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Meteorological fields calculated by numerical weather prediction (NWP) models drive offline chemical transport models (CTMs) to solve the transport, chemical reactions, and atmospheric interaction over the geographical domain of interest. HARMONIE (HIRLAM ALADIN Research on Mesoscale Operational NWP in Euromed) is a state-of-the-art non-hydrostatic NWP community model used at several European weather agencies to forecast weather at the local and/or regional scale. In this work, the HARMONIE WINS50 (cycle 43 cy43) reanalysis dataset at a resolution of 0.025° × 0.025° covering an area surrounding the North Sea for the years 2019–2021 was coupled offline to the LOTOS-EUROS (LOng-Term Ozone Simulation-EURopean Operational Smog model, v2.2.002) CTM. The impact of using either meteorological fields from HARMONIE or from ECMWF on LOTOS-EUROS simulations of NO2 has been evaluated against ground-level observations and TROPOMI tropospheric NO2 vertical columns. Furthermore, the difference between crucial meteorological input parameters such as the boundary layer height and the vertical diffusion coefficient between the hydrostatic ECMWF and non-hydrostatic HARMONIE data has been studied, and the vertical profiles of temperature, humidity, and wind are evaluated against meteorological observations at Cabauw in The Netherlands. The results of these first evaluations of the LOTOS-EUROS model performance in both configurations are used to investigate current uncertainties in air quality forecasting in relation to driving meteorological parameters and to assess the potential for improvements in forecasting pollution episodes at high resolutions based on the HARMONIE NWP model.

Statistical methods, particularly machine learning models, have gained significant popularity in air quality predictions. These prediction models are commonly trained using the historical measurement datasets independently collected at the environmental monitoring stations and their operational forecasts in advance using inputs of the real-time ambient pollutant observations. Therefore, these high-quality machine learning models only provide site-available predictions and cannot solely be used as the operational forecast. In contrast, deterministic chemical transport models (CTMs), which simulate the full life cycles of air pollutants, provide predictions that are continuous in the 3D field. Despite their benefits, CTM predictions are typically biased, particularly on a fine scale, owing to the complex error sources due to the emission, transport, and removal of pollutants. In this study, we proposed a fusion of site-available machine learning prediction, which is from our regional feature selection-based machine learning model (RFSML v1.0), and a CTM prediction. Compared to the normal pure machine learning model, the fusion system provides a gridded prediction with relatively high accuracy. The prediction fusion was conducted using the Bayesian-theory-based ensemble Kalman filter (EnKF). Background error covariance was an essential part in the assimilation process. Ensemble CTM predictions driven by the perturbed emission inventories were initially used for representing their spatial covariance statistics, which could resolve the main part of the CTM error. In addition, a covariance inflation algorithm was designed to amplify the ensemble perturbations to account for other model errors next to the uncertainty in emission inputs. Model evaluation tests were conducted based on independent measurements. Our EnKF-based prediction fusion presented superior performance compared to the pure CTM. Moreover, covariance inflation further enhanced the fused prediction, particularly in cases of severe underestimation.

Satellite-based aerosol optical depth (AOD) has gained popularity as a powerful data source for calibrating aerosol models and correcting model errors through data assimilation. However, simulated airborne particle mass concentrations are not directly comparable to satellite-based AODs. For this, an AOD operator needs to be developed that can convert the simulated mass concentrations into model AODs. The AOD operator is most sensitive to the input of the particle size and chemical composition of aerosols. Furthermore, assumptions regarding particle size vary significantly amongst model AOD operators. More importantly, satellite retrieval algorithms rely on different size assumptions. Consequently, the differences between the simulations and observations do not always reflect the actual difference in aerosol amount. In this study, the sensitivity of the AOD operator to aerosol properties has been explored. We conclude that, to avoid inconsistencies between the AOD operator and retrieved properties, a common understanding of the particle size is required. Accordingly, we designed a hybrid assimilation methodology (hybrid AOD assimilation) that includes two sequentially conducted procedures. First, aerosol size in the model operator has been brought closer to the assumption of the satellite retrieval algorithm via assimilation of Ångström exponents. This ensures that the model AOD operator is more consistent with the AOD retrieval. The second step in the methodology concerns optimization of aerosol mass concentrations through direct assimilation of AOD (standard AOD assimilation). The hybrid assimilation method is tested over the European domain using Moderate Resolution Imaging Spectroradiometer (MODIS) Deep Blue products. The corrections made to the model aerosol size information are validated through a comparison with the ground-based Aerosol Robotic Network (AERONET) optical product. The increments in surface aerosol mass concentration that occur due to either the standard AOD assimilation analysis or the hybrid AOD assimilation analysis are evaluated against independent ground PM2.5 observations. The standard analysis always results in relatively accurate posterior AOD distributions; however, the corrections are hardly transferred into better aerosol mass concentrations due to the uncertainty in the AOD operator. In contrast, the model AOD and mass concentration states are considerably more accurate when using the hybrid methodology.

We present a novel high-resolution inverse modelling system (“FLEXVAR”) based on FLEXPART-COSMO back trajectories driven by COSMO meteorological fields at 7 km×7 km resolution over the European COSMO-7 domain and the four-dimensional variational (4DVAR) data assimilation technique. FLEXVAR is coupled offline with the global inverse modelling system TM5-4DVAR to provide background mole fractions (“baselines”) consistent with the global observations assimilated in TM5-4DVAR. We have applied the FLEXVAR system for the inverse modelling of European CH4 emissions in 2018 using 24 stations with in situ measurements, complemented with data from five stations with discrete air sampling (and additional stations outside the European COSMO-7 domain used for the global TM5-4DVAR inversions). The sensitivity of the FLEXVAR inversions to different approaches to calculate the baselines, different parameterizations of the model representation error, different settings of the prior error covariance parameters, different prior inventories, and different observation data sets are investigated in detail. Furthermore, the FLEXVAR inversions are compared to inversions with the FLEXPART extended Kalman filter (“FLExKF”) system and with TM5-4DVAR inversions at 1∘×1∘ resolution over Europe. The three inverse modelling systems show overall good consistency of the major spatial patterns of the derived inversion increments and in general only relatively small differences in the derived annual total emissions of larger country regions. At the same time, the FLEXVAR inversions at 7 km×7 km resolution allow the observations to be better reproduced than the TM5-4DVAR simulations at 1∘×1∘. The three inverse models derive higher annual total CH4 emissions in 2018 for Germany, France, and BENELUX compared to the sum of anthropogenic emissions reported to UNFCCC and natural emissions estimated from the Global Carbon Project CH4 inventory, but the uncertainty ranges of top-down and bottom-up total emission estimates overlap for all three country regions. In contrast, the top-down estimates for the sum of emissions from the UK and Ireland agree relatively well with the total of anthropogenic and natural bottom-up inventories.

With the explosive growth of atmospheric data, machine learning models have achieved great success in air pollution forecasting because of their higher computational efficiency than the traditional chemical transport models. However, in previous studies, new prediction algorithms have only been tested at stations or in a small region; a large-scale air quality forecasting model remains lacking to date. Huge dimensionality also means that redundant input data may lead to increased complexity and therefore the over-fitting of machine learning models. Feature selection is a key topic in machine learning development, but it has not yet been explored in atmosphere-related applications. In this work, a regional feature selection-based machine learning (RFSML) system was developed, which is capable of predicting air quality in the short term with high accuracy at the national scale. Ensemble-Shapley additive global importance analysis is combined with the RFSML system to extract significant regional features and eliminate redundant variables at an affordable computational expense. The significance of the regional features is also explained physically. Compared with a standard machine learning system fed with relative features, the RFSML system driven by the selected key features results in superior interpretability, less training time, and more accurate predictions. This study also provides insights into the difference in interpretability among machine learning models (i.e., random forest, gradient boosting, and multi-layer perceptron models).

Atmospheric inversions are used to constrain emissions of trace gases using atmospheric mole-fraction measurements. The four-dimensional variational (4DVAR) inversion approach allows optimization of emissions at a higher temporal and spatial resolution than ensemble or analytical approaches but provides limited opportunities for scalable parallelization because it is an iterative optimization method. Multidecadal variational inversions are needed to optimally extract information from the long measurement records of long-lived atmospheric trace gases like carbon dioxide and methane. However, the wall time needed – up to months – complicates these multidecadal inversions. The physical parallelization (PP) method introduced by Chevallier (2013) addresses this problem for carbon dioxide inversions by splitting the period of the chemical transport model into blocks and running them in parallel. Here, we present a new implementation of the PP method which is suitable for methane inversions accounting for the chemical sink of methane. The performance of the PP method is tested in an 11-year inversion using a TM5-4DVAR inversion setup that assimilates surface observations to optimize methane emissions at grid scale. Our PP implementation improves the wall time performance by a factor of 5 and shows excellent agreement with a full serial inversion in an identical configuration (global mean emissions difference =0.06 % with an interannual variation correlation R=0.99; regional mean emission difference % and interannual variation R>0.94). The wall time improvement of the PP method increases with the size of the inversion period. The PP method is planned to be used in future releases of the Copernicus Atmosphere Monitoring Service (CAMS) multidecadal methane reanalysis.

Last spring, super dust storms reappeared in East Asia after being absent for one and a half decades. The event caused enormous losses in both Mongolia and China. Accurate simulation of such super sandstorms is valuable for the quantification of health damage, aviation risks, and profound impacts on the Earth system, but also to reveal the climatic driving force and the process of desertification. However, accurate simulation of dust life cycles is challenging, mainly due to imperfect knowledge of emissions. In this study, the emissions that lead to the 2021 spring dust storms are estimated through assimilation of MODIS AOD and ground-based PM10 concentration data simultaneously. With this, the dust concentrations during these super storms could be reproduced and validated with concentration observations. The multi-observation assimilation is also compared against emission inversion that assimilates AOD or PM10 concentration measurements alone, and the added values are analyzed. The emission inversion results reveal that wind-blown dust emissions originated from both China and Mongolia during spring 2021. Specifically, 19.9×106 and 37.5×106 t of particles were released in the Chinese and Mongolian Gobi, respectively, during these severe dust events. By source apportionment it was revealed that the Mongolian Gobi poses more severe threats to the densely populated regions of the Fenwei Plain (FWP) and the North China Plain (NCP) located in northern China than does the Chinese Gobi. It was estimated that 63 % of the dust deposited in FWP was due to transnational transport from Mongolia. For NCP, the long-distance transport dust from Mongolia contributes about 69 % to the dust deposition.

Atmospheric levels of ammonia (NH3) have substantially increased during the last century, posing a hazard to both human health and environmental quality. The atmospheric budget of NH3, however, is still highly uncertain due to an overall lack of observations. Satellite observations of atmospheric NH3 may help us in the current observational and knowledge gaps. Recent observations of the Cross-track Infrared Sounder (CrIS) provide us with daily, global distributions of NH3. In this study, the CrIS NH3 product is assimilated into the LOTOS-EUROS chemistry transport model using two different methods aimed at improving the modeled spatiotemporal NH3 distributions. In the first method NH3 surface concentrations from CrIS are used to fit spatially varying NH3 emission time factors to redistribute model input NH3 emissions over the year. The second method uses the CrIS NH3 profile to adjust the NH3 emissions using a local ensemble transform Kalman filter (LETKF) in a top-down approach. The two methods are tested separately and combined, focusing on a region in western Europe (Germany, Belgium and the Netherlands). In this region, the mean CrIS NH3 total columns were up to a factor 2 higher than the simulated NH3 columns between 2014 and 2018, which, after assimilating the CrIS NH3 columns using the LETKF algorithm, led to an increase in the total NH3 emissions of up to approximately 30 %. Our results illustrate that CrIS NH3 observations can be used successfully to estimate spatially variable NH3 time factors and improve NH3 emission distributions temporally, especially in spring (March to May). Moreover, the use of the CrIS-based NH3 time factors resulted in an improved comparison with the onset and duration of the NH3 spring peak observed at observation sites at hourly resolution in the Netherlands. Assimilation of the CrIS NH3 columns with the LETKF algorithm is mainly advantageous for improving the spatial concentration distribution of the modeled NH3 fields. Compared to in situ observations, a combination of both methods led to the most significant improvements in modeled monthly NH3 surface concentration and NH4+ wet deposition fields, illustrating the usefulness of the CrIS NH3 products to improve the temporal representativity of the model and better constrain the budget in agricultural areas.

