Using rainfall radar data to improve interpolated maps of dose rate in the
Netherlands
Paul H. Hiemstraa,∗, Edzer J. Pebesmab, Gerard B.M. Heuvelinkc, Chris J.W. Twenh¨ofeld
aUniversity of Utrecht, Department of Physical Geography, P.O. Box 80.115, 3508 TC Utrecht, The Netherlands
bUniversity of M¨unster, Institute for Geoinformatics, Weseler Straße 253, 48151 M¨unster, Germany
cEnvironmental Sciences Group, Wageningen University, P.O. Box 47, 6700 AA Wageningen, The Netherlands
dNational Institute for Public Health and the Environment (RIVM), Antonie van Leeuwenhoeklaan 9, 3721 MA Bilthoven, The Netherlands
Abstract
The radiation monitoring network in the Netherlands is designed to detect and track increased radiation levels, dose rate more specifically, in 10 minute intervals. The network consists of 153 monitoring stations. Washout of radon progeny by rainfall is the most important cause of natural variations in dose rate. The increase in dose rate at a given time is a function of the amount of progeny decaying, which in turn is a balance between deposition of progeny by rainfall and radioactive decay. The increase in progeny is closely related to average rainfall intensity over the last 2.5 hours. We included decay of progeny by usingweighted averaged rainfall intensity, where the weight decreases back in time. The decrease in weight is related to the half-life of radon progeny. In this paper we show for a rain storm on the 20th of July 2007 that weighted averaged rainfall intensity estimated from rainfall radar images, collected every 5 minutes, performs much better as a predictor of increases in dose rate than using the non-averaged rainfall intensity. In addition, we show through cross-validation that including weighted averaged rainfall intensity in an interpolated map using universal kriging (UK) does not necessarily lead to a more accurate map. This might be attributed to the high density of monitoring stations in comparison to the spatial extent of a typical rain event. Reducing the network density improved the accuracy of the map when universal kriging was used instead of ordinary kriging (no trend). Consequently, in a less dense network the positive influence of including a trend is likely to increase. Furthermore, we suspect that UK better reproduces the sharp boundaries present in rainfall maps, but that the lack of short-distance monitoring station pairs prevents cross-validation from revealing this effect.
Keywords: ordinary kriging, universal kriging, interpolation, dose rate, rainfall intensity, rainfall radar, trend, network density
1. Introduction
In case of releases of radioactive material into the atmo-sphere, a fast and accurate estimate of the spatial distribu-tion of radiadistribu-tion levels is needed to estimate health effects on the population. In the Netherlands, radiation levels are measured by 153 monitoring stations of the National Ra-dioactivity Monitoring network (NRM), see figure 1. The NRM provides point information on radiation level, dose rate more specifically, no data are available in between the stations. Interpolated maps provide estimated dose rate in between the monitoring stations and provide an estimate of the spatial distribution of dose rate. EUR 21595 EN (2005), Dubois et al. (2007) and Hiemstra et al. (2009) ex-plored the mapping of dose rate using geostatistics. Geo-statistical mapping, i.e. kriging, has an advantage over more simple interpolation methods in that it can take in
∗Corresponding author.
Email addresses: [email protected](Paul H. Hiemstra),
[email protected](Edzer J. Pebesma)
account trends and provides an estimate of the predicton error. Hiemstra et al. (2009) focused on the interpola-tion of dose rate in non-emergency, background situainterpola-tions, providing a first step towards an interpolation system suit-able for emergency situations. In addition, Hiemstra et al. (2009) suggested to use trend information in a universal kriging (UK) approach (Chil`es and Delfiner, 1999; Chris-tensen, 1996), using soil type to improve the interpolated map. Many other studies (Knotters et al., 1995; Bishop and McBratney, 2001; Bourennane and King, 2003; Lloyd, 2005; Yemefack et al., 2005; Hengl et al., 2007) showed that accounting for a trend can improve an interpolated map.
Rainfall intensity is a major factor determining the spa-tial distribution of dose rate on a short time scale (Smet-sers and Blaauboer, 1997b; Horng and Jiang, 2004). There-fore, we hypothesized that accounting for rainfall inten-sity as predictor would improve the accuracy of the in-terpolated maps of dose rate. Rainfall intensity influences dose rate because radon daughter products or progeny, pri-marily bismuth (214Bi) and lead (214Pb), are washed out
of clouds and the atmosphere and are deposited on the ground. Radioactive decay of the radon progeny increases dose rate at that location. The increase in dose rate at any given time is proportional to the amount of radon progeny that is decaying at that time. In turn, the amount of radon progeny is a balance between the deposition of progeny by rainfall and the radioactive decay of those progeny. We hypothesized that we could model this balance between deposition and decay by taking the weighted average over the history of rainfall intensity. Taking the average over the history of rainfall captured the deposition of radon progeny. In addition, letting the weight drop in time cap-tured the decay of already deposited radon progeny. The rate at which the weight dropped was related to the half-life of the radon progeny.
