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This paper is motivated by the fact that, although temperature readings made by Vaisala RS41 radiosondes at GRUAN sites (https://www.gruan.org/, last access: 30 November 2020) are given at 1 s resolution, for various reasons, missing data are spread along the atmospheric profile. Such a problem is quite common with radiosonde data and other profile data. Hence, (linear) interpolation is often used to fill the gaps in published data products. From this perspective, the present paper considers interpolation uncertainty, using a statistical approach to understand the consequences of substituting missing data with interpolated data. In particular, a general framework for the computation of interpolation uncertainty based on a Gaussian process (GP) set-up is developed. Using the GP characteristics, a simple formula for computing the linear interpolation standard error is given. Moreover, the GP interpolation is proposed as it provides an alternative interpolation method with its standard error. For the Vaisala RS41, the two approaches are shown to provide similar interpolation performances using an extensive cross-validation approach based on the block-bootstrap technique. Statistical results about interpolation uncertainty at various GRUAN sites and for various missing gap lengths are provided. Since both approaches result in an underestimation of the interpolation uncertainty, a bootstrap-based correction formula is proposed. Using the root mean square error, it is found that, for short gaps, with an average length of 5 s, the average uncertainty is less than 0.10 K. For larger gaps, it increases up to 0.35 K for an average gap length of 30 s and up to 0.58 K for a gap of 60 s. It is concluded that this approach could be implemented in a future version of the GRUAN data processing.

During the first wave of the COVID-19 pandemics in 2020, lockdown policies reduced human mobility in many countries globally. This significantly reduces car traffic-related emissions. In this paper, we consider the impact of the Italian restrictions (lockdown) on the air quality in the Lombardy Region. In particular, we consider public data on concentrations of particulate matters (PM10 and PM2.5) and nitrogen dioxide, pre/during/after lockdown. To reduce the effect of confounders, we use detailed regression function based on meteorological, land and calendar information. Spatial and temporal correlations are handled using a multivariate spatiotemporal model in the class of hidden dynamic geostatistical models (HDGM). Due to the large size of the design matrix, variable selection is made using a hybrid approach coupling the well known LASSO algorithm with the cross-validation performance of HDGM. The impact of COVID-19 lockdown is heterogeneous in the region. Indeed, there is high statistical evidence of nitrogen dioxide concentration reductions in metropolitan areas and near trafficked roads where also PM10 concentration is reduced. However, rural, industrial, and mountain areas do not show significant reductions. Also, PM2.5 concentrations lack significant reductions irrespective of zone. The post-lockdown restart shows unclear results.

Functional spatio-temporal data naturally arise in many environmental and climate applications where data are collected in a three-dimensional space over time. The MATLAB D-STEM v1 software package was first introduced for modeling multivariate space-time data and has been recently extended to D-STEM v2 to handle functional data indexed across space and over time. This paper introduces the new modeling capabilities of DSTEM v2 as well as the complexity reduction techniques required when dealing with large data sets. Model estimation, validation and dynamic kriging are demonstrated in two case studies, one related to ground-level air quality data in Beijing, China, and the other one related to atmospheric profile data collected globally through radio sounding.

The RHARM (Radiosounding HARMonization) algorithm is the first to provide homogenized radiosonde-based records of temperature, relative humidity and wind profiles since 1978, alongside an estimatio...

