r.hydro.CASC2D(1)      Grass User's Manual	r.hydro.CASC2D(1)



NNAAMMEE
       rr..hhyyddrroo..CCAASSCC22DD  - Fully integrated distributed cascaded 2D
       hydrologic modeling.

       (GRASS Raster Program)


       Note: This is beta software: version 1.01.



SSYYNNOOPPSSIISS::
       _r_._h_y_d_r_o_._C_A_S_C_2_D_,	 _r_._h_y_d_r_o_._C_A_S_C_2_D   _h_e_l_p_,    _r_._h_y_d_r_o_._C_A_S_C_2_D
       [-smtoepibduq]	   elevation=mapname	  time_step=value
       tot_time=value	discharge=mapname    outlet_eastNnorthNs-
       lope=east,north,bedslope    rain_duration=value	  [water-
       shed_mask=mapname] [initial_depth=mapname] [storage_capac-
       ity=mapname]   [interception_coefficient=mapname]  [rough-
       ness_map=mapname] [Manning_n=value] [conductivity=mapname]
       [capillary=mapname]  [porosity=mapname] [moisture=mapname]
       [pore_index=mapname] [residual_sat=mapname] [lake_map=map-
       name]   [lake_elev=mapname]  [radar_intensity_map=mapname]
       [links_map=mapname]	 [nodes_map=mapname]	   [chan-
       nel_input=mapname] [table_input=mapname] [dis_profile=map-
       name]  [wat_surf_profile=mapname]   [hyd_location=mapname]
       [r_gage_file=mapname]  [unif_rain_int=value] [num_of_rain-
       gages=value]			   [gage_time_step=value]
       [radar_time_step=value]		  [write_time_step=value]
       [unit_el_conv=value] [unit_lake=value]  [unit_space=value]
       [d_thresh=value] 	       [dis_hyd_location=mapname]
       [depth_map=mapname]		  [inf_depth_map=mapname]
       [surf_moist_map=mapname]       [rate_of_infil_map=mapname]
       [dis_rain_map=mapname]



NNOOTTEE
       In above, the command line arguments have been  rearranged
       so  that  the  required	parameters are placed first. When
       doing "_r_._h_y_d_r_o_._C_A_S_C_2_D _h_e_l_p", the user will see a different
       sequence of parameters.



DDIISSCCLLAAIIMMEERR
       Users  with  no	background  in	or  understanding of dis-
       tributed hydrology are strongly advised against using this
       code  in  any  mode,  particularly  in  operational  mode.
       Besides knowledge of basic hydrology, experience with typ-
       ical  numerical techniques used in physically-based hydro-
       dynamic models is recommended as it  will  help	the  user
       grasp  capabilities  and  limitations  of this model. This
       manual is significantly condensed for electronic distribu-
       tion  and is in no way comprehensive. Users are encouraged
       to experiment with the  model  and  venture  in	hydrology
       textbooks  and journal papers to learn more about the top-
       ics touched upon in this manual. The  _r_._h_y_d_r_o_._C_A_S_C_2_D  code
       is continuously being improved. Changes in the source code
       of _r_._h_y_d_r_o_._C_A_S_C_2_D may be made at any time, without notifi-
       cation.	No  claims  are made regarding the suitability of
       _r_._h_y_d_r_o_._C_A_S_C_2_D  for  any  particular  purpose.  The  model
       _r_._h_y_d_r_o_._C_A_S_C_2_D  was  written  for research and educational
       purposes.



HHIISSTTOORRYY
       CASC2D originally began with the two-dimensional  overland
       flow  routing  algorithm  developed  in	APL by Prof. P.Y.
       Julien at Colorado State  University.  The  overland  flow
       routing module was converted from APL to FORTRAN by Bahram
       Saghafian, then at Colorado  State  University,	with  the
       addition of Green & Ampt infiltration and explicit channel
       routing (Julien and Saghafian, 1991, Saghafian, 1992,  and
       Julien  et  al.,  1995).  The Fortran version was reformu-
       lated, significantly enhanced, and  re-written  in  the	C
       programming  language by Bahram Saghafian at the U.S. Army
       Construction Engineering Research  Laboratories.  Implicit
       channel	 routing   code   was	developed  and	added  to
       _r_._h_y_d_r_o_._C_A_S_C_2_D by Fred L. Ogden (Ogden, 1994), formerly at
       Colorado State University, now Asst. Professor, Department
       of Civil and Environmental Engineering, University of Con-
       necticut,  Storrs,  Connecticut. This version became known
       as r.hydro.CASC2D, part of the GRASS  GIS  for  hydrologic
       simulations (Saghafian, 1993).



DDEESSCCRRIIPPTTIIOONN
       _r_._h_y_d_r_o_._C_A_S_C_2_D  is a physically-based, distributed, raster
       hydrologic model which simulates the  hydrologic  response
       of  a  watershed  subject to a given rainfall field. Input
       rainfall is allowed to vary in space and time. Major  com-
       ponents	of  the model include interception, infiltration,
       and surface runoff routing.   Interception  is  a  process
       whereby	rainfall is retained by vegetation.  Interception
       is estimated using an  empirical  three	parameter  model.
       Infiltration  is  the  process whereby rainfall or surface
       water is pulled into the soil  by  capillary  and  gravity
       forces.	The  Green and Ampt equation with four parameters
       is applied to model the event-based infiltration. For con-
       tinuous	soil  moisture accounting, redistribution of soil
       moisture can also be  simulated	whenever  the  non-inter-
       cepted	rainfall  intensity  falls  below  the	saturated
       hydraulic conductivity of  the  soil.  The  redistribution
       option requires two more soil hydraulic parameters. Excess
       rainfall becomes surface runoff and is routed as  overland
       flow  and  subsequently as channel flow. The overland flow
       routing formulation is based on a two-dimensional explicit
       finite  difference  (FD) technique, while two different FD
       techniques, one explicit and one implicit, provide options
       for  routing  one-dimensional channel flow. Through a step
       function, a depression depth may be specified, below which
       no overland flow will be routed.


       The  following  sections  describe  various aspects of the
       model.  In executing the model, the likelihood of making a
       serious	mistake by an inexperienced user is unfortunately
       very high due to complexity of input and  output  options.
       Thus the user must thoroughly read all the details of this
       manual and then select appropriate options for his or  her
       needs.  Since  at  this	time GRASS is an integer GIS, all
       input maps are stored in integer form. This requires  con-
       version	from integer to floating point representation via
       a scaling factor.  The scaling  factor  for  all  floating
       point  values  is  fixed.  Therefore,  the integer maps of
       parameter values are created by multiplying floating point
       values (e.g. volumetric water content) by a multiplier.



PPAARRAAMMEETTEERRSS//OOPPTTIIOONNSS
       The following input/output parameters/options control com-
       plexity of the simulation. Map and file	names  in  square
       brackets [] are optional. Some maps are mutually exclusive
       ( logical -or- ), while some maps require  other  maps  to
       enable  proper  function ( logical -and- ). Carefully read
       the NOTES section.



IINNPPUUTT
       TOPOGRAPHY


       _e_l_e_v_a_t_i_o_n_=_m_a_p_n_a_m_e map of elevation (DEM).


       _o_u_t_l_e_t___e_a_s_t_N_n_o_r_t_h_N_s_l_o_p_e_=_v_a_l_u_e,_e_a_s_t_i_n_g_, _n_o_r_t_h_i_n_g,  and  _b_e_d
       _s_l_o_p_e at the outlet


       value,value (comma delimited)


       TIME


       _t_i_m_e___s_t_e_p_=_v_a_l_u_e	computational  time step duration in sec-
       onds.  (typ. 1 to 30 seconds)


       _t_o_t___t_i_m_e=value total simulation time in sec.


       OVERLAND FLOW


       _[_M_a_n_n_i_n_g___n_=_v_a_l_u_e_] spatially uniform Manning's n	roughness
       value for overland flow.


       -or-


       _[_r_o_u_g_h_n_e_s_s___m_a_p_=_m_a_p_n_a_m_e_]	spatially varied map of Manning's
       n roughness coefficient (values in 1000*Manning's n).


       _[_w_a_t_e_r_s_h_e_d___m_a_s_k_=_m_a_p_n_a_m_e_] map  of  watershed  boundary  (or
       mask).  This option is recommended, as it speeds execution
       greatly.


       _[_d___t_h_r_e_s_h_=_v_a_l_u_e_]  threshold  overland  depth,  in  meters,
       below  which  overland routing will not be performed (i.e.
       average depression storage).


       _[_i_n_i_t_i_a_l___d_e_p_t_h_=_m_a_p_n_a_m_e_]	map  of  initial  overland   (not
       lakes) depth in mm.


       RAINFALL


       _r_a_i_n___d_u_r_a_t_i_o_n_=_v_a_l_u_e total rainfall duration in sec.


       _[_u_n_i_f___r_a_i_n___i_n_t_=_v_a_l_u_e_] spatially uniform rainfall intensity
       in mm/hr.


       -or-


       _[_r___g_a_g_e___f_i_l_e_=_f_i_l_e_n_a_m_e_] raingage rainfall input  file  name
       (ASCII).


       and-


       _[_n_u_m___o_f___r_a_i_n_g_a_g_e_s_=_v_a_l_u_e_] number of recording raingages.


       -and-


       _[_g_a_g_e___t_i_m_e___s_t_e_p_=_v_a_l_u_e_]  time step (temporal resolution) of
       recorded raingage data in sec.


       or-


       _[_r_a_d_a_r___i_n_t_e_n_s_i_t_y___m_a_p_=_m_a_p_n_a_m_e_] prefix  of  time  series  of
       maps of radar- (or otherwise-) generated rainfall intensi-
       ties in mm/hr.


       and-


       [radar_time_step=value] time increment between radar-  (or
       otherwise-) generated rainfall maps in sec.


