Daily precipitation across Chile is monitored by official agencies , yet many ground stations exhibit discontinuities, missing data, or records shorter than 30 years, limiting their suitability for robust climate diagnostics. To ensure spatial completeness and temporal consistency, we employed the CR2MET dataset , a high-resolution (0.05°) gridded product developed specifically for continental Chile and validated against dense observational networks. CR2MET integrates station observations with ERA5 reanalysis via statistical downscaling, capturing precipitation over complex orography more realistically than global products .

From CR2MET we extracted 462 grid points collocated with operational rain gauges with uninterrupted daily records during 1980–2021. Each grid point contributes 123×42=5166 daily austral-winter (May–August; MJJA) observations; frontal systems during MJJA account for approximately 70 %–90 % of annual rainfall between 30 and 44° S , dominating streamflow generation, groundwater recharge, and Andean snow accumulation . The year 2022 is reserved for out-of-sample evaluation. Seasonal totals are primarily modulated by the South Pacific Subtropical High and the Southern Hemisphere storm track ; orographic enhancement along the Andes intensifies rainfall from frontal systems , while persistent blocking can produce substantial deficits even during ENSO-neutral conditions .

Large-scale atmospheric covariates for the nHMM transition model were extracted from ERA5 at 0.25°×0.25° over continental Chile and adjacent oceanic domains (15° N–60° S, 120–60° W). The covariate set comprises geopotential height at 500 hPa (Z500); mean sea-level pressure (MSLP); sea surface temperature (SST); near-surface and maximum temperature; zonal and meridional wind components at 850 hPa (u850, v850); vertically integrated moisture flux and its divergence (VIMF, VIMFD); and the ENSO indices SOI, ONI, and GMSST. The inclusion of VIMF and VIMFD is motivated by their direct link to landfalling moisture flux over Chile : u850 and v850 alone do not fully characterize atmospheric moisture delivery in the presence of orographic blocking and low-level jets. Principal Component Analysis was applied independently to each gridded field; leading components explaining more than 80 % of total variance were retained as predictors in the nHMM transition model.

The nHMM identifies latent climate regimes and models their temporal evolution in daily rainfall sequences. Transitions between states follow the Markov property, and the nHMM extends the conventional HMM by allowing transition probabilities to vary in time through dependence on external covariates.

The nHMM provides a coherent temporal-regime layer, but Assumption 3 is often too restrictive in regions with strong orographic gradients and mesoscale circulations such as Chile . The hybrid framework addresses this through four sequential steps whose conceptual justification is elaborated in Sect. . Full mathematical details and extended diagnostics are in Supplement S1–S4.

We assess model adequacy at two complementary levels: the temporal regime structure encoded by the nHMM, and the residual state-conditioned spatial dependence within DTW zones. Probabilistic skill is verified out-of-sample. Each diagnostic component is described below together with its decision criterion, clarifying how each test leads to a specific modelling choice rather than serving merely as a catalogue of tests applied.

We fitted a grid of 30 nHMMs varying K∈{2,…,6} and the number of Gamma mixture components C∈{2,…,8} (Supplement S9), denoting each as KhsCdg. Model selection uses BIC=plog⁡Nobs-2ℓ(θ^) where Nobs=5166×462=2386692. Table  reports key statistics for the three candidate models.

The BIC surface shows a clear elbow at K=5: moving from K=4 to K=5 yields a large likelihood gain that compensates the penalty, while K=6 increases p sharply with negligible improvement and produces weakly separated regimes confirmed by regime-overlap diagnostics (Supplement S9). Within K=5, the ratio N/p≈82 confirms adequate identifiability: there are roughly 82 observations per estimated parameter. We adopt K=5, C=5 for all subsequent analyses.

All results use nHMM 5hs5dg (K=5, C=5; p=29284; N/p≈82) with residual spatial dependence modelled within G=7 DTW zones (Table ), each with dz∈[50,90] stations. For each zone and state, a state-conditional R-vine copula (Table ) is fit by maximum likelihood estimation (MLE) and used for ensemble simulation. Forecast verification employs central 90 % prediction interval diagnostics (POC, AW, AAD) and strictly proper scoring rules (CRPS, ES, VS) under blocked cross-validation and out-of-sample tests (Tables –; Supplement S5–S9).

