Page History

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The urban water balance tool (Figure 1) has been developed in EXCEL for application in urban area. Recently it has been transformed into a set of Python scripts. The water balance tool describes all possible urban water flows and the associated water resources. Rainfall-runoff, shallow groundwater (saturated and unsaturated), surface water and sewage (both mixed and stormwater drainage) are included. Water exchanges are included with atmosphere, deep groundwater, outside water and waste water treatment plant.

Figure 1      Schematic overview of Urbanwb model

In this figure:

History

Originally the time step was 1 day. That way time series of more than 100-year rainfall and evaporation could be managed in EXCEL. A smaller time step could also be applied (1 hour, 15 minutes, 5 minutes). However, because of the limitations of EXCEL, a smaller time step implies much shorter time series. Transforming the water balance tool to a set of Python scripts solved this limitation. This set of Python scripts that has been combined in the Urbanwb model. This documentation describes the Urbanwb model.

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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

1. 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.
2. 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.
3. 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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Paved Roof (PR) refers to all kinds of buildings in an urban area ranging from low-rise buildings (e.g. single dwelling, apartment complex) to high-rise buildings (e.g. high-rise housing, skyscraper). On rooftop, a roof drainage system collects rainwater in gutters and drains it into a sewer through a downspout pipe. A small amount of rainwater ponded or intercepted on the roof surface is defined as interception storage. It can be emptied only through evaporation. Water exceeding the interception storage capacity becomes runoff on the Paved Roof. Basically, all runoff ends in the sewer system (SWDS and/or MSS). However, the Urbanwb offers the option of disconnecting (part of) the runoff. The disconnected part of the runoff is assumed to flow to the Unpaved area. Figure 4  provides a schematic overview.

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 Figure   4        Schematic overview of Paved Roof (PR) in Urbanwb

2.1.1       Assumptions

• Rainwater falling on the building roof is first retained as interception storage and depleted by evaporation, and then excess water becomes runoff. In other words, only rainfall exceeding interception storage capacity runs off. Provided that a considerably large interception storage capacity on Paved Roof is predefined, there is no runoff generated.
• (Connected) runoff on Paved Roof is redistributed to sewer systems (SWDS and MSS) and Unpaved (UP) by predefined ratios. If part of roof is disconnected to sewer system, for instance a minor fraction of water flows out from the roof edge down to the ground directly, that disconnected fraction of runoff is assumed to flow to Unpaved area. However, given a normally functioning roof drainage system, the majority of the runoff from Paved Roof contributes to the storm water drainage system (SWDS) or (and) combined sewer system (MSS) at predefined proportions.

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2.1.3       Code and input arguments

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class urbanwb.pavedroof.PavedRoof(intstor_pr_t0, pr_no_meas_area, pr_meas_area, pr_meas_inflow_area, intstorcap_pr=1.6, swds_frac=1.0, discfrac_pr=0.0, **kwargs)          [source]

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

Parameters:

• intstor_pr_t0 (float) – initial interception storage on Paved Roof (at t=0) [mm]
• r_no_meas_area (float) – area of Paved Roof without measure [m^2]
• pr_meas_area (float) – area of Paved Roof with measure [m^2]
• pr_meas_inflow_area (float) – measure inflow area from Paved Roof, i.e. runoff inflow area to measure from Paved Roof (>= area of Paved Roof with measure and <= total area of Paved Roof) [m^2]
• intstorcap_pr (float) – predefined interception storage capacity on Paved Roof [mm]
• swds_frac (float) – part of urban paved area with storm water drainage system (SWDS) [-]
• discfrac_pr (float) – part of Paved Roof that is disconnected from sewer system [-]

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Calculates measure inflow factor of Paved Roof.

Returns:                               Measure inflow factor of Paved Roof

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Return type:                         (float)

sol(p_atm, e_pot_ow)       [source]

Calculates states and fluxes on Paved Roof 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]

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

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Closed Paved areas are mainly areas with paved covers like roads, parking lots, driveways, etc. that are made of impermeable material like cement and bituminous concrete pavement. In terms of conceptual modelling mechanisms, Closed Paved is quite similar to Paved Roof. On the surface of a typical impermeable paved area, a small amount of rainwater is intercepted as surface ponding which can only be emptied through evaporation. Rainfall exceeding the interception storage capacity will generate runoff, which flows to the sewer system (SWDS and/or MSS). The disconnected fraction of runoff is assumed to flow to the Unpaved area (UP). Figure 5  provides a schematic overview.

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Figure   5        Schematic overview of Closed Paved (CP) in Urbanwb

2.2.1       Assumptions

• Rainwater falling on the Closed Paved is first ponded as surface interception storage and depleted by evaporation, then the excessive rainwater becomes runoff. In other words, only rainfall exceeding the interception storage capacity runs off. Provided that a very large interception storage capacity on Closed Paved is predefined, there is no runoff generated.
• Runoff on the Closed Paved is redistributed to sewer system (SWDS and MSS) and Unpaved (UP) by predefined ratios. If part of Closed Paved area is disconnected to the sewer system, that disconnected fraction of runoff flows to Unpaved area by assumption. Connected runoff on Closed Paved flows to the storm water drainage system (SWDS) or (and) combined sewer system (MSS) at predefined proportions.

