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a Oregon State Univ., Columbia Basin Agricultural Research Center, P.O. Box 370, Pendleton, OR 97801
b Texas A&M Univ. System, Texas Agricultural Experiment Station, 2301 Experiment Station Road, Bushland, TX 79012
* Corresponding author (w-payne{at}tamu.edu)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSNOTESRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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)], ranging from direct measurement in the laboratory or field, to models that use only basic soil data, e.g., texture or water release curves (WRC). We evaluated K() for a Walla Walla silt loam (coarse-silty, mixed, superactive, mesic Typic Haploxeroll) using two field methods and the Mualem–van Genuchten model (MVG). Field methods were the internal drainage method (ID) and the Klaij and Vachaud method (MKV), which was modified to include hydraulic head (H), and used 20 yr of data from a dryland field experiment. Four approaches to estimate WRC were compared for the MKV, and two approaches to estimate parameters of the MVG. For water contents >0.20 m3 m-3, the MKV gave K values that were two orders of magnitude less than those obtained from internal drainage experiments conducted under wetter conditions. When MVG parameters were predicted by the Rosetta model, which uses pedotransfer functions, K values approached those of the MVK. However, when model parameters were estimated from internal drainage and saturated hydraulic conductivity (Ksat) data, K() values were closer to those of the internal drainage experiments. The study reaffirms the difficulty of reconciling K() determined by different methodologies, and of extrapolating to values of outside those measured. It also demonstrates the sensitivity of the MVG and pedotransfer functions to different sources of input values. Advantages and disadvantages of the different approaches to determining K() are discussed.
Abbreviations: ET, evapotranspiration, H, hydraulic head • h, matric potential • ID, internal drainage method • K, hydraulic conductivity • Ksat saturated hydraulic conductivity • MKV, Modified Klaij and Vachaud method • MVG, Mualem–van Genuchten model • q, flux • SEE, standard error of estimate • WRC, water release curve • Y, yield • z, depth • , volumetric soil water content
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSNOTESRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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) or H is required for many agricultural and other applications, including land-use evaluation (Wösten et al., 1999) and estimates of drainage (Klaij and Vachaud, 1992) or chemical leaching (Normand et al., 1997). There are many field and laboratory methods of determining K() (Klute, 1972; Klute and Dirksen, 1986; Stolte, 1994), each with attendant advantages and disadvantages. Field methods are based on Darcy's law,
 | (1) |
H/z is hydraulic head gradient, z is depth, and h is matric potential. The ID, or instantaneous profile method (Richards et al., 1956; Ogata and Richard, 1957; Rose et al., 1965; van Bavel et al., 1968) has been frequently used as a field method to determine K() for both homogeneous and layered soils (Hillel et al., 1972; Klute, 1972). It requires frequent and concurrent determination of and h over a long period of time. Because the ID is time- and equipment-intensive, it can be costly, especially if several sites must be monitored to estimate spatial variability (Nielsen et al., 1973; Russo and Bresler, 1981).
Klaij and Vachaud (1992) introduced a two-stage field method of estimating K(), using periodic neutron probe measurements, to predict drainage from the root zone of sandy soils of West Africa. In the first stage, when the wetting front had not passed the bottom of the neutron probe access tube, q was calculated from changes in the amount of water stored below the root zone and above the deepest measurement depth. They assumed that the value of the hydraulic head gradient was unity (H/z = 1), because the curvature of the water content profile for sandy soils is generally small so long as wetting fronts are avoided. This simplified Darcy's law to q = -K() and allowed K() to be determined from straightforward regression. During the second stage, once the wetting front had passed the bottom of the access tube, K() was used to calculate drainage.
Advantages of the MKV (Klaij and Vachaud, 1992) are that it does not require a separate internal drainage experiment, and K() can be determined with greater spatial resolution than most internal drainage studies have, because it is calculated for each access tube location. However, for finer-textured soils, the assumption of a hydraulic head gradient of unity is probably not valid. The gradient must therefore be estimated, which requires knowledge of WRC.
