The calculation framework is analogous to elements of risk assessment frameworks (Covello and Merkhoher, 2013), developed to create a systematic process for evaluating freshwater provisioning or regulating services (ES) Under this framework, at least two aspects of provisioning and regulating ES need to be considered: 1) the possibility of demand for the ecosystem service not being met and (2) variability of the occurrence, timing or magnitude of events that leads to unmet demand. The assessment is carried out by dividing the area of interest (river basins for water-related ES) into spatial units in which the delivery of ES can be evaluated, and thus, the objective for non-compliance of demand from the ES can be set. For certain ecosystem services, a univariate or ‘crisp’ threshold-based objective can be defined that will be directly quantifiable, while others will have multi-variable or ‘fuzzy’ threshold-based objectives that may require indirect estimates. For example, for the provision of water to various sectors and cities from a basin, the volume demanded is directly quantifiable and hence, non-compliance can be evaluated based on whether the demand is met or not. On the other hand, when considering the damages from flood events to the inhabited areas within a basin, it is harder to assign a threshold to any reduction or lack of capacity of a freshwater ecosystem to regulate floods and evaluation may depend on the evaluation methods used.

To calculate the ecosystem service indicator (ESI) using the spatial units and objectives or thresholds, three dimensions are evaluated: scope (F1), frequency (F2) and amplitude (or excursion) (F3). These dimensions are similar to those used in the CCME Water quality index (Saffran et al. 2001) and mirror the aspects of ‘risk source,’ ‘exposure’ and ‘consequences’ used in many risk calculations (Merkhofer, 2012; Covello and Merkhoher, 2013). These three dimensions are defined as:

  • Scope (F1): The number of spatial units in area of interest that are unable to meet the objective or threshold.

  • Frequency (F2): The frequency with which the objectives or thresholds are not met.

  • Amplitude (or excursion) (F3): The amplitude or magnitude under which the objectives or thresholds are not met.

The final value for each dimension is scaled between (0-100) before combining into a final score. Data quality and availability to determine the three dimensions will vary based on the ecosystem service being evaluated and the area of assessment: In some cases, only 1-2 of the dimensions can be calculated with any confidence from the available data. In some cases, only one or two dimensions can be calculated with certainty (Modarres, 2006) in which case the robustness or certainty of the evidence should be reported when calculating the final scores, as follows:

  1. If able to only determine F1: $$ESI = 100\ - \ F1$$ (low evidence)

  2. If able to only determine F1 and F2: $$ESI\ = \ 100\ - \ \sqrt{F1 \times F2}$$ (medium evidence)

  3. If able to determine all three: $$ESI\ = \ 100\ - \ \sqrt{F1 \times F3}$$ (high evidence)