The representation of solar cycle signals in stratospheric ozone – Part 1: A comparison of satellite observations

Changes in incoming solar ultraviolet radiation over the 11-year solar cycle affect stratospheric ozone abundances. It is important to quantify the magnitude, structure, and seasonality of the associated solar-ozone response (SOR) to understand the impact of the 11-year solar cycle on climate. Part 1 of this two-part study uses multiple linear regression analysis to extract the SOR in a number of recently updated satellite ozone datasets covering different periods within the epoch 1970 to 2013. The annual mean SOR in the updated version 7.0 (v7.0) Stratospheric Aerosol and Gas Experiment (SAGE) II number density dataset (1984–2004) is very consistent with that found in the previous v6.2. In contrast, we find a substantial decrease in the magnitude of the SOR in the tropical upper stratosphere in the SAGE II v7.0 mixing ratio dataset (∼ 1 %) compared to the v6.2 (∼ 4 %). This difference is shown to be largely attributable to the change in the independent stratospheric temperature dataset used to convert SAGE II ozone number densities to mixing ratios. Since these temperature records contain substantial uncertainties, we suggest that datasets based on SAGE II number densities are currently most reliable for evaluating the SOR. We further analyse three extended ozone datasets that combine SAGE II v7.0 number densities with more recent GOMOS (Global Ozone Monitoring by Occultation of Stars) or OSIRIS (Optical Spectrograph and Infrared Imager System) measurements. The extended SAGE–OSIRIS dataset (1984–2013) shows a smaller and less statistically significant SOR across much of the tropical upper stratosphere compared to the SAGE II data alone. In contrast, the two SAGE–GOMOS datasets (1984–2011) show SORs that are in closer agreement with the original SAGE II data and therefore appear to provide a more reliable estimate of the SOR. We also analyse the SOR in the recent Solar Backscatter Ultraviolet Instrument (SBUV) Merged Ozone Dataset (SBUVMOD) version 8.6 (VN8.6) (1970–2012) and SBUV Merged Cohesive VN8.6 (1978–2012) datasets and compare them to the previous SBUVMOD VN8.0 (1970–2009). Over their full lengths, the three records generally agree in terms of the broad magnitude and structure of the annual mean SOR. The main difference is that SBUVMOD VN8.6 shows a smaller and less significant SOR in the tropical upper stratosphere and therefore more closely resembles the SAGE II v7.0 mixing ratio data than does the SBUV Merged Cohesive VN8.6, which has a more continuous SOR of ∼ 2 % in this region. The sparse spatial and temporal sampling of limb satellite instruments prohibits the extraction of sub-annual variations in the SOR from SAGE-based datasets. However, the SBUVMOD VN8.6 dataset suggests substantial month-to-month variations in the SOR, particularly in the winter extratropics, which may be important for the proposed high-latitude dynamical response to the solar cycle. Overall, the results highlight substantial uncertainties in the magnitude and structure of the observed SOR from different satellite records. The implications of these uncertainties for understanding and modelling the effects of solar variability on climate should be explored

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Content in fatty acids and carotenoids in phytoplankton blooms during the seasonal sea ice retreat in Hudson Bay complex, Canada.

The Hudson Bay complex (HBC) is home to numerous indigenous communities that traditionally have relied heavily on its marine resources. The nutritional quality and stocks of the entire HBC food web depend in large part on the phytoplankton production of bioactive molecules (long chain polyunsaturated fatty acids and carotenoids) and their transfer through trophic levels. The purpose of this study was thus to determine which molecules were produced during spring phytoplankton blooms, as well as the environmental factors driving this production. We investigated 21 stations in 5 sub-regions of the HBC. At the time of sampling, the sub-regions studied had different environmental settings (e.g., ice cover, nutrients, seawater salinity and temperature) conditioning their bloom stages. Pre- and post-bloom stages were associated with relatively low concentrations of bioactive molecules (either fatty acids or carotenoids). In contrast, the highest concentrations of bioactive molecules (dominated by eicosapentaenoic acid and fucoxanthin) were associated with the diatom bloom that typically occurs at the ice edge when silicates remain available. Interestingly, the large riverine inputs in eastern Hudson Bay led to a change in protist composition (larger contribution of Dinophyceae), resulting in lower while more diverse content of bioactive molecules, whether fatty acids (e.g., aa-linolenic acid) or carotenoids (e.g., peridinin). As greater stratification of the HBC is expected in the future, we suggest that a mixotrophic/heterotrophic flagellate-based food web would become more prevalent, resulting in a smaller supply of bioactive molecules for the food web

Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.Comment: 36 pages, 7 figure

Environmental drivers of spring primary production in Hudson Bay

Pertinent environmental factors influencing the microalgal bloom during sea-ice breakup in Hudson Bay were investigated in June 2018, producing the first observations of late spring primary production in the offshore waters of this vast inland sea. Phytoplankton production was found to commence at the onset of ice melt, with surface nutrient depletion leading to the formation of a subsurface chlorophyll maximum in the open waters of western Hudson Bay. Concurrently, the melting mobile ice cover in central Hudson Bay created favorable conditions for a diatom-dominated under-ice bloom, with photosynthetic characteristics and relatively high production confirming that phytoplankton cells were able to acclimate to increasing light levels. Lower mean values of phytoplankton production and total chlorophyll a (TChl a) concentration observed under the sea ice (414 mg C m–2 d–1 and 33.7 mg TChl a m–2) than those observed in open waters during the late bloom stage in the western region (460 mg C m–2 d–1 and 53.5 mgTChl a m–2) were attributed to reduced under-ice light levels and low surface concentrations of dissolved inorganic nitrogen (<2 mmol L–1) in central Hudson Bay. However, the highly abundant subice diatom, Melosira arctica, was estimated to contribute an additional 378 mg C m–2 d–1 to under-ice production in this region. Therefore, this subice algal bloom appears to play a similar role in the seasonally ice-covered sub-Arctic as in the central Arctic Ocean where it contributes significantly to local production. By updating historical total production estimates of Hudson Bay ranging between 21.5 and 39 g C m–2 yr–1 with our late spring observations including the novel observation of M. arctica, annual production was recalculated to be 72 g C m–2 yr–1, which equates to mean values for interior Arctic shelves

