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Development of a coupled hydro-economic model to support groundwater irrigation decisions [1]

['Boyao Tian', 'Department Of Earth', 'Environmental Sciences', 'University Of Waterloo', 'Waterloo', 'Andrea Brookfield', 'Margaret Insley', 'Department Of Economics']

Date: 2026-05 

This model demonstration examines how land values respond to variations in irrigation strategies, aquifer properties, and sustainable extraction rules. To capture these aspects, we selected and tested five variables representing decisions, regulatory, management, and physical conditions (Table 1).

Together, these variables illustrate how the model can assess trade-offs among farmers’ decisions, policy limits, conservation strategies, and aquifer characteristics. For each scenario, 10,000 Monte Carlo simulations were performed to ensure statistical robustness and capture the range of possible outcomes under uncertainty. Each analysis isolates and tests a single objective to evaluate sensitivity. Unless stated otherwise, results assume a 2% discount rate.

Irrigation Strategies

In this section, we evaluate six groups of irrigation strategies (Table 2), designed to reflect local conditions and common irrigation practices, and representing a range of decision-making, regulatory, and management approaches: (A) no regulatory pumping limit ( ) with varying irrigation fractions ( ); (B) constant regulatory pumping limits with varying irrigation fractions; (C) time-varying pumping limits (two-stage) with a fixed irrigation fraction, following a large-to-small pattern; (D) time-varying pumping limits with a fixed irrigation fraction, following a small-to-large pattern; (E) time-varying irrigation fractions (two-stage) with a fixed pumping limit, following a large-to-small pattern; and (F) time-varying irrigation fractions with a fixed pumping limit, following a small-to-large pattern. The tested strategies draw from real-world irrigation practices, focusing on options that are both practically relevant and economically meaningful.

Fig 3 presents the expected land value and 95% CVaR results for Group B under T = 20 years and time to depletion (TD). In Fig 3d, the expected land value peaks at ~$2.5 million when (full irrigation) and the pumping limit is 3800 m3/day. This represents the fair market value of the land if sold. Beyond this point, expected land value is largely insensitive to further increases in the pumping limit. At the same pumping limit, the 95% CVaR is ~$1.9 million (In Fig 3e), indicating that in the worst 5% of cases, land value could fall to roughly ~$1.9 million. When the irrigation fraction is in the range , land value initially increases with the regulatory pumping limit and then stabilizes, as the regulatory pumping rate exceeds the farmer’s decision and no longer constrains pumping. However, when , the regulatory pumping limit does not constrain water use because actual irrigation remains fixed at 50% of crop water demand, resulting in relatively little variation in land value. The variations observed in Fig 3c and 3f arise because, when the pumping limit is ~2400 m3/day, annual profits shift from negative to positive values, resulting in a small total land value and a large difference from the average, leading to a sudden change in the CVaR percentage. In addition to the main cases, we also evaluate a scenario with a 5% discount rate. Relative to the baseline 2% case, this generates a narrower range of land value and CVaR, but a greater relative CVaR. The higher discount rate places greater weight on near-term cash flows, reducing the present value of expected future income. A demonstration of the Monte Carlo results is provided in S8 Fig and S1 Text.

Fig 4a and 4c illustrate the relationship between expected land value and CVaR, with strategies (Table 2) labelled for comparison. Overall, higher expected land values are associated with higher CVaR results, indicating that increases in average land value also correspond to better outcomes in the worst case scenario (bottom 5% of the distribution). Group C (front-loaded pumping with a higher limit in the early period) produces the largest values, particularly under T = TD, as discounting places greater weight on near-term income. For the scenarios with no regulatory limits, strategy A2, which applies 90% of crop water demand, yields substantially lower values than full-demand irrigation (A1). For the remaining strategies, differences in land value are relatively modest, generally less than 10%.

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TIFF original image Download: Fig 4. Relationships between expected land value and risk metrics: (a, c) 95% CVaR; (b, d) standard deviation, across irrigation strategies Groups A, C and D. https://doi.org/10.1371/journal.pwat.0000452.g004

Fig 4b and 4d further illustrate these dynamics. Expected land values and standard deviations follow a characteristic concave (“C-shaped”) pattern, with higher land values generally associated with greater risk.

For farmer’s irrigation decision, the decision variable, we examined the effects of varying irrigation fractions ( ) under (Fig 5a–5c). Expected land value and CVaR both increase with higher irrigation fractions, as greater water application enables more crop demand to be met. However, this gain comes at a cost: operational years decline sharply from 375 to 171 as increases, illustrating the trade-off between short-term profitability and long-term resource availability. While achieves ~90% of the full-irrigation land value and ~80% of its CVaR, reducing to 0.8 cuts land value nearly in half and reduces CVaR to ~30%. Below , land values fall to ~15% and CVaR becomes negative, highlighting increased downside risk and potential financial losses.

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TIFF original image Download: Fig 5. (a–c) Land values and CVaR results for different irrigation fractions, with labels showing operational years; (d–g) results for irrigation strategy Groups E and F. https://doi.org/10.1371/journal.pwat.0000452.g005

To explore dynamic decision-making, we tested eight irrigation strategies about (Groups E and F in Table 2, Fig 5d–5g). Strategies that start with higher and gradually taper (Group E) consistently outperform others. In the T = TD case, most strategies fall within a high-return/high-variability regime (top-right of Fig 5g), indicating that producers often face a trade-off between maximizing profitability and reducing interannual volatility. However, CVaR analysis shows an almost linear relationship with expected land value, indicating that lower mean returns are associated with worse downside outcomes. High pumping strategies result in increased variability: they generate high returns in favorable years but become more sensitive to unfavorable conditions (e.g., droughts, low prices). Notably, strategies with median land values also exhibit median CVaR, reflecting moderate downside risk, yet their standard deviations remain high. This highlights that variability captured by standard deviation does not necessarily reflect greater downside risk, results may fluctuate widely in the middle of the distribution without significantly worsening the worst-case outcomes.

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[1] Url: https://journals.plos.org/water/article?id=10.1371/journal.pwat.0000452

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