       INTERCEPTION


       _[_s_t_o_r_a_g_e___c_a_p_a_c_i_t_y_=_m_a_p_n_a_m_e_]   map   of  vegetation  storage
       capacity in tenths of mm.


       -and-


       _[_i_n_t_e_r_c_e_p_t_i_o_n___c_o_e_f_f_i_c_i_e_n_t_=_m_a_p_n_a_m_e_]  map	of   interception
       coefficient (values in 1000*actual coefficient).


       INFILTRATION


       _[_c_o_n_d_u_c_t_i_v_i_t_y_=_m_a_p_n_a_m_e_]  map  of	soil  saturated hydraulic
       conductivity  in  tenths  of  mm/hr  (Req'd  for  G&A  and
       Redist).


       _[_c_a_p_i_l_l_a_r_y_=_m_a_p_n_a_m_e_] map of soil capillary pressure head at
       the wetting front in tenths  of	mm  (Req'd  for  G&A  and
       Redist).


       _[_p_o_r_o_s_i_t_y_=_m_a_p_n_a_m_e_]  map of soil effective porosity (values
       in 1000*porosity) (Req'd for G&A and Redist).


       _[_m_o_i_s_t_u_r_e_=_m_a_p_n_a_m_e_] map of initial soil moisture (values in
       1000*moisture) (Req'd for G&A and Redist).


       _[_p_o_r_e___i_n_d_e_x_=_m_a_p_n_a_m_e_]  map  of  soil pore-size distribution
       index (Brooks & Corey lambda)  in  1000*index  (Req'd  for
       Redist).


       _[_r_e_s_i_d_u_a_l___s_a_t_=_m_a_p_n_a_m_e_]  map  of	soil  residual saturation
       (values in 1000*residual saturation) (Req'd for Redist).


       LAKES


       _[_l_a_k_e___m_a_p_=_m_a_p_n_a_m_e_] map of lakes categories.


       _[_l_a_k_e___e_l_e_v_=_m_a_p_n_a_m_e_] map of  lakes  initial  water  surface
       elevation (also see unit_lake).


       CHANNEL ROUTING


       _[_c_h_a_n_n_e_l___i_n_p_u_t_=_f_i_l_e_n_a_m_e_]  channel  input  data  file  name
       (ASCII), required for  explicit	(EX)  and  implicit  (IM)
       channel routing methods.


       _[_l_i_n_k_s___m_a_p_=_m_a_p_n_a_m_e_]  map  of channel network link numbers.
       (EX & IM)


       _[_n_o_d_e_s___m_a_p_=_m_a_p_n_a_m_e_] map of channel network  node  numbers.
       (EX & IM)


       _[_t_a_b_l_e___i_n_p_u_t_=_f_i_l_e_n_a_m_e_]  look-up	table file for links with
       breakpoint cross section, link type 8, (ASCII) (IM)


       _[_d_i_s___p_r_o_f_i_l_e_=_f_i_l_e_n_a_m_e_] channel initial  discharge  profile
       file name (ASCII). (IM)


       _[_w_a_t___s_u_r_f___p_r_o_f_i_l_e_=_f_i_l_e_n_a_m_e_]  channel initial water surface
       profile file name (ASCII). (IM)


       _[_h_y_d___l_o_c_a_t_i_o_n_=_f_i_l_e_n_a_m_e_] file name containing link and node
       numbers	of internal locations where discharge hydrographs
       are to be saved (ASCII).


       UNITS


       _[_u_n_i_t___e_l___c_o_n_v_=_v_a_l_u_e_] unit conversion factor by  which  the
       values  in  elevation must be DIVIDED to convert them into
       meters.


       _[_u_n_i_t___l_a_k_e_=_v_a_l_u_e_] unit conversion factor by which the val-
       ues  in lake surface elevation map must be DIVIDED to con-
       vert them into meters.


       _[_u_n_i_t___s_p_a_c_e_=_v_a_l_u_e_] unit conversion  factor  by  which  all
       region easting and northing values must be DIVIDED to con-
       vert them into meters.


       OOUUTTPPUUTT


       _d_i_s_c_h_a_r_g_e_=_f_i_l_e_n_a_m_e outlet hydrograph file name (ASCII).


       _[_d_i_s___h_y_d___l_o_c_a_t_i_o_n_=_f_i_l_e_n_a_m_e_] output file name for discharge
       hydrograph at internal locations (ASCII)


       _[_w_r_i_t_e___t_i_m_e___s_t_e_p_=_v_a_l_u_e_]	time increment for writing output
       raster maps in seconds.


       -and-


       _[_d_e_p_t_h___m_a_p_=_m_a_p_n_a_m_e_] output maps of surface depth in mm.


       _[_i_n_f___d_e_p_t_h___m_a_p_=_m_a_p_n_a_m_e_] output maps of  cumulative  infil-
       tration depth in tenths of mm.


       _[_s_u_r_f___m_o_i_s_t___m_a_p_=_m_a_p_n_a_m_e_] output maps of surface soil mois-
       ture in number of fractions of a thousand.


       _[_r_a_t_e___o_f___i_n_f_i_l___m_a_p_=_m_a_p_n_a_m_e_] output  maps  of  infiltration
       rate in mm/hr.


       _[_d_i_s___r_a_i_n___m_a_p_=_m_a_p_n_a_m_e_] output maps of distributed rainfall
       intensity in mm.


       FFLLAAGGSS


       There are several flags whose utility is  driven  by  data
       availability and/or user's choice.


       _-_s do not check square tolerance of a grid cell. With this
       option non-square grid cell can be simulated  using  width
       of east-west resolution.


       _-_m   r_gage_file  units	in  mm/hr.  Without  this  option
       r_gage_file units in in/hr.


       _-_t spatially interpolates  raingage  rainfall  intensities
       using  Thiessen	polygon  technique. The default technique
       uses inverse-distance-squared proportionality for interpo-
       lation of rainfall intensity over space.


       _-_o  routes  edge-accumulated  overland  flow out of active
       region (ONLY when no mask is specified). Often the surface
       water  accumulated at the edges of the current region cre-
       ates severe backwater effects and may  limit  the  use  of
       longer computational time steps.


       _-_e  performs  one-dimensional  explicit	finite difference
       channel routing. May be suitable for low- to medium-inten-
       sity  rainstorms  over small arid and semi-arid watersheds
       with no base flow discharge. This option often limits  the
       computational  time  step  to  small values (<10 seconds).
       Channel bed smoothing is recommended to eliminate  adverse
       slopes.	No  hydraulic structures, except reservoir spill-
       ways, can be simulated.


       _-_p assumes uniform channel geometry in each link (requires
       -e  option).  If  this option is chosen, the channel input
       file (channel_input) must have only one line  per  fluvial
       link rather than the default of one line per node.


       _-_i performs Preissmann double sweep implicit channel rout-
       ing.  Particularly suitable for watersheds with some  base
       flow  to  avoid dry-bed condition with channel slopes less
       than 1%. Supercritical slopes cannot be handled; a warning
       message	will  be printed if supercritical flow is encoun-
       tered.


       _-_b initializes the channel depth and discharge files (sim-
       ilar  to  -d,  requires -i option) using the standard step
       backwater method.  This option must be used with  -i  flag
       and   replaces	-d  option  to	write  "dis_profile"  and
       &quot;wat_surf_profile&quot; files. At present, only  link
       types 1, 2, and 8 may exist in the channel network.


       _-_d  performs  channel  initialization for implicit routing
       (similar to -b, requires -i option) by flooding the entire
       channel network with a horizontal water surface and drain-
       ing down to normal depth using a y(t) outlet boundary con-
       dition  (similar  to  -b).   It	is essential for implicit
       channel routing technique that a minimum initial base flow
       discharge exist in the channels and also the corresponding
       initial water surface profile at each node in the  channel
       network have a realistic value. When the depth at the out-
       let reaches normal depth, the values  of  depth	and  dis-
       charge  at  each  node  is  written  to	"dis_profile" and
       &quot;wat_surf_profile&quot; files for use in start up  of
       actual simulations. With this option no other component of
       the model is executed; only the implicit  channel  routing
       is  performed  to create initial depth and discharge files
       necessary for start up of actual simulations.


       _-_u writes discharges in cubic feet per  second  (cfs)  and
       volumes	in  cubic  feet in "discharge" file. The internal
       calculations are all in SI units regardless of this  flag.
       The  default SI unit prints the discharges in cubic meters
       per second (cms) and volumes in cubic meters (m3).


       _-_q quietly skips printing iteration, time,  and	discharge
       values to the screen. No status report is printed.



IIMMPPOORRTTAANNTT NNOOTTEESS
       The  user  must pay close attention to the following notes
       prior to any simulation:


       1) watershed_mask: Although optional, preparation of  this
       map  is	highly	recommended as it cuts down on the memory
       requirements by the amount directly  proportional  to  the
       ratio  of  mask	area  over  the  region area (also see -o
       flag). If the basin (mask) delineation has not  been  per-
       formed  correctly,  surface  water may accumulate near the
       edges of the watershed. This excess water has no  way  out
       of the watershed and will accumulate, creating undesirable
       backwater effects within the  watershed	which  eventually
       dictate	use  of shorter time step in order to accommodate
       such effects.  It is recommended, in  such  instances,  to
       re-delineate the watershed along the edges. An alternative
       would be to lower the elevation of the cells being flooded
       by  excessive  surface  runoff near the edges such that no
       artificial backwater is created.


