Radioxenon categorization schemes based on statistical parameters Michael Schoeppner Princeton University, Program on Science and Global Security,
[email protected]
Goal of categorization
Questions about a sample
Once completed the noble gas component of the International Monitoring System (IMS) will collect about 60 air samples per day (depending on the sampling time). A list with the concentrations found in each sample is send to the National Data Centre (NDC) of each CTBT member state. In order to accelerate and optimize the review process in the NDCs each sample should be categorized. This would support the decision process by raising awareness to suspicious samples and would also allow non-scientists to apprehend the significance of a sample. A three-level categorization scheme would give an easy and fast summary of the significance of the sample, also for nonscientists:
LEVEL 1
LEVEL 2
LEVEL 3
No background, guaranteed okay
Explainable background, probably okay
Background with suspicious attributes
Application in categorization
The category of a given sample should answer and reflect the most important questions. Here are a few suggestions: In case of a non-zero background: 1) Is the sample concentration in line with typical concentrations the station?
YES/NO
2) Is the concentration explainable with atmospheric transport modelling and known sources?
YES/NO
3) Are the isotopic ratios pointing to reactor emissions?
YES/NO
More questions are conceivable… The answers to these questions can be incorporated into the categorization process without creating too many different categories by creating a category for every case.
LEVEL 1
LEVEL 2
LEVEL 3
No background, guaranteed okay
Explainable background, probably okay
Background with suspicious attributes
If all questions are positively answered (YES), the sample is unsuspicious and will be categorized as LEVEL 2. If one or more of the questions are negatively answered (NO), the sample has one or more suspicious attributes and will be categorized as LEVEL 3. The details why a sample was categorized as LEVEL 3 can be provided by the IDC in a list of the suspicious attributes. In order to prevent the occurrence of too many falsepositive alarms, the decision parameters can be fine-tuned, as shown in the boxes below.
EXAMPLE 1: Typical concentration, explainable through ATM, unsuspicious isotopic ratios.
EXAMPLE 2: Typical concentration, explainable with ATM, but suspicious isotopic ratios
EXAMPLE 3: Typical concentration, unsuspicious isotopic ratios, but not explainable with ATM.
EXAMPLE 4: Untypical concentration, explainable with ATM, but suspicious isotopic ratios
Fine-tuning of parameters To avoid too many high-level categories the decision parameters can be adjusted until a desired rate of high-level samples is reached. For example a maximum of 5% of all samples could be categorized as Level 3.
Example for fine-tuning the parameters: Is the sample concentration in line with typical concentrations at the station? Typical concentrations at monitoring stations In the figure on the left the simulated Xe133 concentrations for the year 2010 are shown for 39 noble gas stations. Some of these stations are not operable yet. The simulation is based on the assumed emissions from 200 nuclear power plants and 5 medical isotope production facilities. It is seen that • Atmospheric transport modelling can help to establish an understanding of the background even for stations that are not yet operable. • The concentrations often stretch over several orders of magnitude. • Each station has its own fingerprint.
Fine-tuning is possible for each of the questions:
1) Is the sample concentration in line with typical concentrations the station? Instead of a one-sigma confidence interval for samples with unsuspicious concentrations, twosigma or thee-sigma could be used as a threshold. Example for this is demonstrated on the right. 2) Is the concentration explainable with atmospheric transport modelling and known sources? Increase/decrease the allowed discrepancy between model and sample (knowledge of legitimate source terms would improve simulations).
References
[2] Log-normal Distributions across the Sciences: Keys and Clues - E. Limpert, W. Stahel, M. Abbt (BioScience, Vol. 51 No. 5, pp. 341-352, May 2001).
It has been shown previously that concentrations of particles in the atmosphere over time usually do not follow a Gaussian normal distribution [Lim01, Sch12, Sch14]. This is due to the multiplicative nature of the dilution process. Processes that involve adding or subtracting tend to lead to normal distributions (Central Limit Theorem), whereas processes that involve multiplicative factors (such as dilution) tend to lead to log-normal distributions. Gaussian distributions can be described by their arithmetic mean and the standard deviation, where the standard deviation has the same dimension as the mean and adding/subtracting it to/from the mean gives the known confidence intervals of 68.3%, 95.5% and 99.7% of data around the mean. Similarly a log-normal distribution is described by its geometric mean and its standard deviation, where the standard deviation is dimensionless. The confidence intervals are given by multiplying/dividing the mean with/by the standard deviation. This behavior is shown in the figure below for (a) lognormal and (b) its transformed normal distributions [Lim01]. When setting a onesigma threshold for identifying unusually high atmospheric concentrations by multiplying the geometric mean with the dimensionless standard deviation, the result (below in the left figure a value of 200) covers about 84.1% of the data.
One-sigma threshold
3) Are the isotopic ratios pointing to reactor emissions? The allowed distance to the separation line could be increased/ decreased.
[1] Analysis of the Global Radioxenon Background with Atmospheric Transport Modelling for Nuclear Explosion Monitoring - M. Schoeppner (Phd thesis, University Roma Tre, 2012).
Log-normal distributions
Figure 1: Simulated Xe-133 concentrations at 39 noble for one year.
Thus, any categorization scheme must address this with station-specific attributes. This would be provided by the local standard deviation. Special characteristics for the standard deviation of atmospheric concentrations and thresholds are discussed in the box on the right.
Figure 2: The same log-normal distribution in normal form (a) and after log-transformation (b). [2]
