Prediction leaching of potassium using the convective-dispersive and the convective log-normal transfer function models

There is increasing concern about soil enrichment with K+ and subsequent potential losses following long-term application of poor quality water to agricultural land. Different models are increasingly being used for predicting or analyzing water flow and chemical transport in soils and groundwater. The convective-dispersive equation (CDE) and the convective log-normal transfer function (CLT) models were fitted to the potassium (K+) leaching data. The CDE and CLT models produced equivalent goodness of fit. Simulated breakthrough curves for a range of CaCl2 concentration based on parameters of 15 mmol l(-1) CaCl2 were characterised by an early peak position associated with higher K+ concentration as the CaCl2 concentration used in leaching experiments decreased. In another method, the parameters estimated from 15 mmol l(-1) CaCl2 solution were used for all other CaCl2 concentrations, and the best value of retardation factor (R) was optimised for each data set. A better prediction was found. With decreasing CaCl2 concentration the value of R is required to be more than that measured (except for 10 mmol l(-1) CaCl2), if the estimated parameters of 15 mmol l(-1) CaCl2 are used. The two models suffer from the fact that they need to be calibrated against a data set, and some of their parameters are not measurable and cannot be determined independently.

Efficient and cost-effective experimental determination of kinetic constants and data: the success of a Bayesian systematic approach to drug transport, receptor binding, continuous culture and cell transport kinetics

Details about the parameters of kinetic systems are crucial for progress in both medical and industrial research, including drug development, clinical diagnosis and biotechnology applications. Such details must be collected by a series of kinetic experiments and investigations. The correct design of the experiment is essential to collecting data suitable for analysis, modelling and deriving the correct information. We have developed a systematic and iterative Bayesian method and sets of rules for the design of enzyme kinetic experiments. Our method selects the optimum design to collect data suitable for accurate modelling and analysis and minimises the error in the parameters estimated. The rules select features of the design such as the substrate range and the number of measurements. We show here that this method can be directly applied to the study of other important kinetic systems, including drug transport, receptor binding, microbial culture and cell transport kinetics. It is possible to reduce the errors in the estimated parameters and, most importantly, increase the efficiency and cost-effectiveness by reducing the necessary amount of experiments and data points measured. (C) 2003 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

The REFLEX project: Comparing different algorithms and implementations for the inversion of a terrestrial ecosystem model against eddy covariance data

We describe a model-data fusion (MDF) inter-comparison project (REFLEX), which compared various algorithms for estimating carbon (C) model parameters consistent with both measured carbon fluxes and states and a simple C model. Participants were provided with the model and with both synthetic net ecosystem exchange (NEE) of CO2 and leaf area index (LAI) data, generated from the model with added noise, and observed NEE and LAI data from two eddy covariance sites. Participants endeavoured to estimate model parameters and states consistent with the model for all cases over the two years for which data were provided, and generate predictions for one additional year without observations. Nine participants contributed results using Metropolis algorithms, Kalman filters and a genetic algorithm. For the synthetic data case, parameter estimates compared well with the true values. The results of the analyses indicated that parameters linked directly to gross primary production (GPP) and ecosystem respiration, such as those related to foliage allocation and turnover, or temperature sensitivity of heterotrophic respiration, were best constrained and characterised. Poorly estimated parameters were those related to the allocation to and turnover of fine root/wood pools. Estimates of confidence intervals varied among algorithms, but several algorithms successfully located the true values of annual fluxes from synthetic experiments within relatively narrow 90% confidence intervals, achieving >80% success rate and mean NEE confidence intervals <110 gC m−2 year−1 for the synthetic case. Annual C flux estimates generated by participants generally agreed with gap-filling approaches using half-hourly data. The estimation of ecosystem respiration and GPP through MDF agreed well with outputs from partitioning studies using half-hourly data. Confidence limits on annual NEE increased by an average of 88% in the prediction year compared to the previous year, when data were available. Confidence intervals on annual NEE increased by 30% when observed data were used instead of synthetic data, reflecting and quantifying the addition of model error. Finally, our analyses indicated that incorporating additional constraints, using data on C pools (wood, soil and fine roots) would help to reduce uncertainties for model parameters poorly served by eddy covariance data.

Forecasting with difference and trend stationary models

Although difference-stationary (DS) and trend-stationary (TS) processes have been subject to considerable analysis, there are no direct comparisons for each being the data-generation process (DGP). We examine incorrect choice between these models for forecasting for both known and estimated parameters. Three sets of Monte Carlo simulations illustrate the analysis, to evaluate the biases in conventional standard errors when each model is mis-specified, compute the relative mean-square forecast errors of the two models for both DGPs, and investigate autocorrelated errors, so both models can better approximate the converse DGP. The outcomes are surprisingly different from established results.

