Document [original]

Modeling urban evapotranspiration using remote sensing, ﬂux

footprints, and artiﬁcial intelligence

Stenka Vulova

a,1,

⁎,FredMeier

b,2

, Alby Duarte Rocha

a,1

, Justus Quanz

b,c,2

Hamideh Nouri

d,3

, Birgit Kleinschmit

a,1

Geoinformation in Environmental Planning Lab, Department of Landscape Architecture and Environmental Planning, Technische Universität Berlin, 10623 Berlin, Germany

Chair of Climatology, Institute of Ecology, Technische Universität Berlin, 12165 Berlin, Germany

Department of Environmentally Sound Urban and Infrastructure Planning, HafenCity University Hamburg, 20457 Hamburg, Germany

Division of Agronomy, University of Göttingen, 37075 Göttingen, Germany

HIGHLIGHTS

•Evapotranspiration (ET) is key to urban

greening and climate change mitigation.

•Urban ET is challenging to model, with

few available approaches so far.

•Urban ET measured by eddy covariance

is modeled using artiﬁcial intelligence.

•Remote sensing data and footprint

modeling predict the land cover

inﬂuencing ET.

•Incorporating remote sensing data en-

hances the predictive accuracy of

urban ET.

GRAPHICAL ABSTRACT

abstractarticle info

Article history:

Received 2 December 2020

Received in revised form 17 April 2021

Accepted 17 April 2021

Available online 28 April 2021

Editor: Jay Gan

Keywords:

Urban water

Eddy covariance

Latent heat ﬂux

1D convolutional neural networks (CNN)

Deep learning

Harmonized Landsat and Sentinel-2

As climate change progresses, urban areas are increasingly affected by water scarcity and the urban heat island

effect. Evapotranspiration (ET) is a crucial component of urban greening initiatives of cities worldwide aimed

at mitigating these issues.However, ET estimation methods in urban areas haveso far been limited. An expanding

number of ﬂux towers in urbanenvironments provide the opportunity to directly measure ET by the eddy covari-

ance method. In this study, we present a novel approach to model urban ET by combining ﬂux footprint model-

ing, remote sensing and geographic information system (GIS) data, and deep learning and machine learning

techniques. This approach facilitates spatio-temporal extrapolation of ET at a half-hourly resolution; we tested

this approach with a two-year dataset from two ﬂux towers in Berlin, Germany. The beneﬁtofintegratingremote

sensing and GIS data into models was investigated by testing four predictor scenarios. Two algorithms (1D

convolutional neural networks (CNNs) and random forest (RF)) were compared. The best-performing models

were then used to model ET values for the year 2019. The inclusion of GIS data extracted using ﬂux footprints en-

hanced the predictive accuracy of models, particularly when meteorological data was more limited. The best-

performing scenario (meteorological and GIS data) showed an RMSE of 0.0239 mm/h and R

of 0.840 with RF

and an RMSE of 0.0250 mm/h and a R

of 0.824 with 1D CNN for the more vegetated site. The 2019 ET sum

was substantially higher at the site surrounded by more urban greenery (366 mm) than at the inner-city site

Science of the Total Environment 786 (2021) 147293

⁎Corresponding author at: Fachgebiet Geoinformation in der Umweltplanung, Sekretariat EB5, Technische Universität Berlin, Straße des 17. Juni 145, D-10623 Berlin, Germany.

E-mail addresses: stenka.vulova@tu-berlin.de (S. Vulova), fred.meier@tu-berlin.de (F. Meier), a.duarterocha@tu-berlin.de (A.D. Rocha), justus.quanz@hcu-hamburg.de (J. Quanz),

hamideh.nouri@uni-goettingen.de (H. Nouri), birgit.kleinschmit@tu-berlin.de (B. Kleinschmit).

Fachgebiet Geoinformation in der Umweltplanung, Sekretariat EB5, Technische Universität Berlin, Straße des 17. Juni 145, D-10623 Berlin, Germany.

Fachgebiet Klimatologie, Institut für Ökologie, Technische Universität Berlin, Rothenburgstraße 12, D-12165 Berlin, Germany.

Department für Nutzpﬂanzenwissenschaften, Abteilung Pﬂanzenbau, Georg-August-Universität Göttingen Von-Siebold-Straße 8, 37075 Göttingen, Germany.

https://doi.org/10.1016/j.scitotenv.2021.147293

Contents lists available at ScienceDirect

Science of the Total Environment

journal homepage: www.elsevier.com/locate/scitotenv

(223 mm),demonstrating the substantial inﬂuence of vegetation on the urban water cycle. The proposed method

is highly promising for modeling ET in a heterogeneous urban environment and can support climate change mit-

igation initiatives of urban areas worldwide.

creativecommons.org/licenses/by/4.0/).

1. Introduction

Meeting the United Nations' Sustainable Development Goal 11 of

“sustainable cities and communities”is critical as urban residents

worldwide are increasingly affected by climate change and water scar-

city (Liu and Jensen, 2018). By 2050, nearly 70% of the world population

is projected to be urban (United Nations, 2019). The paradigm of inte-

grating green infrastructure to support sustainable urban water man-

agement is growing in importance and is known by various terms

such as water sensitive urban design (WSUD), sponge city, and low im-

pact development (LID) (Liu and Jensen, 2018;Nguyen et al., 2019).

These city policies are part of a “co-beneﬁts approach”of climate change

mitigation, which simultaneously addresses urban ﬂooding and the

urban heat island (He et al., 2019). The ecosystem services provided

by green infrastructure, which include the enhancement of ﬂood

water inﬁltration, air temperature modiﬁcation, energy saving, air qual-

ity, biodiversity, and numerous socio-economic beneﬁts, are central to

this approach (He et al., 2019;Nguyen et al., 2019;Nouri et al., 2013).

Berlin, Germany, a city internationally recognized for its sustainable

water supply system, is one example of a city preparing for climate

change impacts by adopting the sponge city concept (Liu and Jensen,

2018). Taking advantage of the cooling effect of evapotranspiration

(ET) is a key principle of this concept (Gunawardena et al., 2017).

Adding more green infrastructure such as green roofs to the city can

provide an evaporative cooling effect during the increasingly common

heat waves expected in northern Europe (Liu and Jensen, 2018;Meehl

and Tebaldi, 2004;Vulova and Kleinschmit, 2019). Therefore, an en-

hanced understanding of ET in urban areas is essential to implementing

climate change mitigation and urban greening schemes (Gunawardena

et al., 2017).

