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WRM: Water Resources Management Model
The water reouses model WRM is one of the core components of the
WaterWare system. It describes the water flow and avilability,
demand and supply balance on a daily basis across the basin and its
elements, based on conservation and continuity laws.
In order to simulate the behavior of a river basin over time the
river basin is described as a system of nodes and arcs.
These nodes represent the different components of a river system
(i.e., diversions, irrigation areas, reservoirs, etc.),
and can indicate points of water inflow to the basin, storage facilities,
control structures, demand for specific uses.
The nodes are connected by arcs which represent natural or manmade
channels which carry flow through the river system.
The WRM incorporates a number of river basin features (objects)
which are represented by different node types.
WRM node types
 Start node provides the input flow
at the beginning of a water course (main river or a tributary)
considered explicitly in the model;
this could represent:
 a spring,
 an upstream catchment (which in turn can be simulated by the
rainrunoff model),
 a major input of groundwater to the surface water system.
 an interbasin transfer,
 a desalination plant.
Confluence nodes provide for the joining of
several reaches, that could represent
natural tributaries or manmade conveyance channels.
It is characterized by more than one inflow.
Diversion nodes represent branching of flow to
several channels; it is characterized by more than one outflow
and rules to distribute the flow. Abstractions to demand nodes may be
described by diversions (see below).
Demand nodes describe the consumptive use of water.
They include:
 Irrigation node represents water demands for irrigation.
 Municipal node represents municipal water demands.
 Industrial node represents water demands for industry.
Each of them can either be situated on the main water course,
describing their net consumption, or at an abstraction from the main
water course; the latter configuration allows for the explicit treatment
of return flows or waste water (see Figure 4).
 Reservoir nodes represent natural or controlled storage
systems with a set of rules that prescribe outflow from the reservoir
as a function of time, its inflow and storage.
 Control nodes, that do not change the flow but
imposes an instream flow demand (for allocation and performance accounting
purposes), for example, for navigation or environmental purposes.
 Auxiliary or geometry nodes, that again do not affect the
flow directly, but are used to start a new reach or serve as a place
holder to provide a network structure consistent with other models.
 Terminal nodes represent outlets from the basin considered in
the model, including outflow to the sea or inflow to lakes.
WRM reaches
Nodes are connected by reaches. Water is routed along these reaches
considering their length, slope, and channel characteristics including cross
sections and roughness. Along a reach, lateral inflows or outflows
(exfiltration) represent very small tributaries not treated explicitly
and interaction with the groundwater.
Each reach has its own local catchment area, that provides the potential
linkage to spatially distributed water budget models.
Model dynamics
The model operates on a daily time step to represent the dynamics of water
demand and supply, reservoir operations, and the routing through the channel
system. This daily time step can be aggregated, for output and reporting
purposes, to a weekly, monthly, and annual scale.
Inputs at the individual nodes can again be specified at a daily, weekly, or
monthly resolution; different methods than construct a daily input data set
from these more aggregate values.
Start Node
This node provides the input flow to the simulation model, which represents the natural flows and
the intervening flows (lateral inflow, subsurface base flow).
The flow is represented in the following form
where
Q_{j}  outflow from start node in day j [m3/day] 
I_{j}  inflow at a start node in day j [m3/day] 
QI_{j}  input flow to a start node in day j [m3/day] 
beta = 0  in case where the start node represents a head water source. 
Confluence Node
This node provides for the joining of natural tributaries or
manmade conveyance channels. The equation governing the flow at
a confluence node is
where
Q_{j}  outflow from a confluence node in day j [m3/day] 
I_{j}^{i}  ith channel inflow to a confluence node in day j [m3/day]. 
