Errors in water retention curves determined with pressure plates: Effects on the soil water balance

Journal of Hydrology 470–471 (2012) 65–74

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Errors in water retention curves determined with pressure plates: Effects on the soil water balance R. Solone a, M. Bittelli a,⇑, F. Tomei b, F. Morari c a

Department of AgroEnvironmental Science and Technology, University of Bologna, Viale Fanin 44, 40127, Bologna, Italy Regional Agency for Environmental Protection, Hydro-Meteo-Climate Service, Emilia-Romagna, Italy c Department of Agronomy, Food, Natural Resources, Animal and Environment, University of Padova, Italy b

a r t i c l e

i n f o

Article history: Received 19 April 2012 Received in revised form 3 August 2012 Accepted 11 August 2012 Available online 21 August 2012 This manuscript was handled by Peter K. Kitanidis, Editor-in-Chief, with the assistance of J. Simunek, Associate Editor Keywords: Soil water retention curve Pressure plate apparatus Dew point potential meter Hydraulic properties Water budget

a b s t r a c t Pressure plates apparatus are very common experimental devices utilized to measure the soil water retention curve. Many studies have demonstrated the lack of reliability of pressure plates apparatus when they are used to measure the soil water retention curve in the dry range, due to low plate and soil conductance, lack of hydrostatic equilibrium, lack of soil–plate contact and soil dispersion. In this research, we investigated measurements of soil water retention curves obtained with a combination of Stackman’s tables, pressure plates apparatus and the chilled-mirror dew point technique. Specifically, the aim of this research was: (a) to investigate the differences in the measured soil water retention curves by the different experimental methods, (b) evaluate relationships between the experimental differences and soil texture, (c) analyze the effect of experimental differences on hydraulic properties parameterization and (d) investigate the effects of the different parameters set on water transport computation. The results showed differences in measurements made by the combination of Stackman’s tables and Richards’ pressure plates apparatus as compared to the dew point method, for fine textured soils, while no significant differences were detected for coarse textured soils. Computed cumulative drainage and evaporation displayed lower values if soil water retention curves were obtained from data obtained with the Stackman’s tables and Richards’ pressure plates apparatus instead of the dew point method. In soils, where the soil water retention curve was measured with traditional methods (Stackman’s tables and Richards’ pressure plates apparatus) average cumulative drainage was 173 mm, with respect to a combination of methods including the dew point methods, where the average cumulative drainage was 184 mm. Average cumulative evaporation was 77 mm for the traditional methods, while it was 91 mm, for the combination of methods. Overall, when simulation models are used for studies related to solute transport, polluted soil remediation, irrigation management and others, erroneous measurement of the SWRC for fine textured soils, may lead to erroneous computation of the soil water balance. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction The soil water retention curve (SWRC) is the relationship between water content and matric potential. Knowledge of the SWRC is important to solve Richards’ equation (Campbell, 1985) and quantifying soil water flow. Many applications in agriculture and hydrology require the quantification of water flow, such as computation of irrigation volumes, fertilization, remediation of polluted sites and many others. Specifically, the numerical solution of Richards’ equation requires knowledge of the soil hydraulic properties as input parameters, namely the SWRC and the hydraulic conductivity curve (HCC). Several mathematical formulations for describ-

⇑ Corresponding author. Tel.: +39 051 2096779; fax: +39 051 2096641. E-mail addresses: [email protected] (R. Solone), [email protected] (M. Bittelli), [email protected] (F. Tomei), [email protected] (F. Morari). 0022-1694/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jhydrol.2012.08.017

ing the SWRC are available (Brooks and Corey, 1966; Durner, 1994; van Genuchten, 1980; Vogel and Cislerova, 1988). Parameterization of the SWRC can be obtained by: (a) fitting a mathematical model to experimental data using least-squares non-linear fitting algorithms or neural networks (Schaap et al., 2001), (b) employing inverse methods, which are methods where model parameters are iteratively changed so that a given selected hydrological model approximates the observed response (Vrugt et al., 2008) and (c) using pedotransfer functions (PTFs), which are regression equations based on the dependence of the SWRC on basic soil properties such as particle size distribution (PSD), bulk density and organic matter (Guber et al., 2009; Morari et al., 2004; Schaap et al., 2001). In recent decades, PTFs have been widely used because the use of Geographic Information Systems (GIS) coupled with crop and hydrological models, have increased the demand for soil databases at larger scales, such as catchment and regional-scale, requiring

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information on a very high number of spatially distributed soil types (Lin et al., 1997; Kravchenko and Zhang, 1997). The use of PTFs requires a periodic check of the estimated hydraulic properties against experimental SWRC data, because the reliability of the PTFs can be questionable. For instance, PTFs can be checked based on the choice of the regression models selected to estimate the hydraulic properties (Twarakavi et al., 2009), but the most important test should be performed on the reliability of the input experimental data. Since PTFs are more reliable when a high number of soil data and soil types are used, they are commonly developed by employing large soil databases (Leij et al., 1996; Twarakavi et al., 2009). In a review on PTFs, Vereecken et al. (2010) described in details many issues to explain the variability of the results obtained by using PTFs. They listed and discussed problems of predictors choice, soil spatial variability, fitting algorithms, and the functional form of the SWRC. However, they only briefly mentioned a key issue, the quality of the SWRC input data used to derive the PTFs parameters. Indeed, the majority of the soil databases are populated with SWRC data that were obtained by techniques that may have provided incorrect measurements. In particular, most of the SWRC data were measured using pressure plates apparatus (Gee et al., 2002) and therefore most of the current PTFs were obtained by fitting various mathematical equations to SWRC data measured in large part by using this technique (Clapp and Hornberger, 1978; Leij et al., 1996; Rawls et al., 1982; Saxton et al., 1986; Schaap et al., 2001; Vereecken et al., 1989). Clearly, there are questions about the reliability of such estimates if the reliability of the input data is questionable in first place. A discussion on the limitation and errors introduced by pressure plates apparatus is presented.

2. Methodological issues The SWRC can be measured by a variety of techniques. Detailed descriptions of the available techniques can be found in Campbell and Gee (1986) and Dane and Hopmans (2002). Among the available techniques, the most commonly employed are the Richards’ pressure apparatus (Dane and Hopmans, 2002; Richards, 1948, 1965), also called pressure plates (and hereafter called pressure plates apparatus). Since the 1960s several authors have raised questions about the reliability of pressure plates apparatus and presented comparisons between pressure plates apparatus measurements and other methods such as: psychrometry (Richards and Ogata, 1961), coupled osmotic tensiometer and thermocouple psychrometry (Madsen et al., 1986; Peck and Rabbidge, 1969), thermocouple psychrometry (Gee et al., 2002) and the dew point method (Bittelli and Flury, 2009). The results from these studies (performed on different soil types, in different experimental conditions and with different methods) were generally in agreement and demonstrated pronounced differences between pressure plate apparatus and other methods (most commonly based on vapor pressure measurements). In particular, the investigators reported that water potential measured with pressure plates apparatus were higher (Gee et al., 2002; Madsen et al., 1986; Peck and Rabbidge, 1969) and in error at potentials below 50 m-H2O (Campbell, 1988) or below 20 m-H2O (Bittelli and Flury, 2009). The authors attributed these errors to different causes: back flow of water from the membrane of the pressure plates apparatus into the samples, before the applied pressure was released (Richards and Ogata, 1961); failure to achieve hydrostatic equilibrium between the soil samples and the pressure plates apparatus (Campbell, 1988); failure to achieve equilibrium between the soil samples and the pressure plates apparatus at the potential of 150 m-H2O (Gee et al., 2002); loss of hydraulic contact between

sample and plate after the desaturation of the sample and soil dispersion (Campbell, 1988). Gee et al. (2002) performed a number of laboratory experiments and numerical simulations of water flow in pressure plates apparatus. They demonstrated that at low water potential (150 m-H2O), the value of hydraulic conductivity is so small that it would take months to reach hydraulic equilibrium. Indeed, in their simulations and experiments, none of the samples equilibrated at 150 m-H2O reached equilibrium even after 100 days. However, in their simulation the authors ignored the process of isothermal vapor equilibration and therefore they may have overestimated the equilibration time, since vapor flow may occur in these conditions, but they did not include it in their simulated processes. One study by Cresswell et al. (2008), found good agreement and good drainage from the majority of samples with <10% clay content while fine textured swelling soils did not equilibrated fully on pressure plates at either 50 and 150 m-H2O. To avoid introducing these errors in the SWRC measurement, Campbell and Shiozawa (1992) proposed three techniques for determining the water retention curve: hanging water columns and pressure plates apparatus in the wet range (hanging columns from 0 to 1 m-H2O, pressure plates apparatus from 1 to 50 m-H2O) and psychrometry in the dry range (water potentials <50 m-H2O). In general, the methods based on the equilibrium of the liquid phase are less reliable at very negative water potential because at such low values of water potential the unsaturated hydraulic conductivity is also very small, requiring long equilibration times that can lead to lack of equilibrium (Gee et al., 2002). On the other hand, methods based on the equilibration of the vapor phase do not have these problems since the equilibration of the vapor phase is much faster (if proper experimental conditions are set to remove the boundary layer) (Campbell and Norman, 1998). The disadvantage of the methods based on the equilibration of the vapor phase is that, at higher values of water potential (closer to saturation), the measurement becomes less reliable because of the exponential form of Kelvin’s equation (Campbell and Norman, 1998). According to Kelvin’s equation at 20 °C a change in relative humidity from 0.995 to 0.999, corresponds to a change in water potential from 70 m-H2O to 10 m-H2O. Therefore the resolution of water potential measurements with vapor pressure methods depends on the resolution of relative humidity measurements, which in turn depends on the resolution of temperature measurements. For instance, according to the manufacturer (Decagon, 2012), a dew point potentiameter has an accuracy of ±0.05 MPa (±5 m-H2O) from 0 to 5 MPa (from 0 to 500 m-H2O) and 1% from 5 to 300 MPa (from 500 to 30,000 m-H2O). Clearly, an error of ±5 m-H2O, over a measurement of, for instance, 10 m-H2O, corresponds to a 50% error, which is unacceptable. On the other hand, an error of ±5 m-H2O over a measurement of 500 m-H2O, corresponds to a 1% error. At 50 m-H2O (a threshold value used later for using different experimental techniques) the accuracy of the potentiameter is 0.5 m-H2O. Overall, vapor pressure methods are less reliable at high (less negative) values and more reliable at low (more negative) values of water potential. The two techniques (pressure plates and vapor pressure methods) are therefore a good combination, since when the first becomes less reliable (pressure plates at low values of water potential), the second one become more reliable. However, it is cumbersome and time consuming to employ two different methods to measure the SWRC, and a technique covering a wide range of water potentials is still needed. Efforts have been made to develop a method that covers a wide range of water potentials, such as the freezing apparatus proposed by Bittelli et al. (2003), however the device is not yet commercially available.

