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International Journal of Civil Engineering and Technology (IJCIET)
Volume 6, Issue 8, Aug 2015, pp. 15-28, Article ID: IJCIET_06_08_003
Available online at
http://www.iaeme.com/IJCIET/issues.asp?JTypeIJCIET&VType=6&IType=8
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
___________________________________________________________________________
ESTIMATING WATER DEMAND
DETERMINANTS AND FORECASTING
WATER DEMAND FOR NZIOA CLUSTER
SERVICES AREA
Patrick Wanyonyi Munialo
Post Graduate Student, Masinde Muliro University of Science and Technology,
Department of Civil and Structural Engineering, P.O. BOX 190-50100 Kakamega
Carolyne K. Onyancha and Basil Tito Iro Ongo’r
Lecturer, Masinde Muliro University of Science and Technology,
Department of Civil and Structural Engineering, P.O. BOX 190-50100 Kakamega
ABSTRACT
The accuracy of water demand projections depends on the availability of
reliable population and water use data as well as an understanding of the
distribution of different types of users within the community. The underlying
problem for this study is that water demand in Kenya is based on the fact that
operational demand of drinking water is based on experience and appropriated
practices, rather than local empirical evidence. There is limited number of
analytical studies on water demand and supply reliability. In the face of limited
knowledge, per capita use statistics adapted from developed countries are applied
to estimate water consumption in Kenya, and most probably will fail to depict the
water use patterns. At the same time, there is the unknown component of
suppressed consumption induced scarcity and water quality problems. Almost
certainly, will release these constraints, will modify and disrupt the water demand
and design baseline. Finally it is crucial to establish time varying water
consumption patterns and the critical demand values. Correct prediction of these
factors determines the extent to which a network can satisfy critical demand and
maintain economic efficiency. The objective of this study was to model water
demand mathematically to determine the significance of water determinants for
systems design and operations management. To achieve this objective, a survey of
water usage in towns in Bungoma and Trans Nzoia counties was done. The
survey was done in Bungoma town and its environs, Webuye town and its
environs, kitale town and its environs of Nzoia Water Services clustered company
(NZOWASCO). Out of the sample size of 23,000 population a sample size of 517
consumers was chosen across the five categories of consumers namely; domestic,
low income, commercial, industrial and institutional. The presentation has
focused on development of water determinant for domestic and low income
Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r
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consumers. Out of 517 population, the Primary data was collected in the field by
use of structured questionnaire, whereas secondary data was collected from
secondary sources of NZOWASCO. The primary data was used to develop the
regression model. The secondary data was used for sensitivity tests and validation
of the regression model. The results of the model were presented in various forms
and compared with actual data for a period of 2005 and 2014. The model was
able to determine historical water demand and water forecasts for domestic and
low income consumers. The model generated values did not vary significantly
with actual data for historical water demand and forecasting.
Key words: regression model, water demand-determinants, forecasting,
model, primary data and secondary data.
Cite this Article: Munialo, P. W., Onyancha, C. K. and Ongo’r, B. T. I.
Estimating Water Demand Determinants and Forecasting Water Demand for
Nzioa Cluster Services Area. International Journal of Civil Engineering and
Technology, 6(8), 2015, pp 15-28.
http://www.iaeme.com/IJCIET/issues.asp?JTypeIJCIET&VType=6&IType=8
_____________________________________________________________________
1. INTRODUCTION
1.1. BACKGROUND INFORMATION
Forecasting the amount of water to be supplied is a very important factor for design
and operational demand. To guarantee high reliability for water supplies, an intensive
investment to augment flow and operational programme is required. The larger the
flow to be transmitted, the more expensive the investment becomes. Operational
demand of drinking water is presently based more on experience than empirical
evidence and furthermore, water consumption is rarely monitored. When monitoring
does happen, the data is scarcely used to improve day-to-day operations of the water
utilities. Reitveld observes that water supply operations will ordinarily not include
time varying aspects, but is rather fixed. Yet water demand in Kenya’s urban areas is
rapidly changing; the volumes and consumers are rapidly growing, although in a
differentiated manner, and similarly the per capita consumption induced by improving
income and lifestyle. Consequently the water demand is linked to complex
interactions that influence it.
Water demand indicates both current and/or expected water consumption in any
given area over specific time period. While several studies have been conducted in the
developed countries to better understand the characteristics of municipal water uses,
this may not be the case in the developing countries (Hidefumi et al, 2006). This
knowledge is even less understood in Africa. Generally, water demands vary and
consideration of the probabilistic nature of the variations lead to more instructive
assessments of the performance and reliability of water distribution systems
(Tanyimbo et al, 2005).
Little is known about water use statistics in Kenya. Firstly, because Kenya is
developing economy, secondly because of the limited number of analytical studies on
water demand and supply reliability, and finally because of the unknown scarcity
induced consumption patterns and impacts of water quality on consumption.
Convectional analysis may not be applied directly in Kenya and may even fail to
explain the water use patterns. Moreover, previous design and reliability analysis
methods for water distribution systems were based on a fixed value of demand. There
Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster
Services Area
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is little information in the literature on this fixed demand value and how it can be
calculated. In order to understand water supply demand in Kenya, it is necessary to
identify and model the determinants of water use demand and investigate the
disaggregated pattern of use. Plainly a water supply quantity at any given instance is a
chance event limited by social and environmental conditions. Therefore studying the
probabilistic nature of demand should lead to more realistic assessments of the
demand and performance of water distribution systems.
1.2. NEED FOR DEMAND FORECASTING
Water demand forecasting has become an essential ingredient in effective water
resources planning and management. Water forecasts, together with an evaluation of
existing supplies, provide valuable triggers in determining when, or if new sources of
water must be developed. In the NZOWASCO cluster region, this emphasis on
accurate water forecasts is particularly important. There is an increased need for water
demand forecasts as water rights conflicts continue, the area's population grows, the
need for in stream flows is more accurately quantified, and additional uses and needs
of water are identified. Demand for water comprises not only that required for
customers but also leakage from the distribution network, since it is the combined
amount which is put into supply. (Therefore is normally estimated by means of
district metering. Forecasting provides a simulated, though rarely perfect, view of the
future. Forecasting water demand is inherently challenging, as the factors that most
directly affect water demand are difficult to predict. However, effective water
resource planning can account for economic, social, environmental, and political
impacts on water demand. Though water demand models assume various forms,
model developed in this research is for forecasting water demand for a period of at
least five years.)
This research considers, modeling a regression model for domestic water demand
forecasting based on population Size, Price (tariff) and Income. Population size for
domestic consumers comprised of number of persons per connection whereas the
price of water was considered per M3
bearing in mind how the water pricing has
changed over time and income per household variable which was considered during
the survey period. The three variables were considered instrumental in providing
utilities with the ability to micromanage water use, identify specific problem areas,
and negotiate urban development based on resource supply. The modeling focused on
domestic and low income consumption characteristics.
