Evapotranspiration from Natural Vegetation in the Central Valley of California: Monthly Grass Reference-Based Vegetation Coefficients and the Dual Crop Coefficient Approach

In several recent studies, $K_v$ was computed based on a Penman-Monteith equation for ${\mathrm{ET}}_o$ (grass reference) or ${\mathrm{ET}}_r$ (alfalfa reference). Some of these studies were conducted prior to the publication of the ASCE Standardized Reference Evapotranspiration Equation, but used similar equations and standards. If the $K_v$ was developed using a grass reference, it is reported here without modification. If the $K_v$ was based on an alfalfa reference, it was modified to convert it to a grass-reference-based $K_v$. These modifications will be discussed.

In some cases, the standard grass-reference equation could not be used to compute $K_v$. The ${\mathrm{ET}}_{o\text{\_}\text{Study}}$, for example, had to be estimated on a monthly basis for the time frame and the location that the study was conducted. As most ${\mathrm{ET}}_o$ weather stations were not installed in the western United States until the 1980s or later, it was not possible to use the standardized reference evapotranspiration equation for some datasets. Alternatively, the Hargreaves ${\mathrm{ET}}_o$ equation was used in cases where the full set of weather parameters was not available. The Hargreaves equation has been shown to provide relatively accurate ${\mathrm{ET}}_o$ estimates with limited data (maximum and minimum temperature only) in arid regions (Jensen et al. 1990; Allen et al. 1998). Hargreaves ${\mathrm{ET}}_o$ is computed based on temperature and extraterrestrial radiation ($R_a$) as Eq. (4)where temperatures are in degrees Celsius, and $R_a$ and ${\mathrm{ET}}_o$ are in millimeters per unit time. The Hargreaves equation does not include direct information on wind speed or relative humidity, which can cause inaccuracies associated with the Hargreaves ${\mathrm{ET}}_o$. Allen et al. (1998) discusses a calibration method to improve the accuracy of the Hargreaves ${\mathrm{ET}}_o$ estimate on a monthly or annual basis by comparing it to the standardized Penman-Monteith ${\mathrm{ET}}_o$ for years with overlapping data.

${\mathrm{ET}}_{o\text{\_}\text{Study}}$ was determined for each study site depending on the data availability. The list below is used to identify the method used to compute ${\mathrm{ET}}_o$ for each study summarized in the results section. The methods used for determining ${\mathrm{ET}}_o$ were as follows:

If methods (4) or (5) were used to estimate ${\mathrm{ET}}_{o\text{\_}\text{Study}}$, these ${\mathrm{ET}}_o$ values were checked against the long-term (10-year) average ASCE ${\mathrm{ET}}_o$ on an annual basis. The long-term average ASCE ${\mathrm{ET}}_o$ used for the check was either from weather stations within 20–30 miles with similar climate conditions or, for studies in California, from Spatial CIMIS data for the location of the study site (Hart et al. 2009). The difference between the annual ${\mathrm{ET}}_o$ values was set at a threshold of $\pm 15\%$. This reality check ensured that gross errors in the ${\mathrm{ET}}_{o\text{\_}\text{Study}}$ were avoided. If the Hargreaves ${\mathrm{ET}}_o$ was outside of this threshold, alternative means of computing ${\mathrm{ET}}_o$ were attempted or the dataset was abandoned. The alternative method for computing ${\mathrm{ET}}_o$ was to find a nearby NCDC weather station with temperature data for the study’s time frame and use the Hargreaves equation to compute the ${\mathrm{ET}}_o$ based on these data.

The PRISM (Parameter-elevation Regressions on Independent Slopes Model) system maintained by Oregon State University provides a grid of monthly temperatures (minimum and maximum) from 1895 to the present covering the United States (Daly et al. 2002, 2008). PRISM temperature data are computed based on surface weather station data and are interpolated based on factors such as location, coastal proximity, elevation, and topography (Daly et al. 2000).

