Model-data Discrepancies Research Articles

Assessing impacts of observations on ocean circulation models with examples from coastal, shelf, and marginal seas

Ocean observing systems in coastal, shelf and marginal seas collect diverse oceanographic information supporting a wide range of socioeconomic needs, but observations are necessarily sparse in space and/or time due to practical limitations. Ocean analysis and forecast systems capitalize on such observations, producing data-constrained, four-dimensional oceanographic fields. Here we review efforts to quantify the impact of ocean observations, observing platforms, and networks of platforms on model products of the physical ocean state in coastal regions. Quantitative assessment must consider a variety of issues including observation operators that sample models, error of representativeness, and correlated uncertainty in observations. Observing System Experiments, Observing System Simulation Experiments, representer functions and array modes, observation impacts, and algorithms based on artificial intelligence all offer methods to evaluate data-based model performance improvements according to metrics that characterize oceanographic features of local interest. Applications from globally distributed coastal ocean modeling systems document broad adoption of quantitative methods, generally meaningful reductions in model-data discrepancies from observation assimilation, and support for assimilation of complementary data sets, including subsurface in situ observation platforms, across diverse coastal environments.

A revised model of global silicate weathering considering the influence of vegetation cover on erosion rate

Abstract. Silicate weathering, which is of great importance in regulating the global carbon cycle, has been found to be affected by complicated factors, including climate, tectonics and vegetation. However, the exact transfer function between these factors and the silicate weathering rate is still unclear, leading to large model–data discrepancies in the CO2 consumption associated with silicate weathering. Here we propose a simple parameterization for the influence of vegetation cover on erosion rate to improve the model–data comparison based on a state-of-the-art silicate weathering model. We found out that the current weathering model tends to overestimate the silicate weathering fluxes in the tropical region, which can hardly be explained by either the uncertainties in climate and geomorphological conditions or the optimization of model parameters. We show that such an overestimation of the tropical weathering rate can be rectified significantly by parameterizing the shielding effect of vegetation cover on soil erosion using the leaf area index (LAI), the high values of which are coincident with the distribution of leached soils. We propose that the heavy vegetation in the tropical region likely slows down the erosion rate, much more so than thought before, by reducing extreme streamflow in response to precipitation. The silicate weathering model thus revised gives a smaller global weathering flux which is arguably more consistent with the observed value and the recently reconstructed global outgassing, both of which are subject to uncertainties. The model is also easily applicable to the deep-time Earth to investigate the influence of land plants on the global biogeochemical cycle.

The Carbon-to-oxygen Ratio in Cool Brown Dwarfs and Giant Exoplanets. I. The Benchmark Late-T Dwarfs GJ 570D, HD 3651B, and Ross 458C

Measurements of the C/O ratio in brown dwarfs are lacking, in part due to past models adopting solar C/O only. We have expanded the ATMO 2020 atmosphere model grid to include nonsolar metallicities and C/O ratios in the T dwarf regime. We change the C/O ratio by altering either the carbon or oxygen elemental abundances, and we find that nonsolar abundances of these elements can be distinguished based on the shapes of the H and K bands. We compare these new models with medium-resolution (R ≈ 1700), near-infrared (0.8–2.4 μm) Gemini Near-Infrared Spectrograph (GNIRS) spectra of three benchmark late-T dwarfs, GJ 570D, HD 3651B, and Ross 458C. We find solar C/O ratios and best-fitting parameters (T eff, log(g) , Z) broadly consistent with other analyses in the literature based on low-resolution (R ∼ 100) data. The model-data discrepancies in the near-infrared spectra are consistent across all three objects. These discrepancies are alleviated when fitting the Y, J, H, and K bands individually, but the resulting best-fit parameters are inconsistent and disagree with the results from the full spectrum. By examining the model atmosphere properties we find this is due to the interplay of gravity and metallicity on H2–H2 collisionally induced absorption. We therefore conclude that there are no significant issues with the molecular opacity tables used in the models at this spectral resolution. Instead, deficiencies are more likely to lie in the model assumptions regarding the thermal structures. Finally, we find a discrepancy between the GNIRS, SpeX, and other near-infrared spectra in the literature of Ross 458C, indicating potential spectroscopic variability.