The goal of this study was to make interpolated maps of increase in dose rate based on NRM data and rainfall intensity estimated by rainfall radar. We defined the fol-lowing research questions:
1. How well does the weighted averaged rainfall inten-sity perform as a predictor for increase in dose rate in comparison to using non-averaged rainfall intensity, measured at an individual time step?
2. Can the relationship between rainfall intensity and increase in dose rate improve our interpolated map? 3. Is there a relationship between monitoring network density and the improvement mentioned in research question 2?
We fitted a linear model to a rain storm travelling over the Netherlands from southwest to northeast on the 20th of July 2007. We used the goodness of fit R2 as a mea-sure for how well both non-averaged and weighted rainfall intensity explained the variation in increase in dose rate. Consequently, we made maps of increase in dose rate with and without accounting for rainfall, using leave-one-out cross-validation and the mean kriging prediction variance. Furthermore, we reduced monitoring network density and repeated the cross-validation procedure.
2. Methods
In the study we used rainfall and dose rate data from the 20th of July 2007. On this day, a large rainstorm passed over the Netherlands and caused significant in-creases in dose rate.
2.1. Measuring dose rate
Dose rate in the Netherlands is measured at 153 loca-tions (figure 1) every 10 minutes by the NRM (Twenh¨ofel et al., 2005). Dose rate is commonly expressed in ambient dose equivalent rate, H∗(10) (ICRU, 1993), abbreviated in this study to dose rate. The unit used for dose rate in this study was nano Sievert per hour (nSv/h). De-position of radon daughter products by rainfall increases
the dose rate. Consequently, we were only interested in increase of dose rate, not in the absolute value. We deter-mined the increase in dose rate by subtracting the mean dose rate of each NRM station for the 20th of July from the 10-min dose rate data of that station. Note that the mean dose rate was calculate based on times without rain-fall. Using the increase in dose rate has the added advan-tage of eliminating variations between stations, for exam-ple caused by calibration differences or soil type (Smetsers and Blaauboer, 1996).
2.2. Estimating rainfall intensity
In this study rainfall intensity maps were estimated every five minutes using two C-band Doppler radars op-erated by the Royal Netherlands Meteorological Institute (KNMI) (figure 1). The radar emits radio waves and reg-isters reflectivity. Increased reflectivity indicates more wa-ter present in the air, and thus a higher rainfall intensity. The radar provides the spatial distribution of radar re-flectivity (Z, mm6m−3) for 2.5 km × 2.5 km grid cells.
Battan (1973) describes how the radar reflectivity can be converted to the rainfall intensity at the surface (Ru, mm h−1). Figure 2 shows the radar rainfall intensity maps for
the 20th of July 2007 from 8AM to 7PM in hourly time steps. From the rainfall intensity maps we derived the rainfall intensity at the monitoring stations of the NRM. The rainfall intensity at a particular NRM monitoring sta-tion was defined as the closest cell centre of the rainfall intensity map.
2.3. Weighted averaged rainfall intensity
Rainfall intensity was averaged over time using a weighted average where the weight was determined by the half-life of the deposited radon progeny. We calibrated an overall half-life to that part of the data that clearly shows the ef-fect of radon progeny, without disturbances. We used large scale bound constrained optimization (Zhu et al., 1997) to perform the calibration, which lead to an overall half-life of 25.8 minutes. Using weighted averaged rainfall inten-sity assumes that the deposition of radon progeny is only influenced by rainfall intensity and not by how long it has already rained. This assumption is supported by the work of Fujinami (1996).
The weighted averaged rainfall intensity (Rw) at time twas determined by:
Rw(t) = Pm i=0αiRu(ti) Pm i=0αi (1) wheretis the time for which we calculate the average, mis the number of timesteps of five minutes over which we averaged,Ruis rainfall intensity measured at an individual time step andαiis the weight atti=t−i∆t, where ∆tis the size of the timestep. We chosemequal to 30 because at αi=30the weight is very low. The weightαi is determined by: αi= exp −ln2 t1/2 i∆t (2)
wheret1/2is the overall half-life. Figure 3 shows maps
comparing Rw toRu at 5PM.
2.4. Relating dose rate to rainfall intensity
To determine how wellRw described increase in dose rate (H) compared to Ru, we investigated the temporal relationship between both Ru and Rw and H. For the temporal relationship we kept location constant and var-ied time. The temporal relationship was determined using linear regression. The assumption in linear regression is that the nobservations of increase in dose rate, H, at a certain location can be described by the following linear model (Christensen, 1996):
H =Xβ+e, E(e) = 0, Cov(e) =σ2I. (3) where X is then×2 design matrix where the i-th row equals (1, Ru(ti)) or (1, Rw(ti)), β = (β0, β1)0, are
un-known regression coefficients describing the temporal rela-tionship betweenH andRuor Rw, andeis the residual.
