# SWMM-UrbanEVA: A Model for the Evapotranspiration of Urban Vegetation

^{1}

^{2}

^{*}

## Abstract

**:**

_{S}and the crop factor K

_{C}. Both must be derived very carefully to minimize volume errors. Another focus must be set on the soil parameters since they define the soil volume available for ET. Process-oriented differentiation between ET fluxes interception evaporation, transpiration, and soil evaporation, using the leaf area index, behaves realistically but shows a lack in volume errors. Further investigations on process dynamics, validation, and parametrization are recommended.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Description

#### 2.1.1. Model Development

#### 2.1.2. Submodule 1: Shading

^{−1}).

#### 2.1.3. Submodule 2: Evapotranspiration

_{I}takes place out of the vegetation layer. Transpiration E

_{T}and (soil-) evaporation E

_{S}are interacting processes which are both dependent on the soil moisture and are therefore fed out of the soil layer. Evaporation from free water surfaces E

_{W}is allocated in the surface layer.

**Definition of Vegetation-Specific Parameters**

^{2}·m

^{−}

^{2}) describes the leaf area per covered area [35]. It influences the level of interception, radiation reduction, as well as water and carbon gas exchange, and is therefore an important parameter for ET modeling. $LAI$ can be determined directly or indirectly. Literature values can be found at various databases (e.g., [36,37,38]).

^{−1}) describes the water retention capacity of vegetation. The higher the value, the more precipitation intercepts. Various values can be obtained in the literature [24,43,44,45,46,47,48]. Regarding to [31], ${S}_{L}$ can be fixed to 0.29 (mm·h

^{−1}).

^{−1}) can be defined as “the maximum amount of water remaining on the plant at the end of a precipitation event, without evaporation and after stopping the dripping” [36]. It is dependent on the surface condition and the density of the vegetation. Therefore, there is a direct relationship to the $LAI$. The approach according to [49] combines the leaf storage coefficients S

_{L}with the $LAI$.

^{−1}) as an internationally widely used input variable introduces potential ET for the reference crop of a height of 0.12 m, well-watered and under optimal environmental conditions [32]. For modeling various vegetation types the crop factor ${K}_{C}$ (-) is implemented into the calculation as a multiplicator to $E{T}_{0,Ks}$. ${K}_{C}$ is dependent on the climatic conditions and plant characteristics and should be calculated individually, according to [32], with

^{−1}under standard conditions and should be calculated using the Penman–Monteith equation [50] in the standardized format of the American Society of Civil Engineers (ASCE) [51].

^{−1}), ${R}_{n}$ = net radiation (MJ·m

^{−2}·day

^{−1}), $G$ = soil heat flux (MJ·m

^{−2}·day

^{−1}), $\gamma $ = psychrometric constant (kPa·°C

^{−1}), $T$ = air temperature at 2 m height (°C), (${e}_{s}-{e}_{a}$) = saturation vapor pressure deficit (kPa), ${r}_{s}$ = (bulk) surface or canopy resistance (s·m

^{−1}) and ${r}_{a}$ = (bulk) aerodynamic resistance (s·m

^{−1}).

^{2}·Mg

^{−1}·h

^{−1}), $\epsilon $ = ratio of molecular weights of water vapor versus dry air = 0.622 and $R$ = specific gas constant = 0.287 (kJ·kg

^{−1}·K

^{−1}).

^{−1}).

^{−1}). Values for various species can be found in, e.g., [54] or [55]. $LA{I}_{active}$ (- or m

^{2}·m

^{−2}) is the sunlit, ET-active $LAI$. For grouped vegetation such as forests or grass, [32] assume that just the upper half of the vegetation is evaporation-active.

**Potential and Actual (vegetation-Specific) Evapotranspiration (**${\mathit{E}}_{\mathit{S}\mathit{T}\mathit{I},\mathit{p}}$

**and**${\mathit{E}}_{\mathit{S}\mathit{T}\mathit{I},\mathit{a}}$)

^{−1}) [32].

^{−1}) as the sum of interception evaporation, transpiration, (soil) evaporation and evaporation from free water surfaces.

**Interception (**$\mathit{I}$

**)**

^{−1}) is calculated according to [49].

^{−1}). The interception height converges to the limit value ${S}_{max}$, and is thus affected by (i) the precipitation level itself in the case of low precipitation intensities and (ii) the interception capacity in the case of high precipitation intensities.

^{−1}) is calculated depending on the interception capacity ${S}_{max}$ and the remaining interception level of the last timestep (${S}_{I,i-1}$).

^{−1}) is then fed to the following infiltration and runoff processes.

**Interception Evaporation (**${\mathit{E}}_{\mathit{I}}$

**)**

^{−1}), the potential evapotranspiration ${E}_{STI,p}$ is therefore reduced by applying $SCF$ [46].

^{−1}) finally results from the minimum of the level of interception storage and the potential interception evaporation rate.

**Soil Evaporation (**${\mathit{E}}_{\mathit{S}}$

**)**

^{−1}) is already met before the field capacity is reached [25]. For this reason, “$aWCthreshold$” (-) is introduced, which describes the point of reaching the potential evaporation rate as proportion of the available water capacity. In accordance to [25,41], it is set to 0.6.

^{−1}) is then calculated in accordance to [31,62]:

**Transpiration (**${\mathit{E}}_{\mathit{T}}$

**)**

^{−1}) is projected onto $SCF$ [46]. As the actual interception evaporation ${E}_{I,a}$ (mm·h

^{−1}) is integrated into the model as an upstream process ${E}_{T,p}$ is calculated like:

**Evaporation While Ponding (Free Water Surfaces) (**${\mathit{E}}_{\mathit{W}}$

**)**

#### 2.1.4. Software Implementation

#### 2.2. Study Area and Data

^{2}each have been collected since 2016. For this study, one green roof test bed with a substrate layer of 15 cm depth was chosen. It has an underlying drainage mat of 2.5 cm and a vegetation cover of selected sedum species and herbs. In order to model and analyze the hydrological processes, in addition to the climate data runoff, soil moisture, and precipitation are recorded. Rainfall is monitored with $\u2206t$ = 1 min, exfiltration is measured volumetrically with an accuracy of $\u2206h$ = 0.1 mm and $\u2206t$ = 5 min [66].

^{2}consists of a substrate layer of 6 cm depth and a drainage mat of 3 cm. Volumetric exfiltration measurements with $\u2206t$ = 5 min started in 2015.

#### 2.3. Model Sensitivity Analysis, Calibration, and Validation

#### 2.3.1. Set Up and Goodness-of-Fit Criteria

#### 2.3.2. Submodule 1: Shading

#### 2.3.3. Submodule 2: Evapotranspiration

#### 2.3.4. Blue Green Infrastructure

## 3. Results

#### 3.1. Submodule 1: Shading

^{−1}and 1.27 ± 1.15 mm·d

^{−1}for Lincoln. Both are close to the respective values from local data with mean $E{T}_{0,loc}$ being 1.36 ± 1.18 mm·d

^{−1}for Leo and 1.37 ± 1.18 mm·d

^{−1}for Lincoln. The parity plot (Figure 4) illustrates the goodness-of-fit for nearly the whole range of values. The linear fit has a gradient of ± 1 for both locations while the coefficients of determination are R

^{2}= 0.96 for Leo and R

^{2}= 0.98 for Lincoln. Regarding to Section 2.3.1, the evaluation of $NSE$ and $mNSE$ confirms the very good performance of SM1 for the period under consideration with $NSE$ = 0.96 and $mNSE$ = 0.84 for Leo and $NSE$ = 0.98 and $mNSE$ = 0.88 for Lincoln.

#### 3.2. Submodule 2: Evapotranspiration

#### 3.2.1. Sensitivity Analysis

_{aWC}= (FC − WP) · SoDepth) and the air capacity volume (Vol

_{AC}= (Por − FC) · SoDepth) instead of each variable soil depth, porosity, field capacity and wilting point.

_{aWC}and $cor$ = 0.26 for Vol

_{AC}) since large soil volumes result in more ET due to high storage capacities. A slight correlation is observed for the conductivity slope c_sl ($cor$ = 0.08). As a constant regulating soil regeneration, it influences the long-term balance of ET.

