Institutionen för naturgeografi
och kvartärgeologi
Assessment of lead and
cadmium loading in the water
resources of Kingston, Jamaica
An application of input-output assessment
modelling
Khafi Weekes
Examensarbete avancerad nivå
Naturgeografi och kvartärgeologi, 30 hp
Master’s thesis
Preface
This Master’s thesis is Khafi Weekes' degree project in Physical Geography and Quaternary Geology at the Department of Physical Geography and Quaternary Geology, Stockholm University. The Master’s thesis comprises 30 HECs (half a year of full-time studies).
Supervisors have been Jerker Jarsjö and Steve Lyon, Department of Physical Geography and Quaternary Geology, Stockholm University. Examiner has been Peter Schlyter, Department of Physical Geography and Quaternary Geology, Stockholm University.
The author is responsible for the contents of this thesis.
Stockholm, 10 June 2010
Input-Output Assessment (IOA) was employed to quantify a likely range of annual lead and cadmium fluxes and to discern their possible flow paths in the water system of the Kingston hydrological catchment in south-eastern Jamaica. This technique was useful to understand
how cross-sectoral mass exchanges of these heavy metals ultimately impacted the water resources of the basin. Initially, based on deterministic principles of the urban hydrological
cycle, a foundational IOA matrix model was formulated to represent the basin’s typical annual hydrological regime. Here, flows of the water-using or water-impacting sectors that comprise the basin’s water system were identified and quantified. Hereafter the realistically possible cases of minimum, average and maximum direct cross-sectoral mass flows of lead and cadmium were estimated. The heavy metal mass flows of each case were calculated by multiplying the various annual cross-sectoral water flux volumes by corresponding lead and
cadmium concentrations. The resulting direct flow matrices were then stochastically recalculated to succinctly represent the most statistically likely coupled direct and indirect lead and cadmium mass flows in models. After the flux modelling was completed, backward and forward tracing of the mass fluxes identified natural water resources as recipient of most lead and cadmium in the basin. This is arguably the most noteworthy finding of the study as the natural water bodies were loaded even when the water system was modelled to show the minimum likely mass flows of lead and cadmium. From the average and maximum likely fluxes of lead and cadmium, not only did the loading of the natural water resources increase
but they in turn started to distribute lead and cadmium to other water bodies. Tracing also identified anthropogenic activities as the driver of lead and cadmium cycling throughout the system. The study was concluded in the recommendation of a strategy to improve wastewater treatment facilities and coverage as the most efficient and cost effective way to ameliorate the
degree of lead and cadmium cycling and loading in the water resources of the basin.
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1. Introduction 1
1.2. Hydrogeological characterization 4
1.3. Justification of Investigation 5
1.3.1. Toxicity of lead and cadmium 6
1.3.2. Potential Sources of Lead and Cadmium 6
1.3.3. Substantial at-risk Population 9
1.3.4. Implications of water system management 9
2. Materials and Methods 12
2.1 Conceptual premise 12
2.2. Direct Flow Modelling 13
2.2.1. Data Requirements for Direct Water Flow Model (Wij) 13
2.2.2. Data Requirements for Direct Pb and Cd Flow Models (Aij) 20
2.2.3. Modelling concept (Wij and Aij) 22
2.3. Coupled Direct and Indirect Modelling (Cij) 24
2.3.1 Modelling Concept (Cij)...25
2.4. Determining potential water resource loading by Lead and Cadmium 29
2.5. Backward and Forward Tracing 29
3. Results 31
3.1. Cross-sectoral water fluxes 31
3.2. Minimum lead and cadmium cross-sectoral fluxes and annual loading 33 3.3. Average lead and cadmium cross-sectoral fluxes and annual loading 37 3.4. Maximum lead and cadmium cross-sectoral fluxes and annual loading 42
4.2. Sub-sectors that drive lead and cadmium cycling and loading 49
4.3. Extent of loading of Lead and Cadmium in the water resources 53
4.3.1. Minimum Lead and Cadmium prevalence 53
4.3.2. Average and Maximum Lead and Cadmium prevalence 54
5. Conclusion 56
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Integrated water resource management is a term first coined in the United Nations Conference on Water in Mar del Plata, Argentina in 1977. It refers to administration methods that embrace the ever increasing connectedness of natural and engineered elements that are intrinsic to modern water systems. It is the practice of making ‘good’ managerial decisions based on sound scientific evidence to ensure sustained water resource quality, use and
availability (Grigg 1996). Since water quality is ultimately influenced by cross-sectoral fluxes of water between the engineered and natural components in contemporary water systems, in order for water resource management to remain integrated and effective, these flows should be exhaustively understood, quantified and communicated to stakeholders (Baresel, Destouni
2005).
Traditionally, scientific investigation of water exchange and contaminant transport, especially in the subsurface is conceptually flawed as a deterministic approach is used. Hydrological scientific investigation based on determinism is built on the pretext of well defined assumptions and relatively rigid predefinitions. This is impractical to do in nature due to the inherent uncertainty associated with the precept that one cannot possibly conclusively ‘know’ about and quantify all the possible fluxes within a real water system (Beven 2004). Ideally, hydrological data collection should consider both deterministic as well as
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This research proposes the Input Output Assessment (IOA) model as an appropriate scientific tool that can enhance catchment scale integrated water resource management by considering both deterministic and stochastic processes. Originally developed by Wassily Leontief in 1936 to demonstrate capital flow in economic systems, IOA is a linear activity model based on the principles of ‘General Equilibrium’, a branch of theoretical neoclassical economics (International Input- Output Association, 2010). The uses of the IOA model have since diversified. A notable application includes the successful use of the model to account for material flow in socio-political systems seen in its implementation for the widely used
‘IMPLAN’ (IMpact analysis for PLANning) software and ‘RIMS-II‘(Regional Input-Output Modeling System) approach.
More recently and pertinent to the aims of this research, the IOA model has been effectively used to quantify water and potential pollutant flows in catchment scale
hydrological systems. This is because it can communicate a comprehensive representation of water quantity and quality rather simply. It can trace, depict, calculate and predict the cross-sectoral flows between natural and engineered water sub-sectors within and external to a ‘real’ hydrological system.
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This paper is focused on investigating the extent of annual lead and cadmium loading and cross-sectoral fluxes in the Kingston hydrological basin, Jamaica and how they can potentially affect the available water resources. The examination relies on the use of IOA modeling techniques that incorporate deterministic and stochastic methods. The investigation will be completed through:
Formulation of a deterministic balanced hydrological model that reflects the cross-sectoral fluxes that are typical to the Kingston hydrological basin in Jamaica.
Deterministic and stochastic modelling to formulate likely cases of annual lead and cadmium mass flows in the catchment by use of the cross-sectoral water fluxes of the hydrological IOA model and minimum, average and maximum lead and cadmium concentrations contained in the various fluxes.
Determination of the extent of lead and cadmium loading water resources of the basin. Employing backward and forward tracing techniques to establish the water
using/impacting sub-sectors that are most responsible for lead and cadmium mass flows dissolved in the cross-sectoral water fluxes in the basin and loading of the water resources by these heavy metals.
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1.2. Hydrogeological Characterization
Located at 18 15 N, 77 30 W, Jamaica is the most north-westerly island of the Caribbean island archipelago and is a part of the Greater Antilles. The island has a ‘tropical-wet-and-dry climate’ which is characterised by the dry season from December to April and the wet season from May to November (Nkemdirim 1979). The regional climatic
characteristics are more complex as despite Jamaica’s total area of 10,831km2
, its contrasting land elevations enable two, spatially distinct climates. The mountainous interior enjoys a temperate climate while the discontinuous, flatter coastal area is classified as tropical humid (CIA World Fact Book, ‘Jamaica’, 2010).
