some operational applications of geostatistics at hydro ... · some operational applications of...

Dominique TAPSOBAHydro-Québec’s research institute (IREQ),Varennes, Québec, CANADA

Some operational applications of geostatistics at Hydro-Québec

Université de MontréalNICDS Workshop “Statistical Methods for Geographic and Spatial Data in the Management of Natural Resources” March 3-5, 2010

Presentation outline

Hydro-Québec at a glance

Applied geostatistics for :Snow Water Equivalent (SWE) estimation over Hydro-Québec’s watersheds

Wind speed temporal variability analysis over the Gaspe Peninsula (preliminary analysis)

Results and validations

Conclusions

Future work

Focusing interest areas

SWE EstimationHydro-Quebéc’s Watersheds

Wind speed analysisGaspe Peninsula


The main watersheds


Generating facilities by watersheds

Hydroelectric generating stations1 TWh = 1,000,000,000 kWh

• Snow accumulation over Québec and Labrador represents the 2nd largest continental SWE maxima for North America after the western Cordillera

• Annual maximum snow accumulation averages 200-300 mm

• Important resource for hydroelectricity production - estimated that 1 mm of SWE in the headwaters of the Caniapiscau-La Grande hydro corridor is equivalent to $1M in hydro-electric power production (R. Roy, personal communication, 2006).

• Spatial and temporal limitations in both satellite data and in situ snow monitoring networks are a constraint to understanding variability and change in SWE over this region of North America

Mean March SWE, 1979-1997 (Brown et al., 2003; Atmosphere-Ocean, 41, 1-14).

SWE = amount of water stored in the snow pack usually expressed in mm

Geostatistics for SWE estimation at Hydro-Québec

Background


BackgroundLarge interannual variability in SWE over the Hydro-electric corridor of Québec… can vary ± 50-100 mm between years

1965 1970 1975 1980 1985 1990 1995 2000 2005100

150

200

250

300

Mea

n m

onth

ly S

WE

(mm

)

Mean March SWE, La Grande Basin, Quebec

Mean March SWE from snow course observations (52-55°N, 70-77.5°W)

Provide a high quality grid dataset to investigate the spatial and temporal variability in SWE over HQ’s watersheds.

Documenting and understanding variability and change in SWE are important for: seasonal prediction, validation of climate models, and understanding how snow cover may change in the future.

For operational run-off and streamflow forecasts, the maximum SWE grid map generated prior to spring snowmelt is used to assess the a priori potential for getting large run-off and floods.

Used to update the snow-related state variables employed by our hydrological models, which forecast water inflows into reservoirs during spring.

Snow anomaly maps to provide timely and geographic pattern of SWE to assist decision-making related to water management for Hydropower generation.


Snow sampling

Geostatistics for SWE estimation in Hydro-Québec

Data acquisition

Location of snow course observations with 10-years of data from March 01 1970-1979

19301935

19401945

19501955

19601965

19701975

19801985

19901995

20002005

1

10

100

1000

10000

# S

now

Cou

rse

Obs

erva

tions

Number of SWE Observations in Quebec & Adjacent Regions

0

5000

10000

15000

20000

25000

30000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Day of month

No.

of s

now

cou

rses

In situ snow course and snow depth observations:• most observations are concentrated over southern regions • most data available since ~1960• majority of observations are made on the 1st and 15th of each month• gridding SWE at 10-km resolution

Geostatistics for SWE estimation at Hydro-Québec: Data sets

Geostatistics for SWE estimation at Hydro-Québec: Methodology

External Drift Kriging technique

We adopt non-stationary geostatistical techniques such as External Drift Kriging (EDK) (Wackernagel, 1998; Chiles and Delfiner, 1999, p.355)

Integration of auxiliary information such as elevation, as a predictor variable strongly correlated with SWE.

more reasonable result in terms of the known physical relationships, which are imposed on the local mean by the elevation covariate.

Easier to implement than Co-Kriging, collocated-cokriging

There is a strong relationship between topography and SWE. Linear correlation coefficients between SWE and topography over the 1970-2005 period are greater than 0.6.

