Information and Climate Feedback

• ICF is a framework of closed-loop processes linking informational states with climate dynamics across observational, social, and digital contexts.
• It encompasses diverse models including carbon-cycle, radiative, social, and digitalization approaches that shape both climate diagnostics and human behavior.
• ICF employs integrated methods such as Bayesian inversion, CNN-based radiative assessments, and information-theoretic metrics to reduce uncertainties and guide climate action.

Information and Climate Feedback (ICF) denotes a family of formulations in which information—measured, inferred, communicated, or operationalized—enters a feedback loop with climate variables, climate diagnostics, or climate-relevant human behavior. In the cited literature, the term is used for at least six distinct but overlapping constructs: an observing-system loop for constraining carbon–climate feedbacks; near–real-time monitoring of the global radiative feedback parameter $\lambda$ from surface-temperature patterns; a knowledge-base-driven climate-communication loop; information-theoretic detection of couplings among climate variables; coupled social–climate models in which perceptions, norms, or extreme events alter mitigation behavior; and a proposed digitalization–energy–heat–climate loop for information and communication technologies [(Schimel et al., 2016); (Loon et al., 12 Mar 2026); (Rodrigues et al., 2021); (Knuth et al., 2013); (Punnavajhala et al., 14 Sep 2025); (Wyse et al., 29 Oct 2025); (Knar, 8 Jul 2025)].

1. Terminological scope and core forms

The literature does not present a single canonical ICF formalism. Instead, it applies the term to several architectures in which an informational state modifies either climate diagnosis, social response, or physical forcing, and the resulting climatic change then alters subsequent information or decision states.

Formulation	Information component	Feedback target
Carbon observing system	XCO$_2$, XCH$_4$, XCO, SIF, in situ, ocean $p\mathrm{CO}_2$	$\beta_L,\beta_O,\gamma_L,\gamma_O$ and climate projections
Radiative monitoring	Spatial structure of $T(x,y,t)$ interpreted by a CNN and SHAP	Time-varying $\lambda(t)$
ClimateKB	Cause–effect facts and value associations	Tailored messaging, user action, profile/KB update
Information theory	Mutual information and transfer entropy	Statistical and directional climate-variable relationships
Regional social–climate model	Perceived climate-impact cost and social norms	Mitigation support $x_i(t)$ and emissions
Committed-minority model	Extreme-event information stored in decaying memory	Effective committed minority $C_m(t)$ and emissions
Digitalization model	Digital load, greenness, thermal footprint	Climate response and ICT vulnerability

A common architecture appears across these formulations. Information is first harvested or encoded, then transformed through an inference, assimilation, or behavioral module, and finally coupled back to either emissions, feedback parameters, or climate state variables. This suggests that ICF is best understood as a family of closed loops linking informational structure to climate dynamics rather than as a single discipline-specific theory.

2. Earth-system observation, inversion, and radiative diagnosis

In carbon-cycle applications, ICF is formulated around the global carbon budget and the problem of constraining carbon–climate feedbacks from observations. The atmospheric carbon reservoir $C_{atm}$ satisfies

$_2$0

Here $_2$1 is fossil-fuel plus cement CO$_2$2 emissions, given as $_2$3 in 2014; $_2$4 is gross carbon release from land use change, $_2$5; $_2$6 is net terrestrial uptake, $_2$7; and $_2$8 is net ocean uptake, also $_2$9. On average, $_4$0, so about half of anthropogenic CO$_4$1 remains in the atmosphere, driving the observed $_4$2 increase in CO$_4$3 (Schimel et al., 2016).

The standard linear feedback parameters are

$_4$4

$_4$5

with first-order perturbation relations

$_4$6

When normalized to unit warming, the aggregate feedback factor is written as

$_4$7

The observational problem is difficult because fossil CO$_4$8 emissions have an uncertainty of $_4$9 globally but $p\mathrm{CO}_2$0–$p\mathrm{CO}_2$1 in rapidly developing nations; land-use change fluxes are uncertain by $p\mathrm{CO}_2$2 at regional scales; gross primary production and respiration are each uncertain by $p\mathrm{CO}_2$3–$p\mathrm{CO}_2$4; wetland CH$p\mathrm{CO}_2$5 emissions and fossil-fuel CH$p\mathrm{CO}_2$6 leaks are poorly known; and atmospheric transport errors lead to $p\mathrm{CO}_2$7 uncertainty in inverse-modeled fluxes. Divergent Earth System Models yield a $p\mathrm{CO}_2$8–$p\mathrm{CO}_2$9 spread in future airborne fraction and therefore in predicted atmospheric CO$\beta_L,\beta_O,\gamma_L,\gamma_O$0 trajectories (Schimel et al., 2016).

