Temporal variation of (7)Be concentrations in atmosphere for 8y from 2000 at Yamagata, Japan: solar influence on the (7)Be time series

Measurement and analysis of long-term variation of atmospheric 7Be activity concentrations in Dazaifu (western Japan)

Atmospheric 7Be activity concentration was continuously measured in Dazaifu (33°30'N, 130°30'E), western Japan, from 1999 to 2020, and its variation was analyzed. Aerosol samples were collected using quartz fiber filters. The filtered samples were punched into circles, pressed, and molded into a 2-mm-thick disk for accurate 7Be quantification. Daily 7Be data analysis, encompassing an analysis for 7765 days over 22 years, revealed a concentration range of not detected-18 mBq/m3, characterized by substantial monthly variation and smoothed annual variation. An average daily 7Be activity concentration of 5.0 ± 2.6mBq/m3 was considered to be representative at the ground-surface-level in 30-40°N. Results from a two-way Analysis of variance (ANOVA) indicated statistical significance in monthly and annual 7Be variabilities. The monthly variability of 7Be activity concentration was approximately four times greater than the annual variability. Frequency analysis revealed that the monthly variability comprised major 12-month and minor 6-month periodicities. The substantial decrease in 7Be activity concentration during summer, a primary driver of monthly variation, was also observed at other locations in Japan, attributed to a stable high-pressure system in the Pacific Ocean that stalled over Japan's southern seas, followed by the inflow of air masses containing low 7Be activity concentrations. The annual variation was primarily influenced by the 11-year solar activity cycle, which affects the intensity of cosmic rays that produce 7Be.

Variation analysis of atmospheric 7Be activity concentrations with respect to precipitation

Beryllium-7 activity concentrations in the atmosphere and precipitation were continuously measured every day between April 2011 and December 2015 in Dazaifu, western Japan. The measured data were quantitatively analyzed to determine the precipitation-induced variation in 7Be activity concentrations. The average concentrations on nonprecipitation and precipitation days were 5.5 and 3.8 mBq/m3, respectively. This difference of 31% (1.7 mBq/m3) on average, was attributable to the washout effect, which was more significant in the summer. Regarding the association between 7Be activity concentration and precipitation, the concentration remained at a similar level for the small precipitation amount of <5.0 mm/day and showed a decreasing trend (but was insignificant) for the precipitation of 5.0-10.0 mm/day. A significant decrease in the concentration was observed for ≥10 mm/day. Furthermore, when precipitation occurred on two successive days, the 7Be activity concentrations on the second day significantly decreased regardless of precipitation.

Analysis of Factors Contributing to the Increase in 7Be Activity Concentrations in the Atmosphere

In March 2013, increased ⁷Be activity concentrations in the atmosphere were observed for successive days in Dazaifu, western Japan. The daily ⁷Be activity concentration ranged from 0.93 to 14 mBq/m³, with a monthly average of 8.3 mBq/m³. This average was the highest among the monthly averages observed between 1999 and 2015, and higher than the monthly average over this period (4.7 mBq/m³) plus twice the standard deviation. Also, this exceeded the monthly average (6.0 mBq/m³) only for March 1999-2015 (excluding 2013, when the cosmic-ray intensity, a component producing ⁷Be, decreased). Based on the backward trajectory analysis etc. results, the inflow of air from the stratosphere and upper troposphere at high latitudes that frequently occurred in March 2013 was considered the reason for the ⁷Be activity concentration increase.

Online monitoring of lead-214 (214Pb) on atmospheric aerosols by low-resolution gamma-ray spectrometry

This paper provides a new approach that simplifies the monitoring of ²¹⁴Pb activity concentration on aerosols in the atmospheric surface layer. The approach allows obtaining data on ²¹⁴Pb activity concentration with the discreteness of 2 h. The experimental setup described in the paper made it possible to achieve a minimum detectable activity level of 0.4 Bq m^-3. Using this approach, the data on the diurnal variability of ²¹⁴Pb activity concentration in the atmosphere of Sevastopol city for a period of 18 months were obtained. The ²¹⁴Pb activity concentration varied from < 0.4 (less than 1% of the data series) to 8.9 Bq m^-3, mean value 2.0 ± 1.0 Bq m^-3. The analysis of the temporal variability of ²¹⁴Pb activity concentration on different time scales (diurnal, seasonal) was carried out. Annually averaged diurnal variation curve of ²¹⁴Pb activity concentration showed a peak at 6:00 local time and a minimum at 18:00. The maximum variability in the seasonal averaged diurnal cycle of ²¹⁴Pb activity concentration is observed in summer (± 30% of the daily average value) and the minimum in winter (± 13%). The maximum seasonal average value of ²¹⁴Pb activity concentration is observed in winter (2.5 Bq m^-3) and the minimum in summer (1.4 Bq m^-3). A quantitative estimate of the annual effective dose due to exposure to outdoor radon was obtained by using ²¹⁴Pb data, and it was 0.03 mSv a^-1.

