Introduction

In California, recurrent droughts and water shortages have led to competition between agricultural, urban and conservation water needs (Diffenbaugh et al., 2015). Even in the face of these challenges, there are still about 355,000 acres of grapes being cultivated throughout the state (CDFA and USDA, 2021). These vineyards typically use drip irrigation practices, which treat all plants in a management zone identically, even though it is clear that all plants do not require the same amount of water. Water demand heterogeneity can arise from cultivar differences, complex topography, canopy orientation, soil structure and composition, or rogueing practices for disease control, as examples. As a consequence of this variability, treating all plants in a management zone as identical will generally lead to some plants receiving excessive or inadequate water. Beyond the needs of the plant, water balance contributes to fruit quality and yield, layering additional complexity into its management. For example, in perennial woody crops like grapes and almonds, well-timed water stress can help control vegetative vigour and may increase fruit quality (Chaves et al., 2007; Van Leeuwen and Seguin, 2006). Conversely, moderate to severe water stress caused by extreme deficit irrigation can damage cellular components for light harvesting, limiting photosynthesis. If this water stress is prolonged, delays in ripening, sudden vine collapse and reduced fruitfulness can negatively impact berry yield and quality (Dayer et al., 2019). These constraints can create a problem, however, because the irrigation manager's goal is finding this narrow range of applied water by considering the plant's needs, but these needs usually vary in a complex way through space and time. When this variability is combined with complex deficit irrigation schemes, optimization of water use can be nearly impossible using existing technology.

Materials and methods

Results

From May 2020 through August 2022, we collected three seasons of data with our sensors and load cells. All biometeorological parameters are characterised by a strong diurnal pattern (Supplementary Figure 2). Ground truth ET data generated from load cell measurements were recorded at 2-minute intervals. When viewed over time, this data reveals periods of evapotranspiration as well as irrigation events (Supplementary Figure 3). The measured ET rate is computed from the load cell data by taking the derivative of mass with respect to time (Figure 1). It can be seen that the evapotranspiration is highest during times with peak temperature, which occurs around solar noon each day. While these data are reported only for a single vine, other vines exhibited very similar behaviour. Overall, we observed vines using about 30 litres of water per day, which falls within the range of observations from UC ANR in 2002, which measured 22.7 to 37.9 litres of water used per day for mature, vigorous grapevines in the Central Valley of California (Geisel et al., 2002).

Figure 1. Load cell measured ET rate

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^aMeasured ET rate is computed by taking the derivative of load cell mass with respect to time. Irrigation events were ignored using a filter. Data from August 2020

Figure 2. Predicted and measured ET rates over time

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^aEach plot shows the ET rate of water as determined by the load cell and by one the HRI models for a 5-day period in June 2022. In all figures, the purple line represents the load cell measured ET rate. The p-value for all linear regressions was less than 2 ᐧ 10^-16. The CMT r² values ranged from 0.66 to 0.89, the MB r² values ranged from 0.22 to 0.78, and the EM r² values ranged from 0.74 to 0.89. An expanded version of Figure 2 is available in the Supplementary Figures section as Supplementary Figure 4, and includes r², p-value, and linear regression equations, for each vine and model.

