Inverse Modeling Scheme Research Articles

SCIAMACHY formaldehyde observations: constraint for isoprene emission estimates over Europe?

Abstract. Formaldehyde (HCHO) is an important intermediate compound in the degradation of volatile organic compounds (VOCs) in the troposphere. Sources of HCHO are largely dominated by its secondary production from VOC oxidation, methane and isoprene being the main precursors in unpolluted areas. As a result of the moderate lifetime of HCHO, its spatial distribution is determined by reactive hydrocarbon emissions. We focus here on Europe and investigate the influence of the different emissions on HCHO tropospheric columns with the CHIMERE chemical transport model in order to interpret the comparisons between SCIAMACHY and simulated HCHO columns. Europe was never specifically studied before for these purposes using satellite observations. The bias between measurements and model is less than 20% on average. The differences are discussed according to the errors on the model and the observations and remaining discrepancies are attributed to a misrepresentation of biogenic emissions. This study requires the characterisation of: (1) the model errors and performances concerning formaldehyde. The errors on the HCHO columns, mainly related to chemistry and mixed emission types, are evaluated to 2×1015 molecule/cm2 and the model performances evaluated using surface measurements are satisfactory (~13%); (2) the observation errors that define the needs in spatial and temporal averaging for meaningful comparisons. Using SCIAMACHY observations as constraint for biogenic isoprene emissions in an inverse modelling scheme reduces their uncertainties by about a factor of two in region of intense emissions. The retrieved correction factors for the isoprene emissions range from a factor of 0.15 (North Africa) to a factor of 2 (Poland, the United Kingdom) depending on the regions.

Rapid recent warming on Rutford Ice Stream, West Antarctica, from borehole thermometry

[1] The Antarctic Peninsula has warmed faster than the global average rate of warming during the last century. Due to limited availability of long term meteorological records, the geographical extent of this rapid warming is poorly defined. We collected borehole temperature measurements in the upper 300 m of Rutford Ice Stream, West Antarctica, and employed an inverse modeling scheme with a heat diffusion-advection equation to determine the recent surface temperature history of the borehole position. Our results reveal recent warming of 0.17 ± 0.07°C (decade)−1 since 1930. This result suggests that, at least in an attenuated form, the rapid warming observed over the Antarctic Peninsula extends as far south as Rutford Ice Stream. This result agrees with other recent results that show a warming trend across much of the West Antarctic Ice Sheet.

Parameter conditioning with a noisy Monte Carlo genetic algorithm for estimating effective soil hydraulic properties from space

The estimation of effective soil hydraulic parameters and their uncertainties is a critical step in all large‐scale hydrologic and climatic model applications. Here a scale‐dependent (top‐down) parameter estimation (inverse modeling) scheme called the noisy Monte Carlo genetic algorithm (NMCGA) was developed and tested for estimating these effective soil hydraulic parameters and their uncertainties. We tested our method using three case studies involving a synthetic pixel (pure and mixed) where all modeling conditions are known, and with actual airborne remote sensing (RS) footprints and a satellite RS footprint. In the synthetic case studies under pure (one soil texture) and mixed‐pixel (multiple soil textures) conditions, NMCGA performed well in estimating the effective soil hydraulic parameters even with pixel complexities contributed by various soil types and land management practices (rain‐fed/irrigated). With the airborne and satellite remote sensing cases, NMCGA also performed well for estimating effective soil hydraulic properties so that when applied in forward stochastic simulation modeling it can mimic large‐scale soil moisture dynamics. The results also suggest a possible scaling down of the effective soil water retention curve θ(h) at the larger satellite remote sensing pixel compared with the airborne remote sensing pixel. However, it did not generally imply that all effective soil hydraulic parameters should scale down like the soil water retention curve. The reduction of the soil hydraulic parameters was most profound in the saturated soil moisture content (θsat) as we relaxed progressively the soil hydraulic parameter search spaces in our satellite remote sensing studies. Overall, the NMCGA framework was found to be very promising in the inverse modeling of remotely sensed near‐surface soil moisture for estimating the effective soil hydraulic parameters and their uncertainties at the remote sensing footprint/climate model grid.

