Array programming with NumPy.

Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves1 and in the first imaging of a black hole2. Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis.

Simple models for phosphorus loss from manure during rainfall.

Mechanistic, predictive equations for phosphorus (P) transport in runoff from manure-applied fields constitute a critical knowledge gap for developing nonpoint-source pollution models. We derived two simple equations to describe the P release from animal manure during a rainfall event-one based on first-order P desorption kinetics and one based on second-order kinetics. The manure characteristics needed in the two kinetic equations are the maximum amount of water-extractable phosphorus (WEP) and a characteristic desorption time. Water-extractable P can be measured directly but currently the characteristic time can only be obtained by fitting experimental data. In addition, we evaluated two models usually used to estimate P loss from soil, the Elovitch equation and power function, both of which relate P loss to time. The models were tested against previously published data of P release from different manures under laboratory conditions. All equations fit the data well. Of the two kinetic equations, the second-order model showed better agreement with the data than the first-order model; for example, maximum relative differences between the model results and measured data were 2.6 and 4.7%, respectively. The characteristic times varied between 20 min for dairy manure and almost 100 min for poultry manure. The characteristic time did not appear to change with flow rate but decreased with smaller manure aggregates. The parameters for power-function relationships could not be related to measured manure characteristics. These results provide the first step to process-based approximations for predicting P release from manure with time during rainfall shortly after land application, when P losses are the greatest.

Identifying hydrologically sensitive areas: bridging the gap between science and application.

Researchers have noted that current water quality protection strategies, like nutrient management plans, lack a sound hydrological underpinning for pollutant transport processes. This is especially true for areas like the northeastern U.S. where copious research has shown that variable source area hydrology largely governs runoff generation. The goal of this study was to develop a scientifically justified method to identify the locations that generate overland flow. Furthermore, this methodology must be computationally simple enough that it can be utilized or incorporated into nutrient management plans and other established water quality tools. We specifically tested the reliability of the 'distance from a stream,'D(s), and the 'topographic index,'lambda, to predict areas with a high propensity for generating overland flow, i.e. hydrologically sensitive areas (HSA). HSAs were defined by their probability of generating runoff, P(sat), based on 30 year simulations using a physically based hydrological model. Using GIS, each location's P(sat) was correlated with D(s) and lambda. We used three Delaware Co., NY watersheds in the New York City watershed system with areas varying in size from 1.6 to 37 km2 and with forested and agricultural land uses. The topographic index gave stronger, more regionally consistent correlations with P(sat) than did D(s). Equations correlating lambda and P(sat) for each month are presented and can be used to estimate hydrological sensitivity in the region surrounding our study watersheds, i.e. in Delaware Co. This work is currently being incorporated into an Internet Mapping System to facilitate user-friendly, on-line identification of HSAs.