Precipitation and latent heating distributions from satellite passive microwave radiometry. Part I: improved method and uncertainties

A revised Bayesian algorithm for estimating surface rain rate, convective rain proportion, and latent heating profiles from satellite-borne passive microwave radiometer observations over ocean backgrounds is described. The algorithm searches a large database of cloud-radiative model simulations to find cloud profiles that are radiatively consistent with a given set of microwave radiance measurements. The properties of these radiatively consistent profiles are then composited to obtain best estimates of the observed properties. The revised algorithm is supported by an expanded and more physically consistent database of cloud-radiative model simulations. The algorithm also features a better quantification of the convective and nonconvective contributions to total rainfall, a new geographic database, and an improved representation of background radiances in rain-free regions. Bias and random error estimates are derived from applications of the algorithm to synthetic radiance data, based upon a subset of cloud-resolving model simulations, and from the Bayesian formulation itself. Synthetic rain-rate and latent heating estimates exhibit a trend of high (low) bias for low (high) retrieved values. The Bayesian estimates of random error are propagated to represent errors at coarser time and space resolutions, based upon applications of the algorithm to TRMM Microwave Imager (TMI) data. Errors in TMI instantaneous rain-rate estimates at 0.5°-resolution range from approximately 50% at 1 mm h−1 to 20% at 14 mm h−1. Errors in collocated spaceborne radar rain-rate estimates are roughly 50%–80% of the TMI errors at this resolution. The estimated algorithm random error in TMI rain rates at monthly, 2.5° resolution is relatively small (less than 6% at 5 mm day−1) in comparison with the random error resulting from infrequent satellite temporal sampling (8%–35% at the same rain rate). Percentage errors resulting from sampling decrease with increasing rain rate, and sampling errors in latent heating rates follow the same trend. Averaging over 3 months reduces sampling errors in rain rates to 6%–15% at 5 mm day−1, with proportionate reductions in latent heating sampling errors.

Universality of rain event size distributions

We compare rain event size distributions derived from measurements in climatically different regions, which we find to be well approximated by power laws of similar exponents over broad ranges. Differences can be seen in the large-scale cutoffs of the distributions. Event duration distributions suggest that the scale-free aspects are related to the absence of characteristic scales in the meteorological mesoscale.

Non-normal real estate return distributions by property type in the UK

Investment risk models with infinite variance provide a better description of distributions of individual property returns in the IPD UK database over the period 1981 to 2003 than normally distributed risk models. This finding mirrors results in the US and Australia using identical methodology. Real estate investment risk is heteroskedastic, but the characteristic exponent of the investment risk function is constant across time – yet it may vary by property type. Asset diversification is far less effective at reducing the impact of non‐systematic investment risk on real estate portfolios than in the case of assets with normally distributed investment risk. The results, therefore, indicate that multi‐risk factor portfolio allocation models based on measures of investment codependence from finite‐variance statistics are ineffective in the real estate context

Diversification when it hurts? The joint distributions of real estate and equity markets

Much of the literature on the construction of mixed asset portfolios and the case for property as a risk diversifier rests on correlations measured over the whole of a given time series. Recent developments in finance, however, focuses on dependence in the tails of the distribution. Does property offer diversification from equity markets when it is most needed - when equity returns are poor. The paper uses an empirical copula approach to test tail dependence between property and equity for the UK and for a global portfolio. Results show strong tail dependence: in the UK, the dependence in the lower tail is stronger than in the upper tail, casting doubt on the defensive properties of real estate stocks.

Non-normal real estate return distributions by property type in the U.K.

Investment risk models with infinite variance provide a better description of distributions of individual property returns in the IPD database over the period 1981 to 2003 than Normally distributed risk models, which mirrors results in the U.S. and Australia using identical methodology. Real estate investment risk is heteroscedastic, but the Characteristic Exponent of the investment risk function is constant across time yet may vary by property type. Asset diversification is far less effective at reducing the impact of non-systematic investment risk on real estate portfolios than in the case of assets with Normally distributed investment risk. Multi-risk factor portfolio allocation models based on measures of investment codependence from finite-variance statistics are ineffectual in the real estate context.