       2) elevation: The elevation map in  the	form  of  Digital
       Elevation  Model  (DEM)	is  undoubtedly  one  of the most
       important inputs for distributed modeling. Thus the  qual-
       ity  of	the  DEM  plays  a  major role in success of dis-
       tributed hydrologic simulations. DEMs almost  always  con-
       tain errors. Large flat areas in the DEM may be due to the
       limited vertical resolution  of	elevation  data.  Routing
       over  such  flat  areas	usually  creates problems for the
       numerical techniques used in distributed  physically-based
       models.	Unreal pits in the DEM may be artifacts of inter-
       polation scheme used to rasterize digitized  contours,  or
       due  to	coarse resolution in areas of concave topography.
       As a rule of thumb, the user must cross check the DEM with
       topographic  maps  of the area. One way to discover poten-
       tial errors in the DEM is  to  run  _r_._h_y_d_r_o_._C_A_S_C_2_D  itera-
       tively  with no other option except uniform rainfall and a
       relatively short time step.  Writing  surface  depth  maps
       should also be selected (see depth_map and write_time_step
       options).  The simulation may terminate normally, at which
       case  the  surface depth maps must be examined in order to
       determine  where  most  water  accumulation  occurred  and
       whether	such accumulation areas is justified by the topo-
       graphic map of  the  area.  Also  stream  network  may  be
       checked	for  proper connectivity via depth maps. Alterna-
       tively, if the model crashed at a certain location  (whose
       address	is printed on the screen as well as at the bottom
       of discharge file) the user must zoom in and double  check
       the  DEM with the topographic map. Often times some manual
       editing of the DEM is necessary in  order  to  impose  the
       actual drainage trend of the topo map. Prior to editing it
       is recommended that the DEM be multiplied by  10  or  100,
       particularly  if  the  original vertical resolution of the
       DEM is also a concern. To account for this  multiplication
       factor  use unit_el_conv=10 or unit_el_conv=100, whichever
       appropriate.  Note that only the unreal pits  and  depres-
       sions  must be removed since they most likely trap surface
       runoff which would have otherwise contributed to the  out-
       let.  The  real	lakes  and reservoirs may be simulated if
       delineated (see lake_map). In any event, non-smoothed DEMs
       require	short  computational  time  steps, while properly
       smoothed DEMs, particularly those with coarser grid  space
       resolution, allow use of longer time steps. Another source
       of concern, which was briefly  mentioned  in  above  para-
       graph, about the quality of the DEMs is that a nicely con-
       nected stream network cannot be derived from  non-smoothed
       DEM.  If  no  delineated  network (in the form of a vector
       file, for example) is available, an  approach  similar  to
       what  was  described  before may be taken in order to edit
       the DEM. However where a network has been delineated inde-
       pendent	of  the  DEM  then  the elevation of stream cells
       should be checked so that they are not higher  than  those
       of the surrounding cells.  Otherwise the stream cells will
       not properly collect the surface runoff.


       3) initial_depth: This is a  map  which	contains  initial
       overland  depth values, if any. Rarely used since prior to
       the storm overland planes are often dry. For channel  ini-
       tial depth see dis_profile and wat_surf_profile options.


       4)   storage_capacity   &   interception_coefficient:   In
       r.hydro.CASC2D, the interception rate (i) is expressed as:


       _i_(_t_)_=_r_(_t_) _w_h_i_l_e _I _< _a


       _i_(_t_)_=_b_*_r_(_t_) _w_h_i_l_e _I _> _a


       where  r(t) denotes rainfall intensity at time t; a is the
       storage capacity; b is the interception coefficient; and I
       is  the	cumulative  interception  depth. Storage capacity
       map, as well as interception coefficient map, are  usually
       a reclass of vegetation map. For table of storage capacity
       and interception coefficient values see Gray  (1970,  sec-
       tion 4.6) or Bras (1990) p. 233.


       5)  roughness_map: This map represents the spatial distri-
       bution of overland Manning roughness coefficient  n.  This
       map  could be a reclass of vegetation cover map and/or the
       land use map. Tables of Manning's n are available in  most
       hydrology  textbooks. By using Manning resistance equation
       it is assumed that the overland flow over watersheds  sat-
       isfies  the  conditions	of turbulent flow over rough sur-
       faces.


       6) conductivity, capillary,  porosity,  &  moisture:  Four
       soil  property  maps  are needed for modeling infiltration
       process using the Green-Ampt technique. These maps respec-
       tively contain saturated hydraulic conductivity, capillary
       suction head, effective porosity, and initial  soil  mois-
       ture  content.  The  first  three maps may be reclasses of
       soil texture  map  and  the  last  one  must  be  prepared
       considering  antecedent soil moisture conditions. Based on
       soil textural classifications, tables of estimates of  the
       first  three  parameters  can  be  found  in  Rawls et al.
       (1983).	Wherever  reliable  field  measurements  of  such
       parameters are available they may be substituted for table
       values. Note that the saturated hydraulic conductivity map
       must  be  adjusted for the percent of rock fraction within
       the soil, if known. If  these  four  maps  are  specified,
       Green  &  Ampt infiltration calculations are performed. If
       one or more of the maps is not specified, no  infiltration
       calculations are made.


       7)  pore_index & residual_sat: These two maps are required
       when continuous soil moisture  accounting  is  of  primary
       interest.  The model is capable of redistributing the soil
       moisture during periods of no- or low- intensity rainfall,
       over  which infiltration capacity may recover for the next
       burst of storm intensity. The technique	used  herein  for
       hiatus  and  post-hiatus  stages is primarily based on the
       method by Smith el al. (1993). In  this	model  Green-Ampt
       equation  is  used  for post-hiatus stage. Tables of pore-
       size distribution index (Brooks & Corey lambda) and resid-
       ual  saturation	are  given  by Rawls et al. (1982). As in
       (6), measured values should be  substituted  where  avail-
       able.  When  the four maps specified in (6) as well as the
       two maps specified here are given as  command  line  argu-
       ments,  the  redistribution  infiltration routine is used.
       All six maps must be specified  to  enable  redistribution
       infiltration calculations.


       8)  lake_map  & lake_elev: The first map is the delineated
       lake map with different categories corresponding to  indi-
       vidual  lakes  and  the second map holds the initial water
       surface elevation in the lakes. It is best to  number  the
       lakes  categories  sequentially.   If  a lake or reservoir
       connects to the implicit channel network  at  its  outlet,
       then the lake must also be numbered as a link as reflected
       in the channel_input file. See channel_input and links_map
       options	for more details. However isolated pond areas may
       be simulated as well; in fact such ponds  are  recommended
       to  be  delineated  as part of the lake_map. Such isolated
       lakes should not be present in the links map  since  their
       outlet  is not connected to the channel network. The rout-
       ing of the lakes is performed by  linear  reservoir  tech-
       nique.  Rainfall  is added directly to the lake inflow. No
       interception or infiltration is abstracted from	the  lake
       cells.


       9)  radar_intensity_map:  This  is  the	common	prefix of
       radar- or otherwise- generated rainfall maps. One possible
       source  of  this  type  of data could be the NEXRAD system
       (Crum and Albery, 1993).  Alternatively, such time  series
       of  raster  maps may come from the output of an interpola-
       tion software, which takes in the rainfall site data  cor-
       responding  to  different  times  and  generates  the time
       series of raster maps. For instance, where raingage  rain-
       fall data is available, one could run s.surf.rst of GRASS,
       one time for every recording time, and save  the  interpo-
       lated   rainfall   maps	 to   be   used   as   input  for
       r.hydro.CASC2D. In any case one must pay attention to  the
       unit of intensity which is in integer millimeters per hour
       for map values. Also see radar_time_step,  and  rain_dura-
       tion	 options.      Example:      If      one     sets
       radar_intensity_map=rain.map and  there	are  a	total  of
       eight   maps   in   regular   intervals	 of   10  minutes
       (radar_time_step=600 and rain_duration= 4800, both in sec-
       onds),  then  the  actual  name of the maps in the current
       mapset	  would     have     to     be:     "rain.map.1",
       &quot;rain.map.2&quot;  through "rain.map.8", respectively
       corresponding to time periods of 0-10, 10-20 through 70-80
       minutes.


       10) links_map & nodes_map: A link is a channel segment, of
       finite length, which is comprised of two or more  computa-
       tional  nodes  placed at the center of each grid cell. Any
       internal boundary condition (weirs  and	lakes/reservoirs,
       for  example)  is  also	considered  a  link with only two
       nodes, one node upstream of  the  internal  link  and  one
       downstream.  Although all links and nodes must be numbered
       as discussed below, the link and node  maps  only  contain
       trapezoidal  or look-up table cross sections (link types 1
       and 8).	Internal  boundary  condition  link  types  (e.g.
       weirs)  do not appear in the link or node maps. The inter-
       nal boundary condition link types do appear in  the  chan-
       nel_input  file (see attachment).  The purpose of the link
       and node  maps  is  to  provide	connectivity  information
       between	overland  flow grid cells and channel (link,node)
       pairs. This information is used to pass overland  flow  to
       the  1-D  channel  model  as lateral inflow. The nodes map
       must contain the node numbers corresponding to  the  links
       map.  Thus nodes corresponding to internal boundary condi-
       tion links are not present in the nodes	map.  At  a  cell
       where a link terminates and another link begins (junctions
       for example) the node number must comply  with  the  down-
       stream  link;  i.e.  this cell is assigned a value of 1 in
       the nodes map.  However one must note that the  last  node
       of  the	upstream  link	also lies at such junction cells.
       This last node number must be accounted for  in	the  main
       ascii  channel  data  file  (channel_input),  in which the
       total number of nodes per link must be given. An exception
       to  this  rule  is the most downstream link leading to the
       outlet. The links map essentially  describes  topology  of
       the  stream  network  and its strict conformation with the
       stream numbering conventions is	vital.	Output	from  the
       GRASS  command r.watershed cannot be directly used in con-
       junction with r.hydro.CASC2D. The link numbers assigned by
       r.watershed  must  be  re-numbered  in accordance with the
       following rules. Additionally, the node map  may  be  con-
       structed  by  re-numbering the link map. The general rules
       for link and node numbering are:

	      The first link is numbered 1.