Because field measurement of K() is cumbersome, indirect methods have been developed for its estimation. One approach is to calculate K() from WRC based on its theoretical relation to pore-size distribution (Childs and Collis-George, 1950; Marshall, 1958; Millington and Quirk, 1960; Jackson, 1972; Mualem, 1976). The WRC itself has been estimated with varied success from even more easily measured soil physical properties, such as texture and bulk density (e.g., Hall et al., 1977; Gupta and Larsen, 1979; Bache et al., 1981; Campbell, 1985; Vereecken et al., 1989).
More recently, statistical formulae, referred to as pedotransfer functions, have been developed that draw upon existing soil databases to relate basic soil survey data, e.g., soil texture, bulk density, and organic matter content, to hydraulic properties such as WRC and further to K() (Wösten and van Genuchten, 1988; Vereecken et al., 1990; Schaap et al., 1998, Schaap and Leij, 2000; Wösten et al., 1999). When used in conjunction with geographically referenced soil databases, pedotransfer functions facilitate, among other things, assessment or classification of geographical areas for such things as environmental vulnerability or suitable uses, e.g., for agriculture or recreation. Applications of pedotransfer functions include land-use evaluation (Bouma, 1989a, b; van Diepen et al., 1991), prediction of regional pesticide or fertilizer transport (Inskeep et al., 1996; Wilson et al., 1996; Wilson et al., 1993; Bouma et al., 1996), and famine early warning systems.
Despite the importance of K() to so many applications, and the increasing use of pedotransfer functions to influence policy decisions, comparison of different methods of K() estimation is relatively rare.
The objective of this study was to compare measured and modeled K() functions for a Walla Walla silt loam of northeast Oregon. This soil is typical of loess-derived Mollisols in the inland Pacific Northwest. An advantage of the selected experimental site is the existence of a long-term tillage experiment for which there are 20 yr of unpublished soil water content data, and published WRC and K() data (Allmaras et al., 1977; Pikul, 1988).
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSNOTESRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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Three methods were used to estimate K() functions—the ID, the MKV, using four sources of WRC data, and the MVG (van Genuchten, 1980), using two methods of parameter estimation.
Internal Drainage Study
An internal drainage study (Richards et al., 1956; Ogata and Richard, 1957; Hillel et al., 1972) was conducted in six of 32 existing plots used for a long-term wheat (Triticum aestivum L.)–pea (Pisum sativum L.) rotation study at the Columbia Basin Agricultural Research Center (Allmaras et al., 1977; Pikul, 1988; Payne et al., 2000, 2001). Metal rings (1.83 m in diam. by 0.40 m in height) were centered on each of six access tubes that were installed in 1968 and have remained there since. Rings were inserted into soil until 0.20 m was left aboveground. Within each ring, two banks of tensiometers were installed at a distance of 0.30 m around the access tube. Tensiometers were installed to depths of 0.46, 0.91, 1.22, 1.52, and 1.83 m. A Tensimeter pressure transducer1 (Soil Measurement Systems, Tucson, AZ) was used to measure h at each depth.
After determination of initial soil moisture content with a neutron probe (CPN model 503DR, CPN Corporation, Pacheco, CA), water was ponded at a depth of 
3 cm on the soil surface and maintained for 12 h. A wooden block was placed on the soil surface to protect the soil from water impact. Water was added until tensiometers indicated that the wetting front had reached a depth of 1.22 m. The total amount of water added to each ring, based on flow meters, was 0.53 m3.
To minimize evaporation and extreme temperature fluctuation at the surface during subsequent drainage, the soil surface inside each ring was covered with a plastic sheet and a 0.15-m layer of wheat straw. Both and h were then monitored for 71 d. Measurements were taken twice per day for the first 5 d, then once a day for 3 d, and finally once every 3 to 7 d until the end of the experiment. Lateral flow was assumed negligible.
