vvEPA
EPA/600/R-14/296 | September 2014 | www.epa.gov/ged
United States
Environmental Protection
Agency
A Bayesian Belief Network Approach to Explore Alternative Decisions for
Sediment Control and Water Storage Capacity at Lago Lucchetti, Puerto Rico
Office of Research and Development
-------
A Bayesian Belief Network Approach to Explore Alternative
Decisions for Sediment Control and Water Storage Capacity at
Lago Lucchetti, Puerto Rico
Justin Bousquin1, William S. Fisher2, John Carriger2 and Evelyn Huertas3
U.S. Environmental Protection Agency
1 Oak Ridge Institute for Science and Education (ORISE) Fellow
Office of Research and Development,
National Health and Environmental Effects Research Laboratory,
Atlantic Ecology Division, Narragansett Rl 02882
2Office of Research and Development,
National Health and Environmental Effects Research Laboratory,
Gulf Ecology Division, Gulf Breeze FL 32561
3Region 2, Caribbean Environmental Protection Division, San Juan PR
Contents
Executive Summary 4
1. Introduction 5
2. Description of Guanica Bay Watershed and Reservoir System 7
Guanica Bay Watershed 7
Precipitation in Southwestern Puerto Rico 10
Southwest Puerto Rico Project 11
Institutional Authorities 15
3. Issues Facing Decision-Makers 17
Water Availability 17
Land Use and Erosion 18
Sediment Trapping in Reservoirs 19
Decision Options 19
4. Building a Conceptual Diagram 20
Conceptual Diagram for Lago Lucchetti 20
5. Data Sources and Data Acquisition 26
Precipitation in LL Watershed 26
Watershed Water Inflow to LL 27
-------
Water Inflow from Tunnel 28
Total Water Inflow to LL 31
Watershed Sediment input to LL 31
Sediment Input from Tunnel 35
Total Sediment Input to LL 45
Original (T0) Water Storage Capacity 45
Sediment Trapped in LL 45
Remaining (Ti) Water Storage Capacity 45
LL Life Expectancy 46
6. BBN Model for Lago Lucchetti 47
Root Node Precipitation 48
Watershed Water Inflow to Lago Lucchetti 49
Water Inflow from Tunnel 50
Total Inflow of Water 52
Precipitation to sediment runoff 54
Sediment from tunnel 56
Total Sediment into Lucchetti Reservoir 57
To Water Storage Capacity 57
Sediment Trapped in Lucchetti Reservoir 58
Tl Water Storage Capacity 59
Projecting Lucchetti Reservoir Life Expectancy 60
7. Management Options and Results of Model Runs 62
Management Options 62
Conversion to shade-grown coffee 63
Dredging the reservoir 68
Model runs 69
8. Network Evaluation and Sensitivity Analysis 71
Projecting Annual Rates of Sediment Accumulation 72
Effect of Sediment Transfer from Upper Reservoirs 74
Evaluation 77
Sensitivity Analysis 79
9. Discussion 80
2
-------
10. References 85
9. Appendixes 89
Appendix A: Sediment Balance Model Results 89
Appendix B: Precipitation Station Data 95
Appendix C: Building a Bayesian Belief Network and Node Equations 99
Discretization 104
Appendix D: R Script and referenced equations 109
-------
Executive Summary
A Bayesian belief network (BBN) was developed to characterize the effects of sediment accumulation on the
water storage capacity of Lago Lucchetti (located in southwest Puerto Rico) and to forecast the life expectancy
(usefulness) of the reservoir under different management scenarios. The conceptual approach included water
and sediment delivery from two sources, from the Lucchetti watershed and from a tunnel linking Lago Lucchetti
to three upstream reservoirs. Variables in the model included precipitation and erosion factors (soil type,
landscape slope, and land use) applied to the Lucchetti watershed and to watersheds of the upstream
reservoirs. The lack of available data for water and sediment flows in the watershed and through tunnels
connecting the reservoirs led to several unique methods for network data acquisition. Status quo model runs
demonstrated that sediment trapping has continuously declined in all four reservoirs since their construction
and that every year a greater proportion of sediment is moving downstream through tunnels or spillways. The
model compared favorably with incidental measured data in the region. Sensitivity analysis demonstrated that
current sediment accumulation in Lago Lucchetti can be attributed in large part to sediment erosion from the
Lucchetti watershed with only minor influence (~8%) from upstream reservoirs.
Two decision scenarios were explored by including additional nodes for (1) partial and full conversion of
sungrown land use to shadegrown coffee cultivation in the Lucchetti watershed and (2) partial or complete
dredging the reservoir. Both management actions were examined singly and in combination for effects on
reservoir life expectancy (beyond the year 2000) with varying water capacity targets. Using 50% water storage
capacity as a target, model runs for status quo (no decision implemented) resulted in a probability range that
averaged 5.57 years (or 50% water storage capacity in the year 2005). Partial and full conversion of land from
sungrown to shadegrown coffee cultivation raised the life expectancy to 5.89 and 6.57 years, respectively.
Partial and complete dredging of the reservoir resulted in a life expectancy of 37.3 and 40.7 years, and full
implementation of both management options resulted in a life expectancy of 44.4 years.
The advantages of a BBN were apparent from this exercise. A BBN allows consideration of multiple alternative
scenarios such as changing land use from sun-grown to shade-grown coffee or dredging the reservoir. It allows
for both quantitative and qualitative information and retains probabilities throughout the analysis.
Development of a BBN has benefits when working with stakeholders on an issue; it is constructed in simple
modular forms showing relation of causality, and has the flexibility to add or alter nodes as stakeholder
information is learned. Sensitivity analysis of a network provides an ability to examine the relative influence of
factors on the outcome and can thereby guide scientific research or information needs to reduce uncertainty.
-------
1. Introduction
The reservoir system of Puerto Rico serves the public by storing water for domestic, agricultural and
recreational uses, and protects against downstream flooding during extreme precipitation events. Sediment
entering the reservoirs from surrounding watersheds has reduced water storage capacity and threatens the
ability of reservoirs to provide these benefits. It is critical for policy and decision makers to have estimates of
the sedimentation rates and resulting ability of reservoirs to provide these benefits into the future (i.e., life
expectancy). A case study for Lago Lucchetti, a reservoir built in 1952 as part of the Southwest Puerto Rico
Project (SWP), was performed using a Bayesian Belief Network (BBN) to better characterize the likely outcomes
of sedimentation on reservoir life expectancy and the effects on life expectancy from two management
options.
The Guanica Bay watershed in southwestern Puerto Rico includes a network of constructed reservoirs and
irrigation canals built in the 1950s to provide water for agriculture, hydroelectricity and domestic uses. The
impounding reservoirs were a part of the SWP, a massive $35 million (1950 dollars) construction effort to
deliver water from five northern watersheds to the agricultural region of Lajas Valley (PRWRA, 1958). The
project did not bring as much of an economic boost to southwestern Puerto Rico as hoped. Although there
were record sugar cane harvests in 1952, some of the major processing plants (Centrales) were closing and by
1977 only a few remained (Joy, 2012). Nonetheless, the reservoir and water delivery system became central to
the economy and culture of the region. Water from the reservoirs is used for irrigation of pasture land, fruit
and vegetable crops, hydroelectric power generation and domestic water uses (e.g. drinking water) for several
communities. The reservoirs are used for recreational fishing and can provide a level of protection downstream
from flooding during the rainy season.
Another important agricultural commoditycoffeehas affected the hydrology of southwestern Puerto Rico.
Coffee cultivation existed in the mountains of Puerto Rico as early as the mid-1700s and was its most lucrative
export by the end of the 19th century (Wilson, 1899). However, catastrophic losses from hurricanes made
coffee farming a high-risk venture. In an effort to increase production, University of Puerto Rico's Agricultural
Experiment Station advocated a strategy for increasing coffee yield by eliminating shade trees (canopy) and
raising sun-tolerant coffee varieties in full sunlight (Vincente-Chandler et al., 1968). Conversion to sun-grown
coffee reduced biodiversity (from loss of canopy habitat) and increased soil erosion from the steep, poorly-
vegetated and unprotected slopes (Borkhataria et al., 2011). The rate of sedimentation in the reservoirs
increased partly from these new agricultural practices and partly from municipal development in the region
(Soler-Lopez, 2002; Gellis et al., 1999). Today, the reservoirs of the SWP have only about VT. their original water
storage capacity (Soler-Lopez, 2001b).
Lago Lucchetti is a pivotal reservoir in the SWP, serving as a large holding facility capable of receiving water
from the Lucchetti watershed as well as from the three upstream reservoirs. Water from Lago Lucchetti is
distributed via tunnel to the smaller Lago Loco downstream and then into canals for irrigation. Because of its
size, Lago Lucchetti still has a relatively large water storage capacity, but it also has considerable coffee
cultivation in its watershed. Any model developed to estimate the rate of sediment accumulation in Lago
Lucchetti must consider sediment entering from both the watershed and the tunnel from upstream reservoirs,
-------
and must consider sediment leaving over the spillway and through the tunnel downstream to Lago Loco.
Sediment movement in all these cases is dependent on precipitation, which is highly variable in this region of
Puerto Rico. Because of this high variability and uncertainty, a model for Lago Lucchetti was developed using a
probability network approach (BBN). Probability networks are able to simultaneously incorporate multiple
factors for decision analysis while retaining estimates of uncertainty. In this study, a BBN was generated to
explore the likely outcomes of two proposed management options (CWP, 2008) on sedimentation rate and life
expectancy of Lago Lucchetti.
-------
2. Description of Guanica Bay Watershed and Reservoir System
Guanica Bay Watershed
Guanica Bay in southwest Puerto Rico (Fig. 2-1) receives fresh water primarily from a single location, the mouth
of the Rio Loco at the northern end of the bay. The water, however, originates in several different watersheds
and travels different paths to reach the bay. In the 1950s, as part of the Southwest Puerto Rico Project (or the
Southwest Project, SWP) five reservoirs were built in mountain watersheds north of Guanica Bay to provide
irrigation and hydroelectric power. The five dams were connected by tunnels transporting water southward by
gravity flow. At the southernmost reservoir (Lago Loco), canals and channels were constructed to divert water
along the foothills to the west. Water was, and continues to be, pumped into fields for agriculture and drains
south across the broad Lajas Valley. A drainage channel along the southern edge of the valley returns the water
eastward to rejoin the Rio Loco near its mouth at Guanica Bay. Water entering Guanica Bay therefore
originates from and passes through several different watersheds and potentially carries sediment, contaminant
and nutrient loads from all of them (Fig. 2-2).
High sediment loads have been documented from the upper reservoirs (Soler-Lopez, 2001b), much of which
could have eroded from coffee farms on steep, unprotected slopes in mountain regions (Miller & Lugo, 2009).
Additionally, nutrient and contaminant loads increase as waters flow through the agricultural fields of Lajas
Valley. These factors have likely contributed to high levels of sediment, contaminant and nutrient pollution in
Guanica Bay and the coastal region (Fig. 2-3).
-------
«l»-o*» jauWKK
.<<*J
.,,.,
Bosque Estatal da Guanica
Punla Voir.io
Mar Caribe
«^o
Figure 2-1. Southwestern Puerto Rico showing the tunnel systems of the SWP linking (from north to
south) Lagos Yahuecas, Guayo, Prieto, Lucchetti and Loco; the diversion canal from Lago Loco west to
Lajas Valley (Valle de Lajas); the network of irrigation systems across the valley; the drainage canal along
the southern portion of Lajas Valley bringing excess water back to the east; the convergence of the
drainage canal with the Rio Loco north of Guanica Bay; and Guanica Bay. Also shown are wastewater
treatment plants (brown squares), domestic water filtration plants (blue squares), and US Geological
Service stream gauging stations (black triangles). (Map Adapted from Ortiz-Zayas & Terrasa-Soler, 2001)
8
-------
.Yahuecas
Rio Boqueron
Rio Loco
Ridge
Gugnica Bay
Figure 2-2. Flow of water between watersheds that contribute water to Guanica Bay. Water from three
reservoirs north of the Cordillera ridge (Yahuecas, Guayo, and Prieto) is transported by gravity through
tunnels to Lago Lucchetti, which ultimately delivers it to Lago Loco (blue arrows). A diversion channel
from the Loco Reservoir (Lago Loco) transports water across the foothills north of Lajas Valley, into
irrigation canals moving south, and a return drainage ditch that joins the Rio Loco before it enters into
Guanica Bay (red arrows).
Figure 2-3. Sediment from the contributing watersheds is visible as it collects in Guanica Bay (left) and is
dispersed into the coastal zone (right). Biological resources in the Bay and coastal zone are believed to
have been affected by sediment, contaminants and nutrients from the combined watershed areas.
-------
Precipitation in Southwestern Puerto Rico
A notable aspect of southwestern Puerto Rico is the contrast of low coastal plains with high mountain ridges
only a few dozen miles to the north. The mountain range in the center of Puerto Rico (La Cordillera Central)
affects rainfall on the southern coastal plains. The ridges north of Lajas Valley have an orographic effect on
rainfall, where precipitation occurs at higher elevations but air moving down to lower elevations is depleted of
moisture. Average annual precipitation in parts of Lajas Valley is less than half of upper watersheds (Fig. 2-4)
and can be very seasonal, sometimes reaching half its annual level during a single month. Seasons are
considered bimodal in Lajas Valley, with a minor wet season from late April to early June, and a heavier, more
variable wet season from August to November (Fig. 2-5). Severe storms during these months, especially during
hurricane season (June -November), may contribute a major portion of the annual precipitation. Seasonal
precipitation results in intermittent flow in streams and rivers with high flow rates during the wet season or
with storm events.
M«n Annual Precipilalion (mitt)
. MN
1311 . l.ttt
I .MB
Max Month Precipitation (mm)
| | 436 - 520
I | 521 - 573
^B 579 - 659
^B 66° - 73°
^H 731 - 329
Figure 2-4. Average annual precipitation (left) and monthly precipitation during months of greatest
rainfall (right) in Guanica Bay watershed averaged during 1990-2000; note different scales. (NOAA, 2005)
10
-------
Lajas Average Monthly
Precipitation (mm)
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
Figure 2-5. Monthly average precipitation at Lajas Substation. [Source: Southwest Regional Climate
Center (SERCC), Lajas Substation #665097,1/1/1948 to 4/30/2012; SERC, 2012]
The weather patterns of southwestern Puerto Rico make the region especially prone to droughts and flooding.
As noted above, floods are often associated with severe storms, particularly tropical storms and hurricanes.
There have been 31 tropical storms and hurricanes documented since 1899 (NOAA, 2012), most tracking from
southeast to northwest. The largest of these, Hurricane Hugo in 1989, reached Category 5 status just as it
reached Puerto Rico's southeast coastline (NOAA, 2012.
Southwest Puerto Rico Project
Against this backdrop of seasonal and event-driven precipitation, the SWP has significantly altered the natural
flow of water in the area. The SWP (Fig. 2-6) increased the Guanica Bay drainage area from approximately 230
to 390 km2 (57,000 to 97,000 acres; Lucchetti, 1946) with the additional acres reaping water from areas of high
rainfall that would normally drain to the west.
11
-------
^
-------
Table 2-1. Characteristics of five reservoirs constructed in the early 1950s under the Southwestern
Puerto Rico Project (modified from Sheda & Legas, 1968 with lat-long coordinates from Ortiz-Zayas et al.,
2004). Water from a retention pond (Toro, not shown) and from Prieto Reservoir is combined with water
from Guayo Reservoir at an aqueduct intersection flowing to Lago Lucchetti. Lat: Dam Lattitude; Long:
Dam Longitude; Yr: year; Const: Construction; Elev: Elevation
Name
Yahuecas
Guayo
Prieto
Lucchetti
Loco
Lat
18°13'13.6"
18°12'46"
18°11'08"
18°05'37"
18°02'43"
Long
66°49'00.5"
66°50'06"
66°51'48"
66°51'54"
66°53'16"
Yrof
Const
1956
1956
1955
1952
1951
Const
Volume
(Mm3)
1.76
19.20
0.76
20.35
2.40
Elev (m)
449.6
446.5
454.2
179.83
75.54
Spillway
Length (m)
60.96
67.06
51.82
52.12
45.72
Max Spill-
over (m3/s)
1102
885
906
1778
694
Lago Lucchetti (Fig. 2-7) was constructed in 1952 with 20.35 million m3 (Mm3; 16,450 acre-feet) of water
storage capacity. Spill-over water from Lago Lucchetti, which occurs only occasionally and generally in low
volumes, drains south along the Rio Yauco. But much of the water in Lago Lucchetti is transferred westward by
aqueduct to the much smaller (2.4 Mm3; <2,000 acre-ft) Lago Loco. The volume of water leaving Lucchetti
Reservoir via the tunnel to Lago Loco typically exceeds the volume of water entering from the northern
reservoirs. For example, in 1995 upper reservoirs discharged 433 Mm3 of water into Lago Lucchetti and 716
Mm3 were discharged through the tunnel to Lago Loco (Soler-Lopez, 2001a). Assuming this is consistent, water
contributions from upper reservoirs do not add to the frequency or volume of spillover into the Yauco River. In
fact, water that would normally flow down the Yauco River (from the Yauco watershed) is being captured in the
reservoir only to be redirected, along with water from the upper watersheds, to Lago Loco. This reduces the
volume that would naturally flow down the Yauco River to support aquatic habitats and other water uses. The
amounts released to the river are small, as noted by Puerto Rico Planning Board (PRPB, 1970):
"The discharge from Lago Lucchetti to the Rio Yauco is limited to the releases necessary to
supply prior downstream water rights and occasional spills of surplus water".
13
-------
Figure 2-7. Overhead view of Lago Lucchetti (from Google Earth) showing the concrete dam. Water from
upstream reservoirs passes through Power Plant No. 1 (not shown) and then is discharged into the
northwest branch of the reservoir.
The practice of harvesting energy from irrigation flows began in 1908 as a component of the South Coast
Irrigation Service, and was primarily intended to provide electricity for irrigation pumps at remote farms
(Lucchetti, 1936). For the SWP, power production takes place at Yauco Power Plants 1 and 2, which were
placed at the aqueducts coming into and out of Lago Lucchetti, respectively. Water coming from the Guayo-
Prieto tunnel produces energy at Yauco Power Plant No. 1 and is then discharged into the northwest branch of
Lucchetti Reservoir (Fig. 2-7). Water from Lucchetti Reservoir is transferred by another tunnel through Yauco
Power Plant No. 2 and is discharged briefly into the Rio Loco before collecting in Lago Loco (Fig. 2-8). At each of
the power plants the tunnels narrow (penstock) to generate pressure for creating energy.
Spillover from Lago Loco into the Rio Loco is very limited because most of the water entering Lago Loco is
transferred by open canals to Lajas Valley for irrigation. Spillover that occasionally occurs from the Loco
reservoir travels down the lower Rio Loco, eventually draining into Guanica Bay. Flow over the dam into the
lower Rio Loco is typically not increased by water from the upstream watersheds; in fact, as noted above for
Lago Lucchetti and the northern reservoirs, flow into the lower Rio Loco is usually decreased because of the
water diversion for agriculture in Lajas Valley. The water is diverted via a lined concrete canal that starts at the
western edge of the dam and extends west across Lajas Valley. Weirs and pumps are used by farmers to irrigate
from the canal. Most of the water flows south in irrigation channels. Water that does not infiltrate the soil or
evaporate is collected in an unlined drainage canal along the southern edge of Lajas Valley. The drainage ditch
flows to the east and joins the lower Rio Loco near the community of Fuig before discharging into Guanica Bay
(Fig. 2-9).
14
-------
Figure 2-8. View of Yauco Power Plant #2 releasing sediment-laden water into Rio Loco before entering
Lago Loco less than a kilometer downstream. Sediment is transferred with water from upstream
reservoirs. Photo: NOAA
Figure 2-9. Canal diverting water for irrigation (left) Drainage ditch (center) carrying unused irrigation
water back to the east where it converges with the Rio Loco (right) and is ultimately discharged into
Guanica Bay. Photos: NOAA and EPA
Institutional Authorities
The South Coast Irrigation Service was created in 1908, under the Insular Legislature of the Public Irrigation
Law, to support systems that maximize farming potential along the southern coast (Lucchetti, 1936). A
government electric power service emerged as a by-product of this irrigation system with the construction in
1915 of hydroelectric plants at reservoirs in the southeast. Electricity was originally intended to power pumps
used for irrigation. In 1925 the Utilization of the Water Resources Authority was created to survey water
resources and to operate the expanding electric power stations. Because initial private electricity providers
were concentrated only in high-density urban centers, only 12% of Puerto Rico's rural population had electric
15
-------
power by the mid 1940s (PREPA, 2013). The Puerto Rico Water Resources Authority (PRWRA), a public
corporation, was established in 1941 to initiate a vigorous rural electrification program, which started in 1944
and eventually included the SWP system (Sheda & Legas, 1968). During the ensuing years, Puerto Rico
transitioned from hydroelectric to fossil fuel for energy, so in 1979 PRWRA's name was changed (Law #57) to
the Puerto Rico Electric Power Authority (PREPA). The institutional change in this evolution is noteworthy
from a water resources emphasis to a water use emphasis (hydroelectricity) that was declining in importance.
The water supplies designed principally for irrigation and hydroelectric power generation began to be used for
domestic uses. As might be expected, this created inadequate and potentially unsanitary public water supplies,
which led to the Aqueduct Act passed in 1942 and ultimately to establishing the Puerto Rico Aqueduct and
Sewer Authority (PRASA) in 1945. Whereas PRASA has responsibility for most domestic water quality and use,
PREPA retains responsibility for the SWP reservoirs, aqueducts and power plants. PREPA controls the amount of
flow between the reservoirs and, consequently, through the Lajas irrigation system. Major withdrawals from
the system, such as for drinking water, must be approved by PREPA (Ortiz-Zayas et al., 2001).
16
-------
3. Issues Facing Decision-Makers
The situation at Guanica Bay is similar across many Puerto Rican watersheds. Water needed to fulfill various
human uses is limited or unevenly distributed among uses. Reservoirs that were constructed to offset these
needs are filling in with sediment unearthed through land use changes most often related to agriculture and
municipal growth such as roads, housing and industry. Policy and decision makers are faced with the possibility
that the reservoirs will soon be unable to store sufficient water to satisfy human uses and ecological demands,
and will be unable to capture sufficient runoff during severe precipitation events for flood protection. Relevant
issues for decision makers include:
Soil loss: Existing land uses cause soil loss from steep hillsides, especially hillsides cleared of canopy and
ground cover for sungrown coffee farms; soil loss affects agricultural productivity and the clearing of
land and loss of tree canopies affect bird habitat and biodiversity; erosion of soil results in downstream
sediment deposition.
Sediment deposition: Soil lost from hillsides is transported and deposited in streams, rivers, reservoirs,
bays and ultimately the coastal zone; sediment deposition interferes with ecosystem structure and
function, including highly-valued coral reef ecosystems; sediment deposition in man-made structures
(reservoirs, power plants) reduces their effectiveness and adds to their maintenance costs.
Diminishing water storage capacity: Sediment trapping is continually reducing the volume of water
that can be stored in reservoirs; availability of stored water for human uses and reservoir capacity for
protection against floods are both declining.
Increasing water demand: Future human activities are expected to increase demand for stored water,
including municipal growth in Yauco and Lajas Valley (DNER, 2008), increased irrigation needs, and
aquaculture development at Boqueron (Ortiz-Zayas et al., 2001).
Unpredictable weather: Climate change will affect future weather events, potentially changing the
frequency and volume of rainfall with consequences on soil loss and landslides, sediment deposition in
reservoirs, and ultimately water storage capacity and water availability; the frequency, severity and
location of storms are unpredictable and may or may not interfere with flood protection and future
water needs.
A primary goal for decision makers is to maintain reservoir water storage capacity sufficient to meet future
needs for water uses and flood control. Threatening this goal are diminished and continued loss of reservoir
volume, increasing water needs, unpredictable weather scenarios, and division of authority among responsible
agencies. These issues raise concern over the ability of the reservoir to provide future needs; some have called
for immediate action to address these issues (Ortiz-Zayas et al., 2001).
Water Availability
Precipitation in southwestern Puerto Rico is either lost as evapotranspiration back to the atmosphere,
infiltrates the ground surface to become groundwater, or runs off into surface water. A variety of human needs
is met by ground water, surface water or both depending on topography, aquifer characteristics, rainfall
intensity, soil infiltration, accessibility and similar factors. Human water use in the Guanica Bay watershed,
largely because of the Southwestern Puerto Rico Project (SWP), is dominated by surface water. Some
17
-------
groundwater is pumped for irrigation in Lajas Valley but the amounts are limited because of potential saltwater
intrusion (PRPB, 1970).
Estimation of the water volume coming into Lago Lucchetti from the Lucchetti watershed includes calculation
of surface water runoff, which incorporates rainfall, infiltration and evaporation rates across the Lucchetti
watershed. Transfer of water from upper reservoirs can be estimated by volumes recorded at Yauco Power
Station No. 1, which releases the water into Lago Lucchetti. Water storage capacity is the volume of the
reservoir available for water storage; this discounts the volume taken up by accumulated sediment and
consequently is decreasing over time. Reservoir volume above the accumulated sediment surface is calculated
from results of sonic testing for bathymetry (Soler-Lopez, 2001a).
Land Use and Erosion
Both human and natural factors can result in elevated rates of upland soil erosion on the steep slopes of La
Cordillera Central and in the Guanica watershed. Human causes include clearing tree stands and ground cover
for roads, housing and agriculture (Fig. 3-1). The most influential natural causes are hurricanes and severe
storm events, often causing landslides of wet soil from steep slopes. Precipitation is a dominant factor in soil
erosion and transport. High seasonal rains and severe events result in increased surface water runoff and
greater erosion. Channel bed and bank erosion may also increase due to both human factors, such as landuse
changes that destabilize river banks, and natural factors, such as increased stream velocity from severe events
(Rosgen, 2001).
Erosion and sediment transport are also dependent on the type of soil. Different soils have different textures
and structures that are more or less susceptible to initial detachment, and downstream transport is dependent
on grain size and water flow. Soil characteristics also influence permeability, i.e., rates of infiltration and
downward percolation to ground water, which reduces surface water runoff velocity. Finally, land cover is
instrumental in erosion and sediment transport. Vegetation reduces soil erosion by intercepting high-velocity
rain drops, increasing infiltration, and increasing adherence and stability of soil particles.
Figure 3-1. Clearing forest canopies for sun-grown coffee farms (left) and for municipal development
(like road construction, right) causes soil loss through erosion and adds sediment to rivers, reservoirs and
ultimately into Guanica Bay. Photos: EPA
18
-------
Sediment Trapping in Reservoirs
Trapping (deposition) of eroded soil can occur anywhere along the downstream path (land, riparian zone,
streambed, reservoir, lagoon, insular shelf, or oceanic region). Settling is determined by a balance between
settling velocity (or terminal velocity, a function of sediment grain size and density by drag and buoyancy) and
upwards turbulent transfer (which increases with higher flow velocity). This results in both larger and denser
sediment settling first as flow velocity slows. It also means trapping occurs more often in low-velocity pools,
broad channels, reservoirs and embayments.
The trapping efficiency of sediment by reservoirs is related to the ratio of reservoir storage capacity to water
inflow (Brune's Curve; see Brune, 1953). Consequently, trapping efficiency declines as the reservoir is filled,
even when rainfall and erosion are constant. Since their construction in the mid-1950s, the five reservoirs of
the SWP have lost 81, 14, 71, 42 and 64% of the original water storage capacity for Yahuecas, Guayo, Prieto,
Lucchetti, and Loco, respectively (Soler-Lopez, 2001b). The water storage capacity for the smaller reservoirs is
relatively more affected (higher percentage lost). Overall, the five reservoirs of the SWP have declined to about
2/3 the original (1950s) water storage capacity, from 44.5 to 30 Mm3 (36,100 to 24,300 acre-feet of
water;Soler-L6pez, 2001b).
Decision Options
Two actions proposed in the Guanica Bay Management Plan (CWP, 2008) are particularly relevant to this study:
1) Dredging sediment from the reservoir and 2) altering coffee farming practices (converting from sun-grown to
shade-grown coffee). Both actions can be wholly or partly implemented (i.e., partial dredging, partial transition
to shade-grown coffee). Both actions are expected to extend the period of adequate reservoir capacity, but
even both actions fully implemented will not assure adequacy for an indefinite future. Consequently, it is useful
for decision makers to know how long the reservoir will be useful (life expectancy) under different
management scenarios.
19
-------
4. Building a Conceptual Diagram
This report explores a model to characterize the loss of water storage capacity in Lago Lucchetti from
sedimentation. A Bayesian Belief Network (BBN) was developed to examine potential effects of management
actions on the water storage capacity and the ability to provide sufficient water to fulfill current and future
uses. The first step in preparing a BBN is to develop a conceptual diagram to portray the associations among
relevant factors in the Lago Lucchetti water storage problem. Nodes (displayed as boxes) represent variables,
and arcs (displayed as arrows) are used to indicate a relationship between the nodes. This chapter describes a
conceptual diagram to forecast the useful life expectancy of Lago Lucchetti in the face of continued
sedimentation. Components of the diagram are constructed with the expectation that values or quantifiable
estimates and relationships can be found to generate a useful BBN. Therefore, a key aspect of generating the
conceptual diagram, besides the obvious causal connections that are identified, is whether data are available to
populate a node or relationship of the diagram. If not, the data will have to be collected or a different structure
with different data will have to be used. The latter portion of this chapter gathers available evidence for each
factor (node) in the conceptual diagram. The evidence gathered is then integrated into a BBN in the subsequent
chapter (Chapter 5).
Conceptual Diagram for Lago Lucchetti
The conceptual diagram should include the major factors contributing to the sediment problem facing Lago
Lucchetti Reservoir (LL) as well as those factors that will be influenced by management actions. Management
actions to meet water demand can be evaluated by changes in the water storage capacity of the reservoir. In
this approach, that ability is calculated as a reservoir life expectancy.
Problem: Water in Lucchetti reservoir is used for various purposes, including domestic water supply, fish and
wildlife habitat, hydroelectric energy production and irrigation (Ortiz-Zayas et al., 2001). Sediment entering the
Lucchetti reservoir reduces its water storage capacity, impairing the utility of the reservoir, particularly during
periods of drought. When it was constructed in 1952 the reservoir had a capacity of 20.35 Mm3 but by 2000
this had declined to 11.88 Mm3 (58% of original capacity; Soler-Lopez, 2001b). The sediment enters by two
avenues; from the Lucchetti Reservoir watershed and from a tunnel that transports water (and sediment) from
three upstream reservoirs (Soler-Lopez, 2001a).
Management Options: Two management options to reduce sediment in the reservoir have been identified
from the Guanica Bay Watershed Management Plan (CWP, 2008): (1) Dredge the reservoir and (2) convert
sungrown to shadegrown coffee in the watershed areas. The change in reservoir life expectancy (ability to store
water for present and future needs) is examined to evaluate the utility of these alternatives.
The conceptual diagram must account for water and sediment entering Lago Lucchetti Reservoir (LL) from both
the watershed and from the incoming tunnel, and then determine the sediment accumulation in the reservoir
(Fig. 4-1). Forecasting accumulated (trapped) sediment over time will allow an estimation of the life expectancy
(useful service) of the reservoir. The two management options under consideration can be expected to
influence sediment amounts in the reservoir (dredging) and from the watershed (coffee conversion). Following
is a stepwise description of four modules constructed to generate the final conceptual diagram for the BBN
model: water inflow, sediment input, sediment trapping and life expectancy. Relationships in the conceptual
20
-------
diagram were based on literature reviewed both for Lucchetti Reservoir (Soler-Lopez, 2001a) and more
generally for erosion and reservoir sedimentation (Morris & Fan, 1998).
Tunnel Inflow
Watershed Inflow
A\
Spillway
Suspended
Sediment
rapped Sediment
Figure 4-1 Sediment enters the reservoir in watershed runoff (Watershed Inflow) and via water
transported from upstream reservoirs through a tunnel (Tunnel Inflow). Initially, this sediment is
suspended in the reservoir water (Suspended Sediment). Some of the suspended sediment will remain
suspended and flow out of the reservoir through the tunnel outlet or over the spillway. Some of the
suspended sediment will become trapped (accumulated) in the reservoir (Trapped Sediment). The
trapped sediment reduces the reservoir's water storage capacity. (Diagram developed from concepts in
Morris & Fan, 1998 and Soler-Lopez, 2001a).
