A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

Modelling nutrient uptake by crops implies considering and integrating the processes controlling the soil nutrient supply, the uptake by the root system and relationships between the crop growth response and the amount of nutrient absorbed. We developed a model that integrates both dynamics of maize growth and phosphorus (P) uptake. The crop part of the model was derived from Monteith's model. A complete regulation of P-uptake by the roots according to crop P-demand and soil P-supply was assumed. The soil P-supply to the roots was calculated using a diffusion equation and assuming that roots behave as zero-sinks. The actual P-uptake and crop growth were calculated at each time step by comparing phosphate and carbohydrate supply–demand ratios. Model calculations for P-uptake and crop growth were compared to field measurements on a long term P-fertilization trial. Three P-fertilization regimes (no P-fertilization, 42.8 kg P ha⁻¹ year⁻¹ and 94.3 kg P ha⁻¹ year⁻¹) have led to a range of P-supply. Our model correctly simulated both the crop development and growth for all P-treatments. P-uptake was correctly predicted for the two non-limiting P-treatments. Nevertheless, for the limiting P-treatment, P-uptake was correctly predicted during the early period of growth but it was underestimated at the last sampling date (61 day after sowing). Several arguments for under-prediction were considered. However, most of them cannot explain the observed magnitude in discrepancy. The most likely reason might be the fact that biomass allocation between shoot and root must be modelled more precisely. Despite this mismatch, the model appears to provide realistic simulations of the soil–plant dynamic of P in field conditions.     

Gravity currents and intrusions of stratified fluids into a stratified ambient

We consider high-Reynolds-number Boussinesq gravity currents and intrusions systems in which both the ambient and the propagating “current” are linearly stratified. The main focus is on a current of fixed volume released from a rectangular lock; the height ratio of the fluids H, and the stratification parameter of the ambient S, are quite general. We develop a one-layer shallow-water (SW) model which is an extension of previously used and tested formulations for currents and intrusions of constant density. The internal stratification enters as a new dimensionless parameter, s ? [0,1]{\sigma \in [0,1]} . Analytical results are obtained for the initial “slumping” stage during which the speed of propagation is constant, and finite-difference solutions are presented for the more general time-dependent motion. Overall, this is a versatile and robust self-contained prediction tool, which reduces smoothly to the classical case when σ = 0. We show that, in general, the speed of propagation decreases when the internal stratification becomes more pronounced (σ increases). An interesting non-expected behavior was detected: when the stratification of the ambient is weak and moderate then the height of the current decreases with σ, but the opposite occurs when the stratification of the ambient is strong (S ≈ 1, including the case of an intrusion). Moreover, when the stratification of the ambient is strong a current with internal stratification may “run out” of driving power. We also consider the Benjamin-type steady state current with internal linear stratification in a non-stratified ambient, and show that an analytical solution exists, and that the maximal thickness decreases to below half-channel depth when σ increases.     

Regional planning for the siting of local evaporation basins for the disposal of saline irrigation drainage: development and testing of a GIS-based suitability approach

In order to prevent salinisation of the streams of the Riverine Plain of the Murray-Darling Basin in southern Australia, evaporation basins are used to dispose of saline irrigation drainage water. Local on-farm (individual landholder) and community (shared between multiple landholders) basins are increasingly being used to prevent export of salt outside irrigation districts. There are questions regarding the availability of land suitable for these basins and their impact on the surrounding environment. We describe the use of currently available spatial data to assist in regional planning for the environmentally safe use of these basins. A GIS-based approach was developed using suitability criteria expected to minimise the risk of off-site effects of basin leakage. The criteria were proximity to surface water features, urban areas and infrastructure, water table depth and salinity, and soil hydraulic conductivity. The approach was applied to all of the major irrigation districts at 1:250,000, the scale at which data are available over the entire Riverine Plain. Confidence in well-defined parameters such as proximity to infrastructure, urban areas and surface water features was higher than for those involving interpolated point data such as water table depth, salinity, and hydraulic conductivity. Most critically, hydraulic conductivity, the most important factor for basin leakage, was found to be unreliable at this scale. Use of higher resolution data (up to 1:100,000) available for two of the irrigation districts improved confidence in both water table depth and salinity but not in hydraulic conductivity. Despite these limitations, it was found that: (i) on-farm basins can only be used on an opportunistic basis in the eastern irrigation districts, but can be widely used in the western districts; (ii) community basins can be used anywhere there is suitable land; and (iii) the results raise serious questions as to whether there is enough suitable land in the eastern districts to dispose of all of the drainage water that is produced.     

Thin-layer models for gravity currents in channels of general cross-section area,a review

We present a brief review of the recent investigations on gravity currents in horizontal channels with non-rectangular cross-section area (such as triangle, \(\bigvee \)-valley, circle/semi-circle, trapezoid) which occur in nature (e.g., rivers) and constructed environment (tunnels, reservoirs, canals). To be specific, we discuss the propagation of a gravity current (GC) in a horizontal channel along the horizontal coordinate x, with gravity g acting in the \(-z\) direction, and y the horizontal–lateral coordinate. The bottom and top of the channel are at \(z=0,H\). The “standard” problem is concerned with 2D flow in a channel with rectangular (or laterally unbounded) cross-section area (CSA). Recent investigations have successfully extended the standard knowledge to the channels of CSA given by the quite general \(-f_1(z)\le y \le f_2(z)\) for \(0 \le z \le H\). This includes the practical \(\bigvee \)-valley, triangle, circle/semi-circle and trapezoid; these geometries may be in “up” or “down” setting with respect to gravity, e.g., \(\bigtriangleup \) and \(\bigtriangledown \). The major objective of the extended theory is to predict the height of the interface \(z=h(x,t)\) and the velocity (averaged over the CSA) u(x, t), where t is time; the prediction includes the speed and position of the nose \(u_N(t), x_N(t)\). We show that the motion is governed by a set of simplified equations, called “model,” that provides versatile and insightful solutions and trends. The emphasis in on a high-Reynolds-number current whose motion is dominated by buoyancy–inertia balance; in particular a GC released from a lock, which also contains general effects such as front and internal jumps (shocks), and reflected bore. We discuss two-layer, one-layer, and box models; Boussinesq and non-Boussinesq systems; compositional and particle-driven cases; and the effect of stratification of the ambient fluid. The models are self-contained, and admit realistic initial and boundary conditions. The governing equations are amenable to analytical solutions in some special circumstances. Some salient features of the buoyancy-viscous regime, and the estimate for the length at which transition to this regime takes place, are also presented. Some experimental support to the theory, and open questions for further investigations, are also mentioned. The major conclusions are (1) The CSA geometry has significant influence on the motion of the GC; and (2) The new theory is a useful, very significant, extension of the standard two-dimensional GC problem. The standard current is just a particular case, \(f_{1,2} =\) constants, among many other covered by the new theory.