Nationally Consistent, Locally Incomplete: A Bayesian Remote-Sensing Audit of Rooftop Photovoltaic Registries

• A Bayesian framework uses remote sensing to audit energy registries.Source: HIGHLIGHTS · p. 1
• A closed-form rule sets annotation effort for a target precision.Source: HIGHLIGHTS · p. 1
• The corrected French estimate agrees nationally within 3.3%, while local registry coverage gaps reach 61% of local capacity.Source: HIGHLIGHTS · p. 1
• Distribution-chain fragmentation explains 45% of the core missing capacity.Source: HIGHLIGHTS · p. 1

• Keywords: photovoltaics, remote sensing, energy registries, deep learning, data quality, Bayesian calibration, and energy statistics.Source: KEYWORDS · p. 1

• Rooftop PV is difficult to track because individual owners install systems piecemeal across millions of small rooftops.Source: CONTEXT & SCALE · p. 1
• Official statistics on rooftop PV capacity and location are uneven across countries, and their completeness is generally assumed rather than tested.Source: CONTEXT & SCALE · p. 2
• In France, the corrected estimate agrees with the TSO registry within 3.3%, while registry coverage falls to 39% in some regions.Source: CONTEXT & SCALE · p. 2
• A Bayesian framework calibrates remote-sensing detections into rooftop PV capacity estimates with quantified uncertainty.Source: CONTEXT & SCALE · p. 2
• Where high-resolution imagery is available, the approach can check registries or provide a first quantified fleet estimate where no reliable registry exists.Source: CONTEXT & SCALE · p. 2

• Installed capacity is the dominant source of uncertainty in rooftop PV production estimates, ahead of meteorological and technical factors.Source: INTRODUCTION · p. 2
• Administrative registries vary in completeness, and consistency checks cannot detect installations that were never registered.Source: INTRODUCTION · p. 2
• Remote-sensing maps provide scalable PV datasets but remain error-prone, and prior evaluations treated official statistics as ground truth rather than reversing validation nationally.Source: INTRODUCTION · p. 2
• The method models remote-sensing detections as noisy estimates of ground-truth capacity using a Bayesian framework grounded in dual-system estimation, detection-probability modelling, and accuracy-adjusted area estimation.Source: INTRODUCTION · pp. 2–3
• 4.03 GWp [3.96–4.11] (99% credible interval) below 36 kWp agrees with the TSO registry within 3.3%, while local coverage falls to 39%.Source: INTRODUCTION · p. 3
• 45% of core missing capacity is explained by administrative fragmentation; privacy truncation hides over 40% of capacity in over 10% of French departments, mostly rural.Source: INTRODUCTION · p. 3
• Agreement with a mature registry at national scale supports using corrected detections as a primary capacity estimate, with quantified uncertainty, where no comparable reference exists.Source: INTRODUCTION · p. 3

Estimating ground truth rooftop PV capacity to audit registries

• The Bayesian correction reweights detected capacity by department-specific precision and recall, with validity depending on detection errors being sufficiently consistent across installation sizes.For installations at or below 36 kWp, recall shows no meaningful size dependence; a moderate precision-side deviation is carried through the audit explicitly.Source: Estimating ground truth rooftop PV… · pp. 3–4
• The audit’s scope is rooftop PV at or below 36 kWp, and French imagery and registry dates were aligned to the day for each municipality.The reporting unit is the department, with Paris and its three inner-ring departments pooled as one unit.Source: Estimating ground truth rooftop PV… · p. 4

The French case: national convergence, local blind spots

• 4.03 GWp [3.96–4.11 GWp, 99% CI] versus 3.90 GWp in the date-matched TSO registry gives national agreement within 3.3%.The corrected estimate covers rooftop PV installations at or below 36 kWp.Source: The French case: national convergence,… · p. 4
• 25 geographical units show under-reporting totaling 228.2 MWp, while 8 show over-capacity totaling 99.4 MWp; under-reported units carry more than twice the capacity.Units are flagged when registry capacity falls outside the corrected estimate’s 99% credible interval.Source: The French case: national convergence,… · p. 5
• 18 units and 172 MWp remain flagged as missing under the most conservative specification pairing, and Corse-du-Sud coverage is 39% of estimated capacity.The 18-unit hard core is a lower bound on missing capacity identified by the audit.Source: The French case: national convergence,… · p. 5
• The public registry’s privacy rule censors municipalities with fewer than ten installations, affecting 14,019 municipalities; correcting that truncation reduces flagged units from 32 to 8.All 8 remaining units fall within the TSO registry’s hard-core subset.Source: The French case: national convergence,… · p. 5