Despite its signiﬁcance, ET estimation in urban environments re-

mains a nascent area of research, as most ET studies have focused on

natural or agricultural areas (Nouri et al., 2013;Saher et al., 2021). The

urban environment is spatio-temporally heterogeneous, with a mixture

of land cover, microclimate, and soil and water characteristics (Nouri

et al., 2013). Point-based ET measurements such as lysimeters and sap

ﬂow may not be representative or practical in an urban setting (Litvak

et al., 2017).

Surface energy balance (SEB) models use remotely sensed imagery

and auxiliary meteorological data as input and estimate ET as the resid-

ual of the energy balance equation (Norman et al., 1995;Saher et al.,

2021;Su, 2002). Some commonly applied SEB models include the

two-source energy balance (TSEB) model (Norman et al., 1995), Surface

Energy Balance Algorithm for Land (SEBAL) (Bastiaanssen et al., 1998),

and Surface Energy Balance System (SEBS) (Su, 2002). Jiang and Weng

(2017) applied TSEB to model daily ET in an urban area in the United

States; however, ET was not validated with ﬁeld data in this study.

Cong et al. (2017) compared SEBS to a water balance method to esti-

mate ET in Beijing, China, ﬁnding that SEBS severely underestimated an-

nual ET. SEB models are not suitable for characterizing urban ET without

major adjustments, as they omit anthropogenic heat and diurnal advec-

tion effects, assume homogeneous vegetation, operate on a regional

scale, and ignore atmospheric variability in urban areas (Saher et al.,

2021).

Physically based hydrological models simulate hydrological pro-

cesses, including soil evaporation, transpiration, interception, subsur-

face ﬂow, and channel ﬂow, using representations of partial

differential equations (Dwarakish et al., 2015). Recent hydrological

models incorporate remote sensing data such as the Normalized Differ-

ence Vegetation Index (NDVI) as a proxy for leaf area index (LAI), bio-

mass, and urban impervious fraction (Boegh et al., 2009, 2004).

Physically based hydrological models are challenging to implement as

they necessitate the estimation of numerous parameters, which often

require expert knowledge or ﬁeld measurements to be determined

(Boegh et al., 2009;Dwarakish et al., 2015).

Eddy covariance (EC), a micrometeorological technique which mea-

sures turbulent ﬂuxes of sensible and latent heat, momentum and other

gases e.g. CO

, is one of the few methods which can directly measure ET

in a heterogeneous urban environment (Nouri et al., 2013). However,

EC measurements have mostly been used in agricultural, forestryandri-

parian studies so far (Holl et al., 2020;Järvi et al., 2012;Menzer et al.,

2015;Moffat et al., 2007;Papale and Valentini, 2003). Limited EC appli-

cations over urban areas were predominantly used to assess exchanges

of energy, greenhouse gasesandair pollutants rather than LE or ET (Holl

et al., 2020;Järvi et al., 2012;Kordowski and Kuttler, 2010;Menzer

et al., 2015;Moffat et al., 2007;Papale and Valentini, 2003). Moreover,

EC measurements are frequently affected by instrument failures, low

turbulent atmospheric conditions, and system “spikes”,leadingtodata

gaps accounting for 20–60% of data on an annual basis (Moffat et al.,

2007). Gap-ﬁlling or modeling is therefore indispensable in order to ob-

tain daily, monthly, and annual sums of ET, which can be used to better

characterize the urban water cycle.

Current modeling and gap-ﬁlling approaches are insufﬁcient in a

heterogeneous urban environment due to the changing source area of

EC measurements and urban heterogeneity (Kotthaus and Grimmond,

2014;Menzer et al., 2015). Previous studies modeling CO

have ad-

dressed the issue of urban heterogeneity by training models indepen-

dently on different wind direction sectors (Menzer et al., 2015)or

adding wind direction as a binary predictor (Järvi et al., 2012). However,

these approaches do not integrate the inﬂuence of wind speed and at-

mospheric stability in controlling footprint area (Kljun et al., 2002;

Kotthaus and Grimmond, 2014). Footprint models, on the other hand,

can estimate the likely surface area affecting turbulent ﬂux measure-

ments at a given point in time (Kotthaus and Grimmond, 2014). Com-

bining footprint modeling with a geospatial database is highly

beneﬁcial for the interpretation of urban ﬂuxes (Christen et al., 2011;

Kotthaus and Grimmond, 2014). However, footprint modeling has not

thus far been combined with machine learning (ML) regression in

order to model urban ET.

Although studies modeling EC ﬂuxes at a half-hourly scale have ap-

plied ML approaches to gap-ﬁll the datasets, the application of ML

models in new locations has not thus far been assessed. Extracting re-

motely sensed data by footprint modeling opens up the opportunity

to spatially upscale ET to the city scale at a high resolution in the future

(Crawford and Christen, 2015). We therefore test the potential to model

ET in areas where no ﬂux tower is available by training in one location

and testing in another. We model urban ET using 1D convolutional neu-

ral networks (1D CNNs) and random forest (RF), which have never and

rarely been applied to model EC ﬂuxes so far, respectively (Kim et al.,

2020).

In this study, we evaluated an approach combining ﬂux footprint

modeling, deep learning (DL) and ML, and GIS and remotely sensed

data in order to model ET at a half-hourly resolution in a heterogeneous

urban environment. We assessed the hypothesis that integrating re-

mote sensing and GIS data by footprint modeling, rather than relying

solely on meteorological data, can better characterize urban ET. We

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

tested this methodology in Berlin, Germany with a two-year dataset

from two ﬂux towers. Our key objectives were to: 1) assess the beneﬁt

of remote sensing and GIS data extracted by ﬂux footprints to modeling

urban ET; 2) identify the main drivers of ET in an urban environment;

3) compare the performance of two ML and DL algorithms (1D CNN

and RF) and four predictor scenarios in modeling urban ET; 4) compare

model performance at two urban ﬂux tower sites with differing land

cover and evaluate to what extent models can be applied in new loca-

tions; and 5) derive monthly and annual ET estimates.

2. Data

A set of temporally dynamic and static data extracted from satellite

imagery, ﬂux towers, and meteorological stations was used to predict

ET in an urban landscape. An overview of the 23 predictors used to

model ET at a half-hourly resolution is given in Table 1.

2.1. Study area

The study is based in Berlin, the largestcity in Germany with 3.7 mil-

lion inhabitants distributed across 891 km

in 2018 (Statistical Ofﬁce of

Berlin-Brandenburg, 2019)(Fig. 1). Berlin is located in eastern Germany

(52.52°N, 13.40°E) and has a humid warm temperate climate (Kottek

et al., 2006).