The proposed solution is an integrated observing system. Satellite spectrometers measure XCO$\beta_L,\beta_O,\gamma_L,\gamma_O$1, XCH$\beta_L,\beta_O,\gamma_L,\gamma_O$2, XCO, and SIF; in situ networks provide continuous surface flask or sample measurements for CO$\beta_L,\beta_O,\gamma_L,\gamma_O$3, CH$\beta_L,\beta_O,\gamma_L,\gamma_O$4, and CO; eddy covariance towers measure Net Ecosystem Exchange at $\beta_L,\beta_O,\gamma_L,\gamma_O$5 scale; ocean $\beta_L,\beta_O,\gamma_L,\gamma_O$6 is measured by ships, moorings, and emerging Biogeochemical ARGO floats; and biomass and structure are mapped from spaceborne LIDAR and SAR. Required scales are approximately $\beta_L,\beta_O,\gamma_L,\gamma_O$7 monthly for continental fluxes and ENSO-scale variability, $\beta_L,\beta_O,\gamma_L,\gamma_O$8 hourly for urban and point-source attribution, and multi-year continuous time series longer than $\beta_L,\beta_O,\gamma_L,\gamma_O$9 years. Random errors of $T(x,y,t)$0–$T(x,y,t)$1 for XCO$T(x,y,t)$2 and $T(x,y,t)$3–$T(x,y,t)$4 for XCH$T(x,y,t)$5 per sounding are deemed acceptable only if systematic biases remain below $T(x,y,t)$6 in XCO$T(x,y,t)$7 and $T(x,y,t)$8 in XCH$T(x,y,t)$9; otherwise flux-bias errors of $\lambda(t)$0–$\lambda(t)$1 arise. Assimilation proceeds through Bayesian inverse modeling with

$\lambda(t)$2

and posterior regression of $\lambda(t)$3 against $\lambda(t)$4 and $\lambda(t)$5 yields updated estimates of $\lambda(t)$6 (Schimel et al., 2016).

A second Earth-system use of ICF concerns the global radiative feedback parameter $\lambda(t)$7, defined by

$\lambda(t)$8

with Earth’s energy imbalance given by

$\lambda(t)$9

In this formulation, a CNN is trained on climate model simulations to infer the global-mean radiative response from gridded surface-temperature anomalies on a $x_i(t)$0 grid:

$x_i(t)$1

Pre-training uses large-ensemble coupled ESM historical and piClim-histall runs for 1871–2014; fine-tuning uses amip-piForcing data for 1870–2014; and SHAP values decompose $x_i(t)$2 into grid-cell contributions $x_i(t)$3 such that $x_i(t)$4. A 30-year-window regression then defines

$x_i(t)$5

Applied to six surface-temperature reconstructions, the method yields a mid-1990s minimum of $x_i(t)$6 and a recent weakening to $x_i(t)$7 for windows ending around 2015–2025, with inter-reconstruction spread $x_i(t)$8 in the satellite era. An independent satellite-based estimate also shows a mid-1990s minimum and post-2010 rise toward weaker stability, though with slightly higher values because of forcing uncertainties. Removing ENSO or PDO indices alters $x_i(t)$9 by $C_m(t)$0. SHAP-based attribution and E3SMv2 targeted experiments identify subtropical Northeast Pacific warming, especially through the shortwave cloud feedback component, as a major driver of the recent weakening (Loon et al., 12 Mar 2026).

Taken together, these Earth-system formulations use information not as an abstract metaphor but as an operational input: dense observations reduce posterior uncertainty in carbon sinks, while high-dimensional temperature patterns diagnose decadal variation in radiative stability.

