Comparing hybrid data assimilation methods on the Lorenz 1963 model with increasing nonlinearity

We systematically compare the performance of ETKF-4DVAR, 4DVAR-BEN and 4DENVAR with respect to two traditional methods (4DVAR and ETKF) and an ensemble transform Kalman smoother (ETKS) on the Lorenz 1963 model. We specifically investigated this performance with increasing nonlinearity and using a quasi-static variational assimilation algorithm as a comparison. Using the analysis root mean square error (RMSE) as a metric, these methods have been compared considering (1) assimilation window length and observation interval size and (2) ensemble size to investigate the influence of hybrid background error covariance matrices and nonlinearity on the performance of the methods. For short assimilation windows with close to linear dynamics, it has been shown that all hybrid methods show an improvement in RMSE compared to the traditional methods. For long assimilation window lengths in which nonlinear dynamics are substantial, the variational framework can have diffculties fnding the global minimum of the cost function, so we explore a quasi-static variational assimilation (QSVA) framework. Of the hybrid methods, it is seen that under certain parameters, hybrid methods which do not use a climatological background error covariance do not need QSVA to perform accurately. Generally, results show that the ETKS and hybrid methods that do not use a climatological background error covariance matrix with QSVA outperform all other methods due to the full flow dependency of the background error covariance matrix which also allows for the most nonlinearity.

Wave spectra assimilation in typhoon wave modeling for the East China Sea

The East China Sea is a hot area for typhoon waves to occur. A wave spectra assimilation model has been developed to predict the typhoon wave more accurately and operationally. This is the first time where wave data from Taiwan have been used to predict typhoon wave along the mainland China coast. The two-dimensional spectra observed in Taiwan northeast coast modify the wave field output by SWAN model through the technology of optimal interpolation (OI) scheme. The wind field correction is not involved as it contributes less than a quarter of the correction achieved by assimilation of waves. The initialization issue for assimilation is discussed. A linear evolution law for noise in the wave field is derived from the SWAN governing equations. A two-dimensional digital low-pass filter is used to obtain the initialized wave fields. The data assimilation model is optimized during the typhoon Sinlaku. During typhoons Krosa and Morakot, data assimilation significantly improves the low frequency wave energy and wave propagation direction in Taiwan coast. For the far-field region, the assimilation model shows an expected ability of improving typhoon wave forecast as well, as data assimilation enhances the low frequency wave energy. The proportion of positive assimilation indexes is over 81% for all the periods of comparison. The paper also finds that the impact of data assimilation on the far-field region depends on the state of the typhoon developing and the swell propagation direction.

Endophytic bacterial community composition in wheat (Triticum aestivum) is determined by plant tissue type, developmental stage and soil nutrient availability

Aims: To understand effects of tissue type, growth stage and soil fertilisers on bacterial endophyte communities of winter wheat (Triticum aestivum cv. Hereward). Methods: Endophytes were isolated from wheat grown under six fertiliser conditions in the long term Broadbalk Experiment at Rothamsted Research, UK. Samples were taken in May and July from root and leaf tissues. Results: Root and leaf communities differed in abundance and composition of endophytes. Endophytes were most abundant in roots and the Proteobacteria were most prevalent. In contrast, Firmicutes and Actinobacteria, the Gram positive phyla, were most prevalent in the leaves. Both fertiliser treatment and sample time influenced abundance and relative proportions of each phylum and genus in the endosphere. A higher density of endophytes was found in the Nil input treatment plants. Conclusions: Robust isolation techniques and stringent controls are critical for accurate recovery of endophytes. The plant tissue type, plant growth stage, and soil fertiliser treatment all contribute to the composition of the endophytic bacterial community in wheat. These results should help facilitate targeted development of endophytes for beneficial applications in agriculture.

The effects of tannin-containing ground pine bark diet upon nutrient digestion, nitrogen balance, and mineral retention in meat goats

Background Pine bark is a rich source of phytochemical compounds including tannins, phenolic acids, anthocyanins, and fatty acids. These phytochemicals have potential to significantly impact on animal health and animal production. The goal of this work is to measure the effects of tannins in ground pine bark as a partial feed replacement on feed intake, dietary apparent digestibility, nitrogen balance, and mineral retention in meat goats. Results Eighteen Kiko cross goats (initial BW = 31.8 ± 1.49 kg) were randomly assigned to three treatment groups (n = 6). Dietary treatments were tested: control (0 % pine bark powder (PB) and 30 % wheat straw (WS)); 15 % PB and 15 % WS, and 30 % PB and 0 % WS. Although dry matter (DM) intake and digestibility were not affected (P > 0.10) by feeding PB, neutral detergent fiber (linear; P = 0.01), acid detergent fiber (linear; P = 0.001) and lignin digestibility (linear; P = 0.01) decreased, and crude protein (CP) digestibility tended to decrease (P = 0.09) as PB increased in the diet, apparent retention of Ca (P = 0.09), P (P = 0.03), Mg (P = 0.01), Mn (P = 0.01), Zn (P = 0.01) and Fe (P = 0.09) also increased linearly. Nitrogen intake and fecal N excretion were not affected (P > 0.05) by addition of PB in the diet, but N balance in the body was quadratically increased (P < 0.01) in the 15 % PB diet compared to other diets. This may be due to more rumen escape protein and less excreted N in the urine with the 15 % PB diet. The study showed that a moderate level of tannin-containing pine bark supplementation could improve gastrointestinal nitrogen balance with the aim of improving animal performance. Conclusion These results suggest that tannin-containing PB has negative impact on fiber, lignin, and protein digestibility, but positively impacted on N-balance.