The neutron probe was field-calibrated (Payne et al., 2001). The calibration curve for 0.46- to 1.22-m depth was:
 | (2) |
To calculate K() at a depth of 1.22 m, which is the approximate lower boundary of the root zone for peas, q and the gradient H/z at 1.22 m were calculated from neutron probe and tensiometer measurements, and the time lapse between two measurement dates. K() was calculated using Eq. [1].
Modified Klaij and Vachaud Method
Neutron probe data were taken several times during the growing season from 1969 to 1989 using access tubes in the 32 plots of the long-term rotation experiment (Payne et al., 2001). The rotation study consisted of four tillage treatments in a randomized block design, with four replications. The position of peas and wheat was rotated annually within each plot. Individual plots had two access tubes (one for wheat and one for peas) installed to a depth of 1.8 to 2.4 m, depending upon the depth to semipermeable calcareous hardpan or basalt bedrock.
From 1969 to 1974, a Troxler neutron probe (model 1255) (Troxler Laboratories, Research Triangle Park, NC) and scaler rate meter (model 2651) (Troxler Laboratories, Research Triangle Park, NC) were used to measure . Thereafter, a CPN (model 503) neutron probe (Campbell Pacific Nuclear Corp., Pacheco, CA) was used. Both probes were field calibrated regularly, and standard counts were taken at least once on each day of measurement. Payne et al. (2001) gave additional probe calibration information.
For calculation of K(), values were used only if water storage below 1.22 m increased from one measurement date to the next, and only until water content at the deepest measurement depth increased. In other words, q was calculated only when water was moving downward in the soil profile into the compartment between 1.22-m and the deepest measurement depth, and was no longer calculated if the wetting front reached the deepest measurement depth. This constitutes Klaij and Vachaud's (1992) stage one. For our conditions, it corresponded to periods between harvest of wheat, when the profile is dry and flux past the deepest depth of measurement can be considered negligible, and the ensuing winter months, when the soil profile is being replenished by rainfall.
Increases in water stored between 1.22-m and the lowest depth of measurement were divided by the number of days between probe measurements to obtain mean daily q. The value of at 1.22 m was taken as the mean of for the two measurement dates.
The gradient H/z of Eq. [1] was estimated using four different WRC to estimate h at experimentally determined values of . Gravitational head was added to h to obtain estimates of H. The four sources of WRC are described below.
Water Release Curve 1
Volumetric soil water content and h data from this internal drainage study were pooled with data from the internal drainage study of Allmaras et al. (1977), also conducted at the Columbia Basin Agricultural Research Center. Values for and h from the Allmaras et al. (1977) study were obtained using the shareware program WINDIG (Lovy, 1994) on scanned figures. Nonlinear regression (STATGRAPHICS Ver. 7.0, Manugistics, Inc., Rockville, MD) was then used to fit the van Genuchten (1980) equation,
 | (3) |
s is saturated , r is residual (a fitting parameter), and 
and n are shape parameters for the WRC. A positive value of h (kPa) is used for convenience of calculation. For our study, the fitted equation was:
 | (4) |
Water Release Curve 2
The program WINDIG (Lovy, 1994) was also used to obtain and h values from WRC data of Pikul (1988), who combined field neutron probe and tensiometer data near a depth of 40 cm, for which ranged from 0.22 to 0.32 m3 m-3, with psychrometer and pressure plate data measured in the laboratory. The program Tablecurve (SPSS, Chicago, IL) was then used to generate the numerical function
 | (5) |
This equation was used to estimate h for values of measured by neutron probes in the long-term experiment.
