Compute all hydraulic data using Old Morel equations

Calculate rivers width (\(Bm\)), depth (\(H\)) and water travel time (\(TPS\)) with Discharge as input data, using Morel formulas with computed parameters for each segments.

Usage

TnetHydraulic_MorelOld(
  path_data,
  shapefile,
  export_files = c("Bm", "H", "TPS")
)

Arguments

path_data

Path to the folder containing Q

shapefile

Path to the shapefile with all info on segments. Columns needed are detailed in the Shapefile Columns section.

export_files

vector of files that will be exported. It can contain "Bm", "H", "CV" and "TPS", but only "Bm", "H" and "TPS" are needed for T-NET

Value

All hydraulic data as NetCDF files in the folder path_data

Details

With old Morel equation, each parameter used in Morel new depend on segments parameter and needs to be computed for all of them.

Equations used

Pre-computation

\(sSlope = \sqrt{slope}\)

\(ordre = Strahler order - 1\)

Every parameters related to watershed area (_bv) and segment order (_ordr) are puts to 0, so columns containing watershed area (\(Aire\_tronc\)) and Strahler order (\(OSTRAHLER\)) have been removed from mandatory columns in the shapefile

River segment width (\(Bm\))

Computing coefficients

\(ad = \exp\left(ad_0 + ad_{bv} \cdot \log(\text{Aire_tronc}) + ad_{slo} \cdot sSlope + ad_{ordr} \cdot ordre\right)\)

with \(ad_0\) = 2.122, \(ad_{bv}\) = 0, \(ad_{slo}\) = -0.076, \(ad_{ordr}\) = 0

\(bd = bd_0 + bd_q \cdot log(Qmean) + bd_{bv} \cdot log(\text{Aire_tronc}) + bd_{slo} \cdot sSlope + bd_{ordr} \cdot ordre\)

with \(bd_0\) = 0.475, \(bd_{q}\) = 0, \(bd_{bv}\) = 0, \(bd_{slo}\) = 0, \(bd_{ordr}\) = 0

\(b = b_0 + b_q \cdot log(Qmean) + b_{bv} \cdot log(\text{Aire_tronc}) + b_{slo} \cdot sSlope + b_{ordr} \cdot ordre\)

with \(b_0\) = 0.125, \(b_{q}\) = 0, \(b_{bv}\) = 0, \(b_{slo}\) = 0, \(b_{ordr}\) = 0

Equation

$$Bm = ad \cdot (Qmean)^{bd} \cdot \left(\frac{Qaval}{Qmean}\right)^{b}$$

River segment depth (\(H\))

Computing coefficients

\(cd = \exp\left(cd_0 + cd_{bv} \cdot \log(\text{Aire_tronc}) + cd_{slo} \cdot sSlope + cd_{ordr} \cdot ordre\right)\)

with \(cd_0\) = 2.122, \(cd_{bv}\) = 0, \(cd_{slo}\) = -0.076, \(cd_{ordr}\) = 0

\(fd = fd_0 + fd_q \cdot log(Qmean) + fd_{bv} \cdot log(\text{Aire_tronc}) + fd_{slo} \cdot sSlope + fd_{ordr} \cdot ordre\)

with \(fd_0\) = 0.298, \(fd_{q}\) = 0, \(fd_{bv}\) = 0, \(fd_{slo}\) = 0, \(fd_{ordr}\) = 0

\(f = f_0 + f_q \cdot log(Qmean) + f_{bv} \cdot log(\text{Aire_tronc}) + f_{slo} \cdot sSlope + f_{ordr} \cdot ordre\)

with \(f_0\) = 0.302, \(f_{q}\) = 0, \(f_{bv}\) = 0, \(f_{slo}\) = 0, \(f_{ordr}\) = 0

Equation

$$H = cd \cdot (Qmean)^{fd} \cdot \left(\frac{Qaval}{Qmean}\right)^{f}$$

Water speed in river segment (\(CV\))

$$CV = \frac{Qaval}{H \cdot Bm}$$

Water travel time in river segment (\(TPS\))

$$TPS = \frac{Longueur\_m}{CV} \div 3600$$

Shapefile columns

\(gid\_new\)	ID of the river segment (named gid)
\(pente2\)	Slope of the river segment
\(Longueur_m\)	Length of the river segment

References

Maxime Morel, Doug J. Booker, Frédéric Gob, Nicolas Lamouroux, Intercontinental predictions of river hydraulic geometry from catchment physical characteristics, Journal of Hydrology, https://doi.org/10.1016/j.jhydrol.2019.124292.