We used filtered biometeorological parameters to make ET rate predictions using our three models. In Figure 2, the load cell measured ET rate is plotted alongside the model-predicted ET rate over a 5-day period in June 2022. We found a strong linear relationship between model-predicted and load-cell-measured ET rates. The CMT predicted ET rate r² values were 0.89 for Vine 1, 0.85 for Vine 2 and 0.66 for Vine 3; MB predicted ET rate r² values were 0.78 for Vine 1, 0.22 for Vine 2 and 0.45 for Vine 3; and EM predicted ET rate r² values were 0.87 for Vine 1, 0.89 for Vine 2 and 0.74 for Vine 3 (Figure 2). We observed similar agreement over the course of the full 2020, 2021 and 2022 seasons (Table 1). At most times of the day, the CMT model tends to overpredict and the EM model tends to underpredict during the daytime and overpredict during night-time hours. The MB model was both under and overpredicted and was more prone to error. Importantly, we collected some of these data during extended periods of drought stress as well as during periods of typical irrigation. Including stressful periods, noted in Table 1, provides additional evidence that the models generate estimates of crop ET_c and not another concept like reference ET_o, which is more related to evaporative demand. In this experiment, each dry-down event represents 10 consecutive days without receiving any applied irrigation. Note the relatively poor performance of Vine 2 in the MB model in all growing seasons, exhibited in Figure 2 and Table 1. This can be attributed to errors when calculating absolute humidity differences from temperature and individual relative humidity, especially when these differences are small. Sometimes, when absolute humidity inside and outside the canopy is very close, a negative ET rate can be calculated, which is unlikely for grapevine and is probably a result of a lack of sensitivity in the methods used to sense and calculate absolute humidity. Absolute humidity error could also be the result of sensor placement. We noted the outside canopy relative humidity sensors for Vine 2 were placed upwind of prevailing winds relative to Vine 2, while the outside canopy humidity sensors for Vine 1 and 3 were placed downwind relative to their respective vines, thus indicating the importance of proper sensor placement for the successful use of the MB approach. Both the CMT and EM models give generally good predictions of the ET rate. Neither of these approaches uses the external relative humidity sensors on the experimental vines, which means none of the effects seen on Vine 2 are present in these calculations.

Given their physical bases, we hypothesised that the trend in the CMT and MB associated A_s terms over each season could have a consistent relationship to the seasonal trend in other plant physical parameters, such as Leaf Area Index (LAI) or cross-sectional area of the canopy (Orlando et al., 2016; Figure 3). In 2020 and 2022, the CMT model A_s values displayed an overall trend that somewhat or very much resembles annual cycles in canopy physical parameters like LAI, with an increase until approximate veraison with subsequent levelling out, but this trend was reversed in 2021. While in 2022, the MB model A_s trend was somewhat like the expected trend, the trends observed in 2020 and 2021 were not what we would expect for plant growth during a growing season. In several instances during 2020 and 2021, the MB model A_s values were below zero, indicating erroneous predictions likely due to sensitivity issues with sensing and calculating absolute humidity. After these observations, we now believe that the A_s term relationship to physical measurements, such as LAI, is more nuanced and is likely mediated by other factors, such as physiological changes caused by the senescence of older leaves, fruit set, or other seasonal processes.

Figure 3. CMT and MB model area terms over three years

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^aExample of trend in experimentally determined area term (As) values for CMT (top row) and MB (bottom row) models over the 2020 (left column), 2021 (middle column), and 2022 (right column) growing seasons. Legend in top, right panel

With the calculation of A_s terms, we can now directly compare the load cell measured and model predicted ET. Load cell measured ET, ET_c, is calculated by integrating load cell measured ET rate over time. For all vines, we computed the model predicted ET_e and load cell measured ET_c over a 1-hour window from 13:00–14:00 PST, daily using 56 days for Vine 1, 42 days for Vine 2 and 23 days for Vine 3, distributed approximately evenly from May to August 2022 (Figure 4). The days used to calculate model predicted ET_e and load cell measured ET_c were chosen based on the availability of a continuous set of data for a full 24-hour period. The main challenge to finding a full 24 hours of measurements every 2 minutes was frequent gaps in wind speed data, a result of the unprotected needle design of the anemometers. If the anemometer needle comes into contact with anything, such as a leaf, insect or debris, during the measurement window, it will record a zero, negative or unreasonably large value. These erroneous recordings are considered to be gaps or missing data. To understand how the models performed relative to one another over short periods of time during the day, we performed multiple linear regression analyses on all 1-hour vine and model data. The multiple r-squared is 0.6292, suggesting a good overall fit, and all model p-values are significant at the 0.001 level, indicating a significant relationship between all model predictions and ground truth.

Figure 4. Predicted vs. measured ET over 1 hour window

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^aPlot comparing the predicted ET_e from all of the HRI models, and ground truth ET_c from the load cells during a 1 hour window from 13:00–14:00 each day (units = kg). Data are from Vines 1–3 using dates May–August in the 2022 season. Data were fit with a multiple linear regression model, and a 1:1 reference line is shown in black. The multiple r-squared is 0.6292, and all model associated p-values are significant at the 0.001 level of significance.