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2.2.3       Code and input arguments

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class urbanwb.closedpaved.ClosedPaved(intstor_cp_t0, cp_no_meas_area, cp_meas_area, cp_meas_inflow_area, intstorcap_cp=1.6, swds_frac=1.0, discfrac_cp=0.0, **kwargs)         [source]

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

Parameters:

• intstor_pr_t0 (float) – initial interception storage on Closed Paved (at t=0) [mm]
• pr_no_meas_area (float) – area of Closed Paved without measure [m^2]
• cp_meas_area (float) – area of Closed Paved with measure [m^2]
• cp_meas_inflow_area (float) – measure inflow area from Closed Paved, i.e. runoff inflow area to measure from Closed Paved (>= area of Closed Paved with measure and <= total area of Closed Paved) [m^2]
• intstorcap_cp (float) – predefined interception storage capacity on Closed Paved [mm]
• swds_frac (float) – part of urban paved area with storm water drainage system (SWDS) [-]
• discfrac_cp (float) – part of Closed Paved that is disconnected from sewer system [-]

inflowfac()                            [source]

Calculates measure inflow factor of Closed Paved.

Returns:                               Measure inflow factor of Closed Paved

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Return type:                         (float)

sol(p_atm, e_pot_ow)       [source]

Calculates states and fluxes on Closed Paved 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]

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

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Open Paved areas are paths, sidewalks, parking area and other less imperviously paved areas that have relatively limited infiltration capacity. These somewhat permeable pavements use porous material that allows water flowing through it (e.g. pervious concrete, porous asphalt) or spaced nonporous material (e.g. paving stones, permeable interlocking concrete pavement) that allows water infiltrate between the cracks (Figure 6 ). Consequently, compared to the Paved Roof (PR) and Closed Paved (CP) components, the Open Paved (OP) component has an extra infiltration flux from Open Paved surface to groundwater. This infiltration flux is limited by an infiltration capacity as well as by the available interception storage on the Open Paved area. Rainfall exceeding the interception storage capacity will generate runoff, which flows to the sewer system (SWDS and/or MSS). The disconnected fraction of runoff is assumed to flow to the Unpaved area (UP). Figure 7  provides a schematic overview.

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Figure   6        Permeable pavement — porous asphalt and interlocking pavement, source: google images.

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Figure 7      Schematic overview of Open Paved (OP) in Urbanwb 

2.3.1       Assumptions

• On Open Paved, cracks on the pavement and pores in the material that allow infiltration only occupy a very minor fraction of Open Paved surface area. Hence it does not affect the interception storage capacity on Open Paved surface.
• Infiltration starts after interception storage is filled and it is limited by predefined infiltration capacity. Interception storage can only be emptied through evaporation.
• There is no vegetation on the Open Paved area, and consequently no transpiration from root zone below the surface. Hence, for simplicity, the infiltration from Open Paved surface is directly percolating into the groundwater (GW) and passes the Unsaturated Zone.

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2.3.3       Code and input arguments

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class urbanwb.openpaved.OpenPaved(intstor_op_t0, op_no_meas_area, op_meas_area, op_meas_inflow_area, intstorcap_op=1.6, infilcap_op=1.0, swds_frac=1.0, discfrac_op=0.0, **kwargs)         [source]

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

Parameters:

• intstor_pr_t0 (float) – initial interception storage on Closed Paved (at t=0) [mm]
• intstor_op_t0 (float) – initial interception storage on Open Paved (at t=0) [mm]
• op_no_meas_area (float) – area of Open Paved without measure [m^2]
• op_meas_area (float) – area of Open Paved with measure [m^2]
• op_meas_inflow_area (float) – measure inflow area from Open Paved, i.e. runoff inflow area to measure from Open Paved (>= area of Open Paved with measure and <= total area of Open Paved) [m^2]
• intstorcap_op (float) – predefined interception storage capacity on Open Paved [mm]
• infilcap_op (float) – predefined infiltration capacity on Open Paved [mm/d]
• swds_frac (float) – part of urban paved area with storm water drainage system (SWDS) [-]
• discfrac_op (float) – part of Open Paved that is disconnected from sewer system [-]

inflowfac()                            [source]

Calculates measure inflow factor of Open Paved.

Returns:                               measure inflow factor of Open Paved

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Return type:                         (float)

sol(p_atm, e_pot_ow, delta_t)        [source]

Calculates states and fluxes on Open Paved 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]
• delta_t (float) – length of time step [d]

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

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Unpaved area is a land use type that has no paved surface cover, e.g. gardens and grassland, on which the water can much more easily infiltrate than on paved surface. Vegetation (crop) type on the Unpaved area needs to be predefined. The model assumes notable distinction between paved areas (PR, CP and OP) and unpaved areas (UP). From paved areas, excess water is mainly drained through the sewer system. From unpaved areas, excess water mainly infiltrates to the unsaturated zone underneath, percolates to the groundwater and is drained via groundwater flow to the drainage system (open water). Rainfall water stored in the interception layer at the surface simultaneously evaporates to the atmosphere and infiltrates to Unsaturated Zone. Water exceeding the interception storage capacity is assumed to runoff to Open Water (OW). Figure 8  provides a schematic overview.

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Figure   8        Schematic overview of Unpaved (UP) in Urbanwb

2.4.1       Assumptions

• Disconnected runoff from paved area is equally spread over the Unpaved area. This runoff is added to the water available for infiltration and evaporation.
• The interception capacity on Unpaved area is defined as the water depth above which surface runoff generates. Interception capacity of vegetation is not separately defined. Evaporation by the vegetation is taken up in the transpiration from Unsaturated Zone (UZ). Evaporation and infiltration from the Unpaved surface will occur as long as water remains on surface level.
• Infiltration starts after (initial) interception storage contains water. (Initial) interception storage is proportionally emptied by infiltration and evaporation. The excessive part from interception storage capacity becomes runoff. Infiltration is limited by actual infiltration capacity and available storage in the Unsaturated Zone. Evaporation is limited by the potential open water evaporation during that time step. Infiltration and evaporation during a times step occur simultaneously and are limited by the available initial interception storage.
• Actual infiltration capacity during current time step is limited by the actual available free space in the Unsaturated Zone, i.e. the maximum moisture content minus the actual moisture content in root zone during the same time step. However, the anticipated percolation from Unsaturated Zone to Groundwater during the same time step allows more infiltration. The anticipated percolation is limited by the saturated permeability of the soil and the available water for percolation.
• A defined Time factor is that part of the time step that water is remaining on surface level. Potential Open Water evaporation is multiplied with this time factor to get the actual evaporation of the Unpaved area for that time step. The actual infiltration capacity is multiplied with this time factor to get the actual infiltration from the Unpaved area to the Unsaturated Zone for that time step.
• Rainwater falling on Unpaved areas together with runoff from disconnected paved area is first intercepted as (initial) surface interception storage and emptied by evaporation and infiltration, then the excessive rainwater becomes runoff. In other words, only rainfall exceeding the interception storage capacity runs off. Provided that a considerably large interception storage capacity on Unpaved areas is predefined, there is no runoff generated.
• Except runoff from UP to measure when defined possible, all other runoff water on Unpaved flows to Open Water (OW) by assumption. If no Open Water area is present, the water cannot runoff and will be stored on the surface of Unpaved. In that case the water can only evaporate or infiltrate. However, for current version Urbanwb Model, the possibility of no Open Water presence has not yet been fully investigated and tested. Hence, to avoid potential errors, we advise to specify non-zero fraction for Open Water (OW).

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2.4.3       Code and input arguments

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class urbanwb.Unpaved.Unpaved(fin_intstor_up_t0, up_no_meas_area, up_meas_area, up_meas_inflow_area, intstorcap_up=20, infilcap_up=48, soiltype=2, croptype=1, **kwargs)            [source]

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

Parameters:

• fin_intstor_up_t0 – initial final remaining interception storage on Unpaved (at t=0) [mm]
• up_no_meas_area (float) – area of Unpaved without measure [m^2]
• up_meas_area (float) – area of Unpaved with measure [m^2]
• up_meas_inflow_area (float) – measure inflow area from Unpaved, i.e. runoff inflow area to measure from Unpaved (>= area of Unpaved with measure and <= total area of Unpaved) [m^2]
• intstorcap_up (float) – predefined interception storage capacity on Unpaved [mm]
• infilcap_up (float) – predefined infiltration capacity on Unpaved [mm/d]
• soiltype (int) – soil type
• croptype (int) – crop type

inflowfac()                            [source]

Calculates measure inflow factor of Unpaved.

Returns:                               measure inflow factor of Unpaved

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Return type:                         (float)

sol(p_atm, e_pot_ow, r_pr_up, r_cp_up, r_op_up, theta_uz_prevt, pr_no_meas_area, cp_no_meas_area, op_no_meas_area, ow_no_meas_area, delta_t=0.041666666666666664)           [source]

Calculates states and fluxes on Unpaved 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_pr_up (float) – runoff from Paved Roof to Unpaved during current time step [mm]
• r_cp_up (float) – runoff from Closed Paved to Unpaved during current time step [mm]
• r_op_up (float) – runoff from Open Paved to Unpaved during current time step [mm]
• theta_uz_prevt (float) – moisture content of root zone at previous time step [mm]
• 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]
• ow_no_meas_area (float) – area of Open Water without measure [m^2]
• delta_t (float) – length of time step [d]

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

• sum_r_up – Sum of runoff from all paved areas to Unpaved during current time step [mm]
• init_intstor_up – Initial interception storage on Unpaved after rainfall at the beginning of current time step [mm]
• actl_infilcap_up – Actual infiltration capacity on Unpaved during current time step [mm]
• mefac_up – Time factor, i.e. part of time step that interception storage on Unpaved is available for infiltration and evaporation during current time step [-]
• e_atm_up – Evaporation from interception storage on Unpaved during current time step [mm]
• i_up_uz – Infiltration from interception storage on Unpaved to Unsaturated Zone during current time step [mm]
• fin_intstor_up – Final remaining interception storage on Unpaved at the end of current time step [mm]
• r_up_meas – Runoff from Unpaved to measure during current time step (not necessarily on Unpaved itself) [mm]
• r_up_ow – Runoff from Unpaved to Open Water during current time step [mm]

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Figure 9  shows the schematic overview of the Unsaturated Zone. Two important definitions are recapped here. Field capacity is the amount of water that a well-drained soil can hold against gravitational forces. In the absence of water supply, the water content in the root zone decreases as result of water uptake by the crop. As water uptake progresses, the remaining water is held to the soil particles with greater force, lowering its potential energy and making it more difficult for the plant to extract it. Eventually, the so called wilting point is reached where the crop can no longer extract the remaining water in the soil and the water uptake becomes zero. The wilting point is the soil water content at which plants will permanently wilt.

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Figure   9        Schematic overview of Unsaturated Zone (UZ) in Urbanwb

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The threshold pressure h₃ increases with potential transpiration rates, i.e. daily crop-evaporation. For low potential transpiration rate, the threshold pressure h_3l is lower than the threshold pressure h_3h at high potential transpiration rate. Computational simplifications are made here to calculate daily crop-evaporation value. Evaporation data are often provided on daily basis. When the Urbanwb model is applied for smaller time steps (Δt), we derive the hourly values of h₃ based on the daily evaporation values by divided by 2Δt, where Δt is expressed in days (e.g. Δt = 1 hour = 1/24 day). The factor 2 is applied, based on the assumptions that evapotranspiration mainly occurs during day time and that day time lasts on average 12 hours.

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Figure   10      Transpiration reduction coefficient in Urbanwb (i.e. plant water stress factor) in relation to root zone water potential. Source: Dejongvanlier et al, 2008.

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2.5.3       Code and input arguments

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

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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:

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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.

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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.

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Figure 12   Groundwater level h(t) calculation

The basic applied formula is:    Image Added

Seepage: Image Removed  Image Added     Drainage: Image Added         Drainage   Continuity: Image Removed       Continuity: Image Removed

Substitution results in:

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Initial condition:     Image Removed

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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

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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]

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Example (check):

h(t) = 1 m –MV; PP = 1.5 m –MV; H = 2 m –MV; c = 1000 d; w = 50 d :

q_s = (2 – 1) / 1000 = 0.001 m/d = 1 mm/d (downward)

q_d = (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:

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Rewritten:

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Solving:

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Initial condition:     Image Added

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Resulting in:

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Drainage (q_d) and seepage (q_s) 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:

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Rewritten:

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Solving:

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Initial condition:     Image Added

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Resulting in:

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Drainage (q_d) is automatically calculated in depth per day, because the size of the flow resistances (w) is expressed in day.

Seepage (q_s) 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

• 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

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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 Calculates states and fluxes in groundwater during current time step.

Parameters:

• pgwl_uz_gwt0 (float) – percolation from Unsaturated Zone to groundwater during current time step [mm]initial groundwater level (at t=0) [m-SL]
• gwuz_no_meas_area (float) – area of Unsaturated Zone groundwater without measure [m^2]
• pgw_opmeas_gwarea (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]
• 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 owl_prevt (float) – Open Water level at previous time step [m-SL]
• deltadown_seepage_tflux (float) – length of time step [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 Returns:                               A dictionary of computed states and fluxes of groundwater during current time step.

Parameters:

• sump_puz_gw (float) – Sum of percolation from Unsaturated Zone and percolation from Open Paved to groundwater during current time step [mm]
• ruz_no_meas_gwarea (float) – area of Unsaturated Zone without measure [m^2]
• p_op_gw (float) – percolation from Open Paved – 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 [-]
• 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 h_gw – Groundwater level at the end of current 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 s_gw_out – Downward seepage from shallow groundwater to deep groundwater during current time step [mm]
• dr_meas_gw_ow – Groundwater drainage to Open Water – Inflow from measure (if applicable) to groundwater during current time step [mm]
• gwl – Groundwater level below surface _up – First value in predefined lookup table above groundwater level at the end of current previous time step [m-SL]
• gwl_sllow – 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 – Groundwater level above surface level at the end of current time step [m-SL]

...

• 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 (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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• 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].

• Bioswale and green roof
  Figure 16 shows the schematic view of how a bioswale is conceptualized. A bioswale is an infiltration installation. An bioswale can be thought as a 3-layer structure, of which the surface vegetated soil is the interception layer that provides limited storage capacity and facilitates infiltration to the growing medium. The growing medium is the top storage layer where plant transpiration and soil evaporation occur. After evapotranspiration, excessive water infiltrates into the bottom drainage layer. Below the growing medium is the gravel drainage layer encouraging water percolating into the groundwater reservoir. Here the percolation flux can be modelled either as percolation to groundwater limited by saturated permeability of soil, or as a controlled runoff to groundwater dependent on predefined drainage level and resistance to mimic the water jamming. Evaporation from the bottom drainage layer is possible when potential evapotranspiration rate exceeds the transpiration from growing medium (top storage layer), to simulate that the plant roots can uptake water from drainage layer for further transpiration. Overflow from the bottom drainage layer and surface overflow from interception layer together form the uncontrolled runoff, which will be drained to the SWDS. Similar to a bioswale, a green roof is also modelled as a 3-layer structure. However, there are two major differences: 1. A green roof is installed on the building roof, thus controlled runoff directs to the SWDS instead of to GW; 2. The calculation formula for green roofs is specifically modified to make sure no surface submergence from green roof is possible because a normally functioning green roof should have no water logging on the surface.
  
  Figure 16   Conceptualization of a bioswale. Source left figure: [LID].

2.9.1       Assumptions

• A measure can be defined as 3-layer. Even though the area of each layer of measure can be defined different, it is not recommended to do so because it has not been fully tested yet.
• The measure inflow area does not necessarily come from one source. For instance, if a measure is defined in the OP area, it is possible to define the measure inflow area not only in the OP area but also in the PR and the CP area. However, these possibilities have not been fully developed and tested yet. It’s users’ responsibility to pay attention to the boundary conditions of the model.
• Not all measures can be implemented with Measure module or implemented with the Urbanwb model. The user should understand the correct way of using this Urbanwb model and should be careful with the limitations of this model.

...

• 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

2.9.3       Code and input arguments

Image Modified

class urbanwb.measure.Measure(tot_meas_area, runoff_to_stor_layer, intstor_meas_t0, EV_evaporation, num_stor_lvl, infilcap_int_meas, storcap_top_meas, storcap_btm_meas, stor_top_meas_t0, stor_btm_meas_t0, storcap_int_meas, top_meas_area, ET_transpiration, evaporation_factor_meas, IN_infiltration, infilcap_top_meas, btm_meas_area, btm_meas_transpiration, connection_to_gw, limited_by_gwl, k_sat_uz, btm_level_meas, btm_discharge_type, runoffcap_btm_meas, dischlvl_btm_meas, c_btm_meas, surf_runoff_meas_OW, ctrl_runoff_meas_OW, overflow_meas_OW, surf_runoff_meas_UZ, ctrl_runoff_meas_UZ, overflow_meas_UZ, surf_runoff_meas_GW, ctrl_runoff_meas_GW, overflow_meas_GW, surf_runoff_meas_SWDS, ctrl_runoff_meas_SWDS, overflow_meas_SWDS, surf_runoff_meas_MSS, ctrl_runoff_meas_MSS, overflow_meas_MSS, surf_runoff_meas_Out, ctrl_runoff_meas_Out, overflow_meas_Out, greenroof_type_measure, **kwargs)          [source]

...

