Water Balance 1. Precipitation Evapotranspiration Interception and evapotranspiration by vegetation...

Water Balance

1

Jae K. (Jim) Park, ProfessorDept. of Civil and Environmental Engineering

University of Wisconsin-Madison

Water BalancePrecipitation

Evapotranspiration

Interception andevapotranspirationby vegetation

GroundwaterMoisture contentby placement

Leachate escapeto environment

Leachate

Infiltration

PercolationSurfacerunoff

Surfacewaterrun-on

Percolation (% of precipitation)-Active operation: 30~100%; -Final cover installation: 7~20%Computational (Prediction) Method1. Water Balance Method (WBM) 2. Hydrologic Evaluation of Landfill Performance (HELP) Model 2

Definition of Terms

Soil water content: the ratio of the weight of water in a soil or refuse to unit total weight (% wt. of moisture per unit wt. of wet or dry material)

Field capacity: maximum water content before gravity drainage starts (cm/cm) (0.1 ~ 0.84 cm/cm)

Wilting point: water content where water is held so tightly to soil plants cannot take it up

Available moisture (to plants): the difference between the soil water content at field capacity and the wilting point (0.1~ 0.29 cm/cm)

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Hydraulic Property Calculation http://www.pedosphere.com/resources/texture/triangle_us.cfm

This program estimates wilting point, field capacity, saturation, sat. hydraulic conductivity, and available water.

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Move the cursor at the corresponding point in the

triangle and click. Then, you will see the numbers in the

boxes at the right side.

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ExampleSilt - 20%Clay – 50%Sand – 30%

Alternative: [Go to Work Table]

http://www.pedosphere.com/resources/texture/triangle_us.cfm

http://www.pedosphere.ca/resources/texture/worktable_us.cfm



http://www.pedosphere.com/resources/texture/triangle_us.cfm

Water Balance Method (WBM) Determine the major segments of precipitation that detract

from percolation (e.g., interception by vegetation) Incident precipitation: form surface water runoff, evaporate

directly to the atmosphere, transpire to the atmosphere through vegetation surfaces, or infiltration into the cover soils and refuse at the surface of the landfill

Percolation (PERCt) into the refuse from the surface layer

PERCt = Precipitation - R/Ot - STt - AETt

Potential evapotranspiration (PET)and actual evapotranspiration (AET)

Infiltration (I)

Percolation (PERC)

Surface runoff(R/O)

Root zone depthand/or depth ofevapotranspiration

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Storage (S) and change in storage (ST)

WBM Calculation Procedure (1)1. T Enter the average monthly temperature (°F).

http://www.worldclimate.com/

2. i Using the monthly temperature, determine the monthly heat index for each month. For months with T < 32°F, i = 0. Sum the i values to obtain I (the yearly heat index) (see Table C. 1).

January February March April May June July August September October November December

19.30 22.60 32.10 46.10 56.30 66.50 71.30 70.30 61.80 51.60 36.70 24.10F )T (


i 0.00 0.00 0.00 1.97 4.50 7.65 9.31 8.96 6.13 3.25 0.37 0.00 I = 42.14

Year

6


7

April46.1F

April56.3F

WBM Calculation Procedure (2)1. T Enter the average monthly temperature (°F).


2. i Using the monthly temperature, determine the monthly heat index for each month. For months with T < 32°F, i = 0. Sum the i values to obtain I (the yearly heat index) (see Table C. 1).

3. UPET Using the monthly temperature and the yearly heat index, find the Unadjusted Potential Evapotranspiration (see Table C.2).


19.30 22.60 32.10 46.10 56.30 66.50 71.30 70.30 61.80 51.60 36.70 24.10F )T (


i 0.00 0.00 0.00 1.97 4.50 7.65 9.31 8.96 6.13 3.25 0.37 0.00 I = 42.14

Year

January February March April May June July August September October November DecemberUPET 0.00 0.00 0.00 0.04 0.08 0.12 0.14 0.14 0.10 0.06 0.01 0.00

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Yearly heat index = 42.14

WBM Calculation Procedure (3)

4. Using the site latitude find the monthly correction factor for sun-light duration (see Table C.3).

Latitude: 43

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Latitude: 43


4. Using the site latitude find the monthly correction factor for sun-light duration (see Table C.3).

5. PET Multiply the monthly UPET by the monthly r to obtain the Adjusted Potential Evaporation for each month (inches of water).

January February March April May June July August September October November Decemberr 24.30 24.60 30.60 33.60 37.90 38.40 38.70 36.00 31.20 28.50 24.30 23.10


19.30 22.60 32.10 46.10 56.30 66.50 71.30 70.30 61.80 51.60 36.70 24.10

i 0.00 0.00 0.00 1.97 4.50 7.65 9.31 8.96 6.13 3.25 0.37 0.00

UPET 0.00 0.00 0.00 0.04 0.08 0.12 0.14 0.14 0.10 0.06 0.01 0.00

r 24.30 24.60 30.60 33.60 37.90 38.40 38.70 36.00 31.20 28.50 24.30 23.10

PET 0.00 0.00 0.00 1.34 3.03 4.61 5.42 5.04 3.12 1.71 0.24 0.00

F )T (

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6. P Enter the average monthly precipitation (inches of water) from literature.

7. Cr/o Enter the appropriate runoff coefficient to calculate the runoff for each month (see Table 7.6).

Surface conditions:Grass cover (slope) Runoff coefficient

Sandy soil, flat, 2% 0.05~0.10Sandy soil, average, 2~7% 0.10~0.15Sandy soil, steep, 7% 0.15~0.20Heavy soil, flat, 2% 0.13~0.17Heavy soil, average, 2~7% 0.18~0.22Heavy soil, steep, 7% 0.25~0.35Source: Fenn et al., 1975

January February March April May June July August September October November DecemberP(in) 1.57 1.04 2.23 2.90 3.37 3.75 3.66 2.99 3.20 2.13 2.16 1.70

Heavy soil and the grass cover slope 5% Cr/o = 0.18


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8. r/o Multiply the monthly precipitation by the monthly runoff coefficient to calculate the runoff for each month (inches of water).

9. I Subtract the monthly runoff from the monthly precipitation to obtain the monthly infiltration (inches of water).


P(in) 1.57 1.04 2.23 2.90 3.37 3.75 3.66 2.99 3.20 2.13 2.16 1.70r/o 0.28 0.19 0.40 0.52 0.61 0.68 0.66 0.54 0.58 0.38 0.39 0.31I 1.29 0.85 1.83 2.38 2.76 3.08 3.00 2.45 2.62 1.75 1.77 1.39

January February March April May June July August September October November DecemberP(in) 1.57 1.04 2.23 2.90 3.37 3.75 3.66 2.99 3.20 2.13 2.16 1.70C r/o 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18r/o 0.28 0.19 0.40 0.52 0.61 0.68 0.66 0.54 0.58 0.38 0.39 0.31


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10.I-PET Subtract the monthly adjusted potential evapotranspiration from the monthly infiltration to obtain the water available for storage (inches of water).

11. ACCWL (Cumulative Water Balance) Add the negative I-PET values on a cumulative basis to obtain the cumulate water loss. Note: Start the summation with zero accumulated water loss for the last month having I-PET > 0 (inches of water).

January February March April May June July August September October November DecemberPET 0.00 0.00 0.00 1.34 3.03 4.61 5.42 5.04 3.12 1.71 0.24 0.00

I 1.29 0.85 1.83 2.38 2.76 3.08 3.00 2.45 2.62 1.75 1.77 1.39

I-PET 1.29 0.85 1.83 1.03 -0.27 -1.53 -2.42 -2.59 -0.50 0.04 1.53 1.39

January February March April May June July August September October November DecemberI-PET 1.29 0.85 1.83 1.03 -0.27 -1.53 -2.42 -2.59 -0.50 0.04 1.53 1.39

ACCWL 0.00 -0.27 -1.80 -4.22 -6.81 -7.30


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12. ST Determine the monthly soil moisture storage (inches of water) as follows: a. Determine the initial soil moisture storage for the soil

depth and type (see Table 7.7). b. Assign this value to the last month having I-PET > 0. c. Determine ST for each subsequent month having I-PET

< 0 (see Table C.4). d. For months having I-PET 0, add the I-PET value to the

preceding month's storage. Do not exceed the field capacity. Enter the field capacity if the sum exceeds this maximum.

