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] ele-
       vation=mapname  time_step=value	tot_time=value	discharge=mapname out-
       let_eastNnorthNslope=east,north,bedslope  rain_duration=value   [water-
       shed_mask=mapname]  [initial_depth=mapname]  [storage_capacity=mapname]
       [interception_coefficient=mapname]    [roughness_map=mapname]	 [Man-
       ning_n=value] [conductivity=mapname] [capillary=mapname] [porosity=map-
       name]  [moisture=mapname]  [pore_index=mapname]	[residual_sat=mapname]
       [lake_map=mapname]   [lake_elev=mapname]  [radar_intensity_map=mapname]
       [links_map=mapname]  [nodes_map=mapname]  [channel_input=mapname]  [ta-
       ble_input=mapname]   [dis_profile=mapname]   [wat_surf_profile=mapname]
       [hyd_location=mapname]	[r_gage_file=mapname]	 [unif_rain_int=value]
       [num_of_raingages=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 distributed hydrology
       are strongly advised against using this code in any mode,  particularly
       in  operational	mode. Besides knowledge of basic hydrology, experience
       with typical numerical techniques used in physically-based hydrodynamic
       models  is  recommended as it will help the user grasp capabilities and
       limitations of this model. This manual is significantly	condensed  for
       electronic  distribution  and  is  in  no  way comprehensive. Users are
       encouraged to experiment with the model and venture in hydrology  text-
       books and journal papers to learn more about the topics 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 notification. 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 Uni-
       versity. 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 reformulated, 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. Profes-
       sor,  Department  of Civil and Environmental Engineering, University of
       Connecticut,  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 components 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 empiri-
       cal three parameter model.  Infiltration is the process	whereby  rain-
       fall  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  continuous	soil  moisture
       accounting, redistribution of soil moisture can also be simulated when-
       ever  the  non-intercepted 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 tech-
       niques, 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 exe-
       cuting 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 conversion 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 complexity 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 seconds.   (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 over-
       land 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 intensities 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*mois-
       ture) (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 ele-
       vation 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 values in lake
       surface elevation map must be DIVIDED to convert 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 convert 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 infiltration 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 moisture 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 interpolation 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 creates 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-intensity 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). Chan-
       nel bed smoothing  is  recommended  to  eliminate  adverse  slopes.  No
       hydraulic structures, except reservoir spillways, 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 routing.  Particu-
       larly suitable for watersheds with some base flow to avoid dry-bed con-
       dition with channel slopes less than 1%. Supercritical slopes cannot be
       handled;  a  warning  message  will be printed if supercritical flow is
       encountered.


       _-_b initializes the channel depth and discharge files  (similar  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 hori-
       zontal water surface and draining down to normal  depth	using  a  y(t)
       outlet  boundary  condition  (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  real-
       istic  value.  When  the  depth at the outlet reaches normal depth, the
       values of depth and discharge 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  exe-
       cuted; 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 dis-
       charges 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  accommo-
       date  such effects.  It is recommended, in such instances, to re-delin-
       eate 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 quality of the DEM plays a major role in success  of
       distributed  hydrologic simulations. DEMs almost always contain errors.
       Large flat areas in the DEM may be due to the limited vertical  resolu-
       tion  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 interpolation
       scheme used to rasterize digitized contours, or due to  coarse  resolu-
       tion  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  dis-
       cover  potential errors in the DEM is to run _r_._h_y_d_r_o_._C_A_S_C_2_D iteratively
       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 topographic map of the
       area. Also stream network may be checked for  proper  connectivity  via
       depth  maps.  Alternatively, 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	neces-
       sary  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 depressions must be removed  since  they  most
       likely  trap  surface  runoff which would have otherwise contributed to
       the outlet. The real lakes and reservoirs may be  simulated  if	delin-
       eated  (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
       paragraph,  about  the  quality	of the DEMs is that a nicely connected
       stream network cannot be derived from non-smoothed DEM.	If  no	delin-
       eated 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 indepen-
       dent of the DEM then the elevation of stream cells should be checked so
       that  they  are not higher than those of the surrounding cells.	Other-
       wise 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  initial	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 coef-
       ficient	map,  are  usually  a  reclass of vegetation map. For table of
       storage capacity and interception coefficient values  see  Gray	(1970,
       section 4.6) or Bras (1990) p. 233.


