Toxicity-Weighted Exceedance Mapping of Heavy Metals in Urban Soils Using Sequential Indicator Simulation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please refer to the attached file for the detailed review comments.

Comments for author File: Comments.pdf

Author Response

We thank the reviewer for a constructive and thorough review that will improve the clarity, reproducibility and interpretability of the manuscript. We have adopted the great majority of the suggestions and detail each below. Equation and section numbers prefixed "IV” refer to Deutsch and Journel (1998). To preserve the integrity of the main article, all new material in this revision is placed in the Supplementary Material (appended after the existing S-items); existing main-article tables and figures are edited in place, and no main-article item is added or renumbered.

Reviewer comment 1
Although the Introduction mentions several methodological developments, including SISIM-based exceedance probability mapping, threshold sensitivity analysis, and the toxicity-weighted composite exceedance-priority index H(x), the novelty of the present study relative to the previously published Debrecen concentration mapping study is not stated sufficiently clearly. The authors should revise the Introduction to explicitly summarize the original contributions of this manuscript and distinguish them from the previously published concentration mapping and source-analysis results. In addition, the authors should clarify whether any new sampling, laboratory measurements, preprocessing, or QA/QC procedures were conducted for this study, or whether the manuscript entirely reuses analytical data from the earlier publication.

Response.  We have revised the Introduction and Abstract to state the original contributions explicitly: exceedance-probability mapping at regulatory thresholds, the toxicity-weighted exceedance-priority index H(x), the threshold-sensitivity analysis, and the convergence study. We also state plainly that this study reuses the analytical data of [5] – no new sampling or laboratory measurements were undertaken – so the contribution is methodological and interpretive, built on the previously published measurements.

Reviewer comment 2
The manuscript states that the input dataset and companion software package are publicly available. However, the linked Zenodo records appear to have access restrictions or embargoed files. Since the study relies heavily on computational workflows and simulation settings, the authors should clarify the actual availability of the data and code in the Data Availability Statement. To improve reproducibility, they are encouraged to provide the processed input data, key simulation parameters, software/package versions, random seeds, and scripts needed to reproduce the main maps and tables. If some data cannot be shared for privacy or sensitivity reasons, an anonymized or aggregated version should be provided.

Response.  We have expanded the Data Availability Statement and verified the linked records. The companion software is openly licensed and downloadable: the SISIM exceedance-mapping toolkit (DOI 10.5281/zenodo.18805826), together with the DRASTIC (10.5281/zenodo.18805630), XGBoost-SGS (10.5281/zenodo.18805714) and adaptive-sampling (10.5281/zenodo.18805850) toolkits of the same research programme. The measurement dataset (DOI 10.5281/zenodo.15746844) underlies the published open-access data paper [5] and is available from the corresponding author on reasonable request. We now report the GSLIB program versions (sisim, declus), the Python package versions, the random-number seeds used for the realizations (69069–69073 in the batched runs), the declustering cell size, and we provide the parameter files and post-processing scripts needed to reproduce the exceedance maps, Table 5, and the composite index.

Reviewer comment 3
The manuscript states that 295 sampling locations were included, while 198 locations were excluded and shown in Figure S1 of the Supplementary Material. However, the criteria or rationale for excluding these 198 locations are not clearly described. Since sample exclusion may influence spatial coverage, variogram modelling, and exceedance probability estimates, the authors are encouraged to clarify the exclusion criteria and discuss whether this selection could have introduced spatial bias.

Response.  We have clarified this in Section 2.2 and corrected an imprecise wording. The 198 locations were not excluded on any data-dependent criterion. The 295 analysed locations constitute all available EDXRF measurements (the first survey phase); the 198 remaining locations comprise a south-eastern second-phase expansion area – reserved for a later campaign prompted by a recent serious pollution event in southern Debrecen – and a central forested/recreational belt where measurement density was deliberately reduced given its low human-exposure relevance and already-dense coverage. Sampling effort was therefore allocated by exposure relevance rather than by data values, so there is no value-based selection; the non-uniform density is handled by cell declustering of the global marginals and by the correspondingly higher local kriging variance that we report, and the reserved locations provide a prospective validation set (see Reviewer 2, Comments 1 and 9). Figure S1 has been revised accordingly.

Reviewer comment 4
The proposed H(x) index is an important component of the manuscript, but the weighting scheme would benefit from further clarification. The current approach combines several types of toxicological reference values, such as BMDL, TWI, RfD, ARfD, and UL, which may differ in their derivation, exposure duration, and intended use. The authors are encouraged to explain more clearly how these values were harmonized for weighting purposes, including any conversion from weekly to daily intake values and the rationale for using UL values for essential elements such as Cu and Zn. In addition, the exposure relevance factors appear to be based mainly on expert judgment. This may be acceptable for a screening-level prioritization index, but the authors should clarify this point and avoid implying that H(x) represents a validated health-risk metric. A brief table summarizing the rationale for each metal-specific toxicity score and exposure factor would improve transparency.

