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WATER RESOURCES BULLETIN VOL. 13 , NO. 4 AMERICAN WATER RESOURCES ASSOCIATION AUGUST 1977

A COMPARISON OF MULTIVARIATE AND TREND FORECASTING ESTIMATES WITH ACTUAL WATER USE'

Bruce Mitchell and Paul H. Leighton'

ABSTRACT: This paper describes a multivariate water forecasting procedure that is neither complicated, time-consuming nor expensive to operationalize. The forecasting procedure has been used to estimate the water demand for a proposed subdivision in Barrie, Ontario. Reli- ability is checked by applying the procedure to two existing subdivisions in Barrie for which metered consumption is available. For comparison, a trend forecasting procedure is also applied to the proposed subdivision and the existing subdivisions. Both the multivariate and trend fore- casting procedures provide encouragingly accurate results when compared to actual use. While the multivariate procedure allows more precision, both procedures should be useful in forecasting water demand for smaller municipalities. (KEY TERMS: water demand forecasting; multivariate; trend; Barrie; Ontario,)

INTRODUCTION Forecasting urban water use creates several problems. Perhaps the most basic is the

need t o trade-off reliability against time and expense. While it is relatively easy to identify the variables t o include in forecasts, operating constraints frequently exclude their sys- tematic consideration. At the same time, measurement problems may preclude the incor- poration of other variables into forecasts.

The purpose of this study was t o develop a multivariable forecasting procedure which was not overly complicated, time-consuming or expensive. It was thought that such a procedure might allow smaller municipalities to improve estimates. As a result, a multi- variate procedure has been developed and applied t o a proposed subdivision development in Barrie, Ontario. The results of the multivariate procedure are compared with results based upon trend estimates. To check the reliability of the estimates, the multivariate and trend procedures were applied to two existing subdivisions in Barrie for which metered water records were available.

'Paper No. 761 29 of the Wuter Resources Bulletin. Discussions are open until April 1 , 1977. Respectively, Associate Professor, Geography Department, University of Waterloo, Waterloo, On-

tario N 2 L 3G1; Graduate Student, Faculty of Education, University of Toronto, Toronto, Ontario. 2

817

81 8 Mitchell and Leighton

STUDY AREA

Barrie is a city of 33,500 (1976) located 5 5 miles north of Toronto. District 6 is located in the northwestern end of the city and contains the largest tract of undeveloped land, approximately 427 acres. This undeveloped land, owned by three developers - Letitia Heights Development Ltd., Sardinia Development Ltd., and Deer Park Development Ltd. - is presently vacant former agricultural land, sand pits or reforestation areas.

In August 1974, Barrie amended its official plan and changed the designated land use of the 427 acres from industrial to residential. The goal for the district is to create a pleasing and attractive residential community (Barrie, 1974). Particular attention is to be given to the location of roads, schools, recreation, park areas and a convenience com- mercial centre to create a focal point for the residential district.

In the spirit of the plan, the community will be developed so housing will be available to all levels of income and will include single and multiple family units. The population will range from a minimum of 6,625 to a maximum of 9,721.

The official plan offers three possible directions for development. These offer a minimum and maximum number of units and population. A second plan has different unit and population numbers but is within the range specified by the official plan. This plan is a combination of separate projects proposed by the three developers. Whatever plan is adopted, the development will not be completed until five years after it commences (Burrie Examiner, 19 7 5).

One of the basic planning concerns is to determine the amount of water District 6 will require after development. This aspect is of concern for several reasons. First, the Barrie Public Utilities Commission is concerned that there is already a deficiency in storage facilities with respect to the whole water distribution system in the city (Proctor and Redfern, 1975). Second, there is need to provide necessary water works facilities in the district (watermains, fire hydrants, sewers). Since such facilities often have a life time of up to 50 years, it is desirable to know long-term water needs. The third reason relates to economics. Savings could be realized from the avoidance of water shortages and over- investment in supply facilities. Numerous forecastingapproaches to determine future water needs could be used. The general characteristics of the main approaches are reviewed below.

APPROACHES TO FORECASTING

Requirements Approach This approach uses figures for expected population multiplied by the daily per capita

use of water at time of forecast (Hawson, 1955). Water use may or may not be broken down into the major sectors of residential, commercial, and industrial need. This approach was used extensively prior to the 1960’s and still is used by smaller municipalities.

Requirements and Projection Approach T h s technique extends the use of present trends by allowing for increases in domestic

water using devices. Wolff (1957) has recommended that for the period 1955 to 1975 an increase of 2 percent per capita per year be used for design of residential water distri- bution systems. This approach maintains that water resource forecasts should not rely

A Comparison of Multivariate and Trend Forecasting Estimates With Actual Water Use 819

exclusively upon past experience due to the possibility of increased utilization of water consuming equipment in homes over time.