Module 1 (Fig. 4-2): Water inflow. Water inflow is needed to estimate sediment inflow in Module 2 and to
calculate sediment trapped in Module 3. The two main sources of water inflow for Lucchetti Reservoir are from
rainfall on the watershed (the surface of the reservoir is considered to be part of the watershed) and from the
upper reservoirs through the tunnel into Lago Lucchetti (Soler-Lopez, 2001a). Total Water Inflow to LL is
therefore the sum of water entering from the nodes Watershed Water Inflow to LL and Water Inflow from
Tunnel. Precipitation, which can vary annually, is a major driving force behind watershed inflow (GLM, 2008)
and is represented by the node Precipitation in LL Watershed. There is also an expected indirect influence of
precipitation on water flow from the upstream reservoirs, which will be considered later.
21
-------
Precipitation in LL
Watershed
Water
Inflow from
Tunnel
Watershed Water
Inflowto LL
Total Water Inflow
toLL
Figure 4-2. (Module 1) The total water inflow to Lago Lucchetti is the sum of inflows from the watershed
and from the tunnel delivering water from upstream reservoirs. The quantity of water from both sources
is influenced by precipitation. LL= Lago Lucchetti Reservoir
Module 2 (Fig. 4-3): Sediment input. Sediment entering the reservoir is represented by the node Total
Sediment Input to LL. Sediment input is also the sum of two sourcessediment from the watershed
(Watershed Sediment Input to LL) and the tunnel from upstream reservoirs (Sediment Input from Tunnel).
Most erosion models (NOAA, 2005; Renard et al., 1997) indicate that sediment from the watershed is
determined in large part by rainfall (Precipitation in LL Watershed). Precipitation in upstream watersheds may
also influence sediment input from the tunnel; this is considered later, but for simplicity is not included in this
conceptual diagram. Estimating the amount of sediment from the watershed involves an erosion model, the
Universal Soil Loss Equation (LJSLE). USLE calculates sediment from the watershed based on Precipitation in LL
Watershed, an existing node in the conceptual diagram, as well as Soil Type, Slope and Land Use, which are
shown as a single external unit distinguished using dashed lines (Fig. 4-3). These external USLE factors are
variables in the USLE erosion model, used to estimate watershed erosion but not intended to appear as nodes
in the BBN. When management options are considered in the BBN (Chapter 8), the land use factor is the
variable that will be altered and will influence the Watershed Sediment Input to LL node.
22
-------
Precipitation in
LL Watershed
Watershed
Sedimentlnput
toll
Soil Type
Slope
Land Use
Total
Sediment
uttoLL
Sediment
Input from
Tunnel
Figure 4-3. (Module 2) Sediment reaching the Lago Lucchetti Reservoir originates in the Lago Lucchetti
watershed and in upstream reservoirs transported through a connecting tunnel. Precipitation influences
the amount of sediment coming from the watershed, which is estimated using the USLE model (dotted
line box) that accounts for soil type, slope and land use in the watershed. LL = Lago Lucchetti Reservoir.
Module 3 (Fig. 4-4): Sediment trapping. The amount of sediment trapped is determined by the trapping
efficiency (Morris & Fan, 1998; Soler-Lopez, 2001a), which is related to the water inflow and the volume of the
reservoir. This relationship is known as Brune's curve (see side bar in Chapter 5, Sediment Input from Tunnel),
which estimates the percentage of incoming sediment that will be trapped in the reservoir (Brune, 1953).
Greater water inflow and smaller storage capacity (volume) reduces the trapping efficiency. This relationship
can be illustrated conceptually as a separate model component, using a node for sediment accumulation
(Sediment Trapped in LL) that is dependent on water flow (Total Water Inflow to LL), reservoir volume (T0
Water Storage Capacity), and the amount of incoming sediment (Total Sediment Input to LL).
23
-------
Figure 4-4. (Module 3) The amount of sediment trapped in the reservoir is estimated through Brune's
Curve, which incorporates existing water storage capacity and water inflow to calculate sediment
trapping efficiency. Additional nodes are needed to estimate the amount of sediment trapped, including
the existing (To) water storage capacity (reservoir volume) and total water inflow to Lago Lucchetti. LL =
Lago Lucchetti Reservoir.
Module 4 (Fig. 4-5): Calculating reservoir life expectancy. Because of sediment accumulation, water storage
capacity in the reservoir declines during any time period (T0to Ti). The loss in water storage capacity is
estimated by subtracting the volume of sediment trapped in the reservoir at Ti from the water storage volume
at T0; as the volume of sediment increases, the water storage volume decreases. This calculation requires that a
Ti Water Storage Capacity node be added to the diagram (Fig. 4-5), which is estimated from Sediment Trapped
in LL and T0 Water Storage Capacity. The BBN model can be run on a yearly basis, with the T0 Water Storage
Capacity set as desired and then updated based on Ti Water Storage Capacity to allow for annual iterations.
For each time step of the model, one year, the water storage capacity at Ti becomes the new T0 capacity for
the following year. Over the years, declining water storage capacity will eventually fall below the volume
required for a useful reservoir. LL Life Expectancy determines how many years remain until the reservoir water
storage capacity is expected to fall below the useful volume, based on the Ti Water Storage Capacity and
Sediment Trapped in LL. For model development, the useful reservoir volume was set at 0 available water
storage capacity remaining (i.e. serving no purposes). When the modules for each step are combined, the
entire process of Lucchetti Reservoir sedimentation is described (Fig. 4-6).
24
-------
T0 Water Storage
Capacity
Sediment
Trapped in LL
T± Water Stoi
Capacity
LL Life Expectancy
Figure 4-5. (Module 4) The amount of sediment trapped in the reservoir during a run of the model from
To to Ti reduces the water storage capacity equal to the volume of sediment accumulated and ultimately
decreases the reservoir life expectancy. LL = Lago Lucchetti Reservoir.
Watershed Water
Inflow to LL
Precipitation in LL
Watershed
Soil Type
Inflow from
Tunnel
Water
Inflow to
T0 Water Storage
Capacity
SedimentTrapped
inLL
~f1 Water Storage
Capacity
Total
Sediment
Input to LL
Sediment
In put from
Tunnel
LLLJfe Expectancy
Figure 4-6. (Modules 1-4) The combined conceptual diagram to estimate life expectancy for Lago
Lucchetti incorporates all the previous modules. LL= Lago Lucchetti Reservoir.
25
-------
5. Data Sources and Data Acquisition
The conceptual diagram detailed in chapter 4 describes a path for assessing reservoir storage capacity. This
initial illustration was used to guide acquisition of available data and to parameterize a BBN. However,
generating a useful BBN model from the diagram presented some challenges. Data and quantitative
relationships were not available in this part of Puerto Rico for many of the nodes in the diagram so novel
approaches were needed. Data acquisition is described below for each of the modules. For clarity, each section
corresponds to a node in the combined diagram (Fig. 4-6).
Precipitation in LL Watershed
Precipitation is normally measured using rain gauges, but there are no rain gauges in the Lucchetti watershed
area. In previous studies, gauge data from adjacent watersheds (NOAA's National Climate Data Center stations;
NOAA NCDC; NOAA, 2013) have been used to estimate precipitation in the Lucchetti watershed (Table 5-1).
One study for the Puerto Rico Department of Natural and Environmental Resources (DNER; report by Gregory L.
Morris Associates (GLM, 2009)) extracted data from stations in neighboring watersheds with at least 15 years
of consecutive monitoring during the period 1899-2006, and spatially interpolated the data across Puerto Rico
using Geographic Information Systems (GIS).
The interpolated DNER data (GLM, 2009) were used in this study to estimate annual precipitation for the
Lucchetti watershed. Interpolated precipitation values within the Lucchetti watershed were averaged to obtain
a single average annual rainfall value for the watershed (1897 mm/yr). This compared favorably with other
estimates for the watershed (Table 5-1), including an estimate obtained from the RUSLE2 database (USDA,
2008).
Table 5-1. Estimated annual rainfall for the Lago Lucchetti watershed area using four data sets and time
periods. The DNER (GLM, 2009) average was used for precipitation values in this study and the RUSLE2
monthly average precipitation values were used to calculate sediment erosion. Data from Calversbert
(1970) were used for rainfall estimates in the USGS reservoir sedimentation surveys (Soler-Lopez,
2001a). The rainfall maps used by Summit to Sea, NOAA (2005), were averaged within the boundaries of
Lucchetti Watershed using the same method as used for GLM 2009 for an additional point of
comparison.
Catchment
Lucchetti
Area
(km2)
45.09
Avera
Calversbert 1970
2032
ge Rainfall (mr
NOAA 2005
1636
n/yr)
RUSLE2 2008
1953
GLM 2009
1897
For root nodes in our BBN, both a mean and a variance are needed (see Appendix C for more on defining
equations for distributions). The DNER report (GLM, 2009) mapped the average rainfall across space, but did
not provide any measure of variation from year to year. Consequently, the precipitation gauge stations used to
generate the DNER mapped rainfall average were revisited, and the four stations closest to the Lucchetti
Watershed were analyzed to obtain annual variation (Fig. 5-1; Table 5-2). Standard deviation and coefficient of
variation were calculated for these four stations, using only those years with complete datasets (no missing
months). The measures of variance record each station's annual precipitation over time, not variation between
stations or across space. Coefficient of variation was calculated separately for each station and averaged (CoV =
0.20) as an estimate for the watershed area (Table 5-2).
26
-------
Legend
NCDC Stations Selected
Lucchetti Watershed
~| SWP Watersheds
Adjuntas Substation
l;ndiera Altar
ana Grande 2 ENE
Yauco 1 NW
Figure 5-1. Data from four nearby gauging stations were used to estimate rainfall for the Lucchetti
watershed, including Sabana Grande, Yauco 1, Adjuntas substation and Indiera Alta (data shown in Table
5-2).
Table 5-2. Standard deviation (St Dev) and coefficient of variation (CoV) for long-term rainfall data
collected at four rain gauge stations near the Lucchetti watershed.
Station
Sabana Grande 2 ENE
Yauco 1 NW
Adjuntas Substation
Indiera Alta
Record Start
Date
May 1977
Dec 1981
Jan 1970
Oct 1962
Record End
Date
Dec 2006
Dec 2006
Dec 2006
Jun 1990
Annual Average
(mm/yr)
1584.7
1156.2
1869.9
1941.1
St Dev (mm)
349.57
238.60
366.46
366.82
CoV
0.221
0.206
0.196
0.188
Watershed Water Inflow to LL
Surface water runoff from the Lucchetti watershed to the reservoir can be estimated by applying a runoff ratio
(see sidebar) to rainfall volume in the watershed. Surface water volumes were calculated by multiplying rainfall
(1897 mm/yr; Table 5-1) times the area of the Lucchetti watershed (45.09 km2). The amount of water reaching
the pour point, Lucchetti Reservoir, could then be calculated by multiplying the surface water volume by the
runoff ratio. But because there are no gauges in the Lucchetti watershed, there are no documented measured
runoff ratios. Several methods can be used to estimate runoff in ungauged catchments, some of which are
probabilistic (Mclntyre et al., 2005; Wagener et al., 2003; Bulygina et al., 2009). Previous studies that have
estimated runoff for Lucchetti watershed have used measurements from gauges in nearby watersheds (GLM,
2008; Soler-Lopez, 2001a) with the assumption of similar rainfall volume, infiltration and evaporation rates. The
average runoff ratio from these studies (0.38) was chosen to represent Lucchetti watershed and the resulting
water inflow volume was estimated at 32.5 Mm3 per year (Table 5-3).
27
-------
Runoff Ratio: Surface water runoff can be expressed as the ratio of the volume of water that
reaches a point in the watershed to the rainfall volume that was received in the contributing part
of that watershed. The ratio is normally calculated from surface water gauge data and rainfall
volume for the portion of the watershed that flows to the gauge location. Runoff ratios are always
<1 because some of the water is lost to deep groundwater and some evaporates. It is assumed
that the characteristics influencing surface water runoff are similar across the entire watershed, so
once the runoff ratio is determined for a particular gauge location, it is applied to the volume of
rainfall in the entire watershed.
Watershed
Area = B
Contributing Sub-basin
Area = A
Stream Gauge
Volume =VA
Watershed
Outflow Point
Volume = VB
Figure: Runoff ratio (R) = VA / P * A, to get VB it is applied to the entire watershed, where VB = P *
B* R
Table 5-3. Water inflow volume to Lucchetti Reservoir from the watershed using the rainfall average
from a 2009 DNER report (GLM, 2009) and the average runoff ratio from USGS sedimentation reports
(Soler-Lopez, 2001a) and Appendix A from a 2008 DNER report (GLM, 2008).
Watershed
Lucchetti
Rainfall (mm)
1897
Watershed
Area (km2)
45.09
Rainfall *Area
(Mm3)
85.54
Runoff
Ratio
0.38
Inflow Volume
(Mm3)
32.5
Water Inflow from Tunnel
Water entering Lago Lucchetti from upstream reservoirs contributes to the total water inflow for the reservoir.
Estimating inflow from the tunnel is complex with high uncertainty. Variability stems from seasonal
precipitation in each of the upstream watersheds, the runoff from each catchment into the reservoirs, and the
portion that flows into the tunnel. However, it is possible estimate flow through the tunnel using using
28
-------
measurements recorded at Yauco Power Station No. 1 (Yauco 1), which is the hydroelectric plant that receives
all of the water entering Lago Lucchetti from upstream reservoirs.
Water flow through Yauco 1 has been measured and reported in different ways over the years and was
collected from a number of reports and personal communications (Table 5-4). Where water flow has been
reported, it was either determined by actual gauge Measurement of Water Flow (MWF) or the report
calculated flow from the Electricity produced (CElec), measured as gigaWatt-hours (gWh). To include data from
reports where only gWh were provided, a regression was generated from 8 years of data where both flow and
electricity production were reported (water flow (MGD) = 1.3509(gWh) +34.602, R2=0.6018). To add to the
complexity, reports using either MWF or CElec have sometimes included Yauco 1 and Yauco 2 (downstream of
Lago Lucchetti) as a combined value. For the purposes of this study, the aggregated measurements were
disaggregated to estimate average flow at Yauco 1 for that particular year. To do this, a relationship from
known disaggregated data from 5 years was generated [Yl= 0.4733*(Y1+Y2)-5.9603, R2=0.9352] and applied to
aggregated data (Table 5-4).
Table 5-4. Water entering Lago Lucchetti from the tunnel (million gallons per day, MGD) was estimated
by measurement of water flow (MWF) or by calculation from electricity production (CElec). *ln both
measured and calculated cases, some estimates were obtained by disaggregation of data from Yauco 1
and Yauco 2. Certain data were acquired through personal communications (Pers. Comm.)
Year
1980
1981
1982
1986
1987
1988
1989
1990
1995
2002
2005
2009
2010
2011
2012
Method
MWF
MWF
MWF
CElec
CElec
CElec
CElec
CElec
CElec
MWF
MWF
MWF
MWF
MWF
MWF
Yauco 1
MGD
21.55*
26.97*
15.98*
34.68*
45.48*
35.54*
63.69*
29.73*
26.96*
13.37*
40.23
36.06
32.95
49.01
13.15f
Source
(Torres-Siera & Aviles, 1986)
(Torres-Siera & Aviles, 1986)
(Torres-Siera & Aviles, 1986)
(Molina-Rivera & Dopazo, 1995)
(Molina-Rivera & Dopazo, 1995)
(Dopazo & Molina-Rivera, 1995)
(Dopazo & Molina-Rivera, 1995)
(Molina-Rivera, 1997)
(Molina-Rivera, 1998)
(Molina-Rivera, 2005)
(Molina-Rivera & Gomez-Gomez, 2008)
(Pers. Comm. PREPA2012)
(Pers. Comm. PREPA2012)
(Pers. Comm. PREPA2012)
(Pers. Comm. PREPA2012)
*Estimates based on trend (linear regression) between Yauco 1, Yauco 2 and total MGD for
2005, 2009, 2010, 2011, 2012. Yauco 1 was 0.4733*(total)-5.9603 with an R2=0.9352, Yauco 2
was 0.5267(total)+5.9603 with an R2=0.947. Total MGD was treated as Yauco 1 + Yauco 2 in all
cases.
29
-------
CElec: Estimate based on trend (linear regression) between total gWh and MGD for 1986,
1987, 1988,1989, 1995, 2005, 2009, 2011. The equation was MGD = 1.3509(gWh) +34.602;
R2=0.6018.
Represents total energy produced rather than the average because data were not available
for the entire year.
There is an indirect relationship between the flow of water through the tunnel from the upper reservoirs
(Water Inflow from Tunnel) and Precipitation in LL Watershed (Fig. 4-2). If precipitation in Lucchetti watershed
is unusually high during a given year it can be expected that it will also be high in the upper reservoir
watersheds, which would result in more water transferred through the tunnel that year.
To characterize this relationship requires information on precipitation in the upper watersheds with
complimentary information on water flow through the tunnel to Lago Lucchetti. Rainfall in the upper
watersheds can be estimated from the gauging stations used to estimate precipitation for the Lucchetti
watershed as described earlier. Water flow through the tunnel can be estimated, also described above, from
data obtained at Yauco Power Plant 1.
Fifteen years of tunnel flow data (Table 5-4) were available for comparison with precipitation data of
corresponding years (Fig. 5-2). For each year, precipitation data were averaged from the four rain gauges in the
region (Table 5-2). Data for 2012 were omitted completely because precipitation data for the year were
incomplete. Any year where a station was missing data for more than a month resulted in exclusion of that
station for the year. Consequently, data were not collected at Indiera Alta after 1990, the station closest to the
upper reservoirs.
Comparison of upper watershed precipitation with water flow at Yauco 1 (Fig. 5-2) found only a weak
correlation (linear regression R2=0.19). It appeared that the 1981 data may have been an outlier, but when it
was removed the correlation was not greatly improved (R2=0.31; Appendix B). This weak correlation possibly
results from spatial variability in topography and high uncertainty in converting water flow from electricity
generation. A value of the BBN approach is that it can usefully include data with high uncertainty, as in this
case. The units for flow were converted from million gallons per day (MGD) to Mm3/y", where 1 MGD =
1.382589 MmYyr (Table 5-5).
30
-------
'Yauco 1 Flow (MGD)
'Precipitation (mm)
Figure 5-2. Comparison of annual tunnel outflow at Yauco Power Plant 1 (MGD) for available years to
average precipitation (mm) from stations near the upper watersheds that contribute to tunnel outflow.
Both tunnel outflow and precipitation are averaged (represented by solid straight lines) to illustrate
annual variation.
Table 5-5. Descriptive statistics for the relationship of Yauco Power Plant 1 water flow data with
precipitation data from four weather stations in the region at corresponding years.
Average
Standard Deviation
Precipitation (mm)
1651.01
176.15
Flow (MGD)
33.73
13.32
Flow ( Mm 3/y r)
46.63
18.42
Total Water Inflow to LL
The flow of water from the tunnels (averaged 46.63 Mm3/yr, or 33.73 MGD) and from the Lucchetti Watershed
(32.50 Mm3/yr) were summed for the Total Water Inflow to LL. The total inflow value is used as one of the
inputs to determine the amount of sediment trapped in the reservoir.
Watershed Sediment input to LL
The USGS bathymetric survey of Lago Lucchetti (Soler-Lopez, 2001a) provides a measured estimate of sediment
collected in Lucchetti Reservoir since its construction, but does not give any indication what percent of that
sediment came from the tunnel or watershed or how sediment input varied annually. The BBN model can
provide estimates of these variables. An erosion model was used to determine the amount of sediment coming
from the watershed. Several erosion models are available and some have even been performed on watersheds
near Lucchetti (see sidebar). Though several erosion models were explored, and data from some are used later
in comparisons, the Universal Soil Loss Equation (USLE) approach was used in this study because its output is in
specific measureable units.
31
-------
Watershed erosion models can be distinguished as either lumped or distributed, depending on
how the proportion of sediment reaching the outflow point (Lucchetti Reservoir in this case) is
estimated. In distributed erosion models the location of eroded sediment in relation to the
outflow point is the basis for estimating how much would be trapped between the two locations.
The amount of sediment eroded from each point in the watershed is calculated and traced to the
outflow point. Lumped erosion models view the sediment from the watershed as a whole,
meaning that the total sediment eroded is calculated and then reduced by a watershed-wide
factor, often based on the watershed size, to calculate sediment yield. The difference between
the two models is that the reduction factor in distributed models is specific to the location of the
source of the soil, where as in lumped erosion models the reduction factor is generalized for the
entire watershed. One of the tradeoffs is that distributed erosion models are considerably more
data intensive, requiring calibration of the model to existing sediment and flow gauges.
There are two commonly used distributed erosion models. Gridded Surface/Subsurface
Hydrologic Analysis (GSSHA; Downer & Ogden, 2006), Soil and Water Assessment Tool (SWAT;
Neitsch et al., 2005), and two commonly used lumped erosion models, Universal Soil Loss
Equation (USLE; Wischmeier and Smith, 1978), and Summit-to-Sea (S2S; NOAA 2005). GSSHA has
been run successfully for the Lucchetti Reservoir watershed (Yuan, 2011) and SWAT has been run
for the nearby Yahuecas Reservoir watershed (Yuan, 2011). When SWAT and GSSHA were used in
southwestern Puerto Rico, calibrations had to be performed based on data from nearby Adjuntas
watershed which has flow and sediment gauges. The lumped S2S model has also been
implemented in the Lucchetti Reservoir watershed (Bousquin & Fisher, 2013) but its output is in
unitless relative terms, as "Relative Erosion Potential." The S2S output could be used for relative
comparisons between scenarios or between watersheds, but couldn't be validated with
quantitative data. USLE is very similar to S2S but outputs from the model are in specific,
measurable units.
32
-------
The Universal Soil Loss Equation (USLE; Wischmeier and Smith, 1978; RUSLE; Renard et al.,, 1997) was used to
estimate the amount of sediment eroded. Soil erosion (A) is described by four physical factors (Table 5-6),
rainfall erosivity (R), soil erodibility (K), slope length and steepness (LS) and cover management factor (C).
Erosion (A) = R*K*LS*C
Table 5-6. Description of variables used in USLE to estimate sediment erosion
USLE Variable
A
R
K
LS
C
Name
Erosion
Rainfall Erosivity
Soil Erodibility
Slope Length and Steepness
Cover Management Factor
Metric Units
Mg/(hayr)
(MJ mm)/(ha h yr)
(Mg ha h)/(ha MJ mm)
Dimensionless
Dimensionless
Data Source
Modeled in R
RUSLE2 dataset
Summit to sea
Summit to sea
NLCD
Rainfall Erosivity (R) reflects both amount (mm) and intensity of precipitation, which is a measure of rainfall
energy. Precipitation intensity, which is reported as erosivity density (see sidebar) was used from the RUSLE2
database. Both the monthly erosivity density and the monthly precipitation values were available as spatial
datasets from the RUSLE2 database. To calculate average annual rainfall erosivity, the monthly precipitation
and erosivity density values were first multiplied and then all monthly values were summed for the year.
Average annual erosivity is computed as the sum of the erosivity (EI30) which is
the product of the total energy and the maximum 30-minute intensity of
individual storms. Total Storm energy is closely related to storm rainfall amount
and maximum 30-minute intensity is a measure of peak rainfall intensity. Total
energy for a storm is computed by using the following:
M
£
=i
Where E = unit energy (energy per unit rainfall), Delta V = rainfall amount for the
kth period, k = an index for periods during a rain storm where intensity can be
considered to be constant and M = number of periods.
Erosivity density is defined as the number of units of erosivity per unit of rainfall.
These values are used because they are very well-behaved compared to raw
erosivity information. These values are multiplied by the rainfall during a time
period to yield erosivity for that period.
So/7 Erodibility (K) is related to soil type, which has well-documented Kf factors available from the S2S dataset
(originally obtained through the SSURGO database; USDA, 2011).
33
-------
Landscape Slope (LS) is the steepness across the length of the slope. LS is calculated using an equation based on
measured test plots compared to the study area (Stone and Hilborn, 2000). A degree slope shapefile provided
with the S2S dataset was input into the equation (NOAA, 2005; originally derived from the national DEM
dataset, Gesch et al., 2002). The Raster Calculator in the Spatial Analyst Toolbox (ArcGIS 10.1) was used to
convert from degree slope to percent slope and perform the LS calculation (Appendix D).
Cover Management Factor (C-factor) represents the role of land use and land cover management on erosion.
Summit to Sea C factors (based on NASA GeoCover LC, MDA Federal, 2000) were assigned to the different land
use categories used in the 2001 Nation Land Cover Dataset (NLCD; Homer et al., 2007).
All the variables (R, K, LS, C) used to calculate soil erosion (A) were available, or could be calculated, in a spatial
format covering all of Puerto Rico. The Lucchetti watershed boundaries delineated by USDA-NRCS (USDA, 2012)
using Digital Elevation Models were used to clip (in GIS) the datasets to the watershed boundaries. For
calculations, each data layer was divided into 30 x 30 m grid cells which could then be matched to the same
locations in the different layers. Across the Lucchetti watershed the rainfall erosivity values had a Coefficient of
Variation (CoV) of 0.15 (Table 5-7).
Table 5-7. Values for variables used in the calculation of erosivity for Lucchetti watershed. Summary
statistics are measured spatially, between map grid cell values.
USLE Variable
R
K
LS
C
Watershed Average Value
637.54
0.1
14.215
0.049
Minimum
429.496
0.1
0.0712
0.005
Maximum
779.052
0.1
52.1996
0.22
Standard Deviation
109.725
0
8.66499
0.051466
Precipitation, and therefore rainfall erosivity, varies overtime. Precipitation in the Lucchetti watershed was
previously characterized (Precipitation in LL Watershed) as averaging 1810 mm each year, having a normal
distribution and a coefficient of variation of 0.20. This variability and distribution were applied to the average
monthly precipitation values from the RUSLE database for each grid cell to calculate rainfall erosivity
(calculated using a script written for R statistical package (www.r-proiect.org/). further referred to as "the R
script", Appendix D). Each grid cell was randomly assigned 100,000 possible values using a normal distribution
and CoV of 0.20 around the monthly average precipitation. These monthly precipitation distributions were then
multiplied by monthly erosivity density values for each grid cell to obtain monthly rainfall erosivity
distributions. The monthly rainfall erosivity distributions were then summed for annual rainfall erosivity
distributions (R).
The last step in the USLE calculations for erosion was to multiply the annual rainfall erosivity values by the
remaining variables (K, LS and C) in each grid cell. To do this, the annual erosivity values had to be joined with
the other data based on spatial location (grid cell), which was again performed by the R script. When all cells
were summed, this became the total erosion value for the watershed. Since a distribution of 100,000 possible
precipitation values was used for input, a distribution of 100,000 possible total erosion values was calculated.
34
-------
USLE is a lumped erosion model, so it accounts for sediment eroded but does not account for how much is
delivered to the outflow point, the Lucchetti reservoir. Eroded sediment can be deposited anywhere in the
watershed, so a Sediment Delivery Ratio (SDR) was used that is based on the size of the watershed. The SDR is
similar to a rainfall runoff ratio, where ideally a gauge in the watershed would be used to calibrate the ratio of
sediment eroded from the contributing area to the actual sediment that passes through the gauge. Since there
are no sediment gauges in Lucchetti or in neighboring watersheds, the SDR value could not be validated with a
runoff ratio. The SDR used in Summit to Sea (NOAA, 2005) was used here according to the formula:
SDR= 0.41 x basin area"0-3
The watershed area for Lucchetti in the USLE model was 45.09km2, so SDR=0.1308. The SDR calculated here
was lower than other sediment delivery models (Table 5-8).
The delivered sediment was in units of mass from USLE (Mg) and had to be converted to volume to
easily subtract from reservoir capacity. The average sediment dry bulk density of samples from
Yahuecas was 0.98 g/cm3 (Soler- Lopez et al., 1999), estimated in the BBN model as 1 g/cm3. Since this
average sediment density is relatively high it is likely representative of most of the sediment profile
even though sediment cores only penetrated l-3m deep.
Table 5-8. Comparison of SDR equations and SDR results for Lucchetti Reservoir with different SDR
models. A= area of the watershed = 45.09 km2.
SDR Source
USDA(1979)
Vanoni (1975)
Summit to Sea (NOAA, 2005)
Equation
SDR = 0.566 A -an
SDR = 0.473 A -°'125
SDR=0.41 A'03
SDR Result
0.372
0.294
0.1308
Sediment Input from Tunnel
Estimating the volume of sediment entering Lago Lucchetti from upstream reservoirs (Yahuecas, Guayo and
Prieto) presented a unique challenge. The process was broken into two stepsdetermine the amount of
sediment reaching each of the three reservoirs from their respective watersheds and then determine how
much of that sediment flowed into the tunnels leading to downstream reservoirs and ultimately to Lago
Lucchetti.
The first step, determining how much sediment reaches each of the reservoirs, involves the same relationships
described above for the Lucchetti Reservoir. However, instead of using USLE a sediment balance model was
constructed. This sediment balance model used the amount of accumulated sediments trapped from each
reservoir as documented in USGS sedimentation reports (Soler-Lopez, 1999; Soler-Lopez & Webb, 1999; Soler-
Lopez et al. 1999), and then "balanced" this against the sediment input to the reservoirs each year while
accounting for changes in trapping efficiency (see sidebar).
35
-------
Trapping Efficiency: Energy is required to keep sediment moving in water and movement of
larger sediment grains requires more energy. When water flow slows, such as where
streams enter reservoirs, the energy declines and larger grains begin to settle. The amount
of time water stays in a reservoir, or the reservoir turnover rate, also affects settlement. If
the turnover rate is relatively fast, there is less time for settling. In such a case, only larger
sediment grains will settle and smaller ones remain suspended until they are carried out in
effluent water. The percent of the total incoming sediment that settles describes the
trapping efficiency of the reservoir, which is determined by the rate of water inflow and the
reservoir volume.
Brune's Curve: Empirical data were used to generate Brune's Curve (Brune, 1953), which
relates reservoir capacity and water flowing into the reservoir to observed sediment
trapped for those reservoirs. The mathematical relationship to calculate trapping efficiency
(TE) is:
100
£ 80
I 60
2
jj«
1 20
0
- Coarse sediment
TE = 0.
capacity,
10
10 2 10 '
Capacity-inflow ratio
10°
If)1
A large reservoir with a small inflow will retain water longer, allowing more sediment to
settle (higher TE); a small reservoir with high inflow will have a high turnover rate and will
trap less sediment (lowerTE). TE changes overtime because as sediment accumulates,
water storage capacity declines, thereby reducing TE (assuming a constant inflow of
sediment and water).
The conceptual diagram for sediment input for Lucchetti Reservoir (Fig. 4-3) can be adapted slightly to show
the relationships in the sediment balance model for the upper reservoirs (Fig. 5-3). Water Inflow and Water
Storage Capacity T0 influence Trapping Efficiency T0 which, when combined with Sediment Input from
Watershed influences sediment accumulation in the reservoir and creates a reduction in Water Storage
Capacity TI. The sediment balance model was run once for every year between construction and the years that
bathymetric surveys of the upper reservoirs were completed, i.e., those years for which water storage
capacities were known. In the sediment balance model, Sediment Input from Watershed and Water Inflow
were assumed to stay constant, with the same value being used each year, and Trapping Efficiency T0 was
allowed to decline with change in accumulated sediment within each of the upper reservoirs. The difference
36
-------
between Sediment Input from Watershed and Sediment Trapped is the amount of sediment that remained
suspended and left the reservoirs ('effluent sediment). Effluent sediment leaves the upper reservoirs either
through the tunnel or over the spillway.
Water Inflow
Trapping
Efficiency (T0)
Sediment
Trapped (T..,-
Water Storage
Capacity (T0)
Sediment Input
from Watershed
Water Storage
Capacity (Tj)
Figure 5-3. A sediment balance model was run every year from To (time of dam construction) to the time
of a bathymetric survey measuring water storage capacity of each upper reservoir (Tn, where n= 41 or 42
years, depending on the reservoir). The framework shows that sediment trapped in the reservoir after
the first year alters water storage capacity, which affects trapping efficiency and the amount of sediment
trapped the next year.