Jamaica is divided into ten major hydrologic basins. The Kingston hydrological basin is located toward the south east of Jamaica (Figure 1a) and has a total surface area of 202 km2 (Jasminko 2004).
Figure 1a. Map of Jamaica showing hydrological basins delineated with blue lines and the Kingston hydrological basin distinguished in red. (From
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The catchment is surrounded to the north by the Blue Mountains, Red Hills, and Long Mountain and to the south by Kingston Harbour. The Kingston hydrological basin is located in the rain shadow of the Blue Mountains, so in contrast to the north-eastern, windward parishes, it is comparatively drier. Droughts are not uncommon during the dry season which causes the main river that drains the basin, the Hope River, to run dry. The topographically higher extremities of basin are characterised by metamorphosed limestone and sheet wash alluvium. Toward the south, the majority of the basin lies on the Liguanea alluvial plain alongside the Hope River that gently slopes toward the Kingston harbour (Figure 1b).
Figure 1b Topographic Map of Jamaica showing Kingston hydrological Basin delineated by the red line (Adapted from http://commons.wikimedia.org/wiki/File:Jamaica_Topography.png)
1.3. Justification of Investigation
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easily transported and have widespread effects on the water system of the Kingston
catchment. This is because, according to the principles of Darcy’s law, alluvium has a high hydraulic conductivity (Drew 1967). With this in mind, appraisal of potential impacts that lead and cadmium can have on the water resources of the Kingston and St Andrew
municipality is pertinent. The various reasons are outlined in this section.
1.3.1. Toxicity of lead and cadmium
Lead and cadmium are characterised as ‘heavy metals’ because they have an atomic density of ≥ 6 g/cm-3
. Along with other heavy metals, they are generally associated with pollution and toxicity (Knight et al. 1994). Lead and Cadmium are particularly toxic as a comparatively small dose can be harmful to human health (Landrigan 1989). The effects of lead are more pronounced in small children and can lead to damage of the nervous system, anaemia and brain damage. Long term exposure can cause nephropathy and colic-like abdominal pains. According to the World Health Organisation, the maximum allowable concentration of lead in drinking water is 0.010 mg/L (World Health Organization
Publications 2010). Cadmium is a known carcinogen and can cause renal abnormalities. The
maximum allowable concentration of cadmium in drinking water is 0.005 mg/L (World
Health Organization Publications 2010).
1.3.2. Potential sources of Lead and Cadmium
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basin is one of the main centres of industrial activity on the island. Important industrial activities and potential sources of lead and cadmium include cement processing, oil refining, textile industry, port activities and mining. There is also a burgeoning black market car battery stripping industry within the basin that is a significant source lead into the natural environment (Campbell 1991). The natural occurrence and anthropogenic enrichment of these heavy metals can potentially pose a risk to public health as they can become part of the solute load in the water system of the basin.
PLACE Cadmium (mg/kg -1 ) Lead (mg/kg-1) Jamaica 8.4 44 World 0.5 10
Table 1 Comparative concentration of naturally occurring lead and cadmium in Jamaican soils
The effects of past mining activities in Kintyre and Hope Tavern districts of the basin warrant special consideration. Combined, these communities have a population of 8,000 and cover an estimated area of 2 km2 which represents 1% of the Kingston hydrological basin. The communities are also located on one of the 200 multi-metal metalliferous anomalies on the island (Johnson 1993) as it is situated on an occurrence of sphalerite and galena underlain by alluvium. Past lead and gold mining activities have exploited these metal lenses and consequently exposed the community and its natural water resources to lead and cadmium contamination. As evidence, there have been reported cases of heightened blood lead
concentrations as well as associated health effects in the children of the community. Various studies have been undertaken in the area [(Brown et al. 1995), (Brown et al. 1996), (Carby
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audits (one audit of which the residents reportedly use for domestic purposes) contain concentrations of lead and cadmium that surpass the maximum allowable concentrations for drinking and bathing water set by the World Health Organization.
Furthermore, this area is of particular interest since it is situated on the topographically higher, north-eastern water recharge area of the basin. As such, this area’s high natural
concentrations of lead and cadmium as well as the enrichment caused by mining activities could be expected to cause problems in the basin’s water environment (Brown et al. 1995).
Figure 2 shows the spatial extent and concentrations of lead and cadmium in the soils of the
Hope Flats and Kintyre areas.
Figure 2 Map of Kintyre and Hope Flats area showing allotments and levels of lead concentrations in soils (From Brown, A.; Armour-Brown.; Lalor, G. Heavy metal pollution in Jamaica 1: Survey of cadmium, lead and zinc concentrations in
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1.3.3. Substantial at-risk population
As the third most populous nation in the North American region, Jamaica comprises an estimated 2.8 million inhabitants. The Kingston hydrological basin is the most densely populated region with 651,880 inhabitants (CIA World Fact Book, ‘Jamaica’, 2010). The high population is attributable to heavy urbanization as the hydrological basin encompasses the same area and boundary of the Kingston and St Andrew administrative area and the coastal capital city of Kingston is located within its limits (Water Resources Agency 2010). All of the water sourced for municipal use comes from surface water bodies which include the Mona and Hermitage Reservoir (USACE, 2001) and anthropogenic activities known to enrich the natural water environment with lead and cadmium are amplified in any dense urban
population. Thus the risk of lead and cadmium adversely affecting the well being of a significant segment of Kingston residents is considerable.
1.3.4. Implications of water system management
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Reportedly, 97% of households in the Kingston metropolitan area have access to piped, municipal water. The rest use standpipes or gather their own water from springs or rain water collection [(USACE, 2001), (Water Resources Agency, 2002)]. Rain water is often collected for drinking and other forms of domestic use from roof drain pipes especially in the less fortunate and unplanned residential areas in Kingston. A common roofing material in these areas is aluzinc or ‘corrugated iron’. The roof drain pipes supply water that has interacted with this roofing material as well as settled dust from exhaust fumes (exaggerated by congestion and industrial air pollution). There is elevated risk of lead and cadmium leaching into rain water (which is generally slightly acidic) collected under these conditions (Magyar et al. 2004).
Together industrial, urban domestic and tourism water sub-sectors account for 96% of the municipal water used in the basin [(USACE, 2001), (Water Resources Agency, 2002)]. Of the municipal water used for urban domestic purposes, an estimated 33% is treated by the centralized sewage system (National Works Commission 2010). The remaining 67% of untreated water is directly fluxed into the groundwater through soak away pits and to a lesser extent to urban storm water (Interamerican Development Bank 2004). Untreated domestic urban waste water is a confirmed source of lead and cadmium loading into water systems of catchments (da Silva Oliveira et al. 2007).
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The sewage treatment plants within the basin use mainly aeration and settling tanks (primary treatment) to treat collected municipal sewage. All of the water from the treated sewage is discharged into the natural surface water of the hydrological basin [(Water
Resources Agency, 2002), (National Works Commission, 2010)]. Studies show urban waste
water that has only undergone primary treatment still has dangerous concentrations of lead and cadmium (Karvelas 2003). Furthermore, the dewatered settled material or ‘sludge’ is used as fertilizer for agriculture. Based on Earth Trends Country Profiles (2010) statistics, it was estimated that 5 % of land in Kingston hydrological basin is agricultural land. Sludge contains high concentrations of lead and cadmium (Karvelas 2003) and therefore represents a potential source of loading into the natural water of the basin (National Research Council
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In this study, IOA models explicitly represented the fluxes of water, lead and cadmium associated with the sub-sectors that directly and indirectly affected the water system of the Kingston hydrological basin. By determining flow quantities, the extent and key drivers of lead and cadmium cycling and loading of the water resources were assessed.
2.1. Conceptual Premise
The hydrological model is a classical deterministically designed model as it describes water cycling throughout a system through a series of predefined stores and channels. As the basin is classified as an urbanized area, cross-sectoral flow paths depicted in IOA models were defined according to the principles of the ‘urban hydrological cycle’ (see Figure 3).
Based on this deterministic urban water cycling scheme and hydrological interpretation of the Kingston catchment, two types of IOA matrix models were formulated. The first type was the ‘direct’ flow models to represent water and lead and cadmium flows in the basin (Wij and Aij). The lead and cadmium mass flow results of the Aij group of models
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Figure 3 Schematic Representation of an Urban Hydrological Cycle (From writingaboutwater.blogspot.com/)
2.2. Direct Flow Modelling
2.2.1. Data Requirements for Direct Water Flow Model (Wij)
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Data required to calculate the water fluxes were extensive and required multiple data sources. Considering the lack information continuity associated with using multiple data sources and the contrasting methods used to derive them (ranging from quoting reported data to individual calculation), colour coding was used to represent the varying degrees of
certainty in the different flux quantities (see Table 2). Assumptions and sources for deriving the direct cross-sectoral water flow quantities follow.
COLOUR CODE MEANING
XXX Reported data. Empirically certain.
XXX Relatively certain calculation based on data from reliable sources.
XXX Relatively uncertain estimates based on data not directly stated.
XXX Uncertain estimate mainly for mass balance closure.
Table 2 Colour coded degrees of certainty for input data into Wij model.
Annual, average brut precipitation and evapotranspiration
Sources confer that the thirty-year, average, annual brut precipitation for the Kingston water basin is 312 Mm3/yr [(Earth Trends Country Profiles, 2010), (Jasminko, 2004)]. This volume was used as the total input and total output of all of the water sub-sectors that comprise the water system of the basin.
Annual Groundwater Quantity
Total groundwater discharge for the Kingston Hydrological Basin is 50 Mm3/yr(Jasminko,
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Groundwater annual distribution flows
To surface water- the Hope River catchment’s area is 52km2 (Wood, 1977).This is roughly 25% or of the total area of the basin and therefore represents 25% of the total groundwater discharge [(Water Resources Agency 2002), (Jasminko, 2004)]. Therefore, the annual, average groundwater contribution to the Hope River is calculated as 12.5 Mm3.
To exports/outflows- Since the catchment is heavily urbanized, it was assumed that direct
evaporation from groundwater bodies was insignificant due to the prevalence of impermeable surfaces. Thus the difference between the total groundwater discharge and the annual
groundwater flows to surface water was used to calculate this volume: 34 Mm3.
Annual Surface Water Quantity
The annual quantity of surface water in the catchment was tabulated using annual, average surface water runoff and stored water volumes. Surface water runoff includes stream discharge and other significant surface runoff. Net precipitation, base flow and urban storm water inputs comprise the Hope River discharge. Thus, total average surface water runoff is 81 Mm3/year. Added to this was the reported capacity of the two reservoirs within the basin: 6 Mm3/year [(Water Resources Agency 2002), (Jasminko, 2004)]. Thus average surface water quantity is 87 Mm3/yr.
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To groundwater- the exchange ratio between surface water bodies and groundwater was
sourced from (Baresel and Destouni 2005) was used to estimate this figure: 3 Mm3/yr.
To evapotranspiration- this was assumed to be the difference between the total surface water
and the maximum volume of water that can be safely extracted (Earth Trends Country
Profiles, 2010) and was found to be 45.5 Mm3/yr.
To the municipal water supply- reported total water sourced from internal reservoirs per day is
25 million imperial gallons per day: 20 million imperial gallons per day is treated from the Hermitage Reservoir and 5 million imperial gallons of water is treated from the Mona Reservoir (Water Resources Agency 2002). I converted this to metric and multiplied by the number of days in a year. So this is 113, 652.67 m3/ day or 41.5 Mm3/yr.
Imported water inputs to the Municipal water supply
The total municipal water supply sourced from surface water bodies and is 74.3 Mm3/yr (USACE, 2001). The difference between the total municipal water supply per year and the total volume of municipal water sourced from internal surface water bodies is the annual volume of water imported. So 74.3- 41.5 = 32.8 Mm3/yr.
Municipal water distribution flows
Distribution quantities were sourced from the US Army Corps of Engineers (2001) and the Water Resource Agency of Jamaica (2002).
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Domestic urban = 61.8 Mm3/yr.
Industry = 10 Mm3/yr.
Tourism = 0.5 Mm3/yr.
Precipitation annual, average flux to the private water sub-sector
Reportedly, 97% of households in the Kingston metropolitan area have access to piped water [(USACE, 2001), (Water Resources Agency 2002)]. The rest use standpipes or source their own water mainly from rainwater collection. Based on the known per capita water
consumption (Earth Trends Country Profiles, 2010) the figure of 1 Mm3/year was calculated as the figure not supplied by the municipality. As a result, precipitation flux to the private water sub-sector is 1 Mm3/year.
Average, annual water inputs to Wastewater Treatment
From domestic urban wastewater- 33% of the used urban domestic water went to the
centralised sewage system (WHO and UNICEF 2006). Thus, this flux is 33% of 61.8 = 20.39 Mm3/yr.
From wastewater from the tourism sector- all of the tourism facilities in the catchment are
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Domestic Urban Water distribution flows
To groundwater and urban storm water- the difference between the total domestic urban
water and the amount treated by the municipality is 41.41 Mm3/yr. Therefore, using the water distribution ratio provided by Drew (1967), in alluvium, 75% of the sewage water percolates into the groundwater aquifer and 25% into urban storm water conduits. So, the domestic urban annual flux to groundwater is 31.05 Mm3 and to urban storm conduits is 10.36 Mm3/yr.
To wastewater treatment facilities- 33% of the used urban domestic water went to the
centralised sewage system (WHO and UNICEF 2006). Thus, this flux is 33% of 61.8 = 20.39 Mm3/yr.
Wastewater treatment to Surface Water
It is reported that all of the water from the treated sewage is discharged into the natural surface water of the hydrological basin [(Water Resource Agency, 2002), (National Works
Commission, 2010)]. The sludge collected is used as fertiliser for agriculture. This is
calculated as 20.89 Mm3/yr.
Source of Mining water
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Mining water distribution
Using the ratios provided by Drew (1967) for alluvium drainage and the 66% rate of
evapotranspiration for the basin [(Water Resources Agency, 2002), (Jasminko, 2004).], it was calculated that the flux from municipal water to:
Surface Water = 0.27 Mm3/yr.
Groundwater = 0.80 Mm3/yr.
Evapotranspiration = 2.06 Mm3/yr.
Industry water distribution flows
Water used by the industrial sector was 10 Mm3/year. Using the ratios provided by Drew (1967) for alluvium drainage and the 66% rate of evapotranspiration for the Kingston Hydrological basin [(Water Resources Agency, 2002), (Jasminko, 2004).], it was calculated that the water mass transfer from Industrial water to:
Surface Water = 0.85 Mm3/yr.
Groundwater = 2.55 Mm3/yr.
Evapotranspiration = 6.6 Mm3/yr.
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Based on Earth Trends Country Profiles (2010) statistics, 5 % of land in the basin is used for agricultural purposes. Therefore, 5% of the brut precipitation was used to calculate the water mass flow from precipitation to agriculture 15.6 Mm3/yr. Municipal water contribution to agriculture was reported (Jasminko, 2004) as 2 Mm3/yr.
Agricultural water distribution
66% of brut precipitation is lost to evapotranspiration. As such, 66% of brut precipitation to agricultural lands is 10.3 Mm3/yr. The flux of water from the agricultural sub-sector to groundwater was calculated considering the difference between evapotranspiration and the total annual agricultural outflow.
