Adaptive Covariance Estimation with model selection

We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud

Cationic double K-hole pre-edge states of CS2 and SF6

Recent advances in X-ray instrumentation have made it possible to measure the spectra of an essentially unexplored class of electronic states associated with double inner-shell vacancies. Using the technique of single electron spectroscopy, spectra of states in CS2 and SF6 with a double hole in the K-shell and one electron exited to a normally unoccupied orbital have been obtained. The spectra are interpreted with the aid of a high-level theoretical model giving excellent agreement with the experiment. The results shed new light on the important distinction between direct and conjugate shake-up in a molecular context. In particular, systematic similarities and differences between pre-edge states near single core holes investigated in X-ray absorption spectra and the corresponding states near double core holes studied here are brought out

Femtosecond Nuclear Motion of HCl Probed by Resonant X-ray Raman Scattering in the Cl 1s Region

Femtosecond dynamics are observed by resonant x-ray Raman scattering (RXS) after excitation along the dissociative Cl 1s→6ơ* resonance of gas-phase HCl. The short core-hole lifetime results in a complete breakdown of the common nondispersive behavior of soft-x-ray transitions between parallel potentials. We evidence a general phenomenon of RXS in the hard-x-ray region: a complete quenching of vibrational broadening. This opens up a unique opportunity for superhigh resolution x-ray spectroscopy beyond vibrational and lifetime limitations

High resolution measurements of partial photoionization cross sections in hollow lithium: a critical comparison with advanced many-body calculations

Photoelectron data for hollow lithium states obtained with unprecedented high spectral resolution and sensitivity are presented. A critical comparison is made with the most recent theoretical results. Partial cross sections are measured providing the first definitive test of advanced ab initio calculations for this highly excited four-body atomic system

Acetylacetone photodynamics at a seeded freeelectron laser

The first steps in photochemical processes, such as photosynthesis or animal vision, involve changes in electronic and geometric structure on extremely short time scales. Time-resolved photoelectron spectroscopy is a natural way to measure such changes, but has been hindered hitherto by limitations of available pulsed light sources in the vacuum-ultraviolet and soft Xray spectral region, which have insufficient resolution in time and energy simultaneously. The unique combination of intensity, energy resolution, and femtosecond pulse duration of the FERMI-seeded free-electron laser can now provide exceptionally detailed information on photoexcitation–deexcitation and fragmentation in pump-probe experiments on the 50- femtosecond time scale. For the prototypical system acetylacetone we report here electron spectra measured as a function of time delay with enough spectral and time resolution to follow several photoexcited species through well-characterized individual steps, interpreted using state-of-the-art static and dynamics calculations. These results open the way for investigations of photochemical processes in unprecedented detail

Simulation of solute transport in a heterogeneous vadose zone describing the hydraulic properties using a multistep stochastic approach

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95612/1/wrcr10619.pd

Stochastic upscaling of hydrodynamic dispersion and retardation factor in a physically and chemically heterogeneous tropical soil

[EN] Stochastic upscaling of flow and reactive solute transport in a tropical soil is performed using real data collected in the laboratory. Upscaling of hydraulic conductivity, longitudinal hydrodynamic dispersion, and retardation factor were done using three different approaches of varying complexity. How uncertainty propagates after upscaling was also studied. The results show that upscaling must be taken into account if a good reproduction of the flow and transport behavior of a given soil is to be attained when modeled at larger than laboratory scales. The results also show that arrival time uncertainty was well reproduced after solute transport upscaling. This work represents a first demonstration of flow and reactive transport upscaling in a soil based on laboratory data. It also shows how simple upscaling methods can be incorporated into daily modeling practice using commercial flow and transport codes.The authors thank the financial support by the Brazilian National Council for Scientific and Technological Development (CNPq) (Project 401441/2014-8). The doctoral fellowship award to the first author by the Coordination of Improvement of Higher Level Personnel (CAPES) is acknowledged. The first author also thanks the international mobility grant awarded by CNPq, through the Sciences Without Borders program (Grant Number: 200597/2015-9). The international mobility grant awarded by Santander Mobility in cooperation with the University of Sao Paulo is also acknowledged. DHI-WASI is gratefully thanked for providing a FEFLOW license.Almeida De-Godoy, V.; Zuquette, L.; Gómez-Hernández, JJ. (2019). Stochastic upscaling of hydrodynamic dispersion and retardation factor in a physically and chemically heterogeneous tropical soil. Stochastic Environmental Research and Risk Assessment. 33(1):201-216. https://doi.org/10.1007/s00477-018-1624-zS201216331Ahuja LR, Naney JW, Green RE, Nielsen DR (1984) Macroporosity to characterize spatial variability of hydraulic conductivity and effects of land management. Soil Sci Soc Am J 48:699. https://doi.org/10.2136/sssaj1984.03615995004800040001xBellin A, Lawrence AE, Rubin Y (2004) Models of sub-grid variability in numerical simulations of solute transport in heterogeneous porous formations: three-dimensional flow and effect of pore-scale dispersion. Stoch Environ Res Risk Assess 18:31–38. https://doi.org/10.1007/s00477-003-0164-2Brent RP (1973) Algorithms for minimization without derivatives. Prentice Hall, Englewood CliffsBrusseau ML (1998) Non-ideal transport of reactive solutes in heterogeneous porous media: 3. model testing and data analysis using calibration versus prediction. J Hydrol 209:147–165. https://doi.org/10.1016/S0022-1694(98)00121-8Brusseau ML, Srivastava R (1999) Nonideal transport of reactive solutes in heterogeneous porous media: 4. Analysis of the cape cod natural-gradient field experiment. Water Resour Res 35:1113–1125. https://doi.org/10.1029/1998WR900019Brutsaert W (1967) Some methods of calculating unsaturated permeability. Trans ASAE 10:400–404Cadini F, De Sanctis J, Bertoli I, Zio E (2013) Upscaling of a dual-permeability Monte Carlo simulation model for contaminant transport in fractured networks by genetic algorithm parameter identification. Stoch Environ Res Risk Assess 27:505–516. https://doi.org/10.1007/s00477-012-0595-8Cambardella CA, Moorman TB, Parkin TB, Karlen DL, Novak JM, Turco RF, Konopka AE (1994) Field-scale variability of soil properties in central iowa soils. Soil Sci Soc Am J 58:1501. https://doi.org/10.2136/sssaj1994.03615995005800050033xCapilla JE, Rodrigo J, Gómez-Hernández JJ (1999) Simulation of non-Gaussian transmissivity fields honoring piezometric data and integrating soft and secondary information. Math Geol 31:907–927. https://doi.org/10.1023/A:1007580902175Cassiraga EF, Fernàndez-Garcia D, Gómez-Hernández JJ (2005) Performance assessment of solute transport upscaling methods in the context of nuclear waste disposal. Int J Rock Mech Min Sci 42:756–764. https://doi.org/10.1016/j.ijrmms.2005.03.013Corey AT (1977) Mechanics of heterogeneous fluids in porous media. Water Resources Publications, Fort Collins, CO, p 259Dagan G (1989) Flow and transport in porous formations. Springer, Berlin. https://doi.org/10.1007/978-3-642-75015-1Dagan G (2004) On application of stochastic modeling of groundwater flow and transport. Stoch Environ Res Risk Assess. https://doi.org/10.1007/s00477-004-0191-7de Azevedo AAB, Pressinotti MMN, Massoli M (1981) Sedimentological studies of the Botucatu and Pirambóia formations in the region of Santa Rita do Passa Quatro (In portuguese). Rev do Inst Geológico 2:31–38. https://doi.org/10.5935/0100-929X.19810003Deng H, Dai Z, Wolfsberg AV, Ye M, Stauffer PH, Lu Z, Kwicklis E (2013) Upscaling retardation factor in hierarchical porous media with multimodal reactive mineral facies. Chemosphere 91:248–257. https://doi.org/10.1016/j.chemosphere.2012.10.105Diersch H-JG (2014) Finite element modeling of flow, mass and heat transport in porous and fractured media. Springer, Berlin. https://doi.org/10.1007/978-3-642-38739-5Dippenaar MA (2014) Porosity reviewed: quantitative multi-disciplinary understanding, recent advances and applications in vadose zone hydrology. Geotech Geol Eng 32:1–19. https://doi.org/10.1007/s10706-013-9704-9Fagundes JRT, Zuquette LV (2011) Sorption behavior of the sandy residual unconsolidated materials from the sandstones of the Botucatu Formation, the main aquifer of Brazil. Environ Earth Sci 62:831–845. https://doi.org/10.1007/s12665-010-0570-yFenton GA, Griffiths DV (2008) Risk assessment in geotechnical engineering. Wiley, p 463Fernàndez-Garcia D, Gómez-Hernández JJ (2007) Impact of upscaling on solute transport: Traveltimes, scale dependence of dispersivity, and propagation of uncertainty. Water Resour Res. https://doi.org/10.1029/2005WR004727Fernàndez-Garcia D, Llerar-Meza G, Gómez-Hernández JJ (2009) Upscaling transport with mass transfer models: mean behavior and propagation of uncertainty. Water Resour Res. https://doi.org/10.1029/2009WR007764Feyen L, Gómez-Hernández JJ, Ribeiro PJ, Beven KJ, De Smedt F (2003a) A Bayesian approach to stochastic capture zone delineation incorporating tracer arrival times, conductivity measurements, and hydraulic head observations. Water Resour Res. https://doi.org/10.1029/2002WR001544Feyen L, Ribeiro PJ, Gómez-Hernández JJ, Beven KJ, De Smedt F (2003b) Bayesian methodology for stochastic capture zone delineation incorporating transmissivity measurements and hydraulic head observations. J Hydrol 271:156–170. https://doi.org/10.1016/S0022-1694(02)00314-1Forsythe GE, Malcolm MA, Moler CB (1976) Computer methods for mathematical computations. Prentice-Hall, Englewood Cliffs, p 259Freeze R, Cherry J (1979) Groundwater. PrenticeHall Inc, Englewood cliffs, p 604Frippiat CC, Holeyman AE (2008) A comparative review of upscaling methods for solute transport in heterogeneous porous media. J Hydrol 362:150–176. https://doi.org/10.1016/j.jhydrol.2008.08.015Fu J, Gómez-Hernández JJ (2009) Uncertainty assessment and data worth in groundwater flow and mass transport modeling using a blocking Markov chain Monte Carlo method. J Hydrol 364:328–341. https://doi.org/10.1016/j.jhydrol.2008.11.014Gelhar LW, Axness CL (1983) Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour Res 19:161–180. https://doi.org/10.1029/WR019i001p00161Gelhar LW, Welty C, Rehfeldt KR (1992) A critical review of data on field-scale dispersion in aquifers. Water Resour Res 28:1955–1974. https://doi.org/10.1029/92WR00607Giacheti HL, Rohm SA, Nogueira JB, Cintra JCA (1993) Geotechnical properties of the Cenozoic sediment (in protuguese). In: Albiero JH, Cintra JCA (eds) Soil from the interior of São Paulo. ABMS, Sao Paulo, pp 143–175Gómez-Hernandez JJ (1990) A stochastic approach to the simulation of block conductivity fields conditional upon data measured at a smaller scale. Stanford University, StanfordGómez-Hernández JJ, Gorelick SM (1989) Effective groundwater model parameter values: influence of spatial variabiity of hydraulic conductivity, leackance, and recharge. Water Resour Res 25:405–419Gómez-Hernández JJ, Journel A (1993) Joint sequential simulation of multigaussian fields. In: Geostatistics Tróia’92. pp 85–94. https://doi.org/10.1007/978-94-011-1739-5_8Gómez-Hernández JJ, Wen X-H (1994) Probabilistic assessment of travel times in groundwater modeling. Stoch Hydrol Hydraul 8:19–55. https://doi.org/10.1007/BF01581389Gómez-Hernández JJ, Fu J, Fernandez-Garcia D (2006) Upscaling retardation factors in 2-D porous media. In: Bierkens MFP, Gehrels JC, Kovar K (eds) Calibration and reliability in groundwater modelling: from uncertainty to decision making: proceedings of the ModelCARE 2005 conference held in The Hague, The Netherlands, 6–9 June, 2005. IAHS Publication, pp 130–136Goovaerts P (1999) Geostatistics in soil science: state-of-the-art and perspectives. Geoderma 89:1–45. https://doi.org/10.1016/S0016-7061(98)00078-0Jarvis NJ (2007) A review of non-equilibrium water fl ow and solute transport in soil macropores: principles, controlling factors and consequences for water quality. Eur J Soil Sci 58:523–546. https://doi.org/10.4141/cjss2011-050Jellali S, Diamantopoulos E, Kallali H, Bennaceur S, Anane M, Jedidi N (2010) Dynamic sorption of ammonium by sandy soil in fixed bed columns: evaluation of equilibrium and non-equilibrium transport processes. J Environ Manag 91:897–905. https://doi.org/10.1016/j.jenvman.2009.11.006Journel AG, Gomez-Hernandez JJ (1993) Stochastic imaging of the wilmington clastic sequence. SPE Form Eval 8:33–40. https://doi.org/10.2118/19857-PAJournel A, Deutsch C, Desbarats A (1986) Power averaging for block effective permeability. Proc SPE Calif Reg Meet. https://doi.org/10.2118/15128-MSKronberg BI, Fyfe WS, Leonardos OH, Santos AM (1979) The chemistry of some Brazilian soils: element mobility during intense weathering. Chem Geol 24:211–229. https://doi.org/10.1016/0009-2541(79)90124-4Lake LW (1988) The origins of anisotropy (includes associated papers 18394 and 18458). J Pet Technol 40:395–396. https://doi.org/10.2118/17652-PALawrence AE, Rubin Y (2007) Block-effective macrodispersion for numerical simulations of sorbing solute transport in heterogeneous porous formations. Adv Water Resour 30:1272–1285. https://doi.org/10.1016/j.advwatres.2006.11.005Lemke LD, Barrack WA II, Abriola LM, Goovaerts P (2004) Matching solute breakthrough with deterministic and stochastic aquifer models. Groundwater 42:920–934Li L, Zhou H, Gómez-Hernández JJ (2011a) A comparative study of three-dimensional hydraulic conductivity upscaling at the macro-dispersion experiment (MADE) site, Columbus Air Force Base, Mississippi (USA). J Hydrol 404:278–293. https://doi.org/10.1016/j.jhydrol.2011.05.001Li L, Zhou H, Gómez-Hernández JJ (2011b) Transport upscaling using multi-rate mass transfer in three-dimensional highly heterogeneous porous media. Adv Water Resour 34:478–489. https://doi.org/10.1016/j.advwatres.2011.01.001Logsdon Keller KE, Moorman TB (2002) Measured and predicted solute leaching from multiple undisturbed soil columns. Soil Sci Soc Am J 66:686–695. https://doi.org/10.2136/sssaj2002.6860Lourens A, van Geer FC (2016) Uncertainty propagation of arbitrary probability density functions applied to upscaling of transmissivities. Stoch Environ Res Risk Assess 30:237–249. https://doi.org/10.1007/s00477-015-1075-8Mahapatra IC, Singh KN, Pillai KG, Bapat SR (1985) Rice soils and their management. Indian J Agron 30:R1–R41Morakinyo JA, Mackay R (2006) Geostatistical modelling of ground conditions to support the assessment of site contamination. Stoch Environ Res Risk Assess 20:106–118. https://doi.org/10.1007/s00477-005-0015-4Moslehi M, de Barros FPJ, Ebrahimi F, Sahimi M (2016) Upscaling of solute transport in disordered porous media by wavelet transformations. Adv Water Resour 96:180–189. https://doi.org/10.1016/j.advwatres.2016.07.013Osinubi KJ, Nwaiwu CM (2005) Hydraulic conductivity of compacted lateritic soil. J Geotech Geoenviron Eng 131:1034–1041. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:8(1034)Remy N (2004) SGeMS: stanford geostatistical modeling software. Softw Man. https://doi.org/10.1007/978-1-4020-3610-1_89Renard P, de Marsily G (1997) Calculating equivalent permeability: a review. Adv Water Resour 20:253–278. https://doi.org/10.1016/S0309-1708(96)00050-4Robin MJL, Sudicky EA, Gillham RW, Kachanoski RG (1991) Spatial variability of strontium distribution coefficients and their correlation with hydraulic conductivity in the Canadian forces base borden aquifer. Water Resour Res 27:2619–2632. https://doi.org/10.1029/91WR01107Salamon P, Fernàndez-Garcia D, Gómez-Hernández JJ (2007) Modeling tracer transport at the MADE site: the importance of heterogeneity. Water Resour Res. https://doi.org/10.1029/2006WR005522Sánchez-Vila X, Carrera J, Girardi JP (1996) Scale effects in transmissivity. J Hydrol 183:1–22. https://doi.org/10.1016/S0022-1694(96)80031-XScheibe T, Yabusaki S (1998) Scaling of flow and transport behavior in heterogeneous groundwater systems. Adv Water Resour 22:223–238. https://doi.org/10.1016/S0309-1708(98)00014-1Selvadurai PA, Selvadurai APS (2014) On the effective permeability of a heterogeneous porous medium: the role of the geometric mean. Philos Mag 94:2318–2338. https://doi.org/10.1080/14786435.2014.913111Shackelford CD (1994) Critical concepts for column testing. J Geotech Eng 120:1804–1828. https://doi.org/10.1016/0148-9062(95)96996-OŠimůnek J, van Genuchten MT, Šejna M, Toride N, Leij FJ (1999) The STANMOD computer software for evaluating solute transport in porous media using analytical solutions of convection-dispersion equation. Riverside, CaliforniaTaskinen A, Sirviö H, Bruen M (2008) Modelling effects of spatial variability of saturated hydraulic conductivity on autocorrelated overland flow data: linear mixed model approach. Stoch Environ Res Risk Assess 22:67–82. https://doi.org/10.1007/s00477-006-0099-5Tuli A, Hopmans JW, Rolston DE, Moldrup P (2005) Comparison of air and water permeability between disturbed and undisturbed soils. Soil Sci Soc Am J 69:1361. https://doi.org/10.2136/sssaj2004.0332Tyukhova AR, Willmann M (2016) Conservative transport upscaling based on information of connectivity. Water Resour Res 52:6867–6880. https://doi.org/10.1002/2015WR018331van Genuchten MTh (1980) Determining transport parameters from solute displacement experiments. Research Report 118. U.S. Salinity Lab., Riverside, CAVanderborght J, Timmerman A, Feyen J (2000) Solute transport for steady-state and transient flow in soils with and without macropores. Soil Sci Soc Am J 64:1305–1317. https://doi.org/10.2136/sssaj2000.6441305xVanmarcke E (2010) Random fields: analysis and synthesis. World Scientific. MIT Press, Cambridge, MA, p 364Vishal V, Leung JY (2017) Statistical scale-up of 3D particle-tracking simulation for non-Fickian dispersive solute transport modeling. Environ Res Risk Assess, Stoch. https://doi.org/10.1007/s00477-017-1501-1Wen X-H, Gómez-Hernández JJ (1996) Upscaling hydraulic conductivities in heterogeneous media: an overview. J Hydrol 183:ix–xxxii. https://doi.org/10.1016/S0022-1694(96)80030-8Wen XH, Gómez-Hernández JJ (1998) Numerical modeling of macrodispersion in heterogeneous media: a comparison of multi-Gaussian and non-multi-Gaussian models. J Contam Hydrol 30:129–156. https://doi.org/10.1016/S0169-7722(97)00035-1Wen XH, Capilla JE, Deutsch CV, Gómez-Hernández JJ, Cullick AS (1999) A program to create permeability fields that honor single-phase flow rate and pressure data. Comput Geosci 25:217–230. https://doi.org/10.1016/S0098-3004(98)00126-5Wilding LP, Drees LR (1983) Spatial variability and pedology. In: Wilding LP, Smeck NE, Hall GF (eds) Pedogenesis and soil taxonomy: the soil orders. Elsevier, Amsterdam, pp 83–116Willmann M, Carrera J, Guadagnini A (2006) Block-upscaling of transport in heterogeneous aquifers. h2ogeo.upc.edu 1–7Xu Z, Meakin P (2013) Upscaling of solute transport in heterogeneous media with non-uniform flow and dispersion fields. Appl Math Model 37:8533–8542. https://doi.org/10.1016/j.apm.2013.03.070Zech A, Attinger S, Cvetkovic V, Dagan G, Dietrich P, Fiori A, Rubin Y, Teutsch G (2015) Is unique scaling of aquifer macrodispersivity supported by field data? Water Resour Res 51:7662–7679. https://doi.org/10.1002/2015WR017220Zhou H, Li L, Gómez-Hernández JJ (2010) Three-dimensional hydraulic conductivity upscaling in groundwater modeling. Comput Geosci 36:1224–1235. https://doi.org/10.1016/j.cageo.2010.03.008Zhou H, Li L, Hendricks Franssen H-J, Gómez-Hernández JJ (2012) Pattern recognition in a bimodal aquifer using the normal-score ensemble Kalman filter. Math Geosci 44:169–185. https://doi.org/10.1007/s11004-011-9372-

Pattern Recognition in a Bimodal Aquifer Using the Normal-Score Ensemble Kalman Filter

The ensemble Kalman filter (EnKF) is now widely used in diverse disciplines to estimate model parameters and update model states by integrating observed data. The EnKF is known to perform optimally only for multi-Gaussian distributed states and parameters. A new approach, the normal-score EnKF (NS-EnKF), has been recently proposed to handle complex aquifers with non-Gaussian distributed parameters. In this work, we aim at investigating the capacity of the NS-EnKF to identify patterns in the spatial distribution of the model parameters (hydraulic conductivities) by assimilating dynamic observations in the absence of direct measurements of the parameters themselves. In some situations, hydraulic conductivity measurements (hard data) may not be available, which requires the estimation of conductivities from indirect observations, such as piezometric heads. We show how the NS-EnKF is capable of retrieving the bimodal nature of a synthetic aquifer solely from piezometric head data. By comparison with a more standard implementation of the EnKF, the NS-EnKF gives better results with regard to histogram preservation, uncertainty assessment, and transport predictions. © 2011 International Association for Mathematical Geosciences.The authors gratefully acknowledge the financial support by the Spanish Ministry of Science and Innovation through project CGL2011-23295. The first author appreciates the financial aid from China Scholarship Council (CSC No. [2007]3020).Zhou, H.; Li, L.; Hendricks Franssen, H.; Gómez-Hernández, JJ. (2012). Pattern Recognition in a Bimodal Aquifer Using the Normal-Score Ensemble Kalman Filter. Mathematical Geosciences. 44(2):169-185. https://doi.org/10.1007/s11004-011-9372-3S169185442Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans Signal Process 50(2):174–188Bertino L, Evensen G, Wackernagel H (2003) Sequential data assimilation techniques in oceanography. Int Stat Rev 71(2):223–241Burgers G, Jan van Leeuwen P, Evensen G (1998) Analysis scheme in the ensemble Kalman filter. Mon Weather Rev 126(6):1719–1724Carrera J, Neuman SP (1986b) Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability, and solution algorithms. Water Resour Res 22(2):211–227Chen Y, Zhang D (2006) Data assimilation for transient flow in geologic formations via ensemble Kalman filter. Adv Water Resour 29:1107–1122Delhomme JP (1979) Spatial variability and uncertainty in groundwater flow parameters: a geostatistical approach. Water Resour Res 15(2):269–280Evensen G (1994) Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J Geophys Res 99(C5):10143–10162Evensen G (2007) Data assimilation: the ensemble Kalman filter. Springer, Berlin, 279 ppFernàndez-Garcia D, Illangasekare T, Rajaram H (2005) Differences in the scale dependence of dispersivity and retardation factors estimated from forced-gradient and uniform flow tracer tests in three-dimensional physically and chemically heterogeneous porous media. Water Resour Res 41(3):W03012Gómez-Hernández JJ, Journel AG (1993) Joint sequential simulation of multi-Gaussian fields. In: Soares A (ed) Geostatistics Tróia ’92, vol 1. Kluwer Academic, Dordrecht, pp 85–94Gómez-Hernández JJ, Wen XH (1998) To be or not to be multi-Gaussian? A reflection on stochastic hydrogeology. Adv Water Resour 21(1):47–61Gu Y, Oliver DS (2006) The ensemble Kalman filter for continuous updating of reservoir simulation models. J Energy Resour Technol 128:79–87Harbaugh AW, Banta ER, Hill MC, McDonald MG (2000) MODFLOW-2000, the U.S. geological survey modular ground-water model—user guide to modularization concepts and the ground-water