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%% RESPONSE TO REFEREE 1

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We thank Referee 1 for a thorough and expert review. Below we address

each point raised in the General Remarks and in the annotated manuscript.

All page/section references are to the revised manuscript.

Referee's general assessment: "This is a puzzling manuscript: on one

side it delivers evidence that the chosen approach … is a scientifically

fruitful approach … But the presentation of the results is the 'black'

side of the medal."

Authors' response: We fully agree with this characterisation of the

original submission. The revised manuscript has been restructured

substantially to address each of the six specific presentation

deficiencies identified in the General Remarks.

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GENERAL REMARK (1): "In large parts, Section 2 and Section 3 contain

repeated texts."

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Response: This repetition arose because the original Section 2.5

("Experimental Setup") largely duplicated material already presented

in Sections 2.2–2.4. Section 2.5 has been eliminated in the revised

manuscript. Its contents have been either absorbed into the relevant

sub-sections (model selection into Sect. 2.5; DTW zoning criterion

into Sect. 2.3.1; vine-copula setup into Sect. 2.3.4) or removed as

genuinely redundant. The opening paragraph of Section 2 now provides

a concise roadmap, replacing the need for the duplicated summary.

[MANUSCRIPT CHANGE: Section 2.5 "Experimental Setup" removed.

Content redistributed to Sects. 2.3.1, 2.3.4, and 2.5 (now

"Model selection"). Overlap between Methods and Results eliminated.]

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GENERAL REMARK (2): "A very large number of actual results is shifted

into the supplement text S1–S10 (the total supplement covers 20 pages!)

with the additional caveat that S8 is not readable."

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Response: We accept this criticism fully. In the revised manuscript,

the following results have been moved from the Supplement to the main

text as numbered tables:

  Table 1 — DTW CVI consensus (top-ranked zoning candidates)

  Table 2 — GPD parameter estimates with 95% bootstrap CIs

  Table 3 — Vine structure summary for Zone 2 (all states)

  Table 4 — Model selection grid (best per K, with full N_obs/p ratio)

  Table 5 — Transition matrix (1980–2022) with bootstrap CI widths

  Table 6 — Interval uncertainty metrics (AW, POC with 95% CI, AAD)

  Table 7 — Verification summary (CRPSS, CRPS, p_DM, pinball, AUC)

The Supplement has been rewritten and now contains genuinely auxiliary

material: per-zone PIT histograms (S1), full CVI table (S2), full

GPD estimates for all zones (S3), vine structure for all zones (S4),

ES/VS results (S5), areal-CRPS gains and Brier scores (S6), rank

correlation robustness (S7), rolling-origin hindcast details (S8),

and the full 30-configuration model selection grid (S9). Section S8

was rewritten from scratch and is fully readable in the revised version.

[MANUSCRIPT CHANGE: Seven new tables added to main text. Supplement

reduced and reorganised. Former S8 rewritten.]

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GENERAL REMARK (3): "A very large number of evaluation/test variables

is introduced often only by name, and at no stage it is mentioned how

this multitude of tests is used for inferences about the results and

how the actual decision of choosing the appropriate model is influenced

by those test variables."

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Response: Each validation sub-section now contains an explicit

"Retention criterion" or "Decision criterion" paragraph stating what

test outcome leads to retaining or refining the model. Specifically:

  Sect. 2.4.1 (nHMM): "Retention criterion: a configuration is

  retained if PIT histograms are visually flat, KS/CvM tests do not

  reject uniformity at the 5% level for >80% of stations, and no

  significant Ljung–Box autocorrelation is detected. Regime count K

  is selected by BIC, with PIT-based adequacy as a secondary check."

  Sect. 2.4.2 (vine): "Operative criterion for vine adequacy: (i) PIT

  histograms visually consistent with uniformity for states and zones

  used in the verification; (ii) variogram scores lower for the vine

  than for the independence baseline; and (iii) Diebold–Mariano tests

  confirming predictive skill gains out-of-sample."

  Sect. 2.4.3 (scores): "Decision criterion: the vine layer is deemed

  to improve over the independence baseline if the Diebold–Mariano

  test rejects equality at the 10% level for station-wise CRPS or

  zone-wise VS in the majority of zones."

Additionally, the new paragraph in Sect. 2.4.2 explains explicitly

why KS/CvM p-values of zero on individual Rosenblatt components (as

seen in Supplement S1) do not constitute operational failure of the

vine: at training sample sizes of n = 845–1269, these tests have very

high power and will reliably detect even minor residual dependence

of no practical consequence for forecast calibration.

[MANUSCRIPT CHANGE: "Retention criterion" / "Decision criterion"

paragraphs added to Sects. 2.4.1, 2.4.2, 2.4.3. Explanation of

KS/CvM behaviour at large n added to Sect. 2.4.2.]

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GENERAL REMARK (4): "At no stage of the manuscript the actual number

of estimated parameters vs. the actual number of sampling points in

space and time used to perform the inference/estimation is mentioned."

