camels- uncertainties in data

CAMELS- uncertainties in data

Bart Kruijt, Isabel van den Wyngaert, Ronald Hutjes, Celso von Randow, Jan Elbers, Eddy Moors...

Types of data

• Land use, Site parameters•accuracy•representativity

• driving variables (weather)•instrument error/precision•technical/ operational error•siting error

• validation/optimisation data (fluxes)

•stochastic error•technical/ operational error•calculation/conceptual uncertainty•representation of surface

• day • night

vegetation height, LAI, d, z0, rooting …

heterogeneity, sampling

cup anemometer stalling, hygrometers.. calibration, dew on radiation sensor,..Sheltering, shading, …

=(w2c2) *T/ Tscale --> fourth momentscalibration, pump maintenance, window cleaningaveraging time, coordinate rotation, freq. corr

footprint models, heterogeneity, win directioncalm nights drainage, return fluxes

CO2

?

Fc =.w.c

NEE = Fc + z(c/ t)

Eddy correlation

Eddy correlation hopeless?

Raw data

Convert to physical units

Range check and despike

Remove tube delays

High pass filter Rotate, 1, 2, 3

covariances

Frequency correct high low

Convert to area base

Correct calibration

NEE

Pre-rotate?

High pass filter

Rotate, 1, 2, 3 covariances

Storage fluxes

Average T and P

no yes

Each processing step carries uncertainty

Time

Sensitivity to flux calculation methods

Rotation: correction for tilt of mean streamlines

Detrending and averaging:removing non-stationarity

Length scale (m)

1 10 100 1000 10000

Sca

le C

O2

fluxe

s (

mol

/m2 /s

)

-4

-3

-2

-1

0

1

wet seasondry season

CO2 Fluxes (SW Amazon) - Scale contributions

‘Turbulent’ ‘Meso-scale’

Summary effects of rotation and averaging

Relative effects of averaging time and rotation on daily total fluxes, Amazon

Finnigan, Malhi, 2002

Longer averaging times --> better energy closure?

Rio Jaru dry

Time (hours)

0 6 12

Rio Jaru wet

Time (hours)

0 6 12

-10

-5

0

5

Manaus K34 dryManaus K34 wet

Ave

rage

CO

2 flu

x (

mol

m-2

s-1)

-10

-5

0

5

Total uncertainty from rotation and averaging over the day



Correct calibration

NEE

Assess night time,correct

Fill gaps

Cumulate over time


Filter out poor similarity

Ecosystem physiology

Storage fluxes

Average T and P

Manaus K34 1999-2000 CO2 calibration LiCor

[CO2] CIRAS, ppm

330 340 350 360 370 380 390 400 410 420

[CO

2]

Lic

or,

pp

m

340

360

380

400

420

1999 and 2000 DOY<170 2000 DOY 200-230 2000 DOY 230-263 2000 DOY >283

1999 and 2000 DOY<170 :b[0]=-5.81,b[1]=1.02,r ²=0.86

2000 DOY 200-230:b[0]=121.10, b[1]=0.66, r ²=0.75

2000 DOY 230-263:b[0]=-78.92, b[1]=1.22, r ²=0.91

2000, DOY > 283:b[0]=-79.18, b[1]=1.15, r ²=0.96

Uncertainty in calibration

Calibration a posteriori causes problems and uncertainty

Manaus, K34, Oct 1999-April 2000, Low night-time u*

hour of day

0 5 10 15 20

CO

2 flu

x (

mol

m-2

s-1

)

-30

-20

-10

0

10

20

Eddy flux Storage fluxBiotic flux

Manaus, K34, Oct 1999-April 2000, High night-time u*

hour of day

0 5 10 15 20

CO

2 flu

x (

mo

l m-2

s-1

)

-30

-20

-10

0

10

20

Eddy flux, storage flux and Ecosystem (‘biotic’) flux

Windy nights

Calm nights

Eddy correlation integrates everything but misses advection

0 100 200 300 400 500 600 700 800

15

30

45

60

75

90

[CO2] ppmv

Distance (m)

z (

m)

3D Test - [CO2] along topography (early morning)

300 350 400 450 500 550 600 650 700

Morning

CO2 stored in valleys

CO2 return ?