Rheology of magmas with bimodal crystal size and shape distributions: insights from analog experiments

Magmas in volcanic conduits commonly contain microlites in association with preexisting phenocrysts, as often indicated by volcanic rock textures. In this study, we present two different experiments that inves- tigate the flow behavior of these bidisperse systems. In the first experiments, rotational rheometric methods are used to determine the rheology of monodisperse and polydisperse suspensions consisting of smaller, prolate particles (microlites) and larger, equant particles (phenocrysts) in a bubble‐free Newtonian liquid (silicate melt). Our data show that increasing the relative proportion of prolate microlites to equant pheno- crysts in a magma at constant total particle content can increase the relative viscosity by up to three orders of magnitude. Consequently, the rheological effect of particles in magmas cannot be modeled by assuming a monodisperse population of particles. We propose a new model that uses interpolated parameters based on the relative proportions of small and large particles and produces a considerably improved fit to the data than earlier models. In a second series of experiments we investigate the textures produced by shearing bimodal suspensions in gradually solidifying epoxy resin in a concentric cylinder setup. The resulting textures show the prolate particles are aligned with the flow lines and spherical particles are found in well‐organized strings, with sphere‐depleted shear bands in high‐shear regions. These observations may explain the measured variation in the shear thinning and yield stress behavior with increasing solid fraction and particle aspect ratio. The implications for magma flow are discussed, and rheological results and tex- tural observations are compared with observations on natural samples.

Understanding distributions of chess performances

This paper presents evidence for several features of the population of chess players, and the distribution of their performances measured in terms of Elo ratings and by computer analysis of moves. Evidence that ratings have remained stable since the inception of the Elo system in the 1970’s is given in several forms: by showing that the population of strong players fits a simple logistic-curve model without inflation, by plotting players’ average error against the FIDE category of tournaments over time, and by skill parameters from a model that employs computer analysis keeping a nearly constant relation to Elo rating across that time. The distribution of the model’s Intrinsic Performance Ratings can hence be used to compare populations that have limited interaction, such as between players in a national chess federation and FIDE, and ascertain relative drift in their respective rating systems.

Generalized beta generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

Methodology To model the energy and greenhouse gas emissions of electronic software distributions

A new electronic software distribution (ESD) life cycle analysis (LCA)methodology and model structure were constructed to calculate energy consumption and greenhouse gas (GHG) emissions. In order to counteract the use of high level, top-down modeling efforts, and to increase result accuracy, a focus upon device details and data routes was taken. In order to compare ESD to a relevant physical distribution alternative,physical model boundaries and variables were described. The methodology was compiled from the analysis and operational data of a major online store which provides ESD and physical distribution options. The ESD method included the calculation of power consumption of data center server and networking devices. An in-depth method to calculate server efficiency and utilization was also included to account for virtualization and server efficiency features. Internet transfer power consumption was analyzed taking into account the number of data hops and networking devices used. The power consumed by online browsing and downloading was also factored into the model. The embedded CO2e of server and networking devices was proportioned to each ESD process. Three U.K.-based ESD scenarios were analyzed using the model which revealed potential CO2e savings of 83% when ESD was used over physical distribution. Results also highlighted the importance of server efficiency and utilization methods.

Further investigation of the impact of idealised continents and SST distributions on the Northern Hemisphere storm tracks

Building on studies by Brayshaw et al. (2009, 2011) of the basic ingredients of the North Atlantic storm track (land-sea contrast, orography and SST), this article investigates the impact of Eurasian topography and Pacific SST anomalies on the North Pacific and Atlantic storm tracks through a hierarchy of atmospheric GCM simulations using idealised boundary conditions in the HadGAM1 model. The Himalaya-Tibet mountain complex is found to play a crucial role in shaping the North Pacific storm track. The northward deflection of the westerly flow around northern Tibet generates an extensive pool of very cold air in the north-eastern tip of the Asian continent, which strengthens the meridional temperature gradient and favours baroclinic growth in the western Pacific. The Kuroshio SST front is also instrumental in strengthening the Pacific storm track through its impact on near-surface baroclinicity, while the warm waters around Indonesia tend to weaken it through the impact on baroclinicity of stationary Rossby waves propagating poleward from the convective heating regions. Three mechanisms by which the Atlantic storm track may be affected by changes in the boundary conditions upstream of the Rockies are discussed. In the model configuration used here, stationary Rossby waves emanating from Tibet appear to weaken the North Atlantic storm track substantially, whereas those generated over the cold waters off Peru appear to strengthen it. Changes in eddy-driven surface winds over the Pacific generally appear to modify the flow over the Rocky Mountains, leading to consistent modifications in the Atlantic storm track. The evidence for each of these mechanisms is, however, ultimately equivocal in these simulations.

