Simple M-factor algorithm for improved estimation of the basic maximum usable frequency of radio waves reflected from the ionospheric F-region

The equations of Milsom are evaluated, giving the ground range and group delay of radio waves propagated via the horizontally stratified model ionosphere proposed by Bradley and Dudeney. Expressions for the ground range which allow for the effects of the underlying E- and F1-regions are used to evaluate the basic maximum usable frequency or M-factors for single F-layer hops. An algorithm for the rapid calculation of the M-factor at a given range is developed, and shown to be accurate to within 5%. The results reveal that the M(3000)F2-factor scaled from vertical-incidence ionograms using the standard URSI procedure can be up to 7.5% in error. A simple addition to the algorithm effects a correction to ionogram values to make these accurate to 0.5%.

Transition from suppressed to active convection modulated by a weak-temperature gradient derived large-scale circulation

Numerical simulations are performed to assess the influence of the large-scale circulation on the transition from suppressed to active convection. As a model tool, we used a coupled-column model. It consists of two cloud-resolving models which are fully coupled via a large-scale circulation which is derived from the requirement that the instantaneous domain-mean potential temperature profiles of the two columns remain close to each other. This is known as the weak-temperature gradient approach. The simulations of the transition are initialized from coupled-column simulations over non-uniform surface forcing and the transition is forced within the dry column by changing the local and/or remote surface forcings to uniform surface forcing across the columns. As the strength of the circulation is reduced to zero, moisture is recharged into the dry column and a transition to active convection occurs once the column is sufficiently moistened to sustain deep convection. Direct effects of changing surface forcing occur over the first few days only. Afterward, it is the evolution of the large-scale circulation which systematically modulates the transition. Its contributions are approximately equally divided between the heating and moistening effects. A transition time is defined to summarize the evolution from suppressed to active convection. It is the time when the rain rate within the dry column is halfway to the mean value obtained at equilibrium over uniform surface forcing. The transition time is around twice as long for a transition that is forced remotely compared to a transition that is forced locally. Simulations in which both local and remote surface forcings are changed produce intermediate transition times.

Online dietary intake estimation : reproducibility and validity of the Food4Me food frequency questionnaire against a 4-day weighed food record

Background: Advances in nutritional assessment are continuing to embrace developments in computer technology. The online Food4Me food frequency questionnaire (FFQ) was created as an electronic system for the collection of nutrient intake data. To ensure its accuracy in assessing both nutrient and food group intake, further validation against data obtained using a reliable, but independent, instrument and assessment of its reproducibility are required. Objective: The aim was to assess the reproducibility and validity of the Food4Me FFQ against a 4-day weighed food record (WFR). Methods: Reproducibility of the Food4Me FFQ was assessed using test-retest methodology by asking participants to complete the FFQ on 2 occasions 4 weeks apart. To assess the validity of the Food4Me FFQ against the 4-day WFR, half the participants were also asked to complete a 4-day WFR 1 week after the first administration of the Food4Me FFQ. Level of agreement between nutrient and food group intakes estimated by the repeated Food4Me FFQ and the Food4Me FFQ and 4-day WFR were evaluated using Bland-Altman methodology and classification into quartiles of daily intake. Crude unadjusted correlation coefficients were also calculated for nutrient and food group intakes. Results: In total, 100 people participated in the assessment of reproducibility (mean age 32, SD 12 years), and 49 of these (mean age 27, SD 8 years) also took part in the assessment of validity. Crude unadjusted correlations for repeated Food4Me FFQ ranged from .65 (vitamin D) to .90 (alcohol). The mean cross-classification into “exact agreement plus adjacent” was 92% for both nutrient and food group intakes, and Bland-Altman plots showed good agreement for energy-adjusted macronutrient intakes. Agreement between the Food4Me FFQ and 4-day WFR varied, with crude unadjusted correlations ranging from .23 (vitamin D) to .65 (protein, % total energy) for nutrient intakes and .11 (soups, sauces and miscellaneous foods) to .73 (yogurts) for food group intake. The mean cross-classification into “exact agreement plus adjacent” was 80% and 78% for nutrient and food group intake, respectively. There were no significant differences between energy intakes estimated using the Food4Me FFQ and 4-day WFR, and Bland-Altman plots showed good agreement for both energy and energy-controlled nutrient intakes. Conclusions: The results demonstrate that the online Food4Me FFQ is reproducible for assessing nutrient and food group intake and has moderate agreement with the 4-day WFR for assessing energy and energy-adjusted nutrient intakes. The Food4Me FFQ is a suitable online tool for assessing dietary intake in healthy adults.