Response.  We have added a transparency table (new Supplementary Table S8) giving, for each metal, the reference value used, its type and source, any weekly-to-daily conversion, and the assigned exposure-relevance factor with its rationale. We explain that where a chronic oral reference value was unavailable we used the UL as a conservative screening surrogate for the essential elements Cu and Zn, and that the exposure-relevance factors are a structured expert-judgment screening layer. We respectfully note that the manuscript already stated H(x) is not a validated health-risk metric (original lines 120 and 1096); we have reinforced this caveat in the Abstract and Conclusions and adopted consistent “exceedance-priority” language so no health-risk interpretation is implied.

Reviewer comment 5
The dataset includes only total Cr, while Cr toxicity depends strongly on its chemical speciation. The authors’ baseline assumption of Cr(III) and the additional Cr(VI) sensitivity scenarios are useful. However, without measured Cr speciation, the interpretation of Cr-related risk should remain cautious. The authors are encouraged to state more clearly that H(x) is not intended for Cr-specific health-risk inference in the absence of Cr speciation data, and that areas with elevated total Cr, especially near sensitive receptors, may require confirmatory Cr(VI) analysis.

Response.  We agree and have added an explicit statement that, in the absence of Cr speciation, H(x) is not intended for Cr-specific health-risk inference and that areas of elevated total Cr near sensitive receptors may warrant confirmatory Cr(VI) analysis. Our Cr(III)/Cr(VI) sensitivity scenarios (Supplementary) are presented explicitly as bounding cases rather than as a speciation model.

Reviewer comment 6
The exceedance probability maps are presented on a 50 m grid over an approximately 203 km² study area using 295 sampling locations. Although the authors note that the grid represents computational discretization and that the probabilities are point-support estimates, the maps may still imply a finer spatial precision than the sampling density supports. The authors are encouraged to clarify the effective spatial resolution of the results and discuss uncertainty in sparsely sampled areas. For practical management and sensitive receptor screening, it may also be useful to consider whether coarser aggregated maps or block-support exceedance probabilities would be more appropriate.

Response.  We agree the distinction should be explicit. The 50 m grid is a computational discretization, not a claim of 50 m information: it lies well within the range permitted by the fitted variograms (structural ranges of hundreds to a few thousand metres) and is chosen to honour sample locations and render receptor-scale queries. Spatial precision is bounded not by the cell size but by the estimation variance, which increases with distance from data (mean sample spacing ≈ 830 m (nominal, √(A/n); nearest-neighbour mean 326 m)); in sparsely sampled areas the exceedance probability relaxes toward the global marginal and carries correspondingly large uncertainty, which we report alongside the probability. Importantly, the reported quantity is the exceedance probability averaged over the realizations (the E-type indicator estimate), a smooth surface whose per-realization short-scale texture averages out, so a fine grid does not manufacture detail. On block support we note that Deutsch and Journel 1998 (§IV.1.13, Eq. IV.55) cautions that block indicator kriging does not yield the block ccdf and that block-scale uncertainty “should be approached through small-scale stochastic simulations” – i.e. the simulation route we adopt is the recommended one. We have added a grid-sensitivity check (50/100/200 m; new Supplementary Figure S10) confirming the exceedance areas are insensitive to discretization.

Reviewer comment 7
Although the indicator variogram parameters are reported, the manuscript would benefit from a clearer description of how the variogram models were selected and fitted. This is particularly relevant for metals with few exceedance cases and for models with long fitted ranges. The authors are encouraged to provide key fitting details, such as lag spacing, directional variogram checks, fitting criteria, and whether the models were fitted manually or automatically. In addition, the selected declustering cell size and its effect on metal-specific exceedance proportions should be briefly reported. These clarifications would help readers better assess the robustness of the SISIM inputs.

Response.  We have added these details to the Methods: the lag spacing and number of lags, the directional checks performed, the weighted least-squares/visual fitting procedure used for each indicator variogram, and the declustering cell size selected from the declustering summary together with its effect on the declustered marginal proportions that condition SISIM. The experimental and fitted indicator variograms are now shown (the existing Supplementary Figure S7, improved).

Reviewer comment 8
The identification of sensitive receptors with Moderate or Very High Priority is useful for practical screening. However, receptor-level prioritization may be influenced by point-support exceedance probabilities, sampling density, OSM data quality, and the selected H(x) classification thresholds. The authors are encouraged to emphasize in the Abstract and Conclusions that these results should guide confirmatory sampling rather than be interpreted as definitive risk classifications. It would also be helpful to briefly describe how receptor locations were obtained, filtered, geocoded, and matched to grid cells, and whether any privacy or ethical considerations were considered when mapping sensitive sites.

Response.  We have added a short description of how receptor locations were obtained from OpenStreetMap, filtered by category, geocoded and matched to grid cells, and we note the OSM completeness caveat. We added a statement that only public-facility categories (schools, playgrounds, clinics) were used and no personal or private-address data were involved. The Abstract and Conclusions now state explicitly that the receptor prioritization is a screening output to guide confirmatory sampling, not a definitive risk classification.

