Application of a multivariate autoregressive model to generate inflow scenarios using ensemble climate forecast

Transcription

1 Federal University of Rio de Janeiro Department of Civil Engineering - COPPE/ UFRJ Fluminense Federal University Department of Agriculture Engineering and Environmental Studies Application of a multivariate autoregressive model to generate inflow scenarios using ensemble climate forecast William Cossich 1, Marcio Cataldi 2, Otto Corrêa Rotunno Filho 1 wcossich@lamma.ufrj.br 1 Programa de Engenharia Civil PEC/COPPE/ Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil 2 Departmento de Engenharia Agrícola e Meio Ambiente Universidade Federal Fluminense, Niterói, Brazil

2 - Contents Introduction Objective Methodology Results Concluding Remarks CLIVAR VAMOS Workshop on Modeling and Predicting Climate in the Americas

3 Contents Introduction Objective Methodology Results Concluding Remarks

4 Introduction > Brazilian Interconnected System of Generation and Transmission Electricity - SIN Source: ONS.

5 2,3 0,2 0,04-2,3 0,2 0,04 0,2 2,3 0,2 0,04 0,2 2,2 0,4 0,04 0,2 2,1 0,6 0,12 0,7 8,0 8,0 7,9 7,6 7,3 13,1 12,9 13,8 15,2 16,8 76,3 76,4 75,6 74,3 72,4 Introduction > SIN Predominance of Hydroelectric Energy 90,0 Installed capacity in the SIN 2006 to 2010 Source of electric power generation - % 80,0 70,0 60,0 50,0 40,0 30,0 20,0 10,0-2006(4) 2007(5) Hydroelectric Itaipu Conventional thermoelectric Nuclear Wind Energy Biomass Others Source: ONS.

6 Introduction > Inflows Forecasting > use of different types of models / modeling - Weekly horizon: Deterministic forecasts; - Monthly Horizon: Generation of inflow scenarios - Increased uncertainty > Currently, the generation of inflow scenarios made by ONS, for example, does not incorporate any kind of climate information.

7 Contents Introduction Objective Methodology Results Concluding Remarks

8 Objective > Broad Objective - To propose a methodological approach for inflow forecasting into 2- months horizon through the use of stochastic autoregressive models, considering past inflows information jointly with climate information.

9 Contents Introduction Objective Methodology Results Concluding Remarks

10 Methodology Obtain historical records of Natural Affluent Energy - NAE, climate indices and the SST anomalies. Calculate the correlations between NAE and other previous data, to select a watershed for studying. Get and evaluate the historical records of inflows and precipitation for the selected river basin Get the climatology and historical records of rainfall forecasts from ECHAM 4.5 Model (Max-Planck Institute) for the region selected, and use statistical methods to correct these predictions. Apply two different models (AR and ARx-type) to generate inflows scenarios, based on past inflows information and monthly precipitation forecasts. Evaluate the results obtained.

11 Contents Introduction Objective Methodology Results Concluding Remarks

12 > Calculate Pearson correlation between climate indices - SOI, ONI, SAI and SST anomalies on regions of Pacífic Equatorial Ocean- and NAE. SOI: difference in pressure reduced to sea level between Tahiti and Darwin; ONI: average change in three months of SST anomalies in the Niño 3.4 region; SAI: Average SST anomaly in the region of confluence Brazil - Malvinas. Results y x xy n i i n i i n i i i s s s y y x x y y x x Fonte: Tokinaga et al.(2005)

13 Results Linear Correlation Between Climate Indices and ANE 0,5 0,4 0,3 0,2 0,1 0-0,1-0,2-0,3-0,4 SST - Niño 1.2 SST - Niño 3 SST - Niño 3.4 SST - Niño 4 ONI SOI SAI S CW/SE NE N

14 Results > Watershed selected: The Grande River Basin

15 Results Autoregressive Model - AR > Method for estimating parameters: Least Squares Yule-Walker > Order: 1-12 > Inflow Data - Total Natural Inflow Source: Brazilian Operator of Electrical System - ONS > Study Period: Calibration: Validation (Prediction): Tests (Forecasting):

