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• Infiltration from the Open Paved surface (OP) percolates directly to groundwater (GW) without passing Unsaturated Zone. Unsaturated Zone is only relevant beneath Unpaved area. The area of Unsaturated Zone is equal to area of the Unpaved area.
• Since the Urbanwb model is evaluated for smaller time steps Δt than a day (currently Δt = 1 hour), for computing simplicity, hourly reference crop evapotranspiration is divided by 2Δt to get the daily crop-evaporation value as the potential transpiration rate that determines the transpiration reduction point h₃. The factor 2 (in 2 Δt) is applied, because it is assumed that (crop-)evaporation occurs only during day time (half a day). Actually, it would be better to apply the sum of hourly reference crop evapotranspiration for 24 hourly time steps within that day as the daily crop evaporation value, but for the sake of computing efficiency and robustness, we use this simplification and we argue this simplification is a good approximation and has negligible impacts on computed results.
• (Actual) evapotranspiration during current time step is determined by transpiration reduction factor (water stress factor) and reference crop evapotranspiration during the same time step (crop factor =1).
• Percolation to groundwater is limited by the saturated conductivity of the soil.

2.5.2       Calculation order

• Total infiltration from Unpaved area is taken as the influx.
• Calculate runoff from measure to Unsaturated Zone if defined possible.
• Calculate moisture content of soil in the root zone at transpiration reduction point θ_h3. If daily reference evapotranspiration is less than 1 mm/d, θ_h3 = θ_h3l. If daily reference evapotranspiration is more than 5 mm/d, θ_h3 = θ_h3h. If daily reference evapotranspiration is between 1 mm/d and 5 mm/d, θ_h3 is interpolated between θ_h3l and θ_h3h.
• Determine transpiration reduction factor α by linear interpolation between θ_h1 (moisture content of root zone at complete saturation point), θ_h2 (moisture content of root zone at field capacity), θ_h3 (moisture content of root zone at transpiration reduction point), and θ_h4 (moisture content of root zone at permanent wilting point), based on actual moisture content of root zone at previous time step plus the infiltration from Unpaved area during current time step.
• Evapotranspiration from Unsaturated Zone during current time step is the product of transpiration reduction factor α and reference crop evapotranspiration ET₀ during the same time step.
• Determine equilibrium root zone moisture content θ_eq by interpolation, based on the groundwater level at previous time step. In database, for given soil type and crop type, we have information on equilibrium moisture content of root zone for different groundwater levels (from 0 to 10 m-SL). Hence, the equilibrium moisture content of root zone during current time step θ_eq is interpolated from the lookup table based on the groundwater level at previous time step.
• Determine maximum capillary rise by interpolation, based on the groundwater level at the previous time step. In database, for given soil type, we have information on maximum capillary rise for different groundwater levels (from 0 to 10 m-SL). Similarly, to calculating equilibrium moisture content of root zone, the maximum capillary rise during current time step is interpolated from the lookup table based on the groundwater level at previous time step.
• Determine percolation from Unsaturated Zone (UZ) to groundwater (GW). It can be positive (downward deep percolation) and negative (upward capillary rise). Note that deep percolation to groundwater and capillary rise from water table are summarized into one term in the Urbanwb model. If current root zone water budget (root zone moisture content at previous time step + infiltration from UP + runoff from measure to UZ - evapotranspiration) is greater than equilibrium root zone moisture content θ_eq, it is downward deep percolation, otherwise it is upward capillary rise. Deep percolation is limited by saturated permeability of the soil and difference between current water budget and equilibrium root zone moisture content θ_eq; Capillary rise is limited by maximum capillary rise and different between current water budget and equilibrium root zone moisture content θ_eq.
• Determine moisture content of root zone θ at the end of current time step. The root zone moisture content at the end of current time step is the root zone moisture content at the end of previous time step + infiltration + runoff from measure – evapotranspiration percolation, which values are all calculated above.

2.5.3       Code and input arguments

class urbanwb.unsaturatedzone.UnsaturatedZone(theta_uz_t0, uz_no_meas_area, uz_meas_area, soiltype=2, croptype=1, **kwargs)             [source]

Bases: _object

Creates an instance of UnsaturatedZone class with given initial states and properties, iterates sol() function to compute states and fluxes of Unsaturated Zone at each time step.