Inverse modelling of the spatial distribution of NO<sub>x</sub> emissions on a continental scale using satellite data

Abstract. The recent important developments in satellite measurements of the composition of the lower atmosphere open the challenging perspective to use such measurements as independent information on sources and sinks of atmospheric pollutants. This study explores the possibility to improve estimates of gridded NOx emissions used in a continental scale chemistry transport model (CTM), CHIMERE, by employing measurements performed by the GOME and SCIAMACHY instruments. We set-up an original inverse modelling scheme that not only enables a computationally efficient optimisation of the spatial distribution of seasonally averaged NOx emissions (during summertime), but also allows estimating uncertainties in input data and a priori emissions. The key features of our method are (i) replacement of the CTM by a set of empirical models describing the relationships between tropospheric NO2 columns and NOx emissions with sufficient accuracy, (ii) combination of satellite data for tropospheric NO2 columns with ground based measurements of near surface NO2 concentrations, and (iii) evaluation of uncertainties in a posteriori emissions by means of a special Bayesian Monte-Carlo experiment which is based on random sampling of errors of both NO2 columns and emission rates. We have estimated the uncertainty in a priori emissions based on the EMEP emission inventory to be about 1.9 (in terms of geometric standard deviation) and found the uncertainty in a posteriori emissions obtained from our inverse modelling scheme to be significantly lower (about 1.4). It is found also that a priori NOx emission estimates are probable to be persistently biased in many regions of Western Europe, and that the use of a posteriori emissions in the CTM improves the agreement between the modelled and measured data.

Determination of the effective transport coefficients of pore networks from transient immiscible and miscible displacement experiments

Transient immiscible and miscible displacement experiments performed on artificial glass‐etched pore networks are used to determine the capillary and relative permeability curves as well as the hydrodynamic dispersion coefficients. The transient responses of the total and axial distribution of the wetting phase (WP) saturation and the pressure drop across the pore network are introduced into an inverse modeling scheme to estimate the imbibition capillary pressure and relative permeability curves of pore networks by varying the capillary number, the contact angle, and the shear‐thinning rheology of the nonwetting phase (NWP). The temporal evolution of the spatial distribution of the solute concentration profiles over selected areas of the pore network is fitted to analytical one‐dimensional solute dispersion models to estimate the longitudinal dispersion coefficient as a function of the Peclet number, in single‐ and dual‐pore networks. Under an unfavorable viscosity ratio the growth pattern is a two‐dimensional fractal object, its description with the one‐dimensional macroscopic two‐phase flow equations is questionable, a high uncertainty is introduced into the capillary pressure curve, whereas “average” relative permeability functions are estimated. The relative permeability of the NWP may be a decreasing or increasing function of the capillary number over the viscous or capillary fingering pattern, respectively. The relative permeability of the WP is an increasing function of the capillary number and increases weakly with the NWP shear‐thinning rheology strengthening. The longitudinal dispersion coefficient varies nonlinearly with Peclet number following power laws with exponents ranging from 1 to 2 and depending on the relative contribution fraction of the macrodispersion (associated with the spatial variation of pore sizes) and Taylor dispersion (associated with the flow channeling) to the entire process.

Obtaining the Spatial Distribution of Water Content along a TDR Probe Using the SCEM‐UA Bayesian Inverse Modeling Scheme

Time domain reflectometry (TDR) has become one of the standard methods for the measurement of the temporal and spatial distribution of water saturation in soils. Current waveform analysis methodology gives a measurement of the average water content along the length of the TDR probe. Close inspection of TDR waveforms shows that heterogeneity in water content along the probe can be seen in the TDR waveform. We present a comprehensive approach to TDR waveform analysis that gives a quantitative estimate of the dielectric permittivity profile along the length of the probe and, therefore, the distribution of water content. The approach is based on the combination of a multisection scatter function model for the TDR measurement system with the shuffled complex evolution Metropolis algorithm (SCEM‐UA). This combined approach allows for the estimation of the 40 parameters in the transmission line model using a series of simple calibration measurements. The proof of concept is given with measurements in a layered system consisting of air and water. Finally, TDR waveforms from layered soil samples were analyzed to estimate the distribution of the water content along the length of the probe. Results show that the proposed method provides much more reproducible results than obtained with the traditional travel time method. Because the proposed method can be fully automated, it increases the applicability of the TDR method, especially in applications where detailed (real‐time) data are required on heterogeneous infiltration.

