Abstracts
The simple methods of LIBARDI et al. (1980) and SISSON et al. (1980) for K(theta) estimation, although developed on completely different theoretical basis, are rigorously identical for the exponential hydraulic conductivity model. The unit gradient approximation used in these methods seems valid for practical purposes but is theoretically in valid.
soil hydraulic conductivity; unit gradient
Os métodos simplicados de LIBARDI et al (1980) e de SISSON et al (1980), para determinação da função K(teta), apesar de serem desenvolvidos sobre bases teóricas completamente diferentes, são rigorosamente iguais para o modelo exponencial de condutividade hidráulica. A hipótese do gradiente unitário utilizada nestes métodos parece ser válida apenas para efeito prático, mas não o sendo teoricamente.
condutividade hidráulica do solo; gradiente unitário
NOTE
On simple methods for unsaturated soil hydraulic conductivity determination
Sobre métodos simplificados de determinação da condutividade hidráulica do solo
O.O.S. BacchiI, ^{1} 1 Bolsista do CNPq ; K. Reichardt^{II,}^{1} 1 Bolsista do CNPq
^{I}Centro de Energia Nuclear na Agricultura/USP  C.P. 96, CEP: 13400970Piracicaba,SP
^{II}Departamento de Física e Meteorologia  ESALQ/USP  C.P. 9, CEP:13418900Piracicaba,SP
ABSTRACT
The simple methods of LIBARDI et al. (1980) and SISSON et al. (1980) for K(q) estimation, although developed on completely different theoretical basis, are rigorously identical for the exponential hydraulic conductivity model. The unit gradient approximation used in these methods seems valid for practical purposes but is theoretically in valid.
Key Words: soil hydraulic conductivity, unit gradient.
RESUMO
Os métodos simplicados de LIBARDI et al (1980) e de SISSON et al (1980), para determinação da função K(q), apesar de serem desenvolvidos sobre bases teóricas completamente diferentes, são rigorosamente iguais para o modelo exponencial de condutividade hidráulica. A hipótese do gradiente unitário utilizada nestes métodos parece ser válida apenas para efeito prático, mas não o sendo teoricamente.
Descritores: condutividade hidráulica do solo, gradiente unitário.
INTRODUCTION
The goals of this short note are to comment that although the unit gradient assumption can be used under certain limitations in practice for K(q) determination, as successfully shown by LIBARDI et al. (1980) and SISSON et al. (1980), is an approximation without theoretical support. Another objetive is simply to show that the above mentioned methods are identical for exponential K(q) relations.
Many methods used for field determination of unsaturated soil hydraulic conductivity are based on experimental designs involving the drainage of previously saturated soil profiles, preventing soil surface evaporation and using the so called "unit gradient assumption". This assumption first introduced by DAVIDSON et al. (1969), has been used in several field methods (e.g. CHONG et al., 1979; LIBARDI et al., 1980; SISSON et al., 1980) and extensively discussed in the literature (e.g. AHUJAetal., 1988). The validity of this assumption though frequently questioned was formally presented as theoretically invalid by REICHARDT (1993). All hydraulic conductivity determination methods are essentially based on Darcy's equation, K(q) values being calculated from water flux density, hydraulic gradient ratios. The unit gradient assumption implies that conductivities are numerically equal to flux densities. During internal drainage, soil water flux densities vary several orders of magnitude over short time periods, whereas hydraulic gradients vary very little over long periods of time. Therefore the limitations of the use of unit gradient assumption are, in practice, not serious, and minimal the more homogeneous the soil is and the closer to saturation calculations are made. The procedure to calculate K(q) relations presented by HILLEL et al. (1972) clearly indicates the effect of . Gradients deviating 0.2 from unity would introduce errors of about 20% in K(q) calculations.
Since water flow is important in the very wet region of the soil profile, when gradients are close to unity, methods using the unit gradient assumption may yield accurate K(q) values. For the appropriate application of these simplified methods it is therefore recommended that observations of q in space and time during the internal drainage process should not be done over long time periods unless hydraulic gradients are also monitored in order to observe deviations from unity.