Parameters:

• theta_uz_t0 (float) – initial (volumetric) moisture content of soil in the root zone (at t=0) [mm]
• uz_no_meas_area (float) – area of Unsaturated Zone without measure [m^2]
• uz_meas_area (float) – area of Unsaturated Zone with measure [m^2]
• soiltype (int) – soil type
• croptype (int) – crop type

sol(i_up_uz, meas_uz, e_ref, tot_meas_area, gwl_prevt, delta_t=0.041666666666666664)      [source]

Calculates states and fluxes in Unsaturated Zone during current time step.

Parameters:

• i_up_uz (float) – infiltration from interception storage on Unpaved to Unsaturated Zone during current time step [mm]
• meas_uz (float) – inflow from measure to Unsaturated Zone during current time step [mm]
• e_ref (float) – reference crop evapotranspiration during current time step [mm]
• tot_meas_area (float) – total area of measure [m^2]
• gwl_prevt (float) – groundwater level at previous time step [m-SL]
• delta_t (float) – length of time step [d]

Returns:                               A dictionary of computed states and fluxes of Unsaturated Zone during current time step:

• sum_i_uz – Infiltration from Unpaved to Unsaturated Zone during current time step [mm]
• r_meas_uz – Inflow from measure (if applicable) to Unsaturated Zone during current time step [mm]
• theta_h3_uz – Moisture content of root zone at which transpiration reduction starts during current time step [mm]
• t_alpha_uz – Transpiration reduction factor during current time step [-]
• t_atm_uz – Transpiration from Unsaturated Zone during current time step [mm]
• gwl_up – First value in predefined lookup table above the groundwater level at the end of previous time step [m-SL]
• gwl_low – First value in predefined lookup table below the groundwater level at the end of previous time step [m-SL]
• theta_eq_uz – Equilibrium moisture content of root zone during current time step [mm]
• capris_max_uz – Maximum capillary rise in root zone during current time step [mm/d]
• p_uz_gw – Percolation from Unsaturated Zone to groundwater during current time step (positive: deep percolation, negative: capillary rise) [mm]
• theta_uz – Moisture content of root zone at the end of current time step [mm]

Return type:                         (dictionary)

2.6    Groundwater

In the Urbanwb Model, underneath the Unsaturated Zone is the saturated zone, i.e. the Groundwater reservoir (GW). The Groundwater reservoir is modelled as an unconfined aquifer which consists of a pervious layer underlain by a (semi-)impervious layer, below which lies the deep groundwater, one of the boundary components that exchanges water with the Urbanwb model. Percolation from Unsaturated Zone and Open Paved recharges the groundwater, while downward seepage to deep groundwater and drainage to Open Water deplete the Groundwater reservoir. The inflow (percolation from Unsaturated Zone) and outflow (seepage and drainage) are driven by the head difference, so the value of these fluxes can both be positive or negative. Figure 11  shows the schematic overview of the Groundwater reservoir. The area of the Groundwater reservoir is calculated as the area of the total model minus the area of Open Water fraction that is not above the groundwater level and minus the area of Paved Roof fraction of which the basement is below groundwater. The maximum capillary rise and the storage coefficient for the current time step are determined by interpolation based on the groundwater level at the end of the previous time step.

Figure   11      Schematic overview of groundwater reservoir (GW) in Urbanwb

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), q_s is downward seepage to deep groundwater, q_d 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: Image Modified            Drainage: Image Modified       Continuity: Image Modified

Substitution results in:

Initial condition:     Image Modified

2.6.1       Assumptions

• The infiltration water from Open Paved flows directly to the Groundwater (percolation), thus passing the Unsaturated Zone.
• The area of the Groundwater reservoir is equal to the total area minus the part of the Open Water area that lies below the groundwater level minus the part of the Paved Roof area of which the basement is below groundwater level.
• Drainage and seepage are calculated based on the groundwater level at the end of previous time step. Drainage and seepage are reduced due to the changing groundwater level caused by the fluxes. It means that the larger the head difference between shallow groundwater and deep groundwater (or Open Water) is, the larger the driving force is, and thus the larger the water flow is. With water exchanging, the head differences get smaller, so the water flows get smaller.

