2.1 Study area

We measured ground ET_a using a 3-ha, instrumented drainage lysimeter (Figure 1) embedded in an in-service uranium mill tailings disposal cell managed by the U.S. Department of Energy (DOE) near the town of Monticello in southeastern Utah (https://www.energy.gov/lm/office-legacy-management). The Monticello mill was operated from 1942 to 1960 to produce uranium and vanadium for military purposes. Remedial action at the abandoned mill, completed in 2000, was regulated under CERCLA. The disposal cell has an engineered earthen cover designed to limit release of radon gas into the atmosphere and percolation of water into underlying tailings (Waugh et al., 2009).

Monticello is semiarid with cold, windy winters and mild summers. The average annual precipitation (PPT) is 390 mm, the average minimum January temperature is −10.5°C, and the average July maximum temperature is 28.9°C. Three seasons occur with respect to soil–water balance: November–March, the season of deep infiltration and moisture accumulation in soils (PPT averages 160 mm); April–June, a moisture-depletion period when plants are most active (PPT averages 60 mm); and July–October, a season of near-surface moisture accumulation and depletion resulting from monsoonal convection storms (PPT averages 170 mm). Annual snowfall averages 160–170 cm. The clay loam to sandy loam soils (Monticello very fine sandy loam) within the footprint of the Monticello disposal cell were formed in Pleistocene loess (USDA, 1945). The potential natural vegetation for this soil consists primarily of western wheatgrass (Pascopyrum smithii), Sandberg bluegrass (Poa secunda), blue grama (Bouteloua gracilis), mountain big sagebrush (Artemisia tridentata subsp. vaseyana), and rubber rabbitbrush (Ericameria nauseosa) and typically has a canopy coverage of 50%–60% based on annual ground surveys.

The Monticello disposal cell cover, sometimes called an ET cover, was designed to limit percolation into underlying tailings and subsequent leaching of contaminants into groundwater. The design mimics the favourable ecology and water balance of the deep aeolian soils occurring in the landscape surrounding the disposal site (Waugh et al., 2006). The ET cover design relies on the water storage capacity of a 163-cm, fine-textured layer of the aeolian soil overlying a 38-cm sand capillary barrier layer to store PPT and on ET to seasonally release stored water back to the atmosphere (Albright et al., 2004; Waugh et al., 2009; Waugh & Richardson, 1997). Capillary barriers composed of coarse-textured sand and gravel placed below a soil ‘sponge’ can enhance water storage capacity and limit unsaturated flow (Stormont & Morris, 1998; Ward & Gee, 1997). Water movement past the capillary barrier can occur when water accumulation at the fine soil/coarse sand interface approaches saturation and soil water tensions decrease sufficiently for water to enter the larger pores of the sand layer. Hydraulic performance can be evaluated as the probability that ET is sufficient to prevent water accumulation in the soil sponge from exceeding the storage capacity in any given year. The sustainability of the ET cover will depend, in part, on the establishment and resilience of a diverse plant community (Waugh, 1997). Long-term changes in the plant community inhabiting a cover will influence soil water movement, ET rates and the water balance of the cover.

2.2 Ground ET_a measurements

The 3-ha drainage lysimeter at Monticello (Figure 1) functions as a large-scale water collection system. A high-density polyethylene (HDPE) geomembrane, required by the regulator, made creation of the water collection system possible. The geomembrane, placed below the capillary barrier at a depth of 201 cm, formed the floor of the lysimeter. An HDPE flap welded to the geomembrane (Figure 1) directs percolation to a sump at the lower corner of the 3-ha facet of the cover. We collected surface runoff in a 10 × 20-m subplot formed with treated lumber sidewalls and installed within the 3-ha embedded lysimeter (Figure 1).

Lysimeter instruments monitored flow (percolation and runoff), state variables within the cover profile (soil water content and temperature) and meteorology. We routed percolation and runoff from sumps through pipes into separate drainage basins located downslope of the lysimeter (Figure 1). Basins were equipped with tipping buckets, pressure transducers and flouts. The percolation basin has a 70-ml tipper and a 1-L tipper in series (Hydrological Services TB1L/70) for redundant measurement of low and high flows. The runoff basin has a single 1-L tipper. Flouts drain the basins at the high-water point. The basins are capable of measuring percolation and surface runoff flows with a precision better than 1 mm/year (Waugh et al., 2009). We monitored volumetric soil water content with low-frequency (40 MHz) water content reflectometer (WCR) probes (Model 615; Campbell Scientific, Logan, Utah), and soil water matric potential with co-located heat dissipation sensors (HDS) (Model 229; Campbell Scientific). WCRs and HDSs were installed in vertical arrays to a depth of 2 m in three locations at quarter points along a downslope transect through the lysimeter test section (Figure 1). We determined water storage in the profile by integration of the WCR point water content measurements and compared meteorological parameters at an onsite weather station to meteorological data from nearby National Weather Service stations.