2.2.2. Data Requirements for Direct Lead and Cadmium Flow Models (Aij)
21 WATER SOURCE CONCENTRATION (Lead ug/litre-1) CONCENTRATION (Cadmium ug/litre-1) SUPPORTING DATA
Min Average Max Min Average Max
Surface water 0 5.13 12.26 0 0.74 1.5 Knight et al. (1994)
Ground water 0 5.13 12.26 0 0.74 1.5 Hancock (2000)
Municipal Water 0 3.3 10 0 1 3 World Health Organization (2010), Wint (2008) Precipitation to Private water 11 180 350 0 1.3 4 Magyar (2004) Private wastewater 100 240 420 10 60 100 Marin (1999)
Mine water 52 68,5 86 1 1.5 2 Brown (1995)
Domestic urban water
100 240 420 10 60 100 Marin (1999)
Agricultural water
Insignificant Insignificant FAO (2010)
Industry 100 260 510 10 20 100 Marin (1999)
Urban storm water
100 260 510 10 20 100 Marin (1999)
Tourism water 100 240 420 10 60 100 Marin (1999)
Imported water 0 5.13 12.26 0 0.74 1.5 Knight (1994) Wastewater treatment 40 118 168 6 36 60 National Research Council (1996); Karvelas (2003)
Others Varies varies Depends on water
source(s)
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2.2.3. Modelling concept (Wij and Aij)
After the water cross-sectoral fluxes were derived and represented in the Wij
model, the various cases for lead and cadmium cross-sectoral mass flows were calculated and characterized in the Aij group of models. There were six Aij models in
total that signified maximum, average and minimum annual lead and cadmium mass flows in the basin.
Lead and cadmium mass flows were estimated by multiplying concentration of lead and cadmium in water flowing to and from each sub-sector (in Table 3) by the matching water flow volume (in section 2.2.1). In order to convert the concentration per litre (ug/liter-1) to the total annual mass loading in tonnes, the following formula was used:
Mass flow = (W ×109 × C) ÷1012 Equation 1 Heavy metal direct annual mass flow
Where:
W Water flow (litres/yr-1)
C Concentration of heavy metal (ug/liter-1)
Mass Flow Heavy metal mass flow (Millions of cubic metres/yr-1)
23 SU RF A CE W A TE R G RO U N D W A TE R M U N ICI PA L W A TE R PR IV A TE W A TE R M IN IN G W A TE R W A ST EW A TE R TR EA TM EN T D O M ES TI C U RB A N A G RI CU LT U RE IN D U ST RY U RB A N S TO RM TO U RI SM EV A PO CON CE N TR A TI O N O U TF LO W SURFACEWATER GROUNDWATER MUNICIPALWATER PRIVATEWATER MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN AGRICULTURE INDUSTRY URBAN STORM TOURISM PRECIPITATION IMPORTS TOTAL INPUT From To
INTERNAL FLOWS EXTERNAL FLOWS
T O TA L O U TP U T I N TE RN A L F LO WS E X TE RN A L F LO W S
Figure 4 Direct Flow Model Design Template
Direct matrix models were designed to show the significant cross-sectoral fluxes flowing from the sub-sectors in the rows (i) to the respective recipient sub-sector in the columns (j). Insignificant and nonexistent flows were not listed for various reasons. The ‘Internal Flows’ on each model indicated the sub-sectors that use or impact the water system that are located within the basin. These included the fluxes associated with internal natural water: groundwater and surface water. It was also composed exchanges associated with internal engineered economic water: Private, Mining, Municipal water supply, Wastewater Treatment, Urban Storm, Domestic Urban, Tourism, Industry and Agriculture.
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The external flows were essential to compute the complete mass balances of each internal sub-sector within the basin’s hydrological system.
The ‘Total Input’ found at the base of any given j sub-system of a column in the matrix is the summation of annual flux contributed by the row sub-systems. The ‘Total Output’ at the end of the rows (found at the farthest right of the matrix) is the summation of the annual flux distributed from each of the row, i sub-sectors to their various recipient j column sub-sectors. Moreover, the figure at the intersection of the ‘Total Inputs’ and ‘Total Outputs’ (found that the bottom right extremity of each direct flow matrix) is the summation of all annual fluxes of water or dissolved lead or cadmium in the basin. This quantity conveys that the matrices in each case are balanced and that there are no depletion or accumulation flows within the basin as it represents the total annual input which is the same as the total annual output.
Understanding of basic hydrological principles stipulates that there cannot be any water transfer within the same system, thus the diagonal line of the direct flow matrices do not contain any values. The other blank spaces in the matrices show that the corresponding sub-sectors have no direct flow linkages.
2.3. Coupled Direct and Indirect Modelling (C
ij)
As explained before, the deterministic formulation of Aij flow matrices cannot
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in nature. Furthermore, reliable prediction of mass flow paths and contaminant transport quantities by purely deterministic IOA models depends on the accuracy of process-relevant model parameters. Therefore, any error in the predefined heavy metal concentrations in the water, flow paths and structure is likely to lead to gross biases in the direct model results. Nevertheless, use of deterministic implements such as direct flow models (Wij and Aij) and the
urban hydrological cycle were important because they were the basis on which coupled direct and indirect mass flows were derived. A more thorough demonstration of the realistically possible, catchment-scale flow paths and quantities were accounted for by coupled indirect and direct fractional flow modeling.
2.3.1. Modelling concept (Cij)
Coupled direct and indirect matrix models (Cij) were determined using the following
formula:
C ij = (I - Bij)-1
Equation 2 Heavy metal coupled direct and indirect mass flow equation
Where
C ij Direct and indirect lead and cadmium cross-sectoral mass flows
I Identity Matrix
Bij Direct fractional flow matrix
Step 1: Calculating the direct flow fractions (Bij)
This step is done in all cases to produce two sub-groups of matrices: B’ij andB’’ij. The B’ij
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contributing sub-sectors to any given sub-sector (masses found in any given column in the A ij
matrices) by the total direct flow input (at the base of each column). This quantified the fraction of the total inputs that each contributing sub-sector input to their corresponding recipient sub-sector. These matrices should be then considered to be the ‘direct fractional
contribution matrices’.
Conversely, B’’ij matrices were calculated bydividing all the direct mass flow outputs
from any given distributing sub-sector to the corresponding recipient sub-sectors (quantities found in any given row in the A ij matrices) by the total direct flow output (at the end of each
row). This quantified the fraction of the total outputs that a given sub-sector distributed to their corresponding recipient sub-sectors. These matrices should be then considered to be the
‘direct fractional delivery matrices’. Total input and total output sections were not included
in the matrix design of Cij and Bij models (See Figure 5).
SU R FA CE W A TE R G R O U N D W A TE R M U N ICI P A L W A TE R P R IV A TE W A TE R M IN IN G W A TE R W A ST EW A TE R T R EA TM EN T D O M ES TI C U R B A N A G R ICU LT U R E IN D U ST R Y U R B A N S TO R M TO U R IS M WASTEWATER TREATMENT DOMESTIC URBAN AGRICULTURE INDUSTRY URBAN STORM TOURISM From To SURFACEWATER GROUNDWATER MUNICIPALWATER PRIVATEWATER MINING WATER
27
Step 2: Stochastic mathematical modifications to produce coupled direct and indirect
Cij models.