Figure  synthesizes austral-winter (MJJA) precipitation conditioned on the five nHMM regimes. For each column, the main map shows the conditional mean daily precipitation (mm d⁻¹) across the 462 locations for days assigned to that state by the Viterbi path; the inset displays anomalies relative to the MJJA climatology (1980–2021). Climatologically, conditional means peak over southern Chile (40–55° S), consistent with vigorous mid-latitude cyclone activity and Andean orographic enhancement. Northern Chile (north of 30° S) remains dry in all regimes. The anomaly insets reveal a coherent dry-to-wet progression: regimes “0” and “1” exhibit widespread negative anomalies (suppressed frontal activity); regime “2” presents near-neutral, spatially patchy anomalies; and regimes “3” and “4” display robust positive anomalies from ≈35 to ≈45° S, enhanced by windward ascent.

Figure  shows circulation composites for each state. Dry states (e.g., “1”): a ridge–high couplet with positive Z500 over the southeast Pacific and positive MSLP over central Chile displaces the storm track poleward and strengthens subsidence over 30–40° S; weakened westerlies and enhanced coastal southerlies inhibit onshore moisture flux and orographic triggering. Wet states (e.g., “4”): a deep negative Z500 trough extending from the Amundsen–Bellingshausen sector, paired with a negative MSLP minimum south of ≈40° S, intensifies a zonal low-level jet impinging on central–southern Chile; cyclonic curvature favours frontal genesis and baroclinic development. Transitional states (“0”, “2”, “3”) show intermediate synoptic structures consistent with episodic storm incursions. The columnwise correspondence between the MSLP and Z500 composites evidences robust vertical coupling, while the 850 hPa streamlines underscore the state-dependent Pacific moisture corridor intersecting the Andes.

Table  reports the average empirical transition matrix for MJJA 1980–2022. The matrix is diagonally dominant, evidencing persistence: the dry regime S1 has the largest self-transition probability (p^11=0.57), followed by the wet regime S4 (p^44=0.46); S0, S2, S3 are moderately persistent (0.33–0.41), acting as transitional configurations. Direct dry–wet jumps are rare (p^14=0.02, p^41=0.02), dynamically consistent with the gradual synoptic reconfiguration required to transition between anticyclonic and deep cyclonic states . Transitions among S0–S1–S2 are relatively frequent, while S3↔S4 is favoured over links between wet and dry clusters, supporting S3 as a preconditioning stage toward wetness.

Analysis of annual transition proportions {pij(y)}y=19802022 via binomial Generalized Linear Mixed Models (GLMMs; beta-binomial under overdispersion), with Benjamini–Hochberg False Discovery Rate (FDR) correction over all K2=25 transition pairs, reveals a statistically significant decline in S4→S4 self-persistence at ≈0.34 % yr⁻¹ (95 % CI: [0.21, 0.47] % yr⁻¹; p<0.01), indicating shorter wet-regime residence over the study period (Figure ). The S1→S1 self-persistence is trendless (p=0.43). Bridging transitions show compensating behaviour, with modest increases in 0↔3 alongside reduced 3→4 probability, suggesting more frequent cycling through transitional states rather than persistent wet occupancy. Approximately 73 % of the variance in {pij(y)} arises from systematic differences among transition pairs.

Seasonal state occupancy fk(y)=123-1∑t∈Ty1{St=k} is correlated with SOI, Niño 3.4, ONI, and GMSST (Fig. ). Dry-state occupancy f1 correlates positively with SOI and negatively with Niño/ONI; wet-state f4 shows the opposite, consistent with canonical ENSO forcing . Transitional states (k∈{0,2,3}) show weaker, sign-varying associations. GMSST relates negatively to f4, consistent with increased subtropical stability and a poleward baroclinicity shift under global warming . The moderate magnitudes of |ρk,I| reflect the well-established feature that ENSO modulates but does not deterministically control synoptic regimes; the copula component is motivated precisely by these nonlinear, tail-enhanced associations. Spearman and Kendall rank correlations yield qualitatively identical patterns; signs remain invariant under FDR control and block-bootstrap uncertainty bounds (Supplement S7).

We evaluate the hybrid nHMM–Copula–GPD forecaster on MJJA 2022 using M=100 daily ensemble members. The nHMM is trained on 1980–2021; the 2022 state sequence is inferred by Viterbi using observed covariates.

Figure  summarizes the DTW zone design and out-of-sample skill. Panel (A) shows the seven DTW zones with medoids marked by stars. Panel (B) shows, for six medoids (Zone 1 excluded: negligible MJJA totals in the hyperarid far north), monthly boxplots of 2022 predictive distributions (100 daily draws per day) with observed monthly means in orange; insets show daily ensembles versus observations. Ensembles reproduce the seasonal cycle and precipitation intermittency; spreads are smaller in the arid north and larger (and well-centered) in the storm-dominated south, consistent with climatological variance gradients.

