Figure 4: Mutual information between cumulative hyporheic respiration and watershed characteristics. We include Q10-30 as HEF quantiles that were consistently Uncertain in both basins and Q80-100 as quantiles that were consistently Super-linear in both basins. Mutual information values were normalized to the maximum value for each analysis.
As a first step towards generalizing scaling behavior, we plotted the relationship between maximum elevation, precipitation, and cumulative respiration within the context of scaling (Figure 5). Both basins showed significant (p < 0.0001) positive relationships between maximum elevation and cumulative respiration (R2 = 0.48 for WRB and 0.68 for YRB, with a relatively consistent transition from Uncertain scaling behavior at lower respiration and maximum elevation values to Linear then Super-linear with increasing respiration and maximum elevation (Figure 5). This is expected, as maximum elevation positively correlates to watershed area (R2 values of 0.19 and 0.20 for WRB and YRB respectively, Figure S5). We did observe some non-linear behavior in WRB, where reaches with the lowest maximum elevation had a much steeper relationship (higher slope) compared to reaches with higher maximum elevations (Figure 5). In contrast, the YRB showed remarkably consistent linear behavior across the full elevation range with no apparent breakpoint in the relationship. For both basins, we observed a divide along the elevation axis for Uncertain reaches between lower-precipitation and higher-precipitation values. In the YRB in particular, drier reaches generally fall close to the best-fit line, while wetter reaches consistently diverge from the dominant linear pattern.