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.

我感谢 Offer Rozenstein 的评论，我同意他写的大部分内容，那些引用原始文章（Friedman，  2023）以及那些与其主要思想没有直接关系的内容。这篇短文的主要思想是，最佳灌溉（从农艺或经济角度来看）通常高于或低于作物的实际蒸散量 (ET _{c act} ) 率（罗森斯坦同意这一主要观点） 。

例如，图 1 显示了Rozenstein 等人研究的棉花 (cv. Pima ) 的耗水量 (ET _{c act )。}（2018）通过植物指数遥感估计，与使用涡度协方差方法的地面测量非常一致。该图中还显示了以色列推广服务 (IES) 针对该地区的每日灌溉剂量建议（以K _c乘以 ET ₀表示），该建议在大部分灌溉季节期间较高，相当于季节性灌溉这比评估的估计作物蒸散量高出约 10%（截至一年中的某一天 [DOY] 227）。问题出现了：IES 的建议是否高于（农艺或经济）最佳灌溉率？答案可能是：不会。根据 IES 建议进行灌溉，每季的多年平均灌溉量约为 490 毫米，产量约为 5300 千克 ha ⁻¹，收入约为 15,900 美元 ha ⁻¹（目前棉花市场价格约为$3 kg ⁻¹ )。根据不同条件下棉花产量-灌溉生产函数(Dağdelen et al.,  2009 ; Shalhevet et al.,  1979 ; Wanjura et al.,  2002 )，似乎减少季节性灌溉量约10%就会减少产量减少约 5%，种植者利润增加 4%，$650 ha ^-1（仅考虑棉花市场价格和约 0.3 m ^-3美元的灌溉水价）。IES 推荐的关于作物耗水季节的灌溉剂量的季节性过程又如何呢？在早期阶段以高于实际蒸散量并在生长季节结束时低于实际蒸散量（直到最终在 30%–40% 棉铃开放时停止灌溉）的灌溉率是否有意义？是的，这是有道理的。在生长初期，根系较小，不能吸收滴灌点源供给的大部分水分，因此需要过量灌溉。还必须防止有害盐分的积累。另一方面，在生长季节结束时，可以利用土壤剖面中的可用水并将其干燥。就棉花而言，除了节水之外，水分胁迫的激活还可以提高纤维质量并促进自然落叶，从而实现更高效、更有效的收获。

另一个更极端的例子来自以色列内盖夫西部沙质土壤上的甜椒灌溉实验，表明最佳灌溉率远高于作物的耗水量（ET _{c act ）。}在灌溉剂量按照FAO56（Allen等，  1998）的方法和作物系数进行的处理中，6月至12月的季节性灌溉量约为800毫米，我们（硕士生Shani Sperling）在 Shabtai Cohen 和我本人（Sperling， 2013 ）的指导下， 使用热脉冲法测量了低于灌溉率 40% 的日蒸腾率（与用 16 个阵列评估的土壤剖面中的水和盐度平衡非常一致）时域反射计 [TDR] 传感器）。根据我们在初步实验中构建的产量-灌溉剂量生产函数，根据评估的作物耗水量，将灌溉剂量减少到上述灌溉剂量（800毫米）的40%，将导致灌溉剂量减少50%。产量。

大于耗水量（ET _{c act}）的农艺和经济最佳灌溉剂量在密集滴灌果园中也很常见，例如红葡萄柚（Friedman et al.,  2009）和柿子（Kanety et al.,  2014）。经测得（通过热脉冲法）柚园季节性、4月至11月的ET _c行为约为季节性灌溉+降雨深度的60%，减少40%的灌溉剂量将导致大量的产量和利润损失（灌溉剂量减少 20% 导致产量减少约 10%）（Friedman 等，  2009）。同样，柿子的季节性耗水量约为 1000 毫米季节性高灌溉剂量（产量 40 吨/公顷）的 40%，减少 60% 的灌溉剂量将导致约 50% 的产量损失（Kanety 等） .,  2014 )。

另一方面，也存在最佳日灌溉剂量低于作物ET的情况。春夏季，在耶斯列 Newe Ya'ar 农业研究组织 (ARO) 示范农场约 600 毫米的冬季降雨后，在浅层地下水（地下水位深度约 1.5 m）的粘土上种植青贮玉米。以色列山谷 (https://www.modelfarm-aro.org/?lang=en)，每公顷的干物质产量约为 19,500 公斤，季节性灌溉剂量约为 450 毫米（4 月至 7 月期间，季节性灌溉ET ₀约为700mm)。_{在堪萨斯州较低ET 0}的条件下，获得了约20,100 kg DM ha ^-1的相似产量，评估作物耗水量（ET _{c act}）为565 mm，即水生产率约为3.56 kg DM m ^{- 3}（Hattendorf 等人，  1988）。耶斯列河谷气候温暖，水分生产率较低，因此玉米季节性耗水量高于550 mm（19,500 kg DM ha ^-1 /3.56 kg DM m ^-3）。安装在 30、60 和 120 厘米深度的张力计表明，在生长季节的大部分时间里水流向上。根据该地区种植者的经验，增加季节性灌溉量不可能获得更高的产量。因此，在从土壤剖面和浅层地下水吸水的这些条件下，并考虑到水价（~ $0.3 m ^-3）和产量的市场价格（$0.2 kg DM ^-1），最佳灌溉为速率低于作物的耗水量。

罗森斯坦提出的关于空间异质性和空间可变地块的可变灌溉率的问题与我在短文中所写的内容无关，该文章仅提到统一的灌溉实践（与罗森斯坦所写的相反，使用经验生产函数不会“忽略”空间异质性，而是以隐式模式考虑它）。可变流量灌溉的实际和经济可行性仍需要大规模证明。我祝愿罗森斯坦和其他人成功开发这些方法和技术。

我同意 Rozenstein 的观点，即使用作物模型（我确实认为这是一种生产函数）来指导灌溉率是有建设性的，正如我在文章中所写的：“将监测或历史天气数据与作物模型融合，预测生物量积累和农业产量，对于分配每日灌溉量也具有建设性”。使用人工智能方法当然是合法的。根据目前的进展情况，在我看来，至少在目前，它们应该受到农艺方面的限制。

我不认为而且我在那篇文章中也没有写道，使用（经验或建模的）生产函数是一般的最优策略。笔者认为，不同农业环境下的日灌溉剂量的确定并没有单一的最佳方法，需要根据不同的条件和不同的灌溉目标，选择不同的前馈或反馈方法，有时也是它们的组合。当考虑作物的实际ET来指导灌溉剂量时，不仅应考虑作物ET是确定最佳灌溉剂量的几个因素之一，而且还应考虑作物ET取决于灌溉剂量。因此，估计作物的实际蒸散量通常不足以决定灌溉量。