3. Information theory and statistical directionality in climate systems

Knuth et al. formulate an information-theoretic approach in which ICF is associated with the extraction of statistical dependence and possible causal structure from climate data. The central quantities are Shannon entropy,

$C_m(t)$1

joint entropy,

$C_m(t)$2

mutual information,

$C_m(t)$3

and transfer entropy,

$C_m(t)$4

Because $C_m(t)$5 in general, transfer entropy can indicate directional, possible causal influence (Knuth et al., 2013).

The methodological core is a Bayesian histogram-style density estimator with optimal binning. For a piecewise-constant model with $C_m(t)$6 bins, bin probabilities $C_m(t)$7, and equal-width total volume $C_m(t)$8, the density is

$C_m(t)$9

The posterior over $C_{atm}$0 after marginalizing over $C_{atm}$1 is

$C_{atm}$2

and the optimal $C_{atm}$3 maximizes $C_{atm}$4. Once $C_{atm}$5 is fixed, the posterior over bin heights is Dirichlet, permitting explicit posterior means and variances. Error bars on mutual information and transfer entropy are then obtained by sampling many realizations from the Dirichlet posterior, computing the required entropies for each draw, and taking the empirical mean and standard deviation of the resulting ensemble (Knuth et al., 2013).

Two methodological by-products are emphasized. First, the shape of $C_{atm}$6 acts as a sample-size sufficiency diagnostic: for univariate Gaussian-like data, about $C_{atm}$7–$C_{atm}$8 samples are needed for a workable density estimate and about $C_{atm}$9–$_2$00 to be very confident in bin choice. Second, the same diagnostic identifies excessive round-off or compression: a “picket-fence” signature, in which the posterior jumps to the maximum possible number of bins and stops rising, indicates information loss (Knuth et al., 2013).

The case study uses the Cold Tongue Index, a 198-month time series of eastern equatorial Pacific sea-surface-temperature anomalies, together with monthly percent cloud cover at each of 6,596 equal-area pixels over the same 198 months. For each pixel $_2$01, the method computes $_2$02 using 2D optimal binning. The resulting global map highlights maximum dependence in the equatorial Pacific and an artifact in Indian longitudes. Pixel 3231, near $_2$03, shows the largest mutual information. The paper does not demonstrate transfer entropy in this specific case, but states that the same 3D-binning and sampling machinery would yield $_2$04 and $_2$05 (Knuth et al., 2013).

A recurrent caveat is explicit: transfer entropy is an indicator of directed statistical dependence, not proof of physical causation. In this literature, ICF therefore names a data-analytic strategy for identifying potential feedback structure rather than a complete dynamical model.

4. Communication, social learning, and action-mediated climate feedbacks

In communication-oriented work, ClimateKB is described as the “Information” component in an end-to-end Information–Climate–Feedback loop. ClimateKB is a semi-automatically populated knowledge base of impacts, defined as cause–effect statements about climate change drawn from trusted news sources. It contains on the order of $_2$06 articles, yielding on the order of $_2$07 causal sentences and on the order of $_2$08 normalized facts. Each fact is a tuple $_2$09, where the entities are canonical climate concepts and confidence is an optional extraction score. The loop is specified as: retrieve relevant cause–effect facts; present tailored messages based on a profile; record climate-relevant action or expressed preferences; and log feedback to refine the user profile or knowledge-base associations. Causal-sentence detection uses a domain-adapted BERT termed ClimateBERT, further pre-trained on more than $_2$10 tokens of climate news, IPCC reports, and public-facing science books. On a 600-sentence expert test set, causality detection reports Precision $_2$11 and Recall $_2$12. Personalization uses Schwartz’s 10 basic human values, a 10-question Portrait Value Questionnaire, expert-labeled entity–value association vectors $_2$13, and the relevance score

$_2$14

Entities are ranked in descending $_2$15; a proposed online update rule modifies the user vector $_2$16 from feedback $_2$17 (Rodrigues et al., 2021).

