3.1. Stream Order:
It is the mathematical order of the river network through the source to its sink also known as Horton – Strahler. Lines of the river connected to the other by the representative nodes and form the next order number towards the ultimate final number staring from the first starting points. However, if lower and higher-order streams are joined to keep the higher-order (Lindsay et al., 2019). Missed match in stream orders can combine to form the upcoming other order. A segment with index i must be fed by at least 2i − 1 different tributaries of index 1. Shreve noted that Horton’s and Strahler’s Laws (Horton, 1945) should be expected from any topologically random distribution. A later review of the relationships confirmed this argument, establishing that, from the properties the laws describe, no conclusion can be drawn to explain the structure or origin of the stream network (see Fig. 2).
The stream order in the Akaki watershed increases when streams of the same order intersect in the upstream. The intersection of two links of different orders, however, will not result in an increase in order by definition. For the intersection of a first order and second-order link will not create a third-order link but will maintain the order of the highest ordered link. For example, in the Intoto mountainous areas, several 1st order streams joined together to form little Ginfile and grow up fast to form the main channels of Ginfile River. Again, Ginfile River joins a little bit bigger Kebena River. Kebena in the middle of the catchment linked with the Bigger Akaki finally all into Lake Aba Samuel at the order of seven.
The dendritic nature of the stream networks imply that there is enough spaces to share the stormwater and reduce peak flow (Kausarian et al., 2021).
3.2. Gravelius’s index (KG)
Gravelius’s index (KG), which is defined as the relation between the perimeter of the watershed and that of a circle having a surface equal to that of a watershed (Ammar, 2018; Reis et al., 2021).
$${K}_{G}= \frac{P}{2*\sqrt{\pi *A} } \dots \dots \dots \dots \dots \dots \dots .. \left\{1\right\}$$
Where: P is perimeter (km) & A is Area (km2) of Watershed
Accordingly, from the data calculated, Gravelius’s index of Akaki watershed is:
$${K}_{G}= \frac{265}{2*\sqrt{\pi *1504} }=1.93 \dots \dots \dots \dots \dots \dots \dots \dots \dots \left\{2\right\}$$
which defines the catchment as elongated watershed with the value indicating less risk of flooding the catchment (Kausarian et al., 2021).
3.3. Bifurcation ratio (RB)
The bifurcation ratio (RB) is defined as the ratio of the number of streams of any order to the number of streams of the next higher order (Huggett, 2016). It is estimated from ratio of the number Ni of channels of order I to the number Ni+1 of channels of order i + 1 is relatively constant from one order to another (see the results from Table 2).
$${R}_{B}=\frac{{N}_{i}}{{N}_{i+1}} \dots \dots \dots \dots \dots \dots \dots .\left\{3\right\}$$
Where:\(\text{i}=1, 2, 3,\dots \dots ., \text{i}-1\)
3.4. Stream Length (RL)
The law of stream lengths relates the average length of streams of order i (Li+1) to
the successive orders stream length ratio (Li) and the average length would be (RL):
\({R}_{L}= \frac{{L}_{i+1}}{{L}_{i}}\) ………………………….. {4}
Where:\(i=1, 2, 3, \dots \dots \dots , i-1\)
The results of Stream Length for Akaki watershed of seven orders summarized below on Table 2.
3.5. Hypsometric Curve (Ha)
The hypsometric curve is a description of the cumulative relationship between elevation and the area within elevation intervals. The curve is plotted with the elevation plotted as the ordinate and the area within the watershed above the elevation plotted as the abscissa. The hypsometric curve can also be represented in standardized form, with the cumulative fractions in % plotted rather than the actual values. The hypsometric curve for Akaki watershed is shown in Fig. 3 below derived from DEM visualized on RStudio packages.
3.6. Slope Characteristics
Slope represents the rate of change of elevation for each digital elevation model (DEM) cell. It is the first derivative of a DEM. The slope characteristics of the Akaki watershed demonstrated as Fig. 4 below.
3.7. Drainage Density
The progress made by Horton (Horton, 1945) in river morphometry, and in particular the inversion of catchment classification system, also lent impetus to research concerning drainage density. The term was used increasingly, while objections did exist, the same definition was maintained. Drainage density is inversely proportional to the length of overland flow, and that its reciprocal provides a measure of the average distance between rivers. Accordingly, about seven stream orders for an area of 1500 km2 Akaki watershed and the total stream length ranges 2204 kms (Table 2 below.) Therefore, having these catchment data, we can compute equations for different characteristics of the watershed using equations [1–6].
Table 2
Data of stream lengths and stream numbers for Akaki Watershed
| Stream Order | Length (kms) | No. of Streams | Av. Length (meters) | Bifurcation Ratio (RB) | Length Ratio (RL) |
| 1 | 1072.5 | 1631 | 658 | - | 0.5 |
| 2 | 554.6 | 744 | 745 | 2.2 | 0.6 |
| 3 | 307.9 | 436 | 706 | 1.7 | 0.4 |
| 4 | 124.4 | 191 | 651 | 2.3 | 0.4 |
| 5 | 48.5 | 83 | 584 | 2.3 | 1.8 |
| 6 | 85.4 | 154 | 554 | 0.5 | 0.1 |
| 7 | 9.2 | 17 | 541 | 9.1 | - |
| Total | 2204 | 3256 | 541 | 18.1 | 3.7 |
| Average | 314.6 | - | 314.6 | 3 | 0.6 |
3.8. Soil Type Characteristics of Akaki Watershed
Soil is one of the determining hydrogeological system of a watershed. It is a confluence – line of water flow vertical or horizontal interaction of the watershed characteristics and the soil characteristics itself. According to (Berhanu, 2002) and (FAO, 1999) the porosity, permeability, electrostatic attraction, potential dispersion, recharge infiltration and the purifying processes of contaminants in the vadose zone governed by physical and chemical properties of soil.
In the Akaki River watershed depending on the major soils classification and digital soil map of the world database the authors classified the watershed into four main soil type families (Figure. 5). Major soil types in the watershed (FAO, 1999) are Chromic Luvisols, Eutric Nitosols, Vertic Cambisol, and Pellic Vertisols (Fig. 5).
3.9. Topographic Wetness Index (TWI)
The topographic wetness index (TWI) is one of an important tool which used to understand the soil moisture saturated conditions of a watershed. It is simply computed from digital elevation models (DEM) and used to overlook hydrologic responses, how the watershed is dendritic, depression – dominated landscapes investigation and bathymetric survey of a watershed (Grimm et al., 2018; Hojati & Mokarram, 2016).
$$TWI=\text{ln}\frac{\alpha }{\text{tan}\beta +c} ------------Equation 5$$
Where: \(\alpha =Flow accumulation\), \(\beta =Slope \left(Radians\right)\),
$$c=Constant \left(0.01\right)to avoid taking the natural logarithm of zero$$
$$Radians=Degrees\left(\frac{\pi }{180}\right), where \frac{\pi }{180}=0.01745329251$$
DEM is the only input data for the determination of TWI with variations in the spatial resolution can lead to different outputs. It can affect the attributes derived from them and influence models associated with them. The TWI index characterizes the impact parameters of slope on the hydrological processes (Hojati & Mokarram, 2016). In Akaki watershed, TWI explains the water trend accumulating at a given point and the local slope indicates the effect of gravitational forces on water movement (see Fig. 6).
From the Fig. 6 we can understand that how much Akaki watershed is reach in soil moisture contents. The model captures the waterbodies of the watershed very well. All artificial reservoirs within the catchment and natural Lakes, out of the watershed around Bishoftu are identified. The train areas with steep slopes are relatively less in TWI that downstream flat slope areas of the catchment.
3.10. Hydro-geologic Characteristics of the Akaki Watershed
The Akaki catchment is bounded by central volcanic hills and mountains which are not crossed by faults (Fig. 7). Therefore, these areas are treated as a no-flow boundary (Ayenew et al., 2008).
Where: Qb Plato basalt, alkaline basalt, and trachyte
PN a Alajae Formation: Transitional and subalkaline basalt with minor rhyolite and trachyte eruptives.
N c Chilalo Formation: Trachyte, trachy - basalt, per alkaline rhyolite with subordinate alkaline basalt
NQ t b Bishoftu Formation: Alkaline basalt and trachyte
N t b Tarmaber - Megezez Formation: Transitional and alkaline basalt
N n Nazareth Series: Ignimbrites, unwelded tuffs, ash flows, rhyolitic flows, domes and trachyte
3.1.1 Groundwater Recharge Using Soil Water Balance Method
Soil water balance refers to the amount of water held in the soil and is similar to a check book balance. Because soil can hold a limited amount of water, knowing the soil water balance reduces the risk of applying too much water resulting in deep percolation or run-off.
$$\varDelta S+DS=P-AET-RO \dots \dots \dots \dots \dots \dots \dots \dots . \left\{6\right\}$$
Where: ∆S = Change in Soil Storage; P = Precipitation; DS = Deep Seepage; RO = Surface Runoff; AET = Actual Evapotranspiration
This document provides a detailed description of the processing chain applied for the production of the Evapotranspiration data components distributed through the WaPOR portal. Whereas the level-specific WaPOR methodology documents set out the theory that underlies the applied methodology, this document provides details on the input data sources used at all levels and sets out the processing chain for the production of the evapotranspiration data components Evaporation (E), Transpiration (T), Interception (I) and actual Evapotranspiration (AET) as demonstrated in Fig. 8.