When calibrating simulations of dust clouds, both the intensity and the position are important. Intensity errors arise mainly from uncertain emission and sedimentation strengths, while position errors are attributed either to imperfect emission timing or to uncertainties in the transport. Though many studies have been conducted on the calibration or correction of dust simulations, most of these focus on intensity solely and leave the position errors mainly unchanged. In this paper, a grid-distorted data assimilation, which consists of an image-morphing method and an ensemble-based variational assimilation, is designed for realigning a simulated dust plume to correct the position error. This newly developed grid-distorted data assimilation has been applied to a dust storm event in May 2017 over East Asia. Results have been compared for three configurations: a traditional assimilation configuration that focuses solely on intensity correction, a grid-distorted data assimilation that focuses on position correction only and the hybrid assimilation that combines these two. For the evaluated case, the position misfit in the simulations is shown to be dominant in the results. The traditional emission inversion only slightly improves the dust simulation, while the grid-distorted data assimilation effectively improves the dust simulation and forecasting. The hybrid assimilation that corrects both position and intensity of the dust load provides the best initial condition for forecasting of dust concentrations.

This study explores the potential of a new perspective on research into the impact of higher education on students' civic engagement. We propose shifting from viewing engagement as the key dependent variable to two "fundamental constituents": political interest and agency. Both constituents have been presented as either static or determined entirely by factors external to education, such as maturation, but also as dynamic and affected by various aspects of the educational experience in higher education. Furthermore, as analyses of these effects based on sample means do not account sufficiently for the intersectionality of background variables that define the student experience, we propose that data are explored through cluster analysis. Employing this type of analysis, a case study conducted at a small international liberal arts college in the Netherlands showed four distinctly different patterns in the development of both constituents of civic engagement. Based on further data obtained from the same sample, we offer suggestions for specific foci in further research about the impact of higher education on the development of civic engagement.

The evaluation of chemical transport models, CTMs, is essential for the assessment of their performance regarding the physical and chemical parameterizations used. While regional CTMs have been widely used and evaluated over Europe, their validation over Greece is limited. In this study, we investigate the performance of the Long Term Ozone Simulation European Operational Smog (LOTOS-EUROS) v2.2.001 regional chemical transport model in simulating nitrogen dioxide, NO2, over Greece from June to December 2018. In situ NO2 measurements obtained from 14 stations of the National Air Pollution Monitoring Network are compared with surface simulations over the two major cities of Greece, Athens and Thessaloniki. Overall the LOTOS-EUROS NO2 surface simulations compare very well to the in situ measurements showing a mild underestimation of the measurements with a mean relative bias of ∼-10 %, a high spatial correlation coefficient of 0.86 and an average temporal correlation of 0.52. The CTM underestimates the NO2 surface concentrations during daytime by ∼-50 ± 15 %, while it slightly overestimates during night-time ∼ 10 ± 35 %. Furthermore, the LOTOS-EUROS tropospheric NO2 columns are evaluated against ground-based multi-axis differential optical absorption spectroscopy (MAX-DOAS) NO2 measurements in Athens and Thessaloniki. We report that the CTM tropospheric NO2 column simulations over both urban and rural locations represent the diurnal patterns and hourly levels for both summer and winter seasons satisfactorily. The relative biases range between ∼ −2 % and −35 %, depending on season and relative NO2 load observed. Finally, the CTM was assessed also against space-borne Sentinel-5 Precursor (S5P) carrying the Tropospheric Monitoring Instrument (TROPOMI) tropospheric NO2 observations. We conclude that LOTOS-EUROS simulates extremely well the tropospheric NO2 patterns over the region with very high spatial correlation of 0.82 on average, ranging between 0.66 and 0.95, with negative biases in the summer and positive in the winter. Updated emissions for the simulations and model improvements when extreme values of boundary layer height are encountered are further suggested.

The unprecedented order, in modern peaceful times, for a near-total lockdown of the Greek population as a means of protection against severe acute respiratory syndrome coronavirus 2, commonly known as COVID-19, has generated unintentional positive side-effects with respect to the country's air quality levels. Sentinel-5 Precursor/Tropospheric Monitoring Instrument (S5P/TROPOMI) monthly mean tropospheric nitrogen dioxide (NO2) observations show an average change of −34 % to +20 % and −39 % to −5 % with an average decrease of −15 % and −11 % for March and April 2020 respectively, compared with the previous year, over the six larger Greek metropolitan areas; this is mostly attributable to vehicular emission reductions. For the capital city of Athens, weekly analysis was statistically possible for the S5P/TROPOMI observations and revealed a marked decline in the NO2 load of between −8 % and −43 % for 7 of the 8 weeks studied; this is in agreement with the equivalent Ozone Monitoring Instrument (OMI)/Aura observations as well as the ground-based estimates of a multi-axis differential optical absorption spectroscopy ground-based instrument. Chemical transport modelling of the NO2 columns, provided by the Long Term Ozone Simulation European Operational Smog (LOTOS-EUROS) chemical transport model, shows that the magnitude of these reductions cannot solely be attributed to the difference in meteorological factors affecting NO2 levels during March and April 2020 and the equivalent time periods of the previous year. Taking this factor into account, the resulting decline was estimated to range between ∼ −25 % and −65 % for 5 of the 8 weeks studied, with the remaining 3 weeks showing a positive average of ∼ 10 %; this positive average was postulated to be due to the uncertainty of the methodology, which is based on differences. As a result this analysis, we conclude that the effect of the COVID-19 lockdown and the restriction of transport emissions over Greece is ∼ −10 %. As transport is the second largest sector (after industry) affecting Greece's air quality, this occasion may well help policymakers to enforce more targeted measures to aid Greece in further reducing emissions according to international air quality standards.

Emission inversion using data assimilation fundamentally relies on having the correct assumptions about the emission background error covariance. A perfect covariance accounts for the uncertainty based on prior knowledge and is able to explain differences between model simulations and observations. In practice, emission uncertainties are constructed empirically; hence, a partially unrepresentative covariance is unavoidable. Concerning its complex parameterization, dust emissions are a typical example where the uncertainty could be induced from many underlying inputs, e.g., information on soil composition and moisture, land cover and erosive wind velocity, and these can hardly be taken into account together. This paper describes how an adjoint model can be used to detect errors in the emission uncertainty assumptions. This adjoint-based sensitivity method could serve as a supplement of a data assimilation inverse modeling system to trace back the error sources in case large observation-minus-simulation residues remain after assimilation based on empirical background covariance. The method follows an application of a data assimilation emission inversion for an extreme severe dust storm over East Asia (Jin et al., 2019b). The assimilation system successfully resolved observation-minus-simulation errors using satellite AOD observations in most of the dust-affected regions. However, a large underestimation of dust in Northeast China remained despite the fact that the assimilated measurements indicated severe dust plumes there. An adjoint implementation of our dust simulation model is then used to detect the most likely source region for these unresolved dust loads. The backward modeling points to the Horqin desert as the source region, which was indicated as a non-source region by the existing emission scheme. The reference emission and uncertainty are then reconstructed over the Horqin desert by assuming higher surface erodibility. After the emission reconstruction, the emission inversion is performed again, and the posterior dust simulations and reality are now in much closer harmony. Based on our results, it is advised that emission sources in dust transport models include the Horqin desert as a more active source region.