Diversion Node
This node represents diversions of flow to other nodes in the system or to
other tributaries. The diversion rule is such that a minimum downstream release is given priority. The operation rule is described as follows
where
Q_{j}  actual downstream flow from a bifurcation node in day j [m3/day] 
I_{j}  inflow to a bifurcation node in day j [m3/day] 
AD_{j}  actual diversion flow in day j [m3/day] 
DWT_{}  downstream target flow in day j [m3/day] 
TD_{j}  diversion target flow in day j [m3/day] 
Irrigation Node
This node represents diversions of flow to the irrigation area
where
I_{j}  inflow to an irrigation node in day j [m3/day] 
DWT_{j}  minimum downstream flow target in day j [m3/day] 
AD_{j}  actual diversion flow in day j [m3/day] 
TD_{j}  diversion target flow in day j [m3/day] 
To determine the target diversion TD_{j} the following formula is used
where
where
CU_{j}  total area crop water requirements per day j [m3/day] 
ET_{cropj}  crop water requirements per day j [mm/day] 
ET_{0j}  reference crop evapotranspiration per day j [mm/day],
based on climatic data 
K_{c}  crop coefficient 
P_{j}  total area effective precipitation per day j [m3/day] 
P_{effj}  effective precipitation per day j [mm/day] 
P_{totj}  total precipitation per day j [mm/day] 
pl  fixed percentage to account for losses from runoff
and deep percolation. Normally pl = 0.7  0.9 
epsilon  conveyance loss coefficient 
c_{u}  consumptive use coefficient 
A  irrigation area [ha] 
alpha  unit conversion coefficient 
The flow that actually reaches the irrigation area is
The flow that is percolated to groundwater
Figures/mit.eps
Irrigation Return Flow Schemes
The outflow from the irrigation node is
where
R_{j}  amount of flow available after consumptive use by the crop 
GW_{j}  flow percolated to groundwater 
k  river return flow coefficient 
beta  flag for different cases of irrigation, beta = 1 in implicit,
beta = 0 in explicit (Figure irrig.eps 
Municipal and Industrial Water Supply Node
The Municipal and Industrial Water Supply Nodes represent water
demands for industry and other purposes.
The allocation rule for diverting water to the MI node
is described by the following equations:
where
I_{j}  inflow to a MI node in day j [m3/day], 
AD_{j}  actual diversion flow in day j [m3/day], 
DWT_{j}  minimum downstream flow target in day j [m3/day], 
TD_{j}  diversion target flow in day j [m3/day]. 
The downstream flow Q_{j} from the MI node is described by the equation
where
R_{j}  return flow to the river available, 
c_{u}  consumptive use coefficient. 
Reservoir Node
Reservoir node can represent three possible configurations:
 storage reservoir
 storage reservoir and power plant
 run of the river power plant
Storage Reservoir
Figures/res.eps
Reservoir "Standard Operating Policy"
The operating policy of a reservoir used in WRM is the "Standard Operating Policy" [Fiering, 1967].
It is illustrated in Figure res.eps and is described by the following equations:
The release policy is divided into three separate cases:
Similarly, the storage available in the reservoir at the
beginning of day (j+1) corresponds to the three cases as follows:
where
The following notations are used:
I_{j}  inflow to reservoir in day j [m3/day], 
Q_{j}  reservoir reservoir in day j [m3/day], 
W_{j}  available water in day j [m3], 
S_{j}  reservoir storage at the beginning of day j [m3], 
SMIN_{j}  reservoir minimum storage [m3], 
SMAX_{j}  reservoir maximum storage [m3], 
V_{j}  reservoir storage capacity [m3], 
TR_{j}  target reservoir release in day j [m3]day], 
P_{j}  total reservoir area precipitation in day j [m3/day], 
EV_{j}  reservoir evaporation in day j [m3/day], 
pr_{j}  daily precipitation coefficient [mm/day], 
ev_{j}  daily evaporation coefficient [mm/day], 
RA_{j}  reservoir surface area at the beginning of day j [ha],
is a function of the storage RA_{j} = psi[S_{j}], 
alpha  unit conversion coefficient. 
