**1. Introduction**

Marine radars (MR) are designed for navigation and vessel traffic control. Depending on the physical environmental conditions given by precipitation, wind and waves, signatures of the sea surface commonly referred to as *sea clutter* become visible in the near range (<5 km) of the MR radar images. Regarded as a disruptive noise for navigational purposes, *sea clutter* is normally suppressed. Even though *sea clutter* signatures are well known, they are still not completely resolved, and are still under investigation both experimentally and theoretically. Nevertheless, it turns out that *sea clutter* includes valuable information on surface waves [1]. Following Bragg theory, *sea clutter* is caused by the backscatter of the transmitted electromagnetic waves from the short sea surface ripples in the range of half the electromagnetic wavelength (i.e., ~1.5 cm). Longer waves, such as wind sea (~10 m) and swell (~100 m), become visible as they modulate the *sea clutter* signal. Both surface currents and water depth affect the wave propagation [2,3]. As MRs image *sea clutter* simultaneously in time and space, this allows the derivation of multi-directional unambiguous wave information, surface currents, and (in shallow water) also water depth.

Driven by the growing need for precise information about waves and surface currents, commercially available MR-based wave and current monitoring devices, such as WaMoS® II, have

been developed [4–6]. Their capability and performance in a wide range of different applications, ranging from coastal applications [7–9] to vessel-mounted applications [10–12], have been proven.

The *sea clutter* observations of MRs typically range up to 3–5 km, with spatial and temporal resolutions on the order of 7.5 m and 2 s, respectively. This allows MRs to monitor waves longer than 15 m and current conditions over an area of several km2 in real time. As *sea clutter* is caused by the *Bragg* backscatter of the transmitted electromagnetic waves from the short sea surface ripple waves (~2 cm), a minimum wind speed of 2–3 m/s is required for its presence [13]. In calm periods in the absence of ripples, no *sea clutter* can be observed, thereby preventing MR sea state and current observations. Also, signatures of rain or snow (*weather clutter*), or other features in the radar image not related to *sea clutter,* can disturb MR wave and current observations. These environmental limitations reduce the confidence and acceptance of the MR-based measurements, and therefore need to be treated carefully.

The aim of this paper is to assess the present status of the MR-based WaMoS® II system, focusing on its data usability with respect to reliability and accuracy. For this purpose, current measurements obtained onboard the German research vessel *Polarstern* during the Atlantic transit cruise PS113 [14] between Punta Arenas, Chile, and Bremerhaven, Germany, in May 2018 are used. The outline of the paper is as follows: In Section 2, we give a brief introduction on the methods used to estimate the accuracy and precision of fluctuating measurements. Section 3 describes the sensors used, with a focus on WaMoS® II. In Section 4, we present the WaMoS® II real-lime quality control (*rtQC*) used to specify data reliability. Observations made during the Atlantic transit cruise PS113 are presented in Section 5. Results of the accuracy estimation and comparison with acoustic Doppler current profiler (ACDP) measurements are presented in Section 6. Finally, in Section 7, we give a summary and draw conclusions.

#### **2. Methods: Accuracy and Precision**

A common method to evaluate the accuracy and precision of measurements is to perform a direct comparison of data sets from different sensors. In the case of MR-based current measurements, corresponding reference measurements from in situ sensors like ADCPs are used [15]. The underlying assumption of this approach is that both sensors observe the same property (*P*), and it is assumed that spatial and temporal homogeneity and deviations between the data sets can be related directly to inaccuracies in the measurements. However, this method of comparison is limited in that observed deviations do not automatically relate to inaccuracies of the measurement technique [16]. The biggest contribution to independent sensor deviations can be attributed to the different measurement locations of the sensors. For example, an ADCP delivers subsurface current measurements in a limited local volume, while MR-based observation represents current measurements at the sea surface over a spatial domain of several hundreds of square meters. Due to different current structures (e.g., wind-forced surface Ekman flow and geostrophic current shear extending deeply over a large part of the water column), vertical homogeneity is not given at all times. Ref. [17] found that 80%, or more, of the observed deviations between ADCP and HF radar current measurements on the West Florida shelf were associated with horizontal and vertical separation between the measurements.

In addition, the informative value of the direct comparison of two independent data sets might be misleading, as it completely neglects the natural variability of the current as a vector, consisting of mean, oscillatory and chaotic contributions. This makes the results more difficult to compare and properly interpret [18]. Therefore, we use a combination of methods to evaluate the quality, reliability, precision, and accuracy of MR surface current measurements.

