Monomial convergence for holomorphic functions on ℓ_r\ell\_r

Let $\mathcal F$ be either the set of all bounded holomorphic functions or the set of all $m$-homogeneous polynomials on the unit ball of $\ell\_r$. We give a systematic study of the sets of all $u\in\ell\_r$ for which the monomial expansion $\sum\_{\alpha}\frac{\partial^\alpha f(0)}{\alpha !}u^\alpha$ of every $f\in\mathcal F$ converges. Inspired by recent results from the general theory of Dirichlet series, we establish as our main tool, independently interesting, upper estimates for the unconditional basis constants of spaces of polynomials on $\ell\_r$ spanned by finite sets of monomials

Upper Labrador Sea freshwater : seasonal to decadal

The main focus of the thesis is the analysis of freshwater variability in the upper Labrador Sea on seasonal to decadal time scales. The seasonal freshening of the Labrador Sea and its variations play a key role in Labrador Sea deep water formation, since the freshwater has large impact on the stratification of the water column. This stratification as well as atmospheric forcing define in first order the intensity and density - thus depth - of the convection. Therefore it was the aim of this study to understand the origin, variability and path of the freshwater better. A large amount of data sources got combined to get the best possible results, including two online databases of CTD data, float data from the "Labrador Sea Deep Convection Experiment" (1996-1999), ARGO-floats and thermosalinograph data from the North Atlantic. The analyzes concentrate on 9 region within the Labrador Sea that have low horizontal salinity gradients and represent all important surface water masses. The best possible climatological seasonal salinity cycle was constructed for every region. This is for instance important for judging on anomalies in decades with only isolated measurements in a few months. The climatological salinity cycles confirm qualitatively my preliminary work in Schmidt and Send (2007). The further use of satellite SSH-anomaly measurements derived geostrophic surface currents and eddy kinetic energy (EKE) allowed a selection of high and low EKE years from the last 13 years of satellite data. These years show significant hydrographic differences in the central Labrador Sea. Years with low EKE in the Labrador Sea show an early freshening between April and May. The existence, variability and origin of this freshening was so far unsure. The freshwater pulse is not existing in years with high EKE. On the basis of changes in geostrophic surface current and variabilities within the seasonal cycle of some regions I develop a hypothesis. This hypothesis describes the origin, pathway and occurrence of the early freshening pulse in the central Labrador Sea. High EKE in the Labrador Sea seems to reduce the mean velocities of the southern West Greenland Current branch or even stops it. Since this branch is a pathway of freshwater into the northern Labrador Sea and the convection area, high EKE suppresses the freshwater flux into the Labrador Sea. Finally I analyze the pathway of decadal variations in salinity like the Great Salinity Anomaly (GSA) of the 70's. Measurements in the West Greenland Current region during times of large anomalies in the central Labrador Sea ('57, '70, '85), show the origin of these anomalies in the salty Irminger Sea waters with salinities above 34.7. With an average lag of two years these anomalies are found in the fresh shelf water of polar origin, thus significantly past the occurrence in the central Labrador Sea. This order suggests that an origin in the source of the Irminger Current, the North Atlantic Current is more likely than in the Nordic Seas. This would contradict the general believe of Great Salinity Anomalies originating from the Arctic

The surface diurnal warm layer in the Indian Ocean during CINDY/DYNAMO

A surface diurnal warm layer is diagnosed from Seaglider observations, and develops on half the days in the CINDY/DYNAMO Indian Ocean experiment. The diurnal warm layer occurs on days of high solar radiation flux (>80 W m-2) and low wind speed (<6 m s-1), and preferentially in the inactive stage of the Madden-Julian Oscillation. Its diurnal harmonic has an exponential vertical structure with a depth scale of 4-5 m (dependent on chlorophyll concentration), consistent with forcing by absorption of solar radiation. The effective sea surface temperature (SST) anomaly due to the diurnal warm layer often reaches 0.8°C in the afternoon, with a daily mean of 0.2°C, rectifying the diurnal cycle onto longer time scales. This SST anomaly drives an anomalous flux of 4 W m-2 that cools the ocean. Alternatively, in a climate model where this process is unresolved, this represents an erroneous flux that warms the ocean. A simple model predicts a diurnal warm layer to occur on 30-50% of days across the tropical warm pool. On the remaining days, with low solar radiation and high wind speeds, a residual diurnal cycle is observed by the Seaglider, with a diurnal harmonic of temperature that decreases linearly with depth. As wind speed increases, this already weak temperature gradient decreases further, tending towards isothermal conditions

Multidecadal warming of Antarctic waters

Decadal trends in the properties of seawater adjacent to Antarctica are poorly known, and the mechanisms responsible for such changes are uncertain. Antarctic ice sheet mass loss is largely driven by ice shelf basal melt, which is influenced by ocean-ice interactions and has been correlated with Antarctic Continental Shelf Bottom Water (ASBW) temperature. We document the spatial distribution of long-term large-scale trends in temperature, salinity, and core depth over the Antarctic continental shelf and slope. Warming at the seabed in the Bellingshausen and Amundsen seas is linked to increased heat content and to a shoaling of the mid-depth temperature maximum over the continental slope, allowing warmer, saltier water greater access to the shelf in recent years. Regions of ASBW warming are those exhibiting increased ice shelf melt