Modeling Past Hothouse Climates as a Means for Assessing Earth System Models and Improving the Understanding of Warm Climates

Simulating the warmth and equability of past hothouse climates has been a challenge since the inception of paleoclimate modeling. The newest generation of Earth system models (ESMs) has shown substantial improvements in the ability to simulate the early Eocene global mean surface temperature (GMST) and equator-to-pole gradient. Results using the Community Earth System Model suggest that parameterizations of atmospheric radiation, convection, and clouds largely determine the Eocene GMST and are responsible for improvements in the new ESMs, but they have less direct influence on the equator-to-pole temperature gradient. ESMs still have difficulty simulating some regional and seasonal temperatures, although improved data reconstructions of chronology, spatial coverage, and seasonal resolution are needed for more robust model assessment. Looking forward, key processes including radiation and clouds need to be benchmarked and improved using more accurate models of limited domain/physics. Earth system processes need to be better explored, leveraging the increasing ESM resolution and complexity. ▪Earth system models (ESMs) are now able to simulate the large-scale features of the early Eocene.▪Remaining model-data discrepancies exist at regional and seasonal scales and require improvements in both proxy data and ESMs.▪A hierarchical modeling approach is needed to ensure relevant physical processes are parameterized reasonably well in ESMs.▪Future work is needed to leverage the continuously increasing resolution and complexity of ESMs.

Systematic Uncertainties of Atomic Data in Photoionization Modeling

Fitting plasma models to high-quality spectra is a crucial tool for deriving diagnostics about the physical conditions in various astrophysical sources. Despite decades of model development, this prescription often provides an unsatisfying description of observational data. We explore some of the origins of the failure of fits of photoionized plasma models to high-resolution X-ray spectra. In particular, we test whether systematic uncertainties in underlying atomic data can account for data model discrepancies, and whether including model uncertainties during spectral fitting can provide statistically acceptable fits and reasonable parameter estimates. We fit Chandra/HETG spectra of NGC 3783 with the photoionized absorber model warmabs. We use the remaining data model discrepancies to estimate the systematic uncertainties of bound–bound radiative rates for individual transitions quantitatively. We then include these uncertainties into warmabs to return a total model uncertainty. We find residual data model discrepancies which are due to systematic errors that cannot be accounted for solely by a modification of the optical depth of strong absorption lines. Furthermore, statistical uncertainties still dominate the fit statistics. The relevance of model uncertainties in spectral fitting will vary on a case-by-case basis. However, they are likely to have a minor effect on most of the currently existing data sets. We conclude that while the quality of atomic data does have an effect on fitting photoionization models, and so demands further improvement, uncertainties in radiative rates cannot be held solely responsible for statistically unacceptable fits. Other sources of systematic uncertainties are likely to be of comparable importance and require further investigation.

TALKS: A systematic framework for resolving model-data discrepancies

TALKS: A systematic framework for resolving model-data discrepancies

Assessing the theory-data tension in neutrino-induced charged pion production: The effect of final-state nucleon distortion

Pion production on nuclei constitutes a significant part of the total cross section in experiments involving few-GeV neutrinos. Combined analyses of data on deuterium and heavier nuclei points to tensions between the bubble-chamber data and the data of the $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ experiment, which are often ascribed to unspecified nuclear effects. In experimental analysis use is made of approximate treatments of nuclear dynamics, usually in a Fermi gas approach with classical treatments of the reaction mechanism, and fits are often performed by simply rescaling cross sections. To understand the origin of these tensions, check the validity of approximations, and to further advance the description of neutrino pion production on nuclei, a microscopic quantum mechanical framework is needed to compute nuclear matrix elements. We use the local approximation to the relativistic distorted wave impulse approximation to calculate the nuclear matrix elements. We include the distortion of wave functions of the final-state nucleon in a real energy-dependent potential. We compare results with and without distortion. To perform this comparison under conditions relevant to neutrino experiments, we compute cross sections for the $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ and T2K charged-pion production datasets. The inclusion of nucleon distortion leads to a reduction of the cross section up to 10%, but to no significant change in shape of the flux-averaged cross sections. Results with and without distortion compare favorably to experimental data, with the exception of the low-${Q}^{2}$ $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ ${\ensuremath{\pi}}^{+}$ data. We point out that hydrogen target data from BEBC is also overpredicted at low ${Q}^{2}$, and the data-model discrepancy is similar in shape and magnitude as what is found in comparison to $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$ data. Including nucleon distortion alone cannot explain the overprediction of low-${Q}^{2}$ cross sections measured by $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$. The similar overprediction of BEBC data on hydrogen means that it is impossible to ascribe this discrepancy solely to a nuclear effect. Axial form factors might not be constrained in a satisfactory way by the Argonne and Brookhaven National Laboratories (ANL/BNL) data alone. Axial couplings and their ${Q}^{2}$ dependence should ideally be derived from more precise data on hydrogen and deuterium. Nuclear matrix elements should be tested with e.g., electron scattering data for which nucleon level physics is better constrained.