	      Upstream links must have smaller link numbers  than
	      downstream links.

	      Link numbers must change at junctions.

	      Link numbers may not be skipped.

	      Node  numbers increase in the downstream direction.

	      Looped reaches cannot be simulated.

	      Streams may run only  in	x-y  directions  and  not
	      diagonally.

	      Link types cannot be mixed within a link.



       A small example network with three links is given below:


       LINK MAP NODE MAP


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


       0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0


       0 0 0 1 1 0 0 0 0 0 2 0 0 0 0 0 3 2 0 0 0 0 0 1 0 0


       0 0 0 1 0 0 0 0 0 2 2 0 0 0 0 0 4 0 0 0 0 0 3 2 0 0


       0 0 0 1 1 0 0 0 2 2 0 0 0 0 0 0 5 6 0 0 0 5 4 0 0 0


       0 0 0 0 1 0 0 2 2 0 0 0 0 0 0 0 0 7 0 0 7 6 0 0 0 0


       0 0 0 0 1 1 3 2 0 0 0 0 0 0 0 0 0 8 9 1 8 0 0 0 0 0


       0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0


       0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 3 4 0 0 0 0 0


       0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0


       This  network  has three fluvial links, link 1 has 9 nodes
       in the node map, while link 2 has 8 and link 3 has 5. Note
       that the junction of links 1 and 2 is labeled link 3. How-
       ever, links 1 and 2 have hidden nodes  at  this	junction,
       which  must  have the same bed elevation as the first node
       in link 3, but different cross-sections. The  junction  is
       really  not  the  same point in space for all three links,
       but really represents a short distance  from  the  conflu-
       ence.  In  the  channel_input  file,  link 1 really has 10
       nodes and link 2 has 9. Link 3 would only  have	5  nodes,
       because its downstream end is not a junction, rather it is
       the  watershed  outlet.	The  link  and	node  maps   tell
       _r_._h_y_d_r_o_._C_A_S_C_2_D  that the overland flow in the grid cell at
       row 5, column 4 is passed to link 1, node 5. For more dis-
       cussion	 of  links  and  nodes	maps,  see  channel_input
       description and the last  section  of  this  document  for
       channel input and table file options".


       11)  channel_input, table_file: For a detailed description
       of channel data file set-up and requirements: see the last
       section	of  this  document which is a modified version of
       the document presented at  the  CASC2D  Workshop  by  F.L.
       Ogden, June 9-10, 1994, at the University of Memphis, Ten-
       nessee (Revision 2, 10 January 1995).  Also it  is  recom-
       mended  for  the  user  to  refer  to  Ogden (1994) for an
       overview of the implicit channel routing  formulation  and
       numerical  scheme. Note that for explicit channel routing,
       the same channel input file may be used provided that only
       link  types 1 and 4 are present. If explicit channel rout-
       ing is used, the channel talweg elevations are taken  from
       the channel_input file, not from the DEM.


       12)  dis_profile & wat_surf_profile: These two files hold,
       respectively, the discharge profile and the water  surface
       profile	of all nodes within the stream network, including
       internal boundary condition nodes. These files are created
       by running _r_._h_y_d_r_o_._C_A_S_C_2_D with the -i option AND either -d
       or -b. After creation, these files are used to  initialize
       the  implicit  channel routing scheme for actual watershed
       simulations. They must be present for actual  simulations.
       The  -d	flag creates initial discharge and depth files by
       flooding the entire  channel  network  with  a  horizontal
       water  surface, and draining the network using a depth vs.
       time relation at the watershed outlet. This draining  pro-
       ceeds until normal depth is reached at the outlet. At this
       time, the dis_profile and wat_surf_profile files are writ-
       ten  for  use  in channel initialization for later simula-
       tions. The -b flag creates the initialization files  using
       the  standard step backwater method. Note that in dis_pro-
       file the unit of discharge is in cubic meters  per  second
       and  the  unit  of depth in wat_surf_profile is in meters.
       Except for the reservoirs, the water surface profile  file
       actually  holds the flow depth values and thus is measured
       relative to the bed. CAUTION: The implicit channel routing
       routine	must  have  good first approximation of depth and
       discharge at each node in the network.  Inaccurate  values
       (guesses)  will	surely lead to a crash. Additionally, the
       implicit channel routine is for SUBCRITICAL (Froude number
       <  1)  flow  only. A newly created channel input file will
       almost always crash when first run. It is then the task of
       the user to identify the location of the problem. Usually,
       there are regions  of  hydraulically  steep  slopes  which
       cause  supercritical  flow. The channel code will warn the
       user of supercritical flow, including node and link number
       when  it  occurs,  and then exits. The user should look at
       that node/link combination, and alter  the  data  file  to
       eliminate the reach of steep slopes. One workable solution
       to prevent stability problems at low flows is to  use  the
       so-called  "Preissmann  Slot" (see Cunge et al., 1980, for
       example). Be patient, as getting the channel network  run-
       ning  is  a  time  consuming process.  There are a host of
       possible errors including: abrupt  changes  in  cross-sec-
       tion,  DEM-error,  etc.,  which	can  cause  problems. The
       implicit routing method is not applicable to steep  (moun-
       tainous	or  upland)  streams.  If  supercritical  flow is
       encountered in upland (1st order)  streams,  they  can  be
       eliminated  from  the network.  The user should verify the
       suitability of this approach on each watershed.


       13) hyd_location: If a filename is specified,  this  input
       ascii file contains the link and node numbers of the loca-
       tions at which discharge hydrographs are to be written  to
       the  file  named in the dis_hyd_location option. The first
       column in this file should contain link	numbers  and  the
       second  column  must be filled with the corresponding node
       numbers.  For  a  description  of  the  output,	see   the
       dis_hyd_location option.


       14)  r_gage_file:  This	is  an	ascii  file which must be
       provided when raingage rainfall data is	being  simulated.
       At  the top of the file, two-column lines hold the easting
       and the northing for each raingage.  The  number  of  such
       lines is determined by the total number of recording rain-
       gages (num_of_raingages). The location of any of the gages
       does  not  have to be within the current region nor within
       the current watershed mask as long as the easting and  the
       northing are not specified relative to the current region,
       but are based on absolute values in the UTM or SP  coordi-
       nates.  If a gage falls outside in a different zone to the
       left of the active region's zone, then negative values are
       also acceptable.  Note however that raingages well outside
       the watershed under analysis generally provide poor  rain-
       fall  estimates. The subsequent lines at the bottom of the
       raingage file must reflect temporal variation of  rainfall
       intensity.  The number of columns per line is equal to the
       number of raingages (specified via num_of_raingages).  The
       columns	are  separated	by  space. The number of lines in
       this lower portion is equal to number of instances,  sepa-
       rated by a constant time interval, the raingages have made
       a recording. As usually is the case, the unit of  rainfall
       intensity  for  raingage  data must be in inches per hour.
       Example: For  three  raingages,	each  recording  rainfall
       intensity every 2 minutes for a total duration of, say, 10
       minutes, a file called "rain.inp" may look like this:


       205150.0 750212.0


       20545.0 750104.0


       205320.0 750173.0


       0.0 0.0 0.55


       1.75 2.25 0.80


       1.00 1.80 1.50


       0.65 0.90 0.70


       0.0 0.50 0.30


       In above example, the eastings and northing of the  first,
       second,	 and  third  raingages	are  (205150.0,750212.0),
       (20545.0,750104.0), and (205320.0,750173.0)  respectively.
       The  intensities  recorded by the first gage, for example,
       are 0.0, 1.75,  1.00,  0.65,  and  0.0  inches  per  hour,
       respectively,  over  0-2, 2-4, 4-6, 6-8, and 8-10 minutes,
       etc. For this example  r_gage_file=rain.inp,  num_of_rain-
       gages=3,  gage_time_step=120,  and  rain_duration=600. For
       state plane (SP) coordinate system the eastings	and  nor-
       thing will have to be in feet rather than meters.


       15)  outlet_eastNnorthNslope: These three values determine
       the location of the outlet, in terms of	its  easting  and
       northing, and the outlet bed slope. One needs to make sure
       that the outlet described by its easting and  northing  is
       not  only  within the active region but also inside water-
       shed mask. Often times the region is not set to its origi-
       nal  settings  after  zoom-in operations (d.zoom) are per-
       formed and this may put	the  outlet  outside  the  active
       region thus causing the model to eventually crash. The bed
       slope is equal to tangent  of  the  angle  which  is  made
       between	the  bed  profile  at  the  outlet and horizontal
       plane. This slope is primarily used to calculate the  out-
       flow  overland  discharge  at the outlet, if any, based on
       normal depth boundary condition, when no  channel  routing
       is  performed  (all  surface flow treated as overland flow
       and channels essentially assumed wide).	Normal	depth  is
       also  assumed to prevail at the outlet when explicit chan-
       nel routing (-e) has been selected.


