diff --git a/NAMESPACE b/NAMESPACE
index 69b24a9..66eb6b6 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -1,4 +1,4 @@
-# Generated by roxygen2: do not edit by hand
+# Generated by roxygen2: do not edit by hand
 
 S3method(head,rivr)
 S3method(plot,rivr)
diff --git a/cran-comments.md b/cran-comments.md
index 656abfb..b33010d 100644
--- a/cran-comments.md
+++ b/cran-comments.md
@@ -7,7 +7,9 @@ a `stringsAsFactors = FALSE` default.
 ## Test environments
 
 * Local Windows 10 install, R 3.6.2
-* Ubuntu 14.04 (on travis-ci), R-oldrel, R-release, R-devel
+* Ubuntu 14.04 (on travis-ci), R-oldrel, R-release, R-devel 
+
+(confirmed R-devel on Travis was updated to r77865)
 
 ## R CMD check results
 
diff --git a/man/channel_geom.Rd b/man/channel_geom.Rd
index a8dace8..29e9d5b 100644
--- a/man/channel_geom.Rd
+++ b/man/channel_geom.Rd
@@ -1,38 +1,38 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/RcppExports.R
-\name{channel_geom}
-\alias{channel_geom}
-\title{Channel geometry}
-\usage{
-channel_geom(y, B, SS)
-}
-\arguments{
-\item{y}{Flow depth [\eqn{L}].}
-
-\item{B}{Channel bottom width [\eqn{L}].}
-
-\item{SS}{Channel sideslope [\eqn{L L^{-1}}]. For a rectangular channel, \code{SS = 0}.}
-}
-\value{
-Named vector:
-  \item{A}{Flow area [\eqn{L^2}].}
-  \item{P}{Wetted perimeter [\eqn{L}].}
-  \item{R}{Hydraulic radius [\eqn{L}].}
-  \item{dAdy}{Water surface width [\eqn{L}].}
-  \item{dPdy}{First derivative of wetted perimeter w.r.t. flow depth.}
-  \item{dRdy}{First derivative of hydraulic radius w.r.t. flow depth.}
-  \item{DH}{Hydraulic depth [\eqn{L}].}
-  \item{ybar}{Vertical distance from water surface to centroid of flow area [\eqn{L}].}
-}
-\description{
-Compute geometry relations for trapezoidal channels.
-}
-\details{
-Channel geometry relations are routinely calculated in numerical solutions of steady, 
-  gradually-varied and unsteady flows. This function is used extensively by internal 
-  procedures and is made accessible to the user for convenience.
-}
-\examples{
-channel_geom(1.71, 100, 0) # rectangular channel
-channel_geom(5.79, 6.1, 1.5) # trapezoidal channel with sideslope 3H:2V
-}
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/RcppExports.R
+\name{channel_geom}
+\alias{channel_geom}
+\title{Channel geometry}
+\usage{
+channel_geom(y, B, SS)
+}
+\arguments{
+\item{y}{Flow depth [\eqn{L}].}
+
+\item{B}{Channel bottom width [\eqn{L}].}
+
+\item{SS}{Channel sideslope [\eqn{L L^{-1}}]. For a rectangular channel, \code{SS = 0}.}
+}
+\value{
+Named vector:
+  \item{A}{Flow area [\eqn{L^2}].}
+  \item{P}{Wetted perimeter [\eqn{L}].}
+  \item{R}{Hydraulic radius [\eqn{L}].}
+  \item{dAdy}{Water surface width [\eqn{L}].}
+  \item{dPdy}{First derivative of wetted perimeter w.r.t. flow depth.}
+  \item{dRdy}{First derivative of hydraulic radius w.r.t. flow depth.}
+  \item{DH}{Hydraulic depth [\eqn{L}].}
+  \item{ybar}{Vertical distance from water surface to centroid of flow area [\eqn{L}].}
+}
+\description{
+Compute geometry relations for trapezoidal channels.
+}
+\details{
+Channel geometry relations are routinely calculated in numerical solutions of steady, 
+  gradually-varied and unsteady flows. This function is used extensively by internal 
+  procedures and is made accessible to the user for convenience.
+}
+\examples{
+channel_geom(1.71, 100, 0) # rectangular channel
+channel_geom(5.79, 6.1, 1.5) # trapezoidal channel with sideslope 3H:2V
+}
diff --git a/man/compute_profile.Rd b/man/compute_profile.Rd
index af593aa..a52bf2b 100644
--- a/man/compute_profile.Rd
+++ b/man/compute_profile.Rd
@@ -1,72 +1,84 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/graduallyvariedflow_v2.r
-\name{compute_profile}
-\alias{compute_profile}
-\title{Gradually-varied flow profiles}
-\usage{
-compute_profile(So, n, Q, y0, Cm, g, B, SS, z0 = 0, x0 = 0, stepdist,
-  totaldist)
-}
-\arguments{
-\item{So}{Channel slope [\eqn{L L^{-1}}].}
-
-\item{n}{Manning's roughness coefficient.}
-
-\item{Q}{Flow rate [\eqn{L^3 T^{-1}}].}
-
-\item{y0}{The water depth at the control section [\eqn{L}].}
-
-\item{Cm}{Unit conversion coefficient for Manning's equation. For SI units, Cm = 1.}
-
-\item{g}{Gravitational acceleration [\eqn{L T^{-2}}].}
-
-\item{B}{Channel bottom width [\eqn{L}].}
-
-\item{SS}{Channel sideslope [\eqn{L L^{-1}}].}
-
-\item{z0}{Elevation reference datum at control section [\eqn{L}]. Default is 0.}
-
-\item{x0}{Distance reference at control section [\eqn{L}]. Default is 0.}
-
-\item{stepdist}{The spatial interval used in the Standard step method [\eqn{L}].}
-
-\item{totaldist}{The total distance upstream (or downstream) to compute the profile [\eqn{L}].}
-}
-\value{
-data.frame with columns:
-  \item{x}{Along-channel distance.}
-  \item{z}{Elevation.}
-  \item{y}{Flow depth.}
-  \item{v}{Flow velocity.}
-  \item{A}{Flow area.}
-  \item{Sf}{Friction slope.}
-  \item{E}{Total energy.}
-  \item{Fr}{Froude Number.}
-}
-\description{
-Compute the gradually-varied flow profile of a prismatic channel.
