Linear Response Function Research Articles

The Role of Barotropic versus Baroclinic Feedbacks on the Eddy Response to Annular Mode Zonal Wind Anomalies

Abstract The annular mode, the leading pattern of low-frequency variability in the extratropics, owes its temporal persistence to a positive feedback between eddy momentum fluxes and the background zonal wind anomalies associated with the annular mode itself. The mechanisms by which the zonal wind anomalies impact the eddy momentum fluxes fall into two families: 1) baroclinic mechanisms: changes in the amount and location of wave activity generated via baroclinic instability cause the changes in eddy momentum fluxes and 2) barotropic mechanisms: the zonal wind anomalies impact the eddy momentum fluxes directly via critical levels, turning latitudes, and the refraction of meridionally propagating waves. This paper takes a critical look at various methodologies that conclude that baroclinic feedbacks are dominant by developing multiple independent estimates of the relative role of baroclinic versus barotropic processes. All methods conclude that barotropic mechanisms are most important; however, baroclinic mechanisms are not negligible. Additional experiments with the baroclinic feedback turned off (via manipulations to the vertical friction profile) also suggest that barotropic feedbacks are dominant. The methods for estimating the feedbacks are 1) Rossby wave chromatography, 2) forced manipulations of the vertical structure of EOF1 using linear response functions, and 3) quantitatively inferring the meridional wave propagation from the mean wave activity budget and then using this to analyze the wave activity response to anomalies. The last method is also applied to both Northern and Southern Hemisphere reanalysis, and similar conclusions about the feedbacks are reached.

METHOD DEVELOPMENT AND VALIDATION OF CEFOPERAZONE AND SULBACTAM IN DRIED BLOOD SPOTS BY HIGH-PERFORMANCE LIQUID CHROMATOGRAPHY PHOTODIODE ARRAY DETECTOR

Objective: The primary purpose of this research was to develop a simple, precise, fast, and accurate method for measuring cefoperazone and sulbactam simultaneously in dried blood spots (DBS) using HPLC PDA. Methods: A simplified analytical method for quantifying cefoperazone and sulbactam in DBS samples using a High-Performance Liquid Chromatography photodiode array detector with isocratic elution was developed and validated. The best chromatographic conditions were obtained by using a reversed-phase column (250 x 4.6 mm; 5 mm); phosphate buffer 10 mmol pH 3.2–acetonitrile (83:17, v/v) as a mobile phase; a flow rate of 1.0 ml/min; a column temperature of 35 °C; a photodiode array detector at 210 nm, and cefuroxime as internal standard. Samples were prepared by liquid-liquid extraction with 100 ml hydrochloric acid 0.5 mol/l and 1000 ml ethyl acetate, evaporated with nitrogen and reconstituted with 100 mL phosphate buffer–acetonitrile (4:1). Results: The total chromatography run time was 15 min, and the elution times for sulbactam, cefoperazone, and IS (cefuroxime) were 3.46, 10.221, and 6.987 min, respectively. A linear response function was established at 0.5-30 mg/ml with (r) 0.995 for sulbactam and 2.5-250 mg/ml with (r) 0.999 for cefoperazone in dried blood spots. The lower limit quantification (LLOQ) concentration of sulbactam 1 mg/ml and cefoperazone were 5 mg/ml. Conclusion: This method has successfully fulfilled the validation requirement referring to the 2011 EMA and 2018 FDA guidelines.

From Density Functional Theory to Conceptual Density Functional Theory and Biosystems.

The position of conceptual density functional theory (CDFT) in the history of density functional theory (DFT) is sketched followed by a chronological report on the introduction of the various DFT descriptors such as the electronegativity, hardness, softness, Fukui function, local version of softness and hardness, dual descriptor, linear response function, and softness kernel. Through a perturbational approach they can all be characterized as response functions, reflecting the intrinsic reactivity of an atom or molecule upon perturbation by a different system, including recent extensions by external fields. Derived descriptors such as the electrophilicity or generalized philicity, derived from the nature of the energy vs. N behavior, complete this picture. These descriptors can be used as such or in the context of principles such as Sanderson’s electronegativity equalization principle, Pearson’s hard and soft acids and bases principle, the maximum hardness, and more recently, the minimum electrophilicity principle. CDFT has known an ever-growing use in various subdisciplines of chemistry: from organic to inorganic chemistry, from polymer to materials chemistry, and from catalysis to nanotechnology. The increasing size of the systems under study has been coped with thanks to methodological evolutions but also through the impressive evolution in software and hardware. In this flow, biosystems entered the application portfolio in the past twenty years with studies varying (among others) from enzymatic catalysis to biological activity and/or the toxicity of organic molecules and to computational peptidology. On the basis of this evolution, one can expect that “the best is yet to come”.