The second step was to determine how much of the effluent sediment flowed into the tunnels leading to
downstream reservoirs (Fig. 5-4). No measured data were available for water entering or leaving the tunnels
(with the exception of Tunnel P+G in Fig. 5-4 as described earlier using hydroelectric power generation data) so
another method was needed to estimate the proportion of water and sediment leaving each reservoir through
the tunnels or over the spillways. Complicating matters are the recognition that for Guayo Sediment Input
from Watershed originated both from the Guayo watershed and from Yahuecas Reservoir (transported to
Guayo via Tunnel Y, Fig. 5-4). This realization meant the sediment balance model for Guayo could not be
completed until the transfer of sediment from Yahuecas was calculated.
37
-------
Prieto
watershed
Guayo
watershed
Prieto
Reservoir
"urrel F
Yahuecas
watershed
Guayo
Reservoir
Tunnel G
Tunnel P
i Lucchetti
Reservoir
*G
Tunnel Y
Yahuecas
Reservoir
Figure 5-4. Configuration of reservoirs and tunnels that link upstream reservoirs and watersheds to
Lucchetti Reservoir. Water and sediment from Yahuecas Reservoir is transported to Guayo Reservoir
(Tunnel Y); from Guayo Reservoir to Lucchetti Reservoir (Tunnel G); and from Prieto Reservoir to
Lucchetti Reservoir via Tunnel P. Sediment transported in Tunnel G is determined by the input from the
Guayo watershed as well as sediment from the Yahuecas
Reservoir (via Tunnel Y).
Sediment Balance Models:
Total sediment accumulation during the 41-42 years of a reservoir's existence can be calculated as the
difference between initial water storage capacity (at construction in 1955 or 1956) and capacity measured by
bathymetry in 1997 (Soler-Lopez, 2001a). This is because the volume of water capacity displaced by sediment is
equal to the sediment accumulated (Table 5-9). The amount of sediment accumulated on an annual basis could
have been roughly calculated by simply dividing the sediment accumulated by the number of years it
accumulated (41 or 42 years between construction and bathymetry surveys). But this would overlook the effect
of sediment accumulation on trapping efficiency, which declines as sediment accumulates over time. The
sediment balance model was developed to account for annual changes in trapping efficiency in estimates of
accumulated sediment. This concurrently estimates the amount of sediment leaving a reservoir, which is
needed to determine the sediment contribution of upper reservoirs to Lago Lucchetti.
The sediment balance model assumed a constant amount of sediment input to the reservoir (Sediment In) and,
using successive iterative runs of the model, determined a sediment input value that would cause accumulation
to reach the total accumulated volume (Sediment Accumulated) after 41 or 42 years while accounting for
annual changes in trapping efficiency (TE).
Years
Sediment Accumulated = y Sediment In (Sediment In* (I
0-41
38
-------
Table 5-9. Sediment accumulation in each of the upper reservoirs was estimated by the difference in
water storage capacity at construction (initial capacity) and at the time the survey was completed (1997)
41-42 years later. The loss of water storage capacity reflects the total accumulated sediment during that
time period. The values for Guayo Reservoir are used in the next section of the report. Mm3=Million
cubic meters
Reservoir
Yahuecas
Guayo
Prieto
Construction
Year
1956
1956
1955
Initial
Capacity
(Mm3)
1.76
19.20
0.76
Survey
Capacity
(Mm3)
0.33
16.57
0.22
Accumulated
Sediment
(Mm3)
1.43
2.63
0.54
Years
41 ('56-'97)
41 ('56-'97)
42 ('55-'97)
Trapping efficiency is dependent on the water storage capacity, but also on water inflow. Water Inflow was
held constant in the reservoir sediment balance models. Similar to the estimate for Lucchetti Reservoir (Table
5-1), which had no flow gauges, estimates for other watersheds were made from rainfall measurements (GLM,
2009) and runoff ratios (Soler-Lopez, 1999; Soler-Lopez & Webb, 1999; Soler-Lopezet al., 1999) from nearby
watersheds (Table 5-10). Two published runoff ratios were averaged for Prieto and Guayo Reservoirs and a
third runoff ratio was included in the Yahuecas Reservoir average (Yuan et al., 2013).
Table 5-10. Calculation of water inflow volume for three reservoirs. Average rainfall (GLM, 2009)
delineated for each watershed was the product of the watershed area and the Runoff Ratio to obtain
inflow volume (million cubic meters, Mm3).
Watershed
Yahuecas
Guayo
Prieto
Rainfall (mm)
1909
1923
2028
Watershed
Area Km2(ij
45.17
25.10
24.69
Rainfall Area
(Mm3)
86.23
48.27
50.07
Runoff
Ratio (2)
0.463 (3)
0.435
0.37
Inflow Volume
(Mm3)
39.924
20.997
18.526
(1) Area determined using watershed delineations (USDA, 2012) and includes the surface area of the
reservoirs.
(2) Average ratio from USGS sedimentation reports (Soler-Lopez, 1999; Soler-Lopez & Webb, 1999; Soler-
Lopez et al., 1999) and a DNER report (GLM, 2008)
(3) Includes a third value measured by Yuan et al. (2013).
The total sediment accumulated over the 41 or 42 years since a reservoir's construction (Table 5-9) was set as a
target output for the model. Initially, a trial value for Sediment Input from Watershed was entered into the
model. The trial value originated from published estimates of 1430 m3/km2/yr sediment yield for the Yahuecas
watershed and 900 m3/km2/yrforthe Prieto watershed (Soler-Lopez, 2001b). The trapping efficiency for the
first year was calculated from the maximum initial reservoir water capacity (74.88% for Yahuecas and 73.72 for
Prieto), but for subsequent years a new reservoir water capacity value was used, a value that reflected the loss
of capacity from sediment accumulation. Trapping Efficiency (T0) was thus recalculated every year of the model
run until 1997 (Appendix A).
39
-------
Calculations for Guayo Reservoir are different because of the additional input of sediment and water from
Yahuecas Reservoir. A similar procedure, but with the additional water and sediment included, is performed for
Guayo in the next section of the report. The final values for Sediment Input from Watershed were slightly
lower than the estimate of Soler-Lopez (2001b; Table 5-11), which was the value used as a starting point in the
initial model run.
Table 5-11. Annual watershed sediment input for Yahuecas and Prieto reservoirs. The sediment balance
model estimated annual watershed sediment input as total annual volume (m3), which was then
normalized by the area of the watershed (km2). USGS Sediment Input (Soler-Lopez, 2001b) was used as
an initial estimate for the sediment balance model.
Reservoir
Yahuecas
Prieto
Sediment Balance
Model Sediment Input
(mVyr)
56,550
20,050
Sediment Balance
Model Sediment
Input (m3/km2/yr)
1,252
808
USGS
Sediment
Input
(mVkmVyr)
1,430
900
For both reservoirs, sediment accumulation was greatest in the first year after construction and then, due to
declining water storage capacity and trapping efficiency, decreased every year thereafter (Appendix A, Fig. 5-5).
Because trapping efficiency decreased, the amount of sediment leaving the reservoir (effluent sediment)
increased every year; this was calculated by subtracting the amount of sediment accumulated from the
sediment input. Using this model to estimate effluent sediment is much more realistic than simply averaging
the amount of effluent sediment across 41 or 42 years (Table 5-12).
40
-------
0.045
.3
1956 1963 1970 1977 1984 1991 1998
Year
Annual Accumulated Sediment
Annual Effluent Sediment
Annual Water Storage Capacity
Figure 5-5. Annual capacity, accumulated sediment and effluent sediment for Yahuecas Reservoir
between initial construction and 1997 when a bathymetry survey measured the amount of sediment
that had accumulated since construction.
Table 5-12. Sediment balance model forecasts for sediment accumulation and effluent sediment .for
Prieto and Yahuecas Reservoirs for the year 2000. *Annual averages across 41 or 42 years are included
for comparison.
Reservoir
Yahuecas
Prieto
Sediment Inflow
(Constant)
m3
56,550
20,050
mVkmVyr
1,252
808
Trapped Sediment
*Average
m3/yr
34,554.6
12,780.9
m3 (2000)
18,406.6
8,873.2
Effluent Sediment
*Average
m3/yr
21,995.0
7,590.6
Estimated
m3 (2000)
38,143.0
11,321.8
*annual average for 1955 (or 1956) to 1997
Portion of effluent sediment exiting via tunnels:
The second step in determining sediment input from the tunnel into Lago Lucchetti was to estimate the
amount of effluent sediment (the portion of incoming sediment that was not trapped) flowing into reservoir
41
-------
tunnels and the amount flowing over the spillway. Before this can be calculated for Lago Lucchetti, it has to be
calculated for Yahuecas Reservoir to inform the sediment balance model for Guayo Reservoir.
Two methods were used to estimate the proportion of sediment leaving the reservoirs through the tunnels.
Both methods required an assumption that sediment is suspended in the water at a uniform concentration.
This allows effluent water to serve as a proxy for effluent sediment. The first method compared reservoir water
elevations to spillway height and estimated how often (i.e., days per year) water would have escaped over the
dams. The second method estimated the total flow from all the upper reservoirs compared to estimates of
water inflow (Table 5-10).
Reservoir elevations. There are no flow gauges to track the amount of water flowing over reservoir spillways.
During a survey of reservoirs in 1968, Lucchetti was the only reservoir with spillover (8 cfs; 0.227 m3/s),
although the Loco reservoir was reportedly being drawn down at the time (Sheda & Legas, 1968). However,
there are gauges that track the elevation of water in the reservoirs. Water will escape when the elevation is
above the height of the spillway, so the frequency of spillover days (when water elevation is greater than
spillway height) can be an indicator of water effluent over the spillway (Table 5-13). Not captured by this
method is the fact that larger volumes of water flow would be associated with higher elevations.
Although year-to-year variation can be high, frequency of spillover was found to be relatively low (Table 5-13);
when available data were averaged over all days, the reservoir water levels remained below spillway height 80-
90% of the time. Accounting for the days when spillover volume could be much higher, it is reasonable to
project that between 30-50% the water exiting the reservoir exits over the spillway. All the rest (50-70%) exits
through the tunnel. This relationship was roughly equal across all three reservoirs.
Table 5-13. Days (as a percentage of the total) that reservoir water elevation did not exceed spillway
height. Total Days accounts for the number of daily elevation data points and does not include gaps in
data collection.
Reservoir
Yahuecas
Yahuecas
Prieto
Prieto
Guayo
Guayo
Gage Number
50141100
50141100
50142500
50142500
50141500
50141500
% Days Below
Spillway
77%
97%
100%
74%
78%
87%
Total Days
1626
2793
946
2697
1647
8028
Dates
23 Apr 1980 -30 Jan 1985
14 Oct 2004 - 19 May 2013
1 May 1980 -29 Jan 1985
15 Oct 2004 - 28 Sep 2012
23 Apr 1980 -30 Jan 1985
9 Jun 1989 - 19 May 2013
Flow comparison. The second approach to estimate the water flow through tunnels is to compare the
estimated reservoir inflows (Table 5-10) to the gauged flow at Yauco Power Plant 1 (Table 5-4). The total water
inflow for all three reservoirs (39.9 24, 20.997 and 18.526) was 79.45 Mm3/yr. If 100% of the effluent water
were to flow through the reservoir tunnels, there would be 79.45 Mm3 passing through the Yauco Power Plant
1. Gauge measurements at Yauco 1 (Table 5-4, converted to Mm3) document a maximum flow (in 1989) of 88
42
-------
Mm3 and a minimum flow (in 2012) of 18 Mm3 with an average flow of 45 Mm3. The ratio of total inflow for the
three upper reservoirs (79 Mm3) to the average flow through Yauco Power Plant 1 (45 Mm3) is about 57%.
Neither approach for estimating water flow through the tunnels is without limitations, but when combined it is
reasonable to set a tunnel transfer rate of 60%; i.e., 60% of incoming water to each reservoir exits through the
tunnel and 40% over the spillway. By extension, and with the assumption that sediment concentration remains
constant, the proportion of effluent sediment leaving the reservoirs by tunnel is most likely 60%, although it
could range from 0% to 100% on any given year. For example, tunnels could be closed for maintenance (0%), or
at the other extreme, the reservoir could fill with sediment and all the incoming sediment is transferred
through the tunnel (100%).
Sediment Balance Model for Guayo Reservoir:
Guayo Reservoir's sediment balance model is conceptually similar to the model for Prieto and Yahuecas
Reservoirs (Fig. 5-4), but must incorporate the additional sediment and water inflow from Yahuecas Reservoir.
As before, Water Inflow from Guayo watershed was estimated based on precipitation and runoff ratios (Table
5-10); and, as before, the sediment balance model was used to establish the amount of sediment accumulated
during 41 years (Table 5-9). For the initial year of construction (1956) it was assumed that the tunnel wasn't
fully operational, so no contribution from Yahuecas was incorporated. After the initial year, 60% of water
inflow to Yahuecas Reservoir (23.94 Mm3) was added to the watershed inflow for Guayo Reservoir (20.997
Mm3 from Table 5-10) to arrive at a total Water Inflow (44.937 Mm3) for Guayo Reservoir, which remained
constant in the model after the first year.
Likewise, after the initial year, 60% of sediment inflow to Yahuecas Reservoir during the previous year was
added to the watershed sediment input for Guayo Reservoir. Because of declining trapping efficiency in
Yahuecas Reservoir (see Fig. 5-5), the sediment delivered to Guayo from Yahuecas Reservoir increased over
time (Appendix A).
The combined sediment input to Lago Lucchetti from the Guayo watershed and from the Yahuecas Reservoir
tunnel was calculated (Table 5-14). An initial sediment input value (2660 m3/km2/yr (Soler-Lopez, 2001b)) was
entered for the first sediment balance model run and, as before, the accumulated sediment after 42 years was
compared with bathymetry estimates of water storage capacity. The input value was altered and the model re-
run in a trial-and-error approach until the target sediment accumulation was reached. Because the 60%
proportion for water and sediment transfer from Yahuecas to Guayo Reservoir was based on relatively
uncertain methods, a range of possible outcomes was generated by additional runs of the model with transfer
proportions of 0% and 100% (Table 5-14). Results show that additional sediment input from Yahuecas Reservoir
(0, 60 and 100%) caused a commensurate decrease in the contribution of sediment from the watershed. If no
sediment was transferred from Yahuecas Reservoir (0%) the rate of sediment input was very similar to the
value estimated by USGS (Soler-Lopez, 2001b).
43
-------
Table 5-14. Annual watershed sediment input for Guayo Reservoir estimated by the sediment balance
model and accounting for sediment input from Yahuecas Reservoir at 0, 60 and 100% transfer
proportion. The sediment balance model estimated annual watershed sediment input as total annual
volume (m3), which was then normalized by the area of the watershed (km2). USGS Sediment Input
(Soler-Lopez, 2001b) was used as an initial estimate for the sediment balance model.
Transfer Rate
Into Guayo
0%
60%
100%
Yahuecas Sediment
Transferred
(Average)
0
12,991
21,990
Modeled Watershed
Sediment Input
(mVyr)
66,389
56,507
49,800
Modeled Watershed
Sediment Input
(mVkm2/yr)
2,671
2,273
2,003
USGS Sediment
Input
(mVkmVyr)
2660
2660
2660
As presented for Prieto and Yahuecas Reservoirs, completion of the sediment balance model allowed a
projection from 1997, the year that the Guayo bathymetry survey was conducted, to the year 2000 when the
survey was conducted for Lago Lucchetti (Table 5-15). Annual sediment accumulation estimated by the
sediment balance model (which incorporates changes in the trapping efficiency) differs from a simple average
across 41 years. The addition of sediment from Guayo increases both sediment trapped and effluent sediment.
Table 5-15. Sediment balance model forecasts for sediment accumulation and effluent sediment for
Guayo Reservoir assuming 0, 60 and 100% transfer proportions from Yahuecas Reservoir. *Annual
averages across 41 years are included for comparison.
Transfer
Rate Into
Guayo
0%
60%
100%
Watershed Sediment
Inflow (Constant)
m3
66,389
56,507
49,800
mVkmVyr
2,671
2,273
2,003
Sediment Trapped
*Average
m3/yr
64,154
64,305
64,399
m3
(2000)
64,013
72,387
77,770
Effluent Sediment
*Average
m3/yr
2,234
5,194
7,053
m3 (2000)
2,375
7,006
10,180
Total Sediment from Upper Reservoirs:
The projected sediment transfers from upper reservoirs for the year 2000 were summed to obtain the total
tunnel sediment effluent (Table 5-16). The three sediment transfer proportions (60% as 'most likely' and 0%
and 100% to characterize the range) were all run to account for the high level of uncertainty in the transfer
estimate. The same transfer proportion was used simultaneously for all tunnels, including the tunnel between
Yahuecas and Guayo Reservoirs. As expected, the difference between 0% transfer and 100% transfer through
the tunnels was dramatically different. The 'most likely' transfer proportion of 60% resulted in a total sediment
input to Lago Lucchetti of 10,997 m3 for the year 2000.
44
-------
Table 5-16. Total effluent sediment into Lucchetti Reservoir from Prieto, Yahuecas (Table 5-12) and
Guayo (Table 5-15) projected for the year 2000 with three levels of sediment transfer (0, 60 and 100%).
Transfer Rate Into
Lucchetti
0%
60%
100%
Guayo Tunnel
Effluent (m3)
0
4,204
10,180
Prieto Tunnel
Effluent (m3)
0
6,793
11,322
Total Tunnel Sediment
Effluent (m3)
0
10,997
21,502
Total Sediment Input to LL
The total sediment entering Lago Lucchetti Reservoir is the sum of the sediment from the Lago Lucchetti
watershed (based on the USLE erosion model) and sediment from upstream reservoirs delivered through the
Prieto and Guayo Tunnels (Table 5-16).
Original (T0) Water Storage Capacity
Water storage capacity for the reservoir is the volume remaining in the reservoir after sediment accumulation.
In 1952, Lago Lucchetti Reservoir was constructed to hold 20.35 million cubic meters (Mm3) of water; due to
sediment accumulation this capacity was reduced to 15.84 Mm3 (78%) by 1986 and 11.88 Mm3 (58%) by 2000,
which is the last time it was measured. Existing capacity (for 2013 or any future year) could be projected by
extrapolation of these three data points or from BBN model output that incorporates changes to trapping
efficiency.
Sediment Trapped in LL
The amount of sediment trapped in Lago Lucchetti is calculated simply as the Total Sediment Input to LL times
the trapping efficiency for any given year. Trapping efficiency describes the rate of sediment retention in the
reservoir. Sediment enters and leaves the reservoir suspended in the water column. Some settles in the
reservoir and accumulates, reducing the water storage capacity of the reservoir. Trapping efficiency is
determined through application of Brune's curve (Brune, 1953), which incorporates annual inflow and existing
water storage capacity:
TE = 0.97
Trapping efficiency and the equation for Brune's curve were described in greater detail in a sidebar and for the
sediment balance model used on the upper reservoirs
Remaining (Ti) Water Storage Capacity
Water storage capacity of the reservoir declines over time as sediment accumulates. Remaining water storage
capacity is simply the original reservoir volume minus that filled by sediment. Terms must be defined to
calculate remaining storage capacity; for example, original (T0) could mean the initial water capacity for Lago
Lucchetti at construction (20.35 Mm3) and Ti could be the volume remaining in 2000 (11.88 Mm3 or 58%). Or,
the volume in 2000 might be set as T0 to calculate change in storage capacity by 2013 (Ti). For the annual
model runs performed in this study, each Ti became the T0 for the next run. Thus, water storage capacity
45
-------
remaining in the Lucchetti Reservoir at the end of any annual run of the model is simply calculated as the
original storage volume (that of the previous year) minus that volume filled by sediment during the year.
Remaining (Ti) capacity = Original (T0) capacity - Sediment trapped (T0 to Ti)
LL Life Expectancy
It is useful for decision makers to know whether water storage capacity will meet existing or future demands
and, based on the rate of loss, how long into the future the reservoir can be expected to meet those demands.
There are several alternatives for estimating useful life expectancy. By convention, a reservoir is considered to
meet water storage needs if it retains 50% or more of its original water storage capacity (Morris & Fan, 1998).
For model development reservoir life expectancy was set as the number of years after Ti when Water Storage
Capacity became zero and no water demands are being met. A life expectancy threshold could also be set
based on meeting existing and future needs. Although some estimates of future water demands for Lago
Lucchetti are available (Ortiz-Zayas et al., 2001; DNER, 2008), model runs were selected to characterize three
scenarios (0%, 25%, 50% of the original water storage capacity; Chapter 7).
46
-------
6. BBN Model for Lago Lucchetti
The conceptual diagram generated for Lago Lucchetti (Fig. 6-1) captured the linkage of precipitation to
sediment runoff, sediment runoff to sediment trapped in the reservoir, and sediment trapped to water storage
and reservoir life expectancy, which is the outcome that will be examined for utility of different decision
scenarios. The BBN model follows the flow of the conceptual diagram. Node names were altered as needed to
specify the data and units described in Chapter 5.
Water
Inflow from
Tunnel
Water
Inflow to
Sediment Trapped
inLL
Total
Sediment
Input to LL
Sediment
Input from
Tunnel
T Water Storage
Capacity
T Water Storage
Capacity
LLLife Expectancy
Figure 6-1. Conceptual diagram generated in Section 4 (see Fig. 4-6) showing the relationships of
sediment and water flow affecting water storage capacity of Lago Lucchetti (LL).
Bayesian belief networks (BBN; also called Bayesian networks, Bayes nets, probability networks) are directed
acyclic graphs structured to represent conditional independence among variables. Nodes (typically displayed as
circles or boxes) in a BBN represent variables, and arcs (displayed as arrows) are used to indicate a conditional
relationship between the parent (originator) and child (receiver) nodes. Nodes without parents are considered
'root nodes. The uncertainty of a root node is described by the distribution of its values, or prior probability
distribution. Arcs in the BBN represent conditional relationships between nodes. The strength of the
relationship between parent and child node is based on probabilistic evidence stored in the conditional
probability table (CPT) of the child node. The CPT reflects the conditional probability of every combination of
parent and child value (state), and can be constructed from a) frequencies built from standard statistical
methods for developing probabilities and entered directly, b) from observations such as counts or c) from
equations, either deterministic or probabilistic. A brief introduction to BBNs, entering data into them and how
equations are constructed is included in Appendix C. There are several software programs that allow users to
build BBNs, Netica (Norsys, 2000) was the software used for this study and all BBN diagrams are Netica output.
47
-------
These probabilistic outputs for nodes show discretized (continuous values divided into numeric categories, or
states) results as 'belief bars/ which are simply a horizontal histogram showing the distribution between states
of each node. Root node equations provided (Appendix C, Table C-l) are also specifically designed for Netica.
Root Node Precipitation
In the conceptual diagram, Precipitation in LL Watershed is a root node representing the amount of rainfall in
the area contributing water to Lago Lucchetti. Precipitation in the watershed varies from year to year so the
model must describe the probability of all values to project possible rainfall scenarios. These probabilities are
"prior" probabilities (See Appendix C) that can be acquired from past observation.
The BBN node for Precipitation in LL Watershed is called "Annual Precipitation" (Fig. 6-2) and reflects prior
probabilities derived from previous observations. Past records from nearby rainfall gauges were used to
construct a probabilistic equation for the node (Tables 5-1 and 5-2). Entering an equation into the software
requires the type of distribution, the mean, and the variation around that mean (Appendix C). A study by
Bonnin et al. (2006), which measured rainfall in the region during 24 hour periods, showed that rainfall
exhibited a normal distribution. For a normal distribution, an average and standard deviation are entered into
the Netica software. As described in Chapter 5, the annual average rainfall for Lago Lucchetti was 1897 mm
with a Coefficient of Variation (CoV = 0.20). These were used to calculate a standard deviation = 379 mm and
the data were entered into Netica as:
p(Annual_Precipitation |) = NormalDist (Annual_Precipitation, 1897, 379)
The variable "Annual Precipitation" refers to the BBN node where the values are assigned. In Netica, the
"equation to table" function transfers values from the probabilistic equation to the conditional probability table
(CPT) using a series of random values. The number of random values that are used to generate probabilities can
be set within the program and, because of the high uncertainty, 100,000 were used for all steps in this study.
Compiling the network (starting the model in the Netica software) provided a graphic representation of rainfall
distribution on the belief bars (horizontal histogram; Fig. 6-2). The distribution for rainfall was discretized (i.e.,
categorized into ranges) based on standard deviation, where the two middle categories are one standard
deviation above and below the average and the two outer categories include all values higher or lower than
one standard deviation from the average.
Annual Precipitation (mm)
0 to 151 8
1 51 S to 1897
1897 to 2276
>=2276
1 81 0
15.9
34.1
34.1
15.9
! !
i i
±560
Figure 6-2. Continuous node and belief bars (horizontal histogram) representing probabilities for annual
precipitation for the Lucchetti watershed. The precipitation equation was entered into the node as:
p(AnnualPrecip|)= NormalDist (AnnualPrecip, 1897, 379). Discretization of the belief bars (category
ranges) was set at one standard deviation.
48
-------
Watershed Water Inflow to Lago Lucchetti
The contribution of water into Lucchetti Reservoir from the Lucchetti watershed (Watershed Water Inflow to
LL in Fig. 4-2) was estimated from the total volume of precipitation expected to fall across the watershed area
minus that amount lost to infiltration and evapotranspiration. The total volume of rainfall in million cubic
meters (Mm3) was obtained by multiplying the watershed area (45.09 km2) by values in the Annual
Precipitation node. The volume was multiplied by the watershed runoff ratio, estimated at 0.38 (Table 5-3) to
account for infiltration and evapotranspiration. The resulting mechanistic equation describing "Flow from
Lucchetti Watershed" is:
Flow (Annual_Precipitation) = Annual_Precipitation *45.09 *0.001*.38
Where 45.09 = area (km2), 0.001 converts mm x km2 to Mm3; and 0.38 = Runoff Ratio
A report by GL Morris Engineering (GLM, 2008) estimated annual inflow volume to Lucchetti Reservoir from the
watershed as 31.365 Mm3. It was noted earlier (Table 5-3) that using watershed delineations (USDA, 2012), the
map of average rainfall (GLM, 2009) and runoff ratios (GLM, 2008; Soler-Lopez, 2001a), inflow averaged 32.50
Mm3. These independent estimates fall near the middle of the distribution and are similar to the average
described by the BBN (31.2 Mm3; Fig. 6-3).
Annual Precipitation (mm)
0 to 1518 15.9
1518 to 1897 34.1
1897 to 2276 34.1
>= 2276 15.9
L. I I
iii
1810 ±560
Flow from
Oto 15
15 to 20
20 to 25
25 to 28
28 to 32
32 to 35
35 to 40
40 to 45
45 to 50
>=50
Lucchetti Watershed (Mm3)
9.16
3.04
3.06
11.1
21.0
15.8
23.3
7.30
3.37
2.93
M
!
i
^M :
^^^M i
^^m I
^^^^m
i
i
31. 4 ±10
Figure 6-3. BBN describing the probability of water flow from the watershed (Flow from Lucchetti
Watershed) into Lucchetti Reservoir as a condition of Annual Precipitation. The average flow (31.4 Mm3)
was similar to independent estimates.
49
-------
Water Inflow from Tunnel
Estimating the Water Inflow from Tunnel (Fig. 4-2), or "Water Flow from Upper Reservoirs" (Fig. 6-4)
as it is called in the BBN, was based on conversion of data for electricity generation into water flow
(Table 5-4). Since water flow through the tunnel is expected to be related to rainfall in the upper
watershed, these estimates of water flow needed to be compared to precipitation for those same years
(Fig. 5-2). Initially a regression model was explored to compare available flow data to rainfall for the
corresponding years. However, the correlation was very weak and uncertainty (R2 value) was too high
to be useful. In the BBN, the continuous distribution created from such a quantitative model would be
discretized into more general categories where high precision is less important. Consequently, data
were placed into discrete categories based on standard deviation and these categories were used to
define the relationship between the nodes (Water Flow from Upper Reservoirs and Annual
Precipitation) from year to year.
For Water Flow from Upper Reservoirs, three broad qualitative categoriesLow, Average and High
flowswere assigned based on 14 years of available data (Table 5-4) that averaged 46.63 Mm3 with a
standard deviation of 18.42 (Table 6-1, Table 5-5). "Average" was defined as any year when the tunnel
flow was within +/-1 standard deviation of the mean (28.22-65.05 Mm3), and "Low" and "High" were
flows more than 1 standard deviation below (0-28.22 Mm3) or above (>65.05 Mm3) the mean (Table 6-
2).
Table 6-1. (Table 5-5) Descriptive statistics for Yauco Power Plant 1 flow data (million cubic meters per
year; Mm3) for input tunnel and precipitation (mm) for four weather stations in the region on
corresponding years.
Average
Standard Deviation
Precipitation (mm)
1651.01
176.15
Flow (Mm3)
46.63
18.42
Table 6-2. Yauco 1 flow data (million gallons per day; MGD) is categorized into one of three groups based
on the flow for that year in comparison to statistics for all 14 years of available data.
Categories for
Flow
Low
Average
High
Range (Mm3)
<28.22
28.22-65.05
>65.05
Annual fluctuations in precipitation in Lucchetti watershed (Fig. 6-3) were assumed to be proportional to the
fluctuations in the upper watersheds, allowing categories for the two distributions (precipitation in Lucchetti
50
-------
and in upper watersheds) to be considered simultaneously (Table 6-3). Annual Precipitation for Lucchetti was
discretized into four categories based on standard deviation, the same categories were used for annual station
averages (Table 6-1, described in Chapter 5). "Below Average" and "Above Average" were defined as within 1
standard deviation below or above the mean; "Low" and "High" represent values lower than or greater than 1
standard deviation from the mean (Table 6-3). Using categories from Tables 6-2 and 6-3, rainfall and flow were
then characterized qualitatively for each of the 14 years (Table 6-4).
Table 6-3. For each year where flow data were available, precipitation values from stations neighboring
the upper watersheds were averaged. This value for each year was then categorized into one of four
groups based on the precipitation for that year in comparison to statistics for all 14 years of available
data. Each category relates to a range for the node representing rainfall in Lucchetti watershed.
Categories for
Precipitation
Low
Below Average
Above Average
High
Range (mm) Upper Watersheds
<1474.86
1474.86-1651.01
1651.01-1827.16
>1827.16
Range (mm) Lucchetti
<1518
1518-1897
1897-2276
>2276
Table 6-4. Characterization of precipitation and flow from the upper reservoirs
Year
1980
1981
1982
1986
1987
1988
1989
1990
1995
2002
2005
2009
2010
2011
Precipitation
Above Average
High
Low
Below Average
Below Average
Below Average
Above Average
Below Average
Below Average
Below Average
Above Average
Low
High
High
Flow
Average
Average
Below
Average
Average
Average
Above
Average
Average
Below
Average
Average
Average
Above
These results could be integrated into the network either as count data or frequencies. Because there are only
14 data points they were entered as individual occurrences (count data) into the Flow CPT (Table 6-5, Fig. 6-4).
Entering as count data has an advantage over entering data as frequencies because the network integrates the
occurrences with a uniform distribution by adding one additional count experience for each possible outcome.
51
-------
This supplements a limited data set such as this one. In a large dataset with many counts the impact of this is
insignificant and data can be entered by frequencies.
Table 6-5. Conditional Probability Table (CRT) for qualitative categories shown in Table 6-6 for the 14 years of
available flow data.
Node Values
0 to 1518
1518 to 1897
1897 to 2276
>=2276
Precipitation Categories
Low
Below Average
Above Average
High
Water Flow From Upper Reservoirs
Low
1
1
0
0
Average
1
5
2
2
High
0
0
1
1
Annual Precipitation (mm)
Oto1518 15.9
1518 to 1897 34.1
1897 to 2276 34.1
>=2276 15.9
| ;
i i
1810 ±560
k,
^
Water Flow From Upper Reservoirs
Low 22.3
Average 54.1
High 23.6
Figure 6-4. BBN shows the information entered into the conditional probability table as count data,
where frequencies were determined by combining the count data from Table 5-5 with count data from a
uniform distribution to calculate the final probabilities.