January February March April May June July August September October November DecemberACCWL 0.00 -0.27 -1.80 -4.22 -6.81 -7.30

ST (in) 4.00 4.00 4.00 4.00 3.73 2.51 1.35 0.70 0.61 0.65 2.18 3.57

A landfill surfaceDeep rooted crops

Three possible scenarios

1. 3.33 ft of find sand2. 1.67 ft of silt loam3. 0.5 ft of clay overlain

by 0.92 ft of silt loam

1. 1.2 in/ft × 3.33 ft = 4 in.2. 2.4 in/ft × 1.67 ft = 4 in.3. 3.6 in/ft × 0.5 ft + 2.4

in/ft × 0.92 ft = 4 in.

4 inches of moisture storage capacity

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13.ST Calculate the change in soil moisture for each month by subtracting the ST for each month from the preceding month (inches of water).

14. AET Calculate the actual evapotranspiration as follows (inches of water): a) Wet months I-PET 0: AET = PET b) Dry months I-PET < 0: AET = PET + (I-PET - ST) Note: For months when I-PET is negative, the evapotranspired amount is the amount potentially evapotranspired plus that available from excess infiltration that would otherwise add to soil moisture storage plus that available from previously stored soil moisture.

January February March April May June July August September October November DecemberST (in) 4.00 4.00 4.00 4.00 3.73 2.51 1.35 0.70 0.61 0.65 2.18 3.57

0.43 0.00 0.00 0.00 -0.27 -1.22 -1.16 -0.65 -0.09 0.04 1.53 1.39ST


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15. PERC Calculate the percolation as follows (in. of water): a) Dry months I-PET < 0: PERC = 0 b) Wet months I-PET 0: PERC = (I-PET - ST) Sum the percolation values for the year to obtain total annual leachate production per unit area.

16. P P = PERC + AET + ST + r/oJanuary February March April May June July August September October November December

PET 0.00 0.00 0.00 1.34 3.03 4.61 5.42 5.04 3.12 1.71 0.24 0.00P(in) 1.57 1.04 2.23 2.90 3.37 3.75 3.66 2.99 3.20 2.13 2.16 1.70r/o 0.28 0.19 0.40 0.52 0.61 0.68 0.66 0.54 0.58 0.38 0.39 0.31

I-PET 1.29 0.85 1.83 1.03 -0.27 -1.53 -2.42 -2.59 -0.50 0.04 1.53 1.39ACCWL 0.00 -0.27 -1.80 -4.22 -6.81 -7.30

0.43 0.00 0.00 0.00 -0.27 -1.22 -1.16 -0.65 -0.09 0.04 1.53 1.39AET 0.00 0.00 0.00 1.34 3.03 4.30 4.16 3.10 2.71 1.71 0.24 0.00

PERC 0.86 0.85 1.83 1.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00P 1.57 1.04 2.23 2.90 3.37 3.75 3.66 2.99 3.20 2.13 2.16 1.70

S T

WBM Calculation Procedure (11)ST = 4.00 inches C r/o = 0.18

January February March April May June July August September October November December Activity

19.30 22.60 32.10 46.10 56.30 66.50 71.30 70.30 61.80 51.60 36.70 24.10

i 0.00 0.00 0.00 1.97 4.50 7.65 9.31 8.96 6.13 3.25 0.37 0.00 I = 42.14 Table C.1

UPET 0.00 0.00 0.00 0.04 0.08 0.12 0.14 0.14 0.10 0.06 0.01 0.00 Table C.2

r 24.30 24.60 30.60 33.60 37.90 38.40 38.70 36.00 31.20 28.50 24.30 23.10 Table C.3

PET 0.00 0.00 0.00 1.34 3.03 4.61 5.42 5.04 3.12 1.71 0.24 0.00 24.52

P(in) 1.57 1.04 2.23 2.90 3.37 3.75 3.66 2.99 3.20 2.13 2.16 1.70 30.70

C r/o 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 Table 7.6

r/o 0.28 0.19 0.40 0.52 0.61 0.68 0.66 0.54 0.58 0.38 0.39 0.31

I 1.29 0.85 1.83 2.38 2.76 3.08 3.00 2.45 2.62 1.75 1.77 1.39

I-PET 1.29 0.85 1.83 1.03 -0.27 -1.53 -2.42 -2.59 -0.50 0.04 1.53 1.39

ACCWL 0.00 -0.27 -1.80 -4.22 -6.81 -7.30

ST (in) 4.00 4.00 4.00 4.00 3.73 2.51 1.35 0.70 0.61 0.65 2.17 3.57 Table C.4

0.43 0.00 0.00 0.00 -0.27 -1.22 -1.16 -0.65 -0.09 0.04 1.53 1.39AET 0.00 0.00 0.00 1.34 3.03 4.30 4.16 3.10 2.71 1.71 0.24 0.00

