Identification of the hydrological model of a runoff-sourced falaj using empirical methods

Arabic language (Al-Ghafri et al. 2023)

Aflaj

plural of falaj

Ayni

a falaj that transfers the water of a natural spring

Dawoodi

attributed to King Solomon, son of David, a falaj that solely taps groundwater

Falaj

gently sloping subterrain tunnel of open channel that taps and transfers groundwater or valley runoffs mostly for the purpose of irrigation

Ghaili

a falaj that branches off from a valley runoff

Iddi

a falaj that solely taps groundwater

Sarooj

a mixture of clay, soil, and other organic materials, which are typically sourced locally

Spate irrigation

the art and science of water management that is unique to semi-arid environments. Flood water from mountain catchments is diverted from river beds and spread over large areas.

Wadi

valley

The management of scarce water resources is a major challenge for people living in arid and semi-arid countries like Oman. Over the centuries, residents of drylands have overcome this challenge through traditional methods of water harvesting and management, which have ensured the long-term sustainability of water resources through demand management and adequate resource replenishment (Adeel et al. 2008). One of these traditional methods for a rational utilization of water is aflaj, or in its singular form, falaj (Mohtashami et al. 2023a).

The falaj system is one of the most important sustainable resources in Oman for supplying people's demands. These systems, known as engineering heritage, have enabled people in this country to establish their villages and cities for settlement (Khaneiki et al. 2024). The advent of aflaj in Oman dates back to at least 1,000 B.C. (Mohtashami et al. 2023b). Since the ancient times, agriculture in Oman has mainly depended on water extracted through the aflaj. According to a 2001 report by the Ministry of Regional Municipalities, Environment, and Water Resources, there are 4,112 aflaj in Oman, of which 3,017 are actively in use and the rest have dried up (MRMEWR 2001 ¹; Mohtashami & Al-Ghafri 2024). This ample number of aflaj in some cases shows the noticeable role of aflaj in Oman.

The falaj systems are a hydraulic technique to collect and transfer water from different sources flowing under the ground surface through tunnels or open channels, utilizing gravity toward residential and agricultural areas. In Oman, there are three types of aflaj, as noted in all references: aini, ghaili, and iddi (Dawoodi). In aini aflaj, the source of water is a natural spring (ain in Arabic). A ghaili falaj is fed by the water from the base flow of a seasonal stream running down a valley (wadi in Arabic). This type of water source is known as spate irrigation in other countries. The last type of aflaj, iddi falaj, also called Dawoodi, consists of a mother well (Ommol falaj), several ventilation shafts, a tunnel for transferring water, and an outlet point downstream from the source (Al-Ghafri 2004).

According to Figure 1, a ghaili falaj consists of an open channel on the ground that leads to the valley flow to collect the base flow. The length of the channel in this falaj system varies, ranging from 0.5 to 15 km (Al-Khamisi 2011). The geometry of the channel corresponds to the flowrate coming from base flow.

One of the most interesting ghaili aflaj is Falaj Al-Sahamah or Falaj Al-Sahel, located near Izki in the Ad-Dakhiliyah governorate. This study tries to give insight into the hydrological system of this falaj, contributing to the government's future efforts to renovate and repurpose it for human settlement. The hydrological analysis, which includes factors such as flowrate, plays a crucial role in assessing the project's viability. The findings of this research may serve as a guide for the government in effectively utilizing and conserving the falaj's water resources, leading to sustainable benefits for the community and the environment. This falaj, which dates back to approximately 800 years ago, is now out of water and abandoned. The water of this falaj was used mostly for agriculture. At that time, local people constructed around 13 km of open and closed channels from the source point in the valley to a fertile plain where cultivation took place. This fact motivated the authors to conduct this study on the hydrological model of the falaj. The main aim of this study is to estimate the historical flowrate of Falaj Al-Sahamah, with the goal of developing a hydrological model of the falaj.

This study conducts the first-ever estimation of a falaj's flowrate in antiquity. For this purpose, the governed hydraulic equations on open channels, which are similar to the channels of aflaj, can also be applied in this case (Mohtashami & Al-Ghafri 2024). The falaj tunnel in the submerged area lies beneath the water table, however, it may not always be completely filled with water, allowing for the possibility of free surface flow. The partially submerged zone refers to the section of the falaj tunnel enclosed by the unsaturated area and adheres to principles of open channel hydraulics (Azari Rad et al. 2018). The Manning equation is one of these equations that can be used. Therefore, this equation is employed in this research to determine the historical velocity and the following discharge rate of Falaj Al-Sahamah.

Hydrology and hydraulic engineering primarily rely on the Manning empirical formula, particularly in rivers and open channels applications. This formula helps users compute the average flow velocity in such systems (Hauser 1995). The Manning equation was introduced for the first time in 1775 and has since been modified by many scientists over time (Gauckler 1867). Nonetheless, no studies have ever been done on the estimation of flowrate in open channels in terms of falaj systems, and there is a scant scholarship on the falaj irrigation channels in general. In the following paragraph, some of them are reviewed.

Sedghi-Asl & Rahimi (2011) presented a new formulation for the Manning equation by combining the original Manning equation with Darcy–Weisbach's friction loss in pipe flows. They validated their formula with the experimental data obtained from the lab. The results of their proposed method showed good agreement. Choo et al. (2013) used Chiu's velocity equation to develop a model for measuring the mean velocity of water in open channels. They calculated the discharge rate based on the measured velocity and the hydraulic characteristics of the river or channel. Finally they compared their results with the Manning equation. Song et al. (2016) utilized a modified Manning equation for calculation the water velocity in the vertical profile of rivers. Their results revealed that the proposed method has acceptable accuracy. They also recommended their method for application of it in deep and narrow rivers.

This study aims to understand the hydrological model of Falaj Al-Sahamah. The first step is to calculate the flowrate of this falaj using the Manning equation. To achieve this, the authors visited the place more than 12 times to collect and record the required data from the falaj and its channel. After collecting the data, a hydrological model was provided for the falaj. Based on this model, the authors aim to provide answers to the following questions:

• What is the hydrological model of this falaj?

• How much was the inflow rate?

• How much was the outflow rate?

• How long did it take to fill the tank belonging to this falaj with the calculated flowrate?

This research is important for the government's future plans to renovate and repurpose the falaj for human habitation. Understanding the hydrological system of the falaj is significantly important as it serves as the basis for decision-making. By analyzing factors such as flowrate, the government can determine the feasibility of the renovation project. Ultimately, this research will guide the government in utilizing and preserving the falaj's water resources effectively, ensuring a sustainable and beneficial outcome for the community and the environment.

This section provides a comprehensive explanation of the case study and outlines all the hydraulic characteristics of the falaj. Next, the equations applied to calculate the flowrate in different parts of the falaj are presented. In the next part, the procedure for data collection and the field measurements is described. Finally, a flowchart showing the research process is provided.

Sarooj is a local word for artificial pozzolana, produced by calcining clay. For more than 3,600 years, this process has involved mixing calcined clay pozzolana with water and lime to create a cementing material (Cook 1985). In Oman, Sarooj has been used as a durable material for constructing forts, castles, and aflaj (Al-Rawas et al. 1998). For instance, in environments such as furnaces or areas where concentrated stress is likely to occur, people commonly use hair as a reinforcing material, while plants are better suited for flat, thick surfaces. Particularly in hydraulic structures, these reinforcement materials blend effectively with other components without causing any roughness. To create Sarooj, they combine clay and lime in a 6:4 ratio and stir it for 2 days. At the final stage, they add castor oil or white eggs to reduce porosity and enhance workability.

The falaj's water drainage channel extends approximately 728 m eastward from the collection tank, starting at the water outlet point at the bottom of the tank. The water then flows to the first canal intersection, where it branches off to irrigate the plantations. However, the falaj water has ceased to flow due to various factors, such as the centuries-long influence of rainwater and valley runoffs on the main channel in Wadi Halfeen, as well as the neglect of regular maintenance, resulting in the demise of the falaj.