Ammonia emissions into the atmosphere have increased substantially in Europe since 1960, primarily due to the intensification of agriculture, as illustrated by enhanced livestock and the use of fertilizers. These associated emissions of reactive nitrogen, particulate matter, and acid deposition have contributed to negative societal impacts on human health and terrestrial ecosystems. Due to the limited availability of reliable measurements, emission inventories are used to assess large-scale ammonia emissions from agriculture by creating gridded annual emission maps and emission time profiles globally and regionally. The modeled emissions are subsequently utilized in chemistry transport models to obtain ammonia concentrations and depositions. However, current emission inventories usually have relatively low spatial resolutions and coarse categorizations that do not distinguish between fertilization on various crops, grazing, animal housing, and manure storage in its spatial allocation. Furthermore, in assessing the seasonal variation of ammonia emissions, they do not consider local climatology and agricultural management, which limits the capability to reproduce observed spatial and seasonal variations in the ammonia concentrations. This paper describes a novel ammonia emission model that quantifies agricultural emissions with improved spatial details and temporal dynamics in 2010 in Germany and Benelux. The spatial allocation was achieved by embedding the agricultural emission model Integrated Nitrogen Tool across Europe for Greenhouse gases and Ammonia Targeted to Operational Responses (INTEGRATOR) into the air pollution inventory Monitoring Atmospheric Composition and Climate-III (MACC-III), thus accounting for differentiation in ammonia emissions from manure and fertilizer application, grazing, animal houses and manure storage systems. The more detailed temporal distribution came from the integration of TIMELINES, which provided predictions of the timing of key agricultural operations, including the day of fertilization across Europe. The emission maps and time profiles were imported into LOTOS-EUROS to obtain surface concentrations and total columns for validation. The comparison of surface concentration between modeled output and in situ measurements illustrated that the updated model had been improved significantly with respect to the temporal variation of ammonia emission, and its performance was more stable and robust. The comparison of total columns between remote sensing observations and model simulations showed that some spatial characteristics were smoothened. Also, there was an overestimation in southern Germany and underestimation in northern Germany. The results suggested that updating ammonia emission fractions and accounting for manure transport are the direction for further improvement, and detailed land use is needed to increase the spatial resolution of spatial allocation in ammonia emission modeling.

Understanding and quantifying the global methane (CH4) budget is important for assessing realistic pathways to mitigate climate change. Atmospheric emissions and concentrations of CH4 continue to increase, making CH4 the second most important human-influenced greenhouse gas in terms of climate forcing, after carbon dioxide (CO2). The relative importance of CH4 compared to CO2 depends on its shorter atmospheric lifetime, stronger warming potential, and variations in atmospheric growth rate over the past decade, the causes of which are still debated. Two major challenges in reducing uncertainties in the atmospheric growth rate arise from the variety of geographically overlapping CH4 sources and from the destruction of CH4 by short-lived hydroxyl radicals (OH). To address these challenges, we have established a consortium of multidisciplinary scientists under the umbrella of the Global Carbon Project to synthesize and stimulate new research aimed at improving and regularly updating the global methane budget. Following Saunois et al. (2016), we present here the second version of the living review paper dedicated to the decadal methane budget, integrating results of top-down studies (atmospheric observations within an atmospheric inverse-modelling framework) and bottom-up estimates (including process-based models for estimating land surface emissions and atmospheric chemistry, inventories of anthropogenic emissions, and data-driven extrapolations). For the 2008–2017 decade, global methane emissions are estimated by atmospheric inversions (a top-down approach) to be 576 Tg CH4 yr−1 (range 550–594, corresponding to the minimum and maximum estimates of the model ensemble). Of this total, 359 Tg CH4 yr−1 or ∼ 60 % is attributed to anthropogenic sources, that is emissions caused by direct human activity (i.e. anthropogenic emissions; range 336–376 Tg CH4 yr−1 or 50 %–65 %). The mean annual total emission for the new decade (2008–2017) is 29 Tg CH4 yr−1 larger than our estimate for the previous decade (2000–2009), and 24 Tg CH4 yr−1 larger than the one reported in the previous budget for 2003–2012 (Saunois et al., 2016). Since 2012, global CH4 emissions have been tracking the warmest scenarios assessed by the Intergovernmental Panel on Climate Change. Bottom-up methods suggest almost 30 % larger global emissions (737 Tg CH4 yr−1, range 594–881) than top-down inversion methods. Indeed, bottom-up estimates for natural sources such as natural wetlands, other inland water systems, and geological sources are higher than top-down estimates. The atmospheric constraints on the top-down budget suggest that at least some of these bottom-up emissions are overestimated. The latitudinal distribution of atmospheric observation-based emissions indicates a predominance of tropical emissions (∼ 65 % of the global budget, < 30∘ N) compared to mid-latitudes (∼ 30 %, 30–60∘ N) and high northern latitudes (∼ 4 %, 60–90∘ N). The most important source of uncertainty in the methane budget is attributable to natural emissions, especially those from wetlands and other inland waters. Some of our global source estimates are smaller than those in previously published budgets (Saunois et al., 2016; Kirschke et al., 2013). In particular wetland emissions are about 35 Tg CH4 yr−1 lower due to improved partition wetlands and other inland waters. Emissions from geological sources and wild animals are also found to be smaller by 7 Tg CH4 yr−1 by 8 Tg CH4 yr−1, respectively. However, the overall discrepancy between bottom-up and top-down estimates has been reduced by only 5 % compared to Saunois et al. (2016), due to a higher estimate of emissions from inland waters, highlighting the need for more detailed research on emissions factors. Priorities for improving the methane budget include (i) a global, high-resolution map of water-saturated soils and inundated areas emitting methane based on a robust classification of different types of emitting habitats; (ii) further development of process-based models for inland-water emissions; (iii) intensification of methane observations at local scales (e.g., FLUXNET-CH4 measurements) and urban-scale monitoring to constrain bottom-up land surface models, and at regional scales (surface networks and satellites) to constrain atmospheric inversions; (iv) improvements of transport models and the representation of photochemical sinks in top-down inversions; and (v) development of a 3D variational inversion system using isotopic and/or co-emitted species such as ethane to improve source partitioning. The data presented here can be downloaded from https://doi.org/10.18160/GCP-CH4-2019 (Saunois et al., 2020) and from the Global Carbon Project.

