# Prediction of Runoff in Watersheds Located within Data-Scarce Regions

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Hydrologic Data

^{2}area mainly consists of elevated land. The Wadi Wala catchment is classified as arid because of low rainfall in most of the catchment in winter and high temperature in summer [21]. The mean annual rainfall over the catchment is approximately 300 mm, and the mean temperature range is within 150 °C.

#### 2.1.1. Soil Condition

#### 2.1.2. Evaluation and Analysis of Available Data

#### 2.2. Model Structure

- R
_{a}= the total surface runoff depth (mm); - P
_{a}= the total precipitation depth (mm); - F
_{a}= the total infiltration depth (mm); - S
_{in}= the interception storage depth (mm); - PET = the potential evapotranspiration depth (mm);
- D
_{s}= the surface depression storage depth (mm).

#### 2.2.1. Model Components and Conceptualization

_{in}is the difference in interception storage, when the maximum storage capacity is larger than the current interception. P

_{d}refers to the precipitation depth per unit area of the catchment. D

_{c}refers to the canopy density, and E

_{in}is the loss per unit area from the interception due to evaporation and transpiration. Interception storage S

_{in}will be depleted by evapotranspiration PET. Excess water (throughfall) flows to the ground surface upon meeting the requirement of interception storage. Throughfall was estimated using Equation (3):

_{in}indicates throughfall upon exceeding the interception storage capacity. S

_{in}

_{(t−1)}refers to interception storage at time taken (t − 1). S

_{max}refers to the maximum interception storage capacity. Equation (4) describes the condition of throughfall and rainwater reaching the ground surface and infiltrating into the soil [25].

- f = the infiltration capacity rate (mm/h);
- Sa = the available storage capacity depth from the surface (mm).

_{i}(Sa

_{i}is the first model parameter), a and n are the intercept and slope, respectively, of an algorithmic plot of the quantity (f − f

_{c}) versus Sa (a and n are the second and third model parameters).

_{c}= constant rate of infiltration (mm/h) (f

_{c}is the fourth model parameter).

_{s}. At the same time, this storage will be depleted by evaporation (E

_{r}) and infiltration (F

_{a}). Depression storage is depleted by evapotranspiration PET and direct infiltration to the soil moisture storage SMS. Depression storage has a finite capacity D

_{max}(D

_{max}is the fifth model parameter), and when that capacity is exceeded, direct runoff DRO occurs. DRO is computed in agreement with Equations (5) and (6), which are given as follows:

- DRO = the direct surface runoff (mm);
- S
_{ci}= the capacity depth of inflow into interception storage (mm) for each time increment; - Dc = the capacity depth of inflow into surface depression storage for each time increment.

_{C}). The model assumed that percolation is taking place at a rate smaller than f

_{c}. Subsurface flow is estimated according to Equations (7) and (8):

_{w}is gravitational water in mm, SSF is subsurface flow in mm for each time increment, SW is the water sustained above field capacity, and S

_{c}is the coefficient of subsurface flow (S

_{c}is the sixth model parameter).

- PET = the potential evapotranspiration rate (mm/h);
- PER = the percolation (mm);
- SSF = the subsurface flow (mm);
- Δt = the time increment (h);
- t = the time index.

#### 2.2.2. Streamflow Recession

- Q
_{0}= the flow at any time in cumecs; - Q
_{t}= the flow one time unit later in cumecs; - K
_{r}= the recession constant (K_{r}, the seventh model parameter).

#### 2.2.3. Catchment Routing

- T
_{c}= time of concentration in hours; - L
_{c}= channel reach length (m); - S
_{o}= mean slope of channel reach.

- A = the catchment area (km
^{2}), starting point from the Wadi outlet to the most remote point of surface runoff movement): - c & d = regression coefficients.

^{3}/sec versus time, hour). It can predict the flood peak discharges and determines the direct runoff response to rainfall. Both gauged and ungauged basins as well as basin characteristics (drainage area, slope, etc.) are considered in this method. The analysis method of unit hydrograph commonly employs the summation curve (S-curve), instantaneous unit hydrograph, and synthetic unit hydrograph [26]:

- Re = the rainfall excess array (mm/h);
- Aw = the watershed wetted subarea column vector (km
^{2}); - q = the wetted area outflow discharge column vector;
- Nr = the number of ordinates of rainfall excess;
- M = the number of wetted subarea;
- J = the number of wetted area outflow discharge.

- k = the travel time of the flood wave through the channel reach in an hour (k is the eighth model parameter);
- x = the weighing factor ranging from 0 to 0.5 (x is the ninth model parameter. The model performs channel routing using the Muskingum routing equations (Equations (16)–(19)):

_{1}, I

_{2}is the inflow discharge to the reach during successive time increments in cumecs; Q

_{1}, Q

_{2}is the outflow discharge during successive time increments in cumecs; and t

_{v}is the routing time interval for the reach in hours.

#### 2.2.4. Lag Time and Wetted Area Approach

_{L}is the sum of three lag times; the soil absorbed basin time T

_{b}, which is the time from the start of the storm till the surface runoff occurs on the wetted area; the wetted area travel time T

_{a}, which is the time from the start of runoff in the wetted area till the outlet of the wetted area; and the travel time T

_{v}, which is the time from the wetted area outlet till the outlet of catchment or gauging station. This can be expressed by Equation (20):

_{v}, which is divided equally into a number of cascade reaches; the outflow from the first reach is taking as inflow to the next reach and so on. The flow through these reaches is routed by applying the Muskingum method for hydrologic flow routing. Equations (16)–(19) are all used in routing procedures. The parameters x and k in these equations are obtained through optimization technique.

#### 2.2.5. Catchment Area Parceling Condition

#### 2.3. Model Calibration

- OF (LS) = a least-square objective function;
- Qobs
_{i}= the observed flow on any hour i; - Qsim
_{i}= the simulated flow on any hour i; - N = the number of record observations.

#### 2.4. Model Validation

_{i}and NA (which are dependent on catchment initial soil moisture condition and storm event characteristics). Sa

_{i}and NA are optimized individually for each storm.

#### Performance Evaluation of the Proposed Model

- f (Qobs
_{i}) = the observed streamflow; - f (Qsim
_{i}) = the simulated streamflow over the calibration period; - N = the number of record observations.

^{2}indicates the level of agreement between observed and simulated hydrographs. The coefficient of determination r

^{2}is given by Equation (24):

_{i}):

- (Q
_{p})_{obs}= the observed peak; - (Q
_{p})_{sim}= the estimated peak.

## 3. Results and Discussion

^{2}and coefficient of determination r

^{2}are provided with all figures to assess the performance of the simulation process. Storm data were used as input into continuous calibration so that the resulting optimal set of parameters will give the average set of all events. Figure 4 shows both observed and optimized hydrographs with their rainstorm’s hyetograph. For all storms, the values of R

^{2}range from 76% to 98%, whereas r

^{2}ranges from 77% to 98%. Similarly, Figure 5 illustrates a comparison of the validation process for the observed and simulated hydrographs. The R

^{2}values for all storms used in validation ranges from 80% to 92%. Similarly, r

^{2}values for the same storm ranges from 87% to 95%.

_{i}and NA are optimized individually for each storm since they are highly dependent on the storm characteristics, which are different from one storm to other. The values are provided as an average for all the storms.

_{c}) are considered sensitive parameters. This is clearly shown in Table 4 and Table 5. The parameter “a” has a value of SEN 36.8 for a 10% increase in optimal parameter value and 38.4 for a 10% decrease in optimal parameter value, which means that a 10% increase in the optimized value of “a” will result in 36.8% increase in objective function. Similarly, a 10% decrease in the optimized value of “a” will result in a 38.4% decrease in objective function. The parameter “n” has a SEN value of 57.8. This could be explained as for a 10% increase in the value of “n”, there will be a 57.8% increase in objective function. When the value of “n” decreases by 10%, the corresponding decrease in objective function is 55.8%. The parameter “f

_{c}” has a SEN value of 5.9, which means that a 10% increase in the value of “f

_{c}” will result in a 5.9% increase in objective function, while a 10% decrease in “f

_{c}” will decrease the value of the parameter to a value less than its lower constraint. Since the optimal value of “f

_{c}” is equal to the parameter’s lower bound, the SEN value for a 10% decrease in its optimal value is not investigated. The aforementioned analysis reveals that the parameters “a” and “n” are more sensitive than the parameter “f

_{c}”. Therefore, these parameters should be optimized properly in all modeling conditions.

