9.1 DEFINITION
The precipitation rate, P_{r}, is the average volume
of water in the form of rain, snow, hail, or sleet that falls per unit
of area and per unit of time at the site. It is measured in units of volume
per area per time (lT^{1}).
Precipitation is one of the primary processes of the hydrologic cycle,
that is, the endless movement of water through the various elements of
the environment (oceans, atmosphere, land surface water bodies, and subsurface
soil systems). Other processes of the hydrologic cycle include evapotranspiration,
infiltration, overland flow (runoff), streamflow, deep percolation, and
groundwater flow. Thorough descriptions of these processes have been presented
in numerous texts in the hydrology literature (Chow 1964; Linsley et al. 1982;
Bedient and Huber 1988).
A simplified description of the hydrologic cycle could start with considering
the water vapor contained in the atmosphere, which under appropriate conditions,
condenses and precipitates over the oceans and the continental land. The
portion of the water that falls over the surface land, that is, precipitation,
is subsequently dispersed by following different pathways. Thus, from the
precipitation, a parcel of water is retained in the vicinity of the place
where the precipitation falls and is then transferred back to the atmosphere
through evaporation (i.e., the water changes from a liquid at the soil
surface to a vapor) and transpiration (i.e., the indirect loss of water
vapor from the soil to the atmosphere through plant tissue). The combined
effect of evaporation and transpiration is commonly called evapotranspiration.
Another parcel of the precipitation water penetrates the subsurface soil
system, that is, the process of deep percolation, and is added to the groundwater
flow system. Finally, the last parcel of precipitation water (the one that
is not transferred back to the atmosphere and does not percolate deep into
the soil) becomes overland flow, also called surface runoff, and feeds
local streams, rivers, or lakes. Both the surface and the subsurface flows
of water move toward low elevations and eventually reach the oceans. Evaporation,
primarily from the oceans and inland surface waters transfers water vapor
back to the atmosphere, thus completing the hydrologic cycle.
The concept of the hydrologic cycle is applicable to a largescale hydrologic
system on earth and can be represented mathematically by a water balance
(or budget) equation based on the law of the conservation of matter. The
same principle can be applied to any hydrologic system of any scale, whether
it is a small basin or a large watershed, to generate a water balance equation
that, in its simplest form, can be expressed as follows:
where q_{in} is the water inflow rate into the system,
q_{out} is the outflow rate, and ds/dt is the change
in time of the water stored within the system.
To illustrate the application of the water balance concept, consider
a hydrologic system represented by irrigated agricultural land and the
movement of water through it. According to the law of the conservation
of matter, the variation of S (i.e., the change in the volume of
water stored in the soil per unit of surface area of the land) during a
given time period T must be equal to the difference between the
average inflow rate in time and space (i.e., precipitation, P_{r},
plus irrigation, IR_{r}, rates) minus the outflow rate (i.e.,
deep percolation, I_{r}, plus runoff, R_{r},
and evapotranspiration, ET_{r}, rates). The water balance
equation for this system could then be represented as follows:
where all the inflow and outflow rates are expressed in units of lT^{1}.
The precipitation over a specific hydrologic system is an erratic process
with large fluctuations in the time domain. Consequently, because all the
inflow and outflow processes mentioned previously are related to the precipitation,
they also present large and erratic variations along the time. As a result,
the change in S is highly dependent on the period of time (T)
being considered. For short periods, the change in the soilwater storage
(S) is also an erratic process and can present relatively large
values. However, for a long period, such as an entire season or a whole
seasonal cycle of one year, the change in the soilwater storage (S),
particularly in the upper part of the soils, is likely to be small in relation
to the total water balance of the system (Hillel 1980a).
Thus, considering annual averages of the inflow and outflow water rates
in this hypothetical hydrologic system of a generic irrigated agricultural
land, the respective water budget equation can be reduced to the following:
Except for the deep percolation rate, I_{r}, all other
terms of Equation 9.3 can be determined either by direct field measurements
or by using specific coefficients derived from soil and other environmental
characteristics. The experimental methodologies for field measurement of
the precipitation, runoff, irrigation, and evapotranspiration rates are
described in this handbook (Sections 9.2, 10.2, 11.2, and 12.2, respectively).
Direct field measurement of the deep percolation (infiltration) component
of the field water balance has not yet proven to be practical (Hillel 1980a)
and, therefore, the deep percolation rate is often determined from the
other measured components of the equation as follows:
The parameter I_{r}, or the water deep percolation rate,
represents the amount of water that percolates through the upper layers
of the soil and eventually ends up being added to the groundwater flow
underneath the hydrologic system. In the RESRAD model, the parameter I_{r}
is used to calculate the radionuclide leaching from the contaminated zone
and the final contamination of the groundwater. The deep percolation rate
is calculated internally in the code as a function of the precipitation
(P_{r}) and irrigation (IR_{r}) rates and
the runoff (C_{r}) and evapotranspiration (C_{e})
coefficients. The latter two parameters are defined, respectively, as follows:
and
Detailed discussion of the runoff (C_{r}) and evapotranspiration
(C_{e}) coefficients and the irrigation rate (IR_{r})
are presented in Sections 10.1, 12.1, and 11.1, respectively.
Thus, from Equations 9.4, 9.5, and 9.6, the deep percolation rate, I_{r},
can be expressed as follows:
The mass balance equation (Equation 9.7) is the one used in RESRAD to
calculate the deep percolation rate of water into the soil.
9.2 MEASUREMENT METHODOLOGY
Measurement of the precipitation rate at a sitespecific location can
be performed with a precipitation gage, which basically consists of a receptacle
with vertical walls and an opening at the top with a specified area. The
ratio of the volume collected in the receptacle during a specified period
of time to the area of the opening at the top of the receptacle gives the
point estimate of the precipitation rate at a specific location and time.