Commercial real estate return distributions: a review of literature and empirical evidence

This paper review the literature on the distribution of commercial real estate returns. There is growing evidence that the assumption of normality in returns is not safe. Distributions are found to be peaked, fat-tailed and, tentatively, skewed. There is some evidence of compound distributions and non-linearity. Public traded real estate assets (such as property company or REIT shares) behave in a fashion more similar to other common stocks. However, as in equity markets, it would be unwise to assume normality uncritically. Empirical evidence for UK real estate markets is obtained by applying distribution fitting routines to IPD Monthly Index data for the aggregate index and selected sub-sectors. It is clear that normality is rejected in most cases. It is often argued that observed differences in real estate returns are a measurement issue resulting from appraiser behaviour. However, unsmoothing the series does not assist in modelling returns. A large proportion of returns are close to zero. This would be characteristic of a thinly-traded market where new information arrives infrequently. Analysis of quarterly data suggests that, over longer trading periods, return distributions may conform more closely to those found in other asset markets. These results have implications for the formulation and implementation of a multi-asset portfolio allocation strategy.

Precipitation distributions for explicit versus parameterized convection in a large-domain high-resolution tropical case study

Global climate and weather models tend to produce rainfall that is too light and too regular over the tropical ocean. This is likely because of convective parametrizations, but the problem is not well understood. Here, distributions of precipitation rates are analyzed for high-resolution UK Met Office Unified Model simulations of a 10 day case study over a large tropical domain (∼20°S–20°N and 42°E–180°E). Simulations with 12 km grid length and parametrized convection have too many occurrences of light rain and too few of heavier rain when interpolated onto a 1° grid and compared with Tropical Rainfall Measuring Mission (TRMM) data. In fact, this version of the model appears to have a preferred scale of rainfall around 0.4 mm h−1 (10 mm day−1), unlike observations of tropical rainfall. On the other hand, 4 km grid length simulations with explicit convection produce distributions much more similar to TRMM observations. The apparent preferred scale at lighter rain rates seems to be a feature of the convective parametrization rather than the coarse resolution, as demonstrated by results from 12 km simulations with explicit convection and 40 km simulations with parametrized convection. In fact, coarser resolution models with explicit convection tend to have even more heavy rain than observed. Implications for models using convective parametrizations, including interactions of heating and moistening profiles with larger scales, are discussed. One important implication is that the explicit convection 4 km model has temperature and moisture tendencies that favour transitions in the convective regime. Also, the 12 km parametrized convection model produces a more stable temperature profile at its extreme high-precipitation range, which may reduce the chance of very heavy rainfall. Further study is needed to determine whether unrealistic precipitation distributions are due to some fundamental limitation of convective parametrizations or whether parametrizations can be improved, in order to better simulate these distributions.

Groundwater residence time distributions in peatlands: implications for peat decomposition and accumulation

Peat soils consist of poorly decomposed plant detritus, preserved by low decay rates, and deep peat deposits are globally significant stores in the carbon cycle. High water tables and low soil temperatures are commonly held to be the primary reasons for low peat decay rates. However, recent studies suggest a thermodynamic limit to peat decay, whereby the slow turnover of peat soil pore water may lead to high concentrations of phenols and dissolved inorganic carbon. In sufficient concentrations, these chemicals may slow or even halt microbial respiration, providing a negative feedback to peat decay. We document the analysis of a simple, one-dimensional theoretical model of peatland pore water residence time distributions (RTDs). The model suggests that broader, thicker peatlands may be more resilient to rapid decay caused by climate change because of slow pore water turnover in deep layers. Even shallow peat deposits may also be resilient to rapid decay if rainfall rates are low. However, the model suggests that even thick peatlands may be vulnerable to rapid decay under prolonged high rainfall rates, which may act to flush pore water with fresh rainwater. We also used the model to illustrate a particular limitation of the diplotelmic (i.e., acrotelm and catotelm) model of peatland structure. Model peatlands of contrasting hydraulic structure exhibited identical water tables but contrasting RTDs. These scenarios would be treated identically by diplotelmic models, although the thermodynamic limit suggests contrasting decay regimes. We therefore conclude that the diplotelmic model be discarded in favor of model schemes that consider continuous variation in peat properties and processes.

Axonal velocity distributions in neural feld equations

By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.

Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned