Using zero-norm constraint for sparse probability density function estimation

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

Combining satellite data and models to estimate cloud radiative effect at the surface and in the atmosphere

Satellite measurements and numerical forecast model reanalysis data are used to compute an updated estimate of the cloud radiative effect on the global multi-annual mean radiative energy budget of the atmosphere and surface. The cloud radiative cooling effect through reflection of shortwave radiation dominates over the longwave heating effect, resulting in a net cooling of the climate system of –21 Wm-2. The shortwave radiative effect of cloud is primarily manifest as a reduction in the solar radiation absorbed at the surface of -53 Wm-2. Clouds impact longwave radiation by heating the moist tropical atmosphere (up to around 40 Wm-2 for global annual means) while enhancing the radiative cooling of the atmosphere over other regions, in particular higher latitudes and sub-tropical marine stratocumulus regimes. While clouds act to cool the climate system during the daytime, the cloud greenhouse effect heats the climate system at night. The influence of cloud radiative effect on determining cloud feedbacks and changes in the water cycle are discussed.

Multimodel estimate of the global terrestrial water balance: setup and first results

Six land surface models and five global hydrological models participate in a model intercomparison project (WaterMIP), which for the first time compares simulation results of these different classes of models in a consistent way. In this paper the simulation setup is described and aspects of the multi-model global terrestrial water balance are presented. All models were run at 0.5 degree spatial resolution for the global land areas for a 15-year period (1985-1999) using a newly-developed global meteorological dataset. Simulated global terrestrial evapotranspiration, excluding Greenland and Antarctica, ranges from 415 to 586 mm year-1 (60,000 to 85,000 km3 year-1) and simulated runoff ranges from 290 to 457 mm year-1 (42,000 to 66,000 km3 year-1). Both the mean and median runoff fractions for the land surface models are lower than those of the global hydrological models, although the range is wider. Significant simulation differences between land surface and global hydrological models are found to be caused by the snow scheme employed. The physically-based energy balance approach used by land surface models generally results in lower snow water equivalent values than the conceptual degree-day approach used by global hydrological models. Some differences in simulated runoff and evapotranspiration are explained by model parameterizations, although the processes included and parameterizations used are not distinct to either land surface models or global hydrological models. The results show that differences between model are major sources of uncertainty. Climate change impact studies thus need to use not only multiple climate models, but also some other measure of uncertainty, (e.g. multiple impact models).

Attribution of climate change: a methodology to estimate the potential contribution to increases in potato yield in Scotland since 1960

Maincrop potato yields in Scotland have increased by 3035 similar to t similar to ha-1 since 1960 as a result of many changes, but has changing climate contributed anything to this? The purpose of this work was to answer this question. Daily weather data for the period 19602006 were analysed for five locations covering the zones of potato growing on the east coast of Scotland (between 55.213 and 57.646 similar to N) to determine trends in temperature, rainfall and solar radiation. A physiologically based potato yield model was validated using data obtained from a long-term field trial in eastern Scotland and then employed to simulate crop development and potential yield at each of the five sites. Over the 47 similar to years, there were significant increases in annual air and 30 similar to cm soil temperatures (0.27 and 0.30 similar to K similar to decade-1, respectively), but no significant changes in annual precipitation or in the timing of the last frost in spring and the first frost of autumn. There was no evidence of any north to south gradient of warming. Simulated emergence and canopy closure became earlier at all five sites over the period with the advance being greater in the north (3.7 and 3.6 similar to days similar to decade-1, respectively) than the south (0.5 and 0.8 similar to days similar to decade-1, respectively). Potential yield increased with time, generally reflecting the increased duration of the green canopy, at average rates of 2.8 similar to t similar to ha-1 decade-1 for chitted seed (sprouted prior to planting) and 2.5 similar to t similar to ha-1 decade-1 for unchitted seed. The measured warming could contribute potential yield increases of up to 13.2 similar to t similar to ha-1 for chitted potato (range 7.119.3 similar to t similar to ha-1) and 11.5 similar to t similar to ha-1 for unchitted potato (range 7.115.5 similar to t similar to ha-1) equivalent to 3439% of the increased potential yield over the period or 2326% of the increase in actual measured yields.

