In East Africa, many drought events have occurred over the past few decades. Droughts have resulted in severe food crises, especially for countries relying heavily on agriculture. From the perspective of sustainability, utilizing groundwater for crop irrigation could be an avenue toward resilience to drought. In this study, we aim to use AI to identify optimal drilling locations for sustainable irrigation for subsistence agriculture. Our initial focus is the Hare watershed in southern Ethiopia. To identify suitable drilling locations, a hydrogeological model (TOPMODEL) for estimation of discharge and depth to water table will be implemented first; machine learning models will be constructed to estimate the probability of finding groundwater at a particular location; and finally these will be provided as inputs to an optimization model. Since this study is in progress, preliminary intermediate results are presented in this paper. A topographic wetness index (TWI) map was developed. TWI captures topographic features related to groundwater potential and will be an important input to our drilling location model.
In Ethiopia, small farmers comprise 95% of all farmers, and
about 80% of the population (
Understanding the factors that affect groundwater
availability is important for estimating the probability of finding
water at a location. Previous research has shown that
lithology, geological structures, drainage density, soils, lineament
density, geomorphology, slope and land cover land use are
the main factors that have an impact on the occurrence and
movement of groundwater in an area
To estimate groundwater potential, we used TOPMODEL
(a TOPography based hydrological MODEL) proposed by
Optimization approaches have been widely applied in
optimal well placement problems. Ma et al. (2018) developed
a mixed-integer linear programming model to identify the
optimal layout of wells with minimizing the total irrigation
costs in an oasis area in Northwest China. A nonlinear
programming model has been constructed by Liu et al. (2019)
to find the optimal well layouts with minimized pumping
costs in another oasis area in Northwest China.
Applying machine learning requires data on wells. Data
availability will be a challenging problem. A recent study
has addressed challenges in collecting groundwater data
The rest of the paper is organized as follows. Section 2 presents the research questions for this study; Section 3 describes the study area and data; Section 4 discusses the methodologies used in this study; Section 5 shows preliminary results and discussion; Section 6 concludes the paper.
This study reports on research questions related to groundwater recharge, groundwater potential, probability of finding shallow groundwater, and optimal drilling locations. Although this paper focuses on the Hare region, the questions can be generalized to other agricultural regions with similar characteristics such as dry seasons and irrigation difficulties.
• What is the groundwater recharge within the study area?
• What is the depth to the water table for different sites in the study area? • What factors are considered to generate a groundwater potential map?
• What are the factors that affect shallow groundwater availability? • What is the estimated probability of drilling out water at a specific location?
• Without depleting the water table, how many wells can be drilled to help satisfy the irrigation need? • Where are optimal drilling locations that could yield water with an acceptable distance to the crop fields? • What are the optimal distances between wells?
The Hare region is located near the Abaya Lake in southern Ethiopia with latitude 6˚1ʹ to 6˚17ʹ N and longitude 37˚27ʹ to 37˚36ʹ E. The total area is 195.43 2. Elevation of the region ranges from 1161 m to 3465 m.
In this study, observed daily discharge data for the period 1987 to 2006 was collected from the Ministry of Water, Irrigation and Energy of Ethiopia. Units were converted from cubic meters to cubic millimeters. To be consistent with the meteorological data, the plan was to collect data from 1987 to 2016. However, discharge data could be obtained only from 1987 to 2006.
Digital Elevation Model (DEM) data were obtained from Alaska satellite services with a resolution of 25 m by 25 m. For convenience of data analysis, an elevation matrix was created representing a digital elevation model with equally sized pixels and equal NS and EW resolution.
Meteorological data including precipitation and
temperature was collected to estimate streamflow and groundwater
recharge. Daily precipitation data was retrieved from three
different meteorological stations including Arba Minch,
Chencha, and Dorze stations for the period 1987 to 2016.
Since precipitation data in 1987 is missing for the Dorze
station and temperature data from 2006 to 2016 are missing in
both Dorze and Chencha stations, filling in the missing
values is necessary. All the missing data was downloaded from
NASA Power Single Point Data Access
(power.larc.nasa.gov, n.d.) Since we have multiple
precipitation and temperature measurements, measurements from
the three stations were integrated. The Thiessen Polygon
approach
∑
where ̅ is the weighted average; is the measurement at
polygon ; is the area of polygon ; is the total number
of measurement points. After performing the above steps,
we have the finalized weighted average precipitation and
temperature data. To be consistent with the other data, the
period 1987 to 2006 was used.