In principle, any receptacle with an open collector area of known dimensions,
plus a volume measuring device can be used as a precipitation gage. However,
because of some operational features of these devices, unless they are
of the same shape and dimensions and similarly exposed, precipitation rate
measurements are usually not comparable (Linsley et al. 1982).
The standard precipitation gage adopted by the U.S. National Weather
Service has a collector (receiver) with an 8in. (20.3cm) diameter and
can measure the precipitation to the nearest 0.25 mm. Two types of precipitation
gages can be used, recording and nonrecording. The recording gage, the
most commonly used, records on a strip of paper, paper punch, or data logger
every 0.01 in. (0.0254 cm) of precipitation along the time scale. The recorded
data are then reported as an average precipitation rate, total volume,
or intensity variation.
According to Bedient and Huber (1988), a network of five to ten gages
per 260 km^{2} (100 mi^{2}) is usually required in urban
areas to define precipitation variability. The maintenance costs of such
networks are high and, therefore, for a particular application, it is usually
more convenient to rely on data collected locally from existing networks
with gages already installed near the site of interest. Local rain gage
networks that are usually maintained by cities and sewage treatment plants,
for example, could serve as a first source of information on the precipitation
rate at the site. On a larger scale, information on the precipitation rate
could be obtained from national networks. Precipitation gage networks designed
to provide point estimates of precipitation rates in the United States
and its territories are maintained by the U.S. National Weather Service
and the U.S. Geological Survey.
Data on the point estimates of precipitation rates obtained from either
local or national networks can be used to estimate the average areal precipitation
rate over a specific area. The areally averaged values of the precipitation
rate can be derived by three methods (Bedient and Huber 1988): arithmetic
mean, the Thiessen polygon method, and the isohyetal method.
The arithmetic mean of the point precipitation rates provides the simplest
and most straightforward way to obtain an estimate of the areal precipitation
rate at a particular site. For cases in which the gages are uniformly distributed
and the point values have minimal variations, this method provides satisfactory
results.
The Thiessen polygon method consists of areally weighing the point precipitation
from each gage. This is the most commonly used method, although not the
most accurate.
The isohyetal method consists of drawing contour lines of equal precipitation
(isohyets) and areally weighing the average precipitation between pairs
of contour lines crossing over the area of the site being considered. It
is the most accurate among the methods for determining areally averaged
values of the precipitation rate but requires an extensive gage network
to draw the isohyets accurately.
A distribution of values of average annual precipitation rates over
the U.S. continental territory, transcribed from the Water Atlas
of the United States (Geraghty 1973), is shown in Figure 9.1. If measurements
are taken for a sitespecific precipitation rate, users are referred to
DOE's environmental regulatory guide (DOE 1991a) on radiological effluent
monitoring.
9.3 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is requested to input a value for the annual average
areal precipitation rate (P_{r}) that is representative
of the conditions at the site. The precipitation rate is expressed as an
annual average rate in units of meters per year (m/yr).
The precipitation rate and other input parameters, such as the irrigation
rate and the runoff and evapotranspiration coefficients (Sections 11.1,
10.1, and 12.1, respectively), are used in RESRAD to determine the water
deep percolation rate, according to Equation 9.7. The deep percolation
rate is ultimately used to calculate the radionuclide leaching rate of
the contaminated zone and the subsequent contamination of the underlying
groundwater system.
For generic use of the code, a default value of the precipitation rate
(P_{r}) equal to 1 m/yr (about 40 in./yr) was adopted
in the RESRAD model. This value approximately represents the condition
of a relatively humid region. Whenever possible, however, and especially
for sites located in a dry region of the country, such as in the western
United States, sitespecific input data for P_{r} should
be used in the RESRAD calculations.
Annual average values of P_{r} in units of in./yr for
the U.S. continental territory, based on 40 years of recording, are presented
in the Water Atlas of the United States (Geraghty 1973). In the
absence of sitespecific data, the information provided in this atlas can
be used as a provisional and gross estimate of the sitespecific value
of P_{r} at any particular location in the United States.
Sitespecific data on the precipitation rate at a site can be obtained
from a rain gage network installed around the site or from already installed
networks, such as those maintained by cities. In cases in which data are
available on the annual average point precipitation rates at specific locations
in the vicinity of a site, the user can estimate the sitespecific areal
precipitation rate by using one of three averaging methods described in
Section 9.2.
If data on the precipitation rate (P_{r}) are not being
collected at a site or its vicinity, a sitespecific estimation of P_{r}
can be obtained from the U.S. National Weather Service or the U.S. Geological
Survey network database. The user may also refer to Climatological Data,
National Summary and Climatic Atlas of the United States, published
by the U.S. Environmental Data Service, for a sitespecific estimate
of P_{r}, if no local data are available.
10.1 DEFINITION
The average annual runoff coefficient, C_{r}, is the
fraction of the average annual precipitation that does not infiltrate into
the soil and is not transferred back to the atmosphere through evapotranspiration.
The runoff coefficient represents the fraction of the precipitation, in
excess of the deep percolation and evapotranspiration, that becomes surface
flow and ends up in either perennial or intermittent surface water bodies.
The runoff coefficient is a dimensionless parameter.
In a welldesigned and welloperated irrigation system, the flow and
the quantity of the irrigation water are controlled by an appropriate drainage
system (ditching) and the duration of each application. Consequently, under
normal circumstances, the irrigation water does not contribute significantly
to the overall average annual runoff. On the basis of these assumptions,
the average annual runoff coefficient (C_{r}) can be defined
mathematically by the following expression:
where R_{r} is the average annual runoff rate and P_{r}
is the average annual precipitation rate. Because R_{r}
is always smaller than (or at the most equal to) P_{r},
the values of C_{r} vary within the range of zero to one.