_{AC}and $cor$ = 0.36 for Vol

_{aWC}). The sensitivity for the second soil-fed process, ${E}_{S,a}$, is significantly lower ($cor$ = 0.04 for Vol

_{AC}and $cor$ = 0.08 for Vol

_{aWC}), since overall the amount of soil water extracted is much smaller than for ${E}_{T,a}$.

_{aWC}and Vol

_{AC}.

#### 3.2.2. Model Calibration and Validation

_{AC}and factor 5.1 for Vol

_{aWC}) can be observed for changing vegetation. More clearly this effect can be detected when calibrating the current SWMM version (SWMM-current). As there is no other regulation mechanism in the model, the soil volumes are increased even more significantly (factor 1.7 for Vol

_{AC}and factor 7.3 for Vol

_{aWC}).

_{aWC}) for grassland. The high maximum for Vol

_{aWC}can be explained with the high values of WP. As FC is fixed to 0.21 and therefore Vol

_{aWC}is very small, this leads to large relative variations resulting from small absolute deviations of SoDepth and WP. The slightly higher value for ${K}_{C}$ (VarC = 16%) can be explained by the non-negligible sensitivity of soil parameters (Section 3.2.1). Since they also influence ET, ${K}_{C}$ changes depending on the soil parameters applied. For the remaining parameters VarC is small (<10%) so that no significant uncertainty in parameter estimation can be identified.

_{aWC}). Since Vol

_{aWC}has a wider range in contrast to grassland, a maximum value for VarC as for grassland cannot be observed here. Having a higher variation for Vol

_{AC}(VarC = 21%) and Vol

_{aWC}(VarC = 24%), results in wider ranges for SoDepth, Por, and WP as well.

_{(2),median}= −7% whereas current SWMM shows an underestimation of $Vo{l}_{\left(1\right)}$ = −24% ($Vo{l}_{\left(2\right),median}$ = −22%). When using SWMM-UrbanEVA, this means an improvement of the $Vol$ by 71% for calibration period (1). In contrast, the reduction in volume errors by SWMM-UrbanEVA is even stronger for coniferous. Observing a volume error of only $Vo{l}_{\left(1\right)}$ = 3% ($Vo{l}_{\left(2\right),median}$ = 4%) when modeling with SWMM-UrbanEVA, the results of current SWMM show an unacceptable overestimation of infiltration by $Vo{l}_{\left(1\right)}=$ 44% ($Vo{l}_{\left(2\right),median}$ = 53%). Therefore, the improvement by introducing SWMM-UrbanEVA is at 93%.

^{2}the size of the LID leads to slow model reactions to peak changes. The evaluation of performance criteria (Table 9) confirms the good performance of the model.

^{−1}, 1.11 ± 1.08 mm·d

^{−1}modeled by SWMM-UrbanEVA and 1.02 ± 0.99 mm·d

^{−1}by current SWMM. Thus, the linear fit for SWMM-UrbanEVA largely corresponds to the 1:1 reference line, while the linear fit of current SWMM is slightly higher.

^{−1}, SWMM-UrbanEVA gets to 0.52 ± 0.61 mm·d

^{−1}and current SWMM to 0.86 ± 0.82 mm·d

^{−1}on average, which equals a deviation of 62%. This leads to $NSE$ = 0.47 which is poorly satisfactory.

#### 3.2.3. Analysis of the Modeled Process Dynamics

#### 3.3. Blue Green Infrastructure

## 4. Discussion

^{2}test bed cannot be completely modeled by SWMM. This is due to the weakness in modeling detention and exfiltration processes and compensation is found within ${K}_{C}$. The deficit in modeling short-term process dynamics of BGI would fit the findings of [28,89]. It implies that for a good parameterization of vegetated devices such as BGI further investigations are necessary to understand the physical properties (e.g., detention, storage, infiltration, percolation) more precisely and to differentiate them from the processes relevant for ET. Moreover, since this study only analyzes green roofs, a wider range of BGI should also be considered. Additionally, the influence of urban energy balance on BGI should not be neglected and must be investigated separately.

