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100
Seawater enters the pumping wells when (hf) approaches sea level at 0 m. The
freshwater/saltwater response to the reduction in the freshwater head (hf) in order to
attain hydrostatic equilibrium is slow (Howard, 1987). However the low permeable
fractures or conduits along the South Coast Fault Zone and wells drilled to intercept the
saltwater interface (Rushton, 1980) will allow the aquifer to reach equilibrium conditions
at a much faster rate. Therefore, it is pertinent to simulate cells at the saltwater/freshwater
interface along the southern coastline with the equivalent freshwater head hf. The
saltwater interface was simulated as a constant-head boundary along the coastline in these
areas (Figure 4.10). Equivalent freshwater head was calculated is documented in Table 6.
For the purposes of this study, the interface will be treated as a specified-head seepage
boundary to the ground-water flow system.
Submarine Discharge
The quantity of discharge from the White Limestone to the sea along coastal areas
south of the South Coast Fault is unknown. Geophysical investigations conducted by
NASA (1971) failed to show any evidence of freshwater outflow from the White
Limestone aquifer along the immediate coast. However, actual points of discharge into
the sea may be some distance offshore where the White Limestone is exposed to the
seabed. Under natural conditions, the length of the saltwater wedge is directly
proportional to the hydraulic conductivity (K) and thickness of the aquifer (b2 ) squared
and inversely proportional to the flow of freshwater (q) to the sea. Analytical
101
Table 6. Calculation of freshwater head (m) along the constant head boundary at Bernard Lodge, Old Harbor, and Manchester Highlands,
Rio Cobre and Rio Minho-Milk River Basins, Jamaica, West Indies.
Basin Aquifer Location Thickness of Fresh Water Head
Aquifer hf
b (m)
(m)
Rio Cobre Alluvium Bernard Lodge 30 0.78
Rio Cobre Alluvium Old Harbor 30 0.78
Rio Minho-Milk River White Limestone Manchester Highlands 90 2.34
102
EXPLANATION
CONSTANT-HEAD
BOUNDARY
Linstaed Boundary of
physiographic region
Mandeville
Major Towns
May Pen
Old Harbour
River channel
CARIBBEAN SEA
Figure 4.10 Map of study area showing the constant-head boundary.
103
calculations of submarine discharge from the White Limestone aquifer along the
Manchester Highlands and the alluvial aquifers at Bernard Lodge and Old Harbor were
accomplished using the following data provided by the WRAJ (Table 7-8): 1) width of
the coastal boundary across which submarine discharge occurs, 2) the distance inland
from the shoreline, 3) hydraulic conductivity values, 4) aquifer thickness and 5) the
Ghyben Herzberg ratio (á = 0.025). Equation 6 was used to compute the submarine
discharge from the coastline:
ThW
Qs = α (6)
2L
where
Qs is the submarine discharge of freshwater [L3 /t]
T is the aquifer the transmissivity [L/t2 ]
W is the width of the coastal boundary across which submarine discharge
occurs [L]
L is the ldistance inland to the toe of the saltwater wedge [L]
á is the Ghyben-Herzberg ratio (á =0.025) [dimensionless]
As pumpage reduces the flow of freshwater to the sea along coastal margins, the
length of the intruded saltwater wedge increases. The length of the wedge (interface toe)
during the discharge of fresh ground-water to the sea may be found through the relation:
ρs − ρf Kb2
L= (7)
ρ f Qs
104
Distances of 150m from Bernard Lodge, 120m from Old Harbor, and 750m from
the Manchester Highlands along the coast to the seepage face (L) were divided by the
model cell width of 160m to determine the number of cells from the coastline to the
saltwater interface (saline front) (Figure 4.11, Table 7). In order to estimate freshwater
exploitable ground-water resources in the coastal aquifer, knowledge of the amount
ground-water discharge into the sea is required. Values used to determine Qs for the
alluvium aquifer at Bernard Lodge and Old Harbor and the White Limestone aquifers at
Manchester Highlands are provided by the WRAJ and modified in (Figure 4.11, Table 7-
8).