We also computed the model-predicted ET_e and load cell measured ET_c over a 24-hour window, daily for the same 23, 42 or 56 days distributed approximately evenly from May to August 2022 (Figure 5). With the inclusion of night in this multiple linear regression analysis, when little to no ET is occurring, and all models predict more accurately than during the day, the linear relationships between model predicted and ground truth ET now explain up to 82 % of the variation in crop ET_c over a wide range of phenological stages and environmental conditions. The increase in explained variation could also be due to small shifts in prediction compared to ground truth. These shifts have a relatively large effect on the accuracy of predictions during some times of day, but over longer integration periods, this effect is significantly reduced. Overall, only the CMT and EM model p-values are significant at the 0.001 level. MB model predictions are associated with a p-value of 0.17, suggesting a non-significant relationship between MB-predicted ET and ground truth ET over full 24-hour periods.

Figure 5. Predicted vs. measured ET over 24 hour window

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^aPlot comparing the predicted ET_e from all of the HRI models, and ground truth ET_c from the load cells during a 24 hour window each day (units = kg). Data are from Vines 1–3 using dates May–August in the 2022 season. Data were fit with a multiple linear regression model, and a 1:1 reference line is shown in black. The multiple r-squared is 0.8232, and the CMT and EM model associated p-values are significant at the 0.001 level of significance. The MB model p-value is 0.17.

We suggest, based on these results, that crop ET can be modelled effectively using HRI techniques and biometeorological data measured in vine canopies, though accurate calculation of A_s values may be critical to improving these predictions and enhancing generalisability.

Discussion

Given the generally consistent results over multiple seasons, we believe the three novel HRI models for predicting the ET rate of a single vine are a promising new method. With this fine-scale understanding of the water use of individual plants, irrigation managers could, for the first time, adjust water application rates to ensure plants are receiving what they need and nothing more. This vital step towards improved efficiency of applied irrigation, which accounts for the vine-to-vine water use variability that results from the heterogeneity of vineyards, will support further development of important technology capable of addressing the growing problem of water scarcity while maintaining or improving grape quality.

The data presented here is strong evidence that the ET rate can be well described using only simple biometeorological measurements and either first principles or empirical models. Based on the performance criteria of r² and RMSE, the EM model consistently explained more variation in ET rate than other models. However, while the EM gave the best results for these vines, we believe that the CMT model or MB models, which are based on first principles, will prove to be more generalizable, especially to variable canopy architectures and seasonal changes.

Other technologies designed to estimate ET also face challenges, but comparing other models to the HRI model is not straightforward because most other models make predictions at coarser time scales. Generally, data from other ET estimation methods, especially crop coefficient methods, is presented on the scale of months or seasons, such as in Li et al. (2008), not days or hours. However, in Gómez-Candón et al. (2021), researchers captured multispectral images of Durum wheat fields using UAVs and then calculated actual ET using a Two-Source Energy Balance, an application of energy balance which separates energy fluxes, and, therefore, ET, from plant and soil into two components (Norman et al., 1995; Kustas and Anderson, 2009). Using this method, the remotely sensed estimates of ET calculated with the TSEB model only explained 50 % of the variation in daily ground truth ET measurements. While these researchers exemplified how challenging applying ET sensing methods can be in the field, some studies have also reported better performance of the energy balance approach. Anapalli et al. (2018) demonstrated energy balance ET predictions can explain as much as 82 % of the variation in lysimeter ET; however, this study was focused on corn and the ET measurements were less frequent, at once per day. Still, comparing these correlations to those observed in Table 1, it is reasonable to conclude that the HRI models offer a viable alternative to existing methods for estimating ET.

While the observed correlations with ET rate persist over multiple vines and multiple seasons, accurate prediction of ET_e will depend on the accurate calculation of the A_s term, which may vary with plant and over time. The A_s terms for two of the models, CMT and MB, have an actual physical meaning, albeit with the CMT model term incorporating k_cmt, but measuring those parameters directly may not be straightforward and will require further exploration. Again, for a single vineyard, we may not need this term to make good predictions of ET, but to make these predictions generalisable, it will be essential, especially if vines are of different sizes because of replanting or heterogeneities in soil or topography. Calculation of A_s terms directly from physical data, such as ground-based imagery of the vines collected throughout the season during normal tractor passes, would be possible. Downstream image analysis could be automated using a deep learning approach, similar to the approach used in Olenskyj et al. (2022), to extract canopy cross-sectional areas, total leaf area, or other physical parameters of the vine that are well correlated with the model A_s terms.