We used the R2 as a goodness of fit for the fitted re-gression coefficients: R2= 1− SSe SStot = 1− Pn i=1(Hi−Hˆi) 2 Pn i=1(Hi−H¯)2 (4) whereSSeis the residual sums of squares,SStot is the total sums of squares,Hi is the observed H, ˆHi is theH estimated by the linear regression and ¯H is the mean of H.
2.5. Mapping dose rate with- and without trend
We compared ordinary kriging (OK) to universal krig-ing (UK) (Chil`es and Delfiner, 1999; Christensen, 1996) to determine whether including a spatial trend improved the accuracy of the interpolated map. Note that in contrast to section 2.4, the trend is fitted in space and not in time. An important step in kriging is fitting the variogram model to the residuals. For UK these are residuals to a trend, for OK these are residuals to a spatially constant mean. The variogram model was automatically fitted to the residuals as described in Hiemstra et al. (2009). Based on the sam-ple variogram, calculated based on the residuals, we made an initial guess of the variogram parameters, nugget, sill and range. After that, we used iterative reweighted least squares, or Gauss-Newton fitting (Cressie, 1993), to fit the variogram model to the sample variogram. We fitted a sin-gle isotropic variogram model to the entire study area.
We used ordinary least squares (OLS) residuals (as-suming uncorrelated residuals) instead of generalized least squares (GLS) residuals to fit the variogram model. More information on using OLS residuals to find the variogram model is found in Kitanidis (1993). We used the gstat
package (Pebesma, 2004) in the statistical computing en-vironmentR(R Development Core Team, 2010) for all geo-statistical calculations.
2.6. Quantifying the accuracy of the map
We quantified the accuracy of the maps produced by OK and UK using three different measures. The first was the Root Mean Squared Error (RMSE) of the leave-one-out cross-validation residuals:
RM SE= v u u t 1 n n X i=1 ( ˆHcv,i−Hi)2 (5)
wherenis the number of observations, ˆHcv,iis the increase in dose rate estimated by cross-validation and Hi is the measured increase in dose rate. A smaller RMSE indicates a smaller error and thus a more accurate map. The second measure was the Mean Error (ME) and is defined as:
M E= 1 n n X i=1 ( ˆHcv,i−Hi) (6)
ME provides an indication for the systematic error or bias in the cross-validation residuals. The third measure is the Mean Kriging Variance (MKV) defined as the mean of the kriging variance calculated for each prediction location (Christensen, 1996).
3. Results
3.1. Weighted averaged vs. non-averaged rainfall intensity
To compare non-averaged rainfall intensity (Ru) and weighted averaged rainfall intensity (Rw) as a predictor for increase in dose rate (H) figures 4 and 5 show time series of these three variables for four monitoring stations. In addition, scatterplots ofRuversusHandRwversusH are shown with the fitted regression line. The goodness of fit (R2) is shown below the scatterplots in the x-axis caption. At all four monitoring stations theR2increased when we usedRwinstead ofRu. To compare theR2between using RuandRwfor all monitoring stations, figure 6 shows these R2’s. Filled dots represent theR2value forRw, open dots theR2forR
u. On average,R2 increased from 0.17 forRu to 0.78 forRw.
3.2. Estimation of the spatial distribution of dose rate
Figure 7 shows scatterplots of Rw versusH (location varies, time is constant) between 8 AM and 7 PM in hourly timesteps. For all the hourly timesteps the fitted regres-sion parameters are significant (p <0.025). The goodness of fit of the fitted regression parameters varies between 0.42 and 0.71.
Figure 8 shows variograms of Rw and the correlation length in kilometers. The correlation length is determined by fitting a spherical variogram model to the sample vari-ogram and using the range of the varivari-ogram model as the correlation length. The correlation lengths are quite large in comparison to the typical distance between the NRM stations, which is about 12 km. Figure 9 shows the fit-ted variogram models ofH for both OK and UK between
8AM and 7PM. The fitted variogram models show a drop in both sill and range for UK in comparison to OK. The semivariance in these plots is on the log-scale, to make the differences between the fitted models more clear. Fig-ure 10 shows interpolated maps for OK and UK for three moments in time.
Table 1 shows the mean increase in dose rate ( ¯H), root mean squared error (RMSE) of the cross-validation residu-als, the mean error (ME) of the cross-validation residuals and the mean kriging variance (MKV) for OK and UK. The differences between OK and UK in terms of RMSE are small compared to ¯H, indicating that the results for OK and UK are comparable. In addition, ME and MKV for OK and UK are comparable in size. RMSE is large in comparison to the ME, suggesting that there is no bias in the cross-validation residuals.
We reduced the network density to see how this could effect the RMSE. We randomly took out 20%, 40%, 60% and 80% of the stations. We repeated this procedure a number of times for each moment in time. From these randomly reduced networks we selected the one that had the change in RMSE mose favorable to UK. Note that we kept the variogram models and the regression coefficients for cross-validating the reduced network equal to those of the full network. Figure 11 shows the results of reducing the network with panels for different reduction percent-ages, time on the y-axis and the change in RMSE on the x-axis. The vertical lines represent the mean values for the full and reduced network respectively. These lines indicate that the change in RMSE shifts in favor of UK when the network is reduced.
4. Discussion
4.1. Weighted averaged vs. non-averaged rainfall intensity
Weighted averaged rainfall intensity (Rw) performs much better as a predictor for the increase in dose rate (H) than non-averaged rainfall intensity (Ru). TheR2increases for all monitoring stations when we useRwinstead ofRu (fig-ure 6), on average from 0.17 to 0.78. This confirms our hypothesis that taking a weighted averaged rainfall inten-sity is a much better description of the radon washout and decay process. The high R2’s for Rw underline the fact that rain out of radon progeny is an important process in describing the variations in dose rate.
Figure 5 shows that not all monitoring stations show a high R2. We offer two possible explanations: firstly,
the observed dose rate enhancements include contributions from sources other than rainfall. The spiky patterns in e.g. figure 5(a) may well be attributed to the transport of medical radioactive sources or to radiographic screening during welding activities in the vicinity of the monitor-ing station. Secondly, the correlation between rainfall at surface level and the rainfall radar images may fail occa-sionally (figure 5(b)). For example when rainfall detected by the radar system high up in the atmosphere does not
reach the ground surface. In addition, reflectance from buildings or large flocks of birds can produce false rainfall patterns. EUR 20600 EN (2003) provides a more thorough description of complications when using rainfall radar to estimate rainfall intensity. Our estimate of the rainfall intensity could be improved by combining rainfall radar with ground measurements of rainfall intensity (Schuur-mans et al., 2007). Including ground measurements com-bines the spatial coverage of the radar images with the accuracy of ground measurements.
In this study we expressed the temporal structure of the relation between rainfall intensity and increase in dose rate by taking a weighted average. An alternative ap-proach could be to use space-time kriging, see e.g. Jost et al. (2005). Space-time kriging captures the temporal aspect in defining a variogram model not only in space, but also in time.
4.2. Estimation of the spatial distribution of dose rate
The accuracy in terms of RMSE, ME and MKV is more or less the same for OK and UK (table 1). Consequently, there is no significant improvement in our estimate of the distribution of dose rate when we take into account the re-lationship betweenRwandH. This is surprising given the fact that UK takes into account a significant trend with a goodness of fit of up to 0.71 (figure 7). We discuss this fact for MKV and RMSE seperately in the next two sec-tions. Because ME is very small in comparison to RMSE, i.e. there is no bias in the cross-validation residuals, and we will not further discuss ME.
MKV
We expected MKV to drop because the fitted linear model explains part of the variance in the data (sill be-comes lower), decreasing the kriging variance. To illus-trate why the MKV sometimes does not drop for UK, we discuss the way the kriging variance is calculated and the role of the variogram model in this calculation (see figure 9 for the fitted variogram models). The kriging variance at a prediction location is calculated as a weighted average of the semivariance of the surrounding observations, sim-ilar to the kriging prediction. The semivariance of the surrounding observations is obtained from the variogram model and the weights are equal to the kriging weights. In our case the kriging weight is mainly distributed over the points within a 40 km radius. Consequently, the krig-ing variance is mainly determined by the behaviour of the variogram model in this distance interval. When the vari-ogram model shows greater semivariances in this distance interval for UK than for OK, the MKV for UK increases. A good example of the increase when using UK are the fitted variogram models for 9AM (see figure 9). The sill drops, but the decrease in range causes the semivariance values in the range upto 40 km to be greater for UK than for OK. In conclusion: the total variance in the dataset (the sill) drops, but because of the density of the moni-toring network the kriging weights are mainly distributed
over stations that are closer than the range of the vari-ogram model. Consequently, we do not take advantage of the decrease in the sill and the MKV does not drop significantly.
RMSE
The correlation length of Rw is large in comparison to the average distance between the monitoring stations, about 12 km. Figure 8 shows an average correlation length of 184 kilometers. So the NRM is dense compared to the correlation length of the rain storm. The density of the network allows OK to be succesful in interpolating the increases in dose rate caused by rainfall. The succes of OK is also apparent from the interpolated maps in figure 10. The interpolated maps by OK and UK broadly show the same pattern. So the density of the network causes OK and UK to perform equally well in reproducing the spatial pattern ofH, and thus have a comparable RMSE in cross-validation. In conclusion: when the monitoring network is dense in comparison to the phenomenon causing the trend in the data, the increase in accuracy when including the trend is likely to be small. This conclusion is in line with the work of Journel and Rossi (1989).
In case the correlation length is smaller than the typ-ical distance between the monitoring stations, we expect an improvement in the accuracy of the map. This is sup-ported by the results shown in figure 11. The figure shows that for a less dense network UK has smaller RMSE values. This indicates that in a less dense network, the positive in-fluence of adding a trend increases. In addition to a less dense network, we expect an improvement in RMSE for rain storms with a smaller correlation length. Smaller cor-relation lengths occur with more localized thunder storms or in mountainous regions where rain storms are restricted to the valleys.
Although for the current network density UK does not perform much better than OK in terms of cross validation statistics, we consider the maps resulting from UK to be the more realistic ones. OK tends to create highly smooth surfaces, where UK shows much sharper boundaries, see for example the interpolated of 12:00 in figure 10. Rainfall time series show that boundaries are often sharp rather than smooth, see e.g. figure 4(b). That this more realis-tic pattern does not lead to better cross-validation result might be attributed to the even spread of monitoring sta-tions over the country. Lacking monitoring station pairs at short distances prohibit the detection, and thereby val-idation, of sharp boundaries.
5. Conclusions
Our results show that the weighted averaged rainfall intensity performs much better as a predictor for increase in dose rate than the non-averaged rainfall intensity. This conclusion, in combination with the results from literature (Smetsers and Blaauboer, 1997a; Horng and Jiang, 2003;
Fujinami, 1996), show that wash out of radon progeny is a very important process in describing the variations in dose rate.
The accuracy of maps produced by ordinary kriging (OK, no trend) and universal kriging (UK) is compara-ble. This is mainly caused by the density of the NRM in comparison to the scale of the rainfall radar data. When the monitoring network is dense in comparison to the phe-nomenon causing the trend in the data, the increase in accuracy when including the trend is likely to be small. In support of this conclusion, our results show that for networks with a decreased density the performance of UK in comparison to OK increases. In a less dense network the positive effect of including a trend increases. In addi-tion, for rainfall patterns with a shorter correlation length, we expect to see an improved performance of UK in com-parison to OK. Furthermore, we suspect that cross vali-dating the evenly spread monitoring stations works in the advantage of OK, when the external variable (rainfall) ex-hibits sharp boundaries. Maps resulting from UK better follow the sharp boundaries present in rainfall, but the lack of short-distance monitoring station pairs prevents cross-validation to reveal this effect.
Acknowledgements
The authors thank the Royal Dutch Meteorological Institute (KNMI) for supplying the rainfall radar data. We gratefully acknowledge financial support from the in-novation programme Space for Geo-Information (RGI), project RGI-302. This work has been partially funded by the European Commission, under the Sixth Frame-work Programme, by the INTAMAP project Contract N. 033811 with the DG INFSO, action Line IST-2005-2.5.12 ICT for Environmental Risk Management. The views ex-pressed herein are those of the authors and are not nec-essarily those of the RGI or the European Commission. The authors would also like to thank Stephanie Melles and three anonymous reviewers for providing comments that improved the manuscript.
References
Battan, L. J., 1973. Radar Observations of the Atmosphere. Univer-sity of Chicago Press.
Bishop, T. F. A., McBratney, A. B., 2001. A comparison of predic-tion methods for the creapredic-tion of field-extent soil property maps. Geoderma 103 (1-2), 149–160.
Bourennane, H., King, D., 2003. Using multiple external drifts to estimate a soil variable. Geoderma 114 (1-2), 1–18.
Chil`es, J. P., Delfiner, P., 1999. Geostatistics: Modeling Spatial Un-certainty. John Wiley & Sons, New York, 720p.
Christensen, R., 1996. Plane Answers to Complex Questions: The Theory of Linear Models, 2nd Edition. Springer, New York, 496p. Cressie, N. A., 1993. Statistics for Spatial Data. Wiley, NY, 900p. Dubois, G., Pebesma, E. J., Bossew, P., 2007. Automatic mapping
in emergency: A geostatistical perspective. International Journal of Emergency Management 4 (3), 455–467.
Fujinami, N., 1996. Observational study of the scavenging of radon daughters by precipitation from the atmosphere. Environment In-ternational 22 (Supplement 1), 181–185.
Hengl, T., Heuvelink, G. B. M., Rossiter, D. G., 2007. About regression-kriging: From equations to case studies. Computers & Geosciences 33 (10), 1301–1315.
Hiemstra, P. H., Pebesma, E. J., Twenh¨ofel, C. J. W., Heuvelink, G. B. M., 2009. Real-time automatic interpolation of ambient gamma dose rates from the dutch radioactivity monitoring network. Com-puters & Geosciences 35 (8), 1711–1721.
Horng, M., Jiang, S., Dec. 2003. A rainout model for the study of the additional exposure rate due to rainfall. Radiation Measurements 37 (6), 603–608.
Horng, M., Jiang, S., Feb. 2004. In situ measurements of gamma-ray intensity from radon progeny in rainwater. Radiation Measure-ments 38 (1), 23–30.
ICRU, 1993. Quantities and units in radiation protection dosimetry. ICRU report 51. Tech. rep., Bethesda MD.
Jost, G., Heuvelink, G., Papritz, A., 2005. Analysing the space-time distribution of soil water storage of a forest ecosystem using spatio-temporal kriging. Geoderma 128 (3-4 SPEC. ISS.), 258–273. Journel, A. G., Rossi, M. E., Oct. 1989. When do we need a trend
model in kriging? Mathematical Geology 21 (7), 715–739. Kitanidis, P. K., 1993. Generalized covariance functions in
estima-tion. Mathematical Geology 25 (5), 525–540.
