forecasting edwards aquifer water level brian overton budi yulianto chiyan cheung jessica sison...
TRANSCRIPT
Forecasting Edwards Aquifer Water Level
• Brian Overton• Budi Yulianto• ChiYan Cheung• Jessica Sison• Leann Lewis• Terran Fiske
Outline• The Edwards Aquifer,
Background and Objective
• Regression Models and Variables
• Time Series Decomposition Model
• ARIMA Model
• Model Comparisons and Selection
• Conclusion
A Brief Background on the Edwards Aquifer
The Edwards aquifer is a cavernous limestone reservoir in the south-central Texas area. The aquifer is replenished by waters flowing from area rivers and rainfall over its recharge zones (San Antonio, New Braunfels, San Marcos and parts of Austin).
Purpose: To use statistical analysis to determine the most effective model to forecast the water level in the Edwards Aquifer
Edwards Aquifer Water LevelJan 1995 - Dec 1998
620.0
630.0
640.0
650.0
660.0
670.0
680.0
690.0
700.0
Jan-95 Jul-95 Feb-96 Aug-96 Mar-97 Sep-97 Apr-98 Nov-98
Time
Wa
ter
Le
vel (
ab
ove
S.L
.)
Actual Water Level Hold-out Data
‘95 - ‘96 Drought
‘98 Drought
El Nino
Regression Models
• Complete Model
• Comal Springs Model
• Complete without Comal Springs
• Complete Interaction and Interaction2
• Stepwise Raw and Interaction
• Stepwise Raw, Raw2, Interaction, Interaction2
Comal Springs Models: A Special Case
Complete Comal Complete w/oModel Spring Comal Spring
F-Ratio 91.1219 1138.3221 12.6796R-Squared 0.9826 0.9612 0.8778Adj R-Squared 0.9718 0.9603 0.8086Significance of Variables 1/18 100% 50%Line Assumption L-I-E L-I-E L-I-N-EMulticollinearity 5/18 1/1 5/17Outliners/Cooks' D 1 0 1
Water Level vs Comal Spring
620
630
640
650
660
670
680
690
0 100 200 300 400
Comal Spring (cfs)
Wa
ter
Le
ve
l (ft
)Aquifer Water Level versus
the Comal Springs Flow
Regression Variables
• Average Precipitation
• Average Temperature
• Average Salado Treatment Plant In-Flow
• Average Dos Rios Treatment Plant BOD
• Texas Unemployment Rate
• Southwest Retail Sales
• Natural Gas Production
Regression ModelsI and I2 R and I R, R2, I, I2 Complete w/o
Complete Stepwise Stepwise Comal SpringF-Ratio 14.4929 28.1005 38.6935 12.6796R-Squared 0.9919 0.8044 0.8881 0.8778Adj R-Squared 0.9234 0.7758 0.8652 0.8086Significance of Variables 0% 100% 77% 50%Line Assumption L-I-N-E L-I-N-E L-I-N-E L-I-N-EMulticollinearity 31/42 0/6 3/8 3/17Outliners/Cooks' D 0 0 0 1
Edwards Aquifer Water LevelRegression Models
620.0
630.0
640.0
650.0
660.0
670.0
680.0
690.0
700.0
Jan-95 Jul-95 Feb-96 Aug-96 Mar-97 Sep-97 Apr-98 Nov-98
Time
Wa
ter
Le
vel (
ab
ove
S.L
.)
Actual Water Level Hold-out Data
R,R 2,I,I 2 R,I
Complete w/o Comal
Time Series Decomposition Model
1.0
1.0
1.0
1.0
1.0
0.9 2.4 3.8 5.3 6.8
Trend Ratio Chart
Time
1.0
1.0
1.0
1.0
1.0
0.9 2.4 3.8 5.3 6.8
Cycle Ratio Chart
Time
1.0
1.0
1.0
1.0
1.0
0.9 2.4 3.8 5.3 6.8
Season Ratio Chart
Time
1.0
1.0
1.0
1.0
1.0
0.9 2.4 3.8 5.3 6.8
Error Ratio Chart
Time
Edwards Aquifer Water LevelTime Decomposition vs. Actual
620.0
630.0
640.0
650.0
660.0
670.0
680.0
690.0
700.0
Jan-95 Jul-95 Feb-96 Aug-96 Mar-97 Sep-97 Apr-98 Nov-98
Time
Wa
ter
Le
ve
l (a
bo
ve
S.L
.)
Actual WaterLevelHold-out Data
Time-Decomposition
Autocorrelation analysis
PAC’s indicates first order autoregressive
-1.0
-0.5
0.0
0.5
1.0
0.0 7.0 14.0 21.0 28.0
Autocorrelations
Time
-1.0
-0.5
0.0
0.5
1.0
0.0 7.0 14.0 21.0 28.0
Partial Autocorrelations
Time
SAC’s dampens toward 0
Edwards Aquifer Water LevelARIMA vs Actual
620.0
630.0
640.0
650.0
660.0
670.0
680.0
690.0
700.0
Jan-95 Jul-95 Feb-96 Aug-96 Mar-97 Sep-97 Apr-98 Nov-98
Time
Wa
ter
Le
vel (
ab
ove
S.L
.)
Actual Water Level
Hold-out Data
ARIMA Predicted
Upper and LowerBound
Edwards Aquifer Water LevelCompare Regression, Time Series, ARIMA
620.0
630.0
640.0
650.0
660.0
670.0
680.0
690.0
700.0
Jan-95 Jul-95 Feb-96 Aug-96 Mar-97 Sep-97 Apr-98 Nov-98
Time
Wa
ter
Le
vel (
ab
ove
S.L
.)
Actual Water Level
Hold-out Data
R,R^2,I,I^2
Time Predicted
ARIMA
Conclusion
Best Model was ...
Edwards Aquifer Water Level Best Model
620.0
630.0
640.0
650.0
660.0
670.0
680.0
690.0
700.0
Jan-95 Jul-95 Feb-96 Aug-96 Mar-97 Sep-97 Apr-98 Nov-98Time
Wa
ter
Le
vel (
ab
ove
S.L
.)
Actual Water Level
Hold-out Data
R,I,R^2,I^2
R, R2, I, I2 Stepwise
Regression
Questions?