Because generalisability is likely a prerequisite for the viability of this technology, it is critical that we unravel the physical meaning of this term and how to measure it directly. Studying how the experimentally derived A_s terms change over the growing season provides early insights into how we might overcome this problem. As was previously mentioned, we believe the trend in the area term could have some consistent relationship to the trend of other plant physical parameters over the growing season, such as leaf area or leaf area index, which tends to increase until harvest (typically early September in California) when it begins decreasing until leaves are shed shortly thereafter (Netzer et al., 2009). Given these observations and the physical basis of two of the HRI models, we hypothesised that the A_s term will be proportional to other physical measurements such as LAI or canopy cross-section. However, the experimentally derived area terms from the 2021 season did not resemble the expected pattern. Due to the way humidity and temperature sensors were mounted in the centre of the canopy and not in a different or more dynamic position, we believe the calculations of true A_s were masked by other intracanopy effects, such as physiological changes in transpiration rate caused by senescence of older leaves, fruit set, or other seasonal processes. In future studies, we aim to explore ways to mitigate the effect of these other variables.

Other challenges include issues with the relative placement of humidity sensors and vines, which can severely impact the accuracy of MB-predicted mass flux. In future seasons, we will investigate more accurate methods for calculating absolute humidity, including methods that are not sensitive to the relative positioning of vines and sensors or, alternatively, finding the optimal location of sensors for a given vine geometry. This issue is exemplified in Figure 2 and Table 1, which both show the MB predicted ET rate for Vine 2 as underperforming relative to other vines. Moreover, note that in Figure 3, the A_s term for the MB predictions dips below 0 several times in 2020 and 2021, indicating a negative ET rate was erroneously calculated. This sensitivity to sensor and vine location reveals a fundamental weakness of the MB model, as it requires twice as many sensors as the other models and ideal sensor placement, and, therefore, increases the likelihood of incorrect measurements.

In addition to these issues, implementation in a commercial vineyard presents other challenges. For example, it is possible that canopies with less radial symmetry, such as many common trellis systems in California, could be more difficult to measure. It is also possible that certain trellis systems, cultivars, regions, topographical features, or other factors we have yet to consider could limit the performance of the models. In addition, sensors used by the models will need to be inexpensive, especially if every vine or a high density of vines is to be monitored, and robust in an agricultural environment—both topics of further research.

Conclusion

Even with the remaining challenges of increasing generalizability, the algorithms’ prediction of the ET rate of water from single vines is very promising as an inexpensive and high-resolution means of controlling irrigation. Applied correctly, the algorithms presented here provide an option to growers looking for greater efficiency of irrigation and improved crop quality. The HRI algorithms provide a theoretical and practical basis for growers to balance irrigation with the varied water demands of vines growing in heterogeneous environments, all using a non-invasive and automated process.

Acknowledgements

The authors thank Leticia Chacon Rodriguez for viticultural guidance and access to vineyard facilities, Guillermo Federico Garcia Zamora and Gonzalo Ruiz Gonzalez for assistance with vine care and equipment installation at the RMI Vineyard, and Kathryn Prendergast of the Graduate Writing Fellows at the University of California Davis for assistance with editing. This work was made possible through financial support from Till Guldimann and the Ernest Gallo Endowed Chair in Viticulture and Enology.

Author contributions

M.R.J., J.J.L., S.N. and D.E.B. designed and implemented the experimental field setup. K.M. and M.R.J. conceptualised the CMT model. D.E.B., S.N. and M.R.J. conceptualised the MB model. M.R.J. conceptualised the EM model. M.R.J. and A.M. wrote all the code for data capture, analysis and visualisation. M.R.J. and D.E.B. wrote the paper with revisions from all authors. D.E.B., M.B., J.J.L. and J.M.E. provided funding and access to materials.

Data availability

Some of the data used for this publication, including examples from all sensors and the load cell, is available as a CSV file on Zenodo at https://doi.org/10.5281/zenodo.7983157.

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