Extending the Applicability of the Generalized Likelihood Function for Zero‐Inflated Data Series

Oliveira, Debora Yumi de; Chaffe, Pedro Luiz Borges; Sá, João Henrique Macedo

doi:10.1002/2017wr021560

Cited by 10 publications

(10 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Future research on the impact of zero flow treatment in residual error modeling and hydrological prediction in ephemeral catchments could address the following limitations: The explicit approach used in this study generates predictive distributions with a theoretical maximum of 50% probability of zero flows, as explained in section . This limitation could be addressed by allowing the median of the predictive distribution to go below

q_{t}^{{boldθ}_{H}}

using additional shift/skew parameters (e.g., Schoups & Vrugt, ) or by explicitly modeling the probability of zero flows, for example, by using zero‐inflation approaches (e.g., Oliveira et al, ; Smith et al, ). The explicit approach used in this study only censors observed zero flows. In practice, there may be lower/upper detection limits beyond which the instrumentation and methods used to measure streamflow becomes unreliable (Westra et al, ).…”

Section: Discussionmentioning

confidence: 99%

“…Since the cumulative distribution function of the mixed continuous/discrete predictive distribution is discontinuous at Q t = 0, the p value of a zero‐flow observation cannot be computed directly. In this case we draw a uniform random number p * from U [0, p 0 ], where the upper bound p 0 is the probability of zero flow at that time step, and treat p * as the p value of the zero‐flow observation (Oliveira et al, ; Wang & Robertson, ). When predictions are perfectly reliable, the PQQ plot follows the 1:1 line.…”

Section: Case Study Descriptionmentioning

confidence: 99%

“…This theoretical limitation manifests in an overabundance of negative standardized/pseudo-standardized residuals, as seen in Figures 6g and 6h, and could be one (of potentially many) reasons for poor predictive performance in these catchments. Zero-inflation approaches can allow for higher probability of zero flows through a dedicated Bernoulli parameter (e.g., Oliveira et al, 2018;Smith et al, 2010), and may be less susceptible to this problem.…”

Section: Cases Where Explicit Approach Offers Little Benefitmentioning

confidence: 99%

“…For example, Smith et al (2010) presented a two-level zero-inflation approach where a Bernoulli parameter controls the probability of zero flows, with nonzero flows modeled using a transformed Gaussian distribution. In a recent study with a canopy interception model, Oliveira et al (2018) combined a similar zero-inflation approach with the skewed exponential power distribution with dedicated heteroscedasticity, skew, and kurtosis parameters (Schoups and Vrugt (2010).…”

Section: Introductionmentioning

confidence: 99%

“…Censoring approaches are well established in the research literature (e.g., Li et al, 2013;Pagano et al, 2013;Wang & Robertson, 2011) and adopted in operational applications (e.g., Bennett et al, 2016). The application of zero-inflation approaches to hydrological modeling is promising yet still in the development stage, with some notable challenges: (i) The Smith et al (2010) implementation conditions its error model on observed streamflow, making its application in prediction problematic, and (ii) the Oliveira et al (2018) implementation conditions on simulated streamflow but requires further testing in rainfall-runoff modeling beyond its published application to a canopy model. For these reasons, this work focuses on censoring approaches and defers analysis of zero inflation approaches to a dedicated study.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Benefits of Explicit Treatment of Zero Flows in Probabilistic Hydrological Modeling of Ephemeral Catchments

McInerney

Kavetski

Thyer

et al. 2019

Water Resources Research

View full text Add to dashboard Cite

Probabilistic modeling of streamflow in ephemeral catchments, where streamflow is frequently zero or negligible, is a major scientific and operational challenge. This paper evaluates the benefits of an explicit treatment of zero flows in the residual error models used for hydrological model calibration and prediction. In this approach, the lower bound of zero for streamflow is implemented using a censoring approach. The explicit approach is compared to a simpler pragmatic approach, which imposes the zero streamflow bound in prediction but not in calibration. Following a theoretical exposition, empirical comparisons are reported using a daily rainfall‐runoff model (GR4J), four residual error schemes (based on log, log‐sinh, and Box‐Cox [BC] transformations with λ = 0.2 and 0.5), 74 Australian catchments with diverse hydroclimatology, and five performance metrics (reliability, precision, bias, proportion of zero flow days, and Continuous Ranked Probability skill score). The key findings are as follows: (1) in mid‐ephemeral catchments (5–50% zero flows) the explicit approach improves predictive performance, especially reliability, through better characterization of residual errors; (2) BC0.2 and BC0.5 schemes are Pareto optimal in mid‐ephemeral catchments (when the explicit approach is used): BC0.2 achieves better reliability and is recommended for probabilistic prediction, whereas BC0.5 attains lower volumetric bias; (3) in low‐ephemeral catchments (<5% zero flows) the pragmatic approach is sufficient; (4) in high‐ephemeral catchments (>50% zero flows) theoretical limitations result in poor performance of these particular explicit and pragmatic approaches, and further development is needed. The findings provide guidance on improving probabilistic streamflow predictions in ephemeral catchments.

show abstract