Phosphorus is an essential nutrient for every organism on the Earth, yet it is also a potential environmental pollutant, which may cause eutrophication of water bodies. Wastewater treatment plants worldwide are struggling to eliminate phosphorus from effluents, at great cost, yet current research suggests that the world may deplete the more available phosphorus reserves by around 2300. This, in addition to environmental concerns, evokes the need for new phosphorus recovery techniques to be developed, to meet future generations needs for renewable phosphorus supply. Many studies have been, and are, carried out on phosphorus recovery from wastewater and its sludge, due to their high phosphorus content. Chemical precipitation is the main process for achieving a phosphorus-containing mineral suitable for reuse as a fertilizer, such as struvite. This paper reviews the current status and future trends of phosphorus production and consumption, and summarizes current recovery technologies, discussing their possible integration into wastewater treatment processes, according to a more sustainable water-energy-nutrient nexus.

Food production hinges largely upon access to phosphorus (P) fertilizer. Most fertilizer P used in the global agricultural system comes from mining of nonrenewable phosphate rock deposits located within few countries. However, P contained in livestock manure or urban wastes represents a recyclable source of P. To inform development of P recycling technologies and policies, we examined subnational, national, and global spatial patterns for two intersections of land use affording high P recycling potential: (a) manure‐rich cultivated areas and (b) populous cultivated areas. In turn, we examined overlap between P recycling potential and nation‐level P fertilizer import dependency. Populous cultivated areas were less abundant globally than manure‐rich cultivated areas, reflecting greater segregation between crops and people compared to crops and livestock, especially in the Americas. Based on a global hexagonal grid (290‐km² grid cell area), disproportionately large shares of subnational “hot spots” for P recycling potential occurred in India, China, Southeast Asia, Europe, and parts of Africa. Outside of China, most of the remaining manure‐rich or populous cultivated areas occurred within nations that had relatively high imports of P fertilizer (net P import:consumption ratios ≥0.4) or substantial increases in fertilizer demand between the 2000s (2002–2006) and 2010s (2010–2014). Manure‐rich cultivated grid cells (those above the 75th percentiles for both manure and cropland extent) represented 12% of the global grid after excluding cropless cells. Annually, the global sum of animal manure P was at least 5 times that contained in human excreta, and among cultivated cells the ratio was frequently higher (median = 8.9). The abundance of potential P recycling hot spots within nations that have depended on fertilizer imports or experienced rising fertilizer demand could prove useful for developing local P sources and maintaining agricultural independence.

Multivariate polynomial regression (MPR) models were developed for five macrophyte indices. MPR models are able to capture complex interactions in the data while being tractable and transparent for further analysis. The performance of the MPR modeling approach was compared to previous work using artificial neural networks. The data were obtained from hydromorphologically modified Polish rivers with a widely varying water quality. The modeled indices were the Macrophyte Index for Rivers (MIR), the Macrophyte Biological Index for Rivers (IBMR), and the River Macrophyte Nutrient Index (RMNI). These indices measure the trophic and ecological status of the rivers. Additionally, two biological diversity indices, species richness (N) and the Simpson index (D), were modeled. The explanatory variables were physico-chemical properties depicting water quality and river hydromorphological status indices. In comparison to artificial neural networks, the MPR models performed similarly in terms of goodness of fit. However, the MPR models had advantages such as model simplicity and ability to be subject to effective visualization of complex nonlinear input–output relationships, as well as facilitating sensitivity analysis using importance ratios to identify effects of individual input variables.

Multivariate polynomial regression was used to generate polynomial iterators for time series exhibiting autocorrelations. A stepwise technique was used to add and remove polynomial terms to ensure the model contained only those terms that produce a statistically significant contribution to the fit. An approach is described in which datasets are divided into three subsets for identification, estimation, and validation. This produces a parsimonious global model that is can greatly reduce the tendency towards undesirable behaviours such as overfitting or instability. The technique was found to be able to identify the nonlinear dynamic behaviour of simulated time series, as reflected in the geometry of the attractor and calculation of multiple Lyapunov exponents, even in noisy systems. The technique was applied to times series data obtained from simulations of the Lorenz and Mackey – Glass equations with and without measurement noise. The model was also used to determine the embedding dimension of the Mackey – Glass equation.