Ground water model calibration using pilot points and regularization

Use of nonlinear parameter estimation techniques is now commonplace in ground water model calibration. However, there is still ample room for further development of these techniques in order to enable them to extract more information from calibration datasets, to more thoroughly explore the uncertainty associated with model predictions, and to make them easier to implement in various modeling contexts. This paper describes the use of pilot points as a methodology for spatial hydraulic property characterization. When used in conjunction with nonlinear parameter estimation software that incorporates advanced regularization functionality (such as PEST), use of pilot points can add a great deal of flexibility to the calibration process at the same time as it makes this process easier to implement. Pilot points can be used either as a substitute for zones of piecewise parameter uniformity, or in conjunction with such zones. In either case, they allow the disposition of areas of high and low hydraulic property value to be inferred through the calibration process, without the need for the modeler to guess the geometry of such areas prior to estimating the parameters that pertain to them. Pilot points and regularization can also be used as an adjunct to geostatistically based stochastic parameterization methods. Using the techniques described herein, a series of hydraulic property fields can be generated, all of which recognize the stochastic characterization of an area at the same time that they satisfy the constraints imposed on hydraulic property values by the need to ensure that model outputs match field measurements. Model predictions can then be made using all of these fields as a mechanism for exploring predictive uncertainty.

Phylogeny, molecular and fossil dating, and biogeographic history of Annonaceae and Myristicaceae (Magnoliales)

Annonaceae and Myristicaceae, the two largest families of Magnoliales, are pantropical groups of uncertain geographic history. The most recent morphological and molecular phylogenetic analyses identify the Asian-American genus Anaxagorea as sister to all other Annonaceae and the ambavioids, consisting of small genera endemic to South America, Africa, Madagascar, and Asia, as a second branch. However, most genera form a large clade in which the basal lines are African, and South American and Asian taxa are more deeply nested. Although it has been suggested that Anaxagorea was an ancient Laurasian line, present data indicate that this genus is basically South American. These considerations may mean that the family as a whole began its radiation in Africa and South America in the Late Cretaceous, when the South Atlantic was narrower, and several lines dispersed from Africa-Madagascar into Laurasia as the Tethys closed in the Tertiary. This scenario is consistent with the occurrence of annonaceous seeds in the latest Cretaceous of Nigeria and the Eocene of England and with molecular dating of the family. Based on distribution of putatively primitive taxa in Madagascar and derived taxa in Asia, it has been suggested that Myristicaceae had a similar history. Phylogenetic analyses of Myristicaceae, using morphology and several plastid regions, confirm that the ancestral area was Africa-Madagascar and that Asian taxa are derived. However, Myristicaceae as a whole show strikingly lower molecular divergence than Annonaceae, indicating either a much younger age or a marked slowdown in molecular evolution. The fact that the oldest diagnostic fossils of Myristicaceae are Miocene seeds might be taken as evidence that Myristicaceae are much younger than Annonaceae, but this is implausible in requiring transoceanic dispersal of their large, animal-dispersed seeds.

Tracking the Mesozoic distribution of Gunnera: comparison with the fossil pollen species Tricolpites reticulatus Cookson

The morphology of the exine of Late Cretaceous and Tertiary specimens of Tricolpites reticulatus previously documented from Kerguelen, the Antarctic Peninsula, and the Otway Basin of southeastern Australia has been re-examined and compared with the three pollen types identified in the genus Gunnera. An Antarctic specimen of T reticulatus (Maastrichtian) has a uniform reticulum with elongated lumina, similar to that characterising pollen type 3a of Gunnera macrophylla (subgenus Pseudogunnera). Late Cretaceous (Maastrichtian) Australian specimens of T reticulatus differ; specimens from McNamara resemble pollen of subgenera Pseudogunnera and Milligania of type 3a or type 3b, while specimens of T reticulatus from Princes show more rounded and equidimensional lumina and are therefore tentatively attributed to pollen type 2 found in subgenera Gunnera, Misandra and Panke. Kerguelen Island T reticulatus (Miocene) are distinct from Vega Island specimens: a closer resemblance of Kerguelen T reticulatus and pollen type 2 of extant Gunnera is hypothesised. A comparison between specimens of the North American Tricolpites reticulatus/microreticulatus and pollen of Gunnera is also made. The clear similarity of the North American specimens of Tricolpites microreticulatus and pollen of Gunnera in shape and in the exine surface features of pollen suggests that this taxon should not be separated from T reticulatus but should be treated as a synonym of this species. (C) 2004 Elsevier B.V. All rights reserved.