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Response: The following information is now given explicitly:

  — Abstract: "The nHMM comprises p = 29,284 estimated parameters fit

    to N_obs = 2,386,692 daily observations (N_obs/p ≈ 82), confirming

    adequate model identifiability."

  — Table 4: includes columns for p (free parameters) and N/p

    (observations-per-parameter ratio) for all three candidate models.

  — Sect. 2.5: "The ratio N_obs/p ≈ 82 confirms adequate

    identifiability: there are roughly 82 observations per estimated

    parameter."

[MANUSCRIPT CHANGE: N_obs/p ratio added to abstract, Table 4, and

Sect. 2.5.]

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GENERAL REMARK (5): "Very often uncertainty measures such as confidence

intervals or p-values in case of test are not given or even mentioned.

One example is table S8 in the supplements, here the estimated shape

parameter of the Pareto fit of the medoid station is reported … for

each synoptic regime with one close to zero value and two positive and

two negative values which would indicate either clear differences of

the tail behavior or very weak properties of the underlying data set

to estimate the notorious difficult shape value; this is a clear case

to be studied in detail e.g. by bootstrapping across the stations

around the medoid."

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Response: We thank the referee for this specific and constructive

suggestion. We implemented a parametric bootstrap following exactly

the spirit of the recommendation. Specifically, for each (zone, state)

combination we resampled the exceedances of the medoid station itself

(separating body and exceedances to preserve the exceedance proportion)

and re-fitted the GPD 500 times, producing empirical 95% CIs for ξ̂.

The results for Zone 5 (main Table 2) show the following pattern:

States 0, 3, 4 (anticyclonic/transitional): ξ̂ < 0 (bounded tails),

confirmed by CIs that are either entirely negative or straddle zero

only narrowly. States 1 and 2 (episodic frontal): ξ̂ > 0 (heavy

tails), confirmed by CIs with predominantly positive bounds. The

sign contrast is statistically robust and physically interpretable

(bounded tails under weak synoptic forcing; heavy tails under deep

frontal systems). Full per-zone results are in Supplement Table S3.

We also note that the original concern about "two positive and two

negative values" arose partly because the previous table lacked

confidence intervals and partly because it appeared to show the medoid

of a different zone. The revised table explicitly identifies the Zone 5

medoid (southern Chile, storm-dominated) and provides CIs throughout.

[MANUSCRIPT CHANGE: Table 2 (main text) now reports ξ̂, σ̂, 95%

bootstrap CI for ξ, n_exc, and tail classification for all five states.

Supplement Table S3 provides the same information for all six zones.

Physical interpretation of the dry/wet tail contrast added to

Sect. 2.3.2.]

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GENERAL REMARK (6): "Except for the introduction, the remaining

manuscript … reads like a split project report … the selection of

atmospheric variables lacks any moisture-related variables like

specific humidity or vertically integrated moisture transports which

is more than the 850 (u,v) data and which can be easily extracted

from C3S/ERA5 datasets."

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Response: We accept this criticism on both counts.

Regarding presentation: the restructuring described under Remarks (1)

and (2) above has substantially improved the manuscript's coherence.

The Methods section now reads as a continuous, sequentially organised

narrative rather than a collection of sub-reports.

Regarding moisture variables: vertically integrated moisture flux

(VIMF) and its divergence (VIMFD) have been added to the covariate

set in the revised manuscript. The physical motivation is stated

explicitly in Sect. 2.1: "The inclusion of VIMF and VIMFD is motivated

by their direct link to landfalling moisture flux over Chile: u_850 and

v_850 alone do not fully characterize atmospheric moisture delivery in

the presence of orographic blocking and low-level jets." Both fields

were extracted from ERA5 at 0.25°×0.25° resolution over the same domain

used for the other covariates.

[MANUSCRIPT CHANGE: VIMF and VIMFD added to covariate set (Sect. 2.1,

covariate list). Physical justification for their inclusion added.

Manuscript reorganised for coherent narrative flow throughout.]

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ADDITIONAL POINT: Zone 4 characterisation

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During revision we identified an error in the previous version that

characterised Zone 4 as "hyper-arid," which is incorrect. Zone 4

covers the semi-arid Mediterranean transition of central Chile

(approximately 33°S–38°S), a region of significant but highly

heterogeneous precipitation controlled by strong orographic gradients

between coastal and Andean stations.

The zone-level areal-CRPS for Zones 2 and 4 is reported as "n/a" in

the revised Table 7, with a detailed explanation in Sect. 3.5.1

distinguishing the two distinct failure mechanisms:

  — Zone 2 (desert transition, 25°–30°S): dominance of zero-precipitation

    days causes the vine ensemble to occasionally generate positive draws

    on universally zero-observation days, inflating the areal mean and

    causing CRPS to diverge.