**SWMM-UrbanEVA**models ET with good performance. By introducing process-oriented ET-modeling, long-term water balances can be improved significantly in contrast to current SWMM. Being fully integrated into SWMM, the model enables good applicability for urban planning purposes.**SM1**allows the integration of local variability of shading effects on both, pervious and impervious catchments which has not been possible before within urban rainfall runoff models. It only addresses one aspect of urban energy balance. The submodule’s performance depends on the quality of ${K}_{S}$-values.**SM2**is well applicable for vegetation in general. When modeling BGI and urban heat infected vegetation, SWMM-UrbanEVA still implies distinct improvements, but shows needs for further research.- For
**model parameterization**the shading factor ${K}_{S}$ and the crop factor ${K}_{C}$ must be considered as most influential variables. Further sensitive model inputs are the soil characteristics. The $LAI$ controls ET flux interactions. - A proper
**model calibration**is essential for good model performance. The calibration’s set up should be chosen carefully according to later model use (e.g., period, goodness-of-fit, timestep).

## 5. Conclusions

## Supplementary Materials

_{C}values for different types of BGI and the parameters used for calculation; Figure S4: Mean monthly totals for precipitation (top) and ET

_{0}(bottom) of the locations under consideration.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Definition of the vegetation layer and the ET components within the existing LID-soil model. ($P$ = Precipitation, ${K}_{C}$ = crop factor, $E{T}_{0,Ks}$ = shading impacted FAO-grass reference evaporation, ${E}_{STI,p}$ = plant specific potential ET, ${E}_{I,p}$ = pot. interception, ${E}_{T,p}$ = pot. transpiration, ${E}_{S,p}$ = pot. soil evaporation, ${E}_{W,p}$ = pot. evaporation of free water surface, ${E}_{W,a}$ = actual evaporation of free water surface, ${E}_{I,a}$ = actual interception, ${E}_{T,a}$ = actual transpiration, ${E}_{S,a}$ = actual soil evaporation)—modified after [34].

**Figure 3.**Transfer functions $\u2206E{T}_{0}$($\u2206rad$) for locations (

**a**) “Leo” and (

**b**) “Lincoln” with “Geo” as reference station.

**Figure 4.**Parity plots with 1:1 reference line comparing daily $E{T}_{0,Ks}$ and $E{T}_{0,loc}$ in 2017 for (

**a**) Leo and (

**b**) Lincoln.

**Figure 5.**Results of LHS-simulations. Top: Pearson correlation coefficients $cor$, bottom: scatter plots in which each dot represents a parameter sample. Abbreviations for parameters are mentioned in Table 5.

**Figure 6.**Results of SCEUA automatic calibration: Performance criteria of best-fit parameter set for calibration periods (1) total calibration period 1989–1999 and (2) years within 1989 to 1999. Calculation for modelled infiltration of (

**a**) grassland and (

**b**) coniferous.

**Figure 7.**Measured and modeled infiltration in 1992 for calibrated models of (

**a**) grassland and (

**b**) coniferous at full scale lysimeter St. Arnold.

**Figure 8.**Parity plots of daily infiltration in 1992 modeled by SWMM-UrbanEVA and SWMM-current for (

**a**) grassland and (

**b**) coniferous at full scale lysimeter St. Arnold.

**Figure 9.**Time series from SWMM-UrbanEVA for ET relevant processes for a one-week period. Precipitation ($P$) and potential evapotranspiration (${E}_{STI,p}$) as model input variables; soil moisture (SM), interception storage level (Int_Level), interception evaporation (${E}_{I,a}$), transpiration (${E}_{T,a}$) and soil evaporation (${E}_{S,a}$) as model output variables. Simulation done for St. Arnold with ${K}_{S}$ = 1, ${K}_{C}$ = 1, $LAI$ = 2, and WP = 0.15.

**Figure 10.**Proportion of ET fluxes in total ET for different $LAI$. Plotted values are results of LHS (Section 3.2.1).

