3.5 Sensitivity of Age to Input Parameters
The primary uncertainty associated with applying Equation (13) is the background [latex]_{}^{3}H[/latex] concentration (Cbackground) due both to temporal variations at a given location and spatial variation between measurement stations. Hydrodynamic dispersion in the unsaturated zone may effectively smooth intra‑annual variations and hence reduce the age uncertainty. However, hydrodynamic dispersion is complex and depends on many factors (variation in hydraulic conductivity, water content, temporal variations in precipitation, scale, among others), making it difficult to generalize the degree to which average [latex]_{}^{3}H[/latex] values are representative of recharge conditions.
One way to assess the uncertainty in age due to uncertainty in the background concentration is to compute the standard deviation of the background concentration and then construct mean plus standard deviation and mean minus standard deviation curves as shown in Figure 12. The example in Figure 12 uses the Vienna atmospheric curve and a hypothetical sample having 5.5 TU that was collected on January 1st, 2015. The decay curve intersects the mean minus one standard deviation curve in 2009 and the mean plus one standard deviation in 2001. The decay curve intersects the average precipitation curve in 2003 for this example. The age and associated uncertainty are thus calculated in years as 12 years with an uncertainty of +2 to -6 years. However, it is important to point out that the 5.5 TU decay curve for this example also intersects the average precipitation curve in the early 1980s, so a much older age of 35 years cannot be ruled out by the [latex]_{}^{3}H[/latex] data alone. Exercise 4⮧ provides an opportunity to practice using the [latex]_{}^{3}H[/latex] dating method.
Figure 12 ‑ Example of computing the most probable age and uncertainty for a hypothetical sample containing 5.5 TU that was collected near Vienna, Austria, on January 1st, 2015. Section 3.5 provides further discussion. The average precipitation value (PreAve), plus (+ sigma) or minus (- sigma) are plotted to constrain age estimates.