Creating Robust Results
We did not know the best parameter values, nor their distribution, so we assigned a uniform distribution for each parameter and used a Monte Carlo approach so that we could produce more robust results (Paxton et al 2001). We randomly sampled 10,000 values of the six parameters that were used in the algorithm (Table 1). These varying parameters allowed us to simulate many combinations of parameter values. Therefore, each iteration of the algorithm produced a different estimate of our focus variables (e.g. FSC, PT). Thus, we created a rule set to decide how to summarize these Monte Carlo iterations. We narrowed the available pool of iterations for each single precipitation event based on first, how frequently a distinct precipitation event was detected, and second, how often that unique event exhibited a chemograph response.
Subsequently, we considered precipitation events highly likely to represent the reality of conditions and catchment characteristics only if the algorithm detected that unique event within at least 70% of its iterations (7,000 or more instances out of the 10,000). Of the storms that passed the 70% threshold, only those that resulted in a SC response 60% of the time were considered highly likely to have a SC response present (a minimum of between 4,200 responses out of 7,000 existing storm events and 6,000 responses of 10,000 existing storm events). The precipitation events that survived this culling were summarized by the median values of each dependent variable: FSC, DSC, RSC. These were then compared to the independent, environmental factors surrounding the event.