HydroMix v1.0: a new Bayesian mixing framework for attributing uncertain hydrological sources
<p>Tracers have been used for over half a century in hydrology to quantify water sources with the help of mixing models. In this paper, we build on classic Bayesian methods to quantify uncertainty in mixing ratios. Such methods infer the probability density function (PDF) of the mixing ratios...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2020-05-01
|
| Series: | Geoscientific Model Development |
| Online Access: | https://www.geosci-model-dev.net/13/2433/2020/gmd-13-2433-2020.pdf |
| _version_ | 1818428810875371520 |
|---|---|
| author | H. Beria J. R. Larsen A. Michelon N. C. Ceperley N. C. Ceperley B. Schaefli B. Schaefli |
| author_facet | H. Beria J. R. Larsen A. Michelon N. C. Ceperley N. C. Ceperley B. Schaefli B. Schaefli |
| author_sort | H. Beria |
| collection | DOAJ |
| description | <p>Tracers have been used for over half a century in hydrology to quantify
water sources with the help of mixing models. In this paper, we build on
classic Bayesian methods to quantify uncertainty in mixing ratios. Such
methods infer the probability density function (PDF) of the mixing ratios by
formulating PDFs for the source and target concentrations and inferring the
underlying mixing ratios via Monte Carlo sampling. However, collected
hydrological samples are rarely abundant enough to robustly fit a PDF to the
source concentrations. Our approach, called HydroMix, solves the linear
mixing problem in a Bayesian inference framework wherein the likelihood is
formulated for the error between observed and modeled target variables,
which corresponds to the parameter inference setup commonly used in
hydrological models. To address small sample sizes, every combination of
source samples is mixed with every target tracer concentration. Using a
series of synthetic case studies, we evaluate the performance of HydroMix
using a Markov chain Monte Carlo sampler. We then use HydroMix to show that
snowmelt accounts for around 61 % of groundwater recharge in a Swiss
Alpine catchment (Vallon de Nant), despite snowfall only accounting for
40 %–45 % of the annual precipitation. Using this example, we then
demonstrate the flexibility of this approach to account for uncertainties in
source characterization due to different hydrological processes. We also
address an important bias in mixing models that arises when there is a large
divergence between the number of collected source samples and their flux
magnitudes. HydroMix can account for this bias by using composite likelihood
functions that effectively weight the relative magnitude of source fluxes.
The primary application target of this framework is hydrology, but it is by
no means limited to this field.</p> |
| first_indexed | 2024-12-14T15:07:33Z |
| format | Article |
| id | doaj.art-4216e7c84551438f87ffa31da2bd8254 |
| institution | Directory Open Access Journal |
| issn | 1991-959X 1991-9603 |
| language | English |
| last_indexed | 2024-12-14T15:07:33Z |
| publishDate | 2020-05-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Geoscientific Model Development |
| spelling | doaj.art-4216e7c84551438f87ffa31da2bd82542022-12-21T22:56:40ZengCopernicus PublicationsGeoscientific Model Development1991-959X1991-96032020-05-01132433245010.5194/gmd-13-2433-2020HydroMix v1.0: a new Bayesian mixing framework for attributing uncertain hydrological sourcesH. Beria0J. R. Larsen1A. Michelon2N. C. Ceperley3N. C. Ceperley4B. Schaefli5B. Schaefli6Institute of Earth Surface Dynamics, University of Lausanne, Lausanne, SwitzerlandSchool of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham, UKInstitute of Earth Surface Dynamics, University of Lausanne, Lausanne, SwitzerlandInstitute of Earth Surface Dynamics, University of Lausanne, Lausanne, Switzerlandnow at: Institute of Geography, University of Berne, Bern, SwitzerlandInstitute of Earth Surface Dynamics, University of Lausanne, Lausanne, Switzerlandnow at: Institute of Geography, University of Berne, Bern, Switzerland<p>Tracers have been used for over half a century in hydrology to quantify water sources with the help of mixing models. In this paper, we build on classic Bayesian methods to quantify uncertainty in mixing ratios. Such methods infer the probability density function (PDF) of the mixing ratios by formulating PDFs for the source and target concentrations and inferring the underlying mixing ratios via Monte Carlo sampling. However, collected hydrological samples are rarely abundant enough to robustly fit a PDF to the source concentrations. Our approach, called HydroMix, solves the linear mixing problem in a Bayesian inference framework wherein the likelihood is formulated for the error between observed and modeled target variables, which corresponds to the parameter inference setup commonly used in hydrological models. To address small sample sizes, every combination of source samples is mixed with every target tracer concentration. Using a series of synthetic case studies, we evaluate the performance of HydroMix using a Markov chain Monte Carlo sampler. We then use HydroMix to show that snowmelt accounts for around 61 % of groundwater recharge in a Swiss Alpine catchment (Vallon de Nant), despite snowfall only accounting for 40 %–45 % of the annual precipitation. Using this example, we then demonstrate the flexibility of this approach to account for uncertainties in source characterization due to different hydrological processes. We also address an important bias in mixing models that arises when there is a large divergence between the number of collected source samples and their flux magnitudes. HydroMix can account for this bias by using composite likelihood functions that effectively weight the relative magnitude of source fluxes. The primary application target of this framework is hydrology, but it is by no means limited to this field.</p>https://www.geosci-model-dev.net/13/2433/2020/gmd-13-2433-2020.pdf |
| spellingShingle | H. Beria J. R. Larsen A. Michelon N. C. Ceperley N. C. Ceperley B. Schaefli B. Schaefli HydroMix v1.0: a new Bayesian mixing framework for attributing uncertain hydrological sources Geoscientific Model Development |
| title | HydroMix v1.0: a new Bayesian mixing framework for attributing uncertain hydrological sources |
| title_full | HydroMix v1.0: a new Bayesian mixing framework for attributing uncertain hydrological sources |
| title_fullStr | HydroMix v1.0: a new Bayesian mixing framework for attributing uncertain hydrological sources |
| title_full_unstemmed | HydroMix v1.0: a new Bayesian mixing framework for attributing uncertain hydrological sources |
| title_short | HydroMix v1.0: a new Bayesian mixing framework for attributing uncertain hydrological sources |
| title_sort | hydromix v1 0 a new bayesian mixing framework for attributing uncertain hydrological sources |
| url | https://www.geosci-model-dev.net/13/2433/2020/gmd-13-2433-2020.pdf |
| work_keys_str_mv | AT hberia hydromixv10anewbayesianmixingframeworkforattributinguncertainhydrologicalsources AT jrlarsen hydromixv10anewbayesianmixingframeworkforattributinguncertainhydrologicalsources AT amichelon hydromixv10anewbayesianmixingframeworkforattributinguncertainhydrologicalsources AT ncceperley hydromixv10anewbayesianmixingframeworkforattributinguncertainhydrologicalsources AT ncceperley hydromixv10anewbayesianmixingframeworkforattributinguncertainhydrologicalsources AT bschaefli hydromixv10anewbayesianmixingframeworkforattributinguncertainhydrologicalsources AT bschaefli hydromixv10anewbayesianmixingframeworkforattributinguncertainhydrologicalsources |