5.5 Sensitivity of Age to Input Parameters
The procedure outlined in Section 5.4 for calculating a tracer age from a measured concentration of [latex]{SF}_{6}[/latex] involves numerous parameters—recharge temperature, salinity, elevation, and excess air—that are uncertain to some degree. In this section, we summarize the sensitivity of the computed age to uncertainty in some of these parameters.
Figure 23 shows the relationship between the [latex]{SF}_{6}[/latex] tracer age and various input parameters for a water sample having an aqueous concentration of 1.0 fmole/kg [latex]{SF}_{6}[/latex]. An fmole is a femtomole which is an amount of substance equal to 10−15 moles. The sample was assumed to have been collected in the year 2015, and the age was calculated as 2015 minus the computed recharge year. The recharge temperature, recharge elevation, and amount of UA were varied to illustrate the sensitivity of the computed age to these parameters. The sensitivity of the tracer age to recharge temperature is about − 0.5 year/°C between recharge temperatures ranging from 0 to 40 °C. In other words, if the assumed recharge temperature was 1 °C warmer than the true value, the tracer age would be 0.5 years younger than the true age. The sensitivity to recharge elevation is about − 0.3 year/100 m; thus, using a recharge elevation that is 100 m greater than the true elevation results in an age that is 0.3 years younger. The sensitivity of the age to excess air is not constant but instead is about 2 year/(ml kg–1) for smaller amounts of excess air and decreases to about 0.3 year/(ml kg–1) for excess air greater than 20 ml/kg.
Figure 23 ‑ Sensitivity of SF6 tracer age (i.e., apparent age) to input parameters. The tracer age of a hypothetical sample collected in 2015 and having a SF6 concentration of 1.0 fmole/kg was computed for various values of recharge temperature, recharge elevation, and excess air as indicated. The sensitivities (change in age per change in parameter) are shown in red.
The considerable sensitivity of [latex]{SF}_{6}[/latex] tracer ages to excess air suggests that precise dating with this method requires an actual measurement of excess air. As discussed in Section 2.6, the dissolved [latex]Ne[/latex] concentration, expressed as ∆[latex]Ne[/latex], is a sensitive indicator of excess air. For UA, a ∆[latex]Ne[/latex] of ten percent is equal to about 1 ml/kg of excess air. ∆[latex]Ne[/latex] values between 20 and 50 percent are common in groundwater (Aeschbach‑Hertig & Solomon, 2013), and values greater than 200 percent have been reported (Solomon et al., 2011). For the water sample illustrated in Figure 21, a ∆[latex]Ne[/latex] of 50 percent, if not accounted for, would lead to an error of more than 30 percent in the calculated age. If a direct measure of excess air is not available, [latex]{SF}_{6}[/latex] dating can still be useful, but it is important to include the uncertainty in the estimated age that results from the uncertainty in excess air, along with the uncertainty in all other assumed parameters and measurement errors.