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The experimental results and error analysis discussed above were presented in the literature for a few soil samples, but there are still several open questions. Specifically: (a) is the magnitude of the errors introduced by pressure plates apparatus dependent on basic soil properties such as texture or mineralogy?, (b) what is the effect of these experimental differences on the SWRC parameterization? and (c) what is the effect of the different parameterization on water flow computation? The objective of this research was to address these questions, by comparing measurements of SWRC obtained with a combination of Stackman’s tables (Stackman et al., 1969) and pressure plates apparatus against SWRC obtained with the dew point technique for soils with different textural properties and evaluating the effect of the SWRC measurements on the parameterization of hydraulic properties. 3. Materials and methods 3.1. Soil samples: sampling and analysis The soil samples utilized in this study were collected in different areas of the Emilia-Romagna and Veneto region in northern Italy. The samples represented typical soil profiles of the regions, and they were classified in seven different textural classes. Undisturbed soil samples that were exposed from a vertical trench face were sampled with a hammer-driven auger at different depths. Particle size distributions was determined by sieving and pipette (Gee and Or, 2002), bulk density (qb) by the core method (Grossman and Reinsch, 2002), total porosity from knowledge of bulk density and total C was measured with a LECO Carbon Analyzer (LECO Corp., St. Joseph, MI). Soil properties are listed in Table 1. Based on the fractions of sand, silt and clay the samples were classified using the USDA classification. Qualitative and quantitative mineralogical analysis of the clay fraction was performed by X-ray diffraction for the samples from the Emilia-Romagna region (samples 1–11). The analysis was performed with the methodology presented by Harris and White (2008). The minerals that involved the interstratification of the layer clay minerals where the individ-

ual component layers of two or more kinds are stacked in various ways, were classified as interstratified (Fiore et al., 2010). Soils are represented on the textural triangle proposed by Gee and Or (2002) in Fig. 1, where the numbers on the triangle correspond to the soil list and properties presented in Table 1. 3.2. Soil water retention curve measurement Based on the methods and results presented by Bittelli and Flury (2009), two different set of measurements were performed: (1) Stackman tables (Stackman et al., 1969) and pressure plate apparatus, hereafter named STPPA, and (2) Stackman tables, pressure plate apparatus and dew point, hereafter named STPPADP. The rationale was to compare two sets of curves in which, in the first set, the dry range (commonly the range where the pressure plate fails) was measured by pressure plates apparatus, while for the second set the dry range was measured by dew point. For the wet and middle range, the same techniques were employed, using the Stackman tables and pressure plate apparatus. Specifically, the Stackman tables were utilized from 0 to 0.6 m-H2O, and the pressure plates apparatus from 1 to 150 m-H2O. When the dew point was used to replace the pressure plates apparatus, the range was for water potentials <50 m-H2O (Bittelli and Flury, 2009). Samples of 5-cm diameter and 1-cm height were collected, wetted from below with 0.01 M CaSO4 to reduce dispersion and saturated overnight. The samples were then placed into suction tables using the Stackman et al. (1969) method at the following potentials: 0.03, 0.1, 0.5 and 0.6 m-H2O. For potentials below 0.6 m-H2O, pressure plate apparatus were used and equilibrated at the following pressures 1, 2, 5, 25 and 150 m-H2O. We deemed equilibration to be completed after no outflow was measured for at least 2 days. After equilibrium was reached, the samples were removed from the pressure plates apparatus, and the water content was determined gravimetrically. Three replicates were performed for each measurement. A solution of BaCl2 was added to the saturating water solution to prevent microbial growth. The temperature controlled dew point meter device, WP4, (Scanlon et al., 2002; Decagon, 2012), was first calibrated with certified 0.5 molal KCl salt solutions.

Table 1 Soil properties. Number (–)

Sample codea (–)

Profile depth (cm)

Horizon (–)

Sand (%)

Silt (%)

Clay (%)

OM (%)

Textural classb (–)

Illite (%)

Kaolinite (%)

Smectite (%)

Interstratified (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

A1105V0029 A1105V0062 D3401V0050 D3401V0050 D3401V0050 E7103V0001 E7103V0001 E9001P0001 E9001P0002 E9001P0006 E9001P0013 1S5 1S6 2S1 2S5 2S6 LM21 LM22 LL21 LL22 L01 L02

0–40 50–70 0–20 20–38 38–60 0–45 40–85 0–10 0–55 0–55 0–60 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10

Ap Bg Ap Bw Bk Ap Bt Ap Ap Ap Ap Ap Ap Ap Ap Ap Ap Ap Ap Ap Ap Ap

10 2 8 8 10 7 5 5 16 21 50 84 88 88 83 89 31 33 46 45 39 38

66 52 43 46 37 85 76 42 40 56 37 8 4 4 7 5 53 51 42 45 49 48

24 46 49 46 53 8 19 53 44 23 13 8 8 8 10 6 16 15 12 10 12 13

1.2 0.8 2.7 2.5 0.7 na na 1.6 1.5 1.9 1.8 0.5 0.2 0.1 0.5 1.7 0.7 0.7 1 1.2 0.6 0.5

Silt loam Silty clay Silty clay Silty clay Clay Silt Silt loam Silty clay Clay Silt loam Loam Loamy sand Loamy sand Loamy sand Loamy sand Sand Silt loam Silt loam Loam Loam Loam Loam

14.2 16.6 19.3 19.1 19.3 16.1 16.0 23.7 23.0 22.5 23.5 na na na na na na na na na na na

17 18.9 27.4 27.6 24.0 21.0 26.0 24.3 24.1 23.9 23.0 na na na na na na na na na na na

37.7 42.3 35.2 35.1 38.2 32.7 30.9 38.7 39.2 39.9 39.2 na na na na na na na na na na na

31.1 22.2 18.1 18.2 18.5 30.2 27.1 13.3 13.7 13.7 14.3 na na na na na na na na na na na

na, not available. a Soil code. b Classes are according to USDA classification.