The two ﬂux towers are part of the Urban Climate Observatory

(UCO) Berlin maintained by the Chair of Climatology at the Technische

Universität Berlin (TUB) (Scherer et al., 2019). The Rothenburgstraße

(ROTH) ﬂux tower is located in an urban research garden belonging to

the TUB in the southwest of the city (Fig. 1). The TUB Campus

Charlottenburg (TUCC) ﬂux tower is located on top of the main building

of the TUB inthe center of the city (Fig. 1). The measurement heights are

39.75 m and 56 m for the ROTH and TUCC towers, respectively. The

tower at ROTH is situated in a more vegetated area, with 50.6% vegeta-

tion, 26.3% impervious surface, 22.8% buildings, and 0.3% water bodies

within a 1000-m radius. The tower at TUCC, in contrast, is characterized

by 32.6% vegetation, 35.5% impervious surface, 27.2% buildings, and 4.7%

water bodies within a 1000-m radius.

2.2. Meteorological data

Hourly meteorological data were acquired from the German Meteo-

rological Service (DWD) Climate Data Center (DWD, 2020a) and used as

ET predictors (Table 1). Solar radiation data were acquired from the sta-

tion Potsdam (19.2 km and 23.2 km distance from ROTH and TUCC, re-

spectively) for both towers. All other DWD data were acquired at

stations Berlin-Dahlem (1.04 km distance from ROTH) and Berlin-

Tegel (5.94 km distance from TUCC) for ROTH and TUCC, respectively.

Linear interpolation was applied for short (<4 h) gaps. Lastly, all DWD

data were linearly interpolated to a half-hourly resolution.

Reference ET (ETo) was calculated with the hourly ASCE “Standard-

ized Reference Evapotranspiration Equation”for short crops (Allen

et al., 2005) using the “hourlyET”function of the R package “water”

(Olmedo et al., 2016). For further details on the parametrization of

ETo and saturated vapor pressure (SVP), refer to the Appendix.

Fig. 2a–d shows daily air temperature, shortwave downward radia-

tion, precipitation, and NDVI throughout the study period. Fig. 2e

shows the temporal distribution of half-hourly ET after quality control

(in units of mm/h) measured at the two ﬂux towers during the study

period. Both towers follow a typical seasonal pattern for ET, with the

highest maximum values in summertime and the lowest maximum

Table 1

An overview of the predictor variables used to model evapotranspiration (ET) at half-hourly resolution; details of the source of the data, preprocessing method, and their spatial and tem-

poral resolutions are listed. In the “Temporal resolution”column, “static”refers to predictors which remain constant over time (such as building height). In the “Spatial resolution”column,

P refers to point data (derived from a single point in space), while F refers to remote sensing and GIS data extracted with ﬂux footprints. All meteorological data (including ETo) were lin-

early interpolated to a half-hourly resolution.

Predictor (acronym) Unit Data source Preprocessing method Spatial

resolution

(m)

Temporal

resolution

GIS predictors

Building height (BH) m Berlin Digital Environmental Atlas (2014) –1 (F) Static

Impervious surface fraction (ISF) % Urban Atlas 2012 (LULC) Vulova et al. (2020); rasterization with 1-m

resolution

1 (F) Static

Normalized Difference Vegetation Index

(NDVI)

–Harmonized Landsat and Sentinel-2 (HLS)

surface reﬂectance product, NASA

Claverie et al. (2018); cloud-masking; pixel-wise

linear interpolation to daily scale

30 (F) Daily

Vegetation fraction % Berlin Digital Environmental Atlas (2014) VH Conversion of VH higher than 0.01 m to 1 and all

other pixels to 0

1 (F) Static

Vegetation height (VH) m Berlin Digital Environmental Atlas (2014) –1 (F) Static

Water fraction % Urban Atlas 2012 (LULC) Rasterization of water bodies with 1-m resolution

(1 = present, 0 = absent)

1 (F) Static

Meteorological predictors

Air pressure hPa DWD –P Hourly

Air temperature °C DWD –P Hourly

Diffuse solar radiation W/m

DWD Unit conversion from J/cm

to W/m

P Hourly

Dry bulb temperature °C DWD –P Hourly

Longwave downward radiation W/m

DWD Unit conversion from J/cm

to W/m

P Hourly

Reference evapotranspiration (ETo) mm/h DWD Allen et al. (2005) equation for short crops;

“water”R package (Olmedo et al., 2016)

P Hourly

Relative humidity (RH) % DWD –P Hourly

Saturated vapor pressure (SVP) hPa DWD Allen et al. (1998);“MeTo”R package (Dettmann

and Grimma, 2019)

P Hourly

Shortwave downward radiation W/m

DWD Unit conversion from J/cm

to W/m

P Hourly

Soil temperature at 5 cm, 10 cm, 20 cm,

50 cm, and 100 cm depth

°C DWD –P Hourly

Solar zenith angle ° DWD –P Hourly

Vapor pressure deﬁcit (VPD) hPa DWD –P Hourly

Wind speed m/s DWD –P Hourly

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

values in wintertime. As expected, the maximum ET values at the more

vegetated site (ROTH, green dots) are nearly double the values at the

less vegetated site (TUCC, orange dots) in the growing season.

2.3. Flux measurements, ﬁltering and data processing

The EC system at both sites combines an open-path gas analyzer and

a three-dimensional sonic anemometer-thermometer (IRGASON,

Campbell Scientiﬁc) for simultaneous measurements of water vapor

density as well as orthogonal wind components. The EC software pack-

age EddyPro (Version 6.2.1) was used to quality-control EC raw data

and to calculate ET from 20-Hz time series over 30-min intervals.

Data quality control and processing with EddyPro included elimina-

tion of spikes, ﬁltering values based on physical thresholds, and statisti-

cal screening based on the method developed by Vickers and Mahrt

(1997). We applied double coordinate rotation, correction of sonic tem-

perature for humidity, high- and low-frequency spectral corrections

(Moncrieff et al., 1997), and corrections for air density (Webb et al.,

1980). Furthermore, instrument diagnostic ﬂags not equal zero and

data with signal strength <0.8 were withheld. EddyPro output data at

30-min resolution with quality ﬂag 2 were excluded (Foken, 2016)as

well as data during and 4 h after precipitation events based upon

DWD precipitation data. Additionally, data from wind directions 17°–

35° at TUCC and 54°–72° at ROTH were excluded because this sector is

inﬂuenced by ﬂow distortion due to the instrument and mounting

setup (Foken, 2016). De-spiking based on standard deviation (SD) was

applied, with LE data ﬁve times greater than the SD removed as spikes

using the R package “FREddyPro”(Xenakis, 2016). A simple threshold

was applied, excluding data where LE was below −100 W/m

and

above 500 W/m

. Furthermore, negative values of ET were removed as

they represent condensation.