Passing to the Limit in a Wasserstein Gradient Flow: From Diffusion to Reaction

We study a singular-limit problem arising in the modelling of chemical reactions. At finite {\epsilon} > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1/{\epsilon}, and in the limit {\epsilon} -> 0, the solution concentrates onto the two wells, resulting into a limiting system that is a pair of ordinary differential equations for the density at the two wells. This convergence has been proved in Peletier, Savar\'e, and Veneroni, SIAM Journal on Mathematical Analysis, 42(4):1805-1825, 2010, using the linear structure of the equation. In this paper we re-prove the result by using solely the Wasserstein gradient-flow structure of the system. In particular we make no use of the linearity, nor of the fact that it is a second-order system. The first key step in this approach is a reformulation of the equation as the minimization of an action functional that captures the property of being a curve of maximal slope in an integrated form. The second important step is a rescaling of space. Using only the Wasserstein gradient-flow structure, we prove that the sequence of rescaled solutions is pre-compact in an appropriate topology. We then prove a Gamma-convergence result for the functional in this topology, and we identify the limiting functional and the differential equation that it represents. A consequence of these results is that solutions of the {\epsilon}-problem converge to a solution of the limiting problem.Comment: Added two sections, corrected minor typos, updated reference

Formation of Structure in Snowfields: Penitentes, Suncups, and Dirt Cones

Penitentes and suncups are structures formed as snow melts, typically high in the mountains. When the snow is dirty, dirt cones and other structures can form instead. Building on previous field observations and experiments, this work presents a theory of ablation morphologies, and the role of surface dirt in determining the structures formed. The glaciological literature indicates that sunlight, heating from air, and dirt all play a role in the formation of structure on an ablating snow surface. The present work formulates a mathematical model for the formation of ablation morphologies as a function of measurable parameters. The dependence of ablation morphologies on weather conditions and initial dirt thickness are studied, focusing on the initial growth of perturbations away from a flat surface. We derive a single-parameter expression for the melting rate as a function of dirt thickness, which agrees well with a set of measurements by Driedger. An interesting result is the prediction of a dirt-induced travelling instability for a range of parameters.Comment: 28 pages, 13 figure

Recent variability of the solar spectral irradiance and its impact on climate modelling

International audienceThe lack of long and reliable time series of solar spectral irradiance (SSI) measurements makes an accurate quantification of solar contributions to recent climate change difficult. Whereas earlier SSI observations and models provided a qualitatively consistent picture of the SSI variability, recent measurements by the SORCE (SOlar Radiation and Climate Experiment) satellite suggest a significantly stronger variability in the ultraviolet (UV) spectral range and changes in the visible and near-infrared (NIR) bands in anti-phase with the solar cycle. A number of recent chemistry-climate model (CCM) simulations have shown that this might have significant implications on the Earth's atmosphere. Motivated by these results, we summarize here our current knowledge of SSI variability and its impact on Earth's climate.We present a detailed overview of existing SSI measurements and provide thorough comparison of models available to date. SSI changes influence the Earth's atmosphere, both directly, through changes in shortwave (SW) heating and therefore, temperature and ozone distributions in the stratosphere, and indirectly, through dynamical feedbacks. We investigate these direct and indirect effects using several state-of-the art CCM simulations forced with measured and modelled SSI changes. A unique asset of this study is the use of a common comprehensive approach for an issue that is usually addressed separately by different communities.We show that the SORCE measurements are difficult to reconcile with earlier observations and with SSI models. Of the five SSI models discussed here, specifically NRLSSI (Naval Research Laboratory Solar Spectral Irradiance), SATIRE-S (Spectral And Total Irradiance REconstructions for the Satellite era), COSI (COde for Solar Irradiance), SRPM (Solar Radiation Physical Modelling), and OAR (Osservatorio Astronomico di Roma), only one shows a behaviour of the UV and visible irradiance qualitatively resembling that of the recent SORCE measurements. However, the integral of the SSI computed with this model over the entire spectral range does not reproduce the measured cyclical changes of the total solar irradiance, which is an essential requisite for realistic evaluations of solar effects on the Earth's climate in CCMs.We show that within the range provided by the recent SSI observations and semi-empirical models discussed here, the NRLSSI model and SORCE observations represent the lower and upper limits in the magnitude of the SSI solar cycle variation.The results of the CCM simulations, forced with the SSI solar cycle variations estimated from the NRLSSI model and from SORCE measurements, show that the direct solar response in the stratosphere is larger for the SORCE than for the NRLSSI data. Correspondingly, larger UV forcing also leads to a larger surface response.Finally, we discuss the reliability of the available data and we propose additional coordinated work, first to build composite SSI data sets out of scattered observations and to refine current SSI models, and second, to run coordinated CCM experiments