Introduction

Effective irrigation management requires accurate estimates of crop evapotranspiration (ET). Surface renewal (SR) is a biometeorological technique that can be used to estimate the ET of crop surfaces (McElrone et al. 2013). The SR technique uses high frequency air temperature measurements from fine-wire thermocouples to estimate the sensible heat flux density (H) associated with air parcels that transiently reside within crop canopies during the turbulent exchange process (Paw U and Brunet 1991; Paw U et al. 1995). Air temperature time-series data from the fine-wire thermocouples exhibit ramp-like shapes that represent coherent structures that dominate surface-layer energy and mass exchange (Gao et al. 1989), and the amplitude and period of the ramps are resolved using a structure function procedure (Van Atta 1977) to calculate H in the SR methodology (Paw U et al. 1995; Spano et al. 1997). The H captured with SR is then used to estimate latent heat flux density (LE) as the residual of a surface energy balance using the following equation:

$${\text{LE}}={\text{ }}{R_{\text{n}}} - G - H,$$
(1)

where Rn is net radiation and G is the ground heat flux density. Assumptions associated with the energy balance approach are that lateral heat flux and changes of heat storage are negligible. The SR technique has been shown to accurately measure H and subsequently estimate LE on a wide range of crops, such as tomatoes, broccoli, lettuce, wheat, sorghum, maize, cotton, citrus, grapevines, and avocado.

While H measurements obtained with SR have been well correlated with standards such as eddy covariance (EC), SR flux measurements have required calibration to account for linear bias in the data and correct for inconsistencies across sites and crop surfaces (Paw U et al. 1995). Until recently this calibration has been done with an alpha factor that is obtained from the slope of the regression of H from EC measurements versus un-calibrated H measurements from SR. The alpha calibration hypothetically accounts for the uneven heating within the coherent structure that arises from the non-uniform vertical distribution of heat sources in the plant canopy (Paw U et al. 1995). The need for the alpha calibration obtained with expensive research grade sensors (e.g., sonic anemometer) has limited the use of SR to research applications. Shapland et al. (2014) showed that inconsistencies in the alpha calibration measured in previous studies could be corrected by compensating the frequency response characteristics of SR measurement thermocouples, thus causing alpha to converge near the theoretically predicted value. This development provided the opportunity to create an inexpensive, stand-alone SR system to measure H without the need for calibration, and commercial sensors are now available to growers (Shapland et al. 2012b, c). Viable commercial implementation of the SR technique requires that expensive research grade sensors are either replaced with inexpensive ones that provide sufficiently accurate measurements of Rn and G or with modelled values. For example, the original research grade SR system used net radiometers while commercial SR systems now model Rn for sites where clear sky models can be used effectively (i.e., growing locations with limited summer cloud or fog cover like California’s Central Valley). It is currently unknown how effective such replacements are for accurate determination of LE.

Accurate estimates of Rn are extremely important for energy balance approaches used to estimate crop ET (e.g., Nouvellon et al. 2000). Rn at the surface can be either modelled or measured directly, but direct measurement of transmitted radiation through a canopy is often not practical for implementation in commercial agricultural settings with deployment of numerous systems. To evaluate the effectiveness of Rn modelling to replace direct measurements, we compared LE flux measurements in the 2015 and 2016 growing seasons with a combination of direct measurements of Rn and those estimated with three different modelling approaches (Fig. 1 top box). This combination was compared using direct measurements of G and using the assumption that daily G summation = 0 (Fig. 1 right box). SR stations were established in a Vitis vinifera L. cv. Pinot noir vineyard used for the Grape Remote sensing Atmospheric Profile & Evapotranspiration eXperiment (GRAPEX) for comparison with ET estimates from a variety of other techniques.

Fig. 1
figure 1

Schematic of comparisons presented in this manuscript. Latent heat flux (LE) was determined using the surface renewal method to estimate sensible heat flux (H) with a fine-wire thermocouple and combined these with four different radiation inputs (i.e., tower measurements, MODIS output, Modelled from incoming solar radiation (SWi), and DisALEXI output) and with two different estimates of ground heat flux (i.e., the daily sum measured directly and the sum assumed to be zero on a daily basis). Surface Renewal LE estimates were then compared against LE from two eddy covariance (EC) approaches: (1) measured with an infrared gas analyzer (ECIRGA) and solved as a residual in the surface energy balance (ECresid)

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Methods

Site description

As part of the USDA-ARS Grape Remote sensing Atmospheric Profile & Evapotranspiration eXperiment (GRAPEX), the south vineyard of the two Pinot noir vineyards, located at the border of Sacramento and San Joaquin counties, was instrumented in 2015 and 2016 with a surface renewal station to compliment measurements from the existing flux towers. Intensive observation periods (IOPs) covered 2 to 4 phenological stages each year. The smaller southern field (Site 2; 21 ha) contains grapevines that were planted in 2011. The height of the vines ranged between 2 and 2.5 m, row spacing was ~ 3.35 m, and average vine spacing along the row was 1.52 m. The majority of vegetative growth was located within the top ½–1/3 of the vine by the end of the season.

