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Published online 13 September 2005
Published in Vadose Zone J 4:899-907 (2005)
DOI: 10.2136/vzj2004.0156
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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ORIGINAL RESEARCH

Soil Water Extraction with a Suction Cup

Results of Numerical Simulations

Lutz Weihermüller*, Roy Kasteel, Jan Vanderborght, Thomas Pütz and Harry Vereecken

Agrosphere Institute, ICG IV, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
* Corresponding author (l.weihermueller{at}fz-juelich.de)

Received 22 October 2004.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 APPENDIX
 REFERENCES
 
Porous cups are widely used to extract soil water for monitoring solute transport. However, it is not yet clear how the suction cup influences the matric potential in the surrounding soil and which part of the soil is sampled. This research was designed to numerically evaluate the activity domain, the extraction domain, and sampling area of a suction cup under constant infiltration. A finite-element model (HYDRUS-2D) was used to simulate the effect of various applied suctions at two infiltration rates on the water status in three soils (clay loam, sandy clay, and sand). Particle tracking was used to track the streamlines that define the sampling area and extraction domain of the suction cup. In general, the activity domain, the extraction domain, and sampling area of the suction cup depend primarily on the soil hydraulic parameters and the upper boundary, and secondarily on the applied suction. Results showed that the activity domain, the extraction domain, and the sampling area are largest for highest ambient hydraulic conductivities. The activity domain and the sampling area also decrease with increasing infiltration rates. Further, the activity domain of the suction cup depends strongly on the duration of water extraction. Soil heterogeneity seems to play a minor role with respect to the activity domain and sampling area of the cup.

Abbreviations: NMFP, normalized matric flux potential • SCAD, suction cup activity domain • SCED, suction cup extraction domain • SCSA, suction cup sampling area


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 APPENDIX
 REFERENCES
 
POROUS CUPS PROVIDE a simple and direct method for water extraction in the vadose zone and are still widely in use (e.g., Krone et al., 1951; Reeve and Doering, 1965; McGuire and Lowery, 1994; and Williams and Lord, 1997). The presumed advantage of the porous cup method is that the disturbance of the surrounding soil is negligible after installation and, as a consequence, only minor changes in natural percolation behavior are induced (Grossmann and Udluft, 1991). This offers the possibility to sample simultaneously soil water at different depths to record time series of solute breakthrough. The sorption tendencies of suction cups for organic and inorganic compounds have been widely discussed in literature (e.g., Wagner, 1962; Hansen and Harris, 1975; McGuire et al., 1992; and Wessel-Bothe et al., 2000). A serious limitation, however, resides in the fact that the sampling volume and the imposed changes in matric potential during sampling on the natural flow pattern are not well known (Hart and Lowery, 1997). It has also been speculated that porous cups have an inherent bias in preferentially monitoring the chemical composition of larger soil pores at the expense of finer pores (Hansen and Harris, 1975; Severson and Grigal, 1976). To provide a consistent means for the interpretation of the numerical solutions of suction cup behavior three cup characteristics are proposed:

  1. The suction cup activity domain (SCAD) is defined as the spatial extension (cm) of the difference in matric potential between the initial situation without applying suction and the conditions where suction is applied to the cup. It represents the area of influence in matric potential distribution of the natural flow field after suction is applied. For a better comparison between different cases, the activity domain will be plotted as a horizontal transect through the cup.
  2. The suction cup extraction domain (SCED) is an area (cm2), for a two-dimensional case, or volume (cm3), for a three-dimensional case, from which water and solute can be extracted by a suction cup within a certain time of applied suction. If the sampling time is set to infinity, the suction cup extraction domain will eventually reach the soil surface and in the limit will be equal to the suction cup sampling area (SCSA).
  3. The suction cup sampling area (SCSA) is defined as the area at the overlying soil surface from which water could be captured by the suction cup under a continuous application of tension. It is expressed in unit length (cm), for the two-dimensional case, or unit area (cm2) for the three-dimensional case.