2.6.2       Calculation order

• Percolation to groundwater is the sum of percolation from Open Paved and percolation from Unsaturated Zone converted with the area ratios.
• Calculate runoff from measure to groundwater reservoir if defined possible.
• Determine the groundwater storage coefficient μ by interpolation, based on the groundwater level at the previous time step. In a database, for a given soil type, information is stored on storage coefficient for different groundwater levels (from 0 to 10 m-SL). The storage coefficient of groundwater during the current time step is interpolated from a lookup table based on the groundwater level at previous time step.
• Determine the groundwater level at the end of the current time step, based on the calculation formula mentioned above.
• Determine the total seepage to the deep groundwater (positive: downward, negative: upward) during current time step based on predefined seepage conditions. Seepage to deep groundwater can be defined either as a constant flux (0 is fixed flux) or a dynamically-computed flux (1 is level based) which depends on predefined hydraulic head of the deep groundwater and a vertical drainage resistance between the Groundwater reservoir and the deep groundwater.
• Determine the drainage from the Groundwater reservoir to the Open Water during current time step, based on a water balance. Note that here the drainage is a resulting parameter based on the other fluxes and the differences in groundwater volume (groundwater level and storage coefficient).
• Determine the groundwater level below surface level and groundwater above surface level at the end of current time step. They are dependent on groundwater level at the end of previous time step, the calculated percolation, seepage, drainage flux and storage coefficient μ during current time step.

2.6.3       Code and input arguments

class urbanwb.groundwater.Groundwater(gwl_t0, gw_no_meas_area, gw_meas_area, seepage_define=0, w=100, vc=20000, head_deep_gw=21.5, down_seepage_flux=1, soiltype=2, croptype=1, **kwargs)       [source]

Bases: _object

creates an instance of Groundwater class with given initial states and properties, iterates sol() function to compute states and fluxes of groundwater at each time step.

Parameters:

• gwl_t0 (float) – initial groundwater level (at t=0) [m-SL]
• gw_no_meas_area (float) – area of groundwater without measure [m^2]
• gw_meas_area (float) – area of groundwater with measure [m^2]
• seepage_define (int) – seepage to deep groundwater defined as either constant downward flux or dynamic computed flux which is determined by head difference and resistance [0=flux; 1=level]
• w (float) – drainage resistance from groundwater to Open Water [d]
• vc (float) – vertical flow resistance from shallow groundwater to deep groundwater [d]
• head_deep_gw (float) – predefined hydraulic head of deep groundwater [m-SL]
• down_seepage_flux (float) – predefined constant downward flux from shallow groundwater to deep groundwater [mm/d]
• soiltype (int) – soil type
• croptype (int) – crop type

sol(p_uz_gw, uz_no_meas_area, p_op_gw, op_no_meas_area, tot_meas_area, meas_gw, owl_prevt, delta_t=0.041666666666666664)  [source]

Calculates states and fluxes in groundwater during current time step.

Parameters:

• p_uz_gw (float) – percolation from Unsaturated Zone to groundwater during current time step [mm]
• uz_no_meas_area (float) – area of Unsaturated Zone without measure [m^2]
• p_op_gw (float) – percolation from Open Paved to groundwater during current time step [mm]
• op_no_meas_area (float) – area of Open Paved without measure [m^2]
• tot_meas_area (float) – total area of measure [m^2]
• meas_gw (float) – inflow from measure to groundwater during current time step [mm]
• owl_prevt (float) – Open Water level at previous time step [m-SL]
• delta_t (float) – length of time step [d]

Returns:                               A dictionary of computed states and fluxes of groundwater during current time step:

• sum_p_gw – Sum of percolation from Unsaturated Zone and percolation from Open Paved to groundwater during current time step [mm]
• r_meas_gw – Inflow from measure (if applicable) to groundwater during current time step [mm]
• gwl_up – First value in predefined lookup table above groundwater level at the end of previous time step [m-SL]
• gwl_low – First value in predefined lookup table below groundwater level at the end of previous time step [m-SL]
• sc_gw – Storage coefficient of groundwater for current time step [-]
• h_gw – Groundwater level at the end of current time step [m-SL]
• s_gw_out – Downward seepage from shallow groundwater to deep groundwater during current time step [mm]
• d_gw_ow – Groundwater drainage to Open Water during current time step [mm]
• gwl – Groundwater level below surface level at the end of current time step [m-SL]
• gwl_sl – Groundwater level above surface level at the end of current time step [m-SL]

Return type:                         (dictionary)

2.7      Sewer system

The sewer system in Urbanwb model is the combination of a Storm Water Drainage System (SWDS) and a Combined or Mixed Sewer System (MSS). Mixed implies a combined discharge of urban drainage and urban waste water. In urban areas both systems can be applied in practice. Hence, in the Urbanwb model the total paved area (PR, CP and OP) is split proportionally in a SWDS applied area (0 – 100%) and a MSS applied area (the rest). The proportion and system capacity of these systems should be predefined by the user to match the local situation. In dry to normal flow conditions, all water in a combined sewer system is transferred to waste water treatment plant (WWTP) for further treatment. In wet flow conditions (e.g. heavy rainstorms), a relief structure, a so called CSO weir, allows a large part of the combined storm- and waste water to be discharged untreated to an adjacent water body (e.g. a city pond). Combined sewer systems have two phases in wet flow conditions. In phase one, a combined sewer system collects water from paved areas and discharges it together with the urban waste water to a waste water treatment plant and the storage in the sewer system gets filled before sewer overflow through a CSO weir to Open Water occurs (phase 2). Sewer overflow of a combined system may impose pollution problems to the receiving water body. If rainfall is so extreme that the overflow discharge capacity is exceeded, then the sewer overflow into the street will occur. Opposite to combined sewer systems, in separated systems only waste water flows to the waste water treatment plant and only rainfall runoff enters the storm water drainage system, which drains this water directly to the surface water. The storm water drainage system is limited by a predefined system discharge capacity above which the sewer overflow into the street will occur. Figure 1 , in the first section of this document, provides a clear schematic overview of the sewer systems in the Urbanwb model.

2.7.1       Assumptions

• Discharge capacities of sewer systems cannot be directly defined in the configuration file. Since the Urbanwb model is originally developed based on study cases in the Netherlands, there are some localized settings for ease of use. Hence it is user’s responsibility to understand the model and tailor the input for more realistic modelling of their interest. The system discharge capacity of the SWDS and the MSS are derived based on rainfall intensities (T=2year, T=1/6year) and predefined sewer system storage capacities. In the Netherlands, a combined sewer system is designed to overflow approx. 6 times per year, so the MSS discharge capacity to the WWTP above which the sewer overflow occurs is calculated as a rainfall intensity with a return period T of 1/6 year. Sewer overflow through manholes into the street is designed to occur once every 2 year, so the sewer system discharge capacities to Open Water above which the sewer overflow into the street occurs, is calculated as a rainfall intensity with a return period T of 2 year. Storage capacities of sewer systems in the Netherlands are normally estimated at 2 mm (over the paved areas) for SWDS and 9 mm for MSS. Some detailed explanations can be found in the parameter estimation section.
• The total area of the two sewer systems together is equal to the total paved area (PR, CP and OP). The areas of SWDS and MSS are user defined, predefined ratios. The runoff from all three possible paved areas to the sewer systems is divided by these predefined ratios. It means, for example for an urban area that has 60% SWDS and 40% MSS, that 60% of the PR area runoff will be drained to SWDS, and 40% to the MSS. Same runoff division goes for the CP and OP areas. Note that applying adaptation measures, where (part of) the urban runoff flows to these measures, may change this. However, the ratio (in this example 60% : 40%) will be maintained for the part of the runoff that does not flow to these measures.