In regional social–climate dynamics, the loop is fully dynamical. A five-region model stratifies the world into ASIA, LAM, MAF, OECD, and REF, and lets the fraction $_2$18 supporting mitigation evolve according to

$_2$19

Here $_2$20 is the per-capita cost of mitigation; $_2$21 is the perceived cost of climate impacts; and $_2$22 is the empirically inferred social-norm strength. The climate subsystem contains four carbon reservoirs and a temperature equation, with regional mitigation support entering emissions through the atmospheric carbon balance:

$_2$23

The core ICF loop is stated directly as

$_2$24

There is no direct $_2$25 imitation or information flow; cross-region coupling occurs only through the shared global temperature anomaly $_2$26 and atmospheric carbon stock. Baseline calibration uses Approximate Bayesian Computation to match RCP2.6, RCP4.5, or RCP8.5; for the baseline global calibration, reported medians are $_2$27, $_2$28, $_2$29, and $_2$30. Peak global temperature varies by several degrees Celsius across plausible ICF strengths and regional parameters; under the calibrated baseline, the 2100 peak is approximately $_2$31, while parameter variation moves the peak between about $_2$32 and above $_2$33 (Punnavajhala et al., 14 Sep 2025).

A different social–climate formulation centers on a committed minority. In a well-mixed population, each individual holds opinion A (“climate-action”) or B (“business-as-usual”), while a fixed fraction $_2$34 is committed to A and never changes. Uncommitted individuals keep a memory bank of the last $_2$35 opinions heard, generating an opinion-response function

$_2$36

with social steady states satisfying $_2$37. For $_2$38, increasing $_2$39 produces a saddle-node bifurcation; for $_2$40, the threshold is numerically $_2$41. The climate subsystem is a stochastic energy-balance model with CO$_2$42 forcing and Ornstein–Uhlenbeck variability. The coupling is closed by blending a best-case emissions trajectory $_2$43 and a worst-case trajectory $_2$44 as

$_2$45

then letting extreme events feed back into the effective committed minority via

$_2$46

with $_2$47 and $_2$48. The event rate is

$_2$49

where $_2$50 and $_2$51. In 10,000 Monte Carlo runs, about 40% of realizations experience a social tipping event before 2100; early tipping around 2030–2050 locks in SSP1–1.9-like behavior and holds warming below about $_2$52, whereas runs without tipping reach approximately $_2$53 median warming by 2100 (Wyse et al., 29 Oct 2025).

These social and communication literatures treat information as causal content, perceived impact, social norm, or extreme-event signal. The climatic effect is not inferred passively; it is mediated by user choice, imitation, commitment, or mitigation support.

5. Digitalization, thermal footprint, and proposed ICT–climate feedback

A distinct formulation proposes ICF as a nonlinear model of digitalization, energy consumption, thermal footprint, climatic response, and the vulnerability of digital infrastructure. The state variables are $_2$54 for scale of digitalization, $_2$55 for instantaneous energy consumption, $_2$56 for heat emitted, $_2$57 for climatic response, and $_2$58 for greenness. The delay differential system is

$_2$59

$_2$60

$_2$61

$_2$62

$_2$63

Typical calibration values are specified as $_2$64, $_2$65, $_2$66, $_2$67, $_2$68, $_2$69 years, $_2$70, $_2$71, $_2$72 years, $_2$73, and $_2$74 (Knar, 8 Jul 2025).

The loop is described in three parts. First, digitalization increases energy demand, with greenness moderating the energy required per unit digitalization. Second, energy is converted into heat, with a nonlinear $_2$75 term representing overheating. Third, climatic response feeds back on digital growth through the factor $_2$76 and on greening through the denominator $_2$77. If $_2$78, digital growth halts or reverses; this is termed “digital collapse.” Larger delays $_2$79 introduce inertia and can generate oscillatory or resonant dynamics. The paper further states a greenness-compensation condition, $_2$80, and a nonlinear heat threshold near $_2$81 (Knar, 8 Jul 2025).

The numerical analysis uses a custom RK4 integrator for delay differential equations in Python and reports phase reconstructions and thermal cartography. Three critical regimes are identified: Sustainable Growth, Cyclical Overheating, and Infrastructural Collapse. A four-scenario summary reports the following final states:

Scenario	Final $_2$82	Final $_2$83
Base	0.10	1.8
GreenBoost	0.12	1.6
FastDigital	$_2$84	2.5
ClimateSens.	$_2$85	2.0

The same analysis lists a maximum $_2$86 of $_2$87 for Base, $_2$88 for GreenBoost, $_2$89 for FastDigital, and $_2$90 for ClimateSens., with corresponding final greenness values of $_2$91, $_2$92, $_2$93, and $_2$94 (Knar, 8 Jul 2025).

