Rank histograms of stratified Monte-Carlo ensembles

The application of forecast ensembles to probabilistic weather prediction has spurred considerable interest in their evaluation. Such ensembles are commonly interpreted as Monte Carlo ensembles meaning that the ensemble members are perceived as random draws from a distribution. Under this interpretation, a reasonable property to ask for is statistical consistency, which demands that the ensemble members and the verification behave like draws from the same distribution. A widely used technique to assess statistical consistency of a historical dataset is the rank histogram, which uses as a criterion the number of times that the verification falls between pairs of members of the ordered ensemble. Ensemble evaluation is rendered more specific by stratification, which means that ensembles that satisfy a certain condition (e.g., a certain meteorological regime) are evaluated separately. Fundamental relationships between Monte Carlo ensembles, their rank histograms, and random sampling from the probability simplex according to the Dirichlet distribution are pointed out. Furthermore, the possible benefits and complications of ensemble stratification are discussed. The main conclusion is that a stratified Monte Carlo ensemble might appear inconsistent with the verification even though the original (unstratified) ensemble is consistent. The apparent inconsistency is merely a result of stratification. Stratified rank histograms are thus not necessarily flat. This result is demonstrated by perfect ensemble simulations and supplemented by mathematical arguments. Possible methods to avoid or remove artifacts that stratification induces in the rank histogram are suggested.

From ensemble forecasts to predictive distribution functions

The translation of an ensemble of model runs into a probability distribution is a common task in model-based prediction. Common methods for such ensemble interpretations proceed as if verification and ensemble were draws from the same underlying distribution, an assumption not viable for most, if any, real world ensembles. An alternative is to consider an ensemble as merely a source of information rather than the possible scenarios of reality. This approach, which looks for maps between ensembles and probabilistic distributions, is investigated and extended. Common methods are revisited, and an improvement to standard kernel dressing, called ‘affine kernel dressing’ (AKD), is introduced. AKD assumes an affine mapping between ensemble and verification, typically not acting on individual ensemble members but on the entire ensemble as a whole, the parameters of this mapping are determined in parallel with the other dressing parameters, including a weight assigned to the unconditioned (climatological) distribution. These amendments to standard kernel dressing, albeit simple, can improve performance significantly and are shown to be appropriate for both overdispersive and underdispersive ensembles, unlike standard kernel dressing which exacerbates over dispersion. Studies are presented using operational numerical weather predictions for two locations and data from the Lorenz63 system, demonstrating both effectiveness given operational constraints and statistical significance given a large sample.

Altitude acts as an environmental filter on phylogenetic composition, traits and diversity in bee communities.

Knowledge about the phylogeny and ecology of communities along environmental gradients helps to disentangle the role of competition-driven processes and environmental filtering for community assembly. In this study, we evaluated patterns in species richness, phylogenetic structure and life-history traits of bee communities along altitudinal gradients in the Alps, Germany. We found a linear decline in species richness and abundance but increasing phylogenetic clustering in communities with increasing altitude. The proportion of social- and ground-nesting species, as well as mean body size and altitudinal range of bee communities, increased with increasing altitude, whereas the mean geographical distribution decreased. Our results suggest that community assembly at high altitudes is dominated by environmental filtering effects, whereas the relative importance of competition increases at low altitudes. We conclude that inherent phylogenetic and ecological species attributes at high altitudes pose a threat for less competitive alpine specialists with ongoing climate change.

Crooks' fluctuation theorem for a process on a two dimensional fluid field

We investigate the behavior of a two-dimensional inviscid and incompressible flow when pushed out of dynamical equilibrium. We use the two-dimensional vorticity equation with spectral truncation on a rectangular domain. For a sufficiently large number of degrees of freedom, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. We interpret this as doing work to the system. Evolving along a forward and its corresponding backward process, we find numerical evidence that the distributions of the work performed satisfy the Crooks relation. We confirm our results by proving the Crooks relation for this system rigorously.

Examining reliability of seasonal to decadal sea surface temperature forecasts: the role of ensemble dispersion

Useful probabilistic climate forecasts on decadal timescales should be reliable (i.e. forecast probabilities match the observed relative frequencies) but this is seldom examined. This paper assesses a necessary condition for reliability, that the ratio of ensemble spread to forecast error being close to one, for seasonal to decadal sea surface temperature retrospective forecasts from the Met Office Decadal Prediction System (DePreSys). Factors which may affect reliability are diagnosed by comparing this spread-error ratio for an initial condition ensemble and two perturbed physics ensembles for initialized and uninitialized predictions. At lead times less than 2 years, the initialized ensembles tend to be under-dispersed, and hence produce overconfident and hence unreliable forecasts. For longer lead times, all three ensembles are predominantly over-dispersed. Such over-dispersion is primarily related to excessive inter-annual variability in the climate model. These findings highlight the need to carefully evaluate simulated variability in seasonal and decadal prediction systems.Useful probabilistic climate forecasts on decadal timescales should be reliable (i.e. forecast probabilities match the observed relative frequencies) but this is seldom examined. This paper assesses a necessary condition for reliability, that the ratio of ensemble spread to forecast error being close to one, for seasonal to decadal sea surface temperature retrospective forecasts from the Met Office Decadal Prediction System (DePreSys). Factors which may affect reliability are diagnosed by comparing this spread-error ratio for an initial condition ensemble and two perturbed physics ensembles for initialized and uninitialized predictions. At lead times less than 2 years, the initialized ensembles tend to be under-dispersed, and hence produce overconfident and hence unreliable forecasts. For longer lead times, all three ensembles are predominantly over-dispersed. Such over-dispersion is primarily related to excessive inter-annual variability in the climate model. These findings highlight the need to carefully evaluate simulated variability in seasonal and decadal prediction systems.

