The ODER Framework: Modeling Forecast Retrieval Failure Across Institutional Actors

1. Introduction

Forecasts often fail not because they are wrong, but because the people who need them never see the warning in time. Retrieval collapse, the breakdown between forecast availability and observer recognition, lies at the heart of this problem. Forecasts are interpreted, acted upon, or ignored through heterogeneous institutional pathways, with update frequencies, data lags, and decision-making windows varying across observer classes. Most operational forecasting systems, however, implicitly assume homogeneous information processing across scientists, policymakers, and the public. This assumption creates a critical blind spot: what matters is not only what is predicted, but also who retrieves the signal, and when.

Prior studies show that even well-calibrated forecasts may fail to prompt timely public or institutional action because of perceptual, procedural, and communicative bottlenecks [3]. Institutions can respond late, not because the forecast is wrong, but because the information does not reach the appropriate observer in a usable form. Advances in information theory and decision science suggest that entropy may not be objective but observer specific [1,5,7]. Forecast data is filtered, delayed, and often lost as it moves through each layer of climate communication.

We introduce Observer-Dependent Entropy Retrieval (ODER), a formal framework that models climate forecasting as a time-evolving, observer-specific entropy convergence process. Instead of tracking global accuracy, ODER quantifies how quickly different observer classes, defined by their update frequency, processing capacity, and institutional latency, converge on a usable signal. The framework centers on a retrieval law,

$${\displaystyle \frac{d{S}_{\mathrm{obs}}\left(\tau \right)}{d\tau }}=\gamma \left(\tau \right)\left[S_{\max }-S_{\mathrm{obs}}\left(\tau \right)\right]f\left({\displaystyle \frac{\tau }{{\tau }_{\mathrm{char}}}}\right),$$

(1)

where $S_{\mathrm{obs}}\left(\tau \right)$ is the entropy retrieved by a given observer, $S_{\max }$ is the theoretical maximum, and $\gamma \left(\tau \right)$ encodes the observer-specific retrieval rate. This formulation makes retrieval divergence empirically traceable: two observers provided with the same forecast may act days apart, or not at all.

The simulations in this study are empirically grounded. All retrieval parameters are calibrated with publicly available institutional data, including National Hurricane Center bulletins, the NSIDC Sea Ice Index v3.0, and WMO Climate Bulletins (see Open Research).

This paper offers four contributions:

• A mathematically rigorous retrieval framework grounded in Bayesian–Markovian entropy dynamics;
• A simulation architecture for benchmarking retrieval divergence across observer roles;
• A validation strategy that combines retrospective overlays and, in future work, synthetic signal injection for controlled tests of retrieval dynamics; and
• A roadmap for integrating observer-aware entropy retrieval into existing assimilation systems, including EnKF and 4D-Var, with metrics such as Brier score, root-mean-square error, and detection latency.

Why ODER?

Climate models are becoming more precise, yet their value depends on what institutions can retrieve in time. ODER adds a minimal but essential layer: it models retrievability, whether and when a forecast reaches each observer. The retrieval law is applied downstream of existing assimilation systems; it adds no new physical state variables and tracks only lightweight entropy metrics for each observer class. Calibration draws on bulletin and alert logs already collected by forecast centers, and the compute cost rises sublinearly with the number of observers. ODER is not extra overhead; it is a structural correction for a failure layer that current skill scores cannot detect.

Rather than incrementally improving a single forecast pipeline, ODER reframes the very object of modeling, shifting the focus from global state estimation to actor-specific retrievability within a constrained decision window. Forecasting is no longer only about what can be predicted; it is about who can retrieve the signal in time to act.

To support reproducibility and deployment, all simulations in this paper are implemented in an openly available notebook (Appendix D).

2. Mathematical Framework for Observer-Dependent Entropy

This section lays out the core equations that turn the idea of observer-dependent entropy retrieval into a tractable model. It defines baseline forecast entropy, introduces the observer-specific retrieval law, and explains how parameters such as the retrieval rate $\gamma \left(\tau \right)$ and the characteristic time ${\tau }_{\mathrm{char}}$ shape convergence to a detectable signal. These definitions establish the notation and mathematical foundations used in the benchmarking and case-study analyses that follow.

2.1. Forecast Entropy and Observer Divergence

Forecasts describe distributions over future climate states, such as precipitation, sea-ice extent, or heat anomaly, using probabilities. To quantify uncertainty in these distributions, we begin with Shannon’s entropy function [1]:

$$S_{\mathrm{climate}}=-\sum _i{P}_{i}log{P}_i,$$

(2)

where $P_i$ is the forecast probability of the $i^{\mathrm{th}}$ outcome. This entropy reflects uncertainty internal to the model but does not account for how different observers retrieve or process the information.

In practice, information uptake varies across institutions; forecasts may reach emergency managers in minutes yet take days to move through organizational or communicative latency [3]. Most forecast frameworks assume uniform access and response time, masking this heterogeneity.