The predictive power of magnetospheric models for estimating ground magnetic field variation in the United Kingdom

Space weather events can have damaging effects on ground-based infrastructure. Geomagnetically induced currents (GIC) caused by rapid magnetic field fluctuations during geomagnetic storms can negatively affect power networks, railways as well as navigation systems. To reduce such negative impacts, good forecasting capability is essential. In this study we assess the performance of contemporary magnetohydrodynamic (MHD) models in predicting the external-only ground magnetic field perturbations at three United Kingdom observatories during two severe space weather events: September 2017 and March 2015. Simulated magnetic data were acquired via Community Coordinated Modeling Center (CCMC), using the following models: Space Weather Modeling Framework (SWMF), Open Geospace General Circulation Model (Open GGCM) and Lyon–Fedder–Mobarry (LFM) combined with the Rice Convection Model (RCM). All simulations use spacecraft measurements at L1 as their solar wind input in calculating ground perturbations. Qualitative and quantitative comparison between measured and modelled values suggest that the performance of MHD models vary with latitude, the magnetic component and the characteristics of the storm analysed. Most models tend to exaggerate the magnitude of disturbances at lower latitudes but better capture the fluctuations at the highest latitude. For the two storms investigated, the addition of RCM tends to result in overestimation of the amplitude of ground perturbations. The observed data-model discrepancies most likely arise due to the many approximations required in MHD modelling, such as simplified solar wind input or shift in location of the electrojets in the simulated magnetospheric and ionospheric currents. It was found that no model performs consistently better than any other, implying that each simulation forecasts different aspects of ground perturbations with varying level of accuracy. Ultimately, the decision of which model is most suitable depends on specific needs of the potential end user.

Subject-Level Membership Inference Attack via Data Augmentation and Model Discrepancy

Subject-Level Membership Inference Attack via Data Augmentation and Model Discrepancy

Holocene seasonal temperature evolution and spatial variability over the Northern Hemisphere landmass

The origin of the temperature divergence between Holocene proxy reconstructions and model simulations remains controversial, but it possibly results from potential biases in the seasonality of reconstructions or in the climate sensitivity of models. Here we present an extensive dataset of Holocene seasonal temperatures reconstructed using 1310 pollen records covering the Northern Hemisphere landmass. Our results indicate that both summer and winter temperatures warmed from the early to mid-Holocene (~11–7 ka BP) and then cooled thereafter, but with significant spatial variability. Strong early Holocene warming trend occurred mainly in Europe, eastern North America and northern Asia, which can be generally captured by model simulations and is likely associated with the retreat of continental ice sheets. The subsequent cooling trend is pervasively recorded except for northern Asia and southeastern North America, which may reflect the cross-seasonal impact of the decreasing summer insolation through climatic feedbacks, but the cooling in winter season is not well reproduced by climate models. Our results challenge the proposal that seasonal biases in proxies are the main origin of model–data discrepancies and highlight the critical impact of insolation and associated feedbacks on temperature changes, which warrant closer attention in future climate modelling.