Instrumentation

A 10 m radio tower is stationed in the south vineyard and instrumented with a complete surface energy balance eddy covariance flux and wind profile system, providing measurements of net radiation (Rn), ground heat flux (G), incoming solar radiation (SWi), relative humidity (RH), sensible heat flux (H), and latent heat flux (LE). Rn was measured directly onsite with a four-component radiometer (CNR-1, Kipp and Zonen, Delft, Netherlands) mounted at 6 m AGL oriented toward the southwest. Ground heat flux (G) was computed from an average of 5 soil heat flux plates (HFT-3, Radiation Energy Balance Systems, Bellevue, Washington) deployed at a depth 8 cm along a diagonal transect across the inter-row space. Each ground heat flux plate was inserted with a pair of Type E (Chromel-Constantan) thermocouples located at 2 and 6 cm below the soil surface and above the ground heat flux plates. Soil moisture sensors (HydraProbe, Stevens Water Monitoring System, Portland, Oregon) were co-located with each ground heat flux plate at a depth of 5 cm below the surface to provide measured soil water content, which is required to correct the measured ground heat flux plate data to include an estimated soil heat flux storage to arrive at a final total ground heat flux estimate. The turbulent energy fluxes for LE and H heat fluxes were measured via EC by co-locating an infrared gas analyzer (IRGA) (EC-150, Campbell Scientific, Inc., Logan, UT) with the sonic anemometer at the 5 m height on both towers. All sonic anemometers and IRGA sensors were mounted in a vertical configuration facing due west and sampled at a frequency of 20 Hz. Details of the full processing of the EC data are provided in Alfieri et al. (this issue). First, nonphysical values and data spikes were removed from the high frequency data using a moving window algorithm. Then, a two-dimensional coordinate rotation was applied to the wind velocity data so that the coordinate system was aligned into the prevailing wind direction followed by correcting for sensor displacement and frequency response attenuation. The moisture and carbon dioxide fluxes were then corrected for buoyancy and water vapour density effects. Hourly fluxes were calculated.

A SR station was deployed approximately 10 m to the west of the tower. The SR tower measured air temperature (f = 1 Hz) with a 76 micrometer diameter Type E thermocouple (FW3, Campbell Scientific, Inc. Utah, USA) placed approximately 50 cm above the vine canopy and was periodically raised as the canopy grew.

Data analysis

The surface renewal method is used to estimate sensible heat flux (H) using the 1 Hz temperature data that is compensated for the thermocouple size (Shapland et al. 2014), which eliminates the need for calibration against eddy covariance H. Estimates of H by SR were calculated according to the following equation:

$$H=\alpha \times z \times \rho {C_{\text{p}}}~\left( {\frac{a}{{d+s}}} \right)~,$$
(2)

where α is the alpha calibration factor described above, z is the thermocouple height (m), ρ is the air density (g m−3), Cp is the specific heat of air at constant pressure (J g−1 K−1), \(a\) is the average ramp amplitude (K), d is the duration of the air parcel heating (s), s is the quiescent period that follows the sweep-phase of the air parcel (s), and (d + s) are collectively called the ramp period (repetition intervals of ramps) (s).

The ramp characteristics were calculated from the raw temperature signal from the 76 mm thermocouple. The α calibration factor was determined using an empirical compensation method, in which the theoretical alpha coefficient of 0.5 is multiplied by the thermocouple compensation factor specific to the 76 µm diameter thermocouple used here (Shapland et al. 2014). Rather than applying the thermocouple frequency response compensation to the raw thermocouple temperature data, the thermocouple frequency response compensation was applied instead to the SR H values. The 2.16 compensation factor was determined previously as the slope of a regression analysis of H from raw 13 µm data versus H from raw 76 µm temperature data (Shapland et al. 2014).