The interaction between soil water extraction and flow field has been studied using laboratory and field-based experiments (Morrison and Lowery, 1990; McGuire and Lowery, 1994; Wu et al., 1995; Hart and Lowery, 1997), analytical solutions (Warrick and Amoozegar-Fard, 1977; Hart and Lowery, 1997), and numerical simulations (Germann, 1972; van der Ploeg and Beese, 1977; Talsma et al., 1979; Barbee and Brown, 1986; Grossmann, 1988; Wu et al., 1995; Narasimhan and Dreiss, 1986; Weihermüller, 2005). The laboratory-based experiments of Morrison and Lowery (1990) suggest that the SCED is closely connected to the SCAD. The analytical solutions of Warrick and Amoozegar-Fard (1977) and Morrison and Szecsody (1985) showed a dependency of the SCAD on soil properties, with smaller SCADs for coarse soils and larger SCADs for fine soils. Warrick and Amoozegar-Fard (1977) also calculated the dividing streamline which separates the flow field into the region from where water will be extracted by the suction cup and the region where water percolates into the deeper profile. This approach can also be taken to identify the suction cup sampling area, whereby coarser soils result in smaller sampling areas. Numerical simulations of Wu et al. (1995) noted that the source region for the solute collected in the suction cup will be smaller than the activity domain, since water moving in the outer reaches of this activity domain never reaches the cup before cessation of suction. Numerical simulations of Tseng et al. (1995) indicate that the applied suction in the cup decrease the peak concentration and increase the mean and variance of travel times to varying degrees, but the activating process was not identified. In the present work, numerical simulations were conducted to examine the impact of soil water extraction with suction cups on the spatial distribution of the matric potential and to determine the SCED and sampling area in homogeneous and heterogeneous soils. The simulations were performed to obtain data of the influence of different soil hydraulic properties as well as changes of the upper boundary condition to the pressure head field within the flow domain. This approach combines the different experiments conducted by Warrick and Amoozegar-Fard (1977), Morrison and Lowery (1990), Tseng et al. (1995), and Wu et al. (1995) and identifies the influence of the boundary conditions on the SCAD, SCSA, and SCED in homogeneous and heterogeneous soils. However, the study is not concepted to account to preferential flow due to cracks, worm holes, or root channels, which might be important to water and solute transport in natural soils and might influence the SCAD, SCSA, and SCED.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 APPENDIX
 REFERENCES
 
For the simulation of soil water fluxes the finite element code HYDRUS-2D (Simunek et al., 1999) was used, which numerically solves Richards' equation (Eq. [1]) for saturated–unsaturated water flow:

[1]
where {theta} is the volumetric water content (cm3 cm–3), {psi} is the matric potential in head units (cm), x and z are spatial coordinates (cm) in transversal and longitudinal direction, respectively, and K({psi}) is the unsaturated hydraulic conductivity (cm h–1). The parameterization of the soils and the suction cup is based on the Mualem and van Genuchten approach (van Genuchten, 1980) with the effective volumetric water content Se:

[2]
where {theta}r (cm3 cm–3), and {theta}s (cm3 cm–3) are the residual and saturated volumetric water content, respectively, and {alpha} (cm–1), n, and m (m = 1 – 1/n) are shape parameters. Assuming that the tortuosity factor equals 0.5, the Mualem–van Genuchten approach leads to the unsaturated hydraulic conductivity function given by Eq. [3].


[3]
Water flow is simulated in a two-dimensional field 200 cm wide and 200 cm deep. The discretization is nonequidistant with smaller nodal distance in the vicinity of the suction cup (total number of nodes = 40158). The suction cup had an outer radius of 2.4 cm and was implemented in the center of the flow domain. A cross-section of the flow domain is shown schematically in Fig. 1 . The boundary condition of the suction cup was represented as a prescribed head. Infiltration was uniform and constant in time through the upper boundary.



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  		Fig. 1. Cross-section of the flow domain with a suction cup with graphical definitions of the suction cup extraction domain (SCED) and suction cup sampling area (SCSA).