SOURCES AND SINKS
Estimates of Aquifer Recharge
Natural recharge to the saturated zone in a ground-water reservoir may come from
a number sources that include: 1) deep percolation of precipitation, 2) streambed
percolation, 3) subsurface inflow from neighboring basins, and 4) leakage from ponds,
lakes, and reservoirs. Direct recharge, that is precipitation that contributes to soil
moisture content and crosses the water table as recharge to the ground-water system, may
be expressed as:
RE = P − R − AE ± ∆S (8)
where,
RE is the direct recharge
P is the precipitation
105
Table 7. Estimated values used in the determination of submarine discharge from coastal
aquifers of the Rio Cobre and Rio Minho-Milk river basins, Jamaica, WI
(Source: Water Resources Authority of Jamaica).
Hydrologic Aquifer /Location Transmissivity Distance to Aquifer
Basin -T Toe Thickness h
(m2 /d) Of Seawater – (m)
L
(m)
Rio Cobre Alluvium at Old Harbor 745 120 30
Rio Cobre Alluvium at Bernard 14900 150 30
Lodge
Rio Minho-Milk White Limestone at 14900 750 90
River Manchester Highlands
106
Table 8. Calculation of submarine discharge in the Rio Cobre and Rio Minho-Milk River basins, Jamaica, West Indies.
(After Ghyben and Herzberg; 1901).
Location in Coastal Aquifer Length of Submarine Submarine Length Ratio of No of
Aquifer Thickness Saltwater Discharge Discharge of L/Width of Model
Wedge Model Model cell Cells
Cell used to
b L Qs Qs simulate
L
(m) (m) (m3 /d) (m3 /d) (m) (m)
WRA WRA WRA (1990) This study
(1990) (1990)
Alluvium at Bernard
Lodge 30 150 74,500 1,216,000 160 0.94 1
Alluvium at Old
Harbor 30 120 17,694 1,250,000 160 0.75 1
White Limestone at
Manchester
Highlands 90 750 379,950 408,000 160 4.69 4
Total 472,143 2,874,000
107
EXPLANATION
SUBMARINE DISCHARGE
Spauldings
Linstead Submarine discharge
point from The White
Limestone aquifer
Mandeville Spanish
Town Submarine discharge
points from alluvial
aquifer
Old Harbour
Major Towns
Bernard
Lodge
Constant-Head Boundary
Manchester Highlands
CARIBBEAN SEA
Figure 4.11 Map of coastal areas where ground-water is discharged to the sea from coastal aquifers.
108
R is the surface runoff
AE is the actual evapotranspiration
∆S is the change in storage
However the net ground-water recharge rate to the Rio Cobre and Rio Minho-
Milk river basins within the time interval (e.g. 1 year) may be estimated using equation 9
and the change in storage is neglected for steady-state conditions (Maidment, 1992):
P = R + ET + G + I (9)
where,
P is the precipitation
I is the irrigation
R is surface runoff
G is deep percolation leading to ground-water recharge
ET is the evapotranspiration
Major sources of recharge to the alluvial and White Limestone aquifers within the
study area include infiltration from precipitation, natural or induced infiltration from
surface water, irrigation water, and ground and surface water runoff. Mean annual
precipitation rates based on the Jamaica Meteorological Service’s (JMS) 30-year annual
mean for the period 1951 – 1980 were obtained from the WRAJ (Appendix 1, Tables 17-
18). Evapotranspiration from the Rio Cobre and Rio Minho-Milk river basins is
approximately 69% or 3.091 x 109 m3 /yr of the total precipitation of 4.429 x 109 m3 /yr
(Table 9). Net recharge rates from precipitation to the water table (i.e. after the removal
109
of evapotranspiration) were estimated by the WRAJ to be 9.26 x 108 m3 /yr, or
approximately 21 % of the total annual precipitation (Table 9). The equivalent rate of
volumetric recharge to the study area is 2.537 x 106 m3 /d. Recharge is assigned in units of
mm/yr and the conversion represents an average rate of 363.50 mm/yr.
Recharge was assigned to the Rio Cobre and Rio Minho-Milk river basins based
on differences in slope, topography, and relief as used by Torres-Gonzalez et al. (1996)
and by Sepulveda (1996) in similar geologic provinces in Puerto Rico. Steep slopes and
well-drained sinkholes characterize the highland regions of the Rio Cobre and Rio
Minho-Milk river basins. Alluvial sediments with moderately drained overlying soils
cover the irrigated plains.
