EO-HYDRO Progress Meeting – Milan, 9 November 2006 Benefit/Cost analysis for SWE estimation based...

EO-HYDROEO-HYDRO Progress Meeting – Milan, 9 November 2006

Benefit/Cost analysis for SWE estimation based on the EQeau

approachKarem Chokmani

Service utility review, CanadaService utility review, Canada

Pierre Vincent


2

Benefit/cost analysis outlineBenefit/cost analysis outline

• Introduction• Objective• The EQeau model• Benefit/cost analysis methodology• Uncertainties in SWE estimated using EQeau

approach• Uncertainties in SWE estimated using conventional

approach• Benefit/cost ratio calculation• Summary


3

IntroductionIntroduction

• Snow water equivalent (SWE) is a key parameter in

hydroelectric production forecast

• Forecasting models use catchments SWE mean

values in order to estimate water contributions

resulting from spring snow melting

• These values are calculated by interpolating local

SWE measurements

• Expensive and time consuming process


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IntroductionIntroduction• EQeau model: semi-empirical model to estimate

SWE using C-band SAR data (Bernier et Fortin, 1998)

• Tested in a pre-operational mode (2000-2002) over the La Grande river basin (in collaboration with Hydro-Quebec)

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Lac-Roman

Lac-Vianney

Lac-MadiganLac-Frégate

Lac-Falaise

Lac-Cadieux

EOL (Neige)

LG-4 (Neige)

LG-2 (Neige)Lac-Bertrand

Lac-Sauvolles

Lac-Rossignol

Lac-Opiscotéo

Lac-Bienville

Lac-Neokwescau

Lac-Kanaaupscow

Rivière-Caniapiscau

78°0'0"W

76°0'0"W

76°0'0"W

74°0'0"W

74°0'0"W

72°0'0"W

72°0'0"W

70°0'0"W

70°0'0"W 68°0'0"W

68°0'0"W

52°0'0"N

52°0'0"N

54°0'0"N

54°0'0"N

56°0'0"N

mars 2004

0 120 24060 Kilometers

bassin La Grande


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ObjectiveObjective

Assessment of the benefit/cost ratio

related to the use of the EQeau

model for SWE estimation compared

to the conventional method currently

employed by Hydro-Quebec


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The The EQeauEQeau model model

• The increase in the backscattering signal, between a

winter SAR image and late fall snow-free SAR

image, could be associated with a gradual increase

of the soil temperature resulting from snow thermal

resistance (STR) effect (insulating capacity).

• STR is related to SWE via snow depth and density.

• The backscattering signal ratio (BR) can be related

to STR and by the way to SWE


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The The EQeauEQeau model model• Frost penetration depends on the snow thermal resistance

(STR) which is related to SWE via snow depth and density.

• ε of a frozen soil is smaller than that of a wet soil (radiation penetrates deeper into frozen soil).

• The more STR is low (shallow depth and/or high density), the more the soil temperature will decrease, with a corresponding reduction of ε and of the backscattering signal (BS).

• The increase in the BS, between a winter SAR image and late fall snow-free SAR image, could be associated with a gradual increase of the soil temperature resulting from the STR effect.

• The backscattering signal ratio (BR) can be related to STR

• Bernier and Fortin (1998) established a consistent relationship between BR and STR


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The The EQeauEQeau model model• Range application: 80 mm <SWE< 490 mm • Application conditions:

– BS is originating from the snow/soil interface:• sparse vegetation cover;• dry snow pack

– The soil type should be sensitive to freezing conditions (containing a low percentage of coarse materiel);

– The reference image soil should be frozen;– For the winter images, the air temperature << 0ºC for long time

period, as to insure that the snow thermal resistance’s impact is optimal.


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SWE = STRxxK

Local snow density Land Cover Snow density

Fall SAR image Winter SAR image BR image

SWE

STR = mxBR + b

&

CBAK 2

EQeau 2002 version


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• In 2004, EQeau was modified in order

to improve its performances

– A new pre-processing chain with a pixel

size of 375 meters (optimized size)

– Use of either ENVISAT ASAR Wide Swath

or ScanSAR Narrow Radarsat-1 data


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The The EQeauEQeau model model– The modification of EQeau algorithm parameters and the

optimization of the EQeau model

– The correlation between SAR signal and STR is still low at

22%

y = 0.3268x + 4.7098

R2 = 0.2185

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

-2 -1 0 1 2 3 4

BR (dB)

ST

R


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The The EQeauEQeau model model– A new method to interpolate snow density values taking into

account altitude and latitudeAltitudeLocal snow density

50 100 150 200 250 300 350 400 45050

100

150

200

250

300

350

400

450

Densité mesurée (kg/m3)

Den

sité

est

imée

(kg

/m3)

RMSE=21.5 kg/m3R2=0.86

Linear regression+

Inverse distanceinterpolation of

regressionresidues

Interpolated snow density

Cross-validationLinearregression


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• Modified approach explains

78% of SWE variability with

an error of 29 mm

• 6% increase in accuracy is

related to the input of SAR

data into the EQeau model

• The impact of a such

improvement needs to be

specified

50

100

150

200

250

300

350

50 100 150 200 250 300 350

Observed SWE (mm)

Est

imat

ed S

WE

(m

m)

RMSE= 29 mm

R2=0,78

Cross-validation


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Benefit/Cost analysis methodologyBenefit/Cost analysis methodology

Field measurements

(Snow lines)

Uncertainty?

