9 PRECIPITATION RATE

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 large-scale 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 soil-water 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 soil-water 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 site-specific 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 8-in. (20.3-cm) 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 km² (100 mi²) 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 site-specific 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, site-specific 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 site-specific data, the information provided in this atlas can be used as a provisional and gross estimate of the site-specific value of P_r at any particular location in the United States.

Site-specific 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 site-specific 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 site-specific 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 site-specific estimate of P_r, if no local data are available.

10 RUNOFF COEFFICIENT

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 well-designed and well-operated 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.

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, site-specific information should be used for more accurate use of the code. If site-specific 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 IRRIGATION RATE

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 well-designed and well-operated 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 well-designed and well-operated 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 well-distributed 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 site-specific 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 site-specific 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 [(1-C_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 well-irrigated 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 so-called "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) soil-moisture sampling, (2) lysimeter measurement, (3) inflow-outflow 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 1-m diameter and a 2-m 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. 11-27). Two publications from the NOAA (1982a,b) have been used in estimating the potential evapotranspiration on FUSRAP sites for cases in which no site-specific 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 site-specific 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, site-specific 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 time-consuming. Therefore, if data on ET_r have not been collected at the site or its vicinity, a site-specific 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 site-specific 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 SOIL-SPECIFIC EXPONENTIAL b PARAMETER

13.1 DEFINITION

The soil-specific 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 soil-specific 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 soil-specific 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 soil-specific 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 best-fit 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 (0.17-13.6) and even for values of saturation, R_s, near unity (i.e., full saturation). Table 13.1 lists representative values of the soil-specific 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 soil-specific 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 0.17-13.6 (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, site-specific input data for b should be used in the RESRAD calculation.

A relatively more accurate value of parameter b for site-specific 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.

14 EROSION RATE

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 site-specific soils and cover types for the area of interest.

If sufficient site-specific data are available, a site-specific 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 row-crop 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. Long-term 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 site-specific 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 site-specific estimation of the erosion rate for the cover and contaminated zones can be performed by means of the USLE.

15 HYDRAULIC GRADIENT

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 h₁ and h₂ 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 three-dimensional. 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, site-specific information should be used for more accurate use of the code.

Site-specific 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 site-specific 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 m². Whenever possible, however, site-specific 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 (l²). 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 small-scale 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 (m²).

A default value of one million (1 × 10⁶) m² for the watershed area was adopted in the RESRAD model. Whenever possible, however, site-specific information should be used for more accurate use of the code.

Site-specific information on the watershed area can be obtained from small-scale 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 WATER TABLE DROP RATE

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 site-specific 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, site-specific information should be used for more accurate use of the code.

19 WELL-PUMP INTAKE DEPTH

19.1 DEFINITION

The parameter well-pump intake depth is the screened depth of a well within the aquifer (the saturated zone). The well-pump 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 well-pump 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 well-pump intake depth. For more accurate use of the code, however, site-specific data should be used whenever possible.