Total Inflow of Water
The flow from Lucchetti watershed (Fig. 6-3) and the flow from the upper reservoirs (Fig. 6-4) both contribute
to the total inflow of water into Lago Lucchetti so these were added using a simple mechanistic equation. In the
Water Flow from Upper Reservoirs node the categories (Low, Average, and High) were assigned values from
the average and standard deviation of the flow data as described previously (Table 6-2). Once these two steps
were taken, Total Inflow of Water was calculated in the BBN model (Fig. 6-5).
Table 6-6. Values assigned to each characterization of water flow from the upper reservoirs, showing
conversion from million gallons per day (MGD) to million cubic meters (Mm3).
State
Low
Average
High
Lower Bound
(MGD)
0
20.41
47.05
Upper Bound
(MGD)
20.41
47.05
Infinity
52
-------
Annual Precipitation (mm)
Oto 1518
1518 to 1897
1897 to 2276
>= 2276
15.9
34.1
34.1
15.9
1810 ±560
Water Flow From Upper Reservoirs
Low
Average
High
22.3
54.1
23.6
48.1 ±26
Flow from Lucchetti Watershed (Mm3)
Oto 15
15 to 20
20 to 25
25 to 28
28 to 32
32 to 35
35 to 40
40 to 45
45 to 50
>=50
9.14
3.01
3.08
11.1
21.1
15.8
23.2
7.37
3.32
2.92
31.4±10
Total Inflow of Water (Mm3)
Oto 20
20 to 40
40 to 60
60 to 80
80 to 100
100 to 120
120 to 140
140 to 160
160 to 180
180 to 200
>=200
1.70
8.00
15.3
26.3
24.2
10.6
5.86
3.40
1.97
1.10
1.54
83.5 ± 38
Figure 6-5. BBN depicting probabilities for Total Inflow of Water into Lucchetti Reservoir (Mm3) as a
condition of Flow from Lucchetti Watershed and Water Flow from Upper Reservoirs
Water Flow from Upper Reservoirs is an important node for this study because there are actions that can be
taken, such as closing the tunnels for maintenance that could alter the values. There are no anticipated actions
that would directly and significantly alter Water Flow from Upper Reservoirs in the way closing the tunnels
would, so for the sake of model simplicity Flow from Lucchetti Watershed was absorbed into the equation for
Total Inflow of Water (Fig.6-6).
53
-------
Annual rrecipuanon (mm)
0 to 1518 15.9
1518 to 1897 34.1
1897 to 2276 34.1
*> 9O7A \ E* Q
I i I
! i i
1810 ±560
^h
w
Water Flow From
Low
Average
High
48.1
Upper Reservoirs
22.3 ! i i
54.1 ^ i
23.6 ! I I
±26
Total Inflow of Water (Mm3)
Oto20
20 to 40
40 to 60
60 to 80
80 to 100
100 to 120
120 to 140
140 to 160
160 to 180
180 to 200
>=200
83.5
1.75
7.89
15.4
26.5
24.1
10.6
5.79
3.38
1.96
1.14
1.57
^^m
^^^^m
^^^H
^m
m
i
±38
Figure 6-6. BBN showing Total Inflow of Water after absorption (mathematical incorporation) of the
Flow from Lucchetti Watershed node. The Water Flow from Upper Reservoirs node will change with
different decision scenarios examined later.
Precipitation to sediment runoff
Watershed Sediment Input to LL (Module 2 of the conceptual diagram) is determined by precipitation and soil
erosion potential. As described in Chapter 5, the USLE erosion model was applied using a script (Appendix D)
for the R statistical package to estimate erosion in the watershed. The erosion model runs based on erosivity
density values from the RUSLE2 database (USDA, 2008) which are more versatile than aggregated rainfall
erosivity, allowing them to be used with precipitation values from different time periods (sidebar in Chapter 5).
However, the erosivity density values are on a monthly time scale whereas the Annual Precipitation (mm)
node is on an annual time scale. RUSLE2 database provides monthly precipitation values averaged over a 10
year period. Although this time period was shorter than that used for our Annual Precipitation (mm) node, the
annual averages compared favorably (Table 4-1) and were derived from the same set of precipitation stations.
Similar to that of Water Flow from Upper Reservoirs, the monthly rainfall values from the RUSLE2 database
were assumed to have a proportional uncertainty (CoV) and distribution as the Annual Precipitation (mm)
node.
Since uncertainty for the monthly rainfall values was not available, the uncertainty around annual rainfall from
the same area was applied, with the assumption that monthly and annual precipitation variability have similar,
if proportional, patterns. Since the USLE model was to be run on an annual timescale, monthly Rainfall Erosivity
distributions were combined into an annual value before multiplying by the other USLE variables. The result
was a distribution for soil loss for each grid cell of the Lucchetti watershed. The grid cell values were totaled for
each probability, resulting in a distribution for total watershed soil loss. USLE model outputs from R were
54
-------
formatted to align with the original precipitation values based on their distribution, creating a table of samples
from the distribution, i.e., 100,000 outputs with precipitation and eroded sediment (m3/y") side by side. This
table was then imported into Netica as case data.
Netica's case learning function can take lists of "cases," where two pieces of data coincide, such as precipitation
input and sediment soil loss, and create a Conditional Probability Table (CPT) that has probabilities associated
with coincidence of each piece of data. The case learning generated a continuous distribution from the output
table that was then discretized into a Conditional Probability Table (CPT) to create a new "Lucchetti Total Soil
Loss" node that has an arrow (relationship) from the node for annual precipitation (Fig. 5-7). The minor
differences between the precipitation node in Fig 6-7 and Fig 6-6 are due to sampling, where the equation
based sample of 100,000 in Netica ignored sampling error and differed slightly from the value from R. This
difference was considered negligible and would likely disappear with a greater sample size. These minor
changes in the Annual Precipitation node slightly altered values for water flows (Fig 5-6).
Annual Precipitation (mm)
0 to 151 8 15.8
151 8 to 1897 34.1
1397 to 2276 34.3
>=2276 15.8
1810±560
!
;
h.
Lucchetti Total Soil Loss yi >
OtoleG 1.19
1e6to1.25e6 4.40
1.25e6to1.35e6 3.79
1.35e6to1.45e6 5.43
1.45e6to1.55e6 7.12
1.55e6to1.6e6 4.26
1.6e6to 1.65e6 4.72
1.65e6to1.7e6 4.96
1.7e6to1.75e6 5.21
1.75e6 to 1.866 5.29
1. Se6 to 1.85e6 5.33
1.8566 to 1.966 5.55
1.9e6to 1.95e6 5.43
1.95e6to2e6 5.01
2e6to2.1e6 9.00
2.1e6to2.2e6 7.53
2.2e6to2.3e6 5.59
2.3e6to2.4e6 4.08
2.4e6to2.5e6 2.66
2.5e6to3.5e6 3.45
>=3.5e6 .007
I
1840000 ±420000
Figure 6-7. BBN depicting effects of precipitation and other USLE factors on erosion in the Lucchetti
watershed, presented as Total Soil Loss (m3/yr).
As described previously (Chapter 5) Lucchetti Total Soil Loss (M3/yr) quantifies erosion, but must be modified
by the Sediment Delivery Ratio (0.1308) to estimate how much of that soil actually reaches the Lucchetti
reservoir. Multiplying the two provides Lucchetti Sediment Yield (Average 241,000 m3/yr) for the basin (Fig. 6-
8). This represents the amount of sediment leaving the watershed in outflow (at the "pour point") instead of
the amount of sediment eroding from the landscape, some of which may be deposited within the watershed.
55
-------
Annual Precipitaiton (nun)
0 to 151 8 15.8
151 8 to 1897 34.1
1897 to 2276 34.3
>=2276 15.3
1 81 0 ± 560
|M
Mi
h.
Lucchetti Sediment Delivery = 4.4e5 .008
241 000 ±51 000
Figure 6-8. BBN depicting Sediment Delivery (m3/yr) for Lucchetti Watershed, after applying the
Sediment Delivery Ratio (SDR) to Lucchetti Total Soil Loss.
Sediment from tunnel
A sediment balance model was run for the three upper watersheds (see Chapter 4), and the results were used
to construct a root node for sediment entering Lucchetti Reservoir from the input tunnel. The sediment balance
model accounted for sediment entering each reservoir, the amount trapped in each reservoir and the amount
of sediment leaving each reservoir, either through the tunnel or over the spillway. Three scenarios were
applied to sediment leaving the upper reservoirs through the tunnel; no sediment (0%), all the sediment
(100%), and likely normal conditions estimated at 60% of the sediment transferred (Table 6-7, Table 5-16). The
calculation for Guayo includes sediment from Yahuecas that passes through into Lucchetti, with Yahuecas
tunnel transfer using the same three scenarios (0%, 60% & 100%; Table 5-15).
Table 6-7 (Table 5-16). Total effluent sediment from the upper reservoirs into Lucchetti as a result of
three possible tunnel transfer scenarios (0%, 60%, 100%). These sediment predictions are for the year
2000.
Transfer
Scenario
Lucchetti 0%
Lucchetti 60%
Lucchetti 100%
Guayo Tunnel Effluent
(m3)
0
4,204
10,180
Prieto Tunnel
Effluent (m3)
0
6,793
11,322
Total Tunnel Sediment
Effluent (m3)
0
10,997
21,502
56
-------
The three tunnel transfer scenarios were used to create a probability distribution for sediment from the upper
reservoirs. An asymmetrical triangular distribution characterized the uncertainty on the root node for Sediment
from Upper Reservoirs. The distribution's mode was 10,997 m3 (60% tunnel transfer) and it had a range from 0
(0% tunnel transfer) to 21,502m3 (100% tunnel transfer) (Fig. 6-9).
Sediment From Upper Reservoirs
0 to 2500
2500 to 5000
5000 to 7500
7500 to 10000
10000 to 12500
12500 to 15000
15000to 17500
17500 to 20000
>= 20000
10800
2.64
7.93
13.2
18.5
21.8
17.2
11.6
6.09
1.0
1
^M
^^^m
^^^M
^^H
^m
±4500
Figure 6-9. Root node for m3 sediment transported to Lucchetti Reservoir through tunnels from
Yahuecas, Guayo and Prieto Reservoirs.
Total Sediment into Lucchetti Reservoir
The total sediment can be estimated by summing sediment coming from the Lucchetti watershed and sediment
transferred through the tunnels (Fig. 6-10).
To Water Storage Capacity
The water storage capacity of Lago Lucchetti was measured three times (1952, 1986 and 2000). Any of these
three measurements could be used in model runs so all three were included in the root node Start Water
Storage Capacity (T0) (Fig. 6-11). Because the start (T0) capacities for these years are known, there is no
uncertainty (100% probability that it will be the storage capacity for 1952, 1986 or 2000) and the year to be
tested can be selected (100% probability) in the Netica node. For demonstration purposes here, the 2000 water
storage capacity was selected because other components of the model, such as sediment contribution from
upper reservoirs, were calibrated to the year 2000. Using these capacities as starting points, comparisons can
be made between the BBN model performance and actual observations of accumulated sediment. It will also
be demonstrated how projections can be made for a future year (Ti) using the BBN. When used as a new start
capacity, future year projections can provide better estimates of reservoir life expectancy. Such projections will
require the node to be adjusted to accommodate the uncertainty surrounding those projections.
57
-------
Annual Precipitation (mm)
0 to 151 8 15.8
151 8 to 1897 34-1
1897 to 2276 34.3
>=2276 158
1 81 0 ± 560
Ml
Hi
Li.nx I ictli Sediment Delivery (m3/yr)
Oto1e5 0.19
1e5to1.4e5 1.71
1.4e5to1.6e5 2.91
1.6e5to1.75e5 4.00
1.75e5to1.9e5 6.14
1.9e5to2e5 5.36
2e5to2.05e5 3.03
2.05e5to2.1e5 3.37
2.1e5to2.15e5 3.62
2.15e5to2.2e5 3.72
2.2e5to2.25e5 3.93
2.25e5to2.3e5 3.98
2.3e5to2.35e5 4.01
2.35e5to2.4e5 4.14
2.4e5to2.5e5 8.43
2.5e5to2.65e5 11.7
2.65e5to2.8e5 9.78
2.8e5to3e5 9.49
3e5to3.4e5 8.65
3.4e5to4.4e5 1.85
>= 4.4e5 .008
241 000 ±51 000
Total Sediment Delivery i rn.i yi f
0 to 1 .4e5 1 .44
1.4e5to1.8e5 5.85
1.8e5to2e5 7.51
2e5to2.1e5 5.19
2.1e5to2.2e5 6.27
2.2e5to2.3e5 7.24
2.3e5to2.35e5 3.86
2.35e5to2.4e5 3.95
2.4e5to2.45e5 4.03
2.45e5to2.5e5 4.11
2.5e5to2.55e5 4.15
2.55e5to2.6e5 4.13
2.6e5to2.65e5 4.01
2.65e5to2.7e5 3.89
2.7e5to2.8e5 7.24
2.8e5to2.95e5 9.01
2.95e5to3.1e5 6.82
3.1e5to3.3e5 4.92
3.3e5to3.7e5 4.87
3.7e5to4.85eS 1.49
>=4.85e5 .006
I
251 000 ±56000
Sediment From Upper Reservoirs
0 to 2500 2.64
2500 to 5000 7.93
5000 to 7500 13.2
75001010000 18.5
10000 to 12500 21.8
12500to15000 17.2
15000 to 17500 11.6
17500 to 20000 6.09
>= 20000 1 .0
=«
1 0800 ± 4500
Figure 6-10. BBN depicting the contributions of sediment entering Lago Lucchetti from the watershed
(upper center node) and from upper reservoirs (lower right node). Values are shown as exponents (e.g.,
Ie5=10,000).
Start Water Storage Capacity (TO) Mm3
20.35(1952)
15.84(1986)
11.88(2000)
11.88
Figure 6-11. BBN root node for Start Water Storage Capacity showing the original capacity of Lago Lucchetti at
the time of construction (1952) and two measured capacities in 1986 and 2000.
Sediment Trapped in Lucchetti Reservoir
The amount of sediment trapped in Lago Lucchetti is calculated simply as the Total Sediment Input to LL times
the trapping efficiency for any given year. Trapping Efficiency (TE) is determined by the nodes Total Inflow of
Water (Fig. 6-6) for inflow, and Start Water Storage Capacity (T0) (Fig. 6-11) for capacity; based on the equation
given in Chapter 5. Once TE is calculated the amount of sediment trapped can be determined by multiplication
of TE with Total Sediment Delivery (m3/yr) (Fig. 6-10).
58
-------
Sediment trapped = Sediment Delivered x Trapping Efficiency
The final equation used for Sediment Trapped in Lucchetti Reservoir (Fig. 6-13) is:
Sediment_Trapped(Capacity, TotaMnflow, Total_Sediment)
= (0.97A(0.19A(loglO(Capacity/Total_lnflow)))*Total_Sediment)/l,000,000
1 Upper Re
Low
Ave rag
High
22.3
54.1
23.7
Annual Precipitaiton (mm)
0 to 1518 15.8
1513 to 1897 34.1
1897 to 2276 34.3
>= 2276 15.8
1810±560
20 to 40 7.94
40 to 60 15.3
60 to SO 26.4
SO to 100 24.2
100 to 120 10.6
120 to 140 5.33
140 to 160 3-37
160 to 130 1.97
130 to 200 1.14
>= 200 1 .59
^^^m
^^^^f
^
m
I
1
1
S3 .5 ±33
*'
\
^i
Start Water Storage Capacity (TO) Mm3
Construction 1952 0 I
Survey 1986 0
Survey2000 U_g
j j
^^
\
>*
Sed iment Trapped in Lago Luce hetti (Mm^r)
to 0.02S 0.2$
. 2£toO
. StO
. TStO
. 100
. Ito
. 2tO
StO
*to
. 6td
. TtO
. Sto
. Sto 0.2
. to 0.21
. 1 to 0.2
. StO 0.2
. 4 to 0.2
. Sto 0.2
.275 toO
a !>.£>
S 0.2
0.2
0.1
0.1
0.£
1.4$
1.6
$.0
4.6
6.T
T.S
9.0
10.
10.
3.0
T.T
S 1$.
S.S
.StO 0.325 2.6
.325 to 0.35 0.6
.SStBO-STS 0.3
.STStoO.4 0.3
= 0.4 O.S
1
1
1
^H
^H
^^
^^
^^
^^
^^^^^
^m
0.222 ±0.04T
Lucchetti Sediment Delivery(m3/yr)
0 to 1 e5
1 eS to 1.4e5
1.4e5to 1.6e5
1.6e5 to 1.75e5
1.75e5to 1.965
1.9e51o2e5
2e5to2.05e5
2.05e5 to 2.1e5
2.1e5 to 2.15e5
2.15e5to2.265
2.2e5to2.25sS
2.25e5to2.3eS
2.3e5 to 2.35e5
2.35e5to2.4e5
2.465 to 2.565
2.5e5 to 2.65e5
2.S5e5to2.8e5
2.3e5to3e5
3 e5 to 3.4e5
3.465 to 4.465
!= 4.4e5
0.19
1J1
2.91
4.00
6.14
5.36
3.03
3.37
3.62
3.72
3.93
3.98
4.01
4.14
8.43
11.7
9.78
9.49
8.65
1.85
.008
241000 ±51000
Total Sediment Delivery (m3/yr)
0 to 1,4e5
1.4e5to 1.8e5
1.8e5 to 2e5
2e5to2.1e5
2.l65to2.2e5
2.2 e5 to 2.3eS
2.3e5 to 2.35e6
2.35 e5 to 2.4e5
2.4e5 to 2.45e5
2.45 65 to 2.565
2.5e5 to 2.55e5
2.55e5to2.6e5
2.6e5to2.65e5
2.6565 to 2.765
2.7 e5 to 2.8e5
2.8e5 to 2.95e5
2.95e5 to 3.1 e5
3.1 e5 to 3.3e5
3.365 to 3.7eS
3.765 to 4.8565
>= 4.85 e5
1.44
5.85
7.51
5.1Q
6.27
7.24
3.85
3.96
4.03
4.11
4.16
4.12
4.02
3.89
7.23
9.03
6.83
4.91
4.86
1.50
.006
251000 ±56000
Sediment From Upper Reservoirs
0 to 2500
2500 to 5000
5000 to 7500
7500 to 10000
10000 to 12500
12500 to 15000
15000 to 17500
17500 to 20000
»= 20000
2.64
7.93
13.2
18.5
21.8
17.2
11.6
6.09
1.0
1
^
^^m
^^^H
^^^^m !
^^^m j
^H :
1
10800 ±4500
Figure 6-12. BBN depicting annual sediment trapped in Lago Lucchetti (Mm3). Note exponential values in
Total Sediment Delivery (m3/yr). The average sediment trapped was 0.222 + 0.047 Mm3/yr.
Tl Water Storage Capacity
Using the Start Water Storage Capacity (T0) and the Sediment Trapped in Lago Lucchetti (Fig. 6-13), the End
Water Storage Capacity (Ti) was calculated using a simple mechanistic equation where the volume of the
sediment trapped for any year is subtracted from the capacity at the end of the previous year (Fig. 6-14). The
59
-------
discretization used for End Water Storage Capacity (Ti) may need to be adjusted after making observations in
other parts of the model, especially Start Water Storage Capacity (T0), because it must be sensitive enough to
indicate loss of that capacity on an annual basis (see Chapter 8).
Water Flow From Upper Reservoirs
Low
Average
High
22.3
54.1
23.7
Annual Precipitation (mm)
0101518 15.8
1518 to 1397 34.1
1897102276 34.3
>-2276 15.8
18101560
60 to 80 26
80 to 100 24
10010120 10
12010140 5.8
14010160 3.3
160 to 180 1.9
1 80 to 200 1 1
»- 200 1 .5
2 ^^
3
2 !
3 I !
3 I i
4 \
3 I i
83.5 i 38
---^
^\^
^»,
Start Water Storage Capacity (TO) Mm3
Cons
Surv
truction 1 952
ey 1 936
Survey 2000
i '
0
0
0
i
I
__
i
__
End Water Storage Capacity (T1 ) (Mm3)
Oto1
11.5
11. Si
1.5
011.55
to 11. 6
11. 6 to 11. 65
11. 65 to 11. 675
1 1 .675 to 1 1 .7
11. 7 to 11. 725
11.7;
5to11.75
11. 75 to 11. 775
11.7"
5to11 8
11. 3 to 11. 325
11. 825 to 11. 35
11. Si
11.8"
to 11. 875
51015
151017
17to
18.3
183
013.4
18.4 to 18.5
18.5
18.6
018.8
018.64
18.64 to 18.65
18.6;
18.6E
to 18.66
to 20.35
0.60
0.99
7.36
31.5
25.7
19.2
8.62
4.04
0.80
0.28
0.28
0.23
0.28
.056
0
0
0
0
0
0
0
0
0
i
i
i
|
I
I
i
11.62*0.53
/
/
/
If
Ssdirrent Trapped in Lago Lu;cr»tti(Mrrtay)
Oto 0.025 0.23
0.025 to 0.05 0.2S
0.05toO.OT5 0.28
O.OTStoO.1 0.28
0.1to0.11 0.1
0.11 to 0.12 O.t
0.12to0.13 5
0.1 toO.15 6
0.1 to 0.16 9
0 1 too 1? 0
0.1 to 0.18 6
0.18to0.19 ^
0.19to0.2 9
0.2to0.21 0
0.21 to 0.22
0.22 to 0.23
0.23 to 0.24 0
0.24to 0.25 1
0.25to0.2T5
0.3to 0.325 6
0.325 to 0.35 6
0.35to0.3T5 3
0.3T5to 0.4 0.36
>= 0.4 0.32
I
1
^1
^^m
^~
^^
^^m
^^
^^"
0.222± 0.047
Lucchetti Sediment Delivery I m :i y 11
OtaleS
1 e5 to 1.4e5
1.4e5to1.6e5
1.6eSto1.75eS
1 J5e5 to 1.9e5
1.9e5to2e5
2e5to2.05e5
2.05e5to2.1e5
2 1e5 to 2.15e5
2.15e5to2.2e5
2.2e5to2.25e5
225e5to 2.3e5
2.3e5to 2.3565
2.35e5to2.4e5
2.4e5to2.5e5
25e5to2.65e5
2.6565 to 2.8e5
2.8e5to3e5
3e5to3.4e5
3.4e5to4.4e5
>- 4.4e5
0.19
1.71
2.91
4.00
6.14
5.36
3.03
3.37
3.62
3.72
3.93
3.98
4.01
4.14
8.43
11.7
9.78
9.49
8.65
1.85
.008
241000 ±51000
Total Sediment Delivery im3fyr)
0 to 1,4e5
1,4e5 to 1 .Se5
1,8e5 to 2eS
2e5to2.1e5
2.1 e5 to 2.265
2.2e5to2.3e5
2.3e5to2.35e5
2.3565to 2.4e5
2.4e5to2.45e5
2.4565 to 2.565
2.565 to 2.5565
2.55e5to2.6e5
2.6e5to2.65e5
2.65e5to2.7e5
2.7e5to2.8eS
2.8e5to2.95e5
2.95e5to 3.165
3.165 to 3.365
3.3e5to3.7e5
3.7e5to4.85e5
>= 4.8565
1.44
5.85
7.51
5.19
6.27
7.24
3.86
3.95
4.03
4.10
4.17
4.13
4.00
3.90
7.23
9.03
6.82
4.92
4.87
1.49
.006
;, ii -.:.-
Sediment From Upper Reservoirs
0 to 2500
2500 to 5000
5000107500
75001010000
10000 to 12500
12500 to 15000
15000 to 17500
17500 to 20000
>= 20000
108C
2.64
7.93
13.2
18.5
21.8
172
11.6
6.09
1.0
^^m
^^^H i
^^^^m \
^^^m i
^^
I
i
0 ± 4500
Figure 6-14. BBN model depicting reservoir storage capacity after one year for Start Water Storage Capacity
measured in 2000.
Projecting Lucchetti Reservoir Life Expectancy
To this point, the BBN model has the ability to calculate the change in water capacity for a single year (T0 to Ti).
The next steps are to determine what storage capacity is considered 'functioning' (i.e., a level that meets
current demands) and to extend the model beyond a single year. The first issue can be addressed by simply
setting a threshold, or target, for reservoir functioning. Three thresholds will be explored in Chapter 7(0, 25%
and 50% of original capacity) but for simplicity only 0% (no remaining water storage capacity) will be presented
here (Fig. 6-15).
60
-------
Extending the model beyond a single year presents a challenge because trapping efficiency changes over time
as the reservoir capacity changes. BBNs are unable to accommodate such feedback loops directly, so Reservoir
Life Expectancy is calculated by dividing the End Water Storage Capacity (Ti) by the amount of sediment
accumulated in the modeled year. This is the same method used to calculate the reservoir life expectancy in
past studies (Soler- Lopez, 2001b). However, the model can improve this estimate by using the End Water
Storage Capacity (Ti) results from the first modeled year as input to a subsequent run of the model, continuing
annually to complete all the years of the projection up to the target life expectancy threshold. An example of
this is demonstrated and compared to Reservoir Life Expectancy in Chapter 8.
54.1
23.7
Total Inflov
0 to 20
20 to 40
40 to 60
60 to 80
80 to 100
10010 120
120 to 140
1 40 to 1 60
160 to 180
130 to 200
:=-= 200
/of Water [Mm3J
.73
.96
-5.:
6.
4.
0.
.3
.3
.9
.1
.58
i
^Ml i
^^^M
^^^H
^m
I
i
83 .5 ±38
Start Water Storage C-
Construction 1952
Survey 1986
Survey 2000
to 11.5
.5 to 11.55
.55 to 11.B
.6 to 11.65
875
.675 to
.7t
.725 to
.75 to 1
.775 to
25
.75
S.64
S.65t
3.66
7.36
31.5
25.7
19.2
S.62
4.04
0.28
.066
8.64
18.65
11.62 ±0.53
adirrerrt Trapped in Lag.:. 1 ir.- h=.ttn HrrRV I
Oto 0.025
0.025to0.05
O.OSto 0.075
0.075 to 0.1
0.1 to 0.11
0.11toQ.12
0.12to0.13
0.13to0.14
0.14to0.15
Q.I5toQ.16
0.16to0.17
O.ITtoO.18
U 1i
i0.19
0.19 to 0.2
0.2 to 0.21
0.21 to 0.22
0.22to0.23
0.23to0.24
0.24to 0.25
0.25to 0.275
0.275to0.3
0.3 to 0.325
0.325to0.35
0.35to 0.375
0.375to0.4
Re = er....:,ir Life E. pect^nc ./ I Yrs to 0|
0 to 10
10 to 25
25 to 50
50 to 75
75 to 100
>= 100
0.21
0.32
37-6
55.5
4.90
1.37
Lucchetti Sediment Delivery [m3/yr)
0 to 1 e5
1e5to 1.4e5
1.4e5to 1.6e5
1.6e5to 1.75e5
1.75e5to 1.9e5
1.9e5to2e5
2e5 to 2.05e5
2.05e5to2.1e5
2.1e5 to 2.15e5
2.15e5to2.2e5
2.2e5to2.25e5
2.25e5to2.3e5
2.3e5to2.35e5
2.35e5to2.4e5
2.4e5 to 2.5e5
2.5e5 to 2.65e5
2.65e5to2.Se5
2.Be5to3e6
3e5 to 3.4e5
3.4e5 to 4.4e5
>= 4.4e5
241000 ±51000
Total Sediment Delivery (m3/yr)
Oto 1.4e5
1.4e5to 1.8e5
1.Se5 to 2e5
2e5to2.1e5
2.1e5 to 2.2e6
2.2e5to2.3e6
2.3e5to2.35e5
2.35eSto2.4e5
2.4e5to2.45e5
2.45e5to2.5e5
2.5e5to2.55e5
2.55e5to2.6e5
2.6e5to2.65e5
2.65 e5 to2.7e5
2.7e5to2.8e6
2.8e5to2.95e5
2.95eSto3.1eS
3.1e5to3.3e5
3.3e5to3.7e5
3.7e5to4.85e5
>= 4.35e5
1.44
5.85
7.51
5.19
6.27
7.24
3.86
3.95
4.03
4.11
4.16
4.13
4.01
3.90
7.23
9.02
6.82
4.92
4.87
1.49
.006
1
^^M
^^^H
^^
^^B
^^^m
^m
^i
^m
^M
^H
^H
^m
^m
^^^m
^^^^
^^M
^^
^^
251000 ±56000
Sediment Fro
0 to 2500
2500 to 5000
5000 to 7600
7500 to 10000
10000 to 12500
12500 to 15000
15000to 17500
17500 to 20000
>= 20000
10£
m Upper Res
2.6
7.9
13.
13.
21.
17.
11.
60
1.
00 ± 4500
^ j
^^m
^^^m i
^^^^m :
^^^ i
^^ !
^ i
Figure 6-15. BBN Depicting the Lucchetti Reservoir Life Expectancy with Start Water Storage Capacity
value from the survey performed in 2000 (11.88) and the threshold for Lucchetti Reservoir Life
Expectancy (Yrs to 0%) as completely filled.
61
-------
7. Management Options and Model Runs
Management Options
Two management options have been proposed to address sediment accumulation in Lago Lucchetticonvert
from sun-grown to shade grown coffee farming practices in the watershed and dredge accumulated sediment
from the reservoir (CWP, 2008). These options emerged from analysis of watershed issues, but lacked
quantitative projections of their potential to resolve the sedimentation problem. The BBN developed here
provides a tool for estimating the relative effectiveness of these options. This requires that the new
management options are added to the existing network. Consequently, two nodes were incorporated in the
conceptual diagram at positions where the actions would reflect the impact (Fig. 7-1).
To evaluate options requires a criterion, or target, to compare against. The objective of the proposed
management options is to extend the time that the reservoir serves its useful purposes, so any increase in
reservoir life expectancy represents a positive effect. For development of the model, zero water storage
capacity (i.e., reservoir completely filled with sediment) was used as a nominal target for water capacity; but
different values could be selected from zero to 20.35 Mm3, the volume of the reservoir at its construction. The
most useful evaluation would set the target capacity to reflect known or future needs. Future water demand
from PRASA is expected to increase in the southwestern region of Puerto Rico by approximately 0.9 MGD each
year (DNER, 2008). However, future uses of reservoir water are speculative (Ortiz-Zayas et al., 2001), and the
required reservoir storage capacity to maintain water supplies is dependent on weather conditions (Larsen,
2000), so the model was run using a range of target capacities (50%, 25% and 0%).
Wateished
Water Inflow to
Water
Inflow from
Tunnel
T0 Water
Storage
Capacity
Precipitation in
LL Watershed
Water Storage
Capacity
LL Life
Expectancy
Figure 7-1. Conceptual diagram with added nodes for the management options Coffee Conversion and
Dredge Reservoir.
62
-------
Conversion to shade-grown coffee
Conversion of coffee farms from sun-grown to shade-grown cultivation reduces sediment erosion on the
converted land. Coffee conversion affects land use, which is one of the factors used to determine Lucchetti
Total Soil Loss (m3/yr). The land use C factor value assigned to the coffee areas was set to vary dependent on
the land use scenario in the coffee conversion node. The USLE model in R was then re-run for each scenario. As
detailed in chapters 4 and 5, the USLE model was executed external to the BBN in the R statistical package;
however once calculated, the results were incorporated into Lucchetti Sediment Delivery (Fig. 6-15) using
Netica case learning.
Calculating the effect of the land use change for each scenario required that coffee farm areas were included in
the land use map. The 2001 NLCD maps (Homer et al., 2007; Table 5-6) used in USLE for the BBN model in
Chapter 6 did not identify coffee farms as a land use type, so additional data were needed. It was also critical
that this additional data identify the location of the farms, since erosion is influenced by rainfall and slope. A
dataset assembled by The Nature Conservancy (TNC) was used that identified the location of coffee farms by
thermal recognition (TNC, 2006). The dataset did not differentiate between sun-grown and shade-grown
coffee, but farm areas identified by high thermal reflectance are more likely to be in sun-grown cultivation and
available for conversion. A USDA Agricultural Survey in 2002 (USDA, 2004) did differentiate between sun-grown
and shade grown coffee farms, but did not identify locations, instead aggregating farm areas up to the
municipality scale. According to the USDA Agricultural Survey (USDA, 2004) Yauco municipio, which contains
the Lucchetti watershed (Fig. 7-2), had 14.96 km2 under coffee cultivation (4.48 km2 shade-grown, 10.48 km2
sun-grown). The two datasets were compared to estimate the sun-grown coffee farms in the spatial dataset
(TNC, 2006). When the spatial dataset was clipped to the boundaries of Yauco municipio (Fig. 7-2) it had a
coffee coverage of 11.57 km2. This value is closer to the sun-grown coffee area surveyed by USDA (2004) so it
was assumed for our model that all coffee areas in the spatial dataset (TNC, 2006) were for sun-grown coffee.
In the model, the new sun coffee areas replaced the previous NLCD 2001 landuse values for their location,
whereas non-coffee areas or pre-existing shade-grown coffee areas remained unchanged from the original
NLCD 2001 landuse value (Fig. 7-3).
63
-------
Figure 7-2. Left: Map showing the Lucchetti Watershed (light yellow with red outline) within the Yauco municipio (tan).
Right: Map showing coffee areas within Yauco municipio identified by the coffee landuse dataset (TNC, 2006).
64
-------
Lucchetti Reservoir Watershed - NLCD 2001 & Sun Coffee
Kilometers
Figure 7-3. Map showing where sun coffee landuse replaced NLCD 2001 values for an estimated 0.129
landuse C factor in the USLE equation. C Factor values for other NLCD landuse types can be found in
Table 7-1.
With the sun-grown coffee locations assigned, coffee areas still needed to be given land use values (C) to
calculate erosion using USLE. The C values for other types of land use in the NLCD dataset (Table 7-1), as well as
estimates for coffee in other regions of the world, were used to estimate a land use value for coffee in the
Lucchetti watershed. C values as high as 0.394 have been used for coffee in other regions (Angina et al., 2003),
but a value of C= 0.129 was chosen because it is closer to the value for crop/natural vegetation (0.120) than for
full cropland (Gebelein, 2000). This seemed appropriate because it fell between 0.220 (bare earth) and 0.089
(banana trees; Angina et al., 2003). The consideration of banana trees was important since even sun-grown
coffee farms many times grow banana trees alongside the coffee bushes (Borkhataria et al., 2012). When
coffee areas were converted, shade-grown coffee was C= 0.048, a value resembling shrubland (C=0.050). This
value was chosen for shade coffee based on an upper bound of C=0.089 (bananas), and a lower bound of
C=0.015 (natural forest). All other areas, including non-coffee areas and coffee areas originally under shade-
65
-------
grown cultivation, retained the original NLCD land use value. All areas, coffee and non-coffee, also retained the
same slope and soil type (Kf) factors.
Table-7-1. C-value assignments for various land use classifications
NLCD Classification
Barren
Developed
Agriculture
Grassland
Wetlands
Shrubland
Forest
Open Water
C value (Summit to Sea
Geocover)
0.220
0.210
0.200
0.125
0.080
0.050
0.015
0.005
Three options were examined for the coffee conversion alternative: 1) Status Quo means that all the sun-grown
coffee areas retained the 0.129C-value; 2) Partial Implementation means that half of the sun-grown coffee
areas were changed to shade-grown. Since there is uncertainty about the location of converted farms, erosion
values were calculated using the average rainfall erosivity, slope and soil type for all coffee areas. This is not a
concern for status quo or full implementation since both those scenarios use one C-value for all coffee areas; 3)
Full Implementation means all the sun-grown areas become shade-grown areas, so C-values for the converted
sun-grown areas were replaced with those for shade-grown coffee (0.048).
The watershed average C-value for coffee conversion alternatives (Table 7-2) was used while all other variables
were unchanged (compare to Table 5-7). The R statistical package script was re-run with the new C-values for
the coffee conversion alternatives and those results imported into Netica using case learning. For the BBN,
importing the three coffee alternatives required that a third column identifying the alternative was added to
the input file to populate the Conditional Probability Table (CPT).
Table 7-2. Land use C-values used in the calculation of erosivity for Lucchetti watershed for analysis of
alternative coffee conversion scenarios. STD = Standard deviation.
USLE Variable
C-NLCD (from Table 5-7)
C-Status Quo
C-Partial Implementation
C- Full Implementation
Watershed Average Value
0.04899
0.05381
0.04991
0.04600
Min
0.005
0.005
0.005
0.005
Max
0.22
0.22
0.22
0.22
STD (Spatial)
0.051466
0.053487
0.050741
0.047514
The new information was imported several ways to seethe influence of the altered C-value. Separating coffee
areas from non-coffee areas (Fig. 7-4) demonstrated that only 1/3 (66,700/268,000) of sediment coming into
the Lucchetti Reservoir originates on coffee farms. This result can be combined with sediment delivery from all
areas of the Lucchetti watershed (Fig. 7-5) similar to that shown in Fig. 6-10.
66
-------
Annual Precipitation (mm)
0 to 151 8 15.7
1518101897 34.2
1897102276 34.2
>=2276 15.9
1810 ±560
Lucchetti Sediment Delivery (m3.yr)
0 to 60000
60000 to 1.2e5
1.2e5to1.4e5
1.4e5to1.5e5
1.5e5to1.6e5
1.6e5to1.7e5
1.7e5to1.8e5
1.8e5to1.9e5
1.9e5to2e5
2e5to2.1e5
2.1e5to2.2e5
2.2e5to2.3e5
2.3e5to2.4e5
2.4e5to2.5e5
2.5e5to2.6e5
2.6e5to2.7e5
2.7e5to2.8e5
2.8e5to3.4e5
3.4e5to4e5
4e5to4.85e5
>=4.85e5
.025
2.24
4.39
3.86
5.26
6.B4
8.35
9.34
9.79
10.0
9.32
8.05
6.79
5.18
3.92
2.65
1.74
2.22
.035
.004
.004
200000 ±42000
Lucchetti Coffee Sediment Delivery (m3iyr)
Oto 6000
600010 30000
300001035000
350001040000
400001045000
450001050000
500001055000
550001060000
600001065000
650001070000
700001075000
75000 toBOOOO
800001085000
B5000to 90000
90000 to 1e5
1e5to1.2e5
»=1.2e5
.004
0.29
0.63
1.38
2.94
5.25
8.61
11.e
14.3
15.1
13.3
10.8
7.20
4.47
3.37
0.62
.006
66700 + 14000
Conversion Implementation
Status Quo
Partial Implementation
Full Implementation
Total Sediment Delivery (m3.yr)
Oto1.4e5
1.4e5to1.8e5
1.Be5to2e5
2e5to2.1e5
2.1e5to2.2e5
2.2e5to2.3e5
2.3e5to2.35e5
2.35e5to2.4e5
2.4e5to2.45e5
2.45e5to2.5e5
2.5e5to2.55e5
2.55e5to2.6e5
2.6e5to2.65e5
2.65e5to2.7e5
2.7e5to2.Be5
2.8e5to2.95e5
2.95e5to3.1e5
3.1e5to3.3e5
3.3e5to3.7e5
3.7e5to4.85e5
>=4.85e5
1.30
4.13
6.66
3.16
1.59
5.68
3.94
4.25
4.51
4.68
4.50
3.50
1.71
1.16
6.76
13.8
10.6
4.55
11.1
2.46
.009
267000 ±60000
Figure 7-4. BBN showing how Lucchetti Sediment Delivery (m3/yr) from figure 5-15 was divided into non-coffee
areas (Lucchetti Sediment Delivery (m3/yr)), and coffee areas (Lucchetti Coffee Sediment Delivery (m3/yr)).
Having the sediment delivery divided this way allowed for coffee areas to be influenced independently from non-
coffee areas by the decision scenarios for conversion to shade grown (Conversion Implementation).
67
-------
Annual Precipitation (mm)
0 to 1 51 8
1 51 3 to 1 897
1 897 to 2276
>= 2276
15.7 I |
34.2 M j j
34.2 I j
15.9 M
1 31 0 ± 560
1
Total Sediment
0 to 1 .4e5
1 .4e5 to 1 .8e5
1.8e5to2e5
2e5to2.1e5
2.1e5to2.2e5
2.2e5to2.3eS
2.3e5to2.35e5
2.35e5to2.4e5
2.4e5to2.45e5
2.45e5to2.5e5
2.5e5to2.55e5
2.5Se5to2.6e5
2.6e5to2.65e5
2.65e5to2.7e5
2.7e5to2.8e5
2.8e5to2.95e5
2.9Se5to3.1e5
3.1e5to 3.3e5
3.3e5to3.7e5
3.7e5to4.85e5
>= 4.85e5
278000
r
Delivery (m3jyr)
0.88
2.39
4.81
3.64
3.11
2.23
2.06
3.06
3.74
4.18
4.41
4.54
4.28
3.45
4.14
10.6
13.0
9.53
11.9
4.06
.015
I
± 60000
/
Conversion Implementation
Status Quo 0 b^^b
Partial Implementation 0 ! !
Full Implementation 0 | I
/
/
Sediment From Upper Reservoirs
0 to 2500 2.64 I
2500 to 5000 7.93 M
5000 to 7500 13.2 ^H
7500 to 10000 13.5 ^^m
10000 to 12500 21.3 ^^^
12500 to 15000 17.2 ^^
15000 to 17500 11.6 ^m
17500 to 20000 6.09
>= 20000 1 .0
1 0800 ± 4500
Figure 7-5. Integration of the coffee conversion decision node with other watershed sediment sources in
the BBN. This portion of the BBN can now be integrated with the rest of the previous BBN (Fig. 6-15)
based on Total Sediment Delivery (m3/yr).
Dredging the reservoir
Water storage capacity increases if sediment is dredged from the reservoir. This potential management action
is linked to the pre-existing Water Storage Capacity (TO) decision node of the BBN model (Fig. 7-6). Dredging
options were set at 100% removal, 50% removal and no removal of accumulated sediment. If the reservoir is
not dredged (0%), water storage capacity would be at the last measured capacity taken by the bathymetric
survey in 2000 (Soler-Lopez, 2001a), or some more current value projected from the measured capacity. If the
reservoir is dredged completely (100%), water storage capacity would attain its maximum 20.35 Mm3. This
capacity is already in the node as the construction capacity in 1952. To determine the storage capacity if half
the accumulated sediment is dredged, the total accumulation 8.47 Mm3 (years 1952-2000; 20.35Mm3-
ll.SSMm3) is divided in half (4.235 Mm3) and either added to the capacity from 2000 or subtracted from the
original construction capacity. Since the capacity at construction in 1952 and from the survey in 2000 are
already states in the Start Water Storage Capacity, only Dredging 50% had to be added as a state. If dredging
were being modeled to take place in a later year (after 2000), the same method of determining sediment
68
-------
removed could be followed based on the projected capacity in that future year and the original construction
capacity.
Start Water Storage Capacity (TO) Mm3
Construction 1952
Dredge 50
Survey 2000
Figure 7-6. BBN decision node for Start Water Storage Capacity (TO) Mm3, including Dredge 100%
(Construction 1952), Dredge 50%, and not dredging (Survey 2000).
Model runs
With the integration of the coffee Conversion Implementation decision node (Fig. 7-5) and the simple changes
to the Start Water Storage Capacity (T0) Mm3 (Fig. 7-6), the BBN model from Fig. 6-15 can be updated to
include the management options (Fig. 7-7). To change the Reservoir Life Expectancy threshold for 0%, 25% and
50% target capacities (see above), the equation must be updated.
69
-------
Water Flow From Upper Reservoirs
Low
Average
High
i
22.2
54 .1
23.6
! i i
r
Total Inflow of Water (Mm3)
Oto20
20 to 40
40 to SO
60 to 80
80 to 100
100 to 120
120 to 140
14010160
160 to 180
180 to 200
»=200
1 70
7.94
15.3
2tiA
24.2
10.6
5R1
3/lfl
1 B7
1.14
1.58
i
1
83.6 ± 38
x
Annual Precipitation (mm)
Oto1518 15.7
151 8 to 1897 34.2
1897 to 2276 34.2
1 81 0 + 560
X
i i i
^P I I
^H i
\
*r*
~~~
~-~-~,
"*
Sediment Trapped in Lago Lucchetd (Mm3
0100025 017
0.026 to 0.05 0.17
O.OS to 0.075 0.17
0.075 to 0.1 0.17
0.1 to 0.11 .070
0.11 to 0.12
\m
0.12100.13 0.25
0.13 to 0.14 0.53
0.14to 0.15 0.69
rii^tnnifi n R<*
Conversion Implementation
oiatu* Quo
Partial Implementation
Full Implementation
Start Water Storage Capacity (TO) Mm3
Construction 1 952
Survey 1 986
Survey 2000
Dredge 2000
1
0
0
0
0
\ \ I
I i i
[ ! !
r
End Water Storage Capacity (T1) (Mm3)
Oto11.4
11. 4 to 11. 5
11.5to11.6
11. 6 to 11. 65
11.65 1011.7
11. 7 to 11. 75
11. 75 to 11. 8
11. 8 to 11. 85
11.85 1011.9
11.91018.2
18.2 to 18.3
18.3 to 18.4
18.4 to 18.45
18.45 to 18.5
18.5 to 18.55
18.55 to 18.6
18.6 to 18.65
18.65 1018.7
18.71019.9
19.9 to 20
20 to 20.1
20.1 to 20 .15
20.151020.2
20 .2 to 20 .25
20 .25 to 20 .3
20 .3 to 20 .35
20 .35 to 20 .4
11.63
.036
1.61
20.0
41.2
29.4
6.59
0.55
0.34
0.21
0
0
0
0
0
0
0
0
D
0
0
0
0
0
0
0
0
0
|
tO.14
li
0.16100.17 1.72
0.17 to 0.18 2.70
0.18100.19 3.32
0.19 to 0.2 3.80
0.2 to 0.21 4.99
0.21 to 0.22 7.70
0.22 to 0.23 9.60
0.23 to 0.24 3.65
0.24to 0.25 8.48
0.25 to 0.275 20.5
0.275 to 0.3 12.9
0.3 to 0.325 6.72
0.325 to 0.35 1.78
0.35 to 0.375 1.02
0.375 to 0.4 0.97
>=0.4 0.87
0.246 ± 0.051
i
Reservoir Life Expectancy (Yrs to 0)
<0 0
OtolO .013
10to25 0.10
50 to 75 36.6
75 to 100 2.12
»=100 0.83
i i
| |
I |
48.3 + 16
Total Sediment Delivery = 4.85e5
0.88
2.39
4.81
3.64
3.11
2.23
2.06
3.06
3.74
4.18
4.41
4.54
4.28
3.45
4.14
10.6
13.0
9.53
11.9
4.06
.015
278000 ± 60000
Sediment From Upper Reservoirs
0 to 2500
2500 to 5000
5000 to 7500
75001010000
10000 to 12500
125001015000
15000 to 17500
175001020000
»= 20000
10800
2.64
7.93
13.2
18.5
21.8
17.2
11.6
6.09
1.0
I
^
^_
^^^m
^^^M
^^M
^H
±4500
Figure 7-7. BBN from Fig. 6-15, updated with new coffee land use and decisions nodes for coffee
Conversion Implementation and dredging (Start Water Storage Capacity).
For both decision scenarios, the BBN model was run for three water capacity targets, 50% (10.17 Mm3), 25%
(5.09 Mm3) and 0% (no water storage capacity remaining). For coffee conversion, three implementation
scenarios were tested-Status Quo, Partial Implementation and Full Implementation. Three dredging scenarios
were also tested, no dredging, dredging 50% of accumulated sediment, or dredging 100% of the original
volume (Table 7-3).
70
-------
Table 7-3. Life expectancy (years) of Lago Lucchetti under different target water storage volumes (as a percentage
of the original 20.35 Mm3 volume) and with implementation of proposed management actions, conversion of
sun-grown to shade-grown coffee cultivation and dredging the reservoir.
Original Water Capacity Remaining
Coffee conversion
No conversion
Partial Implementation
Full Implementation
Dredging
No dredging
50% of sediment
100% of sediment
Combined
Partial Implementation/50% dredge
Partial Implementation/100% dredge
Full Implementation/50% dredge
Full Implementation/100% dredge
Lago Lucchetti Life Expectancy
Target 50%
5. 57 ±5. 8
5. 89 ±6.7
6.57 ±8.2
5. 57 ±5. 8
37.3 ±11
40.7 ±13
38.6 ±12
42.1 ±14
40.4 ±14
44.4 ± 16
Target 25%
31 ±13
33.4 ±13
35. 8 ±14
31 ±13
54.4 ±17
61.9 ±17
58.1 ±17
64.9 ±17
62 ±18
68.9 ±18
Target 0%
48.3 ± 16
51.7 ±17
56.1 ±18
48.3 ± 16
74.8 ± 18
80.5 ± 19
78.7 ± 19
84.6 ± 18
83.1 ±19
88.9 ± 18
Note: Lago Lucchetti Life Expectancy is measured from 2000, meaning the worst-case scenario, 5.57 years, would
have been May 2005 ± 5.8.
8. Network Evaluation and Sensitivity Analysis
Various aspects of the BBN model can be examined to evaluate the Bayesian Belief Network (BBN), both in
terms of how well it performs compared to measured data and in terms of what information it provides for
decision making. Sensitivity analysis of the network shows how much the value of different nodes in the
network influence the value of a node of interest, in our case Lucchetti Reservoir Life Expectancy. The results
of sensitivity analysis can provide insight to what factors to target with management actions and where more
or more accurate information might be most beneficial.
The model runs performed (Fig. 7-7, Table 7-3) already provided several insights. When the model is run
starting in the year 2000 and assuming no management actions have been taken, it is likely that the Lucchetti
Reservoir would already have dropped below the 50% target (May 2005 ± 5 years). The reservoir would even
be close to dropping below the 25% target (2031 ± 13 years, or 2018-2044). Based on these estimates, there is
still time remaining in 2014 before the reservoir fills completely (0% target; 2048 J^16 years) which we know to
be true. Coffee conversion diminishes the rate of sediment entering the reservoir, meaning the benefits to
Lucchetti Life Expectancy are small but incremental over successive years. This results in minimal benefits (1
year of life gained with full implementation) when short term goals such as the 50% target are considered. But
benefits increase as the horizon to the 0% target increases (7.8 years gained). It is worth noting that coffee
farms only accounted for 4.35 km2 (1/10) of the watershed, yet are the source of 1/3 (66,700/268,000) of the
watersheds total sediment (Fig. 7-4).
Overall, the total life expectancy of the reservoir is extended more significantly by dredging than by coffee
conversion. Dredging the reservoir increases the capacity immediately and significantly, but does not provide
71
-------
any reduction in future sedimentation. Increasing reservoir capacity will concurrently raise the rate of
sedimentation by increasing reservoir trapping efficiency.
Projecting Annual Rates of Sediment Accumulation
Sediment trapping efficiency and therefore the rate of sedimentation in the reservoir has been shown to
change from year to year. Since Lago Lucchetti Reservoir Life Expectancy is based on estimates of sediment
trapping from the BBN model run for 2000 (Fig. 7-7, Table 7-3) it is important to know how much sediment
trapping changes as water storage capacity decreases to determine if it is a significant source of error for
forecasting present (2014) and future storage capacity. The amount of sediment trapped for different water
storage capacities can be calculated using the BBN. Different values for Start Water Storage Capacity (To) were
entered at 0.25 Mm3 increments and the changes in water storage capacity were estimated based on the
Sediment Trapped in Lago Lucchetti (Mm Yyr) (Fig. 8-1). As the starting water storage capacity decreases
(moving right to left in Fig. 8-1) the amount of sediment trapped declines, particularly as the storage capacity
nears zero.
09^ -
"E
m** H 7
2
n n 1 *;
S U.13
Q.
a.
^ n 1
I U.I
4-*
at
E n ric
a
Jf
(
Sensitivity to Water Capacity
^^
X^"
/
^
i i i i i
) 5 10 15 20 25
Start Water Capacity (T0) Mm3
Figure 8-1. Change in sediment trapping as reservoir Start Water Storage Capacity declines.
One way to eliminate this source of error from Reservoir Life Expectancy is to re-calculate sediment trapped
after each year the model is run. To do this, the End Water Storage Capacity (Mm3) from 2001 is used in place
of the Start Water Storage Capacity (Mm3) when the BBN model is run for 2002 (Fig. 8-2). To get a better sense
of how far into the future such error will become a concern in Lucchetti, a future projection of change in water
storage capacity was generated for the years 2000-2015 (Table 8-1). As the amount of sediment that is trapped
declines the life expectancy for that year becomes greater (note in Table 8-1 the change from 2048 to 2049 life
expectancy in the year 2011). However, at this stage of the reservoir's life the error is very low (only 1 year over
72
-------
15 years of calculations). This can also be shown using the relation between water capacity and sediment
trapped (Fig. 8-1); where it appears the decline in sediment trapped doesn't accelerate until the capacity is
below at least 5 Mm3, <25% of the reservoirs original capacity. These observations indicate that the method,
based on 2000 data used in Fig. 1-1, is adequate for Reservoir Life Expectancy projections in the short term (15
years) and for a target Reservoir Life Expectancy that is greater than 25% of original capacity, but that the
more involved BBN method (Fig. 8-2 and Table 8-1) will yield more accurate results when the reservoir is less
than 25% of its original capacity.
Conversion Implementation (2000)
Status Quo
Partial Implementation
Fun Imptementation
^B
Start Water Storage Capacity (2000) Mm3
Survey 2000
Dredge 50
Dredge 100
"
End Water Storage Capacity (2001) (Mm3)
11 to 11. 05
11.05 to 11.1
11.1 to 11. 15
11.15to 11.2
11.2 to 11.25
11.251011.3
11.3 to 11.35
11. 35 to 11. 4
11.4 to 11.45
11.45 to 11.5
11. 5 to 11. 55
11.55 to 11.6
11.6 to 11.65
11.65 to 11.7
11.7to 11. 75
11.75 to 11.8
11.8 to 11.85
11. 85 to 11.9
11.9 to 11.95
11.951012
12 to 20.35
11.634
0
0
0
0
0*
0 +
.004
.031
0.23
1.38
2.64
17.4
41.3
29.4
6.60
0.55
0.34
0.21
0
0
0
^H
^H
1
± 0.055
r
^-».
^~+
/
Sediment Trapped in Lago Lucchetli (Mm3...
0» 0.025
: ::E ;: : :=
0.0500.075
0.075 10 0.1
0.1 1> 0.11
0.11 00.12
:;::;:
0.1300.14
0.1400.15
0.1500.16
0.16C0.17
0.17 O 0.18
0.180019
0.19002
0,2o0.2t
0.2100.22
0.2200.23
02300.24
0.2400.25
02500.275
0.27500.3
0.3 B 0.325
0.32500.35
0.3500.375
0.37500.4
>«0.4
0.246:
0.17
0.17
0.17
0.17
.070
.089
0.25
0.59
0.69
0.89
1.72
2.71
3.31
3.80
4.99
7.71
9.60
9.65
8.49
20.5
12.9
671
1.78
102
0.97
0.87
1
^^M
1
0051
Reservoir Life Expectancy (Yrs to 0)
<0
Oto 10
101025
25 to 50
50 to 75
7510100
>=100
48.3
0
0
.064
60.4
366
2.11
0.83
|
J-
±16
End Water Storage Capacity (2001) (Mm3)
Oto 11
11 to 11 05
11.051011.1
11.1to11.15
11.1510 11.2
112101155
11251011.3
11. 310 11.35
11.351011.4
11.4 to 11.45
11.451011.5
11. 5 to 11.55
11.551011.6
11.6 to 11.65
11.6510 11.7
11.710 11.75
11751011.8
11. 8 to 11.85
11.851011.9
11.9 to 11.95
11.951012
12102035
11 634
1
0
0
0
0
0
»«
0-
.004
031
0.23
1.38
2.64
17.4
41.3
29.4
6.60
0.55
0.34
0.21
0
D
0
j
!
I
= 0.055
i
End Water Storage Capacity (2002) ir.lmS i
-0.60157410 11
11 to 11 05
11.051011.1
11. 11011.15
11.151011.2
11.2 to 11.25
11.251011.3
11. 3 1011.35
11.3510 11.4
1 1 .4 to 1 1 .45
11. 45 ID 11. 5
11. 5 to 11.55
11.551011.6
11.6 to 11.65
11.6510117
11.7to 11.75
11751011.8
11.8 to 11.85
11 85 to 11 9
11. 9to11.95
11.951012
12102035
11 389
.003
012
.055
0.22
0.87
2.53
7.00
17.4
27.7
25.3
13.2
4.14
1.09
0.42
0.15
.028
.004
001
0»
0
0
0
i
0086
Conversion Implementation (2001)
Status Quo
Partial Impiementation
Full Implementation
I
Lj^^^^
I i ; ;
MM
Sediment Trapped in Lago Lucchetli (Mmltyr)
0025 BO 05
0.05 to 0.075
0 075 B 0.1
01B0.11
0.11B0.12
0.12B013
0.13 B 0.14
0.14 B 0.15
015 BO 16
0 16 B 0.17
0.17 B 0.18
: ItkO ;
019B0.2
0.200.21
0.21 BO 22
: i: :-. : 21
0.23 BO 24
0.24 B 0.25
0 25 B 0.275
0.275 BO. 3
0.3 B 0.325
0.325 B 0.35
0.35 B 0.375
: :" :o j i
>«04
0245
1
0.17
0.17
0.17
070
091
0.26
059
0.70
0.90
V75 1
273 1
332 1
3.92 1
511
~ EC'
966 ^
9.64 _
8.5* ^m
205 ^^^^
127 _ i
6 53
1 72 I
102
0.97
083 i
tO.05
1
Reservoir Life Expectancy (Yrs to 0)
<0
> Oto 10
101025
251050
50 to 75
7510100
>»100
47.3
0» 1 i i
0»
0.12
641 . !
33.1
1.87
0.81 j | i
±16
Figure 8-2. Example showing how BBN model run for 2000-2001 (left) can be used to seed a BBN model run for
2001-2002 (right) based on the End Water Storage Capacity Ti for 2000-2001 replacing the Start Water Storage
Capacity (To). The reservoir life expectancy decreases by 1 year, the time that has passed from Ti (2001) to Tz
(2002).
Table 8-1. Projection for 2015 updating Sediment Trapped and Start Water Storage Capacity annually.
73
-------
Year
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
Start Water
Storage
Capacity (T0)
Mm3
11.88
11.634
11.389
11.14
10.9
10.65
10.41
10.16
9.89
9.64
9.4
9.16
8.92
8.68
8.44
8.2
Sediment
Trapped
(Mm3/yr)
0.246
0.245
0.245
0.245
0.244
0.244
0.243
0.242
0.242
0.241
0.24
0.24
0.239
0.238
0.237
End Water
Storage
Capacity (Ti)
Mm3
11.634
11.389
11.14
10.9
10.65
10.41
10.16
9.89
9.64
9.4
9.16
8.92
8.68
8.44
8.2
Year Lago
Lucchetti Will
be Filled
Completely
2048
2048
2048
2048
2048
2048
2048
2048
2048
2048
2048
2049
2049
2049
2049
Effect of Sediment Transfer from Upper Reservoirs
Another concern when constructing the BBN model was the lack of consistent data, and therefore assumptions
about the amount of sediment input to Lago Lucchetti through the tunnel from upper watersheds. In the
model, three different transfer scenarios0 %, 60% and 100%-were entered into a root node with an
asymmetrical triangular distribution across the range (Table 5-16, Fig. 6-9). The potential effect of sediment
transfer can be demonstrated by selecting a low rate of sediment transfer (Fig. 8-3) and a high rate of sediment
transfer (Fig. 8-4). The difference in life expectancy (50.8 years (2051.8) for 0% and 45.4 years (2046.4) for
100% sediment transfer rate) represents the greatest possible impact sediment from upper watersheds on
Lucchetti Reservoir Life Expectancy (Table 8-2). Compared to sediment coming from the watershed (Fig. 7-3,
267,000) sediment from the upper reservoirs is at most <9% of the total sediment going into the reservoir (Fig.
8-4; [291,000-267,000]/291,000).
74
-------
Water Flow From Upper Reservoirs
Low
Average
High
22.2
54.1
23.6
Annual Precipitation (mm)
0101518 1S.7
1518 to 1897 34.2
1897 to 2276 34.2
»=2276 15.9
1810±560
Total Inflow of Water (Mm3)
Oto20
20 to 40
40 to 60
60 to 80
80 to 100
100 to 120
120 to 140
140 to 160
160 to 180
180 to 200
>=200
1.70
7.94
15.3
26.4
24.2
10.6
5.81
3.39
1.97
1.14
1.58
Sediment Trapped in Lago Lutt
0to 0.025
0.025 to 0.05
0.05 to 0.075
0.075 to 0.1
0.1 to 0.11
0.11 to 0.12
0.12 to 0.13
0.13 to 0.14
>0.14to0.15
0.15 to 0.16
0.24
0.24
0.24
0.24
.099
0.13
0.40
0.96
1.11
1.35
Conversion Implementation
status Quo
Partial Implementation
Full Implementation
Start Water Storage Capacity (TO) Mm3
Construction 1 952
Survey 1 986
Survey 2000
Dredge 2000
1
0
0
0
0
! !
f
End Water Storage Capacity (T1) (Mm3)
Oto11.4
11. 4 to 11. 5
11.5to11.6
11. 61011.65
11.65 to11.7
11.7to11.75
11.75 1011.8
11.8to11.85
11.85 to11.9
11.9to18.2
18.21018.3
18.3 to 18.4
18.4to18.45
18.45 to 18.5
18.5 to 18.55
18.55 to18.6
18.6 to 18.65
18.65 to 18.7
18.7to19.9
19.9 to 20
20 to 20.1
20.1 to 20 .15
20 .15 to 20 .2
20 .2 to 20 .25
20 .25 to 20 .3
20 .3 to 20 .35
20 .35 to 20 .4
11.64
.023
1.01
15.6
37.8
34.8
9.10
0.82
0.49
0.29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
I
I
p
I
I
I
I
I
I
i
i
I
I
I
i
I
I
!
|
tO.12
/
0.16 to 0.17 2.34
0.17 to 0.18 3.35
0.18 to 0.19 3.58
0.19 to 0.2 4.60
0.2 to 0.21 7.21
0.21 to 0.22 3.46
0.22 to 0.23 9.99
0.23 to 0.24 8.31
0.24 to 0.25 8.28
0.25 to 0.275 19.4
0.275 to 0.3 9.14
0.3 to 0.325 6.18
0.325 to 0.35 1.40
0.35 to 0.375 0.64
0.375 to 0.4 0.61
>=0.4 0.55
I
0.237 ± 0.051
{
Reservoir Life Expectancy (Yrs to 0)
eO 0
OtolO .008
10 to 25 .064
50 to 75 43.1
75 to 100 3.35
»=100 1.17
it
50.8 ±17
Total Sediment Delivery (m'J.yi I
Oto1.4e5
1.4eSto1.8e5
1.8eSto2e5
2e5to2.1e5
2.1eSto2.2e5
2.2eSto2.3e5
2.3eSto2.35e5
2.3Se5to2.4e5
2.4eSto2.45e5
2.45e5to2.5e5
2.5e5to2.55e5
2.5585 to 2.6e5
2.6e5to2.65e5
2.65e5to2.7e5
2.7e5to2.8e5
2.8eSto2.9Se5
2.95e5to3.1e5
3.1eSto3.3eS
3.3eSto3.7e5
3.7eSto4.85e5
>= 4.85e5
1.24
3.89
6.47
3.42
1.50
S.12
3.83
4.17
4.46
4.62
4.59
3.86
2.20
1.07
5.96
13.9
11.0
4.74
11.4
2.56
0.01
268000 ±60000
Sediment From Upper Reservoirs
0 to 2500
2500 to 5000
5000 to 7500
75001010000
10000 to 12500
12500 to 15000
15000 to 17500
17500 to 20000
>= 20000
1250
100
0
0
0
0
0
0
0
0
^^^^^
I I
i !
