Imagine a student -- let's call him `E', and make him a "he" -- that is enrolled in Calculus 2, and who believes that to pass in maths courses he only needs to memorize methods and apply them quickly and without errors. Let's imagine that `E' is an `E'xtreme case of "bad foundations" and that he knows how to solve $x+2=5$ by doing $x=5-2=3$, but he doesn't know how to substitute the $x$ in $x+2=5$ by 3, and the only way that he knows of "testing the solution" is to apply the same method again and check that he got the same result. When we are teaching Calculus to classes that have many students that are extreme cases of bad foundations we need new strategies and tools; for example, we can't pretend that "taking a particular case" is an obvious operation anymore -- instead we need ways to make these operations easy to visualize. This article shows a way to do that using Maxima.
<p>Aqueous-phase oxidation of biomass-burning phenols is a significant but poorly constrained source of secondary organic aerosol (SOA) in the atmosphere. Laboratory studies replicating aerosol liquid water (ALW) – characterized by high solute and chromophore concentrations – remain scarce due to strong light attenuation and thermal gradients in conventional photoreactors. To address these limitations, we developed a short-pathlength photoreactor (SPP) that minimizes optical screening and provides precise control of temperature, humidity, and illumination conditions. Using guaiacyl acetone (GA) as a model phenol compound and 3,4-dimethoxybenzaldehyde (DMB) as a triplet precursor (<span class="inline-formula"><sup>3</sup></span>C<span class="inline-formula"><sup>∗</sup></span>), the SPP successfully reproduced SOA yields from established photoreactors under dilute conditions and further enabled experiments under strongly light-absorbing ALW regimes. The system maintained stable temperature and relative humidity, consistent photon flux, and reproducible photochemical performance. Positive matrix factorization (PMF) of high-resolution aerosol mass spectra resolved distinct stages of GA-derived aqueous SOA (aqSOA) evolution across a wide range of ionic strengths. The analysis further revealed the formation of GA dimers through photosensitized coupling pathways, with dimer formation rates increasing significantly with ionic strength. Overall, the SPP provides a validated and versatile platform for investigating aqSOA formation and transformation processes under atmospherically relevant droplet and ALW conditions.</p>
Daniel Carranza, Chris Kapulkin, Nathan Kershaw
et al.
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in which to speak of the system's attractors. As a proof of concept, we provide a decomposition theorem for discrete dynamical systems.
<p>Quantifying methane emissions from oil and gas facilities is crucial for emissions management and accurate facility-level greenhouse gas (GHG) inventory development. This paper evaluates the performance of several multi-source methane emission quantification models using the data collected by fixed-point continuous monitoring systems as part of a controlled-release experiment. Two dispersion modeling approaches (Gaussian plume, Gaussian puff) and two inversion frameworks (least-squares optimization and Markov chain Monte Carlo) are applied to the measurement data. In addition, a subset of experiments are selected to showcase the application of computational fluid dynamics (CFD) informed calculations for direct solution of the advection–diffusion equation. This solution utilizes a three-dimensional wind field informed by solving the momentum equation with the appropriate external forcing to match on-site wind measurements. Results show that the Puff model, driven by high-frequency wind data, significantly improves localization and reduces bias and error variance compared to the Plume model. The Markov chain Monte Carlo (MCMC)-based inversion framework further enhances accuracy over least-squares fitting, with the Puff MCMC approach showing the best performance. The study highlights the importance of long-term integration for accurate total mass emission estimates and the detection of anomalous emission patterns. The findings of this study can help improve emissions management strategies, aid in facility-level emissions risk assessment, and enhance the accuracy of greenhouse gas inventories.</p>
<p>Thunderstorm forecasting remains challenging despite advances in numerical weather prediction (NWP) systems. The microphysics scheme that represents clouds in the model partly contributes to the introduction of uncertainties in the simulations. To better understand the discrepancies, synthetic radar data simulated by a radar forward operator (applied to model outputs) are usually compared to dual-polarization radar observations, as they provide insight into the microphysical structure of clouds. However, the modeling of polarimetric values and radar signatures such as the <span class="inline-formula"><i>Z</i><sub>DR</sub></span> column (ZDRC) remains a complex issue, despite the diversity of microphysics schemes and forward operators, especially above the freezing level where values that are too low are often found.</p>
