Foreword: International Space Science Institute (ISSI) workshop on the Earth’s cryosphere and sea level change

Rising sea level is perhaps the most severe consequence of climate warming, as much of the world’s population and infrastructure is located near current sea level (Lemke et al. 2007). A major rise of a metre or more would cause serious problems. Such possibilities have been suggested by Hansen and Sato (2011) who pointed out that sea level was several metres higher than now during the Holsteinian and Eemian interglacials (about 250,000 and 120,000 years ago, respectively), even though the global temperature was then only slightly higher than it is nowadays. It is consequently of the utmost importance to determine whether such a sea level rise could occur and, if so, how fast it might happen. Sea level undergoes considerable changes due to natural processes such as the wind, ocean currents and tidal motions. On longer time scales, the sea level is influenced by steric effects (sea water expansion caused by temperature and salinity changes of the ocean) and by eustatic effects caused by changes in ocean mass. Changes in the Earth’s cryosphere, such as the retreat or expansion of glaciers and land ice areas, have been the dominant cause of sea level change during the Earth’s recent history. During the glacial cycles of the last million years, the sea level varied by a large amount, of the order of 100 m. If the Earth’s cryosphere were to disappear completely, the sea level would rise by some 65 m. The scientific papers in the present volume address the different aspects of the Earth’s cryosphere and how the different changes in the cryosphere affect sea level change. It represents the outcome of the first workshop held within the new ISSI Earth Science Programme. The workshop took place from 22 to 26 March, 2010, in Bern, Switzerland, with the objective of providing an in-depth insight into the future of mountain glaciers and the large land ice areas of Antarctica and Greenland, which are exposed to natural and anthropogenic climate influences, and their effects on sea level change. The participants of the workshop are experts in different fields including meteorology, climatology, oceanography, glaciology and geodesy; they use advanced space-based observational studies and state-of-the-art numerical modelling.

Power allocation strategies for distributed space-time codes in two-way relay networks

We study a two-way relay network (TWRN), where distributed space-time codes are constructed across multiple relay terminals in an amplify-and-forward mode. Each relay transmits a scaled linear combination of its received symbols and their conjugates,with the scaling factor chosen based on automatic gain control. We consider equal power allocation (EPA) across the relays, as well as the optimal power allocation (OPA) strategy given access to instantaneous channel state information (CSI). For EPA, we derive an upper bound on the pairwise-error-probability (PEP), from which we prove that full diversity is achieved in TWRNs. This result is in contrast to one-way relay networks, in which case a maximum diversity order of only unity can be obtained. When instantaneous CSI is available at the relays, we show that the OPA which minimizes the conditional PEP of the worse link can be cast as a generalized linear fractional program, which can be solved efficiently using the Dinkelback-type procedure.We also prove that, if the sum-power of the relay terminals is constrained, then the OPA will activate at most two relays.

Integration of Space and In Situ Observations to Study Global Climate Change

The currently available model-based global data sets of atmospheric circulation are a by-product of the daily requirement of producing initial conditions for numerical weather prediction (NWP) models. These data sets have been quite useful for studying fundamental dynamical and physical processes, and for describing the nature of the general circulation of the atmosphere. However, due to limitations in the early data assimilation systems and inconsistencies caused by numerous model changes, the available model-based global data sets may not be suitable for studying global climate change. A comprehensive analysis of global observations based on a four-dimensional data assimilation system with a realistic physical model should be undertaken to integrate space and in situ observations to produce internally consistent, homogeneous, multivariate data sets for the earth's climate system. The concept is equally applicable for producing data sets for the atmosphere, the oceans, and the biosphere, and such data sets will be quite useful for studying global climate change.

Correlations of long-lived chemical species in a middle atmosphere general circulation model

Correlations between various chemical species simulated by the Canadian Middle Atmosphere Model, a general circulation model with fully interactive chemistry, are considered in order to investigate the general conditions under which compact correlations can be expected to form. At the same time, the analysis serves to validate the model. The results are compared to previous work on this subject, both from theoretical studies and from atmospheric measurements made from space and from aircraft. The results highlight the importance of having a data set with good spatial coverage when working with correlations and provide a background against which the compactness of correlations obtained from atmospheric measurements can be confirmed. It is shown that for long-lived species, distinct correlations are found in the model in the tropics, the extratropics, and the Antarctic winter vortex. Under these conditions, sparse sampling such as arises from occultation instruments is nevertheless suitable to define a chemical correlation within each region even from a single day of measurements, provided a sufficient range of mixing ratio values is sampled. In practice, this means a large vertical extent, though the requirements are less stringent at more poleward latitudes.

Space weather driven changes in lower atmosphere phenomena

During a period of heliospheric disturbance in 2007-9 associated with a co-rotating interaction region (CIR), a characteristic periodic variation becomes apparent in neutron monitor data. This variation is phase locked to periodic heliospheric current sheet crossings. Phase-locked electrical variations are also seen in the terrestrial lower atmosphere in the southern UK, including an increase in the vertical conduction current density of fair weather atmospheric electricity during increases in the neutron monitor count rate and energetic proton count rates measured by spacecraft. At the same time as the conduction current increases, changes in the cloud microphysical properties lead to an increase in the detected height of the cloud base at Lerwick Observatory, Shetland, with associated changes in surface meteorological quantities. As electrification is expected at the base of layer clouds, which can influence droplet properties, these observations of phase-locked thermodynamic, cloud, atmospheric electricity and solar sector changes are not inconsistent with a heliospheric disturbance driving lower troposphere changes.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

On the solvability of a class of second kind integral equations on unbounded domains

We consider integral equations of the form ψ(x) = φ(x) + ∫Ωk(x, y)z(y)ψ(y) dy(in operator form ψ = φ + Kzψ), where Ω is some subset ofRn(n ≥ 1). The functionsk,z, and φ are assumed known, withz ∈ L∞(Ω) and φ ∈ Y, the space of bounded continuous functions on Ω. The function ψ ∈ Yis to be determined. The class of domains Ω and kernelskconsidered includes the case Ω = Rnandk(x, y) = κ(x − y) with κ ∈ L1(Rn), in which case, ifzis the characteristic function of some setG, the integral equation is one of Wiener–Hopf type. The main theorems, proved using arguments derived from collectively compact operator theory, are conditions on a setW ⊂ L∞(Ω) which ensure that ifI − Kzis injective for allz ∈ WthenI − Kzis also surjective and, moreover, the inverse operators (I − Kz)−1onYare bounded uniformly inz. These general theorems are used to recover classical results on Wiener–Hopf integral operators of21and19, and generalisations of these results, and are applied to analyse the Lippmann–Schwinger integral equation.

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

Retrieval of sea surface temperature from space based on modeling of infrared radiative transfer: capabilities and limitations

The retrieval (estimation) of sea surface temperatures (SSTs) from space-based infrared observations is increasingly performed using retrieval coefficients derived from radiative transfer simulations of top-of-atmosphere brightness temperatures (BTs). Typically, an estimate of SST is formed from a weighted combination of BTs at a few wavelengths, plus an offset. This paper addresses two questions about the radiative transfer modeling approach to deriving these weighting and offset coefficients. How precisely specified do the coefficients need to be in order to obtain the required SST accuracy (e.g., scatter <0.3 K in week-average SST, bias <0.1 K)? And how precisely is it actually possible to specify them using current forward models? The conclusions are that weighting coefficients can be obtained with adequate precision, while the offset coefficient will often require an empirical adjustment of the order of a few tenths of a kelvin against validation data. Thus, a rational approach to defining retrieval coefficients is one of radiative transfer modeling followed by offset adjustment. The need for this approach is illustrated from experience in defining SST retrieval schemes for operational meteorological satellites. A strategy is described for obtaining the required offset adjustment, and the paper highlights some of the subtler aspects involved with reference to the example of SST retrievals from the imager on the geostationary satellite GOES-8.

Spatial interaction among nontoxic phytoplankton, toxic phytoplankton and zooplankton: emergence in space and time

In homogeneous environments, by overturning the possibility of competitive exclusion among phytoplankton species, and by regulating the dynamics of overall plankton population, toxin-producing phytoplankton (TPP) potentially help in maintaining plankton diversity—a result shown recently. Here, I explore the competitive effects of TPP on phytoplankton and zooplankton species undergoing spatial movements in the subsurface water. The spatial interactions among the species are represented in the form of reaction-diffusion equations. Suitable parametric conditions under which Turing patterns may or may not evolve are investigated. Spatiotemporal distributions of species biomass are simulated using the diffusivity assumptions realistic for natural planktonic systems. The study demonstrates that spatial movements of planktonic systems in the presence of TPP generate and maintain inhomogeneous biomass distribution of competing phytoplankton, as well as grazer zooplankton, thereby ensuring the persistence of multiple species in space and time. The overall results may potentially explain the sustainability of biodiversity and the spatiotemporal emergence of phytoplankton and zooplankton species under the influence of TPP combined with their physical movement in the subsurface water.

Terrestrial ecosystems from space: a review of earth observation products for macroecology applications

Aim Earth observation (EO) products are a valuable alternative to spectral vegetation indices. We discuss the availability of EO products for analysing patterns in macroecology, particularly related to vegetation, on a range of spatial and temporal scales. Location Global. Methods We discuss four groups of EO products: land cover/cover change, vegetation structure and ecosystem productivity, fire detection, and digital elevation models. We address important practical issues arising from their use, such as assumptions underlying product generation, product accuracy and product transferability between spatial scales. We investigate the potential of EO products for analysing terrestrial ecosystems. Results Land cover, productivity and fire products are generated from long-term data using standardized algorithms to improve reliability in detecting change of land surfaces. Their global coverage renders them useful for macroecology. Their spatial resolution (e.g. GLOBCOVER vegetation, 300 m; MODIS vegetation and fire, ≥ 500 m; ASTER digital elevation, 30 m) can be a limiting factor. Canopy structure and productivity products are based on physical approaches and thus are independent of biome-specific calibrations. Active fire locations are provided in near-real time, while burnt area products show actual area burnt by fire. EO products can be assimilated into ecosystem models, and their validation information can be employed to calculate uncertainties during subsequent modelling. Main conclusions Owing to their global coverage and long-term continuity, EO end products can significantly advance the field of macroecology. EO products allow analyses of spatial biodiversity, seasonal dynamics of biomass and productivity, and consequences of disturbances on regional to global scales. Remaining drawbacks include inter-operability between products from different sensors and accuracy issues due to differences between assumptions and models underlying the generation of different EO products. Our review explains the nature of EO products and how they relate to particular ecological variables across scales to encourage their wider use in ecological applications.