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Library

Types

Sad.Dingman — Type

Dingman river channel cross section.

Uses generalized expressions for cross-section geometry based on at-a-station hydraulic geometry relations.

  • Wb: bankfull width
  • Yb: bankfull depth
  • Ym: flow depth
  • r: geometry exponent
  • S0: bed slope
  • n: Manning roughness coefficient

See also: Rectangular

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Sad.Rectangular — Type

Rectangular river channel cross section.

  • Wb: bankfull width
  • Yb: bankfull depth
  • Ym: flow depth
  • S0: bed slope
  • n: Manning roughness coefficient

See also: Dingman

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Functions

Cross sections

Sad.width — Function
width(xs)

Calculate water surface width of cross section.

Arguments

  • xs: cross section
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Sad.depth — Function
depth(xs)

Calculate average depth of cross section.

Arguments

  • xs: cross section
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Priors

Sad.get_samples — Function
get_samples(p, samples)

Get quantiles from p according to weights provided by Latin Hypercube Sampling samples.

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Sad.lhs_ensemble — Function
lhs_ensemble(nens, args...)

Generate an ensemble of size nens using Latin Hypercube Sampling of the list of distributions or collections provided as args.

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Sad.prior_ensemble — Function
prior_ensemble(x, Qp, np, rp, zp, nens)

Generate a prior ensemble of discharge, roughness coefficient, channel shape parameter, and downstream bed elevation from provided distributions or sample data.

Arguments

  • x: distances between cross sections
  • Qp: discharge prior distribution
  • np: roughness coefficient distribution
  • rp: channel shape parameter distribution
  • zp: downstream bathymetry distribution
  • nens: ensemble size
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Sad.gvf_ensemble! — Function
gvf_ensemble!(H, S, x, hbf, wbf, Qe, ne, re, ze)

Generate an ensemble of water height profiles from Gradually-Varied-Flow simulations and associated profiles of bed elevation.

Arguments

  • H: water surface elevation
  • S: bed slope
  • x: channel chainage
  • hbf: bankfull water surface elevation
  • wbf: bankfull width
  • Qe: ensemble discharge
  • ne: ensemble roughness coefficient
  • re: ensemble channel shape parameter
  • ze: ensemble bed elevation profiles
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Sad.rejection_sampling — Function
rejection_sampling(Qp, np, rp, zp, x, H, S0, hbc, wbf, hbf, nens, nsamples)

Use rejection sampling to select a subset of the prior ensemble.

Arguments

  • Qp: prior discharge distribution
  • np: prior roughness coefficient distribution
  • rp: prior channel shape parameter distribution
  • zp: prior distribution for downstream bed elevation
  • x: channel chainage
  • H: time series of observed water surface elevation profiles
  • S0: prior estimate of channel bed slope
  • hbc: mean downstream flow depth used as boundary condition
  • wbf: bankfull width
  • hbf: bankfull water surface elevation
  • nens: ensemble size
  • nsamples: number of samples
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Sad.priors — Function
priors(ncfile, hmin, id)

Derive prior distributions for discharge, roughness coefficient, channel shape parameter, and bed elevation by reading the SWORD a-priori database.

Arguments

  • ncfile: NetCDF file of SWORD database
  • hmin: minimum observed downstream water surface elevation
  • id: Reach ID in SWORD database
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priors(qwbm, hmin)

Derive distributions for discharge, roughness coefficient, channel shape parameter, and bed elevation using uninformative priors.

Arguments

  • qwbm: mean discharge
  • hmin: minimum downstream water surface elevation
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Kalman filters

Sad.letkf — Function
letkf(A, d, HA, E, xs, ys, ρ, diagR)

Apply the Local Ensemble Transform Kalman Filter algorithm.

Arguments

  • A: state variable ensemble matrix
  • d: observation vector
  • HA: model-predicted observation ensemble matrix
  • E: observation error ensemble matrix
  • xs: indices of state vector that map to observation local patches
  • ys: indices of observation local patches
  • ρ: covariance inflation parameter (optional, default value of 1.05)
  • diagR: force observation error covariance to be diagonal, i.e. no spatial correlation (optional, default is false)
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Gradually Varied Flow

Sad.froude — Function
froude(Q::Float64, xs::CrossSection)

Calculate the Froude number.

Arguments

  • Q: discharge
  • xs: cross section
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Sad.interpolate_hbc — Function
interpolate_hbc(x, H, S)

Interpolate water surface elevation boundary condition by assuming uniform flow, i.e., energy slope is equal to bed slope.