Table  reports interval-based metrics for MJJA 2022. Average Width (AW) increases monotonically from 6.9 mm in Zone 2 to 44.0 mm in Zone 6, reflecting the meridional gradient in climatological precipitation variance. Coverage (POC) is close to or above the nominal 90 % in all zones (88.8 %–97.7 %), confirming well-calibrated prediction intervals. Asymmetry degree (AAD) is small throughout (≤0.07), with mild right-skew in Zone 2 corresponding to occasional outlier events in the arid regime.

The hybrid framework delivers: (i) an interpretable regime taxonomy with physically coherent dry ↔ wet progression and robust vertical coupling; (ii) quantified, statistically significant trends in regime persistence consistent with documented megadrought signals; and (iii) calibrated, sharp probabilistic forecasts with significant vine-layer improvements in the rainfall-active southern zones, robust interval calibration across all zones, and well-understood limitations in semi-arid and orographically heterogeneous regions.

Five hidden regimes organize MJJA precipitation along a coherent dry–wet spectrum with physically interpretable circulation signatures: ridge–high couplets with weakened westerlies in dry anticyclonic states, and trough–low couplets with intensified zonal jets in wet cyclonic states (Sect. ). Regime persistence and connectivity are quantified from 1980–2022, revealing a statistically significant decline in wet-state self-transitions (≈0.34 % yr⁻¹; 95 % CI: [0.21, 0.47] % yr⁻¹), consistent with documented drying signatures in central Chile and the negative trend in S4 associated with rising GMSST. GPD shape parameters range from bounded tails (ξ^<0, anticyclonic states) to heavy tails (ξ^>0, frontal states), with statistically robust differences confirmed by parametric bootstrap CIs (Table ). Out-of-sample probabilistic skill is established in the rainfall-active zones: POC is close to nominal (89–98 %), interval widths increase meridionally as expected, AAD is small (≤0.07), CRPSS is positive in all zones with interpretable scores (Zones 3, 5, 6, 7), and the vine-copula layer yields statistically significant improvements over the independence baseline in the two wettest zones (pDM<0.001). Limitations in Zones 2 and 4 are real and explained by within-zone precipitation heterogeneity rather than methodological failure; interval-based diagnostics confirm adequate calibration at the medoid level.

The novelty lies in the explicit integration of covariate-driven regime transitions, DTW-based zoning that respects temporal asynchronies, and state-conditioned high-dimensional R-vines with GPD tail augmentation for daily totals – a combination not previously assembled in the literature. This design preserves regime-physics interpretability while achieving multivariate coherence and extreme-aware behaviour at daily scales, capabilities difficult to obtain within a single monolithic spatiotemporal likelihood for q=462 sites.

The detected decrease in S4→S4 persistence implies shorter residence times in wet, cyclone-dominated states during MJJA, directly translating into reduced winter accumulation and increasing hydroclimatic stress downstream (streamflow, snowpack, groundwater recharge). The regime classification provides a physically grounded pathway from seasonal predictors (ENSO indices, dynamical fields) to spatially consistent precipitation ensembles – through the state-transition kernel and the copula-GPD simulator – suitable for risk-aware hydroclimate operations including reservoir rule-curve testing, drought early-warning, and flood preparedness.

The most pressing limitation is the inadequacy of zone-level areal-CRPS in climatically heterogeneous zones (2 and 4). The solution is threefold: replace the uniform areal average by an orographically weighted average; implement dedicated zero-inflated marginals for stations with very high dry-day frequencies; and apply stratified validation (separately for coastal and Andean sub-domains) before summarizing at the zone level. These modifications would not change the fundamental framework architecture but would extend its applicability to Chile's most climatically complex zones.

Other limitations include Viterbi-induced state-assignment error that can propagate to the copula layer; within-state nonstationarity that is not explicitly captured; and the modular estimation strategy that assumes conditional spatial independence during EM, though the hierarchical design repairs this in a principled and diagnostically verified manner. Future work should explore hierarchical Bayesian formulations that integrate regime, vine, and tail components with shared priors; regime-aware multivariate fields for compound-risk analysis; and assimilation of sub-seasonal dynamical predictors (MJO diagnostics, RCM output, VIMF forecasts) as transition-model covariates.

By disentangling large-scale regime dynamics from residual spatial dependence and explicitly accounting for extremes, the nHMM–DTW–vine–GPD framework delivers meteorologically coherent regimes, quantified changes in regime persistence consistent with observed megadrought trends, and calibrated, sharp probabilistic forecasts in the rainfall-active zones of Chile. The approach reconciles physical insight with statistical parsimony and computational tractability at continental scale, offering a transferable template for probabilistic hydroclimate modelling in Chile and other mountainous, hydroclimatically heterogeneous regions, with clearly specified conditions for its applicability in arid and orographically complex environments.