-}
-\details{
-Computes the longitudinal water surface profile of a prismatic 
-  channel using the standard step method by solving the non-linear ODE 
-  \deqn{\frac{dy}{dx} = \frac{S_0 - S_f}{1 - Fr^2}} The standard-step 
-  method operates by stepping along the channel by a constant distance 
-  interval, starting from a cross-section where the flow depth is known 
-  (the control section). The flow depth is computed at the adjacent 
-  cross-section (target section). The computed value at the target is then 
-  used as the basis for computing flow depth at the next cross-section, i.e. 
-  the previous target section becomes the new control section for each step. 
-  A Newton-Raphson scheme is used each step to compute the flow depth and 
-  friction slope. Technically, the average friction slope of the control and
-  target section is used to compute the flow depth at the target section.
-}
-\examples{
-# example M1 profile
-compute_profile(0.001, 0.045, 250, 2.7, 1.486, 32.2, 100, 0, stepdist = 10, totaldist = 3000)
-# example M2 profile
-compute_profile(0.001, 0.045, 250, 0.64, 1.486, 32.2, 100, 0, stepdist = 10, totaldist = 3000)
-# example S2 profile
-compute_profile(0.005, 0.01, 250, 2.65, 1.486, 32.2, 10, 0, stepdist = 10, totaldist = 2000)
-# example S3 profile
-compute_profile(0.005, 0.01, 250, 0.5, 1.486, 32.2, 10, 0, stepdist = 10, totaldist = 2000)
-}
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/graduallyvariedflow_v2.r
+\name{compute_profile}
+\alias{compute_profile}
+\title{Gradually-varied flow profiles}
+\usage{
+compute_profile(
+  So,
+  n,
+  Q,
+  y0,
+  Cm,
+  g,
+  B,
+  SS,
+  z0 = 0,
+  x0 = 0,
+  stepdist,
+  totaldist
+)
+}
+\arguments{
+\item{So}{Channel slope [\eqn{L L^{-1}}].}
+
+\item{n}{Manning's roughness coefficient.}
+
+\item{Q}{Flow rate [\eqn{L^3 T^{-1}}].}
+
+\item{y0}{The water depth at the control section [\eqn{L}].}
+
+\item{Cm}{Unit conversion coefficient for Manning's equation. For SI units, Cm = 1.}
+
+\item{g}{Gravitational acceleration [\eqn{L T^{-2}}].}
+
+\item{B}{Channel bottom width [\eqn{L}].}
+
+\item{SS}{Channel sideslope [\eqn{L L^{-1}}].}
+
+\item{z0}{Elevation reference datum at control section [\eqn{L}]. Default is 0.}
+
+\item{x0}{Distance reference at control section [\eqn{L}]. Default is 0.}
+
+\item{stepdist}{The spatial interval used in the Standard step method [\eqn{L}].}
+
+\item{totaldist}{The total distance upstream (or downstream) to compute the profile [\eqn{L}].}
+}
+\value{
+data.frame with columns:
+  \item{x}{Along-channel distance.}
+  \item{z}{Elevation.}
+  \item{y}{Flow depth.}
+  \item{v}{Flow velocity.}
+  \item{A}{Flow area.}
+  \item{Sf}{Friction slope.}
+  \item{E}{Total energy.}
+  \item{Fr}{Froude Number.}
+}
+\description{
+Compute the gradually-varied flow profile of a prismatic channel.
+}
+\details{
+Computes the longitudinal water surface profile of a prismatic 
+  channel using the standard step method by solving the non-linear ODE 
+  \deqn{\frac{dy}{dx} = \frac{S_0 - S_f}{1 - Fr^2}} The standard-step 
+  method operates by stepping along the channel by a constant distance 
+  interval, starting from a cross-section where the flow depth is known 
+  (the control section). The flow depth is computed at the adjacent 
+  cross-section (target section). The computed value at the target is then 
+  used as the basis for computing flow depth at the next cross-section, i.e. 
+  the previous target section becomes the new control section for each step. 
+  A Newton-Raphson scheme is used each step to compute the flow depth and 
+  friction slope. Technically, the average friction slope of the control and
+  target section is used to compute the flow depth at the target section.
