## 3 Results and Discussion
### Revised Equation of Application Efficiency  
We propose a new equation that considers the different components:  
\[\text{REa}=\text{Re }\times\text{DUpa}_{\text{aj}}\times\text{PRR }\times\text{LI} \tag{15}\]  
where REa: revised equation of application efficiency; Re: losses due to evaporation and drift (Equation (2)) and \(\text{DUpa}_{\text{aj}}\): DUpa adjusted according to days after crop emergence, leading to:  
\[\text{DUpa}_{\text{aj}}=\text{DUpa }(\text{control})\times\left[1-\left(- \frac{\text{DDUpa}}{100}\right)\right] \tag{16}\]  
PRR: losses due to partial residue retention obtained from Equation (11) and divided by Id (mm) to make it a dimensionless loss fraction, leading to:  
\[\text{PRR}=1-\left(\frac{0.44+0.05\times\text{MS}}{\text{Id}}-0.02\right) \tag{17}\]  
LI: losses through leaf interception, obtained by summing the components Ta (Equation (12)) and Sa (Equation (14)), replacing and rearranging terms of Equation (13), and dividing by depth (mm) to make it dimensionless, leading to:  
\[\text{LI}=1-\left(\frac{2.75+\text{Id}+3.86\times\text{ H}-11.065\text{ e}^{0.05\times\text{Id}}+0.721\text{ e}^{0.1\times\text{Id}}}{\text{Id}}\right) \tag{18}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Interrow** & & **Crop Line** & **Depth** \\
**(mm)** & & **(mm)** & **(mm)** \\ \hline WI & 12 & WR & 17 \\ Dc & 12 & Intercepted Id & 28 & 40 * \\ Ta & 17 & Sa & 20 & \\ \hline \hline \end{tabular}  
* The sum of the variables in each row is approximately the same as the depth applied (40 mm). WI: water infiltrated in the interrow (mm); WR: water infiltrated in the crop row (mm); Ta: Throughput (mm); Intercepted Id (mm); Dc: Depth collected (mm) and Sa: Stemflow (mm).  
\end{table}
Table 7: Means (mm) of the measured irrigation components estimated both in the crop line and in the interrow, relative to the irrigation depth applied.  
The results for the revised equation of application efficiency are presented in Table 8, with the irrigation depth and dry matter of residue used in this experiment. Values below or above these ranges can determine any inconsistent results of a component, particularly LI. In Equation (18), this new component (LI) has a minimum of 0.895 and a maximum of 0.967, i.e., between 3.3% and 10.5% of losses of the applied irrigation. LI incorporates both throughflow and stemflow and is adjusted for corn. While experiments involving other crops are necessary to validate this equation, the variables included (H and Id) are easily obtained since the mathematical expression combines linear and exponential terms. The component PRR is universal and can be applied to no-tillage systems that include the rotation of gramineous and leguminous species. Dry matter of residue must be measured before the irrigation campaign; this measurement is an easy procedure that only requires an oven for drying the harvest residue. These values may remain constant in long-term rotation of agricultural crops [51] and can be obtained by government research agencies at the regional level.  
The DUpa equation can be applied to a control condition, which can be evaluated using the standards of [19]. The pivot system can be evaluated at least once a year to confirm the functioning of sprinklers. To include the effects of a tall-growing crop (e.g., corn) on the uniformity of distribution, we propose an adjusted equation that includes days after emergence, a measure that is easily obtained by farmers. The REa obtained with the new equation are relatively low, with DUpaaj being the component that most widely affected application efficiency (Table 8). If the texture of the horizontal surface profile allows water redistribution in the soil (CUs \(\geq\) 90%), then DDUpa might not be considered (i.e., it has a value of 0), DUpaaj = DUpa, and therefore, REa increases considerably.