  — Zone 4 (semi-arid to Mediterranean transition, 33°–38°S): extreme

    within-zone orographic heterogeneity (coastal vs. Andean stations

    differ by up to an order of magnitude in annual totals) means that

    rare extreme draws at high-elevation stations — plausible given the

    GPD shape ξ̂ = 0.921 for State 1 at the Zone 4 medoid, the largest

    shape estimate in the dataset, fitted with only n_exc = 34

    exceedances — can dominate the areal mean even when lower-elevation

    stations record near-zero totals. This is a case of unstable tail

    estimation propagating into the areal score, not a fundamental

    failure of the marginal or vine specification.

In both zones, interval-based diagnostics at the medoid level

(Table 6: POC ≈ 96–97%, AAD ≤ 0.07) confirm well-calibrated

performance. The limitation is in the choice of areal-CRPS as an

evaluation metric for heterogeneous zones, not in the framework itself.

Recommendations for addressing this in future work (weighted areal

averages, stratified validation by sub-domain) are given in Sect. 4.4.

[MANUSCRIPT CHANGE: "Hyper-arid" characterisation of Zone 4 removed.

Sect. 3.5.1 expanded with mechanistically distinct explanations for

Zones 2 and 4. Table 7 CRPS entries for Zones 2 and 4 replaced by

"n/a" with footnote. Sect. 4.4 updated.]

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%%  RESPONSE TO REFEREE 2

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We thank Referee 2 for a careful and constructive review. The comments

focused primarily on methodological clarity and organisation, and we

have implemented all suggestions.

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MAIN COMMENT (1): "The methodology section was somewhat challenging to

follow … sections 2.3.2 through 2.4.2 were initially difficult to

navigate, and I had to read them multiple times to fully grasp the

workflow. My impression is that the clarity could be enhanced by

presenting the methodology in a more step-by-step manner … rather than

interleaving statistical theory and its practical application multiple

times."

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Response: We fully agree. The Methods section has been restructured as

a sequential pipeline with four explicitly numbered steps:

  Step 1 — Zoning via DTW (Sect. 2.3.1)

  Step 2 — State-conditional marginal specification (Sect. 2.3.2)

  Step 3 — Transformation to copula space (Sect. 2.3.3)

  Step 4 — Regular vine construction and model selection (Sect. 2.3.4)

A paragraph-map at the opening of Section 2 previews the complete

pipeline, so the reader knows at any point where they are in the

workflow. Within each step, statistical theory and its practical

implementation are presented together in a continuous narrative rather

than interleaved in separate sub-sections. The former "Experimental

Setup" section (which broke the narrative by revisiting already-

presented material in a different order) has been removed.

Regarding Section 2.3.4 specifically, which the referee found unclear

on first reading: the revised version opens with a plain-language

statement of what the vine achieves ("For d_z up to ~90 we represent

C_{z,s} by a Regular Vine (R-vine), decomposing the d_z-variate

density into bivariate pair-copulas"), presents the mathematical

definition, states the candidate family set and selection criterion,

and then immediately provides Table 3 (vine structure for Zone 2) to

ground the abstract description in a concrete example.

[MANUSCRIPT CHANGE: Section 2 entirely reorganised with numbered

steps, paragraph-map, and continuous theory-application narrative.

Former Section 2.5 removed. Sect. 2.3.4 rewritten with concrete

example (Table 3) integrated into the mathematical presentation.]

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MAIN COMMENT (2): "I found it unclear why seven 'zones' were selected

using the clustering approach. If a specific selection criterion was

applied, it would be helpful to state it explicitly, ideally early in

the methodology section, perhaps starting in section 2.3.1."

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Response: The selection criterion is now stated explicitly at the

beginning of Section 2.3.1, before the mathematical formulation.

Specifically, the revised text reads:

  "The optimal number of zones is k* = 7, selected via a consensus of

  five internal cluster validity indices (CVI): Silhouette,

  Calinski–Harabasz, Davies–Bouldin, Dunn, and COP (Table 1; full

  table in Supplement S2). The G = 7 solution achieves the best

  consensus rank across all five CVIs, aligns with established climatic

  subregions of continental Chile, and yields zones with d_z ∈ [50,90]

  stations and at least 200 training days per state, providing

  sufficient data for robust copula estimation."

Table 1 (new in main text) shows the top five candidate configurations

with their CVI scores, making the selection transparent and verifiable.

[MANUSCRIPT CHANGE: Zoning selection criterion (five-CVI consensus)

stated at start of Sect. 2.3.1. Table 1 (CVI table) moved from

Supplement to main text.]

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POSITIVE ASSESSMENT (acknowledged and appreciated)

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The referee noted: "Despite these points, I find this paper highly

engaging and scientifically valuable … The approach combines

sophisticated statistical modeling with practical application, offering

meaningful contributions. The findings not only deepen our

understanding but also have the potential to inform future research

and practical applications in related areas."

We are grateful for this assessment and hope the structural and

clarity improvements in the revised manuscript allow the scientific

contribution to be more readily appreciated by future readers.