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et al., 1993). According to Shiozawa and Campbell (1991), PSD tends to be log-normal, so the appropriate means (l) and standard deviations (r) are log means and log standard deviations. These can be computed from size limits based on the following equations as proposed by Shiozawa and Campbell (1991):

ln l ¼

X

mi ln di

ð1Þ

and

ln r2 ¼

X

mi ðln di Þ2  ðln lÞ2

ð2Þ

where mi is the mass fraction of separate i, and di is the geometric or log mean diameter of the separates. Eqs. (1) and (2) are appropriate for any number of size classes. The geometric means (in lm), dy, dt and dd, are the geometric mean for clay, silt and sand (the subscripts y, t and d refer to the last letters of the words clay, silt and sand). They are calculated from set limits:

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:01  2 ¼ 0:14 pffiffiffiffiffiffiffiffiffiffiffiffiffi dt ¼ 2  50 ¼ 10

dy ¼

ð3Þ ð4Þ

and Fig. 1. Soil textural triangle for classification of the samples. The measured samples are identified on the triangle and represented by numbers from 1 to 22 in Table 1.

The soil samples were fully saturated with distilled water from below (as described above) for about 24 h. Then they were left to evaporate at a constant temperature into a temperature controlled chamber (25 °C), in plastic sample holders, for different times to reach increasingly lower level of water potential. Plastic sample holders were plastic cups of 1.4-cm height and 4-cm diameter. After becoming equilibrated (generally after 1–3 days), samples were measured with the WP4. Equilibration was deemed by measuring water potential changes with the WP4 over time. When water potential did not changed significantly over time, measurements were performed since the sample was deemed equilibrated. This procedure was followed to measure a drying curve for the WP4, which is the same SWRC measurement described above for the pressure plates apparatus. The wetting branch of the SWRC was not measured, therefore no analysis was performed on the effect of the two set of measurements on the SWRC hysteresis. Three repetitions were performed for each sample, by wetting the sample once, letting it evaporate and performing three measurements with the WP4. Then soil samples were covered to prevent further evaporation, and gravimetric water content was determined by oven drying (105 °C for 24 h). Since the WP4 measured the sum of the matric and osmotic potential, the osmotic potential was quantified by measuring the dew point of a saturated paste extract for each sample, as also described by Bittelli and Flury (2009). The paste extract was placed in a plastic cup and measured with the WP4. In this study, we assumed the chilled-mirror technique as the reference method for comparison with the pressure plates apparatus.

4. Particle size distribution To investigate the dependence of the SWRC measurement as function of textural properties, soil PSD was characterized by determining its geometric mean particle diameter. It has been reported that the three typical size fractions (sand, silt and clay) used as diagnostic characteristics in most classification schemes are rather arbitrary, since they do not provide complete information on the soil PSD (Bittelli et al., 1999). On the other hand, PSD can be represented by a variety of mathematical functions (Buchan

dd ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 50  2000 ¼ 316:2

ð5Þ

The lower and the upper limits for the clay fraction were set at 0.01 and 2, while 2 and 50 represent the lower and upper limits for the silt fraction, and 50 and 2000 represent the ones for sand, based on the USDA classification (Shiozawa and Campbell, 1991). Substituting Eqs. (3)–(5) into Eq. (1) leads to:

ln lm ¼ ½my ð1:95Þ þ mt ð2:3Þ þ md ð5:76Þ

ð6Þ

which is the logarithmic mean of the distribution. Its exponent can be computed to use the geometric mean. 5. Hydraulic properties parameterization The functions for SWRC and HCC used in this study were based on the modified formulation of the original van Genuchten (van Genuchten, 1980) and Mualem model (Mualem, 1976), as proposed by Ippisch et al. (2006). Indeed, it has been shown that the van Genuchten–Mualem model, can be problematic when SWRC data are used to predict the HCC (Ippisch et al., 2006; Vogel and Cislerova, 1988). A detailed theoretical description of these limitations was presented by Ippisch et al. (2006). In their paper, the authors specified the conditions for which the classical van Genuchten–Mualem model leads to wrong predictions of the HCC and presented a modified formulation that included an air-entry value. Based on theoretical considerations they concluded that the introduction of an air-entry value in the van Genuchten–Mualem model is obligatory if the parameter n < 2 or ah > 1, where h is the water potential and n and a are the van Genuchten parameters. Bittelli and Flury (2009) also found that the classical van Genuchten–Mualem model predicted erroneous hydraulic conductivity values for their silt loam soil, where the overall trend of the HCC showed an unrealistic behavior, and employed the modified formulation proposed by Ippisch et al. (2006). Overall, one may ask when the modified formulation of Ippisch et al. (2006) should be used instead of the original van Genucthen–Mualem model. By looking at tables of typical van Genuchten parameters, such the one presented by Leij et al. (1996) (Table 4, p. 35), the conditions described above are met by soils belonging to 10 out of 12 textural classes. Therefore the application of the van Genuchten– Mualem formulation will provide erroneous estimates of hydraulic conductivity for the majority of the soils, since the only two textural classes where n > 2 were sand and loamy sand. Also in this

R. Solone et al. / Journal of Hydrology 470–471 (2012) 65–74

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study, a fitting with the traditional van Genuchten formulation led to values of n < 2 for all samples (including the sandy samples), therefore we used this modified formulation. The modified formulation of Ippisch et al. (2006) has the following form:

( Se ¼

1 Sc

½1 þ ðahÞn m

1

if ðh 6 he Þ if ðh > he Þ

ð7Þ

where Se is the degree of saturation, a, m, n are fitting parameters, and Sc = [1 + (ahe)n]m is the water saturation at the air-entry potential he (the water potential is expressed as a negative number). In this work the restriction m = 1  (1/n) was used. The resulting hydraulic conductivity using the Mualem model is:

K¼

8 > <

K s Sle

> :

Ks



1ð1ðSe Sc Þ1=m Þm 1=m 1ð1Sc Þm

2

if ðSe < 1Þ

ð8Þ

if ðSe ¼ 1Þ

where l is the same parameter as in the original Mualem equation. Ippisch et al. (2006) suggested that he can be obtained either from knowledge of the largest pore size, from the SWRC or by inverse modelling. The air entry value could be obtained by letting he as a fitting parameter during the fitting procedure or using a fixed value. In this study a fixed values of he = 0.02 m-H2O was used as also suggested by Vogel and Cislerova (1988). The saturated hydraulic conductivity, Ks, was estimated from the PSD and the bulk density following the approach of Campbell and Shiozawa (1992), while the parameter l was set equal to 0.5. After determining the hydraulic properties, the model was then fitted to the two sets of measured curves as described above: (1) data measured with Stackman tables and pressure plates apparatus (STPPA) and (2) data measured with Stackman tables, pressure plates apparatus and dew point technique (STPPADP). The fitting algorithm, written by the authors in the language Python, was based on the minimization of the sum of least squares, as described by Marquardt (1963) and as implemented by Press et al. (1992). The authors translated the code from the Fortran language presented by Press et al. (1992) into the language Python (the code is available on request by the authors). The effects on the SWRC parameterization were then assessed by analyzing the consequences of these differences on the computation of vertical drainage and evaporation. 6. Comparison of water retention curves To determine at what value of water potential the two curves started to significantly differ, the Root Mean Square Error (RMSE) was used. Specifically, the RMSE between the measured values and the fitted curves were computed for the STPPA and the STPPADP. The two curves were deemed different when the fitted STPPA curve minus its RMSE multiplied by 1.96, was still higher than the fitted STPPADP curve one plus its RMSE multiplied by 1.96. The value 1.96 is the approximate value of the 97.5 percentile point of the normal distribution used in probability and statistics (Rees, 1987). The potential at which this condition was met was named deviation water potential (d). The formulation of this approach is: 

IF ½STPPA  ð1:96 RMSESTPPA Þ > ½STPPADP þ ð1:96 RMSESTPPADP Þ TRUE IF ½STPPA  ð1:96 RMSESTPPA Þ 6 ½STPPADP þ ð1:96 RMSESTPPADP Þ FALSE ð9Þ

where STPPA and STPPADP are the two fitted SWRC curves, while RMSESTPPA and RMSESTPPADP are the two corresponding RMSE. Fig. 2 depicts an example showing the two fitted curves (STPPA

Fig. 2. Example showing the procedure to determine the deviation water potential based on the RMSE times 1.96. The values of RMSE times 1.96, computed for each fitted curve, are subtracted from the STPPA curve and added to the STPPADP.

and STPPADP) and the curves with the error evaluation (STPPA  (1.96 RMSESTPPA) and (STPPADP + (1.96 RMSESTPPADP), as described above. This approach allowed to identify differences in the SWRC that were not within the measurement or fitting error, but that were statistically significant and therefore due to differences between the two set of experimental methods.

7. Numerical simulations The experimental analysis was supported by numerical water flow modelling to evaluate the effect of SWRC measurements on simulated soil water fluxes, water drainage and evaporation. Numerical simulations were performed to compute the soil water balance for each of the soils described in Table 1. Initial and boundary conditions were set equal for all soils, to investigate solely the effect of the different hydraulic properties on soil water redistribution, vertical drainage and evaporation. Indeed, the simulation was a simple redistribution and evaporation numerical experiment, into a 1D profile. The initial condition was of uniform saturated water content in the soil profile. An initial condition of uniform saturated water content was chosen to compare the cumulative annual drainage and evaporation for each soil, and investigate the differences between the STPPA and STPPADP. Simulations were performed for bare soils, using weather data for Carpaneto Piacentino an experimental area of the Italian Agricultural Research Council (CRA-CMA) for the year 2008. Boundary conditions were of atmospheric boundary condition with surface layer for the upper boundary (however since no precipitation was set in the weather file, a water surface layer never developed during the simulation). Indeed, the precipitation input was set to zero in the daily weather data, to remove the processes of infiltration and surface runoff from the computed processes. Although in natural conditions we would have had precipitation, as well as root water uptake, a simplified simulation was performed to analyze solely the effects of hydraulic properties parameterization on fewer processes, namely soil water redistribution, drainage and evaporation. For the lower boundary, a zero-gradient boundary condition (free drainage) was used to simulate a freely draining soil profile. The model employed is called CRITERIA and it is described in details by Bittelli et al. (2010, 2011). CRITERIA is a physicallybased, 1, 2 or 3D model (the domains of simulation can be selected by the user) that simulates saturated and unsaturated soil water dynamics by solving Richards equation for subsurface flow and the St. Venant equation for surface flow. Input parameters needed

