*2.5. Validation Method*

The upscaled results will be validated by comparison to two common methods to estimate ET, namely the Modified Penman Equation for computing reference evapotranspiration (*ETo*) and an equation utilizing normalized difference vegetation index (NDVI) data and meteorological data. The original Penman Equation comprises two terms: energy (radiation) and aerodynamic (wind and humidity) [30]. The Modified Penman Equation includes an amended wind function [31]. According to [32], the Modified Penman Equation has been shown to overestimate *ETo* in conditions with high winds and low evaporation, but it offers the best *ETo* estimates for grass surfaces. The *ETo* (mm/d) was calculated using

$$ET\_o = c[\mathsf{W}R\_n + (1 - \mathsf{W})f(u)(VPD)]\tag{8}$$

where *c* [-] is an adjustment factor compensating for difference in day and night weather conditions, *W* [-] is a temperature related weighting factor, *Rn* (mm/d) is the net solar radiation in equivalent ET, *f*(*u*) [-] is a wind-related function, and VPD (mbar) is the vapor pressure deficit.

The second method for estimating ET is via satellite remote sensing and meteorological data. Remote sensing provides spatial and temporal coverage of the land surface [33]. NDVI is one of the many products that comes from remote sensing and it quantifies the density of green vegetation on a plot of land. Comprising imagery with near-infrared and red spectral bands, NDVI data are useful for monitoring changes in vegetation [34]. Due to chlorophyll in the leaves, vegetated areas absorb visible light and have high near-infrared reflectance. In contrast, non-vegetated features have high visible light reflectance and low near-infrared reflectance, namely rocks, bare soil, water, snow, and clouds. Using an equation by [35], the ET of the riparian forest can be calculated with

$$ET = \frac{R\_n \phi \Delta}{\rho \lambda (\Delta + \gamma)} \left( 1 - 0.583e^{-2.13 \text{NDVI}} \right) \tag{9}$$

where *Rn* (W/m2) is the net solar radiation, *φ* [-] is the aerodynamic and canopy resistance parameter, Δ is the slope of the saturated vapor pressure curve, *ρ* (kg/m3) is the density of water, *λ* (J/kg) is the latent heat of vaporization of water, and *γ* (kPa/K) is a psychrometric constant. The parameter *φ* ∈ (0, *φ*max) was estimated from a scatter plot of site surface temperature *To* and NDVI data using the linear interpolation scheme described in [35], where *φ*max = (Δ + *γ*)/Δ = 1.26.

The *ETo* data set consisted of hourly ET data reported by a California Irrigation Management Information System (CIMIS) automated weather station located 21 km from the study area, in Santa Cruz. The station uses the CIMIS version of the modified Penman-Monteith Equation [30] given by [31] to calculate ET from a standardized grass surface that is well-irrigated and closely cut, while completely shading the soil. NDVI and meteorological data were used to calculate the ET of the riparian forest with Equation (9). The NDVI data were taken from weekly EROS Moderate Resolution Imaging Spectroradiometer (eMODIS) composite sets at 250 × <sup>250</sup> m2 spatial resolution [36]. The weighted average NDVI value of the entire study area each week was calculated in ArcMap by determining the percentage of study area within each pixel. The NDVI values were calculated using NDVI = (IR − R)/(IR + R), where IR and R represents pixel values from the infrared and red bands, respectively. This yielded NDVI values in the range −1 to +1 for use in Equation (9). Required meteorological data comprised air pressure, air temperature, and solar radiation. Two sets of these data were taken from two separate weather stations (CIMIS and Weather Underground) within the general vicinity of the study area in order to compare sap flow based-ET to separate areas with slightly different weather patterns. The second station was a nearby Weather Underground (WU) station, located 5 km from the study area in Davenport, CA. The meteorological data of each weather station were averaged over the same weeks as the eMODIS composite sets.

#### **3. Results**

As stated previously, the objective of the work was to estimate riparian forest ET from sap flow measurements collected in a small sample of the predominant vegetation. The ET estimates are based on estimates of the total sapwood area for the entire riparian forest as well as its canopy areal extent. The results are presented in the following.

#### *3.1. Phreatophytic Vegetation Survey and Sapwood Area*

A total of 159 trees were surveyed in the six sample plots, with 153 of them being phreatophytes. They comprised 83 red alders, 61 arroyo willows, 9 pacific willows, and 6 coastal redwoods. The survey comprised direct measurement of DBH using diameter tape. Sapwood depth was measured directly in a subset of the surveyed phreatophytes by wood coring. The coastal redwoods are not considered phreatophytes, and thus were excluded from the calculations for the total sapwood area of the riparian forest. The survey results, including averages and standard deviations of DBH and sapwood area, are summarized in Table 1. The values in parentheses are for the subsamples that were selected for coring to obtain direct measurements of bark thickness and heartwood/pith radius for sapwood area estimation. Multiple cores were extracted on some trees because the heartwood and/or piths were difficult to sample. Larger trees were especially difficult to sample due to irregularities in radial growth of tree stems. The poor surface quality of the cores and the small difference in color between early wood and late wood made determining the age of trees challenging. Wood cores from young, small red alders (DBH of *d* < 35.6 cm) consistently showed only bark, sapwood, and piths, which agree with [17].

The histograms of the measured diameters at breast height for all surveyed phreatophytes are shown in Figure 5. Theoretical probability density functions are also included for completeness. The arroyo willows and pacific willows were analyzed as one composite group due to their small sample sizes (61 and 9, respectively). Weibull (*p* = 0.090 for willows and *p* > 0.250 for red alders) and lognormal (*p* = 0.079 for willows and *p* = 0.214 for red alders) distribution model fits are also included. When the red alders and willows were analyzed as one composite phreatophytic vegetation group, they appear to follow gamma (*p* = 0.182) and Weibull (*p* = 0.087) distributions based on a 95% confidence interval. All the probability density functions show positive skewness indicating a sampling bias on the small tree diameter end of the range. Figure 5 also shows histograms of cored main stem sapwood areas for red alders, arroyo willows, and pacific willows from the six sample plots.

**Table 1.** Statistics of surveyed phreatophytes within the six sample plots. The values in parentheses indicate the subsamples that were selected for coring to obtain direct measurements of bark thicknesses and heartwood/pith radii for sapwood area estimation.


**Figure 5.** Histograms of *measured* tree stem diameters at breast height (DBH) for (**a**) all phreatophytes, (**b**) red alders, and (**c**) willows within the six sample plots, and histograms of *measured* main stem sapwood areas for (**d**) all phreatophytes, (**e**) red alders, and (**f**) willows within the six sample plots.

Estimates of model parameters in Equations (2)–(4) from tree core data are summarized in Table 2. These parameters were used to estimate sapwood basal area for the trees on which cores were not obtained but for which the diameter *d* at breast height was measured. Estimates of the fractional sapwood basal area and sapwood area across the entire riparian forest using Equations (5) and (6), respectively, are also summarized in Table 2.


