MEASURING SURFACE CURRENTS USING IR CAMERAS. Background. Optical Current Meter 06/10/2010. J.Paul Rinehimer ESS522

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1 J.Paul Rinehimer ESS5 Optical Current Meter 6/1/1 MEASURING SURFACE CURRENTS USING IR CAMERAS Background Most in-situ current measurement techniques are based on sending acoustic pulses and measuring the Doppler Shift of pulses that are reflected back to the transducer. In shallow water (below cm) the signal to noise ratio becomes small and the measurements unreliable. Fig. 1 shows velocity data from an Aquadopp ADCP (Acoustic Doppler Current Profilier), an instrument able to profile the velocity in the entire water column. As the tide falls and the instrument is in less than 1 cm of water, no reliable velocity measurements are obtained. Additionally, velocity measurements near the water surface are often contaminated by high noise levels as the acoustic pulses reflect from the water surface, limiting an ADCP s ability to obtain accurate surface measurements. Figure 1: Example Aquadopp ADCP data from Willapa Channel. Top panel shows along-channel current velocities with depth in m/s. Bottom panel shows salinity and temperature at the aquadopp (AQD) and within the seabed nearby. The Optical Current Meter (OCM) [1] is a data processing technique to obtain surface current measurements from video data. This technique uses a D Fourier Transform to convert a sequence of pixel intensities into an energy spectrum in frequency-wave number space and then into velocity-wave number space. A model of the velocity spectrum is fit to the data and surface velocity estimates and statistics can be calculated. This technique is applicable to any video imagery with a signal that corresponds to surface velocities and can be used to calculate 1 / 9

2 surface currents in shallow water and over larger spatial domains than a traditional one-point measurement. An imaging tower was deployed in Willapa Bay, WA with the camera field of view directed towards a tidal flat channel. Both an infrared (IR) and a visual-band camera (Fig. ) were used on the tower, along with a number of in situ instruments located in the camera field of view. The IR instrumentation was being used to measure the surface water temperature as it leaves the tidal channel in order to determine its source (pore water or drainage of surface water off the flats). An additional advantage of this technique is that a single measurement (IR imagery) can provide multiple parameters of interest in the field (velocity, water temperature, sediment temperature/type). Figure : Sample images from the Willapa Bay imaging tower. Visible light image (left) and IR image (right). The f-stop is open too far for the visible and thus the image is over-exposed and washed out. Darker is colder in the IR imagery. Note the cold buoy used as a marker on the tidal flat and the bubbles in the visible imagery. Dark, cold spots on lower right of IR are footprints from the equipment deployment on the previous day. The main channel is to the bottom of the image with the water in the monitored channel flowing towards the main channel. Before the OCM technique can be applied, the raw IR images (Fig. ) have to be rectified to a real-world coordinate system. The details would probably fill an entire course, but the rectification basically applies a matrix transformation to the raw image data transforming the image intensities at pixels into intensities with physical locations (Fig. 3). For this exercise, a subset of the data was chosen, rectified, and interpolated to a meshed grid. The particular data set chosen was a sequence of IR images along a channel where air-filled, and hence cool, bubbles were moving down the channel. Using this data set, we will obtain surface velocities via the OCM method. / 9 ESS5

3 1 6 y (m, north) y (m, north) x (m, east) x (m, east) 8 1 Figure 3: Rectified IR image. The left panel shows the full field of view while the right panel shows a closeup of the channel. Camera is at origin (,). The x and y axis directions have been reversed so that south is towards the top of the figure. Note how resolution decreases and distortion increase away from the camera. The white pattern in the far field is due to a Matlab aliasing the image when it is written. The red line is the location of the timestack. Method The optical current meter works by transforming a timestack of pixel intensities (Fig. 4) via the Fourier Transform. A timestack consists of the intensities of a single line of pixels as it varies with time. The line is chosen such that its primary axis is in the direction of the velocity you wish to measure. Looking at the example timestack (Fig. 4) the bubble streaks are apparent as regular features with a well-defined slope corresponding to their velocity. The OCM method first calculates the Fourier Transform Z (f,k) of the pixel intensities z(t, x) after multiplying it by a Bartlett taper B(t, x) (the Bartlett taper goes from at the edges to 1 in the center). Z (f,k) = B(t, x)z(t, x)e i πf t e i πkx dtdx (1) Then energy spectral density S(f,k) is then computed: S(f,k) = Z (f,k)z (f,k) () where denotes complex conjugation, producing an energy spectrum in frequency-wavenumber (f k) space. Examining this spectrum (Fig. 5), one can see that there is a large peak of energy along a narrow band with a well defined slope. The slope of this peak corresponds to the primary velocity apparent in the signal, but there are a few more steps need to accurately quantify the measurement. ESS5 3 / 9