Night CO2 drainage ?

RsRs

Rs

Rs

Manaus, Amazon

Systematic error Random error on half-hourly Fc

Total one-sidederror on annualtotals for Amazon *

Spikes / noise 2% 11% 2%Tube delay errors - 3.5% <0.1%Rotation andaveraging

10% - 25% ** - 10- 25% **

Frequency losscorrections - zeroplane

0.27%(d) - 2.7 %

Frequency losscorrections - flowrate

1%(ft)/(ft*(ncf)) - <0.5%

Convert to area base 0.3 % <0.1%Calibrationcorrection

(0% - 20% for 100days)

- 0% - 6 %

Night-time losses 0% - >100% - 0% - 100%General data gaps Bias to daytimeSimilarity filter gaps Bias to night timeMissing data filling - 0.08 - 1 kg ha-1h-1, or

30 - 50 kg ha-1d-1 /(ndfit)0.25 - 1 t ha-1 y-1, or3% - 20%

(d) = uncertainty in zero-plane displacement; (ft) = uncertainty in tube flow rate ft; ncf

= number of cycles in tube flow rate;* assuming the conditions at the Manaus k34 and Jaru towers as described in this paper,(d)=10, (ft)/ft = 0.5 and ncf=4 y-1.** systematic errors appear to partly compensate between seasons, so average uncertaintymay decrease over time.

Total one-sided error for AMAZON on annual totals is, apart from night-time error, between 12.5% and 32%, or 1-2 t ha-1.

Systematic or random error?

• Error depends on measuerement height, surface type, time of day, weather

•Random error vanishes when the number of independent samples increases.

•BUT: when are atmospheric samples independent?

•Systematic error is persistent. • What if maintenance varies or calibration drifts? • What if low frequencies vary with weather or season?•---> when do systematic errors become random?

Bias. Example from the SW Amazon, with cold periods

PA

R(

mo

l.m-2

.s-1

)

0200400600800

100012001400160018002000

PAR C

O2 (

pp

m)

300

350

400

450

500

CO2 Concentrationq

Day 195 (Friagem)

CO

2 f

lux

(m

ol.m

-2.s

-1)

-30-25-20-15-10

-505

10152025303540

FCO2Tair

PA

R(

mo

l.m-2

.s-1

)

0200400600800100012001400160018002000

Sp

ecifi

c H

um

idity

(g.

kg-1

)

0

5

10

15

20

25

Te

mp

era

ture

(o

C)

1012141618202224262830

Day 192 (normal)

Other bias :

transient periods (morning, early evening) are non-stationary and carry high uncertainty

rainy periods carry high uncertainty

ideal weather associated with specific wind directions

Estimates for CAMELS

NEE day NEE night NEE, systematic night u*<0.1NEE night, u*<0.1NEE night, 0.1<u*<0.2LE LE at RH>95%H flux during rain > 10 mm h-1 additional errorsystematic err on all fluxinstrument accuracy sonic 1 1 0 1 1 1 1 1 0 0instrument accuracy licor 1 1 0 1 1 1 1 0 0 0location and footprint (Rehbmann et al) 20 20 0 20 20 30 30 20 0 0stochastic error in turbulence 20 20 0 20 20 20 20 20 0 0night-time 0 0 100 200 100 0 0 0 0 0Angle of attack 5 5 0 5 5 5 5 5 0 5Webb (density) corr (open path only) (???) 0.025515 0.025515 0 0.025515 0.025515 0.025515 0.025515 0.025515 0 0cleaning instrument 5 5 0 5 5 10 15 10 0 0calibration 5 5 0 5 5 10 0 1 0 0tube delay error ( with closed systems only) 4 10 0 10 10 10 20 0 0 0spikes 10 10 0 10 10 10 10 10 100 0lo and hi frequency errors 10 20 0 20 20 10 40 5 0 0relative uncertainty (no perc!) 0.330606 0.384318 1 2.016804 1.033199 0.377492 0.484768 0.255147 1 0.05

numbers are percentages of measured flux, error per (half-hourly) measurement pointassuming good location choice, maintenance and data treatment