COol Companions ON Ultrawide orbiTS (COCONUTS). III. A Very Red L6 Benchmark Brown Dwarf around a Young M5 Dwarf

We present the third discovery from the COol Companions ON Ultrawide orbiTS (COCONUTS) program, the COCONUTS-3 system, composed of the young M5 primary star UCAC4 374−046899 and the very red L6 dwarf WISEA J081322.19−152203.2. These two objects have a projected separation of (1891 au) and are physically associated given their common proper motions and estimated distances. The primary star, COCONUTS-3A, has a mass of 0.123 ± 0.006 M ⊙, and we estimate its age as 100 Myr to 1 Gyr based on its stellar activity (via Hα and X-ray emission), kinematics, and spectrophotometric properties. We derive its bulk metallicity as 0.21 ± 0.07 dex using empirical calibrations established by older and higher-gravity M dwarfs and find that this [Fe/H] could be slightly underestimated according to PHOENIX models given COCONUTS-3A’s younger age. The companion, COCONUTS-3B, has a near-infrared spectral type of L6 ± 1 int-g, and we infer physical properties of T eff = K, = dex, R Jup, and M Jup using its bolometric luminosity, its host star’s age, and hot-start evolution models. We construct cloudy atmospheric model spectra at the evolution-based physical parameters and compare them to COCONUTS-3B’s spectrophotometry. We find that this companion possesses ample condensate clouds in its photosphere (f sed = 1) with the data–model discrepancies likely due to the models using an older version of the opacity database. Compared to field-age L6 dwarfs, COCONUTS-3B has fainter absolute magnitudes and a 120 K cooler T eff. Also, the J − K color of this companion is among the reddest for ultracool benchmarks with ages older than a few hundred megayears. COCONUTS-3 likely formed in the same fashion as stellar binaries given the companion-to-host mass ratio of 0.3 and represents a valuable benchmark to quantify the systematics of substellar model atmospheres.

Ionospheric photoelectrons: A lateral thinking approach

This paper presents a personal account of developments in the solution of two related problems that limited the accuracy of ionosphere calculations in the 1980s. The first problem concerns the model-data discrepancies in the ionosphere photoelectron flux spectrum. Early comparisons between measured and modeled data revealed discrepancies in magnitude and shape. A lateral thinking approach revealed that there were problems with two key photoelectron model inputs: namely, the electron impact cross-sections and the solar extreme ultraviolet irradiance. This work led to the development of a widely used EUVAC solar irradiance model for ionosphere electron density calculations. The second problem relates to the neutral winds that are crucial for modeling variations in the ionosphere ion and electron densities. There is a lack of thermosphere neutral wind data because they are difficult to measure. The winds determine the altitude at which the electron density peaks. An accurate solution to this problem was the development of an algorithm that assimilates the altitude of the peak electron density into ionosphere models. This technique works because the altitude of the peak density is very sensitive to variations in the neutral wind.

Study of an Arctic blowing snow-induced bromine explosion event in Ny-Ålesund, Svalbard

Bromine explosion events (BEEs) are important processes that influence the atmospheric oxidation capacity, especially in the polar troposphere during spring. Although sea ice surface is thought to be a significant bromine source, bromine release mechanisms remain unclear. High-resolution ground-based observations of reactive bromine, such as BrO, are important for assessing the potential impacts on tropospheric ozone and evaluating chemical models. However, previous model studies paid little attention to Svalbard, which is surrounded by both open ocean and sea ice. In this paper, we present continuous BrO slant column densities and vertical column densities derived by Multi-Axis Differential Optical Absorption Spectroscopy deployed at Ny-Ålesund (78.92°N, 11.93°E) in March 2017. We focused on one BEE in mid-March, during which the vertical column densities of BrO surged from 4.26 × 1013 molecular cm−2 to the peak at 1.23 × 1014 molecular cm−2 on March 17, surface ozone depleted from a background level of 46.25 parts per billion by volume (ppbv) to 13.9 ppbv. This case study indicates that the BEE was strongly associated with blowing snow induced by the cyclone systems that approached Svalbard from March 14 to 18. By considering meteorological conditions, sea ice coverage, and airmass trajectory history, we demonstrate that sea salt aerosols (SSAs) from blowing snow on sea ice, rather than from open ocean, are attributed to the occurrence of this BEE. Model results from a parallelized-tropospheric offline model of chemistry and transport (p-TOMCAT) indicate that this BEE was mainly triggered by a blowing snow event associated with a low-pressure cyclone system. The concentration of blowing-snow-sourced SSAs surged to peak when the airmass pass across the sea-ice-covered area under high wind speed, which is a critical factor in the process of bromine explosion observed in Ny-Ålesund. Due to the coarse resolution, the possible delayed timing of bromine release from SSA and the model-data discrepancies still exist.