Exploring strategies for coupled 4D-Var data assimilation using an idealised atmosphere-ocean model

Operational forecasting centres are currently developing data assimilation systems for coupled atmosphere-ocean models. Strongly coupled assimilation, in which a single assimilation system is applied to a coupled model, presents significant technical and scientific challenges. Hence weakly coupled assimilation systems are being developed as a first step, in which the coupled model is used to compare the current state estimate with observations, but corrections to the atmosphere and ocean initial conditions are then calculated independently. In this paper we provide a comprehensive description of the different coupled assimilation methodologies in the context of four dimensional variational assimilation (4D-Var) and use an idealised framework to assess the expected benefits of moving towards coupled data assimilation. We implement an incremental 4D-Var system within an idealised single column atmosphere-ocean model. The system has the capability to run both strongly and weakly coupled assimilations as well as uncoupled atmosphere or ocean only assimilations, thus allowing a systematic comparison of the different strategies for treating the coupled data assimilation problem. We present results from a series of identical twin experiments devised to investigate the behaviour and sensitivities of the different approaches. Overall, our study demonstrates the potential benefits that may be expected from coupled data assimilation. When compared to uncoupled initialisation, coupled assimilation is able to produce more balanced initial analysis fields, thus reducing initialisation shock and its impact on the subsequent forecast. Single observation experiments demonstrate how coupled assimilation systems are able to pass information between the atmosphere and ocean and therefore use near-surface data to greater effect. We show that much of this benefit may also be gained from a weakly coupled assimilation system, but that this can be sensitive to the parameters used in the assimilation.

Joint data assimilation of satellite reflectance and net ecosystem exchange data constrains ecosystem carbon fluxes at a high-elevation subalpine forest

We utilized an ecosystem process model (SIPNET, simplified photosynthesis and evapotranspiration model) to estimate carbon fluxes of gross primary productivity and total ecosystem respiration of a high-elevation coniferous forest. The data assimilation routine incorporated aggregated twice-daily measurements of the net ecosystem exchange of CO2 (NEE) and satellite-based reflectance measurements of the fraction of absorbed photosynthetically active radiation (fAPAR) on an eight-day timescale. From these data we conducted a data assimilation experiment with fifteen different combinations of available data using twice-daily NEE, aggregated annual NEE, eight-day f AP AR, and average annual fAPAR. Model parameters were conditioned on three years of NEE and fAPAR data and results were evaluated to determine the information content from the different combinations of data streams. Across the data assimilation experiments conducted, model selection metrics such as the Bayesian Information Criterion and Deviance Information Criterion obtained minimum values when assimilating average annual fAPAR and twice-daily NEE data. Application of wavelet coherence analyses showed higher correlations between measured and modeled fAPAR on longer timescales ranging from 9 to 12 months. There were strong correlations between measured and modeled NEE (R2, coefficient of determination, 0.86), but correlations between measured and modeled eight-day fAPAR were quite poor (R2 = −0.94). We conclude that this inability to determine fAPAR on eight-day timescale would improve with the considerations of the radiative transfer through the plant canopy. Modeled fluxes when assimilating average annual fAPAR and annual NEE were comparable to corresponding results when assimilating twice-daily NEE, albeit at a greater uncertainty. Our results support the conclusion that for this coniferous forest twice-daily NEE data are a critical measurement stream for the data assimilation. The results from this modeling exercise indicate that for this coniferous forest, average annuals for satellite-based fAPAR measurements paired with annual NEE estimates may provide spatial detail to components of ecosystem carbon fluxes in proximity of eddy covariance towers. Inclusion of other independent data streams in the assimilation will also reduce uncertainty on modeled values.

Prediction of nutrient digestibility and energy concentrations in fresh grass using nutrient composition