Rebmann et al - CARBOEUROFLUX footprint-quality analysis

Table 4: Land-use classification and quality tests for the fluxes of momentum (includingintegral turbulence characteristics), sensible heat H, latent heat E and carbon dioxide fluxFCO2 (only stationarity) and vertical wind component. Numbers are relative to the totalnumber of investigated cases for each site.

Site AOI> 80%

flag 1-2

Hstflag 1

Estflag 1

FCO2

stflag 1wm <0.35m s

-1

BE1 79% 90% 84% 54% 83% 100%BE2 60% 83% 82% 76% 76% 100%CZ1 100% 84% 82% 53% 85% 53%FI1 70% 92% 86% 73% 93% 100%FI2 59% 93% 89% 86% 86% 100%FI3 94% 92% 92% 96% 89% 93%FR1 32% 86% 80% 64% 72% 99%FR2 93% 72% 74% 62% 79% 93%FR4 100% 87% 91% 82% 84% 100%GE1 97% 93% 90% 71% 87% 100%GE2 80% 85% 86% 81% 87% 99%GE3 86% 91% 87% 51% 80% 98%IS1 100% 89% 85% 58% 90% 92%IT4 98% 51% 60% 40% 52% 90%IT5 90% 81% 74% 85% 78% 100%IT-ext 99% 95% 79% 79% 41% 98%NL1 96% 94% 87% 49% 87% 100%UK1 100% 91% 86% 63% 92% 97%average 85% 86% 83% 68% 80% 95%

Discussion:

•How to avoid bias when applying uncertainties to model fitting?

Include more processes?Look at daily totals where day-night cross contamination occurs?

•Can we eliminate bias by better matching models and measurements?

•How to fine-tune uncertainties for specific sites or conditions?

U* • lmFc=f(C,u*,lm,R,Ps)

Advection=f(C)Advection

Consider the area beneath the sensor a leaky, sloshing vesseland fit both physiological and micrometeorological parameters

R, Ps=alpha.PAR

To be tested ….

C=sum(R-Ps-Fc-advection)

time19.8.00 10:00

20.8.00 02:00

20.8.00 06:00

20.8.00 10:00

20.8.00 02:00

20.8.00 06:00

20.8.00 10:00

Fcm

eas,

Fc

mod

el

-20

-10

0

10

20

30

leak rate = 6.8e-4 s-1R = 6.6 umol m2 s-1alpha = -0.024 umol umol-1mixing scaling = 3590.78 m

Some early results look good

Raw data



Remove tube delays


covariances

Pre-rotate?

High pass filter


no yes

CO2 flux (mol m-2 s-1)-40 -20 0 20 40 60

CO

2 f

lux

with

sp

ike

s (m

mol

m-2

s-1

)

-40

-20

0

20

40

60

data with spikes 50 ppm, 1 per 60 sdata with spikes 5 ppm, 1 per 60 s

W

-2-1012

CO

2

380

390

seconds

0 60 120 180 240 300

375

400

425

Manaus K34

GMT=local time + 4 hours

0 6 12 18 24

CO

2 flu

x (

mo

l m-2

s-1)

-25

-20

-15

-10

-5

0

5

10

15

5 ppm spike50 ppm spikeno spike

Manaus k34, July 2000

noise to signal ratio in CO2 concentration

0.1 1 10

Rel

ativ

e un

cert

aint

y in

CO

2 f

lux

0.1

1

10

y = 0.18*x0.72

Effect of spikes in one channel only

5 ppm and 50 ppm spike on CO2.Effect is random relative uncertainty,increasing with spike/signal ratio

Raw data



Remove tube delays


covariances

Pre-rotate?