When SR is used to measure H, one can estimate LE using the residual of the energy balance with Eq. 1. Four different radiation inputs (i.e., tower measurements, MODIS output, modelled from SWi, and DisALEXI output) were used for Rn and two different estimates of G [i.e., the daily sum measured directly and the using the longwave net radiation sub-model in the standardized reference evapotranspiration equation (Blonquist et al. 2010)] with measured SWi, relative humidity, and air temperature from the south vineyard flux tower. The MODIS Rn output was estimated daily using the moderate resolution imaging spectroradiometer—MODIS at 1 km resolution. The DisALEXI Rn output was estimated with each LANDSAT 8 overpasses biweekly to monthly at 30 m resolution. Since The MODIS and DisALEXI Rn are for daytime only, a simple regression with Daily Rn was used to factor in the nighttime effect. This reduced the inherent bias caused using daytime instead of diurnal value. LE estimates from SR were then compared to ECresid and ECIRGA (Fig. 1).

Results and discussion

Direct measurements of net radiation (Rn) collected on the tower at the GRAPEX site matched most closely with modelled Rn based on the SWi (using modelling approaches presented by Parry et al. 2019, this issue) (Fig. 2). While these measurements matched well, there were periods of time in both growing seasons when they diverged. For example in 2015, when dips occurred in both estimates simultaneously (e.g., days 134, 137, 141, 161, 182, and 183) the modelled Rn based on SWi was always slightly lower than that measured directly on the tower (Fig. 2—top panel). A similar pattern was found in 2016 on days (e.g., days 118, 141, 142, and 156) (Fig. 2—bottom panel). Besides these slight differences, the only time that these values consistently diverged was from day 182–207, when the tower Rn value jumped slightly and remained consistently higher for the remainder of the period of observation (Fig. 2—bottom panel). Rn estimates from MODIS and DisALEXI were similar to one another across each season, and were consistent with tower Rn in both years (Fig. 2) similar to results found in previous studies (e.g., Cammalleri et al. 2014). The less frequent estimates of Rn from DisALEXI made it appear as though it was not responding to the intermittent dips measured directly and modelled with the onsite data (e.g., days 212, 216, and 218 in the 2015 season and days 142–144 in the 2016 growing season), and the values from MODIS showed similarly limited response even with a higher frequency of measurements during these periods (Fig. 2).

Fig. 2
figure 2

Net radiation measurements or modelled values (MODIS, Modelled SWi, and DisALEXI) from the GRAPEX site captured across the 2015 (top panel) and 2016 (bottom panel) seasons

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Daily summations of ground heat flux (G) showed that most of the values hovered around zero (Fig. 3); ~ 85% of the G values recorded during the 2015 growing season were within ± 0.5 W m−2 (Fig. 3 left panel). All points recorded across the 2 years of the study fell within ± 2.0 W m−2, and a very small percentage of the total values fell outside of ± 1.0 MJ m−2 day−1 (Fig. 3; only 1 value in 2015 and 5 values in 2016 fell outside ± 1.0 MJ m−2 day−1). G values showed greater scatter and divergence from zero in 2016 compared to 2015. Efforts to apply SR under commercial field conditions would benefit from elimination of G measurements to reduce cost and labour to maintain stations and sensors in the vineyard interrow where farm equipment frequents. Stoy et al. (2013—Supplemental Fig. 3) showed similar results where daily G was close to zero. While our current results show that daily G scatters about zero, this result may not be universally true and should be tested thoroughly in other experimental settings. Moreover, as shown below and in Table 1, assuming G = 0 in all cases results in increase scatter with LE from ECresid and ECIRGA.

Fig. 3
figure 3

Daily summations of ground heat flux (G) measured at the GRAPEX site over the 2015 and 2016 seasons

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Table 1 Statistical analysis for relationships between LE estimates from surface renewal, eddy covariance and water vapour flux as represented in Figs. 6 and 7
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Values of LE from ECresid and from SR using directly measured Rn tracked each other closely in both years of the study (Figs. 4, 5, 6 top left panel). This relationship improved when including daily measured G instead of assuming a value of zero on a daily basis (Table 1; Fig. 6 top row), but the slope for both relationships was essentially unity (Fig. 6 top row). There were some periods during both seasons when the LE from ECresid was higher (e.g., days 222–224 in 2015- Fig. 4) than that from SR estimated with Rn from the tower. Similar relationships were found using a calibrated surface renewal approach over grapes (Shapland et al. 2012a; Spano et al. 2000; Snyder et al. 1996), and more recently in a vineyard containing a weighing lysimeter (Parry et al. in review), where LE estimates from SR matched closely (i.e., R2 > 0.9 and slope ~ 1.0) with those from EC and ET measurements from the weighing lysimeter.

