Our choice to use a binary measure of service provision (“provided”/“not provided”) can be thought of as equivalent to a continuous measure based on a uniform distribution where all streamflow values between the two thresholds are equal to the highest level of service provision (=1). This choice, however, is an arbitrary one; several other measures based on other distributions are possible and may in fact better represent certain aspects of service provision. In order to explore this decision further, we compared the binary (uniform) distribution to three additional continuous measures for flow regulation based on the same thresholds at HBEF. In the first (the “default continuous”), we fit a normal curve to the data range such that the highest possible value of the service (=1) is achieved at a value equidistant to the two thresholds. This represents the situation where beneficiaries are equally concerned about either floods or droughts. We created two additional models, based on beta distributions, in which the highest value of the service is achieved just above the low flow threshold (“flood avoidance”) or just below the high flow threshold (“drought avoidance”) – representing conditions in which beneficiaries are disproportionately concerned about floods or droughts, respectively. Under all four distributions, the value of the service is equal to zero at or beyond either threshold. Streamflow data from the two watersheds were scaled according to each of the four distributions and histograms were generated to summarize the results.
Using our default binary methodology, on more than 90% of measurement days in both watersheds streamflow fell between the two thresholds – within the GLZ. Translating this into a continuous variable using a uniform distribution, we can say that 90% of days achieved a flow provision score of 1.0. Based on this information, we might argue that flow regulation services in the watersheds are extremely high and extremely reliable. Using other distributions to calculate provision scores would result in significantly different interpretations, however. For example, in the default continuous and the drought avoidance scenarios, a majority of measurement days achieve provision scores of less than 0.12. This is because streamflow on most days clusters above, but not far above, the low flow threshold. In these cases, concern about potential drought paints a much more negative picture of the flow regulation services in these watersheds. On the other hand, in the flood avoidance scenario, where concern about drought is assumed to be minimal, any given measurement day is more or less equally likely to achieve any possible provisioning score; the histograms for both watersheds are nearly flat.