       16) Manning_n: The  alternative	to  simulating	spatially
       varied  roughness coefficient is to provide a single value
       of Manning roughness coefficient n via  Manning_n  parame-
       ter.  The  user	is  warned if both roughness_map and Man-
       ning_n have been specified.


       17) unif_rain_int: This option represents the intensity of
       the  spatially-	uniform  temporally-constant  (up  to the
       rainfall duration) rainfall.  Therefore	this  option  may
       replace	r_gage_file  and radar_intensity_map options. The
       unit is in millimeters per hour.


       18) num_of_raingages: The total number of recording  rain-
       gage.  If this variable is set to one, no spatial interpo-
       lation is performed and the rainfall is treated as uniform
       is  space  but  could vary in time. The temporal variation
       will be then provided  by  r_gage_file.	 Note  that  when
       num_of_raingages  is  set to one, the easting and northing
       of the gage is irrelevant although two (arbitrary)  values
       must  still  be	provided  at  the  top	of  raingage file
       (r_gage_file).


       19) time_step: This represents the  duration  of  computa-
       tional  time  step  in  seconds and is a critical variable
       determining the total execution time for a particular sim-
       ulation.  These	is no firm guide for the selection of the
       time step; it comes with experience and	strongly  depends
       on  watershed  and  rainfall  characteristics. The general
       rule for overland routing and explicit channel routing  is
       that  shorter time steps must be used for higher intensity
       storms, finer horizontal grid resolution  (grid	spacing),
       steeper	watershed  slopes,  larger  watershed  areas, and
       smoother surfaces. Stability of explicit  routing  depends
       upon Courant number. Unfortunately, the critical condition
       for Courant number limits the length of the  computational
       time  step  which  must	be used for the entire simulation
       unless variable time step algorithm is implemented in  the
       future.	Shorter  time  steps  must be used when backwater
       effects are generated, mainly in flat areas which are  not
       part of the lake map. If the time step is too long for any
       particular simulation the  surface  water  depth  in  com-
       pletely	flat areas may show a checker-board pattern, i.e.
       oscillations are observed in the water surface level. This
       eventually  results  in	a  crash.  As such, the time step
       should be decreased and the simulation  repeated;  or  the
       flat areas be delineated within the lake map.


       20)  gage_time_step:  This  variable  represents  the time
       interval, in seconds, between recording instances of rain-
       fall  intensities  by  raingage(s). It is implied that the
       rainfall data has been recorded in regular intervals.  See
       the notes under r_gage_file for an example.


       21)  radar_time_step: A value expressing the time interval
       between consecutive rainfall maps. A uniform time step  is
       implied.


       22)  rain_duration: This is the total duration of rainfall
       in seconds.  If multistorm events are simulated, the  time
       from  the  beginning  of the first storm to the end of the
       last storm constitutes the  total  rainfall  duration.  As
       such, selection of soil moisture redistribution capability
       is recommended via specifying pore index (pore_index)  and
       residual saturation (residual_sat) maps.


       23) tot_time: The total simulation time in seconds. If the
       falling limb of the discharge hydrograph is of  particular
       interest  the total simulation time must be set to a value
       greater than total rainfall  duration  plus  the  expected
       recession time.


       24)  write_time_step:  This  time parameter determines the
       frequency of writing output raster maps and  is	equal  to
       the time interval, in seconds, at which output raster maps
       are   saved.   Also    see    depth_map,    inf_depth_map,
       surf_moist_map, rate_of_infil_map, and dis_rain_map output
       options.


       25) unit_el_conv: This conversion factor is used  to  con-
       vert  elevation	values	in DEM (elevation) map to meters.
       This parameter doesn't need to be specified if the DEM  is
       already	in meters since the default is one. For DEM units
       in cm or ft, unit_el_conv must be respectively set to  100
       or 3.281.


       26)  unit_lake:	This conversion factor is used to convert
       the water surface elevation values in the lake_elev map to
       meters. The default is 1.0.


       27)  unit_space: This conversion factor is used to convert
       the horizontal grid  spacing  resolution  to  meters.  The
       default	is 1.0.  For state plane coordinate system in ft,
       set unit_space equal to 3.281.


       28) d_thresh: This parameter represents	an  average  step
       retention  storage below which the overland depth will not
       be routed. Another words, all  depressions  less  than  or
       equal  to  d_thresh  are  filled  before any overland flow
       could begin. The unit must be in meters so  for	2  mm  of
       depression  storage  set  d_thresh=0.002. Higher values of
       depression storage would reduce the total  execution  time
       of  the model as the overland routing consumes most of the
       CPU effort.


       29) discharge: The discharge hydrograph	computed  at  the
       outlet  will be saved in this ascii file under the current
       directory.  Some other  information,  such  as  peak  dis-
       charge, is also printed in this file.


       30)  dis_hyd_location: Whenever the hyd_location option is
       selected, the discharge at individual node/link pairs will
       be  saved  in  this file. The discharge hydrographs at the
       (link,node) locations specified in hyd_location	file  are
       grouped	in  columns.  The number of lines in this file is
       determined by the total	number	of  iterations	equal  to
       tot_time divided by time_step.


       31)	depth_map,     inf_depth_map,	  surf_moist_map,
       rate_of_infil_map, & dis_rain_map: depth_map is the common
       filename  prefix given to the time series of output raster
       maps containing surface depth values  in  millimeters.  At
       the  channel cells the channel flow depth will be recorded
       in the maps. The surface depth maps, and all other  output
       maps,   are  saved  at  regular	intervals  determined  by
       write_time_step option. If write_time_step is not set,  no
       output raster map will be saved. The first map always cor-
       responds to the initial condition and naturally shows  the
       water  surface profile corresponding to the base flow dis-
       charge within the channel network  when	implicit  channel
       routing	is performed. Similarly the last depth map corre-
       sponds to the end-of-simulation time, or to  the  time  at
       which  the program finished abnormally, for example due to
       selection of a  long  step  which  generated  oscillations
       leading to a crash. Abnormal program termination caused by
       oscillating depths may show negative depths in  the  over-
       land  plane.  There  is	a hard-coded limit of 2000 output
       raster  maps  for  each	simulation.   inf_depth_map   and
       rate_of_infil_map  are  two  options  to  save  the output
       raster maps of cumulative infiltration depth, in tenth  of
       mm, and rate of infiltration in mm/hr, respectively. These
       two options can only  be  selected  when  infiltration  is
       being  computed via either the Green & Ampt or redistribu-
       tion methods.  surf_moist_map  output  contains	the  soil
       moisture  values  at the soil surface and it may solely be
       selected with continuous infiltration  option  (pore_index
       and  residual_sat maps are specified). dis_rain_map option
       saves the instantaneous rainfall intensities, in mm/hr, at
       write_time_step	intervals  and may be set for the simula-
       tions involving	spatially  distributed	rainstorms;  i.e.
       raingage rainfall data or radar (or other sources of rain-
       fall  raster   maps)   data.    Example:   If   one   sets
       depth_map=depth.out,  tot_time=1000,  and write_time_step=
       100, then a total of 11 raster depth maps will be saved in
       a     normally-terminated     simulation:    depth.out.00,
       depth.out.01, depth.out.02 through  depth.out.10,  respec-
       tively  corresponding  to  times  equal	to  0,	100, 200,
       through 1000 seconds. These maps  may  be  viewed  sequen-
       tially  in animation form using the GRASS animator program
       xganim.



GGEENNEERRAALL NNOOTTEESS FFOORR CCHHAANNNNEELL__IINNPPUUTT AANNDD TTAABBLLEE__FFIILLEE FFIILLEE OOPPTTIIOONNSS
       The naming convention associated with the Preissmann  dou-
       ble-sweep  1-D implicit channel routing method is based on
       the concept to links  and  nodes.  A  link  is  a  channel
       segment,  or an internal boundary condition, which is com-
       prised of two or more computational nodes.   All  internal
       boundary  conditions  contain  two  nodes,  while  fluvial
       reaches may be of any size greater than or  equal  to  two
       nodes.  The following discussion of input file format must
       first distinguish between different link types. A  few  of
       the possible link types are presented below in Table 1. As
       of August 1995, only link types 1, 2, 4, and  8	are  sup-
       ported. Development is continuing on link types 3 and 7.


       Table 1. Link Types



       Link	Description		  Number of	   Number
       of
       Type    of Link Type		Parameters	 Nodes

       1 Fluvial Link,
	 Trapezoidal Cross-Section	    5		  >=2
       2 Overflow Weir			    8		    2
       3 Culvert/Weir (not yet supported)   8		    2
       4 Reservoir			    5		    2
       7 Bridge Crossing (not yet supported) 8		    2
       8 Fluvial Link, Look-up Table (Breakpoint) 4	   >=2
	 Cross-Section

       At present the channel model  formulation  accepts  cross-
       sectional input for only two different channel geometries,
       namely trapezoidal,  and  breakpoint  via  look-up  table.
       Trapezoidal  channel  parameters which must be provided as
       input at each computation node include: Manning's n,  bot-
       tom  width,  channel depth, side slope, and bed elevation.
       Look-up tables of cross sectional properties must  include
       cross-sectional	area,  top width, and conveyance at equal
       depth intervals. Smooth transition in channel  cross  sec-
       tional  properties  within links of type 8 and between all
       connecting fluvial links often plays a vital role  in  the
       success	of  simulations. Abrupt changes in cross-sections
       can lead to numerical errors in mass conservation.


       As far as handling the reservoirs (link type 4),  flow  is
       not  routed  through  reservoirs  in  this  version of the
       CASC2D channel routing code. Instead the linear	reservoir
       approximation  is used. Among other internal boundary con-
       ditions link types, only weirs can be  simulated  at  pre-
       sent.


       The  channel_input file contains the channel bed elevation
       at each node, which constructs the longitudinal profile of
       channels  in  the  drainage  network. Ideally, the modeler
       should use surveyed cross sections and talweg profiles  of
       the  channel network. However, extensive surveys are often
       impossible for  the  entire  drainage  networks	on  large
       watersheds.  In	lieu  of  an  extensive survey, there are
       existing tools for extracting channel topology from  digi-
       tal  elevation  models (DEM). However, if the channel net-
       work is extracted from a DEM, a smoothing  algorithm  must
       be applied (e.g. Ogden et al., 1994) to produce physically
       realistic longitudinal profiles because of errors inherent
       in any DEM.


       EEXXAAMMPPLLEE OOFF IINNPPUUTT FFIILLEE FFOORRMMAATT AANNDD CCOONNSSTTRRUUCCTTIIOONN


       NOTE: The channel_input file and table_file both follow SI
       unit convention.  All  units  of  length  are  in  meters,
       including elevations.


       In  this example, a channel input data file is constructed
       for a fictitious  watershed.  Note  that  this  particular
       example is merely for demonstration and has not been tried
       in any simulation run.  The stream network will consist of
       trapezoidal  and  look-up table fluvial links, an internal
       reservoir, and an overflow weir. Regarding  the	MASK  map
       (watershed_mask	option),  note	that  all watershed cells
       must be marked with 1, while all raster cells outside  the
       watershed  boundary  are marked with 0. Also all the cells
       in the lake should carry the  value  1  on  the	LAKE  map
       (lake_map  option).   If  there	was  another lake in this
       example, it would be denoted with the number 2, etc.


       The channel link numbering scheme  typically  employed  in
       double-sweep  routing was explained in the main text. With
       reference to the LINK map shown below, (links_map option),
       assume that links 1 and 2 drain into link 3, which in-turn
       drains in to the lake, which is assigned  link  number  4.
       Also links 7 and 8 drain into link 9. Link 5 originates at
       the outlet of the reservoir. Link 5 is split into  link	6
       because	of a change in some cross-section property. Links
       6 and 9 flow into link 10, which is  immediately  upstream
       from  a	weir  which  must be considered link 11. Finally,
       link 12, the most downstream link,  lies  below	the  weir
       (link  11).   Note  that  the LINK map contains continuous
       sequence of link numbers, except for the internal boundary
       conditions  such  as the weir (link 11) and lakes (link 4)
       which does not appear in the LINK map.


       EEXXAAMMPPLLEE LLIINNKK MMAAPP


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


       0 0 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0


       0 0 0 1 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0


       0 0 0 1 1 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0


       0 0 0 0 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0


       0 0 0 0 0 0 1 1 1 0 0 0 2 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 1 0 2 2 2 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 1 1 3 0 0 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


       0 0 7 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


       0 0 0 0 7 7 0 0 0 0 5 0 0 0 0 0 0 0 0 0


       0 0 0 0 0 7 7 0 0 0 5 5 0 0 0 0 0 0 0 0


       0 8 8 8 0 0 7 0 0 0 0 5 6 0 0 0 0 0 0 0


       0 0 0 8 8 8 9 9 0 0 0 0 6 6 0 0 0 0 0 0


       0 0 0 0 0 0 0 9 9 9 0 0 0 6 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 0 9 9 9 9 10 10 10 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 12 12 12 0


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0


       Now, refer to the NODE map (nodes_map option) shown below.
       In  the NODE map, each link is numbered from 1 to the num-
       ber of grid cells spanned by that link, with the exception
       of  the internal boundary conditions. Conceptually, inter-
       nal boundary conditions (including  reservoirs)	have  two
       nodes  but they are not given any node numbers in the NODE
       map. This is how the program recognizes internal  boundary
       conditions.  Furthermore, all links except the one leading
       to the watershed outlet must have an extra node to provide
       connectivity  to  the  downstream  link.  Therefore,  even
       though the NODE map may show link 1 to have 13  nodes,  it
       actually  has  14.  This  implied  extra  node for link 1,
       shared between the most downstream node of link 1 and  the
       most  upstream  node  of  link  3, provides the connection
       between link 1 and link 3. The number  of  nodes  in  each
       link in this example are shown below in Table 2. Note that
       the node map entries for the lake (link 4) are 0.


       EEXXAAMMPPLLEE NNOODDEE MMAAPP


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


       0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0


       0 0 0 2 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0


       0 0 0 3 4 0 0 0 0 0 0 0 5 4 0 0 0 0 0 0


       0 0 0 0 5 6 7 0 0 0 0 0 6 0 0 0 0 0 0 0


       0 0 0 0 0 0 8 9 10 0 0 0 7 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 11 0 10 9 8 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 12 13 1 0 0 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


       0 0 1 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


       0 0 0 0 4 5 0 0 0 0 1 0 0 0 0 0 0 0 0 0


       0 0 0 0 0 6 7 0 0 0 2 3 0 0 0 0 0 0 0 0


       0 1 2 3 0 0 8 0 0 0 0 4 1 0 0 0 0 0 0 0


       0 0 0 4 5 6 1 2 0 0 0 0 2 3 0 0 0 0 0 0


       0 0 0 0 0 0 0 3 4 5 0 0 0 4 0 0 0 0 0 0


       0 0 0 0 0 0 0 0 0 6 7 8 9 1 2 3 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 4 5 0


       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0


       Table 2. Number of Nodes in each Link for  Example  Water-
       shed Stream Network


       Link Number Number of Nodes Number of Nodes


       as in nodes_map in channel-input file


       1 13 14


       2 10 11


       3 3 4


       4 0 2


       (reservoir)


       5 4 5


       6 4 5


       7 8 9


       8 6 7


       9 9 10


       10 3 4


       11 0 2


       (weir)


       12 6 6


       (outlet link)


       The  first  portion  of	the channel input file is used to
       pass physical constants and simulation parameters  to  the
       model.  These  include the gravitational acceleration "g",
       kinetic energy correction  factor  "alpha",  the  friction
       slope  weighting  factor  "beta",  the  spatial derivative
       weighting coefficient "theta", the  length  of  each  node
       &quot;dx&quot;,	the  computational  time  step "dt" (sec-
       onds), the total simulation time "tt" (seconds),  and  the
       discharge  in  all  first  order streams "qmin" (m3/s). At
       present, the time step "dt" must be identical to the  com-
       putational  time  step  used  in the overland flow routing
       portion of r.hydro.CASC2D. The program must  be	told  the
       number  of  links,  and the largest number of nodes in any
       link in the network for dynamic memory allocation.  In our
       example	problem, the number of links is 12, and the maxi-
       mum number of nodes is 14 (in link 1). Remember	that  all
       links  which  are  not  at  the	outlet or not immediately
       upstream of a reservoir must have an extra node	for  con-
       nectivity  purposes.  The  total number of links is called
       "nlinks", and the largest number of nodes in any  link  in
       the  network  is  called  "maxnodes".  In this example, we
       will use the constants and parameters given in Table 3:


       Table 3. physical constants and simulation parameters


       "g" 9.81 m/s2


       "alpha" 1.0


       "beta" 0.5


       "theta" 0.55


       "dx" 100.0 m


       "dt" 30.0 s


       "tt" 3600.0 s


       "qmin" 0.07 cms


       "nlinks" 12


       "maxnodes" 14


       This data constitutes the first portion	of  channel_input
       file  and  is  arranged	into a header which must have the
       form (note floating point and integers):


       9.81


       1.0 0.5 0.55


       100.0


       30.0 3600.0


       0.07


       12


       14


       The second portion of the input file describes link  types
       as  well as the network topology and connectivity. This is
       accomplished using a line-input format, one line for  each
       link in the network.  Each line contains 6 values arranged
       in columns, as shown in Table 4.


       Table 4. Connectivity information format


       Column Data Description


       1 Link number (INT)


       2 Link type (INT)


       3 Number of links upstream from this link (max. 2, min. 0)
       (INT)


       4 Upstream link #1 (INT) (0 if no upstream links)


       5  Upstream  link  #2  (INT) (0 if no or only one upstream
       link)


       6 Downstream link (0 for outlet ) (INT)


       As far as link types in the current example,  assume  that
       links  1 through 9, except reservoir link 4 (link type 4),
       are well-described as trapezoidal (type	1),  and  we  are
       using look-up table data to describe the cross-sections of
       links 10 and 12 (type 8). The weir (link 11)  is  of  link
       type 2. Thus the second portion of input file for describ-
       ing link types and connectivity looks like:


       1 1 0 0 0 3


       2 1 0 0 0 3


       3 1 2 1 2 4


       4 4 1 3 0 5


       5 1 1 4 0 6


       6 1 1 5 0 10


       7 1 0 0 0 9


       8 1 0 0 0 9


       9 1 2 7 8 10


       10 8 2 6 9 11


       11 2 1 10 0 12


       12 8 1 11 0 0


       Note that only the outlet  link	has  0	as  a  downstream
       dependency.   It  is  important that this be the only link
       with 0 as a downstream dependency. Also, the location  and
       topology  of  internal boundary condition links (4 and 11)
       with respect to other links are known via above connectiv-
       ity  information  in the channel_input file.  As an inter-
       pretation, examine link number 10 above.  It  is  of  link
       type  8 (look-up table cross-section data), has 2 upstream
       dependencies (links 6 and 9), and flows into link 11.


       The third portion of the input file contains the  individ-
       ual  hydraulic  property  information for each node in the
       network. Assume for now that all the trapezoidal  channels
       in the network have the properties shown in Table 5.