Comparison of Length, Velocity, and Symmetric Gauges for the Calculation of Absorption and Electric Circular Dichroism Spectra with Real-Time Time-Dependent Density Functional Theory.

A velocity and symmetric gauge implementation for real-time time-dependent density functional theory (RT-TDDFT) in the CP2K package using a Gaussian and plane wave approach is presented, including the explicit gauge-transformed contributions due to the nonlocal part of pseudopotentials. Absorption spectra of gas-phase α-pinene are calculated in length and velocity gauges in the long-wavelength approximation for the application of a δ pulse in linear and full order. The velocity gauge implementation is also applied to a solvated uracil molecule to showcase its use within periodic boundary conditions (PBC). For the calculation of the expectation value of the electric dipole moment in PBC, both the velocity representation and the modern theory of polarization give equivalent absorption spectra if a distributed reference point is used for the nonlocal term of the velocity operator. The discussion of linear response theory takes place in a unified framework in terms of linear response functions in propagator notation, distinguishing the parts of the linear response functions associated with perturbation and response. To further investigate gauge dependence, electric circular dichroism (ECD) spectra of α-pinene were calculated either as magnetic response to an electric field perturbation, in length or velocity gauge, or as electric response to a magnetic field perturbation in the symmetric gauge. Both approaches, electric and magnetic perturbations, have been found to yield equivalent ECD spectra.

Sensitivity of isochrones to surface mass balance and dynamics

AbstractThe interior of an ice sheet consists of layers of accumulated snow, which contain important information on accumulation and ice dynamics that are imprinted on layer shapes over time. This work describes how changes in accumulation influence the stratigraphy of an ice sheet. The thickness of each layer at present day depends both on accumulation and on the effect of dynamic thinning after its deposition. An isochronal numerical model is used to simulate the evolution of a 2-D, idealized ice sheet while explicitly representing the layers. A series of simulations was carried out to quantify the changes that anomalous accumulation at different locations and times has on the stratigraphy. These simulations form the basis of a linear response function. A second set of simulations with more sustained changes in accumulation is then used to describe large-scale and long-term impacts on the layering of the ice sheet as well as to test the quality of the linear approximation. The aim is to examine whether long-term effects can be extrapolated from small differential changes. The result confirms a certain degree of linearity between changes in accumulation and layer thickness that may be exploited for future inverse modeling applications.

Duffing-type digitally programmable nonlinear synthetic inductance for piezoelectric structures

Piezoelectric shunt damping techniques using linear circuits (e.g. resistive-inductive) and switching circuits (e.g. synchronized switch on inductor) have been extremely well studied for suppressing resonant vibrations in flexible structures. Both analog circuits and synthetic impedance circuits with digital control have been explored for linear concepts. In a parallel body of work, from the domain of mechanical methods of vibration attenuation, it is also known that leveraging nonlinearities (e.g. stiffness nonlinearity) can enhance the frequency bandwidth and offer amplitude-dependent suppression over a range of frequencies. However, the existing piezoelectric shunt damping techniques have been mostly limited to linear or switching nonlinear circuits, with the exception of a few nonlinear capacitance efforts. This work aims to introduce cubic inductance to emulate Duffing-type hardening nonlinearity in the shunt circuit with precise digital programming and tuning capability. Experiments are performed on a piezoelectric bimorph cantilever under base excitation for concept demonstration and model validation. First, linear frequency response functions of the cantilever are obtained for the short- and open-circuit conditions, and for linear resistive-inductive synthetic shunt damping, to confirm the standard linear behavior and electromechanical model parameters. Then, cubic inductance is introduced to the circuit and nonlinear experiments (up- and down-frequency sweep) are conducted. Cantilever tip to base motion transmissibility frequency response is measured along with piezoelectric voltage to base motion counterpart for a range of base excitation amplitudes. The distortion of the frequency response curves with increased base acceleration levels is observed. The nonlinear cubic coefficient is then varied to alter the manifestation of nonlinear frequency response at a given base excitation level, demonstrating the ease of tuning and triggering the nonlinear behavior on demand by means of the digitally-controlled synthetic impedance shunt. Nonlinear electromechanical model simulations are also validated against the experiments, yielding a very good agreement.

