Surface water management model

The surface water model is represented as a network with nodes with storage (reser- voirs) or without storage capacity (junction nodes, diversion nodes) and links (natural streams or artificial channels). The demands are also linked to certain nodes.

This network has to have an explicit connectivity given by the actual conditions, and a solution algorithm or how the demands are met by allocating and releasing water from reservoirs. Below we explain the main characteristics of the elements, connectivity, and the algorithm.

5.3.3.1. Reservoirs

Surface reservoirs are represented using a special type of node where water can be stored. Inputs for reservoir definition are maximum capacity, maximum depth, and initial storage. From these parameters the model can calculate automatically a storage- area-elevation curve —given by percentages— or if there is data available the storage- area-elevation curve can be explicitly set. Maximum monthly releases (or maximum capacity of the outlets) are also required as an input.

Besides these main inputs, average monthly evaporation and seepage rates per area (both in [Volume · Area-1 · (Time Step)-1]) are needed to calculate monthly evaporation and infiltration as a function of actual storage.

If the reservoir has a powerhouse the model needs the height (if is a fixed height facili- ty), the turbines efficiency and maximum capacity. With these data, the generated power is:

𝑷 = 𝝁 ∙ 𝝆 ∙ 𝒒 ∙ 𝒈 ∙ 𝒉 Equation 1

where P is the available power (W), μ is the turbine efficiency, ρ is the water density (1000 kg/m3), q is the flow (m3/s), g is the gravity acceleration (m2/s) and h the availa- ble head (m)3. To obtain energy generation from available power we use the average monthly flow and the working hours per month.

5.3.3.2. Nodes

Nodes in the model are at junctions between links. Nodes can represent just the junc- tion between two or more links, and in some cases these nodes will have water de- mands.

The nodes must meet the conservation of mass criteria, i.e. that all the water entering from the upstream link has to be either consumed or returned to the downstream link or aquifer.

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5.3.3.3. Natural streams

Natural streams are represented as links between two nodes where water flows down- stream. Natural streams have a maximum monthly capacity and seepage rate. The cur- rent version of the model assumes that all the rivers can either lose water to the aquifer (if infiltration rate is positive) or just keep the water (infiltration is 0). Future develop- ments will include gaining rivers as well.

5.3.3.4. Artificial channels

Artificial channels are represented as links between two nodes where water can either flow downstream or upstream. If it flows upstream, the link flow will have an energy intensity due to pumping.

5.3.3.5. Connectivity

Each link connects two nodes, but the network will be unidirectional, what means that each of the links only can have one node upstream and one downstream (in the flow direction). Although a node can have more than two links getting in and/or out, but only one link will be the preferred downstream outflow link representing the natural stream that receives return flows.

This connectivity is represented by the connectivity matrix, an n x n matrix (being n the number of nodes) where the row represent upstream nodes and the column represents downstream nodes. Although this matrix could be a weighted matrix (simulating the distance or losses between the nodes), for simplicity only 1 or 0 entries represent con- nectivity between nodes.

5.3.3.6. Water allocation algorithm

An algorithm determines monthly releases from reservoirs and allocations in each time step to meet current demands based on priorities, accounting for current reservoir stor- ages, monthly inflows, evaporation and infiltration from reservoirs, outflows from already met demands, and available connectivity from upstream reservoirs. The main steps of the algorithm are:

i) In the beginning of each period reservoir storages are updated with new inflows.

ii) Each node has priority (1 means first), and according to their priority for

each node:

a. The node looks to meet their demand from water coming from up- stream flows that can come either from outflows from other demands or from reservoirs.

b. If the demand of the node can be met with upstream outflows it will take their water and return its outflows to its downstream link.

c. If node demand cannot be met with upstream outflows then: each node has a reservoir priority to get water. If the demand can be met from the first reservoir in its priority list, demand is met, return flows calculated and released downstream and release from this reservoir updated. If not, the demand looks for the second reservoir in its priori- ty list and tries to meet the demand and so on. The loop finishes either if the total demand has been met or there is no more water in all the reservoirs upstream of the node.

d. If demand is met, surface and aquifer return flows are released. e. If the demand of the node is not totally met, then an optimization

module starts to minimize total scarcity costs according to water pric- es and elasticities for the demands included in that node. Usually ur- ban outdoor demands are more elastic than indoor demands, annual agricultural cops more elastic than perennial crops, and energy more inelastic than anyone else. The minimization problem is defined with the following equations:

Minimize

𝑻𝒐𝒕𝒂𝒍 𝑺𝒄𝒂𝒓𝒄𝒊𝒕𝒚 𝑪𝒐𝒔𝒕 = ∑ 𝑺𝑪

𝒊 𝒊= ∑ (𝑸_𝟎𝒊−𝑸_𝒔𝒊)𝟐_∙𝑷 𝟎𝒊 𝟐∙|𝜺𝒊|∙𝑸𝟎𝒊 𝒊 Equation 2 Subject to: ∑(Q0i− Qsi) = i Total Shortage Q0i≥ Qsi

Where each i is a demand (even differentiating all the different sub- demands included in the urban and agricultural demands), SCi is the scarcity cost for the demand i, Q0i and Qsi are the target demand and the demand actually supplied for the demand i, P0i the price of the wa- ter for the demand i, and Ԑi the water price elasticity for the demand i. The solution of this optimization is which demands are actually sup- plied and then return flows will be assessed.

iii) When all the nodes have tried to meet their demands, the releases from each reservoir will be the sum of the releases for each of the demands plus spills, and then the final month storage is calculated accounting for evapo- ration and infiltration (using the average area between the area for the ini- tial storage and the area of the final storage that are obtained from the ele- vation-area curve).

In document The Water-Energy Nexus: a bottom-up approach for basin-wide management (Page 164-167)