The channel of a falaj, whether above or below ground, closely resembles an open channel in many ways (Tavangari Barzi et al. 2005). Similar to open channels, aflaj channels are pathways for water flow but are often hidden beneath the ground to reduce evaporation. Despite this difference in location, both types of channels follow similar principles of fluid flow and hydraulic behavior (Tavangari Barzi et al. 2005). The partially submerged zone (conveyance section) of the falaj tunnel operates in accordance with open channel hydraulics principles (Azari Rad et al. 2018). Equations governing flow in these channels, such as the Manning equation used to calculate flow rates in open channels, can also be applied to aflaj channels (Mosalman Yazdi 2019).

It should be noted that the hydraulics of a falaj are governed by the regime of groundwater hydraulics, where changes in groundwater potential are not time-dependent and follow the three-dimensional spatial coordinates of length, width, and height. This type of hydraulic regime is referred to as steady-state, exhibiting characteristics very similar to the natural flow behavior of groundwater, which is influenced by gravitational forces and spatial variations. Another aspect of falaj hydraulics is its close alignment with the assumptions made by providers of steady-state groundwater flow formulas (Maleki & Khorsandi 2005). Ultimately, by analyzing various hydraulic formulas concerning falaj, one can cautiously apply the formulas proposed by Behnia (1988) in the field. Behnia (1988) suggested that the Manning equation in the context of aflaj can be used for finding velocity and flowrate (Behnia 1988; Mosalman Yazdi 2019).

In this formula, V (m/s) represents the mean velocity of the fluid in the channel, n signifies the Manning's roughness coefficient (s/m^1/3), R (m) represents the hydraulic radius, which is equivalent to the area of cross section (A) over the wetted perimeter (P) (Equation (2)), and S represents the slope along the channel. According to Equation (1), velocity is positively proportional to the channel cross section hydraulic radius and channel slope, and inversely proportional to channel roughness.

To gather comprehensive data for the hydrological model of Falaj Al-Sahamah, the authors conducted extensive field measurements using a variety of methods. The team employed the hydrological data of the region for a given period of time to understand the general behavior of environment surrounding the case study. In addition to direct measurements, they utilized remote sensing (RS) data and geographical information technology (GIS) to enhance their understanding of hydrological processes. RS data allowed them to analyze land cover patterns, vegetation density, and land use changes in the falaj's catchment area.

To estimate the flowrate in this old falaj, the Manning equation is used. As discussed earlier, the roughness coefficient plays an important role in this equation. Therefore, we must first calculate the roughness coefficient for the materials used in the channel construction. As mentioned previously, Sarooj is the material used for building the channel. Sarooj is a type of water-resistant mortar made from 6 to 4 blended clay and limestone, which is then kneaded for 3 days. A fraction of bath furnace slag is mixed with cattail (Typha) fibers, egg, and straw, and then beaten with a wooden stick for even mixing. As needed, egg whites can be used to reduce the water content. The geotechnical properties of the clay in Birkat Al-Mouz near Izki, as shown in Table 1, were derived from the study by Al-Rawas et al. (1998). This clay, with these properties was used in creation of Sarooj.

The liquid limit (LL) of the soil, which is the moisture content at which the soil transitions from plastic to liquid, is 29%. The plastic limit (PL) is the moisture content at which the soil loses its plasticity is 21%. The plasticity index (PI) is the difference between the LL and PL is 8% (29 − 21 = 8). Finally, the activity index (AI) measures the soil's sensitivity to moisture changes and is calculated as the ratio of the PI to the clay fraction (8/27 = 0.296). These parameters collectively provide insights into a soil's plasticity, compressibility, and potential volume changes, which are crucial for soil classification and engineering analyses. Based on the Casagrande plasticity chart, this soil was classified as clay of low plasticity.

To calculate the roughness coefficient in the Manning's equation, an experiment has been done in the hydraulic laboratory in Iran at the University of Birjand, where the channel bed is made of Sarooj.

In this case, two sections were chosen in a laboratory flume (channel) with a length of 3 m. The reason for selecting two sections is to verify the obtained Manning roughness coefficient. If they equal each other, it indicates that the acquired roughness coefficients are correct.

The first section is placed at x = 1 m, and the second section at x = 2.5 m. The necessary hydraulic data, including the channel slope (S), water flow rate (Q), and channel dimensions (e.g., width (W) and depth (D)), were then collected.

