CITATION.cff

cff-version: 1.0.0
title: funmixer
message: >-
  If you use this software, please cite it using the
  metadata from this file.
type: software
authors:
  - given-names: Richard
    family-names: Barnes
    email: rijard.barnes@gmail.com
    orcid: 'https://orcid.org/0000-0002-0204-6040'
  - given-names: Alexander
    family-names: Lipp
    email: a.lipp@ucl.ac.uk
    orcid: 'https://orcid.org/0000-0003-2130-8576'
identifiers:
  - type: url
    value: 'https://github.com/AlexLipp/funmixer/'
    description: Code Repository
  - type: doi
    value: 10.1029/2023WR036159
    description: Published manuscript DOI
repository-code: 'https://github.com/AlexLipp/funmixer/'
abstract: >-
  Rivers transport elements, minerals, chemicals, and
  pollutants produced in their upstream basins. A sample
  from a river is a mixture of all of its upstream sources,
  making it challenging to pinpoint the contribution from
  each individual source. Here, we show how a nested sample
  design and convex optimization can be used to efficiently
  unmix downstream samples of a well-mixed, conservative
  tracer into the contributions of their upstream sources.
  Our approach is significantly faster than previous
  methods. We represent the river's sub-catchments, defined
  by sampling sites, using a directed acyclic graph. This
  graph is used to build a convex optimization problem
  which, thanks to its convexity, can be quickly solved to
  global optimality---in under a second on desktop hardware
  for datasets of $\sim$100 samples or fewer. Uncertainties
  in the upstream predictions can be generated using Monte
  Carlo resampling. We provide an open-source implementation
  of this approach in Python. The inputs required are
  straightforward: a table containing sample locations and
  observed tracer concentrations, along with a D8
  flow-direction raster map. As a case study, we use this
  method to map the elemental geochemistry of sediment
  sources for rivers draining the Cairngorms mountains, UK.
  This method could be extended to non-conservative and
  non-steady state tracers. We also show, theoretically, how
  multiple tracers could be simultaneously inverted to
  recover upstream run-off or erosion rates as well as
  source concentrations. Overall, this approach can provide
  valuable insights to researchers in various fields,
  including water quality, geochemical exploration,
  geochemistry, hydrology, and wastewater epidemiology.