A review of lognormal estimators forin situ reserves

The term “lognormal kriging” does not correspond to a single well defined estimator. In fact, several types of lognormal estimators forin situ reserves are available, and this may cause confusion. These estimators are based on different assumptions—that is, different models. This paper presents a review of these estimators.     

Continuity for Kriging with Moving Neighborhood

By definition, kriging with a moving neighborhood consists in kriging each target point from a subset of data that varies with the target. When the target moves, data that were within the neighborhood are suddenly removed from the neighborhood. There is generally no screen effect, and the weight of such data goes suddenly from a non-zero value to a value of zero. This results in a discontinuity of the kriging map. Here a method to avoid such a discontinuity is proposed. It is based on the penalization of the outermost data points of the neighborhood, and amounts to considering that these points values are spoiled with a random error having a variance that increases infinitely when they are about to leave the neighborhood. Additional details are given regarding how the method is to be carried out, and properties are described. The method is illustrated by simple examples. While it appears to be similar to continuous kriging with a smoothing kernel, it is in fact based on a much simpler formalism.     

On the Structural Link Between Variables in Kriging with External Drift

Kriging with external drift allows one to estimate a target variable, accounting for a densely sampled auxiliary variable. Contrary to cokriging, kriging with external drift does not make explicit the structural link between target variable and auxiliary variable, for the latter is considered to be deterministic. In this paper, we show that kriging with external drift assumes implicitly an absence of spatial dependence between the auxiliary variable and the residual of the linear regression of target variable on auxiliary variable at same point. This is the simple model with orthogonal residual, where cokriging is collocated and coincides with kriging of the residual. In this model, the cross-structure is proportional to the structure of the auxiliary variable, and the linear regression of target variable on auxiliary variable does not depend on the support.     

A review of lognormal estimators forin situ reserves

The term lognormal kriging does not correspond to a single well defined estimator. In fact, several types of lognormal estimators forin situ reserves are available, and this may cause confusion. These estimators are based on different assumptions—that is, different models. This paper presents a review of these estimators.     

Indicator-Based Geostatistical Models For Mapping Fish Survey Data

Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided.