NG41A-0423 0800h
Geostatistical Estimations of Regional Hydraulic Conductivity Fields
Direct and indirect measurements of hydraulic conductivity ({\it K}) are commonly performed, providing information on the magnitude of this parameter at the local scale (tens of centimeters to hundreds of meters) and at shallow depths. By contrast, field information on hydraulic conductivities at regional scales of tens to hundreds of kilometers and at greater depths is relatively scarce. Geostatistical methods allow for sparsely sampled observations of a variable (primary information) to be complemented by a more densely sampled secondary attribute. Geostatistical estimations of the hydraulic conductivity field in the Carrizo aquifer, a major groundwater flow system extending along Texas, are performed using available primary (e.g., transmissivity, hydraulic conductivity) and secondary (specific capacity) information, for depths up to 2.2 km, and over three regional domains of increasing extent: 1) the domain corresponding to a three-dimensional groundwater flow model previously built (model domain); 2) the area corresponding to the ten counties encompassing the model domain (County domain), and; 3) the full extension of the Carrizo aquifer within Texas (Texas domain). Two different approaches are used: 1) an indirect approach are transmissivity ({\it T}) is estimated first and ({\it K}) is retrieved through division of the {\it T} estimate by the screening length of the wells, and; 2) a direct approach where {\it K} data are kriged directly. Prediction performances of the tested geostatistical procedures (kriging combined with linear regression, kriging with known local means, kriging of residuals, and cokriging) are evaluated through cross validation for both log-transformed variables and back-transformed ones. For the indirect approach, kriging of log {\it T} residuals yields the best estimates for both log-transformed and back-transformed variables in the model domain. For larger regional scales (County and Texas domains), cokriging performs generally better than univariate kriging procedures when estimating both (log {\it T})$^{*}$ and {\it T}$^{*}$. Among univariate procedures using the direct approach, the best prediction performances are obtained using simple kriging of log {\it K} with known local means. Cross validation also indicates that the indirect approach leads to smaller prediction errors than the direct approach, which is likely due to fewer available {\it K} primary data as well as a weaker correlation between primary and secondary attributes in the direct case. Although all procedures used log-transformed variables and incorporate secondary information derived from specific capacity data, none of the investigated techniques provides systematically better predictions for all scales, which stresses the importance of using cross validation to compare performances of alternative approaches and assess the unbiasedness of the back-transform procedure. Overall, estimation of the hydraulic conductivity field at such large regional scales through the tested geostatistical methods appears to be difficult due to both scarcity of sampling in the deeper portions of the formation ($>$ 1 km) and preferential emplacement of well screens in the most productive portions of the aquifer. For example, in the deepest portions of the aquifer in the model domain, the estimated hydraulic conductivity field is obtained by extrapolation and gives origin to unrealistically high hydraulic conductivity values.
NG41A-0424 0800h
Identification of the Time Base in Environmental Archives
One of the major problems with data-processing of proxy records (e.g. stable oxygen or carbon isotopes, or trace elements in shells, sponges, corals, sediment cores, etc.) is the dating of individual observations. All these proxy records are measured as function of a distance, while generally the time series are desired. Due to variations and differences in accretion rate, each record has its unique distance series, which cannot be compared with other records or models. Therefore, distance series are transformed into time series. However, this is only possible if additional information about the accretion rate is available. Unfortunately, this is mostly not the case and thus additional assumptions about the accretion rate are necessary. The most popular method to overcome this problem is the so-called anchor, tie or control point method, where the user assumes that the date of several observations is known. Next, the others are dated by a (linear) interpolation technique. Such methods are often used, especially when growth bands are available. We have proposed an alternative. Therefore, a parametric model for the signal is used, e.g. a periodic signal model. In addition, a new concept is introduced: the time base distortion. Therefore, we started from a previously estimated time base (if this is unknown, we initialize the time base assuming a constant accretion rate). Next, we allow this base to be distorted due to nonlinear accretion rates or hiatuses. This time base distortion can be identified in the frequency domain. When the accretion rate differs from the proposed one the spectral peaks, caused by the periodic component, are broadened and/or side peaks appear. From the latter, the distortion of the initial time base can be decoded, employing a phase demodulation. In order to refine this approach, an automated model selection procedure is employed to estimate how much variation in the time base and in the signal model is significant. The model selection procedure used is an adaptation of Akaike's information criterion, which can now handle small data sets. This results in a refined time base, where each individual observation is dated and where the stochastic disturbances are minimized. Several real world examples are processed to illustrate this methodology. First both methods are compared on the Mg-signal measured in a Saxidomus giganteus (shell) from Kenya. Here, this method was able to identify two hiatuses. Next, the oxygen stable isotope record measured in a coral is discussed. Here growth bands are present. These were used to date the record, using the anchor point method. Because several peaks appeared in its spectrum, the interpretation was not straightforward. The time base distortion approach is used to refine the initially estimated time base and finally one clear peak with a period of 14.4 years remained. This example shows that this method can be used to refine other time bases and that it can be used even when no annual periodicity is present in the signal. Finally, the temperature reconstruction derived from the Vostok ice core record is processed and discussed.
NG41A-0425 0800h
Geostatistical Modeling of the Spatial Variability of Arsenic in Groundwater of Southeast Michigan
The last decade has witnessed an increasing interest in assessing health risks caused by exposure to contaminants present in the soil, air, and water. A key component of any exposure study is a reliable model for the space-time distribution of pollutants. This paper compares the performances of multiGaussian and indicator kriging for modeling probabilistically the space-time distribution of arsenic concentrations in groundwater of Southeast Michigan, accounting for information collected at private residential wells and the hydrogeochemistry of the area. This model will later be combined with a space-time information system to assess the risk associated with exposure to low levels of arsenic in drinking water (typically 5-100 $\mu$g/L), in particular for the development of bladder cancer. Because of the small changes in concentration observed in time, the study has focused on the spatial variability of arsenic. This study confirmed results in the literature that reported intense spatial non-homogeneity of As concentration, resulting in samples that greatly vary even when located a few meters apart. Indicator semivariograms further showed a better spatial connectivity of low concentrations while values exceeding 32 $\mu$g/L (10% of wells) are spatially uncorrelated. Secondary information, such as proximity to Marshall Sandstone, helped only the prediction at a regional scale (i.e. beyond 15 kms), leaving the short-range variability largely unexplained. Several geostatistical tools were tailored to the features of the As dataset: (1) semivariogram values were standardized by the lag variance to correct for the preferential sampling of wells with high concentrations, (2) semivariogram modeling was conducted under the constraint of reproduction of the nugget effect inferred from colocated well measurements, (3) kriging systems were modified to account for repeated measurements at a series of wells while avoiding non-invertible kriging matrices, (4) kriging-based smoothing was combined with multivariate regression to predict the regional background of arsenic concentrations across the study area. Cross-validation indicated the little benefit of secondary information in local prediction of arsenic concentrations. Slightly better results were obtained using univariate indicator kriging which generated the smallest mean absolute error of prediction and the most precise and accurate models of uncertainty.
http://www-personal.engin.umich.edu/~goovaert/publication.html
NG41A-0426 0800h
Singular Spectrum Analysis With Missing Data
A Singular Spectrum Analysis (SSA) with gaps of missing data is presented. SSA is a data-adaptive, non-parametric spectral method based on diagonalizing the lag-covariance matrix of a time series. Using leading oscillatory SSA modes, we iteratively produce estimates of missing data, which are then used to compute a self-consistent lag-covariance matrix. For a univariate record, SSA imputation utilizes only temporal correlations in the data to fill up missing points. For a multivariate record, multi-channel SSA imputation takes advantage of both spatial and temporal correlations. Analyzing the whole available record with the missing points filled, allows for greater accuracy and better significance testing in the spectral analysis. It also provides information on the evolution of the oscillatory modes in the gaps. We use cross-validation to optimize the SSA window width and number of SSA modes to fill the gaps. The algorithm is applied to the extended (A.D. 622--1922) historical records of the low- and high-water levels of the Nile River at Cairo. We fill in the large gaps in the later part of the records (A.D. 1471--1922), and identify statistically significant interannual and interdecadal periodicities. Our analysis suggests that the 7-year periodicity in the records, possibly related to the biblical "Joseph" cycle, is due to North-Atlantic influences. We find that the climate shifts at the beginning and the end of the Medieval Warm Period were fairly abrupt and affected several climatic modes of variability.
NG41A-0427 0800h
Integration of Scale Invariant Generator Technique and S-A Technique for Characterizing 2-D Patterns for Information Retrieve
The scale invariant generator technique (SIG) and spectrum-area analysis technique (S-A) were developed independently relevant to the concept of the generalized scale invariance (GSI). The former was developed for characterizing the parameters involved in the GSI for characterizing and simulating multifractal measures whereas the latter was for identifying scaling breaks for decomposition of superimposed multifractal measures caused by multiple geophysical processes. A natural integration of these two techniques may yield a new technique to serve two purposes, on the one hand, that can enrich the power of S-A by increasing the interpretability of decomposed patterns in some applications of S-A and, on the other hand, that can provide a mean to test the uniqueness of multifractality of measures which is essential for application of SIG technique in more complicated environment. The implementation of the proposed technique has been done as a Dynamic Link Library (DLL) in Visual C++. The program can be friendly used for method validation and application in different fields.