Obtaining the Spatial Distribution of Water Content along a TDR Probe Using the SCEM-UA Bayesian Inverse Modeling Scheme

Time domain reflectometry (TDR) has become one of the standard methods for the measurement of the temporal and spatial distribution of water saturation in soils. Current waveform analysis methodology gives a measurement of the average water content along the length of the TDR probe. Close inspection of TDR waveforms shows that heterogeneity in water content along the probe can be seen in the TDR waveform. We present a comprehensive approach to TDR waveform analysis that gives a quantitative estimate of the dielectric permittivity profile along the length of the probe and, therefore, the distribution of water content. The approach is based on the combination of a multisection scatter function model for the TDR measurement system with the shuffled complex evolution Metropolis algorithm (SCEM-UA). This combined approach allows for the estimation of the 40 parameters in the transmission line model using a series of simple calibration measurements. The proof of concept is given with measurements in a layered system consisting of air and water. Finally, TDR waveforms from layered soil samples were analyzed to estimate the distribution of the water content along the length of the probe. Results show that the proposed method provides much more reproducible results than obtained with the traditional travel time method. Because the proposed method can be fully automated, it increases the applicability of the TDR method, especially in applications where detailed (real-time) data are required on heterogeneous infiltration.

Application of Neural Inverse Modeling Scheme to Optimal Parameter Tuning of Filter Test Equipment

Generally, the yield rate of semiconductors is the major factor that affects directly the price of semiconductors. For a high yield rate of semiconductors, the air inside clean room is needed to be purified and high efficient filters are used for this. The filter are made of super-fine fiber and certain pinholes can be easily produced on the filter's surface by inadvertent manufacturing. As these pinholes are not easily detected with the bare sight, these pinholes exert a negative impact to filtration performance of the filter. In this research, not only the automatic test equipment for detecting pinholes is proposed, but also inverse modeling scheme based on artificial neural network is applied for tuning of its important parameters.

역히스테리시스 모델과 PID-신경회로망 제어기를 이용한 압전구동기의 정밀 위치제어

A piezoelectric actuator yields hysteresis effect due to its composed ferroelectric. Hysteresis nonlinearty is neglected when a piezoelectric actuator moves with short stroke. However when it moves with long stroke and high frequency, the hysteresis nonlinearty can not be neglected. The hysteresis nonlinearty of piezoelectric actuator degrades the control performance in precision position control. In this paper, in order to improve the control performance of piezoelectric actuator, an inverse modeling scheme is proposed to compensate the hysteresis nonlinearty. And feedforward - feedback controller is proposed to give a good tracking performance. The Feedforward controller is an inverse hysteresis model, base on neural network and the feedback control is implemented with PID control. To show the feasibility of the proposed controller and hysteresis modeling, some experiments have been carried out. It is concluded that the proposed control scheme gives good tracking performance.

Inverse modeling of carbon monoxide surface emissions using Climate Monitoring and Diagnostics Laboratory network observations

A three‐dimensional (3‐D) inverse modeling scheme is used to constrain the direct surface emissions of carbon monoxide CO. A priori estimates of CO emissions are taken from various inventories and are included in the IMAGES model to compute the distribution of CO. The modeled CO mixing ratios are compared with observations at 39 CMDL stations, averaged over the years 1990–1996. The interannual variability of CO sources is therefore ignored. We show that the method used (time‐dependent synthesis inversion) is able to adjust the surface fluxes on a monthly basis in order to improve the agreement between the observed and the modeled CO mixing ratios at the stations. The Earth surface is divided into regions. The spatial distribution of CO sources is fixed inside each of these regions. The inversion scheme optimizes the intensities of the emissions fluxes for the following processes: technological activities, forest and savanna burning, agricultural waste burning and fuelwood use, soil/vegetation emissions, and oceanic emissions. The inversion significantly reduces the uncertainties on the surface sources over Europe, North America and Asia. The most striking result is the increase (almost by a factor of 2) of CO flux from Asia in all a posteriori scenarios. The uncertainties on the Southern Hemisphere emissions remain large after the inversion, because the current observational surface network is too sparse at these latitudes. The inversion, moreover, shifts the peak in biomass burning emissions in the Southern Hemisphere by one month. This temporal shift ensures a better match of the observed and modeled CO seasonal cycle at the Ascension Island station. We also attempted to optimize the annual and global productions of CO due to methane and NMHC. With the current set of data, the scheme was not able to differentiate between these two sources, and hence only the total chemical production of CO can be optimized.