Based on overlapping observations from the two towers, the study

period was restricted to two years (1 June 2018 to 1 June 2020). A

total of 16,707 and 16,013 (48% and 46% of the study period) high qual-

ity half-hourly ET observations (in mm/h) then remained available for

modeling at ROTH and TUCC, respectively.

2.4. Turbulent ﬂux footprints

Modeling urban ET measured by ﬂux towers is challenging due to

the dynamic inﬂuence of heterogeneous land cover. Turbulent ﬂuxes

measured by an EC measurement system do not represent the energy

exchange of a ﬁxed radius around the site, but rather that of aconstantly

changing upwind area which contains the sources and sinks contribut-

ing to measurements (Foken, 2016;Kljun et al., 2002;Schmid and Oke,

1990). This area is referred to as a footprint or turbulent ﬂux source area

and can be estimated by footprint models (Crawford and Christen,

2015;Kljun et al., 2002). In this study, footprint areas were estimated

with the Kormann and Meixner (2001) analytical footprint model

using the R package “FREddyPro”(Xenakis, 2016). Further details on

the parametrization of footprint models are given in the Appendix.

The resulting footprint grids were reduced to the 90% probability area.

Weighted averages of the surface cover were extracted by multiplying

these grids with the raster layers and summing the resulting pixel

values on a half-hourly basis (Fig. 3).

2.5. Remote sensing and GIS data

Six remote sensingand GIS datasets were used as predictors of urban

ET (Table 1;Fig. 3), which are referred to as “GIS predictors.”

The Harmonized Landsat and Sentinel-2 (HLS) surface reﬂectance

product provided by NASA was used to compute NDVI, an indicator of

vegetation density and vitality (Claverie et al., 2018;Tucker, 1979).

This open-source product is well-suited for vegetation phenology mon-

itoring in urban areas with a revisit period of 3–5 days and a 30-meter

resolution (Claverie et al., 2018). The preprocessing and interpolation

to daily resolution of HLS data are further described in the Appendix.

Vegetation height (VH) and building height (BH) were provided by

the Berlin Digital Environmental Atlas at 1-meter resolution (Berlin

Senate Department for Urban Development and Housing, 2014). Vege-

tation fraction was derived by converting VH pixels higher than

0.01 m to a value of 1 and all other pixels to 0. Land use and land

cover (LULC) classes data were provided by Urban Atlas 2012

(European Environment Agency, 2018). Water fraction was derived by

assigning the LULC classes “Water”and “Wetlands”to a value of 1 and

Fig. 1. Locations of the two ﬂux towers in Berlin, Germany. A 1-km radius showing vegetation height (VH) and building height (BH) around the towers isdepicted for a) TUCC and b) ROTH.

c) The Normalized Difference Vegetation Index (NDVI) from Landsat 8 is shown for 24 June 2019 in Berlin and its surrounding area. The datum is WGS-84 and the projection is UTM.

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

all other classes to 0. Impervious surface fraction (ISF) was also derived

from the Urban Atlas LULC dataset, as described in Vulova et al. (2020).

3. Methods

3.1. ET modeling

3.1.1. Predictor scenarios

To explore the contribution of different data sources (remote sens-

ing and GIS, meteorological, and ETo) to estimating ET, four predictor

scenarios were tested in models: (1) only ETo as a predictor (one pre-

dictor; “ETo”), (2) ETo and GIS predictors (seven predictors; “ETo and

GIS”), (3) only meteorological predictors (16 predictors; “Met”), and

(4) meteorological and GIS predictors (22 predictors; “Met and GIS”).

GIS predictors refer to the six remote sensing and GIS datasets (BH,

VH, ISF, NDVI, vegetation fraction, and water fraction) (Table 1;Fig. 3).

Meteorological predictors refer to all predictors except GIS predictors

and ETo (Table 1). In total, 32 models were run, with two towers, two

temporal training/testing splits, four predictor scenarios, and two artiﬁ-

cial intelligence (AI) algorithms.

Fig. 3 presents an overview of the entire methodological approach.

3.1.2. ML and DL algorithms

ML and DL algorithms, which broadly fall under the umbrella of AI,

have emerged as particularly accurate methods for gap-ﬁlling urban

ﬂuxes (Järvi et al., 2012;Menzer et al., 2015;Schmidt et al., 2008). ML

and DL algorithms were selected to model urban ET as they can gener-

alize from sample data without relying on a process-based formulation

(Kuhn and Johnson, 2013;Menzer et al., 2015;Schmidt et al., 2008).

Furthermore, ML and DL algorithms allow for the integration of a large

set of predictor variables and the estimation of variable importance

(Kuhn and Johnson, 2013). Here, we tested two supervised regression

DL and ML algorithms: a 1D CNN and RF.

Fig. 2. Meteorological and vegetation greenness conditions during the study period (1 June 2018 to 1 June 2020): (a) daily averaged air temperature (T

air

), (b) daily averaged shortwave

downward radiation (SW), (c) daily precipitation (P), (d) Normalized Difference Vegetation Index (NDVI), and (e) half-hourly ET after quality control measured at the two ﬂux towers

during the study period, with ROTH depicted in green and TUCC in orange. NDVI data were extracted from ﬂux footprint modeling (at a half-hourly temporal scale) at the ROTH ﬂux

tower and averaged to a daily scale. T

air

and P were derived from the German Meteorological Service (DWD) station Berlin-Dahlem (FU) and SW from the DWD station Potsdam. The

study period was drier and warmer than the long-term (1981–2010) mean, with an average annual P of 448 mm (long-term mean: 591 mm) and an average T

air

of 11.3 °C (long-term

mean: 9.5 °C) (DWD, 2020a, 2020b).

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

3.1.2.1. 1D convolutional neural networks (CNN). CNNs are a type of DL

model deﬁned by convolutional layers, which learn local patterns auto-

matically (Chollet and Allaire, 2018). Whereas in computer vision 3D

convolutions are used to extract local spatial features, 1D convolutions

essentially treat time as a spatial dimension, extracting local patterns

in a sequence and recognizing them at a different temporal position

(Chollet and Allaire, 2018). This capacity makes them highly relevant

to sequence processing, with recent applications in hydrological model-

ing (Chollet and Allaire, 2018;Ferreira and da Cunha, 2020;Haidar and

Verma, 2018).

