Conditioning and preconditioning of the variational data assimilation problem

Numerical weather prediction (NWP) centres use numerical models of the atmospheric flow to forecast future weather states from an estimate of the current state. Variational data assimilation (VAR) is used commonly to determine an optimal state estimate that miminizes the errors between observations of the dynamical system and model predictions of the flow. The rate of convergence of the VAR scheme and the sensitivity of the solution to errors in the data are dependent on the condition number of the Hessian of the variational least-squares objective function. The traditional formulation of VAR is ill-conditioned and hence leads to slow convergence and an inaccurate solution. In practice, operational NWP centres precondition the system via a control variable transform to reduce the condition number of the Hessian. In this paper we investigate the conditioning of VAR for a single, periodic, spatially-distributed state variable. We present theoretical bounds on the condition number of the original and preconditioned Hessians and hence demonstrate the improvement produced by the preconditioning. We also investigate theoretically the effect of observation position and error variance on the preconditioned system and show that the problem becomes more ill-conditioned with increasingly dense and accurate observations. Finally, we confirm the theoretical results in an operational setting by giving experimental results from the Met Office variational system.

Analysis of Direct Outdoor Air Cooling Efficency for Combined Variable Air Volume Air-conditioning System in Stores in Cold Climates of China

Direct outdoor air cooling contributes a lot not only to the improvement of the indoor air quality but also to the energy saving. Its full use will reduce the water chiller’s running time especially in some stores where cooling load keeps much higher and longer than that in other buildings. A novel air-conditioning system named Combined Variable Air Volume system (CVAV), combining a normal AHU with a separate outdoor air supply system, was proposed firstly by the authors. The most attractive feature of the system is its full utilization of cooling capacity and freshness of outdoor air in the transition period of the year round. On the basis of the obtain of the dynamic cooling loads of the typical shopping malls in different four cities located in cold climates in China with the aid of DOE-2, the possibility of increasing the amount of outdoor air volume of CVAV system in the transition period instead of operating the water chillers was confirmed. Moreover, a new concept, Direct Outdoor Air Cooling Efficiency (DOACE), was defined as the ratio of cooling capacity of outdoor air to the water chiller, indicating the degree of outdoor air’s utilization. And the DOACE of the CVAV was calculated and compared with that of conventional all-air constant volume air-conditioning systems, the results showed that CVAV bear much more energy saving potential with the 10%~19% higher DOACE and it is a kind of energy efficient systems and can improve the indoor air quality as well.

Conditioning model output statistics of regional climate model precipitation on circulation patterns

Dynamical downscaling of Global Climate Models (GCMs) through regional climate models (RCMs) potentially improves the usability of the output for hydrological impact studies. However, a further downscaling or interpolation of precipitation from RCMs is often needed to match the precipitation characteristics at the local scale. This study analysed three Model Output Statistics (MOS) techniques to adjust RCM precipitation; (1) a simple direct method (DM), (2) quantile-quantile mapping (QM) and (3) a distribution-based scaling (DBS) approach. The modelled precipitation was daily means from 16 RCMs driven by ERA40 reanalysis data over the 1961–2000 provided by the ENSEMBLES (ENSEMBLE-based Predictions of Climate Changes and their Impacts) project over a small catchment located in the Midlands, UK. All methods were conditioned on the entire time series, separate months and using an objective classification of Lamb's weather types. The performance of the MOS techniques were assessed regarding temporal and spatial characteristics of the precipitation fields, as well as modelled runoff using the HBV rainfall-runoff model. The results indicate that the DBS conditioned on classification patterns performed better than the other methods, however an ensemble approach in terms of both climate models and downscaling methods is recommended to account for uncertainties in the MOS methods.

The long-term safety and efficacy of bilateral transplantation of human fetal striatal tissue in patients with mild to moderate Huntington's disease.

