± 1σ is reported although most people think of error as ± 2σ.

AR s

-30%-25%-20%-15%-10%

-5%0%5%

10%15%20%25%30%35%40%45%50%55%60%

0 10 20 30 40 50 60 70 80 90

Index

De

lta

Q (

%)

Total

Delta Q vs Sqrt(Unc.12 + Unc.22)

-This figure shows the result of ~343 recent measurements.-87 Concurrent measurements.

#57#30

#61

AR s Discrepancy in #30

-#30 Mixing length too short.-DQ = 18.5%-Indicators: Shape of pulse not smooth.-DQ is larger than Unc1 + Unc2.-CM measurement was 3.3 m3/s.

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6.5

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10.0

5/20/147:55

5/20/148:02

5/20/148:09

5/20/148:16

5/20/148:24

5/20/148:31

5/20/148:38

5/20/148:45

5/20/148:52

5/20/149:00

5/20/149:07

5/20/149:14

DateTime

EC

.T(u

S/c

m @

25

C)

EC

(u

S/c

m)

0

2

4

6

8

10

12

14

Te

mp

era

ture

(oC

)

FINAL EC.T

Baseline

Start Baseline

End Baseline

S

E

Temp

Temp Spike removed from EC.T

Measurement stopped pre-maturelyEC.T Trace filled in. Q=4.9 m3/s

Unc. =±5.8%

6.0

6.5

7.0

7.5

8.0

8.5

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10.0

5/19/14 7:55 5/19/14 8:02 5/19/14 8:09 5/19/14 8:16 5/19/14 8:24 5/19/14 8:31 5/19/14 8:38 5/19/14 8:45 5/19/14 8:52

DateTime

EC

.T(u

S/c

m @

25

C)

EC

(u

S/c

m)

0

2

4

6

8

10

12

14

Tem

per

atu

re (

oC

)

EC.T

FINAL EC.T

Baseline

Start Baseline

End Baseline

S

E

ALT EC

Temp

Measurement stopped pre-maturelyEC.T Trace wasn't filled in.

Much larger area

Q=4..14 m3/sUnc. =±4.3%


-#57 Mixing length too short.-DQ = 52%-Indicators: Shape of LB pulse and-DQ is larger than Unc1 + Unc2.

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9/12/1416:59

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DateTime

EC

.T(u

S/c

m @

25C

)E

C (

uS

/cm

)

0

5

10

15

20

25

Tem

per

atu

re (

oC

)

FINAL EC.T

Baseline

Start Baseline

End Baseline

S

E

ALT EC

Temp

Center

Q=0.05 m3/sUnc. =±10.2%

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DateTime

EC

.T(u

S/c

m @

25C

)E

C (

uS

/cm

)

0

5

10

15

20

25

Tem

per

atu

re (

oC

)

FINAL EC.T

Baseline

Start Baseline

End Baseline

S

E

ALT EC

Temp

LB

Q=0.10 m3/sUnc. =±14.7%


-#61 Large temperature compensation, temperature change, dosage too low.

-DQ = 18%, 1.1 kg/m3/s.-Indicators: BG ECT not steady-CM measurement was 10.2 m3/s.

70

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130

9/16/14 12:00 9/16/14 12:14 9/16/14 12:28 9/16/14 12:43 9/16/14 12:57 9/16/14 13:12 9/16/14 13:26DateTime

EC

.T(u

S/c

m @

25

C)

EC

(u

S/c

m)

5

5.5

6

6.5

7

7.5

8

Te

mp

era

ture

(oC

)

QM4.0_TM3.1_ECT

QM4.0_TM2.5_ECT

Baseline

Start Baseline

End Baseline

S

E

QM4.0_TM2.5_EC

QM4.0_TM2.5_Temp

TM3.1 on RB

Q = 10.5 m3/s%Unc. = 4.0%

TM2.5 on LB

Q = 8.9 m3/s%Unc. = 4.6%

AR s Experimental Setup

-Typical setup with one probe mid-channel upstream, second probe left bank downstream.