Using meteorological wind data to estimate turbine generation output: a sensitivity analysis

Various studies investigating the future impacts of integrating high levels of renewable energy make use of historical meteorological (met) station data to produce estimates of future generation. Hourly means of 10m horizontal wind are extrapolated to a standard turbine hub height using the wind profile power or log law and used to simulate the hypothetical power output of a turbine at that location; repeating this procedure using many viable locations can produce a picture of future electricity generation. However, the estimate of hub height wind speed is dependent on the choice of the wind shear exponent a or the roughness length z0, and requires a number of simplifying assumptions. This paper investigates the sensitivity of this estimation on generation output using a case study of a met station in West Freugh, Scotland. The results show that the choice of wind shear exponent is a particularly sensitive parameter which can lead to significant variation of estimated hub height wind speed and hence estimated future generation potential of a region.

A study into the accuracy of using meteorological wind data to estimate turbine generation output

Meteorological (met) station data is used as the basis for a number of influential studies into the impacts of the variability of renewable resources. Real turbine output data is not often easy to acquire, whereas meteorological wind data, supplied at a standardised height of 10 m, is widely available. This data can be extrapolated to a standard turbine height using the wind profile power law and used to simulate the hypothetical power output of a turbine. Utilising a number of met sites in such a manner can develop a model of future wind generation output. However, the accuracy of this extrapolation is strongly dependent on the choice of the wind shear exponent alpha. This paper investigates the accuracy of the simulated generation output compared to reality using a wind farm in North Rhins, Scotland and a nearby met station in West Freugh. The results show that while a single annual average value for alpha may be selected to accurately represent the long term energy generation from a simulated wind farm, there are significant differences between simulation and reality on an hourly power generation basis, with implications for understanding the impact of variability of renewables on short timescales, particularly system balancing and the way that conventional generation may be asked to respond to a high level of variable renewable generation on the grid in the future.

Updated estimate of aerosol direct radiative forcing from satellite observations and comparison against the Hadley Centre climate model

The fourth assessment report of the Intergovernmental Panel on Climate Change (IPCC) includes a comparison of observation-based and modeling-based estimates of the aerosol direct radiative forcing. In this comparison, satellite-based studies suggest a more negative aerosol direct radiative forcing than modeling studies. A previous satellite-based study, part of the IPCC comparison, uses aerosol optical depths and accumulation-mode fractions retrieved by the Moderate Resolution Imaging Spectroradiometer (MODIS) at collection 4. The latest version of MODIS products, named collection 5, improves aerosol retrievals. Using these products, the direct forcing in the shortwave spectrum defined with respect to present-day natural aerosols is now estimated at −1.30 and −0.65 Wm−2 on a global clear-sky and all-sky average, respectively, for 2002. These values are still significantly more negative than the numbers reported by modeling studies. By accounting for differences between present-day natural and preindustrial aerosol concentrations, sampling biases, and investigating the impact of differences in the zonal distribution of anthropogenic aerosols, good agreement is reached between the direct forcing derived from MODIS and the Hadley Centre climate model HadGEM2-A over clear-sky oceans. Results also suggest that satellite estimates of anthropogenic aerosol optical depth over land should be coupled with a robust validation strategy in order to refine the observation-based estimate of aerosol direct radiative forcing. In addition, the complex problem of deriving the aerosol direct radiative forcing when aerosols are located above cloud still needs to be addressed.

Heat kernel smoothing via Laplace-Beltrami eigenfunctions and its application to subcortical structure modeling

We present a new subcortical structure shape modeling framework using heat kernel smoothing constructed with the Laplace-Beltrami eigenfunctions. The cotan discretization is used to numerically obtain the eigenfunctions of the Laplace-Beltrami operator along the surface of subcortical structures of the brain. The eigenfunctions are then used to construct the heat kernel and used in smoothing out measurements noise along the surface. The proposed framework is applied in investigating the influence of age (38-79 years) and gender on amygdala and hippocampus shape. We detected a significant age effect on hippocampus in accordance with the previous studies. In addition, we also detected a significant gender effect on amygdala. Since we did not find any such differences in the traditional volumetric methods, our results demonstrate the benefit of the current framework over traditional volumetric methods.