Fire Flow Approach An elaboration of Wolffs approach, this technique goes beyond the projection of past

and present trends plus percentage increases to include fire flow, the amount of water required above daily water demands to meet emergency fire protection. In Canada, flow rates are established by the Insurance Advisory Council of Canada. Different fire flows are established for residential, commercial, public and industrial land uses and are based upon building size, construction type, building use, and fire protection equipmcnt incorporated in building design.

Multivariate Approach Sewell and Bower (1968) have urged that an array of variables, including population

size, nature of the economy, technological changes, social tastes, policy decisions and nature of the physical system, be incorporated in forecasts. Whitford (1968) adds another dimension by suggesting that water requirements should be estimated separately for all sectors (residential, commercial, institutional). Furthermore, he argues that the distribu- tion and expected use of water using fixtures and appliances should be included. His approach requires statistical data for water using appliance ownership for households, in- formation from manufacturers regarding water use of appliances, as well as information about personal behaviour concerning water use.

Grima (1972) expands upon the work of Sewell and Bower and Whltford by dividing residential water use into micro and macro levels. The micro scale includes housing density (apartment, single family, semi-detached, etc.), household density, lot size and frequency of water using appliances. Included in the macro scale are precipitation, temperature, water balance and water retaining characteristics of the soil.

The ideal forecasting procedure ,therefore should draw upon past and present trends, as well as considering the demand for each water using sector in the urban area. Included would be housing density, household size, lot size, climate, number and type of water using appliances, water consumption behaviour and fire protection. These are the variables utilized in the following procedure (Figure 1).

THE FORECASTING PROCEDURE The procedure consisted of a series of progressive steps to determine future water

demand in District 6 for both planning options. A second estimate used the Barrie Public Utilities Commission procedure of basing estimates on 100 gallons per capita per day plus fire flow and peak period estimates (trend procedure). In addition to estimating demand for District 6 , both procedures were applied to two other subdivisions (Chez Belle and Tall Trees) in Barrie for which metered records are available. Comparing estimated and actual use was considered a satisfactory test of the reliability and validity of the forecasting procedures.

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TWO OPTIONS

WATER DMAND

LAWN WATERINO

SOCIAL TASTES

Figure 1. Variables in Water Demand Forecasting

Step 1 The first information calculated was number of units, number of different housing

types, lot size, and population size with reference to the official plan. The number of units was calculated on the basis of low, medium and high residential figures outlined in the plan. This consisted of taking 2150 units as the low and 3010 as the high and averaging for a medium level. A breakdown of unit type was given in the plan and consisted of a 60:40 ratio for single and semi-detached to multiple housing. The Barrie Planning Department indicated that the single family units could be assumed to be 35 percent detached and 65 percent semi-detached.

Lot sizes were determined from zoning bylaws. Subsequently, the percentages of each housing type and lot size were calculated. The resulting figures were applied to each of the three alternatives in the plan to obtain a final breakdown of housing numbers. Population estimates were made using population densities prescribed in the plan.

Step 2 This step was identical to the first step except that figures were calculated for the pro-

posal of Letitia Heights Development. The total number of units, types of units, lot sizes and total population were calculated from the draft plans submitted to the Barrie Planning Office.

Step 3 Lawn watering requirements for the official plan and the developer's plan were estimated

next. The average lot size which would require watering was determined. The actual water

A Comparison of Multivariate and Trend Forecasting Estimates With Actual Water Use 82 1

requirements for lawns was assumed to be 1.5” per week, based upon information pub- lished by the Ministry of Agriculture and Food (1973). A reduction of 0.6” was made to take into account natural rainfall (32”/year average in Barrie). Total water requirements, assuming use approaches Ministry guidelines, became 0.9” per week. This number was then translated into gallons per week and a daily total.

Step 4 Number of water using appliances and fixtures was estimated on the basis of data ob-

tained from Information Canada on numbers of washrooms, toilets, washers, dishwashers, automobiles and air Conditioners. Further data sources were interviews with realtors, con- tractors as well as field observation. Swimming pools and central air conditioners were excluded. Swimming pool contractors indicated that the area could expect about 2 percent growth in pools whereas Information Canada data revealed that only 4 percent of house- holds would have central air conditioners. Given these small percentages, it was assumed that their omission would not be substantial.

Step 5 The amount of water required by appliances and fixtures was calculated. Information

sources included engineering data, manufacturers’ specifications, personal observation, and literature. Information was collected for showers, bathtubs, kitchen, laundry and bath- room sinks, dishwashers, toilets and car washing.

Step 6 While Step 5 determined requirements of appliances and fixtures, the sixth stage dealt

with actual use of this equipment. A simple study was conducted. Twelve people recorded their water using activities for a week. The respondents were 3 universitystudents, 2 senior citizens, 2 housewives, and 5 people employed in jobs ranging from labouring to clerical positions. They recorded their daily routine in terms of number of times facilities were used and amount of water used. Based upon these results, averages were calculated and estimates made. Ten percent then was added to domestic use to account for water main leakages, as well as water for cooking, drinking, air conditioners and swimming pools.