As part of an unrelated, D. J. Howes, unpublished data, 2013, the primary author measured actual evapotranspiration from riparian and wetland habitats in Kern County, CA using a surface energy balance with remote sensing data. Monthly $K_v$ values were computed based on computed ${\mathrm{ET}}_o$ in these investigations and compared to the monthly $K_v$ values from literature. To develop the actual evapotranspiration from the riparian and wetland vegetation, LandSAT 5 images were processed over a two-year period for each site using modified METRIC procedures (Allen et al. 2007a). The primary author has modified the original METRIC procedure to use a grass-reference evapotranspiration and use a semiautomated internal calibration procedure. The values obtained from this separate study proved useful to the research discussed here, and a comparison of the data appears in the “Results and Discussion” section of this paper.

The wetland area that was examined for the comparison is within Kern Wildlife Refuge in northern Kern County, California. The wetland vegetation consists of tules, timothy, and cattails. LandSAT 5 images (Path 42/Row 35) were processed from March through October 2011, which was an unusually wet year that resulted in a portion of the wetland within the refuge having water all season. Because of limited water supplies during the summer, in most years the Kern Wildlife Refuge wetlands are seasonal with limited water supplies during the summer months.

$K_v$ values were computed for each image processed (one per month) using Eq. (2) where the ${\mathrm{ET}}_v$ was the instantaneous value at the time of image acquisition computed with METRIC and ${\mathrm{ET}}_o$ was the instantaneous grass-reference evapotranspiration. The instantaneous ${\mathrm{ET}}_o$ was interpolated from hourly data collected at the CIMIS weather station near Lost Hills, California (Belridge Station, Number 146).

Riparian vegetation in the Central Valley no longer exists in large quantities. However, one of the most significant remaining cottonwood–willow forests in California is located along the Kern River east of Lake Isabella, California in the southern Sierra Nevada mountain range. LandSAT 5 images (Path 41/Row 35) from March through September 2011 and October and November 2010 were used to compute actual evapotranspiration for the riparian forest near Lake Isabella. At least one image per month was used for the evaluation. $K_v$ values were computed as previously described; however, the instantaneous ${\mathrm{ET}}_o$ was computed using the 2005 ASCE Standardized ${\mathrm{ET}}_o$ equation with weather data collected at a Remote Automatic Weather Station (RAWS) near Kernville, California (MesoWest Station KRNC1). Weather data were quality controlled prior to computing ${\mathrm{ET}}_o$ based on procedures of Allen et al. (1998).

The soil–water balance model requires inputs related to plant development, soil-available water-holding capacity, root-zone depth, daily grass reference evapotranspiration, daily precipitation, and basal $K_v$ ($K_v$ for vegetation that is nonstressed with no surface evaporation) during different development periods. While many inputs into the model could be estimated for the Valley Floor based on weather measurements and soil reports, vegetation parameters including basal $K_v$ and plant development timing are unknown. To estimate the vegetation parameters for the grasslands and foothill hardwoods, these parameters were adjusted manually until the modeled ${\mathrm{ET}}_v$ matched the measured ${\mathrm{ET}}_v$. Because only two parameters were modified during the calibration, namely vegetation development and basal $K_v$, manual calibration was used. However, this was a time-consuming process and in the future, an automated calibration tool may be more appropriate.

Daily grass reference evapotranspiration data were obtained from CDWR Cal-SIMETAW program for the Planning Area that included Ione, California based on the spatially averaged ${\mathrm{ET}}_o$ (Orang et al. 2013). Estimated daily precipitation was also provided with ${\mathrm{ET}}_o$. However, the annual precipitation in Valley Floor Planning Area was significantly lower during that year than reported by Baldocchi et al. (2004). This is likely due to the fact that Ione, California is at a higher elevation along the Sierra Nevada foothills and receives more precipitation than other portions of the Planning Area (Planning Area #603). However, daily precipitation data from the original study were not available. To make the adjustment, on days of precipitation in the dataset, the precipitation was increased until the annual precipitation amounts matched those of Baldocchi et al. (2004). In this way, the seasonal precipitation variability was maintained.

For model calibration, the soil-available water-holding capacity (AWHC) was based on the soil retention curves measured by Baldocchi et al. (2004). The reported soil textures were silt loam to rocky silt loam (Miller et al. 2010). The AWHC was computed to be $350\mathrm{mm}/\mathrm{m}$ for the oak savanna and $190\mathrm{mm}/\mathrm{m}$ for the grassland based on the soil–water retention curves. The maximum root-zone depth used for the annual grassland was 0.6 m (Reever Morghan et al. 2007).

