113 9 Models for Design and Evaluation Items of interest in design include estimates of evapotranspiration (ET), sur- face runoff, and deep percolation. In addition, the evaluation should estimate probability for success, thus requiring daily estimates of performance over many years or decades. Interacting processes govern ET landll cover performance; the interaction introduces complexity into the modeling challenge. A model that incorporates all of the important elements of engineering design, including the interactions between weather, plants, and soil, best serves engineering design and evalu- ation of ET covers. The model used for design or evaluation of an ET landll cover should produce estimates that allow the user to evaluate the cumulative effect of each day’s water balance activity and thus identify critical events. 9.1 A MODEL PHILOSOPHY All numerical models calculate an approximation to a specic real-world topic of interest. When used for their intended purpose, they are often useful. However, it is inappropriate to use a model created for one purpose to estimate a solution to a problem not within the scope of the original purpose of the model. For example, an economics model is not suitable for design of a landll cover. In the same way, it may not be appropriate to use a model developed for design of conventional-barrier landll covers to estimate performance of an ET landll cover. The engineer should select a design model that is appropriate for the problem. 9.2 REQUIREMENTS FOR ET LANDFILL COVER MODELS The requirements for model estimates of ET cover performance are different from those for conventional landll covers. Conventional cover design focuses on barrier-layer design and performance. The focus in an ET cover design is on water balance within the cover as controlled by weather, plant growth, soil properties, and related ingredients. The ET landll cover relies on using the soil as a water reservoir, and grass or other plants to empty the reservoir rapidly and completely after a precipitation event. Therefore, the model should accurately estimate daily values of actual evapotranspi- ration, surface runoff, and deep percolation (ET, Q, and PRK). © 2009 by Taylor & Francis Group, LLC 114 Evapotranspiration Covers for Landfills and Waste Sites 9.2.1 Wa t e r ba l a n c e The model must solve the water balance within the cover soil. The hydrologic water balance is the accounting of all water entering and leaving an ET landll cover: a mass balance. The complete mass balance (Chapter 6, Equation 6.1) may be simpli- ed for design as incoming water = outgoing water, or P = ET + Q + PRK + ΔSW (9.1) where P = Precipitation (includes irrigation, if applied) ET = Evapotranspiration (the actual amount) Q = Surface runoff PRK = Deep percolation (below cover or root zone) ∆SW = Change in soil water (SW) storage Two terms in Equation 6.1 are not included in Equation 9.1. Within the cover soil, there is little or no lateral ow, and it is assumed zero. Although the error term is not zero, it should be small if one uses a good model, and it is usually impossible to estimate its size. The error term is unknown and dropped from the design equation. 9.2.2 ac t u a l et Because the amount of water that may percolate through the cover and into the waste is a major design issue for landll remediation, estimates of deep percolation (PRK) are important. However, both PRK and Q are much smaller than ET, as illustrated in Figure 9.1. Daily estimates of water balance are central to ET cover design; it is noteworthy that during most days, ET is 100% of the outgoing water from an ET cover. Evapotranspiration controls the amount of water available for deep percola- tion. The accuracy with which a model predicts ET may dene its usefulness in ET 0% 25% 50% 75% 100% Coshocton, 70–79 Coshocton, 87–93 Bushland, Alfalfa Bushland, Corn PRK & Q ET FIGURE 9.1 Annual outgoing water balance for irrigated crops at Bushland, Texas, and for rain-fed meadow at Coshocton, Ohio. (Drawn from data in Hauser et al. 2005. Environ. Sci. Technol. 39(18), 7226–7233.) © 2009 by Taylor & Francis Group, LLC Models for Design and Evaluation 115 landll cover design even though PRK is the focus of cover performance. Because ET is the largest part of the outgoing water balance, its accurate estimation is a high priority for models. Plant growth, soil water content, root growth and distribution, and related param- eters control the amount of actual ET. The way in which a design model estimates these parameters has profound effects on the accuracy of ET estimates. For example: There are several methods of estimating potential evapotranspiration (PET). • Because ET is calculated from PET, errors in PET estimates affect all other model calculations. Using the wrong method for a site may introduce large errors in estimates of actual ET. The density of soil may control the presence, absence, or number of roots • found in a particular soil layer. The density of plant roots in a soil layer determines how much water plants can remove from the layer and its rate of removal. A model that does not consider the effect of soil density on root growth may not accurately estimate actual ET. Much of the root mass of perennial plants dies during drought or during • dormant periods every year. During a growing season, dryness of a par- ticular soil layer may signicantly reduce the living root mass in that layer; however, new roots grow when the soil is rewet. The entire root system of annual plants dies each year. Therefore, it is important for the model to estimate the changes and the growth of new roots. 9.2.3 mo d e l S a n d ca l I b r a t I o n Some computer-based models are accurate only after “calibration” for the problem in question. In order to make the model output match calibration data, one or more parameters within the model are changed. A complex model suitable for ET cover design may contain parameters that the user may change. Changes in a few internal parameters may create unexpected or unknown changes in other parts of the model. The calibrated model may match the calibration data but become less accurate for general use. A model used to estimate performance of an ET cover should not require cali- bration for two reasons. First, measurements suitable for use in model calibration are seldom, if ever, available for a particular landll site. Second, a requirement for calibration raises the question, “Does this model truly mimic the real world of a landll cover?” 9.2.4 de S I g n mo d e l re q u I r e m e n t S As noted earlier, the focus in an ET cover design is soil, plant growth, and water balance. Scientists use models to estimate the same variables but from a different perspective. Their models often require calibration and trial-and-error testing for every problem; they usually estimate the water balance for a few months or a crop- growing season. Scientists typically use more time to perfect their models for each problem or site than a design engineer can afford. © 2009 by Taylor & Francis Group, LLC 116 Evapotranspiration Covers for Landfills and Waste Sites The factors that affect the hydrologic design of ET covers encompass several sci- entic disciplines, and all of them should be included in a comprehensive computer model. The model should effectively incorporate soil, plant, and climate variables; include their interactions; and estimate their effects on hydrology and water balance. It should be capable of estimating long-term performance for 100 years or more, and the water balance for each day of the evaluation period. The model should correctly estimate the impact of many ingredients on the water balance, including plant bio- mass production, effect of soil density, temperature, plant growth stage, and avail- able plant nutrients. Estimates of long-term performance should include an estimate of long-term loss of primary plant nutrients from the ecosystem. An engineering design model for ET landll covers should be robust and simu- late the entire hydrologic cycle. Model requirements include the following: 1. The model should be tested against eld measurements of P, ET, Q, and PRK, and proved to produce small error. 2. It should be tested and proved in different climates. 3. No calibration should be needed; ready to use. 4. Input data should be easily available. 5. It should provide reliable answers with less than optimum input data. 6. The model should estimate missing input data. 7. It should stochastically generate precipitation (rain and snow), air tempera- ture, wind, solar radiation, and humidity from known local parameters. 8. The model should realistically simulate all parts of the water balance equation. 9. It should simulate daily values of all parameters for decades or centuries. 10. It should contain les of basic data inside the model for numerous site- specic climates, plants, and soils. 11. The model should realistically simulate effect of plant growth and biomass production on water balance. 12. Output data should be complete, user-selectable, exible, and easy to import into other design software. 