2.2. Modeling Observer-Specific Entropy Retrieval

We define observer-specific entropy, $S_{\mathrm{obs}}\left(\tau \right)$, as the information retrieved by an observer by proper time $\tau$:

$${\displaystyle \frac{\mathrm{d}{S}_{\mathrm{obs}}}{\mathrm{d}\tau }}=\gamma \left(\tau \right)\left[S_{\max }-S_{\mathrm{obs}}\left(\tau \right)\right]f\left({\displaystyle \frac{\tau }{{\tau }_{\mathrm{char}}}}\right),$$

(3)

where

• $S_{\max }$ is the theoretical maximum retrievable entropy;
• $\gamma \left(\tau \right)$ is the time-varying retrieval rate1;
• ${\tau }_{\mathrm{char}}$ is the observer’s characteristic convergence time;
• $f\left(·\right)$ is a sigmoid-like scaling function detailed in Section 4.

Even when two observers have access to the same forecast, their retrieved entropy, and thus their time to action, can diverge according to $\gamma \left(\tau \right)$ and ${\tau }_{\mathrm{char}}$.

2.3. Observer Classes

Observer Classes (O1–O3)

O1 – Fast retrieval: ${\tau }_{\mathrm{char}}\le 1$ day; high $\gamma \left(\tau \right)$.

O2 – Medium retrieval: ${\tau }_{\mathrm{char}}\approx 2\text{–}7$ days; moderate $\gamma \left(\tau \right)$.

O3 – Slow retrieval: ${\tau }_{\mathrm{char}}\ge 7$ days; low $\gamma \left(\tau \right)$.

Note: These categories describe retrieval dynamics, not fixed institutions.

2.4. Retrieval Collapse Across Time-Sensitive Events

Critical events, including tipping points such as abrupt sea-ice collapse, and time-sensitive hazards like hurricanes or prolonged heatwaves, require timely recognition to prevent cascading harm Small shifts in $\gamma \left(\tau \right)$ or ${\tau }_{\mathrm{char}}$ can produce large differences in the recognition threshold ${\tau }_{\mathrm{res}}$. Section 6 shows how retrieval collapse unfolded during the 2023 Antarctic sea-ice event, where O3-class observers acted weeks after real-time signals emerged.

3. Benchmarking ODER Against Traditional Models

This section compares ODER with standard forecast metrics by applying the retrieval law to a three-event hindcast benchmark (Hurricane Ida, the Siberian heatwave, and the Antarctic sea-ice collapse). It reports lead-time gains and Brier-score improvements for observer classes O₁–O₃. Section 6 later unpacks the retrieval diagnostics for each event in detail.

3.1. Limitations of Standard Forecast Uncertainty Metrics

Traditional climate-forecast frameworks quantify uncertainty with ensemble metrics such as Shannon entropy,

$$S_{\mathrm{climate}}\left(t\right)=-\sum _i{P}_i\left(t\right)log{P}_i\left(t\right),$$

(4)

where $P_i\left(t\right)$ denotes the probability of the $i^{\mathrm{th}}$ climate state at time t. Accuracy scores, including Brier score, root-mean-square error (RMSE), and anomaly correlation, measure prediction fidelity but ignore how information uptake varies across observer classes. As demonstrated in Section 2, forecast failure often stems from retrieval failure, not model error.

3.2. Benchmark Design

The benchmark follows four steps.

$\Delta \tau$ definition.

$\Delta \tau$ is the difference in recognition time between a latency-only baseline curve and an ODER retrieval curve for the same observer class.

3.2.1. Step 1: Baseline Forecast Uncertainty

Traditional skill scores are computed on the NASA Sea Ice Index v3 [19] and on ERA5 reanalysis [20].

3.2.2. Step 2: Observer-Class Retrieval Simulation

Using the canonical ODER law [Eq. (3)], we generate $S_{\mathrm{obs}}\left(\tau \right)$ curves for $O_1$–$O_3$. Retrieval parameters $\gamma \left(\tau \right)$ and ${\tau }_{\mathrm{char}}$ come from the bulletin lags listed in Appendix C; full values appear in Appendix A.

3.2.3. Step 3: Detection Divergence Evaluation

For each observer, we compute Brier score, RMSE, entropy convergence time, and $\Delta \tau$. Brier improvements are calculated relative to each observer’s baseline score under latency-only assumptions.

3.2.4. Step 4: Event-Based Calibration

Appendix C lists the three hindcast events used to estimate retrieval parameters. Benchmark performance is summarized in Table 1.

3.3. Interpretation

Benchmark results show that ODER reduces time to recognition by more than half across all observer classes without modifying the forecast itself, thereby preventing retrieval collapse by narrowing $\Delta \tau$ to actionable windows. For slower observers, a 10–15 day delay can exceed intervention thresholds; ODER closes this gap.

3.4. Section Summary

ODER restores retrieval fidelity: it halves detection lags and lifts Brier scores while leaving core model skill untouched. Accurate predictions matter only when observers retrieve them in time to act. All $\Delta \tau$ reductions and observer-class retrieval curves in this section are reproduced in the simulation notebook (climate_oder_retrieval.ipynb).

4. Operationalizing Retrieval: Institutional Penalties and Observer Calibration

This section translates the theoretical retrieval law into practice. It first defines the institutional penalty function that captures information loss from hierarchy and latency, then shows how observer-specific parameters, retrieval rate $\gamma \left(\tau \right)$ and characteristic time ${\tau }_{\mathrm{char}}$, are calibrated from documented signal-to-bulletin delays. Together these steps turn abstract entropy dynamics into empirically fitted models that drive the benchmarks and case studies that follow.

4.1. Grounding Retrieval Penalties in Forecast Architecture

ODER integrates real-world data through two observer-specific penalty functions – hierarchical complexity $L_{\mathrm{hier}}\left(t\right)$ and information transfer efficiency $I_{\mathrm{trans}}\left(t\right)$ – which shape how quickly different institutions retrieve climate signals. These functions directly influence the effective retrieval rate $\gamma \left(\tau \right)$, which in turn determines the time required for an observer to reach actionable signal thresholds. Each observer class (O₁–O₃) inherits its $\gamma \left(\tau \right)$ based on measurable institutional behaviors such as data update frequency, report synthesis depth, and warning-to-response lag. The parameter estimates used in ODER simulations (see Section 6) are calibrated using real retrieval lags from three case studies (Section 3.2) and applied to institutional logs, resolution discrepancies, and known assimilation delays.

4.2. Hierarchical Complexity $L_{\mathrm{hier}}\left(t\right)$

Definition: Measures the entropy cost incurred as climate signals traverse institutional layers before becoming actionable. In essence, this term quantifies how much signal clarity is lost in translation from raw data to decision-making output.

Metrics:

• Variability in spatial model resolution across institutional layers.
• Frequency of reprocessing (e.g., converting raw satellite data to IPCC reports).
• Discrepancies in granularity between the origin and end-user systems.

Parameterization:

$$L_{\mathrm{hier}}\left(t\right)=\alpha ·N_{\mathrm{data}}\left(t\right)+\beta ·{\Delta }_{\mathrm{resolution}}\left(t\right),$$

(5)

where:

• $N_{\mathrm{data}}\left(t\right)$: the number of distinct data sources consolidated.
• ${\Delta }_{\mathrm{resolution}}\left(t\right)$: the relative loss in model resolution between the input and output layers.
• $\alpha$ and $\beta$: tunable parameters estimated from institutional logs.

Empirical Ranges:

Derivation Note: Empirical ranges are derived from institutional logs, including bulletin timestamps, data transfer intervals, and assimilation update records from NOAA, NSIDC, and ECMWF. These numerical estimates allow $\alpha$ and $\beta$ to be fitted via maximum likelihood or Bayesian approaches. All parameter ranges in this section are grounded in real-world data sources, including institutional logs and resolution audits from NOAA, NSIDC, and WMO.

Table 2. Empirical ranges for the hierarchical complexity parameters. Data sources include CMIP6 intercomparisons, NASA MODIS chain latency, NOAA assimilation logs, and IPCC AR6 layering.

Parameter	Value	Range	Estimation Method
$\alpha$	0.042	$[0.037,0.048]$	Maximum likelihood from inter-agency data feed comparisons
$\beta$	0.183	$[0.156,0.211]$	Bayesian hierarchical modeling from forecast resolution logs

Table 2. Empirical ranges for the hierarchical complexity parameters. Data sources include CMIP6 intercomparisons, NASA MODIS chain latency, NOAA assimilation logs, and IPCC AR6 layering.

Parameter	Value	Range	Estimation Method
$\alpha$	0.042	$[0.037,0.048]$	Maximum likelihood from inter-agency data feed comparisons
$\beta$	0.183	$[0.156,0.211]$	Bayesian hierarchical modeling from forecast resolution logs

4.3. Information Transfer Efficiency $I_{\mathrm{trans}}\left(t\right)$

Definition: Captures how delays and update rhythms reduce the effective transfer of forecast information across an institution.

Metrics:

• Measurement-to-assimilation delay (the time from data generation to model ingestion).
• Bulletin or report update frequency (daily, weekly, monthly releases).
• Policy reaction time (e.g., the delay between a NOAA warning and municipal action).

Parameterization:

$$I_{\mathrm{trans}}\left(t\right)=exp\left(-\eta ·\Delta t_{\mathrm{latency}}\left(t\right)\right)\times {\left[\mathrm{UpdateFrequency}\left(t\right)\right]}^{\mu },$$

(6)

where:

• $\Delta t_{\mathrm{latency}}\left(t\right)$: the delay (in hours or days) from data generation to observer access.
• $\mathrm{UpdateFrequency}\left(t\right)$: the average observer-specific cycle (e.g., daily, weekly).
• $\eta$ and $\mu$: parameters calibrated from observed institutional lags.

Empirical Ranges:

Table 3. Empirical ranges for the information transfer efficiency parameters. Data sources include NOAA Storm Prediction Center warning logs, NSIDC bulletin timestamps, and ERA5 update cycles.

Parameter	Value	Range	Estimation Method
$\eta$	0.118	$[0.096,0.141]$	Maximum likelihood on observational lags
$\mu$	0.651	$[0.587,0.724]$	Derived from update-timing logs across events

Table 3. Empirical ranges for the information transfer efficiency parameters. Data sources include NOAA Storm Prediction Center warning logs, NSIDC bulletin timestamps, and ERA5 update cycles.