-DQ and %Unc. Calculated in realtime to aid in decision making.

T-HRECS on CH1

QuickFlask

DuckBox

QiQuac

T-HRECS on CH0

QuickFlock on CH1

100

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125

10/15/14 9:46 10/15/14 9:48 10/15/14 9:51 10/15/14 9:54 10/15/14 9:57 10/15/14 10:00 10/15/14 10:03 10/15/14 10:06 10/15/14 10:09

DateTime

EC

.T(u

S/c

m @

25

C)

EC

(u

S/c

m)

US-MID

DS LB

Baseline

Start Baseline

End Baseline

S

EDS-LB Q= 0.078±7%

US-MID Q= 0.087±7%

US-MID Q= 0.090±13%

DS-LB Q= 0.093±15%

-US-MID higher peak, earlier, but approximately the same area (no significant difference between derived Q at 95% confidence)

AR s

Total SDIQ %Uncertainty vs Dosage vs EC.T Unc.

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0 1 2 3 4

Dosage (kg/cms)

To

tal

%U

nc

ert

ain

ty

0.02 µS/cm

0.1 µS/cm

1 µS/cm

Total % Uncertainty

-This figure shows the result of 343 recent measurements (2013-2014).-Lowest Uncertainty when EC.T Unc. is smallest.-Baseline of ~3% Uncertainty from CF.T and NaCl Mass.

Total <10% <5% <3%343 270 57 4

100% 79% 17% 1%

AR s

%Uncertainty due to EC.T Unc.

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30%

0 0.2

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%U

nc

ert

ain

ty

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0.1 µS/cm

1 µS/cm

% Uncertainty due to EC.T Unc.

-Remove Unc. Due to CF.T and Mass.-Unc. Due to SNR steady at 5% until ~0.7 kg/cms

Total <10% <5% <3%343 303 275 225

100% 88% 80% 66%

AR s

EC.T.Uncertainty = 0.1 uS/cm

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10%

15%

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30%

0 0.2

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4

Dosage (kg/cms)

%U

nc

ert

ain

ty

60 mins

30 mins

10 mins

Target Range

-We can further explain variance by transit time of pulse.-The faster the transit time, assuming completely mixed, the lower the

uncertainty.-0.1 µS/cm typical of many commercial sensors for EC.T < 200 µS/cm.

% Uncertainty due to EC.T Unc.:0.1µS/cm

Total <10% <5% <3%185 164 146 115

100% 89% 79% 62%

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30%

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AR s

Inst.Uncertainty = 0.1 uS/cm

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30%

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4

Dosage (kg/cms)

%U

nc

ert

ain

ty

60 mins

30 mins

10 mins




Target Range

I compared to my 2012 estimates of Uncertainty (x0.5 to get 1σ). Good agreement with 0.1 µS/cm above 1 kg/cms, but overestimated for less than 1 kg/cms.

% Uncertainty due to EC.T Unc.:0.1µS/cm

AR s

EC.T.Uncertainty= 0.02uS/cm

0%

5%

10%

15%

20%

25%

30%

0 0.2

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1.8

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2.8

3 3.2

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3.8

4

Dosage (kg/cms)

%U

nc

ert

ain

ty

60 mins

30 mins

10 mins

Target Range

% Uncertainty due to EC.T Unc.: 0.02 µS/cm

-If we can attain EC.T Unc. of 0.02 µS/cm (requires finer than 0.02 µS/cm resolution), then we can reduce the dose to 0.2 kg/cms and remain below 5% Uncertainty.

Total <10% <5% <3%114 114 110 99

100% 100% 96% 87%

AR s

EC.T.Uncertainty= 0.02uS/cm

0%

5%

10%

15%

20%

25%

30%

0 0.2

0.4

0.6

0.8

1 1.2

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1.8

2 2.2

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2.8

3 3.2

3.4

3.6

3.8

4

Dosage (kg/cms)

%U

nc

ert

ain

ty

60 mins

30 mins

10 mins




Target Range

% Uncertainty due to EC.T Unc.: 0.02 µS/cm

- Good agreement with 0.02 µS/cm.- Used 0.02 µS/cm because Inst.Res 0.01 µS/cm but still shows

noise, partly due to temperature.