2.3 Vegetation monitoring

Revegetation goals for the Monticello cover included plants that (1) were well-adapted to the engineered soil habitat, (2) were capable of high transpiration rates, (3) limited soil erosion and (4) were structurally and functionally resilient. Diverse mixtures of native and naturalized plants growing on engineered covers are thought to maximize water removal and remain resilient given variable and unpredictable changes in the environment resulting from pathogen and pest outbreaks, disturbances (overgrazing, fire, etc.) and climatic fluctuations (Link, Waugh, & Downs, 1994).

We seeded and planted the Monticello cover in September 2000 with a mixture of grasses, forbs and shrubs (DOE, 2006). Our goal was to mimic the potential natural vegetation as documented on native soil used to construct the ET cover. We measured species composition, percent cover, and shrub density for most years since 2001 and leaf area index (LAI) from 2001 to 2006 and again in 2011. Vegetation sampling methods included ocular point intercept (Floyd & Anderson, 1982) and quadrat methods (Daubenmire, 1959) for plant foliar cover, a point-quarter-distance method for shrub density (Eberhardt, 1967), and a radiometric method for LAI using an LAI-2000 (www.licor.com), all measured in mid-to-late summer. Invasive weeds, primarily Russian thistle (Salsola tragus) followed by cheatgrass (Bromus tectorum), dominated the plant community from 2000 through 2005 (Figure 2). Foliar cover of native herbaceous species increased as weedy species decreased during that period. Between 2005 and 2006, a rather abrupt decrease in weeds resulted in a burgeoning sagebrush steppe community dominated by western wheatgrass and maturing mountain big sagebrush.

2.4 ET_o calculations

We calculated monthly Penman–Monteith ET_o following the recommendations and methods outlined in Allen et al. (1998) and FAO (2012). The Penman–Monteith equation explicitly incorporates a suite of climatic parameters, but only temperature data were available in our region. Therefore, we calculated Penman–Monteith ET_o for temperature-only datasets assuming the average wind speed was light-moderate and the climate was arid–semiarid. We set the elevation to 2,141 m and centred the location on 37.85°N, 109.33°W (closest to the lysimeter). We obtained daily maximum and minimum temperature from 1-km gridded Daymet data over the lysimeter (Thornton et al., 2020).

2.5 Remote sensing data

Year 2012 represents the period between the decommissioning of Landsat 5 and the launch of Landsat 8. Because of the Scan Line Corrector (SLC) failure on Landsat 7 in 2003, images collected after this period contained streaks of missing data, precluding application of this platform in some areas. Initially, we included Landsat 7 imagery in our analysis but were unable to resolve inconsistencies in the spectral response of the VI over time (explained in the discussion); therefore, 2012 (and Landsat 7) was excluded from our study.

To ensure NDVI data were of sufficient quality for ET calibration, we first eliminated all scenes with >10% cloud cover. We then implemented a per-pixel quality assurance screening that retained only high-quality, clear pixels based on the quality assessment band provided by the USGS. To further minimize the impact of adjacent clouds and cloud shadow, we removed a 4-pixel-wide buffer around all potential cloud or shadow pixels. Finally, we eliminated scenes with less than the full complement of 22 pixels corresponding to the lysimeter. Only data that passed this strict filtering process were retained for further analysis, resulting in two to eight images per growing season and a total of 47 scenes for the period of study (Table 1).

2.6 NDVI scaling

Because this stretching process relies on saturated values of NDVI, we only used scenes acquired during the growing season. We subsequently calculated mean NDVI* for each growing season (mean annual NDVI*) using the scenes that passed the filtering process described above. We digitized the perimeter of the lysimeter and converted this polygon to a 30-m raster registered to the Landsat grid (n = 22 pixels; Figure 1). Mean NDVI* of the 22 lysimeter pixels was used in all subsequent analyses.