For the foothill oak savanna, used as a surrogate for foothill hardwoods, the depth of the root zone was assumed to be 1 m, which is equivalent to the depth of the surface soil (Miller et al. 2010). Both Baldocchi et al. (2004) and Miller et al. (2010) reported that the oaks used groundwater in the summer and fall when soil moisture was limited. While the overall ${\mathrm{ET}}_v$ was significantly lower when soil moisture levels were low, a high percentage of ${\mathrm{ET}}_v$ during this time can be attributed to groundwater (Miller et al. 2010). Oak roots can extend through fractured rock to depths in excess of 24 m (Lewis and Burgy 1964). The lower ${\mathrm{ET}}_v$ during the summer and fall is due to the fact that a relatively shallow soil layer overlaid a fractured rock aquifer that was accessible to a smaller portion of roots. Miller et al. (2012) estimates that groundwater supplies account for approximately 20% of the annual evapotranspiration in the foothill oak savanna. The soil–water balance model did not include contributions from the groundwater in the summer and fall, thus underestimating evapotranspiration for foothill oak savanna. Therefore, the summer evapotranspiration comparison shown in Fig. 2(a) is higher for the measured values than the modeled values. In July and August 2002, the difference between measured and modeled ET was 14 mm and 16 mm, respectively. For the valley oak savanna category, groundwater availability during the summer was assumed.

Vegetation development and basal $K_v$ were calibrated by comparing reported ${\mathrm{ET}}_v$ data from the eddy covariance stations (Baldocchi et al. 2004) to modeled ${\mathrm{ET}}_v$. The processed data for the years reported in the study were obtained from FLUXNET (ORNL DAAC 2013). The development stages and basal $K_v$ were manually adjusted until the modeled and measured monthly average ${\mathrm{ET}}_v$ followed similar patterns and had similar magnitudes, as will be discussed in more detail. The basal $K_v$ is the potential transpiration without water stress and is generally a function of leaf area and vegetation type. The actual $K_v$ is computed using the dual-crop coefficient method in the soil–water balance model, which accounts for vegetation stress due to limited water availability and soil evaporation from a wet soil surface. This is because basal $K_v$ values are not available for these vegetation types and would be dependent on the vegetation cover and health. Vegetation development could be predicted initially through visual examination of the ${\mathrm{ET}}_v$ from the covariance stations. Initial adjustments to the vegetation development were made until the early year trends (not magnitude) in monthly ${\mathrm{ET}}_v$ agreed. The basal $K_v$ required more adjustment during the calibration procedure and were adjusted until the magnitude of monthly modeled and measured ${\mathrm{ET}}_v$ correlated. Additional fine tuning adjustments were made to the vegetative development timing but basal $K_v$ seemed to be the most important for calibration. The root mean square error (RMSE) and normalized RMSE (NRMSE) for rainfed grassland were 6.1 mm and 8%, respectively. The RMSE and NRMSE for foothill oak savanna were 9.1 mm and 11%, respectively. The higher RMSE and NRMSE for the foothill oak savanna is in part due to the model underpredicting ${\mathrm{ET}}_v$ because it was conservatively assumed that the vegetation type did not have access to groundwater. Calibrated values used for the long-term modeling are shown in Table 1. A comparison between the measured and calibration results are shown in Fig. 2.

Evapotranspiration from chaparral vegetation was calibrated using a similar procedure previously discussed based on data used by Claudio et al. (2006). The chaparral leaf area and height were assumed constant throughout the year and therefore the only calibration parameter was basal $K_v$. This assumption, which simplified the calibration procedure, resulted in a best fit between modeled and measured data with a constant basal $K_v$ throughout the year. This indicates that chaparral vegetation is capable of utilizing water if it becomes available and regulates its use as soil moisture depletion increases. Processed eddy covariance data from 2001 through 2002 obtained from FLUXNET (ORNL DAAC 2013) at the Sky Oaks field station located in northern San Diego County were used for the calibration. Grass reference ${\mathrm{ET}}_o$ was obtained from the CIMIS Station #137 near Temecula, California (CIMIS 2013). Calibrated values used for the long-term modeling of chaparral are shown in Table 1. The RMSE and NRMSE for chaparral modeled values were 4.9 mm and 10%, respectively. A comparison between measured and calibrated-modeled ${\mathrm{ET}}_v$ for chaparral is shown in Fig. 2(c).