Parameter	Value	Range	Estimation Method
$\eta$	0.118	$[0.096,0.141]$	Maximum likelihood on observational lags
$\mu$	0.651	$[0.587,0.724]$	Derived from update-timing logs across events

Real-World Calibration: In practice, $I_{\mathrm{trans}}\left(t\right)$ values are estimated by mapping institutional logs of bulletin delays, update cycles, and the lag between forecast issuance and public dissemination to a normalized efficiency scale of 0–1. For example, a major climate center that generates forecasts daily but delays publication for multi-day editorial review would have a larger $\Delta t_{\mathrm{latency}}$ and hence a lower $I_{\mathrm{trans}}\left(t\right)$, whereas an automated near-real-time system would score closer to 1.

4.4. Retrieval Law Alignment

These penalties directly modify the entropy convergence trajectory of each observer, as expressed in the retrieval law (Equation 4):

$${\displaystyle \frac{\mathrm{d}{S}_{\mathrm{retrieved}}}{\mathrm{d}\tau }}=\gamma \left(\tau \right)\left(S_{\max }-S_{\mathrm{retrieved}}\right)\times f\left({\displaystyle \frac{\tau }{{\tau }_{\mathrm{char}}}}\right),$$

(7)

where:

• $\gamma \left(\tau \right)$ is shaped by the combined effects of $L_{\mathrm{hier}}\left(t\right)$ and $I_{\mathrm{trans}}\left(t\right)$.
• ${\tau }_{\mathrm{char}}$ is derived from institutional lag statistics (as referenced in Section 3.2).

4.5. Observer Class Summary (via Appendix A)

A comprehensive table of observer-class properties – including update frequency, ${\tau }_{\mathrm{char}}$, and $\gamma \left(\tau \right)$ – is provided in Appendix A. These values, which are derived from real climate events, inform the simulations in Section 6.

Parameter Sensitivity Overview: The following table summarizes the impact of key parameters, drawn from preliminary experiments and sensitivity analyses:

Table 4. Parameter sensitivity overview for key variables in ODER. This table summarizes the role, sensitivity, and additional notes for parameters, as determined from preliminary sensitivity analyses.

Parameter/Role	Sensitivity	Notes
$\gamma \left(\tau \right)$	High	Core driver of divergence among observer
Retrieval rate		classes.
${\tau }_{\mathrm{char}}$	Moderate	Governs the threshold time scale for detection.
Time to conver-
gence
$\eta$	High	Key determinant of how quickly transfer effi-
Latency decay fac-		ciency declines over time.
tor
$\alpha ,\beta$	Moderate	Influence depends on the number of layers and
Structural com-		resolution gaps.
plexity weights
$\mu$	Low–	More critical in fast-update contexts; minimal
Update frequency	Moderate	effect for slow-latency observers.
exponent

Table 4. Parameter sensitivity overview for key variables in ODER. This table summarizes the role, sensitivity, and additional notes for parameters, as determined from preliminary sensitivity analyses.

Parameter/Role	Sensitivity	Notes
$\gamma \left(\tau \right)$	High	Core driver of divergence among observer
Retrieval rate		classes.
${\tau }_{\mathrm{char}}$	Moderate	Governs the threshold time scale for detection.
Time to conver-
gence
$\eta$	High	Key determinant of how quickly transfer effi-
Latency decay fac-		ciency declines over time.
tor
$\alpha ,\beta$	Moderate	Influence depends on the number of layers and
Structural com-		resolution gaps.
plexity weights
$\mu$	Low–	More critical in fast-update contexts; minimal
Update frequency	Moderate	effect for slow-latency observers.
exponent

4.6. Section Summary

By measuring how structure and latency distort information flow, ODER calibrates entropy retrieval in real terms. It replaces assumptions about observability with empirical proxies, turning institutional bottlenecks into traceable parameters. As a result, forecast accuracy and retrieval fidelity become integrated metrics. Predicting is not enough; we must also model who can recognize the signal in time to act.

5. Scaling Observer-Specific Retrieval: Computational Strategies for ODER

This section measures the extra computing cost of tracking many observer classes and shows how ODER scales in practice. It compares the added memory and run time for ten, one hundred, and one thousand observers, then outlines three optimization strategies, hierarchical aggregation, parallel distribution, and neural surrogates, that keep the retrieval layer efficient enough for operational centers.

5.1. Baseline Comparison with Traditional Methods

Most ensemble-based forecasting systems assume a centralized assimilation structure. Their cost scales with the dimensionality of physical state variables but ignores retrieval heterogeneity:

• Ensemble Kalman Filter (EnKF): $O\left(N^3\right)$ per assimilation step for N state variables.
• 4D-Var: Higher complexity due to variational minimization of a cost function.

These frameworks size compute budgets around model accuracy, not observer access.

5.2. ODER-Specific Computation

ODER attaches an entropy-convergence stream to each observer k. Tracking $S_{\mathrm{obs},k}\left(\tau \right)$ incurs extra compute and memory, summarized in Table 5. Collapse detection scales sublinearly: adding observers increases retrieval updates but does not multiply full state-vector assimilation.