Reviewer comment 9
The manuscript would benefit from a brief practical guidance paragraph in the Discussion or Conclusions. This paragraph could explain how environmental managers may use H(x), CCI, MSI, and single-metal exceedance maps together. For example, H(x) could help identify toxicity-weighted priority areas, CCI and MSI could provide complementary information on multi-metal contamination severity, and single-metal exceedance maps could help determine the specific elements requiring follow-up sampling or management attention.

Response.  We have added such a paragraph to the Discussion: H(x) identifies toxicity-weighted priority areas; the CCI and MSI provide complementary multi-metal severity information; and the single-metal exceedance maps indicate which element drives a given priority cell and should be targeted in follow-up sampling.

Reviewer comment 10
Although the manuscript states that H(x) is not a formal health-risk index, some wording and figure labels may still give readers the impression of a health-risk assessment. The authors are encouraged to check the title, figure labels, and terminology throughout the manuscript for consistency. It would be clearer to use terms such as “toxicity-weighted exceedance-priority index” consistently, and to avoid terms such as “health risk map” or “health risk index” unless formal exposure and risk calculations are performed.

Response.  We have performed a terminology sweep across the title, figure labels, table headings and body text, replacing “health risk” wording with “toxicity-weighted exceedance-priority” throughout, consistent with the screening nature of H(x).
Changes to manuscript.  Global terminology sweep (title, figures, tables, text).

Reviewer comment 11
The manuscript should define SISIM, H(x), CCI, MSI, HQ, HI, and other abbreviations at first use in the Abstract, main text, and figure/table captions as required.

Response.  We have defined all abbreviations at first use in the Abstract, main text, and captions, and added an abbreviations list.

Reviewer comment 12
The supplementary validation-related tables, particularly Table S6 and Table S7, should be reformatted for readability. In Table S6, several column headings and numerical entries are broken across lines, making the cross-validation results difficult to follow. In Table S7, several long column headings and large or negative numerical values are also wrapped awkwardly, which makes interpretation challenging. The authors are encouraged to improve the table layout and use consistent numerical formatting.

Response.  We have reformatted Tables S6 and S7 with non-breaking column headers, consistent significant figures, and aligned numeric columns so the cross-validation and related entries are legible.
Changes to manuscript.  Supplementary Tables S6/S7 reformatted.

Key references cited in this response
Deutsch, C.V., Journel, A.G., 1998. GSLIB: Geostatistical Software Library and User’s Guide, 2nd ed. Oxford University Press, New York.
Goovaerts, P., 1997. Geostatistics for Natural Resources Evaluation. Oxford University Press, New York.
Hengl, T., 2006. Finding the right pixel size. Computers & Geosciences 32, 1283–1298.
We thank the reviewer for the constructive suggestions, which have improved the clarity and reproducibility of the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

General comments

This manuscript falls within the scopes of Soil Systems and potentially of interest for its readers. In the reported study, the choice of SISIM over SGS and over kriging-based point prediction is well argued; the authors are unusually candid about the limitations of their composite index, the difference between point and block support, the path dependence of sequential simulation, and the distinction between H(x) and a formal HQ/HI assessment.

However, several issues should be addressed before the manuscript is suitable for publication. The most consequential are: (i) the manuscript is a direct methodological extension of Fehér et al. 2025 [5] using essentially the same dataset, and the incremental contribution needs to be made sharper; (ii) the composite H(x) is, by construction, an As+Cd index (the two metals carry about 88% of the weight), which limits the interpretive value of the ‘composite’ framing and should be acknowledged more directly; (iii) the Cr ensemble did not converge at N = 100, yet Cr results are reported as a primary finding; (iv) the handling of Pb (58% detection) is opaque; (v) the Cd ‘exceedance’ is partly driven by a regulatory threshold set below the regional median, which raises a background-versus-contamination interpretation issue that the manuscript skirts; (vi) Figure 5 legend and Table 6 use inconsistent terminology for the same classes.

 

Specific comments

Comment 1. The manuscript uses a subset (295 of 493) of the dataset published in [5] and refers back to [5] for sampling design, laboratory protocols, factor analysis, and source attribution. This makes it difficult to read because readers would have to read Reference [5] first and then this manuscript. Moreover, the methodological extension of SISIM plus a toxicity-weighted composite index, is genuine, but the introduction does not state clearly enough what is new and what is inherited. The authors in Section 2.2 should make explicit:

• Why 198 samples were excluded (Figure S1 is referenced but the criterion is not stated in the main text).
• Whether the 295-sample subset was preselected on geographic or chemical grounds, and whether any selection bias could propagate into the indicator-variogram structure.
• What information is genuinely new in this paper beyond what is already in [5]. The current text reads in places as if the SISIM maps could be appended to [5] as a supplementary section rather than constituting a freestanding contribution. Sharpening the novelty claim in the abstract and in the last paragraph of the introduction would strengthen the case for a separate paper.

 

Comment 2. Table 4 shows that the normalised weights w_i for children are: As 0.6765, Cd 0.2030, with the remaining six metals summing to 0.12. The composite H(x) is therefore arithmetically dominated by As and Cd, and the explicit statement at line 207 that the two account for 88% of the weight confirms this. The ‘Composite’ maps and rankings will look essentially identical to a bivariate As/Cd analysis. The reader needs to be told this upfront so they can assess whether the toxicity weighting adds value over simply reporting the two probability surfaces. The interpretation of zone-specific contributions (Figure 6, Section 3.3) depends almost entirely on the As and Cd patterns; the apparent multi-metal ‘compositeness’ of Figure 6 is partly an artefact of the stacked-bar visualisation.

Comment 3. In the Section 3.7 and the supplementary convergence analysis is stated that for Cr, 29.1% misclassification remained at N = 100 relative to the N = 1000 baseline, and that N > 500 was required to fall below 1%. The justification given (Cr contributes only 0.007% of the H(x) weight) is reasonable for H(x), but Cr is reported as a primary single-metal finding (…. ‘61% of the study area exceeds the 75 mg/kg threshold’ …… appears in the abstract). If the Cr exceedance area is itself unstable at N = 100, then the 61% figure should either be regenerated at N equal or greater than 500 and the value updated, or be reported with a clearly stated uncertainty range. As currently written, the abstract and Table 5 give the Cr number the same standing as the other metals, which is inconsistent with what the convergence analysis shows.

 

Comment 4. In Table 2, a median Cd concentration of 1.33 mg/kg against a regulatory threshold of 1 mg/kg is reported. If the median value of an essentially urban-scale sample is already above the legal action level, two interpretations are possible: the city is truly Cd-contaminated at a regional scale, or the Hungarian threshold is set below the regional natural background for soils developed on these Quaternary fluvial/eolian parent materials, possibly in combination with diffuse atmospheric deposition. The authors noted the issue at line 308 but does not resolve it.

 

Comment 5. In Table 2 reports n valid = 171 for Pb (i.e., 124 of 295 samples below the XRF detection limit), and footnote at line 148 acknowledges the low detection rate. The authors do not state what detection limit was used for Pb, how the 124 non-detect samples were treated for the indicator transformation (Equation 1) and which were the consequences for the indicator variogram and for the conditional probability surface. The Pb variogram range reach the upper bound of 6000 m (Table 3) with a low sill, which is consistent with weak spatial structure that is essentially indistinguishable from a pure nugget.

 

Comment 6. In Table 3 there is something unclear. The caption reports ‘Indicator variogram model parameters for the eight heavy metals’, but the Table 3 does not report indicator parameters. These are the parameters of the variograms adapted for different metals. Furthermore, in a manuscript in which variograms are central to the methodological approach, why aren't any variogram figures shown? Furthermore, these metals are compositional data and should be treated as such. That aside, why didn’t the authors apply a multivariate approach? The different metals share variability, and a great deal of information could be extracted from the variance-covariance matrices.

 

Comment 7. In Lines 194-207, the authors justify independent simulation on the grounds that indicator-level correlation between As and Cd is weak (r = 0.24) even though continuous-concentration correlation is strong (r = 0.80). The authors seem to be confused and have not applied any indicator variable approach. This is already evident from the variograms. Here, they discuss simulating the 8 metals individually. When applying the indicator variable approach, the distribution of each metal is divided into n thresholds, and a linear coregionalization model including n indicators is calculated. There is no mention of this in the manuscript. The authors should clarify this and provide specific details.

 

Comment 8. In Figure 5 and Table 6 terminology mismatch. Indeed, Table 6 (and the text) uses the priority labels: ‘Very Low Priority / Low Priority / Moderate Priority / High Priority / Very High Priority’, while Figure 5 legend uses ‘No action needed / Routine monitoring / Enhanced monitoring / Active remediation / Immediate action’. These are mapped to the same five H(x) intervals but the language is different in important ways.

 

Comment 9. In The 10-fold stratified cross-validation (Section 3.7, Table S6) validates the per-metal indicator-kriging predictions, but it does not validate the composite H(x) priority surface against any independent ground-truth. The four high-priority receptors in the east-central area are flagged as warranting confirmatory sampling; would the authors consider, as a future-work addition or as a small validation block, comparing the H(x) priority pattern against any independent indicator (e.g., a moss or lichen biomonitoring survey, a SoilGrids-derived prior, or the source-apportionment results from [5])? Even a qualitative comparison would help calibrate the reader's expectations.

Author Response

We thank the reviewer for a careful and technically engaged assessment, and in particular for recognising our candour regarding the limitations of the composite index, the point–block support distinction, the path dependence of sequential simulation, and the difference between H(x) and a formal HQ/HI assessment. The comments have helped us make the geostatistical design of the study explicit, which we had under-described in the original submission. We address each comment in turn. Unless noted otherwise, equation and section numbers prefixed “IV” refer to Deutsch and Journel (1998), GSLIB: Geostatistical Software Library and User’s Guide, 2nd ed. To preserve the integrity of the main article, all new material introduced in this revision is placed in the Supplementary Material (appended as Figures S9–S11, Tables S8–S10 and Text S4); existing main-article tables and figures are edited in place, and no main-article item is added or renumbered.

