The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.

Effects of forage source and extruded linseed supplementation on methane emissions from growing dairy cattle of differing body weights

Changes in diet carbohydrate amount and type (i.e., starch vs. fiber) and dietary oil supplements can affect ruminant methane emissions. Our objectives were to measure methane emissions, whole-tract digestibility, and energy and nitrogen utilization from growing dairy cattle at 2 body weight (BW) ranges, fed diets containing either high maize silage (MS) or high grass silage (GS), without or with supplemental oil from extruded linseed (ELS). Four Holstein-Friesian heifers aged 13 mo (BW range from start to finish of 382 to 526 kg) were used in experiment 1, whereas 4 lighter heifers aged 12 mo (BW range from start to finish of 292 to 419 kg) were used in experiment 2. Diets were fed as total mixed rations with forage dry matter (DM) containing high MS or high GS and concentrates in proportions (forage:concentrate, DM basis) of either 75:25 (experiment 1) or 60:40 (experiment 2), respectively. Diets were supplemented without or with ELS (Lintec[AU1: Add manufacturer name and location.]; 260 g of oil/ kg of DM) at 6% of ration DM. Each experiment was a 4 × 4 Latin square design with 33-d periods, with measurements during d 29 to 33 while animals were housed in respiration chambers. Heifers fed MS at a heavier BW (experiment 1) emitted 20% less methane per unit of DM intake (yield) compared with GS (21.4 vs. 26.6, respectively). However, when repeated with heifers of a lower BW (experiment 2), methane yield did not differ between the 2 diets (26.6 g/kg of DM intake). Differences in heifer BW had no overall effect on methane emissions, except when expressed as grams per kilogram of digestible organic matter (OMD) intake (32.4 vs. 36.6, heavy vs. light heifers). Heavier heifers fed MS in experiment 1 had a greater DM intake (9.4 kg/d) and lower OMD (755 g/kg), but no difference in N utilization (31% of N intake) compared with heifers fed GS (7.9 kg/d and 799 g/kg, respectively). Tissue energy retention was nearly double for heifers fed MS compared with GS in experiment 1 (15 vs. 8% of energy intake, respectively). Heifers fed MS in experiment 2 had similar DM intake (7.2 kg/d) and retention of energy (5% of intake energy) and N (28% of N intake), compared with GS-fed heifers, but OMD was lower (741 vs. 765 g/kg, respectively). No effect of ELS was noted on any of the variables measured, irrespective of animal BW, and this was likely due to the relatively low amount of supplemental oil provided. Differences in heifer BW did not markedly influence dietary effects on methane emissions. Differences in methane yield were attributable to differences in dietary starch and fiber composition associated with forage type and source.