Determining Characteristic Stressor Scales for Ecosystem Monitoring and Assessment

While most environmental scientists appreciate the importance of appropriate spatial and temporal scales for environmental assessment and monitoring, the issue of how to determine these scales has not (in our view) been addressed in sufficient depth. Here we define thecharacteristic spatial scalefor a stressor as the nearest distance from the source at which stressor values cannot be statistically distinguished from those further away, while thecharacteristic time scaleis the length of time required to detect a statistically significant decline in average stressor values within the defined characteristic spatial scale in response to reduced stressor emission at the source. We show that for a simple model of exponential distance-decay of average stressor values away from the source, the characteristic distanced*for a stressor increase with (1) decreasing spatial signal strength, (2) decreasing spatial noise, (3) increasing sample size and (4) decreasing sampling resolution. By contrast, the characteristic time-scale τ* increases with (1) decreasing sample size and (2) decreasing sampling resolutions. Moreover, unliked*, the relationship between τ*, signal strength and spatial noise is not straightforward. Consequently, neither is the relationship betweend*and τ*; stressors with small characteristic spatial scales need not also have short characteristic time scales. Thus, the accepted wisdom that spatial and temporal scales are positively correlated need not be true in practice primarily because the ability todetectstatisticallly significant spatial or temporal change may vary considerably among different levels of biological organization