The CNN architecture used in this study consisted of three

convolutional layers, with each of the ﬁrst two convolutional layers im-

mediately followed by max pooling layers. The third convolutional layer

was followed by a ﬂatten layer in order to convert the 3D outputs to 2D

outputs (Chollet and Allaire, 2018). The ﬁnal (seventh) layer is a 1-

dimensional dense layer with linear activation, generating the ET pre-

diction. CNN architecture was set up accordingto the recommendations

of Chollet and Allaire (2018) and trial and error experimentation. In

convolutional layers, padding was set to “same”,stridewassetto1,

and the activation function was set to rectiﬁed linear unit (ReLU). To

train the models, the Adam algorithm (Kingma and Ba, 2015) and the

mean squared error (MSE) loss function were used. The learning rate

was set to the default of 0.001. To limit overﬁtting, early stopping was

used to deﬁne the number of training epochs, with a maximum of 100

training epochs and a patience of 10 epochs. In-depth information on

CNNs and their implementation using the R interface to Keras can be

Fig. 3. Flowchart showing an overview of the study, including the data used for ET modeling, footprint modeling, and ML and DL modeling. Abbreviations can be found in the text. The

probability grids diagram is adapted from Christen (2016).

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

found in Chollet and Allaire (2018). A detailed description of

hyperparameter tuning for CNNs is given in the Appendix.

3.1.2.2. Random forest (RF). RF was used to model urban ET due to its ca-

pacity to handle highly nonlinear relationships, avoid overﬁtting, and

produce a stable prediction (Kim et al., 2020;Kuhn and Johnson,

2013). RF is an ensemble decision tree-based algorithm proposed by

Breiman (2001). Further details on RF and its implementation are

given in Kuhn and Johnson (2013). Hyperparameter tuning for RF is de-

scribed in the Appendix.

3.1.2.3. Variable importance. Relative variable importance scores (scaled

from 0 to 100%) were extracted from models trained with the “Met and

GIS”predictor scenario. Variable importance was extracted by the per-

mutation approach describedby Breiman (2001) using the“vip”R pack-

age for CNNs (Greenwell et al., 2020) and the “caret”R package for RF

(Kuhn, 2008).

3.2. ET performance metrics

To evaluate the temporal and spatial extrapolation capability of

models (Roberts et al., 2017), we split the data into training and testing

sets. For the temporal extrapolation capability, we used 2018 and 2020

data for training and 2019 data for testing and vice versa. For ROTH,

8617 and 8090 observations were available for 2018/2020 and 2019, re-

spectively. For TUCC, 8055 and 7958 observations were available for

2018/2020 and 2019, respectively. For the spatial extrapolation capabil-

ity, we tested two scenarios: (1) training and testing on the same tower

and (2) training on one tower and testing on the other.

The model performance was evaluated using the testing set, and the

prediction accuracy was assessed using ﬁve metrics: root mean square

error (RMSE), percent bias (pbias), coefﬁcient of determination (R

mean absolute error (MAE), and normalized root mean square error

(NRMSE). The value used to normalize NRMSE was the difference be-

tween the maximum and minimum observed values.

3.3. Total ET

Monthly and annual ET sums for the year 2019 were calculated by

two methods: (1) by gap-ﬁlling using the ML and DL algorithms and

(2) by exclusively modeling ET using the ML and DL algorithms without

using the high-quality ET data for 2019. All models used for ET sums

were trained in 2018 and 2020 and on the same tower for which data

were predicted. In all cases, the “Met and GIS”predictor scenario was

applied ﬁrst, as it was found to be the best-performing scenario. In

some cases, ﬂux footprints could not be modeled due to unsuitable at-

mospheric conditions for footprint modeling and missing EC input

data. Thus, any remaining gaps were ﬁlled using models trained with

the “Met”predictor scenario. For ROTH, 9430 half-hours in 2019 were

missing and thus gap-ﬁlled (53.8% of the data). For TUCC, 9562 half-

hours in 2019 were missing and thus gap-ﬁlled (54.6% of the data).

Since ET was modeled at a half-hourly scale but is given in units of

mm/h, half-hourly values were averaged to an hourly scale before sum-

ming ET.

Unless stated otherwise, all modeling and analysis were completed

using R version 3.6.3 (2020-02-29) and RStudio (version 1.3.1073) (R

Core Team, 2020). CNNs were implemented through an R interface

using the Keras DL framework and the TensorFlow backend (Allaire

and Chollet, 2020;Chollet and Allaire, 2018). CNN models were trained

on a local workstation using the CUDA environment (GPU-based pro-

cessing) and a NVIDIA graphics card (Quadro P1000). The “caret”R

package was used as a wrapper package for the RF algorithm implemen-

tation in R (Kuhn, 2008). For RF model tuning and training, parallel pro-

cessing was performed on 14 cores using the R package “doSNOW”

(Microsoft Corporation and Weston, 2019).

4. Results

4.1. ET modeling

When modeling both towers independently, the scenarios including

GIS predictors show the highest prediction accuracy. Table 2 presents

the testing performance metrics averaged across the two temporal

training and testing splits, providing an overall performance estimate

of models. The “Met and GIS”scenario shows the lowest RMSE,

NRMSE, and MAE and highest R

in the majority of cases. With RF, the

“Met and GIS”scenario shows the highest accuracy overall, with an

RMSE of 0.0239 mm (R

= 0.840 and MAE = 0.0154 mm) for ROTH

and 0.0170 mm (R

= 0.544 and MAE = 0.0115 mm) for TUCC

(Table 2). The “Met and GIS”scenario has a similar performance with

CNN, with an RMSE of 0.0250 mm (R

= 0.824 and MAE =

0.0160 mm) for ROTH and 0.0178 mm (R

= 0.502 and MAE =

0.0119 mm) for TUCC.

The increase in performance is greater when adding GIS predictors

to a simple “ETo”scenario than a scenario with 16 meteorological pre-

dictors. Comparing the simple predictor scenarios of “ETo”and “ETo

and GIS”,“ETo and GIS”achieves a higher performance (lower RMSE,

NRMSE, and MAE and higher R

) for both towers (Table 2). The “Met

and GIS”scenario shows increased prediction accuracy than the “Met”

scenario (Table 2). For instance, at ROTH with RF, “ETo and GIS”has a

nearly 0.01 mm lower RMSE (26% decrease) and a 0.15 higher R

(22%

increase) than “ETo”, whereas the increased performance of “Met and

GIS”compared to “Met”is less pronounced: 0.002 mm lower RMSE

(7% decrease) and 0.02 higher R

(3% increase).

RF outperforms CNN in most predictor scenarios, although the per-

formance of both algorithms is comparable (Table 2). In a few scenarios,

CNN performs better (“ETo”for ROTH; “ETo”and “ETo and GIS”for

TUCC).

The RMSE and R

values cannot be directly compared between the

two towers, as they are dependent on the variation of ET. The range

and maximum of ET are lower at TUCC, a site with less surrounding veg-

etation, than at ROTH (Fig. 2e), leading to lower RMSE and R

values at

TUCC (Table 2). In the study period, the maximum ET at ROTH is nearly

double (0.29 mm/h) the maximum ET at TUCC (0.16 mm/h) (Fig. 2e).

, in particular, is highly affected by the variation in the dependent var-

iable (Kuhn and Johnson, 2013). NRMSE is normalized RMSE which fa-

cilitates a comparison of the prediction accuracy which takes into

account the different ranges of ET at the two towers. When training

and testing occurs on the same tower, NRMSE is generally lower at

the more vegetated site (ROTH) than at the less vegetated site (TUCC).

In most cases, training on the more vegetated site (ROTH) and testing

on the less vegetated site (TUCC) is associated with a higher NRMSE

than the opposite scenario due to the lower ET range at TUCC.

Models for both towers have a low pbias when training and testing

in different years (Appendix; Tables 5 and 6). However, training and

testing on different towers increases the RMSE substantially while

showing a relatively small effect on the R

(Table 2). This increase in

RMSE occurs due to the considerable difference in the average of ET be-

tween the two towers (0.05 vs. 0.03 mm/h at ROTH and TUCC, respec-

tively), while the similar R

values indicate that the relationship

between most predictors and ET is similar for both towers.

The addition of GIS data is associated with lower RMSE, NRMSE, and

MAE for RF models when training in ROTH and testing in TUCC. Other-

wise, the inclusion of GIS data is associated with a higher RMSE,

NRMSE, and MAE when training and testing on different towers.This ef-

fect can be explained by the contrasting correlations between ET and

the GIS predictors observed at the two towers (Appendix; Fig. 11). At

ROTH, ET correlates positively with indicators of higher vegetation pres-

ence (VH, Pearson's r = 0.30; vegetation fraction, Pearson's r = 0.32)

and negatively with indicators of impervious land cover (ISF, Pearson's

r=−0.45; BH, Pearson's r = −0.27), as expected. In contrast, at

TUCC, ET has a weak positive correlation with BH (Pearson's r = 0.06)

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

and an insigniﬁcant correlation with ISF. Unexpectedly, ET at TUCC cor-

relates negatively with both vegetation fraction (Pearson's r = −0.15)

and VH (Pearson's r = −0.15).

Training on TUCC leads to an underestimation of ET at ROTH, with a

pbias rangingfrom −44% to −55% (Table 2). As ET at TUCC is on average

lower (Figs. 3 and 6), models trained on TUCC data cannot predict the

higher ET observed at ROTH. Conversely, most models trained on

ROTH data overestimate the lower ET observed at TUCC, as indicated

by a positive pbias (52%–87%) for all predictor scenarios except “ETo

and GIS.”The decrease in pbias when including GIS data in models

trained in ROTH and tested in TUCC can be explained by the contradic-

tory relationship between ET and GIS predictors at the two towers (Ap-

pendix; Fig. 11).

Monthly and diurnal modeling accuracy are discussed in the Appen-

dix (Figs. 14–18).

4.2. Variable importance

The relative variable importance of predictors for both towers was

tested. Fig. 4 shows the percentage of relative inﬂuence of predictors

with the “Met and GIS”scenario, which includes most of the predictors

(except ETo). Despite how strongly ET is driven by meteorological con-

ditions, the inﬂuence of GIS predictors is apparent in the RF variable im-

portance. For RF models at ROTH, NDVI, ISF, and BH are the third, ﬁfth,

and sixth most important predictors, respectively. The most important

meteorological predictors at both ROTH and TUCC with RF are wind

speed, air pressure, and solar zenith angle.

RF variable importance differs between the two towers, reﬂecting

thehigher inﬂuence of impervious cover at TUCC. The secondand fourth

most important predictors at TUCC with RF are ISF and BH, respectively.

Water fraction also has a minor inﬂuence in TUCC, whereas in ROTH

water fraction has essentially no inﬂuence due to the lack of water bod-

ies around the tower (Fig. 4).

CNN variable importance differs substantially from RF variable im-

portance. With CNNs, the most important meteorological predictors

are shortwave downward radiation, solar zenith angle, and diffuse

solar radiation at ROTH and solar zenith angle, wind speed, and short-

wave downward radiation at TUCC. ISF is the 7th most important pre-

dictor at ROTH, whereas the other GIS predictors are low ranked in

importance.

4.3. Total ET

Monthly and annual ET sums were computed for both towers

(Fig. 5). ET sums show a substantially higher ET at the more vegetated

site (ROTH), as expected (Fig. 5). The annual ET sum for 2019 is

~140 mm higher at ROTH than at TUCC, with an annual sum of

366 mm and 223 mm, respectively, when gap-ﬁlling with the best-

performing algorithm (RF) (Fig. 5). The highest monthly ET sums are

in the summer months; for ROTH, gap-ﬁlled ET sums with RF are

63mminJune,54mminJuly,and50mminAugust(

Fig. 5). For

TUCC, gap-ﬁlled ET sums with RF are around half the sums at ROTH:

31 mm in June, 28 mm in July, and 27 mm in August. Annual ET sums

differ by only 3–5 mm when modeling the entire year of 2019 rather

than gap-ﬁlling, conﬁrming the dependability of the approach for ET es-

timation. Modeling the entire year without gap-ﬁlling reproduces the

diurnal and annual cycle of the original data well for both algorithms

(Fig. 6). CNN better reproduces the high summer daytime ET at ROTH,

whereas these values are underestimated by RF (Fig. 6; Appendix

Table 5). Nevertheless, differences in annual ET sums between the two

algorithms are negligible, even when solely modeling (4 mm and

10 mm difference at ROTH and TUCC, respectively) (Fig. 5). For both

towers, 14 h remained where ET could not be modeled due to missing

DWD data, which were assigned to zero.

5. Discussion

5.1. ET in an urban environment

Aligning with greening, carbon-neutrality, and sustainability plans

of many cities worldwide and in light of the impact of climate change

on the urban water cycle and urban heat, it is crucial to accurately char-

acterize urban ET.In this study, we presented a novel approach combin-

ing footprint modeling, ML and DL, and remote sensing to accurately

model urban ET at a half-hourly scale. Integrating GIS, remote sensing

and meteorological datasets and using ML and DL techniques paves

the way for new approaches in urban ET estimation and facilitates en-

hancing its accuracy and transferability. When available meteorological

data is more limited (e.g., only ETo data), the addition of remotely

sensed satellite and GIS data is especially beneﬁcial for ET modeling in

an urban environment. Some urban areas, particularly in developing

countries, have limited access to data such as solar radiation

(Shaﬁeiyoun et al., 2020;Shojaei et al., 2018), whereas medium-

resolution satellite imagery is freely available worldwide (Claverie

et al., 2018). Modeling with Penman-Monteith ETo still assumes exten-

sive meteorological data is available for an urban area, which is not the

case for data-scarce regions (Shaﬁeiyoun et al., 2020). Therefore, future

work should consider even more limited data scenarios.

We tested different predictors of urban ET on two EC towers located

in different neighborhoods in Berlin. We found a combination of

Table 2

Testing performance metrics averaged across the two training and testing splits (training in 2018/2020 and testing in 2019 and vice versa). The performance metrics are root mean square

error (RMSE), mean absolute error (MAE), percent bias (pbias), coefﬁcient of determination (R

), and normalized root mean square error (NRMSE). The best performance metricsfor each

tower training and testing combination (e.g., training in ROTH and testing in TUCC) are shown in bold.

Tower (train) Tower (test) Predictors RMSE (mm/h) MAE (mm/h) pbias (%) R

(−) NRMSE (%)

CNN RF CNN RF CNN RF CNN RF CNN RF

ROTH ROTH ETo 0.0304 0.0355 0.0195 0.0226 −6.20 0.95 0.745 0.660 10.55 12.30

ETo and GIS 0.0266 0.0263 0.0177 0.0169 1.05 −0.20 0.801 0.805 9.25 9.10

Met 0.0274 0.0256 0.0178 0.0164 4.65 2.35 0.793 0.817 9.50 8.85

Met and GIS 0.0250 0.0239 0.0160 0.0154 −3.15 1.80 0.824 0.840 8.65 8.30

TUCC TUCC ETo 0.0186 0.0208 0.0121 0.0140 −4.00 0.80 0.486 0.360 11.70 13.05

ETo and GIS 0.0174 0.0175 0.0114 0.0116 −4.65 1.40 0.525 0.514 10.95 11.00

Met 0.0178 0.0173 0.0119 0.0119 −0.60 5.90 0.508 0.529 11.15 10.85

Met and GIS 0.0178 0.0170 0.0119 0.0115 0.35 4.45 0.502 0.544 11.15 10.65

ROTH TUCC ETo 0.0399 0.0475 0.0247 0.0285 70.90 83.95 0.486 0.452 25.05 29.80

ETo and GIS 0.0635 0.0226 0.0398 0.0153 −137.10 −7.45 0.067 0.369 39.90 14.20

Met 0.0473 0.0446 0.0290 0.0273 90.50 87.15 0.507 0.521 29.70 27.95

Met and GIS 0.0636 0.0318 0.0393 0.0202 −119.00 52.10 0.145 0.514 39.70 19.90

TUCC ROTH ETo 0.0509 0.0524 0.0297 0.0311 −48.60 −46.65 0.744 0.524 17.65 18.20

ETo and GIS 0.0583 0.0538 0.0349 0.0321 −61.70 −54.75 0.609 0.703 20.25 18.65

Met 0.0516 0.0491 0.0313 0.0289 −47.10 −44.00 0.665 0.775 17.95 17.05

Met and GIS 0.0582 0.0505 0.0352 0.0297 −61.15 −49.15 0.596 0.780 20.20 17.50

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

meteorological, remote sensing, and GIS data to be the optimal predic-

tor scenario of urban ET. For the tower surrounded by more urban

greenery, meteorological and GIS data shows an RMSE of 0.0239 mm/

handR

of 0.840 with RF and an RMSE of 0.0250 mm/h and a R

0.824 with 1D CNN. For the tower surrounded by a greater proportion

of impervious cover, the same scenario shows an RMSE of 0.0170 mm/

handR

of 0.544 with RF and an RMSE of 0.0178 mm/h and R

0.502 with 1D CNN.

Our approach compares favorably with other modeling approaches

for estimating hourly urban LE; we converted LE (W/m

) from other

studies to ET (mm/h) for comparison. For instance, the Surface Urban

Energy and Water Balance Scheme (SUEWS) was used to model LE on

an hourly scale in Los Angeles, USA and Vancouver, Canada; an RMSE

of 0.0295–0.0826 mm/h and R

0.47–0.79 were reported (Järvi et al.,

2011). SUEWS was applied to estimate urban LE at an hourly scale at

two EC sites in the UK, a dense urban site in London and a suburban

site in Swindon; an RMSE of 0.0364 mm/h and R

of 0.245 and an

RMSE of 0.0333 and R

of 0.721 were reported, respectively (Ward

et al., 2016). Three urban land-surface models (LSMs) were applied to

model EC ﬂuxes in a dense city center site and a suburban site in Hel-

sinki, Finland (Karsisto et al., 2016). The LSMs showed an RMSE of

0.0168 mm/h (winter) to 0.0889 mm/h (summer) at the suburban

site and an RMSE of 0.0226 mm/h (winter) to 0.0733 mm/h (summer)

at the urban site (Karsisto et al., 2016). A micrometeorological approach

(ARM) was applied to model LE in three temperate cities, ﬁnding a poor

to moderate agreement with EC measurements; an RMSE of

0.0268–0.0450 mm/h and R

of 0.37–0.42, an RMSE of 0.0280 mm/h

and R

of 0.09, and an RMSE of 0.0311 mm/h and R

of 0.07 were re-

ported for Basel, Switzerland, London, UK, and Heraklion, Greece, re-

spectively (Chrysoulakis et al., 2018).

Fig. 4. Relative variable importance revealed by models. The “Met and GIS”(meteorologicaland GIS predictors) predictor scenario is depicted. The variable importance wasaveragedacross

the two training and testing splits (training in 2018/2020 and testing in 2019 and vice versa).

Fig. 5. Monthly evapotranspiration (ET) sums for the year 2019 calculated by (a) gap-ﬁlling using random forest (RF) and 1D convolutional neural networks (CNN) and (b) by only

modeling using RF and 1D CNN without using the original ET data for 2019. The ﬁrst annual ET sum values listed represent the RF-based annual sums, while the CNN-based annual

sums are in parentheses. All models used to obtain ET sums were trained in 2018 and 2020 and on the same tower for which data were predicted. In all cases, the “Met and GIS”

(meteorological and GIS) predictor scenario was applied ﬁrst. Any remaining gaps were ﬁlled using models trained with the “Met”(meteorological) predictor scenario (see main text

for further details).