Validation of aquifer parameter determination by extrapolation fitting and treating thickness as an unknown

A genetic algorithm is used here to guess-estimate a close-to-true set of trial values as input to a three-staged quasi-linear inverse modeling scheme for the determination of aquifer parameters. To validate the parameter determination, in addition to the conventional measures of misfit root mean squares (rms) and distribution, the aquifer thickness is treated as an unknown parameter and the model parameters are further evaluated by comparing the expected drawdown with the observed drawdown at wells which are not used for parameter determination (extrapolation fitting). The method is tested with synthetic and observed drawdown data from five partially screened monitoring wells in a water-table aquifer. Test results for synthetic data doped with random errors indicate that modeling based on two or more well data can yield satisfactory parameter values and extrapolation misfits in an ideal aquifer. For field data, the results indicate that a model misfit on par with the standard error of the data is achievable for each individual well or a combination of two wells but the extrapolation misfit distributions are generally biased and their rms are far greater—possibly due to aquifer heterogeneity. Consistent parameter values can be obtained from the geometric means for multiple runs of the genetic-inverse modeling of one-, two-, three-, and four-well data. Our test aquifer can be represented by a set of parameters with 10 to 15% consistency, including transmissivity, storativity, vertical-to-horizontal conductivity ratio, and storativity-to-specific yield ratio, as affirmed by model aquifer thicknesses that deviate less than 10% from the actual thickness.

Inverse modeling for locating dense nonaqueous pools in groundwater under steady flow conditions

In this work we develop an inverse modeling procedure to identify the location and the dimensions of a single‐component dense nonaqueous phase liquid (DNAPL) pool in a saturated porous medium under steady flow conditions. The inverse problem is formulated as a least squares minimization problem and solved by a search procedure based on the Levenberg‐Marquardt method. Model output is calculated by an existing three‐dimensional analytical model describing the transport of solute from a dissolving distributed noise upon the forward model‐generated concentration field. We further test the algorithm's ability to predict the location and size of a DNAPL pool placed in a controlled three‐dimensional bench‐scale experiment. In this case we apply the Levenberg‐Marquardt algorithm to the minimization of three types of residuals: ordinary residuals, weighted residuals with weights equal to the square of the inverse of the observations, and weighted residuals with weights obtained by adding a constant term to the observed concentrations. The results are sensitive to the location of the observation wells and to the type of residuals minimized. In general, better results in terms of pool location and dimensions were obtained by the minimization of weighted residuals with weights obtained by adding a constant term to the observed concentrations. The results also indicate that the inverse problem is nonunique and nonconvex even in the absence of observation errors. Finally, the sensitivity of the inverse modeling scheme to transport parameter uncertainty was addressed. The inverse solution was found to be extremely sensitive to errors in the dispersion coefficients and relatively insensitive to errors in the mass transfer coefficient.

Integrated gravity and wide-angle seismic inversion fortwo-dimensional crustal modelling

An inversion scheme for integrated wide-angle seismic and gravity modelling of 2-D crustal structure is presented. The inversion scheme uses a standard least-squares, linearized iterative approach, which relies on forward algorithms for calculating gravity responses and seismic traveltimes. The presented scheme has been integrated in an existing and widely used program package. Wide-angle seismic data have the potential to provide detailed knowledge about structures in the crust and upper mantle. The corresponding density distribution may, however, provide essential geodynamic information in relation to isostasy, which seismic data cannot provide. In order to describe the interrelation between velocity and density for crustal rock types, numerous empirical relations linking P-wave velocity and density have been estimated over the last 40 years. These experiments have been based on both laboratory experiments and well log data. We use such relations as prior constraints on how velocities and densities should be linked during the joint inversion. These constraints may be narrow in regions of the model where the chosen velocity–density relation is expected to be trustworthy, and broader in parts of the model where the velocity–density relation is believed to be less certain. The velocity–density model of the subsurface is described by a layered, blocky structure defined by velocity, density and depth nodes. During inversion, all three parameter types may vary. The inverse scheme is tested in three synthetic examples, which resemble important problems likely to occur in crustal modelling. In particular, we focus on how the inverse estimates are influenced by the interplay between seismic data and gravity data, and the uncertainties of the relation between velocity and density. Important advantages of the least-squares inverse modelling scheme, as opposed to manual trial-and-error modelling, are that data are assured to be fitted according to a pre-specified norm, the automated interpretation reduces the time used for modelling, and a more exhaustive analysis of the gravimetric and seismic data sets can be made.