PERC 0.86 0.85 1.83 1.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4.57 (in/yr) ResultingP 1.57 1.04 2.23 2.90 3.37 3.75 3.66 2.99 3.20 2.13 2.16 1.70 Pecolation

Cr/o = 0.18 for heavy soil and the grass cover slope 5% http://www.worldclimate.com (reference)

Year

F)T(

ST

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Water Balance Output

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Janu

ary

Febru

ary

Mar

chApr

ilM

ayJu

ne July

Augus

t

Septe

mbe

r

Octob

er

Novem

ber

Decem

ber

Month

Wa

ter

leve

l, i

nch

I

AET

Soil moisturerecharge

Percolation

Soil moistureutilization

Soil moisturerecharge

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Formative Processes Runoff: computed using the Soil Conservation Service (SCS)

runoff curve number (U.S. Dept. of Agriculture, 1972); fraction of precipitation that forms surface runoff; no consideration of surface slope and roughness in estimating runoff and infiltration but through selection of the runoff curve number

Evapotranspiration: evaporation plus transpiration (consumptive use by vegetation); comes from water that has infiltrated into the surface soils or refuse; dependent of capillary flow and the flow through the plant roots to the surface during dry periods; the lake evapotranspiration ( 0.7 times the pan evaporation)

Ex. Determine the max. potential evapotranspiration of available moisture from a 1.5 m deep clay loam cover, vegetated with alfalfa. The root zone depth = 1 m; field capacity = 0.3 cm/cm; wilting point = 0.13 cm/cm

(0.3-0.13) cm/cm × 1 m = 0.17 m

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Formative Processes - continuedMoisture holding capacity (available moisture) = Field capacity -

Wilting point

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Percolation: below the evaporative zone depth The moisture content, or field capacity, for municipal

refuse is approx. 55% moisture on a wet-weight basis.

Formative Processes - continued

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Did not reach field capacity

Closely matched

Formative Processes - continued

Ex. Estimate the available water. A vegetative topsoil depth = 0.65 m; root penetration depth = 0.5 m; moisture content = 200 mm/mRoot zone < topsoil thickness; use 0.5 m.

200 mm/m 0.5 m = 100 mm = 0.1 m Water mass balance models assume plug flow or idealized

conditions, with each layer reaching field capacity before moisture is passed on downward to the next year. In reality, leachate collection at the base of a landfill will occur before the field capacities of the overlying soil and refuse column are reached.

Fungaroli and Steiner (1979)Field capacity = 2.6 ln D - 14.0

where D = wet density (lb/yd3). Although the time required for the refuse and liner to reach field

capacity can be theoretically determined, observed times are found to be shorter than theoretically determined times.

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Example #1 Estimate the time needed to reach field capacity through 10 m

of MSW refuse. Assume 33% of precipitation infiltrates during three years of active site operation (30 cm/yr) and that the infiltration rate is 6 cm/yr following final cover placement. Assume a field capacity of 0.3 cm/cm for the refuse and an initial moisture content of 0.16 cm/cm.

SolutionAdvancement of wetted front during active operation

oninstallaticover finalafter cm 300cm

cm 0.3yr 3

yr

cm 30

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cm/yr 42.8cm

cm 0.16)(0.3

yr

cm 6

yr 16.4m

cm 100

cm/yr 42.8

m 3m 10

yr 19.4yr 16.4yr 3

Example #2 How deep will 10 cm of water penetrate into the soil

profile if the porosity is 0.5 cm/cm and the field capacity is 0.3 cm/cm. Assume soil is at over dry water content.

Solution

Depth of water = Depth of soil × Water content

Depth of soil = Depth of water/Water content

= 10 cm/0.3 cm/cm = 33.3 cm How deep will contaminant in water travel when R

(Retardation factor) = 2.