2. THEREOTICAL BASIS FOR MODELING OF WATER
DEMAND FORECASTING
Modeling of water demand in Nzoia water services cluster company was based on the
existing theoretical regulatory frame work. Water demand forecasting is a function of
an underlying decision making process that takes water usage preferences and
constraints on acquiring water into account (Larson et al. 2006). Essentially, this
implies that the analysis of water demand is critical for designing an effective water
demand policy for efficient use of water resources. Water is a social good that has
attracted a strict administrative framework for both operations and marketing. These
has affected the e fundamental decisions, like the determination of investments and
prices. In such a framework where the regulator has to consult the market or
customers before adjusting the tariff structure or price for water acquires a special
significance, since the decision-makers require sufficient knowledge and information
Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r
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costs (Bithas kostasa and stoforos chrysostomosb,2006) . Furthermore, if the objective
of water policy is t o ensure socially efficient use, demand analysis is a precondition
of designing such a policy, since it defines the optimum socioeconomic water use and
the respective water price (Martiner-Espineira et al. 2004, Espey et al. 1997, Arbues
et al. 2003, Bithas and chrysostomosb,2006) [1–3].
YD = βi ΣCij ln Pj + Σγik ln Zk (1)
Figure 1 Conceptual Model framework for water demand model: Source (Munialo P. W.
2008)
Level of
model
complexity
FORMULATION
Define time and space
domain of water
demand system
Establish and
quantify data
Select criteria to guide the decision
Water demand problem analysis
reformulation and solutions
Data collection
INTERPRETATION
Model testing
Not satisfied
VERIFICATION
SOLUTION
Satisfie
dOutput
Sensitivity
Validation
Problem definition:-outline the
factors influencing Water demand
Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster
Services Area
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Efficient use is defined as a pattern of use that maximizes the benefits arising from
the exploitation of water resources (Tietenberg 1996, Pearce 1999) [7, 8]. Secondly,
whereas in a competitive conditions, the price of water would be determined by the
interaction of market demand and supply forces to reflect the actual costs of water
usage (Bithas and stoforos 2006). The supply of water is a monopoly whose
characteristics closely resemble those of a “natural” monopoly. Specifically, the
extremely high infrastructure costs for transporting, treating and delivering water
make difficult the operation of multiple water suppliers [5, 6].
Modeling of water demand forecasting for Nzoia Water Services Cluster
Company was anchored on economic characteristics of water demand such as,
customer behaviors, income levels, level of industrialization, etc. The mathematical
equation applied in this model is
3. MATERIALS AND METHODS
The ultimate objective of this research was to come up with a mathematical model for
water-demand forecasting. Figure 1 illustrates the conceptual frame work for water
demand adapted in this research.
3.1. Study Design
Domestic water consumption is based on multifold factors including human behavior,
culture, economic status, etc. These obvious seasonal variations too. Availability is
yet another important factor in water consumption. (NGO Forum for Urban Water and
Sanitation report, 2003) [9]. This study design incorporated the major factors
influencing water consumption in Nzoia Water Company cluster region. A survey to
determine spatially explicit characteristics of water demand, its determinants and
forecast was carried out. The survey design incorporated complexities of the
NZOWASCO clustered region morphology, covering three urban centers (Kitale,
Webuye and Bungoma), selected survey instruments and identified procedures to
follow.
The study made use of both primary and secondary sources of data. The primary
data was collected from the users by using both structured (close ended) and
unstructured (open ended) questionnaires. Questionnaires were designed targeting
objectives of the study. Several questions were included to supplement the study and
enhance the results. Besides the direct questions on water and its consumption, several
indirect questions were asked to identify their economic status and sources of water.
Observations were made by the enumerators to supplement grouping of economic
class of the respondents. The survey was Random Sampling (RS) and Probability
Proportional to Size (PPS) methods for selecting customers for domestic and low
income consumers from the three NZOWASCO regions. Survey methodology was
designed strategically in order to include all categories of users from all the three
regions of NZOWASCO as much as possible. The secondary sources involved
review of a variety of documents in order to gain more insight into the subject at
hand. This included review of Company records on production, volume billed,
revenue, customer care over the year, size of population within serving clients, reports
and other published materials. Such documents were used to gain a deeper
understanding of user characteristics.
In this research cluster sampling procedure with probability proportion to size of
each sample was used. The categories of users identified in this study are Domestic
and low income consumers. At the initiation of the study, NZOWASCO provided the
Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r
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researcher with a list and location of consumers. The consumers were based on
volume of use and region. A sample of population 223 respondents consisting of low
and domestic consumers was picked across the three regions (Kitale, Webuye and
Bungoma towns). At first a minimum of 10 consumers were picked per category of
consumers in each region for pretesting purpose. After this the questionnaire was
corrected, areas that need clarification was done, ambiguity in questions was
minimized. The sample frame was done based on Yamane (1967) formula. A sample
is a smaller group or sub group obtained from accessible population (Mugenda and
Mugenda, 2009) [4]. According to Yamane (1967), [10] sample size (n); is obtained
as under:-
Where;
n = the sample size
N = the population size.
e = the error margin.
The sample picked per category was proportionately shared based on the number
of customers per region. Random probability sampling was then used to study water
use characteristics spatially explicit to category of users and to establish and estimate
time varying trends linked to income, lifestyle, climate, price and other factors. A
total of 323 consumers based on Yamane (1967) formula for both domestic and low
income consumers was picked. Apart from the 323 respondents, additional 30 booster
samples were collected from NZOWASCO supply area. The purpose of the 30
booster sampling was to compare water consumption in unconstrained situation.
3.2. Framework of Mathematical Modeling for Water Demand
Forecasting
Analyzing and forecasting changes in demand across the users especially residential
users over the long term is of interest to a wide variety of planning studies. This
theses adopted a model is based on the static theory of optimizing consumer behavior
assuming similarity of preferences, homogeneity of goods and perfect information.
According to microeconomic theory, the individual choice is conceived as an
interrelationship among the quantity of goods that the consumer wishes and is able to
buy in terms of price, income, y, his preferences as well as social and demographic
characteristics. In other words, the consumer divides his income between quantities of
goods and services, so that an increase in the utility level, u, derived by the individual
consumption, is ascribed as: max u = u(q), pq = y pq = Σpiqi Using the appropriate
substitutions, the demand functions are obtained by simple differentiation as follows:
YD= βi ΣCij ln Pj + Σγik ln Zk (2)
Where; lnD is the logarithm of the corresponding demand, lnP is the logarithm of the
price of water depending on customer category and lnZ other shift variables income,
trend, etc.).
The current model is based on a model where the pattern of water consumption is
the endogenous variable and price, income, population and water production are the
main determinants of the system. The functional form of the equations and the
parameters needed for forecasting purposes are derived from Equation 2.
Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster
Services Area
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3.3. Scope of the Model under Study
The objective of the study was to develop the mathematical model to predict the water
demand. The scope consist of mathematical equations for water forecasting based on
water determinants in Nzoia Water Company Cluster. The primary data from the field
was used for model formulation wheas the secondary data was used for testing and
validation of the model.