I I
!
i i
i ]
! \
±720
Figure 8-3. BBN model depicting Lucchetti Reservoir Life Expectancy with no sediment transfer from upper
reservoirs. This situation might have occurred shortly after the upper reservoirs were constructed. Start Water
Storage Capacity (To) was set at 11.88 Mm3, the measured value in 2000.
75
-------
Water Flow From Upper Reservoirs
Low
Average
High
22.2
54.1
23.6
48.1 ± 26
Annual Precipitation (mm)
0101518 15.7
1518 to 1397 34.2
1897 to 2276 34.2
>=2276 15.9
18101560
Conversion Implementation
Status Quo
Partial implementation
Full Implementation
Total Inflow of Water (Mm3)
Oto20
20 to 40
40 to 60
60 to 80
8010100
100 to 120
120 to 140
140 to 160
160 to 180
180 to 200
>=200
1.70
7.94
15.3
26.4
24.2
10.6
5.81
3.39
1.97
1.14
1.58
Sediment Trapped in Lago l.iicditlti (MmSfyr)
0 to 0.025
0.025 to 0.05
0.05 to 0.075
0.075 to 0.1
0.1 to 0.11
0.11 to 0.12
0.12to0.13
0.13 to 0.14
0.14100.15
0.15 to 0.16
.087
.087
.087
.087
.035
.049
0.16
0.40
0.46
0.57
Start Water Storage Capacity (TO) Mm3
Construction 1 952
Survey 1 986
Survey 2000
Dredge 2000
\
0
0
0
0
: i I
I i i
End Water Storage Capacity (T1) (Mm3)
Oto11.4
11.4to11.5
11.5to11.6
11.6to11.65
11.65 to11.7
11.7to 11.75
11.75 1011.8
11.8to11.85
11.85 1011.9
11.9to18.2
18.2 to 18.3
18.3to18.4
18.4 to 18.45
18.45 to 18.5
18.5to18.5S
18.55 to13.6
18.6 to 18.65
18.65 to 13.7
18.7to19.9
19.9 to 20
20 to 20.1
20.1 to 20 .15
20. 15 to 20 .2
20 .2 to 20 .25
20 .25 to 20 .3
20 .3 to 20 .35
20.35 to 20.4
11.61
.061
2.75
25.9
44.2
22.3
4.23
0.32
0.17
0.10
0
a
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
S0.18
/
0.16100.17 1.06
0.17 to 0.18 1.74
0.18 to 0.19 2.53
0.13 to 0.2 3.33
0.2to0.21 3.70
0.21 to 0.22 4.99
0.22 to 0.23 7.68
0.23 to 0.24 9.61
0.24 to 0.25 9.72
0.25 to 0.275 21.4
0.275 to 0.3 17.0
0.3 to 0.325 7.57
0.325 to 0.35 2.62
0.35 to 0.375 1.75
0.375 to 0.4 1.67
>=0.4 1.48
I
I
1
0.257 + 0.051
1
Reservoir Life Expectancy (Yrs to 0)
<0 0
OtolO .023
10to25 0.17
50 to 75 27.7
75 to 100 1.40
>=100 0.42
i i 1
i ! !
45.4 + 15
Total Sediment Delivery < 111) yu
0 to 1.4eS
1.4e5 to 1.8e5
1.8e5 to 2e5
2e5to2.1e5
2.1e5to2.2e5
2.2e5to2.3e5
2.3e5to2.35e5
2.35eSto2.4e5
2.4e5to2.45e5
2.45e5to2.5e5
2.5e5to2.5Se5
2.55e5to2.6e5
2.6e5to2.6Se5
2.65eSto2.7e5
2.7e5to2.8e5
2.8e5to2.9Se5
2.95eSto3.1e5
3.1e5to3.3eS
3.3e5to3.7e5
3.7e5to4.85e5
»= 4.85eS
0.45
1.63
2.79
2.62
3.62
3.51
0.94
0.76
1.68
2.88
3.67
4.08
4.39
4.56
8.63
5.76
12.3
15.8
12.5
6.98
.021
291000 ±61000
Sediment From Upper Reservoirs
0 to 2500
2500105000
5000107500
7500 to 1 0000
100001012500
125001015000
150001017500
175001020000
>= 20000
21250
0
0
0
0
0
0
0
0
100
; ; ;
i i i
i i i
i i i
±720
Figure 8-4. BBN model depicting Lucchetti Reservoir Life Expectancy with 100% sediment transfer from upper
reservoirs. This situation might be expected in the future as the upper reservoirs fill with sediment. Start Water
Storage Capacity (To) was set at 11.88 Mm3, the measured value in 2000.
Table 8-2. Impact of different sediment transfer scenarios on reservoir end of life
Transfer Scenario
0%
60%
100%
Sediment Transfer (m3)
0
11,250
21,250
Reservoir End of Life
2050.8 ±17
2048.2 ±16
2045.4 ±15
76
-------
Evaluation
It is possible to evaluate the accuracy of the overall BBN model by comparing it to previously measured data or
estimates from other methods. Two reservoir water capacity surveys have been performed on Lago Lucchetti
(in 1986 and 2000) since its construction in 1952. Soler-Lopez (2001a) provided a long-term sedimentation rate
for Lago Luccheti between each measurement date (1952-1986 and 1952-2000) and provided two life
expectancy estimates based on each rate. The BBN model can be evaluated against these estimates by
comparing the BBN results for 1986 to the Soler-Lopez (2001a) estimate for 1952-1986 and the BBN results for
2000 to the Soler-Lopez (2001a) estimate for 1952-2000 (Table 8-3).
Table 8-3. Comparison of BBN modeled reservoir life expectancy to results of USGS estimation method from
bathymetric survey data collected in 1986 and 2000 (Soler-Lopez, 2001a). The USGS estimates use a continuous
annual sediment accumulation rate whereas in the BBN model annual sediment accumulation rate changes over
time.
Year (measured
water storage
capacity)
1986 (15.84 Mm3)
2000 (11.88 Mm3)
USGS estimates
Data
1952-1986
1952-2000
Life
Expectancy
2108
2066
BBN Model
Data
1986
2000
Life
Expectancy
2052116
2049 ± 16
The BBN results can be compared to the Soler-Lopez (2001a) estimates in a more piecemeal way by comparing
sediment delivery into the reservoirs . This can be achieved by a simple conversion (Fig. 8-5, originally Fig. 6-8).
If the Lucchetti Sediment Delivery is normalized by the area of the watershed (45.09km2), there is an average
annual sediment delivery of 5,320 m3/km2/yr from the watershed to Lucchetti Reservoir. The U.S. Geological
Survey Report (Soler- Lopez, 2001a) calculated for the year 2000 an average annual sediment delivery of 4,102
m3/km2/yi" to Lucchetti Reservoir from the watershed. This is below the average for the BBN model but falls
within the distribution. The total sediment delivery 278,000 m3/yr (Fig. 7-6) was updated twice from the
original 241,000 m3/yr (Fig. 6-8), first to include sediment coming from the upper reservoirs, and then to
account for changes to landuse in the Lucchetti watershed. The new value after these changes would be about
6,200 m3/km2/yr, but the Soler-Lopez (2001a) estimates do not account for landuse contributions from the
upper reservoirs.
77
-------
Annual Precipitaiton (mm)
0 to 151 8 15.8
151 8 to 1897 34.1
1397 to 2276 34.3
>=2276 15.8
i i
1810 ±560
Average Sediment Delivery i i n 3 hi 1 12 yi t
0 to 1000 .006
1000 to 2000 .097
2000 to 3000 1.41
3000 to 4000 9.23
4000 to 5000 27.5
5000 to 6000 35.7
6000 to 7000 20.3
7000 to 8000 5.12
8000 to 9000 0.58
9000 to 10000 .035
>= 10000 .008
sf-
5320±1100
Figure 8-5. BBN depicting the Average Sediment Delivery for the Lucchetti watershed area in m3/km2/yi",
combining calculations for Sediment Delivery Rate (SDR) and watershed area. These results compared
favorably with and independent estimate made for the year 2000 (Soler- Lopez, 2001a).
Another way to evaluate the BBN is to compare the actual sediment accumulated in the reservoir between
when it was surveyed (1952-1986, 1986-2000, 1952-2000) to the BBN modeled sediment accumulated based
on Sediment Trapped in Lago Lucchetti in the initial year (Fig. 7-7). This comparison (Table 8-4) shows that the
BBN overestimated (almost doubled) sediment accumulation in the first 34 years after construction and slightly
underestimated sediment accumulation in the later 14-yr period. Over the entire 48-yr period the BBN model
overestimated accumulated sediment. It is noted that the model did not account for sediment compaction in
the reservoir directly. Without accurate density estimates for sediment originally entering and settling in
Lucchetti Reservoir, average sediment density was used in place of adjusting for compaction over time. If the
average density (0.98 g/cm3; Soler- Lopez et al., 1999) were adjusted for compaction this would result in a
density of 1.11 g/cm3 after 20 years (Singh and Durgunoglu, 1989). Such compaction would change model
accumulation from 1952-1986 from 8.7 to 7.9 Mm3, if all the sediment had been in the reservoir 20 years (the
actual compaction would be less since compaction rate decreases over time and the average time spent in the
reservoir for sediment would have been 17 years). The BBN model is intended for future projections, making
comparisons to sediment accumulation for the more recent period (1986-2000) most relevant.
Over the 48-yr period several conditions likely contributed to the observed change in sediment accumulation.
Precipitation, particularly from hurricanes, was greater from 1986-2000 than from 1952-1986. Landuse in the
watershed likely changed due to development and shifts in agriculture, such as the shift in the 1980's to sun-
grown coffee. Even the sediment traveling through the tunnels from the upper reservoirs would have increased
for 1986-2000 as those reservoirs filled with sediment and their trapping efficiencies decreased. Given that
current conditions are more likely to resemble the more recent period (1986-2000) the final BBN estimate
being close to the accumulated sediment during the more recent period is preferable over the estimate being
close to the accumulated sediment during the earlier period (1952-1986).
78
-------
Table 8-4. Measured sediment accumulated (Mm3) in Lucchetti reservoir between survey years and the
accumulation rate averaged over those years (Mm3/yr). These measured data are compared to accumulated
sediment for the same years based on the rate of accumulation estimated for the initial year using the BBN model
(Fig. 7-7).
Duration
1952-1986
1986-2000
1952-2000
Number
of years
34
14
48
Measured
Sediment
Accumulated
4.51
3.96
8.47
Rate of
Accumulation
(Average)
0.133
0.283
0.176
Model
Accumulated
Sediment
8.70 ± 1.80
3.53 ±0.73
12.28 ±2.4
Rate of
Accumulation
(Model)
0.256
0.252
0.256
Sensitivity Analysis
The BBN model can be used to explore the relationships between nodes. A sensitivity analysis examines how
responsive the final results of a BBN are to the values for each of the other nodes in the network. The results of
sensitivity analysis are useful in three ways: 1) to look for logical consistency in the model, 2) to identify nodes
where reduced uncertainty (better information) will be valuable to the final results and 3) to identify those
nodes that might have the greatest effect if they are altered through management alternatives. The Netica
Software package (Norsys, 2000) has variance reduction capabilities which provide a single number describing
how strongly related one node is to another (Pearl, 1988). By relating all the other nodes to the final results, in
this case to Lucchetti Reservoir Life Expectancy (Fig. 7-6), the influence of the different nodes can be ranked
(Tables 8-5 and 8-6). Management actions in the network can be treated one of two ways. The condition of the
node can be set (Status Quo and No Dredging; Table 8-5) but the management action will have no variance
reduction measure since it won't be changed from the set value during sensitivity analysis. The alternative is to
give the management action node a distribution, in this case a uniform distribution (Table 8-6).
Table 8-5. Sensitivity Report with nodes ranked by their influence on Lucchetti Reservoir Life Expectancy. Percent
variance reduction was calculated as the variance contributed by each node, divided by the total variance for
Lucchetti Reservoir Life Expectancy (226.6). The decision nodes were set to Status Quo for Conversion
Implementation and Survey 2000 capacity for Start Water Storage Capacity.
Node
Lucchetti Reservoir Life Expectancy
Sediment Trapped in Lago Lucchetti (m3/yr)
End Storage Capacity (Ti)
Total Sediment into Lucchetti (m3)
Annual Precipitation (mm)
Total Inflow of Water (Mm3)
Sediment From Upper Reservoirs
Water Flow From Upper Reservoirs
Variance Reduction
226.6
213.3
201.8
191.0
133.7
17.9
1.4
1.2
Percent
100.000
94.100
89.100
84.300
59.000
7.910
0.623
0.530
79
-------
Table 8-6. Sensitivity Report with nodes ranked by their influence on Lucchetti Reservoir Life Expectancy. Percent
variance reduction was calculated as the variance contributed by each node, divided by the total variance for
Lucchetti Reservoir Life Expectancy (561.7). Management action nodes were given a uniform distribution,
between the three measured Water Storage Capacities (11.88, 15.84, 20.35 Mm3) and between the three possible
coffee Conversion Implementations (status quo, partial implementation, full implementation).
Node
Lucchetti Reservoir Life Expectancy
End Storage Capacity (Ti)
Total Sediment into Lucchetti (m3)
Sediment Trapped in Lago Lucchetti (m3/yr)
Annual Precipitation (mm)
Start Water Storage Capacity (T0)
Total Inflow of Water (Mm3)
Coffee Conversion Implementation
Water Flow from Upper Reservoirs
Sediment from Upper Reservoirs
Variance Reduction
561.7
413.2
284.4
263.7
236.8
178.5
36.4
13.1
2.4
2.0
Percent
100.000
73.600
50.600
47.000
42.200
31.800
6.490
2.330
0.434
0.356
The most sensitive node when variable start capacities are considered (dredging is possible; Table 8-6) is End
Storage Capacity (Tl). This indicates that management actions targeting sediment accumulation (e.g. dredging)
will be very influential. Sediment Trapped in Lago Lucchetti (Mm3/yr) is the most influential node when the
start capacity is set (i.e. no dredging possible). Sediment trapped can be managed through actions that would
alter the reservoir trapping efficiency. An example would be the operation of sluice gates which allow for water
from heavy storm events to flush out suspended sediment. Total Sediment into Lucchetti (m3) is ranked next
on the list [3rd in Fig. 8-5; 2nd in Fig. 8-6). Of the two possible sources of this sediment, sediment coming from
the watershed has a stronger influence than Sediment from Upper Reservoirs. In fact, contributions of both
water and sediment from the upper reservoirs have the least effect on life expectancy, indicating that
management actions targeting the Lucchetti watershed will be more influential than those targeting the upper
reservoirs. Even if Sediment from Upper Reservoirs increases over time, as expected when the upper
reservoirs fill with sediment, the influence of upper reservoirs Lucchetti Reservoir Life Expectancy will still be
small (Table 8-2). The sensitivity analysis of Sediment from Upper Reservoirs and Water Flow from Upper
Reservoirs nodes help to reinforce that additional information/data collection related to these nodes may not
be of high importance.
The remaining nodes, without considering the management options and in order of sensitivity, are Annual
Precipitation and Total Inflow of Water. Of these, Lucchetti Reservoir Life Expectancy is most sensitive to
Annual Precipitation. Based on the BBN structure it is logical that Annual Precipitation is influential despite
having at least two nodes between it and Reservoir Life Expectancy since Annual Precipitation influences both
the flow of water and the flow of sediment into the reservoir.
Last, the sensitivity analysis which included decision nodes (Table 8-6) can be used to quantify how much more
influential dredging is over coffee conversion implementation. The variance reduction attributed to Start Water
80
-------
Storage Capacity was 178.5, compared to 13.1 for Conversion Implementation. The order of magnitude
difference is significant, even though the variance reduction represents the extremes of each state.
9. Discussion
A BBN was developed to characterize the effects of sediment accumulation on Lago Lucchetti water storage
capacity and to forecast the life expectancy of the reservoir. Despite the additional effort required to generate
a BBN there are many advantages over traditional methods. For example, life expectancy for Lago Lucchetti
could have been more simply estimated by applying an average loss per year or extrapolating the change in
water storage capacity from the year of construction (1952) to the year of the latest bathymetry survey (2000).
However, the estimates would be limited to reservoir life expectancy under only one decision alternativeno
change from current practices. A BBN allows consideration of multiple alternative scenarios alternative
scenarios (e.g. changing land use from sun-grown to shade-grown coffee or dredging the reservoir).
Constructing a BBN requires a conceptual understanding of cause-effect relationships, which facilitates
recognition of alternative management actions and gaps in data and information. This is a valuable asset for
stakeholder engagement and adaptive management. As demonstrated here, conceptual diagrams can be
constructed in simple modular forms, modified with new information or concepts, and merged into larger,
more comprehensive representations. Constructing conceptual diagrams and quantifying nodes and arcs
provides a natural forum for communication among scientists, stakeholders and decision-makers. New
information or data, even from external models (e.g., from USLE or sediment balance models), can be used to
update the original BBN for continuous stakeholder discussions. The model can be modified as uncertainty
narrows or as new concerns arise and stakeholders see how each factor changes the model outcomes. The
interactive nature of a BBN model should lead to new ideas, better definition of data gaps, and a better
understanding of tradeoffs with different decision scenarios. The BBN can become the 'working model' to
illustrate and communicate all of these issues.
One of the most revealing aspects of constructing a BBN for Lago Lucchetti was the lack of useable data on
critical aspects of the problem. The lack of gauging stations to document the flow of water and sediment from
the Lucchetti watershed and through the associated tunnels increased the complexity of the collecting data for
the model and uncertainty of the results. Nonetheless, results from the more complicated methods compared
favorably with previously measured data. For example, probabilities for water inflow from the watershed (Fig.
6-3; average 31.4 Mm3) were consistent with estimates from the literature (GLM, 2009; Table 5-3; 32.5 Mm3).
Likewise, probabilities for sediment delivery from the Lucchetti watershed (Fig. 8-5; average 5,320 m3/km2/yr)
were consistent with a previous estimate by Soler-Lopez (2001a; 4,102 m3/km2/y"). The probable amounts of
total sediment entering Lucchetti estimated by the BBN (Fig. 7-7; average 278,000 m3) exceeded a single
estimate by Soler-Lopez (2001a; 183,000 m3). However, with lower trapping efficiencies due to higher
estimates of water flow, the BBN estimated the amount of sediment trapped (Fig. 7-7; 0.246 Mm3) to be less
than that estimates of sediment trapped by Soler-Lopez (2001a; 0.283 Mm3). Again, the advantage of a BBN
model to a decision maker is having parameter estimates with some quantification of uncertainty and the
ability to incorporate changes to parameters under different decision scenarios.
81
-------
It is also worth noting that estimates of life expectancy from the BBN will be more accurate than estimates
made by applying an average loss per year or extrapolating the change in water storage capacity (see Projecting
Rates of Sediment Accumulation section in Chapter 8). These simpler, more traditional methods would
incorporate an average trapping efficiency over the time span tested; yet it is clear from these results that
trapping efficiency declines every year (Fig. 8-1) and more dramatically as the reservoir nearly fills with
sediment. The average used by simpler methods will underestimate sediment trapping in early years and
overestimate it in later years.
The decline in trapping efficiency over time is very relevant to issues under deliberation in the Guanica Bay
watershed. Reservoirs had the highest trapping efficiencies when they were first constructed, and declined
every year thereafter (Fig. 5-5). Consequently, each year a greater proportion of incoming sediment flows
through the outgoing tunnel (or over the spillway) to downstream ecosystems. The amount of sediment
flowing downstream to Lago Lucchetti more than doubled from 1952 to 2000 even though sediment input was
held constant (Fig. 5-5). Combined with increasing sediment loads caused by a growing number of hillside sun-
grown coffee farms during this period, it is easy to see why sediment has become a recent problem for coastal
ecosystems. The reservoirs have been protecting downstream ecosystems from sediment exposure, but their
ability to do that in the future is being compromised by a decreasing ability to trap sediment. Two of the
management options offered by the Guanica Bay Watershed Management Plan (CWP, 2008)altering farm
practices and dredging reservoirswill reduce erosion and restore the ecosystem protection afforded by
higher sediment trapping.
The ability to conduct a sensitivity analysis on a BBN can be a very useful tool (Pearl, 1988). The Netica software
(Norsys, 2000) was used to compare the relationship of values in the final node, Lucchetti Reservoir Life
Expectancy, to the values in all other nodes (Chapter 8). Results indicated that life expectancy was most
sensitive to Sediment Trapped in Lago Lucchetti (Table 8-6), which implies that better information could
reduce uncertainty in this node and places sediment trapping as a high priority for management. In terms of
the BBN model, this result also lends credibility to using iterative model runs to account for annual changes in
trapping efficiency and sediment trapped.
One way to improve the estimation of sediment trapping would be to collect paired data on the amount of
sediment and water entering and leaving Lucchetti Reservoir. Another option, barring new evidence, would be
to add trapping efficiency as a root node using 10% deviation as an uncertainty estimate (Brune, 1948). Other
studies have addressed uncertainty in trapping efficiency by parameterizing uncertainty for different parts of
the trapping efficiency equation (Salas and Shin, 1999). Also, different trapping efficiencies could be applied to
sediment from different sources, incorporating grain size as a variable since larger grains would settle more
quickly in upper reservoirs).
Life expectancy was also sensitive to Total Annual Sediment Yield (m3/km2/yr) from the Lucchetti watershed
(Table 8-5 & 8-6) and could be a target for variance reduction. The USLE method for estimating the Lucchetti
watershed sediment yield is a better method than the unitless Summit to Sea calculation or estimates based on
accumulated sediment (Soler-Lopez, 2001a). One option for greater precision at this node would be to use an
alternative distributed model (see sidebar on distributed/lumped models), although these would require finer
resolution of precipitation data. Using one of these distributed sediment models would characterize where in
82
-------
the watershed the sediment originates and could pinpoint management actions. For example, it might identify
regions of the watershed that should be a high priority of conversion to shade-grown coffee. Other concerns
with using USLE are that it under-estimates soli loss on steep slopes (above 9%; Liu et al., 1994) and under
event driven conditions such as those seen in Puerto Rico (Santos & Canino, 1997).
In general the BBN would benefit from an improved precipitation nodein Puerto Rico where rainfall is very
seasonal and event driven the high variation isn't captured by annual totals. Spatial delineation would also be
useful, such as separate nodes for each individual watershed rather than a single precipitation node for all the
watersheds. This would provide better estimates of rainfall, water flow and sediment flow through the tunnels.
The relationship between precipitation and runoff, here only defined by the runoff ratio, is strongly influenced
by temperature. Since temperature varies annually, seasonally and spatially, a node could be added to account
for differences in temperature that might influence rainfall becoming runoff and impacting the system.
Sediment contribution from the upper watersheds could be better estimated by moving the calculations in the
sediment balance model into their own nodes in the BBN. Doing this would estimate how sediment trapping in
each reservoir is expected to change from year to year and how that change impacts sediment transferred to
Lago Lucchetti (Sediment from Upper Reservoirs).
Three relatively arbitrary thresholds were used to demonstrate how the BBN model could estimate Lucchetti
Reservoir Life Expectancycomplete filling of the reservoir (0% water storage capacity), 75% filling (25% water
storage capacity) and half filling (50% water storage capacity). Better for decision makers would be thresholds
based on actual current and future water demands. Meeting water demands does not, of course, rely solely on
reservoir water storage capacity. High storage capacity will be of little use in periods of drought when the
reservoir cannot be filled. Addressing water needs will require consideration of water demand, storage capacity
and available water.
Conclusions
The BBN model has provided important information for future study and management. Of greatest concern to
watershed managers will be the fact that every year a greater percentage of the sediment from watersheds is
being washed downstream (less is being trapped in the reservoirs). This can only add a sense of urgency to
efforts to reduce erosion and remove sediment from reservoirs. Strategically, it was important to demonstrate
that sediment from the upper watersheds plays only a minor role in sedimentation of Lago Lucchetti. This
allows prioritization of management efforts in the Lucchetti watershed. In the future, however, this may not be
the case. Currently the large Guayo reservoir is trapping much of the sediment from Guayo and Yahuecas
watersheds. As the reservoir continues to accumulate sediment, its trapping efficiency continues to decline and
more sediment is passing through the tunnel to Lago Lucchetti every year.
This exercise has shown that a BBN is a viable option for decision analysis even when data are limited. There
are many improvements that could be made to the existing model and there is great flexibility in developing
models to address data needs or new information. Once constructed, the basic model might serve many
purposes. Whereas this work was designed to address life expectancy of Lago Lucchetti, the same information
and conceptual framework might serve to address additional management questions such as effects of
83
-------
sediment on hydroelectric power generation, quantifying erosion reduction to maintain safe water yield,
limiting sediment transfer to downstream ecosystems, and others.
84
-------
10. References
Angina, S., Stott, D., O'neill, M., Ong, C. & Weesies, G. (2003). Soil erosion prediction using RUSLE for central
Kenyan highland conditions. Agriculture, ecosystems & environment, 97(1), 295-308.
Bonnin, G.M., D. Martin, B. Lin, T. Parzybok, M. Yekta, and D. Riley (2006). Precipitation-Frequency Atlas of the
United States. Volume 3 Version 4.0: Puerto Rico and the US Virgin Islands. Silver Spring, MD: NOAA
National Weather Service.
Borkhataria, R., Collazo, J., Groom, M., and Jordan-Garcia, A. (2012) Shade-grown coffee in Puerto Rico:
Opportunities to preserve biodiversity while reinvigorating a struggling agricultural commodity.
Agriculture, Ecosystems & Environment, 149, 164-170.Brune, G. (1953). Trap Efficience of Reservoirs.
Transactions American Geophysical Union, 34(3), 407-418.
Bousquin, J. & Fisher, W. (2013). A Bayesian Belief Network Approach to Explore Alternative Decisions for
Sediment Control and Water Storage Capacity at Lago Lucchetti, Puerto Rico. Environmental Protection
Agency Internal Report.
Brune, G. (1953). Trap efficiency of reservoirs. Trans. AGU, Vol. 34 No. 3, 407-418
Bulygina, N., Mclntyre, N., & Wheater, H. (2009). Conditioning rainfall-runoff model parameters for ungauged
catchments and land management impacts analysis. Hydrology and Earth System Sciences, 13(6), 893-
904.
Calversbert, R. (1970). Climate of Puerto Rico and US Virgin Islands: Climatography of the United States, no. 60-
52. National Oceanographic and Atmospheric Administration.
Center for Watershed Protection (CWP). (2008). Guanica Bay Watershed Management Plan: A pilot project for
watershed planning in Puerto Rico. Prepared for the NOAA Coral Reef Program by Center for
Watershed Protection, Ellicott City, MD.
Dopazo, T. & Molina-Rivera, W. (1995). Estimated Water Use in Puerto Rico, 1988-89. San Juan, Puerto Rico: US
Geological Survey,no. 95-380.
Downer, C. W. and F.L Ogden. (2006) Gridded Surface Subsurface Hydrologic Analysis (GSSHA) user's manual,
version 1.43 for WMS 6.1, ERDC/CHL SR-06-1. Vicksburg, MS: U.S. Army Engineer Research and
Development Center.
Fenton, N., Neil, M., & Marquez, D. (2008). Using Bayesian networks to predict software defects and
reliability. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and
Reliability, 222(4), 701-712.
Gebelein, J. (2000). Landcover Classification of Landsat Imagery. Classification for spatial dataset.
Gellis, A. C., Webb, R. M. T., Wolfe, W. J., and Mclntyre, S. C. I. (1999) Effects of Land Use on Upland Erosion,
Sediment Transport and Reservoir Sedimentation, Lago Lofza Basin, Puerto Rico. Washington, DC: U.S.
Geological Survey, Water Resources Investigation Report 99-4010.
Gesch, D., Oimoen, M., Greenlee, S., Nelson, C., Steuck, M., & Tyler, D. (2002). The National Elevation Dataset.
Photogrammetric Engineering and Remote Sensing, 68(1), 5-11.
GL Morris Engineering (GLM). (2008). Rendimiento Seguro para las Tomas de Rfos y Embalses de
Abastecimiento Municipal en Puerto Rico. Prepared by GL Morris Engineering for Puerto Rico DNER
(DRNA).
GL Morris Engineering (GLM). (2009). Mean Annual Rainfall Map for Puerto Rico. Prepared by GL Morris
Engineering for Puerto Rico DNER (DRNA).
Homer, C., Dewitz, J., Fry, J., Coan, M., Hossain, N., Larson, C., . . . Wickham, J. (2007). Completion of the 2001
National Land Cover Database for the Counterminous United States. Photogrammetric Engineering and
Remote Sensing, 73 No. 4, pp 337-341.
Howard, R. & Mathesonm J. (2005) Influence diagrams. Decision Analysis. Vol. 2, no. 3: 127-143
Joy, E.B. 2012. The Sugar Industry of Puerto Rico, http://www.preb.com/apuntes5/sugarind.htm ; accessed
April 2013.
85
-------
Larsen, M. (2000). Analysis of 20th century rainfall and streamflow to Characterize Drought and Water
Resources in Puerto Rico. USGS, Guaynabo, Puerto Rico. Physical Geography, 21, 6 pp 494-521.
Liu, B., Nearing, M., & Risse, L. (1994) Slope gradient effects on soil loss for steep slopes. Transactions of the
ASAE, 37 (6), 1835-1840.
Lucchetti, A. (1936). Bulletin of the department of the interior, government of Puerto Rico, concerning the
construction and operation of the hydro-electric and irrigation systems of the south coast and of the
hydro-electric system of utilization of the water resources of the government of Puerto Rico: Puerto
Rico Department of the Interior.
Lucchetti, A. (1946). Second general report of the utilization of the water resources of Puerto Rico 1935-1945
(pp. 38): Water Resources Authority, Government of Puerto Rico.
Mclntyre, N., Lee, H., Wheater, H., Young, A., & Wagener, T. (2005). Ensemble predictions of runoff in
ungauged catchments. Water Resources Research, 41(12).
MDA Federal (2000). NASA GeoCover 1990 and 2000 Land Cover Types. Classification for spatial dataset.
http://www.mdafederal.com/geocover/geocoverortho/
Miller, G. & Lugo (2009). Guide to the Ecological Systems of Puerto Rico. General Technical Report. IITF-GTR-35.
San Juan, PR: U.S. Department of Agriculture, Forest Service, International Institute of Tropical Forestry.
437 p.
Molina-Rivera, W. (1997). Fact Sheet. Guaynabo, Puerto Rico: US Geological Survey.
Molina-Rivera, W. (1998). Estimated Water Use in Puerto Rico, 1995. San Juan, Puerto Rico: US Geological
Survey.
Molina-Rivera, W. (2005). Estimated Water Use in Puerto Rico, 2000. San Juan, Puerto Rico: US Geological
Survey.
Molina-Rivera, W., & Dopazo, T. (1995). Estimated Water Use in Puerto Rico, 1986-87. San Juan, Puerto Rico:
US Geological Survey.
Molina-Rivera, W., & Gomez-Gomez, F. (2008). Estimated Water Use in Puerto Rico, 2005. San Juan, Puerto
Rico: US Geological Survey.
Morris, G.L, & Fan, J. (1998). Reservoir Sedimentation Handbook. McGraw-Hill, New York.
Neitsch, S. L, Arnold, J. G., Kiniry, J. R., Williams, J. R., & King, K. W. (2005). Soil and water assessment tool:
theoretical documentation, version 2005. Texas, USA.
NOAA. (2012). Historical Hurricane Tracks. Retrieved 7/5/2012 from: http://csc.noaa.gov/hurricanes/ft
NOAA. (2005). Summit to Sea Characterization of Coastal Watersheds - Puerto Rico and US Virgin Islands.
Retrieved from: http://ccma.nos.noaa.gov/ecosystems/coralreef/summit_sea/summit_sea2.aspx
NOAA NCDC. (2013). National Climatic Data Center. Climate Data Online Retrieved 4/30/2013
http://www.ncdc.noaa.gov/cdo-web/
Norsys (2000). Netica. http://www.norsys.com
Ortiz-Zayas, J. R., Terrasa-Soler, J. J., & Cruz, J. V. (2001). Allocating water resources for public supply within a
complex hydroelectric system: the case study of Yauco Puerto Rico. Paper presented at the 2nd Latin
American Technical Conference and Exhibition, San Juan, PR.