High pass filter


no yes

2 October 1999, 8:00

Delay (s)

0 2 4 6 8 10

w't'

co

vari

an

ce (

m s

-1 K

)

-0.005

-0.004

-0.003

-0.002

-0.001

0.000

0.001

0.002

w'c

' co

vari

an

ce (

m s

-1

mo

l mo

l-1)

0.102

0.104

0.106

0.108

0.110

0.112

0.114

0.116

0.118

w'q

' co

vari

an

ce

(m s

-1 m

mo

l mo

l-1)

0.0050

0.0052

0.0054

0.0056

0.0058

0.0060

0.0062

0.0064

w't'w'c'w'q'

2 October 1999, 11:30

w't'

cov

aria

nce

(m s

-1 K

)

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.16

w'q

' cov

aria

nce

(m

s-1

mm

ol m

ol-1

)

0.075

0.080

0.085

0.090

0.095

0.100

w'c

' cov

aria

nce

(m s

-1

mol

mol

-1)

-0.40

-0.38

-0.36

-0.34

-0.32

-0.30

-0.28

-0.26

2 October 1999, 11:30

w't'

cov

aria

nce

(m s

-1 K

)

-0.0010

-0.0005

0.0000

0.0005

0.0010

0.0015

0.0020

w'q

' cov

aria

nce

(m

s-1

mm

ol m

ol-1

)

-0.0010

-0.0009

-0.0008

-0.0007

-0.0006

-0.0005

-0.0004

w'c

' cov

aria

nce

(m s

-1

mol

mol

-1)

-0.13

-0.12

-0.11

-0.10

-0.09

-0.08

-0.07

-0.06

Uncertainty in tube delay calculations

Manaus k34

Fc(lag0.5) mol m-2s-1

-40 -30 -20 -10 0 10 20 30 40

Fc(

lag3

.5) m

ol m

-2s-1

-40

-20

0

20

40

Manaus K34

GMT = local + 4 hours

0 6 12 18 24

CO

2 flu

x (

mol

m-2

s-1)

-20

-15

-10

-5

0

5

10

Ave

rage

frac

tion

of s

ucce

ssfu

l de

lay

calc

ulat

ions

0.55

0.60

0.65

0.70

Fc(lag3.5)= -0.35+0.78*Fc(lag0.5)

Raw data



Remove tube delays


covariances

Pre-rotate?

High pass filter


no yes

Cv. Fc

(sd/avg)cv. E(sd/avg)

Abs. Sd Fc

(kg ha-1d-1)Abs. Sd E(MJ m-2d-1)

Total Rnet

(MJ m-2d-1)Manaus K34 average 0.10 1.97Rio Jaru average 0.25 3.47Manaus C14 (wet) 0.10 0.56 13.0 *Manaus K34 wet 0.14 3.29Rio Jaru wet 0.43 0.09 7.56 0.63 12.7Manaus K34 dry 0.15 0.08 2.24 0.61 14.6Rio Jaru dry 0.27 2.83