<p>The aim of this work is to assess the ability of the AROME NWP convective model, when coupled with two distinct microphysics schemes (ICE3 one-moment and LIMA partially two-moment; LIMA: Liquid Ice Multiple Aerosols), to accurately reproduce thunderstorm characteristics. A statistical evaluation is conducted on 34 convective days of 2022 using both a global and an object-oriented approach, and a ZDRC detection algorithm is implemented. Simulations performed with LIMA microphysics showed good agreement with observed <span class="inline-formula"><i>Z</i><sub>H</sub></span>, <span class="inline-formula"><i>Z</i><sub>DR</sub></span>, and <span class="inline-formula"><i>K</i><sub>DP</sub></span> below the melting layer in convective cores. Moreover, it demonstrated a remarkable capacity to generate a realistic number of ZDRCs, as well as a distribution of (1) the ZDRC area and (2) the first ZDRC occurrence, very close to the observations. Enhancements in the forward operator have also been suggested to improve the simulations in the mixed phase and cold phase regions.</p>
<p>These findings are highly encouraging in the context of data assimilation, where one could leverage the combination of advanced microphysics schemes and improved forward operators to improve storm forecasts.</p>
This essay proposes a novel paradigm for a political theory of climate justice: wages for earthwork. Indigenous peoples have disproportionately contributed to the sustainable stewardship of the natural world through ecological systems of governance, which I theorize as “earthwork.” Proponents of climate reparations have focused on reparations for unequal climate damages from emissions. By contrast, I propose “wages” or reparations to Indigenous peoples for debt owed to them for their devalued climate work. This framework makes use of an analogy to the 1970s feminist wages for housework movement, which sought to reveal the exploited and yet indispensable character of systematically devalued work rendered natural and invisible. I contend that (re)valuing earthwork must also be central to projects aimed at decolonizing climate justice, that is, anticolonial climate justice. More than monetary transfers alone, wages for earthwork prioritize the restoration of Indigenous sovereignty and land and wider structural transformation of colonial capitalism.
We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to show the strength and flexibility of such a nonstandard technique for applications in combinatorial number theory.
Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations, have become a popular paradigm. With these models being usually characterized by intuition-driven design or highly intricate components, placing them within the theoretical analysis framework to distill the core concepts, helps understand the key principles that drive the functionality better and guide further development. Given this surge in interest, this article provides a comprehensive summary of the theoretical foundations and breakthroughs concerning the approximation and learning behaviors intrinsic to prevalent graph learning models. Encompassing discussions on fundamental aspects such as expressiveness power, generalization, optimization, and unique phenomena such as over-smoothing and over-squashing, this piece delves into the theoretical foundations and frontier driving the evolution of graph learning. In addition, this article also presents several challenges and further initiates discussions on possible solutions.
Markus de Medeiros, Muhammad Naveed, Tancrède Lepoint
et al.
Differential privacy (DP) has become the gold standard for privacy-preserving data analysis, but implementing it correctly has proven challenging. Prior work has focused on verifying DP at a high level, assuming the foundations are correct and a perfect source of randomness is available. However, the underlying theory of differential privacy can be very complex and subtle. Flaws in basic mechanisms and random number generation have been a critical source of vulnerabilities in real-world DP systems. In this paper, we present SampCert, the first comprehensive, mechanized foundation for differential privacy. SampCert is written in Lean with over 12,000 lines of proof. It offers a generic and extensible notion of DP, a framework for constructing and composing DP mechanisms, and formally verified implementations of Laplace and Gaussian sampling algorithms. SampCert provides (1) a mechanized foundation for developing the next generation of differentially private algorithms, and (2) mechanically verified primitives that can be deployed in production systems. Indeed, SampCert's verified algorithms power the DP offerings of Amazon Web Services (AWS), demonstrating its real-world impact. SampCert's key innovations include: (1) A generic DP foundation that can be instantiated for various DP definitions (e.g., pure, concentrated, Rényi DP); (2) formally verified discrete Laplace and Gaussian sampling algorithms that avoid the pitfalls of floating-point implementations; and (3) a simple probability monad and novel proof techniques that streamline the formalization. To enable proving complex correctness properties of DP and random number generation, SampCert makes heavy use of Lean's extensive Mathlib library, leveraging theorems in Fourier analysis, measure and probability theory, number theory, and topology.
<p>The significance of air quality monitoring for analyzing impact on public health is growing worldwide. A crucial part of smart city development includes deployment of suitable air pollution sensors at critical locations. Note that there are various air quality measurement instruments, ranging from expensive reference stations that provide accurate data to low-cost sensors that provide less accurate air quality measurements. In this research, we use a combination of sensors and monitors, which we call hybrid instruments, and focus on optimal placement of such instruments across a region. The objective of the problem is to maximize a satisfaction function that quantifies the weighted closeness of different regions to the places where such hybrid instruments are placed (here weights for different regions are quantified in terms of the relative population density and relative PM<span class="inline-formula"><sub>2.5</sub></span> concentration). Note that there can be several constraints such as those on budget, the minimum number of reference stations to be placed, or the set of important regions where at least one sensor should be placed. We develop two algorithms to solve this problem. The first one is a genetic algorithm that is a metaheuristic and that works on the principles of evolution. The second one is a greedy algorithm that selects the locally best choice in each iteration. We test these algorithms on different regions from India with varying sizes and other characteristics such as population distribution, PM<span class="inline-formula"><sub>2.5</sub></span> emissions, or available budget. The insights obtained from this paper can be used to quantitatively place reference stations and sensors in large cities rather than using ad hoc procedures or rules of thumb.</p>
<p>Volatile organic compounds (VOCs) have diverse functionality, emission sources, and environmental fates. Speciated measurements of their spatiotemporal variability are thus key to understanding their impacts on air quality, health, and climate. Networks of passive samplers can be used to map VOC concentrations, or in situ instruments can be deployed on mobile platforms. Limitations of existing in situ instruments include high cost, identification of non-target species, differentiation of isomeric species, and low time resolution, which limits how quickly an area can be spatially mapped with mobile measurements. This work describes the development of the Multichannel Organics In situ enviRonmental Analyzer (MOIRA), which has been designed for in situ mobile measurements of target and non-target VOCs from the cargo area of a hybrid hatchback wagon vehicle. Staggered sample collection and analysis by four thermal desorption collectors, four miniature gas chromatography (GC) heaters, and two compact residual gas analyzer (RGA) mass spectrometer (MS) detectors enable continuous measurements at a 10 min time resolution. Non-target species and structural isomers can be identified with electron ionization (EI), and species detected include alkanes (from pentane to pentadecane) and aromatics, as well as more oxidized species such as aldehydes, esters, and carboxylic acids. The instrument is characterized in the laboratory under different environmental conditions and in two pilot field studies of indoor air in a single-family residence and of ambient air during a mobile deployment.</p>
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive in the sense that we do not rely on excluded middle or the axiom of (countable) choice. Domain theory studies so-called directed complete posets (dcpos) and Scott continuous maps between them and has applications in programming language semantics, higher-type computability and topology. A common approach to deal with size issues in a predicative foundation is to work with information systems, abstract bases or formal topologies rather than dcpos, and approximable relations rather than Scott continuous functions. In our type-theoretic approach, we instead accept that dcpos may be large and work with type universes to account for this. A priori one might expect that complex constructions of dcpos result in a need for ever-increasing universes and are predicatively impossible. We show that such constructions can be carried out in a predicative setting. We illustrate the development with applications in the semantics of programming languages: the soundness and computational adequacy of the Scott model of PCF and Scott's $D_\infty$ model of the untyped $λ$-calculus. We also give a predicative account of continuous and algebraic dcpos, and of the related notions of a small basis and its rounded ideal completion. The fact that nontrivial dcpos have large carriers is in fact unavoidable and characteristic of our predicative setting, as we explain in a complementary chapter on the constructive and predicative limitations of univalent foundations. Our account of domain theory in univalent foundations is fully formalised with only a few minor exceptions. The ability of the proof assistant Agda to infer universe levels has been invaluable for our purposes.
