Marginal distributions for cosmic variance limited CMB polarization data

We provide computationally convenient expressions for all marginal distributions of the polarization CMB power spectrum distribution P(C_l|sigma_l), where C_l = {C_l^TT, C_l^TE, C_l^EE, C_l^BB} denotes the set of ensemble averaged polarization CMB power spectra, and sigma_l = {sigma_l^TT, sigma_l^TE, sigma_l^EE, sigma_l^BB} the set of the realization specific polarization CMB power spectra. This distribution describes the CMB power spectrum posterior for cosmic variance limited data. The expressions derived here are general, and may be useful in a wide range of applications. Two specific applications are described in this paper. First, we employ the derived distributions within the CMB Gibbs sampling framework, and demonstrate a new conditional CMB power spectrum sampling algorithm that allows for different binning schemes for each power spectrum. This is useful because most CMB experiments have very different signal-to-noise ratios for temperature and polarization. Second, we provide new Blackwell-Rao estimators for each of the marginal polarization distributions, which are relevant to power spectrum and likelihood estimation. Because these estimators represent marginals, they are not affected by the exponential behaviour of the corresponding joint expression, but converge quickly.Comment: 8 pages, 3 figures; minor adjustment, accepted for publication in ApJ

The two-and three-point correlation functions of the polarized five-year WMAP sky maps

We present the two- and three-point real space correlation functions of the five-year WMAP sky maps, and compare the observed functions to simulated LCDM concordance model ensembles. In agreement with previously published results, we find that the temperature correlation functions are consistent with expectations. However, the pure polarization correlation functions are acceptable only for the 33GHz band map; the 41, 61, and 94 GHz band correlation functions all exhibit significant large-scale excess structures. Further, these excess structures very closely match the correlation functions of the two (synchrotron and dust) foreground templates used to correct the WMAP data for galactic contamination, with a cross-correlation statistically significant at the 2sigma-3sigma confidence level. The correlation is slightly stronger with respect to the thermal dust template than with the synchrotron template.Comment: 10 pages, 5 figures, published in ApJ. v2: New title, minor changes to appendix, and fixed some typos. v3: Matches version published in Ap

A Markov Chain Monte Carlo Algorithm for analysis of low signal-to-noise CMB data

We present a new Monte Carlo Markov Chain algorithm for CMB analysis in the low signal-to-noise regime. This method builds on and complements the previously described CMB Gibbs sampler, and effectively solves the low signal-to-noise inefficiency problem of the direct Gibbs sampler. The new algorithm is a simple Metropolis-Hastings sampler with a general proposal rule for the power spectrum, C_l, followed by a particular deterministic rescaling operation of the sky signal. The acceptance probability for this joint move depends on the sky map only through the difference of chi-squared between the original and proposed sky sample, which is close to unity in the low signal-to-noise regime. The algorithm is completed by alternating this move with a standard Gibbs move. Together, these two proposals constitute a computationally efficient algorithm for mapping out the full joint CMB posterior, both in the high and low signal-to-noise regimes.Comment: Submitted to Ap

CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator

We introduce a new CMB temperature likelihood approximation called the Gaussianized Blackwell-Rao (GBR) estimator. This estimator is derived by transforming the observed marginal power spectrum distributions obtained by the CMB Gibbs sampler into standard univariate Gaussians, and then approximate their joint transformed distribution by a multivariate Gaussian. The method is exact for full-sky coverage and uniform noise, and an excellent approximation for sky cuts and scanning patterns relevant for modern satellite experiments such as WMAP and Planck. A single evaluation of this estimator between l=2 and 200 takes ~0.2 CPU milliseconds, while for comparison, a single pixel space likelihood evaluation between l=2 and 30 for a map with ~2500 pixels requires ~20 seconds. We apply this tool to the 5-year WMAP temperature data, and re-estimate the angular temperature power spectrum, $C_{\ell}$, and likelihood, L(C_l), for l<=200, and derive new cosmological parameters for the standard six-parameter LambdaCDM model. Our spectrum is in excellent agreement with the official WMAP spectrum, but we find slight differences in the derived cosmological parameters. Most importantly, the spectral index of scalar perturbations is n_s=0.973 +/- 0.014, 1.9 sigma away from unity and 0.6 sigma higher than the official WMAP result, n_s = 0.965 +/- 0.014. This suggests that an exact likelihood treatment is required to higher l's than previously believed, reinforcing and extending our conclusions from the 3-year WMAP analysis. In that case, we found that the sub-optimal likelihood approximation adopted between l=12 and 30 by the WMAP team biased n_s low by 0.4 sigma, while here we find that the same approximation between l=30 and 200 introduces a bias of 0.6 sigma in n_s.Comment: 10 pages, 7 figures, submitted to Ap

Biomass production and N2-fixation in seven grass-legume mixtures

Inclusion of forage legumes in low-input grassland mixtures improves biomass production and soil fertility trough addition of nitrogen (N) from N2-fixation. The impacts of different mixture of legumes and companion grasses on the N production of the forage mixture have rarely been investigated under comparable soil and climatic conditions. We conducted a field experiment on a sandy soil at two nitrogen levels with seven two-species grassland mixtures: alfalfa (Medicago sativa), bird’s-foot trefoil (Lotus corniculatus), red clover (Trifolium pratense), or white clover (Trifolium repens) in mixture with perennial ryegrass (Lolium perenne), and white clover in mixture with meadow fescue (Festuca pratensis), timothy (Phleum pratense), or hybrid ryegrass (Lolium hybridum). Red clover and alfalfa fixed 400-500 kg N ha-1 and bird ’s-foot trefoil just above 100 kg N ha-1 in aboveground biomass. The white clover N fixation was affected by the companion grass species and ranged from 150 to 175 kg N ha-1. Fertilization had different effects on N2-fixation among the legumes, but also significant effects on white clover N2-fixation depending on the companion grass species

Nitrogen management on large organic dairy farms

Large dairy herds need much grassland near the farm. Utilisation and losses of nitrogen in such grass-intensive crop rotations can be controlled by management: In grassland, grazing days or fertiliser input can be reduced, and following grassland cultivation, a barley whole crop for silage undersown with Italian ryegrass can reduce leaching to a minimum

Ecosystem services of biodiversity in organic grasslands

The use of multi-species mixtures in herbage production can add value in terms of improved conditions for pollinating insects, better resource utilization, carbon sequestration, yield stability, animal health and product quality. This is the hypothesis of a new project - EcoServe - where the goal is to design grasslands, which increase both the nature value and provide an economically sustainable food production

Productivity and N-leaching in organic dairy grass-arable crop rotations

Increasing size of organic dairy farms makes grazing of all cropped land inexpedient due to long distance to the milking facilities. We investigated nutrient dynamics and feed production in two dairy crop rotations with differences in proportion of grazing and cutting. One six year crop rotation represents close to the farm buildings (barley undersown with grass-clover - 4 years of grass-clover - spring barley/catch crop) and another represents further away (barley undersown with grass-clover, 2 years of grass-clover -barley/catch crop - maize/catch crop - lupin/catch crop). In each of the crop rotations was made five treatments concerning grazing/cutting strategy and manure application. Results shows that herbage production was high in year 1-4 of grass-clover. Nitrate leaching in the crop rotations were highest in grazed and manured 2-4 years old grasslands, but also following maize and lupin considerable losses occurred despite the presence of catch crops. Following grassland cultivation, a barley silage crop undersown with Italian ryegrass reduced leaching to a minimum