2.7.2       Calculation order

• Determine sum of runoff from paved areas (PR, CP, OP) and measure (if defined) to SWDS for the current time step. Determine outflow from SWDS to OW for the current time step based on storage in SWDS at previous time step, runoff from paved areas and measure. Outflow from SWDS to OW is limited by the discharge capacity of the SWDS.
• Determine sum of runoff from paved areas (PR, CP, OP) and measure (if defined) to MSS for the current time step. Determine outflow from MSS to WWTP for the current time step based on storage in MSS at previous time step, runoff from paved areas and measure. Outflow from MSS to WWTP is limited by the discharge capacity of the MSS.
• Determine outflow from MSS to OW for the current time step, which is limited by the discharge capacity of MSS to OW.
• Determine sewer overflow onto the street from SWDS for the current time step. This overflow water is drained at the same time step to Open Water by assumption.
• Determine sewer overflow onto the street from MSS for the current time step. This overflow water is drained the same time step to Open Water by assumption.
• Determine the remaining storage in the SWDS at the end of current time step. Storage is only used when the discharge capacity is exceeded by the inflow volume. Storage is limited to the storage capacity. All other excess water will result in overflow.
• Determine the remaining storage in the MSS at the end of current time step. Storage is only used when the discharge capacity is exceeded by the inflow volume. Storage is limited to the storage capacity. All other excess water will result in overflow.

2.7.3       Code and input arguments

Image Modified

class urbanwb.sewersystem.SewerSystem(swds_no_meas_area, mss_no_meas_area, stor_swds_t0, so_swds_t0, stor_mss_t0, so_mss_t0, q_swds_ow_cap, q_mss_out_cap, q_mss_ow_cap, storcap_swds=2.0, storcap_mss=9.0, **kwargs)                [source]

Bases: _object

Creates an instance of Sewer System class with given initial states and properties, iterates sol() function to compute states and fluxes of sewer system at each time step.

Parameters:

• swds_no_meas_area (float) – area of storm water drainage system (SWDS) without measure [m^2]
• mss_no_meas_area (float) – area of combined sewer system (MSS) without measure [m^2]
• stor_swds_t0 (float) – initial storage in storm water drainage system (SWDS) (at t=0) [mm]
• so_swds_t0 (float) – initial sewer overflow from storm water drainage system (SWDS) (at t=0) [mm]
• stor_mss_t0 (float) – initial storage in combined sewer system (MSS) (at t=0) [mm]
• so_mss_t0 (float) – initial sewer overflow from combined sewer system (MSS) (at t=0) [mm]
• q_swds_ow_cap (float) – discharge capacity of storm water drainage system (SWDS) to Open Water [mm/ timestep]
• q_mss_out_cap (float) – discharge capacity of combined sewer system (MSS) to waste water treatment plant (WWTP) [mm/ timestep]
• q_mss_ow_cap (float) – discharge capacity of combined sewer system (MSS) to Open Water [mm/ timestep]
• stor_swds_cap (float) – predefined storage capacity of storm water drainage system (SWDS) [mm]
• stor_mss_cap (float) – predefined storage capacity of combined sewer system (MSS) [mm]

sol(pr_no_meas_area, cp_no_meas_area, op_no_meas_area, r_pr_swds, r_cp_swds, r_op_swds, r_pr_mss, r_cp_mss, r_op_mss, meas_swds, meas_mss, ow_no_meas_area, tot_meas_area)                                           [source]

Calculates states and fluxes of sewer system during current time step.

Parameters:

• pr_no_meas_area (float) – area of Paved Roof without measure [m^2]
• cp_no_meas_area (float) – area of Closed Paved without measure [m^2]
• op_no_meas_area (float) – area of Open Paved without measure [m^2]
• r_pr_swds (float) – runoff from Paved Roof to storm water drainage system during current time step [mm]
• r_cp_swds (float) – runoff from Closed Paved to storm water drainage system during current time step [mm]
• r_op_swds (float) – runoff from Open Paved to storm water drainage system during current time step [mm]
• r_pr_mss (float) – runoff from Paved Roof to combined sewer system during current time step [mm]
• r_cp_mss (float) – runoff from Closed Paved to combined sewer system during current time step [mm]
• r_op_mss (float) – runoff from Open Paved to combined sewer system during current time step [mm]
• meas_swds (float) – inflow from measure (if applicable) to storm water drainage system during current time step [mm]
• meas_mss (float) – inflow from measure (if applicable) to combined sewer system during current time step [mm]
• ow_no_meas_area (float) – area of Open Water without measure [m^2]
• tot_meas_area (float) – total area of measure [m^2]