flow process. Tech rep. Open-File Report 00-92, U.S. Department of the Interior, U.S. Geological Survey. Reston, Virginia, 121 ppHendricks Franssen HJ, Kinzelbach W (2008) Real-time groundwater flow modeling with the Ensemble Kalman Filter: joint estimation for states and parameters and the filter inbreeding problem. Water Resour Res 44:W09408Hendricks Franssen HJ, Kinzelbach W (2009) Ensemble Kalman filtering versus sequential self-calibration for inverse modelling of dynamic groundwater flow systems. J Hydrol 365(3–4):261–274Houtekamer PL, Mitchell HL (2001) A sequential ensemble Kalman filter for atmospheric data assimilation. Mon Weather Rev 129:123–137Journel AG, Deutsch CV (1993) Entropy and spatial disorder. Math Geol 25(3):329–355Li L, Zhou H, Gómez-Hernández JJ (2011a) A comparative study of three-dimensional hydraulic conductivity upscaling at the macrodispersion experiment (MADE) site, Columbus air force base, Mississippi (USA). J Hydrol 404(3–4):278–293Li L, Zhou H, Gómez-Hernández JJ (2011b) Transport upscaling using multi-rate mass transfer in three-dimensional highly heterogeneous porous media. Adv Water Resour 34(4):478–489Moradkhani H, Sorooshian S, Gupta HV, Houser PR (2005) Dual state-parameter estimation of hydrological models using ensemble Kalman filter. Adv Water Resour 28:135–147Naevdal G, Johnsen L, Aanonsen S, Vefring E (Mar. 2005) Reservoir monitoring and continuous model updating using ensemble Kalman filter. SPE J 10(1):66–74Pardo-Igúzquiza E, Dowd PA (2003) CONNEC3D: a computer program for connectivity analysis of 3D random set models. Comput Geosci 29:775–785Schöniger A, Nowak W, Hendricks Franssen HJ (2011) Parameter estimation by ensemble Kalman filters with transformed data: approach and application to hydraulic tomography. Water Resour Res (submitted)Simon E, Bertino L (2009) Application of the Gaussian anamorphosis to assimilation in a 3-D coupled physical-ecosystem model of the North Atlantic with the EnKF: a twin experiment. Ocean Sci 5:495–510Stauffer D, Aharony A (1994) Introduction to percolation theory. Taylor and Francis, London. 181 ppStrébelle S 2000. Sequential simulation drawing structures from training images. PhD thesis, Stanford University. 187 ppStrebelle S (2002) Conditional simulation of complex geological structures using multiple-point statistics. Math Geol 34(1):1–21Wen X, Chen W (2006) Real-time reservoir model updating using ensemble Kalman filter: the confirming approach. SPE J 11(4):431–442Wen X, Chen W (2007) Some practical issues on real time reservoir updating using ensemble Kalman filter. SPE J 12(2):156–166Zhou H, Gómez-Hernández JJ, Hendricks Franssen H-J, Li L (2011) An approach to handling non-gaussianity of parameters and state variables in ensemble Kalman filtering. Adv Water Resour 34(7):844–864Zinn B, Harvey C (2003) When good statistical models of aquifer heterogeneity go bad: a comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields. Water Resour Res 39(3):105

Angle-resolved photoelectron spectrometry studies of the autoionization of the 2s22p 2P triply excited state of atomic lithium: experimental results and R-matrix calculations

We have measured the angle-resolved energy dependence of the electrons emitted over the energy range of the triply excited 2s22p2P lithium resonance using synchrotron radiation. We have also calculated the behavior of the angular distribution parameter β using the R-matrix approximation. Experimental and theoretical results are in good agreement and show deep minima in the 1s2p1,3P ionic channels. The energy at which the minima occur does not coincide with the resonance energy, but is shifted towards higher energy