Bifurcation analysis of a discrete Phytoplankton–Zooplankton model with linear predational response function and toxic substance distribution

Phytoplanktons are drifting plants in an aquatic system. They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis. Zooplanktons are drifting animals found inside the aquatic bodies. For stable aquatic ecosystem, the growth of both Zooplankton and Phytoplankton should be in steady state but in previous eras, there has been a universal explosion in destructive Plankton or algal blooms. Many investigators used various mathematical methodologies to try to explain the bloom phenomenon. So, in this paper, a discretized two-dimensional Phytoplankton–Zooplankton model is investigated. The results for the existence and uniqueness, and conditions for local stability with topological classifications of the equilibrium solutions are determined. It is also exhibited that at trivial and semitrivial equilibrium solutions, discrete model does not undergo flip bifurcation, but it undergoes Neimark–Sacker bifurcation at interior equilibrium solution under certain conditions. Further, state feedback method is deployed to control the chaos in the under consideration system. The extensive numerical simulations are provided to demonstrate theoretical results.

High-frequency limit of spectroscopy.

We consider an arbitrary quantum mechanical system, initially in its ground-state, exposed to a time-dependent electromagnetic pulse with a carrier frequency ω0 and a slowly varying envelope of finite duration. By working out a solution to the time-dependent Schrödinger equation in the high-ω0 limit, we find that, to the leading order in ω0 -1, a perfect self-cancellation of the system's linear response occurs as the pulse switches off. Surprisingly, the system's observables are, nonetheless, describable in terms of a combination of its linear density response function and nonlinear functions of the electric field. An analysis of a jellium slab and jellium sphere models reveals a very high surface sensitivity of the considered setup, producing a richer excitation spectrum than accessible within the conventional linear response regime. On this basis, we propose a new spectroscopic technique, which we provisionally name the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the traditional dipole selection rules, and the clarity of theoretical interpretation utilizing the linear response time-dependent density functional theory, NLHFPS has a potential to evolve into a powerful characterization method for nanoscience and nanotechnology.

Fluctuation-dissipation theorem with Loewner time

Although the fluctuation-dissipation theorem (FDT) is recognized as a general result of statistical physics, its applicability to the non-equilibrium and nonlinear system has not been completely clarified. In this study, we observe that introducing a new type of time coordinate determined by the stochastic Loewner evolution enables the conversion of a certain class of nonlinear Langevin equations into linear ones. The formulation using Loewner time yields a linear response function for the nonlinear systems under a small perturbation. The proposed approach is expected to provide an extension of the conventional FDT in a form applicable to a wide class of non-equilibrium dynamics.

Development of kinetic energy density functional using response function defined on the energy coordinate

AbstractA kinetic energy functional was developed within the framework of the density‐functional theory (DFT) based on the energy electron density for the purpose of realizing the orbital‐free DFT. The functional includes the nonlocal term described with the linear‐response function (LRF) of a reference system. As a notable feature of the present approach, the LRF is represented on the energy coordinate ϵ defined for each system of interest. In addition, an atomic system is taken as a reference system for the construction of the LRF, which shows a clear difference from the conventional approach based on the homogeneous electron gas. The explicit form of the functional was formulated by means of the Taylor series expansion of the kinetic energy. The functional was applied to the calculations of the kinetic energies of the pseudo atoms that mimics H, He, Ne, and Ar. Explicitly, the kinetic energy of each atom was computed using the functional with respect to the variation of the valence charge Zv of each atom. In these calculations, the electron density n optimized by the Kohn‐Sham DFT was adopted as an argument of the functional. It was found that the results are in excellent agreements with those given by the Kohn‐Sham DFT. We also devised a method to perform the self‐consistent field calculation utilizing the functional . The method was applied to the computation of the radial distribution functions of the electrons in the pseudo Ne and Ar atoms. It was demonstrated that the results reasonably agree with those yielded by the Kohn‐Sham DFT.

