We develop a remote wave gauging technique to estimate wave height and period from imagery of waves in the surf zone. In this proof-of-concept study, we apply the same framework to three datasets: the first, a set of close-range monochrome infrared (IR) images of individual nearshore waves at Duck, NC, USA; the second, a set of visible (i.e. RGB) band orthomosaics of a larger nearshore area near Santa Cruz, CA, USA; and the third, a set of oblique (unrectified) images from the same site. The network is trained using coincident images and in situ wave measurements. The optical wave gauge (OWG) consists of a deep convolutional neural network (CNN) to extract features from imagery — called a ‘base model’, with additional layers to distill the feature information into lower dimensional spaces, and a final layer of dense neurons to predict continuously varying quantities. Four base models are compared. The OWG is trained for both individual wave height and period, and statistical quantities like significant wave height and peak wave period. The best performing OWG on the IR dataset achieved RMS errors of 0.14 m and 0.41 s for height and period, respectively, capturing up to 98% of the variance in these quantities. The best performing OWG on the visible band rectified dataset achieved RMS errors of 0.08 m and 0.79 s, respectively, for height and period. The same values for the oblique RGB imagery were 0.11 m and 0.81 s for height and period, respectively. Overall, wave height and period accuracy is sensitive to choice of base model; OWGs built upon MobilenetV2 tend to perform worst and those built on Inception-ResnetV2 have the smallest RMS error. The presence or otherwise of residual layers in the model makes little systematic difference to the final OWG accuracy. Smaller batch sizes used in model training tend to result in more accurate OWGs. An out-of-calibration validation, using images associated with wave heights or periods outside the range of values represented in the training data, showed that the ability for OWGs to predict the bottom 5% of low wave heights and the top 5% of high wave heights was reasonably good, but the same was not generally true of wave period. The same framework, not optimized for either dataset, predicts both quantities with high accuracy when trained on imagery, despite the differences in electromagnetic band, perspective, and scale. The OWG estimates wave properties from an image in less than 100 ms on a modestly sized CPU, allowing for the possibility of continuous real-time wave estimates.

We apply deep convolutional neural networks (CNNs) to estimate wave breaking type (e.g., non-breaking, spilling, plunging) from close-range monochrome infrared imagery of the surf zone. Image features are extracted using six popular CNN architectures developed for generic image feature extraction. Logistic regression on these features is then used to classify breaker type. The six CNN-based models are compared without and with augmentation, a process that creates larger training datasets using random image transformations. The simplest model performs optimally, achieving average classification accuracies of 89% and 93%, without and with image augmentation respectively. Without augmentation, average classification accuracies vary substantially with CNN model. With augmentation, sensitivity to model choice is minimized. A class activation analysis reveals the relative importance of image features to a given classification. During its passage, the front face and crest of a spilling breaker are more important than the back face. For a plunging breaker, the crest and back face of the wave are most important, which suggests that CNN-based models utilize the distinctive ‘streak’ temperature patterns observed on the back face of plunging breakers for classification.

Thermal infrared (IR) imagery is used to quantify the high spatial and temporal variability of dissipation due to wave breaking in the surf zone. The foam produced in an actively breaking crest, or wave roller, has a distinct signature in IR imagery. A retrieval algorithm is developed to detect breaking waves and extract wave roller length using measurements taken during the Surf Zone Optics 2010 experiment at Duck, NC. The remotely derived roller length and an in situ estimate of wave slope are used to estimate dissipation due to wave breaking by means of the wave-resolving model by Duncan (1981). The wave energy dissipation rate estimates show a pattern of increased breaking during low tide over a sand bar, consistent with in situ turbulent kinetic energy dissipation rate estimates from fixed and drifting instruments over the bar. When integrated over the surf zone width, these dissipation rate estimates account for 40–69% of the incoming wave energy flux. The Duncan (1981) estimates agree with those from a dissipation parameterization by Janssen and Battjes (2007), a wave energy dissipation model commonly applied within nearshore circulation models.