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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]

Bases: _object

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

• inflowfac – measure inflow factor is calculated as (runoff inflow area to measure from Closed Paved - area of Closed Paved with measure) / area of Closed Paved without measure

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

• int_cp – Interception storage on Closed Paved after rainfall at the beginning of current time step [mm]
• e_atm_cp – Evaporation from interception storage on Closed Paved during current time step [mm]
• intstor_cp – Remaining interception storage on Closed Paved at the end of current time step [mm]
• r_cp_meas – Runoff from Closed Paved to measure during current time step (not necessarily on Closed Paved itself) [mm]
• r_cp_swds – Runoff from Closed Paved to storm water drainage system (SWDS) during current time step [mm]
• r_cp_mss – Runoff from Closed Paved to combined sewer system (MSS) during current time step [mm]
• r_cp_up – Runoff from Closed Paved to Unpaved during current time step [mm]

Return type:                         (dictionary)

2.3    Open Paved

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.

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.

2.3.2       Calculation order

• Initial interception storage on Open Paved at the beginning of current time step is the remaining interception storage on Open Paved at the end of previous time step plus rainfall at current time step, and it is limited by predefined interception storage capacity on Open Paved.
• (Actual) evaporation from interception on Open Paved during current time step is limited by potential Open Water evaporation and available initial interception storage on Open Paved during the same time step. Evaporation is possible only if the interception storage contains water.
• (Final) interception storage on Open Paved at the end of current time step is evaporation subtracted from initial interception storage.
• The infiltration (percolation to groundwater) occurs only if interception storage gets fully filled. Infiltration is limited by predefined infiltration capacity on Open Paved. Infiltration directly flows to groundwater (GW), i.e. percolation (skipping Unsaturated Zone).
• (Total) runoff from Open Paved during current time step is rainfall subtracting actual evaporation, the change in interception storage between the same time step and previous time step and percolation to groundwater. Total runoff is redistributed to the measure (Meas), storm water drainage system (SWDS), combined sewer system (MSS) and Unpaved (UP) at predefined ratios.
• Subtracting runoff to the measure from total runoff is the remaining runoff. Connected remaining runoff is reallocated to storm water drainage system (SWDS) and combined sewer system (MSS) at predefined proportions, whilst disconnected remaining runoff flows to Unpaved area (UP) at predefined ratio.

2.3.3       Code and input arguments

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]

Bases: _object

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

• inflowfac – measure inflow factor is calculated as (runoff inflow area to measure from Open Paved - area of Open Paved with measure) / area of Open Paved without measure

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

• int_op – Interception storage on Open Paved after rainfall at the beginning of current time step [mm]
• e_atm_op – Evaporation from interception storage on Open Paved during current time step [mm]
• intstor_op – Remaining interception storage on Open Paved at the end of current time step [mm]
• p_op_gw – Percolation from interception storage on Open Paved to groundwater during current time step [mm]
• r_op_meas – Runoff from Open Paved to measure during current time step (not necessarily on Open Paved itself) [mm]
• r_op_swds – Runoff from Open Paved to storm water drainage system (SWDS) during current time step [mm]
• r_op_mss – Runoff from Open Paved to combined sewer system (MSS) during current time step [mm]
• r_op_up – Runoff from Open Paved to Unpaved during current time step [mm]

Return type:                         (dictionary)

2.4    Unpaved

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.

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).

2.4.2       Calculation order

• Total runoff from disconnected paved area to Unpaved is the sum of runoff from disconnected paved area (PR, CP, OP) to Unpaved area (UP) after conversion with the area ratio.
• (Initial) interception storage on Unpaved land at the beginning of current time step is the final remaining interception storage at the end of previous time step plus precipitation at current time step plus total runoff from disconnected paved area. It is not limited by interception storage capacity because (initial) interception storage is a transient variable which is only relevant in computing process.
• (Actual) infiltration capacity during current time step is limited by predefined infiltration capacity of Unpaved and available free space in root zone for infiltration. Available free space in Unsaturated Zone for infiltration is limited by maximum moisture content of the root zone minus moisture content of soil at previous time step plus anticipated percolation during current time step. Anticipated percolation is limited by the saturated permeability of the soil and the available water for percolation.
• As stated in assumptions, the time factor is that part of the time step that water is remaining on the surface level. Hence the time factor during current time step is limited by 1 and the ratio of initial interception storage over the sum of potential evaporation and actual infiltration capacity during current time step. With the time factor, actual evaporation and actual infiltration can be determined proportionally.
• (Actual) evaporation during current time step is potential evaporation multiplied by the time factor.
• (Actual) infiltration from Unpaved to Unsaturated Zone during current time step is actual infiltration capacity multiplied by the time factor.
• (Final) interception storage on land is limited by the predefined interception storage capacity on Unpaved land and initial interception storage on land subtracting actual evaporation and actual infiltration.
• (Total) runoff on Unpaved land during current time step is part of the (initial) interception storage after evaporation and infiltration still exceeding predefined interception storage capacity on Unpaved. Total runoff is redistributed to the measure (Meas) and Open Water (OW). When inflow runoff from Unpaved to measure defined possible, part of runoff flows to the measure according to predefined ratio, whilst the rest runoff from Unpaved land flows to Open Water (OW) by assumption.