Reviewer - General comments

This manuscript falls within the scopes of Soil Systems and potentially of interest for its readers. In the reported study, the choice of SISIM over SGS and over kriging-based point prediction is well argued; the authors are unusually candid about the limitations of their composite index, the difference between point and block support, the path dependence of sequential simulation, and the distinction between H(x) and a formal HQ/HI assessment. However, several issues should be addressed before the manuscript is suitable for publication. The most consequential are: (i) the manuscript is a direct methodological extension of Fehér et al. 2025 [5] using essentially the same dataset, and the incremental contribution needs to be made sharper; (ii) the composite H(x) is, by construction, an As+Cd index (the two metals carry about 88% of the weight), which limits the interpretive value of the ‘composite’ framing and should be acknowledged more directly; (iii) the Cr ensemble did not converge at N = 100, yet Cr results are reported as a primary finding; (iv) the handling of Pb (58% detection) is opaque; (v) the Cd ‘exceedance’ is partly driven by a regulatory threshold set below the regional median, which raises a background-versus-contamination interpretation issue that the manuscript skirts; (vi) Figure 5 legend and Table 6 use inconsistent terminology for the same classes.

Our reply.  We are grateful for the positive assessment of the modelling choice and welcome the six headline points; each is addressed specifically under Comments 1–9 below.

Reviewer comment 1

The manuscript uses a subset (295 of 493) of the dataset published in [5] and refers back to [5] for sampling design, laboratory protocols, factor analysis, and source attribution. This makes it difficult to read because readers would have to read Reference [5] first and then this manuscript. Moreover, the methodological extension of SISIM plus a toxicity-weighted composite index, is genuine, but the introduction does not state clearly enough what is new and what is inherited. The authors in Section 2.2 should make explicit:

• Why 198 samples were excluded (Figure S1 is referenced but the criterion is not stated in the main text).
• Whether the 295-sample subset was preselected on geographic or chemical grounds, and whether any selection bias could propagate into the indicator-variogram structure.
• What information is genuinely new in this paper beyond what is already in [5]. The current text reads in places as if the SISIM maps could be appended to [5] as a supplementary section rather than constituting a freestanding contribution. Sharpening the novelty claim in the abstract and in the last paragraph of the introduction would strengthen the case for a separate paper.

Response.  We thank the reviewer and have both sharpened the novelty and clarified the composition of the dataset, which we agree was under-described. Reference [5] established the concentration mapping and source attribution; the present paper contributes a distinct product – single-threshold exceedance-probability mapping referenced to regulatory limits, a toxicity-weighted exceedance-priority index H(x), a threshold-sensitivity analysis, and a convergence study – none of which appear in [5]. Regarding the 295/198 split, we have corrected an imprecise description. The 493 locations form a purposively designed, multi-phase survey. The 295 analysed locations are the measured first-phase dataset and constitute all available EDXRF measurements; no selection was made among measured samples on the basis of their values, so the conditioning set is not value-biased. The 198 remaining locations comprise two design elements: (i) a south-eastern second-phase expansion area, reserved for a subsequent campaign prompted by a recent serious environmental pollution event in southern Debrecen close to these newly designated locations, and (ii) locations in the central forested/recreational belt where measurement density was deliberately reduced because this land use combines low human-exposure relevance with already-dense first-phase coverage. Sampling effort was thus allocated in proportion to exposure relevance, consistent with the decision-focused objective of the study. We pre-empt a natural concern – that the denser sampling in the higher-exposure urban core could inflate the apparent exceedance proportions. This is precisely what cell declustering (declus; Deutsch and Journel 1998) corrects: the global marginal proportions pₑ = F(zₑ) that condition SISIM are computed from declustered weights, so over-represented clusters do not bias the target exceedance frequency. We now report the declustering cell size and the declustered versus naive marginals (new Supplementary Table S9) so that this correction is transparent. A second safeguard is that the lower conditioning density in the forested belt and the south-east is reflected in correspondingly higher local indicator-kriging variance, which we report. The reserved locations – in particular those already sampled in the central belt – additionally serve as a prospective, out-of-sample validation set (Comment 9); a targeted confirmatory campaign is planned. We have replaced the word “excluded” with this description throughout and revised the Figure S1 caption accordingly.

Reviewer comment 2
Table 4 shows that the normalised weights wi for children are: As 0.6765, Cd 0.2030, with the remaining six metals summing to 0.12. The composite H(x) is therefore arithmetically dominated by As and Cd, and the explicit statement at line 207 that the two account for 88% of the weight confirms this. The ‘Composite’ maps and rankings will look essentially identical to a bivariate As/Cd analysis. The reader needs to be told this upfront so they can assess whether the toxicity weighting adds value over simply reporting the two probability surfaces. The interpretation of zone-specific contributions (Figure 6, Section 3.3) depends almost entirely on the As and Cd patterns; the apparent multi-metal ‘compositeness’ of Figure 6 is partly an artefact of the stacked-bar visualisation.