Terrorism and cabinet duration

Terrorism can strengthen or weaken electoral support for ruling governments. We show in a simple model of coalition formation that, regardless of the direction of a public opinion shock, the impact of terrorism on cabinet duration is ambiguous. However, in an analysis of a data set including 2,400 cabinets in over 150 countries in the period 1970–2002, we find that terrorism, on average, shortens cabinet duration. This result is robust for a range of alternative terror measures and is present in both democratic as well as autocratic political regimes.

Terrorism and electoral accountability: one strike, you're out!

We examine the relationship between terrorism and electoral accountability. We find that terror has a robust positive effect on the probability that the incumbent government is replaced. The magnitude of the effect increases with the severity of the terrorist attack.

Examining reliability of seasonal to decadal sea surface temperature forecasts: the role of ensemble dispersion

Useful probabilistic climate forecasts on decadal timescales should be reliable (i.e. forecast probabilities match the observed relative frequencies) but this is seldom examined. This paper assesses a necessary condition for reliability, that the ratio of ensemble spread to forecast error being close to one, for seasonal to decadal sea surface temperature retrospective forecasts from the Met Office Decadal Prediction System (DePreSys). Factors which may affect reliability are diagnosed by comparing this spread-error ratio for an initial condition ensemble and two perturbed physics ensembles for initialized and uninitialized predictions. At lead times less than 2 years, the initialized ensembles tend to be under-dispersed, and hence produce overconfident and hence unreliable forecasts. For longer lead times, all three ensembles are predominantly over-dispersed. Such over-dispersion is primarily related to excessive inter-annual variability in the climate model. These findings highlight the need to carefully evaluate simulated variability in seasonal and decadal prediction systems.Useful probabilistic climate forecasts on decadal timescales should be reliable (i.e. forecast probabilities match the observed relative frequencies) but this is seldom examined. This paper assesses a necessary condition for reliability, that the ratio of ensemble spread to forecast error being close to one, for seasonal to decadal sea surface temperature retrospective forecasts from the Met Office Decadal Prediction System (DePreSys). Factors which may affect reliability are diagnosed by comparing this spread-error ratio for an initial condition ensemble and two perturbed physics ensembles for initialized and uninitialized predictions. At lead times less than 2 years, the initialized ensembles tend to be under-dispersed, and hence produce overconfident and hence unreliable forecasts. For longer lead times, all three ensembles are predominantly over-dispersed. Such over-dispersion is primarily related to excessive inter-annual variability in the climate model. These findings highlight the need to carefully evaluate simulated variability in seasonal and decadal prediction systems.

A gradual depth-dependent change of connectivity features of supragranular pyramidal cells in rat barrel cortex

Recent experimental evidence suggests a finer genetic, structural and functional subdivision of the layers which form a cortical column. The classical layer II/III (LII/III) of rodent neocortex integrates ascending sensory information with contextual cortical information for behavioral read-out. We systematically investigated to which extent regular-spiking supragranular pyramidal neurons, located at different depths within the cortex, show different input-output connectivity patterns. Combining glutamate-uncaging with whole-cell recordings and biocytin filling, we revealed a novel cellular organization of LII/III: (i) “Lower LII/III” pyramidal cells receive a very strong excitatory input from lemniscal LIV and much fewer inputs from paralemniscal LVa. They project to all layers of the home column, including a feedback projection to LIV whereas transcolumnar projections are relatively sparse. (ii) “Upper LII/III” pyramidal cells also receive their strongest input from LIV, but in addition, a very strong and dense excitatory input from LVa. They project extensively to LII/III as well as LVa and Vb of their home and neighboring columns, (iii) “Middle LII/III” pyramidal cell show an intermediate connectivity phenotype that stands in many ways in-between the features described for lower versus upper LII/III. “Lower LII/III” intracolumnarly segregates and transcolumnarly integrates lemniscal information whereas “upper LII/III” seems to integrate lemniscal with paralemniscal information. This suggests a finegrained functional subdivision of the supragranular compartment containing multiple circuits without any obvious cytoarchitectonic, other structural or functional correlate of a laminar border in rodent barrel cortex.

