Reply to commentary by Offer Rozenstein on ‘Is the crop evapotranspiration rate a good surrogate for the recommended irrigation rate?’

I thank Offer Rozenstein for his commentary, and I agree with most of the things he wrote, those that refer to the original article (Friedman, 2023) and those that are not directly related to its main idea. The main idea of that short article was that optimal irrigation (from an agronomic or economic point of view) is usually at a rate higher or lower than the actual evapotranspiration (ET_{c act}) rate of the crop (Rozenstein agrees with this main idea).

For example, Figure 1 displays the water consumption (ET_{c act}) of cotton (cv. Pima) that Rozenstein et al. (2018) estimated by remote sensing of plant indices, in very good agreement with ground measurements using the eddy covariance method. Also displayed in this figure are the daily irrigation dose recommendations (in terms of K_c to be multiplied by ET₀) of the Israeli Extension Service (IES) for that region, which were higher during most of the irrigation season and amounted to seasonal irrigation that was about 10% higher than the evaluated estimated crop evapotranspiration (until day of year [DOY] 227). The question arises: Are the recommendations of the IES higher than the (agronomical or economical) optimal irrigation rate? The answer is probably: No. Irrigation according to the IES recommendations which are at a multi-annual average rate of about 490 mm per season results in a yield of about 5300 kg ha⁻¹ and an income of about $15,900 ha⁻¹ (current cotton market price is about $3 kg⁻¹). According to the cotton yield–irrigation production functions under various conditions (Dağdelen et al., 2009; Shalhevet et al., 1979; Wanjura et al., 2002), it seems that reducing the seasonal irrigation amount by about 10% would have reduced the yield by about 5% and the grower's profit by 4%, $650 ha⁻¹ (accounting for only the cotton market price and irrigation water price of ~ $0.3 m⁻³). And what about the seasonal course of the irrigation dose recommended by the IES concerning the seasonal course of the crop's water consumption? Does it make sense to irrigate at rates higher than the actual ET at earlier stages and lower than the ET towards the end of the growing season (until eventually stopping irrigation at 30%–40% open bolls)? Yes, that makes sense. In the first growth stages, the root systems are small and cannot take up most of the water supplied from the point sources in drip irrigation, so it is necessary to irrigate in excess. It is also necessary to prevent the accumulation of harmful salinity. On the other hand, towards the end of the growing season, the available water in the soil profile can be utilized and it can be dried. In the case of cotton, in addition to water saving, the activation of water stress may improve fibre quality and promote natural defoliation resulting in a more efficient and effective harvest.

Another, more extreme example indicating that the optimal irrigation rate is much higher than the water consumption (ET_{c act}) of the crop is from an experiment of bell pepper irrigation on a sandy soil in Western Negev, Israel. In the treatment in which the irrigation dosing was according to the approach and the crop coefficients of the FAO56 (Allen et al., 1998) and seasonal irrigation from June to December amounted to about 800 mm, we (Shani Sperling, a master's degree student under the guidance of Shabtai Cohen and myself, Sperling, 2013) measured daily transpiration rates of less than 40% of the irrigation rates using the heat pulse method (in good agreement with water and salinity balances in the soil profile evaluated with an array of 16 time-domain reflectometry [TDR] sensors). According to a yield–irrigation dose production function that we constructed in a preliminary experiment, reducing the irrigation dose to 40% of that mentioned above (800 mm), following the evaluated water consumption of the crop, would have caused a 50% reduction in the yield.

Agronomic and economic optimal irrigation dose larger than the water consumption (ET_{c act}) is common in also intensively drip-irrigated orchards, for example, red grapefruit (Friedman et al., 2009) and persimmon (Kanety et al., 2014). The measured (via the heat pulse method) seasonal, April till November, ET_{c act} of the grapefruit grove was approximately 60% of the seasonal irrigation + rainfall depth, and reducing the irrigation dose by 40% would have caused substantial yield and profit losses (irrigation dose reduction of 20% caused ~ 10% yield reduction) (Friedman et al., 2009). Similarly, the seasonal water consumption of the persimmon was approximately 40% of a high seasonal irrigation dose of 1000 mm (yielding 40 tons/ha), and reducing the irrigation dose by 60% would have caused approximately 50% yield loss (Kanety et al., 2014).

On the other hand, there are also circumstances where the optimal daily irrigation dose is lower than the crop ET. In the spring–summer cultivation of silage corn on a clayey soil with shallow groundwater (water table depth of about 1.5 m), after about 600 mm of winter rains at the Agricultural Research Organization (ARO) model farm in Newe Ya'ar, Jezreel Valley, Israel (https://www.modelfarm-aro.org/?lang=en), a yield of about 19,500 kg dry matter per hectare was obtained with a seasonal irrigation dose of about 450 mm (during April to July, seasonal ET₀ of about 700 mm). Under conditions of lower ET₀ in Kansas, a similar yield of about 20,100 kg DM ha⁻¹ was obtained with an evaluated crop water consumption (ET_{c act}) of 565 mm, that is, a water productivity of about 3.56 kg DM m⁻³ (Hattendorf et al., 1988). The water productivity in the warmer conditions in the Jezreel Valley is lower, thus the seasonal water consumption of corn there is higher than 550 mm (19,500 kg DM ha⁻¹/3.56 kg DM m⁻³). Tensiometers installed at depths of 30, 60 and 120 cm indicated an upward water flow during most of the growing season. Based on the experience of growers in the region, it is not possible to obtain a higher yield with an increased seasonal irrigation rate. Therefore, under these conditions of water uptake from the soil profile and the shallow groundwater, and taking into account the water price (~ $0.3 m⁻³) and the market price of the yield ($0.2 kg DM⁻¹), optimal irrigation is at a rate lower than the water consumption of the crop.

The issues that Rozenstein raised concerning spatial heterogeneity and variable-rate irrigation of spatially variable plots are not related to what I wrote in the short article that referred only to a uniform irrigation practice (contrary to what Rozenstein wrote, the use of an empirical production function does not ‘ignore’ the spatial heterogeneity, but takes it into account in an implicit mode). The practical and economic feasibility of variable-rate irrigation still needs to be proven on a wide scale. I wish Rozenstein and others success in developing these methodologies and technologies.

I agree with Rozenstein that using crop models (which I indeed consider a type of production function) to direct the irrigation rate is constructive, as I wrote in the article: ‘Fusion of monitored or historical weather data with crop models, predicting biomass accumulation and agricultural yields, can also be constructive for allocating daily irrigation amounts’. Using artificial intelligence methods is of course legitimate. According to the current state of progress, it seems to me that, at least for the time being, they should be agronomically constrained.

I do not think and I did not write in that article that using (empirical or modelled) production functions is a general optimal strategy. In my humble opinion, there is no single optimal approach for determining the daily irrigation dose in different agricultural circumstances, and depending on the different conditions and the different irrigation goals, it is necessary to choose different feed-forward or feed-back approaches, and sometimes also a combination of them. When considering the actual ET of the crop to direct the irrigation dose, one should take into account not only that the crop ET is one of several factors that determine the optimal irrigation dose, but also that the crop ET depends on the irrigation dose. Therefore, estimating the actual ET of the crop is usually not sufficient for deciding on the irrigation rate.