In this Reply, we address the concerns of Knoben and Clark (2023, https://doi.org/10.1029/2022WR034294) or KC23 that “the assumptions needed to effectively use difference‐based variance estimation ...methods are not always met by hourly streamflow records.” There should be little doubt that the assumptions of our difference‐based estimator will sometimes be violated in hourly streamflow records but the results from de Oliveira and Vrugt (2022, https://doi.org/10.1029/2022wr032263) and confirmed by the findings in our Reply show that such violations are sporadic enough not to affect much the error variance estimates. Snowmelt as pointed out by KC23 (https://doi.org/10.1029/2022WR034294) may not have received sufficient attention in our paper, yet their 365‐day record is simply not long enough to demonstrate bias of our discharge error variance estimates (and their dependence on flow level). This would require analysis of a much longer, multi‐year, streamflow record of a snowmelt‐driven watershed. The snowmelt catchment analyzed in dOV22 (https://doi.org/10.1029/2022wr032263) did not demonstrate bias in the discharge error variance estimates. We also provide additional clarification on the interpretation of the variance estimates obtained with the nonparametric estimator, and discuss the main issues in the test case presented in Knoben and Clark (2023, https://doi.org/10.1029/2022WR034294)).
Key Points
We address the concerns of Knoben and Clark (2023) on the use of the nonparametric estimator with hourly discharge data
We provide further clarification on the interpretation of the variance estimates obtained with the nonparametric estimator
In this paper, we introduce a relatively simple data‐driven method for the representation of the uncertainty in daily discharge records. The proposed method relies only on hourly discharge data and ...takes advantage of a nonparametric difference‐based estimator in the characterization of random errors in discharge time series. We illustrate with corrupted streamflow data that the nonparametric estimator provides an accurate characterization of the nature (homoscedastic or heteroscedastic) and magnitude of these errors. In addition, we demonstrate the practical usefulness of the estimator using discharge time series of 500+ watersheds of the Catchment Attributes and MEteorology for Large‐sample Studies data set. This analysis reveals that the magnitude of errors of aleatory nature in the investigated discharge records is rather small (less than 3% for 80% of the records). We then combine the effect of random errors and measurement frequency into a daily variance estimate, which serves as input to a streamflow generation approach. This procedure produces replicates of the discharge record which portray accurately the assigned streamflow uncertainty, preserve key statistical properties of the discharge record and are hydrologically realistic. The proposed method facilitates Bayesian analysis and supports tasks such as model diagnostics, data assimilation, uncertainty quantification and regionalization.
Key Points
We present a model‐agnostic method for the generation of replicates of discharge records
The nonparametric estimator provides an accurate estimate of random errors, which for the investigated discharge records are rather small
The replicates portray accurately the assigned streamflow uncertainty and preserve statistical and hydrologic properties
Electrostatic assembly is used here to couple CdS nanorods with Co3O4 nanoparticles into photocatalytic systems that simultaneously oxidize water and mediate electron transfer. Layered films of CdS ...nanorods and Co3O4 nanoparticles are first used to generate high photocurrents electrochemically as opposed to CdS or Co3O4 alone. Dispersed clusters of CdS nanorods conjugated with Co3O4 nanoparticles are next shown to efficiently oxidize water and reduce methylene blue in solution.
•The confidence intervals of the KG efficiency do not have a closed-form description.•The uncertainty of KG efficiency is attributed to measurement errors of training data.•Statistical inference with ...an informal goodness-of-fit metric is coined diagnostic regression.•Parameter confidence regions of KG efficiency in agreement with linear regression theory.•Marginal parameter distributions of KG efficiency are approximately Gaussian.
The Kling-Gupta efficiency, hereafter referred to as KG efficiency rather than its common abbreviation KGE, proposed by Gupta et al. (2009) has become a widely used metric for evaluating the goodness-of-fit of n-vectors of observations, ỹ=ỹ1ỹ2…ỹn⊤, and corresponding model simulations, yθ=y1θy2θ…ynθ⊤. This metric rectifies some of the shortcomings of the coefficient of determination, R2, also known to hydrologists as the efficiency of Nash and Sutcliffe (1970), by using a Euclidean-distance based weighting of the correlation, bias and temporal variability of the observed, ỹ, and simulated, yθ, data. But as the KG efficiency is not borne out of assumptions with respect to the statistical distribution of the residuals, eθ=ỹ-yθ, we cannot formally characterize its uncertainty. The NS efficiency suffers a similar problem, yet, statistical theory postulates that its confidence intervals should follow a beta distribution in certain special cases. Without a formal description of the confidence intervals of the KG efficiency, we cannot (amongst others) quantify parameter uncertainty, compute confidence and prediction limits on simulated model responses, inform decision makers about critical modeling uncertainties, evaluate model adequacy and assess the information content of calibration data. More fundamentally, without confidence intervals we cannot establish whether the KG efficiency is a consistent, efficient and unbiased estimator. In this paper we present an empirical description of the confidence intervals of the KG efficiency. We relate the unknown probability distribution of the KG efficiency to the measurement errors of the training data record, ỹ, and use the bootstrap method to carry out statistical inference. We illustrate our method by application to a simple linear regression function for which the least squares parameter confidence regions are exactly known and two hydrologic models of contrasting complexity. The empirical parameter confidence regions and/or intervals of the KG efficiency are compared to those derived from generalized least squares, objective function contouring and Bayesian analysis using Markov chain Monte Carlo simulation. The marginal parameter distributions of the KG efficiency are generally well described by a normal distribution. Results further confirm that the distribution of the KG efficiency is a complex function of data length and the magnitude, distribution and structure of the measurement errors. This prohibits an analytic description of the empirical confidence regions and/or intervals of the KG efficiency and reiterates the need for the bootstrap method.
This study compares single-site, multi-site and multi-variable SWAT calibration. The SWAT model was applied to a large basin (63 884 km
2
) and calibrated at a monthly time step with the SUFI-2 ...algorithm, using the Kling-Gupta efficiency (KGE) as the objective function. Multi-variable calibration was performed by combining streamflow and remote sensing-derived actual evapotranspiration data. Parameter transferability was also investigated, by daily time step validation. The KGE for the outlet ranged from 0.73 to 0.86, and the average KGE of all streamflow gauge stations ranged from 0.73 to 0.80, reflecting a good overall simulation performance for the monthly time step. In daily time step validation, KGE ranged from 0.62 to 0.68, and the Nash-Sutcliffe efficiency ranged from 0.40 to 0.60, for the average of all gauge stations. Multi-site and multi-variable calibrations did not significantly improve inner sub-basin simulation performance but improved streamflow uncertainty when compared to single-site calibration.
The innovation process has traditionally been understood as a predefined sequence of phases: idea generation, selection, development, and launch/diffusion/sales. Drawing upon contingency theory, we ...argue that innovation process may follow a number of different paths. Our research focuses on a clear theoretical and managerial question, i.e., how does a firm organize and plan resource allocation for those innovation processes that do not easily fit into traditional models. This question, in turn, leads to our research question: Which configuration of innovation processes and resource allocation should be employed in a given situation, and what is the rationale behind the choice? Based on a large-scale study analyzing 132 innovation projects in 72 companies, we propose a taxonomy of eight different innovation processes with specific rationales that depend on a project׳s contingencies.
•Not all innovation projects fit in the traditional linear process from-idea-to-launch.•Which configuration and rationale of the innovation process for which situation?•We researched 132 cases of innovation projects in 72 companies.•We propose eight types of innovation processes according to specific contingencies.•Uncertainties shape the structure and the content of the innovation process.
Core‐Shell (CS) polymeric particles have attracted great interest due to their high mechanical, thermal, and chemical stability and their surface properties. In this study, functionalizable CS ...poly(propylene/styrene)/poly(acrylonitrile) (PP/PS/PAN) particles were prepared through heterogeneous polymerizations in a batch reactor. Commercial PP particles and PP/PS particles (prepared by seeded suspension polymerization of styrene (Sty) on PP spheres) were applied as core components of the final structure, while the shell was prepared through acrylonitrile dispersion polymerization. The degree of swelling of the core particles by Sty played an important role for the adhesion of the PAN shell, which for PP particles was 24 wt%, whereas for PP/PS hybrid particles it was 57 wt%. The particles (PP/PS and CS) were characterized through image analysis, revealing a uniform and smooth surface for PP/PS spheres and a uniform porous shell for CS particles. Particle size distributions, thermal degradation, chemical structures, degrees of crystallinity, and textural properties were also evaluated. The PAN shell adhered to the PP/PS particles without forming a copolymer, and the CS particles formed by a PP/PS core and PAN shell had sizes of 4.54 ± 1.24 mm, specific area of 2.70 m2g−1 and PAN content of 15.98 ± 0.82% (m/m) of total particles.
Graphical summary of the synthesis of core and shell particles of the final core‐shell structure (PP/PS/PAN).
This work reports new results about the solvent-free enzymatic production of ethylene glycol monostearate, an industrially important emollient ester conventionally produced by a chemical route. For ...this purpose, reactions were carried out using two commercial immobilized lipases, evaluating the effect of temperature, agitation, and enzyme concentration on the reaction conversion. It was shown that, for most tested conditions, reaction conversions around 100% were achieved. The reuse of the enzyme was also evaluated with satisfactory results up to four enzyme cycles. System scale-up by 9-fold allowed reaching conversions of up to 99%. Chemical analyzes showed that the product obtained through enzymatic synthesis presented very good characteristics, which makes the enzymatic esterification process employed in this work an interesting and promising route for possible application at industrial scale.
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