Long-term conditioning of soil by plantation eucalypts and pines does not affect growth of the native jarrah tree

Plant species can condition the physico-chemical and biological properties of soil in ways that modify plant growth via plant–soil feedback (PSF). Plant growth can be positively affected, negatively affected or neutrally affected by soil conditioning by the same or other plant species. Soil conditioning by other plant species has particular relevance to ecological restoration of historic ecosystems because sites set aside for restoration are often conditioned by other, potentially non-native, plant species. We investigated changes in properties of jarrah forest soils after long-term (35 years) conditioning by pines (Pinus radiata), Sydney blue gums (Eucalyptus saligna), both non-native, plantation trees, and jarrah (Eucalyptus marginata; dominant native tree). Then, we tested the influence of the conditioned soils on the growth of jarrah seedlings. Blue gums and pines similarly conditioned the physico-chemical properties of soils, which differed from soil conditioning caused by jarrah. Especially important were the differences in conditioning of the properties C:N ratio, pH, and available K. The two eucalypt species similarly conditioned the biological properties of soil (i.e. community level physiological profile, numbers of fungal-feeding nematodes, omnivorous nematodes, and nematode channel ratio), and these differed from conditioning caused by pines. Species-specific conditioning of soil did not translate into differences in the amounts of biomass produced by jarrah seedlings and a neutral PSF was observed. In summary, we found that decades of soil conditioning by non-native plantation trees did not influence the growth of jarrah seedlings and will therefore not limit restoration of jarrah following the removal of the plantation trees.

Soil conditioning and plant-soil feedbacks in a modified forest ecosystem are soil-context dependent

Aims There is potential for altered plant-soil feedback (PSF) to develop in human-modified ecosystems but empirical data to test this idea are limited. Here, we compared the PSF operating in jarrah forest soil restored after bauxite mining in Western Australia with that operating in unmined soil. Methods Native seedlings of jarrah (Eucalyptus marginata), acacia (Acacia pulchella), and bossiaea (Bossiaea ornata) were grown in unmined and restored soils to measure conditioning of chemical and biological properties as compared with unplanted control soils. Subsequently, acacia and bossiaea were grown in soils conditioned by their own or by jarrah seedlings to determine the net PSF. Results In unmined soil, the three plant species conditioned the chemical properties but had little effect on the biological properties. In comparison, jarrah and bossiaea conditioned different properties of restored soil while acacia did not condition this soil. In unmined soil, neutral PSF was observed, whereas in restored soil, negative PSF was associated with acacia and bossiaea. Conclusions Soil conditioning was influenced by soil context and plant species. The net PSF was influenced by soil context, not by plant species and it was different in restored and unmined soils. The results have practical implications for ecosystem restoration after human activities.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.