The runoff rate at a specific location is influenced by the morphology
of the region, the degree of the slopes, the type of soil material, and
the type of soil utilization. Table 10.1 lists values for the runoff
coefficient, C_{r}, under various conditions of soils and
soil uses.
10.2 ESTIMATION METHODOLOGY
A methodology for estimating the runoff coefficient (C_{r})
is presented in Table 10.1. The value of C_{r} can be evaluated
on the basis of the type of soil and its land utilization at the specific
site.
10.3 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is requested to input a value for the average annual
runoff coefficient (C_{r}) that represents conditions at
the site. The runoff coefficient is a dimensionless parameter and its input
value should be entered in the form of a decimal fraction rather than as
a percentage.
TABLE 10.1 Runoff Coefficient Values  
Type of Area 
Coefficient 
Value 
Agricultural environment^{a} Flat land with average slopes of 0.30.9 m/mi Rolling land with average slopes of 4.66.1 m/mi Hilly land with average slopes of 4676 m/mi Open sandy loam Intermediate combinations of clay and loam Tight, impervious clay Woodlands Cultivated lands Urban environment Flat, residential area  about 30% impervious Moderately steep, residential area  about 50% impervious Moderately steep, builtup area  about 70% impervious 
c_{1} c_{1} c_{1} c_{2} c_{2} c_{2} c_{3} c_{3} C_{r} C_{r} C_{r} 
0.3 0.2 0.1 0.4 0.2 0.1 0.2 0.1 0.4 0.65 0.8 
^{a} The runoff coefficient for an agricultural environment is given by C_{r} = 1  c_{1}  c_{2}  c_{3}. Source: Gilbert et al. (1989). 
For generic use of the code, a default value of 0.2 was adopted in the
RESRAD model for the runoff coefficient. According to the methodology presented
in Table 10.1, this default value of C_{r} represents an
agricultural environment of cultivated flat land with a sandy loam type
of soil. Whenever possible, however, sitespecific information should be
used for more accurate use of the code. If sitespecific data are not available,
Table 10.1 may be used to estimate the average annual runoff coefficient
(C_{r}).
The runoff coefficient and other input parameters, such as the precipitation
and irrigation rates and the evapotranspiration coefficient (Sections 9.1,
11.1, and 12.1, respectively), are used in RESRAD to determine the water
deep percolation rate according to a mass balance equation (Equation 9.7)
presented in Section 9.1. The water deep percolation rate is ultimately
used to calculate the radionuclide leaching rate of the contaminated zone
and the subsequent contamination of the underlying groundwater system.
11.1 DEFINITION
The irrigation rate, IR_{r}, is the average volume of
water that is added to the soil at the site, per unit of surface area and
per unit of time. It is measured in units of volume per area per time,
or lT^{1}. In the RESRAD code, the irrigation rate is expressed
as an annual average rate in units of meters per year (m/yr).
Irrigation is the practice of supplying water artificially to the soil
in order to permit agricultural use of the land in an arid region or to
compensate for occasional droughts in semidry or semihumid regions. Irrigation
is closely dependent on the precipitation rate at the site, in the sense
that a welldesigned and welloperated irrigation system should optimize
the spatial and temporal availability of water in the soil.
As discussed earlier (Section 9.1), irrigation, in conjunction with
precipitation, provides the inflow water into a hydrologic system formed
by the soil in an agricultural land and the water that circulates through
it. The outflow of water in this system is the result of processes such
as surface runoff and evapotranspiration and deep percolation rates.
The irrigation rate and other input parameters such as the precipitation
rate and the runoff and evapotranspiration coefficients (Sections 9.1,
10.1, and 12.1, respectively) are used in RESRAD to determine the water
deep percolation rate according to Equation 9.7 in Section 9.1. The
water deep percolation rate is ultimately used to calculate the radionuclide
leaching rate of the contaminated zone and the subsequent contamination
of the underlying groundwater system.
11.2 MEASUREMENT METHODOLOGY
The average annual irrigation rate at a site is determined as a ratio
of the total volume of irrigation water added to the field during the year
to the surface area of the irrigated land. This quantity is not measured
in the field per se but is obtained from the operational activities of
the irrigation system.
A welldesigned and welloperated irrigation system should be able to
supply water to plants at a rate sufficient to balance their transpiration
rate requirements. The objective is to provide water to the soil in a welldistributed
manner during the crop season so that the plants can maintain their own
hydration without loss of continuity. As long as the water uptake rate
from the plants' roots matches the water loss due to the plants' transpiration
from their foliage, they can maintain their hydration. As soon as the water
intake from the roots becomes lower than the transpiration, however, the
plants start losing moisture, resulting in a stressful situation for the
development of the crop (Hillel 1980a).
Therefore, the required rate of irrigation at a specific agricultural
site is governed by the properties of the soil and the plants, and, fundamentally,
by the meteorological conditions at the site. The soil/plant system properties
determine the ability of the soil to supply and transmit water to the roots,
as well as the ability of the roots to extract water from the soil at a
rate needed to overcome transpiration. The meteorological conditions, however,
dictate the rate at which the plants are required to transpire and, therefore,
the amount of water needed for their survival.
Estimation of the annual irrigation rate at a specific site can be obtained
in different ways, depending on the degree of knowledge about site agricultural
activities. When information on irrigation systems in operation at the
site or at its vicinity is available, the annual irrigation rate can be
obtained from operational records. When little information is available
on the irrigation procedures at a site, an estimation of the irrigation
rate can be obtained on the basis of the measured (or assessed) values
of the potential evapotranspiration and precipitation rates and on the
basis of an estimated "irrigation efficiency."
