Comparative assessment of monthly evaporation reliability in desert regions using Monte Carlo simulation, Curve method, Point Estimate Method and machine learning

Study region Two climatically contrasting desert stations in southeast Iran were examined: Zabol (31°02′N, 61°30′E; 489 m a.s.l.) is an inland continental desert site (Köppen BWk) at the centre of the endorheic Sistan Basin, where the “120-day wind” phenomenon and > 300 clear-sky days per year drive among the highest pan-evaporation rates in the world. Chabahar (25°17′N, 60°37′E; 8 m a.s.l.) is a maritime-modified arid site (BWh) on the Makran coast of the Gulf of Oman, where oceanic thermal inertia and the southwest monsoon compress the annual evaporation cycle. Together these two stations span the full aridity gradient of southeastern Iran and provide an ideal natural laboratory for probabilistic evaporation analysis under contrasting desert hydroclimates. Study focus The study benchmarks four reliability frameworks for the bi-directional (minimum and maximum) historical-constraint problem in monthly pan evaporation: Monte Carlo simulation (MCS), the First-Order Reliability Method (FORM, also referred to as the Curve method), the Point Estimate Method (PEM), and an ensemble machine-learning (ML) framework. A consistent 31-year monthly record (1993–2024; n = 31 for January–July, n = 30 for August–December) is used throughout. Shapiro–Wilk tests reject normality at every month at both stations (p < 10⁻¹⁰); MCS and FORM are therefore used as Gaussian-approximation screening tools, with Gamma and Log-normal fits retained for sensitivity checks. Prediction accuracy, predictive uncertainty and reliability interpretation are deliberately kept as three distinct analytical layers rather than conflated into a single index. New hydrological insights for the region System reliability indices fall within βsys ∈ [1.36, 1.94] at Zabol and [1.41, 1.91] at Chabahar; no calendar month at either station reaches the conventional engineering threshold of β = 3.0, indicating that monthly evaporation regularly exceeds its 31-year historical experience envelope at frequencies of 4–9% per month under the current climate. Despite a roughly fivefold contrast in absolute evaporation magnitude (Zabol 85.9–840.4 mm; Chabahar 147.4–260.0 mm), the two stations return near-identical βsys ranges — demonstrating that, in desert hydrology, reliability of monthly evaporation is governed by the normalised mean-to-bound distance rather than the absolute evaporation scale; this is a region-transferable insight for arid-zone water-budget design across the Iranian plateau. Critical operational months are May, July and November at continental Zabol and April, July and October–December at coastal Chabahar (βsys < 1.5), aligning physically with the 120-day-wind onset/decay at Zabol and with the spring warm-advection and monsoon-transition windows at Chabahar. FORM reproduces MCS within < 3% across all months. PEM, in contrast, overstates βmax by as much as 102% at Chabahar and yields failure-probability errors exceeding two orders of magnitude in five Chabahar months and one Zabol month — every instance coinciding with |γ₁| > 0.5, establishing a clean empirical skewness threshold beyond which two-point reliability approximations should not be used in arid hydroclimates. These findings translate directly into operational guidance for the Sistan and Makran-coast water-supply systems and, more broadly, for probabilistic evaporation modelling under accelerating climatic variability.