This study contributes to identifying and spatializing the different types of nitrate sources by combining hydrogeochemical and isotopic data with principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE) multicriteria statistical methods. The methodology is applied to the strategic Mons Basin chalk aquifer (Belgium). The results are based on a whole dataset containing 72 water samples with analyses of the hydrogeochemical parameters (temperature, pH, electrical conductivity (EC), redox potential, dissolved O2), alkalinity, total organic carbon (TOC), silica (SiO2), major and minor ions (NO3–, NH4+, Ca2+, dissolved Fe and Mn, K+, Mg2+, Na+, Sr2+, Cl–, F–, SO4–, B) and multiple stable isotope ratios (δ11B, δ15N–NO3–, δ18O–NO3–). Compared to classical PCA, the recently developed t-SNE method, which considers nonlinear relationships between variables and preserves local-scale similarities in a low-dimensional space, showed much better performance in discriminating different groups of samples and related zones in the aquifer. t-SNE results combined with isotope ratios highlighted four zones in the aquifer (grouped as A–D) and the presence of denitrification fronts. Group A presents a manure signature (δ15N–NO3– – mean (μ) +12.78‰, standard deviation (σ) 6.48‰; δ11B – μ 29.96‰, σ 6.91‰). Group B exhibits both manure and inorganic fertilizer signatures (δ15N–NO3– – μ 6.27‰, σ 2.55‰; δ11B – μ 15.86‰, σ 9.69‰). Group C shows a contamination by sewage (δ15N–NO3– – μ 12.67‰, σ 5.60‰; δ11B – μ 9.97‰, σ 7.08‰). Group D presents a mixed signature (δ15N–NO3– – μ 9.25‰, σ 2.94‰; δ11B – μ 20.00‰, σ 6.70‰).
We present a new method to solve the problem of initial orbit determination of any binary system. This method is mainly based
on the material available for an observer, for example relative positions at a given time of the couple in the “plane of sky”,
namely the tangent plane to the celestial sphere at the position of the primary component. The problem of orbit determination
is solved by splitting in successive stages in order to decorrelate the parameters of each other as much as possible. On one
hand, the geometric problem is solved using the first Kepler’s law from a single observing run and, on the other hand, dynamical
parameters are then inferred from the fit of the Kepler’s equation. At last, the final stage consists in determining the main
physical parameters involved in the secular evolution of the system, that is the spin axis and the J2 parameter of the primary if we assume that it is a quasi-spherical body. As a matter of fact there is no need to make too
restrictive initial assumptions (such as circular orbit or zero eccentricity) and initial guesses of parameters required by
a non-linear least-squares Levenberg–Marquardt algorithm are finally obtained after each stage. Such a protocol is very useful
to study systems like binary asteroids for which all of the parameters should be considered a priori as unknowns. As an example of application, we used our method to estimate the set of the Pluto–Charon system parameters from
observations collected in the literature since 1980. 相似文献