Long-term stasis in ecological assemblages: Evidence from the fossil record

Studies of plant and animal assemblages from both the terrestrial and the marine fossil records reveal persistence for extensive periods of geological time, sometimes millions of years. Persistence does not require lack of change or the absence of variation from one occurrence of the assemblage to the next in geological time. It does, however, imply that assemblage composition is bounded and that variation occurs within those bounds. The principal cause for these patterns appears to be species-, and perhaps clade-level, environmental fidelity that results in long-term tracking of physical conditions. Other factors that influence persistent recurrence of assemblages are historical, biogeographic effects, the law of large numbers, niche differentiation, and biotic interactions. Much research needs to be done in this area, and greater uniformity is needed in the approaches to studying the problem. However, great potential also exists for enhanced interaction between paleoecology and neoecology in understanding spatiotemporal complexity of ecological dynamics.

Calibration of the channel that determines the omega-hydroxylation regiospecificity of cytochrome P4504A1 - Catalytic oxidation of 12-halododecanoic acids

The fatty acid omega-hydroxylation regiospecificity of CYP4 enzymes may result from presentation of the terminal carbon to the oxidizing species via a narrow channel that restricts access to the other carbon atoms. To test this hypothesis, the oxidation of 12-iodo-, 12-bromo-, and 12-chlorododecanoic acids by recombinant CYP4A1 has been examined. Although all three 12-halododecanoic acids bind to CYP4A1 with similar dissociation constants, the 12-chloro and 12-bromo fatty acids are oxidized to 12-hydroxydodecanoic acid and 12-oxododecanoic acid, whereas the 12-iodo analogue is very poorly oxidized. Incubations in (H2O)-O-18 show that the 12-hydroxydodecanoic acid oxygen derives from water, whereas that in the aldehyde derives from O-2. The alcohol thus arises from oxidation of the halide to an oxohalonium species that is hydrolyzed by water, whereas the aldehyde arises by a conventional carbon hydroxylation-elimination mechanism. No irreversible inactivation of CYP4A1 is observed during 12-halododecanoic acid oxidation. Control experiments show that CYP2E1, which has an omega-1 regiospecificity, primarily oxidizes 12-halododecanoic acids to the omega-aldehyde rather than alcohol product. Incubation of CYP4A1 with 12,12-[H-2](2)-12-chlorododecanoic acid causes a 2-3-fold increase in halogen versus carbon oxidation. The fact that the order of substrate oxidation (Br > Cl >> I) approximates the inverse of the intrinsic oxidizability of the halogen atoms is consistent with presentation of the halide terminus via a channel that accommodates the chloride and bromide but not iodide atoms, which implies an effective channel diameter greater than 3.90 angstrom but smaller than 4.30 angstrom.

Fossil biotas from the Okanagan Highlands, southern British Columbia and northeastern Washington State: climates and ecosystems across an Eocene landscape

The late Early to early Middle Eocene Okanagan Highlands fossil sites, spanning -1000 km north-south (northeastern Washington State, southern British Columbia) provide an opportunity to reconstruct biotic communities across a broad upland landscape during the warmest part of the Cenozoic. Plant taxa from these fossil sites are characteristic of the modern eastern North American deciduous forest zone, principally the mixed mesophytic forest, but also include extinct taxa, taxa known only from eastern Asian mesothermal forests, and a small number of taxa restricted to the present-day North American west coast coniferous biome. In this preliminary report, paleoclimates and forest types are reconstructed using collections from Republic in Washington State, USA., and Princeton, Quilchena, Falkland, McAbee, Hat Creek, Horsefly, and Driftwood Canyon in British Columbia, Canada. Both leaf margin analysis (LMA) and quantitative bioclimatic analysis of identified nearest living relatives of megaflora indicated upper microthermal to lower mesothermal moist environments (MAT -10-15 degrees C, CMMT > 0 degrees C, MAP > 100 cm/year). Some taxa common to most sites suggest cool conditions (e.g., Abies, other Pinaceae; Alnus, other Betulaceae). However, all floras contain a substantive broadleaf deciduous element (e.g., Fagaceae, Juglandaceae) and conifers (e.g., Metasequoia) with the bioclimatic analysis yielding slightly higher MAT than LMA. Thermophilic (principally mesothermal) taxa include various insects, the aquatic fern Azolla, palms, the banana relative Ensete, taxodiaceous conifers, Eucommia and Gordonia, taxa which may have occurred near their climatic limits. The mixture of thermophilic and temperate insect and plant taxa indicates low-temperature seasonality (i.e., highly equable climate).

delta O-18, Sr/Ca and Mg/Ca records of Porites lutea corals from Leizhou Peninsula, northern South China Sea, and their applicability as paleoclimatic indicators

Combined seasonal to monthly resolution coral skeletal delta(18)O, Sr/Ca, and Mg/Ca records are reported for one modem and two late Holocene Porites lutea corals from a fringing reef at Leizhou Peninsula, the northern coast of the South China Sea (SCS). All the profiles for the period 1989-2000 reveal annual cycles well correlated with instrumental sea surface temperatures (SST), and display broad peaks in summer and narrow troughs in winter, reflecting seasonal growth rate variations. Calibration against instrumental SST yields the following equations: delta(18)O=-0.174(+/- 0.010)xSST(degrees C)-1.02(+/- 0.27) (MSWD=5.8), Sr/Ca-(mmol/mol)=-0.0424(+/- 0.0031)xSST(degrees C)+9.836(+/- 0.082) (MSWD=8.6), and Mg/Ca-(mmol/mol)=0.110(+/- 0.009)XSST(degrees C)+ 1.32(+/- 0.23) (MSWD=55). The scatter in the Mg/Ca-SST relationship is much larger than analytical uncertainties can account for, suggesting the presence of SST-unrelated components in the Mg/Ca variation. Calculated Sr/Ca-SST values for two later Holocene Porites lutea samples (U-series ages similar to 541 BC and similar to 487 AD, respectively) from the same reef suggest that SST in the SCS at similar to 541 BC was nearly as warm as in the 1990s (the warmest decade of the last century), but at similar to 487 AD, it was significantly cooler. This observation is consistent with climatic data reported in Chinese historic documents, confirming that the Sr/Ca-SST relationship is a reliable thermometer. Removing the SST component in the delta(18)O variation based on calculated Sr/Ca-SST values, the residual delta(18)O reflects the deviation of the Holocene seawater delta(18)O from the modem value, which is also a measure of the Holocene sea surface salinity (SSS) or the summer monsoon moisture level in mainland China. Such residual delta(18)O was close to zero at similar to 541 BC and -0.3 parts per thousand at similar to 487 AD, suggesting that it was as wet as in the 1990s at similar to 541 BC but significantly drier at similar to 487 AD in mainland China, which are also consistent with independent historic records. Calculated Mg/Ca-SST values for the two late Holocene corals are significantly lower than the Sr/Ca-SST values and are also in conflict with Chinese historic records, suggesting that coral Mg/Ca is not reliable proxy for SST. At comparable Sr/Ca ranges, fossil corals always display negative Mg/Ca offsets if compared with the modem coral of the same site. We interpret this observation as due to preferential loss of Mg during meteoric dissolution of cryptic Mg-calcite-bearing microbialites in the exposed fossil corals. Microbialites (MgO up to 17%, Sr only 100-300 ppm) are ubiquitous during reef-building processes and their presence in only a trace amount will have a significant impact on coral Mg/Ca ratios without detectable influence on coral Sr/Ca ratios. (c) 2004 Elsevier B.V. All rights reserved.

Review of tropospheric bomb C-14 data for carbon cycle modeling and age calibration purposes

Comprehensive published radiocarbon data from selected atmospheric records, tree rings, and recent organic matter were analyzed and grouped into 4 different zones (three for the Northern Hemisphere and one for the whole Southern Hemisphere). These C-14 data for the summer season of each hemisphere were employed to construct zonal, hemispheric, and global data sets for use in regional and global carbon model calculations including calibrating and comparing carbon cycle models. In addition, extended monthly atmospheric C-14 data sets for 4 different zones were compiled for age calibration purposes. This is the first time these data sets were constructed to facilitate the dating of recent organic material using the bomb C-14 curves. The distribution of bomb C-14 reflects the major zones of atmospheric circulation.

A planar microwave imaging system with step-frequency synthesized pulse using different calibration methods

An experimental study of a planar microwave imaging system with step-frequency synthesized pulse for possible use in medical applications is described. Simple phantoms, consisting of a cylindrical plastic container with air or oil imitating fatty tissues and small highly reflective objects emulating tumors, are scanned with a probe antenna over a planar surface in the X-band. Different calibration schemes are considered for successful detection of these objects. (c) 2006 Wiley Periodicals, Inc.

An advanced regularization methodology for use in watershed model calibration

A calibration methodology based on an efficient and stable mathematical regularization scheme is described. This scheme is a variant of so-called Tikhonov regularization in which the parameter estimation process is formulated as a constrained minimization problem. Use of the methodology eliminates the need for a modeler to formulate a parsimonious inverse problem in which a handful of parameters are designated for estimation prior to initiating the calibration process. Instead, the level of parameter parsimony required to achieve a stable solution to the inverse problem is determined by the inversion algorithm itself. Where parameters, or combinations of parameters, cannot be uniquely estimated, they are provided with values, or assigned relationships with other parameters, that are decreed to be realistic by the modeler. Conversely, where the information content of a calibration dataset is sufficient to allow estimates to be made of the values of many parameters, the making of such estimates is not precluded by preemptive parsimonizing ahead of the calibration process. White Tikhonov schemes are very attractive and hence widely used, problems with numerical stability can sometimes arise because the strength with which regularization constraints are applied throughout the regularized inversion process cannot be guaranteed to exactly complement inadequacies in the information content of a given calibration dataset. A new technique overcomes this problem by allowing relative regularization weights to be estimated as parameters through the calibration process itself. The technique is applied to the simultaneous calibration of five subwatershed models, and it is demonstrated that the new scheme results in a more efficient inversion, and better enforcement of regularization constraints than traditional Tikhonov regularization methodologies. Moreover, it is argued that a joint calibration exercise of this type results in a more meaningful set of parameters than can be achieved by individual subwatershed model calibration. (c) 2005 Elsevier B.V. All rights reserved.

Efficient accommodation of local minima in watershed model calibration

The Gauss-Marquardt-Levenberg (GML) method of computer-based parameter estimation, in common with other gradient-based approaches, suffers from the drawback that it may become trapped in local objective function minima, and thus report optimized parameter values that are not, in fact, optimized at all. This can seriously degrade its utility in the calibration of watershed models where local optima abound. Nevertheless, the method also has advantages, chief among these being its model-run efficiency, and its ability to report useful information on parameter sensitivities and covariances as a by-product of its use. It is also easily adapted to maintain this efficiency in the face of potential numerical problems (that adversely affect all parameter estimation methodologies) caused by parameter insensitivity and/or parameter correlation. The present paper presents two algorithmic enhancements to the GML method that retain its strengths, but which overcome its weaknesses in the face of local optima. Using the first of these methods an intelligent search for better parameter sets is conducted in parameter subspaces of decreasing dimensionality when progress of the parameter estimation process is slowed either by numerical instability incurred through problem ill-posedness, or when a local objective function minimum is encountered. The second methodology minimizes the chance of successive GML parameter estimation runs finding the same objective function minimum by starting successive runs at points that are maximally removed from previous parameter trajectories. As well as enhancing the ability of a GML-based method to find the global objective function minimum, the latter technique can also be used to find the locations of many non-global optima (should they exist) in parameter space. This can provide a useful means of inquiring into the well-posedness of a parameter estimation problem, and for detecting the presence of bimodal parameter and predictive probability distributions. The new methodologies are demonstrated by calibrating a Hydrological Simulation Program-FORTRAN (HSPF) model against a time series of daily flows. Comparison with the SCE-UA method in this calibration context demonstrates a high level of comparative model run efficiency for the new method. (c) 2006 Elsevier B.V. All rights reserved.