Optical remote sensing of marine constituents in coastal waters: a feasibility study

Optical remote sensing of ocean color is a well-established technique for inferring ocean properties. However, most retrieval algorithms are based on the assumption that the radiance received by satellite instruments is affected only by the phytoplankton pigment concentration and correlated substances. This assumption works well for open ocean water but becomes questionable for coastal waters. To reduce uncertainties associated with this assumption, we developed a new algorithm for the retrieval of marine constituents in a coastal environment. We assumed that ocean color can be adequately described by a three-component model made up of chlorophyll a, suspended matter, and yellow substance. The simultaneous retrieval of these three marine constituents and of the atmospheric aerosol content was accomplished through an inverse-modeling scheme in which the difference between simulated radiances exiting the atmosphere and radiances measured with a satellite sensor was minimized. Simulated radiances were generated with a comprehensive radiative transfer model that is applicable to the coupled atmosphere-ocean system. The method of simulated annealing was used to minimize the difference between measured and simulated radiances. To evaluate the retrieval algorithm, we used simulated (instead of measured) satellite-received radiances that were generated for specified concentrations of aerosols and marine constituents, and we tested the ability of the algorithm to retrieve assumed concentrations. Our results require experimental validation but show that the retrieval of marine constituents in coastal waters is possible.

Radial profiles of temperature and viscosity in the Earth's mantle inferred from the geoid and lateral seismic structure

In the framework of dynamical modelling of the geoid, we have estimated basic features of the radial profile of temperature in the mantle. The applied parameterization of the geotherm directly characterizes thermal boundary layers and values of the thermal gradient in the upper and lower mantle. In the inverse modelling scheme these parameters are related to the observables (geoid and seismic structure of the mantle) through the viscosity profile which is parameterized as an exponential function of pressure and temperature. We have tested ∼10 4 model geotherms. For each of them we have found proper rheological parameters by fitting the geoid with the aid of a genetic algorithm. The geotherms which best fit the geoid show a significant increase of temperature (∼600–800°C) close to the 660-km discontinuity. The value of the thermal gradient in the mid-mantle is found to be sub-adiabatic. Both a narrow thermal core–mantle boundary layer and a broad region with a superadiabatic regime can produce a satisfactory fit of the geoid. The corresponding viscosity profiles show similarities to previously presented models, in particular in the viscosity maximum occurring in the deep lower mantle. The best-fitting model predicts the values of activation volume V ∗ and energy E ∗ which are in a good agreement with the data from mineral physics, except for V ∗ in the lower mantle which is found somewhat lower than the estimate based on melting temperature analysis. An interesting feature of the viscosity profiles is a local decrease of viscosity somewhere between 500 and 1000 km depth which results from the steep increase of temperature in the vicinity of the 660-km discontinuity.

Thermal Remote Sensing of Surface Soil Water Content with Partial Vegetation Cover for Incorporation into Climate Models

This study outlines a method for the estimation of regional patterns of surface moisture availability (M(sub 0)) and fractional vegetation (Fr) in the presence of spatially variable vegetation cover. The method requires relating variations in satellite-derived (NOAA, Advanced Very High Resolution Radiometer (AVHRR)) surface radiant temperature to a vegetation index (computed from satellite visible and near-infrared data) while coupling this association to an inverse modeling scheme. More than merely furnishing surface soil moisture values, the method constitues a new conceptual and practical approach for combining thermal infrared and vegetation index measurements for incorporating the derived values of M(sub 0) into hydrologic and atmospheric prediction models. Application of the technique is demonstrated for a region in and around the city of Newcastle upon Tyne situated in the northeast of England. A regional estimate of M(sub 0) is derived and is probabbly good for fractional vegetation cover up to 80% before errors in the estimated soil water content become unacceptably large. Moreover, a normalization scheme is suggested from which a nomogram, `universal triangle,' is constructed and is seen to fit the observed data well. The universal triangle also simplifies the inclusion of remotely derived M(sub 0) in hydrology and meteorological models and is perhaps a practicable step toward integrating derived data from satellite measurements in weather forecasting.