Benefit / Cost Ratio

Martin et al. study

GAIN OR LOSS OF

ACCURACY

Extrapolation to one

sub-watershed SWE

Uncertainty?

Integrated SWE at the

sub-watershed level

Uncertainty?

EQeau model

SWE at the pixel scale

Uncertainty?


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MethodologyMethodology• Benefit/cost ratio resulting from the improvement of the SWE estimation

accuracy related to the use RADARSAT-1 imagery (Martin et al., 1999)– 3 acquisition modes were evaluated (ScanSAR, Wide and Standard) – Investments in R & D, project exploitation costs and incomes resulting from

an increase in forecasts accuracy were taken into account– The study involved the period 1994-2007 (results remain valid)– 2 initial reservoir levels

• Linear relation between error reduction and B/C ratio

Martin et al. study


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0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

-5 -4 -3 -2 -1 0 1 2 3 4 5

Backscattering ratio (dB)

Err

or'

s co

effi

cien

t o

f va

riat

ion

100 kg/m3

200 kg/m3

300 kg/m3

400 kg/m3 500 kg/m3

Snow density

Uncertainties in SWE estimated using EQeau approachUncertainties in SWE estimated using EQeau approach

• Total error for SWE values estimated by EQeau for a pixel size of 375 m x 375 m (ET) is the resultant of two components:

– Ep: error resulting from uncertainty on the model parameters (random error) ≈ 38% -26%;

– EA: model fitting error :

– Var() is error variance (≈ 28.5 mm, random error) and b is the bias (≈ 4.5 mm, systematic error)

-4.5

-80

-60

-40

-20

0

20

40

60

80

50 100 150 200 250 300 350

Observed SWE (mm)

SW

E r

esid

uals

(m

m)

EP

EA2)var( bRMSEEA

2222 )var( bEEEE PAPT

EQeau model

SWE at the pixel scale

Uncertainty?


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Uncertainties in SWE estimated using EQeau approachUncertainties in SWE estimated using EQeau approach

• When averaging the SWE values at the sub-basin level, the random error component is cancelled:

• The final error associated with SWE estimation at this level from the EQeau method is quite low ≈ 4.5 mm representing only 2% for mean SWE values of 250 mm.

2)var(2

bE n

E

mp

bEn m

Integrated SWE at the

sub-watershed level

Uncertainty?


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Uncertainties in SWE estimated using conventional approachUncertainties in SWE estimated using conventional approach

• Local SWE measurements are interpolated over a regular grid (10x10 km2) using inverse-distance interpolation

• Interpolated values are averaged over the sub-basin level

– Starting from field measurements error (≈6.5 mm) and using Monte Carlo simulation, we find Ep ≈ 2.5 mm

– Interpolation technique error (EA) is ≈ 30 mm and the mean bias is ≈ 1.4 mm

• The SWE estimation error at the sub-basin level is represented by the bias which varies according to the SWE value

y = -0.3016x + 56.856

-120

-80

-40

0

40

80

120

0 50 100 150 200 250 300 350 400

Observed SWE (mm)

SWE

resi

dual

s (m

m)

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300 350 400

Observed SWE (mm)

Estim

ated S

WE(m

m)

RMSE= 30,3 mm

R2=0,76

Field measurements

(Snow lines)

Uncertainty?

Extrapolation to one

sub-watershed SWE

Uncertainty?


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Benefit/cost ratio calculationBenefit/cost ratio calculation

-5

0

5

10

15

20

25

30

35

100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300

SWE (mm)

Err

or

(%)

EQeau Inverse Distance Difference [EQeau - (Inverse Distance)]

-4

1

6

11

16

21

26

100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300

SWE (mm)

B/C

Ra

tio

B/C-60 B/C-44

Benefit / Cost Ratio

Martin et al. study

GAIN OR LOSS OF

ACCURACY


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SummarySummary

• Benefit/Cost (B\C) ratio of less than 1 is obtained with the EQeau Model when the (SWE) estimation is close to the field measurements average value – B/C ratio is unfavourable with EQeau in spatially

homogenous snow conditions

• In spatially variable snow conditions (high SWE variance), the B/C ratio is very favourable with EQeau – La Grande River watershed: huge basin (200 000 km2)

where, snow conditions are not homogenous and vary spatially from East to West.


Thank you

EO-HYDRO Progress Meeting – Milan, 9 November 2006 Benefit/Cost analysis for SWE estimation based...

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