<p>This study presents a simulation framework for cloud and
precipitation measurements via spaceborne millimeter-wave radar composed of
eight submodules. To demonstrate the influence of the assumed physical
parameters and to improve the microphysical modeling of the hydrometeors, we
first conducted a sensitivity analysis. The results indicated that the radar reflectivity was highly sensitive to the particle size distribution (PSD) parameter of the median volume diameter and particle density parameter, which can cause reflectivity variations of several to more than 10 dB. The variation in the prefactor of the mass–power relations that related to the riming degree may result in an uncertainty of approximately 30 %–45 %. The
particle shape and orientation also had a significant impact on the radar
reflectivity. The spherical assumption may result in an average
overestimation of the reflectivity by approximately 4 %–14 %, dependent on
the particle type, shape, and orientation. Typical weather cases were
simulated using improved physical modeling, accounting for the particle
shapes, typical PSD parameters corresponding to the cloud precipitation
types, mass–power relations for snow and graupel, and melting modeling. We
present and validate the simulation results for a cold-front stratiform
cloud and a deep convective process with observations from a W-band cloud
profiling radar (CPR) on the CloudSat satellite. The simulated bright band
features, echo structure, and intensity showed a good agreement with the
CloudSat observations; the average relative error of radar reflectivity in
the vertical profile was within 20 %. Our results quantify the
uncertainty in the millimeter-wave radar echo simulation that may be caused
by the physical model parameters and provide a scientific basis for optimal
forward modeling. They also provide suggestions for prior physical parameter constraints for the retrieval of the microphysical properties of clouds and precipitation.</p>
<p>The MethaneSAT satellite instrument and its aircraft precursor, MethaneAIR, are imaging spectrometers designed to measure methane concentrations with wide spatial coverage, fine spatial resolution, and high precision compared to currently deployed remote sensing instruments. At 12 960 m cruise altitude above ground (13 850 m above sea level), MethaneAIR datasets have a 4.5 km swath gridded to 10 m <span class="inline-formula">×</span> 10 m pixels with 17–20 ppb standard deviation on a flat scene. MethaneAIR was deployed in the summer of 2021 in the Permian Basin to test the accuracy of the retrieved methane concentrations and emission rates using the algorithms developed for MethaneSAT. We report here point source emissions obtained during a single-blind volume-controlled release experiment, using two methods. (1) The modified integrated mass enhancement (mIME) method estimates emission rates using the total mass enhancement of methane in an observed plume combined with winds obtained from Weather Research Forecast driven by High-Resolution Rapid Refresh meteorological data in Large Eddy Simulations mode (WRF-LES-HRRR). WRF-LES-HRRR simulates winds in stochastic eddy-scale (100–1000 m) variability, which is particularly important for low-wind conditions and informing the error budget. The mIME can estimate emission rates of plumes of any size that are detectable by MethaneAIR. (2) The divergence integral (DI) method applies Gauss's theorem to estimate the flux divergence fields through a series of closed surfaces enclosing the sources. The set of boxes grows from the upwind side of the plume through the core of each plume and downwind. No selection of inflow concentration, as used in the mIME, is required. The DI approach can efficiently determine fluxes from large sources and clusters of sources but cannot resolve small point emissions. These methods account for the effects of eddy-scale variation in different ways: the DI averages across many eddies, whereas the mIME re-samples many eddies from the LES simulation. The DI directly uses HRRR winds, while mIME uses WRF-LES-HRRR wind products. Emissions estimates from both the mIME and DI methods<span id="page5772"/> agreed closely with the single-blind volume-controlled experiments (<span class="inline-formula"><i>N</i></span> <span class="inline-formula">=</span> 21). The York regression between the estimated emissions and the released emissions has a slope of 0.96 [0.84, 1.08], <span class="inline-formula"><i>R</i></span> <span class="inline-formula">=</span> 0.83 and <span class="inline-formula"><i>N</i></span> <span class="inline-formula">=</span> 21, with 30 % mean percentage error for the whole dataset, which indicates that MethaneAIR can quantify point sources emitting more than 200 kg h<span class="inline-formula"><sup>−1</sup></span> for the mIME and 500 kg h<span class="inline-formula"><sup>−1</sup></span> for the DI method. The two methods also agreed on methane emission estimates from various uncontrolled sources in the Permian Basin. The experiment thus demonstrates the powerful potential of the MethaneAIR instrument and suggests that the quantification method should be transferable to MethaneSAT if it meets the design specifications.</p>