By determination of cross-sectional area (A) and wetted perimeter (P) for the two cross-sections, the hydraulic radius (R) was calculated. After that, velocities for the two distances were computed using flow velocity probes.

Utilizing the Manning equation, the roughness coefficient was obtained ⁠. Table 2 provides the dimensions of two cross-sections and eventually the obtained Manning roughness coefficients.

According to this table, the roughness coefficient for Sarooj is calculated to be 0.013 s/m^1/3 for both cross-sections and it indicates that the measurements were performed correctly and this value is accurate.

After identifying the healthy parts, the measurement operations started. The water depth and channel width were measured and recorded. Along the channel, six healthy parts were found. All the measurements for these parts are illustrated in Table 3.

In these six sections, the flowrate was calculated. According to the table, the discharge rates are similar to each other. On average, the flowrate of the channel is 0.048 m³/s, or 48 L/s. This value is not constant over time due to the variability of the ghaili falaj, however, on average, it was 48 L/s.

and represent the discharge rates from the two outlet points. Subscript 1 corresponds to the outlet point placed on the wall, while subscript 2 refers to the one situated at the bottom of the tank. H denotes the height of the water inside the tank. When the height of the water reaches d = 2.3 m, water starts to flow out from both outlet points. Changes in the flowrates from the two outlet points are shown in Figure 12.

These graphs show the changes in discharge rates from two outlet points in the tank. All the graphs exhibit an exponential trend due to Torricelli's law. Figure 12(a) shows the discharge rate from outlet point #1, Figure 12(b) displays the discharge rate from outlet point #2, and Figure 12(c) represents the overall discharge rate from both outlet points combined. A flowrate of zero means that there is no water inside the falaj's tank. Figure 12 demonstrates how the rate of water discharge from the tank decreases as the water level inside the tank drops. When the water height reaches 0.16 m, no water exits from outlet point #1 due to its higher elevation relative to the water level. In this case, only outlet point #2 has outflow, leading to a discontinuity or ‘break’ in the graph.

With the substitution of the values, it is found that it takes 4 h to fill the tank from 0 to 2.3 m.

The hydrological model of Falaj Al-Sahamah is summarized as follows:

• (1) Water from the mother source flows through a network of open and covered channels, as well as two siphons, before reaching the downstream tank. This design was intended for the transportation and distribution of water from the source to the storage facility.

• (2) The flow rate of Falaj Al-Sahamah is determined to be 48 L/s. This value represents the inflow of water into the tank and serves as a crucial parameter for the hydrological model.

• (3) The downstream tank is equipped with two outlet points: one positioned on the wall and the other located at the bottom of the tank floor. These outlet points serve as discharge points for the stored water.

• (4) The hydraulic structure of the tank is designed to release water once the water level reaches a height of 2.3 m. This design enables controlled flow and prevents any overflow out of the tank.

• (5) The discharge rate of the second outlet point is higher than that of the first due to their respective placements within the tank. The strategic placement of the outlets ensures efficient water flow and distribution within the falaj system.

• (6) The discharge rate at the first outlet point is measured at 33 L/s, while the second outlet point has a discharge rate of 34 L/s. Combined, the overall flow rate of the system is 67 L/s. These measurements are crucial for understanding water distribution capabilities and for managing the flow within the system.

• (7) It takes approximately 4 h for the tank to be filled to the desired water level of 2.3 m. This timing is an important factor to consider when planning water usage and ensuring a consistent supply to the downstream areas.

• (8) In the event of heavy rainfall or an inflow rate exceeds 67 L/s, the falaj system experiences surplus water. To manage this excess water, an auxiliary channel is designed to divert the overflow towards the cultivation areas downstream. This ensures that the surplus water is utilized effectively and does not lead to waterlogging or waste.

This research is very important for researchers, scientists, archaeologists, water historians, hydrologists, and decision-makers. The results of this study will be key to solving the mystery of this falaj from agricultural, economic, social, historical, cultural, engineering, and archaeological perspectives. With the help of the results of this study, along with the satellite images from different periods, historical documents, and an analysis of the agricultural pattern of that region, it will be possible to calculate the area of agricultural land and subsequently, the agricultural yield.

