A probabilistic method for the estimation of ocean surface currents from short time series of HF radar data

Highlights

• Probabilistic approach to estimate radial surface currents from HF radar data.

• Does not use the Doppler spectrum but the radar complex time series.

• Robust to noise and adapted to short time series.

• Assessment with synthetic and experimental radar data.

• Promising results for rapidly changing currents and surface current mapping.

Abstract

We present a new method for inverting ocean surface currents from beam-forming HF radar data. In contrast with the classical method, which inverts radial currents based on shifts of the main Bragg line in the radar Doppler spectrum, the method works in the temporal domain and inverts currents from the amplitude modulation of the I and Q radar time series. Based on this principle, we propose a Maximum Likelihood approach, which can be combined with a Bayesian inference method assuming a prior current distribution, to infer values of the radial surface currents. We assess the method performance by using synthetic radar signal as well as field data, and systematically comparing results with those of the Doppler method. The new method is found advantageous for its robustness to noise at long range, its ability to accommodate shorter time series, and the possibility to use a priori information to improve the estimates. Limitations are related to current sign errors at far-ranges and biased estimates for small current values and very short samples. We apply the new technique to a data set from a typical 13.5 MHz WERA radar, acquired off of Vancouver Island, BC, and show that it can potentially improve standard synoptic current mapping.

Introduction

In the past four decades, High Frequency (HF) radars have routinely been used to monitor ocean surface currents in coastal regions (see, e.g., the reviews Barrick (1978); Prandle (1991)) and, more recently, to estimate other sea state parameters (see the recent review in Paduan and Washburn (2013), Wyatt et al. (2013) and Heron et al. (2016)). HF radars take advantage of two specific physical mechanisms occurring in the HF electromagnetic (EM) wave regime, namely the over-the-horizon propagation of EM surface waves, for a vertically polarized electric field, and the dominance in the backscattered signal of a single resonant component of the ocean wave field, a process known as “Bragg scattering”. The estimation of ocean surface currents along the radar looking direction (referred to as “radial surface currents”) is typically based on identifying the frequency shift caused by the current in the backscattered Doppler spectrum to the well-defined Bragg frequency line. The performance of this estimation, in terms of accuracy, reliability, achievable range, and spatial resolution, depends on several parameters related to the radar system (e.g., carrier frequency, antenna system, integration time, emitted power), the environment (e.g., sea state, Radio Frequency Interferences (“RFI”), or a combination of both (signal-to-noise ratio (“SNR”)).

Even though the physics underlying the estimation of ocean surface currents through Bragg scattering has been well understood for a long time, we show in this paper that the processing of the radar signal can still be improved. To this effect, we propose a new non-spectral estimator that can recover (or invert) radial currents from complex radar time series, based on a Maximum Likelihood Bayesian optimization approach. The main principle of the new estimator is that, in the HF regime, ocean surface currents cause a slow amplitude modulation of the real and imaginary parts of the backscattered radar signal which, depending on the level and nature of the environmental noise affecting the data, may in some cases be easier to identify than a shift in the main spectral peak in the Doppler spectrum. Additionally, the estimation based on the amplitude modulation can be improved by resorting to Bayesian inference, in which an a posteriori probability distribution is derived for the estimated parameter (here the radial current), given the observations and some a priori information. The estimation then results from maximizing the likelihood of the a posteriori probability distribution (i.e., minimizing errors). The introduction of a priori information on radial surface currents reduces the undesirable occurrence of outliers and the dispersion of the estimates. As a result, with the new estimator, shorter time series of radar signal can in principle be used to achieve a specified confidence interval on the inverted currents, than with the Doppler-based estimation. These properties of the new estimator will be made clear in the paper.