**Figure 11.**Measured and modeled exfiltration for two green roofs at locations “Leo” and “FHZ”. Plotted periods are (

**a**) calibration period and (

**b**,

**c**) two validation periods. Note poor data quality and exclusion from analysis at “Leo” in October 2017.

**Table 1.**Mean annual totals for precipitation and $E{T}_{0}$ of the locations under consideration. The years in brackets indicate the analyzed periods.

Parameter | Unit | St. Arnold | Geo | Leo | Lincoln |
---|---|---|---|---|---|

(1966–2008) | (2017–2018) | (2017–2018) | (2017–2018) | ||

Precipitation | mm·a^{−1} | 793 | 596 | 691 | 647 |

ET_{0} | mm·a^{−1} | 460 | 648 | 490 | 524 |

Parameter | STEP 1: Shading (SM1) | STEP 2: ET Vegetation (SM2) | STEP 3 BGI (SM1 + SM2) | |
---|---|---|---|---|

Sensitivity | Calibration | |||

Location | Münster (“Leo” and “Lincoln”) | St. Arnold | Münster (“Leo” and “FHZ”) | |

Reference station | “Geo” | St. Arnold (no shading) | “Geo” | |

Measurement | ET_{0,loc} “Leo” and “Lincoln” | infiltration grassland/coniferous | exfiltration green roofs “Leo” and “FHZ” | |

Timestep | 5 min | daily | 5 min | |

Methods | - | LHS | SCEUA | SCEUA |

Period | 2017 | 1989/1999 | 1989/1999, 1989, …, 1999 | 2017-01/2017-03; 2017-04/2017-06; 2017-02-21/2017-02-27; 2017-03-07/2017-03-17 |

Varied input parameters | K_{S,spring}, K_{S,summer}, K_{S,winter}, (see Table 4) | all LID + SWMM-UrbanEVA variables, (see Table 5) | K_{C}, SoDepth, Por, WP, c_sl(see Table 7) | K_{C}, Por, WP, c_sl, FCoef, FEx(see Table 7) |

Evaluated result parameters | $E{T}_{0,Ks}$ “Leo” and “Lincoln” | ET, E_{I,a}, E_{T,a}, E_{S,a} | infiltration grass./ conif. | exfiltration green roofs “Leo” and “FHZ” |

Goodness-of-fit | NSE, mNSE, Vol |

Goodness-of-Fit Criterion | Formula | Equation No. |
---|---|---|

Nash-Sutcliffe model efficiency | $NSE=1-\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({Q}_{m,i}-{Q}_{o,i}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{\left({Q}_{o,i}-\overline{{Q}_{o}}\right)}^{2}}$ | (43) |

Modified Nash-Sutcliffe model efficiency | $mNSE=1-\frac{{{\displaystyle \sum}}_{i=1}^{n}\left|{Q}_{m,i}-{Q}_{o,i}\right|}{{{\displaystyle \sum}}_{i=1}^{n}\left|{Q}_{o,i}-\overline{{Q}_{o}}\right|}$ | (44) |

Volume Error | $Vol=\frac{{{\displaystyle \sum}}_{i=1}^{n}{Q}_{o,i}}{{{\displaystyle \sum}}_{i=1}^{n}{Q}_{m,i}}-1$ | (45) |

**Table 4.**Reduction in shortwave radiation ($\u2206rad$) and resulting ${K}_{S}$-values used for the estimation of $E{T}_{0,Ks}$. All values have been calculated for spring equinox as well as winter and summer solstice.

Parameter | Unit | Leo | Lincoln | |||||
---|---|---|---|---|---|---|---|---|

Spring | Summer | Winter | Spring | Summer | Winter | |||

(i) | $\u2206rad$ | - | −0.15 | −0.12 | −0.25 | −0.13 | −0.07 | −0.12 |

(ii) | ${K}_{S}$ | - | 0.75 | 0.78 | 0.66 | 0.78 | 0.84 | 0.79 |

**Table 5.**LID parameter ranges for sensitivity analysis and model calibration. (grey = fixed parameter, black = varied parameter).