0 100 200 300 400 500 600 700 800 900

0

100

200

300

400

R= 0.6

March 15th 1970

SWE(

mm

)

Elevation(m)Elevation(m)

100 200 300 400 500 600

0

100

200

SWE(

mm

)February 15th 2003

R=0.8

Geostatistics for SWE estimation at Hydro-Québec: MethodologyExternal Drift Kriging technique

External drift kriging (EDK) is a classical approach that aims at integrating, in the modeling of a target variable Z(x), the knowledge of an auxiliary field s(x) linearly correlated with Z(x), s(x) providing a large scale information about the spatial trend of Z(x). EDK only requires the kwnoledge of the variogram of the residuals (see e.g. Chilès & Delfiner, 1999).

In the case of the snow water equivalent (SWE), EDK at a given location x relies on the following decomposition:

with:

– D(x) derived from topography T(x):

– R(x) stationary residuals with mean 0.

To ensure robustness of the temporal SWE estimates, a constant variogram model is assumed for each season, fitted on average empirical variograms derived from the 1st and 15th of every month from December to May for the period from 1970 to 2005.

)()()( xRxDxSWE +=

bxaTxD += )()(

Geostatistics for SWE estimation at Hydro-Québec: MethodologyExternal Drift Kriging techniqueSWE spatio-temporal variability

Example of normalized variograms of residuals from SWE regression with topography (1970-1980).No significant differences in the global shape between monthly variograms.

JANUARY

0 100 200 300 400

Distance (km)

0.00

0.25

0.50

0.75

1.00

Variogram: Residuals

FEBRUARY

0 100 200 300 400

Distance (km)

0.00

0.25

0.50

0.75

1.00


MARCH

0 100 200 300 400

Distance (km)

0.00

0.25

0.50

0.75

1.00


0 100 200 300 400 500 600 700

Distance (km)

0.00

0.25

0.50

0.75

1.00

Variogram: Residuals Combined use of two model variograms focusing

on small and large distances for variogram fitting.

Choice of a variogram model based on two spherical nested structures

Geostatistics for SWE estimation at Hydro-Québec: Results

EDK shows a realistic spatial structure consistent with the structure of DEM but with SWE values honouring observation sites.

Polygonal technique was formerly used to generate Hydro-Québec forecasts. This technique was just based on the influence zone of each SWE measurement, without any additional information and any uncertainty estimate.

Maps of SWE spatial distribution for February 25th 2008 over Hydro-Quebec River basins: polygonal technique, SWE estimate usingelevation as external drift, standard deviation, anomaly in % (value minus reference period 1971-2000).

SWE-EDKSWE-Thiessen

SWE-StDev SWE- Anomaly

DEM

Geostatistics for SWE estimation at Hydro-QuébecOperational application of interpolation methodology for real-time monitoring of SWE.

SWE-EDK SWE-Stdev

Difference between current observed interpolated SWE map and the mean map (anomaly)

SWE anomaly maps are generated automatically bi-weekly from December to May to provide temporal information on the spatial distribution of SWE for decision-makers at Hydro-Québec.

Graphical User Interface Design for SWE estimation Over Hydro-Quebec River Basins (Internet website)

SWE-ANOMALY

Geostatistics for SWE estimation at Hydro-QuébecValidations

• Cross-validation carried out for March 15 (approx date of max annual SWE for most of Quebec) for a random selection of 25% of the observations (~130 observations/yr) over the 1970-2005 period

• rmse computed for interpolation results with EDK and a simple interpolation procedure (Thiessen polygon method) formely used as a reference

Conclusions:

• EDK had lower rmse than ThiessenEDK Thiessen

rmse (mm)1970-2005

33.6 44.5

Geostatistics for SWE estimation at Hydro-Québec : Validations

Maximal annual SWE over 2 watersheds exploited by 2 corporations

By Prof. Slivitzky(2007) Max

imal

SW

E (m

m)

Max

imal

SW

E (m

m)