Global burned-land estimation in Latin America using MODIS composite data

This paper presents results of the AQL2004 project, which has been develope within the GOFC-GOLD Latin American network of remote sensing and forest fires (RedLatif). The project intended to obtain monthly burned-land maps of the entire region, from Mexico to Patagonia, using MODIS (moderate-resolution imaging spectroradiometer) reflectance data. The project has been organized in three different phases: acquisition and preprocessing of satellite data; discrimination of burned pixels; and validation of results. In the first phase, input data consisting of 32-day composites of MODIS 500-m reflectance data generated by the Global Land Cover Facility (GLCF) of the University of Maryland (College Park, Maryland, U.S.A.) were collected and processed. The discrimination of burned areas was addressed in two steps: searching for "burned core" pixels using postfire spectral indices and multitemporal change detection and mapping of burned scars using contextual techniques. The validation phase was based on visual analysis of Landsat and CBERS (China-Brazil Earth Resources Satellite) images. Validation of the burned-land category showed an agreement ranging from 30% to 60%, depending on the ecosystem and vegetation species present. The total burned area for the entire year was estimated to be 153 215 km2. The most affected countries in relation to their territory were Cuba, Colombia, Bolivia, and Venezuela. Burned areas were found in most land covers; herbaceous vegetation (savannas and grasslands) presented the highest proportions of burned area, while perennial forest had the lowest proportions. The importance of croplands in the total burned area should be taken with reserve, since this cover presented the highest commission errors. The importance of generating systematic products of burned land areas for different ecological processes is emphasized.

Rainfall estimation by rain gauge-radar combination: a concurrent multiplicative-additive approach

A procedure (concurrent multiplicative-additive objective analysis scheme [CMA-OAS]) is proposed for operational rainfall estimation using rain gauges and radar data. On the basis of a concurrent multiplicative-additive (CMA) decomposition of the spatially nonuniform radar bias, within-storm variability of rainfall and fractional coverage of rainfall are taken into account. Thus both spatially nonuniform radar bias, given that rainfall is detected, and bias in radar detection of rainfall are handled. The interpolation procedure of CMA-OAS is built on Barnes' objective analysis scheme (OAS), whose purpose is to estimate a filtered spatial field of the variable of interest through a successive correction of residuals resulting from a Gaussian kernel smoother applied on spatial samples. The CMA-OAS, first, poses an optimization problem at each gauge-radar support point to obtain both a local multiplicative-additive radar bias decomposition and a regionalization parameter. Second, local biases and regionalization parameters are integrated into an OAS to estimate the multisensor rainfall at the ground level. The procedure is suited to relatively sparse rain gauge networks. To show the procedure, six storms are analyzed at hourly steps over 10,663 km2. Results generally indicated an improved quality with respect to other methods evaluated: a standard mean-field bias adjustment, a spatially variable adjustment with multiplicative factors, and ordinary cokriging.

Sparse density estimation on the multinomial manifold

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators.

Estimation after subpopulation selection in adaptive seamless trials

During the development of new therapies, it is not uncommon to test whether a new treatment works better than the existing treatment for all patients who suffer from a condition (full population) or for a subset of the full population (subpopulation). One approach that may be used for this objective is to have two separate trials, where in the first trial, data are collected to determine if the new treatment benefits the full population or the subpopulation. The second trial is a confirmatory trial to test the new treatment in the population selected in the first trial. In this paper, we consider the more efficient two-stage adaptive seamless designs (ASDs), where in stage 1, data are collected to select the population to test in stage 2. In stage 2, additional data are collected to perform confirmatory analysis for the selected population. Unlike the approach that uses two separate trials, for ASDs, stage 1 data are also used in the confirmatory analysis. Although ASDs are efficient, using stage 1 data both for selection and confirmatory analysis introduces selection bias and consequently statistical challenges in making inference. We will focus on point estimation for such trials. In this paper, we describe the extent of bias for estimators that ignore multiple hypotheses and selecting the population that is most likely to give positive trial results based on observed stage 1 data. We then derive conditionally unbiased estimators and examine their mean squared errors for different scenarios.

Synergistic angular and spectral estimation of aerosol properties using CHRIS/PROBA-1 and simulated Sentinel-3 data

We develop a method to derive aerosol properties over land surfaces using combined spectral and angular information, such as available from ESA Sentinel-3 mission, to be launched in 2015. A method of estimating aerosol optical depth (AOD) using only angular retrieval has previously been demonstrated on data from the ENVISAT and PROBA-1 satellite instruments, and is extended here to the synergistic spectral and angular sampling of Sentinel-3. The method aims to improve the estimation of AOD, and to explore the estimation of fine mode fraction (FMF) and single scattering albedo (SSA) over land surfaces by inversion of a coupled surface/atmosphere radiative transfer model. The surface model includes a general physical model of angular and spectral surface reflectance. An iterative process is used to determine the optimum value of the aerosol properties providing the best fit of the corrected reflectance values to the physical model. The method is tested using hyperspectral, multi-angle Compact High Resolution Imaging Spectrometer (CHRIS) images. The values obtained from these CHRIS observations are validated using ground-based sun photometer measurements. Results from 22 image sets using the synergistic retrieval and improved aerosol models show an RMSE of 0.06 in AOD, reduced to 0.03 over vegetated targets.

