Model Development
System model development began with a compilation of parameters identified during data collection interviews, which were then used to develop causal loop diagrams. In a causal loop diagram (CLD), relationships between factors are assigned polarities of or , depending on whether a change in one factor or variable positively or negatively impacts another (e.g., indicates that more of A leads to more of B, while indicates that more of A leads to less of B). The loop created by or connections can then be characterized as reinforcing or balancing, based on whether the resulting effect on the initiating factor perpetuates or dampens the initiating behavior. The CLDs consist of feedback loops that drive the changes in borehole functionality seen over time in the region.
The causal connections identified in the CLDs inform the development of stock-flow models, which enable quantifying the parameters, their interactions, and how these change over time. Stock-flow models consist of stocks, which represent the size or state of parameters at a given time (e.g., the volume of water or number of boreholes); and flows, which are events or activities that cause stocks to change over time (e.g., pumping water or boreholes breaking). Our stock-flow models were developed with the STELLA version 2.0.3 Architect software from isee systems and integrate quantitative data, parameter estimates, and time.
CLDs and stock-flow models capture the most influential factors for borehole functionality from two perspectives: repair response times and borehole failure rates. Borehole functionality is defined in the model as the percentage of working over the total number of boreholes in the region/county at a given time. Factors influencing repair times include funding for operations and maintenance (O&M), availability of spare parts and vehicles, travel time to the site, delays in information sharing, and the priority assigned to the repair based on breakdown type (
). Seasonality was captured in the models based on historical wet and dry seasons, and informed the probability of flooding events, which affect repair rates. New construction increases the number of working boreholes and is based on capital expenditure allocations and water access coverage targets under the United Nation’s Sustainable Development Goals (SDGs) (
United Nations 2015).
The stock-flow model simulation begins in the past to calibrate to historical data from January 1, 2018, and then runs for a simulated 12 years (629 weeks by one week time steps), ending at the end of 2029. This time frame was chosen to observe values for 2030, the end of the SDGs.
At each stage of the modeling process (Fig.
1), we re-evaluated the dynamic hypothesis, model structure, and parameter values to correspond with an evolving understanding of the system. Sterman (
2000) and Ford (
2009) have laid out iterative processes for system dynamics modeling that we have adapted to incorporate time-series data, calibration, and interface development (
Ford 2009;
Sterman 2000). Full details on parameters and calculations are available in the Supplemental Materials (Table
S1).
System Dynamics Model Components
Borehole status, functionality, and runtime: The model is structured to track the transition of boreholes through the states of Working, Broken, and Repaired. The availability of allocated government budget and target installation rates from both government and donor organizations determines the rate at which new schemes enter the Working stock. The breakdown rates are a function of pump usage, with minor and major breakdowns occurring every time a certain usage threshold in hours is passed. Borehole weekly pumping hours (runtime) were imported into the model directly for the calibration timeframe and then repeated for the remainder of the simulation. Broken boreholes are fixed based on response times, which are a function of the varying vehicle, spare parts, and technician availability. The remoteness or distance of a borehole site from the Water Department office is also a factor affecting response time and is a graphical distribution fit to existing distances.
Borehole functionality is a simulated calculation calibrated to historical data. Sensor-supplied borehole runtime data from 2018 to 2021 was accessed from Sweetsense Inc. and averaged every week to determine the regional/county functionality levels using R.
Borehole runtime, or hours of pumping per week, was also aggregated weekly from the historical sensor data. Actual borehole pumping ranges from 0 to 133 h per week in Afar and 0 to 63 h per week in Turkana. The weekly pumping data was imported directly into STELLA to account for the high variability in runtime between sites observed and a graphical distribution was fit to the data for the remainder of the simulation.
Water demand and storage: The breakdown rates are informed by borehole usage, based on cumulative hours pumped. The water storage stock was set based on current reservoir capacities in cubic meters and the water demand was calculated from average per capita water use, population estimates based on growth rates, and water access levels. When all reservoirs are empty, groundwater use goes to zero until stored water becomes available again.
Breakdowns: Borehole runtime affects the breakdown rates via thresholds of pumping hours after which a minor or a major breakdown is expected, according to the historical fraction of minor to major breakdowns. This breakdown threshold parameter for the calibration was set at a minimum of 1,000 h and a maximum of 20,000 h. Each time the number of cumulative pumped hours crossed a multiple of the specified breakdown threshold, an additional breakdown was tallied. The breakdowns per week are the number of boreholes over the threshold of pumping hours, and those boreholes then change status from Working to Broken. We used Monte Carlo distributions to specify the probability of a major breakdown (20% of breakdowns in Turkana and 70% of breakdowns in Afar), based on self-reported breakdown histories from the government maintenance staff.
Maintenance response times: The maintenance response times are a sum of the average time taken to identify a breakdown (monitoring), to access vehicles (rented or owned), to access spare parts (immediate or time to procure), and the time to deploy staff to the field. Delays due to conflict were assessed to have a 10% risk, while inaccessibility to sites due to flooding or other disasters was estimated as a 5%–15% risk in Turkana and Afar, respectively, during the wet season, based on historical inaccessibility (e.g., flooded roads) by repair teams. Response delays were calculated for minor and major breakdowns separately, as major repairs are prioritized over minor ones.
