\begin{thebibliography}{23}
\newcommand{\enquote}[1]{``#1''}
\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi

\bibitem[{url()}]{url:Delft3Dbranch}
\enquote{Delft3D Hirano ellipticity check branch.}
\newblock
  \urlprefix\url{https://svn.oss.deltares.nl/repos/delft3d/branches/research/Technical
  University of Delft/20161020_ellipticity_check}.

\bibitem[{Blom(2008)}]{Blom08}
Blom, A., 2008.
\newblock \enquote{Different approaches to handling vertical and streamwise
  sorting in modeling river morphodynamics.}
\newblock \emph{Water Resour. Res.} 44~(3): {W03415}.
\newblock DOI {10.1029/2006WR005474}, ISSN 1944-7973,
  \urlprefix\url{http://dx.doi.org/10.1029/2006WR005474}.
\newblock \urlprefix\url{http://dx.doi.org/10.1029/2006WR005474}.

\bibitem[{Blom \emph{et~al.}(2006)Blom, Parker, Ribberink and
  De~Vriend}]{Blom06_2}
Blom, A., G.~Parker, J.~S. Ribberink and H.~J. de~Vriend, 2006.
\newblock \enquote{Vertical sorting and the morphodynamics of
  bed-form-dominated rivers: An equilibrium sorting model.}
\newblock \emph{J. Geophys. Res., Earth Surface} 111: F01006.
\newblock DOI {10.1029/2004JF000175}, ISSN 2156-2202,
  \urlprefix\url{http://dx.doi.org/10.1029/2004JF000175}.
\newblock \urlprefix\url{http://dx.doi.org/10.1029/2004JF000175}.

\bibitem[{Blom \emph{et~al.}(2008)Blom, Ribberink and Parker}]{Blom08_2}
Blom, A., J.~S. Ribberink and G.~Parker, 2008.
\newblock \enquote{Vertical sorting and the morphodynamics of bed
  form-dominated rivers: A sorting evolution model.}
\newblock \emph{J. Geophys. Res., Earth Surface} 113: F01019.
\newblock DOI {10.1029/2006JF000618}, ISSN 2156-2202,
  \urlprefix\url{http://dx.doi.org/10.1029/2006JF000618}.
\newblock \urlprefix\url{http://dx.doi.org/10.1029/2006JF000618}.

\bibitem[{Blom \emph{et~al.}(2003)Blom, Ribberink and De~Vriend}]{Blom03}
Blom, A., J.~S. Ribberink and H.~J. de~Vriend, 2003.
\newblock \enquote{Vertical sorting in bed forms: Flume experiments with a
  natural and a trimodal sediment mixture.}
\newblock \emph{Water Resour. Res.} 39~(2): 1025.
\newblock DOI {10.1029/2001WR001088}, ISSN 1944-7973,
  \urlprefix\url{http://dx.doi.org/10.1029/2001WR001088}.
\newblock \urlprefix\url{http://dx.doi.org/10.1029/2001WR001088}.

\bibitem[{Chavarr\'ias \emph{et~al.}()Chavarr\'ias, Stecca, Labeur and
  Blom}]{ChavarriasXX}
Chavarr\'ias, V., G.~Stecca, R.~J. Labeur and A.~Blom.
\newblock \enquote{Ill-posedness in modelling mixed-sediment river
  morphodynamics.} (in preparation).

\bibitem[{Egiazaroff(1965)}]{Egiazaroff65}
Egiazaroff, I.~V., 1965.
\newblock \enquote{Calculation of nonuniform sediment concentrations.}
\newblock In \emph{Proceedings ASCE}, vol.~91, pages 225--247.

\bibitem[{Engelund and Hansen(1967)}]{Engelund67}
Engelund, F. and E.~Hansen, 1967.
\newblock \emph{Monograph on sediment transport in alluvial streams}.
\newblock {T}ech. {R}ep., Hydraul. Lab., Tech. Univ. of Denmark, Copenhagen,
  Denmark.

\bibitem[{Exner(1920)}]{Exner20}
Exner, F.~M., 1920.
\newblock \enquote{Zur {P}hysik der {D}{\"u}nen.}
\newblock \emph{Akad. Wiss. Wien Math. Naturwiss} 129(2a): 929--952.
\newblock (in German).

\bibitem[{Frings \emph{et~al.}(2014)Frings, D\"{u}ring, Beckhausen,
  Sch\"{u}ttrumpf and Vollmer}]{Frings14_2}
Frings, R.~M., R.~D\"{u}ring, C.~Beckhausen, H.~Sch\"{u}ttrumpf and S.~Vollmer,
  2014.
\newblock \enquote{Fluvial sediment budget of a modern, restrained river: The
  lower reach of the {R}hine in {G}ermany.}
\newblock \emph{Catena} 122~(0): 91--102.
\newblock DOI {10.1016/j.catena.2014.06.007}, ISSN 0341-8162,
  \urlprefix\url{http://www.sciencedirect.com/science/article/pii/S0341816214001714}.
\newblock
  \urlprefix\url{http://www.sciencedirect.com/science/article/pii/S0341816214001714}.

\bibitem[{Hirano(1971)}]{Hirano71}
Hirano, M., 1971.
\newblock \enquote{River bed degradation with armouring.}
\newblock \emph{Trans. Jpn. Soc. Civ. Eng} 3~(2): 194--195.