Knotters, M., Brus, D. J., Oude Voshaar, J. H., 1995. A comparison of kriging, co-kriging and kriging combined with regression for spatial interpolation of horizon depth with censored observations. Geoderma 67 (3-4), 227–246.
Lloyd, C. D., 2005. Assessing the effect of integrating elevation data into the estimation of monthly precipitation in great britain. Jour-nal of Hydrology 308 (1-4), 128–150.
EUR 20600 EN, 2003. Quality and assimilation of radar data for NWP. Alberoni, P. P., Ducrocq, V., Gregoric, G., Haase, G., Holleman, I., Lindskog, M., Macpherson, B., Nuret, M. and A. Rossa (Eds). Office for Official Publications of the European Com-munities, Luxembourg., 38 p.
EUR 21595 EN, 2005. Automatic mapping algorithms for routine and emergency monitoring data. Report on the Spatial Interpo-lation Comparison (SIC2004) exercise. Dubois G. (Ed). Office for Official Publications of the European Communities, Luxembourg, 150 p.
Pebesma, E. J., 2004. Multivariable geostatistics in S: the gstat package. Computers & Geosciences 30 (7), 683–691.
R Development Core Team, 2010. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Comput-ing, Vienna, Austria, ISBN 3-900051-07-0.
URLhttp://www.R-project.org
Schuurmans, J. M., Bierkens, M. F. P., Pebesma, E. J., Uijlenhoet, R., 2007. Automatic prediction of high-resolution daily rainfall fields for multiple extents: The potential of operational radar. Journal of Hydrometeorology 8 (6), 1204–1224.
Smetsers, R. C. G., Blaauboer, R. O., 1996. Variations in outdoor radiation levels in the Netherlands. Ph.D. thesis, Rijksuniversiteit Groningen.
Smetsers, R. C. G., Blaauboer, R. O., 1997a. A dynamic compen-sation method for natural ambient dose rate based on 6 years data from the dutch radioactivity monitoring network. Radiation Protection Dosimetry 69 (1), 19–31.
Smetsers, R. C. G., Blaauboer, R. O., 1997b. Source-dependent prob-ability densities explaining frequency distributions of ambient dose rate in the Netherlands. Radiation Protection Dosimetry 69 (1), 33–42.
Twenh¨ofel, C. J. W., de Hoog van Beynen, C., van Lunenburg, A. P. P. A., Slagt, G. J. E., Tax, R. B., van Westerlaak, P. J. M., Aldenkamp, F. J., 2005. Operation of the Dutch 3rd generation national radioactivity monitoring network. In: EUR 21595 EN, 2005. Automatic mapping algorithms for routine and emergency monitoring data. Report on the Spatial Interpolation Comparison (SIC2004) exercise. Dubois G. (Ed). Office for Official Publica-tions of the European Communities, Luxembourg, pp. 19–31. Yemefack, M., Rossiter, D. G., Njomgang, R., 2005. Multi-scale
char-acterization of soil variability within an agricultural landscape mo-saic system in southern Cameroon. Geoderma 125 (1-2), 117–143. Zhu, C., Byrd, R., Lu, P., Nocedal, J., 1997. Algorithm 778: L-bfgs-b: Fortran subroutines for large-scale bound-constrained op-timization. ACM Transactions on Mathematical Software 23 (4), 550–560.
t 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 ¯H 0.27 2.99 3.60 4.47 9.93 12.32 10.37 8.00 5.31 5.11 3.73 2.01 RMSE OK 3.58 2.66 3.11 3.71 6.69 4.69 3.94 3.46 3.20 3.63 3.25 2.95 RMSE UK 2.85 3.18 3.04 4.18 6.19 4.51 4.40 3.29 3.50 3.69 3.24 3.41 ∆RMSE -0.73 0.53 -0.08 0.47 -0.50 -0.18 0.46 -0.17 0.30 0.05 -0.01 0.46 MKV OK 9.20 9.62 11.34 12.39 26.43 15.75 13.76 11.37 8.37 8.22 6.18 4.96 MKV UK 6.95 20.07 11.08 13.06 28.48 15.29 27.83 10.43 11.05 11.39 6.38 4.97 ∆MKV -2.26 10.45 -0.26 0.67 2.04 -0.46 14. 07 -0.94 2.67 3.17 0.20 0.01 ME OK 0.00 0.03 0.00 -0.04 0.02 0.07 0.07 0.04 0.02 0.04 0.03 -0.01 ME UK 0.03 -0.03 -0.02 -0.07 0.04 0.01 -0.02 0.03 0.00 0.01 -0. 02 0.04 T able 1: Mean increase in dose ra te ( ¯H), Ro ot M ean Squared Error (RMSE) and Mean Error (ME) o f the lea v e-one-out cross-v alidation residuals, the Mean Kriging V ariance (MKV) for Ordinary and Univ ersal kriging and the difference b et w een them. W e p erformed cro ss-v alidation for the data b et w een 8AM and 7PM. A negativ e difference for either MKV or RMSE means that UK w as p erforming b etter than OK. 7