For practical handling of a fluctuating quantity, *P*, its temporal averages *P* over a suitable period (averaging time τ) are used. This allows to describe *P* as *P* = *P* + *P* , where *P* is the fluctuation with *P* = 0. Based on this assumption, the resulting measurement is represented by the average *P*, which depends, among other things, also on the used sampling and averaging intervals.

In this paper, we aim to evaluate the general performance of WaMoS® II data by directly comparing both the mean current, *U*, and the corresponding standard deviation, σ*U*, representing the

short-term oceanic fluctuating component of the current. To evaluate the accuracy of the WaMoS® II measurements, a direct comparison of *U*, with the corresponding ADCP measurements is carried out, where the accuracy is described by correlation coefficient (*r*), bias (Δ) and standard deviation (σΔ) of the difference:

$$\sigma = \frac{\sum\_{i=1}^{N} \left( \mathbf{X}\_{i} - \overline{\mathbf{X}} \right) \left( \mathbf{Y}\_{i} - \overline{\mathbf{Y}} \right)}{\sqrt{\sum\_{i=1}^{N} \left( \mathbf{X}\_{i} - \overline{\mathbf{X}} \right) \cdot \sum\_{i=1}^{N} \left( \mathbf{Y}\_{i} - \overline{\mathbf{Y}} \right)}} \tag{1}$$

$$\overline{\Delta}\_{\cdot} = \frac{1}{N} \sum\_{i=1}^{N} \Delta\_{i\cdot} \text{ with } \Delta\_{i} = |X\_{i} - Y\_{i}| \tag{2}$$

$$
\sigma\_{\Lambda} = \sqrt{\frac{1}{N-1} \left( \sum\_{i=1}^{N} \left( \Delta\_{i} - \Delta \right)^{2} \right)} \tag{3}
$$

where *X* = <sup>1</sup> *N* %*<sup>N</sup> <sup>i</sup>* <sup>=</sup> <sup>1</sup> *Xi* and *<sup>Y</sup>* = <sup>1</sup> *N* %*<sup>N</sup> <sup>i</sup>* <sup>=</sup> <sup>1</sup> *Yi* represent the mean measurement of the data sets *X* and Y, respectively. The resulting combined standard deviation is defined as σ<sup>Δ</sup> = σ2 *<sup>X</sup>* <sup>+</sup> <sup>σ</sup><sup>2</sup> *Y*. Assuming that the measurement errors of the two sensors are uncorrelated and of equal magnitude, the individual (single) standard deviation σ*<sup>s</sup>* = σ*<sup>X</sup>* = σ*Y*, and can hence be estimated by:

$$
\sigma\_S = \frac{1}{2}\sqrt{2}\,\sigma\_\Lambda. \tag{4}
$$

Note that *r*, Δ, and σ*<sup>S</sup>* include deviations related to horizontal (σΔ*h*) and vertical (σΔ*v*) gradients, as well as temporal variation (σ*t*) of *P*, which are not related to inaccuracies of the measurement device. Using the mean instead of the instantaneous measurements leads to statistically more stable and reliable results as the effect of uncorrelated natural variability is minimized.

To evaluate the precision of an individual sensor itself, we use a more general approach. This approach is based on statistical analysis of a property *P*, represented by a statistical population {*P1*, *P2*, ... , *PN*}. The precision of the measurement of *P* can be estimated by the standard deviation σ *P* of the mean *P*, which is given by:

$$\sigma(\overline{P}) = \sqrt{\frac{1}{N-1} \sum\_{i=1}^{N} \left( P\_i - \overline{P} \right)^2} \tag{5}$$

where *i* = 1, *N* denotes individual values over the averaging interval τ.

Following this strategy, the precision of a measurement is estimated by the standard deviation σ*<sup>P</sup>* of the mean *P*. Using an averaging interval of τ = 20–30 min in combination with typical update rates of WaMoS® II measurements ranging between 1–3 min allows us to obtain a sufficient number of independent measurements, and hence gives statistically significant results for our investigation.

#### **3. Data**

The data used for the WaMoS® II-ADCP comparison were acquired on board *Polarstern* during the Atlantic transit cruise PS 113 (May 2018) [14].