 
The lower boundary was chosen to be a seepage face, which is typical for zero-tension lysimeters. No-flow conditions were imposed on the remaining boundary nodes. For the simulation three different soils (i.e., clay loam, sandy clay, and sand) were chosen from the HYDRUS soil catalog.

The hydraulic properties of the soils and suction cup are listed in Table 1 and are shown in Fig. 2 . The applied suction inside the cups as well as the potential differences (picked at the border of the flow field at the depth of the suction cup) of the matric potentials between a simulation with and without applied suction are listed in Table 2.


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  		Table 1. Hydraulic properties of the soil and suction cup.

 


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  		Fig. 2. Hydraulic properties of the soils and suction cup: (a) water retention function and (b) hydraulic conductivity function.

 

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  		Table 2. Applied suction in the suction cup and potential differences.

 
The initial condition was a hydrostatic equilibrium with the groundwater table at the lower boundary. The simulation period was chosen to be 9000 h, which was sufficiently long to reach a stationary flow field in all cases. The global water mass balance error was always <1% for all time-steps. All outputs were taken at the final time step.

The sampling area and the extraction domain of the suction cup were calculated by tracking the streamlines using particles. In total 2000 particles were uniformly applied at the soil surface. The sampling area was determined by assigning the initial start position at the soil surface to each particle. This procedure backtraced the initial position of particles trapped in the suction cup. To determine the SCED, the water flow field was inverted and 2000 particles were released from the suction cup outer surface. The end positions of the particles then delineate the extraction domain as a function of the extraction time.

Local-scale heterogeneity in hydraulic properties was generated using Miller-Miller scaling theory (Miller and Miller, 1956). The spatial correlation structure of the scaling factor is given by an exponential auto-covariance model with variance, {sigma}2f = 0.0625, and correlation length, {lambda}f = 10 cm. The heterogeneous profile is plotted in Fig. 3 .



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  		Fig. 3. Random heterogeneous (Miller-Miller-similar) field generation of the scaling factor with standard deviation of 0.25 and a correlation length, {lambda}f, of 10 cm.

 

   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
SUMMARY AND CONCLUSIONS
 APPENDIX
 REFERENCES
 
The SCAD for the clay loam, sandy clay, and sandy soil with various applied suctions (see Table 2) and a constant infiltration rate Jw = 0.013 cm h–1 is shown in Fig. 4 . As expected, the highest matric potential differences occur in the direct vicinity of the suction cup and decline to the periphery. Increasing the applied suction results in larger differences in matric potential. Suctions larger than 300 cm result in only small changes in matric potential differences. Therefore, the SCAD does not change much. In the case of the sandy soil, changes in matric potential differences are hardly noticeable for all applied suctions. The matric potential differences of the sandy soil are somewhat smaller than for the sandy clay and largest for the clay loam.



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  		Fig. 4. Suction cup activity domain (SCAD) on a horizontal transect through the suction cup plotted as matric potential differences for all applied suctions. Upper boundary constant flux Jw = 0.013 cm h–1: (a) clay loam, (b) sandy clay, and (c) sand. Note that the ordinate has been split to visualize small differences in the periphery of the cup.

 
If we look at the hydraulic conductivity function (Fig. 2b) and compare the hydraulic conductivities for the applied suction higher than 30 cm a ranking of the three soils occurs with lowest conductivities for the sandy soil, slightly higher values for the sandy clay, and highest for the clay loam.

If these results are compared with the activity domain of the three soil types, a dependency is obvious. The activity domain is the smallest for sandy soil, slightly larger for sandy clay, and largest for clay loam. It becomes clear that the maximum activity domain of a suction cup is primarily determined by the hydraulic conductivity of the soils. In general, the maximum of the activity domain will be reached for an applied suction where the first derivative of the hydraulic conductivity function converges to zero. This stage is reached at matric potentials <30, 60, and 100 cm for the sand, sandy clay, and clay loam, respectively. The limiting factor for the activity domain of the suction cup is, therefore, the hydraulic conductivity at ambient matric potentials. Higher hydraulic conductivities result in larger activity domains for the suction cup.