the topographic wetness index computed from the digital
elevation data, a delay function derived by DEM and outlet
data, a set of parameters that need to be calibrated (Table 2),
and hydrometeorological and geological variables including
precipitation data, potential evapotranspiration, and
observed discharge.
formed on the validation data set to evaluate the goodness
are
adof the calibrated parameters. The calibration metric is the
Nash-Sutcliffe efficiency criterion. Values close to 1
indicate a good fit; a value of 1 indicates a perfect match
∑ =1(
∑ =1( − − ̅ ) 2 )2 is the total number of time steps. where discharge; ̅ is the observed discharge; is the simulated is the mean of the observed discharge; and
The depth to water table is simulated based on the saturation deficit, which is simulated using TOPMODEL. To evaluate the goodness of the simulation result of the depth to water table, information on the depth of the existing wells should be collected, which requires field work.
As mentioned in previous section, to find optimal drilling locations, we need to make predictions on the probability of drilling water out of a well in Hare region. This would be an input parameter for the optimization model. We divide the Hare region into small pixels with equal area. A machine learning model, such as logistic regression, could be constructed to predict the probability of water availability for each pixel in Hare. The binary dependent variable is whether the well at the location yield water. The independent variables may include precipitation, elevation, ETP, land cover land use, soil texture, and percentage of topsoil moisture, the data will be collected along with the dependent variable by launching a field work.
To find the optimal drilling locations, a two-stage stochastic
mixed integer programming (SMIP) problem could be
formulated. The two-stage SMIP approach allows users to
make decisions under uncertainty with two decision
variables, one in the first stage and the other in the second stage
(
The general idea of the two-stage SMIP optimization will be described from the initial formulation including the objective functions, decision variables for each stage, uncertainty and possible constraints, reformulation of the problem, and how to solve the problem.
For the initial formulation, the first stage objective function could be minimizing the total construction cost with decision variable denoting whether there is a well ( = 0
1) at location . The second stage objective function could be minimizing the pumping cost with decision variable denoting the pumping hours. Uncertainty could be the yield of water which has a distribution that should be determined prior the optimization model. A set of constraints (e.g. restriction on the pumping hours and total amount of water withdrawn) will be added to fulfill the groundwater sustainability considerations. Reformulation will be generated based on the initial formulation to make the problem tractable. Gurobi, an optimization solver, will be used to solve this optimization problem.
The topographic wetness index map of Hare Ethiopia derived from digital elevation data shows the potential for where water may tend to accumulate (Figure 2). Areas with higher values of topographic index indicate large contributing areas and low slopes. Higher topographic indices (darker green to purple) are mainly found in the southern part of the watershed, and a little in the central and northern parts. These regions have greater potential to become saturated with rainfall. Higher TWI values are found in the areas with surface water, such as streams and wetlands. Lower TWI values indicate the area has small contributing areas and high slope. In our study, lower TWI values (yellow) are found in the central and northern parts of the watershed. Since lower TWI indicates lower moisture storage in the soils, there may be little accumulation in many parts of the Hare watershed. As such, it could be challenging to find shallow good drilling locations for drawing groundwater. Before finalizing the formulation of the optimization problem, we need to estimate the parameters for an initial formulation from the collected data in our study area. As mentioned, data collection is the most challenging task in this study. If the collection for some data items requires too much effort and cost to be practical, the formulation would be modified to adjust. The research questions related to optimal drilling locations would be answered after completing the data collection, parameter estimation and optimization.
This study focuses on using AI to identify optimal drilling locations for sustainable irrigation for subsistence farmers in Hare Ethiopia. We have found that collecting hydrogeological data has become the main challenge to develop an AI model. After data items are collected, we will first construct the TOPMODEL to estimate discharge and depth to water table, which will be used as inputs in machine learning models for an estimation of the probability of finding water at a particular location. With the probabilities as input, an optimization model for identifying optimal drilling locations for sustainable irrigation for subsistence agriculture will be constructed. Our preliminary intermediate result is the topographic wetness index map of Hare Ethiopia. The TWI map indicates that southern part of the watershed has greater potential to accumulate water; central and northern parts of the watershed show lower moisture storage in soils, which make it challenging to identify shallow groundwater. As the study moves forward, more results will be provided.
This research is performed by the MODL (Modeling Optimal Drilling Locations) team, which comprises researchers from the George Mason University Center for Resilient and Sustainable Communities (C-RASC), the Arba Minch University Water Technology Institute, and Global MapAid, with support from Czech Geological Survey. Wanru Li gratefully acknowledges support from a C-RASC fellowship for her efforts on this project.