The Regional Aquifer-System Analysis (RASA) Program was started in 1978 following a congressional mandate to develop quantitative appraisals of the major groundwater systems of the United States. The RASA Program represents a systematic effort to study a number of the Nation's most important aquifer systems, which in aggregate underlie much of the country and which represent an important component of the Nation's total water supply. In general, the boundaries of these studies are identified by the hydrologic extent of each system and accordingly transcend the political subdivisions to which investigations have often arbitrarily been limited in the past. The broad objective for each study is to assemble geologic, hydrologic, and geochemical information, to analyze and develop an understanding of the system, and to develop predictive capabilities that will contribute to the effective management of the system. The use of computer simulation is an important element of the RASA studies, both to develop an understanding of the natural, undisturbed hydrologic system and the changes brought about in it by human activities, and to provide a means of predicting the regional effects of future pumping or other stresses. The final interpretive results of the RASA Program are presented in a series of U.S. Geological Survey Professional Papers that describe the geology, hydrology, and geochemistry of each regional aquifer system. Each study within the RASA Program is assigned a single Professional Paper number, and where the volume of interpretive material warrants, separate topical chapters that consider the principal elements of the investigation may be published. The series of RASA interpretive reports begins with Professional Paper 1400 and thereafter will continue in numerical sequence as the interpretive products of subsequent studies become available.

Motivation Due to new technology for efficiently generating genome data, machine learning methods are urgently needed to analyze large sets of gene trees over the space of phylogenetic trees. However, the space of phylogenetic trees is not Euclidean, so ordinary machine learning methods cannot be directly applied. In 2019, Yoshida et al. introduced the notion of tropical principal component analysis (PCA), a statistical method for visualization and dimensionality reduction using a tropical polytope with a fixed number of vertices that minimizes the sum of tropical distances between each data point and its tropical projection. However, their work focused on the tropical projective space rather than the space of phylogenetic trees. We focus here on tropical PCA for dimension reduction and visualization over the space of phylogenetic trees. Results Our main results are twofold: (1) theoretical interpretations of the tropical principal components over the space of phylogenetic trees, namely, the existence of a tropical cell decomposition into regions of fixed tree topology; and (2) the development of a stochastic optimization method to estimate tropical PCs over the space of phylogenetic trees using a Markov Chain Monte Carlo (MCMC) approach. This method performs well with simulation studies, and it is applied to three empirical datasets: Apicomplexa and African coelacanth genomes as well as sequences of hemagglutinin for influenza from New York. Availability Dataset: http://polytopes.net/Data.tar.gz, Code: http://polytopes.net/tropica_MCMC_codes.tar.gz Supplementary information Supplementary data are available at http://polytopes.net/supplement.pdf.

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Merced and vicinity comprises about 112 square miles in the northeastern part of the San Joaquin Valley of California. Two physiographic units occur in the area: (1) Dissected uplands, and (2) low alluvial plains and fans. Physiography from Davis AREA and others, 1959,pi. 1 FIGURE 1. Location and physiography of the study area. MAP OF CALIFORNIA The scope of this study was to appraise groundwater conditions in Merced and vicinity with regard to source, occurrence, and movement. Further, groundwater quality was investigated to determine the relationship, if any, between occurrence of water and its chemical type. Method of Study Planning for this study was begun in June 1975, and the fieldwork was completed in September 1975. Boundaries of the study area (fig. 1) were drawn to include the major communities in the immediate area of Merced and a sufficient number of wells and water-level data for contouring water levels ' ' around Merced. The method of study was to collect, assemble, and evaluate data to show the source, occurrence, movement, and chemical quality of ground water in the Merced area. All available drillers' logs, chemical analyses of ground water, water data for irrigation, water-level records, and pumpage data were collected. These data were analyzed and are shown on graphs, maps, and geologic sections.

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