Returns:                               A dictionary of computed states and fluxes of sewer system during current time step:

• sum_r_swds – Sum of runoff from paved area to storm water drainage system during current time step [mm]
• r_meas_swds – Inflow from measure (if applicable) to storm water drainage system during current time step [mm]
• sum_r_mss – Sum of runoff from pave area to combined sewer system during current time step [mm]
• r_meas_mss – Inflow from measure (if applicable) to combined sewer system during current time step [mm]
• q_swds_ow – Outflow from storm water drainage system to Open Water during current time step [mm]
• q_mss_out – Discharge from combined sewer system to Waste Water Treatment Plant (WWTP) during current time step [mm]
• q_mss_ow – Outflow from combined sewer system to Open Water during current time step [mm]
• so_swds_ow – Sewer overflow from storm water drainage system during current time step [mm]
• so_mss_ow – Sewer overflow from combined sewer system during current time step [mm]
• stor_swds – Storage in storm water drainage system at the end of current time step [mm]
• stor_mss – Storage in combined sewer system at the end of current time step [mm]

Return type:                         (dictionary)

2.8      Open Water

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.

Image Modified

Figure   13      Schematic overview of Open Water (OW) in Urbanwb

2.8.1       Assumptions

• All runoff from UP in a time step flows to OW in that same time step.
• All sewer overflow into the street from SWDS and MSS in a time step flows directly to OW in that same time step.
• A target OW level is defined as a level below the surface level. This is the lower limit of the OW level. For instance, the target OW level is set 1.5 m-SL, then the computed OW level x can only be higher than this level (x ≤ 1.5). Above this level (x < 1.5), discharge from OW to outside water starts. The outside water is not part of the model, and discharge from OW to outside is only limited by a predefined pumping capacity. Note, this pumping capacity can be applied as the discharge capacity in the Storage-Discharge-Frequency (SDF) curves, where the storages are calculation results of the Urbanwb.

2.8.2       Calculation order

• Determine total runoff from UP to OW for the current time step.
• Determine drainage from GW to OW for the current time step.
• Determine total outflow from SWDS and MSS to OW and the total sewer overflow into the street from SWDS and MSS to OW for the current time step.
• Determine inflow from measure (if applicable) to OW for the current time step.
• Determine discharge from OW to outside water for the current time step.
• Determine OW level at the end of the current time step.

2.8.3       Code and input arguments

Image Modified

class urbanwb.openwater.OpenWater(ow_no_meas_area, q_ow_out_cap, ow_level, **kwargs)                  [source]

Bases: _object

Creates an instance of OpenWater class with given initial states and properties, iterates sol() function to compute states and fluxes of Open Water at each time step.

Parameters:

• ow_no_meas_area (float) – area of Open Water without measure [m^2]
• q_ow_out_cap (float) – discharge capacity from Open Water (internal) to outside water (external) [mm/d]
• ow_level (float) – predefined target Open Water level, also the initial Open Water level (at t=0) [m-SL]

sol(p_atm, e_pot_ow, r_up_ow, d_gw_ow, q_swds_ow, q_mss_ow, so_swds_ow, so_mss_ow, meas_ow, up_no_meas_area, gw_no_meas_area, swds_no_meas_area, mss_no_meas_area, tot_meas_area, tot_area, delta_t=0.041666666666666664)                [source]

Calculates states and fluxes on Open Water during current time step.

