2.4 Computed and used parameters for the experiment
Parameters such as soil texture, bulk density, irrigation water requirement, effective rainfall, water productivity and yield response factor are calculated according to their adopted formulas.
The soil bulk density was determined from undisturbed soil samples using a core sampler. The core soil sample was dried at 105\(℃\) for 24 hours and the bulk density was calculated using the following equation[11]
$${ {\rho }}_{\text{b}}=\frac{{\text{W}}_{\text{s}}}{{\text{V}}_{\text{c}}} \left(1\right)$$
Where: - \({{\rho }}_{\text{b} }\)is soil bulk density (g/cm3), Ws is the mass of dry soil (g) and Vc is the volume of soil in the core (cm3).
Determination of moisture content of the soil was carried out during the experiment using the gravimetric method. The soil samples were collected at different root depths based on the growth stage as root depth increased with the growth stage. Its gravimetric water content was determined using the equation
$${ {\theta }}_{\text{m}}=\frac{\left({\text{W}}_{\text{w}}-{\text{W}}_{\text{d}}\right)}{{\text{W}}_{\text{d}}}\times 100 \left(2\right)$$
Where: θm is water content on a weight basis (%), \({W}_{d}\) is the weight of dry soil (g), and Ww is the weight of wet soil (g). The moisture content in the weighted base was converted to a volumetric base by multiplying it with bulk density [11]
$${ {\theta }}_{\text{v}}={{\theta }}_{\text{m}}\times \frac{{{\rho }}_{\text{b}}}{{{\rho }}_{\text{w}}} \left(3\right)$$
Where: θv is the volumetric moisture content in (%), ρb is soil bulk density (g/cm3), and ρw is water density (g/cm3). For determination of moisture content at field capacity (FC) and permanent wilting point (PWP), soil samples were collected from four depths (0–15 cm, 15–30 cm, 30–45 cm and 45–60 cm). Hydrometer methods were used to analyze particle size distribution and determination of textural class based on the percent of sand, silt and clay in a textural triangle. The textural of the soil profile was determined using USDA textural triangle.
Crop water requirement is the depth of water needed to meet the loss through evapotranspiration of a disease-free crop growing in large fields under non-restricting soil conditions including soil water and fertility and achieving full production potential under the given growing environment. Reference evapotranspiration (ETO) is the rate of evapotranspiration from a reference surface with no shortage of water. It was estimated using the Penman-Monteith method from climatological data collected from Melkassa station using CROP WAT 8.0 model. ETO is calculated based on the FAO Penman-Monteith method[12]. Evapotranspiration of the crop (ETc) was calculated from the ETo and the crop coefficient (Kc).
$$ETc=KcETo \left(4\right)$$
The crop coefficient was adopted from FAO 56. The total available water (TAW) in mm, stored in a unit volume of soil was determined by taking the difference between the water content at FC and PWP as the following equation.
$$\text{T}\text{A}\text{W}= \left(\text{F}\text{C}-\text{P}\text{W}\text{P}\right)\times \frac{{\text{B}\text{D}}_{\text{s}}}{{ \text{B}\text{D}}_{\text{w}}}\times {\text{D}}_{\text{Z}} \left(5\right)$$
Where: FC and PWP are soil water content in % (weight basis), \({\text{B}\text{D}}_{\text{s}}\) and \({\text{B}\text{D}}_{\text{w}}\) are the bulk density of the soil and water in gm cm− 3 and Dz is the maximum effective root zone depth in mm.
The RAW is the amount of water that crops can extract from the root zone without experiencing any water stress. For maximum crop production, the irrigation schedule should be fixed based on RAW. Thus RAW was computed from the following equation
$$\text{R}\text{A}\text{W}={\rho }\times \text{T}\text{A}\text{W} \left(6\right)$$
Where; RAW in mm, ρ is an infraction for allowable permissible soil moisture depletion for no stress (40–50%) and TAW is total available water in mm. RAW was taken as the applied depth at that age of crops or 100% ETc requirement.
The net irrigation water requirement is water required by irrigation to satisfy crop evapotranspiration.
$$\text{F}\text{n}={\text{E}\text{T}}_{\text{c}}-{\text{P}}_{\text{e}} \left(7\right)$$
Where; Fn is the net irrigation depth in mm, \({\text{E}\text{T}}_{\text{c}}\) is the crop water requirement in mm and \({\text{P}}_{\text{e}}\) is the effective rainfall in mm.
Gross irrigation water requirement is the actual amount of water supplied to meet crop evapotranspiration or percolation/seepage observed under field conditions. Taking application efficiency of a short, end diked furrow as 60% the gross irrigation requirement was calculated as:
$$\text{G}\text{W}\text{R}=\frac{\text{F}\text{n}}{\text{E}\text{a}} \left(8\right)$$
Where: Fn is the net irrigation depth in mm and Ea is the furrow application efficiency (%).
Effective rainfall is only the rainwater that is retained in the root zone and can be used by the plant. The Pe is, therefore, the difference between the total rainfall and the losses. Various approaches can be used to estimate the effective rainfall from the total monthly rainfall. However, FAO developed a formula based on the analysis carried out for different climates
\({\text{P}}_{\text{e}}=0.6{\text{P}}_{\text{d}\text{e}\text{p}}-10 \text{f}\text{o}\text{r} {\text{P}}_{\text{d}\text{e}\text{p}}<70 \text{m}\text{m} \left(9\right)\)
\({\text{P}}_{\text{e}}=0.8{\text{P}}_{\text{d}\text{e}\text{p}}-24 \text{f}\text{o}\text{r} {\text{P}}_{\text{d}\text{e}\text{p}}>70 \text{m}\text{m} \left(10\right)\)
Where: Pe is Monthly effective rainfall (mm), \({P}_{dep}\)is Monthly dependable rainfall (mm). Dependable rainfall is defined as rainfall with a probability of exceedance (P) of 80%.
Water productivity refers to the ratio between output derived from water use and the water input (value of water derived). The irrigation water productivity was calculated by dividing harvested yield in (kg/ha) by the net amount of seasonal irrigation water (m3/ha) used by crops. It was calculated as:
$$\text{W}\text{P}=\frac{\text{Y}}{\text{n}\text{e}\text{t} \text{i}\text{r}\text{r}\text{i}\text{g}\text{a}\text{t}\text{i}\text{o}\text{n} \text{w}\text{a}\text{t}\text{e}\text{r}} \left(11\right)$$
Where WP is water productivity (kg/m3), Y is yield produced (kg/ha) and net irrigation is in (m3/ha).
Yield response is the relative yield decrease to relative evapotranspiration deficit[13]
$$(1-\frac{{\text{Y}}_{\text{a}}}{{\text{Y}}_{\text{m}}})={\text{K}}_{\text{Y}}(1-\frac{{\text{E}\text{T}}_{\text{a}}}{{\text{E}\text{T}}_{\text{m}}}) \left(12\right)$$
Where Ya is actual yield (kg/ha), Ym is maximum yield (kg/ha), ETa is actual evapotranspiration (mm), ETm is maximum evapotranspiration (mm), and ky is yield response factor