Lessons from the French case study

• Local-operator municipalities have 38% lower registry coverage after controlling for municipality size, and coverage is lower in 16 of 19 departments with both operator types represented.The unadjusted coverage difference is 42%; detected capacity itself does not differ between the groups within departments.Source: Lessons from the French case study · p. 6
• Reporting-chain fragmentation accounts for 77 of 172 MWp, or 45% of hard-core missing capacity; the remaining 95 MWp across 12 units is unexplained by tested mechanisms.Non-declaration and residual registry defects remain possibilities, not established explanations.Source: Lessons from the French case study · p. 6

Summary of the findings

• A Bayesian detection-probability framework adapts ecological abundance estimation to image-based rooftop PV detection, accounting for errors that survive downstream processing.Recall alone falls from 0.84 to 0.61 across the pipeline; corrections are direction-agnostic and require checking size-dependent detection performance.Source: Summary of the findings · p. 8
• In France, two independent instruments converge at the national scale where system operation aggregates, but registry completeness diverges sharply below that level, with local gaps principally linked to operator-reporting integration.A separate publication rule hides capacity below a reporting threshold in 14,019 municipalities without removing it from the fleet.Source: Summary of the findings · p. 8
• Local planning against the public registry can miss substantial PV capacity, while registry censoring and dating artefacts can be absorbed into reported detection-model error.The discussion notes that local under-reporting is concentrated in rural areas where hosting-capacity and voltage-management considerations are sensitive to fleet size.Source: Summary of the findings · p. 8

Limitations of the study

• Binary detection and an approximately 11 m2 detection floor leave possible solar-thermal confusion and small kilowatt installations outside the audit’s reliable scope.A shared detector-and-annotator confusion would not be visible to the label-reliability checks; any thermal contamination would inflate, not deflate, corrected capacity.Source: Limitations of the study · pp. 8–9
• OpenStreetMap-seeded recall ground truth passes a source-concordance test, but residual intra-rural selection cannot be tested.The limitation concerns the spatial representativeness of the seed data, not the reported source-concordance result.Source: Limitations of the study · p. 9
• The surface-to-capacity conversion is the audit’s largest single sensitivity, and detected PV-like material does not establish electrical connection or prove that local gaps are registry omissions.Results describe the registry and data vintage from 2022–2025, rather than a permanent characterization of operator practice.Source: Limitations of the study · p. 9

Broader applicability

• The method can be transposed to another country with new data rather than a new statistical implementation, using orthoimagery and bounded annotation effort.The estimator is released as a standalone package and accepts any reporting unit with a raw total and validation sample.Source: Broader applicability · p. 9
• The French operator-interface mechanism predicts larger effects in more fragmented operator-mediated systems, while direct owner registration offers a contrasting case to test.The passage names the United States and Germany as candidate settings for these respective comparisons.Source: Broader applicability · p. 9

Detailed audit methodology

• The correction is interpretable as true capacity only under four assumptions: homogeneous detection by capacity, exhaustive coverage, representative samples, and unbiased capacity conversion.These assumptions are H1–H4.Source: Detailed audit methodology · pp. 10–11
• Under H1–H4, Cadj = (P/R) Craw equals Ctrue at the true P and R values, and its estimator is consistent as annotation samples grow.The result requires exhaustive geographic coverage and representative sampling for consistency.Source: Detailed audit methodology · p. 11
• The audit propagates sampled precision and recall posteriors through the capacity correction, then flags registry values outside the corrected 99% credible interval after robustness checks.The pipeline filters aerial-image detections to the ≤36 kWp segment and compares date-matched registry values.Source: Figure S1. Flowchart of the audit… · p. 12