<p>The Earth Cloud, Aerosol and Radiation Explorer (EarthCARE) is a combination of multiple active and passive instruments on a single platform. The Atmospheric Lidar (ATLID) provides vertical information of clouds and aerosol particles along the satellite track. In addition, the Multi-Spectral Imager (MSI) collects multi-spectral information from the visible to the infrared wavelengths over a swath width of 150 km across the track. The ATLID–MSI Column Products processor (AM-COL) described in this paper combines the high vertical resolution of the lidar along track and the horizontal resolution of the imager across track to better characterize a three-dimensional scene. ATLID Level 2a (L2a) data from the ATLID Layer Products processor (A-LAY), MSI L2a data from the MSI Cloud Products processor (M-CLD) and the MSI Aerosol Optical Thickness processor (M-AOT), and MSI Level 1c (L1c) data are used as input to produce the synergistic columnar products: the ATLID–MSI Cloud Top Height (AM-CTH) and the ATLID–MSI Aerosol Column Descriptor (AM-ACD). The coupling of ATLID (measuring at 355 nm) and MSI (at <span class="inline-formula">≥670</span> nm) provides multi-spectral observations of the aerosol properties. In particular, the Ångström exponent from the spectral aerosol optical thickness (AOT 355/670 nm) adds valuable information for aerosol typing. The AOT across track, the Ångström exponent and the dominant aerosol type are stored in the AM-ACD product. The accurate detection of the cloud top height (CTH) with lidar is limited to the ATLID track. The difference in the CTH detected by ATLID and retrieved by MSI is calculated along track. The similarity of MSI pixels across track with those along track is used to transfer the calculated CTH difference to the entire MSI swath. In this way, the accuracy of the CTH is increased to achieve the EarthCARE mission's goal of deriving the radiative flux at the top of the atmosphere with an accuracy of 10 W m<span class="inline-formula"><sup>−2</sup></span> for a 100 km<span class="inline-formula"><sup>2</sup></span> snapshot view of the atmosphere. The synergistic CTH difference is stored in the AM-CTH product. The quality status is provided with the products. It depends, e.g., on day/night conditions and the presence of multiple cloud layers. The algorithm was successfully tested using the common EarthCARE test scenes. Two definitions of the CTH from the model truth cloud extinction fields are compared: an extinction-based threshold of 20 Mm<span class="inline-formula"><sup>−1</sup></span> provides the geometric CTH, and a cloud optical thickness threshold of 0.25 describes the radiative CTH. The first CTH definition was detected with ATLID and the second one with MSI. The geometric CTH is always higher than or equal to the radiative CTH.</p>
The consequence of human activity in the field of construction is an increase in the density of buildings. As a result, areas that were previously considered risky from the point of view of the quality of soil conditions or increased saturation of the soil stratum with underground communications are allocated for development. All these factors are of direct importance when it comes to the use of loess soils as a basis for the design, erection and operation of new construction facilities. Loess soils cover about 80% of the territory of Ukraine. These soils have a negative feature - the ability to reduce their mechanical properties when in contact with water and give additional collapse deformations. Therefore, a significant part of the buildings is erected in such soil conditions. That's why, the foundation structures of these buildings and structures must be designed taking into account the possibility of uneven deformations. For this reason, the relevance of taking into account the joint work of the "collapsible base - foundation - above-ground structures" system does not decrease, but even increases. Loess soils in a dry state have good physical and mechanical characteristics due to structural bonds. However, with increasing humidity, the soil porosity undergoes a sharp change, the compressive strength decreases rapidly, structural bonds are destroyed and collapse deformations occur. The search for a reliable and economical option for foundation structures is an urgent issue in the design of buildings and structures at the modern level. This is especially relevant in the conditions of construction on soils capable of collapsing with possible water saturation. The work presents a variant design of the foundations of the building. At the same time, the impact of possible water saturation of the loess soils of the base on the stress-strain state of the foundations was considered. Different schemes of possible soaking of loess soils were considered. Different sizes and locations of water saturation zones within the building plan were considered. An analysis of the results of the numerical simulation of the joint work of the elements of the "base - foundation - above-ground structures" system was performed. The choice of the most reliable foundation option is substantiated. It has been confirmed that the size and location of loess soil water saturation zones influence the redistribution of stresses in foundation structures. It is shown that the use of variable design of foundations allows choosing an economical and reliable foundation option, if we consider different options for their parameters and take into account the negative factors of the soil conditions of the construction site and emergency situations that may occur during the operation of the building.