0 25 km
time 0 10 20 30 06:00 09:00 12:00 15:00 18:00 21:00 ●● ● ● ● ● ● ● ● ● ●●● ●●● ● ● ● ● ●●●●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ●● ● ●
H: Increase in dose rate (nSv/h)
0.0 0.5 1.0 1.5 2.0 2.5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ● ● ●●●● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ●
Rw: Weighted averaged rainfall intensity (mm/h)
0 1 2 3 4 5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Ru: Rainfall intensity (mm/h) Ru (mm/h, R 2 = 0.19 ) H (nSv/h) 0 10 20 30 0 1 2 3 4 5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Rw (mm/h, R2 = 0.9 ) H (nSv/h) 0 10 20 30 0.0 0.5 1.0 1.5 2.0 2.5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● (a) time 0 10 20 30 40 50 06:00 09:00 12:00 15:00 18:00 21:00 ● ●● ● ● ● ●● ●● ●● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ● ●● ●● ●● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●●● ●
H: Increase in dose rate (nSv/h)
0 1 2 3 4 5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ● ● ● ●● ●●● ● ●● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●
Rw: Weighted averaged rainfall intensity (mm/h)
0 5 10 15 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Ru: Rainfall intensity (mm/h) Ru (mm/h, R2 = 0.26 ) H (nSv/h) 0 10 20 30 40 50 0 5 10 15 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Rw (mm/h, R2 = 0.94 ) H (nSv/h) 0 10 20 30 40 50 0 1 2 3 4 5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● (b)
Figure 4: Non-averaged rainfall intensity (Ru), weighted averaged rainfall intensity (Rw) and increase in dose rate (H) versus time (left), and scatterplots ofRuandRwvsH (right) for two stations (a, b) that show a high correlation betweenRw andH.
time 0 20 40 60 06:00 09:00 12:00 15:00 18:00 21:00 ● ●● ●● ● ● ● ●●● ● ● ●● ● ●● ● ●● ● ● ● ●● ●● ● ● ● ●●● ● ● ● ● ● ●● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ●
H: Increase in dose rate (nSv/h)
0.0 0.5 1.0 1.5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ●● ● ●● ● ● ● ● ●● ● ● ●●● ●● ● ● ● ●● ● ● ● ● ● ● ●● ●● ●● ●● ● ●● ● ●● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●● ●●
Rw: Weighted averaged rainfall intensity (mm/h)
0 2 4 6 8 10 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Ru: Rainfall intensity (mm/h) Ru (mm/h, R 2 = 0.01 ) H (nSv/h) 0 20 40 60 0 2 4 6 8 10 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Rw (mm/h, R2 = 0.16 ) H (nSv/h) 0 20 40 60 0.0 0.5 1.0 1.5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● (a) time 0 5 10 15 06:00 09:00 12:00 15:00 18:00 21:00 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●
H: Increase in dose rate (nSv/h)
0 1 2 3 4 5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ●●● ●● ●● ● ● ● ● ● ●● ● ●● ●●● ● ●● ●● ● ●● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ● ●● ● ● ● ● ● ● ●●● ● ● ● ● ●
Rw: Weighted averaged rainfall intensity (mm/h)
0 10 20 30 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●●● ●●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Ru: Rainfall intensity (mm/h) Ru (mm/h, R2 = 0 ) H (nSv/h) 0 5 10 15 0 10 20 30 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Rw (mm/h, R2 = 0.14 ) H (nSv/h) 0 5 10 15 0 1 2 3 4 5 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● (b)
Figure 5: Non-averaged rainfall intensity (Ru), weighted averaged rainfall intensity (Rw) and increase in dose rate (H) versus time (left), and scatterplots ofRuandRwvsH (right) for two stations (a, b) that show a low correlation betweenRwandH.
R
2
stations
0.0
0.2
0.4
0.6
0.8
1.0
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●Weighted averaged rainfall intensity
Rainfall intensity
●
●
Figure 6: Goodness of fit (R2) between increase in dose rate and non-averaged rainfall intensity (open dots) and weighted averaged rainfall intensity (filled dots) per station. Note how theR2 shifts in favor of weighted averaged rainfall intensity.