Response.  We agree, and we have made this explicit rather than implicit. As and Cd carry ≈88% of the child weight by construction, because H(x) is a toxicity-weighted index and these two elements combine the lowest toxicological reference values with the highest exposure relevance. We now state this in the Abstract and at the head of the H(x) section, and we have added a quantitative demonstration: the rank correlation between H(x) and a pure As+Cd index (ρ = 0.998), together with a map of the cells where the remaining six metals (≈12% of weight) change the priority class – only 1.9% of the study area (new Supplementary Figure S9). This reframes the dominance as an intended, documented property and identifies precisely where the other metals matter. The existing Figure 6 has been revised in place (no renumbering) to separate the As+Cd contribution from the remaining metals so the stacked bars are not read as spurious multi-metal balance.

Reviewer comment 3

In the Section 3.7 and the supplementary convergence analysis is stated that for Cr, 29.1% misclassification remained at N = 100 relative to the N = 1000 baseline, and that N > 500 was required to fall below 1%. The justification given (Cr contributes only 0.007% of the H(x) weight) is reasonable for H(x), but Cr is reported as a primary single-metal finding (‘61% of the study area exceeds the 75 mg/kg threshold’  appears in the abstract). If the Cr exceedance area is itself unstable at N = 100, then the 61% figure should either be regenerated at N equal or greater than 500 and the value updated, or be reported with a clearly stated uncertainty range. As currently written, the abstract and Table 5 give the Cr number the same standing as the other metals, which is inconsistent with what the convergence analysis shows.

Response.  We agree, and the reviewer is correct that the Cr number was under-converged. Cr is the one metal whose indicator proportion lies near 0.50 (p ≈ 0.523), where the between-realization variance of the exceedance indicator is maximal (binomial variance p(1−p)); the P > 0.50 area is therefore highly sensitive to ensemble size. We quantified this directly: the Cr over-threshold area rises from ≈61% at N = 100 to ≈82% at N = 1000 (a ≈21 percentage-point, ≈34% relative, increase), whereas the mean Cr exceedance probability is stable (≈0.52). We have accordingly regenerated Cr at N = 1000 and updated the reported single-metal Cr exceedance area to ≈82% in the abstract, Table 5, Results and Conclusions. A convergence check confirms the other seven metals agree with the N = 1000 baseline to within <1% already at N = 100 (Table S4), so they are retained at N = 100; the full per-metal convergence is documented in Supplementary Table S4 and Figure S3, and interpreted in Supplementary Text S4 (pixel-level versus areal convergence; the near-boundary residual reflects ergodic Monte-Carlo fluctuation, SE = √(p(1−p)/N)). We also reconciled a bookkeeping discrepancy between the realization count in the Cr parameter file and the text.

Reviewer comment 4

In Table 2, a median Cd concentration of 1.33 mg/kg against a regulatory threshold of 1 mg/kg is reported. If the median value of an essentially urban-scale sample is already above the legal action level, two interpretations are possible: the city is truly Cd-contaminated at a regional scale, or the Hungarian threshold is set below the regional natural background for soils developed on these Quaternary fluvial/eolian parent materials, possibly in combination with diffuse atmospheric deposition. The authors noted the issue at line 308 but does not resolve it.

Response.  We thank the reviewer and have resolved the interpretation with national reference data. The Hungarian soil geochemical background for Cd is low: the expected value across the dominant geochemical macro-region is < 0.5 mg/kg (Geochemical Atlas of Hungary; Ódor et al. 1998; Fügedi et al. 2006), and the national Soil Information and Monitoring (TIM) survey reports topsoil Cd of 0.3–0.6 mg/kg (Marth and Karkalik 2004) – both below the 1 mg/kg regulatory limit. The regulatory threshold is therefore not set below the regional background. The Debrecen median Cd (1.33 mg/kg) exceeds the expected background (< 0.5 mg/kg) and the threshold (1 mg/kg), while remaining within the broad characteristic regional range (up to ≈1.5 mg/kg), indicating genuine but moderate Cd enrichment consistent with the mixed lithogenic and diffuse anthropogenic sources identified in [5], and with the earlier finding of strong arsenic, mercury and cadmium contamination in Debrecen soils (Szegedi 1999). One measurement caveat: Cd near the threshold lies close to the XRF Cd detection limit (2 mg/kg; Supplementary Table S10), so the precise exceedance magnitude carries analytical uncertainty and is best read as pervasive low-level enrichment rather than a precise contamination surface. The Discussion now states this explicitly.

Reviewer comment 5

In Table 2 reports n valid = 171 for Pb (i.e., 124 of 295 samples below the XRF detection limit), and footnote at line 148 acknowledges the low detection rate. The authors do not state what detection limit was used for Pb, how the 124 non-detect samples were treated for the indicator transformation (Equation 1) and which were the consequences for the indicator variogram and for the conditional probability surface. The Pb variogram range reach the upper bound of 6000 m (Table 3) with a low sill, which is consistent with weak spatial structure that is essentially indistinguishable from a pure nugget.