       5) roughness_map: This map represents the spatial distribution of over-
       land 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 satisfies
       the conditions of turbulent flow over rough surfaces.


       6) conductivity, capillary, porosity, & moisture:  Four	soil  property
       maps  are needed for modeling infiltration process using the Green-Ampt
       technique. These maps respectively contain saturated hydraulic  conduc-
       tivity,	capillary  suction  head, effective porosity, and initial soil
       moisture content. The first three maps may be reclasses of soil texture
       map and the last one must be prepared considering antecedent soil mois-
       ture 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 satu-
       rated hydraulic conductivity map must be adjusted for  the  percent  of
       rock  fraction within the soil, if known. If these four maps are speci-
       fied, 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 continu-
       ous  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-hia-
       tus  stage.  Tables  of	pore-size  distribution  index (Brooks & Corey
       lambda) and residual saturation are given by Rawls et al. (1982). As in
       (6),  measured  values  should be substituted where available. When the
       four maps specified in (6) as well as the two maps specified  here  are
       given  as  command line arguments, the redistribution infiltration rou-
       tine 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 individual 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 iso-
       lated pond areas may be simulated as well; in fact such ponds are  rec-
       ommended  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  con-
       nected to the channel network. The routing of the lakes is performed by
       linear reservoir technique. 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	other-
       wise- 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 interpo-
       lation software, which takes in the rainfall site data corresponding to
       different  times  and  generates  the  time  series of raster maps. For
       instance, where raingage rainfall data  is  available,  one  could  run
       s.surf.rst  of  GRASS,  one time for every recording time, and save the
       interpolated 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_duration   options.	Example:   If  one  sets  radar_inten-
       sity_map=rain.map and there are a total of eight maps in regular inter-
       vals  of  10 minutes (radar_time_step=600 and rain_duration= 4800, both
       in seconds), 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 computational 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 sec-
       tions (link types 1 and 8).  Internal  boundary	condition  link  types
       (e.g.  weirs)  do  not  appear  in  the link or node maps. The internal
       boundary condition link types do appear in the channel_input file  (see
       attachment).   The purpose of the link and node maps is to provide con-
       nectivity 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 condition 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 downstream 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 down-
       stream 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 conjunction with r.hydro.CASC2D.
       The link numbers assigned by r.watershed must be re-numbered in	accor-
       dance  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. However, 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 rep-
       resents a short distance from  the  confluence.	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 discussion of links and nodes maps, see chan-
       nel_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  docu-
       ment  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,  Tennessee  (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
       routing is used, the channel talweg elevations are taken from the chan-
       nel_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  proceeds  until
       normal  depth  is  reached at the outlet. At this time, the dis_profile
       and wat_surf_profile files are written for use in  channel  initializa-
       tion  for  later  simulations.  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 dis-
       charge 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	elimi-
       nate  the  reach of steep slopes. One workable solution to prevent sta-
       bility problems at low flows is to use the so-called "Preissmann  Slot"
       (see Cunge et al., 1980, for example). Be patient, as getting the chan-
       nel network running is a time consuming process.  There are a  host  of
       possible  errors including: abrupt changes in cross-section, DEM-error,
       etc., which can cause problems. The  implicit  routing  method  is  not
       applicable  to  steep (mountainous or upland) streams. If supercritical
       flow is encountered in upland (1st order) streams, they can  be	elimi-
       nated 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 locations 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
       raingages (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  coordinates.   If  a  gage falls outside in a different zone to the
       left of the active region's zone, then negative values are also accept-
       able.   Note  however  that  raingages well outside the watershed under
       analysis generally provide  poor  rainfall  estimates.  The  subsequent
       lines  at  the bottom of the raingage file must reflect temporal varia-
       tion 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, separated 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_raingages=3, gage_time_step=120,
       and rain_duration=600. For state plane (SP) coordinate system the east-
       ings and northing 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
       watershed  mask. Often times the region is not set to its original set-
       tings after zoom-in operations (d.zoom) are performed and this may  put
       the  outlet outside the active region thus causing the model to eventu-
       ally 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 outflow 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  channel  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  coeffi-
       cient  n  via  Manning_n  parameter.  The user is warned if both rough-
       ness_map and Manning_n have been specified.


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


       18)  num_of_raingages: The total number of recording raingage.  If this
       variable is set to one, no spatial interpolation 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  pro-
       vided at the top of raingage file (r_gage_file).