Jackson Trager, Alireza S. Ziabari, Elnaz Rahmati
et al.
Moral framing and sentiment can affect a variety of online and offline behaviors, including donation, environmental action, political engagement, and protest. Various computational methods in Natural Language Processing (NLP) have been used to detect moral sentiment from textual data, but achieving strong performance in such subjective tasks requires large, hand-annotated datasets. Previous corpora annotated for moral sentiment have proven valuable, and have generated new insights both within NLP and across the social sciences, but have been limited to Twitter. To facilitate improving our understanding of the role of moral rhetoric, we present the Moral Foundations Reddit Corpus, a collection of 16,123 English Reddit comments that have been curated from 12 distinct subreddits, hand-annotated by at least three trained annotators for 8 categories of moral sentiment (i.e., Care, Proportionality, Equality, Purity, Authority, Loyalty, Thin Morality, Implicit/Explicit Morality) based on the updated Moral Foundations Theory (MFT) framework. We evaluate baselines using large language models (Llama3-8B, Ministral-8B) in zero-shot, few-shot, and PEFT (Parameter-Efficient Fine-Tuning) settings, comparing their performance to fine-tuned encoder-only models like BERT (Bidirectional Encoder Representations from Transformers). The results show that LLMs continue to lag behind fine-tuned encoders on this subjective task, underscoring the ongoing need for human-annotated moral corpora for AI alignment evaluation. Keywords: moral sentiment annotation, moral values, moral foundations theory, multi-label text classification, large language models, benchmark dataset, evaluation and alignment resource
<p>The cube root of the energy dissipation rate (EDR), as a
standard reporting metric of atmospheric turbulence, is estimated using 1 Hz
quick access recorder (QAR) data from Korean-based national air carriers
with two different types of aircraft (Boeing 737 (B737) and Boeing 777 (B777)), archived
for 12 months from January to December 2012. The EDRs are estimated using
three wind components (zonal, meridional, and derived vertical wind) and the
derived equivalent vertical gust (DEVG) of the 1 Hz post-flight data by
applying all possible EDR methods. Wind components are used to calculate
three different EDRs, utilizing the second-order structure function, power
spectral density, and von Kármán wind spectrum and maximum-likelihood method. In addition, two DEVG-based EDRs are calculated using the
lognormal mapping technique and the predefined parabolic relationship
between the observed EDR and DEVG. When the reliability of lower-rate (1 Hz)
data to estimate the EDR is examined using the higher-rate (20 Hz) wind data
obtained from a tall tower observatory, it is found that the 1 Hz EDR can be
underestimated (2.19 %–12.56 %) or overestimated (9.32 %–10.91 %). In this
study, it is also found that the structure-function-based EDR shows lower
uncertainty (2.19 %–8.14 %) than the energy spectrum-based EDRs
(9.32 %–12.56 %) when the 1 Hz datasets are used. The observed EDR estimates
using 1 Hz QAR data are examined in three strong turbulence cases that are
relevant to clear-air turbulence (CAT), mountain wave turbulence (MWT), and
convectively induced turbulence (CIT). The observed EDR estimates derived
from three different wind components show different characteristics
depending on potential sources of atmospheric turbulence at cruising
altitudes, indicating good agreement with selected strong turbulence cases
with respect to turbulence intensity and incident time. Zonal wind-based
EDRs are stronger in the CAT case that is affected by synoptic-scale forcing
such as upper-level jet/frontal system. In the CIT case, vertical wind-based
EDRs are stronger, which is related to convectively induced gravity waves
outside the cloud boundary. The MWT case has a peak of the EDR based on both
the zonal and vertical winds, which can be related to the propagation of
mountain waves and their subsequent breaking. It is also found that the CAT
and MWT cases occurred by synoptic-scale forcing have longer variations in
the observed EDRs before and after the turbulence incident, while the CIT
case triggered by a mesoscale convective cell has an isolated peak of the
EDR. Current results suggest that the 1 Hz aircraft data can be an
additional source of the EDR estimations contributing to expand more EDR
information at the cruising altitudes in the world and that these data can
be helpful to provide a better climatology of aviation turbulence and a
situational awareness of cruising aircraft.</p>