Estimation of the true rooftop PV capacity

• 0.84 model-level recall versus 0.61 pipeline recall; using model metrics would understate error by about 40%, so precision and recall are measured on final pipeline output.The pipeline metrics are measured after all filtering steps.Source: Estimation of the true rooftop PV… · pp. 12–13
• The H1 check found no meaningful size-dependence in recall, while a moderate precision deviation is retained through a capacity-weighted specification.Capacity-weighted and count-based recall were 0.649 and 0.645; corresponding precision was 0.733 and 0.766.Source: Estimation of the true rooftop PV… · p. 13
• Registry comparisons are date-matched to the day; a department is flagged only when its registry value falls outside the corrected 99% credible interval.Reported gaps are computed against the posterior mean, and the interval is deliberately wide to avoid flagging every possible discrepancy.Source: Estimation of the true rooftop PV… · p. 14

Uncertainty of the rooftop PV power estimation

• The delta-method interval narrows with more reliable detection and larger annotation samples, and its inversion budgets the minimum labels needed for a target precision.Departmental 95% interval half-widths sat at or below the prediction curve because annotation effort targeted weaker-performing locations.Source: Uncertainty of the rooftop PV power… · pp. 14–15

Collection of the precision and recall samples

• Precision sampling began with 120 detections per department and added annotations where measured precision was closest to 0.5; recall ground truth combined OSM points with manual imagery review.The final campaigns comprised 18,023 precision annotations and 13,847 deduplicated recall points.Source: Collection of the precision and recall… · p. 16
• Weighted recall was statistically indistinguishable from count-based recall (0.649 against 0.645), while weighted precision was lower (0.733 against 0.766).The authors interpret the precision difference as evidence that false positives are somewhat larger than true positives on average.Source: Collection of the precision and recall… · p. 16

Precision and recall posteriors and their uncertainty

• Empirical-Bayes priors partially pool department estimates, with prior weights of about 5% for precision and 25% for recall at the annotation floor.The prior choice did not change results, but tightened bounds where annotations were fewer.Source: Precision and recall posteriors and… · p. 18
• ±13% for departments with F1 ≥0.7 and ±21% where F1 < 0.55 are the 95% capacity-interval half-widths; the median is ±16%, and none exceeds ±25%.National precision is 0.82 and pipeline recall is 0.61.Source: Precision and recall posteriors and… · p. 18
• The achieved interval precision is wider than the ±10% initial target because budgeting used measured deployed error rates rather than test-set metrics.National pipeline recall is reported as 0.61, versus 0.96 in the initial test-set calculation.Source: Collection of the precision and recall… · p. 15, Precision and recall posteriors and… · p. 18

Capacity correction

• 0.999 correlation links the bootstrap-based capacity interval to the closed-form prediction, so the annotation-budgeting rule applies without modification.Most departments are corrected upward, consistent with pipeline recall being lower than precision.Source: Capacity correction · p. 20, Figure S5. Posterior capacity… · p. 20

Temporal alignment: implementation

• Year-level matching to archived RNI snapshots systematically includes some capacity connected after imagery acquisition, creating a level-artefact overshoot.Imagery dates are matched to the registry snapshot for the same year rather than the exact acquisition day.Source: Temporal alignment: implementation · p. 20

A recipe for applying the protocol elsewhere

• At regional rather than departmental resolution, the minimum annotation budget would fall from 19,200 to 2,600 samples, but a national unit removes spatial resolution.The required effort depends on the chosen geographic stratification.Source: A recipe for applying the protocol… · p. 21
• Coarsening produces a lower corrected capacity; its penalty is 1.3% in France at regional level, but could reach 5 to 9% if recall varied three times as much.The penalty vanishes when recall is homogeneous within the pooled unit.Source: A recipe for applying the protocol… · p. 21
• The audit corrects any detector’s output through unit-level precision and recall posteriors, the ratio P/R, bootstrap draws, and comparison with a registry or primary-estimate reporting.Its five steps cover detector use, target and sample-size choices, annotation, assumption checks, and corrected-capacity estimation.Source: A recipe for applying the protocol… · pp. 21–22
• The protocol assumes constant error rates or correction for heterogeneity, area-wide detections, representative and sufficiently broad recall sampling, and capacity factors of 5.0–6.0.Recall points should align with imagery dates and cover installations geographically and by type.Source: A recipe for applying the protocol… · pp. 21–22

Robustness checks

• Unit-level diagnoses survive alternative error aggregation and the full conversion-coefficient range, but the national aggregate’s sign depends on that coefficient.The authors therefore report a local diagnosis rather than a national correction.Source: Robustness checks · p. 22

Surface-to-capacity conversion

• 5.63 m2/kWp on medians and 5.71 m2/kWp on means are both within the 5.0–6.0 specification range, supporting the retained 5.5 m2/kWp coefficient.The comparison uses 60 reporting units selected to avoid circularity.Source: Surface-to-capacity conversion · p. 23, Figure S6. Surface-to-capacity agreement · p. 23
• 18 units are under-reported and 7 over-reported under both specifications, with no units changing sign; across 5.0–6.0 m2/kWp, 15 of 25 and 5 of 8 baseline flags persist.The two specifications’ concordance table defines the hard core as units flagged by both.Source: Specification batteries · p. 24, Table S1 · p. 25, Figure S7. Effect of the conversion… · p. 25
• −42% and −38% are the implied registry-coverage gaps without and with controls; coverage is lower in 16 of 19 paired departments (p = 0.0003).The extensive-margin estimate is directionally consistent only, and detected capacity alone does not differ between operator groups.Source: Empirical strategy of the… · pp. 27–28

TSO connection data

• The TSO connection data records rooftop PV installations, capacities, locations, and lifecycle history; after temporal alignment, the audited reference contains 853,469 installations totaling 3.90 GWp.Before alignment, it comprises 1,034,283 installations totaling 4.89 GWp.Source: Data sources · pp. 28–29

Public registry (RNI)

• The public RNI aggregates systems below 36 kWp by city and withholds capacity where a municipality has fewer than 10 systems.The study compares the registry as published with a truncation-corrected variant that reintegrates capacity aggregated at departmental level.Source: Data sources · p. 29

Aerial orthoimagery

• National aerial orthoimagery has 20 cm/pixel native resolution, with departmental acquisition dates varying across 2022–2025.Each municipality is matched to its most recent available tile and acquisition date.Source: Data sources · p. 29

Materials availability

• The study did not generate new materials.Source: Materials availability · p. 29

Data and code availability

• The detection product, replication data, original code, analysis code, and statistical audit package are publicly available or released with the paper.The study’s code is open source under an MIT license.Source: Data and code availability · pp. 29–30
• Municipality-level date matching and fixed-effects regression cannot be reproduced because the raw connection extract and municipality-level registry values are not released.The non-parametric mechanism test can be rerun from released departmental medians, reproducing 16 of 19 negative differences and p = 0.0003.Source: Data and code availability · p. 30

Declaration of generative AI and AI-assisted technologies

• Claude Cowork was used to help create source code and notebooks.Source: DECLARATION OF GENERATIVE AI AND… · p. 31
• Claude Cowork also helped adjust figure and table layout and redact the final manuscript.Source: DECLARATION OF GENERATIVE AI AND… · p. 31
• The authors reviewed and edited the content as needed and take full responsibility for the publication.Source: DECLARATION OF GENERATIVE AI AND… · p. 31

• Two authors are or were affiliated with RTE, whose registry is audited in the study.Source: DECLARATION OF INTERESTS · p. 31
• The audit design avoids dependence on privileged access or favoring RTE, and its findings include under-reporting in RTE’s own reference dataset.Source: DECLARATION OF INTERESTS · p. 31
• The other authors declare no competing interests.Source: DECLARATION OF INTERESTS · p. 31

Note S1: theoretical properties of the capacity correction

• Under H1–H4, the capacity correction converges to true capacity, but its plug-in ratio has finite-sample bias of order O(1/n_R).H1 is a sufficient condition for equal mean estimated and true capacities; H2–H3 support consistent estimates of precision and recall, while H4 requires the true-positive capacity component to be unbiased. The study therefore propagates posterior draws through a bootstrap rather than reporting a point correction.Source: Note S1: theoretical properties of the… · p. 32

Note S2: ground truth validity

• 94.0% raw agreement and κ = 0.864 indicate near-perfect precision-label reproducibility overall, but Paris labels were less reliable and were replaced after relabelling.Paris had κ = 0.435 and measured precision shifted from 0.175 to 0.275; every other sampled department had κ ≥ 0.763. Agreement between annotation passes cannot rule out errors shared by both passes. For recall, 17 of 250 reviewed false-negative points (6.8%) were invalid, and OSM-seeded versus manually annotated recall was statistically indistinguishable at fixed department (OR 0.85, p = 0.11).Source: Note S2: ground truth validity · pp. 33–34