16 Inflow (m 3 s -1 ) Results Total Natural Inflow - The upstream of the Furnas Hydroelectric Power Plant AR Model - 1 st Month X Observed Data Months LS1 LS2 LS3 LS4 LS5 LS6 LS7 LS8 LS9 LS10 LS11 LS12 YW1 YW2 YW3 YW4 YW5 YW6 YW7 YW8 YW9 YW10 YW11 YW12 MEDIA MAXIMUM MINIMUM OBS

17 Inflow (m 3 s -1 ) Results Total Natural Inflow - The upstream of the Furnas Hydroelectric Power Plant AR Model - 2 nd Month X Observed Data Months LS1 LS2 LS3 LS4 LS5 LS6 LS7 LS8 LS9 LS10 LS11 LS12 YW1 YW2 YW3 YW4 YW5 YW6 YW7 YW8 YW9 YW10 YW11 YW12 MEDIA MAXIMUM MINIMUM OBS

18 Results Autoregressive Model with Exogenous Variable - ARx > Method for estimating parameters: Least Squares > Best Order Between 1 and 12 > Inflow Data - Total Natural Inflow Font: Brazilian Operator of Electrical System - ONS > Study Period: Calibration: Validation (Prediction): Tests (Forecasting):

19 Results > Precipitation Data > Simulated and Predicted ECHAM 4.5 Model Max-Plack Institute (Roeckner et al, 1996). Source: IRI - Horizontal resolution =~2.8 (Spectral model at T42 resolution) - Vertical resolution = 19 Levels > Observed - 22 rainfall stations from Water Brazilian Agency ANA > Climatology: > Rainfall Predicted Data: Jan/2002 Dec/2007

20 Precipitation (mm) 300 The upstream of the Furnas Hydroelectric Power Plant - Climatology ( ) Echam 4.5 Model X Observed Data Results correction factor: Months ECHAM 4.5 Model - porvided by IRI Data Climatology Observed Data

21 Inflow (m 3 s -1 ) Results Total Natural Inflow - The upstream of the Furnas Hydroelectric Power Plant ARx Model - 1 st Month X Observed Data M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 M21 M22 M23 M24 M-Medium MAXIMUM MINIMUM Arx-with observed precipitation OBS Months

22 Inflow (m 3 s -1 ) Results Total Natural Inflow - The upstream of the Furnas Hydroelectric Power Plant ARx Model - 2 nd Month X Observed Data M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 M21 M22 M23 M24 M-Medium MAXIMUM MINIMUM Arx-with observed precipitation OBS Months

23 Contents Introduction Objective Methodology Results Concluding Remarks

24 Concluding Remarks > Both the AR and the ARx models represented well the inflow seasonal behavior, however the AR models didn t anticipate the inflow change; > The AR models represent the inflow with a phase shift of one month, this is a feature common to univariate AR models; > The ARx model performs better than the AR models. It is possible to note that the observed inflow was within range of maximum and minimum of model predictions, in majority of data from analyzed period; > The ensemble mean from precipitation forecast showed a good correlation with the observed inflow; > There was an increase in variance estimate of second month ahead in both types of models. This was more pronounced in AR models; > It is needed a supplement evaluation of results, using statistical methods to get a better measure of forecast accuracy.

25 Thank You!

26 Federal University of Rio de Janeiro Department of Civil Engineering - COPPE/ UFRJ Fluminense Federal University Department of Agriculture Engineering and Environmental Studies Application of a multivariate autoregressive model to generate inflow scenarios using ensemble climate forecast William Cossich 1, Marcio Cataldi 2, Otto Corrêa Rotunno Filho 1 wcossich@lamma.ufrj.br 1 Programa de Engenharia Civil PEC/COPPE/ Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil 2 Departmento de Engenharia Agrícola e Meio Ambiente Universidade Federal Fluminense, Niterói, Brazil