In order to represent randomness in nature in the coupled direct and indirect Cij
models, as dictated in Equation 2, the fractional flow interactions between the various water systems in the matrix groups B’ ij and B’’ ij were subtracted from an Identity Matrix (I), an
example of which is seen in Figure 6. The results were inverted to finally result in C’ij and
C’’ij models. SU RF A CE W A TE R G RO U N D W A TE R M U N ICI PA L W A TE R PR IV A TE W A TE R M IN IN G W A TE R W A ST EW A TE R TR EA TM EN T D O M ES TI C U RB A N A G RI CU LT U RE IN D U ST RY U RB A N S TO RM TO U RI SM SURFACEWATER 1 0 0 0 0 0 0 0 0 0 0 GROUNDWATER 0 1 0 0 0 0 0 0 0 0 0 MUNICIPALWATER 0 0 1 0 0 0 0 0 0 0 0 PRIVATEWATER 0 0 0 1 0 0 0 0 0 0 0 MINING WATER 0 0 0 0 1 0 0 0 0 0 0 WASTEWATER TREATMENT 0 0 0 0 0 1 0 0 0 0 0 DOMESTIC URBAN 0 0 0 0 0 0 1 0 0 0 0 AGRICULTURE 0 0 0 0 0 0 0 1 0 0 0 INDUSTRY 0 0 0 0 0 0 0 0 1 0 0 URBAN STORM 0 0 0 0 0 0 0 0 0 1 0 TOURISM 0 0 0 0 0 0 0 0 0 0 1 From To
Figure 6 Identity Matrix Template
28
I = inv (M)*M
Equation 3 Equation of an Identity Matrix. Where
M Square Matrix and I Identity Matrix
The method prescribed in Equation 2 for coupled direct and indirect fractional flow modeling accounts for the complexities associated with flow paths and quantification within the basin. Instead of dealing with only one possible reality of how dissolved lead and
cadmium is processed within the basin as was represented in the A ij and B’ij models, in a
stochastic or random process there is some indeterminacy in its future evolution. This indeterminacy is described by probability distributions. This means that even if the initial condition is known, there are many possibilities the process might go to, but some paths may be more probable and others less (Finsterle and Kowalsky 2006). Therefore, the figures in the
Cij group of models are the flow fractions that correspond to the most probable cross-sectoral
flow paths and total annual loading.
The elements for on the main diagonal of all matrices in the Cij group (see Figure 5)
are always equal to or greater than 1. This is because 1 represents the total flow that any given sub-sector contributes or distributes (derived from the total inputs and total outputs from the
Aij models). When the figure is greater than 1, this shows the influence of indirect flow from
other systems through pathways that are not explicitly defined. These indirect flows are not defined in the Aij, Bij or Wij groups of IOA matrices because they are beyond the scope of the
29
2.4. Determining potential water resource loading by lead and cadmium
In order to comprehensively assess the extent of lead and cadmium loading in the water resources used by Kingstonians, the proportions of total contribution and total
distribution flows in the coupled direct and indirect models were multiplied by the direct total inputs and outputs of the various subsectors (seen in the total input and total output sections of
Aij models). After the actual annual input and output mass flux was determined, the extent of
annual loading of the water resources of the basin by lead and cadmium was assessed. This was calculated using:
Accumulation = Input – Output
Equation 4 Accumulation Formula
Where
Input = Total annual input in Aij X Contribution flow fraction in Cij Output = Total annual output in Aij X Distribution flow fraction in Cij
2.5. Backward and Forward Tracing
30
31
3
3
.
.
R
R
E
E
S
S
U
U
L
L
T
T
S
S
3.1. Cross-sectoral water fluxes
SU R FA CE W A TE R G R O U N D W A TE R M U N ICI P A L W A TE R P R IV A TE W A TE R M IN IN G W A TE R W A ST EW A TE R T R EA TM EN T D O M ES TI C U R B A N A G R ICU LT U R E IN D U ST R Y U R B A N S TO R M TO U R IS M EV A P O TR A N SP IR A TI O N O U TF LO W SURFACEWATER 3 41.5 42.5 87 GROUNDWATER 15 35 50 MUNICIPALWATER 61.8 2 10 0.5 74.3 PRIVATEWATER 0.11 0.33 0.56 1 MINING WATER 0.27 0.8 2.06 3.13 WASTEWATER TREATMENT 20.89 20.89 DOMESTIC URBAN 31.05 20.39 10.36 61.8 AGRICULTURE 7.3 10.3 17.6 INDUSTRY 0.85 2.55 6.6 10 URBAN STORM 11.63 11.63 TOURISM 0.5 0.5 PRECIPITATION 38.25 4.97 1 3.13 15.6 1.27 IMPORTS 32.8 87 50 74.3 1 3.13 20.89 61.8 17.6 10 11.63 0.5 338 T O TA L O U TP U T E X TE RN A L TOTAL INPUT
INTERNAL FLOWS EXTERNAL FLOWS
From To I N TE R N A L F LO WS
Figure 7 (Wij) Internal and External Annual Average Water Flows (Millions of cubic metres/yr-1) for the Kingston Hydrological
Basin water system.
Figure 7 represents the volumes of water fluxed between sectors that comprise the
water system of Kingston and the total volumes of water that is input and output from these systems annually. As the volumes represented in the total input and outputs are equal, it shows that there is no depletion or accumulation flows within the basin. Importantly, Wij
32
transfer of water between internal groundwater and internal surface water bodies (internal natural water bodies). Therefore, groundwater is also considered to be important to the water quality of the surface water bodies as it supplements more water to surface water than it receives from surface water bodies. For the intents and purposes of this research, groundwater bodies are considered to be a secondary component of the water resource of the basin.
To demonstrate how water is cycled through the water system, Wij shows that the
quantity of water supplied by the municipality for all agricultural, domestic, tourism and industrial activities in the basin annually is 74.3 Mm3. In turn, 38% of the water directly contributed to the surface water bodies came from engineered subsectors within the basin. The most significant direct contributor was the flux from waste water treatment plants as 33% of the used urban domestic water went to the centralized sewage system [(WHO and
UNICEF, 2006), (National Works Commission, 2010)]. Domestic urban water not only
influences the flux from wastewater treatment plants but also groundwater (through soak away pits) and to a lesser extent urban storm water.
33
3.2. Minimum lead and cadmium cross-sectoral fluxes and annual
loading
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU LT U R E IN D U S T R Y U R B A N S T O R M T O U R IS M E V A P O CON CE N T R A T IO N O U T F LO W SURFACEWATER 0 0 0 0 GROUNDWATER 0 0 0 MUNICIPALWATER 0 0 0 0 0 PRIVATEWATER 0.011 0.033 0.066 0.11 MINING WATER 0.01404 0.0416 0.10712 0.16276 WASTEWATER TREATMENT 0.8356 0.8356 DOMESTIC URBAN 3.105 2.039 1.036 6.18 AGRICULTURE 0 0 0 INDUSTRY 0.085 0.255 0.66 1 URBAN STORM 1.163 1.163 TOURISM 0.05 0.05 PRECIPITATION 0 0 0.011 0.16276 0 0.127 IMPORTS 0 2.10864 3.4346 0 0.011 0.16276 2.089 0 0 0 1.163 0 9 From ToINTERNAL FLOWS EXTERNAL FLOWS
T O T A L O U T P U T I N T E R N A L F LO WS E X TE R N A L TOTAL INPUT
Figure 8 (Lead_Min, Aij) Matrix of the Direct Minimum Annual Lead Flows (tonnes/year-1) between natural water and
engineered-economic systems in the Kingston Hydrological Basin water system
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU LT U R E IN D U S T R Y U R B A N S T O R M T O U R IS M E V A P O CON CE N T R A T IO N O U T F LO W SURFACEWATER 0 0 0 0 GROUNDWATER 0 0 0 MUNICIPALWATER 0 0 0 0 0 PRIVATEWATER 0.0011 0.0033 0.0056 0.01 MINING WATER 0.00027 0.0008 0.00206 0.00313 WASTEWATER TREATMENT 0.75204 0.75204 DOMESTIC URBAN 0.3105 0.2039 0.1036 0.618 AGRICULTURE 0 0 0 INDUSTRY 0.0085 0.0255 0.066 0.1 URBAN STORM 0.1163 0.1163 TOURISM 0.005 0.005 PRECIPITATION 0 0 0 0.00313 0 0.0127 IMPORTS 0 0.87821 0.3401 0 0 0.00313 0.2089 0 0 0 0.1163 0 1.5 TOTAL INPUT From To
INTERNAL FLOWS EXTERNAL FLOWS
T O T A L O U T P U T I N T E R N A L F LO WS E X T E R N A L
Figure 9 (Cadmium_Min, Aij). Matrix of the Direct Minimum Annual Cadmium Flows (tonnes/year-1) between natural water and
34
In the minimum direct case, water fluxes via urban storm conduits mainly cycle lead and cadmium through the system in the same amounts as they receive. Agriculture and the abandoned mining area receive and distribute no lead and cadmium fluxes. The rest of the subsystems in the basin are the net loaders as they distribute more lead and cadmium to other systems (mainly natural) than they receive. Most importantly, there is no transfer of lead or cadmium from surface water bodies within and external to the system to the municipal water supply. Moreover, the natural water resource and municipal water do not distribute/output any lead or cadmium. However, all of the direct lead and cadmium contributions to surface water and groundwater come from engineered water systems, most notably from waste water treatment plant discharge. Overall, there are more heavy metal inputs into the natural water bodies than there are outputs from them which suggest that they are being loaded.