Once the vegetation parameters were calibrated, the other model inputs were modified to represent average conditions on the Valley Floor (as opposed to the upper foothills). The calibrated model for the rainfed grasslands, chaparral, and foothill hardwoods was used as the basis of the long-term modeling of these vegetative types for the Valley Floor. However, modifications were made to the rooting depth and soil AWHC to account for differing characteristics near the Valley Floor. A root-zone depth of 1.5 m was used for the foothill hardwood, which coincides with the measured root-zone depth of older blue oaks (Millikin and Bledsoe 1999). Oak roots in the Valley Floor can be much deeper to tap into the groundwater, but because the grassland and foothill hardwoods oaks are modeled as a system (as opposed to independently), a deeper root zone would lead to overestimation of ET from the grasslands within the foothill hardwood, while underestimating ET from the hardwood themselves. In the foothill regions on the edge of the Valley Floor, Millikin and Bledsoe (1999) found that the majority of the blue oak root biomass was in the top 0.5 to 1 m of soil, and a smaller percentage below that reached to a depth of 1.5 m. However, Miller et al. (2010) found that blue oaks reach and rely on stores of groundwater more than 10 m below the surface. Thus, the approach used here would underestimate ${\mathrm{ET}}_v$ from foothill hardwoods.

The rainfed grasslands’ root zone was maintained at 0.6 m based on field studies of annual and perennial bunchgrass on the Valley Floor (Holmes and Rice 1996). Major soil types covering the grassland and valley/foothill hardwood habitat were examined in GIS by overlaying the vegetation types with a large-scale soils map of California (Soil Survey Staff 2006). The major soil texture in both vegetative categories was silt loam, covering 28% of the valley/foothill hardwood and 18% of the grassland areas. Other major soil textures in these regions included gravelly loam, sandy loam, loam, and clay loam. General published values of AWHC for these soil types range from 110 to $200\mathrm{mm}/\mathrm{m}$ (Allen et al. 1998). An average value of $150\mathrm{mm}/\mathrm{m}$ was used for the modeling of both vegetation types.

Urbanization and agriculture have replaced the valley oak savannas that once covered a significant area within the Central Valley. Unlike the blue oaks that make up the majority of the foothill hardwood savannas, valley oaks are not as drought tolerant and studies have indicated that they have deep roots that tap into groundwater reserves (Griffin 1973; Knops and Koenig 1994). Valley oaks tend to grow in bottomlands where groundwater is available. Because the water table was much higher predevelopment, it is reasonable to assume that the valley oaks had unrestricted access to groundwater in a significant portion of the Valley Floor. However, no information on evapotranspiration for natural valley oak savannas was found during this investigation. Valley oaks are dormant from December to approximately March in California (Pavlik et al. 1991). During this time frame, the grass and scrub understory would continue to use water (rainfed). It was assumed that the evapotranspiration on the Valley Floor would be similar to the foothill hardwoods during the winter and spring until the soil moisture was depleted in the primary understory root zone. After this period, a $K_v$ value of 0.4 was used throughout the summer and fall to account for groundwater use by the valley oaks. The value of 0.4 was selected to account for a medium density overstory with a shallower rooted understory that either senesces or has significantly reduced evapotranspiration during the summer and early fall. The tree density of the valley oaks during predevelopment was likely mixed, as it is today (Pavlik et al. 1991), having higher densities on the fringe of the riparian forests to wider spacing towards the foothills on the edge of the Valley Floor. An estimated minimum summer and fall $K_v$ of 0.4 represents an average tree density that would underestimate the evapotranspiration in the dense oak forests. However, the distribution of valley oak tree densities throughout the Valley Floor predevelopment is currently unknown so an average density was assumed.