Improved nutrient utilization efficiency is strongly related to enhanced economic performance and reduced environmental footprint of dairy farms. Pasture-based systems are widely used for dairy production in certain areas of the world, but prediction equations of fresh grass nutritive value (nutrient digestibility and energy concentrations) are limited. Equations to predict digestible energy (DE) and metabolizable energy (ME) used for grazing cattle have been either developed with cattle fed conserved forage and concentrate diets or sheep fed previously frozen grass, and the majority of them require measurements less commonly available to producers, such as nutrient digestibility. The aim of the present study was therefore to develop prediction equations more suitable to grazing cattle for nutrient digestibility and energy concentrations, which are routinely available at farm level by using grass nutrient contents as predictors. A study with 33 nonpregnant, nonlactating cows fed solely fresh-cut grass at maintenance energy level for 50 wk was carried out over 3 consecutive grazing seasons. Freshly harvested grass of 3 cuts (primary growth and first and second regrowth), 9 fertilizer input levels, and contrasting stage of maturity (3 to 9 wk after harvest) was used, thus ensuring a wide representation of nutritional quality. As a result, a large variation existed in digestibility of dry matter (0.642-0.900) and digestible organic matter in dry matter (0.636-0.851) and in concentrations of DE (11.8-16.7 MJ/kg of dry matter) and ME (9.0-14.1 MJ/kg of dry matter). Nutrient digestibilities and DE and ME concentrations were negatively related to grass neutral detergent fiber (NDF) and acid detergent fiber (ADF) contents but positively related to nitrogen (N), gross energy, and ether extract (EE) contents. For each predicted variable (nutrient digestibilities or energy concentrations), different combinations of predictors (grass chemical composition) were found to be significant and increase the explained variation. For example, relatively higher R(2) values were found for prediction of N digestibility using N and EE as predictors; gross-energy digestibility using EE, NDF, ADF, and ash; NDF, ADF, and organic matter digestibilities using N, water-soluble carbohydrates, EE, and NDF; digestible organic matter in dry matter using water-soluble carbohydrates, EE, NDF, and ADF; DE concentration using gross energy, EE, NDF, ADF, and ash; and ME concentration using N, EE, ADF, and ash. Equations presented may allow a relatively quick and easy prediction of grass quality and, hence, better grazing utilization on commercial and research farms, where nutrient composition falls within the range assessed in the current study.

Ectomycorrhizal symbiosis can enhance plant nutrition through improved access to discrete organic nutrient patches of high resource quality

It is known that roots can respond to patches of fertility; however, root proliferation is often too slow to exploit resources fully, and organic nutrient patches may be broken down and leached, immobilized or chemically fixed before they are invaded by the root system. The ability of fungal hyphae to exploit resource patches is far greater than that of roots due to their innate physiological and morphological plasticity, which allows comprehensive exploration and rapid colonization of resource patches in soils. The fungal symbionts of ectomycorrhizal plants excrete significant quantities of enzymes such as chitinases, phosphatases and proteases. These might allow the organic residue to be tapped directly for nutrients such as N and P. Pot experiments conducted with nutrient-stressed ectomycorrhizal and control willow plants showed that when high quality organic nutrient patches were added, they were colonized rapidly by the ectomycorrhizal mycelium. These established willows (0.5 m tall) were colonized by Hebeloma syrjense P. Karst. for 1 year prior to nutrient patch addition. Within days after patch addition, colour changes in the leaves of the mycorrhizal plants (reflecting improved nutrition) were apparent, and after I month the concentration of N and P in the foliage of mycorrhizal plants was significantly greater than that in non-mycorrhizal plants subject to the same nutrient addition. It seems likely that the mycorrhizal plants were able to compete effectively with the wider soil microbiota and tap directly into the high quality organic resource patch via their extra-radical mycelium. We hypothesize that ectomycorrhizal plants may reclaim some of the N and P invested in seed production by direct recycling from failed seeds in the soil. The rapid exploitation of similar discrete, transient, high-quality nutrient patches may have led to underestimations when determining the nutritional benefits of ectomycorrhizal colonization.

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.

Balanced Ocean-Data Assimilation near the Equator

The question is addressed whether using unbalanced updates in ocean-data assimilation schemes for seasonal forecasting systems can result in a relatively poor simulation of zonal currents. An assimilation scheme, where temperature observations are used for updating only the density field, is compared to a scheme where updates of density field and zonal velocities are related by geostrophic balance. This is done for an equatorial linear shallow-water model. It is found that equatorial zonal velocities can be detoriated if velocity is not updated in the assimilation procedure. Adding balanced updates to the zonal velocity is shown to be a simple remedy for the shallow-water model. Next, optimal interpolation (OI) schemes with balanced updates of the zonal velocity are implemented in two ocean general circulation models. First tests indicate a beneficial impact on equatorial upper-ocean zonal currents.

Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

The weak-constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak-constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. they also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. the feasibility of the new methods is illustrated in a two-layer quasigeostrophic model.

Assimilation of Geosat Altimeter Data for the Agulhas Current Using the Ensemble Kalman Filter with a Quasigeostrophic Model

The ring-shedding process in the Agulhas Current is studied using the ensemble Kalman filter to assimilate geosat altimeter data into a two-layer quasigeostrophic ocean model. The properties of the ensemble Kalman filter are further explored with focus on the analysis scheme and the use of gridded data. The Geosat data consist of 10 fields of gridded sea-surface height anomalies separated 10 days apart that are added to a climatic mean field. This corresponds to a huge number of data values, and a data reduction scheme must be applied to increase the efficiency of the analysis procedure. Further, it is illustrated how one can resolve the rank problem occurring when a too large dataset or a small ensemble is used.