*2.1. Water Limited Yield—WLY*

The yielding potential of a particular crop plant expresses its genetic potential for the exploitation of solar radiation and CO2 fixation [28]. Yield potential (Yp), as proposed by Evans and Fisher [29], defines the maximum attainable yield of a crop cultivar grown under conditions of the non-limiting supply of nutrients, and effective control of pests and diseases. These growth conditions can be achieved provided the implementation of irrigation to the currently grown crop [30]. Water and nitrogen are classified as factors limiting yield [28].

The importance of water supply to crop plants during the growing season is wellknown to farmers. A temporary shortage of water is a natural feature of natural, i.e., non-irrigated agriculture [31]. Therefore, in practice a much more adequate term is water limited-yield (WLY, Y w), i.e., Yp defined under natural water supply to crop plants. The really attained yield, in fact, depends on the unit productivity of water (water-useefficiency—WUE). This index expresses the amount of yield per total volume of evaporated and transpired water during a life-cycle of a currently grown crop [32]:

$$\text{WUE} = \text{Y}\_{\text{a}} / \text{ET}\_{\text{a}} \tag{1}$$

where:

> WUE—water-use-efficiency, kg yield mm<sup>−</sup><sup>1</sup> or m<sup>−</sup><sup>3</sup> of water;

Ya—actual yield, kg, t ha−1;

ETa—water use (transpired and evaporated water), mm, m3.

Two methods can be used as simple and practical tools to calculate Y w. The first is the FAS procedure (French and Schulz approach—FAS). This method is based on the assumption that the yield increase under the same environmental conditions is directly related to the increase in WUE [33]. The FAS method of water productivity calculation

is composed of three components: (i) the maximum water productivity (TE), (ii) the quantities of water from current precipitation, (iii) the size of water resources in the soil volume rooted by the currently grown crop. The water-limited yield, (WLY) is calculated based on the equation:

$$\text{WLIY} = \text{TE} \left( \text{R-} \Sigma \text{E}\_{\text{s}} \right) + \text{WR} \tag{2}$$

where: TE refers to the transpiration efficiency TE (TE = *k*/VPD; *k*—biomass/transformation ratio; VPD—vapor pressure deficit; R—the sum of rainfall during the growth period; Es—the seasonal soil evaporation, equal to 110 mm, WR -water reserves in the rooted soil volume.

The yield gap can be defined as the difference between the yield resulting from the effect of water available to plants during the growing season, i.e., the water-limited yield (WLY) and the actual yield (Ya):

$$\text{YG} = \text{WLY} - \text{Y}\_{\text{a}} \tag{3}$$

$$\text{YG}\_{\text{f}} = 1 - \left(\text{Y}\_{\text{a}}/\text{CPY}\right) \tag{4}$$

The key component in Equation (2) is the TE index. Originally, it was set for wheat grown in Australia at the level of 20 kg grain mm<sup>−</sup><sup>1</sup> of available water. Under favorable growth conditions, as stated by Passioura [34], this index can reach up to 30 kg grain mm<sup>−</sup>1. As reported by Grzebisz et al. [26], TE is sensitive to the amount of supplied water and nutrients, ranging during the critical stages of spring triticale growth, from 14 to 39 kg grain mm<sup>−</sup>1. The practical advantage of the Yw calculation, based on the FAS approach, is to quantify the yield loss due to inefficient water management. The fraction of the yield gap (YGf) is a relative measure (a value, extending from 0 to 1) of the yield gap (YG) due to unfavorable growth conditions with respect to those created by the potential water supply (WLY) to the currently grown plant. As shown in Figure 1, the highest WLY was recorded in the wet year (1997). Irrigation applied to winter wheat during the critical stages of yield component formation, i.e., stem elongation and heading did not result in a yield increase. The highest values of the YGf, measured on the irrigated plots, indicate that water was not exploited by wheat due to the presence of other growth constraints. In contrast, the artificial reduction in the water supply (the treatment with imposed drought—D) to wheat during the critical period of yield component formation, resulted in a slightly lower grain yield. However, a much higher level of water exploitation was recorded, as indicated by much lower YGf indices, especially on the K fertilized plot (0.11 vs. 0.29 on the irrigated plot, I). The other two years were characterized by a natural water shortage during the stem elongation period (1998), or during the grain filling period (1999). As a result, the YGf, in general, approached zero, indicating that actual yields were close to the potential productivity of water. The negative values of YGf stress the effect of other growth factors, which increased water productivity. This phenomenon was observed on treatments with the imposed drought, revealed most frequently on the K-treated plots. The presented data corroborates the main assumption of the FAS procedure of WLY calculation that WUE depends on the amount of water available to the currently grown crop. The YGf index clearly reflects both the status of water managemen<sup>t</sup> and soil fertility status.
