Saving Water with Statistics

Transcription

1 Saving Water with Statistics Natalie Smith John Henstridge Meredith Regan Data Analysis Australia

2 Outline The problems Measuring the effect of water restrictions Predicting future water use For each problem: Background Model Structure Data and model fitting Applications Saving Water with Statistics - Page 2

3 Problem 1 - Background By the end of 2001 Perth dam levels were extremely low Low rainfall and runoff into the dams over winter High water consumption Water restrictions were introduced in September 2001 Perth sprinkler use was restricted to two days a week Households were only allowed to water their gardens on specified days Saving Water with Statistics - Page 3

4 Dam Storage % Storage in Gigalitres (Millions of Kilolitres) % 35% 30% 25% Percentage of Full Capacity % 80 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 15% Source: Water Corporation, WA Saving Water with Statistics - Page 4

5 Measuring the Effect Water Corporation needed to measure the effect of water restrictions on water usage Daily water consumption was modelled To quantify the two day a week effect Basis of model Data Analysis Australia had successfully modelled water consumption in 2000 to measure the impact of advertising on water usage The model was used to separate effects such as weather and time of year from the advertising effect Now interested in the impact of restrictions Saving Water with Statistics - Page 5

6 Model Structure Models daily consumption for Perth and Mandurah Because weather has an effect felt on the day Used consumption data from 1980 A Gamma Distribution Data is positive, skewed to the right Linear on a log scale Fitted using a Generalised Linear Model R statistical system Saving Water with Statistics - Page 6

7 Model Structure Long Term Trend Season of the Year Day of the Week Weather Restrictions Advertising Linear Model Exponential Consumption Saving Water with Statistics - Page 7

8 Model Parameters (1) Trend over time Essentially linear Contains a lot of issues growth of Perth, changing housing and gardens, economy etc Annual cycle Fourier series representation gives continuity with not too many parameters Day of the week Also by Fourier series Advertising, restrictions, free water allowances etc Need to know the precise timing Saving Water with Statistics - Page 8

9 Model Parameters (2) Weather is complex Maximum and minimum temperatures Includes carry over from previous days Borderline non-linear effect Rainfall Also non-linear (square root) And lots of interactions For example, rain in winter has different effect from rain in summer Giving over 100 parameters But also lots of data available since it is daily data since Saving Water with Statistics - Page 9

10 Results Advertising and restrictions after Sept 2001 could not be separated Were introduced at the same time Effect of two day a week water restrictions Biggest effect is in summer and on extreme days Examination of residuals Differences between predicted and actual values Residuals were high on extreme days Added non-linear terms to the model (square root of rainfall) Saving Water with Statistics - Page 10

11 Quantifying Effect 1,600 1,400 Modelled Water Use with and without Restrictions and Advertising Difference between Predicted Consumption (with no ads and restrictions) and Actual Consumption since 1 September 2004 is GL. 700, ,000 Consumption (ML) 1,200 1, , , , , Sep-04 Oct-04 Nov-04 Dec-04 Jan-05 Feb-05 Mar-05 Apr-05 May-05 Jun-05 Jul-05 Aug-05 Sep-05 Oct-05 Nov-05 Dec-05 Jan-06 Feb-06 Mar-06 Apr-06 May-06 Jun-06 Jul-06 Aug-06 Sep-06 Oct-06 Nov-06 Cummulative Consumption (ML) 100,000 0 Actual Predicted - With Restrictions Predicted - No Restrictions Saving Water with Statistics - Page 11

12 Problem 1 - Conclusions Can measure the effect of two day a week restrictions Greater in summer and on extreme days Clearer decision making Removing weather and other effects leaves the behavioural pattern Decide whether consumer behaviour needs modification How long should the restrictions be maintained? Is there a need for further restrictions? Saving Water with Statistics - Page 12

13 Problem 2 - Background There are a number of water sources that service Perth Metropolitan area Need to manage the distribution of water. Water pressure Storage Predict Metropolitan Daily Water Consumption Using weather forecasts. Permit optimisation of pumping and water sources. Saving Water with Statistics - Page 13

14 Predicting Water Use Needed to be able to predict water consumption Forecasted Weather Previous water consumption Four daily water consumption models were created One-day ahead model Two-day ahead model Three-day ahead model Four-day ahead model Saving Water with Statistics - Page 14

15 Model Structure Long Term Trend Season of the Year Day of the Week Actual Weather Forecasted Weather Previous Consumption Linear Model Exponential Consumption Saving Water with Statistics - Page 15

16 Model Parameters (1) Trend over time Annual cycle Fourier terms Hot season indicator Day of the week Weather forecasts Maximum and minimum temperatures Rainfall Actual weather Previous day s maximum and minimum temperatures Previous day s rainfall Saving Water with Statistics - Page 16

17 Model Parameters (2) Previous Water Consumption Previous 3 days Same day last week plus the 2 days before that Interactions Hot season with Previous actual weather Day of the week with Previous consumption Day of the week and Previous consumption with the Hot season Saving Water with Statistics - Page 17

18 Results A model that predicts water consumption Four days into the future Weather forecasts Examination of residuals Differences between predicted and actual values Accuracy decreases as predicting further ahead More accurate in colder months Saving Water with Statistics - Page 18

19 Quantifying Effect Oct-05 8-Oct Oct Oct Oct-05 5-Nov Nov Nov Nov-05 3-Dec Dec Dec Dec Dec-05 7-Jan Jan Jan Jan-06 4-Feb Feb Feb Feb-06 4-Mar Mar Mar Mar-06 1-Apr-06 8-Apr Apr Apr-06 Water Consumption (ML) 29-Apr-06 Actual Consumption 1 Day Ahead Predictions 2 Day Ahead Predictions 3 Day Ahead Predictions 4 Day Ahead Predictions Saving Water with Statistics - Page 19

20 Problem 2 - Conclusions Can estimate future consumption Using weather forecasts Up to four days in advance Can predict four days into the future Less accurate the further into the future you predict Further development Geographical segmentation Saving Water with Statistics - Page 20

21 Thank You Natalie Smith Data Analysis Australia (08)