Lin S.D. Water and Wastewater Calculations Manual

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Chapter

Lakes and Reservoirs

1 Lakes and Impoundment Impairments 125

2 Lake Morphometry 126

3 Water Quality Models 130

4 Evaporation 131

4.1 Water budget method 132

4.2 Energy budget method 132

5 The Clean Lakes Program 137

5.1 Types of funds 138

5.2 Eligibility for ﬁnancial assistance 138

5.3 State lake classiﬁcation survey 139

5.4 Phase 1: Diagnostic/feasibility study 140

5.5 Phase 2: Implementation 145

5.6 Phase 3: Post-restoration monitoring 145

5.7 Watershed protection approach 146

5.8 In-lake monitoring 146

5.9 Trophic state index 156

5.10 Lake use support analysis 158

5.11 Lake budgets (ﬂuxes) 168

5.12 Soil loss rate 173

References 176

This chapter includes mainly lake morphometry, evaporation, and the

Clean Lakes Program (CLP). Since most lake management programs in

the United States are based on the CLP, the CLP is discussed in detail.

Regulatory requirements and standardization of research and applica-

tion are provided with a focus on the Phase 1, diagnostic/feasibility study.

1 Lakes and Impoundment Impairments

Lakes are extremely complex systems whose conditions are a function

of physical, chemical, and biological (the presence and predominance of

125

the various plants and organisms found in the lake) factors. Lakes

inherently function as traps or sinks for pollutants from tributaries,

watersheds (drainage basins) or from atmospheric deposits and

precipitation.

Like streams, lakes are most often impaired by agricultural activ-

ities (main sources in the United States), hydrologic/habitat modifi-

cation (stream channelization), and point pollution sources. These

activities contribute to nutrient and sediment loads, suspended solids,

and organic matter, and subsequently cause overgrowth of aquatic

plants. The resulting decline in water quality limits recreation,

impairs other beneficial uses, and shortens the expected life span of

a lake.

Common lake problems are eutrophication, siltation, shoreline ero-

sion, algal bloom, bad taste and/or odor, excessive growth of aquatic

vegetation, toxic chemicals, and bacterial contamination. Eutrophication,

or aging, the process by which a lake becomes enriched with nutrients,

is caused primarily by point and nonpoint pollution sources from

human activities. Some man-made lakes and impoundments may

be untrophic from their birth. These problems impact esthetic and

practical uses of the lake. For example, the growth of planktonic algae

in water supply impoundments may cause taste and odor problems,

shortened filter runs, increased chlorine demand, increased turbidity,

and, for some facilities, increased trihalomethane precursors. The effects

ultimately lead to increased water treatment costs and, in some

instances, even to abandonment of the lake as a public water supply

source.

Lakes and reservoirs are sensitive to pollution inputs because they

flush out their contents relatively slowly. Even under natural condi-

tions, lakes and reservoirs undergo eutrophication, an aging process

caused by the inputs of organic matters and siltation.

2 Lake Morphometry

Lake morphometric data can be calculated from either a recent hydro-

graphic map or a pre-impoundment topographic map of the basin. In

general, pre-impoundment maps may be obtainable from the design

engineering firm or local health or environmental government agencies.

If the map is too old and there is evidence of significant siltation, sec-

tions of the lake, such as the upper end and coves with inflowing

streams, will need to be remapped.

In some cases, it is necessary to create a new lake map. The proce-

dures include the following:

126 Chapter 2

1. The outline of the shoreline is drawn either from aerial photographs

or from United States Geological Survey (USGS) 7.5-minute topo-

graphic maps.

2. The water depth for transacts between known points on the shore-

line of the lake is measured by a graphing sonar.

3. The sonar strip chart of the transacts is interpreted and drawn on

to an enlarged copy of the lake outline.

4. Contours may be drawn by hand or with a computer on the map.

5. All maps are then either digitized or scanned and entered into a geo-

graphic information system (GIS).

6. Coverages are then converted into sea level elevations by locating

the map on a 7.5-minute USGS topographic map and digitizing ref-

erence points both on the map and on the quadrangle for known sea

level elevations.

7. Depths are assigned to the contour. The GIS gives the length of

each contour and areas between adjacent contour lines.