Spare parts: Spare parts costs include inflation and are based on whether the maintenance performed is categorized as minor or major. When a part is used, a procurement order is placed to replace it depending on the availability of funds and can take between a month and two years to fulfill. Spare parts costs for major and minor repairs are average costs of the following types of maintenance activities:
•
Minor: sensor replacement, generator repair, switchboard repair or replacement, reservoir repair, other repair or replacement (requiring a light vehicle, average driving speed).
•
Major: submersible pump repair or replacement, generator replacement, borehole cleaning, structural repair to pump house, total rehabilitation (requiring a heavy vehicle, 50km/hr average driving speed).
Vehicle availability: Vehicle availability is the sum of rented and owned vehicles not currently in use. Both regions owned two light vehicles in 2017 and the Afar Water Bureau owned two pieces of heavy equipment (drilling rigs and cranes required for major repairs and rehabilitations). When owned light vehicles are unavailable or if a major breakdown requires an advance site visit to assess the repair needs, a vehicle will be rented. Deployment rates of light and heavy vehicles were determined based on the number of technicians available to drive and the length of time needed for the repair, based on the driving distance to the site. Both regions have a stated goal to purchase one new vehicle a year, so rentals and repair delays reduce as new vehicles are purchased.
Technicians/Contractors availability: The availability of a technician for a repair is determined by the total number of staff, the number already deployed, and their daily expenses (per diem and salary). The technician demand at any time is two persons per broken borehole; however, there must be sufficient repair funds to actually conduct the repair. In the case of Turkana, contractors are hired for major rehabilitation works, which constitute approximately 10% of significant breakdowns, for an all-inclusive cost for parts, equipment, vehicles, and per diems.
Government funds: All funds in the model start from national government allocations to the regional/county governments, which are then allocated to the water departments. The water department then determines what fraction of the total budget will go towards capital expenditure, capital maintenance expenditure (major repairs and rehabilitations), operations and maintenance (minor repairs), and monitoring (also called direct support). Certain expenses, like administration and overhead, are fixed. In Afar, the use of funds for monitoring is based on the number of sensors, and the use of funds for repairs is based on the numbers and types of repairs conducted in a calendar year. In Turkana, the water department has not allocated funds for sensor-based monitoring, as this is currently covered through outside aid. New construction spending is based on borehole unit costs, target installation rates by the local government, an estimated maximum capacity of one new borehole per week, and a universal access target in 2030.
The components previously described are interconnected throughout the model. Pump use rates based on groundwater demand and population growth determine breakdown frequencies, informing the rate at which schemes transition from stocks of Working to Broken. Maintenance response times are a function of the availability of spare parts, vehicles and skilled technicians, as well as rates of flooding and insecurity, informing the rate at which schemes transition from Broken to Repaired. Resources for maintenance activities are contingent on the availability of budgeted funds, as well as procurement times. Lastly, the availability of funds is based on the government allocations towards repair and maintenance activities. Complete details of every model parameter, including equations used for calculations and data sources, are provided in Table S1.
A number of assumptions were made throughout model development. Data on government budget allocations, installation and target repair rates were obtained from annual government reports and were assumed to be representative of future allocations, adjusting for inflation. The inflation rate is an average of the past five years. The model assumes pump use is the primary factor contributing to wear and tear and breakdowns, and does not take into account the effects of environmental conditions, groundwater quality, system age, or other factors that are likely to affect breakdown frequency. Cost estimates for vehicles, spare parts, and contractors are assumed to follow historical prices observed by regional repair teams, adjusted for inflation. Similarly, time delays associated with procurement and contracting are also assumed to follow historical averages.
Model Outputs: Sensitivity Analysis and Optimization
Following model calibration, we tested model performance under a wide range of parameter inputs using sensitivity analysis, selecting input values iteratively. The input variables are different fractional allocations of the water office’s budget to different uses. In the case of Afar, the budget is divided into capital expenditure (CapEx), O&M, monitoring, capital maintenance (CapManEx), and other water expenditure. In Turkana, the budget is divided into allocations for borehole maintenance and new installations, with the proportion for all other water expenditures (e.g., rain/surface water storage, water testing) considered constant. The measured output variables from the sensitivity analysis are the values for functionality and the number of working boreholes at the end of the simulation in 2030.
Within each sensitivity analysis model run, we performed a multicriteria optimization of factors to meet two goals: reduce the maintenance response time delay, therefore increasing the repair rate, and maximizing the overall functionality. Multicriteria optimization in STELLA Architect selects a set of model parameters where the tradeoff between payoff goals can be analyzed. The optimized factors are O&M team operations that determine operational efficiency at conducting repairs. These include the target purchase rates of spare parts per week and vehicles per year, the target for new installations per year, and the average driving distance per day. We chose to optimize the allocation of resources for maintenance between capital maintenance expenditures (vehicles and spare parts), and operational maintenance expenditures (travel and technicians) to simulate best practices for decision-making in a maintenance service provider financial department.
The impacts of the different sensitivity analysis runs are translated into the number of working boreholes and estimated number of households served under the current budget allocation, the sensitivity-analysis-identified optimal allocation, and a scenario where the optimal allocation is applied to a doubled total water department budget. Household size estimates are from asset inventory surveys done in each region, cross-verified against national and regional census data.