+}
+\examples{
+# example M1 profile
+compute_profile(0.001, 0.045, 250, 2.7, 1.486, 32.2, 100, 0, stepdist = 10, totaldist = 3000)
+# example M2 profile
+compute_profile(0.001, 0.045, 250, 0.64, 1.486, 32.2, 100, 0, stepdist = 10, totaldist = 3000)
+# example S2 profile
+compute_profile(0.005, 0.01, 250, 2.65, 1.486, 32.2, 10, 0, stepdist = 10, totaldist = 2000)
+# example S3 profile
+compute_profile(0.005, 0.01, 250, 0.5, 1.486, 32.2, 10, 0, stepdist = 10, totaldist = 2000)
+}
diff --git a/man/conveyance.Rd b/man/conveyance.Rd
index 4d57524..9c9ecdc 100644
--- a/man/conveyance.Rd
+++ b/man/conveyance.Rd
@@ -1,28 +1,28 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/RcppExports.R
-\name{conveyance}
-\alias{conveyance}
-\title{Channel conveyance}
-\usage{
-conveyance(n, A, R, Cm)
-}
-\arguments{
-\item{n}{Manning's roughness coefficient (dimensionless).}
-
-\item{A}{Flow area [\eqn{L^2}].}
-
-\item{R}{Hydraulic radius [\eqn{L}].}
-
-\item{Cm}{Unit conversion coefficient for Manning's equation. For SI units, Cm = 1.}
-}
-\value{
-The channel conveyance.
-}
-\description{
-Calculate the channel conveyance.
-}
-\details{
-Channel conveyance is routinely calculated in numerical solutions of steady, 
-  gradually-varied and unsteady flows. This function is used extensively by internal 
-  procedures and is made accessible to the user for convenience.
-}
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/RcppExports.R
+\name{conveyance}
+\alias{conveyance}
+\title{Channel conveyance}
+\usage{
+conveyance(n, A, R, Cm)
+}
+\arguments{
+\item{n}{Manning's roughness coefficient (dimensionless).}
+
+\item{A}{Flow area [\eqn{L^2}].}
+
+\item{R}{Hydraulic radius [\eqn{L}].}
+
+\item{Cm}{Unit conversion coefficient for Manning's equation. For SI units, Cm = 1.}
+}
+\value{
+The channel conveyance.
+}
+\description{
+Calculate the channel conveyance.
+}
+\details{
+Channel conveyance is routinely calculated in numerical solutions of steady, 
+  gradually-varied and unsteady flows. This function is used extensively by internal 
+  procedures and is made accessible to the user for convenience.
+}
diff --git a/man/critical_depth.Rd b/man/critical_depth.Rd
index e138b04..1bc0c68 100644
--- a/man/critical_depth.Rd
+++ b/man/critical_depth.Rd
@@ -1,39 +1,39 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/RcppExports.R
-\name{critical_depth}
-\alias{critical_depth}
-\title{Critical depth}
-\usage{
-critical_depth(Q, yopt, g, B, SS)
-}
-\arguments{
-\item{Q}{Flow rate [\eqn{L^3 T^{-1}}].}
-
-\item{yopt}{Initial guess for normal depth [\eqn{L}].}
-
-\item{g}{Gravitational acceleration [\eqn{L T^{-2}}].}
-
-\item{B}{Channel bottom width [\eqn{L}].}
-
-\item{SS}{Channel sideslope [\eqn{L L^{-1}}].}
-}
-\value{
-The critical depth \eqn{y_c} [\eqn{L}].
-}
-\description{
-Calculate the critical depth.
-}
-\details{
-The critical depth is the water depth at which a channel 
-  flow regime will transition from supercritical to subcritical (or vice versa).
-  Calculation of the critical depth is based on a specific energy formulation, 
-  i.e. \deqn{E = y + z + \frac{Q^2}{2gB^2y^2}} where \eqn{y} is the flow depth, \eqn{z} is 
-  the elevation relative to some datum (assumed to be 0), and the last term 
-  represents kinetic energy. More specifically, the function operates
-  by finding the point where the derivative of specific energy w.r.t. \eqn{y} is zero, i.e.
-  \eqn{y = y_c} when \deqn{\frac{dE}{dy} = 1 - \frac{Q^2}{gA^3}\frac{dA}{dy} = 0}.
-}
-\examples{
-critical_depth(250, 2, 32.2, 100, 0) # rectangular channel
-critical_depth(126, 1, 9.81, 6.1, 1.5) # trapezoidal channel with sideslope 3H:2V
-}
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/RcppExports.R
+\name{critical_depth}
+\alias{critical_depth}
+\title{Critical depth}
+\usage{
+critical_depth(Q, yopt, g, B, SS)
+}
+\arguments{
+\item{Q}{Flow rate [\eqn{L^3 T^{-1}}].}
+
+\item{yopt}{Initial guess for normal depth [\eqn{L}].}
+
+\item{g}{Gravitational acceleration [\eqn{L T^{-2}}].}
+
+\item{B}{Channel bottom width [\eqn{L}].}
+
+\item{SS}{Channel sideslope [\eqn{L L^{-1}}].}
+}
+\value{
+The critical depth \eqn{y_c} [\eqn{L}].
+}
+\description{
+Calculate the critical depth.
+}
+\details{
+The critical depth is the water depth at which a channel 
+  flow regime will transition from supercritical to subcritical (or vice versa).
+  Calculation of the critical depth is based on a specific energy formulation, 
+  i.e. \deqn{E = y + z + \frac{Q^2}{2gB^2y^2}} where \eqn{y} is the flow depth, \eqn{z} is 
+  the elevation relative to some datum (assumed to be 0), and the last term 
+  represents kinetic energy. More specifically, the function operates
+  by finding the point where the derivative of specific energy w.r.t. \eqn{y} is zero, i.e.
