a=0.54; w=1.4e-4; % tidal amplitude, tidal radian frequency
wt=2*pi*(0:50)/50; hour=12.42*wt/(2*pi); % time in radians and hours
eta=a*sin(wt); % tidal elevation time-series
deta_dt=w*a*cos(wt); % time-derivative of tidal elevation time-series
gam=1.8; r=0.01; % Boon & Bryne parameter values
h_H=(.94+.78)/2+.5*(.94-.78)*sin(wt); % h/H depth time-series over tidal cycle
G=(1-h_H).^gam; % time-varying value for Boon & Bryne G parameter
a_A=G./(r+G*(1-r)); % a/A area time-series over tidal cycle
Ab=27.4e6*(1-a_A); % Bay flooded surface area time-series over tidal cycle
Ac=500*(5+eta); % tidal channel cross-sectional area time-series over tidal cycle
u=Ab./Ac.*deta_dt; % cross-sectionally-averaged velocity time-series over tidal cycle
subplot(121); plot(hour,u); ylabel('velocity (m/s)'); xlabel('time (hour)');
subplot(122); plot(u,eta); ylabel('eta (m)'); xlabel('velocity (m/s)');