\bibitem[{Hoey and Ferguson(1994)}]{Hoey94}
Hoey, T.~B. and R.~Ferguson, 1994.
\newblock \enquote{Numerical simulation of downstream fining by selective
  transport in gravel bed rivers: Model development and illustration.}
\newblock \emph{Water Resour. Res.} 30~(7): 2251--2260.
\newblock DOI {10.1029/94WR00556}, ISSN 1944-7973,
  \urlprefix\url{http://dx.doi.org/10.1029/94WR00556}.
\newblock \urlprefix\url{http://dx.doi.org/10.1029/94WR00556}.

\bibitem[{Kalkwijk and Booij(1986)}]{Kalkwijk86}
Kalkwijk, J. P.~T. and R.~Booij, 1986.
\newblock \enquote{Adaptation of secondary flow in nearly-horizontal flow.}
\newblock \emph{J. Hydraul. Res.} 24~(1): 19-37.
\newblock DOI {10.1080/00221688609499330},
  \urlprefix\url{http://dx.doi.org/10.1080/00221688609499330}.
\newblock \urlprefix\url{http://dx.doi.org/10.1080/00221688609499330}.

\bibitem[{Meyer-Peter and M{\"u}ller(1948)}]{MeyerPeter48}
Meyer-Peter, E. and R.~M{\"u}ller, 1948.
\newblock \enquote{Formulas for bed-load transport.}
\newblock In \emph{Proc. 2nd Meeting Int. Assoc. Hydraul. Struct. Res.}, pages
  39--64. Stockholm.

\bibitem[{Parker(1991)}]{Parker91_1}
Parker, G., 1991.
\newblock \enquote{Selective Sorting and Abrasion of River Gravel. {I}:
  Theory.}
\newblock \emph{J. Hydraul. Eng.} 117~(2): 131--147.
\newblock DOI {10.1061/(ASCE)0733-9429(1991)117:2(131)},
  \urlprefix\url{http://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9429%281991%29117%3A2%28131%29}.
\newblock
  \urlprefix\url{http://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9429%281991%29117%3A2%28131%29}.

\bibitem[{Parker \emph{et~al.}(1982)Parker, Klingeman and McLean}]{Parker82_3}
Parker, G., P.~C. Klingeman and D.~G. McLean, 1982.
\newblock \enquote{Bedload and size distribution in paved gravel-bed streams.}
\newblock \emph{Journal of the Hydraulics Division} 108~(4): 544--571.

\bibitem[{Ribberink(1987)}]{Ribberink87_PhD}
Ribberink, J.~S., 1987.
\newblock \emph{Mathematical modelling of one-dimensional morphological changes
  in rivers with non-uniform sediment}.
\newblock Ph.D. thesis, Delft University of Technology, The Netherlands.

\bibitem[{Saint-Venant(1871)}]{SaintVenant71}
Saint-Venant, A. J. C.~B., 1871.
\newblock \enquote{Th\'{e}orie du mouvement non permanent des eaux, avec
  application aux crues des rivi\`{e}res et \`{a} l'introduction des mar\'{e}es
  dans leur lit.}
\newblock \emph{Comptes Rendus des s\'{e}ances de l'Acad\'{e}mie des Sciences}
  73: 237--240.
\newblock (in French).

\bibitem[{Sieben(1994)}]{Sieben94}
Sieben, A., 1994.
\newblock \emph{Notes on the mathematical modelling of alluvial mountain rivers
  with graded sediment}.
\newblock Tech. Rep. 94--3, Delft University of Technology.

\bibitem[{Sieben(1997)}]{Sieben97_PhD}
Sieben, J., 1997.
\newblock \emph{Modelling of hydraulics and morphology in mountain rivers}.
\newblock Ph.D. thesis, Delft University of Technology.

\bibitem[{Sloff(1992)}]{Sloff92}
Sloff, C.~J., 1992.
\newblock \emph{The method of characteristics applied to analyse 2DH models}.
\newblock Tech. Rep. 92--4, Delft University of Technology.

\bibitem[{Stecca \emph{et~al.}(2014)Stecca, Siviglia and Blom}]{Stecca14}
Stecca, G., A.~Siviglia and A.~Blom, 2014.
\newblock \enquote{Mathematical analysis of the {S}aint-{V}enant-{H}irano model
  for mixed-sediment morphodynamics.}
\newblock \emph{Water Resour. Res.} 50: 7563--7589.
\newblock DOI {10.1002/2014WR015251}, ISSN 1944-7973,
  \urlprefix\url{http://dx.doi.org/10.1002/2014WR015251}.
\newblock \urlprefix\url{http://dx.doi.org/10.1002/2014WR015251}.

\bibitem[{Viparelli \emph{et~al.}(2016)Viparelli, Moreira and
  Blom}]{Viparelli16}
Viparelli, E., R.~R.~H. Moreira and A.~Blom, 2016.
\newblock \enquote{Modelling stratigraphy-based {GBR} morphodynamics.}
\newblock In \emph{Proc. {G}ravel {B}ed {R}ivers 8, Kyoto, Japan.}
\newblock In press.

\end{thebibliography}