Hydroelectric Power Generation
The production of energy is calculated as a function of the output variables
from the reservoir node Q_{j} and S_{j}:
where
in case of a runoftheriver plant.
PG_{j}  energy generated at plant in day j [KWH/day], 
ef  efficiency of power plant, 
nh_{j}  number of hours in day j, 
H_{j}  average turbine head in day j, 
H_{j}^{*}  average turbine head between the base of
the dam and the elevation of the water surface of the reservoir in day j, 
HC_{j}  depth between turbine and the base of the dam, 
beta = 0 
Storage Routing in Tributaries
The Muskingum flood routing method [Engineer School, Ft.Belvoir, Va.,1940] is
applied in WRM. In this method the conditions relating inflows into and outflows from
a river reach to the water stored within the reach are described by the continuity
equation and an empirical linear storage equation:
where
I  rate of inflow [m3/day], 
Q  rate of outflow [m3/day], 
K  storage coefficient [day], approximates the time of travel of the wave through the reach, 
sigma  weighting factor, in natural channels usually varies between 0.1 and 0.3,
specifying the relative importance of the inflow and outflow in determining storage. 
where
WRM Data Requirements
 Start Node
I_{j}  inflow to a start node in day j [m3/day], 
QI_{j}  input flow to a start node in day j [m3/day]. 
 Confluence Node
 Diversion Node
DWT_{j}  target flow in day j [m3/day], 
TDSUB>j  diversion target flow in day j [m3/day]. 
 Irrigation Node
DWT_{j}  downstream flow target in day j [m3/day], 
ET_{0j}  reference crop evapotranspiration per day j [mm/day], 
K_{c}  crop coefficient, 
P_{totj}  total precipitation per day j [mm/day], 
pl  fixed percentage to account for losses from runoff and deep percolation, 
varepsilon  conveyance loss coefficient, 
k  river return flow coefficient, 
A  irrigation area [HA], 
Notice that to calculate ET_{0j} different methods, depending on available
data might be used. For areas where available climatic data cover air temperature data
only the relationship recommended by the BlaneyCriddle method, representing mean value
over the given month, is expressed as
where
T  mean daily temperature over the month considered [centigrade], 
p  mean daily percentage of total annual daytime hours, 
c  adjustment factor which depends on minimum relative humidity, sunshine hours and day time wind estimates. 
For areas where measured data on temperature, humidity, wind and sunshine duration
or radiation are available an adaptation of the Penman method is suggested.
The equation used in this method is:
where
W  temperature related weighting factor, 
R_{n}  net radiation in equivalent evaporation [mm/day], 
phi(u)  windrelated function, 
ea  saturation vapor pressure at mean temperature [mbar], 
ed  mean actual vapor pressure of the air [mbar], 
c  adjustment factor. 
 Municipal Node
consumptive use coefficient.
DWT_{j}  minimum downstream flow target in day j [m3/day], 
TD_{j}  diversion target flow in day j [m3/day], 
c_{u} 
 Industrial Node
DWT_{j}  minimum downstream flow target in day j [m3/day], 
TD_{j}  diversion target flow in day j [m3/day], 
c_{u}  consumptive use coefficient. 
 Reservoir Node
S_{j}  reservoir storage at the beginning of day j [m3], 
SMIN_{j}  reservoir minimum storage [m3], 
SMAX_{j}  reservoir maximum storage [m3], 
TR_{j}  target reservoir release in day j [m3]day], 
pr_{j}  daily precipitation coefficient [mm/day], 
ev_{j}  daily evaporation coefficient [mm/day], 
RA_{j}  reservoir surface area at the beginning of day j [HA], 
Additional data for power plants:
ef  efficiency of power plant, 
nh_{j}  number of hours in day j, 
HC_{j}  is the depth between turbine and the base of the dam. 
 Terminal Node
Storage Routing in Tributaries
L  reach length, 
AD  reach altitude difference. 