3.4. Background to the model
Nzoia Water Services Company has in operation since 2005. The clustered company
covers a companied coverage area of over 300 Km2
. Nzoia water Services Company
covers the area of 110 km2
in Trans-Nzoia county specifically Kitale town with its
environs , Webuye and Bungoma towns and their environs covering an area of 50
Km2
and 65 Km2
respectively. Both towns are in Bungoma County. Kimilili covers
110 Km2
, whereas Malaba, Kocholia, Malakisi and Amukura covers companied area
of 80 Km2
. The study focused on the three towns, Kitale, Webuye and Bungoma. The
three towns have a companied population served of 360,000. The water coverage in
these towns is over 80%. The companied customer base is about 21,000. Nzowasco
cluster area has a typical tropical climate with a mean temperature at. NZOWASCO
cluster region has a typical mean temperature of 27.3 °C with the highest temperature
on the highlands being at Kitale at 25 °C and highest temperatures in low areas like
Bungoma being at 29.3 °C . The minimum temperature during the day is in the range
of 18 °C. The mean total precipitation of the area is 1400 mm/year, Relative Humidity
is between 65% and 63% in July and the average maximum temperature is 31 °C in
January. Nzoia cluster is located in a hot and wet climate region. Nowadays, water is
almost exclusively provided by the Nzoia water Services Company, which until 2004
was under Local authorities and ministry of water development and national water
and conservation management. The state is still the main decision-maker for water
policy. The state mandated the regulator i.e. Water Services Regulatory Board
(WASREB) through Lake Victoria North Water Services Board to regulate the
provision of water services for water services providers of which Nzoia water
Services Company was licensed to operate in tran-nzoia and Bungoma counties.
This research examines water use across the domestic users in Nzoia cluster with
a purpose of developing a mathematical model to predict water demand forecasting.
Domestic use in Nzoia cluster accounts for over 80% whereas other categories of
users account for less than 20%. Furthermore, the case of demand for water in the
region presents some interesting history in water pricing for the last eleven years
where by the water tariff has changed three times that is phase one pricing was
between 2005 to 2008, phase two was between 2008 to 2011 and phase three was
between 2011 to 2014.
Between 2008 and 2014 major investments were undertaken in the cluster and
water prices were increased and as the public realized, through strict administrative
measures and extensive water coverage, the water coverage increased and customer
base also increased from a mere 6000 connections to 21000 connections level in
2014. In this context, water demand management is of paramount importance for the
sustainability of the Nzowasco cluster water system.
3.5. Sources of Data for demand forecasting model.
In order to estimate water demand determinants, annual time series across the
category of users for the NZOWASCO cluster area. The data was captured by a
Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r
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questionnaire tool on water pricing consumption or demand, size of household or
number of persons per connection, the income per household, hours of supply across
category of consumers. The data collected during the survey was used for modeling.
Secondary data from NZOWASCO covering the period of 2005 and 2014 that is time
varying trends like pricing (pricing, consumption trends, population growth trends,
population were used for validation of the model).
3.6. Model Formulation
3.6.1. Normality Test
The normality test among the categories i.e. Domestic, Low income, industrial,
institutional and commercial was done to investigate the skewness of demand. The
consumption of water in all categories of consumption in study area is normal based
on the probabilistic normal graph drawn over the demand pattern for water within a
year hence no positive or negative skewness for the demand. The mean and standard
deviation of the data was considering the sample of 517.
Figure 2 Water demand normality test
3.6.2. Modelling
According to the methodology described in chapter three, the following equation was
used to validate mathematical model for demand forecasting.
YD = α + βi ln Pw + γi ln + δi ln X + εi (3)
Where YD stands for the quantity of residential water demanded, Pw for the water
price, in real disposable income, X for the vector of other variables (in this particular
case a trend variable as a proxy to weather variations) and ε the error term. Moreover
price and income are expressed in real terms using CPI as the deflator.
It is important to stress that income captured under domestic and low income and
the size of household population was used for deriving domestic and low income
consumer’s category. Equation 3 was transformed depending on the variables used to
Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster
Services Area
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estimate water demand for Nzoia cluster region. The results of multiple regression
analysis model was generated and recorded in the Tables below. (Tables 1 and 2).
Table 1 Regression Analysis for the determinant of water for the Domestic and Low income
Independent
Variables
Coefficients
T Sig.Unstandardized Coefficients
Standardized
Coefficients
B Std. Error Beta
(Constant) 6210.923 3845.739 1.615 .000
Household
Size
29.452 119.482 .099 .247 .000
Income 26.029 678.245 .072 .038 .000
Tariff -12.066 37.707 -.018 -.320 .000
a. Dependent Variable: Quantity Supplied Month
Table 2 Model Summary for domestic and low income consumers
Model R R Square Adjusted R
Square
Std. Error of the Estimate
1 .024a
.0567 .099 20319.339
a. Predictors: (Constant), Tariff, Household Size, Income
4. DISCUSSION OF RESULTS
4.1. Domestic and Low income water determinant Regression Model
The result showed a positive correlation of r=0.024 with a high coefficient
determination of r2
=0.0567 and its adjusted value of 0.0829 at 95% significance level.
YD = f (α, HHz, In, Tariff, £) (4)
Where YD - the water consumption demand
Α - Constant
HHz - Household Size
In - income per month
Tariff = price of water per month
£ - Error term
YD=α+βHHz+µIn- Tariff+£
YD=6210.92+0.099HHz+0.072In-0.018Tariff+£
The result above shows that Income, Population size and Tariff were statistically
significant determinant of water demand in the study area. The tariff applied on water
use has a strong negative effect on residential water consumption. As such, water
consumption decreases when tariff growth is recorded. Thus, according to the
literature, tariffs are frequently used as a tool for improving water savings. The
implementation of efficient water-pricing practices that promote equity, efficiency
and sustainability in the water sector is probably the simplest conceptual instrument.
Using tariffs as a manner in which to regulate water consumption could potentially
have a greater effect on lower income households, since water has no substitutes for
basic uses and there is an amount of water that is highly insensitive to price changes.
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While income per capita and household size has a positive effect of 0.099 and 0.072
on water consumption for domestic and low income hence for any change by a unit in
income and population size leads to a corresponding significant increase in water
demand. Figure 3 illustrate the model generated based on determinant of water
demand. Figure 3 below shows the estimation of water demand under domestic and
low income categories using different population size, income and tariffs.
Figure 3 Model generated based on determinant of water demand for domestic and low
income consumers
4.2. Sensitivity of the Model in the Area
Sensitivity of the model in estimating water demand was investigated through
estimating water supplied against water demand over the years. The model was used
to forecast the demand over the years and comparing the water supplied that time. The
line of best fit was drawn over the estimated water estimate line over the years.
In order to assess the sensitivity of the model and its credibility of results, the
model was run over the sample period (2005–2014). In Figures 3 and 4, comparisons
between actual and fitted values are presented. It is clear that the actual demand and
estimated demand are reasonably close. Additionally, two statistics for examining the
forecasting accuracy, namely the correlation between determinants of water demand
(R2
) and the standards deviation error of the estimates are reported as indicated in
Table 1 demand for domestic and low income and Table 2 for other consumer
categories. The statistics suggest that the model tracks historical water demand
patterns fairly well. Overall, the results for both stages can be considered promising, a
fact that permits us to continue with the post sample prediction through policy
scenarios.