Parameter | Unit | Min | Max | Reference | ||
---|---|---|---|---|---|---|

vegetation | crop factor | Kc | - | 1 | 3 | [32] |

leaf area index | LAI | - | 1 | 16 | [36] | |

leaf storage coefficient | S_{L} | - | 0 | 1 | - | |

aWCthreshold | aWC-th | - | 0 | 1 | - | |

surface | surface storage | SuStor | mm | 1 | 10 | site specific |

surface roughness | SuManN | s·m^{−1/3} | 0.001 | 0.8 | [87] | |

surface slope | SuSlope | % | 0 | 6 | site specific | |

soil | soil depth | SoDepth | mm | 1 | 2000 | site specific |

porosity | Por | - | 0.22 | 0.65 | [88] | |

field capacity | FC | - | 0.21 | 0.21 | [88] | |

wilting point | WP | - | 0 | 0.20 | [88] | |

conductivity | cond | mm·h^{−1} | 0.25 | 360 | [87] | |

conductivity slope | c_sl | - | 1 | 100 | [34] | |

suction head | SucH | mm | 49 | 320 | [34] | |

storage | storage height | StHeight | mm | 1 | 5000 | site specific |

void ratio | VoidR | - | 0 | 1 | [88] | |

seepage rate | SR | mm·h^{−1} | 0.25 | 360 | [87] |

**Table 6.**Comparison of $E{T}_{0}$ out of local measurements ($E{T}_{0,loc}$) with the ${K}_{S}$-modified $E{T}_{0}$ of the reference station ($E{T}_{0,Ks}$) for 2017.

Month in 2017 | Leo | Lincoln | ||||||
---|---|---|---|---|---|---|---|---|

ET_{0,loc} | ET_{0,Ks} | Diff. | ET_{0,loc} | ET_{0,Ks} | Diff. | |||

(mm) | (mm) | (mm) | (%) | (mm) | (mm) | (mm) | (%) | |

January | 2.9 | 7.4 | 4.5 | 153.2 | 5.5 | 8.4 | 3.0 | 54.4 |

February | 13.0 | 13.1 | 0.1 | 0.6 | 12.5 | 14.2 | 1.7 | 13.5 |

March | 37.8 | 32.9 | −4.9 | −13.0 | 38.7 | 34.2 | −4.5 | −11.6 |

April | 49.4 | 47.3 | −2.2 | −4.4 | 52.3 | 49.5 | −2.7 | −5.3 |

May | 77.5 | 75.4 | −2.1 | −2.7 | 81.2 | 80.3 | −0.9 | −1.1 |

June | 82.3 | 82.6 | 0.3 | 0.3 | 88.8 | 89.1 | 0.4 | 0.4 |

July | 80.0 | 77.3 | −2.8 | −3.4 | 84.3 | 82.7 | −1.6 | −1.9 |

August | 58.7 | 61.9 | 3.3 | 5.6 | 64.7 | 65.2 | 0.5 | 0.8 |

September | 34.2 | 35.6 | 1.4 | 4.1 | 37.9 | 37.0 | −0.8 | −2.2 |

October | 17.2 | 21.8 | 4.6 | 26.5 | 20.7 | 23.4 | 2.7 | 13.1 |

November | 6.3 | 7.2 | 0.9 | 14.5 | 7.1 | 8.1 | 1.0 | 14.5 |

December | 4.7 | 4.3 | −0.5 | −9.5 | 5.8 | 5.1 | −0.7 | −12.1 |

∑ | 464 | 467 | 3 | 1 | 499 | 497 | −2 | −0.4 |

**Table 7.**LID parameters obtained from model calibration. (grey = fixed parameter, black = varied parameter).

Parameter | Unit | Full Scale Lysimeter St. Arnold | Green Roofs | |||||||
---|---|---|---|---|---|---|---|---|---|---|

