1	BroadBand ADCP Basics 3 Discussion of Concepts re How It Works
2	Autocovariance Function Decorrelation Effects
3	Autocovariance Function Water speed: U_water= C/2 x p / (Df x T_apart) p is determined from autocovariance function (acvf) of echo time series for each depth cell ACVF tells the average delay and similarity between recurring patterns in a time series ACVF outputs correlation Measure of similarity between recurring patterns Says how well you detect and measure pulse separation Key point Low correlation => poor estimate of water velocity i.e., sd (p) varies inversely with correlation
4	Information In Acvf Water speed: U_water= C/2 x p / (Df x T_apart) p = N x carrier cycles + fraction of cycle (1) (2) Complex autocovariance function has 2 types of information Magnitude (correlation): used to measure (1) Phase information: used to measure (2) Key point Phase values are only reliable if correlation is high Poor correlation results in noisy (or none) water velocity measurements
5	Velocity and Correlation Water speed: U_water= C/2 x p / (Df x T_apart) p = N x carrier cycles + fraction of cycle (1) (2) Standard deviation of U_water= sd (U_water) sd (U_water) = C/2 x 1/ (Df x T_apart)x sd (p ) Factors affecting sd (p ) Part (1) .. quantizing noise (N±1) Parts (1), (2) .. correlation between 1st, 2nd pulses
6	Decorrelation Effects
7	Decorrelation Effects ACVF => measures AVERAGE delay and similarity between patterns recurring in a time series Poor correlation => due to TOO MUCH VARIABILITY in the delay or similarity between these patterns over the duration of time series Consider separately 2 aspects of too much variability Delay between pulses Similarity between pulses
8	Varying Inter-pulse Delay (Figure) Too much variability in the delay between pulses Blurs 2nd pulse and its average location when ACVF is computed for each depth cell Result: Low correlation => noisy or no velocity Causes High Shear: velocity changes too much across the depth of the bin (notably the ambiguity resolving bin) Beam divergence: differences between velocity measured at edges of beams greater at higher speed
9	Velocity Shear Effect Figure Velocity profile vs. Pulse Separation in Echo
10	Velocity Shear In Bin Figure Velocity shear vs. Pulse Separation in Echo
11	Beam Divergence Effect Figure Beam Width vs. Pulse Separation in Echo
12	Action: Inter-pulse Delay Options to improve correlation Smaller bins .. Reduce range of velocities in cell Slow down .. Reduce range between Doppler shifts measured at beam edges
13	Rapidly Varying Scatterers Too much variability in the similarity between pulses Back-scattering sources change too fast before the 2nd pulse arrives Degrades the signature of 2nd pulse compared with 1st pulse Result: Low correlation => noisy or no velocity Causes Turbulence and Boat Heave: scatterers move rapidly between bins (or along beam) High boat speed, Pitch and Roll: scatterers move rapidly across beam (short residence time)
14	Rapidly Varying Scatterers Figure
15	Action: Varying Scatterers Options to improve correlation Slow down .. Scatterers move across beam slower Use larger bins .. fractional change in scatterers is less Increase ambiguity velocity (reduce inter-pulse delay at transmit) .. 2nd pulse arrives sooner after 1st pulse sees more of same scatterers Move measurement section to place with smoother bottom or calmer surface .. Vertical water motions are reduced
16	BroadBand ADCP Basics 3 Discussion of Concepts re How It Works