+  \eqn{y = y_c} when \deqn{\frac{dE}{dy} = 1 - \frac{Q^2}{gA^3}\frac{dA}{dy} = 0}.
+}
+\examples{
+critical_depth(250, 2, 32.2, 100, 0) # rectangular channel
+critical_depth(126, 1, 9.81, 6.1, 1.5) # trapezoidal channel with sideslope 3H:2V
+}
diff --git a/man/demo_shiny.Rd b/man/demo_shiny.Rd
index 0916b88..841ee9d 100644
--- a/man/demo_shiny.Rd
+++ b/man/demo_shiny.Rd
@@ -1,27 +1,27 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/shinydemos.r
-\name{demo_shiny}
-\alias{demo_shiny}
-\title{Shiny Demonstrations}
-\usage{
-demo_shiny(ex)
-}
-\arguments{
-\item{ex}{Example to run.}
-}
-\description{
-Demonstrate package functionality via Shiny apps
-}
-\details{
-Demonstrations available:
-  \code{"gvf"} Gradually-varied flow.
-}
-\examples{
-\dontrun{
-# get list of available demos
-demo_shiny()
-# run the gradually-varied flow demo
-demo_shiny("gvf")
-}
-
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/shinydemos.r
+\name{demo_shiny}
+\alias{demo_shiny}
+\title{Shiny Demonstrations}
+\usage{
+demo_shiny(ex)
+}
+\arguments{
+\item{ex}{Example to run.}
+}
+\description{
+Demonstrate package functionality via Shiny apps
+}
+\details{
+Demonstrations available:
+  \code{"gvf"} Gradually-varied flow.
+}
+\examples{
+\dontrun{
+# get list of available demos
+demo_shiny()
+# run the gradually-varied flow demo
+demo_shiny("gvf")
+}
+
 }
diff --git a/man/froude.Rd b/man/froude.Rd
index 1926c78..58bcb2c 100644
--- a/man/froude.Rd
+++ b/man/froude.Rd
@@ -1,38 +1,38 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/RcppExports.R
-\name{froude}
-\alias{froude}
-\title{Froude Number}
-\usage{
-froude(Q, g, A, DH)
-}
-\arguments{
-\item{Q}{Flow rate [\eqn{L^3 T^{-1}}].}
-
-\item{g}{Gravitational acceleration [\eqn{L T^{-2}}].}
-
-\item{A}{Flow area [\eqn{L^2}].}
-
-\item{DH}{Hydraulic depth [\eqn{L}].}
-}
-\value{
-The Froude Number (dimensionless).
-}
-\description{
-Calculate the Froude Number.
-}
-\details{
-The Froude number is a dimensionless measure of bulk flow 
-  characteristics that represents the relative importance of inertial 
-  forces and gravitational forces. For open channel flow, the Froude 
-  number of open channel flow is defined as \deqn{Fr = \frac{v}{\sqrt{gD_H}}} 
-  where \eqn{v = \frac{Q}{A}} is the flow velocity, \eqn{g} is the gravitational 
-  acceleration and \eqn{D_H} is the hydraulic depth. The Froude number is related
-  to the energy state of the flow and can be used to identify flows as
-  either supercritical (\eqn{Fr < 1}) or subcritical (\eqn{Fr > 1}).
-}
-\examples{
-froude(250, 32.2, 171, 1.71) # subcritical flow
-froude(250, 32.2, 57.9, 0.579) # critical flow
-froude(250, 32.2, 45, 0.45) # supercritical flow
-}
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/RcppExports.R
+\name{froude}
+\alias{froude}
+\title{Froude Number}
+\usage{
+froude(Q, g, A, DH)
+}
+\arguments{
+\item{Q}{Flow rate [\eqn{L^3 T^{-1}}].}
+
+\item{g}{Gravitational acceleration [\eqn{L T^{-2}}].}
+
+\item{A}{Flow area [\eqn{L^2}].}
+
+\item{DH}{Hydraulic depth [\eqn{L}].}
+}
+\value{
+The Froude Number (dimensionless).
+}
+\description{
+Calculate the Froude Number.
+}
+\details{
+The Froude number is a dimensionless measure of bulk flow 
+  characteristics that represents the relative importance of inertial 
+  forces and gravitational forces. For open channel flow, the Froude 
+  number of open channel flow is defined as \deqn{Fr = \frac{v}{\sqrt{gD_H}}} 
+  where \eqn{v = \frac{Q}{A}} is the flow velocity, \eqn{g} is the gravitational 
+  acceleration and \eqn{D_H} is the hydraulic depth. The Froude number is related
+  to the energy state of the flow and can be used to identify flows as
+  either supercritical (\eqn{Fr < 1}) or subcritical (\eqn{Fr > 1}).
+}
+\examples{
+froude(250, 32.2, 171, 1.71) # subcritical flow
+froude(250, 32.2, 57.9, 0.579) # critical flow
+froude(250, 32.2, 45, 0.45) # supercritical flow
+}
diff --git a/man/normal_depth.Rd b/man/normal_depth.Rd
index e525bc0..7edd2d8 100644
--- a/man/normal_depth.Rd
+++ b/man/normal_depth.Rd
@@ -1,44 +1,44 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/RcppExports.R
-\name{normal_depth}
-\alias{normal_depth}
-\title{Normal depth}
-\usage{
-normal_depth(So, n, Q, yopt, Cm, B, SS)
-}
-\arguments{
-\item{So}{Channel slope [\eqn{L L^{-1}}].}
-
-\item{n}{Manning's roughness coefficient.}
-
-\item{Q}{Flow rate [\eqn{L^3 T^{-1}}].}
-
-\item{yopt}{Initial guess for normal depth [\eqn{L}].}
-
-\item{Cm}{Unit conversion coefficient for Manning's equation. For SI units, Cm = 1.}
-
-\item{B}{Channel bottom width [\eqn{L}].}
-
-\item{SS}{Channel sideslope [\eqn{L L^{-1}}].}
-}
-\value{
-The normal depth \eqn{y_n} [\eqn{L}].
