*2.2. Sap Flow Measurements*

Four trees of the dominant phreatophytes at the study site were selected for monitoring based on their stem diameters (7.6–12.7 cm) and proximity (less than 33 m) to the data acquisition station. The location of the sap flow probe area is shown on the site map in Figure 1. A pair of probes was installed in each tree. The installation procedure involved removal of the outer bark at 1.22–1.45 m above the ground to minimize radiative temperature effects from land surface. Two pilot holes, 40 mm apart vertically, were then bored into the tree stem to a depth of 30 mm using a 1.5-mm diameter drill bit. The pilot holes and drill bit were flushed with 10% chlorine bleach prior to and after boring the holes in each tree to minimize the introduction and spread of pathogens. The probes were then carefully inserted into the bores and adhesive putty applied around the base of each probe to provide a water-tight seal. Foam covers were placed over the probes for thermal insulation and to protect the electrical wiring. Reflective bubble insulation was wrapped around the probes, foam, and tree stem to minimize thermal gradients caused by direct solar radiation. Saran wrap was wrapped around the tree stem and upper portion of the reflective bubble insulation to prevent water from flowing down the stem surface and into the probes. Figure 3 depicts the probe installation steps (a)–(d) and the aftermath of tree healing that occurred over the study period (e).

**Figure 3.** Pictures of the probe installation and insulation procedure. (**a**) the dual probe after insertion into stem drill holes and sealing with putty, (**b**) foam insulation cover over probes, (**c**) reflective blanket, (**d**) saran wrapped installation, and (**e**) post-study period probe condition shown growth over probe.

The probes were part of the FLGS-TDP XM1000 sap velocity system (Dynamax Inc., Huston, TX, USA), which includes a CR1000 measurement and control data logger with a AM16/32 relay multiplexer (Campbell Scientific, Logan, UT, USA) housed in a rugged weather-resistant instrument enclosure. Communication, programming, and data extraction between the data logger and a computer were facilitated using the PC400 data logger support software (Campbell Scientific). The data logger and solar panel were mounted

on a 10-ft UT10 aluminum tower in a forest canopy gap. The tower was secured in an 8-ft3 concrete pad with a J-bolt kit for stability during rough weather and flooding. Probe cords were placed inside 1.0-inch diameter schedule 40 PVC conduit pipes and installed approximately 30 cm underground for protection against weather, flooding, and wildlife. The conduit pipe openings were covered with duct seal putty to keep out moisture. Upon completion of probe installation and mounting the data logger to the tower, sap temperature differentials were recorded at one-minute intervals and their averages were recorded every 15 min. The data were downloaded from the data logger every two months. A sap flow computation spreadsheet, provided by Dynamax Inc., and modified appropriately to implement the theoretical equations of [14], was used to calculate the volumetric rate of sap flow.

#### *2.3. Measurement and Estimation of Tree Diameter and Sapwood Depth*

Determination of the sapwood area, *SA*, requires knowledge of tree stem diameters, *d*, and sapwood depth, *D*sap. Hence, for this work, tree stem diameter, *d*, at breast height (herein *d* = DBH) was measured for all woody vegetation greater than 0.025 m in diameter in each of the six representative sample plots. For this work, the breast height used was 1.37 m. The stem diameters were measured manually with a standard English diameter tape. The tree diameter tape is based on the assumption that tree stems are perfect circles such that *d* = *C*/*π*, where *C* is tree stem circumference. Within each plot, the number of species, and number of trees for each species were also recorded.

Whereas tree stem diameter was measured for all woody vegetation in each of the sample plots, sapwood depths, *D*sap, were measured from cores extracted from a small representative subset of the riparian phreatophytic trees within each plot. A stratified random sampling design was used to estimate phreatophytic vegetation composition. Woody vegetation was sampled in six random plots, each of area 400 m2, within the riparian corridor. Environmental Systems Research Institute's (ESRI) ArcMap 10.7 was used to determine the locations of these random plots. First, a fishnet with 20 m × 20 m sections was laid over the study area in ArcMap. Then, random sections were chosen on the grid. The coordinates of the northwest corner of each plot were programmed into a Trimble Geo 7X handheld GPS for locating in the field. The locations of the remaining three corners for each plot were determined with an open reel measuring tape and a compass.

To measure *D*sap, wood cores were extracted at breast height (1.37 m) from select phreatophytes using an increment borer (Haglöf Sweden AB) within each plot. The bark thickness, sapwood depth, and heartwood/pith radius of each core were measured in the field with a ruler. In most trees, the sapwood's lighter color made it simple to distinguish from the heartwood. However, in some trees (e.g., red alders and arroyo willows), there was very little color difference between the sapwood and heartwood [24]. In order to determine the sapwood depth, *D*sap, wood cores were first stained with a 0.2% safranin dye by applying the dye to each core in a series of continuous drops using a small pipette. The dye was applied immediately after extracting the cores because the vessels of vascular system lose uptake pressure [25]. Because the dye is absorbed more easily by sapwood than by heartwood [26], it allows one to locate the sapwood and heartwood boundaries from which *D*sap could then be estimated. Figure 4 depicts (a) the bore from which a core sample was retrieved, (b) an example of a retrieved tree core stained with dye, and (c) a close-up of the core showing sap wood to heartwood transition.