2.4.3       Code and input arguments

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]

Bases: _object

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

• inflowfac – measure inflow factor is calculated as (runoff inflow area to measure from Unpaved - area of Unpaved with measure) / area of Unpaved without measure

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]

Return type:                         (dictionary)

2.5    Unsaturated Zone

Underneath Unpaved areas (UP) is an Unsaturated Zone (UZ). The Unsaturated Zone, often called the vadose zone, is the portion of the subsurface above the groundwater table. As mentioned before the Urbanwb does not apply an Unsaturated Zone in paved areas (PR, CP and OP), thus by assumption the Unsaturated Zone has the same area size as the Unpaved area. Infiltration from the Unpaved surface is an inflow to the Unsaturated Zone and percolation from the Unsaturated Zone to the groundwater (GW) is an outflow. In the Unsaturated Zone, we focus on the root zone from where the plant transpiration take place as the water uptake through plant roots. The root zone can be represented by means of a container in which the water content may fluctuate. Rainfall infiltration and capillary rise of groundwater towards the root zone add water to the root zone and decrease root zone depletion, while soil evaporation, crop transpiration and percolation removes water from root zone and increase depletion (Allen et al, 1998). Evapotranspiration the from root zone is modelled as the product of reference crop evapotranspiration (using Penman-Monteith evaporation or Makkink evaporation) and transpiration reduction coefficient (Panman, 1948; Montheith, 1965). Transpiration reduction coefficient is derived from the concept of Feddes plant water stress factor in the literature (Feddes et al, 1978).

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.

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

Figure 10  shows how the transpiration reduction factor is related to soil water pressure head h (i.e. root zone water potential). In the range between h₃ (transpiration reduction point) and h₂ (field capacity), root water uptake is optimal (maximal), so the transpiration reduction factor α= 1.

When h < h₃, there is drought stress, and α linearly reduces to zero at h₄ (wilting point).

When h > h₂, α linearly reduces to zero at h₁ (fully saturated, i.e. anoxic moisture condition).

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.

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.

Some applied concepts regarding evapotranspiration based on literature are:

• Evapotranspiration: Evapotranspiration is an important component of the water cycle and is composed of two-subprocesses: evaporation from soil and vegetation surfaces and transpiration from plant through root-stomata system. Evaporation and transpiration occur simultaneously and there is no easy way of distinguishing between the two processes.
• Reference crop evapotranspiration ET₀: The evapotranspiration rate from a reference surface, not short of water, is called reference crop evapotranspiration or reference evapotranspiration and is denoted as ET₀. The reference surface is a hypothetical grass reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s/m and an albedo of 0.23. As a result of an Expert Consultation held in May 1990, the FAO Penman-Monteith method is recommended as the sole standard method for the definition and computation of the reference crop evapotranspiration method for determining ET₀. ET₀ can also be estimated from pan evaporation. Pans have proved their practical value and have been used successfully to estimate ET₀ by observing the water loss from the pan and using empirical coefficients to relate pan evaporation to ET₀. However, special precautions and management must be applied. Besides, Makkink evaporation commonly used in the Netherlands can be used to estimate ET₀ as well. Makkink evaporation = 0.8982 * Penman Monteith evaporation according to STOWA (2009).
• Crop evapotranspiration under standard conditions ET_c: The crop evapotranspiration under standard conditions, denoted as ET_c, is the evapotranspiration from disease-free, well fertilized crops, grown in large fields, under op mum soil water conditions, and achieving full production under the given climatic conditions. ET_c = K_cET₀.
  K_c is the crop factor (crop coefficient). The effect of both crop transpiration and soil evaporation are integrated into this single crop coefficient K_c. K_c varies with crop type, growth stage and other factors, the range of which is commonly (0.2 < K_c < 1.3). For simplicity, we say that the crop factor K_c = 1 for a hypothetical grass reference crop.
• (Actual) evapotranspiration ET: As stated above, the ET from crop surfaces under standard conditions is determined by a crop coefficient K_c that relates ET_c to ET₀. However, actual evapotranspiration is usually under non-standard conditions. The ET from crop surfaces under non-standard conditions is adjusted by a water stress coefficient (α) and/or by modifying the crop coefficient. Hence, the (actual) evapotranspiration is ET = α ∗ K_c ∗ ET₀. In the Urbanwb model, we take 1.0 for crop factor, Penman-Monteith evaporation (or Makkink evaporation) for reference crop evapotranspiration, transpiration reduction factor as water stress factor, so the modelled evapotranspiration is ET = α ∗ 1 ∗ E_PM .
• Makkink evapotranspiration: Though Penman-Monteith method is solely recommended by FAO to calculate reference crop evapotranspiration and has been commonly used world widely, there are several other methods popular in certain area or nations. Makkink method is named after Gerrit François Makkink, a Dutch hydrologist (Makkink, 1957). The Makkink method is simple but must be calibrated to a specific location. Since 1987, the national Dutch Weather services KNMI used Makkink method as standard method to calculate reference crop evapotranspiration. Hence, Makkink evaporation can be used as the forcing “reference crop evapotranspiration” and can replace of Penman-Monteith evaporation, especially for study cases in the Netherlands. The relationship between Makkink evaporation and Penman-Monteith evaporation is Makkink evaporation = 0.8982 * Penman-Monteith evaporation according to STOWA (2009).

2.5.1       Assumptions

• 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

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