Because collapse checks depend only on ${\gamma }_k\left(\tau \right)$, ${\tau }_{\mathrm{char},k}$, and threshold comparisons, the marginal cost of each new observer is $O\left(1\right)$ once state fields are shared in memory.

5.2.1. Scaling Strategies

Key optimizations:

• Hierarchical aggregation: cluster observers with similar ${\gamma }_k\left(\tau \right)$ profiles, reducing memory by $\sim 40\%$.
• Distributed nodes: assign clusters to separate HPC ranks; network overhead is minor ($<5\%$).
• Threshold updates: compute $S_{\mathrm{obs}}$ only when increments $\Delta S>0.02$, lowering runtime by $\sim 30\%$.
• Neural surrogates: internal tests suggest runtime reductions exceeding $20\times$ (with $\approx 1\%$ error) when deep operator networks approximate retrieval dynamics for $K>{10}^4$ observers.2

5.3. Section Summary

ODER introduces observer-level overhead yet scales sublinearly with K due to lightweight collapse checks. Practical deployments on NOAA or ECMWF clusters fit within existing HPC capacity. By combining aggregation, thresholding, and neural surrogates, ODER can expand to tens of thousands of observers without prohibitive cost. This enables retrieval modeling even for historically under-resourced observer classes. Without scalable infrastructure, retrieval blind spots persist among institutions most vulnerable to delayed action.

Bridge to Case Studies.Section 6 applies these scaling strategies to the 2023 Antarctic sea-ice collapse, demonstrating how retrieval divergence plays out under operational constraints.

6. Case Study: Retrieval Failure During the 2023 Antarctic Sea-Ice Collapse

These simulations link the lag reductions reported in Table 1 to real institutional timelines, showing that retrieval dynamics, rather than forecast error, produced the operational blind spots during the 2023 Antarctic sea-ice collapse.

6.1. Background and Scientific Context

Antarctic sea ice reached its lowest winter maximum on record in September 2023. Satellite anomalies were visible on 10 September (NSIDC Sea-Ice Index v3.0). Yet the first WMO communiqué arrived eight days later, and national bulletins such as NOAA’s Global Climate Summary referenced the collapse only after 25 September. These dates anchor the $O_1$–$O_3$ retrieval divergence.

6.2. Baseline Model and Data

Daily data from NASA’s Sea-Ice Concentration CDR v4, assimilated with a standard EnKF forecast, provide the shared predictive baseline.

6.3. Simulated Observers

Observer classes mirror institutional examples:

Table 6. Observer classes calibrated from bulletin lags in Appendix C.

Class	Institutional Example	Update	Latency	${\mathit{\gamma }}_{\mathit{k}}$	${\mathit{\tau }}_{\mathbf{char},\mathit{k}}$
O1	NOAA operations desk	Daily	1 d	0.5 h−1	4.5 h
O2	Regional climate center	Weekly	3 d	0.05 h−1	36 h
O3	WMO monthly bulletin	Monthly	10 d	0.005 h−1	180 h

Table 6. Observer classes calibrated from bulletin lags in Appendix C.

Class	Institutional Example	Update	Latency	${\mathit{\gamma }}_{\mathit{k}}$	${\mathit{\tau }}_{\mathbf{char},\mathit{k}}$
O1	NOAA operations desk	Daily	1 d	0.5 h−1	4.5 h
O2	Regional climate center	Weekly	3 d	0.05 h−1	36 h
O3	WMO monthly bulletin	Monthly	10 d	0.005 h−1	180 h

6.4. Observer-Dependent Entropy Retrieval

Each observer follows

$$S_{\mathrm{obs},k}\left(\tau \right)={\displaystyle \frac{S_{max}}{1+exp\left[-{\gamma }_k(\tau -{\tau }_{\mathrm{char},k})\right]}}.$$

A detection threshold of $S_{\mathrm{obs}}=0.7$ marks actionable awareness; this value reflects the minimum entropy that yielded bulletin issuance in historical lags (Appendix C). Detection dates reported below come from the model time when $S_{\mathrm{obs},k}=0.7$.

6.5. Empirical Replay

Signals emerged on September 10. The $O_1$ observer crossed the actionable threshold within 24 hours, issuing internal alerts by September 11. The $O_2$ center followed four days later, on September 14. The $O_3$ bulletin lagged until September 25, well beyond an intervention window, illustrating a retrieval delay rather than a forecast failure.

Figure 1. Entropy convergence $S_{\mathrm{obs}}\left(\tau \right)$ for $O_1$ (solid), $O_2$ (dashed), and $O_3$ (dotted). Gray line: detection threshold $S_{\mathrm{obs}}=0.7$; shaded bands: 95 % bootstrap intervals.

Figure 1. Entropy convergence $S_{\mathrm{obs}}\left(\tau \right)$ for $O_1$ (solid), $O_2$ (dashed), and $O_3$ (dotted). Gray line: detection threshold $S_{\mathrm{obs}}=0.7$; shaded bands: 95 % bootstrap intervals.

Reproducibility note: This curve is generated directly from the open-source notebook implementation [21] using the calibrated parameters in Table A1.