Energy Harvesting from Human Walking Motion using Pendulum-based Electromagnetic Generators

Wearable devices find many applications in health monitoring, communications, and entertainment devices; however, battery life is still a major limitation to their functionality. The kinetic energy from the walking motion can be employed as an energy source for wearable devices with the use of vibration-based energy harvesters. This paper investigates energy harvesting from a pendulum-based system with an electromagnetic generator when placed on different human body joints. The coupled electromechanical equations of motion for the pendulum-based system with an electromagnetic generator energy harvester under combined in-plane movements and the body segment rotation are derived from the Lagrange formulation. The linearized coupled electromechanical equations for small amplitude oscillations are applied for the system parameter identification. The system's nonlinear response depends on identified parameters from linear frequency response functions, while the system's behavior is explored as a function of several critical parameters: excitation frequency, excitation amplitude, resistance load, and placement on the body. The system jumps from the chaotic non-rotary to the periodic rotary solution at the limit point bifurcation (i.e., saddle-node appears on the limit cycle). After this bifurcation point, the harvested energy increases multiple times. To estimate the output power from the walking motion, the trajectories generated by the walking simulation program are substituted into the coupled electromechanical equations of motion. The system's response is always an oscillatory type with the same period as the walking motion, and the output power can be maximized by varying the external load resistance at each specific relative walking velocity. Moreover, a higher walking velocity results in higher output power from the generator. The output voltage and power from wearable energy harvesters can be predicted accurately by using more precise walking trajectories.

Delayed elastic contributions to the viscoelastic response of foams.

We show that the slow viscoelastic response of a foam is that of a power-law fluid with a terminal relaxation. Investigations of the foam mechanics in creep and recovery tests reveal that the power-law contribution is fully reversible, indicative of a delayed elastic response. We demonstrate how this contribution fully accounts for the non-Maxwellian features observed in all tests, probing the linear mechanical response function. The associated power-law spectrum is consistent with soft glassy rheology of systems with mechanical noise temperatures just above the glass transition [Fielding et al., J. Rheol. 44, 323 (2000)] and originates from a combination of superdiffusive bubble dynamics and stress diffusion, as recently evidenced in simulations of coarsening foam [Hwang et al., Nat. Mater. 15, 1031 (2016)].

Rider control identification in cycling taking into account steering torque feedback and sensory delays

Experiments and human rider models were used to investigate bicycle balance and steering using visuo/vestibular motion and proprioceptive feedback taking into account sensory delays. An instrumented steer-by-wire bicycle designed and built at the TU Delft bicycle laboratory was used to investigate rider responses with and with reduced steering torque feedback. Steering responses and bicycle motions were measured perturbing balance with impulsive forces at the seat post. The rider was commanded to follow a straight lane at unstable (2.6 and 3.7 ) and stable speeds (4.5 and 5.6 ). Bicycle speed was controlled with an electric drive and cruise control. Balance and steering responses could well be captured by linear impulse response functions which were consistent across participants. The impulse response functions were used to develop neuromuscular control models capturing rider–bicycle interaction. The Carvallo–Whipple bicycle model was extended with rider inertia and an additional degree of freedom for the steer-by-wire system. Rider behaviour was modelled as a balance and heading controller. This controller used visuo/vestibular motion feedback of roll angle and roll rate, heading angle and heading rate, and proprioceptive feedback of steering angle, velocity and torque. Results showed that the rider model followed the necessary stability condition of steer into the fall and was capable of stabilising the bicycle. Sensory delays had a negative effect on the model fit, which was resolved with an internal model and prediction algorithm. A model without steer angle and steer velocity feedback could not well capture the human response at the highest speeds and the absence of torque feedback had similar effects for all speeds, supporting the relevance of steer angle and torque feedback in bicycle control.

A Speech-Level-Based Segmented Model to Decode the Dynamic Auditory Attention States in the Competing Speaker Scenes.