Solar and meteorological influences on seasonal atmospheric 7Be in Europe for 1975 to 2018

Assessing the transport of natural radionuclides in the atmosphere provides a powerful tool to study air mass circulation. Here, we investigated the seasonal atmospheric distribution of the naturally produced ⁷Be in surface air over Europe between 40° N and 68° N during the period 1975-2018. The results suggest that the inter-annual variability of ⁷Be reflects production rates of the radionuclide induced by solar modulation of cosmic rays. Further analysis of the meteorological influences indicates that the meteorological influences on ⁷Be concentrations are geographically and seasonally dependent. We found that, in general, the tropopause pressure plays an important factor influencing ⁷Be activity for winter and spring seasons while the sea level pressure and temperature are more dominant during summer and autumn seasons. The combination of tropospheric production rates and meteorological parameters explains 24%-79% variances of the seasonal ⁷Be activity. We further applied a three-box model to study the influence of stratosphere-troposphere exchanges on ⁷Be concentrations. The simulation supports that the seasonal cycle of ⁷Be in Europe is controlled by two main factors: the changing height of the troposphere (seasonality of the tropopause height) and seasonal variations of the stratosphere-troposphere exchanges.

Meteorological Factors Controlling 7Be Activity Concentrations in the Atmospheric Surface Layer in Northern Spain

This work presents the analysis of weekly 7Be activity concentrations in the air measured in Bilbao (northern Spain) by collecting aerosols in filters over a ten years period (2009–2018). 7Be level is in the 0.35–7.3 mBq/m3 range, with a mean of 3.20 ± 1.12 mBq/m3. The trend, cycle, seasonal and monthly variability are evaluated using time series analysis techniques. The results indicate the impact of sunspots (24th solar cycle) on interannual 7Be activity concentrations, and a significant seasonal and monthly variation, with maximum concentrations occurring in spring-summer and minimum in the winter. The correlation of different 7Be ranges with local meteorological parameters, such as precipitation, temperature, relative humidity, and pressure, is also addressed, with precipitation having the greatest impact on 7Be activity values. The analysis of synoptic airflows, by calculating the back-trajectory clusters, and local winds at surface level reveals the important influence of the arrival of slow northwest Atlantic flows and the development of breezes on reaching high 7Be activity concentrations in this area.

Assessment of temporal variations of natural radionuclides Beryllium-7 and Lead-212 in surface air in Tanay, Philippines

Detection of radionuclides in surface air allows researchers to gain further insight on the behavior of radionuclides that may affect human radiation exposure especially in the event of a nuclear emergency. In this study, activity concentrations of naturally-occurring radionuclides Beryllium-7 (⁷Be) and Lead-212 (²¹²Pb) in surface air and meteorological data collected in Tanay, Philippines from January 2012 to December 2017 were evaluated to determine the impact of atmospheric conditions and processes to airborne radioactivity. Surface air concentrations of ⁷Be and ²¹²Pb were found to range from 0.00779 ± 0.00188 to 11.2 ± 0.116 mBq/m³ and from 1.371 ± 0.036 to 106.6 ± 1.075 mBq/m³, respectively. ⁷Be and ²¹²Pb show distinct annual trends, suggesting that atmospheric conditions affect both radionuclides differently and independently. ⁷Be shows two peak concentrations annually, with the first peak occurring between January to April and the second lower peak occurring between October and November. ²¹²Pb, on the other hand, shows annual peak concentrations occurring between April and June. Ambient temperature showed strong positive correlation with ²¹²Pb concentration in surface air and a weak negative correlation with ⁷Be; relative humidity and precipitation showed varying degrees of negative correlation with radionuclide concentrations in surface air. Source locations for the unusually high ²¹²Pb activity concentrations detected on 11-13 May 2013 and 19-31 May 2015 determined using WEB-GRAPE and HYSPLIT atmospheric transport models are presented as a case study. The data and findings of this study shall serve as basis for further studies on local and regional atmospheric transport and radiological impact assessment for the implementation of an effective nuclear and radiological emergency preparedness and response system in the country.