When comparing methods, differences in K values are not only due to estimates, and the evaluation of the limitations of the unit gradient assumption becomes difficult. As an illustration, Table 1 presents data of an internal drainage test, performed on a fairly homogeneous Haplustox soil profile (sandy yellowred latosol) of the Piracicaba County, SP, Brazil, showing the evolution in time of , q and K values, calculated using measured values of , according to HILLEL et al. (1972), and K values assuming unit gradient, according to LIBARDI et al. (1980). It can be seen that oscilates around 1 up to about 5 days, from there on decreasing consistently. Although is approximately 1 over the period of 5 days, values indicate that DK values calculated by HILLEL et al. (1972) and LIBARDI et al. (1980) deviate consistently over time.
BACCHI & REICHARDT (1991) analysed the simplified methods of LIBARDI et al. (1980) and SISSON et al. (1980) and showed that although developed on completely different theoretical basis they are rigorously identical. Applying the same exponential model used by LIBARDI et al (1980) for K(q) in SISSON's formulation, the authors derived the following equation relating the soil water content q(cm^{3}.cm"^{3}) and the time of drainage t (day):
LIBARDI et al. (1980) expresses the same relation by the following equation:
where z = depth (cm), positive downwards; q_{0} (cm^{3}.cm"^{3}) and K_{0} (cm.day^{1}) the values of qand K during steadystate infiltration; a parameter relating q at a given depth z to the average q over the interval 0 to z and b a dimensionless coefficient of the exponential K(q) relation.
Although the approach of SISSON et al. (1980) also permits solutions for other than the exponential K(q) model, and was extended to layered soils (SISSON, 1987), it is important to point to the fact that equations (1) and (2) are identical for a = 1. For field soils, for which most likelydiffers from unity, different results should be expected when using both methods. Although LIBARDI et al. (1980) combine thevalue with 6 and SISSON et al. (1980) with z, both are related to deviations from homogeneity.
Results obtained for the same sandy yellowred latosol show the equivalence of the methods, as presented in Table 2.
Received May 15, 1993
Accepted May 25, 1993
Trabalho enviado para publicação em 15.05.1993
Trabalho aceito para publicação em 25.05.1993
 AHUJA, L.R.; BARNES, B.B.; CASSEL, O.K.; BRUCE, R.R.; NOFZIGER, D.L. Effect of assumed unit gradient during drainage on the determination of unsaturated conductivity and infiltration parameters. Soil Science, Baltimore, v.145, p.235243, 1988.
 BACCHI, O.O.S.; REICHARDT, K. Análise comparativa de dois métodos simplificados de determinação da condutividade hidráulica de solos. Revista Brasileira de Ciência do Solo, Campinas, v.15, p.249252, 1991.
 CHONG, S.R.; GREEN, R.E.; AHUJA, L.R. Simple in situ determination of hydraulic conductivity by power function descriptions of drainage. Water Resources Research, Washington, v.17, p.11091114, 1979.
 DAVIDSON, J.M.; STONE, L.R.; NIELSEN, D.R. LARUE, M.E. Field measurement and use of soilwater properties. Water Resources Research, Washington, v.5, p.13121321, 1969.
 HILLEL, D.; KRENTOS, V.D.; STILIANOU, Y. Procedure and test of an internal drainage method for measuring soil hydraulic characteristics in situ. Soil Science, Baltimore, n.114, p.395400, 1972.
 LIBARDI, P.L.; REICHARDT, K.; NIELSEN, D.R. BIGGAR, J.W. Simple field methods for estimating soil hydraulic conductivity. Soil Science Society of America Journal, Madison, v.44, p.37, 1980.
 REICHARDT, K. Unit gradient in internal drainage experiments for the determination of soil hydraulic conductivity. Scientia Agricola, Piracicaba, v.50, n.1, p.151153, 1993.
 SISSON, J.B. Drainage from layered field soils: fixed gradient models. Water Resources Research, Washington, v.23, p.20712075, 1987.
 SISSON, J.B.; FERGUSON, A.H. van GENUCHTEN, M.Th. Simple method for predicting drainage from field plots. Soil Science Society of America Journal, Madison, v.44, p.11471152, 1980.

1
Bolsista do CNPq
Publication Dates

Publication in this collection
10 Aug 2005 
Date of issue
Sept 1993
History

Accepted
25 May 1993 
Received
15 May 1993