Arnald Puy

For five decades, refining models and datasets has been regarded as central to reducing uncertainty in global irrigation water withdrawal estimates. However, whether these efforts have succeeded remains unclear. Here we compile 1,621 global estimates from 65 studies published between 1974 and 2025 and evaluate them across 360 analytical pathways, spanning a comprehensive range of plausible statistical designs. Our results indicate that uncertainty in global irrigation water withdrawals has not declined: only 18% of pathways show any reduction over time, falling to 10% once projections to 2100 are excluded. Paths split between an unstable trend (42%) and an increase in uncertainty (35%), and where a net direction exists, it is an increase by more than two to one. Progress may therefore require the field to renounce the goal of reducing uncertainty and instead double down on what it has historically done best: expanding it, until uncertainty reaches the boundary of what current knowledge of global irrigation cannot exclude.

It leverages the network-like architecture of scientific models together with software quality metrics to identify chains of function calls that are more prone to generating and propagating errors. It operates on tbl_graph objects representing call dependencies between functions (callers and callees) and computes risk scores for individual functions and for paths (sequences of function calls) based on cyclomatic complexity, in-degree and betweenness centrality. The package supports variance-based uncertainty and sensitivity analyses after Puy et al. (2022) to assess how risk scores change under alternative risk definitions.

Many global water models contain an irrigation module that simulates irrigation water withdrawals based on several assumptions on climate conditions, crop management, soil moisture, irrigation practices or water source. However, we do not know how many of these assumptions are grounded on empirical data and how many are pragmatic; that is, based on practical considerations rather than on observational evidence. Given that pragmatic assumptions are more flexible and can be altered, replaced or removed without compromising the model's representational capacity, this knowledge gap constrains our ability to delineate the uncertainties in these models and assess how reliable their results are. Here we address this issue through the lens of sensitivity auditing and philosophy of science and analyze 50 studies across nine global irrigation models (GIM), identifying a total of 102 model assumptions. Our results suggest that 70% of these assumptions are pragmatic, 35% are shared by multiple models and that most of these in turn are pragmatic. This indicates that the uncertainty space of GIMs may be larger than currently addressed using traditional uncertainty analyses. Our findings underscore the need for systematic appraisal of model assumptions to enhance transparency and improve the robustness of GIMs for decision‐making in water resource management and policy.

A prevailing notion in sustainability science is that irrigated agriculture underpins global food and water security because it accounts for 40% of crop production and 70% of freshwater withdrawals. Through a network citation analysis of 3,500 documents, we reveal that this belief has spread through the literature with minimal empirical support: 60–80% of all citation paths lead to sources that lack supporting data or that do not even contain the 40 or 70% numbers. We also demonstrate that these figures mask a much more uncertain contribution of irrigation to global crop production and water withdrawals, which can lie anywhere between 18–50 and 45–90%, respectively. These ranges should be understood as lower bounds on the true uncertainty. Our findings underscore the need to rigorously evaluate foundational claims in sustainability science and embrace ambiguity to produce robust research and policy-making.

We look at the issue of “analytic flexibility” discovered in the context of recent multianalyststudies, and reconnect it to procedures long advocated across disciplines to test thequality of a quantification. In particular, we recall Leamer’s 1985 work suggesting globalsensitivity analysis (GSA) to test the robustness of a quantitative inference, and illustratehow GSA has been successfully applied to this effect in mathematical modelling in the pastdecades. We show how this approach permits analysts to properly chart statistical gardensof forking paths before venturing into one, or to make sense of a multi-analyst experimentafter it has been done. GSA offers procedures for efficient exploration of the multidimensionalspace scanned by the modelling choices, and easily allows the thus-far unexplained“universe of uncertainty” hidden in multi-analyst studies to be unveiled (uncertainty quantification)and characterised (sensitivity analysis). We describe some essential elementsfrom the GSA toolbox and illustrate their application to a recent multi-analyst study fromBreznau, Rinke and Wuttke (2022). We call our application of GSA to the garden of theforking path a “modelling of the modelling process” (MOMP), detailing the differencesbetween this and a more recently proposed “multiverse analysis”. We conclude offering aprogramming environment for these studies.

Sensitivity analysis (SA) studies how much the uncertainty of a model output depends upon its inputs. Though it is generally agreed in existing guidelines that uncertainty and sensitivity analyses are both crucial for the validation or verification of a model, their application is hampered by practical difficulties, scarce awareness, and at times reluctance to expose the weakness of a model. We present here global sensitivity analysis, mainly through one class of global SA methods known as ‘variance-based’— considered by most practitioners as a recommended practice - and offer pointers on additional methods. We also suggest several hints for a successful and effective use these of these techniques.