From this data, surface area, maximum depth of the lake, and shore-

line length can be computed. Lake volume (V ), shoreline development

index (SDI) or shoreline configuration ratio, and mean depth ( ) can

be calculated by the formula in Wetzel (1975):

1. Volume

(2.1)

where V ⫽ volume, ft

, acre ⭈ ft, or m

h ⫽ depth of the stratum, ft or m

i ⫽ number of depth stratum

⫽ area at depth i, ft

, acre, or m

2. Shoreline development index

(2.2)

where L ⫽ length of shoreline, miles or m

⫽ surface area of lake, acre, ft

, or m

SDI 5

2!p 3 A

V 5

⌺

i50

1 A

i11

1 2A

3 A

i11

Lakes and Reservoirs 127

3. Mean depth

(2.3)

where ⫽ mean depth, ft or m

V ⫽ volume of lake, ft

, acre ⭈ ft, or m

⫽ surface area, ft

, acre, or m

Other morphometric information also can be calculated by the follow-

ing formulas:

4. Bottom slope

(2.4)

where S ⫽ bottom slope

⫽ mean depth, ft or m

⫽ maximum depth, ft or m

5. Volume development ratio, V

(Cole, 1979)

(2.5)

6. Water retention time

(2.6)

where RT ⫽ retention time, year

7. Ratio of drainage area to lake capacity R

(2.7)

Example: A reservoir has a shoreline length of 9.80 miles. Its surface area is

568 acres. Its maximum depth is 10.0 ft. The areas for each foot depth are 480,

422, 334, 276, 205, 143, 111, 79, 30, and 1 acres. Annual rainfall is 38.6 in. The

watershed drainage is 11,620 acres. Calculate morphometric data with the for-

mulas described above.

solution: Compute the following parameters:

R 5

drainage area, acre or m

storage capacity, acre

ft or m

RT 5

storage capacity, acre

ft or m

annual runoff, acre

ft/yr or m

/yr

5 3 3

S 5

D 5

128 Chapter 2

1. The volume of the lake

2. Shoreline development index or shoreline configuration ratio

⫽ 2.93

3. Mean depth

⫽ 4.14 ft

4. Bottom slope

5. Volume development ratio

5 3 3

5 3 3 0.41 5 1.23 sor 1.23:1d

S 5

4.13 ft

10.0 ft

5 0.41

2354 acre

568 acres

9.80

3.34

9.80 miles

2!3.14 3 0.8875 sq. miles

SDI 5

2!p 3 A

5 568 acres 5 568 acres 3

1 sq. miles

640 acres

5 0.8875 sq. miles

5 2,902,000m

5 2354sacre

ftd

[7062]

1 s422 1 324 1 2422 3 324

d 1

1 s30 1 1 1 230 3 1d]

[s568 1 480 1 2568 3 480d 1 s480 1 422 1 2480 3 422d

V 5

⌺

i50

1 A

i11

1 2A

3 A

i11

Lakes and Reservoirs 129

6. Water retention time

Storage capacity V ⫽ 2354 acre ⭈ ft

⫽ 0.063 years

7. Ratio of drainage area to lake capacity

3 Water Quality Models

Lakes and reservoirs are usually multipurpose, serving municipal and

industrial water supplies, recreation, hydroelectric power, flood control,

irrigation, drainage, and/or agriculture, due to the importance of pro-

tecting these natural resources. Water quality involves the physical,

chemical, and biological integrity of water resources. Water quality stan-

dards promulgated by the regulatory agencies define the water quality

goals for protection of water resources in watershed management.

Modeling the water quality in lakes and reservoirs is very different

from that in rivers (Chapter 1) or estuaries. A variety of models are

based on some of physical, chemical, and biological parameters and/or

combinations. Physical models deal with temperature, dissolved oxygen

(DO), energy budget diffusion, mixing, vertical and horizontal aspects,

seasonal cycles, and meteorological data setting. Chemical models

involve mass balance and toxic substances. Biological models deal with

nutrients and the food chain, biological growth, perdition, oxygen bal-

ance, and tropical conditions, etc.

4.94 acres

1 acre

or 5 4.94 acres/sacre

ftd

11,620 acres

2354 acre

R 5

drainage area

storage capacity

2354 acre

37,378 acre

ft/yr

RT 5

storage capacity

annual runoff

5 37,378 acre

ft/yr

5 38.6 in/yr 3

1 ft

12 in

3 11,620 acres

Annual runoff 5 38.6 in/yr 3 11,620 acres

130 Chapter 2

A detailed modeling of lake water quality is given in a book by Chapra

and Reckhow (1983). Clark et al. (1977), Tchobanoglous and Schroeder

(1985), and James (1993) also present modeling water quality in lakes

and reservoirs. However, most of those models are not used for lake

management practices.

For construction of a new lake or reservoir, it is required that the

owner submit the prediction of water quality in the future new lake

to the US Army Corps of Engineers. For example, Borah et al. (1997)

used the US Army Corps of Engineers’ HEC-5Q model (US Army Corps

of Engineers, 1986, 1989) for a central Illinois lake and two proposed

new lakes. The model was calibrated and verified on the existing water

supply lake used monitored data in the draft years of 1986 and 1988.

Eight water quality constituents were simulated. Calibration, verifi-

cation, and predictions were made only for water temperature, DO,

nitrate nitrogen, and phosphate phosphorus. The calibrated and ver-

ified model was used to predict water surface elevations and con-

stituent concentrations in the three lakes, individually and in

combination, with meteorological and estimated flow data for a 20-

month period from May 1953 through December 1954, the most severe

drought of record. The HEC-5Q model provided a useful tool in the

water quality evaluation of the three lakes. The HEC-5Q model was

developed by the Hydraulic Engineering Center in Davis, California,

for simulation of flood control and conservation systems with water

quality analysis. The details of these models are beyond the scope of

this book.

The major portion of this chapter will cover evaporation and lake

management programs in the Clean Lakes Program. Because these

subjects are general, they are not usually included in environmental

engineering textbooks.

4 Evaporation

Evaporation converts water in its liquid or solid state into water vapor

which mixes with the atmosphere. The rate of evaporation is controlled

by the availability of energy at the evaporating surface, and the ease

with which water vapor can diffuse into the atmosphere.

Shuttleworth (1993) presented a detailed description with modeling

of evaporation and transpiration from soil surfaces and crops. Modelings

include fundamental and empirical equations. Measurements of evap-

oration and methods for estimating evaporation are also given.

Evaporation of water from a lake surface uses energy provided by the

sun to heat the water. The rate of evaporation is controlled primarily

by the water temperature, air temperature, and the level of moisture

saturation in the air. Knowledge of evaporative processes is important

Lakes and Reservoirs 131

in understanding how water losses through evaporation from a lake or

reservoir are determined. Evaporation increases the storage require-

ment and decreases the yield of lakes and reservoirs.

Determination of evaporation from a lake surface can be modeled by

the water budget method, the mass transfer method, and the energy

budget method (Robert and Stall, 1967). Many empirical equations have

been proposed elsewhere (Fair et al., 1966, Linsley and Franzinni, 1964).

4.1 Water budget method

The water budget method for lake evaporation depends on an accurate

measurement of the inflow and outflow of the lake. The simple mathe-

matical calculation shows that the change in storage equals the input

minus output. It is expressed as

(2.8)

where ⌬S ⫽ change in lake storage, mm (or in)

P ⫽ precipitation, mm

R ⫽ surface runoff or inflow, mm

GI ⫽ groundwater inflow, mm

GO ⫽ groundwater outflow, mm

E ⫽ evaporation, mm

T ⫽ transpiration, mm

O ⫽ surface water release, mm

For the case of a lake with little vegetation and negligible groundwater

inflow and outflow, lake evaporation can be estimated by

(2.9)

The water budget method has been used successfully to estimate lake

evaporation in some areas.

4.2 Energy budget method

The principal elements in energy budget of the lake evaporation are

shown in Fig. 2.1. The law of conservation of energy suggests that the

total energy reaching the lake must be equal to the total energy leav-

ing the lake plus the increase in internal energy of the lake. The energy

budget in Fig. 2.1 can be expressed as (US Geological Survey, 1954)

(2.10)Q

5 Q

2 Q

6 Q

E 5 P 1 R 2 O 6 ⌬S

⌬S 5 P 1 R 1 GI 2 GO 2 E 2 T 2 O

132 Chapter 2

where Q

⫽ energy available for evaporation

⫽ solar radiation energy

⫽ reflected solar radiation

⫽ net long-wave radiation

⫽ energy transferred from the lake to the atmosphere

␪

⫽ increase in energy stored in the lake

⫽ energy transferred into or from the lake bed

The energy budget shown in Fig. 2.1 can be applied to evaporation

from a class A pan (illustrated in Fig. 2.2). The pan energy budget

(Fig. 2.2) contains the same elements as the lake budget (Fig. 2.1) except

that heat is lost through the side and the bottom of the pan. Equation (2.10)

is also applied to pan energy budget calculation.

A pioneering and comprehensive research project centered on tech-

niques for measuring evaporation was conducted at Lake Hefner,

Oklahoma, in 1950–51 with the cooperation of five federal agencies (US

Geological Survey, 1954). The energy budget data from a Weather

Bureau class A evaporation pan was used to evaluate the study. Growing

out of that project was the US Weather Bureau nomograph, a four-

gradient diagram (Fig. 2.3) for general use for lake evaporation (Kohler

et al., 1959). Subsequently, the formula for a mathematical solution

of the nomograph was adapted from computer use (Lamoreux, 1962).

Lakes and Reservoirs 133

Figure 2.1 Elements of energy budget method for determining

lake evaporation (Robert and Stall, 1967).

134 Chapter 2

Figure 2.2 Energy budget method applied to class A

pan (Robert and Stall, 1967).

Figure 2.3 Lake evaporation nomograph (Kohler et al., 1959).