The assignment of weights based on the percent slope calculated in a GIS using
spatial analysis, relief, and topography were used to demarcate net recharge zones in the
model (Figure 4.12). The estimated net recharge value of 363.50 mm/yr was applied to 6
zones ranging from 0% slope – greater than 12.85% slope. For example, the highest
weight of 1.2 was assigned to highland plateaus, 0.7, 0.5 was assigned to the irrigation
plains, and 0 assigned to no-flow boundaries (Table 10). Ground-water recharge of
upland areas was initially assumed to be influenced primarily by slope, with steep-sloped
regions having lower recharge than low-sloped regions of the lowlands. A map of the
distribution of simulated recharge for the Rio Cobre and Rio Minho-Milk river basins is
shown in figure 4.13.
110
Table 9. Water Balance, Water Use and Future Demands of the Rio Cobre and Rio Minho-Milk River basins, Jamaica
In MCM/yr (after Water Resources Authority of Jamaica, 1990).
ITEM RIO COBRE RIO MINHO TOTAL
Rainfall 2009 2420 4429
Evapotranspiration 1450 1641 3091
Surface water Runoff 187 225 412
Ground-water recharge
(Exploitable surface) 372 554 926
Water runoff 15 32 47
Exploitable ground-water 404 439 843
NON AGRICULTURAL SEC TOR:
Present Use 45 39 84
Expected Demand 2015 59 50 109
AGRICULTURAL SECTOR:
Present Use 589
Possible demand 2015 391 582 973
111
EXPLANATION
PERCENT SLOPE (%)
0 – 4.285
4.285-8.569
8.569-12.854
12.854 –17.138
17.138 – 38.562
Major Town S
Major highways
CARIBBEAN SEA
Slope calculated using GIS ArcView Spatial A nalyst, Base from United Nations Development Program/OAS – Government of Jamaica,
Underground Water Authority of Jamaica (now WRAJ) Map of Watershed Management. Digitized by the author from 1:250,000 scale,
Lambert Conical Orthomorphic Projection, UTM Zone 18.
Figure 4.12 Map of percent slope used in the assignment of recharge in the study region.
112
Table 10. Assignment of net recharge zones applied to the three-dimensional ground-water-flow model
Model Recharge Zones A B C D E F G H I
Xi % Weight§ (WiXi) WiXi % AreaWiXi CF CF
ΣArea Area Wi
∑WiXi ∑ WiXi CF * Vol ∑ CF
∑ RchRt
No-flow boundary 0 0 0 0 0 0 0 0 0
Urban Centers 1.93E+14 0.076 0.1 36.35 0.022 0.002 0.009 8.007E+15 3.140
Irrigated Coastal Plains 1.40E+15 0.549 0.5 181.75 0.111 0.061 0.313 2.904E+17 113.884
(Slopes < 4.28) and river
reaches
Upland regions (slopes 4.08E+14 0.188 2 727 0.444 0.084 0.430 3.983E+17 156.183
4.28 - 12. 85)
Hilly Terrane (slopes > 3.00E+13 0.012 0.7 254.45 0.156 0.002 0.009 8.713E+15 3.147
12.85
Highland Plateaus 4.45E+14 0.175 1.2 436.2 0.267 0.047 0.239 2.216E+17 86.877
Total Recharge 2.55E+15 1.000 5 1635.75 1.000 0.259 1.000 9.27E+17 363.5
§
C is based on slope (See Figure 4. 13)
113
Simulated Rivers
River interaction with ground-water-flow was simulated with the River Package
in MODFLOW (McDonald and Harbaugh; 1988). A total of 1650 river cells were used in
the simulation and specified in model layer 1 (Figure 4.14). The Rio Cobre was divided
into 384 reaches; Rio Minho into 938, Pindars River into 141, Milk River into 129, Rio
D'Oro into 73, Rio Magno into 118, and Rio Pedro into 114.
The River Package (RIV) requires that a known river head and a streambed
conductance be specifed by the user. The model simulates leakage to and from the river
based on the head in the river and the simulated head in the model. The rate of leakage
between the river and the aquifer (Q RIV) is calculated from (Source: Anderson and
Woessner, 1992):
QRIV = CRIV (H RIV − h) h>RBOT (10a)
where
HRI is the head in the source reservoir
h is the head in the aquifer directly below the surface reservoir
RBOT is the bottom of the streambed
CRIV is the stream conductance
When the water table falls below the bottom of the streambed (RBOT), the leakage
stabilizes and QRIV is calculated from:
QRIV = CRIV ( H RIV − RBOT ) h RBOT (10b)
114
EXPLANATION
RECHARGE
Values expressed in mm/yr
0 mm/yr (no-flow cell)
3 mm/yr
3.4 mm/yr
87 mm/yr
110 mm/yr
150 mm/yr
Boundary of
physiographic region
CARIBBEAN SEA
River
Figure 4.13 Aquifer recharge used in the model analysis.
