GeoENV 2010 – Gent, 13-15 Sept. 2010

Improved mapping of daily precipitation over Quebec daily precipitation over Quebec

using the i i i hmoving-geostatistics approach

N. Jeannée (GEOVARIANCES) & D. Tapsoba (HYDROQUEBEC)

Contact: jeannee@geovariances.comTel: +33 (0)1 60 74 74 54 – Mob: +33 (0)6 84 04 35 41

Contents

Motivation

Input dataInput data

Methodology: the M-GS approachgy pp

Results

Conclusions and Perspectives

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MotivationContext

− Daily precipitation: key parameter for predicting hydropower generationin Québec (Canada)

Several modeling issues: scarce monitoring network large spatial − Several modeling issues: scarce monitoring network, large spatial variability, local anisotropies, non stationarity, ...

− Development of the “Moving-Geostatistics” framework by Estimages & Geovariances dedicated to the local optimization of parameters involved Geovariances, dedicated to the local optimization of parameters involved in variogram-based models

Obj tiObjectives− Present the M-GS approach

i) Determination of local modeling parameters (ranges, sills, anisotropy directions…);

ii) Use of these parameters in subsequent estimation/simulation algorithms.

− Test its efficiency for the modeling of daily precipitationy g y p p

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Input Data 6000 Data (mm)

22.40 1

Dataset from the « Réseau 5750

m)

Alti(m)

800

0.1No rainBasins

Météorologique Coopératif du Québec », a partnership initiave from the managers of

5250

5500

Y (km 800

700

600

500

400

300from the managers of meteorological networks.

0 500 1000

5000

300

200

100

0

Focus on daily precipitations for a specific day: January 18, 2009.

0.4 Nb Samples: 176Minimum: 0.0Maximum: 22.4Mean: 2.3

X (km)

Characteristics:

0.3

encies

Mean: 2.3Std. Dev.: 2.7

Characteristics:skewness, non stationarity, local anisotropies... 0.1

0.2

Frequ

0 10 20

Rainfall (mm)

0.0 ⇒ Which modeling framework?

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Methodology

Moving-Geostatistics:Moving Geostatistics:− Methodology developed since 2007, dedicated to the local

optimization of variogram-based models.optimization of variogram based models.

− Numerous applications initially dedicated to the Oil & Gas Industry:

Gridding (reservoir geometry or properties)

Noise filtering (seismic processing)

Facies modeling (reservoir characterization)

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Methodology

Common modelling issues addressed by M-GS:g y

« Structural » non stationarity(Bathymetry data)

Local accuracy

Small scale structures,strong anisotropy

Highlycontinuous

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Methodology

Idea: estimate and use parameters mapsp p

Main challenge: determining local parameters− Several approaches:

Local cross-validation

Local variogram analysis

Mathematical morphology approach (Ray tracing) to convert images into structural characteristics

− Ability to integrate exogenous information

Then, use of the local parameters in estimation or simulation algorithmsg

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Results

Application to daily precipitationApplication to daily precipitation− Comparison between two approaches:

U i l k i i ( ith li t d )Universal kriging (with linear trends)

Kriging with moving parameters (M-kriging)

− Elements of comparison:

Visual control of results

Use of a validation subset

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ResultsM-kriging approach

Determination of local parameters:− Determination of local parameters:

Definition of an analysis grid, use of overlapping

M-parameter 1: main direction of anisotropy (local Cross-Validation)p py ( )

M-parameter 2: variogram sill (computation of local variances)

Other M-parameters: ranges (not shown)

6500 6500

6000

(km) Angle

90

6000

(km)

Sill

5500

Y (

80

70

60

50

40

30

5500

Y Sill

10 9 8 7 6 5

0 500 1000 1500

X (km)

5000 20

10

0 0 500 1000 1500

X (km)

5000 4 3 2 1 0

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Results

Comparisonp− Visual control of daily precipitation maps

5750

6000

5750

6000

5250

5500

Y (km)

5250

5500

Y (km)

[mm]

10 98

0 500 1000

5000

5250

M-kriging

0 500 1000

5000

Univ. Kriging

8 7 6 5 4 3 2 1

0 500 1000

X (km)

0 500 1000

X (km)0

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Results

Comparisonp− Visual control of daily precipitation maps

5750

6000

5750

6000

5250

5500

Y (km)

[mm]

5.04.50

5250

5500

Y (km)

0 500 1000

5000

5 50

Univ. Kriging StDev

4.03.53.02.52.01.51.00.5 0 500 1000

5000

M-kriging StDev

0 500 1000

X (km)0.0

X (km)

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Results

Comparisonp− Visual control of daily precipitation maps

5750

6000

5750

6000

5250

5500

Y (km)

[mm]

5.04.50

5250

5500

Y (km)

0 500 1000

5000

5 50

Univ. Kriging StDev

4.03.53.02.52.01.51.00.5 0 500 1000

5000

M-kriging StDev

− Validation results (34 points - 20% subset)

0 500 1000

X (km)0.0

X (km)

Method rho RMSE

UK 0.63 1.75

M-GS 0.70 1.56

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Conclusions and Perspectives

Conclusions− Accounting for local parameters: a promising and pragmatic

approach to improve the modeling of variables presenting structural characteristics which are locally varyingcharacteristics which are locally varying.

− Daily precipitation case: local anisotropies, non stationarity…

Perspectives− Several theoretical aspects still need to be addressed: model

authorization, local anamorphosis for simulations, distinguishingstructural variations vs. statistical fluctuations…

− Daily precipitation case: integration of radar data as an auxiliaryvariable, which might also be useful to guide the estimation of precipitation parametersprecipitation parameters.

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