In physical studies of ocean surface currents inverted from HF radar data based on the standard Doppler method, the time scales considered are typically on the order of 2–60 min, depending on radar frequency, the antenna system (compact antenna or large arrays), and signal-to-noise ratio. The selected observation time results from a trade-off between the conflicting requirements of using a large enough integration time to accurately compute the spectra and achieve sufficient resolution on the currents, and a short enough time to capture the temporal variability of mesoscale oceanic features. A number of studies of ocean surface currents at such spatial scales have shown that an integration/observation time on the order of 20 min is in general adequate to characterize most classical patterns of background oceanic currents, such as rapidly evolving eddies, tidal and subtidal fluctuations, and the ocean response to a changing wind stress (see references in Paduan, Washburn, 2013, Wyatt, et al., 2013). However, for some emerging applications, such as the early detection of tsunamis (e.g. Lipa, Barrick, Bourg, Nyden, 2006, Gurgel, Dzvonkovskaya, Pohlmann, Schlick, Gill, 2011, Lipa, Isaacson, 2016) and particularly the non-seismic tsunamis (e.g., meteotsunamis, landslide tsunamis), which have shorter wavelengths, a shorter integration time is required to properly capture the signature of such events in ocean surface currents, whose typical period is on the order of a few to a few tens of minutes (Grilli et al., 2017). Other applications such as the prediction of Lagrangian transport in oil spill tracking (e.g., Berta et al., 2014), the distribution of plankton blooms in ecological systems (Helbig and Pepin, 2002), or the identification of small-scale coherent structures (e.g. Parks et al., 2009; Haza et al., 2010), while not restricted to, would clearly benefit from a higher temporal resolution in the inverted surface currents. The reliable estimate of small magnitude surface currents varying at minute temporal scales would also make it possible observing infragravity waves, through the measurement of their orbital motion, which have a typical period of 30 s to a few minutes (Webb et al., 1991). Such waves, which are generated and grow in parallel with large storm systems, are key contributors to the coastal flooding and erosion such storms cause upon landing.

Estimating the Bragg frequency shift in the time domain is not new, and several attempts have been made in the literature to carry it out using non-spectral parametric methods (see Stoica et al., 2005 for a comprehensive review). Khan and radar (1991) studied the rapid variations (at the sub-minute time scale) of oceanic HF backscattered signal in the context of target detection and sea clutter suppression. He observed amplitude modulations of the HF radar time signal (his Figs. 2 and 3), which he attributed to velocity variations of ocean waves. He then proposed tracking short term variations of the main frequency around the Bragg line via an autoregressive, low-order linear, prediction model, which he showed predicted well the observed modulations of the radar signal. This made it possible demodulating the radar signal and discriminating the target, by filtering out the rapid variations of the Bragg peak. An interesting application of this for surface current estimation at a rapid time scale is the interpretation of the shifted Bragg frequency in terms of the complex roots of the prediction-error filter on the unit circle. The idea of using an autoregressive approach in the time domain for improving the estimation of surface currents was later applied by Martin et al. (1997). An instantaneous Bragg frequency, calculated on short samples (256 points), was obtained through the coefficient of the autoregressive model and the resulting estimated current was shown to be more realistic, in the sense that it did not suffer from rapid non-physical fluctuations in time, such as observed with the Doppler approach. This technique has no physical basis or constraint other than that the difference between the positive and negative Bragg peak frequencies must be twice the Bragg frequency. Another method dealing with instantaneous variations in the Bragg peak frequency was the Instantaneous-Filtering technique proposed by Middleditch and Wyatt (2006), who used it to identify and remove the frequency modulation due to the ocean variability. Our probabilistic approach belongs to the same family of parametric non-spectral techniques, as it accurately estimates instantaneous frequencies. Its main difference in purpose with these earlier approaches, however, is that it is not based on a filtering techniques but instead constrains the signal to match a physical (albeit simplistic) analytical model, namely the first-order Bragg theory, while other methods proposed earlier were entirely empirical. Another important feature of the new method is the possibility to incorporate a priori information in the current estimation. We did not yet perform a systematic comparison of our method with the earlier alternative methods for estimating radial surface currents; this task will be left out for future work.

In this paper, in Section 2, we first review the classical spectral estimation method and summarize its main features and limitations. In Section 3 we introduce a key simplified representation of the radar signal, within the frame of first-order Bragg theory, which in Section 4 naturally leads to the formulation of the new estimator of radial surface currents. The general performance of the estimator is then assessed in Sections 5 and 6, first on the basis of synthetic radar data. In Section 7, the new method is finally applied to an actual data set of HF data, recently acquired by a WERA radar system installed in Tofino (BC, Canada) to monitor ocean surface currents off of Vancouver Island. Based on a few test cases, we show that the new method has the potential of both better capturing the variability of surface currents at short time scales and extending the spatial coverage of standard synoptic current mapping. A critical discussion of the method is provided in Section 8, where its potential limitations and improvements are presented.