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.