Huntington's disease (HD) is a fatal autosomal dominant neurodegenerative disease involving progressive motor, cognitive and behavioural decline, leading to death approximately 20 years after motor onset. The disease is characterised pathologically by an early and progressive striatal neuronal cell loss and atrophy, which has provided the rationale for first clinical trials of neural repair using fetal striatal cell transplantation. Between 2000 and 2003, the 'NEST-UK' consortium carried out bilateral striatal transplants of human fetal striatal tissue in five HD patients. This paper describes the long-term follow up over a 3-10-year postoperative period of the patients, grafted and non-grafted, recruited to this cohort using the 'Core assessment program for intracerebral transplantations-HD' assessment protocol. No significant differences were found over time between the patients, grafted and non-grafted, on any subscore of the Unified Huntington's Disease Rating Scale, nor on the Mini Mental State Examination. There was a trend towards a slowing of progression on some timed motor tasks in four of the five patients with transplants, but overall, the trial showed no significant benefit of striatal allografts in comparison with a reference cohort of patients without grafts. Importantly, no significant adverse or placebo effects were seen. Notably, the raclopride positron emission tomography (PET) signal in individuals with transplants, indicated that there was no obvious surviving striatal graft tissue. This study concludes that fetal striatal allografting in HD is safe. While no sustained functional benefit was seen, we conclude that this may relate to the small amount of tissue that was grafted in this safety study compared with other reports of more successful transplants in patients with HD.

Pre-conditioning the epigenetic response to high vapor pressure deficit increases the drought tolerance of Arabidopsis thaliana

Epigenetic modification of the genome via cytosine methylation is a dynamic process that responds to changes in the growing environment. This modification can also be heritable. The combination of both properties means that there is the potential for the life experiences of the parental generation to modify the methylation profiles of their offspring and so potentially to ‘pre-condition’ them to better accommodate abiotic conditions encountered by their parents. We recently identified high vapor pressure deficit (vpd)-induced DNA methylation at two gene loci in the stomatal development pathway and an associated reduction in leaf stomatal frequency.1 Here, we test whether this epigenetic modification pre-conditioned parents and their offspring to the more severe water stress of periodic drought. We found that three generations of high vpd-grown plants were better able to withstand periodic drought stress over two generations. This resistance was not directly associated with de novo methylation of the target stomata genes, but was associated with the cmt3 mutant’s inability to maintain asymmetric sequence context methylation. If our finding applies widely, it could have significant implications for evolutionary biology and breeding for stressful environments.

Preoperative predictors for postoperative problems in heart transplantation: psychiatric and psychosocial considerations

The psychiatric and psychosocial evaluation of the heart transplant candidate can identify particular predictors for postoperative problems. These factors, as identified during the comprehensive evaluation phase, provide an assessment of the candidate in context of the proposed transplantation protocol. Previous issues with compliance, substance abuse, and psychosis are clear indictors of postoperative problems. The prolonged waiting list time provides an additional period to evaluate and provide support to patients having a terminal disease who need a heart transplant, and are undergoing prolonged hospitalization. Following transplantation, the patient is faced with additional challenges of a new self-image, multiple concerns, anxiety, and depression. Ultimately, the success of the heart transplantation remains dependent upon the recipient's ability to cope psychologically and comply with the medication regimen. The limited resource of donor hearts and the high emotional and financial cost of heart transplantation lead to an exhaustive effort to select those patients who will benefit from the improved physical health the heart transplant confers.

Intrastriatal transplantation of adult human neural crest-derived stem cells improves functional outcome in parkinsonian rats

Parkinson's disease (PD) is considered the second most frequent and one of the most severe neurodegenerative diseases, with dysfunctions of the motor system and with nonmotor symptoms such as depression and dementia. Compensation for the progressive loss of dopaminergic (DA) neurons during PD using current pharmacological treatment strategies is limited and remains challenging. Pluripotent stem cell-based regenerative medicine may offer a promising therapeutic alternative, although the medical application of human embryonic tissue and pluripotent stem cells is still a matter of ethical and practical debate. Addressing these challenges, the present study investigated the potential of adult human neural crest-derived stem cells derived from the inferior turbinate (ITSCs) transplanted into a parkinsonian rat model. Emphasizing their capability to give rise to nervous tissue, ITSCs isolated from the adult human nose efficiently differentiated into functional mature neurons in vitro. Additional successful dopaminergic differentiation of ITSCs was subsequently followed by their transplantation into a unilaterally lesioned 6-hydroxydopamine rat PD model. Transplantation of predifferentiated or undifferentiated ITSCs led to robust restoration of rotational behavior, accompanied by significant recovery of DA neurons within the substantia nigra. ITSCs were further shown to migrate extensively in loose streams primarily toward the posterior direction as far as to the midbrain region, at which point they were able to differentiate into DA neurons within the locus ceruleus. We demonstrate, for the first time, that adult human ITSCs are capable of functionally recovering a PD rat model.

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.