Multiscale evaluation of CMIP5 models using wavelet-based descriptive and diagnostic techniques

Time–frequency localization of model-data discrepancies may provide useful information for climate models inter-comparison, and especially for the goals of climate model refinement and improvement. CMIP5 models of the long-term historical (1850–2005) run experiment are compared using wavelet-based multiscale descriptive and diagnostic techniques with interesting results. Wavelet coherence maps can visualize the ability of alternative CMPI5 models to capture the observed climate variability at different time scales, while the performance of each CMIP5 model is assessed using goodness of fit relative measures on a scale-by-scale basis. Finally, the plots of wavelet decompositions of CMIP5 models and observed temperature series at different scales can detect and locate model/data disagreements across frequencies and over time, thus providing useful information to researchers for model diagnostic refinement and improvement.

Base Models for Configural Frequency Analysis - Data Generation Processes.

In Configural Frequency Analysis (CFA), model-data discrepancies are interpreted with reference to CFA base models. Thus far, CFA base models are defined as probability models that differ in the constraints they place on variable relations. In this article, it is proposed extending the scope of CFA base models. Specifically, it is proposed that the specification of base models is conducted with reference to data generation processes (DGPs). These processes result in uni- or multivariate distributions that reflect variable relations, probability distributions, or processes that result in change in series of observations. The new, DGP-based definition of CFA base models retains the concept of unique interpretability of CFA results, but it opens the doors to many more forms of base models than considered before. Four classes of base models are defined. Data examples illustrate various CFA base models.

Computer Model Calibration with Time Series Data Using Deep Learning and Quantile Regression

Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiment is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer input parameters by combining information from model runs and observational data. The existing standard calibration framework suffers from inferential issues when the model output and observational data are high-dimensional dependent data such as large time series due to the difficulty in building an emulator and the non-identifiability between effects from input parameters and data-model discrepancy. To overcome these challenges we propose a new calibration framework based on a deep neural network (DNN) with long-short term memory layers that directly emulates the inverse relationship between the model output and input parameters. Adopting the 'learning with noise' idea we train our DNN model to filter out the effects from data model discrepancy on input parameter inference. We also formulate a new way to construct interval predictions for DNN using quantile regression to quantify the uncertainty in input parameter estimates. Through a simulation study and real data application with WRF-hydro model we show that our approach can yield accurate point estimates and well calibrated interval estimates for input parameters.

Talks: A Systematic Framework for Resolving Model-Data Discrepancies

Talks: A Systematic Framework for Resolving Model-Data Discrepancies

General characteristics of climate change over China and associated dynamic mechanisms during the Last Interglacial based on PMIP4 simulations

Investigation of climate change during the Last Interglacial (LIG, ~130–115 ka BP) may deepen our understanding of the response of climate to Earth's orbit. Here we examine climate change over China and associated mechanisms during the LIG using the lig127k experiments from the Paleoclimate Modeling Intercomparison Project Phase 4. We illustrate that annual mean surface air temperature over China decreases by 0.22 °C during the LIG relative to the preindustrial, with a colder climate in winter and spring, whereas a warmer climate in summer and autumn. Annual mean precipitation increases (up to 54%) over northern and southwestern China during the LIG, whereas it decreases (up to 11%) over the other parts. This pattern largely holds for precipitation change in summer during the LIG, but precipitation generally decreases in winter. According to the moisture budget equation, the nonlinear and horizontal dynamic terms contribute largely to the drier (wetter) conditions in summer over the south (north) of eastern China, whereas the horizontal dynamic term and the horizontal thermodynamic term is more important in regulating drier conditions over south and north of eastern China in winter, respectively. Furthermore, East Asian summer monsoon is intensified during the LIG manifested by anomalous southerly at 850 hPa, a westward shift of western North Pacific subtropical high, and poleward migration of East Asian westerly jet. East Asian winter monsoon also gets stronger during the LIG, with anomalous northerly at low-level troposphere, enhanced mid-tropospheric East Asian trough, and an equatorward shift of westerly jet at upper troposphere. Additionally, we note obvious data-model discrepancies in annual temperature change over China during the LIG, with cooling seen in the models but warming suggested by multiproxies. This highlights close collaboration between model and data communities in future to deepen our understanding of climate change during the LIG.