-}
-\description{
-Calculate the normal (equilibrium) depth using Manning's equation.
-}
-\details{
-The normal depth is the equilibrium depth of a channel for a given 
-  flow rate, channel slope, geometry and roughness.
-  Manning's equation is used to calculate the equilibrium depth. Manning's 
-  equation for normal flow is defined as \deqn{Q = \frac{C_m}{n} AR^{2/3}S_0^{1/2}}
-  where \eqn{Q} is the channel flow, \eqn{S_0} is the channel slope, \eqn{A} is the 
-  cross-sectional flow area, \eqn{R} is the hydraulic depth and \eqn{C_m} is a conversion factor
-  based on the unit system used. This function uses a Newton-Raphson root-finding approach 
-  to calculate the normal depth, i.e.
-  \eqn{y = y_n} when \deqn{f(y) = \frac{A^{5/3}}{P^{2/3}} - \frac{nQ}{C_mS_0^{1/2}} = 0}.
-}
-\examples{
-normal_depth(0.001, 0.045, 250, 3, 1.486, 100, 0) # rectangular channel
-normal_depth(0.0008, 0.013, 126, 5, 1, 6.1, 1.5) # trapezoidal channel with sideslope 3H:2V
-}
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/RcppExports.R
+\name{normal_depth}
+\alias{normal_depth}
+\title{Normal depth}
+\usage{
+normal_depth(So, n, Q, yopt, Cm, B, SS)
+}
+\arguments{
+\item{So}{Channel slope [\eqn{L L^{-1}}].}
+
+\item{n}{Manning's roughness coefficient.}
+
+\item{Q}{Flow rate [\eqn{L^3 T^{-1}}].}
+
+\item{yopt}{Initial guess for normal depth [\eqn{L}].}
+
+\item{Cm}{Unit conversion coefficient for Manning's equation. For SI units, Cm = 1.}
+
+\item{B}{Channel bottom width [\eqn{L}].}
+
+\item{SS}{Channel sideslope [\eqn{L L^{-1}}].}
+}
+\value{
+The normal depth \eqn{y_n} [\eqn{L}].
+}
+\description{
+Calculate the normal (equilibrium) depth using Manning's equation.
+}
+\details{
+The normal depth is the equilibrium depth of a channel for a given 
+  flow rate, channel slope, geometry and roughness.
+  Manning's equation is used to calculate the equilibrium depth. Manning's 
+  equation for normal flow is defined as \deqn{Q = \frac{C_m}{n} AR^{2/3}S_0^{1/2}}
+  where \eqn{Q} is the channel flow, \eqn{S_0} is the channel slope, \eqn{A} is the 
+  cross-sectional flow area, \eqn{R} is the hydraulic depth and \eqn{C_m} is a conversion factor
+  based on the unit system used. This function uses a Newton-Raphson root-finding approach 
+  to calculate the normal depth, i.e.
+  \eqn{y = y_n} when \deqn{f(y) = \frac{A^{5/3}}{P^{2/3}} - \frac{nQ}{C_mS_0^{1/2}} = 0}.
+}
+\examples{
+normal_depth(0.001, 0.045, 250, 3, 1.486, 100, 0) # rectangular channel
+normal_depth(0.0008, 0.013, 126, 5, 1, 6.1, 1.5) # trapezoidal channel with sideslope 3H:2V
+}
diff --git a/man/rivr-package.Rd b/man/rivr-package.Rd
index 85323c3..12aeaae 100644
--- a/man/rivr-package.Rd
+++ b/man/rivr-package.Rd
@@ -1,15 +1,15 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/graduallyvariedflow_v2.r
-\docType{package}
-\name{rivr-package}
-\alias{rivr-package}
-\alias{rivr}
-\title{Steady and Unsteady Open-Channel Flow Computation}
-\description{
-This package is designed as an educational tool for students and 
-instructors of undergraduate courses in open channel hydraulics. 
-Functions are provided for computing normal and critical depths, 
-steady (e.g. backwater curves) and unsteady (flood wave routing) 
-flow computations for prismatic trapezoidal channels. See the vignettes
-to get started.
-}
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/graduallyvariedflow_v2.r
+\docType{package}
+\name{rivr-package}
+\alias{rivr-package}
+\alias{rivr}
+\title{Steady and Unsteady Open-Channel Flow Computation}
+\description{
+This package is designed as an educational tool for students and 
+instructors of undergraduate courses in open channel hydraulics. 
+Functions are provided for computing normal and critical depths, 
+steady (e.g. backwater curves) and unsteady (flood wave routing) 
+flow computations for prismatic trapezoidal channels. See the vignettes
+to get started.