According to the historical records and an examination of past economic patterns in rural areas of the region, the exchanges value of these agricultural products for income generation and economic issues will be calculated. Then, based on the remaining crop yields, the population of upstream users and beneficiaries will be estimated. Eventually, in light of hydrological, economic, social, and historical aspects, relationships between these components will be determined and the secret of the past oases over that region will be unraveled. This can be applicable to all dried ghaili aflaj. Therefore, this article will lead to the completion of several scientific and interdisciplinary articles in the near future.

The falaj has been one of the important techniques to extract groundwater from the past up until now in Oman. These sustainable groundwater resources fall into three categories: aini, ghaili and iddi. This study concentrates on one of the ghaili aflaj named Al-Sahamah or Al-Sahel whose hydrological system serves as a fundamental component in the decision-making process. Through a meticulous analysis of such factors as flowrate, the government can assess the feasibility of a renovation project. Ultimately, the insights gained from this research can provide valuable guidance to the government for optimizing the utilization and conservation of the falaj's water resources, ensuring sustainable benefits for both local communities and the environment. Moreover, the findings of this research can serve as a stepping stone for further studies in other scientific fields, such as archaeology. We employed an engineering methodology to reconstruct the hydraulic characteristics of a 12th-century water system from the medieval period when it was functional. Archaeologists now know the precise dimensions and directions of the canals and tank of this falaj, the amount of water flowing in and out of the tank, the tank's fluctuation regime, and other essential information required to answer archaeological questions, such as how much land was irrigated by this water system in the past, how much crop this irrigation system could yield, and what type of economy crystallized around this irrigation system at the time.

We aimed to find the hydrological model of this falaj in an engineering framework where the first and the most important step is flowrate estimation. The following are all the conclusion points achieved from this study:

• (1) The Falaj Al-Sahamah, also known as Falaj Al-Sahel, is one of the ghaili aflaj in Oman, located in Izki, Ad-Dakhiliyah governorate. It is fed by Wadi Halfeen and plays a crucial role in sustainable groundwater resource management.

• (2) The hydrological model of Falaj Al-Sahamah involves the abstraction of water from a mother well located at the center of the wadi. The water is then channeled into a tank downstream, followed by another channel for irrigating a cultivation area.

• (3) The flow rate of Falaj Al-Sahamah was estimated using the Manning equation. By measuring the dimensions of six healthy parts of the channel and analyzing the data, the flow rate was determined to be 48 L/s. This represents the inflow of water into the tank.

• (4) On the opposite side of the tank, there are two connected outlet points positioned at the bottom. Using Torricelli's law, it was observed that the flow rates from these points depend on the water height inside the tank. The outflow starts at 67 L/s and decreases to 0 L/s, indicating that the outflow exceeds the inflow. As a result, no water is stored in the tank unless the inflow significantly exceeds 67 L/s.

• (5) The hydrological model shows that the outlet points start to discharge water when the water level inside the tank reaches a height of 2.3 m. Calculations suggest that it takes approximately 4 h to fill the tank up to this height.

This article acts like a key to the doors of future studies. Subsequent studies will follow one another like links in a continuous chain. With the estimation of the flowrate carried out in this article, scientists can work on estimating the downstream cultivation area. Consequently, the next study could focus on population estimation, based on the cultivation area and the resulting agricultural products. After that, a comprehensive study can be conducted to unravel the relationships among people, water, and agriculture.

The authors would like to express their sincere gratitude to the Ministry of Heritage and Tourism for their cooperation throughout the research process. Special thanks are extended to Mr Amjad Al-Rawahi for providing the photographs. We are also indebted to Mr Ishaq Al-Shabibi and Ms Zahra Al-Abri for their diligent efforts in data collection.

All authors, A.A.-G., A.M., M.L.K., H.A.-B., and A.H.A.-M. contributed to the study conception and design. Material preparation and data collection were performed by A.A.-G., A.M., H.A.-B., and A.H.-M. Analysis and the first draft of the manuscript was written by A.M. and M.L.K. and all authors commented on final versions of the manuscript. All authors read and approved the final manuscript.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.