ABSTRACT An important aspect in the study and understanding of the physical phenomena involved in water movement in the soil-plant system is the need to carry out the hydrodynamic characterization (HC) of non-saturated field soils. Studies of this type have been widely developed in soils of temperate climates, but they are infrequent in the tropics, hence there is a need for further research in tropical Vertisols under field conditions. Hydrodynamic characterization consists of finding the functional relationship between soil hydraulic conductivity (K), matric head (h) and soil moisture content (θ), widely known as K(θ) and h(θ) relationships, being the main objective of this study. The instantaneous profile method (IPM) was applied, in which splines were used for the HC of a bare, tropical agricultural field soil classified as a Vertisol. Field measurements of h and θ were made at five different soil depths (0.15, 0.30, 0.45, 0.60 and 0.90 m) and values of K at the same depths were estimated with the IPM, which allowed for the estimation of pairs of values of the K(θ) relationships in the soil profile. Unlike in other studies with the same objective, the use of splines was proposed to represent the spatial variation of the H(z) and θ(z) functions in the IPM. Subsequently, the van Genuchten equation was adjusted to the specific values determined for the h(θ) relations (r2 value ranged from 0.65 to 0.87), and the Ks values and the point data of K and θ were used to estimate the accuracy of the equation proposed by Mualem–van Genuchten (M-vG): in this case negative values for the exponent l of the M-vG function were determined for the five soil depths under study, ranging from –7.04 (0.45 m deep), to -13.26 (0.90 m deep). In addition, pedotransfer functions for tropical soils proposed in the literature, based on different soil physical properties, were used to estimate the h(θ) and K(θ) relationships and the saturated hydraulic conductivity (Ks). Best square root of the mean squared error (SRMSEθ) observed was 0.02853 cm3 cm-3 at 0.15 m depth and 0.02262 cm3 cm-3 at 0.9 m depth for h(θ) relations, and in all cases, the SRMSEk values are less than 0.0018 m day-1 for K(θ) relationships. The results reveal the utility of splines in the IPM for characterizing the soil profile K(θ) relationships in field studies, as well as the need for more research to the generation of pedotransfer functions in tropical Vertisols.