SWMM-UrbanEVA | SWMM-Current | |||||||||

Grass | Conif. | Grass | Conif. | Leo | FHZ | |||||

General | area | Area | M^{2} | 400 | 400 | 400 | 400 | 3 | 80 | |

width | Width | m | 20 | 20 | 20 | 20 | 1 | 9 | ||

initial saturation | InitSat | - | 0 | 0 | 0 | 0 | 0 | 0 | ||

slope | Slope | % | 2 | 2 | 2 | 2 | 3 | 3 | ||

SM1 | shading factor spring | K_{S,spring} | - | 1 | 1 | - | - | 0.75 | 1 | |

shading fact. summer | K_{S,summer} | - | 1 | 1 | - | - | 0.78 | 1 | ||

shading factor winter | K_{S,winter} | - | 1 | 1 | - | - | 0.66 | 1 | ||

SM2 | vegetation | crop factor | Kc | - | 1.04 | 1.56 | - | - | 1.80 | 1.14 |

leaf area index | LAI | - | 2 | 11 | - | - | 3 | 3 | ||

leaf storage coefficient | S_{L} | % | 0.29 | 0.29 | - | - | 0.29 | 0.29 | ||

aWCthreshold | aWC-th | % | 0.6 | 0.6 | - | - | 0.6 | 60 | ||

gf scheme | gf | - | Table S1, no. 7 | |||||||

surface | surface storage | SuStor | mm | 2 | 2 | 2 | 2 | 20 | 20 | |

surface roughness | SuManN | s·m^{−1/3} | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | ||

surface slope | SuSlope | % | 1 | 1 | 1 | 1 | 3 | 3 | ||

soil | soil depth | SoDepth | mm | 1596 | 1639 | 1616 | 2331 | 150 | 60 | |

porosity | Por | - | 0.48 | 0.57 | 0.46 | 0.50 | 0.29 | 0.40 | ||

volume air capacity | Vol_{AC} | mm | 431 | 590 | 404 | 676 | 14 | 10 | ||

field capacity | FC | - | 0.21 | 0.21 | 0.21 | 0.21 | 0.20 | 0.23 | ||

wilting point | WP | - | 0.18 | 0.10 | 0.19 | 0.11 | 0.10 | 0.07 | ||

volume avail. water cap. | Vol_{aWC} | mm | 35 | 180 | 32 | 233 | 15 | 10 | ||

conductivity | cond | mm·h^{−1} | 250 | 250 | 250 | 250 | 61 | 27 | ||

conductivity slope | c_sl | - | 40.6 | 28.4 | 36.5 | 34.8 | 63.8 | 37.6 | ||

suction head | SucH | mm | 58 | 58 | 58 | 58 | 58 | 58 | ||

storage | storage height | StHeight | mm | 3000 | 3000 | 3000 | 3000 | 25 | 30 | |

void ratio | VoidR | - | 0.27 | 0.27 | 0.27 | 0.27 | 0.75 | 0.30 | ||

seepage rate | SR | mm·h^{−1} | 250 | 250 | 250 | 250 | 0 | 0 | ||

drain | flow coefficient | FCoef | 1·h^{−1} | - | - | - | - | 53 | 43 | |

flow exponent | FEx | - | - | - | - | - | 0.9 | 0.2 | ||

offset | Off | mm | - | - | - | - | 0 | 0 |

**Table 8.**Mean (mean), standard deviation (SD) and variation coefficient (VarC) for last population of calibration-runs for grassland and coniferous.

Parameter | Unit | Grassland | Coniferous | |||||
---|---|---|---|---|---|---|---|---|

Mean | SD | VarC | Mean | SD | VarC | |||

crop factor | Kc | - | 1.05 | 0.17 | 16% | 1.57 | 0.19 | 15% |

soil depth | SoDepth | mm | 1463 | 146 | 10% | 1555 | 268 | 17% |

porosity | Por | - | 0.50 | 0.02 | 4% | 0.55 | 0.04 | 8% |

volume air capacity | Vol_{AC} | mm | 431 | 40 | 9% | 545 | 113 | 21% |

wilting point | WP | - | 0.18 | 0.02 | 9% | 0.10 | 0.02 | 21% |

volume available water capacity | Vol_{aWC} | mm | 29 | 20 | 67% | 167 | 39.5 | 24% |

Parameter | Unit | SWMM-UrbanEVA | SWMM-Current | ||
---|---|---|---|---|---|

Grassland | Coniferous | Grassland | Coniferous | ||

NSE | - | 0.74 | 0.87 | 0.73 | 0.47 |

mNSE | - | 0.59 | 0.75 | 0.63 | 0.41 |

Vol | - | −0.06 | −0.14 | −0.04 | 0.59 |

**Table 10.**ET partitioning validation for different species. (frac. = fraction of ET, abs. dev. = absolute deviation, rel. dev. = relative deviation).