+}
diff --git a/man/route_wave.Rd b/man/route_wave.Rd
index 0eb9c46..d27c67d 100644
--- a/man/route_wave.Rd
+++ b/man/route_wave.Rd
@@ -1,121 +1,135 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/route_wave_v4.r
-\name{route_wave}
-\alias{route_wave}
-\title{Flood wave routing}
-\usage{
-route_wave(So, n, Cm, g, B, SS, initial.condition, boundary.condition,
-  downstream.condition, timestep, spacestep, numnodes, monitor.nodes,
-  monitor.times, engine = c("Dynamic", "Kinematic"),
-  scheme = c("MacCormack", "Lax"), boundary.type = c("QQ", "Qy", "yQ",
-  "yy"))
-}
-\arguments{
-\item{So}{Channel slope [\eqn{L L^{-1}}].}
-
-\item{n}{Manning's roughness coefficient.}
-
-\item{Cm}{Unit conversion coefficient for Manning's equation. For SI units, Cm = 1.}
-
-\item{g}{Gravitational acceleration [\eqn{L T^{-2}}].}
-
-\item{B}{Channel bottom width [\eqn{L}].}
-
-\item{SS}{Channel sideslope [\eqn{L L^{-1}}].}
-
-\item{initial.condition}{The initial flow rate [\eqn{L^3 T^{-1}}], assumed constant 
-throughout the channel.}
-
-\item{boundary.condition}{Vector specifying the upstream boundary condition 
-for the full duration of the model. If \code{engine = "Kinematic"}, values are 
-assumed to be flow [\eqn{L^3 T^{-1}}]. If \code{engine = "Dynamic"}, the form of the 
-boundary condition is determined by the argument \code{boundary.type}.}
-
-\item{downstream.condition}{Only used if \code{engine = "Dynamic"}. Vector specifying 
-the upstream boundary condition for the full duration of the model. Must be the same
-length as \code{boundary.condition}.}
-
-\item{timestep}{Temporal resolution of the model. Also the assumed time interval [\eqn{T}] 
-between elements of \code{boundary.condition} and \code{downstream.condition}. 
-The user is responsible for ensuring numerical stability.}
-
-\item{spacestep}{the spatial resolution of the model, interpreted as the distance [\eqn{L}]
-between nodes in the model domain. The user is responsible for ensuring numerical stability.}
-
-\item{numnodes}{The number of nodes used to discretize the channel. The total channel extent is
-computed as \code{spacestep*(numnodes - 1)}.}
-
-\item{monitor.nodes}{the nodes to be monitored every time step. Specified as a vector of node 
-indices, with 1 being the upstream boundary and \code{numnodes} being the downstream boundary.}
-
-\item{monitor.times}{the time steps at which to monitor every node. Specified as a vector of 
-indices of \code{boundary.condition}. Defaults to five equally-spaced time steps including 
-the first and last time steps.}
-
-\item{engine}{The engine to be used for routing the flood wave. 
-May be either "Kinematic" or "Dynamic".}
-
-\item{scheme}{Only used if \code{engine = "Dynamic"}. Specifies whether to use the 
-Lax Diffusive scheme or the MacCormack predictor-corrector scheme.}
-
-\item{boundary.type}{Only used if \code{engine = "Dynamic"}. Specifies what boundary data
-is supplied. Possible characters are If \code{boundary.type = "QQ"}, both \code{boundary.condition}
-and \code{downstream.condition} are assumed to be flows [\eqn{L^3 T^{-1}}]. If 
-\code{boundary.type = "Qy"} the upstream boundary is assumed to be flow
-while the downstream boundary is assumed to be depth [\eqn{L}]. Other possibilities
-are \code{"yQ"} and \code{"yy"}.}
-}
-\value{
-data.frame with columns:
-  \item{step}{Time step.}
-  \item{node}{Node index.}
-  \item{time}{Time since start.}
-  \item{distance}{Downstream distance.}
-  \item{flow}{Flow rate.}
-  \item{depth}{Flow depth.}
-  \item{velocity}{Flow velocity.}
-  \item{area}{Flow area.}
-  \item{monitor.type}{Row refers to a monitored node ("node") or timestep ("timestep").}
-}
-\description{
-Route a flood wave down a prismatic channel.
-}
-\details{
-Provides implementations of a Kinematic Wave Model (KWM) and 
-  a Dynamic Wave Model (DWM) with the choice of two numerical schemes. The MacCormack 
-  scheme is a second-order accurate predictor-corrector scheme that provides efficient 
-  flood wave routing. The Lax diffusive scheme can be used to obtain smooth solutions for
-  problems with discontinuities in the boundary conditions, e.g. sudden gate closures.
-  The DWM implementation uses the Method of Characteristics (MOC) to compute the flow 
-  regime at the model boundaries, and allows the user to specify boundaries in terms of 
-  depths and/or flows. the KWM implementation assumes the normal depth at the upstream
-  boundary and is only first-order accurate.
