Development of grids, contour plots, and profiles for model

Further analysis of the modelling results was focused on comparisons of the predicted and measured deposition (surface contamination, Bq/m²) within the grid area (the area with measurements), using an approach developed for this exercise. Although some model predictions extended to distances greater than 50 m, there are no measured values at those distances for comparison. Measurement points used during Tests 3 and 4 are shown in Appendix I. All sets of model predictions were first represented in the same Cartesian coordinate system as the measurements, in terms of predicted deposition at the same points for which measured deposition was available, designating the dispersion point (origin of the explosion) at grid coordinates (0,0). Comparisons were then made of the measured and predicted maximum activity concentrations within the grid area and of the total measured or predicted activity within the grid area (Section 2.5.3). Deposition profiles were defined in terms of profiles from the dispersion point through the point with the maximum measured or predicted deposition (Section 2.5.4), and from the dispersion point through the cloud axis, defined as the approximate centre of the measured or predicted plume (Section 2.5.5). Figure 2.5 provides a schematic illustration of these two profiles.

TABLE 2.4. PREDICTED RADIUS OR AREA OF ZONES OF 50%, 75%, AND 95%

CONTAMINATION FOR TESTS 3 AND 4

Model Scale Contamination zone

50% 75% 95%

FIG. 2.5. Schematic diagram showing the profile through the point of maximum deposition (left) or through the cloud axis (right). For any given set of activity concentrations, the point of maximum

To better characterize the measured or predicted deposition, not only at the measurement points, but in the entire grid area, values of activity concentrations were first calculated from measurements using a Multilevel B-Spline interpolation methodology [2.6] with SAGA GIS⁹ software. Each set of model predictions was similarly interpolated using the same methodology and settings as for the measured data and using the same set of grid coordinates as for the measurements. Negative values produced by the calculations were replaced with zeros. Section 2.5.3 discusses the predictions of the total activity deposited in the grid area and of the maximum deposited activity.

Figures 2.6 to 2.11 show the predicted and measured deposition by model type (computational fluid dynamics (CFD) models, Gaussian models, and Lagrangian models) for Tests 3 and 4, in terms of contour plots of the measured or predicted activity concentrations (deposition, Bq/m²).

These plots of the normalized data sets show the predictions and measurements in the same coordinate system and with the same color scale. The plots thus permit a visual comparison of the two dimensional predicted or measured surface contamination. For Test 3, the measurements show deposition largely to the grid north. In contrast, the models predicted the primary deposition in a range from northwest to northeast. For Test 4, the measurements show deposition largely to the grid northwest, then to the southwest. Model predictions included a range from northwest to west, southwest, and south. For Test 4, the measurements indicate that the plume was not stable in direction during the deposition event, and the models did not fully reproduce this effect.

For the contour maps and for the comparisons of profiles (Sections 2.5.4 and 2.5.5), each set of measured or predicted activity concentrations was normalized to the maximum value in the set, i.e. rescaled to a range of 0 to 1, using the following formula:

𝑒𝑒𝑖𝑖,𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑖𝑖𝑛𝑛𝑛𝑛𝑛𝑛 = _𝑛𝑛^{𝑛𝑛𝑖𝑖− 𝑛𝑛𝑚𝑚𝑖𝑖𝑚𝑚}

𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑛𝑛_{𝑚𝑚𝑖𝑖𝑚𝑚} (2.1)

where:

ei,normalized is the normalized value of the activity concentration at a given point i;

ei is the measured or predicted value of the activity concentration at a given point i;

emin is the minimum value of the set of measured or predicted activity concentrations; and emax is the maximum value of the set of measured or predicted activity concentrations.

The maximum and minimum values were acquired for each of two ‘profiles’ for each set of measurements or model predictions, as follows:

(1) A line from the dispersion point to the point with the maximum activity concentration (measured or modelled; see Fig. 2.5, left panel); and

(2) A line from the dispersion point along the axis (centreline) of the cloud (measured or modelled), as determined manually from the contour plot (Fig. 2.5, right panel).

The normalization was performed independently for each set of measurements or predictions;

thus, the maximum value for a given set of normalized activity concentrations is 1 and the minimum value is 0.

9 http://www.saga-gis.org/

Profiles of the measurements and of each set of model predictions were developed for each of the two descriptions above (from the dispersion point to the point of maximum activity concentration, and from the dispersion point through the cloud axis), according to the following steps:

(1) A profile line X was defined from ‒65 to +65 m, in a shape file format, with the centre at coordinates (0,0).

(2) The profile line was converted to points in SAGA GIS.

(3) The maximum value and its coordinates were acquired for each set of measurements or model outputs (for the first profile), or the cloud axis was manually defined (or provided by the participant) for the measurements or model outputs (for the second profile).

(4) The rotation angle was calculated for each profile; this is a simple calculation using goniometry¹⁰.

(5) The line of the profile was rotated using the measured angle in SAGA GIS (module Transform Shapes).

(6) Coordinates were added to the line.

(7) Measurements or model predictions from the grid were added to profile points using the Nearest Neighbor method.

(8) The predicted values were processed using the software LibreOffice Calc¹¹ and Scidavis/QTIplot¹².

Two profile integrals were calculated for Tests 3 and 4 (Sections 2.5.4 and 2.5.5):

(1) A profile integral describing the predicted pattern of deposition along a line from the dispersion point through the point of maximum deposited activity; and

(2) A profile integral describing the predicted pattern of deposition from the dispersion point along the cloud axis (plume centreline).

The rectangle method was used to calculate these integrals. The distance range for the calculation was set as wide as possible in order to include values for all models. For the first profile, the distance ranged from approximately ‒10 m to 24 m for Test 3 and from approximately ‒10 m to 17 m for Test 4. For the second profile, the distance ranged from approximately ‒10 m to 21 m for Test 3 and from approximately ‒10 m to 15 m for Test 4. The x-axis variable for the profile integrals was in units of m (distance from the dispersion point), and the y-axis variable for the profile integrals was in units of Bq/m² (deposited activity per unit ground area, at a distance of x m). The profile was assumed to have a width of 0.01 m (1 cm); thus, the profile integral has units of Bq (total activity under the profile).