4.3. Further Sensitivity and Forecasting Demand
In order to be able to recognize the possible policy and theoretical implications of the
results, it was considered important to conduct a further sensitivity analysis. Five
scenarios were examined. The first scenario considered the Forecasting demand for a
constant tariff, 10 ten percent increase in connections and five percent increase in
income. In the second scenario the model was used for projection of Demand
0
5000
10000
15000
20000
2005/06 2006/07 2007/08 2008/09 2009/10 2010/11 2011/12 2012/13 2013/14
ESTIMATED WATER DEMAND BY THE MODEL
OVER THE YEARS
Estimated_Demand
AverageDemandOverthe
Years
YD=6210.92+0.099HHz+0.072In-0.018Tariff+£
Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster
Services Area
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forecasting for a reducing tariff of (10%), increment in connections (10%) and income
(5%) across the five year period. In both scenarios, real historical figures to carry out
projections prices are assumed to be fixed for the period 2015–2020 and the income,
house hold size growth of customer base is determined from historical figures. In third
scenario demand forecasting for increment in tariff by 4% annually, connections
(10%) and income (5%). The fourth scenario was demand forecasting for increment in
tariff (20%), is applied during the base year and is to run for five years, connections
(10%) and income (5%). The fifth scenario was forecasting demand for %increment
tariff by 20% and connection (10%). Finally the sixth scenario forecasting demand
for %increment in tariff by 4% and connection (10%). The explanations of the
findings are illustrated in the following figures.
Figure 1 Estimating water demand using the regression model
Figure 5 Forecasting demand for a constant tariff, %increment in connection (10%) and
income (5%)
0
5000
10000
15000
20000
25000
2005/06 2006/07 2007/08 2008/09 2009/10 2010/11 2011/12 2012/13 2013/14
ESIMATED WATER DEMAND OVER THE YEARS
Av. Demand Estimated_Demand
AverageDemandOverthe
Years
0
5000
10000
15000
20000
25000
Demand Forecasting
Estimated_Demand
Av.Demand
YD=6210.92+0.099HHz+0.072In-0.018Tariff+£
Trend Line of best fit
YD=6210.92+0.099HHz+0.072In-0.018Tariff+£
Actual Demand
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When a forecast was conducted to investigate the rate of consumption over the years
until 2020, the results showed that for any increment of connections by 10% and
income 5% p.a at a constant tariff there is increase in water demand by 3.2%. The
graph above illustrate the estimated forecast values of water demand based on
domestic consumption category.
Figure 6 Demand forecasting for a reducing tariff (10%), increment in connections (10%)
and income (5%)
Investigation on the variation of water demand when the tariff reduced by 10%
and increment of connections at 10% and income increase at 5%. The result illustrated
above shows that for any indicated change there is a change in water demand at a rate
of 3.3%. The change shows that water price is significant in determining the
consumption such that for any reduction made there will be an increase in water
demand under domestic category.
Figure 7 Demand forecasting for increment in tariff (20%), connections (10%) and income
(5%)
0
5000
10000
15000
20000
25000
Demand Forecasting
Estimated_Demand
Av.ConnectionGrowth
v.ConnectionGrowth
YD=6210.92+0.099HHz+0.072In-0.018Tariff+£
0
5000
10000
15000
20000
25000
Demand Forecasting
Estimated_Demand
Av.ConnectionGrowth
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Further investigation was tested based on increase of tariff by 20%, connections
by 10% and income by 5%. The results showed that for any increment in water tariff
there will be a significant reduction in water demand by 1.5% as compared to a case
where the tariff was reduced by 10%. These results reveals that for any larger percent
increment of tariff will lead to a significant reduction in water demand.
Figure 8 Demand forecasting for increment in tariff (4%), connections (10%) and income
(5%)
A test was conducted to investigate what will happen to demand when a tariff
changes with smaller percentage of 4% and increment in connections by 10% income
5%pa. The results reveals that for any above changes effected there will be water
demand at a rate of 2.4%. As compared to above case where there was increase of
tariff by 20% the demand rate for smaller percent change is higher than a larger
percent. Therefore the model stands advise that if the company would like to increase
water demand, the percentage increase in tariff should be reasonable.
1. This Research in water resource management has revealed the key parameters to
forecast water demand for domestic and low income consumers are price for water,
population size/ Household size or number of persons per connection and income for
consumers
2. The model thus, ( YD = 6210.92+0.099HHz + 0.072In – 0.018Tariff + £ )
Where YD-the water consumption demand, α- Constant, HHz-Household Size In-
income per month, Tariff = price of water per month, £-Error term
YD = α + βHHz + µIn- Tariff + £, to predict water demand for domestic users has been
developed.
These conclusions also represent hopeful applications of the research completed in
this thesis. Water demand forecasting model has been estimated using the following
equations/models;
YDdl=f (α, HHz, In, Tariff, £) (5)
YDics=α + βHHz + µIn – Tariff + £ (6)
Combined Equation YD = YDdl + YDics
0
5000
10000
15000
20000
25000
Demand Forecasting
Estimated_Demand
Av.ConnectionGrowth
YD=6210.92+0.099HHz+0.072In-0.018Tariff+£
Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r
http://www.iaeme.com/IJCIET/index.asp 28 editor@iaeme.com
REFERENCES
[1] Arbues, F., Garcia-Valinas M. A. and Martinez-Espineira, R. Estimation of
residential water demand: a state-of-the-art review. The Journal of Socio-
Economics, 32, 2003, pp. 81–102.
[2] Espey, M., Espey, J. and Shaw, W. D. Price elasticity of residential demand for
water: a meta-analysis. Water Resource Research, 33(6), 1997, pp. 1369–1374.
[3] Martinez-Espineira, R. and Nauges, C. Is All Domestic Water Consumption
Sensitive to Price Control? Applied Economics, 36, 2004, pp. 1697–1703.
[4] Mugenda, M. O. Research Methods: Quantitative and qualitative approaches.
African Center for Technology Studies, 1999.
[5] Surendra, H. J. and Deka, P. C. Effects of Statistical Properties of Dataset in
Predicting Performance of Various Artificial Intelligence Techniques for Urban
Water Consumption Time Series. International Journal of Civil Engineering &
Technology, 3(2), 2012, pp. 60–69
[6] Das, K. K., Kumar, D. V., Udayalaxmi, G. and Muralidhar, M. Fluoride
Contamination in the Groundwater in Mathadi Vague Basin in Adilabad District,
Telangana State, India. International Journal of Civil Engineering & Technology,
5(7), 2014, pp. 55–63.
[7] Pearce, D. (Pricing Water: Conceptual and Theoretical Issues, Paper for European
Commission for the Conference on Pricing Water: Economics, Environment and
Society. Portugal: Sintra, 1999.
[8] Tietenberg, T. Environmental and Natural Resources. N Y.: Harper Collins, 1996.
[9] NGO Forum for Urban Water and Sanitation Report. International Institute for
Sustainable Development. 82(40), 2003.