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.40 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.88 0.90 0.00 0.00 0.00 0.98 1.00 0.00 0.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.04 0.07 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.01 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.00 1.00 From To SURFACEWATER GROUNDWATER MUNICIPALWATER PRIVATEWATER MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN TOURISM AGRICULTURE INDUSTRY URBAN STORM
Figure 10 (Lead_Min, C’ij) Quantification of Total (Direct and Indirect) Contribution Flows from System (row i) to System
35 S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.86 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.95 0.91 0.00 0.00 0.00 0.98 1.00 0.00 0.00 0.89 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.01 0.07 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.02 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.00 1.00 TOURISM AGRICULTURE INDUSTRY URBAN STORM MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN GROUNDWATER MUNICIPALWATER PRIVATEWATER From To SURFACEWATER
Figure 11 (Cadmium_Min, C’ij) Quantification of Total (Direct and Indirect) Contribution Flows from System (row i) to System
(column j) relative to the Total Annual Minimum Cadmium Inflow
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU LT U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.30 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.09 0.26 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.50 0.50 0.00 0.00 0.00 0.33 1.00 0.00 0.00 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.09 0.26 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 From To SURFACEWATER GROUNDWATER MUNICIPALWATER PRIVATEWATER MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN TOURISM AGRICULTURE INDUSTRY URBAN STORM
Figure 12 (Lead_Min, C’’ij) Quantification of Total (Direct and Indirect) Distribution Flows from System (row i) to System
36 S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.11 0.33 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.09 0.26 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.50 0.50 0.00 0.00 0.00 0.33 1.00 0.00 0.00 0.17 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.09 0.26 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 TOURISM AGRICULTURE INDUSTRY URBAN STORM MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN GROUNDWATER MUNICIPALWATER PRIVATEWATER From To SURFACEWATER
Figure 13 (Cadmium_Min, C’'ij) Quantification of Total (Direct and Indirect) Distribution Flows from System (row i) to System
(column j) relative to the Total Annual Minimum Cadmium Outflow
In the C’ij contribution and C’'ij distribution models, the total contribution flow and
distribution flow of all of the sub-sectors that comprise the water system are not directly or indirectly loaded by other subsystems. This is because they all remain at 1 which represents the total annual input and output mass quantity in their corresponding Aij direct flow model.
37
3.3. Average lead and cadmium cross-sectoral fluxes and annual loading
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M E V A P O CON CE N T R A T IO N O U T F L O W SURFACEWATER 0.01539 0.212895 0.218025 0.43092 GROUNDWATER 0.07695 0.17442 0.25137 MUNICIPALWATER 0.20394 0.0066 0.033 0.00165 0.24519 PRIVATEWATER 0.0264 0.0792 0.1584 0.264 MINING WATER 0.018495 0.0548 0.14111 0.214405 WASTEWATER TREATMENT 2.46502 2.46502 DOMESTIC URBAN 7.452 4.8936 2.4864 14.832 AGRICULTURE 0 0 0 INDUSTRY 0.221 0.663 1.716 2.6 URBAN STORM 3.0238 3.0238 TOURISM 0.12 0.12 PRECIPITATION 0.1962225 0.0254961 0.18 0.214405 0 0.3302 IMPORTS 0.168264 6.027888 8.289886 0.381159 0.18 0.214405 5.0136 0.20394 0.0066 0.033 2.8166 0.00165 24 From To
INTERNAL FLOWS EXTERNAL FLOWS
T O T A L O U T P U T I N T E R N A L F L O WS E X T E R N A L TOTAL INPUT
Figure 14(Lead_Average, Aij). Matrix of the Direct Average Annual Lead Flows (tonnes/year-1) between natural water and
engineered-economic systems in the Kingston Hydrological Basin water system
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M E V A P O CON CE N T R A T IO N O U T F L O W SURFACEWATER 0.00222 0.03071 0.03145 0.06438 GROUNDWATER 0.0111 0.02516 0.03626 MUNICIPALWATER 0.0618 0.002 0.01 0.0005 0.0743 PRIVATEWATER 0.0066 0.0198 0.0336 0.06 MINING WATER 0.000405 0.0012 0.00309 0.004695 WASTEWATER TREATMENT 0.75204 0.75204 DOMESTIC URBAN 1.863 1.2234 0.6216 3.708 AGRICULTURE 0 0 0 INDUSTRY 0.017 0.051 0.132 0.2 URBAN STORM 0.2326 0.2326 TOURISM 0.03 0.03 PRECIPITATION 0.0283050.0036778 0.0013 0.004695 0 0.0254 IMPORTS 0.024272 1.04805 1.940898 0.054982 0.0013 0.004695 1.2534 0.0618 0.002 0.01 0.647 0.0005 5 TOTAL INPUT From To
INTERNAL FLOWS EXTERNAL FLOWS
T O T A L O U T P U T I N T E R N A L F L O WS E X T E R N A L
Figure 15 (Cadmium_Average,Aij). Matrix of the Direct Average Annual Cadmium Flows (tonnes/year-1) between natural
38
In the average direct flow case, the natural water resource entities of the basin continue to be loaded with just over half of the total lead and cadmium inputs to the system. However, there is 15 Mm3/yr more lead and 4.5 Mm3/yr more cadmium cycled through the water system of the basin than in the minimum case. The consequence is that though the natural water and municipal water bodies continue to distribute less lead and cadmium than they receive, unlike the minimum cases, they begin to output these heavy metals to other water using or impacting sub-sectors. Combined flux from these three sub-sectors account for 3% of the total direct outputs of the water system.