Response.  We thank the reviewer and have clarified the censoring treatment, which we agree was under-specified. The Pb XRF detection limit is 5 mg/kg, which lies far below the regulatory cutoff (100 mg/kg) used for the Pb indicator; the full Skyray XRF detection limits for all eight metals are listed in Supplementary Table S10 (CRM calibration from [5]). A below-detection sample is therefore a hard-inequality datum in the sense of Deutsch and Journel 1998 Eq. IV.36 and IV.44: for a cutoff zₑ well above the detection limit, the indicator I(u;zₑ) = 0 is fully defined, not missing. The non-detects thus carry correct, unambiguous indicator information at the regulatory threshold, and we have re-run the Pb indicator using all 295 locations, with the 124 non-detects entered as i = 0 alongside the 171 detects (the constraint-interval handling of ik3d/sisim); the exceedance surface is negligibly changed, confirming that the earlier exclusion did not materially affect the result. We now state this explicitly. The near-pure-nugget Pb indicator variogram correctly reflects the genuinely weak spatial structure of a rare, near-background exceedance field, and we report it as such rather than over-interpreting the fitted range.

Reviewer comment 6

In Table 3 there is something unclear. The caption reports ‘Indicator variogram model parameters for the eight heavy metals’, but the Table 3 does not report indicator parameters. These are the parameters of the variograms adapted for different metals. Furthermore, in a manuscript in which variograms are central to the methodological approach, why aren’t any variogram figures shown? Furthermore, these metals are compositional data and should be treated as such. That aside, why didn’t the authors apply a multivariate approach? The different metals share variability, and a great deal of information could be extracted from the variance-covariance matrices.

Response.  We appreciate the opportunity to clarify, as our original text did not make the single-threshold design explicit. Table 3 does report indicator (semi)variogram parameters. Following Deutsch and Journel 1998 Eq. IV.27–IV.30, indicator kriging at a single cutoff zₑ requires exactly one indicator covariance C_I(h;zₑ) and one cdf value F(zₑ); Table 3 reports precisely that quantity for each metal – the nugget, sill, range and anisotropy of the indicator semivariogram of I(u;zₑ). We have revised the caption to name the cutoff and added the exceedance proportion pₑ and the pₑ(1−pₑ) sill so the indicator nature is unambiguous, and we now include the experimental and fitted indicator variograms in the existing Supplementary Figure S7 (improved for clarity and now cited from §2.3). On the multivariate/compositional point: we considered it and explain why it is not adopted here. The eight regulated trace metals (mg/kg) are a small sub-composition of the bulk soil and are not closed to a constant sum, so the closure artefacts that motivate compositional log-ratio analysis do not apply to them; moreover each element is assessed against its own absolute regulatory limit, and a log-ratio coordinate has no regulatory threshold. A joint indicator treatment would be full indicator cokriging, which Deutsch and Journel 1998 (§IV.1.10, Eq. IV.41) notes requires K² direct and cross indicator covariances and is “impractical for large K”, adding that for cumulative indicators “the loss from using IK instead of coIK is not as large as it appears.”

Reviewer comment 7

In Lines 194-207, the authors justify independent simulation on the grounds that indicator-level correlation between As and Cd is weak (r = 0.24) even though continuous-concentration correlation is strong (r = 0.80). The authors seem to be confused and have not applied any indicator variable approach. This is already evident from the variograms. Here, they discuss simulating the 8 metals individually. When applying the indicator variable approach, the distribution of each metal is divided into n thresholds, and a linear coregionalization model including n indicators is calculated. There is no mention of this in the manuscript. The authors should clarify this and provide specific details.

Response.  We are grateful for the chance to state the design precisely. The analysis is indicator-based throughout: SISIM (the sisim program of Deutsch and Journel 1998, single-threshold indicator mode) draws each realisation from the binary indicator ccdf at the regulatory cutoff, and we now give the indicator definition (Eq. 1) and the sisim configuration explicitly in Section 2.x. The n-threshold, linear-coregionalization construction the reviewer describes is full indicator cokriging (Deutsch and Journel 1998 Eq. IV.41), or its median-IK simplification (Deutsch and Journel 1998 Eq. IV.32–IV.34); it is required only when the full conditional cdf is reconstructed from several cutoffs, so that order relations among cutoffs must be enforced. Our estimand is a single regulatory exceedance probability per metal. With one cutoff there is only one indicator, hence a single indicator variogram (Deutsch and Journel 1998 Eq. IV.29–IV.30) and no second threshold to coregionalize – a coregionalization model is not defined for a single indicator. This single-threshold design is standard for regulatory exceedance mapping (Goovaerts 1997; Van Meirvenne and Goovaerts 2001, who map the probability of exceeding a soil-Cd threshold in exactly this way). On the r = 0.24 versus 0.80 point, the observation is intentional and correct: the co-dependence of two indicators at their respective thresholds is a different quantity from the correlation of the underlying concentrations, and its weakness is precisely what makes independent single-threshold simulation appropriate here. Because the two metals exceed at very different frequencies (As is a rare exceedance, Cd a common one), the co-dependence attainable between their threshold indicators is intrinsically limited, so a joint indicator model would add little even in principle.