9.3 POTENTIAL MODEL ACCURACY Designers, owners, and regulators should understand the limits of accuracy that are reasonable to expect from design, construction, and implementation of remediation measures on landlls. Therefore, knowledge of possible limits to model accuracy is helpful when choosing a model for design. Field measurements and observations typically provide the basis for model development and testing. Because the accuracy of eld measurement is limited, it is unlikely that the models developed from the data will be perfect. In order to improve the quality of the model, the developer should use eld measurements from sev- eral sources during development and testing, thus reducing the potential error of the model during general use. An understanding of the potential accuracy of eld research measurements provides useful insight into possible model accuracy. © 2009 by Taylor & Francis Group, LLC Models for Design and Evaluation 117 Hauser et al. (2005) evaluated measurements by three high-quality lysimeter facilities that measured all parts of the hydrologic water balance. The records included 17 years of measurements from Coshocton, Ohio, and two lysimeter records of 2 years each from Bushland, Texas. These experimental sites are among the best in the world, and the precision of the lysimeters was better than that of a single class- A rain gage measurement. The lysimeter at Coshocton is sufciently sensitive to provide accurate measurements of daily ET, and those at Bushland are capable of measuring hourly values of ET. The precision of the Coshocton and Bushland lysim- eters was 0.25 and 0.045 mm/day, respectively. The data were independent mea- surements of all parts of the water balance; as a result, one can readily estimate measurement errors. The annual water balance errors from these high-quality lysim- eter facilities, with widely differing climate, ranged between 5 and 15% of precipita- tion, measured by a standard rain gage at each site. Model developers usually use measured data from several sites during development and testing. Models developed from measurements at several locations are expected to be more accurate for general use than those developed at a single site. As a result, one should expect annual total water balance estimates by good models to be in error by about 5%, with possible errors up to 10% of annual precipitation. 9.4 MODELING SOIL WATER MOVEMENT In order to estimate deep percolation below a soil prole, it is rst necessary to esti- mate water movement within the soil prole. There are two leading methods to estimate water ow within the soil. Some numerical programs compute water ow within the soil using the “Richards’ equation.” These models are sometimes called theoretical or scientic models because they use the Richards’ equation. Other mod- els employ “water storage routing” to simulate water movement within the cover. 9.4.1 rI c h a r d S ’ eq u a t I o n The “theoretical” models utilize numeric approximations to a complex set of equa- tions based on Richards’ equation (Richards 1931). Warrick (1990) discusses both the development and status of this equation. No one has mathematically solved the equa- tion, but assumptions allow a numeric solution. Warrick (1990) presents four different forms of Richards’ equation. Numeric methods employ numerous calculations using complex equations; therefore, computer simulation is required for their solutions. Important assumptions are used to allow numeric solutions for the Richards’ equation; they may compromise the theoretical basis of the equation. They include the following: 1. Darcy’s law is incorporated into the solution. 2. The density of water is constant. 3. A unique relationship exists for each soil between water content (theta) and water pressure (head) for unsaturated soil. 4. A unique relationship exists for each soil between water content (theta) and unsaturated hydraulic conductivity (K unsat ). © 2009 by Taylor & Francis Group, LLC 118 Evapotranspiration Covers for Landfills and Waste Sites Darcy’s law was developed for saturated sand lters. ET cover soils are unsaturated soil; thus, the assumption that Darcy’s law applies may be questionable. The density of water in unsaturated soil is beyond the scope of this book. When applied to the ET landll cover problem, the denition of the relationship between theta and head or between theta and K unsat is particularly troublesome. The relationships are logarithmic, and small changes in water content may cause large changes in the value of head or K unsat . Small changes in particle size distribution, particle arrangement, organic content, or soil density can signicantly alter these relationships. In addition, the soil within an ET cover or natural eld is not homoge- neous. It is difcult to dene these logarithmic functions with sufcient accuracy for use in model estimates of ET cover performance. To add to the difculty, the relation between these parameters is different for the wetting and drying soil situations. There are other assumptions, but these are important and serve for discussion purposes. In spite of the possible discrepancies introduced by the assumptions, the numerical solutions to Richards’ equation have produced good results when applied to scientic studies of unsaturated ow that are limited in time and space. Richards’ equation is superior to other methods in many applications; however, it may or may not be superior for engineering design of ET covers. 9.4.2 Wa t e r St o r a g e ro u t I n g Some models use water storage routing to simulate water movement through the soil. This section describes water storage routing by the Environmental Policy Integrated Climate (EPIC) model; other models use similar methods. Within the model, ow out of a soil layer occurs when the soil water content exceeds eld capacity. Water drains downward from the layer until the storage returns to eld capacity. The saturated hydraulic conductivity controls ow rate through the layer. The routing process applies layer by layer from the surface downward through the deepest layer. Because the hydraulic conductivity of some layers may be lower than that for layers above them, the routing scheme can create the impossible situation where the water content of the layer exceeds the pore volume. For that situation, a back pass upward moves water into upper layers until none holds more water than the volume of the pore space. EPIC may move water upward from a layer if that layer’s storage exceeds eld capacity, but movement is dependent on the water tension in that layer and the layer immediately above. When the water content of all layers is less than or equal to the eld capacity, the water storage routing method does not allow water to move upward through the prole. The water storage routing method assumes a simplistic model of water ow within the soil. In spite of its limitations, this method performs well in the EPIC and other models. 9.5 PREVIOUS MODEL EVALUATIONS There are several reports of model evaluations for vegetative landll covers. One report compared 18 models with one another and evaluated them against incomplete eld measurements. They stated, “Drainage could be estimated to within about © 2009 by Taylor & Francis Group, LLC Models for Design and Evaluation 119 ±64% by most codes” (Scanlon et al. 2002). Others evaluated one or more models (Roesler et al. 2002; Khire et al. 1999; Khire et al. 2000; Choo and Yanful 2000; Anderson et al. 1993). These investigations had common characteristics. All compared model esti- mates against predictions by other models or incomplete eld measurements of short duration. Even though actual ET is the largest and most important part of the site water balance, none measured it; instead, they either calculated potential ET from weather measurements or estimated actual ET by difference from the other measure- ments. None of the investigators assessed the accuracy of the measurements that they used to test model accuracy. Neither the models nor the tests met the requirements for designing ET landll covers contained in Section 9.2.4. Although these comparisons may be useful to model developers or others, none provided recommendations that are useful to the landll cover design engineer. 9.6 EVALUATION OF THREE MODELS This section compares estimates by three models with excellent quality eld mea- surements made by three lysimeters at two locations. The models are (1) the Hydro- logic Evaluation of Landll Performance (HELP) model, version 3.07 (Schroeder et al. 1994a,b), (2) the Environmental Policy Integrated Climate (EPIC) model, ver- sion 8120 (Mitchell et al. 1998; Sharpley and Williams 1990; Williams et al. 1990; Williams 1995), and (3) the HYDRUS-1D version 3.0 (Simunek et al. 2005). The HELP and EPIC models are engineering models; HYDRUS-1D was developed as a scientic model, but it has been used to solve engineering problems. These models are uniquely different from one another and represent three classes of models. The developer and others extensively tested each of them; they were widely acclaimed for their intended use. The purpose was to evaluate fully developed and tested models for use in engi- neering design of ET landll covers. The models estimated the major input and out- put terms of the water balance (P, ET, Q, and PRK). The model estimates were compared to independent eld measurements of all terms in the water balance. The accuracy of the eld measurements was known. 9.6.1 helP mo d e l The HELP model was developed during the early deployment of barrier landll cov- ers. It is an engineering model designed for analysis and design of barrier-type land- ll covers. It is widely used and accepted for that purpose. The primary purpose of the HELP model is to provide water balance estimates with which to examine the expected performance of barrier design alternatives and the resulting effect on land- ll contents. The HELP model uses climate, soil, and design data to estimate daily landll hydrologic performance as expressed by surface storage, snowmelt, runoff, inltra- tion, ET, soil moisture storage, leachate recirculation, and leakage through barrier layers. It is capable of modeling landll systems for up to 100 years. The HELP model © 2009 by Taylor & Francis Group, LLC 120 Evapotranspiration Covers for Landfills and Waste Sites was extensively tested during development; however, it failed to meet expectations for the evaluation of vegetative covers (Benson and Pliska 1996; Khire et al. 1997). 9.6.2 ePIc mo d e l The EPIC model is an engineering model designed to estimate all parts of the daily water balance, soil erosion, plant production, and soil’s physical and nutrient status. The development of EPIC began in 1981; from the beginning, it was built for use on ungaged watersheds. EPIC estimates the hydrologic water balance, including all terms in Equation 9.1. It uses a daily time step to simulate climate and hydrologic parameters for a wide range of soils, climates, and plants. EPIC uses readily avail- able input data and can simulate hydrologic response for hundreds of years. The EPIC model was tested for water balance estimates in dry and wet cli- mates, including sites with signicant accumulation of snow in winter. Gassman et al. (2004) cite 200 research papers reporting testing and use of the EPIC model worldwide. Testing of the EPIC model against measured eld data demonstrated that it estimated PRK with satisfactory accuracy (Chung et al. 1999; Chung et al. 2001; Hauser et al. 2005). In addition, Meisinger et al. (1991) offered convincing evidence that EPIC estimates PRK accurately (see Figure 9.2). EPIC has no easy provisions to model barrier layers, although it would be pos- sible to specify soil layers with very low hydraulic conductivity. It can estimate lat- eral ow; however, it would be difcult to describe layer properties for solid waste and the barrier-layer -drainage system under the waste. 9.6.3 hydruS-1d mo d e l HYDRUS-1D is primarily a scientic model, although it has been used to solve engineering problems. The model numerically solves Richards’ equation for variably saturated water ow and convection-dispersion type equations for heat and solute transport. HYDRUS-1D is available in three versions: one-, two-, and three-dimen- sional water, heat, and solute ow. HYDRUS-1D is the one-dimensional model and 0 20 40 60 80 100 mm EPIC Measured DNOSAJJMAMFJ FIGURE 9.2 Lysimeter measured, monthly percolation during 3 years at Coshocton, Ohio, compared with estimates by the EPIC model. (Drawn from data in Meisinger et al. 1991. Proceedings, Cover Crops for Clean Water. Soil Conservation Society, Ankeny, Iowa, pp. 57–68.) © 2009 by Taylor & Francis Group, LLC Models for Design and Evaluation 121 is most suitable for ET landll cover design. It is described in the manual and in the online Web page, PC-Progress Discussion Forums (Simunek et al. 2005). HYDRUS-1D estimates actual ET; however, the user must separately calculate and enter daily values of precipitation, potential soil evaporation, and potential plant transpiration. The user obtains actual ET from the model output by adding the model estimates for “actual root uptake” and “actual surface evaporation.” It estimates inl- tration with a model-supplied inltration equation, and surface runoff as the differ- ence between precipitation and inltration. HYDRUS-1D is sensitive to time-step denition, and may require iterative runs to nd an acceptable time-step denition for a particular problem. 9.6.4 mo d e l dI f f e r e n c e S There are signicant differences between the models. The EPIC model contains a complete plant growth model, as well as hydrological estimates. The others provide less complete plant growth simulation. The estimate of ET dominates hydrologic modeling accuracy, because it is the largest part of the water balance and it controls the size of the other terms esti- mated by the model. The mass of plant roots in a soil layer limits the amount of water that plants can remove from the layer during each day; therefore, root mass and rate of root growth are important for accurate ET estimates. The stage of plant growth, soil density, and temperature control root mass and growth rate processes. Table 9.1 shows the differences between model characteristics that are important to root growth estimates. The HELP model treats frozen soils as impermeable; however, the EPIC model treats them as having reduced permeability. The HYDRUS-1D model allows snow accumulation, but the manual does not indicate how it handles inltration into frozen soil. These differences may signicantly affect water balance estimates. Both EPIC and HELP are engineering models that estimate all hydrologic terms important to ET landll cover design. They have different origins, but both evalu- ate the hydrologic cycle and satisfy basic requirements for engineering design. The HELP model was designed to evaluate barrier covers; EPIC was designed to simu- late the water balance in a soil prole in response to weather, plant growth, and soil TABLE 9.1 Characteristics of the EPIC, HELP, and HYDRUS-1D Models That Are Important for Root Growth Estimates Characteristic EPIC HELP HYDRUS-1D Actual root growth a Yes No Y/N b Soil density vs. root growth Yes No No Soil temperature vs. root growth Yes No No a Root growth in response to season, soil conditions, and plant parameters. b Estimates root growth one time, and no further change. © 2009 by Taylor & Francis Group, LLC 122 Evapotranspiration Covers for Landfills and Waste Sites properties. The HYDRUS-1D model began as a scientic model for soil physics investigations; it does not share the same focus as the other two. 9.7 MODEL TEST DATA The models were tested against accurate eld measurements made by the Agri- cultural Research Service (ARS) of the U.S. Department of Agriculture (USDA) at two locations. At Coshocton, Ohio, the ARS measured the hydrologic response of meadow with a lysimeter for a total of 17 years. At Bushland, Texas, ARS measured the hydrologic response of alfalfa and corn with two lysimeters for 2 years. At both locations, the investigators measured all parts of the water balance directly (P, ET, Q, and PRK). The lysimeters measure ET and P by weighing the mass of the lysimeter each hour of the day or more often. Percolation from the soil and surface runoff were continuously measured. The measurements of Q and PRK were independent of each other and the ET and P measurements. These model tests used daily measurements of each parameter of the water balance. Hauser et al. (2005) described the data. 9 . 7 . 1 c o S h o c t o n da t a ARS, USDA personnel made the Ohio measurements at the North Appalachian Experimental Watershed (NAEW). The site is located about 16 km (10 mi) northeast of Coshocton, Ohio, at 40.4° N latitude and 81.5° W longitude. The vegetation was meadow and similar to plant cover that might be established on an ET landll cover in that region. The dimensions of the soil block contained in the lysimeter are 4.3 m (14 ft) long, 1.9 m (6.2 ft) wide, and 2.4 m (8 ft) deep, with the long dimension up- and down- hill. The lysimeter soil block is an undisturbed natural soil prole from the site; it includes bedrock in the bottom layers, thus ensuring natural percolation processes. The land slope is about 23%, and the lysimeter precision was 0.25 mm/day. The lysimeter is similar to that shown in Chapter 6, Figure 6.3. Precipitation, air temperature, humidity, wind, and solar radiation measurements were available from a nearby weather station, and precipitation was measured at the site. Percolation outow was about 31% of precipitation (Harrold and Dreibelbis 1958,1967; Malone et al. 1999). 9.7.2 bu S h l a n d da t a Personnel at the Conservation and Production Research Laboratory, ARS, USDA, made the Texas measurements. The lysimeters were located near Bushland, Texas, on the Texas High Plains in a semiarid climate at 35.2° N latitude and 102.0° W longitude (about 24 km west of Amarillo). The two weighing and recording monolithic lysim- eters contained undisturbed columns of Pullman clay loam soil with surface area of 9 m 2 . The soil depth was 2.3 m. Irrigated corn grew in one lysimeter during 1989 and 1990, and irrigated alfalfa grew in the other lysimeter during 1996 and 1997. Precipitation, air temperature, humidity, wind, and solar radiation measurements were available from a weather station operated at the site over irrigated grass and from © 2009 by Taylor & Francis Group, LLC [...]... Coshocton, Meadow, 197 0– 197 9 EPIC 753 −2 HELP 547 − 29 HYDRUS 1000 +30 3.4 71 +100 Bushland, Corn (Growing Season)b, 198 9 and 199 0 22 EPIC 867... HYDRUS 6, 890 22 185 1 59 0.8 2 2 . only for 198 9 and 199 0. © 20 09 by Taylor & Francis Group, LLC 126 Evapotranspiration Covers for Landfills and Waste Sites TABLE 9. 3 Total P, ET, Q, and PRK Measured at Coshocton and Bushland for. 214 −24 Bushland, Alfalfa, 199 6 and 199 7 2 ,95 3 3,028 0 0 EPIC 2 ,92 0 −4 0 0 0 0 HELP 2 ,95 7 −2 0 0 142 5 HYDRUS 3,065 1 0 0 2 <1 Bushland, Corn (Growing Season) 2 , 198 9 and 199 0 1,664 1,616. 5,472 −20 6 69 6 4 ,91 7 11 HYDRUS 9, 997 −21 0.2 −1 1,064 −24 Coshocton, Meadow, 198 7– 199 3 7,170 5,351 14 1 ,93 0 EPIC 5,125 −3 185 2 1,815 −2 HELP 3 ,98 7 − 19 1 59 2 3,005 15 HYDRUS 6, 890 22 0.8 <−1