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.