Tropical deoxygenation sites revisited to investigate oxygen and nutrient trends

An oxygen decrease of the intermediate-depth low-oxygen zones (300 to 700 m) is seen in time series for selected tropical areas for the period 1960 to 2008 in the eastern tropical Atlantic, the equatorial Pacific and the eastern tropical Indian Ocean. These nearly 5-decade time series were extended to 68 years by including rare historic data starting in 1950 and more recent data. For the extended time series between 1950 and 2018, the deoxygenation trend for the layer 300 to 700 m is similar to the deoxygenation trend seen in the shorter time series. Additionally, temperature, salinity, and nutrient time series in the upper-ocean layer (50 to 300 m) of these areas were investigated since this layer provides critical pelagic habitat for biological communities. Due to the low amount of data available, the results are often not statistically significant within the 95 % confidence interval but nevertheless indicate trends worth discussing. Generally, oxygen is decreasing in the 50 to 300 m layer, except for an area in the eastern tropical South Atlantic. Nutrients also showed long-term trends in the 50 to 300 m layer in all ocean basins and indicate overlying variability related to climate modes. Nitrate increased in all areas. Phosphate also increased in the Atlantic Ocean and Indian Ocean areas, while it decreased in the two areas of the equatorial Pacific Ocean. Silicate decreased in the Atlantic and Pacific areas but increased in the eastern Indian Ocean. Hence, oxygen and nutrients show trends in the tropical oceans, though nutrients trends are more variable between ocean areas than the oxygen trends; therefore, we conclude that those trends are more dependent on local drivers in addition to a global trend. Different positive and negative trends in temperature, salinity, oxygen and nutrients indicate that oxygen and nutrient trends cannot be completely explained by local warming

Mismatch between observed and modeled trends in dissolved upper-ocean oxygen over the last 50 yr

Observations and model runs indicate trends in dissolved oxygen (DO) associated with current and ongoing global warming. However, a large-scale observation-to-model comparison has been missing and is presented here. This study presents a first global compilation of DO measurements covering the last 50 yr. It shows declining upper-ocean DO levels in many regions, especially the tropical oceans, whereas areas with increasing trends are found in the subtropics and in some subpolar regions. For the Atlantic Ocean south of 20° N, the DO history could even be extended back to about 70 yr, showing decreasing DO in the subtropical South Atlantic. The global mean DO trend between 50° S and 50° N at 300 dbar for the period 1960 to 2010 is –0.066 μmol kg−1 yr−1. Results of a numerical biogeochemical Earth system model reveal that the magnitude of the observed change is consistent with CO2-induced climate change. However, the pattern correlation between simulated and observed patterns of past DO change is negative, indicating that the model does not correctly reproduce the processes responsible for observed regional oxygen changes in the past 50 yr. A negative pattern correlation is also obtained for model configurations with particularly low and particularly high diapycnal mixing, for a configuration that assumes a CO2-induced enhancement of the C : N ratios of exported organic matter and irrespective of whether climatological or realistic winds from reanalysis products are used to force the model. Depending on the model configuration the 300 dbar DO trend between 50° S and 50° N is −0.027 to –0.047 μmol kg−1 yr−1 for climatological wind forcing, with a much larger range of –0.083 to +0.027 μmol kg−1 yr−1 for different initializations of sensitivity runs with reanalysis wind forcing. Although numerical models reproduce the overall sign and, to some extent, magnitude of observed ocean deoxygenation, this degree of realism does not necessarily apply to simulated regional patterns and the representation of processes involved in their generation. Further analysis of the processes that can explain the discrepancies between observed and modeled DO trends is required to better understand the climate sensitivity of oceanic oxygen fields and predict potential DO changes in the future

Global oxygen changes and oxygen variability in the eastern Pacific off Peru

Numerical model runs predict decreasing ocean oxygen with increasing CO2 emission scenarios. Oxygen measurements are generally sparse in the ocean, nonetheless at some key locations longer-term oxygen time series exist and trends for the global ocean can be estimated. In many regions especially the tropical oceans oxygen has decreased during the last 50 years, however especially in the subtropical ocean regions with increasing oxygen values exist. Typical oxygen trends range from -0.5 to +0.4 mol kg-1 yr-1 in the upper ocean for the last few decades, with a global mean oxygen trend of -0.066 mol kg-1yr-1 between 50°S and 50°N at 300 dbar for the period 1960 to 2010 [Stramma et al., 2012]. In a measurement to model comparison for the last 50 years the model reproduce the overall sign and to some extent magnitude of observed ocean deoxygenation, though with a mismatch in regional pattern. Further analysis of the processes that can explain the discrepancies between observed and modeled oxygen trends is required to better understand the climate sensitivity of oceanic oxygen fields and predict potential oxygen changes in the future. Further expansion of low oxygen regions in conjunction with overfishing may threaten the sustainability of pelagic fisheries and accelerate shifts in animal distributions and changes in ecosystem structure. In the eastern Pacific Ocean multidecadal variability (Pacific Decadal Oscillation) and also El Nino phases have a strong influence on long-term oxygen trends [e.g. Czeschel et al., 2012]. Historical data combined with new hydrographic measurements from two ship expeditions in the eastern tropical Pacific in 2009 and 2012 as well as oxygen sensor data from floats allow an enhanced view at the circulation, oxygen variability and trends in the oxygen minimum zone off Peru. Oxygen differences derived by comparison of ship sections show large variability in some locations. This local variability from eddies, seasonal and longer-term variability obscure trends in oceanic dissolved oxygen. Caution in interpretation of the data is necessary