Network Replicability & Generalizability: Exploring the Effects of Sampling Variability, Scale Variability, and Node Reliability

Work surrounding the replicability and generalizability of network models has increased in recent years, prompting debate as to whether network properties can be expected to be consistent across samples. To date, certain methodological practices may have contributed to observed inconsistencies, including the common use of single-item indicators to estimate nodes, and use of non-identical measurement tools. The current study used a resampling approach to systematically disentangle the effects of sampling variability from scale variability when assessing network replicability. Additionally, we explored the extent to which consistencies in network characteristics were improved when precision in node estimation was increased. Overall, scale variability produced less stability in network properties than sampling variability, however under more optimal measurement conditions (i.e. larger sample, greater node precision), discrepancies were markedly reduced. Findings also importantly underscored the value of improving node reliability: Use of multi-item indicators led to denser networks, higher network sensitivity, greater estimates of global strength, and greater levels of consistency in network properties (e.g., edge weights, centrality scores). Taken together, variability in network properties across samples may be less indicative of a lack of replicability, but may arise from poor measurement precision, and/or may reflect properties of the underlying true network model or scale-specific properties. All data and syntax are openly available online (https://osf.io/m37q2/).

On the physical constraints for the exceeding probability of deep water rogue waves

<p><strong>(manuscript accepted into Applied Ocean Research https://www.researchgate.net/publication/344786014)</strong></p><p><strong>Abstract</strong></p><p>Nearly four decades have elapsed since the first efforts to obtain a realistic narrow-banded model for extreme wave crests and heights were made, resulting in a couple of dozen different exceeding probability distributions. These models reflect results of numerical simulations and storm records measured from oil platforms, buoys, and more recently, satellite data. Nevertheless, no consensus has been achieved in either deterministic or operational approaches. Typically, distributions found in the literature analyze a very large set of waves with large variations in sea-state parameters while neglecting homogeneous smaller samples, such that we lack a suitable definition for the sample size and homogeneity of sea variables, also known as sampling variability (Bitner-Gregersen et al., 2020). Naturally, a possible consequence of such sample size inconsistency is the apparent disagreement between several studies regarding the prediction of rogue wave occurrence, as some studies can report less rogue wave heights while others report more rogue waves or the same statistics predicted by Longuet-Higgins (1952), sometimes a combination of the three in the very same study (Stansell, 2004; Cherneva et al., 2005). In this direction, we have obtained a dimensionless parameter capable of measuring how large the deviations in sea state variables can be so that accuracy in wave statistics is preserved.  In particular, we have defined which samples are too heterogeneous to create an accurate description of the uneven distribution of rogue wave likelihood among different storms (Stansell, 2004). Though the literature is rich in physical bounds for single waves, here we describe empirical physical limits for the ensemble of waves (such as the significant steepness) devised to bound these variables within established and prospective wave distributions. Furthermore, this work supplies a combination of sea state parameters that provide guidance on the influence of sea states influence on rogue wave occurrence. Based on these empirical limits, we conjecture a mathematical model for the dependence of the expected maximum of normalized wave heights and crests on the sea state parameters, thus explaining the uneven distribution of rogue wave likelihood among different storms collected by infrared laser altimeters of the North Alwyn oil platform discussed in Stansell (2004). Finally, we demonstrate that for heights and crests beyond 90% of their thresholds (H>2H<sub>1/3</sub> for heights), the exceeding probability becomes stratified, i.e. they resemble layers of probability curves according to each sea state, suggesting the existence of a dynamical definition for rogue waves rather than purely statistical.</p><p> </p><p><strong>References</strong></p><p>Bitner-Gregersen, E. M., Gramstad, O., Magnusson, A., Malila, M., 2020. Challenges in description of nonlinear waves due to sampling variability. J. Mar. Sci. Eng. 8, 279.</p><p>Longuet-Higgins, M., 1952. On the statistical distribution of the heights of sea waves. Journal of Marine Research 11, 245–265.</p><p>Stansell, P., 2004. Distribution of freak wave heights measured in the north sea. Appl. Ocean Res. 26, 35–48.</p><p>Cherneva, Z., Petrova, P., Andreeva, N., Guedes Soares, C., 2005. Probability distributions of peaks, troughs and heights of wind waves measured in the black sea coastal zone. Coastal Engineering 52, 599–615.</p>

Wave height return periods from combined measurement–model data: a Baltic Sea case study

This paper presents how to account for the lack of sampling variability in model data when they are combined with wave measurements. We addressed the dissimilarities between the types of data by either (i) low-pass filtering the observations or (ii) adding synthetic sampling variability to the model. Measurement–model times series combined with these methods served as the basis for return period estimates of a high wave event in January 2019. During this storm northerly wind speeds in the Baltic Sea rose to 32.5 m s−1 and an unprecedented significant wave height of 8.1 m was recorded in the Bothnian Sea sub-basin. Both methods successfully consolidated the combined time series but produced slightly different results: using low-pass-filtered observations gave lower estimates for the return period than using model data with added sampling variability. Extremes in both types of data followed the same type of theoretical distributions, and our best estimate for the return period was 104 years (95 % confidence 39–323 years). A similar wave event can potentially be more likely in the future climate, and this aspect was discussed qualitatively.

Wave height return periods from combined measurement–model data: A Baltic Sea case study

This paper presents how to account for the lack of sampling variability in model data when they are combined with wave measurements. We addressed the dissimilarities between the types of data by either: i) low-pass filtering the observations or ii) adding synthetic sampling variability to the model. Measurement–model times series combined with these methods served as the basis for return period estimates of a high wave event in January 2019. During this storm northerly wind speeds in the Baltic Sea rose to 32.5 m s−1 and an unprecedented significant wave height of 8.1 m was recorded in the Bothnian Sea sub-basin. Both methods successfully consolidated the combined time series but produced slightly different results: using low-pass filtered observations gave lower estimates for the return period than using model data with added sampling variability. Extremes in both types of data followed the same type of theoretical distributions, and our best estimate for the return period was 104 years (95 % confidence 39–323 years). A similar wave event can potentially be more likely in the future climate, and this aspect was discussed qualitatively.

Challenges in Description of Nonlinear Waves Due to Sampling Variability

Wave description is affected by several uncertainties, with sampling variability due to limited number of observations being one of them. Ideally, temporal/spatial wave registrations should be as large as possible to eliminate this uncertainty. This is difficult to reach in nature, where stationarity of sea states is an issue, but it can in principle be obtained in laboratory tests and numerical simulations, where initial wave conditions can be kept constant and intrinsic variability can be accounted for by changing random seeds for each run. Using linear, second-order, and third-order unidirectional numerical simulations, we compare temporal and spatial statistics of selected wave parameters and show how sampling variability affects their estimators. The JONSWAP spectrum with gamma peakedness parameters γ = 1, 3.3, and 6 is used in the analysis. The third-order wave data are simulated by a numerical solver based on the higher-order spectral method which includes the leading-order nonlinear dynamical effects. Field data support the analysis. We demonstrate that the nonlinear wave field including dynamical effects is more sensitive to sampling variability than the second-order and linear ones. Furthermore, we show that the mean values of temporal and spatial wave parameters can be equal if the number of simulations is sufficiently large. Consequences for design work are discussed.