Multi-axis differential optical absorption spectroscopy (MAX-DOAS) tropospheric NO2 column retrievals from four European measurement stations are compared to simulations from five regional air quality models which contribute to the European regional ensemble forecasts and reanalyses of the operational Copernicus Atmosphere Monitoring Service (CAMS). Compared to other observational data usually applied for regional model evaluation, MAX-DOAS data are closer to the regional model data in terms of horizontal and vertical resolution, and multiple measurements are available during daylight, so that, for example, diurnal cycles of trace gases can be investigated. In general, there is good agreement between simulated and retrieved NO2 column values for individual MAX-DOAS measurements with correlations between 35 % and 70 % for individual models and 45 % to 75 % for the ensemble median for tropospheric NO2 vertical column densities (VCDs), indicating that emissions, transport and tropospheric chemistry of NOx are on average well simulated. However, large differences are found for individual pollution plumes observed by MAX-DOAS. Most of the models overestimate seasonal cycles for the majority of MAX-DOAS sites investigated. At the urban stations, weekly cycles are reproduced well, but the decrease towards the weekend is underestimated and diurnal cycles are overall not well represented. In particular, simulated morning rush hour peaks are not confirmed by MAX-DOAS retrievals, and models fail to reproduce observed changes in diurnal cycles for weekdays versus weekends. The results of this study show that future model development needs to concentrate on improving representation of diurnal cycles and associated temporal scalings.

We present an observing simulated system experiment (OSSE) dedicated to evaluate the potential added value from the Sentinel-4 and the Sentinel-5P observations on tropospheric ozone composition. For this purpose, the ozone data of Sentinel-4 (Ultraviolet Visible Near-infrared) and Sentinel-5P (TROPOspheric Monitoring Instrument) on board a geostationary (GEO) and a low-Earth-orbit (LEO) platform, respectively, have been simulated using the DISAMAR inversion package for the summer 2003. To ensure the robustness of the results, the OSSE has been configured with conservative assumptions. We simulate the reality by combining two chemistry transport models (CTMs): the LOng Term Ozone Simulation – EURopean Operational Smog (LOTOS-EUROS) and the Transport Model version 5 (TM5). The assimilation system is based on a different CTM, the MOdèle de Chimie Atmosphérique à Grande Echelle (MOCAGE), combined with the 3-D variational technique. The background error covariance matrix does not evolve in time and its variance is proportional to the field values. The simulated data are formed of six eigenvectors to minimize the size of the dataset by removing the noise-dominated part of the observations. The results show that the satellite data clearly bring direct added value around 200 hPa for the whole assimilation period and for the whole European domain, while a likely indirect added value is identified but not for the whole period and domain at 500 hPa, and to a lower extent at 700 hPa. In addition, the ozone added value from Sentinel-5P (LEO) appears close to that from Sentinel-4 (GEO) in the free troposphere (200–500 hPa) in our OSSE. The outcome of our study is a result of the OSSE design and the choice within each of the components of the system.

Tropospheric O3 remains a major air-quality issue in the Mediterranean region. The combination of large anthropogenic emissions of precursors, transboundary contributions, a warm and dry aestival climate, and topographical features results in severe cases of photochemical pollution. Chemical transport models (CTMs) are essential tools for studying O3 dynamics and for assessing mitigation measures, but they need to be evaluated specifically for each air basin. In this study, we present an optimisation of the LOTOS-EUROS CTM for the Madrid air basin. Five configurations using different meteorological datasets (from the European Centre for Medium-Range Weather Forecast, ECMWF; and the Weather Research and Forecasting Model, WRF), horizontal resolution and number of vertical levels were compared for July 2016. LOTOS-EUROS responded satisfactorily in the five configurations reproducing observations of surface O3 with notable correlation and reduced bias and errors. However, the best-fit simulations for surface O3 were obtained by increasing spatial resolution and using a large number of vertical levels to reproduce vertical transport phenomena and the formation of reservoir layers. Using the optimal configuration obtained in the evaluation, three characteristic events have been described: recirculation (REC) episodes and northern and southern advection (NAD and SAD, respectively) events. REC events were found to produce the highest O3 due to the reduced ventilation associated with low wind speeds and the contribution of reservoir layers formed by vertical transport of O3 formed near the surface in the previous days of the event. NAD events, usually associated with higher wind speeds, present the lowest ground-level O3 concentrations in the region. During SAD episodes, external contributions along with low wind speeds allow O3 to increase considerably but not as much as in REC events because steady southerly winds disperse local emissions and hinder the formation of reservoir layers.

We present an Observing System Simulation Experiment (OSSE) dedicated to the evaluation of the added value of the Sentinel-4 and Sentinel-5P missions for tropospheric nitrogen dioxide (NO2). Sentinel-4 is a geostationary (GEO) mission covering the European continent, providing observations with high temporal resolution (hourly). Sentinel-5P is a low Earth orbit (LEO) mission providing daily observations with a global coverage. The OSSE experiment has been carefully designed, with separate models for the simulation of observations and for the assimilation experiments and with conservative estimates of the total observation uncertainties. In the experiment we simulate Sentinel-4 and Sentinel-5P tropospheric NO2 columns and surface ozone concentrations at 7 by 7 km resolution over Europe for two 3-month summer and winter periods. The synthetic observations are based on a nature run (NR) from a chemistry transport model (MOCAGE) and error estimates using instrument characteristics. We assimilate the simulated observations into a chemistry transport model (LOTOS-EUROS) independent of the NR to evaluate their impact on modelled NO2 tropospheric columns and surface concentrations. The results are compared to an operational system where only ground-based ozone observations are ingested. Both instruments have an added value to analysed NO2 columns and surface values, reflected in decreased biases and improved correlations. The Sentinel-4 NO2 observations with hourly temporal resolution benefit modelled NO2 analyses throughout the entire day where the daily Sentinel-5P NO2 observations have a slightly lower impact that lasts up to 3–6 h after overpass. The evaluated benefits may be even higher in reality as the applied error estimates were shown to be higher than actual errors in the now operational Sentinel-5P NO2 products. We show that an accurate representation of the NO2 profile is crucial for the benefit of the column observations on surface values. The results support the need for having a combination of GEO and LEO missions for NO2 analyses in view of the complementary benefits of hourly temporal resolution (GEO, Sentinel-4) and global coverage (LEO, Sentinel-5P).