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

Parameters:

• tot_meas_area (float) – total area of measure [m^2]
• num_stor_lvl (int) – predefined number of storage layers [1, 2 or 3]
• runoff_to_stor_layer (int) – predefined selection at which measure layer runoff from other area is stored, inflow runoff can only take place at interception layer (1) or at bottom storage layer (3) [1 or 3]
• Active processes (#) –
• EV_evaporation (int) – predefined selection if evaporation from measure interception layer is possible (1) or not (0) [0 or 1]
• ET_transpiration (int) – predefined selection if evapotranspiration from measure is possible (1) or not (0) [0 or 1]
• IN_infiltration (int) – predefined selection if infiltration from measure is possible (1) or not (0) [0 or 1]
• SD_delay (int) – predefined selection if slow drainage from measure is possible (1) or not (0) [0 or 1]
• FD_pumping (int) – predefined selection if fast drainage from measure is possible (1) or not (0) [0 or 1]
• RTC_realtime (#) – predefined selection if real- me-control release from measure is possible (1) or not (0) [0 or 1]
• Interception layer (#) –
• storcap_int_meas (float) – predefined storage capacity of interception layer of measure [mm]
• infilcap_int_meas (float) – predefined infiltration capacity of interception layer of measure [mm/d]
• stor_int_meas_t0 (float) – initial storage in interception layer of measure (at t=0) [mm]
• Top storage layer (#) –
• top_meas_area (float) – predefined area of top storage layer of measure [m^2]
• storcap_top_meas (float) – predefined storage capacity of top storage layer of measure [mm]
• infilcap_top_meas (float) – predefined infiltration capacity of top storage layer of measure [mm/d]
• stor_top_meas_t0 (float) – initial storage in top storage layer of measure (at t=0) [mm]
• Bottom storage layer (#) –
• btm_meas_area (float) – predefined area of bottom storage layer of measure [m^2]
• storcap_btm_meas (float) – predefined storage capacity of bottom storage layer of measure [mm]
• connection_to_gw (int) – predefined percolation (connection) from measure bottom storage layer to groundwater is possible (1) or not (0) [0 or 1]
• limited_by_gwl (int) – predefined limitation of percolation from measure to groundwater if groundwater level is below measure bottom level, limited (1) or unlimited (0) [0 or 1]
• btm_level_meas (float) – predefined bottom level of measure [m-SL]
• btm_meas_transpiration (int) – predefined selection if transpiration from bottom storage layer of measure is possible (1) or not (0) [0 or 1]
• btm_discharge_type (int) – predefined discharge type from bottom storage layer of measure [0:flux or 1:level]
• runoffcap_btm_meas (float) – predefined runoff capacity from bottom storage layer of measure [mm/d]
• dischlvl_btm_meas (float) – predefined discharge level from bottom storage layer of measure [mm]
• c_btm_meas (float) – predefined hydraulic resistance for level induced discharge from bottom storage layer of measure [d]
• k_sat_uz (float) – saturation permeability of soil [mm/d]
• evaporation_factor_meas (float) – predefined evaporation factor of measure [-]
• stor_btm_meas_t0 (float) – initial storage in bottom storage layer of measure (at t=0) [mm]
• Runoff from measure flows to (#) –
• surf_runoff_meas_OW (int) – predefined definition of surface runoff from measure storage 1 (interception level) to Open Water (0 = no, 1 = yes)
• ctrl_runoff_meas_OW (int) – predefined definition of controlled runoff from measure storage 3 (bottom level) to Open Water (0 = no, 1 = yes)
• overflow_meas_OW (int) – predefined definition of overflow from measure storage 3 (bottom level) to Open Water (0 = no, 1 = yes)
• surf_runoff_meas_UZ (int) – predefined definition of surface runoff from measure storage 1 (interception level) to Unsaturated Zone (0 = no, 1 = yes)
• ctrl_runoff_meas_UZ (int) – predefined definition of controlled runoff from measure to Unsaturated Zone (0 = no, 1 = yes)
• overflow_meas_UZ (int) – predefined definition of overflow from measure to Unsaturated Zone (0 = no, 1 = yes)
• surf_runoff_meas_GW (int) – predefined definition of surface runoff from measure to groundwater (0 = no, 1 = yes)
• ctrl_runoff_meas_GW (int) – predefined definition of controlled runoff from measure to groundwater (0 = no, 1 = yes)
• overflow_meas_GW (int) – predefined definition of overflow from measure to groundwater (0 = no, 1 = yes)
• surf_runoff_meas_SWDS (int) – predefined definition of surface runoff from measure to storm water drainage system (0 = no, 1 = yes)
• ctrl_runoff_meas_SWDS (int) – predefined definition of controlled runoff from measure to storm water drainage system (0 = no, 1 = yes)
• overflow_meas_SWDS (int) – predefined definition of overflow from measure to storm water drainage system (0 = no, 1 = yes)
• surf_runoff_meas_MSS (int) – predefined definition of surface runoff from measure to mixed sewer system (0 = no, 1 = yes)
• ctrl_runoff_meas_MSS (int) – predefined definition of controlled runoff from measure to mixed sewer system (0 = no, 1 = yes)
• overflow_meas_MSS (int) – predefined definition of overflow from measure to mixed sewer system (0 = no, 1 = yes)
• surf_runoff_meas_Out (int) – predefined definition of surface runoff from measure to outside water (0 = no, 1 = yes)
• ctrl_runoff_meas_Out (int) – predefined definition of controlled runoff from measure to outside water (0 = no, 1 = yes)
• overflow_meas_Out (int) – predefined definition of overflow from measure to outside water (0 = no, 1 = yes)

sol(p_atm, e_pot_ow, r_pr_meas, r_cp_meas, r_op_meas, r_up_meas, pr_no_meas_area, cp_no_meas_area, op_no_meas_area, up_no_meas_area, gw_no_meas_area, gwl_prevt, delta_t)          [source]

Calculates states and fluxes in measure 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_pr_meas (float) – runoff from Paved Roof to measure during current time step [mm]
• r_cp_meas (float) – runoff from Closed Paved to measure during current time step [mm]
• r_op_meas (float) – runoff from Open Paved to measure during current time step [mm]
• r_up_meas (float) – runoff from Unpaved to measure during current time step [mm]
• pr_no_meas_area (float) – area of Paved Roof without measure [m^2]
• cp_no_meas_area (float) – area of closed pave without measure [m^2]
• op_no_meas_area (float) – area of Open Paved without measure [m^2]
• up_no_meas_area (float) – area of Unpaved without measure [m^2]
• gw_no_meas_area (float) – area of groundwater without 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 measure during current time step:

• prec_meas – Direct rainfall on measure during current time step [mm]
• sum_r_meas – Total runoff from Paved Roof, Closed Paved, Open Paved, Unpaved to measure during current time step [mm]
• int_meas – Interception storage on interception layer of measure after rainfall at the beginning of current time step [mm]
• e_atm_meas – Evaporation form interception layer of measure during current time step [mm]
• interc_down_meas – Downward flow from interception layer of measure during current time step [mm]
• surf_runoff_meas – Surface runoff from interception layer of measure during current time step [mm]
• intstor_meas – Remaining interception storage on interception layer of measure during current time step [mm]
• ini_stor_top_meas – Storage in top storage layer of measure at the beginning of current time step [mm]
• t_atm_top_meas – Transpiration from top storage layer of measure during current time step [mm]
• perc_top_meas – Percolation from top layer of measure at the current time step [mm]
• fin_stor_top_meas – top layer storage at the end of current time step [mm]
• ini_stor_btm_meas – bottom layer storage at the beginning of current time step [mm]
• t_atm_btm_meas – transpiration from bottom layer of measure at the current time step [mm]
• p_gw_btm_meas – percolation from bottom layer of measure to groundwater during current time step [mm]
• runoff_btm_meas – runoff from the bottom layer of the measure during current time step [mm]
• fin_stor_btm_meas – bottom storage at the end of the current time step [mm]
• overflow_btm_meas – bottom storage overflow during current time step [mm]
• q_meas_ow – Measure outflow to Open Water during current time step [mm]
• q_meas_uz – Measure outflow to Unsaturated Zone during current time step [mm]
• q_meas_gw – Measure outflow to groundwater during current time step [mm]
• q_meas_swds – Measure outflow to storm water drainage system during current time step [mm]
• q_meas_mss – Measure outflow to mixed sewer system during current time step [mm]
• q_meas_out – Measure outflow to outside water during current time step [mm]

...

Dynamic _input : The forcing — Hourly time series of Precipitation, potential Open Water evaporation and potential reference crop evapotranspiration. The user is responsible for data preprocessing — clean data, fill vacancy, remove unrealistic data and make sure the data is in float type. Make sure the column name is the same because the script use uses the column name to index which data is precipitation and evaporation.

Static _input : All the static input parameters are stored in the configuration file suffixed with _.ini . Currently, two configuration files are indispensable for every function to use — one is neighbourhood configure file, the other is measure configuration file. If no measure is included in the modelling, please specify _{measure_appledapplied=false} in measure configuration file. Though the script will automatically do some checks after reading the configuration file to make it fool proof, for example it will update the measure-related area with zero if no measure is applied even if it is not zero due to the user’s carelessness, it is highly recommended that the user carefully deal deals with the configuration input. Besides, the user should modify the parameters according to the local context of his area of interest and expected setups. Be aware of not changing the parameter name, otherwise the model goes wrong. The descriptions of the parameter parameters are in the configuration file, documentation and script docstrings for the user’s cross check.

5.2   Input time series and parameters

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• precipitation (only rainfall considered)
• potential Open Water evaporation (i.e. Penman evaporation – Penman, 1948)
• potential reference crop evapotranspiration (i.e. Penman-Monteith evaporation – Montheith, 1965 or Makkink evaporation – Makkink, 1957)

Note:

Sometimes, If Penman evaporation is not directly available, since it is not straightly measured, while but (class-A) pan evaporation data is easier to find. Pan evaporation Usually, pan evaporation is multiplied a correlation are available, Pan evaporation can be multiplied by a factor 0.77 to convert to Penman evaporation (Linacre, 1994). The model assumes potential Open Water evaporation from actual interception evaporation on paved surfacesurfaces. Evapotranspiration for the unpaved areas (and reference crop grass) is assumed to be 0.8982 * Penman evaporation (Droogers, 2009).