Observational records are essential for assessing long-term changes in our climate. However, these records are more often than not influenced by residual non‐climatic factors which must be detected and adjusted prior to their usage. Ideally, measurement uncertainties should be properly quantified and validated. In the context of the Copernicus Climate Change Service (C3S), a novel approach, named RHARM (Radiosounding HARMonization), has been developed to provide a harmonized dataset of temperature, humidity and wind profiles along with an estimation of the measurement uncertainties for about 650 radiosounding stations globally. The RHARM method has been applied to IGRA daily (0000 and 1200 UTC) radiosonde data holdings on 16 standard pressure levels (from 1000 to 10 hPa) from 1978 to present. Relative humidity adjustment and data provision has been limited to 250 hPa owing to pervasive issues on sensors' performance in the upper troposphere and lower stratosphere. The applied adjustments are interpolated to all reported significant levels to retain information content contained within each individual ascent profile. Each historical station time series is harmonized using two distinct methods. Firstly, the most recent period of the records when modern radiosonde models have been in operation at each station (typically starting between 2004 and 2010 but varying on a station-by-station basis) are post-processed and adjusted using reference datasets from the GCOS Reference Upper Air Network (GRUAN) and from the 2010 WMO/CIMO (World Meteorological Organization/Commission for Instruments and Methods of Observation) radiosonde intercomparison. Subsequently, at each mandatory pressure level, the remaining historical data are scanned backward in time to detect structural breaks due to prolonged systematic effects in the measurements and then adjusted to homogenize the time series. This paper describes the dataset portion related to the adjustment of post-2004 measurements only. A step-by-step description of the algorithm is reported and comparisons with GRUAN and atmospheric reanalysis data for temperature and relative humidity data are discussed. The evaluation shows that the strongest benefit of RHARM compared to existing products is related to the substantive adjustments applied to relative humidity time series for values below 15 % and above 55 % as well as to the provision of the uncertainties for all variables. Uncertainties have been validated using the ECMWF reanalysis short-range forecast outputs. The RHARM algorithm is the first to provide homogenized time series of temperature, relative humidity and wind profiles alongside an estimation of the observational uncertainty for each single observation at each pressure level. A subset of RHARM dataisavailable at https://doi.org/10.5281/zenodo.3973353 (Madonnaet al., 2020a)

Most urban areas of the Po basin in the North of Italy are persistently affected by poor air quality and difficulty in disposing of airborne pollutants. In this context, the municipality of Milan started a multi-year progressive policy based on an extended limited traffic zone (Area B). Starting on 25 February 2019, the first phase partially restricted the circulation of some classes of highly polluting vehicles on the territory, in particular, Euro 0 petrol vehicles and Euro 0 to 3 diesel vehicles, excluding public transport. This is the early-stage of a long term policy that will restrict access to an increasing number of vehicles. The goal of this paper is to evaluate the early-stage impact of this policy on two specific vehicle-generated pollutants: total nitrogen oxides (NO x ) and nitrogen dioxide (NO 2 ), which are gathered by Lombardy Regional Agency for Environmental Protection (ARPA Lombardia). We use a statistical model for time series intervention analysis based on unobservable components. We use data from 2014 to 2018 for pre-policy model selection and the relatively short period up to September 2019 for early-stage policy assessment. We include weather conditions, socio-economic factors, and a counter-factual, given by the concentration of the same pollutant in other important neighbouring cities. Although the average concentrations reduced after the policy introduction, this paper argues that this could be due to other factors. Considering that the short time window may be not long enough for social adaptation to the new rules, our model does not provide statistical evidence of a positive policy effect for NO x and NO 2 . Instead, in one of the most central monitoring stations, a significant negative impact is found.

In this study, a spatiotemporal land use regression (LUR) model using distributed space-time expectation maximization (D-STEM) software was developed. We trained the model using daily mean ambient particulate matter ≤2.5 μm (PM2.5) data measured hourly in 2015 at 30 regulatory monitoring network stations within the megacity of Tehran, Iran. Since a substantial amount of measured data were missing (48% of the total number of daily PM2.5 observations), we used the D-STEM to impute missing data and compared the missing imputation performance between different fitted models and the mean substitution method. We used h-block cross-validation (h-block CV) method in order to account for spatial autocorrelation in the model building and validation. In the imputation of missing data, the D-STEM LUR model had a mean absolute percentage error (MAPE) of 25.3%, outperforming the mean substitution method, which resulted in MAPE of 28.3%. The spatiotemporal R-squared was 0.73 and the average CV R-squared of 2-block and 5-block cross-validations was 0.60. These values were 0.68 and 0.47 when the spatial aspect of the LUR model was assessed, and 0.995 and 0.992 when the temporal aspect of the LUR model was assessed. This study demonstrated the competence of D-STEM software in spatiotemporal modeling, missing data imputation, and mapping of daily ambient PM2.5 at a very high spatial resolution (20 m × 20 m). These estimations are available for future research, especially for epidemiological studies on short- and/or long-term health effects of ambient PM2.5. Generally, we found D-STEM as a promising tool for spatiotemporal LUR modeling of ambient air pollution, especially for those models that rely on regulatory network monitoring stations with a considerable amount of missing data.

