1. Water Balance
Jae K. (Jim) Park, Professor Dept. of Civil and Environmental Engineering University of Wisconsin-Madison

2. Water Balance Precipitation Interception and evapotranspiration
by vegetation
Evapotranspiration
Infiltration
Surface
runoff
Percolation
Moisture content
by placement
Surface
water
run-on
Groundwater
Leachate
Leachate escape
to environment
Percolation (% of precipitation)
-Active operation: 30~100%; -Final cover installation: 7~20%
Computational (Prediction) Method
1. Water Balance Method (WBM)
2. Hydrologic Evaluation of Landfill Performance (HELP) Model

3. 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)

4. Hydraulic Property Calculation*
07/16/96
Hydraulic Property Calculation
This program estimates wilting point, field capacity, saturation, sat. hydraulic conductivity, and available water.
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.
Example
Silt - 20%
Clay – 50%
Sand – 30%
Alternative: [Go to Work Table] 30 *

5. 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)
Surface runoff
(R/O)
Storage (S) and
change in storage (ST)
Infiltration (I)
Root zone depth
and/or depth of
evapotranspiration
Percolation (PERC)

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

7. April
46.1F
April
56.3F

8. WBM Calculation Procedure (2)
T Enter the average monthly temperature (°F).
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).
UPET Using the monthly temperature and the yearly heat index, find the Unadjusted Potential Evapotranspiration (see Table C.2).

9. Yearly heat index = 42.14

10. WBM Calculation Procedure (3)
Using the site latitude find the monthly correction factor for sun-light duration (see Table C.3).
Latitude: 43

11. Latitude: 43

12. WBM Calculation Procedure (4)
Using the site latitude find the monthly correction factor for sun-light duration (see Table C.3).
PET Multiply the monthly UPET by the monthly r to obtain the Adjusted Potential Evaporation for each month (inches of water).

13. WBM Calculation Procedure (5)
P Enter the average monthly precipitation (inches of water) from literature.
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% 0.05~0.10
Sandy soil, average, 2~7% 0.10~0.15
Sandy soil, steep, 7% 0.15~0.20
Heavy soil, flat, 2% 0.13~0.17
Heavy soil, average, 2~7% 0.18~0.22
Heavy soil, steep, 7% 0.25~0.35
Source: Fenn et al., 1975
Heavy soil and the grass cover slope 5%
Cr/o = 0.18

14. WBM Calculation Procedure (6)
r/o Multiply the monthly precipitation by the monthly runoff coefficient to calculate the runoff for each month (inches of water).
I Subtract the monthly runoff from the monthly precipitation to obtain the monthly infiltration (inches of water).

15. WBM Calculation Procedure (7)
I-PET Subtract the monthly adjusted potential evapotranspiration from the monthly infiltration to obtain the water available for storage (inches of water).
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).

16. WBM Calculation Procedure (8)
ST Determine the monthly soil moisture storage (inches of water) as follows:
Determine the initial soil moisture storage for the soil depth and type (see Table 7.7).
Assign this value to the last month having I-PET > 0.
Determine ST for each subsequent month having I-PET < 0 (see Table C.4).
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.

17. A landfill surface
Deep rooted crops
Three possible scenarios
ft of find sand
ft of silt loam
ft of clay overlain by 0.92 ft of silt loam
in/ft × 3.33 ft = 4 in.
in/ft × 1.67 ft = 4 in.
in/ft × 0.5 ft in/ft × 0.92 ft = 4 in.
4 inches of moisture storage capacity

19. WBM Calculation Procedure (9)
ST Calculate the change in soil moisture for each month by subtracting the ST for each month from the preceding month (inches of water).
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.

20. WBM Calculation Procedure (10)
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.  
P P = PERC + AET + ST + r/o

21. WBM Calculation Procedure (11)

22. Water Balance Output

23. 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
( ) cm/cm × 1 m = 0.17 m

24. Formative Processes - continued
Moisture holding capacity (available moisture) = Field capacity - Wilting point

25. Formative Processes - continued
Percolation: below the evaporative zone depth
The moisture content, or field capacity, for municipal refuse is approx. 55% moisture on a wet-weight basis.
Closely matched
Did not reach field capacity

26. Formative Processes - continued
Ex. Estimate the available water. A vegetative topsoil depth = m; root penetration depth = 0.5 m; moisture content = 200 mm/m
Root 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
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.

27. 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.
Solution
Advancement of wetted front during active operation

28. 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.
Depth of soilcontaminant = 33.3 cm/2 = cm

29. 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 = ΔS
ΔS = 5.29 cm
Depth of water penetration = 5.29/( ) = 40.7 cm
Depth of contaminant penetration = 40.7/5 = 8.14 cm

30. 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

31. 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

32. 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.

33. 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.
Evapotranspiration
Precipitation
Vegetation/infiltration
Runoff
Vegetative layer
Lateral drainage layer
Cover
Barrier soil layer
Waste layer
Lateral drainage layer
Liner
Barrier soil layer
Slope

34. 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

35. 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

36. Hydrologic Evaluation of Landfill Performance (HELP) - continued
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.

37. Hydrologic Evaluation of Landfill Performance (HELP) - continued
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.