Investigating hydrological regimes and processes in a set of catchments with temporary waters in Mediterranean Europe

Seven catchments of diverse size in Mediterranean Europe were investigated in order to understand the main aspects of their hydrological functioning. The methods included the analysis of daily and monthly precipitation, monthly potential evapotranspiration rates, flow duration curves, rainfall runoff relationships and catchment internal data for the smaller and more instrumented catchments. The results showed that the catchments were less dry than initially considered. Only one of them was really semi-arid throughout the year. All the remaining catchments showed wet seasons when precipitation exceeded potential evapotrans-piration, allowing aquifer recharge, wet runoff generation mechanisms and relevant baseflow contribution. Nevertheless, local infiltration excess (Hortonian) overland flow was inferred during summer storms in some catchments and urban overland flow in some others. The roles of karstic groundwater, human disturbance and low winter temperatures were identified as having an important impact on the hydrological regime in some of the catchments.

Growth factor receptor-bound protein 2 contributes to (hem)immunoreceptor tyrosine-based activation motif-mediated signaling in platelets

Rationale: Platelets are anuclear cell fragments derived from bone marrow megakaryocytes (MKs) that safeguard vascular integrity but may also cause pathological vessel occlusion. One major pathway of platelet activation is triggered by 2 receptors that signal through an (hem)immunoreceptor tyrosine-based activation motif (ITAM), the activating collagen receptor glycoprotein (GP) VI and the C-type lectin-like receptor 2 (CLEC-2). Growth factor receptor–bound protein 2 (Grb2) is a ubiquitously expressed adapter molecule involved in signaling processes of numerous receptors in different cell types, but its function in platelets and MKs is unknown. Objective: We tested the hypothesis that Grb2 is a crucial adapter protein in (hem)immunoreceptor tyrosine-based activation motif signaling in platelets. Methods and Results: Here, we show that genetic ablation of Grb2 in MKs and platelets did not interfere with MK differentiation or platelet production. However, Grb2-deficiency severely impaired glycoprotein VI–mediated platelet activation because of defective stabilization of the linker of activated T-cell (LAT) signalosome and activation of downstream signaling proteins that resulted in reduced adhesion, aggregation, and coagulant activity on collagen in vitro. Similarly, CLEC-2–mediated signaling was impaired in Grb2-deficient platelets, whereas the cells responded normally to stimulation of G protein–coupled receptors. In vivo, this selective (hem)immunoreceptor tyrosine-based activation motif signaling defect resulted in prolonged bleeding times but affected arterial thrombus formation only after concomitant treatment with acetylsalicylic acid, indicating that defective glycoprotein VI signaling in the absence of Grb2 can be compensated through thromboxane A2–induced G protein–coupled receptor signaling pathways. Conclusions: These results reveal an important contribution of Grb2 in (hem)immunoreceptor tyrosine-based activation motif signaling in platelets in hemostasis and thrombosis by stabilizing the LAT signalosome.

Resolution and discrimination - two sides of the same coin

The notions of resolution and discrimination of probability forecasts are revisited. It is argued that the common concept underlying both resolution and discrimination is the dependence (in the sense of probability theory) of forecasts and observations. More specifically, a forecast has no resolution if and only if it has no discrimination if and only if forecast and observation are stochastically independent. A statistical tests for independence is thus also a test for no resolution and, at the same time, for no discrimination. The resolution term in the decomposition of the logarithmic scoring rule, and the area under the Receiver Operating Characteristic will be investigated in this light.

Probabilistic wind power forecasts with an inverse power curve transformation and censored regression

Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 h are generally made by using statistical methods to post-process forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the non-linear relationship between wind speed and power production and the limited range of power production between zero and nominal power of the turbine. In practice, these problems are often tackled by using non-linear non-parametric regression models. However, such an approach ignores valuable and readily available information: the power curve of the turbine's manufacturer. Much of the non-linearity can be directly accounted for by transforming the observed power production into wind speed via the inverse power curve so that simpler linear regression models can be used. Furthermore, the fact that the transformed power production has a limited range can be taken care of by employing censored regression models. In this study, we evaluate quantile forecasts from a range of methods: (i) using parametric and non-parametric models, (ii) with and without the proposed inverse power curve transformation and (iii) with and without censoring. The results show that with our inverse (power-to-wind) transformation, simpler linear regression models with censoring perform equally or better than non-linear models with or without the frequently used wind-to-power transformation.

Assessing the performance of dynamical trajectory estimates

Estimating trajectories and parameters of dynamical systems from observations is a problem frequently encountered in various branches of science; geophysicists for example refer to this problem as data assimilation. Unlike as in estimation problems with exchangeable observations, in data assimilation the observations cannot easily be divided into separate sets for estimation and validation; this creates serious problems, since simply using the same observations for estimation and validation might result in overly optimistic performance assessments. To circumvent this problem, a result is presented which allows us to estimate this optimism, thus allowing for a more realistic performance assessment in data assimilation. The presented approach becomes particularly simple for data assimilation methods employing a linear error feedback (such as synchronization schemes, nudging, incremental 3DVAR and 4DVar, and various Kalman filter approaches). Numerical examples considering a high gain observer confirm the theory.