Abstract. This paper studies a 3-D state space representation of Budyko's framework designed to capture the mutual interdependence among long-term mean actual evapotranspiration (E), potential evapotranspiration (E p ) and precipitation (P ). For this purpose we use three dimensionless and dependent quantities: = E/P , = E p /P and = E/E p . This 3-D space and its 2-D projections provide an interesting setting to test the physical soundness of Budyko's hypothesis. We demonstrate analytically that Budyko-type equations are unable to capture the physical limit of the relation between and in humid environments, owing to the unfeasibility of E p /P = 0 when E/E p → 1. Using data from 146 sub-catchments in the Amazon River basin we overcome this inconsistency by proposing a physically consistent power law: = k e , with k = 0.66, and e = 0.83 (R 2 = 0.93). This power law is compared with two other Budyko-type equations. Taking into account the goodness of fits and the ability to comply with the physical limits of the 3-D space, our results show that the power law is better suited to model the coupled water and energy balances within the Amazon River basin. Moreover, k is found to be related to the partitioning of energy via evapotranspiration in terms of . This suggests that our power law implicitly incorporates the complementary relationship of evapotranspiration into the Budyko curve, which is a consequence of the dependent nature of the studied variables within our 3-D space. This scaling approach is also consistent with the asymmetrical nature of the complementary relationship of evapotranspiration. Looking for a physical explanation for the parameters k and e, the interannual variability of individual catchments is studied. Evidence of space-time symmetry in Amazonia emerges, since both between-catchment and between-year variability follow the same Budyko curves. Finally, signs of co-evolution of catchments are explored by linking spatial patterns of the power law parameters with fundamental characteristics of the Amazon River basin. In general, k and e are found to be related to vegetation, topography and water in soils.

From a socioeconomic and environmental standpoint, rubber cultivation is potentially important for Colombia, because it not only constitutes an alternative to the traditional mining, agricultural, and livestock activities, but also a beneficial option in the substitution of illegal crops. Thus, there is need to determine the factors restricting the productivity of the species, particularly soil-related aspects. In this context, the current research undertook the description and identification of soil physical and chemical properties in three rubber plantations located in a region known as Bajo Cauca Antioqueño, at the lower course of the Cauca river. The results indicate that these soils are classified as Ultisols, they are deep, with acid reaction and low levels of soil organic matter. Essential elements also exhibited low levels, except Cu. Fe and Al are also present in very high concentrations, while the cation exchange capacity is limited. These observations alert on the need for agronomic management techniques that allow the crop to express its full potential under conditions that are not very adequate for its growth and development.

The expansion and modernization of the cocoa area under new strategies, such as the use of adapted genetic material and the establishment of Agroforestry Systems with cocoa, under criteria of competitiveness and sustainability, require selecting sites with adequate biophysical conditions, which facilitate the optimization of resources for production. In this sense, we conducted a study in the Estación Agraria Cotové, of the Universidad Nacional de Colombia, located in a tropical dry forest life zone (TDF), at 540 meters of elevation, with an average temperature of 27 ºC, average annual precipitation annual of 1,031 mm and relative humidity less than 70 %. The yield components and productive potential of four cocoa clones, ICS 95, TSH565, CCN 51, and ICS 60, were evaluated. The cocoa clones were planted under two controlled sunlight habitats, generated by the timber species Gmelina arborea Roxb. (single-row and double-row arrangement), and two different canopy management of the cocoa plants (plagiotropic and orthotropic growth stimulus). The clones TSH 565 and CCN 51 showed the highest yields in the two harvest years. ICS 95 showed the lowest bean index. Regarding the pod index, no differences were observed between the cocoa clones. Clones TSH 565 and CCN 51 stood out as the earliest and most productive clones.

Abstract. This paper studies a 3-D generalization of Budyko's framework designed to capture the mutual interdependence among long-term mean actual evapotranspiration (E), potential evapotranspiration (Ep) and precipitation (P). For this purpose we use three dimensionless and dependent quantities: Ψ = E/P, Φ = Ep/P and Ω = E/Ep. This 3-D space and its 2-D projections provide an interesting setting to test the physical soundness of Budyko's hypothesis. We demonstrate analytically that Budyko-type equations are unable to capture the physical limit of the relation between Ω and Φ in humid environments, owing to the unfeasibility of Ep/P → 0 at E/Ep = 1. Using data from 146 sub-catchments in the Amazon River basin we overcome this inconsistency by proposing a physically consistent power law: Ψ = k Φe, with k = 0.66, and e = 0.83 (R2 = 0.93). This power law is compared with two other Budyko-type equations. Taking into account the goodness of fits and the ability to comply with the physical limits of the 3-D space, our results show that the power law is better suited to model the coupled water and energy balances within the Amazon River basin. Moreover, k is found to be related to the partitioning of energy via evapotranspiration in terms of Ω. This suggests that our power law implicitly incorporates the complementary relationship of evapotranspiration into the Budyko curve, which is a consequence of the dependent nature of the studied variables within our 3-D space. This scaling approach is also consistent with the asymmetrical nature of the complementary relationship of evapotranspiration. Looking for a physical explanation for the parameters k and e, the inter-annual variability of individual catchments is studied. Evidence of space–time symmetry in Amazonia emerges, since both between-catchment and between-year variability follow the same Budyko curves. Finally, signs of co-evolution of catchments are explored by linking spatial patterns of the power law parameters with fundamental characteristics of the Amazon River basin. In general, k and e are found to be related to vegetation, topography and water in soils.