AR s

-EC.T Unc. Ceiling 1 µS/cm or greater. Combined sensor resolution, background noise, and return to background EC.T.

-Only two measurements in target range.-Possible to get high quality measurement, but requires larger dose.

EC.T. Uncertainty = 1uS/cm

0%

5%

10%

15%

20%

25%

30%

0 0.2

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1 1.2

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2.8

3 3.2

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4

Dosage (kg/cms)

%U

nc

ert

ain

ty

60 mins

30 mins

10 mins

Target Range

% Uncertainty due to EC.T Unc.: 1µS/cm

Total <10% <5% <3%44 25 19 11

100% 57% 43% 25%

AR s

EC.T. Uncertainty = 1uS/cm

0%

5%

10%

15%

20%

25%

30%

0 0.2

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1 1.2

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3 3.2

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3.8

4

Dosage (kg/cms)

%U

nc

ert

ain

ty

60 mins

30 mins

10 mins



Target Range

% Uncertainty due to EC.T Unc.: 1µS/cm

- Unc. Overestimated for EC.T Unc. = 1 us/cm. Not sure why yet

AR s Recommendations

– The relationship shown in previous figures is tabulated here for two data classes. NaCl dose depends on EC.T Unc. and transit time.

– Most common EC.T Unc. and transit time (0.1 uS/cm and 30 mins) requires 1.1 kg/cms to attain ±5% at 95%confidence.

– Shorter transit time or lower EC.T Unc. results in lower dose required.– Rule of Thumb:

• 10x the EC.T Unc. at 30 mins. Except at 1uS/cm use 2kg/cms.• Half the dose for 10 mins, double for 60 mins.

– Best Practice: Pre-dissolve or inject slowly (>30 second).

C:\Users\gsentlin\AQUARIUS_R&D\BUSINESS\Research&Development\Conferences\AWRA_Virginia\CF.T Calcs\[Raffuse_SD-CM_Apr 13 2012_InstrumentNoiseModel_v0.9.xls]SNR_%Error 10/31/14

(2.5% SE) (5.0% SE)EC.T Unc. (µS/cm) 10 30 60 EC.T Unc. (µS/cm) 10 30 60

0.01 0.04 0.11 0.21 0.01 0.02 0.06 0.130.02 0.07 0.21 0.42 0.02 0.04 0.13 0.250.1 0.35 1.1 2.1 0.1 0.2 0.6 1.31 1.2 2 5 1 0.8 1.2 6

NOTES

B) Dose estimates from the EC.T Unc. = 1 uS/cm are estimated visually from scatter plots.

VER 0.6

A) EC.T Unc. Is the total uncertainty in the measurement due to Instrument Resolution, BG Noise, drifting background (due to temperature or EC).

Transit Time (mins)Transit Time (mins)Dose (kg/cms) Required for 5% Uncertainty at 95% Dose (kg/cms) Required for 10% Uncertainty at 95%

AR s Acknowledgements

T-HRECS on CH1

QuickFlask

DuckBox

QiQuac

T-HRECS on CH0

QuickFlock on CH1

100

105

110

115

120

125

10/15/14 9:46 10/15/14 9:48 10/15/14 9:51 10/15/14 9:54 10/15/14 9:57 10/15/14 10:00 10/15/14 10:03 10/15/14 10:06 10/15/14 10:09

DateTime

EC

.T(u

S/c

m @

25

C)

EC

(u

S/c

m)

US-MID

DS LB

Baseline

Start Baseline

End Baseline

S

EDS-LB Q= 0.078±7%

US-MID Q= 0.087±7%

US-MID Q= 0.090±13%

DS-LB Q= 0.093±15%

Thank you

Jane Bachman, EDI YukonDave Hutchinson, WSCRobin Pike, BC MOEDan Moore, UBC

Questions?

quantifying and controlling error in salt dilution flow measurements gabe sentlinger (ard), andre...

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