4 .5 Distance (m) Time (s) Figure 4: Example timestack. Colormap has been inverted so that white is cool and black is warm. Note the long white streaks corresponding to dark bubbles crossing our section. 9 8 Wave Number (m 1 ) v =.66 m/s Frequency (Hz) Figure 5: Log-energy spectral density log(s( f, k)) of the timestack. The peak corresponds to the line with slope v = f /k =.66m/s. 4 / 9 ESS5

5 Next, the spectra is converted to velocity-wavenumber (v k) space following the transformation: S(k, v) = S(f,k) k (3) Multiplication by k is required in order to preserve the variance of the signal. The narrow, sloped band of energy has now been converted into a vertical band in S(v,k) (Fig. 6). A large amount of noise near low wave numbers is also apparent along with the large blank regions in the upperleft and upper-right corresponding to areas beyond the Nyquist frequency (f nyq and wave number (k nyq ). 9 8 Wavenumber (m 1 ) Velocity (m/s Figure 6: Log-energy spectral density log(s(v, k)) of the timestack. In v, k space, the velocity peak is a sharp vertical band. The S(k, v) spectrum can now be integrated to get a one-dimensional velocity spectrum S(v). If we choose the k limits carefully, we can eliminate a lot of the low-frequency noise while still maintaining much of our spectrum. For this exercise, I have chosen k min =1. Then we can compute S(v) by knyq S(v) = S(v,k)dk (4) k min and thus obtain a single spectrum of velocity (Fig. 7). In this example, the background noise is relatively small, so the maximum velocity peak is not far from the mean of the spectrum, however, the long tail towards negative velocities influences the value somewhat. Also, there is a small energy peak near velocity. This peak is due to background noise and spectral leakage and can often be much larger, and in some spectra may dwarf the actual velocity peak. ESS5 5 / 9

6 . Velocity Spectrum, S(v) Mean v =.51 Max v = S (v)/σs (v) Velocity (m/s) Figure 7: Spectrum of S(v). Note how velocity estimates using the mean and the max of the spectra are different due to the noise throughout all v values. In order to account for the background noise field, a model of the velocity spectrum can be developed: S m (v) = S b (v) + S noi se (v) (5) where S m (v) is the model spectrum, S b (v) is the spectrum due to the moving bubbles, and S noi se (v) is a white-noise spectrum (equal at all frequencies). If the bubble spectrum is modeled as a gaussian with mean v, standard deviation σ b, and a signal amplitude of A b then S b (v) = A b exp [ ( ) ] v v while a white noise spectrum with amplitude A noi se will follow f nyq A noi se v f nyq v S noi se (v) = k nyq knyq A noi se v > f (7) nyq k nyq this gives us a set of 4 unknowns v,σ b, A b, and A noi se that can be fit to the model and allow us to derive a useful statistics such as confidence intervals (Fig. 8). Fitting these equations requires non-linear curve fitting and optimization techniques and will not be covered here. Finally, by subwindowing a long timestack, a velocity timeseries can be produced (Fig. 9). σ b (6) 6 / 9 ESS5

7 1.8 S(v) S model (v).6 S(v) Velocity (m/s) Figure 8: Comparsion of S(v) and modelled S model (v) spectra. Black dashed lines indicate ±σ b Velocity (m/s) Time (s) Figure 9: Timeseries of estimated velocities with ±95% confidence intervals. ESS5 7 / 9

8 Conclusions The OCM technique provides robust, remote way to measure the velocity of surface features. The method works well for shallow water environments where in situ observations are sparse and difficult to obtain, as well as with data sets ill-suited for PIV due to the lack of image texture. Improvements to the technique include extending the analysis to a 3-D timestack, and calculating velocities along an orthogonal component, in order to rectify both the velocity magnitude and direction. Ease of setup, fast data processing, and low-cost make the OCM technique a useful tool to gain current information where traditional instrumentation fail. References [1] Chickadel, CC, RA Holman, and MH Freilich. 3 An optical technique for the measurement of longshore currents. Journal of Geophysical Research 18: C11, doi: 1.19/3JC / 9 ESS5