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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 man-made 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

  1. 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 rain-runoff model),
    • a major input of groundwater to the surface water system.
    • an inter-basin transfer,
    • a desalination plant.

  2. Confluence nodes provide for the joining of several reaches, that could represent natural tributaries or man-made conveyance channels. It is characterized by more than one inflow.

  3. 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).

  4. 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).

  5. 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.

  6. Control nodes, that do not change the flow but imposes an in-stream flow demand (for allocation and performance accounting purposes), for example, for navigation or environmental purposes.

  7. 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.

  8. 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

Qj outflow from start node in day j [m3/day]
Ij inflow at a start node in day j [m3/day]
QIjinput 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 man-made conveyance channels. The equation governing the flow at a confluence node is

where

Qjoutflow from a confluence node in day j [m3/day]
Ijii-th 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

Qjactual downstream flow from a bifurcation node in day j [m3/day]
Ijinflow to a bifurcation node in day j [m3/day]
ADjactual diversion flow in day j [m3/day]
DWTdownstream target flow in day j [m3/day]
TDjdiversion target flow in day j [m3/day]

Irrigation Node

This node represents diversions of flow to the irrigation area

where

Ijinflow to an irrigation node in day j [m3/day]
DWTjminimum downstream flow target in day j [m3/day]
ADjactual diversion flow in day j [m3/day]
TDjdiversion target flow in day j [m3/day]

To determine the target diversion TDj the following formula is used

where
where
CUjtotal area crop water requirements per day j [m3/day]
ETcropjcrop water requirements per day j [mm/day]
ET0jreference crop evapotranspiration per day j [mm/day], based on climatic data
Kccrop coefficient
Pjtotal area effective precipitation per day j [m3/day]
Peffjeffective precipitation per day j [mm/day]
Ptotjtotal precipitation per day j [mm/day]
plfixed percentage to account for losses from runoff and deep percolation. Normally pl = 0.7 - 0.9
epsilonconveyance loss coefficient
cuconsumptive use coefficient
Airrigation area [ha]
alphaunit 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
Rjamount of flow available after consumptive use by the crop
GWjflow percolated to groundwater
kriver return flow coefficient
betaflag 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

Ij inflow to a MI node in day j [m3/day],
ADj actual diversion flow in day j [m3/day],
DWTjminimum downstream flow target in day j [m3/day],
TDj diversion target flow in day j [m3/day].

The downstream flow Qj from the MI node is described by the equation

where

Rjreturn flow to the river available,
cuconsumptive 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:

Ij inflow to reservoir in day j [m3/day],
Qj reservoir reservoir in day j [m3/day],
Wj available water in day j [m3],
Sj reservoir storage at the beginning of day j [m3],
SMINj reservoir minimum storage [m3],
SMAXj reservoir maximum storage [m3],
Vj reservoir storage capacity [m3],
TRj target reservoir release in day j [m3]day],
Pj total reservoir area precipitation in day j [m3/day],
EVj reservoir evaporation in day j [m3/day],
prj daily precipitation coefficient [mm/day],
evj daily evaporation coefficient [mm/day],
RAj reservoir surface area at the beginning of day j [ha], is a function of the storage RAj = psi[Sj],
alpha unit conversion coefficient.

Hydroelectric Power Generation

The production of energy is calculated as a function of the output variables from the reservoir node Qj and Sj:

where

in case of a run-of-the-river plant.
PGj energy generated at plant in day j [KWH/day],
ef efficiency of power plant,
nhj number of hours in day j,
Hj average turbine head in day j,
Hj*average turbine head between the base of the dam and the elevation of the water surface of the reservoir in day j,
HCjdepth 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

Irate 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

  1. Start Node
  2. Ijinflow to a start node in day j [m3/day],
    QIjinput flow to a start node in day j [m3/day].

  3. Confluence Node
  4. Diversion Node
  5. DWTjtarget flow in day j [m3/day],
    TDSUB>j diversion target flow in day j [m3/day].

  6. Irrigation Node
  7. DWTj downstream flow target in day j [m3/day],
    ET0j reference crop evapotranspiration per day j [mm/day],
    Kc crop coefficient,
    Ptotj 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 ET0j 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 Blaney-Criddle 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,
    Rn net radiation in equivalent evaporation [mm/day],
    phi(u) wind-related function,
    ea saturation vapor pressure at mean temperature [mbar],
    ed mean actual vapor pressure of the air [mbar],
    c adjustment factor.

  8. Municipal Node
  9. consumptive use coefficient.
    DWTj minimum downstream flow target in day j [m3/day],
    TDj diversion target flow in day j [m3/day],
    cu

  10. Industrial Node
  11. DWTj minimum downstream flow target in day j [m3/day],
    TDj diversion target flow in day j [m3/day],
    cu consumptive use coefficient.
  12. Reservoir Node
  13. Sj reservoir storage at the beginning of day j [m3],
    SMINj reservoir minimum storage [m3],
    SMAXj reservoir maximum storage [m3],
    TRj target reservoir release in day j [m3]day],
    prj daily precipitation coefficient [mm/day],
    evj daily evaporation coefficient [mm/day],
    RAj reservoir surface area at the beginning of day j [HA],
    Additional data for power plants:
    ef efficiency of power plant,
    nhj number of hours in day j,
    HCj is the depth between turbine and the base of the dam.
  14. Terminal Node
Storage Routing in Tributaries
L reach length,
AD reach altitude difference.

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