A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

Selenium supplementation of lactating dairy cows: effects on milk production and total selenium content and speciation in blood, milk and cheese

Forty-multiparous Holstein cows were used in a 16-wk continuous design study to determine the effects of either selenium (Se) source, selenized yeast (SY) (derived from a specific strain of Saccharomyces cerevisiae CNCM I-3060 Sel-Plex®) or sodium selenite (SS), or inclusion rate of SY on Se concentration and speciation in blood, milk and cheese. Cows received ad libitum a TMR with 1:1 forage:concentrate ratio on a dry matter (DM) basis. There were four diets (T1-T4) which differed only in either source or dose of Se additive. Estimated total dietary Se for T1 (no supplement), T2 (SS), T3 (SY) and T4 (SY) was 0.16, 0.30, 0.30 and 0.45 mg/kg DM, respectively. Blood and milk samples were taken at 28 day intervals and at each time point there were positive linear effects of SY on Se concentration in blood and milk. At day 112 blood and milk Se values for T1-T4 were 177, 208, 248, 279 ± 6.6 and 24, 38, 57, 72 ± 3.7 ng/g fresh material, respectively and indicate improved uptake and incorporation of Se from SY. While selenocysteine (SeCys) was the main selenised amino acid in blood its concentration was not markedly affected by treatment, but the proportion of total Se as selenomethionine (SeMet) increased with increasing inclusion rate of SY. In milk, there were no marked treatment effects on SeCys content, but Se source had a marked effect on the proportion of total Se as SeMet. At day 112 replacing SS (T2) with SY (T3) increased the SeMet concentration of milk from 36 to 111 ng Se/g and its concentration increased further to 157 ng Se/g as the inclusion rate of SY increased further (T4) to provide 0.45 mg Se/kg TMR. Neither Se source nor inclusion rate effected the keeping quality of milk. At day 112, milk from T1, T2, and T3 was made into a hard cheese and Se source had a marked effect on total Se and the proportion of total Se comprised as either SeMet or SeCys. Replacing SS (T2) with SY (T3) increased total Se, SeMet and SeCys content from 180 to 340 ng Se/g, 57 to 153 ng Se/g and 52 to 92 ng Se/g, respectively. Key words: dairy cow, milk and cheese, selenomethionine, selenocysteine, milk keeping quality

Selenium supplementation of lactating dairy cows: Effect on selenium concentration in blood, milk, urine and feces

The objectives were to determine effects of graded levels of selenized yeast derived from a specific strain of Saccharomyces cerevisiae (CNCM I-3060) on animal performance and in selenium concentrations in the blood, milk, feces, and urine of dairy cows compared with sodium selenite; and to provide preliminary data on the proportion of selenium as selenomethionine in the milk and blood. Twenty Holstein cows were used in a 5 × 5 Latin square design study in which all cows received the same total mixed rations, which varied only in source or concentration of dietary selenium. There were 5 experimental treatments. Total dietary selenium of treatment 1, which received no added selenium, was 0.15 mg/kg of dry matter, whereas values for treatments 2, 3, and 4, derived from selenized yeast, were 0.27, 0.33, and 0.40 mg/kg of dry matter, respectively. Treatment 5 contained 0.25 mg of selenium obtained from sodium selenite/kg of dry matter. There were no significant treatment effects on animal performance, and blood chemistry and hematology showed few treatment effects. Regression analysis noted significant positive linear effects of increasing dietary selenium derived from selenized yeast on selenium concentrations in the milk, blood, urine, and feces. In addition, milk selenium results indicated improved bioavailability of selenium from selenized yeast, compared with sodium selenite. Preliminary analyses showed that compared with sodium selenite, the use of selenized yeast increased the concentration of selenomethionine in the milk and blood. There was no indication of adverse effects on cow health associated with the use of selenized yeast.

Effects of different calcium salts on properties of milk related to heat stability

Insoluble calcium salts were added to milk to increase total calcium by 30 mM, without changing properties influencing heat stability, such as pH and ionic calcium. There were no major signs of instability associated with coagulation, sediment formation or fouling when subjected to ultra high temperature (UHT) and in-container sterilisation. The buffering capacity was also unaltered. On the other hand, addition of soluble calcium salts reduced pH, increased ionic calcium and caused coagulation to occur. Calcium chloride showed the largest destabilising effect, followed by calcium lactate and calcium gluconate. Milk became unstable to UHT processing at lower calcium additions compared to in-container sterilisation.

Measurement of ionic calcium, pH and soluble divalent cations in milk at high temperature

Dialysis and ultrafiltration were investigated as methods for measuring pH and ionic calcium and partitioning of divalent cations of milk at high temperatures. It was found that ionic calcium, pH, and total soluble divalent cations decreased as temperature increased between 20 and 80°C in both dialysates and ultrafiltration permeates. Between 90 and 110°C, ionic calcium and pH in dialysates continued to decrease as temperature increased, and the relationship between ionic calcium and temperature was linear. The permeabilities of hydrogen and calcium ions through the dialysis tubing were not changed after the tubing was sterilized for 1h at 120°C. There were no significant differences in pH and ionic calcium between dialysates from raw milk and those from a range of heat-treated milks. The effects of calcium chloride addition on pH and ionic calcium were measured in milk at 20°C and in dialysates collected at 110°C. Heat coagulation at 110°C occurred with addition of calcium chloride at 5.4mM, where pH and ionic calcium of the dialysate were 6.00 and 0.43mM, respectively. Corresponding values at 20°C were pH 6.66 and 2.10mM.