_{c}) depend on the type of surface soil profile and the antecedent soil moisture condition. These three parameters significantly influence the value of infiltration capacity. Infiltration capacity is directly related to the moisture content preserved in the soil at the start of the rain.

_{c}is taking value equal to its lower constraint, and that the estimated infiltration rate does not reach its final steady rate f

_{c}. This may be attributed to the prevailing soil type at the catchment under study (silty clay loam), which is considered heavy soil and usually having a lower infiltration rate. The other reason is the nature of the storm rainfall at arid and semiarid catchments, which is usually marked by short duration and high intensity.

_{max}is found to be very sensitive; this is clearly shown in Table 4 and Table 5. The SEN values for an increase and decrease in the value of D

_{max}are 20 and 91, respectively. Generally, the value of D

_{max}is relatively small and closer to its lower constraints. This low value of D

_{max}can be attributed to the catchment’s higher relief in its prevailing steep slope. An accurate estimation of D

_{max}requires that a major field works, and a complete land survey should be performed on the catchment under study.

_{i}is a major parameter involved in several modeling processes. The sensitivity measure SEN for decreasing the parameter value by 10% is very high. This is clearly shown in Table 5. The value of SEN takes as much as 94, which is a very high value. Therefore, Sa

_{i}must be optimized in all modeling applications.

_{i}, one can observe that the majority of the values are closer to the lower constraint of the parameter. In other words, the available soil moisture storage capacity is very limited, and mostly, for all storms, the moisture level at the catchments soil is greater than the field capacity. This low value of Sa

_{i}is justified by the fact that the time lag between each consecutive storm event is relatively short. This is true since in this study, many storms are neglected due to suspicion that they contained errors.

_{c}takes value near its lower constraint. The sensitivity measure SEN is equal to zero, which indicates that S

_{c}is an insensitive parameter. Interflow commonly takes place in mountain soils where vegetative cover can produce a layer on the surface characterized by high porosity, but in a relatively bare soil, as the condition in most arid and semiarid catchments, the situation is reversed. Since it is very hard to anticipate the occurrence of interflow in the catchment, the interflow parameter S

_{c}should always be optimized. S

_{c}may be set to a value of zero if a rough estimate of runoff is only needed. It is hard to associate S

_{c}with any watershed characteristics, and its value should always be optimized.

_{r}is important in discrete event modeling. The sensitivity measure SEN is somewhat high. The parameter K

_{r}depends mainly on storm characteristics (intensity, duration, and frequency) and catchment characteristics (such as soil type and catchment relief).

_{i}is the most sensitive model parameter, and therefore, care should be taken when optimizing this parameter; the initial soil moisture storage should be assessed carefully in the catchment before conducting the calibration.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Parameter | Lower Bound | Upper Bound | Optimum Value |
---|---|---|---|

a | 0.08 | 0.9 | 0.658 |

n | 0.1 | 1.5 | 0.336 |

f_{c} (mm/h) | 1.27 | 3.8 | 1.27 |

S_{c} | 0.0 | 0.9 | 0.272 |

D_{max} (mm) | 0.0 | 50.0 | 11.924 |

K_{r} | 0.1 | 0.99 | 0.91 |

K (h) | 0.0 | T_{L} | 1.255 |

X | 0.0 | 0.5 | 0.002 |

Sa_{i} (mm) | 0.0 | 141.6 | 26.8 (average) |

NA (h) | 1.0 | 9 | 2.8 (average) |

Storm Event | Observed | Simulated | IVF | RE | ||||
---|---|---|---|---|---|---|---|---|

Time to Peak (h) | Peak Flow (m^{3}/s) | Runoff Volume (m^{3} × 10^{6}) | Time to Peak (Hours) | Peak Flow (m^{3}/s) | Runoff Volume (m^{3} × 10^{6}) | |||

31 December 1991 | 11 | 28.97 | 3.73 | 11 | 31.3 | 3.33 | 0.893 | 0.080 |

7 February 1992 | 13 | 348 | 38.27 | 14 | 337.51 | 37.23 | 0.973 | 0.030 |

25 February 1992 | 24 | 120.5 | 19.88 | 24 | 98. 13 | 19.33 | 0.972 | 0.186 |

4 January 1994 | 11 | 176 | 11.99 | 10 | 159.7 | 11.36 | 0.947 | 0.093 |

24 November 1994 | 3 | 286 | 22.00 | 5 | 222.4 | 20.90 | 0.950 | 0.222 |

Storm Event | Peak Flow (m ^{3}/s) | Rainfall Depth (mm) | Runoff Depth (mm) | Sa_{i}(mm) | NA | Runoff Coefficient C |
---|---|---|---|---|---|---|

31 December 1991 | 31.3 | 13 | 1.43 | 7.7 | 2 | 0.11 |

7 February 1992 | 337.51 | 14.2 | 6.39 | 0.02 | 6 | 0.45 |

25 February 1992 | 98.13 | 33 | 13.2 | 1.4 | 5 | 0.4 |

4 January 1994 | 159.7 | 33 | 6.6 | 27.9 | 3 | 0.2 |

24 November 1994 | 222.4 | 32.6 | 11.41 | 11.9 | 2 | 0.35 |

Parameter | Optimum Value | O.F. (m ^{3}/s) | Increase of 10% in Parameter Value | O.F. (m ^{3}/s) | SEN * |
---|---|---|---|---|---|

a | 0.658 | 9053 | 0.724 | 42,381 | 36.8 |

n | 0.336 | 9053 | 0.369 | 61,417 | 57.8 |

f_{c} | 1.27 | 9053 | 1.397 | 5.9 | |

S_{c} | 0.272 | 9053 | 0.299 | 9053 | 0 |

D_{max} | 11. 924 | 9053 | 13.116 | 26,909 | 20 |

K_{r} | 0.91 | 9053 | - | - | - |

K | 1.255 | 9053 | 1.381 | 12,361 | 3.7 |

x | 0.002 | 9053 | 0.0022 | 9053 | 0 |

Sa_{i} | 141.29 | 9053 | - | - | - |

NA | 1.187 | 9053 | 2 | 21,867 | 14 |

Parameter | Optimum Value | O.F. (m ^{3}/s) | Decrease of 10% in Parameter Value | O.F. (m ^{3}/s) | SEN * |
---|---|---|---|---|---|

a | 0.658 | 9053 | 0.592 | 43,790 | 38.4 |

n | 0.336 | 9053 | 0.302 | 59,572 | 55.8 |

f_{c} | 1.27 | 9053 | - | - | - |

S_{c} | 0.272 | 9053 | 0.245 | 9053 | 0 |

D_{max} | 11.924 | 9053 | 10.732 | 91,775 | 91 |

K_{r} | 0.91 | 9053 | 0.819 | 22,220 | 14.5 |

K | 1.255 | 9053 | 1.129 | 10,913 | 2.1 |

x | 0.002 | 9053 | 0.0018 | 9053 | 0 |

Sa_{i} | 141.29 | 9053 | 127.16 | 94,166 | 94 |

NA | 1.187 | 9053 | - | - | - |

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**MDPI and ACS Style**

Ghanim, A.A.J.; Beddu, S.; Abd Manan, T.S.B.; Al Yami, S.H.; Irfan, M.; Mursal, S.N.F.; Mohd Kamal, N.L.; Mohamad, D.; Machmudah, A.; Yavari, S.;
et al. Prediction of Runoff in Watersheds Located within Data-Scarce Regions. *Sustainability* **2022**, *14*, 7986.
https://doi.org/10.3390/su14137986

**AMA Style**

Ghanim AAJ, Beddu S, Abd Manan TSB, Al Yami SH, Irfan M, Mursal SNF, Mohd Kamal NL, Mohamad D, Machmudah A, Yavari S,
et al. Prediction of Runoff in Watersheds Located within Data-Scarce Regions. *Sustainability*. 2022; 14(13):7986.
https://doi.org/10.3390/su14137986

**Chicago/Turabian Style**

Ghanim, Abdulnoor A. J., Salmia Beddu, Teh Sabariah Binti Abd Manan, Saleh H. Al Yami, Muhammad Irfan, Salim Nasar Faraj Mursal, Nur Liyana Mohd Kamal, Daud Mohamad, Affiani Machmudah, Saba Yavari,
and et al. 2022. "Prediction of Runoff in Watersheds Located within Data-Scarce Regions" *Sustainability* 14, no. 13: 7986.
https://doi.org/10.3390/su14137986