Irrigation efficiency is the ratio of the volume of water used consumptively
(such as in evapotranspiration) to the total volume of water applied to
the field (Hillel 1980a). This definition is similar to the one for the
evapotranspiration coefficient, C_{e}, (Section 12.1) and
can be expressed as follows:
According to Hillel (1980a), most irrigation projects are inherently
inefficient and although irrigation efficiencies of 80 to 90% can be achieved
in actual practice with proper water management, the average irrigation
efficiency is less than 50%. Thus, by assuming a value for the irrigation
efficiency (e.g., around 50%) at a specific site with little available
data on agricultural activities; and by determining the potential evapotranspiration
rate, ET_{r}, the precipitation rate, P_{r},
and the runoff coefficient, C_{r}; the predicted, necessary
average annual irrigation rate, IR_{r}, at the site can
be estimated as follows:
11.3 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is required to input a value for the annual average
irrigation rate, IR_{r}, that represents conditions at the
site. The IR_{r} should be entered in units of meters per
year (m/yr).
A default value of IR_{r} equal to 0.2 m/yr was adopted
in the RESRAD model. This value approximately represents the conditions
of a relatively humid region where only a small amount of irrigation is
needed per year. For an arid region, 1 m/yr is considered to be an
appropriate generic value for IR_{r}.
When there is no sitespecific information on the annual average irrigation
rate, the input value of IR_{r} at the site can be estimated
on the basis of the irrigation efficiency (usually below 50%) and the measurement
(or estimation) of another parameter such as the potential evapotranspiration
rate, ET_{r}, the precipitation rate, P_{r},
the runoff coefficient, C_{r}, and the evapotranspiration
coefficient, C_{e} (i.e., irrigation efficiency), according
to the following expression:
12 EVAPOTRANSPIRATION COEFFICIENT
12.1 DEFINITION
Evapotranspiration is one of the processes of the hydrologic cycle and
represents the total volume of water that changes phase, that is, from
the liquid or solid state to the gaseous state, near the ground surface
and is transferred to the atmosphere during a fixed period of time. Consequently,
it represents the combination of two separate processes: (1) evaporation
(i.e., the change of phase of water near the ground surface and the direct
transfer of water vapor from the ground to the atmosphere) and (2) transpiration
(i.e., the transfer of water from the ground to the atmosphere through
the plants and their foliage).
Evapotranspiration is also called "consumptive use" in the
hydrology literature and is defined as the quantity of water used by either
cropped or natural vegetation in transpiration or in the building of plant
tissue, together with water evaporated from the adjacent soil or from intercepted
precipitation, during a fixed period of time (Veihmeyer 1964).
Two parameters need to be defined in relation to the concept of evapotranspiration:
(1) the evapotranspiration rate, ET_{r}, and (2) the
evapotranspiration coefficient, C_{e}.
The evapotranspiration rate, ET_{r}, is the total volume
of water vapor that is transferred to the atmosphere because of the combined
effect of evaporation and transpiration, per unit of the ground surface
area and per unit of time at the site. It is measured in units of volume
per area per time (lT^{1}). The evapotranspiration rate is neither
required as input data to the RESRAD code, nor is it used implicitly within
the model. However, the measured or estimated sitespecific value of ET_{r}
is used to estimate the input value of the evapotranspiration coefficient,
which is used in the code. For consistency with other correlated parameters
handled in the RESRAD code, the evapotranspiration rate is expressed as
an annual average rate in units of meters per year (m/yr).
The evapotranspiration coefficient, C_{e}, is the ratio
of the total volume of water leaving the ground as the result of evapotranspiration,
ET_{r}, to the total volume of water available within the
root zone of the soil [(1C_{r})P_{r} + IR_{r}]
during a fixed period of time. It can then be expressed as follows:
where P_{r} is the precipitation rate (m/yr), IR_{r}
is the irrigation rate (m/yr), and C_{r} is the runoff coefficient
(dimensionless). (All these parameters are defined in this handbook; see
Sections 9.1, 11.1, and 10.1, respectively.)
In wellirrigated agricultural land, transpiration predominates over
evaporation in composing the total evaporation. Under these circumstances,
the evapotranspiration coefficient represents the efficiency by which the
water available in the root zone of the soil is actually transferred through
the plant system and into the atmosphere. Thus, for cultivated land, the
evapotranspiration coefficient (C_{e}) is also called the
"irrigation efficiency." Most irrigation projects are inherently
inefficient; the average irrigation efficiency is less than 50% (Hillel
1980a).
The evapotranspiration process is fundamentally governed by the meteorological
conditions at the site, as well as by the properties of the soil/plant
system. Meteorological parameters such as air temperature, wind speed,
atmospheric pressure, air humidity, and exposure to the sun, all have an
important role in determining the evapotranspirational demand at a specific
location and time of year. However, it is the amount of water available
in the root zone of the soil that limits the occurrence of the evapotranspiration
process. Thus, the power of the atmosphere to extract water from the ground
surface because of evaporation decreases as the moisture content of the
soil decreases. The smaller the moisture content is, the more strongly
the water is bound to the porous matrix of the soil because of capillarity,
and thus more energy is needed to extract it. Transpiration is also limited
by the availability of water at the root zone, the ability of the soil
to supply and transmit water toward the root zone, and the ability of the
root system to absorb water from the soil in its vicinity. Below a certain
value of soil moisture called the wilting point, the roots of the plants
are not able to extract water from the soil, and the transpiration process
is broken, resulting in dehydration and wilting. Therefore, as a combination
of evaporation and transpiration, the actual evapotranspiration at a specific
site depends on external climatic conditions and on the type and density
of vegetation covering the ground surface as well as on soil moisture,
root distribution, and other soil properties.