       Table 5. Cross-Sectional Properties of Example Trapezoidal
       Channels


       Manning roughness coefficient varies


       Bottom width (m) varies


       Channel depth (m) 1.75


       Side slope H:V varies


       Talweg elevation dependent upon location


       Now, build the input file section for link #1 which has 13
       nodes  on  the NODE map, plus an extra for connectivity at
       the upstream end of link 3 (total of 14 nodes). This input
       file section will look like:


       1 14


       0.035 2.10 1.75 2.00 264.40


       0.035 2.10 1.75 2.00 263.85


       0.035 2.10 1.75 2.00 263.41


       0.035 2.10 1.75 2.00 262.98


       0.035 2.10 1.75 2.00 262.75


       0.035 2.10 1.75 2.00 262.54


       0.035 2.10 1.75 2.00 262.37


       0.035 2.10 1.75 2.05 262.02


       0.035 2.20 1.75 2.05 261.87


       0.035 2.20 1.75 2.10 261.75


       0.035 2.20 1.75 2.10 261.67


       0.035 2.20 1.75 2.15 261.52


       0.035 2.30 1.75 2.15 261.25


       0.035 2.40 1.75 2.15 261.00


       The 1 and 14 on the first line indicate that it is link 1,
       with 14 nodes. The columns represent Manning's  n,  bottom
       width, channel depth, trapezoidal side slope H/V, and tal-
       weg elevation, respectively.


       Link 2 might have an entry which looks like:


       2 11


       0.035 1.80 1.75 1.80 264.21


       0.035 1.80 1.75 1.80 264.10


       0.035 1.90 1.75 1.90 263.81


       0.035 1.90 1.75 1.90 263.56


       0.035 2.00 1.75 1.90 263.34


       0.035 2.10 1.75 1.90 262.86


       0.035 2.10 1.75 2.00 262.24


       0.035 2.10 1.75 2.00 261.76


       0.035 2.20 1.75 2.10 261.48


       0.035 2.30 1.75 2.10 261.26


       0.035 2.30 1.75 2.10 261.00


       The cross-section entry for link 3 would then look like:


       3 4


       0.035 2.60 1.75 2.20 261.00


       0.035 2.60 1.75 2.40 260.20


       0.035 2.80 1.75 2.90 259.67


       0.035 2.80 1.75 2.90 259.17


       The elevation of the downstream end of links 1 and 2  must
       be  equal to the bed elevation of the upstream end of link
       3. It is required that the bed elevation  of  all  channel
       inverts	at  each  junction be equal. Even though they are
       not exactly the same points in  space,  they  are  assumed
       close enough to have the same elevation.


       Flow Flow




					/
				  /  /	   /
		      v 	  /  v	   /
				 /	  /
		      link 1	/link 2  /
		       node 14 / node 11/
				  /
			    /
		   |	      |
		   |   link 3	 |
		   |   node 1	 |





       The  input  for other links with trapezoidal cross section
       is similar to the input for link 1 (see the  next  section
       for the complete input file).


       Additionally,  assume  that  the  reservoir (link 4) has a
       surface area of 0.498 square km,  a  rectangular  spillway
       width of 12m, a spillway discharge coefficient of 0.97, an
       initial water surface elevation of 260.10m, and a spillway
       crest  elevation  of  260.50m.	The  resulting input file
       entry is shown below.


       4 2


       0.498 12.0 0.97 260.10 260.50


       0.000 0.0 0.00 0.00 0.00


       The number of nodes (line entries)  in  the  channel_input
       file per reservoir link is two, but the numbers entered in
       the second row entry are for further improvements and  for
       now their value is irrelevant. Also note that the bed ele-
       vation at the downstream limit of link  3  MUST	be  lower
       than  the initial water surface elevation in the reservoir
       (link 4). This is mandatory at all  downstream  boundaries
       between	channels  flowing into the reservoirs. Reservoirs
       serve as downstream boundary conditions at upstream links.
       The  elevation  of  reservoirs  should  therefore never be
       allowed to fall below critical depth in any channels which
       flow  into  the reservoir.  If this happens, the code will
       crash.


       The input for links 5, 6, 7, 8, and 9 will be  similar  to
       links  1,  2, and 3. See the constructed input file at the
       end of this text. Trapezoidal channel links are simple  in
       terms  of  input.   The channel depth field is intended to
       represent the average bank-full depth of the channel. This
       number is not used in the present version of the code, but
       will be in the future when the overland	flood  plane  and
       channel	flows  are  coupled  iteratively.  At present the
       flows are not fully coupled. Water can flow only from  the
       overland  flow plane into the channels, not from the chan-
       nels back to the flood plane.


       If look-up table data are used (link type 8), the  look-up
       tables  are  stored  in a separate file. The GRASS command
       line option for this look-up table file is table_file.  If
       there  are any link type 8 in the channel_input data file,
       the program will attempt to open the file table_file (typ-
       ically  called "table.dat").  If this file is not present,
       the program will terminate.  In	channel_input  file,  all
       that  is needed is the table number for a particular cross
       section, and the talweg elevation. Assume that the 4 nodes
       in link 10 are approximated by one cross-section, which is
       given as table entry 1, then the channel_input file  entry
       for link 10 would look like:


       10 4


       1 244.0 1 243.5 1 243.0 1 242.5


       In  this  format,  the first column represents the look-up
       table number for the given node,  and  the  second  column
       represents  the bed elevation for that node. Table numbers
       can be mixed within a link.  However,  abrupt  changes  in
       cross-section should be avoided because they cause signif-
       icant continuity errors in the formulation.  The format of
       the table_file is discussed later in this document.


       Link  11  is an overflow weir link. While this link has no
       nodes which appear in the node map for overland flow  con-
       nectivity,  it  does  have  two	nodes in terms of channel
       topology. The meaning of the  columns  in  the  weir  node
       input section is presented in Table 6.


       Table 6. Parameter Description for Weirs


       Line Entry Column Parameter Description


       1 1 forward direction weir discharge coefficient


       1 2 reverse direction weir discharge coefficient


       1 3 0.0 (reserved for future use)


       1 4 crest length, meters


       1 5 elevation of weir crest, meters


       2 1-4 0.0 (reserved for future use)


       2 5 downstream bed elevation, meters


       The  first  (upstream)  node  represents  the crest of the
       rectangular weir. The second (downstream) node  represents
       the  bed  of  the  channel  just downstream from the weir.
       Assume that this weir has a crest elevation of 244.4 m,	a
       crest width of 8 m, a discharge coefficient in the forward
       direction of 0.92, a discharge coefficient for flow in the
       reverse	direction equal to 0.85, and the channel bed ele-
       vation immediately downstream from the weir is 239.8m. The
       entry  for  this weir in the channel_input file would thus
       appear as:


       11 2


       0.92 0.85 0.00 8.00 244.4


       0.00 0.00 0.00 0.00 239.8


       Link 12 uses table entry 2 for the its  first  four  nodes
       and entry 4 for the remaining two nodes. Note that link 12
       has 6 nodes in the node map, and  6  nodes  in  the  chan-
       nel_input  file. Because link 12 is the outlet link, we do
       not add an extra node at the downstream end for connectiv-
       ity  purposes.  The  portion of the channel_input file for
       link 12 looks like:


       12 6


       2 239.80


       2 239.47


       2 239.33


       2 239.05


       3 238.54


       3 238.44


       Hence, 238.44 is the talweg elevation at the outlet of the
       catchment.   Also  notice that the upstream end of link 12
       and the downstream node of link 11 have the same bed  ele-
       vation.


       Weirs  cannot be used as the outlet boundary condition for
       this channel model. If your watershed has a  weir  at  the
       outlet,	just  place a short link downstream from the weir
       with appropriate characteristics.


       FFIINNAALL CCHHAANNNNEELL FFIILLEE FFOORRMMAATT


       The example channel data file (typically  called  chn.dat)
       developed for this example looks like:


       ----------------------BEGIN	 channel_input	     FILE
       HERE----------------------------