Often hourly potential Open Water evaporation data are not available, or even daily evaporation time series are not available. Then assumptions and simplifications will be made on evaporation interpolation. For instance, when only monthly potential evaporation data and daily sunrise and sunset data are available, you can transform to hourly data by:

Even though Forcing: Hourly time series of precipitation (actually only rainfall) [mm] and potential evaporation of Open Water [mm]. (for grass, it is approximately 0.8982 * Penman evaporation – Droogers, 2009) Length should better be most recent 30 years. Atmosphere is the most crucial exchange to the model. 1. Format: CSV format is preferred with corresponding column names. Make sure the data has no vacancy or unrealistic data. Make sure the data is in float type. 2. Note: Sometimes hourly potential Open Water evaporation is not findable, and it may be easier to get access to data like class-A pan evaporation time series. However, pan evaporation cannot be used as input directly. Conversion from pan evaporation to Penman Open Water evaporation should be done before running the model. Sometimes it is possible that only daily evaporation time series is available or even daily evaporation time series is not available, then assumptions and simplifications will be made on evaporation interpolation. For instance, in Area H, we only have annual potential evaporation data. First, we will divide this value by 365 to get the average daily evaporation. Then, interpolate by daily dynamics as assumed

First, divide the monthly values by the number of days of these months. Second, assume zero evaporation during night hours and determine the hourly evaporation by dividing the daily values by the number of daily hours between sunrise and sunset.

All conversion required to retrieve hourly evaporation have to be done before entering these input data in the model.

The length of the time series of rainfall and evaporation is advised to be 30 years or more, preferably ending as recent as possible.

Regarding formats, CSV file format is preferred with corresponding column names. Check the data on vacancies and unrealistic values. Make sure the data is in float type.

5.2.2    Parameters (Static input)

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%. And we need total area . The minimum required size of the open water area is larger than 0. In addition, the total area [m2] of the study area in [m2] is required input. Besides, for paved areas (PR, CP, OP), we also can define three additional types of fractions have to be defined:

1. disconnected fraction of three paved areas: “Part disconnected from sewer”: This disconnect fraction means how much represents the percentage of the each paved area (say Paved Roofs) that is disconnected from the sewer system. If For instance if this fraction is 5% for Paved Roofs, then it means implies that 5% of the Paved Roofs (PR) is disconnected to sewer system. Consequently, 5% of the runoff from the Paved Roofs (PR) will not end in the sewer system but will presumably is assumed to flow to the Unpaved area.
2. part of building above groundwater (GW): “part of buildings above GW”: This  This fraction means, in terms of Paved Roofs only, how much percentage of Paved Roofs (PR) has its bottom of foundation above the phreatic table. As we know, the relationship between the bottom level of building foundation and variation of groundwater level is essential to building stability, but this safety concern is not the model concern. What this fraction really matters water table. This fraction in the model is defines the total area size of the (shallow) groundwater (GW).
3. part of Open Water above groundwater (GW): “Part of OW above GW”: This  This fraction is more or less similar to part of building above groundwater (GW). It affects the calculation of the size of the groundwater area. Say we have 300m2 Open Water. If this fraction is zero, then groundwater will not contain any m2 of area is limited by this 300m2. If this fraction is 100%, then groundwater will also contain this extra 300m2 as all Open Water is assumed to be above the groundwater table.

To sum up, type 2 and type 3 fractions influence the total area of (shallow) groundwater (GW).

...

This area is important since all the storage and fluxes in the model are calculated in depth [mm], so the conversion from one component to another component is dependent on the area ratio of these two components.

...

Therefore, these two additional fractions (type 2 and type 3) are defined to

...

determine the actual groundwater area

...

in the model.

Runoff from paved surface to sewer system systems only occurs when the surface interception storage capacity can no longer handle excessive rainfall. This runoff can flow to either of the two available sewer systems. The division is defined by the fraction (X%) flowing to the “Storm Water Drainage System”: Part of urban area with , the part of paved area that has a storm water drainage system. The rest of the paved runoff (100% – X%) is automatically defined to flow to the “Mixed Sewer System”: Part of urban area with mixed sewer system (i.e. combined sewer system). These two fractions should sum up to 100%, the part of paved area that has a combined sewer system.

Design standard / Design rainfall of sewer system. This part may be a bit confusing, please don’t get puzzled by the nota on used i. Circle 3.b is discharge capacity of SWDS to Open Water, discharge capacity of MSS to Open Water (wet flow condition), discharge capacity of MSS to waste water treatment plant (dry flow condition). These three discharge capacities in circle 3.b are used in the model. Circle 3.a is design rainfall. Parameters in Circle 3.a are not directly used in the model. They are actually used to calculated Circle 3.b parameters if there is no direct information on design discharge capacity of sewer system. In the Netherlands, say if there is no direct information on discharge capacity of SWDS to Open Water (actually there is and it is around 21mm/hr to 30mm/hr), then we can do below calculations: “t = 2 rainfall” (in Fig 2): Design rainfall intensity of sewer system. In the Netherlands, the sewer overflow on the street is designed to occur once every two years. Hence t = 2 year is chosen as the design rainfall return period. Its corresponding rainfall intensity is 58.7 mm/hr by rainfall statistics. Consequently, for SWDS, the predefined discharge capacity of the SWDS is then calculated as 58.7(rainfall intensity of t=2) - 1.6 (interception on paved area) – 2 (storage in SWDS) = 55.1 mm/hr. This 55.1mm/hr is the discharge capacity of SWDS to Open Water above which sewer water will overflow onto the street. Similar to SWDS, discharge capacity of MSS to Open Water is calculated as 48.1mm/hr above which sewer overflow from MSS onto street will occur. “t = 1/6 rainfall” (in Fig 2): Design rainfall intensity of combined sewer overflow. In the Netherlands, the combined sewer overflow onto the Open Water is designed to occur six to seven times a year. Hence t= 1/6 is chosen as the design rainfall return period of combined sewer overflow. Its corresponding rainfall intensity is 27.9 mm/hr by statistics. Consequently, for MSS, the predefined discharge capacity of the MSS to waste water treatment plant (WWTP) is in fact the sewer discharge capacity above which sewer overflow to Open Water (CSO) will occur, and this discharge capacity is calculated as 27.9 – 1.6 = 26.3mm/hr.