The concept of the "potential evapotranspiration rate," ET_{pr},
has been introduced into the hydrology literature to represent the socalled
"climatic demand" for water, independently of the transient properties
of the soil (Hillel 1980a). As such, the potential evapotranspiration rate,
ET_{pr} (or the evaporating power of the atmosphere), is
defined as the evapotranspiration rate that occurs on the ground of a land
area totally covered with vegetation and where sufficient water is continuously
available for the needs of plants. The actual evapotranspiration rate,
ET_{r}, is then a function of the potential evapotranspiration
rate, ET_{pr}, and the quantity of water available in the
root zone of the soil. Where there is an excess of water in the root zone,
the value of ET_{r} is at its maximum, equal to ET_{pr},
and the excess water percolates the soil toward the groundwater system.
During a water shortage period, however, the value of ET_{r}
becomes lower than ET_{pr}, with no resulting percolation.
The potential evapotranspiration rate, ET_{pr}, at any location in the contiguous U.S. territory can be estimated from Evaporation Atlas for the Contiguous 48 United States (National Oceanic and Atmospheric Administration [NOAA] 1982a), Mean Monthly Seasonal and Annual Pan Evaporation for the United States (NOAA 1982b), and Water Atlas of the United States (Geraghty 1973). A distribution of average potential evapotranspiration over the U.S. continental territory is shown in Figure 12.1.
The evapotranspiration coefficient and other input parameters such as
the precipitation rate, the irrigation rate, and the runoff coefficient
are used in RESRAD to determine the water percolation rate, according to
Equation 9.7 in Section 9.1. The water percolation rate is ultimately used
to calculate the radionuclide leaching rate of the contaminated zone and
the subsequent contamination of the underlying groundwater system.
12.2 MEASUREMENT METHODOLOGY
Estimation of the evapotranspiration coefficient, C_{e}
(to be used as input data to the RESRAD code), should be obtained from
measured (or otherwise estimated) values of the evapotranspiration rate,
ET_{r}, the precipitation rate, P_{r}, the
irrigation rate, IR_{r}, and the runoff coefficient, C_{r},
according to Equation 12.1.
There are many methods of measuring or estimating the actual (ET_{r})
and the potential (ET_{pr}) evapotranspiration rate. However,
no one method can be used for all purposes (Veihmeyer 1964). Most of the
methods used for estimating ET_{r} can also be used for
estimating ET_{pr}, provided that the available water supply
is sufficient for the area under observation during the duration of the
test. These methods can be classified into three broad categories: (1)
the theoretical approach, based on physical principles governing the process;
(2) the analytical approach, based on conservation principles, either
as a mass or as an energy balance; and (3) the empirical approach, based
on experimental results expressing the correlation between measured evapotranspiration
and local climatic conditions.
A generic description of various methods used for measuring evapotranspiration
can be found in Veihmeyer (1964). The methods available are (1) soilmoisture
sampling, (2) lysimeter measurement, (3) inflowoutflow measurements,
(4) integration method, (5) energy balance, (6) vapor transfer, and
(7) groundwater fluctuations. For example, the lysimeter method consists
of using a large barrel (also called a tank or evapotranspirometer) with
about a 1m diameter and a 2m depth that is filled with soil and buried
in the ground so that its top is flush with the ground surface. Individual
crops and/or natural vegetation are grown on and around the lysimeter.
The evapotranspiration rate can then be determined on the basis of the
mass balance by measuring the infiltration flux seeping out of the bottom
of the lysimeter and the rainfall rate. The loss of water necessary to
maintain satisfactory plant growth represents the evapotranspiration. When
operated properly, the lysimeter can provide reasonably reliable values
of potential evapotranspiration. However, reliable measurements of actual
evapotranspiration (particularly when it is much lower than the potential)
are rarely attainable because of the difficulty in maintaining comparable
soil moisture and vegetation cover conditions on and around the lysimeter
(Linsley et al. 1982).
Because of the inherent difficulties of field methods for measuring evapotranspiration, several empirical formulas have been developed to relate the potential evapotranspiration to some readily available climatic data, such as temperature, sunshine, wind velocity, and so forth. A list of typical evapotranspiration equations is presented in
Table 11.2 of the Handbook of Applied Hydrology (Veihmeyer
1964, pp. 1127). Two publications from the NOAA (1982a,b) have been used
in estimating the potential evapotranspiration on FUSRAP sites for cases
in which no sitespecific data are available.
12.3 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is requested to input a value for the annual average
evapotranspiration coefficient, C_{e}, that is representative
of conditions at the site. The input value of C_{e} is given
in dimensionless units.
In the process of estimating the value of C_{e} as an
input value for RESRAD, it is assumed that the cultivated land at the site
under consideration is maintained with the necessary level of moisture
in the soil for the growth and development of the crop. This condition
is achieved either by natural precipitation or by the combination of precipitation
and irrigation. In other words, it is assumed that the required moisture
content for potential evapotranspiration based on the annual average is
maintained in the soil.
Therefore, the estimation of the input value of C_{e}
for some sitespecific conditions is based on a previously measured (or
otherwise determined) value of the potential evapotranspiration, ET_{pr},
the precipitation rate, P_{r}, the irrigation rate, IR_{r},
and the runoff coefficient, C_{r}, according to the definition
of C_{e} presented in Equation 12.1.
A default value of C_{e} equal to 0.5 (dimensionless)
was adopted in the RESRAD model. This value represents the condition of
50% efficiency in the irrigation process at a generic site. Under this
condition, 50% of the water available in the root zone of the soil is transferred
to the atmosphere, and 50% of the water infiltrates the soil and percolates
toward the aquifer system. Whenever possible, however, sitespecific input
data for C_{e} should be used in the RESRAD calculations.