Water Release Curve 3
Percentages of sand, silt, and clay, and bulk density were used as inputs to the Rosetta model (Schaap et al., 1998, 1999; Schaap and Leij, 2000), developed at the U.S. Salinity Laboratory, to predict WRC. The percentages of sand (10.1), silt (77.0), and clay (12.9), and the value of bulk density (1.15 Mg m-3) at 1.22 m, were taken from Allmaras et al. (1977). The Rosetta model predicted the following WRC function:
 | (6) |
Water Release Curve 4
A model proposed by Campbell (1985) was used to predict WRC. It also uses percentages of sand, silt, and clay, and bulk density as inputs:
 | (7) |
s is saturated soil water content, and b is the slope of loge h vs. loge . The parameter b was calculated from geometric mean particle diameter and standard deviation (Campbell, 1985). The soil texture and bulk density input values for this model were also from Allmaras et al. (1977). When s as predicted from the Rosetta model (0.49 m3 m-3) was used, the resulting WRC equation was:
 | (8) |
Mualem–van Genuchten Model
The MVG (van Genuchten, 1980), which was derived from Mualem's (1976) pore-size distribution model, was used to model K:
 | (9) |
In this equation, K0 is a matching point at saturation that is similar but not necessarily equal to Ksat, and L is sometimes considered to indicate tortuosity. Mualem (1976) and others have assumed L to be 0.5, but its value can also be predicted by the Rosetta model. The variable Se is relative saturation, defined as
 | (10) |
In this study, we used the same model, i.e., Eq. [9] and [10], to predict K(), but the parameters were estimated in two different ways: Method 1. The Rosetta model was used to estimate the parameters K0, s, r, n, and L, using percentages of sand, silt, and clay, and bulk density as inputs. The resulting model [with K(Se) in mm d-1] was:
 | (11) |
 | (12) |
Method 2. Parameters s, r, and n were obtained from the field measured WRC1 (Eq. [4]). A value of 0.5 was used for L, and a value of 345.6 mm d-1 for Ksat, which was from Allmaras (1982), who used the double-tube method (Bouwer, 1962). The resulting model of K(Se) (in mm d-1) was:
 | (13) |
 | (14) |
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSNOTESRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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) functions obtained for the six individual plots are given in Table 1. Although slope magnitude for individual plots ranged from 16 to 29, it did not differ significantly at p = 0.05. Pooling points from all six plots (Fig. 1)
increased scatter and reduced model r2 (Table 1), reflecting spatial variability of K(). Data redrawn from Allmaras et al. (1977) for the 0.6- to 0.9-m depth interval were in good agreement with our results, but had less scatter (Fig. 1). Allmaras et al. (1977) used two monoliths (dimensions 1.22 by 1.83 by 1.60 m) from two adjacent plots, and wrapped the sides of the monolith to prevent side flow. The six plots for our internal drainage experiment were spaced unevenly over a distance of 120 m. Increased distance between internal drainage sites is probably the main source of increased variability.
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H/z from periodic measurements of are shown in Fig. 2
. At greater values of , the four curves tended to converge; however, at lower values, they diverged considerably. In particular, the Campbell (1985) model (WRC4) tended to estimate more negative values for h as decreased to <0.30 m3 m-3. The curve of Pikul (1988) (WRC2) was very close to that from the internal drainage experiments (WRC1), especially at values >0.28 m3 m-3. Increased divergence of WRC2 at lower water contents may be because of slight differences in pore-size distribution associated with depth and, perhaps, tillage. Pikul's (1988) measurements were concentrated near a depth of 40 cm in the soil profile, where there was some compaction because of tillage.
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H/z. This, in addition to its much less demanding input requirements, would appear to make it an attractive source of WRC for soils similar to the Walla Walla silt loam.
The K() functions determined by the MKV are shown in Fig. 3
, with 95% confidence intervals, for the four WRC. Because of the very large amount of neutron probe data for this experiment, there were over 1700 mean values of at 1.22 m used to determine q of Eq. [1]. Such a large data set is not required by the method, however. Klaij and Vachaud (1992) and Payne (1997) were able to obtain acceptable K() functions from only 1 yr of data, but for the sandy soils in West Africa, weekly neutron probe readings were required.