[10] Yamane, T. Elementary Sampling Theory. Englewood Cliffs, New Jersey:
Prentice Hall, 1967

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  • 1. http://www.iaeme.com/IJCIET/index.asp 15 editor@iaeme.com International Journal of Civil Engineering and Technology (IJCIET) Volume 6, Issue 8, Aug 2015, pp. 15-28, Article ID: IJCIET_06_08_003 Available online at http://www.iaeme.com/IJCIET/issues.asp?JTypeIJCIET&VType=6&IType=8 ISSN Print: 0976-6308 and ISSN Online: 0976-6316 © IAEME Publication ___________________________________________________________________________ ESTIMATING WATER DEMAND DETERMINANTS AND FORECASTING WATER DEMAND FOR NZIOA CLUSTER SERVICES AREA Patrick Wanyonyi Munialo Post Graduate Student, Masinde Muliro University of Science and Technology, Department of Civil and Structural Engineering, P.O. BOX 190-50100 Kakamega Carolyne K. Onyancha and Basil Tito Iro Ongo’r Lecturer, Masinde Muliro University of Science and Technology, Department of Civil and Structural Engineering, P.O. BOX 190-50100 Kakamega ABSTRACT The accuracy of water demand projections depends on the availability of reliable population and water use data as well as an understanding of the distribution of different types of users within the community. The underlying problem for this study is that water demand in Kenya is based on the fact that operational demand of drinking water is based on experience and appropriated practices, rather than local empirical evidence. There is limited number of analytical studies on water demand and supply reliability. In the face of limited knowledge, per capita use statistics adapted from developed countries are applied to estimate water consumption in Kenya, and most probably will fail to depict the water use patterns. At the same time, there is the unknown component of suppressed consumption induced scarcity and water quality problems. Almost certainly, will release these constraints, will modify and disrupt the water demand and design baseline. Finally it is crucial to establish time varying water consumption patterns and the critical demand values. Correct prediction of these factors determines the extent to which a network can satisfy critical demand and maintain economic efficiency. The objective of this study was to model water demand mathematically to determine the significance of water determinants for systems design and operations management. To achieve this objective, a survey of water usage in towns in Bungoma and Trans Nzoia counties was done. The survey was done in Bungoma town and its environs, Webuye town and its environs, kitale town and its environs of Nzoia Water Services clustered company (NZOWASCO). Out of the sample size of 23,000 population a sample size of 517 consumers was chosen across the five categories of consumers namely; domestic, low income, commercial, industrial and institutional. The presentation has focused on development of water determinant for domestic and low income
  • 2. Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r http://www.iaeme.com/IJCIET/index.asp 16 editor@iaeme.com consumers. Out of 517 population, the Primary data was collected in the field by use of structured questionnaire, whereas secondary data was collected from secondary sources of NZOWASCO. The primary data was used to develop the regression model. The secondary data was used for sensitivity tests and validation of the regression model. The results of the model were presented in various forms and compared with actual data for a period of 2005 and 2014. The model was able to determine historical water demand and water forecasts for domestic and low income consumers. The model generated values did not vary significantly with actual data for historical water demand and forecasting. Key words: regression model, water demand-determinants, forecasting, model, primary data and secondary data. Cite this Article: Munialo, P. W., Onyancha, C. K. and Ongo’r, B. T. I. Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster Services Area. International Journal of Civil Engineering and Technology, 6(8), 2015, pp 15-28. http://www.iaeme.com/IJCIET/issues.asp?JTypeIJCIET&VType=6&IType=8 _____________________________________________________________________ 1. INTRODUCTION 1.1. BACKGROUND INFORMATION Forecasting the amount of water to be supplied is a very important factor for design and operational demand. To guarantee high reliability for water supplies, an intensive investment to augment flow and operational programme is required. The larger the flow to be transmitted, the more expensive the investment becomes. Operational demand of drinking water is presently based more on experience than empirical evidence and furthermore, water consumption is rarely monitored. When monitoring does happen, the data is scarcely used to improve day-to-day operations of the water utilities. Reitveld observes that water supply operations will ordinarily not include time varying aspects, but is rather fixed. Yet water demand in Kenya’s urban areas is rapidly changing; the volumes and consumers are rapidly growing, although in a differentiated manner, and similarly the per capita consumption induced by improving income and lifestyle. Consequently the water demand is linked to complex interactions that influence it. Water demand indicates both current and/or expected water consumption in any given area over specific time period. While several studies have been conducted in the developed countries to better understand the characteristics of municipal water uses, this may not be the case in the developing countries (Hidefumi et al, 2006). This knowledge is even less understood in Africa. Generally, water demands vary and consideration of the probabilistic nature of the variations lead to more instructive assessments of the performance and reliability of water distribution systems (Tanyimbo et al, 2005). Little is known about water use statistics in Kenya. Firstly, because Kenya is developing economy, secondly because of the limited number of analytical studies on water demand and supply reliability, and finally because of the unknown scarcity induced consumption patterns and impacts of water quality on consumption. Convectional analysis may not be applied directly in Kenya and may even fail to explain the water use patterns. Moreover, previous design and reliability analysis methods for water distribution systems were based on a fixed value of demand. There
  • 3. Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster Services Area http://www.iaeme.com/IJCIET/index.asp 17 editor@iaeme.com is little information in the literature on this fixed demand value and how it can be calculated. In order to understand water supply demand in Kenya, it is necessary to identify and model the determinants of water use demand and investigate the disaggregated pattern of use. Plainly a water supply quantity at any given instance is a chance event limited by social and environmental conditions. Therefore studying the probabilistic nature of demand should lead to more realistic assessments of the demand and performance of water distribution systems. 1.2. NEED FOR DEMAND FORECASTING Water demand forecasting has become an essential ingredient in effective water resources planning and management. Water forecasts, together with an evaluation of existing supplies, provide valuable triggers in determining when, or if new sources of water must be developed. In the NZOWASCO cluster region, this emphasis on accurate water forecasts is particularly important. There is an increased need for water demand forecasts as water rights conflicts continue, the area's population grows, the need for in stream flows is more accurately quantified, and additional uses and needs of water are identified. Demand for water comprises not only that required for customers but also leakage from the distribution network, since it is the combined amount which is put into supply. (Therefore is normally estimated by means of district metering. Forecasting provides a simulated, though rarely perfect, view of the future. Forecasting water demand is inherently challenging, as the factors that most directly affect water demand are difficult to predict. However, effective water resource planning can account for economic, social, environmental, and political impacts on water demand. Though water demand models assume various forms, model developed in this research is for forecasting water demand for a period of at least five years.) This research considers, modeling a regression model for domestic water demand forecasting based on population Size, Price (tariff) and Income. Population size for domestic consumers comprised of number of persons per connection whereas the price of water was considered per M3 bearing in mind how the water pricing has changed over time and income per household variable which was considered during the survey period. The three variables were considered instrumental in providing utilities with the ability to micromanage water use, identify specific problem areas, and negotiate urban development based on resource supply. The modeling focused on domestic and low income consumption characteristics. 2. THEREOTICAL BASIS FOR MODELING OF WATER DEMAND FORECASTING Modeling of water demand in Nzoia water services cluster company was based on the existing theoretical regulatory frame work. Water demand forecasting is a function of an underlying decision making process that takes water usage preferences and constraints on acquiring water into account (Larson et al. 2006). Essentially, this implies that the analysis of water demand is critical for designing an effective water demand policy for efficient use of water resources. Water is a social good that has attracted a strict administrative framework for both operations and marketing. These has affected the e fundamental decisions, like the determination of investments and prices. In such a framework where the regulator has to consult the market or customers before adjusting the tariff structure or price for water acquires a special significance, since the decision-makers require sufficient knowledge and information
  • 4. Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r http://www.iaeme.com/IJCIET/index.asp 18 editor@iaeme.com costs (Bithas kostasa and stoforos chrysostomosb,2006) . Furthermore, if the objective of water policy is t o ensure socially efficient use, demand analysis is a precondition of designing such a policy, since it defines the optimum socioeconomic water use and the respective water price (Martiner-Espineira et al. 2004, Espey et al. 1997, Arbues et al. 2003, Bithas and chrysostomosb,2006) [1–3]. YD = βi ΣCij ln Pj + Σγik ln Zk (1) Figure 1 Conceptual Model framework for water demand model: Source (Munialo P. W. 2008) Level of model complexity FORMULATION Define time and space domain of water demand system Establish and quantify data Select criteria to guide the decision Water demand problem analysis reformulation and solutions Data collection INTERPRETATION Model testing Not satisfied VERIFICATION SOLUTION Satisfie dOutput Sensitivity Validation Problem definition:-outline the factors influencing Water demand
  • 5. Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster Services Area http://www.iaeme.com/IJCIET/index.asp 19 editor@iaeme.com Efficient use is defined as a pattern of use that maximizes the benefits arising from the exploitation of water resources (Tietenberg 1996, Pearce 1999) [7, 8]. Secondly, whereas in a competitive conditions, the price of water would be determined by the interaction of market demand and supply forces to reflect the actual costs of water usage (Bithas and stoforos 2006). The supply of water is a monopoly whose characteristics closely resemble those of a “natural” monopoly. Specifically, the extremely high infrastructure costs for transporting, treating and delivering water make difficult the operation of multiple water suppliers [5, 6]. Modeling of water demand forecasting for Nzoia Water Services Cluster Company was anchored on economic characteristics of water demand such as, customer behaviors, income levels, level of industrialization, etc. The mathematical equation applied in this model is 3. MATERIALS AND METHODS The ultimate objective of this research was to come up with a mathematical model for water-demand forecasting. Figure 1 illustrates the conceptual frame work for water demand adapted in this research. 3.1. Study Design Domestic water consumption is based on multifold factors including human behavior, culture, economic status, etc. These obvious seasonal variations too. Availability is yet another important factor in water consumption. (NGO Forum for Urban Water and Sanitation report, 2003) [9]. This study design incorporated the major factors influencing water consumption in Nzoia Water Company cluster region. A survey to determine spatially explicit characteristics of water demand, its determinants and forecast was carried out. The survey design incorporated complexities of the NZOWASCO clustered region morphology, covering three urban centers (Kitale, Webuye and Bungoma), selected survey instruments and identified procedures to follow. The study made use of both primary and secondary sources of data. The primary data was collected from the users by using both structured (close ended) and unstructured (open ended) questionnaires. Questionnaires were designed targeting objectives of the study. Several questions were included to supplement the study and enhance the results. Besides the direct questions on water and its consumption, several indirect questions were asked to identify their economic status and sources of water. Observations were made by the enumerators to supplement grouping of economic class of the respondents. The survey was Random Sampling (RS) and Probability Proportional to Size (PPS) methods for selecting customers for domestic and low income consumers from the three NZOWASCO regions. Survey methodology was designed strategically in order to include all categories of users from all the three regions of NZOWASCO as much as possible. The secondary sources involved review of a variety of documents in order to gain more insight into the subject at hand. This included review of Company records on production, volume billed, revenue, customer care over the year, size of population within serving clients, reports and other published materials. Such documents were used to gain a deeper understanding of user characteristics. In this research cluster sampling procedure with probability proportion to size of each sample was used. The categories of users identified in this study are Domestic and low income consumers. At the initiation of the study, NZOWASCO provided the
  • 6. Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r http://www.iaeme.com/IJCIET/index.asp 20 editor@iaeme.com researcher with a list and location of consumers. The consumers were based on volume of use and region. A sample of population 223 respondents consisting of low and domestic consumers was picked across the three regions (Kitale, Webuye and Bungoma towns). At first a minimum of 10 consumers were picked per category of consumers in each region for pretesting purpose. After this the questionnaire was corrected, areas that need clarification was done, ambiguity in questions was minimized. The sample frame was done based on Yamane (1967) formula. A sample is a smaller group or sub group obtained from accessible population (Mugenda and Mugenda, 2009) [4]. According to Yamane (1967), [10] sample size (n); is obtained as under:- Where; n = the sample size N = the population size. e = the error margin. The sample picked per category was proportionately shared based on the number of customers per region. Random probability sampling was then used to study water use characteristics spatially explicit to category of users and to establish and estimate time varying trends linked to income, lifestyle, climate, price and other factors. A total of 323 consumers based on Yamane (1967) formula for both domestic and low income consumers was picked. Apart from the 323 respondents, additional 30 booster samples were collected from NZOWASCO supply area. The purpose of the 30 booster sampling was to compare water consumption in unconstrained situation. 3.2. Framework of Mathematical Modeling for Water Demand Forecasting Analyzing and forecasting changes in demand across the users especially residential users over the long term is of interest to a wide variety of planning studies. This theses adopted a model is based on the static theory of optimizing consumer behavior assuming similarity of preferences, homogeneity of goods and perfect information. According to microeconomic theory, the individual choice is conceived as an interrelationship among the quantity of goods that the consumer wishes and is able to buy in terms of price, income, y, his preferences as well as social and demographic characteristics. In other words, the consumer divides his income between quantities of goods and services, so that an increase in the utility level, u, derived by the individual consumption, is ascribed as: max u = u(q), pq = y pq = Σpiqi Using the appropriate substitutions, the demand functions are obtained by simple differentiation as follows: YD= βi ΣCij ln Pj + Σγik ln Zk (2) Where; lnD is the logarithm of the corresponding demand, lnP is the logarithm of the price of water depending on customer category and lnZ other shift variables income, trend, etc.). The current model is based on a model where the pattern of water consumption is the endogenous variable and price, income, population and water production are the main determinants of the system. The functional form of the equations and the parameters needed for forecasting purposes are derived from Equation 2.