Rio Tinto Alcan CFLCo (Churchill Falls and Labrador Corporation)

discrepancies forsome years

Churchill Falls watershedSaint-Jean watershed

Pow

er g

ener

atio

n(G

Wh) Churchill Falls watershed

Good agreement with a change in the mean level of power generation around 1985 Perreault(2000)

By Prof. Slivitzky(2007)


Uncertainty analysis

Essentially kriging produces:a simple map of the «best » local estimates a mean squared prediction error

Estimates are “smoothed” such that low values will tend to be overestimated and high values will tend to be underestimated

Deleterious consequences forModeling variabilityQuantifying uncertainty in the predictionUnderstanding risk

We use geostatistical simulation to produce multiple realizations all honouring the data and the statistics derived from the data


Uncertainty analysis

Model uncertainty by generating a set of maps of the spatial distribution of SWE values. For this analysis, we generated 200realizations by Turning Bands technique (Journel, 1974; Chilès, 1977, Tompson et al., 1989)

Each realization is conditional to the original data and approximately reproduces the spatially weighted sample frequency distribution and the variogram. Therefore, the set of mean SWE values generated will be similar to that of kriging.

The Turning Bands algorithm used here assumes the data are normally distributed, although other probability models (including nonparametric) could be selected.

Journel ,(1974) Simulation Conditionnelle. Théories Pratique, thèse de Docteur-Ingénieur, Université de Nancy Chilès, J.P.(1977). Géostatistique des phénomènes non stationnaires. Thes, Doct.-Ing. Nancy.Tompson A.F.B. Abadou R.and Gelhar L. W.(1989). Implementation of a three-domensional Turning Bands random field generator, W.Ress.Res., Vol.25, no10, p.2227-2243


Uncertainty analysis (Ex: Kenogami river basin 3390km2)

740 750 760 770 780 790 800 740 750 760 770 780 790 800 740 750 760 770 780 790 800 740 750 760 770 780 790 800

X (km)

5280

5290

5300

5310

5320

5330

5340

5350

5360

5370

Y (km)

740 750 760 770 780 790 800 740 750 760 770 780 790 800

Exp. 6 simulated realizations of SWE

40.037.535.032.530.027.525.022.520.017.515.012.510.0

740 750 760 770 780 790 800

SWE(cm)DEM

Elev.(m) SWE_Estimation with EDK

Ex. March 31 1999


Uncertainty analysis (Ex: Kenogami river basin 3390km2)

740 750 760 770 780 790 800

X (km)

5280

5290

5300

5310

5320

5330

5340

5350

5360

5370

Y (km)

EEN_31_03 1999 Quantiles{2.500000}

40.037.535.032.530.027.525.022.520.017.515.012.510.0

740 750 760 770 780 790 800

X (km)

5280

5290

5300

5310

5320

5330

5340

5350

5360

5370

Y (km)

EEN_31_03 1999 Quantiles{50.000000}

740 750 760 770 780 790 800

X (km)

5280

5290

5300

5310

5320

5330

5340

5350

5360

5370

Y (km)

EEN_31_03 1999 Quantiles{97.500000}

SWE(cm)

Geostatistical analysis of wind speed temporal variability

Background

Integrating wind power into a large, primarily hydroelectric generating fleet presents a real challenge. Hydro-Québec is therefore developing cutting-edge expertise in order to:

Plan the integration of wind farms into its grid

Develop method to characterize and forecast fluctuating wind power output (in collaboration with Environment Canada) that will maximize the contribution of wind energy without compromising the reliability of the transport

Maintain safe, reliable operation of the power system


Background


Wind speed is essential for wind power generation however :

Wind speed varies quickly in time and the power output is dependent on how fast the wind is blowing. Therefore, it is desirable that wind speed temporal variability (patterns) be investigated and described

One way for predicting a wind farm power would be forecast wind speed through a numerical weather prediction (NWP) model and convert them into a production value by means of a wind farm power curve. Therefore it could be interesting to analyse NWP Outputs and observations

A simple equation for the Power in the Wind P

P = 1/2 ρ Π r2 V3

ρ = Density of the Airr = Radius of your swept areaV = Wind Velocity

Power is proportional to theCUBE of wind speed


The purpose of the study

Extract the maximum information of wind speed time series properties over an area of interest using geostatistical framework.