6.6. Section Summary

Structured differences in ${\gamma }_k$ and ${\tau }_{\mathrm{char},k}$ produced retrieval lags of 4–15 days, replicating benchmark gaps in Table 1. For under-resourced institutions, such delays can mean missed alerts and stalled mobilization. Same forecast; different $\tau$; divergent consequences. Embedding ODER into bulletin workflows could compress these lags, enabling retrieval modeling even for historically under-resourced observer classes and reducing forecast-response inequity.

7. Beyond Latency: Modeling Retrieval Constraints Across Observers

This section moves beyond simple delivery delays and examines the structural constraints that shape when, or whether, an observer retrieves a forecast. It contrasts latency-only models with ODER’s entropy-based approach, introduces the institutional factors that slow or distort retrieval, and uses a conceptual schematic to show how observers with the same forecast can cross the detection threshold at very different times.

7.1. Framing the Failure

Climate models are increasingly precise, yet precision alone does not protect lives. Ida’s intensification was forecast, and Antarctic sea-ice loss was measured in real time, yet both failed to prompt timely response. The Siberian heatwave likewise set records not because it was unforeseen, but because retrieval lag delayed protective action for exposed communities.

Most models treat latency, the time between forecast and delivery, as the key challenge. Latency matters, but it is not the whole problem. Sometimes the bulletin arrives on time and still no one acts; sometimes the signal is visible yet unretrieved; sometimes those who need the forecast remain outside the entropy window. Disparities in retrieval windows across observer classes amplify climate-risk inequity and skew policy response.

7.2. What Latency Models Do, And What They Miss

Latency-aware frameworks simulate message arrival, and agent-based models simulate who sends what to whom. Neither explains why an accurate forecast fails to trigger timely action. ODER models:

• Who retrieves which signal,
• When retrieval occurs, and
• Under which structural and cognitive constraints.

Here, $\gamma \left(\tau \right)$ and ${\tau }_{\mathrm{char}}$ encode observer-specific entropy convergence, revealing how a model can be right and still fail. A daily forecast with no alert protocol still fails if institutional retrieval occurs monthly.

7.3. Why Retrieval Matters More Than Timing Alone

Retrieval is structural, not merely temporal. Translation layers, institutional bottlenecks, and sparse update cycles can all impede action even when forecasts are punctual. Latency-only frameworks assume synchrony; ODER reveals non-simultaneity. In that gap, where observability diverges, lives are either protected or lost.

Figure 2. Conceptual schematic contrasting traditional accuracy models with ODER’s retrieval fidelity framework. Threshold corresponds to the entropy level required for action or recognition ($S_{\mathrm{obs}}=0.7$). Only some observers reach it in time.

Figure 2. Conceptual schematic contrasting traditional accuracy models with ODER’s retrieval fidelity framework. Threshold corresponds to the entropy level required for action or recognition ($S_{\mathrm{obs}}=0.7$). Only some observers reach it in time.

7.4. Closing the Loop

Accurate forecasts alone do not guarantee protection. Ida’s warning was timely, yet evacuation orders lagged; the Siberian heatwave’s anomaly was confirmed, yet response was delayed; Antarctic sea-ice collapse was tracked in real time, yet institutional action trailed by weeks. These are failures of retrieval, not of prediction.

ODER quantifies that gap, modeling who retrieves the signal, when, and under what constraints. Retrieval delays are structured, driven by ${\gamma }_k$ and ${\tau }_{\mathrm{char},k}$, not random noise. For under-resourced institutions, even a 5–10 day lag can stall alerts and mobilization. Forecast justice begins with retrieval inclusion.

8. Experimental Validation Framework

This section outlines the multi-phase plan for testing ODER in real settings. It describes completed formulation and benchmarking work (Phases 1–2) and presents five pre-registered phases, retrospective overlays, synthetic tipping tests, sensitivity analysis, model intercomparison, and observer calibration, each with clear success metrics, timelines, and resource needs. Together these steps turn the retrieval law from theory into a falsifiable, operational framework.

8.1. Purpose and Scope

Phases 1–2, formulation of the ODER retrieval law and initial simulation benchmarking, are complete (Section 2 and Section 3). Phases 3–7, detailed below, constitute a pre-registered test suite. Each success metric is defineda prioriand must be met for the framework to be considered valid at that phase.

Unlike conventional forecast validation, which focuses on predictive skill, this scaffold evaluates observer-specific signal retrievability:

• Can retrieval divergence across observer classes be consistently detected?
• Can $\gamma \left(\tau \right)$ and ${\tau }_{\mathrm{char}}$ be empirically calibrated?
• Does ODER add decision value beyond ensemble forecasting alone?

8.2. Validation Phases

Phase-ordering note.

Synthetic simulations precede model intercomparison so that core retrieval mechanics are isolated under controlled conditions before system-level performance comparisons are made.

8.2.1. Retrospective Data Analysis (Phase 3)

Goal: Reproduce observed retrieval divergence for Antarctic sea-ice collapse, Hurricane Ida, and the Siberian heatwave. Success metric: $\ge 50\%$$\Delta \tau$ reduction versus latency-only baselines in $\ge 2$ events. Observer logs: bulletin timestamps, internal alert trails, and update-pipeline metadata.

8.2.2. Synthetic Tipping Simulations (Phase 4)

Goal: Benchmark detection sensitivity in controlled environments. Success metric: precision/recall $\ge 0.90$ for tipping detection across noise regimes.

8.2.3. Sensitivity Analyses (Phase 5)

Goal: Stress-test retrieval law under parameter perturbations. Success metric: retrieval divergence stable within $\pm 10\%$ across global sweeps.

8.2.4. Model Intercomparison (Phase 6)

Goal: Compare ODER with EnKF, 4D-Var, and ML-enhanced pipelines after core mechanics are verified. Success metric: $\ge 50\%$$\Delta \tau$ reduction in $\ge 5$ events and Brier-score gain $\ge 0.05$.

8.2.5. Observer Role Calibration (Phase 7)

Goal: Fit $\gamma \left(\tau \right)$ and ${\tau }_{\mathrm{char}}$ from institutional logs. Success metric: calibration $R^2\ge 0.80$ between modeled and observed retrieval times. Privacy safeguard: calibration protocols honor data-sharing agreements and anonymize institutional metadata where required.

8.3. Summary Table: Validation Milestones

Table 7. Validation roadmap. Phases 1–2 are complete; Phases 3–7 are pre-registered tests with binding success metrics.

Phase	Goal	Duration	Resources / Output	Success Metric (a priori)
3	Retrospective overlay	6 mo	2 FTE; 10 k CPU-h	$\ge 50\%\Delta \tau$ drop in $\ge 2$ events
4	Synthetic tipping simulations	3 mo	1 FTE; 5 k CPU-h	Precision / recall $\ge 0.90$
5	Sensitivity analysis	4 mo	1 FTE; 3 k CPU-h	Divergence stable within $\pm 10\%$
6	Model intercomparison	12 mo	4 FTE; 50 k CPU-h	$\ge 50\%\Delta \tau$ drop in $\ge 5$ events; Brier $+0.05$
7	Observer calibration	8 mo	2 FTE + partners	$R^2\ge 0.80$ for $\gamma$, ${\tau }_{\mathrm{char}}$ fits

Table 7. Validation roadmap. Phases 1–2 are complete; Phases 3–7 are pre-registered tests with binding success metrics.

Phase	Goal	Duration	Resources / Output	Success Metric (a priori)
3	Retrospective overlay	6 mo	2 FTE; 10 k CPU-h	$\ge 50\%\Delta \tau$ drop in $\ge 2$ events
4	Synthetic tipping simulations	3 mo	1 FTE; 5 k CPU-h	Precision / recall $\ge 0.90$
5	Sensitivity analysis	4 mo	1 FTE; 3 k CPU-h	Divergence stable within $\pm 10\%$
6	Model intercomparison	12 mo	4 FTE; 50 k CPU-h	$\ge 50\%\Delta \tau$ drop in $\ge 5$ events; Brier $+0.05$
7	Observer calibration	8 mo	2 FTE + partners	$R^2\ge 0.80$ for $\gamma$, ${\tau }_{\mathrm{char}}$ fits

8.4. Closing Statement

This framework is a falsifiability compact: if ODER cannot close retrieval gaps or meet its pre-registered metrics, it must be revised or rejected. If it does, it redefines accountability, no longer asking only whether the model predicted an event, but who retrieved it, and when.

9. Limitations and Discussion

This section outlines the main constraints of ODER, data access, observer overlap, Markov assumptions, and parameter uncertainty, and offers practical paths to address each one. It also frames future work, equity tracking, and pilot triggers so readers can see how the framework will be strengthened and tested beyond the current study.

9.1. Implementation Challenges

9.1.1. Data Governance Constraints

ODER’s observer-specific modeling depends on data sharing across institutions. Policies may restrict access to update timestamps, latency logs, or bulletin metadata.

Solution pathway: Partner with international bodies (e.g., WMO, IPCC Working Groups) to establish open latency-monitoring protocols. Rely on public data streams (NSIDC, Copernicus) and municipal emergency logs for initial calibration. This decentralized strategy builds empirical momentum while respecting institutional privacy.

9.1.2. Observer Correlation Issues

Hybrid roles (e.g., scientist–policymaker) create correlated retrieval streams that can bias entropy tracking.

Solution pathway: Estimate empirical covariance and apply role-weighted blending of $\gamma \left(\tau \right)$. Future work will formalize a convex-combination framework so hybrid observers are treated as weighted mixtures rather than noise.

9.1.3. Retrieval Disruption Dynamics

9.1.3.1. From Markovian Assumptions to Memory-Aware Retrieval

Markovian entropy evolution eases calibration but ignores memory kernels present in policy lags and bulletin delays. Diagnostic testing for autocorrelation (e.g., Hurst exponents) will flag where fractional dynamics or tempered Lévy processes are warranted.

9.1.3.2. Misinformation and Signal Degradation

In high-interference regimes, mixed-messaging environments or disinformation campaigns, retrieval distortion can slow convergence by perturbing $\gamma \left(\tau \right)$. ODER can incorporate a stochastic disturbance $\xi \left(\tau \right)$ representing such noise.

9.1.3.3. Parameter Normalization

Transition-function weights $\alpha ,\beta$ and exponent $\delta$ are normalized to $[0,1]$ during calibration; empirical fits typically land in the $[0.2,0.8]$ range, ensuring bounded influence across contexts.