Fig. 4
figure 4

Estimates of latent heat flux (LE) from Eddy covariance and Surface Renewal using direct measurements and modelled values of net radiation from the GRAPEX site captured during the 2015 growing season. Three different modelled net radiation values were used from the MODIS, Modelled SWi, and DisALEXI (see comparison in Fig. 2), and were the residual was calculated using the ground heat flux measured directly (top panel) or assumed to equal zero on a daily basis (bottom panel)

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Fig. 5
figure 5

Estimates of latent heat flux (LE) from Eddy covariance and Surface Renewal using direct measurements and modelled values of net radiation from the GRAPEX site captured during the 2016 growing season. Three different modelled net radiation values were used from the MODIS, Modelled SWi, and DisALEXI (see comparison in Fig. 2), and were the residual was calculated using the ground heat flux measured directly (top panel) or assumed to equal zero on a daily basis (bottom panel)

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Fig. 6
figure 6

Relationships between latent heat flux (LE) residual estimates derived using Eddy Covariance and Surface Renewal with direct measurements of net radiation (top row) and modelled radiation (bottom 3 rows) with ground heat flux measured directly (left column) or assumed to equal zero on a daily basis (right column)

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For most of the 2015 growing season, LE estimates from SR using the three Rn modelling approaches followed LE from SR and from ECresid using tower Rn measured directly (Fig. 4). The LE estimate from SR using modelled Rn from SWi fell below that of the other technique at several points in 2015 (Fig. 4), which corresponded with the dips in Rn measured onsite described above (e.g., days 134, 137, and 141—Fig. 2). Despite these differences, the SR LE estimated using modelled Rn from SWi tracked closely with the LE from ECresid with the tower Rn data (r of ~ 0.88), albeit with a significant slope of 1.35 or 1.39 due to the bias (Table 1; Fig. 6). The LE estimate using MODIS Rn spiked higher than LE from the other methods on several days in the middle of the 2015 growing season (Fig. 4), but was in line with other methods throughout much of the 2016 growing season. LE estimates from SR based on the Rn from DisALEXI showed the best fit of all the model approaches (r of ≥ 0.96), but the LE values generated by this approach were much greater compared to the LE from ECresid (Fig. 6—bottom row; Table 1) that could be due far fewer data points for the DisALEXI comparison.

LE estimates obtained from SR with the various Rn inputs were compared with LE from ECIRGA (Fig. 7), and showed similar patterns to the LE from ECresid comparisons in Fig. 6. Inclusion of direct measurements of G improved the relationships (i.e., higher r values and lower RMSE—see Table 1) for the directly measured Rn from the tower and MODIS Rn approaches (Fig. 7 top two rows), but showed little effect for the DisALEXI approach (Fig. 7 right vs. left hand column; Table 1). LE from ECIRGA was most strongly correlated with LE from SR estimated with tower Rn (r of 0.8), while the other approaches exhibited weaker fits (r of 0.58–0.7 and larger RMSE values; see Table 1). The slopes (and bias) of the relationships were consistent within a given approach regardless of the EC approach they were compared against (i.e., slopes were similar within a given approach across both comparisons in Figs. 6, 7). For example, direct Rn measurements from the tower resulted in near unity slopes, while modelled Rn from SWi and DisALEXI Rn consistently overestimated LE compared to that of both ECresid and ECIRGA.

Fig. 7
figure 7

Relationships between latent heat flux (LE) from Eddy Covariance using water vapour concentration measurements and LE residual estimates derived using Surface Renewal with direct measurements of net radiation (top row) and modelled radiation (bottom 3 rows) with ground heat flux measured directly (left column) or assumed to equal zero on a daily basis (right column)

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Conclusions

The SR technique is currently being used as a commercial product to provide site specific crop ET estimates for growers and irrigation managers for a variety of crops in California’s Central Valley. To make this application cost-effective, Rn is being modelled and G is assumed to equal zero on a daily basis. We evaluated the effectiveness of various Rn modelling approaches to replace direct measurements, and compared output using direct measurements of G and using daily G summation equal to zero. The SR LE estimates using direct measurements of Rn and G were strongly correlated with LE from ECresid and from ECIRGA. Estimates of LE from SR derived with modelled SWi and DisALEXI Rn approaches were both significantly correlated with LE from ECresid, but both overestimated LE from ECresid and ECIRGA at higher fluxes. LE residual derived from MODIS Rn performed the weakest overall. Neglecting G had minimal impact on the general agreement between LE from SR and LE from both EC approaches, but assuming G = 0 did cause greater scatter. Our results suggest that LE from SR requires a more rigorous Rn modelling approach using satellites if there are no local net radiation measurements that can be used. For example, errors of LE estimations using the modelled Rn from SWi and the DisALEXI (Figs. 6, 7) are consistent with the error structures of the corresponding Rn estimations (shown in Fig. 2) such as the modelled Rn from SWi being consistent with Rn tower measurements at high values while tending to underestimate Rn at low values. Otherwise significant bias in daily LE could result (Table 1).