scholarly journals Synthesizing the impacts of baseflow contribution on concentration–discharge (<i>C</i>–<i>Q</i>) relationships across Australia using a Bayesian hierarchical model

2022 ◽  
Vol 26 (1) ◽  
pp. 1-16
Author(s):  
Danlu Guo ◽  
Camille Minaudo ◽  
Anna Lintern ◽  
Ulrike Bende-Michl ◽  
Shuci Liu ◽  
...  
Keyword(s):  
Hierarchical Model ◽  
Soluble Reactive Phosphorus ◽  
Bayesian Hierarchical Model ◽  
Temporal Variations ◽  
Variable Flow ◽  
Bayesian Hierarchical ◽  
Wide Range ◽  
Flow Pathways ◽  
Nitrate And Nitrite ◽  
The Impact

Abstract. Understanding concentration–discharge (C–Q) relationships can inform catchment solute and particulate export processes. Previous studies have shown that the extent to which baseflow contributes to streamflow can affect C–Q relationships in some catchments. However, the current understanding on the effects of baseflow contribution in shaping the C–Q patterns is largely derived from temperate catchments. As such, we still lack quantitative understanding of these effects across a wide range of climates (e.g. arid, tropical and subtropical). The study aims to assess how baseflow contributions, as defined by the median and the range of daily baseflow indices within individual catchments (BFI_m and BFI_range, respectively), influence C–Q slopes across 157 catchments in Australia spanning five climate zones. This study focuses on six water quality variables: electrical conductivity (EC), total phosphorus (TP), soluble reactive phosphorus (SRP), total suspended solids (TSS), the sum of nitrate and nitrite (NOx) and total nitrogen (TN). The impact of baseflow contributions is explored with a novel Bayesian hierarchical model. For sediments and nutrient species (TSS, NOx, TN and TP), we generally see largely positive C–Q slopes, which suggest a dominance of mobilization export patterns. Further, for TSS, NOx and TP we see stronger mobilization (steeper positive C–Q slopes) in catchments with higher values in both the BFI_m and BFI_range, as these two metrics are positively correlated for most catchments. The enhanced mobilization in catchments with higher BFI_m or BFI_range is likely due to the more variable flow pathways that occur in catchments with higher baseflow contributions. These variable flow pathways can lead to higher concentration gradients between low flows and high flows, where the former is generally dominated by groundwater/slow subsurface flow while the latter by surface water sources, respectively. This result highlights the crucial role of flow pathways in determining catchment exports of solutes and particulates. Our study also demonstrates the need for further studies on how the temporal variations of flow regimes and baseflow contributions influence flow pathways and the potential impacts of these flow pathways on catchment C–Q relationships.

scholarly journals Synthesizing the impacts of baseflow contribution on C-Q relationships across Australia using a Bayesian Hierarchical Model

2021 ◽  
Author(s):  
Danlu Guo ◽  
Camille Minaudo ◽  
Anna Lintern ◽  
Ulrike Bende-Michl ◽  
Shuci Liu ◽  
...  
Keyword(s):  
Water Quality ◽  
Hierarchical Model ◽  
Spatial Scales ◽  
Bayesian Hierarchical Model ◽  
Spatial And Temporal Variation ◽  
Strong Impact ◽  
Climate Zones ◽  
Bayesian Hierarchical ◽  
Flow Pathways ◽  
The Impact