  • 7. Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster Services Area http://www.iaeme.com/IJCIET/index.asp 21 editor@iaeme.com 3.3. Scope of the Model under Study The objective of the study was to develop the mathematical model to predict the water demand. The scope consist of mathematical equations for water forecasting based on water determinants in Nzoia Water Company Cluster. The primary data from the field was used for model formulation wheas the secondary data was used for testing and validation of the model. 3.4. Background to the model Nzoia Water Services Company has in operation since 2005. The clustered company covers a companied coverage area of over 300 Km2 . Nzoia water Services Company covers the area of 110 km2 in Trans-Nzoia county specifically Kitale town with its environs , Webuye and Bungoma towns and their environs covering an area of 50 Km2 and 65 Km2 respectively. Both towns are in Bungoma County. Kimilili covers 110 Km2 , whereas Malaba, Kocholia, Malakisi and Amukura covers companied area of 80 Km2 . The study focused on the three towns, Kitale, Webuye and Bungoma. The three towns have a companied population served of 360,000. The water coverage in these towns is over 80%. The companied customer base is about 21,000. Nzowasco cluster area has a typical tropical climate with a mean temperature at. NZOWASCO cluster region has a typical mean temperature of 27.3 °C with the highest temperature on the highlands being at Kitale at 25 °C and highest temperatures in low areas like Bungoma being at 29.3 °C . The minimum temperature during the day is in the range of 18 °C. The mean total precipitation of the area is 1400 mm/year, Relative Humidity is between 65% and 63% in July and the average maximum temperature is 31 °C in January. Nzoia cluster is located in a hot and wet climate region. Nowadays, water is almost exclusively provided by the Nzoia water Services Company, which until 2004 was under Local authorities and ministry of water development and national water and conservation management. The state is still the main decision-maker for water policy. The state mandated the regulator i.e. Water Services Regulatory Board (WASREB) through Lake Victoria North Water Services Board to regulate the provision of water services for water services providers of which Nzoia water Services Company was licensed to operate in tran-nzoia and Bungoma counties. This research examines water use across the domestic users in Nzoia cluster with a purpose of developing a mathematical model to predict water demand forecasting. Domestic use in Nzoia cluster accounts for over 80% whereas other categories of users account for less than 20%. Furthermore, the case of demand for water in the region presents some interesting history in water pricing for the last eleven years where by the water tariff has changed three times that is phase one pricing was between 2005 to 2008, phase two was between 2008 to 2011 and phase three was between 2011 to 2014. Between 2008 and 2014 major investments were undertaken in the cluster and water prices were increased and as the public realized, through strict administrative measures and extensive water coverage, the water coverage increased and customer base also increased from a mere 6000 connections to 21000 connections level in 2014. In this context, water demand management is of paramount importance for the sustainability of the Nzowasco cluster water system. 3.5. Sources of Data for demand forecasting model. In order to estimate water demand determinants, annual time series across the category of users for the NZOWASCO cluster area. The data was captured by a
  • 8. Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r http://www.iaeme.com/IJCIET/index.asp 22 editor@iaeme.com questionnaire tool on water pricing consumption or demand, size of household or number of persons per connection, the income per household, hours of supply across category of consumers. The data collected during the survey was used for modeling. Secondary data from NZOWASCO covering the period of 2005 and 2014 that is time varying trends like pricing (pricing, consumption trends, population growth trends, population were used for validation of the model). 3.6. Model Formulation 3.6.1. Normality Test The normality test among the categories i.e. Domestic, Low income, industrial, institutional and commercial was done to investigate the skewness of demand. The consumption of water in all categories of consumption in study area is normal based on the probabilistic normal graph drawn over the demand pattern for water within a year hence no positive or negative skewness for the demand. The mean and standard deviation of the data was considering the sample of 517. Figure 2 Water demand normality test 3.6.2. Modelling According to the methodology described in chapter three, the following equation was used to validate mathematical model for demand forecasting. YD = α + βi ln Pw + γi ln + δi ln X + εi (3) Where YD stands for the quantity of residential water demanded, Pw for the water price, in real disposable income, X for the vector of other variables (in this particular case a trend variable as a proxy to weather variations) and ε the error term. Moreover price and income are expressed in real terms using CPI as the deflator. It is important to stress that income captured under domestic and low income and the size of household population was used for deriving domestic and low income consumer’s category. Equation 3 was transformed depending on the variables used to
  • 9. Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster Services Area http://www.iaeme.com/IJCIET/index.asp 23 editor@iaeme.com estimate water demand for Nzoia cluster region. The results of multiple regression analysis model was generated and recorded in the Tables below. (Tables 1 and 2). Table 1 Regression Analysis for the determinant of water for the Domestic and Low income Independent Variables Coefficients T Sig.Unstandardized Coefficients Standardized Coefficients B Std. Error Beta (Constant) 6210.923 3845.739 1.615 .000 Household Size 29.452 119.482 .099 .247 .000 Income 26.029 678.245 .072 .038 .000 Tariff -12.066 37.707 -.018 -.320 .000 a. Dependent Variable: Quantity Supplied Month Table 2 Model Summary for domestic and low income consumers Model R R Square Adjusted R Square Std. Error of the Estimate 1 .024a .0567 .099 20319.339 a. Predictors: (Constant), Tariff, Household Size, Income 4. DISCUSSION OF RESULTS 4.1. Domestic and Low income water determinant Regression Model The result showed a positive correlation of r=0.024 with a high coefficient determination of r2 =0.0567 and its adjusted value of 0.0829 at 95% significance level. YD = f (α, HHz, In, Tariff, £) (4) Where YD - the water consumption demand Α - Constant HHz - Household Size In - income per month Tariff = price of water per month £ - Error term YD=α+βHHz+µIn- Tariff+£ YD=6210.92+0.099HHz+0.072In-0.018Tariff+£ The result above shows that Income, Population size and Tariff were statistically significant determinant of water demand in the study area. The tariff applied on water use has a strong negative effect on residential water consumption. As such, water consumption decreases when tariff growth is recorded. Thus, according to the literature, tariffs are frequently used as a tool for improving water savings. The implementation of efficient water-pricing practices that promote equity, efficiency and sustainability in the water sector is probably the simplest conceptual instrument. Using tariffs as a manner in which to regulate water consumption could potentially have a greater effect on lower income households, since water has no substitutes for basic uses and there is an amount of water that is highly insensitive to price changes.