**Figure 4.** Core sampling to measure of sap wood and heartwood depth. (**a**) tree bore after core retrieval, (**b**) retrieved tree core, and (**c**) a close-up of the core showing sap wood to heartwood transition.

The sapwood depth, *D*sap, of phreatophytic trees in each plot was measured in only a subset of the trees on the plot. Here, we outline the approach used to estimate *D*sap, and the sapwood areas, *SA*, of the non-sampled trees. Sapwood depth is defined as

$$D\_{\rm sap} = \frac{d}{2} - D\_B - D\_{H\prime} \tag{1}$$

where *d* is tree diameter at breast height (DBH), *DB* is bark thickness, and *DH* heartwood/pith radius. Estimates of bark thickness *DB* for non-cored trees of known diameter, *d*, were estimated using the relation of [27], namely

$$D\_B = a\_1 e^{\beta\_1 d},\tag{2}$$

where *a*<sup>1</sup> and *β*<sup>1</sup> are empirical parameters determined using data from cored trees. Estimates of heartwood/pith radii were obtained using the relation

$$D\_H = a \circ \epsilon^{\beta\_2 d},\tag{3}$$

for red alders, and

$$D\_H = a\_2 d + \beta\_{2'} \tag{4}$$

for willows, where *a*<sup>2</sup> and *β*<sup>2</sup> are empirical parameters determined using data from cored trees. For cored trees, the measured bark thicknesses and heartwood/pith radii were plotted against the measured stem diameters and best fits of the models given in above were obtained to determine the values of the empirical parameters. With the empirical constants thus determined, Equations (2)–(4) were then used to estimate values of *DB* and *DH* for the non-cored trees given their measured diameter *d*.

For cored samples, the dye droplet method was used to determine the boundary between sapwood and heartwood. The dye was applied to every core immediately after extraction from the tree but yielded mixed results depending on the quality of the wood cores and the tree. On some cores, especially those from small trees, the sapwood absorbed the dye immediately. Heartwood in cores from older trees absorbed the dye at very slow rates, making it challenging to make the distinction between heartwood and sapwood in a timely manner. There were multiple instances where sapwood and heartwood could not be distinguished from each other based on dye absorption. In these cases, changes in color and/or texture were used to determine the sapwood/heartwood boundary. Overall, determining the boundary between sapwood and heartwood was very difficult, even with the dye droplet method.

#### *2.4. Upscaling Plot Measurements to Forest Scale*

Sapwood area is a measure of the actual tree stem area through which water extracted from the subsurface flows on its way to be transpired to the atmosphere from the canopy. The sapwood areas of all phreatophytic trees in six sample plots of the riparian forest were used to estimate the fractional sapwood basal area, *α<sup>k</sup>* (expressed in m2/ha), for each

phreatophytic species over the riparian forest within the study area using the following relation adapted from [28]:

$$\alpha\_k = \frac{1}{M} \sum\_{p=1}^{M} \left( \frac{1}{A\_p} \sum\_{n=1}^{N\_p} A\_{n,p}^{(k)} \right) \tag{5}$$

where *M* is the number of sample plots, *Np* is the number of trees of *k*th species in the *p*th sample plot, *Ap* is the forest floor area of the *<sup>p</sup>*th sample plot, and *<sup>A</sup>*(*k*) *<sup>n</sup>*,*<sup>p</sup>* is the sapwood area of the *n*th tree of the *k*th species in the *p*th plot. In this work, the area of each of the six (*M* = 6) sample plots in which trees were counted and core samples collected, was fixed at *Ap* = 400 m2. The total sapwood area, *As*,*k*, of a given phreatophytic species over the entire riparian forest within the study area was then estimated as simply

$$A\_{s,k} = \mathfrak{a}\_k A\_{\rm rf} \tag{6}$$

where *A*rf is the measured total ground area of the forest. For this study, *A*rf = 9.2 ha.

The total riparian forest sapwood area determined with this equation was then with sap flow data from the four instrumented trees to upscale measured sap flow to the riparian forest ET. First, the ET from each instrumented tree was calculated based on the areal extent of its canopy [29]. The canopy extent of each instrumented tree was determined with a Trimble Geo 7x GNSS handheld. In ArcMap, the GPS points of each tree were connected to create a polygon that represented the areal extent of the canopy. A modified version of an equation from [16] was used to calculate ET above the riparian corridor canopy viz.,

$$ET = \frac{1}{A\_{\text{cp}}} \sum\_{k=1}^{N} \mu\_k A\_{s,k} = \frac{A\_{\text{rf}}}{A\_{\text{cp}}} \sum\_{k=1}^{N} \mu\_k a\_k \tag{7}$$

where *N* is the number of tree species, *uk* is the mean sap flux density of the *k*th phreatophytic species and *A*cp is the combined canopy areal extent of the riparian forest. For simplicity, arroyo and pacific willows are treated as one species for this study such that the number of species was *N* = 2 (red alders and willows). This was necessitated by the fact that only one willow was instrumented.