Sparse probability density function estimation using the minimum integrated square error

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.

Is DARTEL-based voxel-based morphometry affected by width of smoothing kernel and group size? A study using simulated atrophy

Purpose: To quantify to what extent the new registration method, DARTEL (Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra), may reduce the smoothing kernel width required and investigate the minimum group size necessary for voxel-based morphometry (VBM) studies. Materials and Methods: A simulated atrophy approach was employed to explore the role of smoothing kernel, group size, and their interactions on VBM detection accuracy. Group sizes of 10, 15, 25, and 50 were compared for kernels between 0–12 mm. Results: A smoothing kernel of 6 mm achieved the highest atrophy detection accuracy for groups with 50 participants and 8–10 mm for the groups of 25 at P < 0.05 with familywise correction. The results further demonstrated that a group size of 25 was the lower limit when two different groups of participants were compared, whereas a group size of 15 was the minimum for longitudinal comparisons but at P < 0.05 with false discovery rate correction. Conclusion: Our data confirmed DARTEL-based VBM generally benefits from smaller kernels and different kernels perform best for different group sizes with a tendency of smaller kernels for larger groups. Importantly, the kernel selection was also affected by the threshold applied. This highlighted that the choice of kernel in relation to group size should be considered with care.

Assessment of the Wind Gust Estimate Method in mesoscale modelling of storm events over West Germany

A physically based gust parameterisation is added to the atmospheric mesoscale model FOOT3DK to estimate wind gusts associated with storms over West Germany. The gust parameterisation follows the Wind Gust Estimate (WGE) method and its functionality is verified in this study. The method assumes that gusts occurring at the surface are induced by turbulent eddies in the planetary boundary layer, deflecting air parcels from higher levels down to the surface under suitable conditions. Model simulations are performed with horizontal resolutions of 20 km and 5 km. Ten historical storm events of different characteristics and intensities are chosen in order to include a wide range of typical storms affecting Central Europe. All simulated storms occurred between 1990 and 1998. The accuracy of the method is assessed objectively by validating the simulated wind gusts against data from 16 synoptic stations by means of “quality parameters”. Concerning these parameters, the temporal and spatial evolution of the simulated gusts is well reproduced. Simulated values for low altitude stations agree particularly well with the measured gusts. For orographically exposed locations, the gust speeds are partly underestimated. The absolute maximum gusts lie in most cases within the bounding interval given by the WGE method. Focussing on individual storms, the performance of the method is better for intense and large storms than for weaker ones. Particularly for weaker storms, the gusts are typically overestimated. The results for the sample of ten storms document that the method is generally applicable with the mesoscale model FOOT3DK for mid-latitude winter storms, even in areas with complex orography.

An improved sum-product estimate for general finite fields

An improved sum-product estimate for subsets of a finite field whose order is not prime is provided. It is shown, under certain conditions, that max{∣∣∣A+A∣∣∣,∣∣∣A⋅A∣∣∣}≫∣∣A∣∣12/11(log2∣∣A∣∣)5/11. This new estimate matches, up to a logarithmic factor, the current best known bound obtained over prime fields by Rudnev

Global estimate of aerosol direct radiative forcing from satellite measurements

Atmospheric aerosols cause scattering and absorption of incoming solar radiation. Additional anthropogenic aerosols released into the atmosphere thus exert a direct radiative forcing on the climate system1. The degree of present-day aerosol forcing is estimated from global models that incorporate a representation of the aerosol cycles1–3. Although the models are compared and validated against observations, these estimates remain uncertain. Previous satellite measurements of the direct effect of aerosols contained limited information about aerosol type, and were confined to oceans only4,5. Here we use state-of-the-art satellitebased measurements of aerosols6–8 and surface wind speed9 to estimate the clear-sky direct radiative forcing for 2002, incorporating measurements over land and ocean. We use a Monte Carlo approach to account for uncertainties in aerosol measurements and in the algorithm used. Probability density functions obtained for the direct radiative forcing at the top of the atmosphere give a clear-sky, global, annual average of 21.9Wm22 with standard deviation, 60.3Wm22. These results suggest that present-day direct radiative forcing is stronger than present model estimates, implying future atmospheric warming greater than is presently predicted, as aerosol emissions continue to decline10.