Abstract. The spatial and temporal variation of concentration-discharge (C-Q) relationships inform solute and particulate export processes. Previous studies have shown that the extent to which baseflow contributes to streamflow can affect C-Q relationships in some catchments. However, these patterns have not yet been investigated across large spatial scales. To address this, the study aims to assess how baseflow contributions, as defined by the median catchment baseflow index (BFI_m), influence C-Q slopes across 157 catchments in Australia spanning five climate zones. This study focuses on six water quality variables: electrical conductivity (EC), total phosphorus (TP), soluble reactive phosphorus (SRP), total suspended solids (TSS), nitrate–nitrite (NOx) and total nitrogen (TN). The impact of baseflow contribution is explored with a novel Bayesian hierarchical model. We found that BFI_m has a strong impact on C-Q slopes. C-Q slopes are largely positive for nutrient species (NOx, TN, SRP and TP) and are steeper in catchments with higher BFI_m across all climate zones (for TN, SRP and TP). On the other hand, we also found a generally higher variation in instantaneous BFI for catchments with high BFI_m. Thus, the steeper C-Q slopes found in catchments with high BFI_m may be a result of a larger variation in water sources and flow pathways between low (baseflow-dominated) and high (quickflow-dominated) flow conditions. In contrast, catchments with low BFI_m may have more homogeneous flow pathways at both low and high flows, resulting in less variable concentrations and thus a flatter C-Q slope. Our model can explain over half of the observed variability in concentration of TSS, EC and P species across all catchments (93 % for EC, 63 % for TP, 63 % for SRP, and 60 % for TSS), while being able to predict C-Q slopes across space by BFI_m. This indicates that our parsimonious model has potential for predicting the C-Q slopes for catchments in different climate zones, and thus improving the predictive capacity for water quality across Australia.

scholarly journals Measuring spatial allocative efficiency in basketball

2020 ◽  
Vol 16 (4) ◽  
pp. 271-289
Author(s):  
Nathan Sandholtz ◽  
Jacob Mortensen ◽  
Luke Bornn
Keyword(s):  
Spatial Distribution ◽  
Hierarchical Model ◽  
Opportunity Cost ◽  
Allocative Efficiency ◽  
Bayesian Hierarchical Model ◽  
National Basketball Association ◽  
Spatial Context ◽  
Bayesian Hierarchical ◽  
The Impact

AbstractEvery shot in basketball has an opportunity cost; one player’s shot eliminates all potential opportunities from their teammates for that play. For this reason, player-shot efficiency should ultimately be considered relative to the lineup. This aspect of efficiency—the optimal way to allocate shots within a lineup—is the focus of our paper. Allocative efficiency should be considered in a spatial context since the distribution of shot attempts within a lineup is highly dependent on court location. We propose a new metric for spatial allocative efficiency by comparing a player’s field goal percentage (FG%) to their field goal attempt (FGA) rate in context of both their four teammates on the court and the spatial distribution of their shots. Leveraging publicly available data provided by the National Basketball Association (NBA), we estimate player FG% at every location in the offensive half court using a Bayesian hierarchical model. Then, by ordering a lineup’s estimated FG%s and pairing these rankings with the lineup’s empirical FGA rate rankings, we detect areas where the lineup exhibits inefficient shot allocation. Lastly, we analyze the impact that sub-optimal shot allocation has on a team’s overall offensive potential, demonstrating that inefficient shot allocation correlates with reduced scoring.

A point-based Bayesian hierarchical model to predict the outcome of tennis matches

2019 ◽  
Vol 15 (4) ◽  
pp. 313-325 ◽  
Author(s):  
Martin Ingram
Keyword(s):  
Random Walk ◽  
Hierarchical Model ◽  
Bayesian Hierarchical Model ◽  
Bayesian Hierarchical ◽  
Gaussian Random Walk ◽  
Over Time ◽  
Modelling Approach ◽  
Independent And Identically Distributed

Abstract A well-established assumption in tennis is that point outcomes on each player’s serve in a match are independent and identically distributed (iid). With this assumption, it is enough to specify the serve probabilities for both players to derive a wide variety of event distributions, such as the expected winner and number of sets, and number of games. However, models using this assumption, which we will refer to as “point-based”, have typically performed worse than other models in the literature at predicting the match winner. This paper presents a point-based Bayesian hierarchical model for predicting the outcome of tennis matches. The model predicts the probability of winning a point on serve given surface, tournament and match date. Each player is given a serve and return skill which is assumed to follow a Gaussian random walk over time. In addition, each player’s skill varies by surface, and tournaments are given tournament-specific intercepts. When evaluated on the ATP’s 2014 season, the model outperforms other point-based models, predicting match outcomes with greater accuracy (68.8% vs. 66.3%) and lower log loss (0.592 vs. 0.641). The results are competitive with approaches modelling the match outcome directly, demonstrating the forecasting potential of the point-based modelling approach.

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