Analysis of trends, periodicities, and correlations in the beryllium-7 time series in Northern Europe

The activity concentrations of beryllium-7, a natural radiotracer that is considered as a tracer of the stratospheric-tropospheric exchange, shows a distinct behaviour in Northern Europe compared to the central and southern parts of the continent. In this study, we use the measurements collected at four sampling stations in Scandinavia (Ivalo, Umea, Kista, Risoe) between 2001 and 2010 and investigate their trends, periodicities and residuals with the aim to further understand the common features in the beryllium-7 data records in northern sampling sites. The beryllium-7 activity concentrations exhibit statistically significant positive trends that range from an average value of 1.50%/year to an average value of 2.96%/year. We detect a one-year periodicity in all the sites, and in the southernmost site, Risoe in Denmark, additional higher-frequency harmonics. In the residual time series, we find outliers that represent occurrences of extremely high beryllium-7 activity concentration. Cross-correlations of the beryllium-7 residuals across the four sites decrease with increasing distance; similarly, as indicated by local Hurst exponents the records exhibit long-range correlations that weaken towards the end of the investigated period. To investigate the causes of the detected trends, we also calculate correlations between beryllium-7 and factors related to its production, transport and removal from the atmosphere: in particular, cross-correlations of the beryllium-7 residuals with residuals in sunspot number, local temperature, atmospheric pressure and precipitation, as well as Arctic Oscillation index and North Atlantic Oscillation index. Most of the obtained correlations, however, are not statistically significant, highlighting the need to analyse a longer time period in order to evaluate the impact of different factors on the airborne beryllium-7 activity concentration.

7Be concentration in the near-surface layer of the air in Bialystok (north-eastern Poland) in the years 1992-2010

Weekly measurements of air ⁷Be concentrations (n = 769) were performed in the years 1992-2010 in Bialystok (north-eastern Poland) using gamma spectrometry. The arithmetic mean (AM) concentration of ⁷Be was 2.51 mBq m^-3, and the median (M) was 2.24 mBq m^-3 (range 0.47-7.81 mBq m^-3). The observed ⁷Be concentrations were within the range of levels recorded in Europe. Typical seasonal variability was observed. Concentrations of ⁷Be in the warm season (May, June, July) were almost twice as high as those in the cold season (November, December, January). A correlation was found between weekly ⁷Be concentrations and mean weekly values of relative humidity, temperature, and wind speed throughout the observation period. Pearson's correlation coefficients were -0.63, p < 0.001; 0.477, p < 0.001; -0.288, p < 0.001, respectively. The correlation coefficient between sunspot number and mean annual ⁷Be concentrations in the air in the years 1992-2010 was -0.609.

Influence of broadleaf forest vegetation on atmospheric deposition of airborne radionuclides

The activities of airborne radionuclides ⁷Be and unsupported ²¹⁰Pb (²¹⁰Pb_us) were measured in moss samples taken from 17 different locations. The objective was to estimate the influence of the broadleaf forest vegetation on atmospheric deposition of airborne radionuclides attached to aerosols. Two moss samples were collected at each location: within the forest stand (inside the area of the tree canopy projection) and within forest openings (outside the area of the tree canopy projection). Samples were taken in the spring season, before the leaves of trees came forth and in the autumn season, right before fall defoliation. A measurement indicates an absence of variation in ²¹⁰Pb_us concentration, however spring/autumn ratios of ⁷Be concentrations in mosses showed the expected seasonal difference in ⁷Be deposition. It was also noted that atmospheric deposition of ⁷Be at the forest openings was about two times higher than deposition in the forest. Using very simplified models, these measurements can be used to get estimation at how long ⁷Be and aerosols can reside on the leaves before precipitation eventually wash it to the ground mosses. It was estimated that the mean residence time of aerosols in the leaves was up to 50 days.