Testing the CMIP6 GCM Simulations versus Surface Temperature Records from 1980–1990 to 2011–2021: High ECS Is Not Supported

The last-generation CMIP6 global circulation models (GCMs) are currently used to interpret past and future climatic changes and to guide policymakers, but they are very different from each other; for example, their equilibrium climate sensitivity (ECS) varies from 1.83 to 5.67 °C (IPCC AR6, 2021). Even assuming that some of them are sufficiently reliable for scenario forecasts, such a large ECS uncertainty requires a pre-selection of the most reliable models. Herein the performance of 38 CMIP6 models are tested in reproducing the surface temperature changes observed from 1980–1990 to 2011–2021 in three temperature records: ERA5-T2m, ERA5-850mb, and UAH MSU v6.0 Tlt. Alternative temperature records are briefly discussed but found to be not appropriate for the present analysis because they miss data over large regions. Significant issues emerge: (1) most GCMs overestimate the warming observed during the last 40 years; (2) there is great variability among the models in reconstructing the climatic changes observed in the Arctic; (3) the ocean temperature is usually overestimated more than the land one; (4) in the latitude bands 40° N–70° N and 50° S–70° S (which lay at the intersection between the Ferrel and the polar atmospheric cells) the CMIP6 GCMs overestimate the warming; (5) similar discrepancies are present in the east-equatorial pacific region (which regulates the ENSO) and in other regions where cooling trends are observed. Finally, the percentage of the world surface where the (positive or negative) model-data discrepancy exceeds 0.2, 0.5 and 1.0 °C is evaluated. The results indicate that the models with low ECS values (for example, 3 °C or less) perform significantly better than those with larger ECS. Therefore, the low ECS models should be preferred for climate change scenario forecasts while the other models should be dismissed and not used by policymakers. In any case, significant model-data discrepancies are still observed over extended world regions for all models: on average, the GCM predictions disagree from the data by more than 0.2 °C (on a total mean warming of about 0.5 °C from 1980–1990 to 2011–2021) over more than 50% of the global surface. This result suggests that climate change and its natural variability remain poorly modeled by the CMIP6 GCMs. Finally, the ECS uncertainty problem is discussed, and it is argued (also using semi-empirical climate models that implement natural oscillations not predicted by the GCMs) that the real ECS could be between 1 and 2 °C, which implies moderate warming for the next decades.

Earth System Model Analysis of How Astronomical Forcing Is Imprinted Onto the Marine Geological Record: The Role of the Inorganic (Carbonate) Carbon Cycle and Feedbacks.

Astronomical cycles are strongly expressed in marine geological records, providing important insights into Earth system dynamics and an invaluable means of constructing age models. However, how various astronomical periods are filtered by the Earth system and the mechanisms by which carbon reservoirs and climate components respond, particularly in absence of dynamic ice sheets, is unclear. Using an Earth system model that includes feedbacks between climate, ocean circulation, and inorganic (carbonate) carbon cycling relevant to geological timescales, we systematically explore the impact of astronomically modulated insolation forcing and its expression in model variables most comparable to key paleoceanographic proxies (temperature, the δ13C of inorganic carbon, and sedimentary carbonate content). Temperature predominately responds to short and long eccentricity and is little influenced by the modeled carbon cycle feedbacks. In contrast, the cycling of nutrients and carbon in the ocean generates significant precession power in atmospheric CO2, benthic ocean δ13C, and sedimentary wt% CaCO3, while inclusion of marine sedimentary and weathering processes shifts power to the long eccentricity period. Our simulations produce reduced pCO2 and dissolved inorganic carbon (DIC) δ13C at long eccentricity maxima and, contrary to early Cenozoic marine records, CaCO3 preservation in the model is enhanced during eccentricity‐modulated warmth. Additionally, the magnitude of δ13C variability simulated in our model underestimates marine proxy records. These model‐data discrepancies hint at the possibility that the Paleogene silicate weathering feedback was weaker than modeled here and that additional organic carbon cycle feedbacks are necessary to explain the full response of the Earth system to astronomical forcing.