Data assimilation algorithms rely on a basic assumption of an unbiased observation error. However, the presence of inconsistent measurements with nontrivial biases or inseparable baselines is unavoidable in practice. Assimilation analysis might diverge from reality since the data assimilation itself cannot distinguish whether the differences between model simulations and observations are due to the biased observations or model deficiencies. Unfortunately, modeling of observation biases or baselines which show strong spatiotemporal variability is a challenging task. In this study, we report how data-driven machine learning can be used to perform observation bias correction for data assimilation through a real application, which is the dust emission inversion using PM10 observations. PM10 observations are considered unbiased; however, a bias correction is necessary if they are used as a proxy for dust during dust storms since they actually represent a sum of dust particles and non-dust aerosols. Two observation bias correction methods have been designed in order to use PM10 measurements as proxy for the dust storm loads under severe dust conditions. The first one is the conventional chemistry transport model (CTM) that simulates life cycles of non-dust aerosols. The other one is the machine-learning model that describes the relations between the regular PM10 and other air quality measurements. The latter is trained by learning using 2 years of historical samples. The machine-learning-based non-dust model is shown to be in better agreement with observations compared to the CTM. The dust emission inversion tests have been performed, through assimilating either the raw measurements or the bias-corrected dust observations using either the CTM or machine-learning model. The emission field, surface dust concentration, and forecast skill are evaluated. The worst case is when we directly assimilate the original observations. The forecasts driven by the a posteriori emission in this case even result in larger errors than the reference prediction. This shows the necessities of bias correction in data assimilation. The best results are obtained when using the machine-learning model for bias correction, with the existing measurements used more precisely and the resulting forecasts close to reality.

An operational multimodel forecasting system for air quality has been developed to provide air quality services for urban areas of China. The initial forecasting system included seven state-of-the-art computational models developed and executed in Europe and China (CHIMERE, IFS, EMEP MSC-W, WRF-Chem-MPIM, WRF-Chem-SMS, LOTOS-EUROS, and SILAMtest). Several other models joined the prediction system recently, but are not considered in the present analysis. In addition to the individual models, a simple multimodel ensemble was constructed by deriving statistical quantities such as the median and the mean of the predicted concentrations. The prediction system provides daily forecasts and observational data of surface ozone, nitrogen dioxides, and particulate matter for the 37 largest urban agglomerations in China (population higher than 3 million in 2010). These individual forecasts as well as the multimodel ensemble predictions for the next 72 h are displayed as hourly outputs on a publicly accessible web site (http://www.marcopolo-panda.eu, last access: 27 March 2019). In this paper, the performance of the prediction system (individual models and the multimodel ensemble) for the first operational year (April 2016 until June 2017) has been analyzed through statistical indicators using the surface observational data reported at Chinese national monitoring stations. This evaluation aims to investigate (a) the seasonal behavior, (b) the geographical distribution, and (c) diurnal variations of the ensemble and model skills. Statistical indicators show that the ensemble product usually provides the best performance compared to the individual model forecasts. The ensemble product is robust even if occasionally some individual model results are missing. Overall, and in spite of some discrepancies, the air quality forecasting system is well suited for the prediction of air pollution events and has the ability to provide warning alerts (binary prediction) of air pollution events if bias corrections are applied to improve the ozone predictions.

An operational multi-model forecasting system for air quality including nine different chemical transport models has been developed and provides daily forecasts of ozone, nitrogen oxides, and particulate matter for the 37 largest urban areas of China (population higher than 3 million in 2010). These individual forecasts as well as the mean and median concentrations for the next 3 days are displayed on a publicly accessible website (http://www.marcopolo-panda.eu, last access: 7 December 2018). The paper describes the forecasting system and shows some selected illustrative examples of air quality predictions. It presents an intercomparison of the different forecasts performed during a given period of time (1–15 March 2017) and highlights recurrent differences between the model output as well as systematic biases that appear in the median concentration values. Pathways to improve the forecasts by the multi-model system are suggested.

A Lagrangian particle dispersion model, the FLEXible PARTicle dispersion chemical transport model (FLEXPART CTM), is used to simulate global three-dimensional fields of trace gas abundance. These fields are constrained with surface observation data through nudging, a data assimilation method, which relaxes model fields to observed values. Such fields are of interest to a variety of applications, such as inverse modelling, satellite retrievals, radiative forcing models and estimating global growth rates of greenhouse gases. Here, we apply this method to methane using 6 million model particles filling the global model domain. For each particle, methane mass tendencies due to emissions (based on several inventories) and loss by reaction with OH, Cl and O(1D), as well as observation data nudging were calculated. Model particles were transported by mean, turbulent and convective transport driven by 1° × 1° ERA-Interim meteorology. Nudging is applied at 79 surface stations, which are mostly included in the World Data Centre for Greenhouse Gases (WDCGG) database or the Japan–Russia Siberian Tall Tower Inland Observation Network (JR-STATION) in Siberia. For simulations of 1 year (2013), we perform a sensitivity analysis to show how nudging settings affect modelled concentration fields. These are evaluated with a set of independent surface observations and with vertical profiles in North America from the National Oceanic and Atmospheric Administration (NOAA) Earth System Research Laboratory (ESRL), and in Siberia from the Airborne Extensive Regional Observations in SIBeria (YAK-AEROSIB) and the National Institute for Environmental Studies (NIES). FLEXPART CTM results are also compared to simulations from the global Eulerian chemistry Transport Model version 5 (TM5) based on optimized fluxes. Results show that nudging strongly improves modelled methane near the surface, not only at the nudging locations but also at independent stations. Mean bias at all surface locations could be reduced from over 20 to less than 5 ppb through nudging. Near the surface, FLEXPART CTM, including nudging, appears better able to capture methane molar mixing ratios than TM5 with optimized fluxes, based on a larger bias of over 13 ppb in TM5 simulations. The vertical profiles indicate that nudging affects model methane at high altitudes, yet leads to little improvement in the model results there. Averaged from 19 aircraft profile locations in North America and Siberia, root mean square error (RMSE) changes only from 16.3 to 15.7 ppb through nudging, while the mean absolute bias increases from 5.3 to 8.2 ppb. The performance for vertical profiles is thereby similar to TM5 simulations based on TM5 optimized fluxes where we found a bias of 5 ppb and RMSE of 15.9 ppb. With this rather simple model setup, we thus provide three-dimensional methane fields suitable for use as boundary conditions in regional inverse modelling as a priori information for satellite retrievals and for more accurate estimation of mean mixing ratios and growth rates. The method is also applicable to other long-lived trace gases.

We present a consistent intercomparison of the mean age of air (AoA) according to five modern reanalyses: the European Centre for Medium-Range Weather Forecasts Interim Reanalysis (ERA-Interim), the Japanese Meteorological Agency's Japanese 55-year Reanalysis (JRA-55), the National Centers for Environmental Prediction Climate Forecast System Reanalysis (CFSR) and the National Aeronautics and Space Administration's Modern Era Retrospective analysis for Research and Applications version 1 (MERRA) and version 2 (MERRA-2). The modeling tool is a kinematic transport model driven only by the surface pressure and wind fields. It is validated for ERA-I through a comparison with the AoA computed by another transport model.The five reanalyses deliver AoA which differs in the worst case by 1 year in the tropical lower stratosphere and more than 2 years in the upper stratosphere. At all latitudes and altitudes, MERRA-2 and MERRA provide the oldest values ( ∼ 5–6 years in midstratosphere at midlatitudes), while JRA-55 and CFSR provide the youngest values ( ∼ 4 years) and ERA-I delivers intermediate results. The spread of AoA at 50 hPa is as large as the spread obtained in a comparison of chemistry–climate models. The differences between tropical and midlatitude AoA are in better agreement except for MERRA-2. Compared with in situ observations, they indicate that the upwelling is too fast in the tropical lower stratosphere. The spread between the five simulations in the northern midlatitudes is as large as the observational uncertainties in a multidecadal time series of balloon observations, i.e., approximately 2 years. No global impact of the Pinatubo eruption can be found in our simulations of AoA, contrary to a recent study which used a diabatic transport model driven by ERA-I and JRA-55 winds and heating rates.The time variations are also analyzed through multiple linear regression analyses taking into account the seasonal cycles, the quasi-biennial oscillation and the linear trends over four time periods. The amplitudes of AoA seasonal variations in the lower stratosphere are significantly larger when using MERRA and MERRA-2 than with the other reanalyses. The linear trends of AoA using ERA-I confirm those found by earlier model studies, especially for the period 2002–2012, where the dipole structure of the latitude–height distribution (positive in the northern midstratosphere and negative in the southern midstratosphere) also matches trends derived from satellite observations of SF6. Yet the linear trends vary substantially depending on the considered period. Over 2002–2015, the ERA-I results still show a dipole structure with positive trends in the Northern Hemisphere reaching up to 0.3 yr dec−1. No reanalysis other than ERA-I finds any dipole structure of AoA trends. The signs of the trends depend strongly on the input reanalysis and on the considered period, with values above 10 hPa varying between approximately −0.4 and 0.4 yr dec−1. Using ERA-I and CFSR, the 2002–2015 trends are negative above 10 hPa, but using the three other reanalyses these trends are positive. Over the whole period (1989–2015) each reanalysis delivers opposite trends; i.e., AoA is mostly increasing with CFSR and ERA-I but mostly decreasing with MERRA, JRA-55 and MERRA-2.In view of this large disagreement, we urge great caution for studies aiming to assess AoA trends derived only from reanalysis winds. We briefly discuss some possible causes for the dependency of AoA on the input reanalysis and highlight the need for complementary intercomparisons using diabatic transport models.

Background: Deaf and hard-of-hearing (DHH) children may experience difficulties in word decoding development. Aims: We aimed to compare and predict the incremental word decoding development in first grade in Dutch DHH and hearing children, as a function of kindergarten reading precursors. Methods and procedures: In this study, 25 DHH, and 41 hearing children participated. Kindergarten measures were phonological awareness (PA), letter knowledge (LK), rapid naming (RAN), and verbal short-term memory (VSTM). Word decoding (WD) was assessed at three consecutive time points (WD1, 2, 3) during reading instruction in first grade. Outcomes and results: The hearing children scored higher than the DHH children on PA and VSTM only, although the distribution of WD scores differed between the groups. At WD1, PA and RAN predicted WD efficiency in both groups; but PA was a stronger predictor for hearing children. At WD2, LK, RAN, and the autoregressor were predictors for both groups. While at WD3, only the autoregressor was a significant predictor. Conclusions and implications: WD development in DHH children on average shows similar levels as in hearing children, though within the DHH group more variation was observed. WD development in DHH children is not as much driven by PA; they may use other skills to compensate.

To keep up with technological advances and macro-economic trends, higher education has increasingly focused on developing students' employability competences through mentoring programs. However, measuring the effectiveness of such mentoring programs has remained difficult, because many mentoring measurements are not validated or grounded in theory. Furthermore, existing questionnaires have mostly focused on one or two types of support, ignoring the wide variety of support types offered by a mentor. Therefore, the current study's aim was to develop and validate a new questionnaire measuring various types of mentoring support. Based on a systematic literature review, a 35-item questionnaire was developed and data were collected from mentoring programs at four higher education institutions. Data were analyzed through exploratory factor analysis (n = 225), confirmatory factor analysis (n = 208), and cross-validation (n = 101). The results support a 6-factor model (21 items) that is statistically valid and reliable for use in universities (of applied sciences). The model includes the following factors, referring to types of support and their features: trust and availability, emotional support, networking support, autonomy support, similarity, and empathy. This questionnaire makes an original contribution insofar as (1) it is based on a sound, theoretical framework, and (2) it was demonstrated to be valid and reliable across different sub-populations in higher education. The questionnaire provides educational practitioners with a sound and valid tool to evaluate the quality of their mentoring program. It can also be used to assess what types of support could be offered to a greater extent.