Influence of long-range atmospheric transport pathways and climate teleconnection patterns on the variability of surface 210Pb and 7Be concentrations in southwestern Europe

The variability of the atmospheric concentration of the ⁷Be and ²¹⁰Pb radionuclides is strongly linked to the origin of air masses, the strength of their sources and the processes of wet and dry deposition. It has been shown how these processes and their variability are strongly affected by climate change. Thus, a deeper knowledge of the relationship between the atmospheric radionuclides variability measured close to the ground and these atmospheric processes could help in the analysis of climate scenarios. In the present study, we analyze the atmospheric variability of a 14-year time series of ⁷Be and ²¹⁰Pb in a Mediterranean coastal city using a synergy of different indicators and tools such as: the local meteorological conditions, global and regional climate indexes and a lagrangian atmospheric transport model. We particularly focus on the relationships between the main pathways of air masses and sun spots occurrence, the variability of the local relative humidity and temperature conditions, and the main modes of regional climate variability, such as the North Atlantic Oscillation (NAO) and the Western Mediterranean Oscillation (WeMO). The variability of the observed atmospheric concentrations of both ⁷Be and ²¹⁰Pb radionuclides was found to be mainly positively associated to the local climate conditions of temperature and to the pathways of air masses arriving at the station. Measured radionuclide concentrations significantly increase when air masses travel at low tropospheric levels from central Europe and the western part of the Iberian Peninsula, while low concentrations are associated with westerly air masses. We found a significant negative correlation between the WeMO index and the atmospheric variability of both radionuclides and no significant association was observed for the NAO index.

The Fourier analysis applied to the relationship between (7)Be activity in the Serbian atmosphere and meteorological parameters

Air sample monitoring in Serbia, Belgrade started in the 1960s, while (7)Be activity in air and total (dry and wet) deposition has been monitored for the last 22 years by the Environment and Radiation Protection Department of the Institute for Nuclear Sciences, Vinca. Using this data collection, the changes of the (7)Be activity in the air and the total (wet and dry) deposition samples, as well as their correlation with meteorological parameters (temperature, pressure, cloudiness, sunshine duration, precipitation and humidity) that affect (7)Be concentration in the atmosphere, were mathematically described using the Fourier analysis. Fourier analysis confirmed the expected; the frequency with the largest intensity in the harmonic spectra of the (7)Be activity corresponds to a period of 1 year, the same as the largest intensity frequency in Fourier series of meteorological parameters. To analyze the quality of the results produced by the Fourier analysis, we compared the measured values of the parameters with the values calculated according to the Fourier series. Absolute deviations between measured and predicted mean monthly values are in range from 0.02 mBq/m(3) to 0.7 mBq/m(3) for (7)Be activity in air, and 0.01 Bq/m(2) and 0.6 Bq/m(2) for (7)Be activity in deposition samples. Relatively good agreement of measured and predicted results offers the possibility of prediction of the (7)Be activity.

Analytical Model for Estimating the Zenith Angle Dependence of Terrestrial Cosmic Ray Fluxes

A new model called "PHITS-based Analytical Radiation Model in the Atmosphere (PARMA) version 4.0" was developed to facilitate instantaneous estimation of not only omnidirectional but also angular differential energy spectra of cosmic ray fluxes anywhere in Earth's atmosphere at nearly any given time. It consists of its previous version, PARMA3.0, for calculating the omnidirectional fluxes and several mathematical functions proposed in this study for expressing their zenith-angle dependences. The numerical values of the parameters used in these functions were fitted to reproduce the results of the extensive air shower simulation performed by Particle and Heavy Ion Transport code System (PHITS). The angular distributions of ground-level muons at large zenith angles were specially determined by introducing an optional function developed on the basis of experimental data. The accuracy of PARMA4.0 was closely verified using multiple sets of experimental data obtained under various global conditions. This extension enlarges the model's applicability to more areas of research, including design of cosmic-ray detectors, muon radiography, soil moisture monitoring, and cosmic-ray shielding calculation. PARMA4.0 is available freely and is easy to use, as implemented in the open-access EXcel-based Program for Calculating Atmospheric Cosmic-ray Spectrum (EXPACS).