Parameters:

• p_atm (float) – rainfall during current time step [mm]
• e_pot_ow (float) – potential Open Water evaporation during current time step [mm]
• r_up_ow (float) – runoff from Unpaved to Open Water during current time step [mm]
• d_gw_ow (float) – drainage from groundwater to Open Water during current time step [mm]
• q_swds_ow (float) – Outflow from storm water drainage system (SWDS) to Open Water during current time step [mm]
• q_mss_ow (float) – Outflow from combined sewer system (MSS) to Open Water during current time step [mm]
• so_swds_ow (float) – Sewer overflow of storm water drainage system (SWDS) during current time step [mm]
• so_mss_ow (float) – Sewer overflow of combined sewer system (MSS) during current time step [mm]
• meas_ow (float) – inflow from measure (if applicable) to Open Water during current time step [mm]
• up_no_meas_area (float) – area of Unpaved without measure [m^2]
• gw_no_meas_area (float) – area of groundwater without measure [m^2]
• swds_no_meas_area (float) – area of storm water drainage system (SWDS) without measure [m^2]
• mss_no_meas_area (float) – area of combined sewer system (MSS) without measure [m^2]
• tot_meas_area (float) – total area of measure [m^2]
• tot_area (float) – total area of study area [m^2]
• delta_t (float) – length of time step [d]

Returns:                               A dictionary of computed states and fluxes of Open Water during current time step:

• prec_ow – Direct rainfall on Open Water during current time step [mm]
• e_atm_ow – Evaporation from Open Water during current time step [mm]
• sum_r_ow – Total runoff from Unpaved to Open Water during current time step [mm]
• sum_d_ow – Drainage from groundwater to Open Water during current time step [mm]
• sum_q_ow – Total outflow from sewer systems to Open Water during current time step [mm]
• sum_so_ow – Total sewer overflow from sewer systems to Open Water during current time step [mm]
• r_meas_ow – Inflow from measure (if applicable) to Open Water during current time step [mm]
• q_ow_out – Discharge from Open Water to outside water during current time step [mm]

Return type:                         (dictionary)

2.9      Measure 

Urban flooding is usually attributed to three types: pluvial flooding, fluvial flooding and coastal flooding. Pluvial flooding occurs when an extremely heavy rainfall saturates the storage capacity of the water system and excess water cannot be absorbed. Fluvial flooding occurs when rivers burst their bank as a result of sustained or intense rainfall. Coastal flooding occurs in coastal area as a result of extreme tidal conditions like storm surges. Unlike other types of flooding, pluvial flooding is a direct, quick and localized consequence of rainfall, and it is a predominantly urban phenomenon as it is in urban area where the effects are most pronounced and damaging (Susana). The Urbanwb model simulates only the pluvial flooding in urban water systems through two indicators, sewer overflow into the street and storage height above the target open water level. Climate change is predicted to increase the intensity and frequency of extreme rainfall events. Together with further urbanization and rapid growing population, this may result in increased urban pluvial flood risks. To effectively adapt to increasing flood risks, a combination of intervention strategies is required, including structural infrastructure, nature-based solutions, early warning system, risk financing instrument, etc. The Urbanwb model is capable of modelling all kinds of physical adaptation measures. Physical measures can be categorized into artificial structural infrastructure and nature-based solutions. Structural infrastructure refers to grey infrastructure are considered to be engineering projects that use concrete and steel, while nature-based solutions refer to blue-green infrastructure that depend on water, plants and ecosystem services. Blue-green infrastructure is the strategic use of networks of natural lands, working landscapes, and other open spaces to conserve ecosystem values and functions and provide associated benefits to human populations (Benedict & McMahon, 2006). Blue-green infrastructure is generally decentralized. Water is captured and treated where it falls, rather than being transported to a treatment facility. Blue-green infrastructure terminology can also be used in the context of low impact development (LID). Grey infrastructure refers to the human-engineered infrastructure for water resources such as water and wastewater treatment plants, pipelines, and reservoirs. Grey infrastructure typically refers to components of a centralized approach to water management. Examples of grey infrastructure are canals, levees, ditches, raised curbs, underground off-line tanks, etc. Examples of blue-green infrastructure are rainwater harvesting, water squares, urban wetlands, green roofs, bioswales, etc. A module named Measure is creatively developed in the Urbanwb model to model the physical urban adaptation measures. With the ingenious setup of this module, underlying mechanisms of these physical measures are simulated and incorporated into the dynamics of the entire modelling of water system. The next sections provide detailed descriptions on the structure of the Measure module.