115
EXPLANATION
4
.
5 SIMULATED RIVER
3 .
. LEAKAGE
6 BOUNDARIES
2 .
. 7
Inactive cell
1.
CARIBBEAN SEA
Figure 4.14 Simulated river leakage in the Rio Cobre and Rio Minho-Milk River Basins, Jamaica, WI. 1 – Milk River, 2 – Danks at Rio
Minho, 3 – Pindars River, 4 – Rio Pedro, 5 – Rio D’Oro, 6 – Rio Pedro,
and 7 – Rio Cobre.
116
Streambed hydraulic conductivity is unknown. The streambed commonly consists
of unconsolidated cobble, gravel, sand, clay, minor limestone, and volcanogenics on the
inside of meanders or impoundments. The initial value of streambed hydraulic
conductivity was set to 0.0834 m/d for all reaches, based on values computed from
variable head permeameter and field tests conducted on various materials (Rosenshein et
al., 1968). Since there were no data available on stream conductance values, the
simulated values of the streambed hydraulic conductivity are within the range of reported
values for unconsolidated stream sediments (Rosenshein et al., 1968). Thickness of
streambed sediments is often assumed to be 1ft in most modeling studies. The thickness
of the streambed sediments in the Rio Cobre and Rio Minho-Milk river basins was
h
assumed to be 1 m because there is mostly a t ick accumulation of cobbles, gravel, and
sand. The area of the river was estimated by choosing the widths of rivers (20 m to 100
m) and using 200 m as the length per model cell. River conductance values ranging from
1.125 to 20 m/d were calculated for the area of the river channel in the model cell, the
thickness of the streambed sediments, and the vertical streambed hydraulic
conductivities.
AQUIFER PARAMETERS USED IN MODEL SIMULATION
Computed Hydraulic Conductivity
Specific-capacity tests conducted in the Rio Cobre and Rio Minho-Milk river
basins by several previous investigators (Versey, 1962); FAO, 1974; H. Humphrey’s
Limited, 1974, and Botbol, 1982) were performed to determine aquifer transmissivity.
The distributions of transmissivity in the alluvial and White Limestone aquifers are
117
shown in Figures 4.15 - 4.16. The transmissivity value at a given well was obtained using
the Theis equation below:
Q ∞ e −u r2 S
ho − h =
4πT ∫
u u
du , u =
4Tt
(11)
where
Q is the constant pumping rate [L3 /t]
h is the hydraulic head [L]
ho is the hydraulic head before pumping started [L]
h - ho is the drawdown [L]
T is aquifer transmissivity [L2 /t]
t is the time since pumping began [t]
r is the radial distance from the pumping well [ L]
S is aquifer storativity [dimensionless]
Aquifer transmissivity (T) values for the alluvial and White Limestone aquifers in
the Rio Cobre and Rio Minho-Milk river basins were divided by aquifer thickness to
compute the hydraulic conductivity (K) values (T/b = K) (Appendix 1, Tables 23-26).
Thicknesses of both layers were determined from well logs. Thickness ranges from 1 m
to 150 m in layer 1 and 2 m to 260 in layer two. Due to variations in lithology and
thickness associated with the alluvial and White Limestone aquifers of the Rio Cobre and
Rio Minho-Milk River basins, it was necessary to assign a number of hydraulic
118
EXPLANATION
WELL LOCATION –
specific capacity
transmissivity in
RIO COBRE BASIN
meters squared per
RIO MINHO-MILK RIVER day
BASIN
Boundary of
physiographic region
CARIBBEAN SEA
Figure 4.15 Transmissivity estimates from specific-capacity tests in the alluvial aquifer in the Cobre and Rio Miho-Milk River Basins.
119
EXPLANATION
WELL LOCATION –
specific capacity
transmissivity in meters
squared per day
Rio Cobre Boundary of
Rio Minho-Milk River
Basin physiographic region
Basin
CARIBBEAN SEA
Figure 4.16 Transmissivity estimates from specific-capacity tests in the White Limestone aquifer in the Cobre and Rio Miho-Milk
River Basins
120
conductivity zones for each model layer. The average hydraulic conductivity value for
each zone was assigned by finding the geometric mean of all values within each zone.