Observing systems consisting of a finite number of in situ monitoring stations can provide high-quality measurements with the ability to quality assure both the instruments and the data but offer limited information over larger geographic areas. This paper quantifies the spatial coverage represented by a finite set of monitoring stations by using global data—data that are possibly of lower resolution and quality. For illustration purposes, merged satellite temperature data from Microwave Sounding Units are used to estimate the representativeness of the Global Climate Observing System Reference Upper-Air Network (GRUAN). While many metrics exist for evaluating the representativeness of a site, the ability to have highly accurate monthly averaged data is essential for both trend detection and climatology evaluation. The calculated correlations of the monthly averaged upper-troposphere satellite-derived temperatures over the GRUAN stations with all other pixels around the globe show that the current 9 certified GRUAN stations have moderate correlations (r ≥ 0.7) for approximately 10% of the earth, but an expanded network incorporating another 15 stations would result in moderate correlations for just over 60% of the earth. This analysis indicates that the value of additional stations can be quantified by using historical, satellite, or model data and can be used to reveal critical gaps in current monitoring capabilities. Evaluating the value of potential additional stations and prioritizing their initiation can optimize networks. The expansion of networks can be evaluated in a manner that allows for optimal benefit on the basis of optimization theory and economic analyses.

Francesco Finazzi and Alessandro Fassò use location data collected by an earthquake‐monitoring app to gauge compliance with lockdown measures in Italy, Francesco Finazzi and Alessandro Fassò use location data collected by an earthquake‐monitoring app to gauge compliance with lockdown measures in Italy.

Visualizing both conditional and marginal associations in contingency tables by using simple diagrams is discussed

In this paper, motivated by a multiple profile monitoring problem, we introduce general functional exponentially weighted moving average (EWMA) control charts. When functional data to be monitored are smooth enough to be representable by a finite dimensional basis, a particular version of these functional EWMAs is shown to be a multivariate EWMA applied to basis coefficients. Hence, it is called f-EWMA for monitoring single profiles and f-MEWMA for multiple profiles. The use of f-MEWMA is illustrated in connection to health monitoring of a steam sterilizer during its life cycle. Indeed, each sterilization run gives several profiles related to machine health, and degradation of the steam sterilizer during its life cycle modifies profile curvature in an unpredictable way. Hence, a control chart capable to monitor multiple sterilization profiles during the sterilizer life cycle is needed. The f-EWMA thresholds or control limits have been computed using Monte Carlo simulations. Moreover, the f-EWMA performance has been assessed using experimental data generated in laboratory according to anomalies considered relevant to the sterilizer maintenance program. Consequently, the average run length for these anomalies has been computed applying Monte Carlo simulation to experimental results. Copyright © 2016 John Wiley & Sons, Ltd.

Measurement uncertainty of atmospheric profiles obtained by radiosoundings is crucial in climate change studies. This paper shows how the understanding of geographic gaps of radiosonde networks calls for a functional approach able to handle spatio-temporal profile data, and related complexity issues are addressed.

Multivariate spatio-temporal statistical models are deserving for increasing attention for environmental data in general and for air quality data in particular because they can reveal dependencies and spatio-temporal dynamics across multiple variables and can be used to obtain dynamic concentration maps over specified areas. In this frame, we introduce a multivariate generalization of a known spatio-temporal model referred to as the hidden dynamic geostatistical model. Maximum likelihood parameter estimates are obtained implementing the expectation maximization algorithm and suitably extending the D-STEM software, recently introduced for alternative model specifications, allowing to handle multiple variables with heterogeneous spatial support, covariates, and missing data. A case study illustrates some of the statistical issues typical of a medium complexity problem related to air quality data modeling. Considering air quality and meteorological data over the Apulia region, Italy, the usual approach using meteorological variables as regressors is not possible because these data are observed on different monitoring networks, and preliminary spatial interpolation to co-locate the data is to be avoided. Hence, an eight-variate model is considered for understanding the relations between daily concentrations of particulate matters (PM10) and nitrogen dioxides (NO2) and six non co-located meteorological variables. Model interpretation is given, and its use for dynamic map construction, uncertainty included, is illustrated. Moreover, some preliminary evidence of the model capability to detect a Saharan dust event is presented. Copyright © 2015 John Wiley & Sons, Ltd.