2.7 ET modelling

ET was modelled on both an annual scale and the 48-day period prior to each Landsat acquisition date. Sixteen- and 32-day timesteps were also tested, but, because of the immense volume of the lysimeter, a significant lag was discovered between the onset of rainfall and resultant changes in soil water storage and percolation. This lag sometimes led to negative or near-zero ET values over periods <32 days. The 48-day timestep was chosen because it both resolved this lag over all Landsat acquisition periods and corresponded to the Landsat acquisition repeat period of 16 days. We subsequently added daily ET_o, ET_a and PPT over each 48-day period. We excluded the Landsat image from 19 June 2010 because of spurious lysimetry data recorded during this period. To ensure the 48-day period did not include a significant portion of the non-growing season, we also excluded scenes acquired before 15 June, resulting in a total of 36 imagery periods. On an annual scale, we added lysimeter ET_a and PPT to derive water-year totals (October 1–September 30) for each component.

2.8 Statistical procedures

All statistical modelling was conducted in RStudio (RStudio Team, 2016). Ordinary least squares (OLS) regression was initially used to model the relationship between ET_a, ET_a normalized by ET_o (ET_a/ET_o), PPT and NDVI* on 48-day and annual timescales. Assumptions of independence and homogeneity were then assessed, and models were selected following methods in Zuur et al. (2009). For the 48-day ET_a/ET_o models, residual heterogeneity was resolved using generalized least squares (GLS) regression with a fixed variance structure proportional to NDVI*. A linear correlation function was also included in the GLS to resolve significant temporal autocorrelation observed at lag step 1. Multiple variance and correlation structures were compared and ranked by the corrected Akaike information criterion (AICc), and those with the lowest AICc were selected. We also included spatial correlation functions in this process because they can potentially handle missing and irregularly spaced data better than temporal functions (Zuur et al., 2009). The optimal fixed component of the GLS was subsequently determined by dropping all non-significant terms from the full model.

3.1 Annual modelling of ET_a

Our lysimetry NDVI* dataset ranged from a mean growing season high of 0.2609 in 2019 to a low of 0.0800 in 2018 (Table 1). Annual ET_a ranged from 225.3 mm in 2018 to 602.4 mm in 2019, which was 18 to 53% of ET_o, respectively (Table 1). NDVI* was a decent predictor of annual ET_a (r² = 0.75; SEE = 54.6 mm, p < 0.001), but annual PPT best explained ET_a over the same period (r² = 0.99; SEE = 13.1 mm; p < 0.001; Figure 3). This finding is not surprising for an upland semiarid ecosystem, where ET is expected to be balanced with PPT (Glenn et al., 2016; Wilcox et al., 2003). Also as expected, annual PPT was correlated with growing season NDVI* (r = 0.88). To test the assumption that peak seasonal NDVI* (compared to mean NDVI*) would not adequately explain annual ET_a of upland vegetation on the lysimeter, we constructed and compared the simple NDVI*–ET_a linear models using both forms of NDVI*. Mean NDVI* outperformed peak NDVI* based on AICc.

3.2 Subannual modelling of ET_a

On the 48-day scale, NDVI* ranged from a low of 0.0501 on 25 June 2018 to a high of 0.2862 on 28 June 2019 (Table 2). NDVI* was highly correlated with ET_a (r = 0.89; SEE = 17.3 mm; p < 0.001; Figure 4), while PPT alone was not (r = 0.39; SEE = 35.1 mm; p = 0.02). Although NDVI* and ET_a were correlated, NDVI* alone fails to account for evaporative demand of the local environment, limiting or precluding application of this model to other sites with different evaporative forcing; however, this limitation can be overcome by incorporating ET_o, which accounts for variation in evaporative driving force of the atmosphere (Groeneveld et al., 2007; Nagler et al., 2013).

A plot of ET_a versus ET_a predicted (modelled) by Equation 9 revealed a good, balanced fit, without any strong outliers (Figure 5).

3.3 Error in ET estimates

In order to quantify the error resulting from ET_a estimates predicted using Equation 9, we compared the 48-day modelled ET_a values to ET_a measured by the lysimeter. While individual residual errors (% of ET_a) ranged from −33.11% to +103.83%, these errors tended to cancel each other out, with an average of only 9.92% across all observations (Table 2). The highest residual error is likely explained by rainfall that occurred just prior to that 48-day period, resulting in a substantial overprediction of ET_a. PMRE in the current study was also reasonably low at 22.23%.

Average error in our ET_a model was similar to that reported by Groeneveld et al. (2007), who modelled ET_a in phreatophytic vegetation communities using Landsat NDVI. Average error across sites in their study ranged from 2.2% to 12.5%, with individual errors as high as 175.1%. Ramón-Reinozo et al. (2019) used Landsat NDVI and EVI to estimate ET_a in a high elevation region of Ecuador and reported a mean percent error of −36.0% and −32.1%, respectively. Error in our study was higher than that reported by Nagler et al. (2013), who calibrated an ET_a equation using MODIS EVI. Average error across sites in their study was 5.4%, with a lower range of values compared to our study (2.9%–9.3%). PMRE in our study was comparable to the global MODIS ET product (24.1%–24.6%; Mu et al., 2011). Overall, our VI-ET_a model performed as well as, and in some cases better than, similar models described in the literature.