Step 7 Included in this stage were estimated water demands for proposed commercial, institu-

tional and public use. For commercial use, the proposed facilities’needs were estimated by examining meter records of comparable facilities elsewhere in the city. Institutional uses (schools) were also estimated using meter records from similar facilities elsewhere in the city.

Step 8 The eighth step related to fire flow requirements. Using the guide issued by the Insur-

ance Services Office, water demand for fire flow was calculated. Estimateswere made for residential, commercial and institutional buildings based upon the insurance guidelines.

82 2 Mitchell and Leighton

Step 9

visions (Chez Belle and Tall Trees). Steps 1 through 8 were then applied to the water demand for the two existing subdi-

Step 10 Water use for Chez Belle and Tall Trees was calculated from existing meter records.

Figures were determined for low, medium and high use from summer records (July- August) and winter records (January-March). The medium level was taken as the average daily need. Fire flow was added to this figure to give total water requirements.

Step 11

This step applied the Barrie Public Utilities procedure of multiplying the expected population by 100 gallons per day plus adding expected fire flow for District 6 . Com- parable calculations were made of the Chez Belle and Tall Trees subdivisions.

Step 12 Water demand for the three options under the official plan and under the developer’s

proposal was determined. Total water demand was calculated for low, medium and high projections for each alternative. For the low daily need the calculated domestic water demand was added to the low commercial, institutional and public water requirements. Fire flow then was added to this calculation. Mediumand high projectionsvaried only from changes in water demand for the commercial, institutional and public uses, with domestic use and fire flow remaining constant. Medium projections used medium water demand for the non-residential land use, while the high projection used the high projections plus lawn watering and car washing.

RESULTS AND IMPLICATIONS The forecasts for the three alternatives under the official plan and the developers’ pro-

posal are shown in Table 1. The trend procedure produces comparable results to the multi- variate procedure. Furthermore, the reliability and validity of both procedures is validated by the forecasts for the two existing subdivisions (Table 2). The ability of the two proce- dures to approximate reality is heartening.

It is still important, however, not to overlook the importance of the multivariate approach since it breaks down water usage into sectors. Some sectors (commercial, in- dustrial) might use larger amounts of water (e.g., soft drink company) than would be accounted for by using population multiplied by an average rate of use.

In addition, the forecasts illustrate that changes, even of a minor nature, can change water usage sharply. Deviations of only 300 units can have a significant impact upon water use. The effect of such a change after a water demand analysis could result in expensive service changes being required after houses and roads were completed. It also could lead to water shortages which might be critical at the time of a fire. In contrast, significantly overdesigning a water supply facility may result in resources being unnecessarily committed which could better be used elsewhere in the community.

A Comparison of Multivariate and Trend Forecasting Estimates With Actual Water Use 823

TABLE 1. Results of Water Demand From Multivariate and Trend Approaches (imperial gallons per minute)

Alternative Population Multivariate Procedure Trend Procedure

Official Plan LOW Medium Hi@

Alternative 1 6,625 609.8 617 840 772.6 Alternative 2 7,950 667.5 675 1,004 864.6 Alternative 3 9,271 725 732.5 1,115 956.3 Developers’ Alternative 6,790 614 621 9 24 784

TABLE 2. Results for Two Established Subdivisions (Chez Belle and Tall Trees) (imperial gallons per minute)

Subdivision Population Multivariate Procedure Trend Procedure Metered Results

Low Medium High Low Medium High

Chez Belle Tall Trees

358 377 403.8 380.5 339 371 403 371 408 446.6 413.5 354 379 404

The attraction of the multivariate procedure as described here is that it is relatively straightforward and relies upon information readily available. The only “new” data were that collected from the survey of water use behaviour. However, the success of the forecast results suggests that a small scale survey is adequate. As a result, the procedure can be operationalized without major costs. On the other hand, the procedure is weak in that it does not explicitly incorporate the impact of changing technology or social taste upon water use patterns. These two variables represent further avenues for research.

LITERATURE CITED Barrie, Ontario, 1974. Amendment No. 12 to the Official Plan of the City of Barrie. Barrie Examiner, 1975. District 6 Mainly Low Density. February 15, 1975, p. 1. Grima, A. P., 1972. Residential Demand, Alternative Choices for Management. University of Toronto

Hawson, L. R., 1955. Forecasting of the Needs of the Chicago Metropolitan Area. Journal of the

Ministry of Agriculture and Food, 1973. Lawns. Toronto, prepared by J. C. Taylor. Proctor and Redfern, 1975. South Reservoir Studies. Barrie Public Utilities Commission.

Press.

American Water Works Association, Vol. 47, p. 1031.

824 Mitchell and Leighton

Sewell, W. R. D., and B. Bower, eds., 1968. Forecasting the Demands for Water. Queen's Printer. Whitford, P. W., 1968. Forecasting Demand for Urban Water Supply. Stanford University Press. Wolff, J. B., 1957. Forecasting Residential Water Requirements. Journal of the American Water Works

Association, Vol. 49, pp. 1225-1235.