Seasonal dynamics and operational monitoring of hedgerow olive tree transpiration in response to applied water

We used 2012 sap flow measurements to assess the seasonal dynamics of daily plant transpiration (ETc) in a high-density olive orchard (Olea europaea L. cv. ‘Arbequina’) with a well-watered (HI) control treatment A to supply 100 % of the crop water needs, and a moderately (MI) watered treatment B that replaced 70% of crop needs. To assure that treatment A was well-watered, we compared field daily ETc values against ETc obtained with the Penman-Monteith (PM) combination equation incorporating the Orgaz et al. (2007) bulk daily canopy conductance (gc) model, validated for our non-limiting conditions. We then tested the hypothesis of indirectly monitoring olive ETc from readily available vegetation index (VI) and ground-based plant water stress indicator. In the process we used the FAO56 dual crop coefficient (Kc) approach. For the HI olive trees we defined Kcb as the basal transpiration coefficient, and we related Kcb to remotely sensed Soil Adjusted Vegetation Index (SAVI) through a Kcb-SAVI functional relationship. For the MI treatment, we defined the actual transpiration ETc as the product of Kcb and the stress reduction coefficient Ks obtained as the ratio of actual to crop ETc, and we correlated Ks with MI midday stem water potential (ψst) values through a Ks-ψ functional relationship. Operational monitoring of ETc was then implemented with the ETc = Kcb(SAVI)Ks(ψ)ETo relationship stemmed from the FAO56 approach and validated taking as inputs collected SAVI and ψst data reporting to year 2011. Low validation error (6%) and high goodness-of-fit of prediction were observed (R2 = 0.94, RSME = 0.2 mm day-1, P = 0.0015), allowing to consider that under field conditions it is possible to predict ETc values for our hedgerow olive orchards if SAVI and water potential (ψst) values are known.

Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelas- ticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibrium and reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration. In contrast, relative Green–Lagrange strains (which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. In addition, the adequacy of several objective stress rates in the semi-implicit context is studied. We para- metrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use coinciding configurations. A single constitutive framework provides quantities needed by common discretization schemes. This is computationally convenient and robust, as all elements only need to provide pre-established quantities irrespectively of the constitutive model. In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complemen- tarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewer than one-tenth of the typical number of time increments can be used with a quantifiable effect in accuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plastic models can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.