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Figure 1 provides a schematic overview of Urbanwb model with its fundamental elements included. Under this conceptual framework, major hydrological dynamics in an urban water system can be quickly and indicatively modelled modeled to provide users with a general idea of the water quantity distribution and how the water system behaves under certain conditions.
Below you find a brief introduction of the major components of the Urbanwb model. Chapter 2 describes these components into much more detail.
1.2 Major components
In the Urbanwb, the land use area is divided into:
Notes
- The Urbanwb model is based on a Dutch urban area in a polder system (Figure 3) with a controlled target water level. However it can also be applied in other areas than polders. In those cases the target water level is the applied drainage water level of that area.
- The open water area is an essential part of the Urbanwb model. All excess water in the urban area first flows to the open water area, before it is discharged from the urban area (except for the water of the mixed sewer system that flow to the WWTP). Therefore the open water area size always has to be larger than 0.
- In case an urban area is modeled that contains no open water, an open water area has to be added to the model artificially (advised is to add in those cases an open water area size of a few percent of the total urban area).
1.2 Major components
In the Urbanwb, the land use area is divided into:
- Paved area above floor level
o Paved Roof (PR), i.e. buildings. - Paved area at floor level
o Closed Paved (CP), completely sealed.
o Open Paved (OP), allowing some infiltration. - Unpaved area at floor level
o Unpaved (UP). - Paved area above floor level
o Paved Roof (PR), i.e. buildings. - Paved area at floor level
o Closed Paved (CP), completely sealed.
o Open Paved (OP), allowing some infiltration. - Unpaved area at floor level
o Unpaved (UP). - Surface water at floor level
o Open Water (OW).
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The formula of groundwater level during current time step h(t) and its derivation are shown below (Figure 12 ). In this figure, P is percolation (assumed to be constant during a time step), qs is downward seepage to deep groundwater, qd is drainage to Open Water. All these water flows can get positive as well as negative values, negative meaning flow in the other direction. In Urbanwb all relevant levels are relative to the surface level, where the unit (m-SL) means meter below surface level.
Figure 12 Groundwater level h(t) calculation
Seepage: 
Drainage: 
Continuity: 
Substitution results in:
Initial condition: 
Figure 12 Groundwater level h(t) calculation
The basic applied formula is: 
Seepage: 
Drainage: 
Continuity: 
Example (check):
h(t) = 1 m –MV; PP = 1.5 m –MV; H = 2 m –MV; c = 1000 d; w = 50 d :
qs = (2 – 1) / 1000 = 0.001 m/d = 1 mm/d (downward)
qd = (1.5 – 1) / 50 = 0.01 m/d = 10 mm/d (outflow)
Two options for seepage are available.
In option 1 the seepage is dependent of the difference between the variable groundwater level and a user defined constant hydraulic head of the deep groundwater (H) over a hydraulic resistance (c) of the layer in-between.
In option 2 the seepage is defined as a constant water flow.
Important note: all parameters in these formulas are in meters and days. For different time step sizes water flows expressed in meter per time step need to be adapted.
Option 1. Seepage is groundwater level dependent
Substitution in continuity equation results in:
Rewritten:
Solving:
Initial condition: 
Resulting in:
Drainage (qd) and seepage (qs) are automatically calculated in depth per day, because the sizes of both flow resistances (w and c) are expressed in days.
Percolation (P) is expressed in depth per time step, hence must be divided by the time step size (t [d])
Option 2. Seepage is constant
Substitution in continuity equation results in:
Rewritten:
Solving:
Initial condition:
Resulting in:
Drainage (qd) is automatically calculated in depth per day, because the size of the flow resistances (w) is expressed in day.
Seepage (qs) is defined as a constant flow, expressed in depth per day.