Measures mitigate urban flooding by means of creating extra storage, encouraging evapotranspiration, facilitating infiltration, increasing drainage and the combination of these interventions. Consequently, despite many types/terms of urban adaptation measures, they can be categorized and modelled under certain framework with specific settings. The underlying idea and fundamental principle of this Measure module is to provide a general adaptive framework that represents the measures’ physical dimensions and that mimics the measures’ predominant functionality.

Measures in the Urbanwb model can be defined in a 1-layer, 2-layer or 3-layer structure (Figure 14 ).

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Figure   14      Layer principle of measures in Urbanwb

1-layer structures contain only an interception layer (layer no. 1), which can represent the type of measures that creates storage and allows evaporation. A typical example of a 1-layer measure is a blue roof.

2-layer structures consist of 2 layers, an interception layer (layer no. 1) and a bottom storage layer (layer no.3). The bottom storage layer is the most sophisticated part of the measure module. In the bottom storage layer, evapotranspiration, percolation to groundwater and controlled runoff (to anywhere) can be defined by the user. Controlled runoff means the runoff volume that is first stored in the measure is discharged in a controlled way. Basically, controlled runoff implies either “continuously delayed released” to the urban water system or “instantaneously released at a much later time”, when the urban water system is able to handle this runoff again, most likely by means of real time control systems. Urban water system is referring to the entire water system, hence incorporating all elements described in the sections above. In the current Urbanwb model real time control is not incorporated and is simulated by a small constant discharge over a large number of time steps to one of the subsystems SWDS, GW, OW. Continuous slow release is defined as a dynamically-computed flux that dependents on a head difference and a flow resistance. Examples of 2-layer measures are rain barrel, wet pond, infiltration box, etc.

3-layer structures consist of 3 layers, an interception layer (layer no. 1), a top storage layer (layer no. 2) and a bottom storage layer (layer no.3). Extra, compared to the 2-layer measures is the top storage layer. This layer is especially added to model measures like green roofs and bioswales. These measures have a growing medium that encourages evapotranspiration and a drainage layer beneath the growing medium that drains excessive water to the sewer system. Some examples are provided in next paragraph to inspire the user how to conceptualize a measure into this Measure module.

The setup of the measures involves expert judgement: “the model is only as good as the modeler”.

Below some examples of how to conceptualize measures are provided:

• Blue roof
  Blue roofs (without drainage) create extra water storage on buildings from where water can evaporate. A blue roof can be considered as a storage installation. In the Urbanwb model, it can be simulated with the basic model or with the Measure module. Simulating a blue roof with the basic model can be done by increasing the PR interception capacity. However, then interception capacity of the entire PR area increases. To simulate that in only part of the PR area blue roofs are applied, the Measure module can be used. A blue roof can be conceptualized as a 1-layer structure of which an interception layer with certain storage capacity is defined from where only evaporation is possible. Exceedance of the storage capacity results in overflow. Overflow from a blue roof is considered to be uncontrolled runoff and will be drained to the SWDS.
• Wet pond:
  Figure 15 shows the schematic view of how a wet pond is conceptualized. An artificial wet pond can be seen as a 2-layer structure, of which the interception layer is a pseudo layer that has no storage capacity and infinite infiltration capacity, allowing all water (precipitation and inflow runoff from contributing area) to flow directly into the bottom storage layer. A wet pond usually has a sealed concrete bottom to prevent it from falling dry thus percolation is defined not possible. The wet pond has a certain threshold (drainage level) above which the excess water is slowly drained. This runoff is called controlled runoff. The higher the water level in the pond above this threshold, the faster it drains. In addition, a drainage resistance has to be defined by the user to determine how fast it drains. Evaporation from the pool is possible and is limited by Penman evaporation. In case of very extreme rainfall events, incoming runoff may completely fill the storage capacity of wet pond, hence overflow from the wet pond occurs. Unlike controlled runoff from bottom storage layer, this overflow is an uncontrolled runoff, and will be drained eventually to SWDS.
  
  Figure 15   Conceptualization of a wet pond. Source left figure: [LID].

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