5.3   Functions

In the Netherlands, the sewer overflow on the street is designed to occur once every two years. Hence 2 year is chosen as the design rainfall return period. Its corresponding rainfall intensity (16.8 mm/hour) is determined by rainfall statistics.
Consequently, for SWDS, the predefined hourly discharge capacity from SWDS to OW is determined by subtracting the interception capacity of the paved areas (1.6 mm) and the storage capacity of the SWDS (2 mm) from the T=2year rainfall intensity (16.8 mm), resulting in 13.2 mm/hr. This 13.2 mm/hour is the discharge capacity of SWDS to Open Water above which sewer water will overflow onto the street.
For the MSS the discharge capacity to the waste water treatment plant (WWTP) is calculated in a similar way. In the Netherlands the combined sewer overflow onto the Open Water is designed to occur approx. six times a year (T=1/6year). The corresponding rainfall intensity is 6.7 mm/hour. This will only occur when the discharge capacity of to the WWTP is exceeded. Hence the discharge capacity from MSS to WWTP is 6.7 – 1.6 (paved area interception) = 5.2 mm/hour.
The storage capacity of the MSS in the Netherlands is assumed to be 9 mm, hence MSS overflow onto street will occur above 16.8 – 1.6 – 9 = 6.2 mm/hour.
Please note that these values can (and have to be) adapted by the user dependent on the actual climate and sewer design of the study area.

5.3   Functions

5.3.5.3.1    save_to_csv

This function performs single run of the model. It can save all results or selected results in to an output csv file.

5.3.2    batch_run_sdf

This function performs batch run on different pumping capacity to produce database which can be used to plot Storage-Discharge-Frequency (SDF) Curve

The SDF function can be used to get an indication of the return period of the runoff depth that a catchment can withstand, based on the storage and discharge capacity. It can provide insights in whether it is more cost-efficient to invest in storage capacity or if it is more efficient to increase the drainage capacity. The values needed for the SDF function are obtained using the 'batch_run_sdf' function. Below it is described how these values are obtained and what has to be done in order to create a SDF curve.

Input

The required parameters are as following:

 Process

1. The model runs using the user-defined neighbourhood/catchment and measure parameters.
2. When the runoff in the model is exceeding the discharge capacity of the open water leaving the model, then the open water level increases. This open water level deviation is calculated using the target open water level and represents the storage depth for the SDF function.
3. For each time step, there will be a storage depth. All depths are grouped in events, where an event is divided by a 6-hour interval of no storage depth.
4. From each event, the maximum storage depth is obtained. The maxima are sorted, and a rank is assigned to each maximum.
5. In order to investigate what happens to the storage depths at different open water discharge capacities, several discharges are assigned by the user in ‘q_list’. The model runs for each of the specified discharges and follows steps 2-4.

Output

A dataframe with a series of storage depths (in m) for the baseline_q and the values in q_list is created. Figure 18 shows an example of the output, obtained using the following parameters:

q_list                              = [4, 6, 4]
baseline_q                     = 3
arithmetic_progression = True

Image Added

Figure   18      An example of part of the output of the SDF function. The headers ‘rank’ and ‘q_ow_out_cap’ are not in the output. This has been manually edited for the explanation.

These storage depths are the excess of water on top of the open water level. It is an accumulation of all the runoff in the model, which could not be discharged out of the model. Therefore, this can be interpreted as the required storage in the model in order to cope with runoffs at a specific return period.

SDF Curve

The SDF curve can be made using the values from the output. Plot the discharge capacity of the open water (q_ow_out_cap) on the x-axis and the storage depths on the y-axis. For each of the storage depths, the return period can be calculated as following:

                T = t_total / (rank + 1)

where t_total is the amount of years of input data. This assigns a return period to each of the storage depths for all values of ‘q_ow_out_cap’. When the return period is plotted on a logarithmic x-axis against the storage depth on the y axis, the line is close to linear. Based on this, the return period formula for that specific ‘q_ow_out_cap’ can be derived. Figure 19 shows the result for the example at a q_ow_out_cap of 3 mm/d and the formula for the fitted trendline. This formula is accurate for the lower return periods, however, at higher return periods there is more uncertainty as there is only one storage depth for those return periods. To increase the accuracy for those return periods, a longer timeseries should be used as input.

Image Added

Figure   19      The return period for each storage depth, plotted on a logarithmic x-axis. The red line is a fitted trendline.

This equation can be obtained for each of the q_ow_out_cap values. Using these equations, the storage depths can be calculated for the q_ow_out_cap values at every return period. Plotting the values results in the SDF curve, shown in Figure 20.

Image Added

Figure   20      The SDF curve for several return periods

5.3.3    batch_run_meas

This function performs batch run on measure. First do batch run with different (pairs of) values, then do baseline run (no measure). In the end, save the runoff time series into a csv file.

It can vary one parameter with a list of values or vary two parameters at the same time.

5.4   References

• DROOGERS, P. Verbetering bepaling actuele verdamping voor het strategisch waterbeheer. Definitiestudie. STOWA, 2009.
• PENMAN, Howard Latimer. Natural evaporation from Open Water, bare soil and grass. Proc. R. Soc. Lond. A, 1948, 193.1032: 120-145.
• MONTEITH, John L., et al. Evaporation and environment. In: Symp. Soc. Exp. Biol. 1965. p. 4.
• LINACRE, Edward T. Estimating US Class A pan evaporation from few climate data. Water International, 1994, 19.1: 5-14.