3.4 Assumptions and limitations

Although the average residual error of our ET_a model was reasonably low, the algorithm has several key limitations and assumptions that must be considered prior to its application over a particular area. (1) Plants primarily moderate soil water loss, and soil evaporation is limited. One unique feature of our algorithm is that it predicts ET in an upland plant community, as opposed to phreatophytic systems where canopy expression is not limited by availability of water. While phreatophytes predominantly moderate soil water loss, soil evaporation will likely be a larger contributor to ET_a in upland environments. Our algorithm likely performed well for the upland species in Monticello because the area is cool and the lysimeter was mostly shaded or covered by plants and mulch, which both reduce soil evaporation (20-year mean bare ground = 13.7%). For this reason, in areas that are warmer and/or more exposed (e.g., large areas of bare soil), evaporation will likely contribute more to ET_a, which will not be captured by NDVI*. (2) The climate must be arid to semiarid, emphasizing the point that plants and atmospheric evaporative demand (via ET_o) predominantly moderate soil water loss. (3) Because greenup of upland plants will primarily be dependent on local PPT, mean NDVI* of these communities must adequately capture canopy expression over the growing season.

It must be stressed that our model is limited to Landsat 5 TM and Landsat 8 OLI sensors. We initially included Landsat 7 ETM+ in our calibration but found a disproportionate spectral response between NDVI₀ and NDVI_s that the scaling process did not resolve. It is unclear if the issues we encountered were due to the SLC failure on Landsat 7 (resulting in missing pixels), but the Groeneveld and Baugh (2007) scaling technique may not properly stretch values over a scene if true NDVI_s is not captured. Therefore, we do not recommend Landsat 7 data be applied to our ET_a model. Another factor that could limit temporal continuity of our model is the lag between rainfall and resultant changes in soil water storage and percolation (i.e., 48-day periodicity). This could be problematic where cloud cover is likely to contaminate Landsat scenes.

The linear relationship between ET_a and NDVI* in the current study is consistent for a sagebrush steppe (Prater & DeLucia, 2006); however, as we observed in the current study, low NDVI* values characterize these plant communities (Kremer & Running, 1993; Prater & DeLucia, 2006); therefore, it is unknown how the ET_a–NDVI* relationship might change for higher VI values. In other vegetation communities, a similar linear relationship was observed between ET_a/ET_o and low VI values, while the relationship was distinctly non-linear at higher values (Nagler et al., 2013). For this reason, our model should not be applied to areas where NDVI* values greatly exceed those included in our calibration. Additionally, because we were limited to approximating Penman–Monteith ET_o for temperature-only datasets, this likely contributed to additional uncertainty in our model. Ideally, a complete set of meteorological variables measured onsite would be used in the calculation of ET_o, but, since these variables are rarely available, our approach broadens its applicability to areas where only temperature is known.

3.5 Management implications

Traditionally, VI-ET_a studies, especially in the arid Desert Southwest, have focused on phreatophytic systems and groundwater discharge (e.g., Glenn et al., 2016; Jarchow et al., 2020; Jarchow, Nagler, Glenn, Ramírez-Hernández, & Rodríguez-Burgueño, 2017; Nagler et al., 2016). To our knowledge, this is the first VI-ET_a algorithm calibrated in a semiarid upland plant community using field-scale lysimetry. Despite the limitations discussed in the previous section, our algorithm has important management implications, especially for situations where vadose zone water use is of interest. For example, in waste disposal areas such as Uranium Mill Tailings Radiation Control Act sites, accurate and spatially explicit ET_a estimates are important for monitoring potential mobilization and transport of contaminants past the root zone into local aquifers and for monitoring and modelling effects of recharge on flow and transport of contaminants in underlying aquifers. Therefore, in such areas dominated by shallow rooted upland species, it is imperative to determine if PPT exceeds ET_a, which could mobilize vadose zone contaminants and increase flow and transport of groundwater contaminants. Landscape-scale monitoring of ET_a is also important for evaluations of engineered covers overlying waste contained in disposal cells, like at the Monticello site, that rely on ET to limit percolation into underlying waste. Additionally, because plant communities, soil properties and soil covers vary across the landscape, detection of spatial variability in ET_a is needed to identify localized areas where recharge may occur (Link, Waugh, Downs, Thiede, et al., 1994).