Reviewer comment 8

In Figure 5 and Table 6 terminology mismatch. Indeed, Table 6 (and the text) uses the priority labels: ‘Very Low Priority / Low Priority / Moderate Priority / High Priority / Very High Priority’, while Figure 5 legend uses ‘No action needed / Routine monitoring / Enhanced monitoring / Active remediation / Immediate action’. These are mapped to the same five H(x) intervals but the language is different in important ways.

Response.  We agree and have unified the vocabulary. Both Figure 5 and Table 6 now use a single five-class “exceedance-priority” scale, with the management interpretation given once in the caption rather than as a second, competing label set.

Reviewer comment 9

In The 10-fold stratified cross-validation (Section 3.7, Table S6) validates the per-metal indicator-kriging predictions, but it does not validate the composite H(x) priority surface against any independent ground-truth. The four high-priority receptors in the east-central area are flagged as warranting confirmatory sampling; would the authors consider, as a future-work addition or as a small validation block, comparing the H(x) priority pattern against any independent indicator (e.g., a moss or lichen biomonitoring survey, a SoilGrids-derived prior, or the source-apportionment results from [5])? Even a qualitative comparison would help calibrate the reader's expectations.

Response.  We agree this is a distinct and worthwhile check. A fully independent biomonitoring survey is not available for the study period, but we have added a quantitative validation of the H(x) priority pattern against the independent anthropogenic source factor of [5] (its Factor 1: log As, log Pb, log Zn, Co). Reconstructed from the published factor loadings and mapped as Supplementary Figure S11, this factor correlates significantly with H(x) (Spearman ρ = 0.51, p < 0.001, at the 167 sample sites where Factor 1 could be reconstructed from the published loadings), confirming that the high-priority zones coincide with the documented traffic- and settlement-associated contamination sources while remaining a distinct, non-circular construct. In addition, and more directly, the reserved locations described in our response to Comment 1 – in particular those already sampled in the densely-covered central belt – constitute a prospective held-out validation set: the planned measurement campaign will provide an independent, out-of-sample test of both the per-metal exceedance maps and the composite H(x) priority surface at locations that did not condition the model, while the south-eastern second phase will extend the mapped domain to the recently affected area. The qualitative comparison against [5] is added as new Supplementary Figure S11 and a short Discussion subsection. We present it as corroborative, not confirmatory, and state clearly that H(x) is a screening surface to be confirmed by this targeted sampling.

Key references cited in this response

Deutsch, C.V., Journel, A.G., 1998. GSLIB: Geostatistical Software Library and User’s Guide, 2nd ed. Oxford University Press, New York.

Goovaerts, P., 1997. Geostatistics for Natural Resources Evaluation. Oxford University Press, New York.

Van Meirvenne, M., Goovaerts, P., 2001. Evaluating the probability of exceeding a site-specific soil cadmium contamination threshold. Geoderma 102, 75–100.

Ódor, L., Horváth, I., Fügedi, U., 1998. Magyarország geokémiai atlasza [Geochemical Atlas of Hungary]. Magyar Állami Földtani Intézet (MÁFI), Budapest.

Fügedi, U., Horváth, I., Ódor, L., 2006. Geokémiai háttér és a természetes eredetű környezeti terhelés Magyarország felszíni képződményeiben [Geochemical background and naturally occurring environmental load in Hungary's surface formations]. In: Szendrei, G. (Ed.), Magyarország környezetgeokémiai állapota [Hungary's environmental geochemical conditions]. Innova Print, Budapest, pp. 11–22.

Marth, P., Karkalik, A., 2004. A Talajvédelmi Információs és Monitoring (TIM) rendszer módszertana, működése, informatikai rendszere [The methodology, operation, and information system of the Soil Protection Information and Monitoring (TIM) system]. Manuscript, Budapest, 29 p.

Szegedi, S., 1999. Közlekedés eredetű nehézfémek Debrecen talajaiban és növényzetében, ennek talajtani összefüggései és városökológiai hatásai [Traffic-derived heavy metals in the soils and vegetation of Debrecen]. PhD dissertation, Debrecen, 138 p.

We thank the reviewer again; the clarifications above have materially improved the rigour of the methodological description.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

No more comments!

Reviewer 2 Report

Comments and Suggestions for Authors

The revised manuscript is substantially clearer than the original. All my main comments have been addressed and, particularly, methodological transparency has been substantially improved. Only in the discussion regarding the multivariate/compositional approach (Comment 6) and not in the SISIM methodology itself, some risks of misunderstanding for readers remain, but I believe this version of the manuscript is acceptable.