Field measurements of the average annual evapotranspiration rate, ET_{r},
usually are expensive and timeconsuming. Therefore, if data on ET_{r}
have not been collected at the site or its vicinity, a sitespecific estimation
of ET_{r} (and ultimately of C_{e}) should
be obtained from information in the literature. For a gross estimation
of ET_{pr}, the user can consult the annual average values
of potential evapotranspiration for the U.S. continental territory as shown
in Figure 12.1 (Geraghty 1973). Two NOAA publications (NOAA 1982a,b) provide
useful information that can be used to estimate the value of ET_{r}
(and ultimately of C_{e}) at any particular location in
the United States. For most applications, in the absence of sitespecific
data, this approach should suffice because of the intrinsic uncertainties
associated with the model itself and the natural variability of the potential
evapotranspiration at any site.
13 SOILSPECIFIC EXPONENTIAL b PARAMETER
13.1 DEFINITION
The soilspecific exponential b parameter is one of several hydrological
parameters used to calculate the radionuclide leaching rate of the contaminated
zone. (See also precipitation rate, irrigation rate, runoff coefficient,
evapotranspiration coefficient, hydraulic conductivity, and soil porosity.)
The soilspecific b parameter is an empirical and dimensionless
parameter that is used to evaluate the saturation ratio (or the volumetric
water saturation), R_{s}, of the soil, according to a soil
characteristic function called the conductivity function (i.e., the relationship
between the unsaturated hydraulic conductivity, K, and the saturation
ratio, R_{s}).
It has been suggested that a power function is an acceptable form of
representing the conductivity function. As cited by Clapp and Hornberger
(1978), Campbell (1974) derived a partly empirical and partly theoretical
conductivity function on the basis of the power function model; this function
proved to be reasonably accurate over a large number of cases. Campbell
suggested the following power expression to represent the working relationship
for the conductivity function:
where k is the relative conductivity (or relative permeability,
dimensionless), R_{s} is the saturation ratio (dimensionless),
and b is the fitting parameter, called the soilspecific exponential
parameter, which must be determined experimentally.
The relative permeability, k, at any location in the unsaturated
zone, is defined as a ratio of the unsaturated hydraulic conductivity,
K, at that point, to the saturated hydraulic conductivity, K_{sat}.
Thus, k can be expressed as follows:
Substituting the definition of the relative permeability k into
Equation 13.1 yields
or
In downward water infiltration into the unsaturated upper layer of the
soil, the infiltration rate, I_{r} (see also precipitation
rate), can be approximated by the unsaturated hydraulic conductivity, K
(Hillel 1980a). Therefore, substituting I_{r} for K
in Equation 13.4 yields
Equation 13.5 is used internally in the RESRAD model to evaluate the
volumetric water saturation, R_{s}, in all unsaturated regions
of the soil system. According to Equation 13.5, under unsaturated
infiltration conditions, the saturation ratio R_{s} is a
function of the infiltration rate I_{r}, the saturated hydraulic
conductivity K_{sat}, and the texture of the soil, as determined
by the fitting parameter b. When the medium is fully saturated,
I_{r} equals K_{sat}, and R_{s}
equals unity.
13.2 MEASUREMENT METHODOLOGY
The soilspecific b parameter is an empirical fitting parameter
and, therefore, must be determined experimentally. For each type of soil,
the best estimate of b can be obtained by adjusting the bestfit
values of each soil to an experimentally determined curve of relative permeability
versus saturation, according to the power function model proposed above
(Equation 13.1).
Determining the conductivity function of a soil sample experimentally
by measuring the relative permeability and the saturation is not an easy
laboratory task because of many technical and procedural difficulties.
Yet some data have been reported in the literature that demonstrate reasonable
agreement with the proposed model. For example, Clapp and Hornberger (1978)
have reported that Campbell's model (Campbell 1974) for the conductivity
function has proven to be acceptable under different conditions of soil
saturation over a wide range of b values (0.1713.6) and even
for values of saturation, R_{s}, near unity (i.e., full
saturation). Table 13.1 lists representative values of the soilspecific
exponential b parameter for various soil textures. Section 2.1.2
provides a discussion on soil textures.
13.3 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is requested to define an input value for the soilspecific
b parameter for (1) the contaminated zone, (2) the
unsaturated zone strata, and (3) the saturated zone. Input for the
saturated zone b parameter will only be required if the water table
drop rate (Section 18.1) is greater than zero.
Reported measured data indicate that values of b vary within
the range of 0.1713.6 (Clapp and Hornberger 1978). A default value of
5.3 was adopted in the RESRAD model. This value represents the condition
of a silty loam soil material. Whenever possible, however, sitespecific
input data for b should be used in the RESRAD calculation.
A relatively more accurate value of parameter b for sitespecific
soil materials can be obtained from the data listed in Table 13.1. For
most applications, this approach should suffice because of the difficulties
in obtaining laboratory determinations of the soil conductivity function.
TABLE 13.1 Representative
Values of SoilSpecific Exponential b Parameter 

Texture 
SoilSpecific Exponential Parameter, b 
Sand Loamy sand Sandy loam Silty loam Loam Sandy clay loam Silty clay loam Clay loam Sandy clay Silty clay Clay 
4.05 4.38 4.90 5.30 5.39 7.12 7.75 8.52 10.40 10.40 11.40 
Source: Clapp and Hornberger (1978). 
14.1 DEFINITION
The erosion rate is the average volume of soil material that is removed
from one place to another by running water, waves and currents, wind, or
moving ice per unit of ground surface area and per unit of time. The erosion
rate represents the average depth of soil that is removed from the ground
surface per unit of time at the site and is expressed in units of length
per time (lT^{1}).
14.2 MEASUREMENT METHODOLOGY
Erosion rates can be estimated by means of the Universal Soil Loss Equation
(USLE), an empirical model that has been developed for predicting the rate
of soil loss by sheet and rill erosion. It should be emphasized, however,
that orders of magnitude errors can result by using the USLE method without
proper orientation. An appropriate guide for using the USLE method can
be obtained from the U.S. Soil Conservation Service (SCS), which conducts
county soil surveys on a regular basis. The SCS office near the site should
be able to provide the USLE parameters mapped out for the sitespecific
soils and cover types for the area of interest.