There are different ways to do that, such are spectral methods, wavelets but we focus here on the semivariogram method for its robustness.

For wind power generation, the mean behaviour of wind speed over a time period (month, annual) for a given area (farm) is essential. We apply geostatistical tools, namely Mean Regional Temporal Semivariogram (MRTS) to capture the structure.

MRTS is also a way to ensure the robustness of semivariogram inference

Compare the temporal variability of wind speed recorded at the 10m meteorological stations and the GEM-LAM (Global Environmental MultiscaleLimited Area Model) model outputs.

Geostatistical analysis of wind speed temporal variability: Methodology

Mean regional temporal semivariograms (MRTS) definition and computation

Given N data points z1, z2,…, sampled at a regular interval d, the sample variogram can be computed for any lag h=kd, k=1, 2,…, by

Mean Regional Temporals Variogram is computed by:

∑=

=P

jkdR j

P 1

)(1 γγ

Where P is the number of stations within the area R

Rγ

∑=

=kdN

ikdstationkd N

j12

1)(γ


Application of MRTS to wind speed analysis

300 400 500 600 700 800 900 1000 110

X (km)

4900

5000

5100

5200

5300

5400

5500

5600

Y (km)

GEM-LAM 2.5km+ 10m sites

V(m/s)

10

9

8

7

6

5

4

3

2

1

0

01/01/2009-11h

Environment Canada records a wind velocity (speed and direction) at every hour at 41 sites at 10m

Estimates GEM-LAM value at station locations using a bilinear method(SMC)

GEM-LAM= Global Environmental Multiscale Limited Area ModelNumerical model employed operationally by Environment Canada’s – Canadian Meteorological Centre (CMC)

•forecast periods up to 24 hours•initial and boundary conditions derived from CMC’s operational regional GEM 15 km resolution forecast system (GEM 15).•presently run for two configurations: SW Canada/Pacific Northwest, and southern Ontario and Québec

Data and domain


MRTS - Observations 2001

June July August September

January October November December

February March April May


MRTS - Observations 2007

June July August September

January October November December

February March April May


MRTS –FITTING

Tapsoba Dominique. Regional-temporal patterns of wind speed over the Gaspe peninsula suggested by 1-D Variogram. (Renewable Energy)

Time (heure)

Ex: May 2007

Var

iogr

am Choice of a variogram model based on two (spherical and exponential cosine) nested structures


How well did the GEM-LAM capture the hourly variability of wind speed?

Hourly mean wind speed bias (Obs minus GEM-LAM Ouputs)


MRTS – Observations and GEM-LAM Outputs 2009

observation

GEM-LAM

Cross Vario


MRTS – Observations and GEM-LAM Outputs 2009va

riog

ram

vari

ogra

m

Time(h) Time(h)

observation

GEM-LAM

GEM-Cross Vario



observation

GEM-LAM

Cross Vario



MRTS method allows to characterize timescalesof wind speed varying signals

MRTS clearly show for the observations and the GEM-LAM model output a periodic component of 24h during summer

– For several years– For such behaviour have physical explanations

Both MRTS and GEM-LAM variograms do not show a clearly periodic signal during winter

GEM-LAM model systematically underestimated wind speed variability through time

Terminal conclusions : Future work

SWE estimation

Will investigate the usefulness of additional covariates e.g. vegetation characteristics (e.g. vegetation density and tree type play an important role in sublimation loss)

Take into account of an uncertainty of the variogram model parameters

Terminal conclusions : Future work

Wind speed variability analysis

We have to continue to study the wind speed behaviour both spatially and temporally in order to predict the wind characteristics at a specific farm from the general characteristics appropriate for a region.

Combine temporal and spatial models in order to correct the GEM-LAM Outputs.

Merci

• Ministère du Développement durable, de l'Environnement et des Parcs

• Ontario Ministry of Natural Resources

• New Brunswick Environment

• Environment Canada

Thanks to the data providers:

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