39 S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 2.01 1.10 1.12 0.00 0.00 1.12 1.12 1.12 1.12 0.99 1.12 0.03 1.01 0.01 0.00 0.00 0.01 0.01 0.01 0.01 0.01 0.01 1.81 1.97 2.01 0.00 0.00 2.01 2.01 2.01 2.01 1.78 2.01 0.01 0.01 0.01 1.00 0.00 0.01 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.82 0.45 0.46 0.00 0.00 1.46 0.46 0.46 0.46 0.41 0.46 1.72 1.84 0.96 0.00 0.00 1.94 1.96 0.96 0.96 1.73 0.96 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.08 0.12 0.04 0.00 0.00 0.04 0.04 0.04 1.04 0.04 0.04 1.01 0.55 0.56 0.00 0.00 0.56 0.56 0.56 0.56 1.50 0.56 0.02 0.01 0.01 0.00 0.00 0.03 0.01 0.01 0.01 0.01 1.01 From To SURFACEWATER GROUNDWATER MUNICIPALWATER PRIVATEWATER MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN TOURISM AGRICULTURE INDUSTRY URBAN STORM
Figure 16 (Lead_Average, C’ij) Quantification of Total (Direct and Indirect) Contribution Flows from System (row i) to System
(column j) relative to the Total Annual Average Lead Inflow
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 2.15 1.19 1.20 0.00 0.00 1.20 1.20 1.20 1.20 1.15 1.20 0.02 1.01 0.01 0.00 0.00 0.01 0.01 0.01 0.01 0.01 0.01 2.06 2.12 2.15 0.00 0.00 2.15 2.15 2.15 2.15 2.07 2.15 0.01 0.02 0.01 1.00 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1.54 0.85 0.86 0.00 0.00 1.86 0.86 0.86 0.86 0.83 0.86 1.99 2.06 1.11 0.00 0.00 2.09 2.11 1.11 1.11 2.03 1.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.04 0.05 0.02 0.00 0.00 0.02 0.02 0.02 1.02 0.02 0.02 0.48 0.26 0.27 0.00 0.00 0.27 0.27 0.27 0.27 1.26 0.27 0.04 0.02 0.02 0.00 0.00 0.04 0.02 0.02 0.02 0.02 1.02 TOURISM AGRICULTURE INDUSTRY URBAN STORM MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN GROUNDWATER MUNICIPALWATER PRIVATEWATER From To SURFACEWATER
Figure 17 (Cadmium_Average, C’ij) Quantification of Total (Direct and Indirect) Contribution Flows from System (row i) to
40 S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 1.41 0.36 0.70 0.00 0.00 0.19 0.58 0.02 0.09 0.10 0.00 0.43 1.11 0.21 0.00 0.00 0.06 0.18 0.01 0.03 0.03 0.00 0.79 0.66 1.39 0.00 0.00 0.38 1.16 0.04 0.19 0.19 0.01 0.27 0.37 0.13 1.00 0.00 0.04 0.11 0.00 0.02 0.02 0.00 0.23 0.32 0.11 0.00 1.00 0.03 0.10 0.00 0.02 0.02 0.00 1.41 0.36 0.70 0.00 0.00 1.19 0.58 0.02 0.09 0.10 0.00 0.92 0.74 0.45 0.00 0.00 0.45 1.38 0.01 0.06 0.23 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.23 0.31 0.11 0.00 0.00 0.03 0.09 0.00 1.02 0.02 0.00 1.41 0.36 0.70 0.00 0.00 0.19 0.58 0.02 0.09 1.10 0.00 0.06 0.01 0.03 0.00 0.00 0.05 0.02 0.00 0.00 0.00 1.00 From To SURFACEWATER GROUNDWATER MUNICIPALWATER PRIVATEWATER URBAN STORM MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN TOURISM AGRICULTURE INDUSTRY
Figure 18 (Lead_Average, C’'ij) Quantification of Total (Direct and Indirect) Distribution Flows from System (row i) to System
(column j) relative to the Total Annual Average Lead Outflow
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU LT U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 1.41 0.37 0.70 0.00 0.00 0.20 0.58 0.02 0.09 0.10 0.00 0.43 1.11 0.21 0.00 0.00 0.06 0.18 0.01 0.03 0.03 0.00 0.81 0.66 1.40 0.00 0.00 0.39 1.16 0.04 0.19 0.20 0.01 0.30 0.41 0.15 1.00 0.00 0.04 0.12 0.00 0.02 0.02 0.00 0.23 0.32 0.11 0.00 1.00 0.03 0.10 0.00 0.02 0.02 0.00 1.41 0.37 0.70 0.00 0.00 1.20 0.58 0.02 0.09 0.10 0.00 0.92 0.74 0.46 0.00 0.00 0.46 1.38 0.01 0.06 0.23 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.23 0.31 0.11 0.00 0.00 0.03 0.09 0.00 1.02 0.02 0.00 1.41 0.37 0.70 0.00 0.00 0.20 0.58 0.02 0.09 1.10 0.00 1.41 0.37 0.70 0.00 0.00 1.20 0.58 0.02 0.09 0.10 1.00 TOURISM AGRICULTURE INDUSTRY URBAN STORM MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN GROUNDWATER MUNICIPALWATER PRIVATEWATER From To SURFACEWATER
Figure 19 (Cadmium_Average, C’'ij) Quantification of Total (Direct and Indirect) Distribution Flows from System (row i) to
41
In this case, the total annual inputs of lead and cadmium to surface water and groundwater in C’ij models were 101% and 1% more respectively than the total input
quantities calculated in the average Aij models. This indelibly affected the annual distribution
flows from surface water and groundwater in C’'ij models as the total outputs of lead and
cadmium were 41% and 11% higher than the average Aij model results respectively.
By multiplying the total quantities produced in the Aij models with the proportions in
the C’ij and C’’ij models, the actual contribution flows of lead and cadmium into surface water
were 12 Mm3/year and 2.1Mm3/year respectively. The total contribution flux into groundwater bodies calculated as being 8.37 Mm3/year of lead and 1.95 Mm3/year for cadmium. In turn, surface water distributed 0.60 Mm3/year of lead and 0.09 Mm3/year of cadmium and groundwater bodies distributed 0.27 Mm3/year of lead and 0.04 Mm3/year of cadmium.
42
3.4. Maximum lead and cadmium cross-sectoral fluxes and annual
loading
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU LT U R E IN D U S T R Y U R B A N S T O R M T O U R IS M E V A P O CON CE N T R A T IO N O U T F LO W SURFACEWATER 0.03678 0.50879 0.52105 1.06662 GROUNDWATER 0.1839 0.41684 0.60074 MUNICIPALWATER 0.618 0.02 0.1 0.005 0.743 PRIVATEWATER 0.0462 0.1386 0.2772 0.462 MINING WATER 0.02322 0.0688 0.17716 0.26918 WASTEWATER TREATMENT 3.50952 3.50952 DOMESTIC URBAN 13.041 8.5638 4.3512 25.956 AGRICULTURE 0 0 0 INDUSTRY 0.4335 1.3005 3.366 5.1 URBAN STORM 5.9313 5.9313 TOURISM 0.21 0.21 PRECIPITATION 0.4689450.0609322 0.35 0.26918 0 0.6477 IMPORTS 0.402128 10.59659 14.64661 0.910918 0.35 0.26918 8.7738 0.618 0.02 0.1 4.9989 0.005 42.5 TOTAL INPUT From To EXTERNAL FLOWS INTERNAL FLOWS T O T A L O U T P U T I N T E R N A L F LO WS E X T E R N A LFigure 20 (Lead_Max, Aij) Matrix of the Direct Maximum Annual Lead Flows (tonnes/year-1) between natural water and
engineered-economic systems in the Kingston Hydrological Basin water system
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M E V A P O CON CE N T R A T IO N O U T F L O W SURFACEWATER 0.0045 0.06225 0.06375 0.1305 GROUNDWATER 0.0225 0.051 0.0735 MUNICIPALWATER 0.1854 0.006 0.03 0.0015 0.2229 PRIVATEWATER 0.011 0.033 0.056 0.1 MINING WATER 0.00054 0.0016 0.00412 0.00626 WASTEWATER TREATMENT 1.2534 1.2534 DOMESTIC URBAN 3.105 2.039 1.036 6.18 AGRICULTURE 0 0 0 INDUSTRY 0.085 0.255 0.66 1 URBAN STORM 1.163 1.163 TOURISM 0.05 0.05 PRECIPITATION 0.057375 0.007455 0.004 0.00626 0 0.127 IMPORTS 0.0492 2.592815 3.406555 0.11145 0.004 0.00626 2.089 0.1854 0.006 0.03 1.163 0.0015 10 From To
INTERNAL FLOWS EXTERNAL FLOWS
T O T A L O U T P U T I N T E R N A L F L O WS E X T E R N A L TOTAL INPUT
Figure 21 (Cadmium_Max, Aij).Matrix of the Direct Maximum Annual Cadmium Flows (tonnes/year-1) between natural water
43
In comparing the direct average and maximum cases, there was 18 Mm3/yr more lead and 5 Mm3/yr more cadmium cycled though the water system of the Kingston hydrological basin. As such, this translated into slight increases in the distribution and contribution proportions in lead and cadmium cycling throughout the water system. To illustrate, the natural water bodies distributed 2% more of the total lead and cadmium outputs of the system as compared to that of the average case.
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 1.96 1.08 1.09 0.00 0.00 1.09 1.09 1.09 1.09 0.95 1.09 0.03 1.02 0.02 0.00 0.00 0.02 0.02 0.02 0.02 0.02 0.02 1.72 1.92 1.96 0.00 0.00 1.96 1.96 1.96 1.96 1.70 1.96 0.01 0.01 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.65 0.36 0.36 0.00 0.00 1.36 0.36 0.36 0.36 0.32 0.36 1.62 1.78 0.90 0.00 0.00 1.88 1.90 0.90 0.90 1.66 0.90 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.08 0.13 0.05 0.00 0.00 0.05 0.05 0.05 1.05 0.04 0.05 1.10 0.60 0.61 0.00 0.00 0.61 0.61 0.61 0.61 1.53 0.61 0.02 0.01 0.01 0.00 0.00 0.03 0.01 0.01 0.01 0.01 1.01 WASTEWATER TREATMENT MINING WATER PRIVATEWATER DOMESTIC URBAN AGRICULTURE INDUSTRY URBAN STORM From To SURFACEWATER GROUNDWATER MUNICIPALWATER TOURISM
Figure 22 (Lead_Max, C’ij) Quantification of Total (Direct and Indirect) Contribution Flows from System (row i) to System
44 S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 2.07 1.14 1.15 0.00 0.00 1.15 1.15 1.15 1.15 1.03 1.15 0.02 1.01 0.01 0.00 0.00 0.01 0.01 0.01 0.01 0.01 0.01 1.91 2.04 2.07 0.00 0.00 2.07 2.07 2.07 2.07 1.84 2.07 0.01 0.01 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.55 0.56 0.00 0.00 1.56 0.56 0.56 0.56 0.50 0.56 1.82 1.92 1.02 0.00 0.00 1.99 2.02 1.02 1.02 1.80 1.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.07 0.11 0.04 0.00 0.00 0.04 0.04 0.04 1.04 0.03 0.04 0.93 0.51 0.52 0.00 0.00 0.52 0.52 0.52 0.52 1.46 0.52 0.02 0.01 0.01 0.00 0.00 0.04 0.01 0.01 0.01 0.01 1.01 GROUNDWATER MUNICIPALWATER PRIVATEWATER From To SURFACEWATER TOURISM AGRICULTURE INDUSTRY URBAN STORM MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN
Figure 23 (Cadmium_Max, C’ij) Quantification of Total (Direct and Indirect) Contribution Flows from System (row i) to System
(column j) relative to the Total Annual Maximum Cadmium Inflow
S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU L T U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 1.39 0.35 0.66 0.00 0.00 0.19 0.55 0.02 0.09 0.09 0.00 0.43 1.11 0.20 0.00 0.00 0.06 0.17 0.01 0.03 0.03 0.00 0.80 0.65 1.38 0.00 0.00 0.39 1.15 0.04 0.19 0.19 0.01 0.27 0.37 0.13 1.00 0.00 0.04 0.11 0.00 0.02 0.02 0.00 0.23 0.31 0.11 0.00 1.00 0.03 0.09 0.00 0.01 0.02 0.00 1.39 0.35 0.66 0.00 0.00 1.19 0.55 0.02 0.09 0.09 0.00 0.91 0.73 0.43 0.00 0.00 0.45 1.36 0.01 0.06 0.23 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.23 0.31 0.11 0.00 0.00 0.03 0.09 0.00 1.01 0.02 0.00 1.39 0.35 0.66 0.00 0.00 0.19 0.55 0.02 0.09 1.09 0.00 1.39 0.35 0.66 0.00 0.00 1.19 0.55 0.02 0.09 0.09 1.00 From To SURFACEWATER GROUNDWATER MUNICIPALWATER DOMESTIC URBAN PRIVATEWATER MINING WATER AGRICULTURE INDUSTRY URBAN STORM TOURISM WASTEWATER TREATMENT
Figure 24 (Lead_Max, C’'ij) Quantification of Total (Direct and Indirect) Distribution Flows from System (row i) to System
45 S U R F A CE W A T E R G R O U N D W A T E R M U N ICI P A L W A T E R P R IV A T E W A T E R M IN IN G W A T E R W A S T E W A T E R T R E A T M E N T D O M E S T IC U R B A N A G R ICU LT U R E IN D U S T R Y U R B A N S T O R M T O U R IS M 1.39 0.35 0.66 0.00 0.00 0.19 0.55 0.02 0.09 0.09 0.00 0.43 1.11 0.20 0.00 0.00 0.06 0.17 0.01 0.03 0.03 0.00 0.80 0.65 1.38 0.00 0.00 0.39 1.15 0.04 0.19 0.19 0.01 0.29 0.40 0.14 1.00 0.00 0.04 0.12 0.00 0.02 0.02 0.00 0.23 0.31 0.11 0.00 1.00 0.03 0.09 0.00 0.01 0.02 0.00 1.39 0.35 0.66 0.00 0.00 1.19 0.55 0.02 0.09 0.09 0.00 0.91 0.73 0.43 0.00 0.00 0.45 1.36 0.01 0.06 0.23 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.23 0.31 0.11 0.00 0.00 0.03 0.09 0.00 1.01 0.02 0.00 1.39 0.35 0.66 0.00 0.00 0.19 0.55 0.02 0.09 1.09 0.00 1.39 0.35 0.66 0.00 0.00 1.19 0.55 0.02 0.09 0.09 1.00 GROUNDWATER MUNICIPALWATER PRIVATEWATER From To SURFACEWATER TOURISM AGRICULTURE INDUSTRY URBAN STORM MINING WATER WASTEWATER TREATMENT DOMESTIC URBAN
Figure 25 (Cadmium_Max, C’'ij) Quantification of Total (Direct and Indirect) Distribution Flows from System (row i) to System
(column j) relative to the Total Annual Maximum Cadmium Outflow
The annual contribution and distribution flow proportions remained much the same in the maximum case as compared to the fractions in average settings e.g. the quantity of total annual lead and cadmium received by surface water bodies is double the result shown in average direct models. As such, the total annual loading is conveyed in Table 4.
Water Resource Total Contribution Mass flow (quantity in Aij x fraction in Cij)
Total Distribution Mass flow (quantity in Aij x fraction in Cij) Annual Loading Pb Cd Pb Cd Pb Cd Surface Water 20.75 5.3 1.47 0.18 19.28 5.12 Groundwater 15 3.43 0.666 0.08 14.33 3.35