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.

A joint state and parameter estimation scheme for nonlinear dynamical systems

We present a novel algorithm for concurrent model state and parameter estimation in nonlinear dynamical systems. The new scheme uses ideas from three dimensional variational data assimilation (3D-Var) and the extended Kalman filter (EKF) together with the technique of state augmentation to estimate uncertain model parameters alongside the model state variables in a sequential filtering system. The method is relatively simple to implement and computationally inexpensive to run for large systems with relatively few parameters. We demonstrate the efficacy of the method via a series of identical twin experiments with three simple dynamical system models. The scheme is able to recover the parameter values to a good level of accuracy, even when observational data are noisy. We expect this new technique to be easily transferable to much larger 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.

Short communication: estimation of the financial benefit of using Jersey milk at different inclusion rates for Cheddar cheese production using partial budgeting

Partial budgeting was used to estimate the net benefit of blending Jersey milk in Holstein-Friesian milk for Cheddar cheese production. Jersey milk increases Cheddar cheese yield. However, the cost of Jersey milk is also higher; thus, determining the balance of profitability is necessary, including consideration of seasonal effects. Input variables were based on a pilot plant experiment run from 2012 to 2013 and industry milk and cheese prices during this period. When Jersey milk was used at an increasing rate with Holstein-Friesian milk (25, 50, 75, and 100% Jersey milk), it resulted in an increase of average net profit of 3.41, 6.44, 8.57, and 11.18 pence per kilogram of milk, respectively, and this additional profit was constant throughout the year. Sensitivity analysis showed that the most influential input on additional profit was cheese yield, whereas cheese price and milk price had a small effect. The minimum increase in yield, which was necessary for the use of Jersey milk to be profitable, was 2.63, 7.28, 9.95, and 12.37% at 25, 50, 75, and 100% Jersey milk, respectively. Including Jersey milk did not affect the quantity of whey butter and powder produced. Althoug further research is needed to ascertain the amount of additional profit that would be found on a commercial scale, the results indicate that using Jersey milk for Cheddar cheese making would lead to an improvement in profit for the cheese makers, especially at higher inclusion rates.

Improving the estimation of probability of bidder participation in procurement auctions

Anticipating the number and identity of bidders has significant influence in many theoretical results of the auction itself and bidders' bidding behaviour. This is because when a bidder knows in advance which specific bidders are likely competitors, this knowledge gives a company a head start when setting the bid price. However, despite these competitive implications, most previous studies have focused almost entirely on forecasting the number of bidders and only a few authors have dealt with the identity dimension qualitatively. Using a case study with immediate real-life applications, this paper develops a method for estimating every potential bidder's probability of participating in a future auction as a function of the tender economic size removing the bias caused by the contract size opportunities distribution. This way, a bidder or auctioner will be able to estimate the likelihood of a specific group of key, previously identified bidders in a future tender.

CO2 emission estimation in the urban environment: measurement of the CO2 storage term

Eddy covariance has been used in urban areas to evaluate the net exchange of CO2 between the surface and the atmosphere. Typically, only the vertical flux is measured at a height 2–3 times that of the local roughness elements; however, under conditions of relatively low instability, CO2 may accumulate in the airspace below the measurement height. This can result in inaccurate emissions estimates if the accumulated CO2 drains away or is flushed upwards during thermal expansion of the boundary layer. Some studies apply a single height storage correction; however, this requires the assumption that the response of the CO2 concentration profile to forcing is constant with height. Here a full seasonal cycle (7th June 2012 to 3rd June 2013) of single height CO2 storage data calculated from concentrations measured at 10 Hz by open path gas analyser are compared to a data set calculated from a concurrent switched vertical profile measured (2 Hz, closed path gas analyser) at 10 heights within and above a street canyon in central London. The assumption required for the former storage determination is shown to be invalid. For approximately regular street canyons at least one other measurement is required. Continuous measurements at fewer locations are shown to be preferable to a spatially dense, switched profile, as temporal interpolation is ineffective. The majority of the spectral energy of the CO2 storage time series was found to be between 0.001 and 0.2 Hz (500 and 5 s respectively); however, sampling frequencies of 2 Hz and below still result in significantly lower CO2 storage values. An empirical method of correcting CO2 storage values from under-sampled time series is proposed.