If sufficient sitespecific data are available, a sitespecific erosion
rate can be calculated by using the USLE method. Wischmeier and Smith (1978)
and Foster (1979) discuss details of the calculation. Estimates based on
the range of erosion rates for typical sites in humid areas east of the
Mississippi River (based on model site calculations for locations in New
York, New Jersey, Ohio, and Missouri) can also be used (Knight 1983). For
example, for a site with a 2% slope, these model calculations predict a
range of 8 × 10^{7} to 3 × 10^{6}
m/yr for natural succession vegetation, 1 × 10^{5} to 6 × 10^{5}
m/yr for permanent pasture, and 9 × 10^{5} to 6 × 10^{4}
m/yr for rowcrop agriculture. The rate increases by a factor of about
3 for a 5% slope, 7 for a 10% slope, and 15 for a 15% slope. If these generic
values are used for a farm/garden scenario in which the dose contribution
from food ingestion pathways is expected to be significant, an erosion
rate of 6 × 10^{4} m/yr should be assumed for
a site with a 2% slope. This would lead to erosion of 0.6 m of soil in
1,000 yr. A proportionately higher erosion rate must be used if the slope
exceeds 2%. An erosion rate of 6 × 10^{5} m/yr,
leading to erosion of 0.06 m of soil in 1,000 yr, can be used for a site
with a 2% slope if it can be reasonably shown that the farm/garden scenario
is unreasonable; for example, if the site is, and will likely continue
to be, unsuitable for agricultural use.
Erosion rates are more difficult to estimate for arid than for humid
sites. Although water erosion is generally more important than wind erosion,
the latter can also be significant. Water erosion in the West is more difficult
to estimate because it is likely to be due to infrequent heavy rainfalls
for which the empirical constants used in the USLE may not be applicable.
Longterm erosion rates are generally lower for sites in arid locations
than for sites in humid locations. A more detailed discussion and data
on soil erosion are presented in Soil Physics (Marshall and Holmes
1979), Universal Soil Loss Equation: Past, Present, and Future (Peterson
and Swan 1979), and the Nature and Properties of Soils (Brady 1984).
14.3 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is requested to input a value for the annual average
erosion rate for the cover zone and the contaminated zone. The dimensions
of these input values of the erosion rate are given in units of meters
per year (m/yr).
For generic use of the code, a default value of the annual erosion rate
equal to 0.001 m/yr was adopted in the RESRAD model for both the cover
and the contaminated zones. This default value should suffice for screening
estimates. For a particular site, however, a more accurate sitespecific
estimation of the erosion rates for both the cover and the contaminated
zones should be attempted. The erosion rate of the contaminated zone only
becomes significant if and when the cover zone is completely eroded, thus
exposing the contaminated zone to the erosive effects of the environmental
elements. If there is no initial cover, a greater erosion rate will remove
the contaminated material faster. This may lead to lower doses than found
for an initial cover case.
A sitespecific estimation of the erosion rate for the cover and contaminated
zones can be performed by means of the USLE.
15.1 DEFINITION
The hydraulic gradient is the change in hydraulic head per unit of distance
of the groundwater flow in a given direction. The hydraulic gradient, J_{x},
in the flow direction x, is expressed as follows:
where h_{1} and h_{2} represent the hydraulic
head at points 1 and 2, respectively, and x is the distance between
these two points. Mathematically, the hydraulic gradient is a vector that
can be expressed as grad h. The norm of the vector represents the maximum
slope of the hydraulic gradient; its orientation represents the direction
along the maximum slope. The hydraulic gradient is a dimensionless parameter,
usually represented as a fraction rather than as a percentage.
In an unconfined (water table) aquifer, the horizontal hydraulic gradient
of groundwater flow is approximately the slope of the water table. In a
confined aquifer, it represents the difference in potentiometric surfaces
over a unit distance. The potentiometric surface is the elevation to which
water rises in a well that taps a confined aquifer. It is an imaginary
surface analogous to a water table. In general, the hydraulic gradient
of groundwater flow in a highly permeable geologic material, such as sand
or gravel, is far less than that in a geologic material with a low permeability,
such as silt and clay.
15.2 MEASUREMENT METHODOLOGY
The hydraulic head at a point in the saturated zone can be measured
in the field by installing a piezometric nest at the site. A piezometer
is basically a tube or pipe long enough to be introduced through the unsaturated
zone down into the saturated zone. Its walls must be completely sealed
along all its length, but it must be open to the atmosphere at the top
and to the water flow at the bottom. The water level measured inside the
piezometer, as compared with a defined reference level (such as mean sea
level), gives the hydraulic head of the aquifer at the point of measurement.
The distribution of the hydraulic head in a groundwater system is actually
threedimensional. Thus with the installation of three or more piezometers
spatially distributed in an aquifer, it is possible to determine the spatial
distribution of the hydraulic head at the site. By knowing the distances
between the piezometers, the hydraulic gradient of the dominant aquifer
flow at the site can be evaluated. A detailed description of piezometer
nests can be found in Freeze and Cherry (1979).
15.3 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is requested to input a value for the hydraulic
gradient in the dominant groundwater flow direction in the underlying aquifer
at the site. This parameter is dimensionless and should be entered as a
decimal fraction rather than as a percentage.
For generic use of the code, a default value of 0.02 was adopted for
the hydraulic gradient in the RESRAD model. Because the hydraulic gradient
varies significantly from one site to another, whenever possible, sitespecific
information should be used for more accurate use of the code.
Sitespecific data on the hydraulic gradient and the general flow pattern
of the groundwater system at the site can be obtained by installing a piezometric
nest in the area, as suggested above. RESRAD users should also consider
contacting a local or state hydrologist or geologist as a possible source
of sitespecific information.
16 LENGTH OF CONTAMINATED ZONE PARALLEL
TO THE AQUIFER FLOW
16.1 DEFINITION
The length, , of the contaminated zone parallel to the aquifer flow
is the maximum horizontal distance measured in the contaminated zone, from
its upgradient edge to the downgradient edge, along the direction of the
groundwater flow in the underlying aquifer.
The parameter is used in RESRAD to evaluate the dilution of the contaminated
inflow water (which percolates the contaminated zone vertically and reaches
the aquifer underneath) by the uncontaminated inflow groundwater in the
Nondispersion Model for a well located near the contaminated zone.
16.2 MEASUREMENT METHODOLOGY
To evaluate the value of parameter at a specific site, it is first necessary
to determine the hydraulic gradient of groundwater flow at the site. As
described in Section 15.2, the groundwater flow direction in the aquifer
can be determined locally by installing a piezometric nest composed of
three or more piezometers spatially distributed throughout the hydrogeological
system. With a known groundwater flow direction and the horizontal extension
of the contaminated zone, the parameter can be determined by measuring
the largest horizontal length of the contaminated zone parallel to the
groundwater flow direction.
16.3 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is required to input a value of , that is, the length
of the contaminated zone parallel to the groundwater flow, that represents
the conditions at the site. The dimensions of should be entered in units
of meters (m).
A default value of 100 m was adopted in the RESRAD model for parameter
. The default value of 100 m is the square root of the default contaminated
zone area of 10,000 m^{2}. Whenever possible, however, sitespecific
information should be used for more accurate use of the code.
17 WATERSHED AREA FOR NEARBY STREAM OR POND
17.1 DEFINITION
A watershed is a region contoured by an imaginary line connecting ridges
or summits of high land and drained by or draining into a river, river
system, or a body of water such as a lake or pond. The watershed area is
the surface area of the draining region above the discharge measuring points.
This parameter is expressed in units of length squared (l^{2}).
In the RESRAD code, the watershed area parameter represents the area of
the region draining into the nearby stream or pond located at the vicinity
of the site.
The watershed area parameter is used in the RESRAD model to evaluate
the dilution factor for the contamination of the water at the nearby stream
or pond as it gets mixed with the inflow of water from the contaminated
aquifer. Thus, the evaluation of the dilution factor for the ground/surface
water pathway is based on the following assumptions (Gilbert et al. 1989):
(1) the nearby body of water is a pond, (2) the inflow and outflow
of water in the pond are in equilibrium, (3) the average annual inflow
of radioactivity into the pond is equal to the average annual quantity
of radioactivity that is leached from the contaminated zone into the groundwater
system, and (4) the infiltrating water flow through the contaminated
zone is vertically downward. Under these conditions and assumptions, the
dilution factor is then defined as the ratio of the average annual volume
of water that percolates through the contaminated zone to the average annual
total inflow of water into the pond. More specifically, the dilution factor
is calculated internally in the code as the ratio of the contaminated zone
area (AREA) to the watershed area (WAREA).
17.2 MEASUREMENT METHODOLOGY
The area of the watershed draining toward the pond located at the vicinity
of the site can be evaluated by using a smallscale morphologic map of
the region.
17.3 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is requested to input a value for the area of the
watershed region draining into the stream or pond located at the vicinity
of the site. The dimensions of the watershed area should be entered in
units of square meters (m^{2}).
A default value of one million (1 × 10^{6})
m^{2} for the watershed area was adopted in the RESRAD model. Whenever
possible, however, sitespecific information should be used for more accurate
use of the code.
Sitespecific information on the watershed area can be obtained from
smallscale hydrological and morphological maps covering the region under
study. In the RESRAD code, the watershed area must be larger than or equal
to the area of the contaminated zone. The code will issue a warning if
this condition is violated and will not proceed with the calculations until
it is corrected.
18.1 DEFINITION
The water table drop rate is the rate, in units of length per time (lT^{1}),
at which the depth of the water table is lowered. The level of the water
table in a groundwater system fluctuates seasonally because of the erratically
temporal variations of the processes involved in the hydrologic cycle (Section 9.1),
as well as extra use of the water from the system. Under normal circumstances,
the level of the water table is approximately stationary if averaged over
long periods of time such as one year. For unusually high consumptive use
of groundwater in the region, however, the water table may experience a
significant drop during the annual period. In these cases, the average
annual water table drop rate is not zero and results in the creation of
an increase in the unsaturated zone thickness.
18.2 MEASUREMENT METHODOLOGY
The sitespecific water table drop rate can be estimated by observing
the change of the water level of a monitoring well appropriately installed
at the site. It can also be estimated by consulting water table records
of past decades.
18.3 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is required to input a value for the average annual
water table drop rate that represents conditions at the site. The dimensions
of the water table drop rate should be given in units of meters per year
(m/yr).
A default value of 0.001 m/yr was adopted in the RESRAD model for the
water table drop rate. This value is the same as the default value used
for the erosion rate. Whenever possible, however, sitespecific information
should be used for more accurate use of the code.
19.1 DEFINITION
The parameter wellpump intake depth is the screened depth of a well within the aquifer (the saturated zone). The wellpump intake depth is measured in units of length (l).
19.2 RESRAD DATA INPUT REQUIREMENTS
In RESRAD, the user is required to input a value for the wellpump intake depth that represents conditions at the site. Its dimensions should be given in units of meters (m).
A default value of 10 m was adopted in the RESRAD model for the wellpump
intake depth. For more accurate use of the code, however, sitespecific
data should be used whenever possible.