  • 10. Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r http://www.iaeme.com/IJCIET/index.asp 24 editor@iaeme.com While income per capita and household size has a positive effect of 0.099 and 0.072 on water consumption for domestic and low income hence for any change by a unit in income and population size leads to a corresponding significant increase in water demand. Figure 3 illustrate the model generated based on determinant of water demand. Figure 3 below shows the estimation of water demand under domestic and low income categories using different population size, income and tariffs. Figure 3 Model generated based on determinant of water demand for domestic and low income consumers 4.2. Sensitivity of the Model in the Area Sensitivity of the model in estimating water demand was investigated through estimating water supplied against water demand over the years. The model was used to forecast the demand over the years and comparing the water supplied that time. The line of best fit was drawn over the estimated water estimate line over the years. In order to assess the sensitivity of the model and its credibility of results, the model was run over the sample period (2005–2014). In Figures 3 and 4, comparisons between actual and fitted values are presented. It is clear that the actual demand and estimated demand are reasonably close. Additionally, two statistics for examining the forecasting accuracy, namely the correlation between determinants of water demand (R2 ) and the standards deviation error of the estimates are reported as indicated in Table 1 demand for domestic and low income and Table 2 for other consumer categories. The statistics suggest that the model tracks historical water demand patterns fairly well. Overall, the results for both stages can be considered promising, a fact that permits us to continue with the post sample prediction through policy scenarios. 4.3. Further Sensitivity and Forecasting Demand In order to be able to recognize the possible policy and theoretical implications of the results, it was considered important to conduct a further sensitivity analysis. Five scenarios were examined. The first scenario considered the Forecasting demand for a constant tariff, 10 ten percent increase in connections and five percent increase in income. In the second scenario the model was used for projection of Demand 0 5000 10000 15000 20000 2005/06 2006/07 2007/08 2008/09 2009/10 2010/11 2011/12 2012/13 2013/14 ESTIMATED WATER DEMAND BY THE MODEL OVER THE YEARS Estimated_Demand AverageDemandOverthe Years YD=6210.92+0.099HHz+0.072In-0.018Tariff+£
  • 11. Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster Services Area http://www.iaeme.com/IJCIET/index.asp 25 editor@iaeme.com forecasting for a reducing tariff of (10%), increment in connections (10%) and income (5%) across the five year period. In both scenarios, real historical figures to carry out projections prices are assumed to be fixed for the period 2015–2020 and the income, house hold size growth of customer base is determined from historical figures. In third scenario demand forecasting for increment in tariff by 4% annually, connections (10%) and income (5%). The fourth scenario was demand forecasting for increment in tariff (20%), is applied during the base year and is to run for five years, connections (10%) and income (5%). The fifth scenario was forecasting demand for %increment tariff by 20% and connection (10%). Finally the sixth scenario forecasting demand for %increment in tariff by 4% and connection (10%). The explanations of the findings are illustrated in the following figures. Figure 1 Estimating water demand using the regression model Figure 5 Forecasting demand for a constant tariff, %increment in connection (10%) and income (5%) 0 5000 10000 15000 20000 25000 2005/06 2006/07 2007/08 2008/09 2009/10 2010/11 2011/12 2012/13 2013/14 ESIMATED WATER DEMAND OVER THE YEARS Av. Demand Estimated_Demand AverageDemandOverthe Years 0 5000 10000 15000 20000 25000 Demand Forecasting Estimated_Demand Av.Demand YD=6210.92+0.099HHz+0.072In-0.018Tariff+£ Trend Line of best fit YD=6210.92+0.099HHz+0.072In-0.018Tariff+£ Actual Demand
  • 12. Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r http://www.iaeme.com/IJCIET/index.asp 26 editor@iaeme.com When a forecast was conducted to investigate the rate of consumption over the years until 2020, the results showed that for any increment of connections by 10% and income 5% p.a at a constant tariff there is increase in water demand by 3.2%. The graph above illustrate the estimated forecast values of water demand based on domestic consumption category. Figure 6 Demand forecasting for a reducing tariff (10%), increment in connections (10%) and income (5%) Investigation on the variation of water demand when the tariff reduced by 10% and increment of connections at 10% and income increase at 5%. The result illustrated above shows that for any indicated change there is a change in water demand at a rate of 3.3%. The change shows that water price is significant in determining the consumption such that for any reduction made there will be an increase in water demand under domestic category. Figure 7 Demand forecasting for increment in tariff (20%), connections (10%) and income (5%) 0 5000 10000 15000 20000 25000 Demand Forecasting Estimated_Demand Av.ConnectionGrowth v.ConnectionGrowth YD=6210.92+0.099HHz+0.072In-0.018Tariff+£ 0 5000 10000 15000 20000 25000 Demand Forecasting Estimated_Demand Av.ConnectionGrowth
  • 13. Estimating Water Demand Determinants and Forecasting Water Demand for Nzioa Cluster Services Area http://www.iaeme.com/IJCIET/index.asp 27 editor@iaeme.com Further investigation was tested based on increase of tariff by 20%, connections by 10% and income by 5%. The results showed that for any increment in water tariff there will be a significant reduction in water demand by 1.5% as compared to a case where the tariff was reduced by 10%. These results reveals that for any larger percent increment of tariff will lead to a significant reduction in water demand. Figure 8 Demand forecasting for increment in tariff (4%), connections (10%) and income (5%) A test was conducted to investigate what will happen to demand when a tariff changes with smaller percentage of 4% and increment in connections by 10% income 5%pa. The results reveals that for any above changes effected there will be water demand at a rate of 2.4%. As compared to above case where there was increase of tariff by 20% the demand rate for smaller percent change is higher than a larger percent. Therefore the model stands advise that if the company would like to increase water demand, the percentage increase in tariff should be reasonable. 1. This Research in water resource management has revealed the key parameters to forecast water demand for domestic and low income consumers are price for water, population size/ Household size or number of persons per connection and income for consumers 2. The model thus, ( YD = 6210.92+0.099HHz + 0.072In – 0.018Tariff + £ ) Where YD-the water consumption demand, α- Constant, HHz-Household Size In- income per month, Tariff = price of water per month, £-Error term YD = α + βHHz + µIn- Tariff + £, to predict water demand for domestic users has been developed. These conclusions also represent hopeful applications of the research completed in this thesis. Water demand forecasting model has been estimated using the following equations/models; YDdl=f (α, HHz, In, Tariff, £) (5) YDics=α + βHHz + µIn – Tariff + £ (6) Combined Equation YD = YDdl + YDics 0 5000 10000 15000 20000 25000 Demand Forecasting Estimated_Demand Av.ConnectionGrowth YD=6210.92+0.099HHz+0.072In-0.018Tariff+£
  • 14. Patrick Wanyonyi Munialo, Carolyne K. Onyancha and Basil Tito Iro Ongo’r http://www.iaeme.com/IJCIET/index.asp 28 editor@iaeme.com REFERENCES [1] Arbues, F., Garcia-Valinas M. A. and Martinez-Espineira, R. Estimation of residential water demand: a state-of-the-art review. The Journal of Socio- Economics, 32, 2003, pp. 81–102. [2] Espey, M., Espey, J. and Shaw, W. D. Price elasticity of residential demand for water: a meta-analysis. Water Resource Research, 33(6), 1997, pp. 1369–1374. [3] Martinez-Espineira, R. and Nauges, C. Is All Domestic Water Consumption Sensitive to Price Control? Applied Economics, 36, 2004, pp. 1697–1703. [4] Mugenda, M. O. Research Methods: Quantitative and qualitative approaches. African Center for Technology Studies, 1999. [5] Surendra, H. J. and Deka, P. C. Effects of Statistical Properties of Dataset in Predicting Performance of Various Artificial Intelligence Techniques for Urban Water Consumption Time Series. International Journal of Civil Engineering & Technology, 3(2), 2012, pp. 60–69 [6] Das, K. K., Kumar, D. V., Udayalaxmi, G. and Muralidhar, M. Fluoride Contamination in the Groundwater in Mathadi Vague Basin in Adilabad District, Telangana State, India. International Journal of Civil Engineering & Technology, 5(7), 2014, pp. 55–63. [7] Pearce, D. (Pricing Water: Conceptual and Theoretical Issues, Paper for European Commission for the Conference on Pricing Water: Economics, Environment and Society. Portugal: Sintra, 1999. [8] Tietenberg, T. Environmental and Natural Resources. N Y.: Harper Collins, 1996. [9] NGO Forum for Urban Water and Sanitation Report. International Institute for Sustainable Development. 82(40), 2003. [10] Yamane, T. Elementary Sampling Theory. Englewood Cliffs, New Jersey: Prentice Hall, 1967