-}
-\examples{
-\dontrun{ 
-# kinematic wave routing
-times = seq(0, 30000, by = 25)
-floodwave = ifelse(times >= 9000, 250,
-  250 + (750/pi)*(1 - cos(pi*times/(60*75))))
-route_wave(0.001, 0.045, 1.486, 32.2, 100, 0, initial.condition = 250, 
-  boundary.condition = floodwave, timestep = 25, spacestep = 50, 
-  numnodes=301, monitor.nodes = c(1, 101, 201, 301), 
-  monitor.times = seq(1, length(times), by = 10), engine = "Kinematic")
-# dynamic wave routing with zero-gradient downstream condition using MacCormack scheme
-route_wave(0.001, 0.045, 1.486, 32.2, 100, 0, initial.condition = 250, 
-  boundary.condition = floodwave, downstream.condition = rep(-1, length(times)), 
-  timestep = 25, spacestep = 500, numnodes = 31, engine = "Dynamic", 
-  scheme = "MacCormack", monitor.nodes = c(1, 11, 21, 31), 
-  monitor.times = seq(1, length(times), by = 10))
-# mixed boundary conditions (sudden gate closure) using Lax scheme
-lax = route_wave(0.00008, 0.013, 1, 9.81, 6.1, 1.5, 
-  initial.condition = 126, boundary.condition = rep(5.79, 2001), 
-  downstream.condition = rep(0, 2001), timestep = 1, spacestep = 10, 
-  numnodes = 501, monitor.nodes = c(1, 151, 251, 301, 501), 
-  monitor.times = c(1, 501, 1001, 1501, 2001), 
-  engine="Dynamic", scheme="Lax", boundary.type="yQ")
-# extract data for a monitored point
-require(dplyr)
-filter(lax, monitor.type == "node", node == 151)
-}
-}
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/route_wave_v4.r
+\name{route_wave}
+\alias{route_wave}
+\title{Flood wave routing}
+\usage{
+route_wave(
+  So,
+  n,
+  Cm,
+  g,
+  B,
+  SS,
+  initial.condition,
+  boundary.condition,
+  downstream.condition,
+  timestep,
+  spacestep,
+  numnodes,
+  monitor.nodes,
+  monitor.times,
+  engine = c("Dynamic", "Kinematic"),
+  scheme = c("MacCormack", "Lax"),
+  boundary.type = c("QQ", "Qy", "yQ", "yy")
+)
+}
+\arguments{
+\item{So}{Channel slope [\eqn{L L^{-1}}].}
+
+\item{n}{Manning's roughness coefficient.}
+
+\item{Cm}{Unit conversion coefficient for Manning's equation. For SI units, Cm = 1.}
+
+\item{g}{Gravitational acceleration [\eqn{L T^{-2}}].}
+
+\item{B}{Channel bottom width [\eqn{L}].}
+
+\item{SS}{Channel sideslope [\eqn{L L^{-1}}].}
+
+\item{initial.condition}{The initial flow rate [\eqn{L^3 T^{-1}}], assumed constant 
+throughout the channel.}
+
+\item{boundary.condition}{Vector specifying the upstream boundary condition 
+for the full duration of the model. If \code{engine = "Kinematic"}, values are 
+assumed to be flow [\eqn{L^3 T^{-1}}]. If \code{engine = "Dynamic"}, the form of the 
+boundary condition is determined by the argument \code{boundary.type}.}
+
+\item{downstream.condition}{Only used if \code{engine = "Dynamic"}. Vector specifying 
+the upstream boundary condition for the full duration of the model. Must be the same
+length as \code{boundary.condition}.}
+
+\item{timestep}{Temporal resolution of the model. Also the assumed time interval [\eqn{T}] 
+between elements of \code{boundary.condition} and \code{downstream.condition}. 
+The user is responsible for ensuring numerical stability.}
+
+\item{spacestep}{the spatial resolution of the model, interpreted as the distance [\eqn{L}]
+between nodes in the model domain. The user is responsible for ensuring numerical stability.}
+
+\item{numnodes}{The number of nodes used to discretize the channel. The total channel extent is
+computed as \code{spacestep*(numnodes - 1)}.}
+
+\item{monitor.nodes}{the nodes to be monitored every time step. Specified as a vector of node 
+indices, with 1 being the upstream boundary and \code{numnodes} being the downstream boundary.}
+
+\item{monitor.times}{the time steps at which to monitor every node. Specified as a vector of 
+indices of \code{boundary.condition}. Defaults to five equally-spaced time steps including 
+the first and last time steps.}
+
+\item{engine}{The engine to be used for routing the flood wave. 
+May be either "Kinematic" or "Dynamic".}
+
+\item{scheme}{Only used if \code{engine = "Dynamic"}. Specifies whether to use the 
+Lax Diffusive scheme or the MacCormack predictor-corrector scheme.}
+
+\item{boundary.type}{Only used if \code{engine = "Dynamic"}. Specifies what boundary data
+is supplied. Possible characters are If \code{boundary.type = "QQ"}, both \code{boundary.condition}
+and \code{downstream.condition} are assumed to be flows [\eqn{L^3 T^{-1}}]. If 
+\code{boundary.type = "Qy"} the upstream boundary is assumed to be flow
+while the downstream boundary is assumed to be depth [\eqn{L}]. Other possibilities
+are \code{"yQ"} and \code{"yy"}.}
+}
+\value{
+data.frame with columns:
+  \item{step}{Time step.}
+  \item{node}{Node index.}
+  \item{time}{Time since start.}
+  \item{distance}{Downstream distance.}
+  \item{flow}{Flow rate.}
+  \item{depth}{Flow depth.}
+  \item{velocity}{Flow velocity.}
+  \item{area}{Flow area.}
+  \item{monitor.type}{Row refers to a monitored node ("node") or timestep ("timestep").}
+}
+\description{
+Route a flood wave down a prismatic channel.
+}
+\details{
+Provides implementations of a Kinematic Wave Model (KWM) and 
+  a Dynamic Wave Model (DWM) with the choice of two numerical schemes. The MacCormack 
+  scheme is a second-order accurate predictor-corrector scheme that provides efficient 
+  flood wave routing. The Lax diffusive scheme can be used to obtain smooth solutions for
+  problems with discontinuities in the boundary conditions, e.g. sudden gate closures.