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by the model are: a digital elevation model (DEM), a soil map, meteorological measurements (hourly shortwave radiation, relative humidity, air temperature, wind speed, and precipitation), soil physical properties (bulk density, texture, soil water retention curves, and vertical hydraulic conductivity) and crop parameters. The profile depth was 1 m. To evaluate the potential differences on the water budget terms scatter plots were analyzed, as well as cumulative curves for evaporation and drainage. 8. Results and discussion 8.1. Soil water retention measurement Fig. 3 shows four representative examples of SWRC measured with two different combination of techniques: the STPPA and the STPPADP. Table 2 show the fitting parameters obtained by fitting Eq. (7) with the experimental data. SWRC data points are the average of three replicates, for which the standard deviation was computed. Standard deviations between the three repetitions were always <0.04 m3 m3 in the wet range (water potential >50 mH2O) and <0.01 m3 m3 in the dry range (water potential <50 m-H2O), indicating a small variability among replicates for both measuring techniques; i.e., the precision of the measurements was good. The saturated paste extracts all showed no measurable potentials, i.e., the osmotic potential was too close to 0 m-H2O, and could not be measured with the dew point methods. Based on these results, we assume that the osmotic potential did not significantly affect the total water potential for our samples, and we neglected its effect in the measurements. As it is shown in Fig. 3, for some soils the drier portion of the two soil water retention curves deviated. Where the curves deviated, at the same water potential, the water content measured

with the STPPADP curve was lower as compared to the STPPA curves. This trend was detected for fine textured soils (sample numbers from 1 to 11). In coarse soils the deviations between the two curves were always smaller than the error, therefore not significant. The deviation water potentials (d) are shown in Table 3. These results are in agreement with the ones of Cresswell et al. (2008), where they found good agreement from the majority of samples with <10% clay, while they could not equilibrate swelling clay soil at either 50 and 150 m-H2O. Our hypothesis to explain these results is that drainage is impeded by loss of soil–plate contact as samples shrinks during drying. Indeed, a visual analysis during sample preparation and saturation, showed evident shrinking and swelling phenomena for the fine textured soils, as described below. 8.2. Errors as function of textural properties To assess if the textural properties of the different samples had an effect of these differences we plotted the geometric mean diameter (as computed from Eqs. (1)–(6)) against the water potential where the two curves deviated (Fig. 4). The data were log-transformed to allow for a linear regression analysis. This transformation is also supported by the assumption of a log-normal distribution of the grain size (Eqs. (1)–(6)), and of pore size distribution. The relationship depicts that when the geometric mean diameter was smaller, the two curves diverged at lower values of water potential (note that the water potential is expressed as absolute value), therefore when the soil was drier. On the other hand, for soils with larger geometric mean diameter (soils with a smaller fraction of fine particles), the deviation occurred at higher values. In soil with finer textures, water transport processes can still be significant at more negative water potential, since the unsaturated

Fig. 3. Examples of four soil water retention curves, measured with Stackman plates and pressure plates apparatus (STPPA) and Stackman plates, pressure plates apparatus and dew point potential meter (STPPADP). The points are experimental data from STPPA, triangles are experimental data from STPPADP, and the lines are fitted curves for the two sets of experimental data.

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R. Solone et al. / Journal of Hydrology 470–471 (2012) 65–74 Table 2 Soil water retention parameters obtained by using van modified Genuchten’s equation, for data measured with STPPA and STPPADP. Soil code

A1105V0029 A1105V0062 D3401V0050 D3401V0050 D3401V0050 E7103V0001 E7103V0001 E9001P0001 E9001P0002 E9001P0006 E9001P0013 1S5 1S6 2S1 2S5 2S6 LM21 LM22 LL21 LL22 L01 L02

Depth (m)

0–40 50–70 0–20 20–38 38–60 0–40 40–85 0–10 0–55 0–55 0–60 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10

Texture (–)

Silt loam Silty clay Silty clay Silty clay Clay Silt Silt loam Silty clay Silty clay Silt loam Loam Loamy sand Loamy sand Loamy sand Loamy sand Sand Silt loam Silt loam Loam Loam Loam Loam

STPPA

STPPADP 1

hs (–)

hr (–)

a (m )

m (–)

n (–)

he (m)

hs (–)

hr (–)

a (m1)

m (–)

n (–)

he (m)

0.46 0.48 0.45 0.46 0.38 0.42 0.41 0.50 0.60 0.35 0.37 0.52 0.51 0.47 0.53 0.49 0.42 0.42 0.46 0.47 0.38 0.44

0.001 0.001 0.184 0.160 0.063 0.001 0.001 0.001 0.001 0.002 0.095 0.063 0.050 0.045 0.061 0.047 0.001 0.001 0.022 0.001 0.056 0.002

0.301 0.040 0.091 0.040 0.037 0.028 0.016 0.122 0.488 0.381 0.267 0.353 0.349 0.328 0.354 0.360 0.067 0.085 0.035 0.067 0.014 0.057

0.124 0.112 0.140 0.173 0.150 0.163 0.210 0.062 0.073 0.117 0.164 0.719 0.730 0.733 0.729 0.731 0.234 0.184 0.323 0.236 0.398 0.275

1.142 1.126 1.163 1.209 1.177 1.194 1.266 1.066 1.078 1.133 1.195 3.564 3.700 3.749 3.693 3.711 1.305 1.226 1.476 1.309 1.661 1.380

0.04 0.42 0.42 0.22 0.22 0.11 0.17 0.53 0.14 0.34 0.09 0.11 0.07 0.09 0.07 0.09 0.14 0.14 0.42 0.22 0.82 0.22

0.46 0.48 0.44 0.45 0.37 0.43 0.41 0.49 0.60 0.34 0.37 0.52 0.51 0.47 0.53 0.46 0.41 0.41 0.46 0.47 0.38 0.44

0.001 0.001 0.001 0.001 0.001 0.001 0.073 0.001 0.001 0.001 0.001 0.038 0.040 0.036 0.053 0.041 0.001 0.001 0.016 0.001 0.045 0.001

0.188 0.023 0.024 0.010 0.015 0.068 0.018 0.011 0.056 0.050 0.112 0.364 0.351 0.329 0.356 0.352 0.050 0.064 0.034 0.052 0.014 0.053