A model analysis of climate and CO2 controls on tree growth in a semi-arid woodland

We used a light-use efficiency model of photosynthesis coupled with a dynamic carbon allocation and tree-growth model to simulate annual growth of the gymnosperm Callitris columellaris in the semi-arid Great Western Woodlands, Western Australia, over the past 100 years. Parameter values were derived from independent observations except for sapwood specific respiration rate, fine-root turnover time, fine-root specific respiration rate and the ratio of fine-root mass to foliage area, which were estimated by Bayesian optimization. The model reproduced the general pattern of interannual variability in radial growth (tree-ring width), including the response to the shift in precipitation regimes that occurred in the 1960s. Simulated and observed responses to climate were consistent. Both showed a significant positive response of tree-ring width to total photosynthetically active radiation received and to the ratio of modeled actual to equilibrium evapotranspiration, and a significant negative response to vapour pressure deficit. However, the simulations showed an enhancement of radial growth in response to increasing atmospheric CO2 concentration (ppm) ([CO2]) during recent decades that is not present in the observations. The discrepancy disappeared when the model was recalibrated on successive 30-year windows. Then the ratio of fine-root mass to foliage area increases by 14% (from 0.127 to 0.144 kg C m-2) as [CO2] increased while the other three estimated parameters remained constant. The absence of a signal of increasing [CO2] has been noted in many tree-ring records, despite the enhancement of photosynthetic rates and water-use efficiency resulting from increasing [CO2]. Our simulations suggest that this behaviour could be explained as a consequence of a shift towards below-ground carbon allocation.

On the observability of turbulent transport rates by Argo: supporting evidence from an inversion experiment

Although estimation of turbulent transport parameters using inverse methods is not new, there is little evaluation of the method in the literature. Here, it is shown that extended observation of the broad scale hydrography by Argo provides a path to improved estimates of regional turbulent transport rates. Results from a 20 year ocean state estimate produced with the ECCO v4 non-linear inverse modeling framework provide supporting evidence. Turbulent transport parameter maps are estimated under the constraints of fitting the extensive collection of Argo profiles collected through 2011. The adjusted parameters dramatically reduce misfits to in situ profiles as compared with earlier ECCO solutions. They also yield a clear reduction in the model drift away from observations over multi-century long simulations, both for assimilated variables (temperature and salinity) and independent variables (bio-geochemical tracers). Despite the minimal constraints imposed specifically on the estimated parameters, their geography is physically plausible and exhibits close connections with the upper ocean ocean stratification as observed by Argo. The estimated parameter adjustments furthermore have first order impacts on upper-ocean stratification and mixed layer depths over 20 years. These results identify the constraint of fitting Argo profiles as an effective observational basis for regional turbulent transport rates. Uncertainties and further improvements of the method are discussed.

How much flower-rich habitat is enough for wild pollinators? Answering a key policy question with incomplete knowledge

In 2013, an opportunity arose in England to develop an agri-environment package for wild pollinators, as part of the new Countryside Stewardship scheme launched in 2015. It can be understood as a 'policy window', a rare and time-limited opportunity to change policy, supported by a narrative about pollinator decline and widely supported mitigating actions. An agri-environment package is a bundle of management options that together supply sufficient resources to support a target group of species. This paper documents information that was available at the time to develop such a package for wild pollinators. Four questions needed answering: (1) Which pollinator species should be targeted? (2) Which resources limit these species in farmland? (3) Which management options provide these resources? (4) What area of each option is needed to support populations of the target species? Focussing on wild bees, we provide tentative answers that were used to inform development of the package. There is strong evidence that floral resources can limit wild bee populations, and several sources of evidence identify a set of agri-environment options that provide flowers and other resources for pollinators. The final question could only be answered for floral resources, with a wide range of uncertainty. We show that the areas of some floral resource options in the basic Wild Pollinator and Farmland Wildlife Package (2% flower-rich habitat and 1 km flowering hedgerow), are sufficient to supply a set of six common pollinator species with enough pollen to feed their larvae at lowest estimates, using minimum values for estimated parameters where a range was available. We identify key sources of uncertainty, and stress the importance of keeping the Package flexible, so it can be revised as new evidence emerges about how to achieve the policy aim of supporting pollinators on farmland.

Genetic parameters and evaluations from single- and multiple-trait analysis of dairy cow fertility and milk production

Genetic parameters and breeding values for dairy cow fertility were estimated from 62 443 lactation records. Two-trait analysis of fertility and milk yield was investigated as a method to estimate fertility breeding values when culling or selection based on milk yield in early lactation determines presence or absence of fertility observations in later lactations. Fertility traits were calving interval, intervals from calving to first service, calving to conception and first to last service, conception success to first service and number of services per conception. Milk production traits were 305-day milk, fat and protein yield. For fertility traits, range of estimates of heritability (h(2)) was 0.012 to 0.028 and of permanent environmental variance (c(2)) was 0.016 to 0.032. Genetic correlations (r(g)) among fertility traits were generally high ( > 0.70). Genetic correlations of fertility with milk production traits were unfavourable (range -0.11 to 0.46). Single and two-trait analyses of fertility were compared using the same data set. The estimates of h(2) and c(2) were similar for two types of analyses. However, there were differences between estimated breeding values and rankings for the same trait from single versus multi-trait analyses. The range for rank correlation was 0.69-0.83 for all animals in the pedigree and 0.89-0.96 for sires with more than 25 daughters. As single-trait method is biased due to selection on milk yield, a multi-trait evaluation of fertility with milk yield is recommended. (C) 2002 Elsevier Science B.V. All rights reserved.