We review the origin and the meaning of the term seismomatics. In doing, this historical and recent seismicity of Chile is discussed. Moreover, the papers appearing in the special issue on seismomatics are briefly reviewed.

In this paper, we estimate the distribution of population by exposure to multiple airborne pollutants, taking into account the spatio-temporal variability of daily air quality and the high-resolution spatial spread of human population around Europe. In particular, we consider monitoring network data for five pollutants, namely carbon monoxide, nitrogen dioxide, ozone, coarse and fine particulate matters. The spatial information contained in the large dataset of daily continental air quality is exploited using a multivariate spatio-temporal model capable to cover cross correlation among pollutants, covariates, and missing data as well as spatial and temporal variability and correlation. At the same time, the model is simple enough to be feasible for the large dataset of daily continental air quality over three years. Maximum likelihood estimation is performed using the EM algorithm, and kriging-like spatial estimates are used to compute high-resolution exposure distribution. Moreover, a novel semi-parametric bootstrap technique is used to assess the exposure distribution uncertainty. In this way, we compare the daily population exposure of 33 European countries and three important metropolitan areas in years 2009–2011 using a single flexible model. Extensive tabulations and graphs are reported in the supplementary material.

In recent literature there has been a growing interest in the construction of covariance models for multivariate Gaussian random fields. However, effective estimation methods for these models are somehow unexplored. The maximum likelihood method has attractive features, but when we deal with large data sets this solution becomes impractical, so computationally efficient solutions have to be devised. In this paper we explore the use of the covariance tapering method for the estimation of multivariate covariance models. In particular, through a simulation study, we compare the use of simple separable tapers with more flexible multivariate tapers recently proposed in the literature and we discuss the asymptotic properties of the method under increasing domain asymptotics.

Satellite product validation is a key to ensure the delivery of quality products for climate and weather applications. To do this, a fundamental step is the comparison with other instruments, such as radiosonde. This is especially true for essential climate variables such as temperature and humidity. Thanks to a functional data representation, this paper uses a likelihood-based approach that exploits the measurement uncertainties in a natural way. In particular, the comparison of temperature and humidity radiosonde measurements collected within the network of the Universal Rawinsonde Observation Program (RAOB) and the corresponding atmospheric profiles derived from the infrared atmospheric sounding interferometer aboard MetOp-A and MetOp-B satellites is developed with the aim of understanding the vertical smoothing mismatch uncertainty. Moreover, conventional RAOB functional data representation is assessed by means of a comparison with radiosonde reference measurements given by the Global Climate Observing System (GCOS) Reference Upper-Air Network (GRUAN), which provides high-resolution fully traceable radio-sounding profiles. In this way, the uncertainty related to coarse vertical resolution, or sparseness, of the conventional RAOB is assessed. It has been found that the uncertainty of vertical smoothing mismatch averaged along the profile is 0.50 K for temperature and 0.16 g/kg for water-vapor mixing ratio. Moreover, the uncertainty related to RAOB sparseness, averaged along the profile, is 0.29 K for temperature and 0.13 g/kg for water-vapor mixing ratio.

The Earthquake Network research project implements a crowdsourced earthquake early warning system based on smartphones. Smartphones, which are made available by the global population, exploit the Internet connection to report a signal to a central server every time a vibration is detected by the on-board accelerometer sensor. This paper introduces a statistical approach for the detection of earthquakes from the data coming from the network of smartphones. The approach allows to handle a dynamic network in which the number of active nodes constantly changes and where nodes are heterogeneous in terms of sensor sensibility and transmission delay. Additionally, the approach allows to keep the probability of false alarm under control. The statistical approach is applied to the data collected by three subnetworks related to the cities of Santiago de Chile, Iquique (Chile) and Kathmandu (Nepal). The detection capabilities of the approach are discussed in terms of earthquake magnitude and detection delay. A simulation study is carried out in order to link the probability of detection and the detection delay to the behaviour of the network under an earthquake event.

During the conference of the Italian Statistical Society on ‘‘Advances in Latent Variables’’ held in Brescia, Italy, June 19–21, 2013, the working group on environmental statistics, named GRASPA (http://www.graspa.org), organized the special track on ‘‘Space and space-time models: methods and environmental applications’’. This scientific activity was intended to celebrate the new condition as a permanent group of the Italian statistical society and renew GRASPA’s long life, which dates back to 1989. The idea of a special issue on the track main theme arose considering not only the number and scientific quality of the track contributions, but also the general interest of the topic, which exceeds the conference coverage. The result, raising from both track attendance and space-time statistical scientific community, is an interesting blend of various topics, which amounts at fourteen papers covering various environmental problems. To a large extent climate problems are considered, including upper atmosphere monitoring, rain simulation, air and water temperature and sea currents. Moreover, applications considered water body ecology, seismology and radon emissions. From the methodological point of view, areas covered by the special issue are scalar and vector-valued stochastic processes with continuous index over space or over spacetime. Moreover, functional data, point processes and time series methods are taken into account. Latent variables enter in a natural way in many of these papers either as spatial or temporal components. This methodological key is loosely used in the rest of this editorial to briefly review the special issue contributions. As for spatial processes methods, the work by RuizMedina and Porcu (2014) puts the theoretical basis for understanding the equivalence of Gaussian measures that index multivariate Gaussian fields. Their work will open the lines for research in estimation of Gaussian fields through tapering techniques as well as for assessing the properties of estimators of spatial dependence under infill asymptotics. For binary spatial data, which are built on the basis of a truncated latent Gaussian model, Bevilacqua et al. (2014) explore the possibility of building Euclidean likelihoods, obtaining high computational benefits and ensuring a reasonable level of statistical efficiency. In the same framework of spatial data, Verdin et al. (2014) introduce a stochastic weather generator for the variables of minimum and maximum temperature, as well as precipitation occurrence. In particular, temperature variables are modeled in a vector autoregressive framework, conditional on precipitation occurrence, whilst this last arises via a probit model. Both temperature and occurrence are spatially correlated using spatial Gaussian processes. Fontanella et al. (2014) consider a generalized latent-spatialquantile regression (GLSQR) model for the understanding of indoor radon gas monitoring in central Italy. Vallejo et al. (2014) consider a method for image landscape classification based on the assumption that the vector of image bands is a spatial multivariate process. They build such classification using the divergence of a modified Mahalanobis distance, given by the codispersion matrix. Methods for space-time processes are faced with great detail in this issue. If spatial design represents a critical issue, the paper by Stehlik et al. (2014) gives a clear picture A. Fasso (&) University of Bergamo, Viale Marconi 5, 24044 Dalmine BG, Italy e-mail: alessandro.fasso@unibg.it

Atmospheric thermodynamic data are gathered by high technology remote instruments such as radiosondes, giving rise to profiles that are usually modelled as functions depending only on height. The radiosonde balloons, however, drift away in the atmosphere resulting in not necessarily vertical but three-dimensional trajectories. To model this kind of functional data, we introduce a “point based” formulation of an heteroskedastic functional regression model that includes a trivariate smooth function and results to be an extension of a previously introduced unidimensional model. Functional coefficients of both the conditional mean and variance are estimated by reformulating the model as a standard generalized additive model and subsequently as a mixed model. This reformulation leads to a double mixed model whose parameters are fitted by using an iterative algorithm that allows to adjust for heteroskedasticity. The proposed modelling approach is applied to describe collocation mismatch when we deal with couples of balloons launched at two different locations. In particular, we model collocation error of atmospheric pressure in terms of meteorological covariates and space and time mismatch. Results show that model fitting is improved once heteroskedasticity is taken into account.