Percolation (P) is expressed in depth per time step, hence must be divided by the time step size (t [d])
2.6.1 Assumptions
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Return type: (dictionary)
2.8 Open Water (required area > 0)
Open Water in the Urbanwb model refers to all controlled Open Water bodies, e.g. ditches, canals and ponds. In the Urbanwb model the open water has a fixed target level. Above this level, water will be discharged to outside water, limited by a user defined discharge capacity. In the Urbanwb model, the minimum open water level is the defined target water level. If evaporation losses result in water level below the target level, water will be let in (with unlimited capacity) from outside water to maintain the target water level. Open Water can be deemed as an abstract term reflecting system storage capacity. By assumption, all runoff from Unpaved and all sewer overflow into the street flow directly to the Open Water. Also, sewer system outflow and groundwater drainage will recharge the Open Water. During simulation, under successive heavy rain events, Open Water level may exceed the target level due to insufficient storage capacity and discharge capacity, indicating there is excessive water that the urban water system cannot handle. This can represent all kinds of real urban flood phenomena. In the current version of the Urbanwb model water above surface elevation level cannot flow (directly) to the other surface areas and cause flooding in these areas. Hence the maximum water level in the Open Water is not limited. The storage height above the target Open Water level is calculated to understand the storage requirements of the water system. Maximum storage height on Open Water for a certain flood event multiplied with the Open Water area reflects the required storage capacity for the total study area for that event. To sum up, Open Water component is an abstract recipient water body that indicates the required storage capacity of the system. Figure 13 shows the schematic overview of the Open Water.
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- Determine the rainfall on the measure for the current time step.
- Determine the runoff from the measure inflow area to the measure for the current time step.
- Determine the initial interception storage of measure. Initial interception water budge budget includes interception storage at the end of previous time step + rainfall + runoff from measure inflow area in case runoff is defined to flow to interception layer.
- Determine the evaporation from the interception layer of the measure, limited by Penman evaporation.
- Determine the downward infiltration from the interception layer. Downward infiltration from the interception layer is only possible when the measure structures contain at least 2 layers.
Note: Downward infiltration calculation for a green roof is separately defined. - Determine the surface overflow from the interception layer of the measure.
- Determine the final interception storage on the interception layer of the measure.
- Determine initial storage in top storage layer of measure. When measure structure contains only 2 layers. This storage is zeros (when 2 layer — no top storage layer is involved, all the variable related to top storage layer will be zero.) When 3 layer, initial storage in top storage layer of measure is storage at previous time step + downward infiltration from interception layer.
- Determine transpiration from top storage layer of measure, limited by water availability and Penman evaporation multiplied with a predefined reduction factor.
- Determine the percolation from the top storage layer of the measure to the bottom storage layer of the measure.
Note: This variable is separately defined for green roof type measures. - Determine the final storage in the top storage layer of the measure, limited by the predefined storage capacity of the top storage layer of the measure.
- Determine the initial storage in the bottom storage layer of the measure.
- Determine the evapotranspiration from the bottom storage layer of the measure. Transpiration from the bottom storage layer can only occur when defined possible and when the transpiration capacity exceeds the transpiration from the top storage layer in case of 3 layers.
- Determine the percolation from the bottom storage layer of the measure to the groundwater. Specify whether this percolation is limited by the groundwater level or not. If not, the limitation will only be the saturated permeability. It is recommended to specify percolation being not limited by the groundwater level.
- Determine the controlled runoff from the bottom storage level of the measure. The controlled runoff can be modelled as either a constant flux or as a dynamically-computed flux that depends on a user defined drainage level and resistance.
- Determine the final storage of the bottom storage layer of the measure.
- Determine the overflow from the bottom storage layer of the measure if the bottom layer is completely filled.
- Determine the outflow from the measure to OW, UZ, GW, SWDS, MSS, Out
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Land use at or above surface level are divided into 5 components, namely Paved Roofs (buildings), Closed Paved (roads, etc.), Open Paved (pavements, parkings, etc.), Unpaved (grass land, etc.) and Open Water (ditches, canals, ponds, etc.). The fractions of the five land use types should sum up to 100%. The minimum required size of the open water area is larger than 0. In addition, the total area [m2] of the study area is required input. Besides, for paved areas (PR, CP, OP), three additional types of fractions have to be defined:
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