Beryllium-7 and (210)Pb atmospheric deposition measured in moss and dependence on cumulative precipitation

This paper focuses on analysis of the time series of (7)Be and (210)Pb activity measured in moss, and the amount, as well as duration of precipitation, to gain a better understanding of the possible relationships between airborne radionuclide deposition and precipitation. Here we consider whether the amount of these airborne radionuclides in moss samples is a cumulative measure of radionuclide deposition and decay, and a new approach for analyses of the relationships between precipitation and moss activity concentrations is suggested. Through these analyses it was shown that comparison of cumulative activity measured at one location using moss, normalized by values of cumulative amount or duration of precipitation, showed different regimes of airborne radionuclide deposition.

Analytical Model for Estimating Terrestrial Cosmic Ray Fluxes Nearly Anytime and Anywhere in the World: Extension of PARMA/EXPACS

By extending our previously established model, here we present a new model called "PHITS-based Analytical Radiation Model in the Atmosphere (PARMA) version 3.0," which can instantaneously estimate terrestrial cosmic ray fluxes of neutrons, protons, ions with charge up to 28 (Ni), muons, electrons, positrons, and photons nearly anytime and anywhere in the Earth's atmosphere. The model comprises numerous analytical functions with parameters whose numerical values were fitted to reproduce the results of the extensive air shower (EAS) simulation performed by Particle and Heavy Ion Transport code System (PHITS). The accuracy of the EAS simulation was well verified using various experimental data, while that of PARMA3.0 was confirmed by the high R2 values of the fit. The models to be used for estimating radiation doses due to cosmic ray exposure, cosmic ray induced ionization rates, and count rates of neutron monitors were validated by investigating their capability to reproduce those quantities measured under various conditions. PARMA3.0 is available freely and is easy to use, as implemented in an open-access software program EXcel-based Program for Calculating Atmospheric Cosmic ray Spectrum (EXPACS). Because of these features, the new version of PARMA/EXPACS can be an important tool in various research fields such as geosciences, cosmic ray physics, and radiation research.

A climatology of ⁷Be in surface air in European Union

This study presents a European-wide analysis of the spatial and temporal distribution of the cosmogenic isotope (7)Be in surface air. This is the first time that a long term database of 34 sampling sites that regularly provide data to the Radioactivity Environmental Monitoring (REM) network, managed by the Joint Research Centre (JRC) in Ispra, is used. While temporal coverage varies between stations, some of them have delivered data more or less continuously from 1984 to 2011. The station locations were considerably heterogeneous, both in terms of latitude and altitude, a range which should ensure a high degree of representativeness of the results. The mean values of (7)Be activity concentration presented a spatial distribution value ranging from 2.0 to 5.4 mBq/m(3) over the European Union. The results of the ANOVA analysis of all (7)Be data available indicated that its temporal and spatial distributions were mainly explained by the location and characteristic of the sampling sites rather than its temporal distribution (yearly, seasonal and monthly). Higher (7)Be concentrations were registered at the middle, compared to high-latitude, regions. However, there was no correlation with altitude, since all stations are sited within the atmospheric boundary layer. In addition, the total and yearly analyses of the data indicated a dynamic range of (7)Be activity for each solar cycle and phase (maximum or minimum), different impact on stations having been observed according to their location. Finally, the results indicated a significant seasonal and monthly variation for (7)Be activity concentration across the European Union, with maximum concentrations occurring in the summer and minimum in the winter, although with differences in the values reached. The knowledge of the horizontal and vertical distribution of this natural radionuclide in the atmosphere is a key parameter for modelling studies of atmospheric processes, which are important phenomena to be taken into account in the case of a nuclear accident.

Atmospheric deposition patterns of (210)Pb and (7)Be in Cienfuegos, Cuba

The radiometric composition of bulk deposition samples, collected monthly for one year, February 2010 until January 2011, at a site located in Cienfuegos (22° 03' N, 80° 29' W) (Cuba), are analysed in this paper. Measurement of (7)Be and (210)Pb activity concentrations were carried out in 12 bulk deposition samples. The atmospheric deposition fluxes of (7)Be and (210)Pb are in the range of 13.2-132 and 1.24-8.29 Bq m(-2), and their mean values are: 56.6 and 3.97 Bq m(-2), respectively. The time variations of the different radionuclide have been discussed in relation with meteorological factors and the mean values have been compared to those published in recent literature from other sites located at different latitudes. The annual average flux of (210)Pb and (7)Be were 47 and 700 Bq m(-2) y(-1), respectively. Observed seasonal variations of deposition data are explained in terms of different environmental features. The atmospheric deposition fluxes of (7)Be and (210)Pb were moderately well correlated with precipitation and well correlated with one another. The (210)Pb/(7)Be ratios in the monthly depositions samples varied in the range of 0.05-0.10 and showed a strong correlation with the number of rainy days.

