2.3. Hydrodynamic measurements
The shear velocity in the stream (u) was calculated using the following formula (Loga 2016):
u = \(\sqrt{h;g;S}\)
where:
u – shear velocity (m∙s-1),
h – average water depth (m),
g – gravitational acceleration (m ∙s-2),
S – channel bed slope (%).
Hydrodynamic measurements were conducted using a VALEPORT Model 801 Flat EM Flow Meter, which measures the average velocity at set time intervals. Approximately 0.01 m·s-1 of accuracy is provided by the device, measured at a height of 0.4 m above the riverbed. Using the diagrams of velocity distribution above the bottom in a semilogarithmic system, the dynamic velocity was calculated based on the maximum and instantaneous velocities (measured just above the bottom) (Gordon et al., 2007):
\begin{equation} V=\frac{a}{5.75}\nonumber \\ \end{equation}
where:
a – line slope coefficient of V = f (h) with the equation y = ax + b,
where:
x – height above the bottom on which the velocity measurement (m·s-1) was made,
b – intercept of the equation (Loga 2016):
\(Dt,y=0.6;h;u\)
where:
(Dt,y) – turbulent diffusion coefficient for transverse mixing of the cross-section (m2·s-1),
h – average water depth (m), u – shear velocity (m·s-1).
The relation between the turbulent diffusion index, inorganic nutrients, and TSS (physicochemical indices) randomly distributed in the surface water was studied by spatial autoregression (SAR) using a lagged response model (Rangel et al., 2010):
Y = ρ·Wy+Xβ+ε
where:
Y – vector (N · 1) of responsive (explained) variable,
Wy – weight matrix of adjacent variables at different measuring points (N · N matrix of spatial weights),
ρ – spatial autoregression parameter reflecting the relationship between the variables (spatial interaction parameter),
X – matrix (N · K) of the explanatory process,
β – vector (K · 1) of structure index,
ε – vector (N · 1) of the random component (error of spatial estimation not described by the model; random effect).