In the competing speaker environments, human listeners need to focus or switch their auditory attention according to dynamic intentions. The reliable cortical tracking ability to the speech envelope is an effective feature for decoding the target speech from the neural signals. Moreover, previous studies revealed that the root mean square (RMS)–level–based speech segmentation made a great contribution to the target speech perception with the modulation of sustained auditory attention. This study further investigated the effect of the RMS-level–based speech segmentation on the auditory attention decoding (AAD) performance with both sustained and switched attention in the competing speaker auditory scenes. Objective biomarkers derived from the cortical activities were also developed to index the dynamic auditory attention states. In the current study, subjects were asked to concentrate or switch their attention between two competing speaker streams. The neural responses to the higher- and lower-RMS-level speech segments were analyzed via the linear temporal response function (TRF) before and after the attention switching from one to the other speaker stream. Furthermore, the AAD performance decoded by the unified TRF decoding model was compared to that by the speech-RMS-level–based segmented decoding model with the dynamic change of the auditory attention states. The results showed that the weight of the typical TRF component approximately 100-ms time lag was sensitive to the switching of the auditory attention. Compared to the unified AAD model, the segmented AAD model improved attention decoding performance under both the sustained and switched auditory attention modulations in a wide range of signal-to-masker ratios (SMRs). In the competing speaker scenes, the TRF weight and AAD accuracy could be used as effective indicators to detect the changes of the auditory attention. In addition, with a wide range of SMRs (i.e., from 6 to –6 dB in this study), the segmented AAD model showed the robust decoding performance even with short decision window length, suggesting that this speech-RMS-level–based model has the potential to decode dynamic attention states in the realistic auditory scenarios.

Subdiffusion and Many-Body Quantum Chaos with Kinetic Constraints.

We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic timescales are given by the inverse gap of an effective Hamiltonian-or equivalently, a transfer matrix describing a classical Markov process. Our approach allows us to connect directly the Thouless time, t_{Th}, determined by the spectral form factor, to transport properties and linear-response correlators. Using tensor network methods, we determine the dynamical exponent z for a number of constrained, conserving models. We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics, depending on the severity of the constraints. In particular, we show that quantum systems with "Fredkin" constraints exhibit anomalous transport with dynamical exponent z≃8/3.

Spectral analysis method of electrophysical non-destructive testing data

A computational method for spectral analysis of the electrophysical test results based on sequential mathematical algorithm transformations using a discrete linear response function has been developed. The procedure for constructing spectral functions has a certain order and is aimed at obtaining adequate results of the experimental sample approximation in the frequency domain. It is shown that use of the low-frequency FIR filter function as part of the convolution, together with the fast Fourier transform, gives accurate results for structural inhomogeneities localization in welded joints.

First Demonstration of Calibrated Color Imaging by the CAOS Camera

The Coded Access Optical Sensor (CAOS) camera is a novel, single unit, full spectrum (UV to short-wave IR bands), linear, high dynamic range (HDR) camera. In this paper, calibrated color target imaging using the CAOS camera and a comparison to a commercial HDR CMOS camera is demonstrated for the first time. The first experiment using a calibrated color check chart indicates that although the CMOS sensor-based camera has an 87 dB manufacturer-specified HDR range, unrestricted usage of this CMOS camera’s output range greatly fails quality color recovery. On the other hand, the intrinsically linear full dynamic range operation CAOS camera color image recovery generally matches the restricted linear-mode commercial CMOS sensor-based camera recovery for the presented 39.5 dB non-HDR target that also matches the near 40 dB linear camera response function (CRF) range of the CMOS camera. Specifically, compared to the color checker chart manufacturer provided XYZ values for the calibrated target, percentage XYZ mean errors of 8.3% and 10.9% are achieved for the restricted linear range CMOS camera and CAOS camera, respectively. An alternate color camera assessment gives CIE ΔE00 mean values of 4.59 and 5.7 for the restricted linear range CMOS camera and CAOS camera, respectively. Unlike the CMOS camera lens optics and its photo-detection electronics, no special linear response optics and photo-detector designs were used for the experimental CAOS camera, nevertheless, a good and equivalent color recovery was achieved. Given the limited HDR linear range capabilities of a CMOS camera and the intrinsically wide linear HDR capability of a CAOS camera, a combined CAOS-CMOS mode of the CAOS smart camera is prudent and can empower HDR color imaging. Applications for such a hybrid camera includes still photography imaging, especially for quantitative imaging of biological samples, valuable artworks and archaeological artefacts that require authentic color data generation for reliable medical decisions as well as forgery preventing verifications.