       9.81


       1.0 0.5 0.55


       100.0


       30.0 3600.0


       0.07


       12


       14


       1 1 0 0 0 3


       2 1 0 0 0 3


       3 1 2 1 2 4


       4 4 1 3 0 5


       5 1 1 4 0 6


       6 1 1 5 0 10


       7 1 0 0 0 9


       8 1 0 0 0 9


       9 1 2 7 8 10


       10 8 2 6 9 11


       11 2 1 10 0 12


       12 8 1 11 0 0


       1 14


       0.035 2.10 1.75 2.00 264.40


       0.035 2.10 1.75 2.00 263.85


       0.035 2.10 1.75 2.00 263.41


       0.035 2.10 1.75 2.00 262.98


       0.035 2.10 1.75 2.00 262.75


       0.035 2.10 1.75 2.00 262.54


       0.035 2.10 1.75 2.00 262.37


       0.035 2.10 1.75 2.05 262.02


       0.035 2.20 1.75 2.05 261.87


       0.035 2.20 1.75 2.10 261.75


       0.035 2.20 1.75 2.10 261.67


       0.035 2.20 1.75 2.15 261.52


       0.035 2.30 1.75 2.15 261.25


       0.035 2.40 1.75 2.15 261.00


       2 11


       0.035 1.80 1.75 1.80 264.21


       0.035 1.80 1.75 1.80 264.10


       0.035 1.90 1.75 1.90 263.81


       0.035 1.90 1.75 1.90 263.56


       0.035 2.00 1.75 1.90 263.34


       0.035 2.10 1.75 1.90 262.86


       0.035 2.10 1.75 2.00 262.24


       0.035 2.10 1.75 2.00 261.76


       0.035 2.20 1.75 2.10 261.48


       0.035 2.30 1.75 2.10 261.26


       0.035 2.30 1.75 2.10 261.00


       3 4


       0.035 2.60 1.75 2.20 261.00


       0.035 2.60 1.75 2.40 260.20


       0.035 2.80 1.75 2.90 259.67


       0.035 2.80 1.75 2.90 259.17


       4 2


       0.498 12.0 0.97 260.10 260.50


       0.000 0.0 0.00 0.00 0.00


       5 5


       0.035 2.50 1.75 2.10 249.20


       0.035 2.50 1.75 2.10 248.65


       0.035 2.50 1.75 2.15 247.94


       0.035 2.50 1.75 2.20 247.31


       0.035 2.50 1.75 2.20 246.97


       0.035 2.50 1.75 2.25 246.42


       6 5


       0.035 2.50 1.75 2.00 246.42


       0.035 2.50 1.75 2.00 245.97


       0.035 2.50 1.75 2.00 245.24


       0.035 2.50 1.75 2.00 244.73


       0.035 2.50 1.75 2.00 244.00


       7 9


       0.035 1.75 1.75 2.00 254.20


       0.035 1.75 1.75 2.00 253.55


       0.035 1.75 1.75 2.00 252.92


       0.035 1.90 1.75 2.00 252.29


       0.035 1.90 1.75 2.00 251.71


       0.035 1.90 1.75 2.00 251.24


       0.035 2.00 1.75 2.00 250.82


       0.035 2.00 1.75 2.00 250.34


       0.035 2.00 1.75 2.00 250.08


       8 7


       0.035 1.60 1.75 2.00 253.71


       0.035 1.90 1.75 2.00 253.21


       0.035 1.90 1.75 2.00 252.94


       0.035 2.00 1.75 2.00 252.55


       0.035 2.10 1.75 2.00 251.80


       0.035 2.10 1.75 2.00 251.11


       0.035 2.10 1.75 2.00 250.08


       9 10


       0.035 3.10 1.75 2.90 250.08


       0.035 3.20 1.75 2.90 249.16


       0.035 3.30 1.75 3.00 248.63


       0.035 3.40 1.75 3.00 248.02


       0.035 3.40 1.75 3.10 247.33


       0.035 3.20 1.75 3.10 246.65


       0.035 3.10 1.75 3.10 246.05


       0.035 3.20 1.75 3.10 245.88


       0.035 3.20 1.75 3.10 245.52


       0.035 3.50 1.75 3.10 245.24


       0.035 3.70 1.75 3.40 244.74


       0.035 3.50 1.75 3.40 244.51


       0.035 3.10 1.75 3.40 244.00


       10 4


       1 244.00


       1 243.50


       1 243.00


       1 242.50


       11 2


       0.92 0.85 0.00 8.00 244.40


       0.00 0.00 0.00 0.00 239.80


       12 6


       2 239.80


       2 239.47


       2 239.33


       2 239.05


       3 238.54


       3 238.44


       ---------------------   END    OF    channel_input    FILE
       ---------------------------


       TTAABBLLEE__FFIILLEE IINNPPUUTT FFOORRMMAATT


       If  link  type 8 (look-up table x-sections) are present in
       the channel_input file, we require a file typically called
       "table.dat",  to store all look-up table values. This file
       must begin with an integer equal to the number  of  tables
       contained  within the file.  In our example this number is
       3. Then we require 3 tables. The first line of each  table
       is  an integer equal to the table number.  The second line
       in the table entry contains two numbers, an integer, and a
       floating  point (real) value. The first number is equal to
       the number of entries (rows)  in  each  particular  table,
       designated  by "numhts". The second number is the vertical
       distance between hydraulic property points, which must  be
       a  constant  for each table. For instance, if you describe
       the variation of cross-sectional area, topwidth, and  con-
       veyance	at  0.5 m vertical intervals, this number will be
       0.5.


       Each table entry must then contain  "numhts"  lines,  each
       with four entries. The first line must be:


       0.0 0.0 0.0 0.0


       subsequent lines must contain the following:


       height topwidth x-section_area x-section_conveyance.


       For instance, assume we know geometric variables for table
       entries 1, 2, and  3.  The  file  "table.dat"  (table_file
       option) may look like:


       3


       1 5 1.0


       0.0 0.0 0.0 0.0


       1.0 2.1 5.9 13.5


       2.0 6.9 22.3 122.2


       3.0 14.7 72.1 312.8


       4.0 19.6 145.6 789.4


       2 8 0.5


       0.0 0.0 0.0 0.0


       0.5 1.1 1.5 7.5


       1.0 1.7 3.4 17.1


       1.5 3.1 11.2 43.9


       2.0 5.2 32.4 98.5


       2.5 7.2 49.2 187.4


       3.0 9.2 86.4 312.5


       3.5 12.1 143.1 624.9


       3 5 1.0


       0.0 0.0 0.0 0.0


       1.0 2.2 5.4 15.5


       2.0 6.6 15.3 132.2


       3.0 15.7 81.8 352.8


       4.0 21.4 155.2 839.6


       For  further clarification, consider table 2 above, corre-
       sponding to cross sectional properties of  the  four  most
       upstream  nodes	of  link  12. Table 2 has 8 entries, each
       separated by 0.5 meter of depth. At a depth of 3.0 m,  for
       example, the channel has a top-width of 9.2m, a cross-sec-
       tional area of 86.4 m2, and a conveyance  of  312.5  m3/s.
       The conveyance K is used to calculate the discharge using:


       _Q_=_K_*_s_q_r_t_(_S_l_o_p_e_)


       Where using Manning's equation, K is defined (in SI units)
       as:


       _K _= _1_/_n _* _(_A_r_e_a_) _* _(_H_y_d_r_a_u_l_i_c___r_a_d_i_u_s_)_^_(_2_/_3_)


       These  tables  can  be produced easily using a spreadsheet
       using measured channel cross-section data.



RREEFFEERREENNCCEESS
       Bras, R. L., 1990, Hydrology: An  introduction  to  hydro-
       logic science, Addison-Wesley, Reading, Mass., 643 p.


       Crum,  T. D., and R. L. Alberty, 1993, The WSR-88D and the
       WSR-88D operational  support  facility,	Bulletin  of  the
       American Meteorological Soc., 74(9), pp. 1669-1687.


       Cunge,  J.A.,  F.M.  Holly, and A. Verwey, 1980, Practical
       Aspects of Computational River Hydraulics, Iowa	Institute
       of  Hydraulic Research, 404HL The University of Iowa, Iowa
       City, IA 52242. 420 p.


       Gray, D.M., 1970, Handbook on the Principles of Hydrology,
       National  Research  Council  of	Canada, Water Information
       Center Inc., Water Research Building, Manhasset Isle, Port
       Washington, N.Y., 11050.


       Julien, P. Y., and B. Saghafian, 1991, CASC2D users manual
       - A two dimensional watershed rainfall-runoff model, Civil
       Engr.  Report,  CER90-91PYJ-BS-12,  Colorado State Univer-
       sity, Fort Collins, CO.


       Julien, P. Y., Saghafian,  B.,  and  F.	L.  Ogden,  1995,
       "Raster-Based Hydrologic Modeling of Spatially-Varied Sur-
       face Runoff", Water Resources Bulletin, AWRA,  31(3),  pp.
       523-536.


       Ogden,  F.L.,  1994,  de-St Venant channel routing in dis-
       tributed hydrologic modeling., Proc. Hydraulic Engineering
       `94,  ASCE  Hydraulics Specialty Conference, G.V. Cotroneo
       and R.R. Rumer, eds., Vol.  1, pp. 492-496.


       Ogden, F.L., Saghafian, B., and W.F. Krajewski, 1994, GIS-
       based  channel extraction and smoothing algorithm for dis-
       tributed hydrologic modeling, Proc. Hydraulic  Engineering
       `94,  ASCE  Hydraulics Specialty Conference, G.V. Cotroneo
       and R.R. Rumer eds., August 1-5, 1994, Buffalo, N.Y.,  pp.
       237-241.


       Rawls,  W.  J.,	Brakensiek,  D.  L., and N. Miller, 1983,
       Green-Ampt infiltration parameters from soils data, J.  of
       Hydraulic Engineering, ASCE, 109(1), pp. 62-70.


       Rawls,  W.  J., Brakensiek, D. L., and K. E. Saxton, 1982,
       Estimation of soil water properties, Trans. of  ASAE,  pp.
       1316-1320.


       Saghafian,  B.,	1992,  Hydrologic  analysis  of watershed
       response to spatially varied infiltration, Ph.D. Disserta-
       tion,  Civil Engr.  Dept., Colorado State University, Fort
       Collins, CO.


       Saghafian,  B.,	1993,  Implementation  of  a  distributed
       hydrologic model within Geographic Resources Analysis Sup-
       port   System   (GRASS),   Proceedings	of   the   Second
       International Conference on Integrating Environmental Mod-
       els and GIS, Breckenridge, CO.


       Smith, R. E., Corradini, C., and F. Melone, 1993, Modeling
       infiltration for multistorm runoff events, Water Resources
       Research, 29(1), pp. 133-144.


       CASC 2D page

AAUUTTHHOORRSS
       B. Saghafian and F. L. Ogden, Colorado State University

       _L_a_s_t _c_h_a_n_g_e_d_: _$_D_a_t_e_: _2_0_0_2_/_0_1_/_2_5 _0_5_:_4_5_:_3_4 _$



GRASS 5.0					r.hydro.CASC2D(1)