Weighted averaged rainfall intensity (mm/h) Increase in r adioactivity le v el (nSv/h) 0 20 40 60 80 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● R2=0.56 0800 0 2 4 6 8 ● ● ● ● ● ● ● ●● ● ● ●● ●●● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● R2=0.55 0900 ● ● ● ● ●●● ● ● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● R2=0.54 1000 0 2 4 6 8 ●●● ● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●●●●●●●● ●●● ●● ● ● ● ● ●●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●●●● ● ● ● ● ● ●● ● R2=0.71 1100 ● ●●●● ●● ● ● ●●● ● ● ● ●●●●●●● ● ● ● ● ● ● ● ● ● ● ●●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● R2=0.48 1200 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●●● ● ● ● ● ● ● ● ● ● ● R2=0.47 1300 ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● R2=0.5 1400 0 20 40 60 80 ● ● ● ●● ●● ●● ● ● ● ● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ●● ● R2=0.61 1500 0 20 40 60 80 0 2 4 6 8 ● ● ● ●● ● ● ● ● ● ● ● ●● ● ●● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●●● ● ● ● ● ●●●● ●●● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● R2=0.59 1600 ● ● ● ●● ●●● ● ● ● ● ● ● ● ● ● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●●●●●●● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ●●● ● ● ● ● ● R2=0.51 1700 0 2 4 6 8 ●●● ● ● ● ● ● ● ●● ● ●● ●● ● ● ● ● ● ● ●●● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ●● ● ● ● ● ●● ●● ● ● ● ● ●● ● ● ● ●● ● ● ●●● ● ●● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● R2=0.42 1800 ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●● ●●● ● ●●●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ●● ● ● ● ●● ●● ● ● ● ●●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ● ●●●● ●● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● R2=0.52 1900
Figure 7: Weighted averaged rainfall intensity versus increase in dose rate from 8 AM to 7 PM. Line fitted using linear regression. The numbers in the plots represent the goodness of fit (R2).
Distance (km) Semiv ar iance (nSv/h) 0.0 0.2 0.4 0.6 0.8 ● ● ● ● ● ● ● ● ● ● ● ● range : 144 km 0800 0 50 100 150 200 250 ●● ● ● ● ● ● ● ● ● ● ● range : 187 km 0900 ● ● ● ● ● ● ● ● ● ● ● ● range : 147 km 1000 0 50 100 150 200 250 ●● ● ● ● ● ● ● ● ● ● ● range : 175 km 1100 ● ●● ●● ● ● ● ● ● ● ● range : 239 km 1200 ●● ● ● ● ● ● ● ● ● ● ● range : 263 km 1300 ●● ● ● ● ● ● ● ● ● ● ● range : 255 km 1400 0.0 0.2 0.4 0.6 0.8 ● ● ● ● ● ● ● ● ● ● ● ● range : 221 km 1500 0.0 0.2 0.4 0.6 0.8 0 50 100 150 200 250 ● ● ● ● ● ● ● ● ● ● ● ● range : 186 km 1600 ● ● ● ● ● ● ● ● ● ● ● ● range : 165 km 1700 0 50 100 150 200 250 ● ● ● ● ● ● ● ● ● ● ● ● range : 150 km 1800 ●● ●●● ● ● ● ● ● ● ● range : 220 km 1900
Figure 8: Spherical variogram models fitted to weighted averaged rainfall intensity from 8 AM to 7 PM. The number in the lower right corner is the correlation length.
Distance (km) Semiv ar iance (nSv/h) 2.7 7.4 20.1 54.6 148.4 ●● ● ● ● ● ● ● ● ● 0800 20 40 60 80 100 120 ● ● ● ● ● ● ● ● ● ● 0900 ●● ● ● ● ● ● ● ● ● 1000 20 40 60 80 100 120 ● ●● ● ● ● ● ● ● ● 1100 ● ●● ● ● ● ● ● ● ● 1200 ● ● ● ● ● ● ● ● ● ● 1300 ● ● ● ● ● ● ● ● ● ● 1400 2.7 7.4 20.1 54.6 148.4 ● ●● ● ● ● ● ● ● ● 1500 2.7 7.4 20.1 54.6 148.4 20 40 60 80 100 120 ● ● ● ● ● ● ● ● ● ● 1600 ● ● ●● ● ● ● ● ● ● 1700 20 40 60 80 100 120 ● ●●● ● ● ● ● ● ● 1800 ● ● ● ● ● ● ● ● ● ● 1900 OK UK
Figure 9: Hourly sample variograms and fitted models for ordinary kriging (o) and universal kriging (+) from 8AM to 7PM. Note that semivariances are shown on the log-scale.
Change in Cross−validation RMSE
Time 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 −2.0 −1.5 −1.0 −0.5 0.0 0.5 x x x x x x x x x x x x + + + + + + + + + ++ + Decrease of 20% 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 x x x x x x x x x x x x + + + + + + + + + + + + Decrease of 40% 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 x x x x x x x x x x x x + + + + + ++ + + ++ + Decrease of 60% 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 x x x x x x x x x x x x + + + + + + + + + + + + Decrease of 80% Normal Decreased density x+UK better
OK better
Figure 11: The effect of reducing the size of the network by 20%, 40%, 60% and 80% on the change in cross-validation RMSE between OK and UK. Time is on the y-axis, the change in RMSE on the x-axis. A negative change in RMSE means that UK is outperforming OK and vice versa. The plusses (+) show the best ∆RMSE in favor of UK for the reduced network and the crosses (×) show the ∆RMSE for the full network. The vertical lines represent the mean values for ∆RMSE for the reduced and the full network.