Solar ultraviolet-B radiation and vitamin D: a cross-sectional population-based study using data from the 2007 to 2009 Canadian Health Measures Survey

Background: Exposure to solar ultraviolet-B (UV-B) radiation is a major source of vitamin D3. Chemistry climate models project decreases in ground-level solar erythemal UV over the current century. It is unclear what impact this will have on vitamin D status at the population level. The purpose of this study was to measure the association between ground-level solar UV-B and serum concentrations of 25-hydroxyvitamin D (25(OH)D) using a secondary analysis of the 2007 to 2009 Canadian Health Measures Survey (CHMS). Methods: Blood samples collected from individuals aged 12 to 79 years sampled across Canada were analyzed for 25(OH)D (n=4,398). Solar UV-B irradiance was calculated for the 15 CHMS collection sites using the Tropospheric Ultraviolet and Visible Radiation Model. Multivariable linear regression was used to evaluate the association between 25(OH)D and solar UV-B adjusted for other predictors and to explore effect modification. Results: Cumulative solar UV-B irradiance averaged over 91 days (91-day UV-B) prior to blood draw correlated significantly with 25(OH)D. Independent of other predictors, a 1 kJ/m 2 increase in 91-day UV-B was associated with a significant 0.5 nmol/L (95% CI 0.3-0.8) increase in mean 25(OH)D (P =0.0001). The relationship was stronger among younger individuals and those spending more time outdoors. Based on current projections of decreases in ground-level solar UV-B, we predict less than a 1 nmol/L decrease in mean 25(OH)D for the population. Conclusions: In Canada, cumulative exposure to ambient solar UV-B has a small but significant association with 25(OH)D concentrations. Public health messages to improve vitamin D status should target safe sun exposure with sunscreen use, and also enhanced dietary and supplemental intake and maintenance of a healthy body weight.

On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.