The convergence of the SCAD up to the maximum SCAD also depends on the hydraulic conductivity for ambient matric potentials. Larger changes in the SCAD occur with larger changes in the hydraulic conductivity.

If we compare the activity domain of the homogeneous medium to that of the simulated heterogeneous Miller-Miller-similar medium (heterogeneous field with {lambda}f = 5 cm and {sigma}2f = 0.0625 not shown) (Fig. 5) , only slightly smaller activity domains were found for all soils and applied suctions. In general, the underlying heterogeneous hydraulic structure seems to play a minor role in the differences in matric potential due to the fact that the gradient for the total head is the driving force for water flow, which will be minimized. Therefore, soil heterogeneity will not be directly reflected in the matric potential distribution, in comparison to the water content.



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  		Fig. 5. Suction cup activity domain (SCAD) on a horizontal transect through the suction cup plotted as matric potential differences for all applied suctions in a heterogeneous Miller-Miller-similar medium . Upper boundary constant flux Jw = 0.013 cm h–1: (a) clay loam, (b) sandy clay, and (c) sand. Note that the ordinate has been split to visualize small differences in the periphery of the cup.

 
Suction Cup Sampling Area
Figure 6 shows the SCSA (2r) as a function of applied suction for the three soils under stationary conditions with varying applied suctions (from 30–1000 cm) both for a homogeneous and heterogeneous medium. In general, the sampling area increases with increasing suction in the cup and reaches a maximum value for suctions larger than 300 cm. If we compare the sampling area for each set of simulations, clay loam shows the largest SCSA, and sand the smallest. These results confirm the findings of the analytical solution presented by Warrick and Amoozegard-Fard (1977), who found the same ranking (see Fig. 7) . In the analytical solutions the streamline labeled 1.0 is the dividing streamline and separates water going into the cup from water that goes past the cup and downstream. For suction smaller than 50 cm this ranking is not valid (Fig. 6a and 6b), because differences in ambient matric potential for the three soils is not negligible for the case without suction. The hydraulic gradient of the sandy soil, sandy clay, and clay loam are 30, 41, and 20 cm, respectively. Simulations with the same hydraulic gradient showed comparable results in ranking even for low applied suctions.



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  		Fig. 6. Suction cup sampling area (SCSA) (2r) for stationary conditions for a clay loam, sandy clay, and sandy soil for all applied suctions: (a) for a homogeneous medium and a constant flux Jw = 0.013 cm h–1, and a constant flux Jw = 0.051 cm h–1, and (b) a heterogeneous Miller-Miller medium ({lambda} = 10 cm and {sigma}2f = 0.0625) and a constant flux Jw = 0.013 cm h–1.

 


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  		Fig. 7. Flow net of the streamlines for a suction cup with dividing stream line q = 1.0 for an applied suction of 100 cm for (a) clay loam, (b) sandy clay, and (c) sand soil. All calculations were done using Eq. [13] after Warrick and Amoozegar-Fard (1977) with {alpha} = 0.0236 (cm–1), q = 2914 (cm–3 h–1), {psi}1 = –31.2 (cm), and Ks = 0.26 (cm h–1) for the clay loam, {alpha} = 0.0279 (cm–1), q = 2834 (cm–3 h–1), {psi}1 = –7.2 (cm), and Ks = 0.12 (cm h–1) for the sandy clay, and {alpha} = 0.0978 (cm–1), q = 2734 (cm–3 h–1), {psi}1 = –20.5 (cm), and Ks = 29.7 (cm h–1) for the sand soil.

 
Comparison of the two infiltration rates indicated that the sampling area decreases for increasing fluxes. This decrease can be ascribed to the smaller suction cup activity domain shown in Fig. 4 and 5. The simulated soil heterogeneity does not influence the sampling area for all three soils.

To confirm these results the sampling area is plotted against the normalized matric flux potential (NMFP), which is the integral of the hydraulic conductivity (K) function from matric potential at the given infiltration rate to applied suction divided by the flux rate (Fig. 8) .