EffectIncreasing averaging time

30-120 min.True lateral

rotationDetrended

lateral rotationC

on

dit

ion

Ver

tica

lro

tati

on

on

ly

Ver

tica

l an

dla

tera

lro

tati

on

Ver

tica

l an

dd

etre

nd

edla

tera

lro

tati

on

30 m

in

120

min

30 m

in

120

min

Manaus K34 Fc 0.96 0.95 0.95 0.94 0.93 0.97 0.95

Rio Jaru Fc 0.74 0.71 0.85 0.84 0.92 1.00 1.15

Manaus K34 E 0.99 1.08 1.03 0.94 1.01 0.99 1.02

Rio Jaru E 0.98 1.13 1.07 0.88 0.99 0.97 1.04

Manaus C14 E 1.04 1.10 1.09 0.92 0.97 0.93 0.98

Summary effects of rotation and averaging

Variation in sensitivities to treatments

Relative effects of averaging time and rotation

Reference Run1 Run2 Run3 Run4 Run5 Run6 Run7Time constant 200 s * * * * *

800 s * * *Averaging time 30 min * * * * *

120 min * * *Low freq.correction

Yes * * * * *

No * * *Lateral rotation Yes * * * * *

No * * *

reference run1 run2 run3 run4 run5 run6 run7

Car

bon

flux

(g C

m-2

)

-20

-15

-10

-5

0



Correct calibration

NEE


Fill gaps

Cumulate over time




Storage fluxes

Average T and P

K34, 2-12 October 1999

GMT = local time+4 h

0 6 12 18 24

Frequen

cy correc

tion ( m

ol m

-2s-1

)

-2

-1

0

1

2

Only high frequency correctionsOnly high frequency corrections, low flow rateAll frequency correctionsAll frequency corrections, d=30 m

Frequency corrections

Zero-plane, tube NOT important. Low frequencies ARE important.



Correct calibration

NEE


Fill gaps

Cumulate over time




Storage fluxes

Average T and P

Manaus k34

GMT= local + 4 hours

0 6 12 18 24

Ave

rag

e ai

r m

ola

r de

nsity

(m

ol m

-3)

40.0

40.2

40.4

40.6

40.8

41.0

Atm

osp

he

ric P

ress

ure

(h

Pa)

1006

1007

1008

1009

1010

1011

1012

1013

1014

Conversion ppm m s-1 to area based fluxes

Small potential errors average out over days



Correct calibration

NEE


Fill gaps

Cumulate over time




Storage fluxes

Average T and P

Similarity relations - representativity for surface

Filtering for poor similarity will discard important periods such as early morning

Jaru, 1999-2000

u*

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w

)

0.0

0.5

1.0

1.5

2.0

b[0]=0.05b[1]=1.16r ²=0.91

(z-d)/L (stable)

0.1 1 10 100

1

10

-(z-d)/L (unstable)

0.1110100

(w

)/u*

1

10

-0.1 < z/L < 0.1

Jaru 50%-100%

Ave

rag

e d

aily

car

bo

n fl

ux

(T h

a-1 d

-1)

-0.04

-0.02

0.00

0.0210-day average daily total fluxfit to only even 10-day periodsfit to only odd 10-periods

Col 61 vs fit tots

Jaru 25%

Jan 99 Jul 99 Jan 00 Jul 00 Jan 01

Ave

rage

dai

ly c

arbo

n flu

x (T

ha-1

d-1)

-0.04

-0.02

0.00

0.02 10-day average daily total fluxfit to every 2nd in 4 10-day periodsfit to every 4th in 4 10-day periodsfit to every 1st in 4 10-day periodsfit to every 3rd in 4 10-day periods

Jaru 12.5%

Jan 99 Jul 99 Jan 00 Jul 00 Jan 01

10-day average daily total fluxfit to every 1st in 8 10-day periodsfit to every 2nd in 8 10-day periodsfit to every 3rd in 8 10-day periodsfit to every 4th in 8 10-day periods

Uncertainty as a function of the percentage good data - Rebio Jaru

Percentage annual data coverage

0 10 20 30 40 50 60 70 80 90 100

Cum

ula

tive

sta

nda

rd e

rror

of e

stim

ate

(T h

a-1y-1

)

0.0

0.5

1.0

1.5

2.0

2.5

Number of full data days per year

0 50 100 150 200 250 300 350

JaruManaus K34

Uncertainty on annual totals from (well distributed) data gaps

And finally….

camels- uncertainties in data

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