0.141 0.138 0.178 0.182 0.155 0.228 0.542 0.174 0.163 0.190 0.201 0.673 0.713 0.719 0.716 0.719 0.256 0.219 0.320 0.251 0.374 0.282

1.164 1.160 1.216 1.223 1.183 1.295 2.182 1.210 1.195 1.235 1.252 3.054 3.490 3.563 3.517 3.563 1.344 1.280 1.471 1.336 1.598 1.392

0.04 0.42 0.42 0.22 0.22 0.11 0.17 0.53 0.14 0.34 0.09 0.11 0.07 0.09 0.07 0.09 0.14 0.14 0.42 0.22 0.82 0.22

Table 3 Root Mean Square Errors of the experimental data and water retention curves fitting (using Eq. (7)) for data measured with STPPA and STPPADP.

a b c

Number (–)

Sample codea (–)

Profile depth

Textural classb (cm)

RMSESTPPA (m3 m3)

RMSESTPPADP (m3 m3)

d (m-H2O)c

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

A1105V0029 A1105V0062 D3401V0050 D3401V0050 D3401V0050 E7103V0001 E7103V0001 E9001P0001 E9001P0002 E9001P0006 E9001P0013 1S5 1S6 2S1 2S5 2S6 LM21 LM22 LL21 LL22 L01 L02

0–40 50–70 0–20 20–38 38–60 0–45 40–85 0–10 0–55 0–55 0–60 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10

Silt loam Silty clay Silty clay Silty clay Clay Silt Silt loam Silty clay Clay Silt loam Loam Loamy sand Loamy sand Loamy sand Loamy sand Sand Silt loam Silt loam Loam Loam Loam Loam

0.0068 0.0035 0.0046 0.0035 0.0046 0.0114 0.0052 0.0045 0.0074 0.0045 0.0049 0.0267 0.0166 0.0247 0.0145 0.0207 0.0184 0.0148 0.0130 0.0128 0.0153 0.0089

0.0103 0.0119 0.0084 0.0119 0.0084 0.0052 0.0175 0.0081 0.0114 0.0101 0.0045 0.0131 0.0145 0.0208 0.0145 0.0191 0.0147 0.0216 0.0150 0.0128 0.0149 0.0105

25 4958 9.6 111.6 1039.7 1.6 4.9 29.3 12 57.2 3.9 ns ns ns ns ns ns ns ns ns ns ns

Soil code. Classes are according to USDA classification. ns, no statistical significance.

hydraulic conductivity is higher. However, if the soil–plate contact is reduced, this ability to drain water is lost. Mineralogical analysis of the soil sample showed that the samples 1–11, had high swelling–shrinking clay types, with high amounts of smectite. Indeed, from the mineralogical point of view, the soils are classified by the Geological Survey Service of the Emilia-Romagna region as smectitic. Shrinking–swelling processes depends on clay types and their quantitative distribution within the sample (Marshall et al., 1996). The relationships between the volumetric fractions of clay minerals and the deviation water potential (d) were investigated, however, no clear relationships were found. This was probably due to the fact that all the analyzed soils had high quantities of smectite (ranging from 30.9% to 42.3 %) and to the complexity of the dynamic of shrinking and swelling.

Overall, these results demonstrated that when pressure plates apparatus are used in fine textured soils with high content of clay types determining swelling–shrinking, errors in the measurement of the SWRC are already introduced at relatively high water potentials (less negative), as compared to coarse soils where pressure plates apparatus and the dew point methods showed no significant differences. It is also interesting to note that when the traditional textural fractions (sand, silt and clay) were plotted against the deviation water potential, the data were scattered and no relationship was found (data not showed). When texture was represented by a geometric mean diameter, instead of the traditional textural classes, a clear inverse relationship appeared (Fig. 4). These results confirm the conclusions of previous studies suggesting that statistical

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Log of Deviation water potential [m]

4 3.5 3 2.5 2 1.5

y= -1.42x + 2.33

1 0.5 0 0

0.5

1

1.5

2

Log of Geometric mean diameter [µm] Fig. 4. Relationship between log of geometric mean diameter and of deviation water potential. The water potential is expressed as absolute value.

parameters should be used to characterize soil texture instead of arbitrary defined textural classes, such as geometric diameters (Shiozawa and Campbell, 1991) or fractal dimensions (Bittelli et al., 1999). 8.3. Hydraulic properties parameterization Table 2 shows the parameters obtained from fitting the Ippisch et al. (2006) for the two sets STPPA and STPPADP. The parameter sets showed marked differences between the STPPA and STPPADP data sets. This difference was caused by the deviation of the experimental data. Examples of the corresponding water retention curves and their fitting are shown in Fig. 3. The RMSE (Table 3) were always <0.026 m3 m3 indicating that the model employed was a good estimator of the experimental data. The correlation coefficient among parameters was always |r| < 0.1, indicating that the parameters were not correlated. The parameters hs were the same for the two sets since the data close to saturation were obtained from the same data obtained with the Stackman’s tables and pressure plates apparatus, while the other parameters differed since they are affected by the shape of the curve. The residual water (hr) content is one of the parameters that differed the most, since the most pronounced differences between the two set of measurement were in the dry range. Indeed, the STPPA set had an average hr = 0.03, while the STPPADP displayed an average of hr = 0.01. The a parameter was consistently larger for the STPPA than for the STPPADP data. These results are consistent with the results described by Bittelli and Flury (2009). The parameters m and n, which describe the shape and slope of the curve, were higher for the STPPADP. This was due to the generally steeper shape of the STPPADP curves, a result of the lower water content values at the same water potential when measured with the dew point method. 8.4. Computation of water content, drainage and evaporation Fig. 5 shows cumulative drainage and evaporation for the whole simulation period, for both sets of measurement. Each single data point represents the annual cumulative evaporation, (a) and drainage, (b), for each soil textural class. Cumulative evaporation and drainage were higher, for fine textured soils, measured with STPPADP as compared to the ones measured with the STPPA. As discussed above, the coarse soils displayed no significant differences between the SWRC measured with STPPADP and STPPA. Indeed, in Fig. 5, the samples located closer to the 1:1 line (therefore with no significant deviations be-

