Some operational applications of geostatistics at Hydro-Québec

Some operational applications of geostatistics at Hydro-Québec Dominique TAPSOBA Hydro-Québec s research institute (IREQ),Varennes, Québec, CANADA NICDS Workshop Statistical Methods for Geographic and Spatial Data in the Management of Natural Resources March 3-5, 2010 Université de Montréal

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 Estimation Hydro-Quebéc s Watersheds Wind speed analysis Gaspe Peninsula

Hydro-Québec at a glance The main watersheds

Hydro-Québec at a glance Generating facilities by watersheds 1 TWh = 1,000,000,000 kwh Hydroelectric generating stations

Geostatistics for SWE estimation at Hydro-Québec Background Mean March SWE, 1979-1997 (Brown et al., 2003; Atmosphere-Ocean, 41, 1-14). Snow accumulation over Québec and Labrador represents the 2 nd 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 hydroelectric 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 SWE = amount of water stored in the snow pack usually expressed in mm

Geostatistics for SWE estimation at Hydro-Québec Background Large interannual variability in SWE over the Hydro-electric corridor of Québec can vary ± 50-100 mm between years 300 Mean March SWE, La Grande Basin, Quebec Mean monthly SWE (mm) 250 200 150 100 1965 1970 1975 1980 1985 1990 1995 2000 2005 Mean March SWE from snow course observations (52-55 N, 70-77.5 W)

Geostatistics for SWE estimation at Hydro-Québec 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.

Geostatistics for SWE estimation in Hydro-Québec Data acquisition Snow sampling

Geostatistics for SWE estimation at Hydro-Québec: Data sets 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 1 st and 15 th of each month gridding SWE at 10-km resolution Number of SWE Observations in Quebec & Adjacent Regions 10000 Location of snow course observations with 10-years of data from March 01 1970-1979 # Snow Course Observations 1000 100 10 1 1930 1940 1950 1960 1970 1980 1990 2000 1935 1945 1955 1965 1975 1985 1995 2005 No. of snow courses 30000 25000 20000 15000 10000 5000 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Day of month

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 400 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. SWE(mm) 300 200 R= 0.6 200 SWE(mm) 100 R=0.8 100 0 March 15 th 1970 0 100 200 300 400 500 600 700 800 900 Elevation(m) 0 February 15 th 2003 100 200 300 400 500 600 Elevation(m)

Geostatistics for SWE estimation at Hydro-Québec: Methodology External 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: SWE ( x) = D( x) + R( x) D(x) derived from topography T(x): D ( x) = at ( x) + b 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 1 st and 15 th of every month from December to May for the period from 1970 to 2005.

Geostatistics for SWE estimation at Hydro-Québec: Methodology External Drift Kriging technique SWE 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. 1.00 1.00 1.00 Variogram: Residuals 0.75 0.50 0.25 JANUARY Variogram: Residuals 0.75 0.50 0.25 FEBRUARY Variogram: Residuals 0.75 0.50 0.25 MARCH 0.00 0 100 200 300 400 Distance (km) 0.00 0 100 200 300 400 Distance (km) 0.00 0 100 200 300 400 Distance (km) Variogram: Residuals 1.00 0.75 0.50 0.25 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 0.00 0 100 200 300 400 500 600 700 Distance (km)

Geostatistics for SWE estimation at Hydro-Québec: Results DEM Maps of SWE spatial distribution for February 25th 2008 over Hydro-Quebec River basins: polygonal technique, SWE estimate using elevation as external drift, standard deviation, anomaly in % (value minus reference period 1971-2000). SWE-Thiessen SWE-EDK SWE-StDev SWE- Anomaly 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.

Geostatistics for SWE estimation at Hydro-Québec Operational application of interpolation methodology for real-time monitoring of SWE. SWE-EDK SWE-Stdev Graphical User Interface Design for SWE estimation Over Hydro-Quebec River Basins (Internet website) Difference between current observed interpolated SWE map and the mean map (anomaly) SWE-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.

Geostatistics for SWE estimation at Hydro-Québec Validations 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 Thiessen rmse (mm) 1970-2005 EDK Thiessen 33.6 44.5

Geostatistics for SWE estimation at Hydro-Québec : Validations Maximal annual SWE over 2 watersheds exploited by 2 corporations Saint-Jean watershed Churchill Falls watershed discrepancies for some years Maximal SWE (mm) Rio Tinto Alcan By Prof. Slivitzky(2007) Maximal SWE (mm) CFLCo (Churchill Falls and Labrador Corporation) By Prof. Slivitzky(2007) Good agreement with a change in the mean level of power generation around 1985 Perreault(2000) Power generation(gwh) Churchill Falls watershed

Geostatistics for SWE estimation at Hydro-Québec 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 for Modeling variability Quantifying uncertainty in the prediction Understanding risk We use geostatistical simulation to produce multiple realizations all honouring the data and the statistics derived from the data