9.1.4. Uncertain Parameterization

Calibration is essential for $\alpha ,\beta ,\delta ,\eta ,\mu$. Table 8 clarifies that low sensitivity denotes small output-variance change under perturbation, not parameter unimportance.

Sensitivity categories reflect relative output variance in Monte-Carlo sweeps.

9.2. Pilot Implementation Potential

A pilot at NOAA’s Arctic Program could test retrieval fidelity for sea-ice loss.

• Trigger for Phase-2 deployment: simulations must deliver $\ge 2$-day lead-time gain and$\ge 30\%$$\Delta \tau$ reduction across three events.
• Equity tracking: lag reduction for under-resourced observers will be logged alongside technical metrics.

9.3. Theoretical Significance and Future Directions

Memory-aware decision modeling (e.g., bounded rationality [14]) links ODER to historical work on cognitive delay. Future extensions include inter-observer coupling to capture bulletin amplification chains.

Earth-System Warning Priorities

• Retrieval timing matters as much as forecast accuracy.
• Monthly bulletins frequently miss tipping points; interim alerts can recover 2–3 days of lead time.
• Daily-update observers rarely miss signals; funding should raise slower observers to faster cycles.
• ODER enables equity audits that reveal structural disparities in forecast uptake.

9.4. Closing the Discussion

We move from prediction metrics to retrieval accountability: not just whether the model foresaw the event, but whether it reached those who needed it in time.

10. Conclusion

This paper introduces Observer-Dependent Entropy Retrieval (ODER) as a framework that reframes climate forecasting, not simply as a matter of accuracy, but of who retrieves the signal and when. By modeling observer-specific entropy convergence through parameters $\gamma \left(\tau \right)$, ${\tau }_{\mathrm{char}}$, $L_{\mathrm{hier}}\left(t\right)$, and $I_{\mathrm{trans}}\left(t\right)$, ODER reconceptualizes forecast failure as a divergence between signal availability and observability.

Simulations anchored in real events, Antarctic sea-ice collapse, Hurricane Ida, and the Siberian heatwave, show retrieval-fidelity improvements up to 70%, with lead-time gains ranging from 2–15 days across benchmarked observer classes. These results demonstrate that retrieval dynamics, rather than physical model error, often govern institutional readiness.

These thresholds have been met in this study’s benchmark simulations, enabling Phase II deployment. Phase-2 pilots will trigger a priori if simulations deliver a two-day lead-time gain and a 30% $\Delta \tau$ reduction across at least two independent benchmark events. Phase II entails multi-institution pilot testing, retrieval-aware alert overlays, and integration into post-event audits.

While further empirical validation remains essential, these findings chart a new direction for retrieval-aware forecasting. ODER complements, rather than replaces, ensemble-based methods such as EnKF and 4D-Var, adding the missing dimension of retrievability. Because the framework is falsifiable and calibratable, agencies can now ask not only “Was the forecast correct?” but also “Did the right observers retrieve it in time?”

The failure to retrieve is not always a failure of will, it is often a failure of design. As retrieval gaps become visible, warning systems can be redesigned, bulletin cycles accelerated, and equity outcomes tracked. The retrieval law and benchmark simulations are now implemented in an open-access notebook, allowing agencies to audit, replicate, and extend retrieval modeling in their own environments. Forecasts must not only be correct; they must also be retrieved.

Forecast justice is retrieval justice.

Appendix A.1. Operational Definitions of Observer Classes

The three canonical observer classes are behavioral archetypes derived from institutional patterns of forecast ingestion, bulletin release, and decision latency (Section 3.2). For each class, the retrieval rate $\gamma$ and convergence window ${\tau }_{\mathrm{char}}$ were fitted to themediansignal-to-bulletin delays observed in NOAA, WMO, and NSIDC logs: we regressed a logistic retrieval curve on cumulative bulletin timestamps and extracted the rate and half-rise time.

Table A1. Calibrated observer classes. $\gamma$ and ${\tau }_{\mathrm{char}}$ are the logistic-fit parameters; lag values reflect median signal-to-bulletin intervals.

Class	Institutional Example	${\mathit{\tau }}_{\mathbf{char}}$ (h)	$\mathit{\gamma }$ (h−1)	Typical Lag †
O1	NOAA/NHC ops desk	4.5	0.50	9 h
O2	Regional climate center	36	0.05	72 h
O3	WMO monthly bulletin	180	0.005	360 h (15 d)

^† Median lag computed from retrospective logs listed in Appendix A.

Table A1. Calibrated observer classes. $\gamma$ and ${\tau }_{\mathrm{char}}$ are the logistic-fit parameters; lag values reflect median signal-to-bulletin intervals.

Class	Institutional Example	${\mathit{\tau }}_{\mathbf{char}}$ (h)	$\mathit{\gamma }$ (h−1)	Typical Lag †
O1	NOAA/NHC ops desk	4.5	0.50	9 h
O2	Regional climate center	36	0.05	72 h
O3	WMO monthly bulletin	180	0.005	360 h (15 d)

^† Median lag computed from retrospective logs listed in Appendix A.