Mapping rates associated with polygons

Suppose that geographic data under investigation are rates associated with polygons. For example, disease incidence, mortality, and census undercount data may be displayed as rates. Spatial analysis of data of this sort can be handled very naturally through Bayesian hierarchical statistical modeling, where there is a measurement process at the first level, an explanatory process at the second level, and a prior probability distribution on unknowns at the third level. In our paper, we shall feature epidemiological data, specifically disease-incidence rates, and the “polygons” referred to in the title are typically states or counties.     

Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates

The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and computational load of the integration of the multivariate probability density function. Contributions of this work are twofold. First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid, at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions.     

Characterization of multipath phase rates in different multipath environments

A well-known effect of multipath propagation is multipath fading that typically causes periodic signal variations. Such signal variations may become visible in some basic GNSS observables such as the code minus carrier observable, single or double differences or in C/N ₀ time series. The frequency of these variations—also called fading frequency or multipath phase rate—strongly depends on the multipath environment, i.e. on the actual geometric conditions which can be described by the location of the satellite causing the multipath signal and the reflector location with respect to the receiving antenna. This paper gives a detailed insight on the expected multipath phase rates in different multipath environments. Different geometric conditions are analyzed, from arbitrary reflector positions to the point of dealing with the special case of ground multipath. Fading frequencies are determined by means of an empirical approach using the characteristics of real satellite passes. The approach results in distributions of multipath phase rates which are computed for a multitude of possible reflector locations and from which minimum, mean and maximum multipath phase rates can be derived.     

Identifying a low-frequency oscillation in Galileo IOV pseudorange rates

Galileo, the European global navigation satellite system, is in its in-orbit validation phase and the four satellites which have been available for some months now have allowed a preliminary analysis of the system performance. Previous studies have showed that Galileo will be able to provide pseudorange measurements more accurate than those provided by GPS. However, a similar improvement was not found for pseudorange rate observations in the velocity domain. This fact stimulated additional analysis of the velocity domain, and, in particular, an unintended oscillatory component was identified as the main error source in the velocity solution. The magnitude of such oscillation is less than 10 cm/s, and its period is in the order of few minutes. A methodology was developed to identify oscillatory components in the Galileo IOV pseudorange rate observables, and it was verified that the measurements from Galileo IOV PFM and Galileo IOV FM2 are affected by a small oscillatory disturbance. This disturbance stems from the architecture adopted for combining the frequency references provided by the two active clocks present in the Galileo satellites. The issue has been solved in Galileo IOV FM3 and Galileo IOV FM4, and the oscillatory component has been eliminated. We also propose a methodology for removing this unwanted component from the final velocity solution and for determining the performance that Galileo will be able to achieve. The analysis shows that Galileo velocity solution will provide a root-mean-square error of about 8 cm/s even in the limited geometry conditions achieved using only four satellites. This shows the potential of Galileo also in the determination of user velocity.     

Global carbon dioxide removal rates from forest landscape restoration activities

Background

Forest landscape restoration (FLR) has been adopted by governments and practitioners across the globe to mitigate and adapt to climate change and restore ecological functions across degraded landscapes. However, the extent to which these activities capture CO₂ with associated climate mitigation impacts are poorly known, especially in geographies where data on biomass growth of restored forests are limited or do not exist. To fill this gap, we developed biomass accumulation rates for a set of FLR activities (natural regeneration, planted forests and woodlots, agroforestry, and mangrove restoration) across the globe and global CO₂ removal rates with corresponding confidence intervals, grouped by FLR activity and region/climate.

Results

Planted forests and woodlots were found to have the highest CO₂ removal rates, ranging from 4.5 to 40.7 t CO² ha^?1 year^?1 during the first 20 years of growth. Mangrove tree restoration was the second most efficient FLR at removing CO₂, with growth rates up to 23.1 t CO₂ ha^?1 year^?1 the first 20 years post restoration. Natural regeneration removal rates were 9.1–18.8 t CO₂ ha^?1 year^?1 during the first 20 years of forest regeneration, followed by agroforestry, the FLR category with the lowest and regionally broad removal rates (10.8–15.6 t CO₂ ha^?1 year^?1). Biomass growth data was most abundant and widely distributed across the world for planted forests and natural regeneration, representing 45% and 32% of all the data points assessed, respectively. Agroforestry studies, were only found in Africa, Asia, and the Latin America and Caribbean regions.

Conclusion

This study represents the most comprehensive review of published literature on tree growth and CO₂ removals to date, which we operationalized by constructing removal rates for specific FLR activities across the globe. These rates can easily be applied by practitioners and decision-makers seeking to better understand the positive climate mitigation impacts of existing or planned FLR actions, or by countries making restoration pledges under the Bonn Challenge Commitments or fulfilling Nationally Determined Contributions to the UNFCCC, thereby helping boost FLR efforts world-wide.

     

Improved convergence rates for the truncation error in gravimetric geoid determination

 When Stokes's integral is used over a spherical cap to compute a gravimetric estimate of the geoid, a truncation error results due to the neglect of gravity data over the remainder of the Earth. Associated with the truncation error is an error kernel defined over these two complementary regions. An important observation is that the rate of decay of the coefficients of the series expansion for the truncation error in terms of Legendre polynomials is determined by the smoothness properties of the error kernel. Previously published deterministic modifications of Stokes's integration kernel involve either a discontinuity in the error kernel or its first derivative at the spherical cap radius. These kernels are generalised and extended by constructing error kernels whose derivatives at the spherical cap radius are continuous up to an arbitrary order. This construction is achieved by smoothly continuing the error kernel function into the spherical cap using a suitable degree polynomial. Accordingly, an improved rate of convergence of the spectral series representation of the truncation error is obtained. Received: 21 April 1998 / Accepted: 4 October 1999     

Microwave observations of daily Antarctic sea-ice edge expansion and contraction rates

Algorithms for estimating sea-ice extent from remotely sensed microwave sensor data can benefit from knowledge of the "a priori" distribution of the daily expansion and contraction of the sea-ice pack. To estimate the probability distribution of daily Antarctic sea-ice extent change, two independent sea-ice datasets are analyzed: sea-ice extent derived from the QuikSCAT scatterometer and ice concentration estimates from the Special Sensor Microwave/Imager. The daily sea-ice advance and retreat is tracked over a four-year period. The distribution of the daily sea-ice advance/retreat from each sensor is similar and is approximately double-exponential. Daily ice-pack statistics are presented.     

Characterization of the effects of high multipath phase rates in GPS

GPS multipath has been studied since the early 1970s. Prior to the investigation described in this paper, however, the effects due to the relative Doppler shift between the direct and multipath signal components have received scant attention. The single previous study that did address the issue indicated coherent receivers had significant performance advantages over noncoherent receivers. Specifically, it was stated that under the condition of fast-fading multipath, noncoherent receivers would yield a bias error, whereas coherent receivers would not. After reviewing the background theory, this paper describes a revised model of the phenomenon and shows the results of hardware simulations which validate the existence of the bias in both receiver types and offer support for the new model. A case study of a specific commercial receiver is presented. Electronic Publication     

New Year,New You

新鲜的感觉总是很容易就会消失，看过、听过、经历过，或许就不再新鲜，可是对于新的一年要发生的，总是还有期待。     

Modelling small-area inequality in premature mortality using years of life lost rates

Analysis of premature mortality variations via standardized expected years of life lost (SEYLL) measures raises questions about suitable modelling for mortality data, especially when developing SEYLL profiles for areas with small populations. Existing fixed effects estimation methods take no account of correlations in mortality levels over ages, causes, socio-ethnic groups or areas. They also do not specify an underlying data generating process, or a likelihood model that can include trends or correlations, and are likely to produce unstable estimates for small-areas. An alternative strategy involves a fully specified data generation process, and a random effects model which “borrows strength” to produce stable SEYLL estimates, allowing for correlations between ages, areas and socio-ethnic groups. The resulting modelling strategy is applied to gender-specific differences in SEYLL rates in small-areas in NE London, and to cause-specific mortality for leading causes of premature mortality in these areas.     

中国省域离婚率的时空格局及趋同演变研究

针对现有离婚率研究时间、空间割裂,整体性探讨不足及实证研究缺乏的问题,该文运用空间自相关、空间马尔可夫链等空间统计方法对中国大陆各省域1979—2012年离婚率数据的时空分布及趋同演变进行了研究,结果发现:除东北、西北地区离婚率一直居高不下之外,中国大陆高离婚率地区逐步向中部延伸并聚集,离婚率存在着较强的空间自相关且空间聚集现象明显;省域离婚率的"两极分化"现象和"俱乐部趋同"现象均经历了由弱到强再减弱的波动变化趋势。     

Vertical displacement rates in the Upper Rhine Graben area derived from precise leveling

The recent vertical displacement field of the Upper Rhine Graben (URG) located in the tri-national region between Germany, France and Switzerland is investigated using repeatedly measured leveling data. We estimate vertical displacement rates at leveling benchmarks by applying a kinematic network adjustment on more than 40,000 height differences measured by German, French and Swiss surveying agencies. Focusing on an optimal solution for the adjusted rates in the URG area also historical data (measured before 1900) are used, significantly increasing the time span of available measurements and the number of transnational connections between the three countries. To account for inhomogeneities apparent in the database, we apply an iterative variance component estimation within the adjustment procedure, particularly revealing more realistic information on the accuracy of the estimated rates. A special focus within our analysis is put on the statistical testing of gross errors in the observations and model-related errors at benchmarks with non-linear movement. As some of the estimated vertical rates behave significantly different compared to the vertical rates of adjacent benchmarks, a filtering of outliers is applied after the adjustment procedure. The resulting map of linear height changes in an area of 280 km in N–S and 230 km in E–W direction provides detailed insight into the recent vertical displacements of the URG and neighboring regions. In the German part of the study area, it was possible for the first time to consistently constrain an average subsidence rate of 0.5 mm/a ( \(\pm \) 0.2 mm/a) of the Graben interior w.r.t. the Black Forest. In addition to the tectonic displacements, some man-induced surface movements, e.g., caused by oil and groundwater extraction, are observed and discussed.     