Solution

Depth of soilcontaminant = 33.3 cm/2 = 16.75 cm

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Example #3

Compute how deep a contaminant with R of 5 will travel in a loam soil. P = 13.6 cm, R/O = 1.0 cm; ET = 7.31 cm; FC = 0.29, initial water content = 0.16 cm/cm

Solution

Depth of water penetration = Depth of water/(FC-WCinit)

P = ET + R/O + ΔS; 13.6 = 7.31 + 1.0 + ΔS

ΔS = 5.29 cm

Depth of water penetration = 5.29/(0.29-0.16) = 40.7 cm

Depth of contaminant penetration = 40.7/5 = 8.14 cm

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Example #4

Water Balance

Percolation into the top soil layer (mm/yr) = Precipitation × (1-Runoff coefficient) – Storage within the soil or waste (mm/yr) – Evapotranspiration (mm/yr)

Example: 10-m deep landfill with a 1-m cover of sandy loam soil in southern Ohio

Precipitation = 1025 mm/yr; R = 0.15; E = 660 mm/yr; soil field capacity = 200 mm/m; refuse field capacity = 300 mm/m as packed

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Example #4 - continued

Assume soil is at field capacity when applied and the incoming refuse has a moisture content of 150 mm/m.

Percolation = 1025 (1-0.15) – 0 – 660 = 211 mm/yr

The moisture front movement

The time to produce leachate

m/yr 1.4mm/m 150

mm/yr 211

yr 7.1 m/yr 1.4

m 10

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Water Balance Method (WBM) Evapotranspiration (ET) = Potential evapotranspiration Actual

soil moisture content Field capacity A heat index is obtained for each of the 12 months of the year and

summed to create an annual index. The daily potential evapotranspiration is obtained from the heat

index by use of tables. The potential evapotranspiration is adjusted for month and day

lengths with correction factors. Actual ET Potential ET Basic assumptions

The sole source of infiltration/percolation is percipitation falling directly on the landfill’s surface.

Groundwater does not enter the landfill. All water movement through the landfill is vertically

downward. The landfill is at field capacity at the start of calculations No recycle of leachate or co-disposal of liquid occurs. 32

Hydrologic Evaluation of Landfill Performance (HELP)

Is based on the same hydrologic principles as the WBM but utilizes a much more detailed sequence of calculations.

Has the ability to examine water fluxes throughout the complete vertical profile of a landfill.

Lateral drainage layer

Barrier soil layer

Lateral drainage layerBarrier soil layer

Vegetative layer

Waste layer

Liner

Cover

PrecipitationVegetation/infiltration

Evapotranspiration

Runoff

Slope

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HELP Model

Quasi-Two Dimensional Model Performs daily water budget calculation over a

one-dimensional landfill column

Three Types of Layers Vertical percolation layers Lateral drainage layers Barrier soil layers

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Hydrologic Evaluation of Landfill Performance (HELP) - continued

1. The model carries out the calculation sequence on a daily basis. Climate data - daily precipitation, mean monthly solar

radiation (generated by the model), and mean monthly temperature (generated by the model)

Soil data - saturated hydraulic conductivity, soil porosity, evaporation coefficient, field capacity, wilting point, minimum infiltration rate, SCS runoff curve number, initial soil water content (vol/vol)

Vegetation data - crop type, crop cover, leaf area indices, winter cover factor, evaporative zone depth

Design data - number of layers, layer thickness, layer slope, lateral flow distance, surface layer of landfill, leakage fraction, runoff fraction from waste

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2. Moisture that enters the topsoil layer is determined by a daily infiltration procedure that considers the amount of antecedent moisture, the density of vegetation on the surface, and the evaporative and runoff potential.

3. The rate of vertical moisture flow in the soil varies with the soil moisture content.

4. Lateral drainage in the drainage layers is computed analytically from a linearized Boussinesq equation.

5. Snow is assumed to remain as snowpack when the daily mean temperature is less than 32°F.

6. The HELP model does not include special leachate migration routes; the existence of a main wetting front is assumed.

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Limitations Does not model the aging of a liner. Does not develop a water balance over the history of

development of a landfill site. Does not model leachate quality. Tends to underpredict the surface runoff coefficient,

because the rainfall rate from a short, intensive rainfall is averaged out over the daily time increment, making the intensity much lower.

The synthetic-liner leakage fraction is a function of hole size, depth of leachate ponding, and saturated hydraulic conductivity of the underlying soil.

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Water Balance 1. Precipitation Evapotranspiration Interception and evapotranspiration by vegetation...

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