Fig. 5. Comparison of cumulative annual drainage and evaporation for the two different measurement sets.

tween the two methods) were the loamy, loamy sand and sandy soils, as indicated by the ovals in the plate (b). Coarse soils displayed higher values of cumulative drainage, as also indicated by the oval in the upper right of plate (b). This is due to the shape of the SWRC for coarse soils and to the initial and boundary conditions of the numerical experiment. The soil initial conditions were of saturation water content and no precipitation was set during the numerical experiment, therefore in a sandy soil the initial drainage was higher because the saturated hydraulic conductivity is higher than in fine textured soils, as shown in the example of Fig. 6. In fine textured soils (samples 1–11) where the SWRC was measured with the STPPADP, average cumulative drainage was 184 mm, as compared to the STPPA, where the average cumulative drainage was 173 mm. Average cumulative evaporation for STPPADP was 91, while for the STPPA it was 77. The differences between STPPADP and STPPA were more pronounced for evaporation, where the slope of the curve is 1.14, as compared to the drainage prediction, where the slope was 1.03. The differences in cumulative evaporation and drainage as function of time during the numerical simulation are shown in Fig. 7 for a representative soil sample (number 3 in Table 1). The difference in the SWRC between the two methods (STPPA and STPPADP) determines a different magnitude of drainage and evaporation and with different dynamics. The differences in drainage are larger at the beginning of the simulation when the soil is saturated and therefore drainage is a dominant process, while there are no differences in evaporation between STPPA and STPPADP until the day of year is equal to approximately 50 (end of February). These differences are explained by the shapes of the SWRC and HCC and to the deviation water potential between STPPA and STPPADP (Table 3). Soil number 3, displayed a deviation water potential (d) at

R. Solone et al. / Journal of Hydrology 470–471 (2012) 65–74

Hydraulic Conductivity [cm/day]

10 10 10 10 10 10 10 10

the deviation between the two SWRC curves increased at decreasing values (more negative) of water potential (Fig. 3). Overall, these results show that the differences in SWRC measurements between STPPA and STPPADP, are important for the computation of water flow (therefore on drainage and evaporation processes). These differences are dependent upon the water potential at which the two SWRC deviates, and they differ in magnitude and dynamics depending on the processes analyzed and on the initial and boundary conditions.

5

Clay (5) Sand (16)

0

-5

-10

-15

-20

-25

9. Summary and conclusions -30

-2

10

-1

10

0

10

1

10

2

10

10

3

4

10

5

10

| Soil Water Potential [m] | Fig. 6. Comparison of hydraulic conductivity curves for a clay (number 5 in Table 1) and a sand sample (number 16 in Table 1).

160

Evaporation (mm)

140 120 100 80 60 40 STPPA STPPADP

20 0 70 60

Drainage (mm)

73

50 40 30 20

The conclusions of this study are the following: (a) the fine textured soil samples, measured with the two sets of methods displayed differences ranging from 1.6 to 4958 m-H2O; (b) errors introduced by using pressure plates apparatus were dependent on textural properties, where errors were found for fine textured soils while no significant errors were found for coarse textured soils; (c) these errors had an effect on hydraulic properties parameterization and (d) the differences in hydraulic properties parameterization determined differences in the computation of vertical drainage and evaporation. Specifically, the results of this study, performed over a wider range of textures with respect to previous ones, showed the limitation of pressure plate apparatus for measuring the SWRC in fine textured soils. It is suggested therefore that the use of pressure plates apparatus should be avoided in fine textured soils and other methods, such as the dew point technique, should be used. It is problematic that a multitude of data collected with pressure plates apparatus are still utilized for many applications in hydrology and agriculture, including the use of pedotransfer functions. This study suggests that common pedotransfer functions (obtained from pressure plates apparatus data) may provide erroneous hydraulic properties estimations and therefore erroneous estimates of drainage and evaporation. In summary, when simulation models are used for researches related to solute transport, polluted soil remediation, irrigation management and others, where the computation of water fluxes are key, erroneous measurement of the SWRC may lead to erroneous results and interpretation. Acknowledgments

STPPA STPPADP

10 0 0

50

100

150

200

250

300

350

Day of year Fig. 7. Example of cumulative evaporation and drainage as function of time (day of year) for the STPPA and STPPADP, for the soil sample number 3.

9.6 m-H2O (in absolute value). Since the simulation started with a saturated soil, the soil desaturated during the first few days, afterwhile the drainage process displayed differences in magnitude because the two SWRC curves differed already at relatively high values of water potential (less negative). This process is clearly depicted in plate (b) in Fig. 7. On the other hand, when the soil has a high water content, evaporation at the soil surface is high and depends on atmospheric conditions, but water vapor diffusion within the soil is limited by the low value of air filled porosity (Bittelli et al., 2008). Therefore, differences in evaporation rates, due to the shape of the SWRC and HCC curve, between STPPA and STPPADP, became more important at reduced values of soil water content. This is also the reason why the differences between the two methods were more pronounced for cumulative evaporation than for cumulative drainage, since

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