Ortiz-Zayas, J., F. Quinones, S. Palacios, A. Velez and H. Mas (2004). Caracterfsticas y Condicion de los Embalses
Principales en Puerto Rico. S.I. : Departamento de Recursos Naturales y Ambientales.
Pearl, Judea (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan
Kaufmann, San Mateo, CA. 2nd edition 1991.
Puerto Rico Department of Natural and Environmental Resources (DNER). (2008). Plan Integral de Recursos de
Agua de Puerto Rico.
Puerto Rico Planning Board (PRPB). (1970). Water Resources of Puerto Rico Phase II Ground Water Appraisal
(pp. 6-40 to 46-65): Puerto Rico Planning Board.
Puerto Rico Electric Power Authority (PREPA) (2012). Personal Communication.
Puerto Rico Electric Power Authority (PREPA) (2013). http://www.prepa.com/historia eng.asp.
86
-------
Puerto Rico Water Resources Authority (PRWRA). (1958). Power and Irrigation in Puerto Rico 1945-1955, A
Third General Report on the Utilization of the Water Resources of Puerto Rico.
Renard, K.G., Foster, G. R., Weesies, G.A., McCool, O.K., & Yoder, D.C. (1997). Predicting soil erosion by water: a
guide to conservation planning with the revised universal soil loss equation (RUSLE). Agriculture
Handbook. Washington, 703.
Rosgen, D.L (2001). A practical method of computing streambank erosion rate. In Proceedingsof the seventh
Federal Interagency Sedimentation Conference. Vol. 2 No. 2
Salas, J. & Shin, H. (1999). Uncertainty analysis of reservoir sedimentation. Journal of Hydraulic Engineering,
Vol. 125 No. 4, 339-350
Santos, J. R., & Canino, G. (1997). Erosion and sediment transport in a proposed regional sanitary landfill. Paper
presented at the Congreso Regional de AIDIS para Norteamerica y El Caribe.
Schachter, R. & Heckermen, D. (1987). Thinking Backward for knowledge acquisition. Al magazine, 8(3), 55.
Sheda, H. E., & Legas, J. (1968). Condition of Concrete Dams in Puerto Rico (B. o. Reclamation, Trans.). Denver,
Colorado: US Department of the Interior.
SERC (2012). Historical Climate Summary for Lajas Substation. Southeast Regional Climate Services Support
Program. Chapel Hill, NC. www.sercc.com . Accessed 4/30/2012.
Singh, K. and A. Durgunoglu (1989). A New Method for Estimating Future Reservoir Storage Capacities. Water
Resources Bulletin. Vol. 25 No. 2.
Soler-Lopez, L. R. (1999). Sedimentation Survey of Lago Guayo, Puerto Rico, October 1997. San Juan, Puerto
Rico: USGS Water-Resources Investigations Report.
Soler-Lopez, L. R. (2001a). Sedimentation Survey of Lago Lucchetti, Puerto Rico, March 2000. San Juan, Puerto
Rico: USGS Water-Resources Investigations Report.
Soler-Lopez, L. R. (2001b). Sedimentation survey results of the principal water supply reservoirs of Puerto Rico.
Paper presented at the Sixth Caribbean Islands Water Resources Congress, Mayaguez, Puerto Rico.
Soler-Lopez, L. R. (2002). Sedimentation Survey of Lago Loco, Puerto Rico, March 2000. San Juan, Puerto Rico:
USGS Water-Resources Investigations Report.
Soler-Lopez, L. R., & Webb, R. (1999). Sedimentation Survey of Lago Prieto, Puerto Rico, October 1997. San
Juan, Puerto Rico: USGS Water-Resources Investigations Report.
Soler-Lopez, L. R., Webb, R., & Rerez-Blair, F. (1999). Sedimentation Survey of Lago Yahuecas, Puerto Rico,
March 1997. San Juan, Puerto Rico: USGS Water-Resources Investigations Report.
Stone, R& Hilborn (2000). Universal Soil Loss Equation, USLE Fact Sheet. Ontario Ministry of Agriculture, Food
and Rural Affairs.
The Nature Conservancy (TNC) (2006) Coffee, Puerto Rico Spatial Vector Dataset. Available from Florida
International University Information Systems and Remote Sensing Center (FIU-RSC) Revised: 08/01/06
Accessed: 4/23/13
Torres-Siera, H., & Aviles, A. (1986). Estimated Water Use in Puerto Rico, 1980-82 Open-File Data Report. San
Juan, Puerto Rico: US Geological Survey.
USDA (1979) United States Department of Agriculture - Soil Conservation Service. National
Engineering Handbook, Sec. 4. Hydrology.
USDA (2012). Personal Communication with Rodriguez of the Natural Resources Conservation Service (NRCS),
US Department of Agriculture.
USDA (2004). Puerto Rico 2002 Census of Agriculture.
USDA (2008). Revised Universal Soil Loss Equation, Version 2 (RUSLE2) Database. Natural Resources
Conservation Service, United States Department of Agriculture. Retrieved 8/1/2013
http://fargo.nser!. purdue.edu/RUSLE2_ftp/Climate_data/
USDA (2011). Soil Survey Geographic (SSURGO) Database. Natural Resources Conservation Service, United
States Department of Agriculture. Available online at http://sdmdataaccess.nrcs.usda.gov/.
87
-------
USGS (1996). US Geological Service Programs in Puerto Rico. US Geological Survey Fact Sheet FS-051-96. US
Geological Survey, Department of the Interior. 4pp.
Vanoni, V. A. (1975). Sedimentation engineering. ASCE. Manuals and Reports on Engineering Practive No. 54.
American Society of Civil Engineers, New York, New York
Vincente-Chandler, J., F. Abruna, R. Bosque-Lugo and S. Silva 1968. Intensive Coffee Culture in Puerto Rico.
University of Puerto Rico Agriculture Experiment Station Bulletin 211, August 1968, 84 pp.
Wagener, T., Mclntyre, N., Lees, M. J., Wheater, H. S., & Gupta, H. V. (2003). Towards reduced uncertainty in
conceptual rainfall-runoff modelling: Dynamic identifiability analysis. Hydrological Processes, 17(2),
455-476.
Wischmeier, W., and Smith, D. (1978) Predicting Rainfall Erosion Losses: A Guide to Conservation Planning.
USDA, Science and Education Administration, Agriculture Handbook No. 537,
Wilson, H. M. (1899). Water Resources of Puerto Rico Water-Supply and Irrigation Papers of the United States
Geological Survey. Washington D.C.: Department of the Interior.
Yuan, Y., Mbonimpa, Hu, W. Fisher & Casper, A. (2013). Quantifying sediment contributions to Guanica Bay
Puerto Rico. American Water Resources Association Meeting.
88
-------
9. Appendixes
Appendix A: Sediment Balance Model Results
Table A-l: Prieto Sediment Balance. Sediment Balance Model for Prieto Reservoir. Model was
calibrated to survey data from 1997 (shaded value for Capacity T0; Soler-Lopez and Webb, 1999).
Year
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
Total Inflow
(Mm3)
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
Reservoir Capacity
(T0)(Mm3)
0.76
0.7452
0.7305
0.7159
0.7013
0.6868
0.6723
0.6579
0.6436
0.6294
0.6153
0.6012
0.5873
0.5734
0.5596
0.5459
0.5322
0.5187
0.5053
0.4920
0.4788
0.4657
0.4527
0.4398
0.4271
0.4144
0.4019
0.3896
0.3773
0.3652
0.3533
0.3415
Trapping
Efficiency
0.7372
0.7340
0.7307
0.7274
0.7239
0.7204
0.7167
0.7130
0.7091
0.7052
0.7011
0.6970
0.6927
0.6883
0.6837
0.6790
0.6742
0.6693
0.6642
0.6589
0.6535
0.6479
0.6421
0.6361
0.6300
0.6237
0.6171
0.6104
0.6034
0.5962
0.5887
0.5810
Sediment
Yield (Mm3)
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
Accumulated
Sediment (Mm3)
0.01478
0.01472
0.01465
0.01458
0.01451
0.01444
0.01437
0.01429
0.01422
0.01414
0.01406
0.01397
0.01389
0.01380
0.01371
0.01361
0.01352
0.01342
0.01332
0.01321
0.01310
0.01299
0.01287
0.01275
0.01263
0.01250
0.01237
0.01224
0.01210
0.01195
0.01180
0.01165
Effluent
Sediment (Mm3)
0.005269
0.005333
0.005399
0.005466
0.005536
0.005607
0.005680
0.005755
0.005832
0.005911
0.005992
0.006076
0.006162
0.006250
0.006341
0.006435
0.006532
0.006631
0.006734
0.006839
0.006948
0.007060
0.007176
0.007295
0.007418
0.007545
0.007677
0.007812
0.007952
0.008096
0.008246
0.008400
89
-------
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
18.53
0.3298
0.3183
0.3070
0.2958
0.2849
0.2741
0.2635
0.2530
0.2428
0.2328
0.2230
0.2134
0.2041
0.1949
0.5731
0.5649
0.5564
0.5477
0.5386
0.5293
0.5196
0.5097
0.4994
0.4889
0.4780
0.4667
0.4552
0.4433
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.02005
0.01149
0.01133
0.01116
0.01098
0.01080
0.01061
0.01042
0.01022
0.01001
0.00980
0.00958
0.00936
0.00913
0.00889
0.008559
0.008724
0.008894
0.009069
0.009250
0.009438
0.009631
0.009830
0.010036
0.010248
0.010467
0.010692
0.010923
0.011161
Table A-2: Yahuecas Sediment Balance. Sediment Balance Model for Yahuecas
was calibrated to survey data from 1997 (shaded value for Capacity T0; Soler-Lopez
Reservoir. Model
atal., 1999).
Year
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
Total Inflow
(Mm3)
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
Reservoir Capacity
(T0)(Mm3)
1.76
1.7177
1.6755
1.6336
1.5920
1.5505
1.5093
1.4684
1.4277
1.3873
1.3472
1.3074
1.2679
1.2287
1.1898
1.1513
1.1131
1.0753
1.0379
1.0009
0.9642
0.9281
0.8923
0.8571
Trapping
Efficiency
0.7488
0.7450
0.7410
0.7369
0.7327
0.7283
0.7238
0.7192
0.7143
0.7093
0.7041
0.6987
0.6932
0.6874
0.6813
0.6751
0.6686
0.6618
0.6548
0.6475
0.6399
0.6319
0.6236
0.6150
Sediment
Yield (Mm3)
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
Accumulated
Sediment (Mm3)
0.0423
0.0421
0.0419
0.0417
0.0414
0.0412
0.0409
0.0407
0.0404
0.0401
0.0398
0.0395
0.0392
0.0389
0.0385
0.0382
0.0378
0.0374
0.0370
0.0366
0.0362
0.0357
0.0353
0.0348
Effluent
Sediment (Mm3)
0.0142
0.0144
0.0146
0.0149
0.0151
0.0154
0.0156
0.0159
0.0162
0.0164
0.0167
0.0170
0.0174
0.0177
0.0180
0.0184
0.0187
0.0191
0.0195
0.0199
0.0204
0.0208
0.0213
0.0218
90
-------
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
39.9
0.8223
0.7880
0.7543
0.7211
0.6885
0.6565
0.6251
0.5944
0.5644
0.5350
0.5065
0.4787
0.4517
0.4256
0.4003
0.3759
0.3525
0.3300
0.3085
0.2880
0.2686
0.6060
0.5966
0.5868
0.5766
0.5659
0.5548
0.5432
0.5310
0.5184
0.5052
0.4914
0.4772
0.4623
0.4469
0.4309
0.4144
0.3975
0.3800
0.3621
0.3439
0.3255
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.05655
0.0343
0.0337
0.0332
0.0326
0.0320
0.0314
0.0307
0.0300
0.0293
0.0286
0.0278
0.0270
0.0261
0.0253
0.0244
0.0234
0.0225
0.0215
0.0205
0.0194
0.0184
0.0223
0.0228
0.0234
0.0239
0.0245
0.0252
0.0258
0.0265
0.0272
0.0280
0.0288
0.0296
0.0304
0.0313
0.0322
0.0331
0.0341
0.0351
0.0361
0.0371
0.0381
Table A-3: Guayo (0% Transfer) Sediment Balance. Sediment Balance Model for Guayo Reservoir.
Model was calibrated to survey data from 1997 (shaded value for Capacity T0; Soler-Lopez, 1999), with
no additional sediment considered from sources outside the Guayo Reservoir watershed.
Year
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
Total Inflow
(Mm3)
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
Reservoir Capacity
(T0)(Mm3)
19.200
19.136
19.071
19.007
18.943
18.879
18.814
18.750
18.686
18.622
18.558
18.493
18.429
18.365
18.301
18.237
18.172
18.108
Trapping
Efficiency
0.9680
0.9680
0.9679
0.9678
0.9677
0.9676
0.9676
0.9675
0.9674
0.9673
0.9673
0.9672
0.9671
0.9670
0.9669
0.9668
0.9668
0.9667
Sediment
Yield (Mm3)
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
Accumulated
Sediment (Mm3)
0.0643
0.0643
0.0643
0.0643
0.0642
0.0642
0.0642
0.0642
0.0642
0.0642
0.0642
0.0642
0.0642
0.0642
0.0642
0.0642
0.0642
0.0642
Effluent
Sediment (Mm3)
0.0021
0.0021
0.0021
0.0021
0.0021
0.0021
0.0022
0.0022
0.0022
0.0022
0.0022
0.0022
0.0022
0.0022
0.0022
0.0022
0.0022
0.0022
91
-------
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
20.997
18.044
17.980
17.916
17.851
17.787
17.723
17.659
17.595
17.531
17.467
17.403
17.338
17.274
17.210
17.146
17.082
17.018
16.954
16.890
16.826
16.762
16.698
16.634
16.570
16.505
16.441
16.377
0.9666
0.9665
0.9664
0.9663
0.9663
0.9662
0.9661
0.9660
0.9659
0.9658
0.9657
0.9656
0.9655
0.9655
0.9654
0.9653
0.9652
0.9651
0.9650
0.9649
0.9648
0.9647
0.9646
0.9645
0.9644
0.9643
0.9642
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.06639
0.0642
0.0642
0.0642
0.0642
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0641
0.0640
0.0640
0.0640
0.0640
0.0640
0.0640
0.0022
0.0022
0.0022
0.0022
0.0022
0.0022
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0023
0.0024
0.0024
0.0024
0.0024
Table A-4: Guayo (60% Transfer) Sediment Balance. Sediment Balance Model for Guayo
Reservoir. Model was calibrated to survey data from 1997(shaded value for Capacity T0; Soler-Lopez,
1999), while also considering sediment contribution from Yahuecas Reservoir based on 60% (23.94
Mm3) transference of water and effluent sediment through the tunnel after 1956.Effluent sediment
from Yahuecas is transferred within the same year, meaning Sediment Transferred (Yahuecas) (Mm3)
in 1957 = Table A-2 Effluent Sediment *60%. Two trapping efficiencies are calculated, one for sediment
from the Guayo watershed and one for sediment transferred from Yahuecas.
Year
1956
1957
1958
1959
1960
1961
1962
1963
1964
Total Inflow
(Mm3)
20.997
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
Capacity
(T0)(Mm3)
19.2
19.145
19.085
19.024
18.963
18.902
18.840
18.779
18.718
Trapping
Efficiency
(Guayo)
0.9680
0.94520
0.94508
0.94495
0.94483
0.94470
0.94458
0.94445
0.94432
Trapping
Efficiency
(Yahuecas)
0.8507
0.8506
0.8505
0.8503
0.8502
0.8501
0.8500
0.8499
Watershed
Sediment
Yield (Mm3)
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
Sediment
Transferred
(Yahuecas) (Mm3)
0.00865
0.00879
0.00893
0.00907
0.00922
0.00937
0.00953
0.00969
Total Accumulated
Sediment (Mm3)
0.0547
0.0608
0.0609
0.0610
0.0611
0.0612
0.0613
0.0615
0.0616
Total Effluent
Sediment
(Mm3)
0.0018
0.0044
0.0044
0.0044
0.0045
0.0045
0.0045
0.0046
0.0046
92
-------
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
44.937
18.656
18.594
18.532
18.470
18.408
18.346
18.283
18.221
18.158
18.095
18.032
17.968
17.904
17.841
17.777
17.712
17.648
17.583
17.518
17.452
17.387
17.321
17.254
17.188
17.121
17.053
16.986
16.917
16.849
16.780
16.710
16.640
16.570
16.499
16.428
16.356
0.94420
0.94407
0.94393
0.94380
0.94367
0.94354
0.94340
0.94326
0.94313
0.94299
0.94285
0.94271
0.94256
0.94242
0.94228
0.94213
0.94198
0.94183
0.94168
0.94153
0.94137
0.94122
0.94106
0.94090
0.94074
0.94057
0.94041
0.94024
0.94007
0.93990
0.93972
0.93955
0.93937
0.93919
0.93900
0.93881
0.8498
0.8497
0.8495
0.8494
0.8493
0.8492
0.8491
0.8489
0.8488
0.8487
0.8486
0.8484
0.8483
0.8482
0.8480
0.8479
0.8478
0.8476
0.8475
0.8474
0.8472
0.8471
0.8470
0.8468
0.8467
0.8465
0.8464
0.8462
0.8461
0.8459
0.8458
0.8456
0.8454
0.8453
0.8451
0.8449
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.05651
0.00986
0.01004
0.01022
0.01041
0.01061
0.01081
0.01102
0.01124
0.01147
0.01171
0.01196
0.01222
0.01249
0.01277
0.01306
0.01337
0.01369
0.01402
0.01437
0.01473
0.01511
0.01550
0.01591
0.01634
0.01679
0.01726
0.01774
0.01824
0.01877
0.01931
0.01987
0.02044
0.02104
0.02164
0.02226
0.02289
0.0617
0.0619
0.0620
0.0622
0.0623
0.0625
0.0627
0.0628
0.0630
0.0632
0.0634
0.0636
0.0639
0.0641
0.0643
0.0646
0.0648
0.0651
0.0654
0.0657
0.0660
0.0663
0.0667
0.0670
0.0674
0.0678
0.0682
0.0686
0.0690
0.0694
0.0699
0.0704
0.0709
0.0714
0.0719
0.0724
0.0046
0.0047
0.0047
0.0047
0.0048
0.0048
0.0049
0.0049
0.0049
0.0050
0.0050
0.0051
0.0051
0.0052
0.0052
0.0053
0.0054
0.0054
0.0055
0.0056
0.0056
0.0057
0.0058
0.0058
0.0059
0.0060
0.0061
0.0062
0.0063
0.0064
0.0065
0.0066
0.0067
0.0068
0.0069
0.0070
Table A-5: Guayo (100% Transfer) Sediment Balance Sediment Balance Model for Guayo
Reservoir. Model was calibrated to survey data from 1997(shaded value for Capacity T0; Soler-Lopez,
1999), while also considering sediment contribution from Yahuecas Reservoir based on 100% (39.9
Mm3) transference of water and effluent sediment through the tunnel after 1956.Effluent sediment
from Yahuecas is transferred within the same year, meaning Sediment Transferred (Yahuecas) (Mm3)
in 1957 = Table A-2 Effluent Sediment *60%. Two trapping efficiencies are calculated, one for sediment
from the Guayo watershed and one for sediment transferred from Yahuecas.
Year
1956
1957
1958
1959
1960
1961
Total Inflow
(Mm3)
20.997
60.897
60.897
60.897
60.897
60.897
Capacity
(T0)(Mm3)
19.200
19.152
19.093
19.035
18.976
18.917
Trapping
Efficiency
(Guayo)
0.9680
0.9322
0.9321
0.9320
0.9318
0.9317
Trapping
Efficiency
(Yahuecas)
0.839024
0.838894
0.838763
0.83863
0.838497
Watershed
Sediment
Yield (Mm3)
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
Sediment
Transferred
(Yahuecas) (Mm3)
0.01442
0.01465
0.01488
0.01512
0.01536
Total
Accumulated
Sediment (Mm3)
0.04821
0.05853
0.05871
0.05889
0.05908
0.05928
Total Effluent
Sediment
(Mm3)
0.00159
0.00570
0.00574
0.00579
0.00583
0.00588
93
-------
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
60.897
18.857
18.798
18.738
18.678
18.618
18.558
18.497
18.436
18.375
18.314
18.252
18.190
18.128
18.065
18.002
17.939
17.875
17.811
17.747
17.682
17.616
17.551
17.484
17.418
17.351
17.283
17.214
17.146
17.076
17.006
16.935
16.864
16.792
16.719
16.645
16.570
16.495
16.419
16.342
0.9315
0.9314
0.9312
0.9311
0.9309
0.9307
0.9306
0.9304
0.9303
0.9301
0.9299
0.9298
0.9296
0.9294
0.9293
0.9291
0.9289
0.9287
0.9286
0.9284
0.9282
0.9280
0.9278
0.9276
0.9274
0.9272
0.9270
0.9268
0.9266
0.9264
0.9262
0.9260
0.9258
0.9255
0.9253
0.9251
0.9248
0.9246
0.9244
0.838363
0.838227
0.83809
0.837952
0.837812
0.837672
0.83753
0.837386
0.837241
0.837095
0.836947
0.836798
0.836647
0.836495
0.83634
0.836184
0.836026
0.835866
0.835705
0.835541
0.835375
0.835207
0.835037
0.834864
0.834689
0.834511
0.834331
0.834148
0.833962
0.833773
0.833581
0.833386
0.833187
0.832985
0.83278
0.83257
0.832357
0.83214
0.831919
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.0498
0.01562
0.01588
0.01615
0.01644
0.01673
0.01704
0.01735
0.01768
0.01802
0.01837
0.01874
0.01912
0.01952
0.01993
0.02037
0.02081
0.02128
0.02177
0.02228
0.02281
0.02336
0.02394
0.02455
0.02518
0.02583
0.02652
0.02724
0.02798
0.02876
0.02957
0.03041
0.03128
0.03218
0.03311
0.03407
0.03506
0.03607
0.03710
0.03814
0.05948
0.05969
0.05991
0.06014
0.06038
0.06062
0.06088
0.06114
0.06141
0.06170
0.06200
0.06230
0.06263
0.06296
0.06331
0.06367
0.06405
0.06445
0.06486
0.06529
0.06574
0.06621
0.06670
0.06722
0.06775
0.06831
0.06889
0.06950
0.07013
0.07079
0.07147
0.07218
0.07292
0.07367
0.07446
0.07526
0.07608
0.07692
0.07777
0.00593
0.00599
0.00604
0.00610
0.00615
0.00621
0.00628
0.00634
0.00641
0.00647
0.00654
0.00662
0.00669
0.00677
0.00686
0.00694
0.00703
0.00712
0.00722
0.00732
0.00742
0.00753
0.00764
0.00776
0.00788
0.00801
0.00815
0.00828
0.00843
0.00858
0.00874
0.00890
0.00907
0.00924
0.00942
0.00960
0.00979
0.00998
0.01018
94
-------
Appendix B: Precipitation Station Data
Table B-l Data from the four stations used to represent rainfall in the upper reservoirs when
paired with flow data from the upper reservoirs (NOAA,2013).
Year
1980
1981
1982
1986
1987
1988
1989
1990
1995
2002
2005
2009
2010
2011
Station Name
Sabana Grande
1267.46
1678.94
1153.67
1589.02
1393.44
1760.98
1536.70
1392.43
1755.65
1531.37
1171.19
1386.33
1487.42
Yauco 1
1056.39
1082.55
1388.11
1223.77
1046.48
1452.12
1079.25
892.56
1552.70
1299.72
1641.35
Adjuntas Substation
1912.37
1927.61
1639.82
1821.94
1866.39
1531.11
2008.12
1974.09
1943.35
1786.64
2310.89
1876.81
2551.18
2292.60
Indiera Alta
2027.17
2151.13
1671.32
1851.91
1908.81
1503.93
2430.53
Year's Average
1735.67
1919.22
1380.30
1586.36
1639.19
1504.95
1755.46
1606.21
1511.30
1478.28
1798.32
1449.24
1859.62
1890.01
Omitted years were missing more than one month of precipitation data. Years that are highlighted are
missing one month of data from their total. For Yauco and Adjuntas stations these years still had total
precipitation values that were above that station's average. Sabana Grande data for 1990 and 2010 are
below both the station average and that year's average from the four stations. Both years with a
missing month of data for Indiera Alta (1987 & 1988) are below the station's average, but are at or
above the average from the four stations for that year. Although Indiera Alta station has the highest
average precipitation values, absence of the station's data after 1990 did not seem to have a significant
impact. Substituting data from nearby stations (Adjuntas 1 NW, when available) or substituting with
the station's average value decreased the correlation between precipitation and flow through Yauco 1.
This may be due to a general increasing trend in precipitation from the 1990s to the 2000s.
Table B-2 Summary Statistics for Station Data Used for Upper Watersheds
Station Name
Sabana Grande
Yauco 1
Adjuntas Substation
Indiera Alta
Average
1469.59
1246.82
1960.21
1934.97
Standard Deviation
200.39
239.09
268.99
306.51
COV
0.136
0.192
0.137
0.158
95
-------
Figure B-l Linear Regression between Yauco 1 Flow (Table 5-4) and Station Precipitation (Table B-l)
Yauco 1 Flow (MGD) Linear Regression
7n
"ZZ" fin
Q DU
(S
^ cn -
s-
> 4U -
_O
u- an .
T-H
O on -
(j ^U
3
J" m -
>- 1U
y = 0.0328X - 20.48 +
Rz = 0.1885
* * ^v ^*
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Average of Station Precipitation (mm)
Figure B-2: Logarithmic Trend between Yauco 1 Flow (Table 5-4) and Station Precipitation (Table B-l)
Yauco 1 Flow (MGD) Logarithmic Trend
7n
IT" fin
(S
^ c;n -
£.
S An -
_o
LL. on -
t-H
o on -
3
.ro m -
> 1U
y = 55.836ln(x)- 379.67 4
Rz = 0.2005
* *
* * ~^E *" ^
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Average of Station Precipitation (mm)
96
-------
Figure B-3: Linear Regression between Yauco 1 Flow (Table 5-4) and Average Station Precipitation
(Table B-l) omitting data From 1981.
Linear Regression without 1981
vn
Q 60 -
5 ^n -
5 An -
_o
U- 30
u
m 10 -
Q
.0466x - 41.775
R2 = 0.3138
« _^^
* * _*^^^^ +
"""""""
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Average of Station Precipitation (mm)
Figure B-4: Linear Regression between Yauco 1 Flow (Table 5-4) and Average Station Precipitation
(Table B-l); omitting data from 1981 and 1980.
Linear Regression without 1980 or 1981
vn
(D
=
5 An -
g 40
LL. 7n
tH
(j
3
0 -
y = 0.053x - 50.683 *
R2 = 0.4237
^ ~~~"^
* + Jl~--~~~~~~~~~~
^ ^r
^~^^*
^
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Average of Station Precipitation (mm)
97
-------
Figure B-5: Linear regression between Yauco 1 Flow (Table 5-4) and Average Station Precipitation
(Table B-l); where Yauco Station average values have been substituted for missing years 1980 and
1981.
Linear Regression with adjusted 1980 and 1981
7fl
Q fin
0 bu
5 sn
5 An
_o
LL. Of)
iH
o 9n
o zu
ra 10
y - 0.048 Ix - 44. /43
R2 = 03311
* _^~^
* * ±f^ *
_- -^ *
+
* 4
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
Average of Station Precipitation (mm)
Figure B-6: Linear Regression between Yauco 1 Flow (Table 5-4) and Average Station Precipitation
(Table B-l), where Adjuntas 1 NW Station Data were substituted for Indiera Alta after its closer (1990-
2011).
Linear Regression with Adjuntas 1 NW after 1990
70
(D
I.50
0
" 30
rH
O 20
3
>
0
y = 0.021x- 2.1713
» A
R* = 0.1296 ^
+ 4^
^ - ^ ^r
^ ^
A
*
i i i i i i i
1000 1200 1400 1600 1800 2000 2200 2400
Average of Station Precipitation (mm)
98
-------
Appendix C: Building a Bayesian Belief Network and Node Equations
Bayesian belief networks (BBN; also called Bayesian networks, Bayes nets, probability networks) are directed
acyclic graphs structured to represent conditional independence among variables. Nodes (typically displayed as
circles or boxes) in a BBN represent variables, and arcs (displayed as arrows) are used to indicate a conditional
relationship between the parent (originator) and child (receiver) nodes. There are several software programs
that allow users to build BBNs and generate probability calculations. For this study, Netica (Norsys, 2000)
software was used and all BBN diagrams are Netica output.
A simple example BBN is useful for discussion: it is intuitive that rain is more likely on a day with cumulonimbus
clouds overhead. Nodes and arrows to represent this situation would show a parent node for variable Clouds
with an arc pointing toward the child node for the variable Rain. In this example, Clouds is considered a 'root
node because it is without parents influencing its outcome in the model. This does not mean that variables like
humidity and temperature don't affect cloudiness, but they are not represented in the model. Bayesian
networks have three levels of representation that make them attractive for solving complex problems (Howard
& Matheson, 2005). The first level (relation) reflects the relationships among variables (Fig. C-l). In this case,
the diagram depicts a relationship between clouds and rain.
Clouds
(J^ajnj
Figure C-l. The first level of a BBN characterizes a cause-effect relationship but does not quantify it. In the
example, the presence of cumulonimbus clouds is known to have an effect on the probability of rain.
The second level (number) is where prior distributions are assigned to root nodes (Fig. C-2). A variable's 'prior
distribution' characterizes the uncertainty about the value (state) that variable holds. The states identified for a
node must be mutually exclusive, meaning that states do not overlap. The states must also be collectively
exhaustive, meaning they represent all of the values a variable can take. In the example, clouds are either
present or absent, and there is either rain or no rain; the variables cannot maintain both states simultaneously.
For root nodes, the prior probability distribution reflects the uncertainty over its possible values. In the
example, prior probabilities are known for both nodes: on any given day, there is a 60% probability
cumulonimbus clouds will be present and on any given day there is a 40% chance there will be rain. This
reflects our prior beliefs about rain because even if the Clouds node were removed from the network Rain
would retain the same probability.
99
-------
Present
Absent
Clouds
60.CT
40.0
Rain
Rain
No Rain
Figure C-2. The second level of a BBN assigns a prior distribution, which is the probability of occurrence without
considering any other factors. In the example, there is a 60% chance of clouds on any given day and a 40% chance
of rain on any given day. The 'belief bars' are simply a horizontal histogram showing the distribution between the
two states of each node. The quantitative relationship between clouds and rain has not been incorporated in this
BBN although the cause-effect association is shown.
The third level (function) provides probabilistic evidence for the strength of relationships between different
nodes. Each relationship between a child node and its parent requires a conditional probability, which
describes the strength of the relationship and the conditional probability of every combination of parent and
child states. These are captured in a Conditional Probability Table (CRT). For child nodes this evidence is stored
as the conditional probability of every combination of parent and child value (state). Root nodes have CRT
tables as well, but these CRTs contain the unconditional or marginal probability distributions for the node's
possible states, without considering the condition of any other nodes. Observations can be input to the model
and this will change the prior probability for rain to a posterior probability (Fig. C-3), which characterizes the
probability of a node having a particular state when given the state of a parent node. Reading the conditional
probability table, there is a 60% chance of rain on any day when cumulonimbus clouds are present and a 10%
chance when they are absent.
Clouds
Present
Absent
o
Rain
Rain 60c
No Rain 40.0
Clouds
Present
Absent
Rain
60
10
No Rain
40
90
Figure C-3. A BBN diagram (left) shows the posterior probability for rain after an observation has been made for
the presence of clouds (100% probability clouds are present). The conditional probability table for this
relationship (right) shows the percent probabilities for rain given presence or absence of clouds.
100
-------
Conditional Probability Tables (CPT) can be constructed from a) frequencies built from standard statistical
methods for developing probabilities and entered directly, as in the cloud example, b) from observations such
as counts or c) from equations, either deterministic or probabilistic.
Direct counts (which are called 'case files' in Netica) are used to learn probabilities from observed occurrences
(b, above). Paired data from a daily log of cloudiness and rain during a previous year, for example, can be
entered into the program which will automatically calculate the posterior probabilities and enter them into the
CPT. As new data sets or distributions are entered the program can integrate them with former data sets.
When mechanistic or probabilistic equations are used to generate a CPT (c, above), the software generates
random values to apply in the equation, and this provides projected outcomes that are then entered
(automatically) as though they were count data (b, above). The software does this by assigning the outcome
from each random value to one of several bins (ranges within all possible outcomes), thereby establishing the
probability of occurrence for each bin. The number of random values that are used to generate probabilities for
the CPT can be set within the program.
Mechanistic equations are deterministic, where one value for a parent node results in a single value for the
child node. The equation could be extremely simple, like y = x + 1, where y is the child node and x is the parent.
For mechanistic equations, the software randomly selects values for x based on their frequency of occurrence.
Uncertainty is transferred into child nodes because of the uncertainty in the parent node.
Entering probabilistic equations into the software typically requires three pieces of information to characterize
their distribution (Fig. C-4):
1) Type of distribution (e.g., a normal distribution as shown in Fig. C-4.)
2) 1st moment for the distribution, typically the mean
3) 2nd moment for the distribution, which typically describes the variation around the mean
These input requirements are a generalization and may change depending on the type of the distribution.
Normal distributions and their derivatives (e.g., lognormal distribution) are the most common and will be the
only distribution type described here. Netica requires probability equations to be entered using a specific
format. The name of the variable and the parent variables must appear on the left side of the equation. For
prior distributions this is simply p(x), where x is the name of the root node; and for posterior distributions it is
entered as:
p(child_variable | parent_variable) =
which is read as "the probability of the child variable given the parent variable".
The variables (nodes) involved will always appear on both sides of the equation. Being listed on the left of the
equation means that the variables (nodes) are related (1st level). How a prior for a root node is defined (2nd
level) and how variables relate (3rd level) is defined by the right of the equation.
How the distribution is characterized goes on the right side of the equation. For a root node (x) with a normal
distribution this would be:
p(x)=[l/(o sqrt(2n))] exp (-[(x-u)/ o]A2/2)
101
-------
where u. is mean, o is standard deviation and x gets a random value picked by the software based on the
frequency the variable (node) would have that value. This also helps explain why x appears on the left side of
this equation, because x is the variable this distribution describes. If for example, x were randomly selected the
value 1, the equation would read "probability (1) =" and the value 1 would be substituted in on the right to get
a probability for the value equaling 1.
Netica has functions that can be used to replace the long equations that describe the common distributions.
For a normal distribution, the above equation is simply replaced by entering p(x) = NormalDist(x, [i, a), where x
is the name of the node (variable), u. is the mean and o is the standard deviation. The format (notation) for
entering these parameters in the equation is specific to each type of distribution, and can be found in the
program's index.
Figure C-4: A normal distribution with the first moment (u. = mean) and second moment (a = standard deviation)
indicated. In Netica, the probabilistic equation is entered as p(variable) = NormalDist(variable, u, a).
The equations for each of the nodes in the BBN (Fig. 6-15) have been summarized based on the type of data
used to generate the node's distribution (C-l Root nodes; C-2 nodes that used direct input of data; C-3 Nodes
based on mechanistic equations)
Table C-l Root Nodes
Node
Annual Precipitation
(mm)
Sediment From
Upper Reservoirs
Start Water Storage
Capacity (T0) Mm3
Distribution
Normal
Asymetrical
Triangular
Uniform
Equation
p(Annual_Precipitation | )= NormalDist (Annual_Precipitation,
1897, 379)
p(Sediment_From_Upper_Reservoirs | )=
TriangularEnd3Dist(Sediment_From_Upper_Reservoirs, 10997, 0, 21502)
102
-------
Table C-2 Direct Input Nodes
Node
Water Flow From Upper Reservoirs
Start Water Storage Capacity (T0) Mm3
Lucchetti Sediment Delivery (m3/y")
Source
Table
USGS Survey (Soler-Lopez, 2001a)
R Script (Appendix D)
Table C-3 Mechanistic Nodes
Node
Total Sediment Delivery (m3/yr)
Total Inflow of Water (Mm3)
Sediment Trapped in Lago Lucchetti (Mm3/yr)
End Water Storage Capacity (Ti) (Mm3)
Reservoir Life Expectancy (Yrs to 0)
Equation
Total_Sediment (Lucchetti_Sediment_Delivery, Upper_Sediment) =
Upper_Sediment + (45.09*Lucchetti_Sediment_Delivery)
Total_lnflow (Tunnel_Flow, Annual_Precipitation) =
Tunnel_Flow+(((Annual_Precipitation *45.09) *0.001) *0.38)
Sediment_Trapped(Capacity, TotaMnflow, Total_Sediment) =
(0.97A(0.19A(loglO
(Capacity/Total_lnflow)))*Total_Sediment)/1000000
End_Capacity (Capacity, Sediment_Trapped) =
Capacity - (Sediment_T rapped/1000000)
Reservoir_Life (End_Capacity, Sediment_Trapped) =
End_Capacity/Sediment_Trapped
Further development ofBayesian Belief Networks
As more data is collected and analysis gets more detailed, BBNs often develop from using qualitative variables
(such as light rain and heavy rain) into more quantitative variables (such as rainfall in mm). Quantitative nodes
are often continuous variables, meaning they could have virtually any value within a range. For example, rain
depths between 1 mm and 2 mm could equal 1.1 mm, 1.01 mm, 1.001mm, and so on. This quickly makes
defining exhaustive probability distributions very computationally intensive. The solution is to discretize the
continuous variable into states defined by ranges (Fig. C-5). Discretization divides the continuous probability
distribution into bins (ranges of values).
Figure C-5. Left: Continuous probability distribution with normal shape. Right: Normal probability distribution
broken into 9 bins through discretization.
103
-------
Discretization of continuous variables can cause loss in statistical power and has been called the "Achilles heel"
of Bayesian networks (Fenton et al., 2008). If too few bins are used, thresholds or important details may be
lost. If too many bins are used, computing time increases and some outlier values (observational data that are
numerically distant from the rest of the data set) may be given too much weight.
Another important aspect of BBNs is the ability to aggregate or merge (fold) different networks. For example, a
network representing the causes for cloudiness could be added to the existing network. This is useful for a
more comprehensive 'systems' approach to solving a problem.
Once a BBN has data and relationships entered, it can be queried to calculate probable outcomes of scenarios .
The calculations can propagate to both upstream and downstream variables in the network depending on the
network structure, the existing evidence in the network, and resulting relationship dependencies (Schachter
and Heckermann, 1987). Thus, observed variables (measured indicators) might be queried to find the likely
status of unobserved variables.
Discretization
The constructed BBN (Fig. 7-7) can be used to estimate the life expectancy of Lucchetti Reservoir under
different scenarios. Each scenario will alter values in the network's nodes, at times significantly changing these
values from what they were when the categories that summarize these values were decided on. It is
particularly important to re-examine the discretization of nodes that contain outputs useful to decision-makers.
In this case Lucchetti Reservoir Life Expectancy, End Water Storage Capacity (Ti), and Sediment Trapped in
Lucchetti Reservoir are all output nodes that are meaningful to decisions and must convey the data as
accurately as possible. Some examples of the effects of discretization on distributions and summary statistics
follow, using data from the Lago Lucchetti BBN.
When choosing a discretization there are two decisions to make, where to set the upper and lower intervals
and how many intervals (categories) to use. The upper and lower range limits can extend to (+/-) infinity,
meaning that > and < symbols can be used in the node. For summary statistics, the actual value is used (i.e.
>=0.3 is averaged as 0.3). Fig. C-6 shows Sediment Trapped in Lago Lucchetti using >=0.3, >=0.4 and >=0.5 at
the upper extent. When a change in discretization doesn't cause a change in summary statistics (e.g., Fig. C-6
center vs. C-6 right) it is assumed that both are adequate for discretization and the tighter limit can be chosen.
Sediment Trapped in Lago Lucchetti (Mm3fyr)
0 to 0.1 10.5
0.1 to 0.15 18.7
0.15 to 0.175 22.3
0.1 75 to 0.2 24.4
0.2 to 0.225 14.0
0.225(00.25 5.43
0.25 to 0.3 2.17
>= 0.3 2.49
^"
0.167 ±0.059
Sediment Trapped in Lago Lucchetti (Mm3/yr)
0 to 0.1 10.5
0.1 to 0.15 18.7
0.1 5 to 0.1 75 22.3
0.175 to 0.2 24.4
0.2 to 0.225 14.0
0.225 to 0.25 5.42
0.25 to 0.3 2.17
0.3 to 0.4 1.86
>= 0.4 0.63
i
0.169 ±0.063
Sediment Trapped in Lago Lucchetti (MmSlyr)
0 to 0.1 10.5
0.1 to 0.15 18.7
0.15 to 0.175 22.3
0.175 to 0.2 24.4
0.2 to 0.225 14.0
0.225 to 0.25 5.43
0.25 to 0.3 2.17
0.3 to 0.4 1.85
0.4 to 0.5 0.62
>=0.5 .013
^^^
0.1 69 ±0.063
Figure C-6. Comparison of three different discretization approaches. The average and standard deviation were
identical in nodes with >+0.4 and >=0.5, so both are considered adequate.
104
-------
Generally it is better to have a higher number of intervals between upper and lower limits (finer resolution).
The exception to this is when nodes are based directly on paired observation data, where using more intervals
than the original data had will negatively impact results. Most of the BBN nodes in this analysis are equation
based, and increasing the number of intervals until the summary statistics no longer show a change is the
conventional approach that was used here (Fig. C-7). Going from five even intervals (Fig. C-7 far left) to 41
intervals (Fig. C-7 center left) showed an improvement, but increasing the number of intervals further to 61
(Fig. C-7 center right) did not. By using uneven intervals (Fig. C-7 far right) the total number of intervals may
also be decreased without changing the accuracy of the node's summary statistics.
105
-------
Sediment Trapped in Lago Lucclietti (HmSfyii
0 to 0.1 10.5 1
0.1 to 0.2 65.4 Mbdil
02to0.3 216
0.3 to 0 4 1 85
>=0.4 0.63
0.167 ±0.071
Sediment Trapped in Lago Lutthetb (Mm3hfl
0 to 0.01 0.91
0.01 to 0.02 0.91
0.02 to 0.03 0.91
0.03100.04 0.91
0.04 to 0.05 1.03
0.05to0.06 1.16
O.OStoO.07 1.17
0.07100.08 1.16
0.08to0.09 1.17
0.09to 0.1 1.17
0.1 to 0.11 1.23
0.11 to 0.12 2.05
0.12to0.13 2.45
0.13to0.14 5.32
0.14to0.15 7.58
0.15100.16 8.45
0.16 to 0.17 8.92
0.17to0.18 10.1
0.18to0.19 10.2
0.19 to 0.2 3.02
0.2to0.21 6.67
0.21 to 0.22 5.34
0.22to0.23 3.57
0.23 to 0.24 2.34
0.24to0.25 1.54
0.25 to 0.26 1.02
0.26to0.27 0.54
0.27 to 0.28 0.24
0.28 to 0.29 0.19
0.29to0.3 0.19
0.3 to 0.31 0.19
0.31 to 0.32 0.19
0.32to0.33 0.19
0.33 to 0.34 0.19
0.34100.35 0.19
0.35 to 0.36 0.19
0.36 to 0.37 0.19
0.37to0.38 0.19
0.38 to 0.39 0.19
0.39to0.4 0.18
s- 0.4 0.63
^^B
^^^m
i^^H
^^^
^p
^m
«
0.17*0.06
Sediment Trapped in Lago LuccheUi (Mn^Vr)
Ob (U)l 0.9!
O.OIbO.O: 0.91
(i.i): b (1.0 :. 0.91
0. (1st (1.04 0.91
(1.04 b (U)5 1.0:
0. 05 b 0.055 0.55
0.055 b 0. »h 0.5!
0.06 b d.065 0.5*
0.065 b 0.07 0.5!
0.07 b 0.075 0.55
0.075*0.0* 0.51
0.05 * O.OtS 0.55
0.055 fcO.OM 0.5!
0.09 * 0.0)5 0.55
0.095 b O.I 0.51
0. ibD. 105 0.59
O.IOSbO. II 0.64
0.11*0.115 0.93
0. 1 15 b 0. ii 1.1!
0.12*0.125 1.11
0.125*0.11 1.21
0.13*0.135 I(i4
0.115*0.14 J.JO
0.14*0.145 J.71
0.145*0.15 i.55
0.15*0.155 4.15
0. 155b0.ii. 4JO
O.K* 0.1(5 4.i'l
0.1(5*0.17 4.55
0.17*0.17! 4.95
0.175*0.11 5.22
0. 1!b0. 155 5.20
0.115*0.19 5.0J
0.19*0.195 4.74
0.195*0.2 4.25
0.2 * 0.205 1.57
0.205*0.21 J.10
0.21*0.215 2.13
0.215*0.22 2.52
0.22*0.225 2.01
0.225*0.23 1.5i
0.2J * 0.235 1.21
0.235*0.24 1.05
0.24*0.245 0.15
0.245*0.25 0.69
0.25 * 0.2! 1.02
0.2(*0.27 0.5J
0.27 * 0.2( 0.24
0.21*0.29 .19
0.29*0.3 .19
0.3*0.31 .19
O.J 1*0.32 .19
0.32*0.33 .19
0.33*0.34 .19
0.34*0.35 .19
O.J5*0.3( .19
0.3(*O.S7 .19
0.37*0.31 .19
0.3t*0.39 .19
0.39*0.4 .11
;-=0.4 0.63
1
1
1
1
1
^
^^m
^^H
^^B
^^m
^^^^H
^^^^
^^^B
^^^^
^^^^^
^^H
^^^^
^^^B
^^^f
^^_
~
^m
HH
B
m
m
i
i
i
i
0.17±0.0(
Sediment Tra|
0 to 0.025
0.025 to 0.05
0.05to 0.075
0.075 to 0.1
0.1 to 0.11
0.11 to 0.12
0.12to0.13
0.13 to 0.14
0.14to0.15
0.15to0.16
0.16to0.17
0.17 to 0.18
0.18 to 0.19
0.19 to 0.2
0.2 to 0.21
0.21 to 0.22
0.22to0.23
0.23 to 0.24
0.24to 0.25
0.25 to 0.275
0.275to0.3
0.3to 0.325
0.325 to 0.35
0.35to 0.375
0.375to0.4
s=0.4
ped in Lago Lucchetd O.lniJfjn
2.28
2.39
2.91
2.91
1.23
2.06
2.46
5.33
7.56
8.45
8.94
10.1
10.2
9.01
6.68
5.34
3.57
2.34
1.54
1.70
0.43
0.47
0.47
0.47
0.46
0.63
1
^i
^^H
^^^m
^^^H
^^^^m
^^^^m
I^^^H
^^H
^^
^m
m
i
0.17 ± 0.06
Figure C-7. Demonstration of the effect of discretization on summary statistics using data from the Lago Lucchetti BBN.
Coarse discretization (far left; 5 even intervals) may not provide the accuracy or precision needed. Fine discretization
(middle left; 41 even intervals) alters the summary statistics. Increasing the number of intervals (middle right; 61 even
intervals) did not show any change in summary statistics so the 41 intervals was adequate. Reducing the number of
intervals (far right; 26 uneven intervals) without changing summary statistics can be achieved by using smaller intervals for
maximum and minimum categories.
106
-------
A second example from the Lucchetti BBN shows how different scenarios will change the values in nodes in a
way that makes the original discretization less useful. In this example, the results for Sediment Trapped in
Lucchetti Reservoir varied in response to changing precipitation. The discretization originally selected (Fig. C-8,
left) provided a distribution curve in the middle of the category ranges. When precipitation was changed (not
shown) the values in the sediment trapped node moved higher and lower within the original discretization.
When the values move to the edge of the category range the distribution becomes lumped and less
meaningful.
Sediment Trapped in Lago Lucchetti (Mm3fyi)
0 to 0.025
0.025 to 0.05
0.05 to 0.075
0.075 to 0.1
0.1 to 0.11
0.11 to 0.12
0.12to0.13
0.13to0.14
0.14to0.15
0.15to0.16
0.16to0.17
0.17to0.18
0.18to0.19
0.19 to 0.2
0.2 to 0.21
0.21 to 0.22
0.22 to 0.23
0.23 to 0.24
0.24 to 0.25
0.25 to 0.275
0.275 to 0.3
0.3 to 0.325
0.325 to 0.35
0.35 to 0.375
0.375 to 0.4
>=0.4
2.28
2.33
2.91
2.92
1.24
2.05
2.46
5.34
7.56
8.44
8.94
10.1
10.2
9.01
6.66
5.35
3.57
2.34
1.54
1.69
0.47
0.46
0.47
0.47
0.46
0.63
M
^M
^^M
^^^
^^^m
^^^M
^^^i
^^^m
^^m
^M
M
0.17 ±0.06
Sediment Trapped in Lago Lucchetti (MmSfyi)
0 to 0.025 0
0.025 to 0.05 0
0.05 to 0.075 0
0.075 to 0.1 0
0.1 to 0.11 0
0.11 to 0.12 0
0.12to0.13 0 +
0.13 to 0.14 .004
0.14to0.15 .052
0.15to0.16 0.24
0.16to0.17 0.42
0.17to0.18 0.84
0.18 to 0.19 1.99
0.19to0.2 5.45
0.2to0.21 9.93
0.21 to 0.22 12.7
0.22 to 0.23 15.3
0.23 to 0.24 14.1
0.24 to 0.25 9.69
0.25 to 0.275 10.7
0.275 to 0.3 2.99
0.3 to 0.325 2.93
0.325 to 0.35 2.93
0.35 to 0.375 2.94
0.375 to 0.4 2.90
>= 0.4 3.98
I
1
M
^^m
^^^
^^^M
^^^m
^^
^^H
0.25 ± 0.057
Sediment Trapped in Lago Lucchetti (Mm3fyi)
0 to 0.025 14.4
0.025 to 0.05 15.1
0.05 to 0.075 18.4
0.075 to 0.1 18.4
0.1 to 0.11 7.28
0.11 to 0.12 6.85
0.12to0.13 6.27
0.13 to 0.14 4.97
0.14to0.15 2.76
0.15to0.16 2.16
0.16to0.17 1.65
0.17to0.18 1.23
0.18to0.13 0.60
0.19 to 0.2 .082
0.2 to 0.21 .001
0.21 to 0.22 0 +
0.22 to 0.23 0 +
0.23 to 0.24 0 +
0.24to0.25 0 +
0.25 to 0.275 0
0.275 to 0.3 0
O.Sto 0.325 0
0.325 to 0.35 0
0.35 to 0.375 0
0.375 to 0.4 0
>= 0.4 0
^^_
^^^
^^^_
^^^H
^
H
H
m
m
i
0.0786 ± 0.045
Figure C-8. Comparison of probability distributions for Sediment trapped in Lago Lucchetti derived from different
decision scenarios (11.88). (Left) BBN using the probability distribution for Annual Precipitation and a Start
Water Storage Capacity of 11.88 Mm3. (Center) BBN with Annual Precipitation >=2276. (Right) BBN with Annual
Precipitation <1518.
Another example re-emphasizes how the range may need to be adjusted when input variables affect results. In
this example, the node End Water Storage Capacity (Ti) varies depending on the value set for Start Water
Storage Capacity (T0). Discretization was initially set by calculating the highest possible value and then
decreasing each category in even 0.02 Mm3 increments (Fig. C-9). This discretization worked well with several
Annual Precipitation scenarios (e.g., Fig. C-9 left, center). This discretization would work for performing
multiple iterations of the model, assuming only minor changes in starting water capacity. However, the
discretization did not work well when starting water capacity was changed significantly (Fig. C-9 right). This
suggests that discretizations must be adjusted anytime the Start Water Storage Capacity (T0) changes
significantly, which can occur after several iterations.
107
-------
El ill Water Stui
0 to 11. 44
11. 44 to 11. 46
11. 46 to 11. 43
11. 48 to 11. 5
11. 5 to 11. 52
11. 52 to 11. 54
11. 54 to 11. 56
11. 56 to 11. 53
11. 53 to 11. 6
11. 6 to 11. 62
11. 62 to 11. 64
11. 64 to 11. 66
11. 66 to 11. 68
11.68(011.7
11. 7 to 11. 72
11. 72 to 11. 74
11. 74 to 11. 76
11. 76 to 11. 78
11. 73 to 11. 8
11. 8 to 11. 82
11. 82 to 11. 84
11. 84 to 11. 86
11. 86 to 11. 88
11.881011.9
>= 1 1 .9
11
age Capacity (T1
0
0 +
0 +
0 +
.005
.038
0.29
2.15
0.37
0.78
2.56
5.90
12.0
19.2
19.1
16.0
7.79
3.29
2.33
2.33
2.19
1.82
1.82
0
0
712 + 0.056
) (Mm3)
I
I
^^m
^^^H
^^^H
^^^m
^m
End Water Storage C
0 to 11. 44
11.44to11.46
11.46 to 11. 48
11.481011.5
11. 5 to 11. 52
11.52 to 11. 54
11.54to11.56
11.56to11.58
11. 58 to 11. 6
11. 6 to 11. 62
11. 62 to 11. 64
11.64 to 11. 66
11. 66 to 11. 68
11. 68 to 11. 7
11. 7 to 11. 72
11. 72 to 11. 74
11. 74 to 11. 76
11. 76 to 11. 78
11.781011.3
11. 8 to 11. 82
11.82 1011.84
11. 34 1011.86
11. 36 1011.88
11.881011.9
«=1i.g
11.639 +
ipacity(T
0
0 +
0 +
.005
.031
0.24
1.85
13.6
2.35
4.89
16.1
29.3
22.7
7.43
1.26
0.30
.004
0 +
0
0
0
0
0
0
0
0.039
) (Mm3)
^f
I
^H
^^HB
^^H
End Water Storage Capacity IT
01011.44 0
11.44to11.46 0
11. 46 to 11. 48 0
11.481011.5 0
11.51011.52 0
11. 52 to 11. 54 0
11. 54 to 11. 56 0
11. 56 to 11. 513 0
11. 58 to 11. 6 0
11. 6 to 11. 62 0
11. 62 to 11. 64 0
11. 64 to 11. 66 0
11. 66 to 11. 68 0
11.681011.7 0
11.7to11.72 0
11. 72 to 11. 74 0
11. 74 to 11. 76 0
11. 76 to 11. 78 0
11.781011.8 0
11.81011.32 0
11. 82 to 11. 84 0
11. 84 to 11. 86 0
11. 86 to 11. 88 0
11. 88 to 11. 9 0
>=11.9 100
11.91 ±0.0058
)(
Mil
13)
Figure C-9. Comparison of End Water Storage Capacity (Ti) node discretization performance for (left) BBN using
the probability distribution for Annual Precipitation and Start Water Capacity 11.88 Mm3; (center) BBN with
Annual Precipitation >=2470 and Start Water Capacity 11.88; and (right) BBN using the probability distribution
for Annual Precipitation and Start Water Capacity 15.84 Mm3.
108
-------
Appendix D: R Script and referenced equations
ptm <- proc.time()
#This script generates R values for various R groups from a watershed
#Using multiple R values maintains pre-existing spatial variation
#Applying a distribution to the precipitation values used to calculate the R value
#also maintains variation overtime
#First all files are read into R and attached
# read in the monthly precipitation and erosivity density data from .csv
precip <- read.csv("C:/Users/jbousquin/Desktop/R_Files/precip2.csv", sep=",")
attach(precip)
#Next read in the data from GIS
smpl_cofl<- read.csv("C:/Users/jbousquin/Desktop/R_Files/Simple_Grids/smple_cofl.csv")
smpl_ncof2<- read.csv("C:/Users/jbousquin/Desktop/R_Files/Simple_Grids/smple_ncof2.csv")
smpl_scof3 <- read.csv("C:/Users/jbousquin/Desktop/R_Files/Simple_Grids/smple_scof3.csv")
smpl_scof4<- read.csv("C:/Users/jbousquin/Desktop/R_Files/Simple_Grids/smple_scof4.csv")
smpl_nlcdl<- read.csv("C:/Users/jbousquin/Desktop/R_Files/Simple_Grids/smple_nlcdl.csv")
#set parameter n as the number of samples
n <-100000
#Set parameter rainfall Coefficient of Variation (CoV) to be applied to the dataset for variation over time
CoV<-0.2
#set parameter rg as number of R groups from the file
rg <- nrow(precip)
#set average rainfall value for watershed
rain <-1897
#Designate dataset vectors for 1st and 2nd moment, to apply distribution to
mean Jan <- with(precip, ppt.jan)
std_jan <- meanJan*CoV
mean_feb <- with(precip, ppt.feb)
std_feb <- mean_feb*CoV
mean_mar <- with(precip, ppt.mar)
std_mar <- mean_mar*CoV
mean_apr <- with(precip, ppt.apr)
std_apr<- mean_apr*CoV
mean_may <- with(precip, ppt.may)
std_may <- mean_may*CoV
mean Jun <- with(precip, ppt.jun)
std_jun <- meanJun*CoV
mean Jul <- with(precip, ppt.jul)
stdjul <- meanJul*CoV
mean_aug <- with(precip, ppt.aug)
109
-------
std_aug <- mean_aug*CoV
mean_sep <- with(precip, ppt.sep)
std_sep <- mean_sep*CoV
mean_oct <- with(precip, ppt.oct)
std_oct <- mean_oct*CoV
mean_nov<- with(precip, ppt.nov)
std_nov <- mean_nov*CoV
mean_dec <- with(precip, ppt.dec)
std_dec<- mean_dec*CoV
#The following process will be looped n times, with each entry becoming a row in table x
z<- l:n
x <- matrix(nrow=0, ncol=9)
for(i in seq(along=z)){
#Produce random probability
rprob <- runif(l, 0,1)
#Get n random samples from the normal distribution around the moments
#The new value is sampled by the random probability for each original mean, rg X n
samplejan <- qnorm(rep(rprob, each=rg), meanjan, stdjan)
sample_feb <- qnorm(rep(rprob, each=rg), mean_feb, std_feb)
sample_mar<- qnorm(rep(rprob, each=rg), mean_mar, std_mar)
sample_apr<- qnorm(rep(rprob, each=rg), mean_apr, std_apr)
samplejmay <- qnorm(rep(rprob, each=rg), mean_may, stdjmay)
samplejun <- qnorm(rep(rprob, each=rg), meanjun, stdjun)
sample_jul <- qnorm(rep(rprob, each=rg), mean Jul, std_jul)
sample_aug <- qnorm(rep(rprob, each=rg), mean_aug, std_aug)
sample_sep <- qnorm(rep(rprob, each=rg), mean_sep, std_sep)
sample_oct <- qnorm(rep(rprob, each=rg), mean_oct, std_oct)
sample_nov<- qnorm(rep(rprob, each=rg), mean_nov, std_nov)
sample_dec <- qnorm(rep(rprob, each=rg), mean_dec, std_dec)
#Now multiply the monthly ppt values by the corresponding erosivity density value
rjan<- samplejan * precip$edjan
r_feb<- sample_feb * precip$ed_feb
r_mar<- sample_mar * precip$ed_mar
r_apr<- sample_apr * precip$ed_apr
r_may<- sample_may * precip$ed_may
rjun<- samplejun * precip$edjun
rjuk- samplejul * precip$edjul
r_aug<- sample_aug * precip$ed_aug
r_sep<- sample_sep * precip$ed_sep
r_oct<- sample_oct * precip$ed_oct
r_nov<- sample_nov * precip$ed_nov
r_dec<- sample_dec * precip$ed_dec
110
-------
#Now add the monthly R values together to get annual R values
r_annual <- (rjan + r_feb + r_mar + r_apr + r_may + rjun + rjul + r_aug + r_sep + r_oct + r_nov+ r_dec)
#To check the math
#write.csv(r_annual, "C:/Users/jbousquin/Desktop/USLE_exports/r_annual.csv")
#Now turn the list of possible values into a martix with 25 rows
r_matrix <- matrix(r_annual, nrow=rg, ncol=l)
#Make sure the matrix has the R groups IDs too
r_matrix <- cbind(r_matrix, R_ID)
#This completes phase 1
attach(smpl_nlcdl)
nlcdl <- merge(r_matrix, smpl_nlcdl, by.x= "R_ID", by.y = "r_group")
nlcdl <- cbind(nlcdl, nlcdl$Vl * nlcdl$LS5_K_CCOF)
nlcdl <- rbind(nlcdl, apply(nlcdl, 2, sum))
nlcdl_row<- nrow(nlcdl)
nlcdl_col <- ncol(nlcdl)
nlcd_l <- unlist(nlcdl [nlcdl_row, nlcdl_col])
detach(smpl_nlcdl)
attach(smpl_cofl)
cofl <- merge(r_matrix, smpl_cofl, by.x= "R_ID", by.y = "r_group")
cofl <- cbind(cofl, cofl$Vl * cofl$LS5_K_CCOF)
cofl <- rbind(cofl, apply(cofl, 2, sum))
cofl_row <- nrow(cofl)
cofl_col <- ncol(cofl)
cof_l <- unlist(cofl [cofl_row, cofl_col])
detach(smpl_cofl)
attach(smpl_ncof2)
ncof2 <- merge(r_matrix, smpl_ncof2, by.x= "R_ID", by.y = "r_group")
ncof2 <- cbind(ncof2, ncof2$Vl * ncof2$LS5_K_CCOF)
ncof2 <- rbind(ncof2, apply(ncof2, 2, sum))
ncof2_row <- nrow(ncof2)
ncof2_col <- ncol(ncof2)
ncof_2 <- unlist(ncof2 [ncof2_row, ncof2_col])
detach(smpl_ncof2)
attach(smpl_scof3)
scofS <- merge(r_matrix, smpl_scof3, by.x= "R_ID", by.y = "r_group")
scofS <- cbind(scof3, scof3$Vl * scof3$LS5_K_CCOF)
scofS <- rbind(scof3, apply(scof3, 2, sum))
111
-------
scof3_row <- nrow(scofS)
scof3_col <- ncol(scofS)
scof_3 <- unlist(scof3 [scof3_row, scof3_col])
detach(smpl_scof3)
attach(smpl_scof4)
scof4 <- merge(r_matrix, smpl_scof4, by.x="R_ID", by.y = "r_group")
scof4_l <- cbind(scof4, scof4$Vl * scof4$LS5_K * 0.0734)
scof4_l <- rbind(scof4_l, apply(scof4_l, 2, sum))
scof_4_l<- unlist(scof4_l [scof3_row, scof3_col])
y<-c(0.0734, 0.129)
scof4_2 <- cbind(scof4, rep(sample(y, 1, replace=TRUE), nrow(scof4)))
scof4_2 <- cbind(scof4, scof4$Vl * scof4$LS5_K * samplefy, 4832, replace=TRUE))
scof4_2 <- rbind(scof4_2, apply(scof4_2, 2, sum))
scof_4_2 <- unlist(scof4_2 [scof3_row, scof3_col])
#This last one should match scofS
scof4_3 <- cbind(scof4, scof4$Vl * scof4$LS5_K * 0.129)
scof4_3 <- rbind(scof4_3, apply(scof4_3, 2, sum))
scof_4_3 <- unlist(scof4_3 [scof3_row, scof3_col])
detach(smpl_scof4)
ptp <- qnorm(rprob, rain, rain*CoV)
xl <- cbind(rprob, ptp, nlcd_l, cof_l, ncof_2, scof_3, scof_4_l, scof_4_2, scof_4_3)
x <- rbind(x,xl)
write.csv(x, "C:/Users/jbousquin/Desktop/R_output.csv")
proc.time() - ptm
The following equation was used to calculate LS using Raster Calculator in ArcGIS 10.1. Since LS was originally developed
for a slope of 9% and length of 72.6 ft, all lengths and slopes had to be related to that reference LS. If slope <5% NN=05,
otherwise NN=0.3.
where LS = Con(100*Sin("pr_dslope" * (math.pi/180))<5, (0.065 + 0.0456 * (100*Sin("pr_dslope" * (math. pi/180))) +
0.006541 * Power (100*Sin("pr_dslope" * (math. pi/180)), 2)) * Power (30/22.1, 0.3), (0.065 + 0.0456 *
(100*Sin("pr_dslope" * (math. pi/180))) + 0.006541 * Power (100*Sin("pr_dslope" * (math. pi/180)), 2)) * Power (30/22.1,
0.5))
112
------- |