An Adaptive Metropolis Algorithm Haario, Heikki; Saksman, Eero; Tamminen, Johanna
Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability,
04/2001, Volume:
7, Issue:
2
Journal Article
Peer reviewed
Open access
A proper choice of a proposal distribution for Markov chain Monte Carlo methods, for example for the Metropolis-Hastings algorithm, is well known to be a crucial factor for the convergence of the ...algorithm. In this paper we introduce an adaptive Metropolis (AM) algorithm, where the Gaussian proposal distribution is updated along the process using the full information cumulated so far. Due to the adaptive nature of the process, the AM algorithm is non-Markovian, but we establish here that it has the correct ergodic properties. We also include the results of our numerical tests, which indicate that the AM algorithm competes well with traditional Metropolis-Hastings algorithms, and demonstrate that the AM algorithm is easy to use in practical computation.
In this paper, we present the new multi-wavelength dataset of aerosol extinction profiles, which are retrieved from the averaged transmittance spectra by the Global Ozone Monitoring by Occultation of ...Stars instrument aboard the Envisat satellite.
In this paper, we present the MErged GRIdded Dataset of Ozone Profiles (MEGRIDOP) in the stratosphere with a resolved longitudinal structure, which is derived from data from six limb and occultation ...satellite instruments: GOMOS, SCIAMACHY and MIPAS on Envisat, OSIRIS on Odin, OMPS on Suomi-NPP, and MLS on Aura. The merged dataset was generated as a contribution to the European Space Agency Climate Change Initiative Ozone project (Ozone_cci). The period of this merged time series of ozone profiles is from late 2001 until the end of 2018.
To be able to meet global grand challenges (climate change; biodiversity loss; environmental pollution; scarcity of water, food and energy supplies; acidification; deforestation; chemicalization; ...pandemics), which all are closely interlinked with each other, we need comprehensive open data with proper metadata, along with open science. The large data sets from ground-based in situ observations, ground and satellite remote sensing, and multiscale modeling need to be utilized seamlessly. In this opinion paper, we demonstrate the power of the SMEAR (Station for Measuring Earth surface–Atmosphere Relations) concept via several examples, such as detection of new particle formation and the particles' subsequent growth, quantifying atmosphere–ecosystem feedback loops, and combining comprehensive observations with emergency science and services, as well as studying the effect of COVID-19 restrictions on different air quality and climate variables. The future needs and the potential of comprehensive observations of the environment are summarized.
The Dutch-Finnish Ozone Monitoring Instrument (OMI) on board NASA's Aura spacecraft provides estimates of erythemal (sunburning) ultraviolet (UV) dose rates and erythemal daily doses. These data were ...compared with ground-based measurements at 13 stations located throughout the Arctic and Scandinavia from 60 to 83° N. The study corroborates results from earlier work, but is based on a longer time series (8 versus 2 years) and considers additional data products, such as the erythemal dose rate at the time of the satellite overpass. Furthermore, systematic errors in satellite UV data resulting from inaccuracies in the surface albedo climatology used in the OMI UV algorithm are systematically assessed. At times when the surface albedo is correctly known, OMI data typically exceed ground-based measurements by 0-11 %. When the OMI albedo climatology exceeds the actual albedo, OMI data may be biased high by as much as 55 %. In turn, when the OMI albedo climatology is too low, OMI data can be biased low by up to 59 %. Such large negative biases may occur when reflections from snow and ice, which increase downwelling UV irradiance, are misinterpreted as reflections from clouds, which decrease the UV flux at the surface. Results suggest that a better OMI albedo climatology would greatly improve the accuracy of OMI UV data products even if year-to-year differences of the actual albedo cannot be accounted for. A pathway for improving the OMI albedo climatology is discussed. Results also demonstrate that ground-based measurements from the center of Greenland, where high, homogenous surface albedo is observed year round, are ideally suited to detect systematic problems or temporal drifts in estimates of surface UV irradiance from space.
The Ozone Monitoring Instrument (OMI) flies on NASA's Earth Observing System AURA satellite, launched in July 2004. OMI is an ultraviolet/visible (UV/VIS) nadir solar backscatter spectrometer, which ...provides nearly global coverage in one day, with a spatial resolution of 13 km/spl times/24 km. Trace gases measured include O/sub 3/, NO/sub 2/, SO/sub 2/, HCHO, BrO, and OClO. In addition OMI measures aerosol characteristics, cloud top heights and cloud coverage, and UV irradiance at the surface. OMI's unique capabilities for measuring important trace gases with daily global coverage and a small footprint will make a major contribution to our understanding of stratospheric and tropospheric chemistry and climate change along with Aura's other three instruments. OMI's high spatial resolution enables detection of air pollution at urban scales. Total Ozone Mapping Spectrometer and differential optical absorption spectroscopy heritage algorithms, as well as new ones developed by the international (Dutch, Finnish, and U.S.) OMI science team, are used to derive OMI's advanced backscatter data products. In addition to providing data for Aura's prime objectives, OMI will provide near-real-time data for operational agencies in Europe and the U.S. Examples of OMI's unique capabilities are presented in this paper.