       19)  time_step: This represents the duration of computational time step
       in seconds and is a critical variable determining the  total  execution
       time for a particular simulation. These is no firm guide for the selec-
       tion 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 completely flat areas may show a checker-board  pattern,
       i.e. oscillations are observed in the water surface level. This eventu-
       ally 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 sec-
       onds,  between  recording  instances  of  rainfall intensities by rain-
       gage(s). It is implied that the rainfall data has been recorded in reg-
       ular intervals. See the notes under r_gage_file for an example.


       21)  radar_time_step: A value expressing the time interval between con-
       secutive 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 sat-
       uration (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 simula-
       tion  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 sec-
       onds, 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 out-
       put options.


       25) unit_el_conv: This conversion factor is used to  convert  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 sur-
       face  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  horizon-
       tal  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 stor-
       age  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 over-
       land 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 discharge, 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 mil-
       limeters. 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 corresponds 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 per-
       formed.	Similarly the last depth map corresponds to the end-of-simula-
       tion 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 overland 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 redistribution 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 inten-
       sities,	in  mm/hr, at write_time_step intervals and may be set for the
       simulations involving spatially distributed rainstorms;	i.e.  raingage
       rainfall data or radar (or other sources of rainfall 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, respectively corresponding to times
       equal to 0, 100, 200, through 1000 seconds. These maps  may  be	viewed
       sequentially 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  double-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  comprised  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 supported. Devel-
       opment 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,
       bottom  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 sectional  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 inter-
       nal boundary conditions link types, only  weirs	can  be  simulated  at
       present.


       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 digital elevation models (DEM). However, if the
       channel network is extracted from a DEM, a smoothing algorithm must  be
       applied	(e.g. Ogden et al., 1994) to produce physically realistic lon-
       gitudinal 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 conven-
       tion. All units of length are in meters, including elevations.


       In  this example, a channel input data file is constructed for a ficti-
       tious watershed. Note that this particular example is merely for demon-
       stration and has not been tried in any simulation run.  The stream net-
       work 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 number of grid	cells  spanned
       by  that  link, with the exception of the internal boundary conditions.
       Conceptually, internal 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.  Further-
       more,  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 Watershed Stream Net-
       work


       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 deriv-
       ative   weighting   coefficient	 "theta",  the	length	of  each  node
       &quot;dx&quot;, the computational time step "dt" (seconds),  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	computational time step used in the overland flow routing por-
       tion 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  maximum  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 connectivity 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 describing
       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 connectivity
       information in the channel_input file.  As an  interpretation,  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 individual 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 talweg 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 dis-
       charge 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 reser-
       voir  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 elevation 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 there-
       fore 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.	Trape-
       zoidal  channel	links are simple in terms of input.  The channel depth
       field is intended to represent the average bank-full depth of the chan-
       nel.  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 channels 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 chan-
       nel_input data file, the program will attempt  to  open	the  file  ta-
       ble_file  (typically 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 ele-
       vation. 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
       significant 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 connectivity, 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 for-
       ward direction of 0.92, a discharge coefficient for flow in the reverse
       direction  equal  to  0.85,  and  the channel bed elevation 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 channel_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 elevation.


       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 chan-
       nel_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  exam-
       ple  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 conveyance  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, corresponding 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-
       sectional  area	of  86.4  m2, and a conveyance of 312.5 m3/s. The con-
       veyance 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 hydrologic science,
       Addison-Wesley, Reading, Mass., 643 p.


       Crum, T. D., and R. L. Alberty, 1993, The WSR-88D and the WSR-88D oper-
       ational 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 Com-
       putational  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 University, Fort Collins, CO.


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


       Ogden, F.L., 1994, de-St Venant channel routing in  distributed	hydro-
       logic  modeling., Proc. Hydraulic Engineering `94, ASCE Hydraulics Spe-
       cialty 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 distributed 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 infil-
       tration 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  spa-
       tially  varied  infiltration,  Ph.D.  Dissertation, Civil Engr.	Dept.,
       Colorado State University, Fort Collins, CO.


       Saghafian, B., 1993, Implementation of a distributed  hydrologic  model
       within  Geographic  Resources Analysis Support System (GRASS), Proceed-
       ings of the Second International Conference on Integrating  Environmen-
       tal Models 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)