Targeting deforestation rates in climate change policy: a "Preservation Pathway" approach

We present a new methodological approach to incorporating deforestation within the international climate change negotiating regime. The approach, called "Preservation Pathway" combines the desire for forest preservation with the need to reduce emissions associated with forest loss by focusing on the relative rate of change of forest cover as the criteria by which countries gain access to trading preserved forest carbon stocks. This approach avoids the technically challenging task of quantifying historical or future deforestation emission baselines. Rather, it places emphasis on improving quantification of contemporary stocks and the relative decline in deforestation rates necessary to preserve those stocks. This approach places emphasis on the complete emissions trajectory necessary to attain an agreed-upon preserved forest and as such, meets both forest conservation and climate goals simultaneously.     

Impact of different sampling rates on precise point positioning performance using online processing service

In this study, the effect of different sampling rates (i.e. observation recording interval) on the Precise Point Positioning (PPP) solutions in terms of accurac...     

Ocean loading effects on the prediction of Antarctic glacial isostatic uplift and gravity rates

The effect of regional ocean loading on predicted rates of crustal uplift and gravitational change due to glacial isostatic adjustment (GIA) is determined for Antarctica. The effect is found to be significant for the ICE-3G and ICE-5G loading histories (up to ?8 mm/year and ?3 mm/year change in uplift rate and ?3 cm/year and ?1 cm/year equivalent water height change (EWHC) of surface mass, respectively). The effect is smaller (+1 mm/year; +0.25 cm/year) for the IJ05 loading history. The impact of ocean loading on the rate of change of the long-wavelength zonal harmonics of the Earth’s gravitational field is also significantly smaller for IJ05 than ICE-3G. A simple analytical formula is derived that is accurate to about 3% in a root-mean-square sense that relates predicted or observed gravitational change at the surface of the Earth (r = a) to the EWHC. A fundamental difference in the definition of the load histories accounts for the differing sensitivities to ocean loading. IJ05 defines its surface load history relative to the present-day surface load, rather than specifying an absolute loading history, and thus implicitly approximates the temporal and spatial mass exchange between grounded ice and open ocean. In contrast, ICE-3G and ICE-5G specify an absolute load history and explicit regional ocean loading substantially perturbs predicted GIA rates. Conclusions of previous studies that used IJ05 predictions without ocean loading are relatively robust.     

Monument-antenna effects on GPS coordinate time series with application to vertical rates in Antarctica

We examine the electromagnetic coupling of a GPS antenna–monument pair in terms of its simulated affect on long GPS coordinate time series. We focus on the Earth and Polar Observing System (POLENET) monument design widely deployed in Antarctica and Greenland in projects interested particularly in vertical velocities. We base our tests on an absolute robot calibration that included the top ~0.15 m of the monument and use simulations to assess its effect on site coordinate time series at eight representative POLENET sites in Antarctica over the period 2000.0–2011.0. We show that the neglect of this calibration would introduce mean coordinate bias, and most importantly for velocity estimation, coordinate noise which is highly sensitive to observation geometry and hence site location and observation period. Considering only sub-periods longer than 2.5 years, we show vertical site velocities may be biased by up to ±0.4 mm/year, and biases up to 0.2 mm/year may persist for observation spans of 8 years. Changing between uniform and elevation-dependent observation weighting alters the time series but does not remove the velocity biases, nor does ambiguity fixing. The effect on the horizontal coordinates is negligible. The ambiguities fixed series spectra show noise between flicker and random walk with near-white noise at the highest frequencies, with mean spectral indices (frequencies <20 cycles per year) of approximately −1.3 (uniform weighting) and −1.4 (elevation-dependent weighting). While the results are likely highly monument specific, they highlight the importance of accounting for monument effects when analysing vertical coordinate time series and velocities for the highest precision and accuracy geophysical studies.     

Strain rates in the Alpine Mediterranean region: insights from advanced techniques of data processing

Strain rates and Euler poles for various subregions of the Alpine Mediterranean region were calculated by using global navigation satellite system data from permanent stations. The main scope of the study is to compare and analyze strain rate maps that were calculated using different approaches. This area presents a complex tectonic setting due to the interaction of the Eurasian and Nubian plates. The horizontal velocity gradient tensor was computed starting from a new set of site velocities determined by using continuous long-series geodetic data, state-of-the-art antenna calibrations and recomputed precise orbits. Geodesy provides velocities for a sparsely distributed, discrete number of sites, while deformation has a spatially continuous distribution. For this reason, the interpolation method and the geometric approach to the problem play a fundamental role in the estimation of the strain rate field. In the present study, principal deformation axes and principal angle were estimated by applying two different approaches: the Delaunay triangulation and a grid solution. Both methods produce results with broad coherence, providing new information about the deformation throughout the entire study area. Moreover, an evaluation and analysis of Euler poles related to the different velocity patterns, give complementary information to reconstruct the active deformation in the Mediterranean area.