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) functions tended to converge at greater values of . However, WRC4 from the Campbell (1985) model, which estimated more negative values of h for < 0.30 m3 m-3 (Fig. 2), gave very low estimates of K in this same range. Also, similar to trends for WRC, K() calculated from WRC3 (from the Rosetta model) was close to that calculated from WRC2 (from Pikul's data).
Because of the large number of data points acquired from 32 tubes, which were evenly spaced over a distance of nearly 250 m, Payne (1998) could detect statistically significant differences among plots for the slope of the line relating log10 K to . Thus, the modified method appears to retain the advantage of increased spatial resolution that Klaij and Vachaud (1992) originally found for sandy soils of West Africa.
Mualem–van Genuchten Model
Results of K() predicted by the MVG are shown in Fig. 4
, using the two different methods to estimate parameters. Results show that Method 1, which uses the Rosetta model to predict model parameters from texture and bulk density, predicts values of K that are approximately two orders of magnitude less than Method 2, which used parameters obtained from WRC1 and Ksat from Allmaras (1982). The large discrepancy resulted mainly from differences in the parameters Ksat (17.1 mm d-1 for Method 1 and 346 mm d-1 for Method 2) and, to a lesser extent, s (0.49 m3 m-3 for Method 1, and 0.40 m3 m-3 for Method 2).
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) curves generated from internal drainage data (Measured-ID) and from the MKV, using WRC1 (Measured-MKV), are also shown in Fig. 4. The internal drainage experiment gave values of K that were one to two orders of magnitude greater than those predicted by the MKV for similar values of . Thus, when using output from the Rosetta model for its parameters, the MVG gave results similar to those of the MKV, but when using field WRC from the internal drainage experiment and Ksat from the double-tube method (Allmaras, 1982), it gave results similar to those of the internal drainage experiment. |
DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSNOTESRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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) naturally raises questions about the accuracy and appropriateness of the different methods used in this study, particularly given the large differences in the amount of resources they require. The ID, for example, requires considerable financial and labour investment, as well as specialized and costly equipment. Furthermore, it would take several months for the soil to dry to water contents normally observed under dryland conditions. This imposes additional logistical constraints, because the experimental plots must be protected from rainfall. The MVG, in contrast, only requires soil texture and bulk density data when the Rosetta model is used for parameter estimation.
Mathematically, the ID, which used neutron probe and tensiometric data to calculate q and H/z, is similar to the MKV, which used neutron probe data and a numerical approximation of the WRC. However, the two methods differ fundamentally in the way in which q was calculated. In the ID, q was determined from the reduction in water stored in the profile above 1.22 m after the soil profile was saturated. By contrast, the MKV calculated q from the increase in water stored below 1.22 m and above the greatest depth of measurement. The size of this lower volume varied because of differences in depth to impermeable contact. Perhaps more importantly, the range of over which q was measured was quite different for the two methods. For the MKV, had a median value of 0.22 m3 m-3 and ranged from a minimum of 0.079 m3 m-3 to a maximum of 0.320 m3 m-3, with a standard deviation of 0.047m3 m-3. The median value of the Allmaras et al. (1977) data, on the other hand, was >0.30 m3 m-3 (see Fig. 1). Thus, the internal drainage data were obtained under much wetter conditions than are normally observed in the field.
As decreased to values of 0.23 m3 m-3, measured K() values from both internal drainage studies fell below those predicted by linear extrapolation of the regression curve to lower values (Fig. 1), which illustrates the hazards of linear extrapolation to values not experimentally measured.
As a practical matter, from the standpoint of drainage calculation, at a water content of 0.25 m3 m-3, which is typically maintained or surpassed at a depth of 1.22 m for many weeks in late winter or early spring, the linear equation fitted to the internal drainage data (Fig. 1) predicts a daily drainage rate of 4 mm for a gradient of unity. This suggests that a fairly substantial percentage of the mean annual rainfall is lost to deep drainage, and that there is some potential for leaching of chemicals. When we tested this K() function to correct water use of peas and wheat for deep drainage (Payne et al., 2001), however, we found that it lead to unrealistically low values of crop evapotranspiration (ET), and much greater ratios of yield (Y) to ET than are physiologically possible, based upon existing literature. Thus, even though some might view the internal drainage experiment as giving more accurate results for K(), we do not necessarily view it as such. At this same water content of 0.25 m3 m-3, the MKV, using the WRC1 data (Fig. 3), predicts a daily drainage rate of only 0.02 mm. This K() result, which is based on 20 yr of field observations under rainfed conditions, gave ET and Y/ET values that were much more realistic physiologically. On the other hand, we certainly wouldn't recommend using the MKV to extrapolate to greater water contents that might be obtained under irrigated conditions, and which were measured during the internal drainage experiment.
The MKV was designed for soil water balance studies that require an estimate of drainage after the wetting front surpasses the depth of neutron probe access tubes. Its only additional costs are associated with more frequent measurements before this occurs. Frequent measurements provide more q values for the subsequent regression to obtain K(), and help to avoid large differences in between successive measurements at a particular depth.
Because the ID and MKV methods used different soil volumes to calculate q, one may speculate that divergence for K() in the wetter range may have been partly because of soil macropore flow in the internal drainage experiment, which began under saturated initial conditions in the upper layers of the soil profile. Macropores from dead plant roots and soil fauna would exist mostly in the upper soil horizons, and may have accelerated water flux of water through the initially very dry soil. Additionally, tillage effects upon soil pore-size distribution would be more pronounced in the upper 40 cm (Pikul, 1988), and therefore influence the soil volume above 1.22 m and not that below. We note that Inskeep et al. (1996) also found that Ksat estimated from soil texture data using a regression equation was significantly lower than measured Ksat in the soil horizons below 0.30 m for a silt loam. They attributed the underestimation to lack of consideration of soil structure and macroporosity. Finally, because the internal drainage experiment essentially measures q from a drying upper soil volume, whereas the MKV measures q from a wetting lower volume, hysteresis may have contributed to differences in K().
The MVG model is attractive because it requires relatively few, simple and inexpensive inputs when used with the Rosetta model. But the Rosetta model draws upon a large database of hydraulic properties determined by different field and laboratory methods, which itself introduces error.
As shown by our results, both the MVG and MKV methods are very sensitive to the input data from which K() is calculated. For the MVG, the Ksat value of 346 mm d-1, measured by Allmaras (1982) with the double-tube method, was one order of magnitude greater than the value of 17 mm d-1 predicted by the Rosetta model for K0. This resulted in K() values that differed by one to two orders of magnitude when used in the MVG model (Fig. 4). Similarly, K() results for the MKV were sensitive to the selection of WRC (Fig. 3) because of the subsequent effect on H/z.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSNOTESRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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) probably depends upon the intended application. The best method will depend upon such additional factors as available human and financial resources, and existing data sets. For our purpose, which was to estimate root zone drainage in a dryland water balance study, the MKV appeared to be the most accurate method, based on the parameter Y/ET. But for irrigated or other conditions under which higher soil water contents are typical, the ID method appears to be more appropriate. The MVG is a very attractive alternative if one has confidence in its input parameters, especially where only limited data and financial resources are available. We recommend caution when using the Rosetta model for its input parameters, however, unless the intended application is purely heuristic. Considerable acumen is required for the selection of data inputs for both the MKV and MVG methods when estimating K(). We suspect that such acumen will come in large part from training and experience not easily duplicated by computer algorithms. |
ACKNOWLEDGMENTS |
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NOTES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSNOTESRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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Received for publication July 5, 2000.
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), which represents laboratory- and field-measured data of 
), calculated data from the Rosetta model, using percentages of clay, silt, and sand, and bulk density reported by 
), calculated data using the 
