Mapping mesoscale currents by optimal interpolation of satellite radiometer and altimeter data

 Mapping the mesoscale surface velocity stream function by combining estimates of surface height from satellite altimetry and surface currents from sequential infrared (sea-surface temperature) imagery using optimal interpolation is described. Surface currents are computed from infrared images by the method of maximum cross-correlations (MCC) and are combined with altimeter sea-level anomaly data from the TOPEX/Poseidon and ERS satellites. The analysis method was applied to 6 years of data from the East Australian Current region. The covariance of velocity and sea-level data is consistent with the statistical assumptions of homogeneous, isotropic turbulence, with typical length scales of order 220 km and time scales of 10 days in this region. Augmenting the analysis of altimeter data with MCC velocity observations improves the resolution of the surface currents, especially near the Australian coast, and demonstrates that the two data sources provide consistent and complementary observations of the surface mesoscale circulation. The volume of MCC data is comparable to that from a satellite altimeter, but with a more variable distribution of spatial and temporal resolution. In concert with altimetry, satellite radiometer velocimetry represents a technique useful for retrospective analysis of currents from high-resolution satellite radiometer data-sets. Received: 3 July 2001 / Accepted: 16 November 2001     

Variograms of Order ω: A Tool to Validate a Bivariate Distribution Model

The multigaussian model is used in mining geostatistics to simulate the spatial distribution of grades or to estimate the recoverable reserves of an ore deposit. Checking the suitability of such model to the available data often constitutes a critical step of the geostatistical study. In general, the marginal distribution is not a problem because the data can be transformed to normal scores, so the check is usually restricted to the bivariate distributions. In this work, several tests for diagnosing the two-point normality of a set of Gaussian data are reviewed and commented. An additional criterion is proposed, based on the comparison between the usual variogram and the variograms of lower order: the latter are defined as half the mean absolute increments of the attribute raised to a power between 0 and 2. This criterion is then extended to other bivariate models, namely the bigamma, Hermitian and Laguerrian models. The concepts are illustrated on two real data-sets. Finally, some conditions to ensure the internal consistency of the variogram under a given model are given.     

Quantifying Uncertainty in Mineral Resources by Use of Classification Schemes and Conditional Simulations

Mineral inventory determination consists of estimating the amount of mineral resources on a block-by-block basis and classifying individual blocks into categories with increasing level of geologic confidence. Such classification is a crucial issue for mining companies, investors, financial institutions, and authorities, but it remains subject to some confusion because of the wide variations in methodologies and the lack of standardized procedures. The first part of this paper considers some of the criteria used to classify resources in practice and their impact through a sensitivity study using data from a Chilean porphyry copper deposit. Five classification criteria are compared and evaluated, namely: Search neighborhoods, absolute and relative kriging variances, absolute and relative conditional simulation variances. It is shown that some classification criteria either favor or penalize the high-grade areas if the grade distribution presents a proportional effect. In the second part of the paper, conditional simulations are used to quantify the uncertainty on the overall mineral resources. This approach is promising for risk analysis and decision-making. Unlike linear kriging, simulations allow inclusion of a cutoff grade in the calculation of the resources and also provide measures of their joint uncertainty over production volumes.     

Conditioning Simulations of Gaussian Random Fields by Ordinary Kriging

Conditioning realizations of stationary Gaussian random fields to a set of data is traditionally based on simple kriging. In practice, this approach may be demanding as it does not account for the uncertainty in the spatial average of the random field. In this paper, an alternative model is presented, in which the Gaussian field is decomposed into a random mean, constant over space but variable over the realizations, and an independent residual. It is shown that, when the prior variance of the random mean is infinitely large (reflecting prior ignorance on the actual spatial average), the realizations of the Gaussian random field are made conditional by substituting ordinary kriging for simple kriging. The proposed approach can be extended to models with random drifts that are polynomials in the spatial coordinates, by using universal or intrinsic kriging for conditioning the realizations, and also to multivariate situations by using cokriging instead of kriging.     

Reducing fluctuations in the sample variogram

In the analysis of regionalized data, irregular sampling patterns are often responsible for large deviations (fluctuations) between the theoretical and sample semi-variograms. This article proposes a new semi-variogram estimator that is unbiased irrespective of the actual multivariate distribution of the data (provided an assumption of stationarity) and has the minimal variance under a given multivariate distribution model. Such an estimator considerably reduces fluctuations in the sample semi-variogram when the data are strongly correlated and clustered in space, and proves to be robust to a misspecification of the multivariate distribution model. The traditional and proposed semi-variogram estimators are compared through an application to a pollution dataset.     

Solar wind structure sources and periodicities of auroral electron power over three solar cycles

We assess the contributions of various types of solar wind structures (transients, coronal hole high-speed streams (HSS), and slow-speed wind) to hourly average auroral electron power (P_e). The time variation of the solar wind velocity (V_sw) and P_e are determined by HSS, which contribute ～47% to P_e and V_sw. Transients contribute ～42% of P_e in solar maxima, and ～6% in solar minimum. Cross-correlations of P_e with V_sw|B| for negative B_z are significant. P_e exhibits solar rotational periodicities similar to those for V_sw, with strong 7- and 9-day periodicities in 2005–2008 and equinox semiannual periodicities in 1995–1999.     

Long-term evolution (1988–2008) of Zostera spp. meadows in Arcachon Bay (Bay of Biscay)

The spatial variability of seagrass meadows in Arcachon Bay, was studied between 1988 and 2008 using a combination of mapping techniques based on aerial photographs for intertidal dwarf-grass (Zostera noltii) beds and acoustic sonar for permanently submerged eelgrass (Zostera marina) populations. The results show a severe decline over the period for both species, as well as an acceleration of the decline since 2005 for Z. noltii. The total surface regression over the studied period is estimated to be 22.8 km² for Z. noltii and 2.7 km² for Z. marina, which represent declines of 33 and 74% respectively.     

On the Existence of Mosaic and Indicator Random Fields with Spherical,Circular, and Triangular Variograms

This paper focuses on two specific families of stationary random fields (namely, mosaic and indicator random fields) and examines the question of whether the variogram of a member of these two families could be spherical, circular, or triangular. It is shown that there are such examples in one-dimensional spaces, while there are counterexamples in higher-dimensional spaces for mosaic random fields, indicators of Boolean random sets and indicators of excursion sets of Gaussian random fields. Further results concerning the spherical plus nugget and circular plus nugget variograms are provided.