Extraction of SC Patterns
The algorithm we developed extracted information from in situstream sensors and weather data and sequentially assessed the three aforementioned patterns that occur in response to precipitation events: the flush, dilution, and recovery. This algorithm fully processed the available data 10,000 times, with each iteration using our defined parameters sampled randomly from a uniform distribution (Table 1). The range for each distribution was chosen through trial and error and visual assessment of the SC time series of the catchment.
The algorithm first identified unique precipitation events, defined by a parameter, B , which was the amount of time between non-zero precipitation measurements (Figure 4). The time between each precipitation measurement was calculated, and if the gap between one measurement and the previous measurement exceeded B , the latter measurement was determined to be the start of a new, separate event. The total amount of precipitation for each of these unique precipitation events was then calculated, and if that value was lower than a fixed amount, defined by a parameter, A , the streamwater SC characteristics associated with that event were not analyzed.
If a storm was detected, the algorithm then analyzed the changes in streamwater SC. It first determined the pre-storm trajectory (PST): the trend of the stream’s SC prior to precipitation, projected forward in time as if no rainwater had been added to the catchment. To find the PST, a Sen (1968) slope estimate of the SC data was fit to the time series. The time period used for the estimate ranged between the first precipitation measurement of the event and B . The PST was then projected forward in time to the periods during and after the occurrence of rain. The algorithm determined the residuals surrounding the PST line and using those residuals, found the SC values that deviated far enough from the PST to be considered a flush or dilution caused by the rain event. The magnitude of the deviation was defined by the number of standard deviations of the residuals, and represented by the parameterG .
To find the peak of the flush, the algorithm created a temporal window ranging between the event’s first precipitation measurement and a period of time defined by parameter D , and then found the maximum value of SC during the period. If that maximum value was greater than Gstandard deviations from the PST, it was accepted as a legitimate response to the precipitation event.
The algorithm found the maximum dilution differently whether a flush was detected or not. If a flush was found, the range to look for a maximum dilution was set between the time at which the peak flush occurred and a time period after the storm’s last precipitation defined by parameterE . If a flush was not detected, the range was created to be between the 6 hours prior to a storm’s last precipitation and E . In either instance, the algorithm then found the minimum value of SC within that window. If that minimum value was less than Gstandard deviations from the PST, it was accepted as a legitimate response to the precipitation event.
The values of both the peak flush and maximum dilution were added or subtracted, respectively, from what the SC would have been if no precipitation had occurred. This value was determined by calculating the SC value on the PST at the time in which both responses reached their apex. The difference resulting from our observed stream SC behavior and what the PST suggested the SC would otherwise be was defined as the FSC and DSC, both having units of µS cm-1.
To calculate the RSC, a Sen’s slope estimation was again used. The time range for this estimate began at the point of maximum dilution, if one was determined to be present, and ended an amount of time later defined by parameter F . The slope of the resulting line was classified as the RSC, having a unit of µS cm-1 day-1.
If a flushing response was either not detected or was not deemed different enough from normal variations in the SC, the algorithm still searched for a dilution response. However, if a dilution was not detected or deemed variable enough, the RSC was not calculated, because there would be no beginning point from which to conduct the Sen’s slope estimation.