The proposed policy layer is the Green Digital Accord, accompanied by 16 metrics. Selected metrics include Digital Thermal Density, Infoclimatic Sensitivity, Digitalization Growth Rate, Greening Rate, Total Digital Thermal Footprint, Digital Overheating Threshold, and Digital Climate Justice Index. The proposed provisions include mandatory reporting of energy use, heat, and greenness for major ICT players; a global cap on the digital thermal footprint; certification of “Thermally Stable” data centers; quotas and regional thresholds on digital-growth rates; a Digital Adaptation Fund; and yearly publication of a Digital Climate Resilience Index and a Thermal Density Map (Knar, 8 Jul 2025).

Because this framework is introduced explicitly as a proposed theory, its place within ICF is different from the observational and information-theoretic literatures. It extends the term to the climatic consequences of information infrastructure itself.

6. Shared logic, methodological limits, and interpretive issues

Across these formulations, a recurring sequence can be identified: information acquisition or encoding, state estimation or behavioral transformation, and feedback to climate variables or climate-relevant action. In the carbon-observing framework, observations are assimilated into inversion systems such as CarbonTracker, CMS-Flux, JENA Inversion, GEOS-Chem 4D-Var, and Ensemble Kalman Filters to constrain $_2$95 and $_2$96 parameters; in radiative monitoring, a CNN and SHAP map spatial temperature information to $_2$97; in ClimateKB, a graph of cause–effect facts and value associations is used to personalize messages; in Knuth et al., Bayesian density estimation converts raw data into mutual information and transfer entropy with error bars; in the regional and committed-minority models, perceived impacts, norms, or extreme events alter mitigation and emissions; and in the digitalization model, digital load, greenness, and climatic stress co-evolve through delayed nonlinear feedbacks [(Schimel et al., 2016); (Loon et al., 12 Mar 2026); (Rodrigues et al., 2021); (Knuth et al., 2013); (Punnavajhala et al., 14 Sep 2025); (Wyse et al., 29 Oct 2025); (Knar, 8 Jul 2025)].

Several misconceptions are explicitly countered in the source material. Transfer entropy is not proof of physical causation; it is a directional indicator requiring physical interpretation (Knuth et al., 2013). High-density satellite data are not sufficient unless systematic bias is controlled, because small XCO$_2$98 or XCH$_2$99 biases produce large flux-bias errors (Schimel et al., 2016). Decadal weakening of the global radiative feedback parameter is not reduced to ENSO or PDO removal, although forcing uncertainty still affects independent satellite-based estimates (Loon et al., 12 Mar 2026). In the five-region social model, cross-regional effects do not come from direct imitation, but only through the shared climate state (Punnavajhala et al., 14 Sep 2025). ClimateKB’s empirical evaluation is currently strongest for causality detection, while the tailored-message user study remains planned (Rodrigues et al., 2021). The digitalization paper presents a multiscenario proposal and a governance program, not an established component of mainstream carbon-cycle or radiative-feedback monitoring (Knar, 8 Jul 2025).

The literatures also differ in what “feedback” means. In Earth-system monitoring, it denotes biogeochemical or radiative response coefficients such as $_4$00, $_4$01, or $_4$02. In information-theoretic work, it denotes statistically coupled and possibly directional interactions. In social models, it denotes endogeneity between temperature, perceived impacts, norms, committed minorities, mitigation support, and emissions. In digitalization research, it denotes a physical and infrastructural loop connecting computational load to heat and climate. This suggests that ICF is less a single theory than a cross-domain schema for closing loops between informational states and climatic dynamics.

The broad significance of the term therefore lies in its integrative role. Whether the object of inference is airborne fraction, radiative stability, motivational relevance, directed statistical dependence, mitigation support, or ICT vulnerability, the underlying research program attempts to replace one-way climate analysis with closed-loop systems in which information changes the trajectory being observed.