Species | LAI | Literature | SWMM-UrbanEVA | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

E_{I,a}/ET | E_{T,a}/ET | E_{S,a}/ET | E_{I,a}/ET | E_{T,a}/ET | E_{S,a}/ET | ||||||||

Frac. | Frac. | Frac. | Frac. | Abs. Dev. | Rel. Dev | Frac. | Abs. Dev. | Rel. Dev | Frac. | Abs. Dev. | Rel. Dev | ||

(-) | (-) | (-) | (-) | (-) | (-) | (-) | (-) | (-) | (-) | (-) | (-) | ||

grassland | 2 | 0.25 ^{1} | 0.50 ^{1} | 0.25 ^{1} | 0.15 | −0.10 | −0.60 | 0.42 | −0.08 | −0.19 | 0.43 | 0.18 | 0.72 |

pine | 8 | 0.45 ^{2.} | 0.47 ^{2} | 0.08 ^{2} | 0.49 | 0.04 | 0.09 | 0.42 | −0.05 | −0.07 | 0.09 | 0.01 | 0.13 |

spruce | 12 | 0.50 ^{3} | 0.44 ^{3} | 0.06 ^{3} | 0.56 | 0.06 | 0.12 | 0.40 | −0.04 | −0.10 | 0.04 | −0.02 | -0.33 |

**Table 11.**Performance criteria of the different models for the green roofs “Leo” and “FHZ”. The analysis was done with a daily timestep.

Model | (a) Calibration (2017-01 and 2017-06) | (b) Validation 1 (2017-07 and 2017-09) | (c) Validation 2 (2017-10 and 2017-12) | 2017 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

NSE | mNSE | Vol | NSE | mNSE | Vol | NSE | mNSE | Vol | NSE | mNSE | Vol | ||

Leo | UE SM1+2 | 0.84 | 0.71 | 0.01 | 0.85 | 0.72 | −0.06 | 0.71 | 0.61 | −0.01 | 0.79 | 0.69 | −0.02 |

UE SM2 | 0.82 | 0.69 | −0.24 | 0.82 | 0.70 | −0.21 | 0.72 | 0.62 | −0.11 | 0.78 | 0.68 | −0.17 | |

current | 0.79 | 0.65 | 0.25 | 0.83 | 0.73 | 0.21 | 0.70 | 0.60 | 0.06 | 0.77 | 0.67 | 0.15 | |

FHZ | UE SM1+2 | - | - | - | - | - | - | - | - | - | - | - | - |

UE SM2 | 0.95 | 0.81 | −0.08 | 0.88 | 0.78 | 0.18 | 0.81 | 0.78 | −0.03 | 0.89 | 0.81 | 0.00 | |

current | 0.90 | 0.74 | −0.28 | 0.89 | 0.79 | −0.13 | 0.80 | 0.74 | −0.15 | 0.87 | 0.78 | −0.18 |

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**MDPI and ACS Style**

Hörnschemeyer, B.; Henrichs, M.; Uhl, M.
SWMM-UrbanEVA: A Model for the Evapotranspiration of Urban Vegetation. *Water* **2021**, *13*, 243.
https://doi.org/10.3390/w13020243

**AMA Style**

Hörnschemeyer B, Henrichs M, Uhl M.
SWMM-UrbanEVA: A Model for the Evapotranspiration of Urban Vegetation. *Water*. 2021; 13(2):243.
https://doi.org/10.3390/w13020243

**Chicago/Turabian Style**

Hörnschemeyer, Birgitta, Malte Henrichs, and Mathias Uhl.
2021. "SWMM-UrbanEVA: A Model for the Evapotranspiration of Urban Vegetation" *Water* 13, no. 2: 243.
https://doi.org/10.3390/w13020243