[Insert Fig. 3 here]
In theory, window sizes of 80 s can be used, but in practice the quality
of recorded temperature data deteriorates as temperatures level off and
noise thus becomes increasingly prominent. For example, if we exclude
temperature rises of less than 0.015 K (3 times the standard deviation
of temperature noise due to sensor resolution), sap velocities
> 80 cm h-1 could not be deciphered using
a 100 s window. Optimal window sizes generally decrease as flow rates
increase. To simplify, we suggest a fixed window of 40 s forV DRM calculations – the same window size as
recommended for the HRM.
In minimizing SEs, the DRM algorithm identifies both the optimal size
and timing of the averaging window. There is a distinct transition of
optimal window size and timing in the range of velocities at which the
intrinsic uncertainties of V 12 andV 23 are similar, which occurs at around
~ 20 cm h-1. At lower sap velocities,V 12 is less uncertain thanV 23 (hence V DRM =V 12, Eqn. 7 ), giving an optimal
averaging window 40 s wide and centred between 60 and 70 s (Fig.4 ) – very similar to the averaging window commonly used for
the HRM (40 s wide and centered at 80 s, see Chen et al. (2012)). At
intermediate sap velocities, V 23 is less
uncertain than V 12 (henceV DRM = V 23), and the
optimal averaging window is centered at > 200 s – roughly
when the temperature traces for Probe #2 and #3 intersect (see blue
and red lines in Fig. 4 ). Note that the velocity at which the
transition from V 12 to V 23occurs will depend on conditions and will differ with probe positions
and heat pulse strength and length. For example, greater heat intensity
(Q /t 0) will lead to a transition at
greater flux.