[4]
The NMFP combines the hydraulic properties of the soil, the applied suction in the cup, and the given infiltration rate at the upper boundary. In Fig. 7 the NMFP is plotted vs. the sampling area. The plot shows that no unique characteristic for all soils is deducible, but for each soil and flow rate we find an estimation of the SCSA by changes of applied suction in the cup.



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  		Fig. 8. Normalized matric flux potential (NMFP) for two infiltration rates Jw = 0.013 cm h–1, and 0.051 cm h–1 in correlation with the SCSA for a clay loam, sandy clay, and sand soil. NMFP calculated using Eq. [4].

 
The breakthrough of the particles in the suction cups (travel time) indicates a faster arrival of the particles directly applied above the cup and a slower breakthrough for particles trapped at the bottom of the cup compared to the undisturbed flow field (no suction applied within the cup). As a result, an earlier arrival and a pronounced tailing occurs compared to an undisturbed fictive point at the same depth (see Fig. 9) . As shown in Fig. 10 , the arrival time in the cup, as well as the amount of trapped particles, depends on the applied suction in the cup because higher potential gradients induced by applied suction increase the pore-water velocities. The pronounced tailing of the particle breakthrough is a result of a longer travel distance of the particles trapped at the bottom of the cup.



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  		Fig. 9. Travel time for all particles trapped either in the suction cup or at the lower boundary for a simulation in a clay loam with constant flux Jw = 0.013 cm h–1 (a) for no applied suction in the cup, and (b) an applied suction of 100 cm in the cup.

 


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  		Fig. 10. Travel time for all particles trapped in the suction cup for a simulation in a clay loam with constant flux Jw = 0.013 cm h–1 and applied suction of 50, 100, 300, 600, and 1000 cm in the cup.

 
Apart from the activity domain in the direct vicinity of the cup, the extraction of soil water also influences the arrival of particles deeper down in the profile. As shown in Fig. 9 the arrival of particles at the lower boundary of the flow domain is decelerated if water was extracted. Particles trapped at the lower boundary directly below the suction cup are slower (by a factor of two) than the undisturbed particle flow (see Fig. 9) due to deflection of streamlines in the flow domain by water extraction of the suction cup. The magnitude of deceleration at the bottom of the flow field depends on the infiltration rate and the applied suction, whereby higher applied suctions result in a larger deceleration and a more pronounced tailing of the arrival time. This fact has to be taken into account when lysimeter or column experiments were equipped with suction cups operating in a continuous mode.

Suction Cup Extraction Domain
The SCED is plotted in Fig. 11 and 12 as a function of extraction time for two applied suctions, 100 and 1000 cm, respectively. The infiltration rate for both cases was set to Jw = 0.013 cm h–1. The activity domain is also shown as differences in matric potential with smallest changes for an applied suction of 100 cm than for the higher applied suction of 1000 cm. Both figures clearly show that the SCED increases with increasing extraction time. If the time is set to infinity the SCED will eventually reach the soil surface and then delineates the SCSA. The geometry of the SCED differs between both cases. The case with larger suction leads to more pronounced water extraction from below the cup. The SCED for water flow to the cup predicted by the simulations does not have a static geometry and, therefore, a comparison with the analytical solutions of the normalized Stokes stream function by Warrick and Amoozegard-Fard (1977) (see Fig. 8), and other SCED equation (e.g., Hart and Lowery, 1997) are not applicable. It should also be noted that the source region for water extracted by the cup will be smaller and out of a different region than the activity domain delineated by the deformation of the water content field.



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  		Fig. 11. Suction cup activity domain (SCAD) (background) and suction cup extraction domain (SCED) (black contour) for a clay loam with constant flux Jw = 0.013 cm h–1 and an applied suction of 100 cm for a travel time of (a) 100, (b) 500, (c) 1000, and (d) 2000 h.

 


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  		Fig. 12. Suction cup activity domain (SCAD) (background) and suction cup extraction domain (SCED) (black contour) for a clay loam with constant flux Jw = 0.013 cm h–1 and an applied suction of 1000 cm for a travel time of (a) 100, (b) 500, (c) 1000, and (d) 2000 h.

