Yaoyang Xu | Search USGS

USGS2023

Approaching the upper boundary of driver-response relationships: Identifying factors using a novel framework integrating quantile regression with interpretable machine learning

The identification of factors that may be forcing ecological observations to approach the upper boundary provides insight into potential mechanisms affecting driver-response relationships, and can help inform ecosystem management, but has rarely been explored. In this study, we propose a novel framework integrating quantile regression with interpretable machine learning. In the first stage of the framework, we estimate the upper boundary of a driver-response relationship using quantile regression. Next, we calculate “potentials” of the response variable depending on the driver, which are defined as vertical distances from the estimated upper boundary of the relationship to observations in the driver-response variable scatter plot. Finally, we identify key factors impacting the potential using a machine learning model. We illustrate the necessary steps to implement the framework using the total phosphorus (TP)-Chlorophyll a (CHL) relationship in lakes across the continental US. We found that the nitrogen to phosphorus ratio (N:P), annual average precipitation, total nitrogen (TN), and summer average air temperature were key factors impacting the potential of CHL depending on TP. We further revealed important implications of our findings for lake eutrophication management. The important role of N:P and TN on the potential highlights the co-limitation of phosphorus and nitrogen and indicates the need for dual nutrient criteria. Future wetter and/or warmer climate scenarios can decrease the potential which may reduce the efficacy of lake eutrophication management. The novel framework advances the application of quantile regression to identify factors driving observations to approach the upper boundary of driver-response relationships.

Frontiers of Environmental Science & Engineering↗

USGS2021

A statistical framework to track temporal dependence of chlorophyll–nutrient relationships with implications for lake eutrophication management

A reliable chlorophyll–nutrient relationship (CNR) is essential for lake eutrophication management. Although the spatial variability of CNRs has been extensively explored, temporal variations of CNRs at the individual lake scale has rarely been discussed. The paucity of information about temporal dependence in CNRs may in part be due to the lack of a suitable statistical framework that helps guide such investigations. In order to reveal temporal dependence of CNR, this study develop a novel statistical framework. In the framework, we employ quantile regression to generate overall (the entire dataset), annual (subsets for each year), and accumulative (subsets collected before a certain year) CNRs. We aim to 1) show biases of annual relationships by comparing the overall and annual relationships and 2) determine whether or not data accumulation is enough to develop a reliable CNR. We use Lake Champlain and Lake Kasumigaura as case studies to illustrate the necessary steps needed to utilize this novel framework. Results show that large interannual variations exist for CNRs. Accumulative relationships tend to converge to the overall relationship, indicating that overall relationships are reliable for informing lake-specific eutrophication management in the two case study lakes. The novel statistical framework that we propose for a procedure to estimate reliable CNRs is important for informing lake-specific eutrophication control decision-making processes.

Ibaraki Prefecture, Lake Champlain, Lake Kasumigau↗

USGS2021

A statistical framework to track temporal dependence of chlorophyll–nutrient relationships with implications for lake eutrophication management

A reliable chlorophyll–nutrient relationship (CNR) is essential for lake eutrophication management. Although the spatial variability of CNRs has been extensively explored, temporal variations of CNRs at the individual lake scale has rarely been discussed. The paucity of information about temporal dependence in CNRs may in part be due to the lack of a suitable statistical framework that helps guide such investigations. In order to reveal temporal dependence of CNR, this study develop a novel statistical framework. In the framework, we employ quantile regression to generate overall (the entire dataset), annual (subsets for each year), and accumulative (subsets collected before a certain year) CNRs. We aim to 1) show biases of annual relationships by comparing the overall and annual relationships and 2) determine whether or not data accumulation is enough to develop a reliable CNR. We use Lake Champlain and Lake Kasumigaura as case studies to illustrate the necessary steps needed to utilize this novel framework. Results show that large interannual variations exist for CNRs. Accumulative relationships tend to converge to the overall relationship, indicating that overall relationships are reliable for informing lake-specific eutrophication management in the two case study lakes. The novel statistical framework that we propose for a procedure to estimate reliable CNRs is important for informing lake-specific eutrophication control decision-making processes.

Journal of Hydrology↗

USGS2021

Bayesian change point quantile regression approach to enhance the understanding of shifting phytoplankton-dimethyl sulfide relationships in aquatic ecosystems

Dimethyl sulfide (DMS) serves as an anti-greenhouse gas, plays multiple roles 7 in aquatic ecosystems, and contributes to the global sulfur cycle. The chlorophyll 8 a (CHL, an indicator of phytoplankton biomass)-DMS relationship is critical for 9 estimating DMS emissions from aquatic ecosystems. Importantly, recent research has 10 identified that the CHL-DMS relationship has a breakpoint, where the relationship 11 is positive below a CHL threshold and negative at higher CHL concentrations. 12 Conventionally, mean regression methods are employed to characterize the CHL-DMS 13 relationship. However, these approaches focus on the response of mean conditions 14 and cannot illustrate responses of other parts of the DMS distribution, which could 15 be important in order to obtain a complete view of the CHL-DMS relationship. In 16 this study, for the first time, we proposed a novel Bayesian change point quantile 17 regression (BCPQR) model that integrates and inherits advantages of Bayesian change 18 point models and Bayesian quantile regression models. Our objective was to examine 19 whether or not the BCPQR approach could enhance the understanding of shifting 20 CHL-DMS relationships in aquatic ecosystems. We fitted BCPQR models at five 21 regression quantiles for freshwater lakes and for seas. We found that BCPQR models 22 could provide a relatively complete view on the CHL-DMS relationship. In particular, 23 it quantified the upper boundary of the relationship, representing the limiting effect of 24 CHL on DMS. Based on the results of paired parameter comparisons, we revealed the 25 inequality of regression slopes in BCPQR models for seas, indicating that applying 26 the mean regression method to develop the CHL-DMS relationship in seas might not 27 be appropriate. We also confirmed relationship differences between lakes and seas at 28 multiple regression quantiles. Further, by introducing the concept of DMS emission 29 potential, we found that pH was not likely a key factor leading to the change of the 30 CHL-DMS relationship in lakes. These findings cannot be revealed using piecewise 31 linear regression. We thereby concluded that the BCPQR model does indeed enhance 32 the understanding of shifting CHL-DMS relationships in aquatic ecosystems and is 33 expected to benefit efforts aimed at estimating DMS emissions. Considering that 34 shifting (threshold) relationships are not rare and that the BCPQR model can easily 35 be adapted to different systems, the BCPQR approach is expected to have great 36 potential for generalization in other environmental and ecological studies.

Water Research↗