Spatial Resolution and Frequency Characteristics for Dose Modulation on the TrueBeam Medical Accelerator

Purpose: To study the spatial resolution achievable by dose modulation in a water phantom using a multi-leaf collimator, jaws and their combination. To estimate the power spectrum density of the useful signal (dose distribution) and statistical noise, evaluate the frequency interval containing the useful signal.
 Material and methods: Using the Gafchromic EBT2 radiochromic film, nested squares dose patterns formed in a water-equivalent phantom by 6 and 15 MV photon beams of the TrueBeam medical accelerator, jaws, a multi-leaf collimator, and a combination of these devices were measured. Dose response to step function (ESF) data was extracted from the penumbra and the linear photon source dose response function (LSF) was calculated. To move to frequency domain, fast Fourier transform was performed over the obtained datasets, as well as over individual LSF peaks, and then power spectra densities were calculated. The Nyquist frequency associated with data sampling was 1.42 mm-1, the Hann window was used to minimize leakage effect.
 Results: The shape of the obtained LSF peaks was approximated by a sum of two Gaussian distributions with the same center positions but different widths. The LSF peak width at half maximum (FWHM) was 1.7-3.9 mm depending on the modulation device. No significant difference was observed in the peak widths at energies of 6 and 15 MV. In most cases, the width of the peak along the X-axis was wider than along the Y-axis. The power spectrum of the useful signal had a maximum near zero frequency, a 50 % level was near 0.09 mm-1 and its high frequency limit was about 0.4 mm-1. Above this value, only the spectrum of statistical noise was recorded, uniformly distributed over frequency.
 Conclusion: The obtained values of the LSF peak width in the range 1.7-3.9 mm characterize the ability of dose modulation by the considered devices or their combination, which can be significant for treatment of small targets (less than 3-4 cm), where these limits of spatial resolution can be reached. The obtained relationships in frequency domain can be used for optimal removal of statistical noise using Wiener filters from profiles or two-dimensional dose distributions.

Toward witnessing molecular exciton entanglement from spectroscopy

Entanglement is a defining feature of quantum mechanics that can be a resource in engineered and natural systems, but measuring entanglement in experiment remains elusive especially for large chemical systems. Most practical approaches require determining and measuring a suitable entanglement witness which provides some level of information about the entanglement structure of the probed state. A fundamental quantity of quantum metrology is the quantum Fisher information (QFI) which is a rigorous witness of multipartite entanglement that can be evaluated from linear response functions for certain states. In this work, we explore measuring the QFI of molecular exciton states of the first-excitation subspace from spectroscopy. In particular, we utilize the fact that the linear response of a pure state subject to a weak electric field over all possible driving frequencies encodes the variance of the collective dipole moment in the probed state, which is a valid measure for QFI. The systems that are investigated include the molecular dimer, $N$-site linear aggregate with nearest-neighbor coupling, and $N$-site circular aggregate, all modeled as a collection of interacting qubits. Our theoretical analysis shows that the variance of the collective dipole moment in the brightest dipole-allowed eigenstate is the maximum QFI. The optical response of a thermally equilibrated state in the first-excitation subspace is also a valid QFI. Theoretical predictions of the measured QFI for realistic linear dye aggregates as a function of temperature and energetic disorder due to static variations of the host matrix show that 2- to 3-partite entanglement is realizable. This work lays some groundwork and inspires measurement of multipartite entanglement of molecular excitons with ultrafast pump-probe experiments.

Identification of linear response functions from arbitrary perturbation experiments in the presence of noise – Part 1: Method development and toy model demonstration

Abstract. Existent methods to identify linear response functions from data require tailored perturbation experiments, e.g., impulse or step experiments, and if the system is noisy, these experiments need to be repeated several times to obtain good statistics. In contrast, for the method developed here, data from only a single perturbation experiment at arbitrary perturbation are sufficient if in addition data from an unperturbed (control) experiment are available. To identify the linear response function for this ill-posed problem, we invoke regularization theory. The main novelty of our method lies in the determination of the level of background noise needed for a proper estimation of the regularization parameter: this is achieved by comparing the frequency spectrum of the perturbation experiment with that of the additional control experiment. The resulting noise-level estimate can be further improved for linear response functions known to be monotonic. The robustness of our method and its advantages are investigated by means of a toy model. We discuss in detail the dependence of the identified response function on the quality of the data (signal-to-noise ratio) and on possible nonlinear contributions to the response. The method development presented here prepares in particular for the identification of carbon cycle response functions in Part 2 of this study (Torres Mendonça et al., 2021a). However, the core of our method, namely our new approach to obtaining the noise level for a proper estimation of the regularization parameter, may find applications in also solving other types of linear ill-posed problems.