We present the comparison of satellite-based OMI (Ozone Monitoring Instrument) NO2 products with ground-based observations in Helsinki. OMI NO2 total columns, available from NASA's standard product ...(SP) and KNMI DOMINO product, are compared with the measurements performed by the Pandora spectrometer in Helsinki in 2012. The relative difference between Pandora no. 21 and OMI SP total columns is 4 and -6% for clear-sky and all-sky conditions, respectively. DOMINO NO2 retrievals showed slightly lower total columns with median differences about -5 and -14% for clear-sky and all-sky conditions, respectively. Large differences often correspond to cloudy fall-winter days with solar zenith angles above 65°. Nevertheless, the differences remain within the retrieval uncertainties. The average difference values are likely the result of different factors partly canceling each other: the overestimation of the stratospheric columns causes a positive bias partly compensated by the limited spatial representativeness of the relatively coarse OMI pixel for sharp NO2 gradients. The comparison between Pandora and the new version (V3) of OMI NO2 retrievals shows a larger negative difference (about -30%) than the current version (V2.1) because the revised spectral fitting procedure reduces the overestimation of the stratospheric column. The weekly and seasonal cycles from OMI, Pandora and NO2 surface concentrations are also compared. Both satellite- and ground-based data show a similar weekly cycle, with lower NO2 levels during the weekend compared to the weekdays as a result of reduced emissions from traffic and industrial activities. The seasonal cycle also shows a similar behavior, even though the results are affected by the fact that most of the data are available during spring-summer because of cloud cover in other seasons. This is one of few works in which OMI NO2 retrievals are evaluated in a urban site at high latitudes (60°N). Despite the city of Helsinki having relatively small pollution sources, OMI retrievals have proved to be able to describe air quality features and variability similar to surface observations. This adds confidence in using satellite observations for air quality monitoring also at high latitudes.
We discuss uncertainty quantification for aerosol-type selection in satellite-based atmospheric aerosol retrieval. The retrieval procedure uses precalculated aerosol microphysical models stored in ...look-up tables (LUTs) and top-of-atmosphere (TOA) spectral reflectance measurements to solve the aerosol characteristics. The forward model approximations cause systematic differences between the modelled and observed reflectance. Acknowledging this model discrepancy as a source of uncertainty allows us to produce more realistic uncertainty estimates and assists the selection of the most appropriate LUTs for each individual retrieval.This paper focuses on the aerosol microphysical model selection and characterisation of uncertainty in the retrieved aerosol type and aerosol optical depth (AOD). The concept of model evidence is used as a tool for model comparison. The method is based on Bayesian inference approach, in which all uncertainties are described as a posterior probability distribution. When there is no single best-matching aerosol microphysical model, we use a statistical technique based on Bayesian model averaging to combine AOD posterior probability densities of the best-fitting models to obtain an averaged AOD estimate. We also determine the shared evidence of the best-matching models of a certain main aerosol type in order to quantify how plausible it is that it represents the underlying atmospheric aerosol conditions.The developed method is applied to Ozone Monitoring Instrument (OMI) measurements using a multiwavelength approach for retrieving the aerosol type and AOD estimate with uncertainty quantification for cloud-free over-land pixels. Several larger pixel set areas were studied in order to investigate the robustness of the developed method. We evaluated the retrieved AOD by comparison with ground-based measurements at example sites. We found that the uncertainty of AOD expressed by posterior probability distribution reflects the difficulty in model selection. The posterior probability distribution can provide a comprehensive characterisation of the uncertainty in this kind of problem for aerosol-type selection. As a result, the proposed method can account for the model error and also include the model selection uncertainty in the total uncertainty budget.
Atmospheric emissions from anthropogenic hotspots, i.e., cities, power plants and industrial facilities, can be determined from remote sensing images obtained from airborne and space-based imaging ...spectrometers. In this paper, we present a Python library for data-driven emission quantification (ddeq) that implements various computationally light methods such as the Gaussian plume inversion, cross-sectional flux method, integrated mass enhancement method and divergence method. The library provides a shared interface for data input and output and tools for pre- and post-processing of data. The shared interface makes it possible to easily compare and benchmark the different methods. The paper describes the theoretical basis of the different emission quantification methods and their implementation in the ddeq library. The application of the methods is demonstrated using Jupyter notebooks included in the library, for example, for NO2 images from the Sentinel-5P/TROPOMI satellite and for synthetic CO2 and NO2 images from the Copernicus CO2 Monitoring (CO2M) satellite constellation. The library can be easily extended for new datasets and methods, providing a powerful community tool for users and developers interested in emission monitoring using remote sensing images.
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