+  The DWM implementation uses the Method of Characteristics (MOC) to compute the flow 
+  regime at the model boundaries, and allows the user to specify boundaries in terms of 
+  depths and/or flows. the KWM implementation assumes the normal depth at the upstream
+  boundary and is only first-order accurate.
+}
+\examples{
+\dontrun{ 
+# kinematic wave routing
+times = seq(0, 30000, by = 25)
+floodwave = ifelse(times >= 9000, 250,
+  250 + (750/pi)*(1 - cos(pi*times/(60*75))))
+route_wave(0.001, 0.045, 1.486, 32.2, 100, 0, initial.condition = 250, 
+  boundary.condition = floodwave, timestep = 25, spacestep = 50, 
+  numnodes=301, monitor.nodes = c(1, 101, 201, 301), 
+  monitor.times = seq(1, length(times), by = 10), engine = "Kinematic")
+# dynamic wave routing with zero-gradient downstream condition using MacCormack scheme
+route_wave(0.001, 0.045, 1.486, 32.2, 100, 0, initial.condition = 250, 
+  boundary.condition = floodwave, downstream.condition = rep(-1, length(times)), 
+  timestep = 25, spacestep = 500, numnodes = 31, engine = "Dynamic", 
+  scheme = "MacCormack", monitor.nodes = c(1, 11, 21, 31), 
+  monitor.times = seq(1, length(times), by = 10))
+# mixed boundary conditions (sudden gate closure) using Lax scheme
+lax = route_wave(0.00008, 0.013, 1, 9.81, 6.1, 1.5, 
+  initial.condition = 126, boundary.condition = rep(5.79, 2001), 
+  downstream.condition = rep(0, 2001), timestep = 1, spacestep = 10, 
+  numnodes = 501, monitor.nodes = c(1, 151, 251, 301, 501), 
+  monitor.times = c(1, 501, 1001, 1501, 2001), 
+  engine="Dynamic", scheme="Lax", boundary.type="yQ")
+# extract data for a monitored point
+require(dplyr)
+filter(lax, monitor.type == "node", node == 151)
+}
+}
diff --git a/man/waterolympics.Rd b/man/waterolympics.Rd
index d08ecd8..6ae542f 100644
--- a/man/waterolympics.Rd
+++ b/man/waterolympics.Rd
@@ -1,38 +1,38 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/route_wave_v4.r
-\docType{data}
-\name{waterolympics}
-\alias{waterolympics}
-\title{California Water Olympics}
-\format{A data frame with 40 rows and 3 variables}
-\usage{
-data(waterolympics)
-}
-\description{
-Digitized results from the California Water Olympics. The variables are as follows:
-\itemize{
-  \item t The time (in seconds) since the start of the model run.
-  \item Q The flow rate [\eqn{ft^3 s^{-1}}].
-  \item x The distance downstream [\eqn{ft}] at which the hydrograph was recorded.
-}
-The data can be used to validate numerical solutions to flood wave routing for a channel 
-under the following conditions:
-\itemize{
-  \item Channel width is 100 feet.
-  \item Channel slope is 0.001.
-  \item Channel extent is 150,000 feet.
-  \item Channel roughness (Manning's n) is 0.045.
-  \item Channel sideslope is 0 (rectangular channel).
-  \item Initial flow rate is 250 cfs.
-  \item Upstream boundary condition is defined as 
-    \deqn{Q(t < 9000) = 250 + \frac{750}{\pi}(1 - \cos{\frac{\pi t}{4500}})} 
-    \deqn{Q(t >= 9000) = 250}
-}
-}
-\references{
-Sobey, Rodney. "H11: Hydrograph Routing." 
-  Review of One-Dimensional Hydrodynamic and Transport Models. Bay-Delta 
-  Modeling Forum, 15 June 2001. Web. 13 Mar. 2015. 
-  <http://www.cwemf.org/1-DReview/>.
-}
-\keyword{datasets}
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/route_wave_v4.r
+\docType{data}
+\name{waterolympics}
+\alias{waterolympics}
+\title{California Water Olympics}
+\format{A data frame with 40 rows and 3 variables}
+\usage{
+data(waterolympics)
+}
+\description{
+Digitized results from the California Water Olympics. The variables are as follows:
+\itemize{
+  \item t The time (in seconds) since the start of the model run.
+  \item Q The flow rate [\eqn{ft^3 s^{-1}}].
+  \item x The distance downstream [\eqn{ft}] at which the hydrograph was recorded.
+}
+The data can be used to validate numerical solutions to flood wave routing for a channel 
+under the following conditions:
+\itemize{
+  \item Channel width is 100 feet.
+  \item Channel slope is 0.001.
+  \item Channel extent is 150,000 feet.
+  \item Channel roughness (Manning's n) is 0.045.
+  \item Channel sideslope is 0 (rectangular channel).
+  \item Initial flow rate is 250 cfs.
+  \item Upstream boundary condition is defined as 
+    \deqn{Q(t < 9000) = 250 + \frac{750}{\pi}(1 - \cos{\frac{\pi t}{4500}})} 
+    \deqn{Q(t >= 9000) = 250}
+}
+}
+\references{
+Sobey, Rodney. "H11: Hydrograph Routing." 
+  Review of One-Dimensional Hydrodynamic and Transport Models. Bay-Delta 
+  Modeling Forum, 15 June 2001. Web. 13 Mar. 2015. 
+  <http://www.cwemf.org/1-DReview/>.
+}
+\keyword{datasets}