 

   SUMMARY AND CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
APPENDIX
 REFERENCES
 
In this study we analyzed the impact of suction cups on the state variables of water flow and solute transport using numerical simulations in homogeneous and heterogeneous soils. The numerical simulations were done for three soil types and two different boundary conditions. As a result three typical properties of the suction cups were defined: (i) SCAD, (ii) SCED, and (iii) SCSA.

The SCAD was found to be dependent on the soil hydraulic properties, the infiltration rate, and the applied suction in the cup. In general, the SCAD is detectable within decimeters in the flow field, with the smallest SCAD for coarser soils. The spatial extend of the activity domain showed a pronounced propagation of the matric potential differences below the suction cup. The SCAD decreased with increasing infiltration. The suction cup sampling area was found to be dependent on the soil hydraulic properties, the infiltration rate, and the applied suction in the cup. Again, smallest SCSAs were found for coarser soils. The SCSA decreased with increasing infiltration. The analysis of the sampling area resulted in qualitative estimations that corresponded to those derived using the analytical solutions of Warrick and Amoozegard-Fard (1977) with a dependency of the SCAD on the soil hydraulic properties and smallest SCAD for coarser soils. The SCED reflects the region where water is extracted. Therefore, it is not useful to interpret changes in matric potential (SCAD) as the extraction domain. Furthermore, the extraction domain is a function of time, and therefore, not a static region. For prolonged sampling, soil water will be sampled that is not in the direct vicinity of the cup. Thus, soil water sampled from the profile will not represent the solute concentration at the depth of the suction cup and it might also be extracted from below the cup.

If hydrodynamic dispersion and diffusion is negligible the calculated mean arrival time of the sampling area are transferable to conservative tracers (e.g., bromide or chloride). For sorbing chemicals the retardation factor also has to be considered into the travel time. The detected arrival time of the tracer pulse in the suction cup was lower compared to an undisturbed case. At the same time the tailing of the breakthrough will be more pronounced using suction cups, because of the deflection of the streamlines, which result in a longer percolation distance. As a consequence, an enhanced spreading of the breakthrough curve will occur compared to undisturbed solute transport at the same depth. The mean travel time of the tracer pulse at the lower boundary (seepage face) will be delayed if extraction of soil water is performed by suction cups under continuous applied suction. This effect should be taken into account if lysimeter experiments with installed suction cups are used for solute transport prediction. However, the study cannot give any information about the behavior of the SCAD, SCSA, and SCED in soils where preferential flow might be a major transport phenomena due to cracks, worm holes, root-channels etc. In general, the findings of theses study can help to interpret suction cup results in homogeneous and heterogeneous soil under stationary conditions. But still no estimations about the SCAD, SCSA, and SCED can be drawn for nonstationary conditions due to the dependency on the infiltration rate and the resulting variations in water content. Therefore, results of water extraction via suction cups under natural field conditions should be interpreted carefully in terms of mass recovery, effective transport parameters, mean pore water velocity, and dispersivity.


   APPENDIX
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 APPENDIX
REFERENCES
 
Abbreviations
{alpha} (cm–1), reciprocal value of the air entry value (bubble point)

f (-), logarithm of scaling factor

Jw (cm h–1), water flux density

{lambda}f (cm), correlation length of f

K (cm h–1), hydraulic conductivity

m (-), van Genuchten parameter

n (-), van Genuchten parameter

NMFP (cm), normalized matric flux potential

{theta} (cm3 cm–3), volumetric water content

{theta}r (cm3 cm–3), residual water content

{theta}s (cm3 cm–3), saturated water content

{sigma}2f (-), variance of f

Se (-), effective water content

t (h), time

{psi} (cm), matric potential expressed in equivalent height

x (cm), horizontal transversal direction

z (cm), longitudinal direction, mean flow direction


   ACKNOWLEDGMENTS
 
This study was funded by BayerCropScience AG Landwirtschaftszentrum Mohnheim, Germany and the Forschungszentrum Jülich GmbH (member of the Helmholtz Gesellschaft, Germany).


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 APPENDIX
 REFERENCES
 




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