Background: Reading comprehension is an interactive process. Yet, instructional needs are usually identified with isolated componential tests. This study examined whether a dynamic approach, in which componential abilities are measured within the same text and global text comprehension is facilitated via feedback, can help in understanding variation in children's reading comprehension. Objectives: With a pretest-posttest control group design, componential abilities before and after feedback were related to growth in global text comprehension within the same text. Methods: At pretest, third to fifth graders read 30 short texts, each followed by one global text comprehension question. This was repeated at posttest, but additional questions were asked with feedback prior to each global text comprehension question. The vocabulary group received two vocabulary questions with feedback (n = 97). The vocabulary plus integration group received two vocabulary questions and one sentence-integration question with feedback (n = 98). The control group (n = 98) only answered the global text comprehension questions. Results and Conclusion: Participants in the experimental conditions who needed feedback (i.e., lower-skilled) experienced a decrease in global text comprehension, whereas this was not found for the control group and participants in the experimental groups who did not need feedback (i.e., higher-skilled). There was also less decrease among those lower-skilled participants who had profited from the feedback. Implications: It is concluded from explorative analyses that not feedback but the overall design caused the decrease. Conceptually, the dynamic approach is worth further research.

The paper presents the first modelling experiment of the European-scale olive pollen dispersion, analyses the quality of the predictions, and outlines the research needs. A 6-model strong ensemble of Copernicus Atmospheric Monitoring Service (CAMS) was run throughout the olive season of 2014, computing the olive pollen distribution. The simulations have been compared with observations in eight countries, which are members of the European Aeroallergen Network (EAN). Analysis was performed for individual models, the ensemble mean and median, and for a dynamically optimised combination of the ensemble members obtained via fusion of the model predictions with observations. The models, generally reproducing the olive season of 2014, showed noticeable deviations from both observations and each other. In particular, the season was reported to start too early by 8 days, but for some models the error mounted to almost 2 weeks. For the end of the season, the disagreement between the models and the observations varied from a nearly perfect match up to 2 weeks too late. A series of sensitivity studies carried out to understand the origin of the disagreements revealed the crucial role of ambient temperature and consistency of its representation by the meteorological models and heat-sum-based phenological model. In particular, a simple correction to the heat-sum threshold eliminated the shift of the start of the season but its validity in other years remains to be checked. The short-term features of the concentration time series were reproduced better, suggesting that the precipitation events and cold/warm spells, as well as the large-scale transport, were represented rather well. Ensemble averaging led to more robust results. The best skill scores were obtained with data fusion, which used the previous days' observations to identify the optimal weighting coefficients of the individual model forecasts. Such combinations were tested for the forecasting period up to 4 days and shown to remain nearly optimal throughout the whole period.

In this study, we investigate a strategy to accelerate the data assimilation (DA) algorithm. Based on evaluations of the computational time, the analysis step of the assimilation turns out to be the most expensive part. After a study of the characteristics of the ensemble ash state, we propose a mask-state algorithm which records the sparsity information of the full ensemble state matrix and transforms the full matrix into a relatively small one. This will reduce the computational cost in the analysis step. Experimental results show the mask-state algorithm significantly speeds up the analysis step. Subsequently, the total amount of computing time for volcanic ash DA is reduced to an acceptable level. The mask-state algorithm is generic and thus can be embedded in any ensemble-based DA framework. Moreover, ensemble-based DA with the mask-state algorithm is promising and flexible, because it implements exactly the standard DA without any approximation and it realizes the satisfying performance without any change in the full model.

We use the technique of Observing System Simulation Experiments (OSSEs) to quantify the impact of spaceborne carbon monoxide (CO) total column observations from the Sentinel-5 Precursor (S-5P) platform on tropospheric analyses and forecasts. We focus on Europe for the period of northern summer 2003, when there was a severe heat wave episode associated with extremely hot and dry weather conditions. We describe different elements of the OSSE: (i) the nature run (NR), i.e., the truth; (ii) the CO synthetic observations; (iii) the assimilation run (AR), where we assimilate the observations of interest; (iv) the control run (CR), in this study a free model run without assimilation; and (v) efforts to establish the fidelity of the OSSE results. Comparison of the results from AR and the CR, against the NR, shows that CO total column observations from S-5P provide a significant benefit (at the 99 % confidence level) at the surface, with the largest benefit occurring over land in regions far away from emission sources. Furthermore, the S-5P CO total column observations are able to capture phenomena such as the forest fires that occurred in Portugal during northern summer 2003. These results provide evidence of the benefit of S-5P observations for monitoring processes contributing to atmospheric pollution.

Using data assimilation (DA) to improve model forecast accuracy is a powerful approach that requires available observations. Infrared satellite measurements of volcanic ash mass loadings are often used as input observations for the assimilation scheme. However, because these primary satellite-retrieved data are often two-dimensional (2-D) and the ash plume is usually vertically located in a narrow band, directly assimilating the 2-D ash mass loadings in a three-dimensional (3-D) volcanic ash model (with an integral observational operator) can usually introduce large artificial/spurious vertical correlations.In this study, we look at an approach to avoid the artificial vertical correlations by not involving the integral operator. By integrating available data of ash mass loadings and cloud top heights, as well as data-based assumptions on thickness, we propose a satellite observational operator (SOO) that translates satellite-retrieved 2-D volcanic ash mass loadings to 3-D concentrations. The 3-D SOO makes the analysis step of assimilation comparable in the 3-D model space.Ensemble-based DA is used to assimilate the extracted measurements of ash concentrations. The results show that satellite DA with SOO can improve the estimate of volcanic ash state and the forecast. Comparison with both satellite-retrieved data and aircraft in situ measurements shows that the effective duration of the improved volcanic ash forecasts for the distal part of the Eyjafjallajökull volcano is about 6 h.

In this quasi-experimental study involving 23 fourth grade teachers, we investigated the effect of implementing teacher-child dynamic mathematics interviews to improve mathematics teaching behavior in the classroom. After a baseline period of 13 months, the teachers participated in a professional development program to support the use of dynamic mathematics interviews followed by a period of practice in mathematics interviewing to identify children's mathematics learning needs. To determine the effects of the teacher professional development program, pretest and posttest videos of mathematics interviews were compared. To analyse the effects of the intervention, mathematics teaching behavior, mathematics teaching self-efficacy and perceived mathematical knowledge for teaching were measured. Results showed not only the effect of the program on the quality of the dynamic mathematics interviews, but also the effects of the intervention on mathematics teaching behavior, mathematics teaching self-efficacy and mathematical knowledge for teaching.