Note S3: consistency of the estimate across aggregation scales

• Regional and national pooling lower the corrected national total by 1.31% and 1.26%, respectively, within the unit-level 95% credible interval half-width of 1.8% (Figure S8).Pooling yields a smaller correction because recall varies across units; the gap tracks within-region recall dispersion, and the finest calibrated level is weakly preferable. Under a Jeffreys prior, totals rise 1.9% while the between-level gap ranking and signs remain unchanged.Source: Note S3: consistency of the estimate… · p. 34

Note S4: statistical robustness

• 25 below- and 8 above-threshold units at baseline, versus 18 and 7 after unanimity, cannot be explained by multiplicity; the negative control remained stable at 7 units.At the two-sided 1% threshold across 93 units, fewer than one false flag is expected under the global null. Recomputing under the unpooled Jeffreys prior leaves every hard-core unit flagged.Source: Note S4: statistical robustness · p. 35

Note S5: truncation bias in the public registry

• 14,019 municipalities (40.3%) are absent from the public municipal view, censoring 363 MWp or 11.6% of detected capacity and altering local under-reporting flags (Figure S9).The censored capacity share exceeds 40% in eleven reporting units and reaches 100% in Corse-du-Sud. The truncated view flags 32 units versus 8 against departmental totals; 24 flags disappear and none are added. The surviving eight are within the independently established hard core against transmission-operator connection data.Source: Note S5: truncation bias in the public… · pp. 35–36, Figure S9 · p. 36

Note S6: imagery acquisition — coverage and vintage effect

• After controlling for local detection quality, pipeline recall shows no imagery-year effect across 2022–2025 campaigns (p = 0.54).The raw recall gradient reflects geographic composition, supporting comparison of units imaged in different years; stable recent IGN orthoimagery radiometry may help explain the absence of distribution shift.Source: Note S6: imagery acquisition —… · pp. 36–37

Connection lags

• At a realistic three-month connection window, under-reporting gaps survive in all 18 hard-core units, while over-reporting excesses exceed pre-image connected capacity in all 7 negative controls.Even assuming all post-image transit capacity was already installed, gaps survive in 12 of 18 hard-core units. Annual RNI dating raises the national reference by 10.8%, but growth does not predict which units are flagged as over-reported (r = +0.02, p = 0.84).Source: Connection lags · p. 38

Sensitivity to dating

• 16 of 18 hard-core units remain flagged at natural month-end dating, and 14–18 survive across the ±3-month sweep; all 7 negative controls remain flagged (Figure S11).National surplus varies from +8.5% to −3.1% across the sweep, so national comparisons are dating-sensitive. The per-unit dating bracket has median 11.5%, maximum 37.4%, and correlates with local registry growth at r = 0.998; the hard-core gaps therefore do not depend on biannual reporting cadence.Source: Sensitivity to dating · p. 39, Figure S11. Audit stability under… · p. 39

Note S8: the detection pipeline (DeepPVMapper)

• DeepPVMapper derives installation characteristics from detected polygons, then filters detections by building attachment and perimeter thresholds.Tilt is inferred from a geographic-cell and projected-surface-cluster look-up table; the deployed product has an effective detection floor of ≈11 m2 and an upper bound of 36 kWp.Source: Note S8: the detection pipeline… · p. 40

Note S9: statistical lineage

• Dual-system estimation compares two imperfect population counts, using their overlap and divergence to infer the unobserved total [27,28]; capture–recapture extends this logic across repeated samples [29].This motivates comparing a corrected detection product against a registry.Source: Note S9: statistical lineage · p. 42
• Occupancy modeling separates non-detection from absence by estimating detection probability alongside the quantity of interest [30,39,40].This supports treating undetected installations as correctable false negatives rather than evidence that no installation exists.Source: Note S9: statistical lineage · p. 42
• Accuracy-adjusted area estimation uses a stratified reference sample and confusion matrix to correct a mapped class’s area estimate, with uncertainty reported alongside it [31–33].The paper’s correction follows this structure, applying a validated-sample confusion matrix to a raw estimate and propagating an interval.Source: Note S9: statistical lineage · p. 42