Arguments

  • x: channel chainage
  • H: water surface elevation profile
  • S: bed slope
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Sad.dydx — Function
dydx(y, p, x)

Ordinary differential equation describing the Gradually-Varied-Flow model.

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Sad.gvf — Function

Calculate a water surface profile by solving the Gradually-Varied-Flow equation.

  • Q: discharge
  • ybc: downstream boundary condition for depth
  • S0: bed slope for reach
  • n: roughness coefficient
  • x: downstream distance for each cross section
  • wbf: bankfull width for each cross section
  • ybf: bankfull depth for each cross section
  • r: channel geometry coefficient for each cross section
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Sad

Sad.drop_unobserved — Function
drop_unobserved(x, H, W, S)

Remove cross sections with no valid observations.

Arguments

  • x: channel chainage
  • H: time series of water surface elevation profiles
  • W: time series of width profiles
  • S: time series of water surface slope profiles
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Sad.assimilate — Function
assimilate(H, W, S, x, wbf, hbf, S0, Qp, np, rp, zp, nens, constrain)

Assimilate SWOT observations for river reach.

Arguments

  • H: time series of water surface elevation profiles
  • W: time series of water surface width profiles
  • S: time series of water surface slope profiles
  • x: downstream distance for each cross section
  • wbf: bankfull width
  • hbf: bankfull depth
  • Qₚ: prior probability distribution for discharge
  • nₚ: prior probability distribution for roughness coefficient
  • rₚ: prior probability distribution for channel shape parameter
  • zₚ: prior distribution for downstream bed elevation
  • nens: ensemble size
  • constrain: switch for applying AHG constraint
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Sad.bathymetry! — Function
bathymetry!(ze, S, S0, Qe, ne, re, x, hbf, wbf, H, ϵₒ)

Estimate channel bed slope and thalweg (elevation) by assimilating SWOT water surface elevation observations.

Arguments

  • ze: ensemble of bed elevations
  • S: time series of water surface slope profiles
  • S0: bed slope
  • Qe: ensemble of discharge
  • ne: ensemble of roughness coefficient
  • re: ensemble of channel shape parameters
  • x: channel chainage
  • hbf: bankfull water surface elevation
  • wbf: bankfull width
  • H: time-averaged water surface elevation observed
  • ϵₒ: observation error (default value of 10 cm)
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Sad.ahg_constrain! — Function
ahg_constrain!(Qa, hbc, hbf, wbf, S0, x, ne, re, ze, tol=1e-3)

Constrain assimilated discharge with At-a-Station hydraulic geometry (AHG) relationships.

Arguments

  • Qa: assimilated ensemble discharge
  • hbc: downstream boundary water surface elevation
  • hbf: bankfull water surface elevation
  • wbf: bankfull width
  • S0: bed slope
  • x: channel chainage
  • ne: ensemble roughness coefficient
  • re: ensemble channel shape parameter
  • ze: ensemble bed elevation
  • tol: numeric tolerance for closing the AHG relationships
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Sad.calc_bed_slope — Function
calc_bed_slope(x, S)

Estimate initial channel bed slope.

Arguments

  • x: channel chainage
  • S: time series of water surface slope profiles
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Sad.calc_dA — Function
calc_dA(Qa, na, W, S)

Calculate changes in cross-sectional area.

Arguments

  • Qa: time series of estimated discharge
  • na: time series of estimated roughness coefficient
  • W: time series of width profiles
  • S: time series of water surface slope profiles
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Sad.flow_parameters — Function
flow_parameters(Qa, na, W, S, dA)

Estimate flow parameters (roughness coefficient and baseflow cross-sectional area) from assimilated discharge.

Arguments

  • Qa: time series of estimated discharge
  • na: time series of estimate roughness coefficient
  • W: time series of observed width (reach)
  • S: time series of observed slope (reach)
  • dA: time series of changes in reach-averaged cross-sectional area (from minimum observed)
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Sad.estimate — Function
estimate(x, H, W, S, Qp, np, rp, zp, nens)

Estimate discharge and flow parameters from SWOT observations.

Arguments

  • x: channel chainage
  • H: time series of water surface elevation profiles
  • W:time series of width profiles
  • S: time series of water surface slope profiles
  • Qp: discharge prior distribution
  • np: roughness coefficient prior distribution
  • rp: channel shape parameter prior distribution
  • zp: downstream bed elevation prior distribution
  • nens: ensemble size
  • nsamples: sample size for rejection sampling
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