Because of the regional scale of the model, local variations in hydraulic conductivity are
not simulated. Hydraulic conductivity ranges from 50 to 200 m/d in layer 1 and from 10
to 870 m in layer 2. Estimates of hydraulic conductivity in layer 1 range from 50 to 200
m/d and 10 m/d to 820 m/d in layer 2. Figures 4.17 – 4.18 define each of the hydraulic
conductivity zones in both layers. Table 11 lists a summary of the initial estimates of
hydraulic conductivity assigned to each zone in the model. These values fall within the
range of typical values of hydraulic conductivity reported for karst limestone and alluvial
aquifers (Brahana et al., 1988) (Appendix I, Table 22).
Vertical Hydraulic Conductance
Vertical conductance was assigned as a function of the hydraulic conductivity values
in each layer. Conductance refers to movement of water through a layer of material that
has a vertical hydraulic conductivity lower than that of the aquifer. The vertical hydraulic
conductivity, K , assigned to cells in the model was initially set to 5 percent of the horizontal
z
hydraulic conductivity. The ratio of horizontal to vertical hydraulic conductivity varies
from 4:1 to 20:1 because there is heterogeneity in geology and permeability. The lowest
ratio is associated with the highly permeable section in the White Limestone aquifer of
the Rio Minho-Milk River basin. Vertical conductance was calculated for the leakance
between the alluvial and White Limestone aquifers and the confining unit in the lower
Rio Cobre and Rio Minho-Milk river basins. The vertical conductance, V between these
c
cells is computed from the equation:
121
EXPLANATION
ESTIMATED HYDRAULIC
CONDUCTIVITY OF THE
1 ALLUVIAL AQUIFER
3
25 m/d
2
25 m/d
12
25 m/d
11 40 m/d
4
13 40 m/d
9
135 m/d
8 135 m/d
15 14
135 m/d
CARIBBEAN SEA 10
165 m/d
165 m/d
780 m/d`
222 m/d
10 Assigned hydraulic
conductivity zone
Figure 4.17 Distribution of hydraulic conductivity zones in model layer 1- alluvial aquifer.
122
EXPLANATION
ESTIMATED HYDRAULIC
CONDUCTIVITY OF THE WHITE
LIMESTONE AQUIFER
1
3
25 m/d
2
7 25 m/d
40 m/d
5
40 m/d
8 4
5 135 m/d
9
135 m/d
135 m/d
15
165 m/d
10
165 m/d
222 m/d
780 m/d
10 Assigned hydraulic
Figure 4.18 Distribution of hydraulic conductivity zones in model layer 2 – White conductivity zone
Limestone aquifer.
123
Table 11. Estimated values of hydraulic conductivity used in model analysis (m/d)
(Source: WRAJ, 1997).
Aquifer Zone Estimated Estimated Vertical
Horizontal Hydraulic
Hydraulic Conductivity
Conductivity Kz
Kx
WHITE (m/d) (m/d)
LIMESTONE
Zone 1 135 26
Zone 2 135 26
Zone 3 135 26
Zone 4 165 32
Zone 5 780 78
Zone 6 25 12
Zone 7 25 12
Zone 8 222 222
Zone 9 40 8
Zone 10 40 8
ALLUVIUM:
Zone 11 25 12
Zone 12 25 12
Zone 13 782 78
Zone 14 30 15
Zone 15 165 32
124
2 K1 K2
Vc = (12)
K1b2 + K2 b1
where
K1 is the vertical hydraulic conductivity assigned to model cell in layer 1
K2 is the vertical hydraulic conductivity assigned to model cell in layer 2
b1 is the corresponding thickness of cell in layer 1
b2 is the corresponding thickness of cell in layer 2
Computed values of vertical conductance between the alluvial and White Limestone
aquifer is listed in Table 12.
125
Table 12. Computed values for vertical conductance between the White Limestone and alluvial aquifers, Rio Cobre and Rio Minho-
Milk river basins, Jamaica, West Indies (m/d).
Conductivity Zone Hydraulic Thickness Conductivity Zone Hydraulic Conductivity Thickness Conductance
(Alluvial Aquifer) Conductivity Layer 1 (White Limestone K2 Layer 2
K1 b Aquifer) (m/d) b
(m/d) (m) (m)
Zone 11 7 30 6 25 30 1.944 x 10-1
Zone 12 10 30 7 25 30 3.333 x 10 -1
Zone 13 20 50 5 120 50 5.014 x 10 -1
Zone 14 14 50 5 120 50 1.043
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