Geostatistics for SWE estimation at Hydro-Québec Uncertainty analysis Model uncertainty by generating a set of maps of the spatial distribution of SWE values. For this analysis, we generated 200 realizations 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

Geostatistics for SWE estimation at Hydro-Québec Uncertainty analysis (Ex: Kenogami river basin 3390km2) Elev.(m) SWE_Estimation with EDK Ex. March 31 1999 DEM SWE(cm) 40.0 37.5 35.0 32.5 30.0 27.5 25.0 22.5 20.0 17.5 15.0 12.5 10.0 740 750 760 770 780 790 800 Exp. 6 simulated realizations of SWE 5370 5360 5350 5340 Y (km) 5330 5320 5310 5300 5290 5280 740 750 760 770 780 790 800 740 750 760 770 780 790 800 740 750 760 770 780 790 800 740 750 760 770 780 790 800 740 750 760 770 780 790 800 740 750 760 770 780 790 800 X (km)

Geostatistics for SWE estimation at Hydro-Québec Uncertainty analysis (Ex: Kenogami river basin 3390km2) EEN_31_03 1999 Quantiles{2.500000} 5370 5360 5350 EEN_31_03 1999 Quantiles{50.000000} 5370 5360 5350 EEN_31_03 1999 Quantiles{97.500000} 5370 5360 5350 5340 5340 5340 Y (km) 5330 5320 5310 5300 5290 5280 740 750 760 770 780 790 800 X (km) SWE(cm) Y (km) 40.0 37.5 35.0 32.5 30.0 27.5 25.0 22.5 20.0 17.5 15.0 12.5 10.0 5330 5320 5310 5300 5290 5280 740 750 760 770 780 790 800 X (km) Y (km) 5330 5320 5310 5300 5290 5280 740 750 760 770 780 790 800 X (km)

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

Geostatistical analysis of wind speed temporal variability Background

Geostatistical analysis of wind speed temporal variability Wind speed is essential for wind power generation however : A simple equation for the Power in the Wind P P = 1/2 ρ Πr 2 V 3 ρ = Density of the Air r = Radius of your swept area V = Wind Velocity Power is proportional to the CUBE of wind speed 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

Geostatistical analysis of wind speed temporal variability 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 Multiscale Limited Area Model) model outputs.

Geostatistical analysis of wind speed temporal variability: Methodology Mean regional temporal semivariograms (MRTS) definition and computation Given N data points z 1, z 2,, sampled at a regular interval d, the sample variogram can be computed for any lag h=kd, k=1, 2,, by γ kd ( j station ) = 1 2N kd N kd i= 1 Mean Regional Temporals Variogram γ R is computed by: γ R = 1 P γ kd ( j) P j= 1 Where P is the number of stations within the area R

Geostatistical analysis of wind speed temporal variability Application of MRTS to wind speed analysis Data and domain GEM-LAM= Global Environmental Multiscale Limited Area Model Numerical 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 V(m/s) 10 9 8 7 6 5 4 3 2 1 0 Y (km) 5600 5500 5400 5300 5200 5100 5000 GEM-LAM 2.5km + 10m sites 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) 4900 01/01/2009-11h 300 400 500 600 700 800 900 1000 110 X (km)

Geostatistical analysis of wind speed temporal variability MRTS - Observations 2001 June July August September February March April May January October November December

Geostatistical analysis of wind speed temporal variability MRTS - Observations 2007 June July August September February March April May January October November December

Geostatistical analysis of wind speed temporal variability MRTS FITTING Tapsoba Dominique. Regional-temporal patterns of wind speed over the Gaspe peninsula suggested by 1-D Variogram. (Renewable Energy) Variogram Choice of a variogram model based on two (spherical and exponential cosine) nested structures Ex: May 2007 Time (heure)

Geostatistical analysis of wind speed temporal variability How well did the GEM-LAM capture the hourly variability of wind speed? Hourly mean wind speed bias (Obs minus GEM-LAM Ouputs)

Geostatistical analysis of wind speed temporal variability MRTS Observations and GEM-LAM Outputs 2009 observation GEM-LAM Cross Vario

Geostatistical analysis of wind speed temporal variability MRTS Observations and GEM-LAM Outputs 2009 variogram observation variogram GEM-LAM GEM-Cross Vario Time(h) Time(h)

Geostatistical analysis of wind speed temporal variability MRTS Observations and GEM-LAM Outputs 2009 observation GEM-LAM Cross Vario

Geostatistical analysis of wind speed temporal variability MRTS Observations and GEM-LAM Outputs 2009 observation GEM-LAM Cross Vario

Geostatistical analysis of wind speed temporal variability MRTS Observations and GEM-LAM Outputs 2009 MRTS method allows to characterize timescales of 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 Thanks to the data providers: Ministère du Développement durable, de l'environnement et des Parcs Ontario Ministry of Natural Resources New Brunswick Environment Environment Canada