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

Frequency of educational computer use as a longitudinal predictor of educational outcomes in young people with specific language impairment

Computer use draws on linguistic abilities. Using this medium thus presents challenges for young people with Specific Language Impairment (SLI) and raises questions of whether computer-based tasks are appropriate for them. We consider theoretical arguments predicting impaired performance and negative outcomes relative to peers without SLI versus the possibility of positive gains. We examine the relationship between frequency of computer use (for leisure and educational purposes) and educational achievement; in particular examination performance at the end of compulsory education and level of educational progress two years later. Participants were 49 young people with SLI and 56 typically developing (TD) young people. At around age 17, the two groups did not differ in frequency of educational computer use or leisure computer use. There were no associations between computer use and educational outcomes in the TD group. In the SLI group, after PIQ was controlled for, educational computer use at around 17 years of age contributed substantially to the prediction of educational progress at 19 years. The findings suggest that educational uses of computers are conducive to educational progress in young people with SLI

Determination of quantitative trait loci (QTL) for early maturation in rainbow trout (Oncorhynchus mykiss)

To identify quantitative trait loci (QTL) influencing early maturation (EM) in rainbow trout (Oncorhynchus mykiss), a genome scan was performed using 100 microsatellite loci across 29 linkage groups. Six inter-strain paternal half-sib families using three inter-strain F(1) brothers (approximately 50 progeny in each family) derived from two strains that differ in the propensity for EM were used in the study. Alleles derived from both parental sources were observed to contribute to the expression of EM in the progeny of the brothers. Four genome-wide significant QTL regions (i.e., RT-8, -17, -24, and -30) were observed. EM QTL detected on RT-8 and -24 demonstrated significant and suggestive QTL effects in both male and female progeny. Furthermore, within both male and female full-sib groupings, QTL on RT-8 and -24 were detected in two or more of the five parents used. Significant genome-wide and several strong chromosome-wide QTL for EM localized to different regions in males and females, suggesting some sex-specific control. Namely, QTL detected on RT-13, -15, -21, and -30 were associated with EM only in females, and those on RT-3, -17, and -19 were associated with EM only in males. Within the QTL regions identified, a comparison of syntenic EST markers from the rainbow trout linkage map with the zebrafish (Danio rerio) genome identified several putative candidate genes that may influence EM. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s10126-008-9098-5) contains supplementary material, which is available to authorized users

Atlantic cod (Gadus morhua) hemoglobin genes: multiplicity and polymorphism

Background: Hemoglobin (Hb) polymorphism, assessed by protein gel electrophoresis, has been used almost exclusively to characterize the genetic structure of Atlantic cod (Gadus morhua) populations and to establish correlations with phenotypic traits such as Hb oxygen binding capacity, temperature tolerance and growth characteristics. The genetic system used to explain the results of gel electrophoresis entails the presence of one polymorphic locus with two major alleles (HbI-1; HbI-2). However, vertebrates have more than one gene encoding Hbs and recent studies have reported that more than one Hb gene is present in Atlantic cod. These observations prompted us to re-evaluate the number of Hb genes expressed in Atlantic cod, and to perform an in depth search for polymorphisms that might produce relevant phenotypes for breeding programs. Results: Analysis of Expressed Sequence Tags (ESTs) led to the identification of nine distinct Hb transcripts; four corresponding to the α Hb gene family and five to the β Hb gene family. To gain insights about the Hb genes encoding these transcripts, genomic sequence data was generated from heterozygous (HbI-1/2) parents and fifteen progeny; five of each HbI type, i.e., HbI-1/1, HbI-1/2 and HbI-2/2. β Hb genes displayed more polymorphism than α Hb genes. Two major allele types (β1A and β1B) that differ by two linked non-synonymous substitutions (Met55Val and Lys62Ala) were found in the β1 Hb gene, and the distribution of these β1A and β1B alleles among individuals was congruent with that of the HbI-1 and HbI-2 alleles determined by protein gel electrophoresis. RT-PCR and Q-PCR analysis of the nine Hb genes indicates that all genes are expressed in adult fish, but their level of expression varies greatly; higher expression of almost all Hb genes was found in individuals displaying the HbI-2/2 electrophoretic type. Conclusion: This study indicates that more Hb genes are present and expressed in adult Atlantic cod than previously documented. Our finding that nine Hb genes are expressed simultaneously in adult fish suggests that Atlantic cod, similarly to fish such as rainbow trout, carp, and goldfish, might be able to respond to environmental challenges such as chronic hypoxia or long-term changes in temperature by altering the level of expression of these genes. In this context, the role of the non-conservative substitution Lys62Ala found in the β1 Hb gene, which appears to explain the occurrence of the HbI-1 and HbI-2 alleles described by gel electrophoresis, and which was found to be present in other fish such as eel, emerald rockcod, rainbow trout and moray, requires further investigation

Climate induced temperature effects on growth performance, fecundity and recruitment in marine fish: developing a hypothesis for cause and effect relationships in Atlantic cod (Gadus morhua) and common eelpout (Zoarces viviparus).

Effects of global warming on animal distribution and performance become visible in many marine ecosystems. The present study was designed to develop a concept for a cause and effect understanding with respect to temperature changes and to explain ecological findings based on physiological processes. The concept is based on a wide comparison of invertebrate and fish species with a special focus on recent data obtained in two model species of fish. These fish species are both characterized by northern and southern distribution limits in the North Atlantic: eelpout (Zoarces viviparus), as a typical non-migrating inhabitant of the coastal zone and the cod (Gadus morhua), as a typical inhabitant of the continental shelf with a high importance for fisheries. Mathematical modelling demonstrates a clear significant correlation between climate induced temperature fluctuations and the recruitment of cod stocks. Growth performance in cod is optimal at temperatures close to 10 degreesC, regardless of the population investigated in a latitudinal cline. However, temperature specific growth rates decrease at higher latitudes. Also, fecundity is less in White Sea than in North and Baltic Sea cod or eelpout populations. These findings suggest that a cold-induced shift in energy budget occurs which is unfavorable for growth performance and fecundity. Thermal tolerance limits shift depending on latitude and are characterized by oxygen limitation at both low or high temperatures. Oxygen supply to tissues is optimized at low temperature by a shift in hemoglobin isoforms and oxygen binding properties to lower affinities and higher unloading potential. Protective stimulation of heat shock protein synthesis was not observed. According to a recent model of thermal tolerance the downward shift of tolerance limits during cold adaptation is associated with rising mitochondrial densities and, thus, aerobic capacity and performance in the cold. especially in eurythermal species. At the same time the costs of mitochondrial maintenance reflected by mitochondrial proton leakage should rise leaving a lower energy fraction for growth and reproduction. The preliminary conclusion can be drawn that warming will cause a northern shift of distribution limits for both species with a rise in growth performance and fecundity larger than expected from the Q(10) effect in the north and lower growth or even extinction of the species in the south. Such a shift may heavily affect fishing activities in the North Sea