Analysis of (7)Be behaviour in the air by using a multilayer perceptron neural network

A multilayer perceptron artificial neural network (ANN) model for the prediction of the (7)Be behaviour in the air as the function of meteorological parameters was developed. The model was optimized and tested using (7)Be activity concentrations obtained by standard gamma-ray spectrometric analysis of air samples collected in Belgrade (Serbia) during 2009-2011 and meteorological data for the same period. Good correlation (r = 0.91) between experimental values of (7)Be activity concentrations and those predicted by ANN was obtained. The good performance of the model in prediction of (7)Be activity concentrations could provide basis for construction of models which would forecast behaviour of other airborne radionuclides.

Time lag between the tropopause height and ⁷Be activity concentrations on surface air

A strong positive correlation between the seasonal changes of the tropopause height and the concentration of (7)Be in the surface air (R = 0.94, p < 0.0001) was observed at 40°N. Moreover, a strong positive correlation was revealed between the activity concentrations of (7)Be and the temperature T (°C) (R = 0.97, p < 0.001), confirming that the increased rate of vertical transport within the troposphere, especially during warmer months, has as a result the descent to the surface of air masses enriched in (7)Be. The results of the present work suggest that the temperature and the tropopause height are good indicators for transport time of air masses enriched in (7)Be to the surface. Higher values of temperature or tropopause height seem to result to shorter transport times. This is attributed to atmospheric convection which provides an effective mechanism for vertical transport of air masses. Increasing tropospheric temperature has generally as a result that convection penetrates more deeply which in turn leads to an increase in tropopause height. But, the atmospheric procedures do not occur immediately after the fluctuations of correlated factors. Thus, a time lag is expected between the tropopause height and (7)Be activity concentrations on surface air that might be from hours to days or weeks. The result suggests that (7)Be concentrations fully respond within three days after the changes in the tropopause height.

7Be in ground level air in Daejeon, Korea

(7)Be concentrations in the ground level air in Daejeon, Korea were determined during the period of January 1998 to December 2009 by gamma-ray spectrometric analysis of particulate samples collected on filter paper with a high-volume air sampler. The monthly concentrations of (7)Be in the ground level air were in the range of 1.3-7.7 mBq m(-3) with strong seasonal trends of low values in the summer and high values in the spring and autumn. The annual mean values of (7)Be concentrations showed weak reverse correlation with the annual average sunspot number.

Comparative trends and seasonal variation of ⁷Be, ²¹⁰Pb and ¹³⁷Cs at two altitude sites in the central part of France

The atmospheric concentrations of ¹³⁷Cs, ²¹⁰Pb, and ⁷Be were measured over a three-year period at two research stations located less than 12 km apart and at different altitudes (puy de Dôme, 1465 m a.s.l. and Opme, 660 m a.s.l., France). Seasonal trends in all radionuclides were observed at both stations, with high concentration measured during the summer and low concentrations during the winter. The ²¹⁰Pb concentrations at both stations were similar to each other. Higher concentrations of both ⁷Be and ¹³⁷Cs were measured at puy de Dôme than at Opme. These observations can be explained by the stratospheric and upper tropospheric sources of ⁷Be and the long-range transportation of ¹³⁷Cs at high altitudes. Air mass origins during sampling periods were classified into several groups by their route to the stations (marine, marine modified, continental and mediterranean). We observed that ⁷Be concentrations were constant regardless of the air mass origins, unlike ¹³⁷Cs and ²¹⁰Pb concentrations that increased when influenced by continental air masses. Higher ⁷Be concentrations were observed when air masses were arriving from the upper troposphere than from the boundary layer, the opposite was observed for ¹³⁷Cs. The temporal trend in concentrations of ⁷Be shows good agreement with previous modelling studies suggesting that there is a good understanding of its sources and the atmospheric vertical mixing of this radionuclide. The sources and mixing of ²¹⁰Pb, however, seem to be more complex than it appeared to be in previous modelling studies.