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

5.2. Modeling ET

Comparing ML and DL algorithms used in our study, RF showed a

slightly higher accuracy than CNN, although the performance of the al-

gorithms was comparable. RF also outperformed ANNs and SVM in a

study gap-ﬁlling methane ﬂuxes (Kim et al., 2020). Kim et al. (2020) at-

tributed the superior performance of RF for methane gap-ﬁlling to its

capacity to incorporate a variety of model inputs, including noise,

while avoiding overﬁtting. 1D CNNs are nevertheless promising for hy-

drological modelingdue totheir high computational speed and capacity

to extract temporal patterns (Ferreira and da Cunha, 2020;Haidar and

Verma, 2018). As data-driven empirical models, the ML and DL algo-

rithms needed to be trained at each location to perform optimally,

shown by the increase in RMSE when training and testing on different

towers. However, the similar R

values whether training and testing

on the same or different towers show that the relationship between

the predictors and ET are similar for both towers. The inclusion of re-

mote sensing and GIS data opens up the possibility to ﬁt general models

incorporating the inﬂuence of surface cover.

5.3. ET drivers in an urban environment

Deeper investigation of predictors by variable importance analysis

highlighted the contribution of remote sensing and GIS data to models,

even though ET is primarily driven by meteorological variables. The

most important GIS predictors based on RF were NDVI, ISF, and BH at

ROTH and ISF, BH, and vegetation fraction at TUCC. Land cover may play

a role in which predictors are most relevant. For instance, NDVI may be

more relevant for modeling in a more vegetated urban area

(e.g., ROTH), as NDVI has been shown to be very beneﬁcial to modeling

ET of urban vegetation (Boegh et al., 2009;Nouri et al., 2015). CNN models

assigned lower importance to GIS predictors, with ISF as the most impor-

tant GIS predictor at ROTH and BH as the most important GIS predictor at

TUCC. Wind speed, air pressure, and solar zenith angle are highly relevant

in ET estimation according to RF models. CNN models also emphasized a

similar set of meteorological variables: shortwave downward radiation,

solar zenith angle, diffuse solar radiation, and wind speed.

The ET sums showed a substantial difference between the less vege-

tated site and the more vegetated site, demonstrating how green

Fig. 6. Annual and diurnal course of (a) observed evapotranspiration (ET) at ROTH, (b) observed ET at TUCC, (c) modeled ET at ROTH with 1D convolutional neural networks (CNN),

(d) modeled ET at TUCC with 1D CNN, (e) modeled ET at ROTH with random forest (RF), and (f) modeled ET at TUCC with RF. ET depicted in (c)–(f) is exclusively modeled with ML

algorithms (not gap-ﬁlled). All models used to model ET were trained in 2018 and 2020 and on the same tower for which data were predicted. White areas represent missing data

(for (a) and (b)) and modeled negative values (for (c)–(f)).

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

infrastructure can substantially alter the urban water cycle. In summer-

time, monthly ET sums of a more highly vegetated site (ROTH) were

double the ET sums of the less vegetated site (TUCC). ET at ROTH consti-

tuted a larger share of available precipitation (P) annually (72% of

506 mm P measured at Berlin-Dahlem) than at TUCC (56% of 400 mm

P measured at Berlin-Tegel or 38% of 584 mm P measured at the TUCC

ﬂux tower), which can be attributed to the greater vegetation cover at

ROTH. P was not calculated from the ROTH ﬂux tower due to large

data gaps in the dataset. A study in a suburban area (Swindon) in the

UK estimated annual ET to be 370 mm using EC data (Ward et al.,

2013), closely matching the annual ET sum at the more vegetated site

(ROTH) in our study (366 mm). The study area in Swindon, UK was sim-

ilar to our study site at ROTH, as their ﬂux tower was also installed in a

residential garden with signiﬁcant surrounding vegetation cover (44%

within a 500-m radius) (Ward et al., 2013). However, the ratio of ET

to P annually at Swindon (57%) was lower than the ratio at ROTH

(Ward et al., 2013). A study simulating annual ET in Copenhagen,

Denmark with an ecohydrological model estimated an annual ET of

210 mm, corresponding to 27% of P (Boegh et al., 2009); this ET sum

is comparable to the value at the less vegetated site (223 mm), although

the percentage of P is lower in Copenhagen than in both sites in this

study. The site in Copenhagen was surrounded by 28% vegetation

cover in the averaged daily ﬂux footprint (Boegh et al., 2009), which is

even lower than the fraction of vegetation cover at TUCC (33%). A source

of uncertainty for ET sums are precipitation events, during which the EC

system cannot accurately record ﬂuxes. On average, modeled ET was

lower during precipitation events, likely reﬂecting the reduced short-

wave radiation during rain events (Appendix;Fig. 12 and Table 7). In re-

ality, a rapid evaporation may occur directly following rainfall from

rainwater that is intercepted by impervious surfaces or vegetation

(Ward et al., 2013). Methods relying on open-path gas analyzers there-

fore underestimate ET sums (Ward et al., 2013).

5.4. Future applications

The future of sustainable cities, elaborated in the sponge city or

WSUD concept, hinges upon ecosystem services provided by green in-

frastructure (He et al., 2019;Liu and Jensen, 2018). ET is a key indicator

of the ecosystem services provided by urban green spaces due to its role

in the water balance and its cooling capacity; as such, urban initiatives

are already explicitly aiming to enhance ET by integrating more vegeta-

tion, green facades, and green roofs into the urban landscape (Liu and

Jensen, 2018). Expanding green infrastructure in cities, however, brings

trade-offs in urban sustainability, as more water resources are used for

landscape irrigation (Litvak et al., 2017;Nouri et al., 2019;Pataki et al.,

2011). While urban water scarcity has mainly been the concern of

(semi-)arid regions so far (Litvak et al., 2017;Pataki et al., 2011;Saher

et al., 2021), extreme drought and heat waves in recent years in western

and northern Europe have demonstrated that these challenges are also

increasingly relevant for temperate cities suffering from summer heat

waves such as Paris or Berlin (Dousset et al., 2011;Fenner et al., 2019;

Gabriel and Endlicher, 2011).

The growing interest in managing and quantifying the impacts of cli-

mate change on cities therefore demands accurate ET modeling ap-

proaches (Boegh et al., 2009;Cong et al., 2017;Saher et al., 2021). The

proposed methodology can be applied to simulate the effects of climate

change and land use scenarios on urban ET, with implications for the

urban energy and water balance. Furthermore, the presented approach

can be used to upscale urban ET spatially at the city scale at a high res-

olution in the presence of EC and GIS data as the most important model

inputs are freely available. Spatial upscaling can facilitate the explora-

tion of how adding green infrastructure such as green roofs in cities

can augment evaporative cooling and where to install them for the

greatest beneﬁt to urban residents (Besir and Cuce, 2018). Furthermore,

large-scale urban land use change, such as the conversion of the former

Berlin Tempelhof Airport to a built-up area, can be simulated to

anticipate its effect on ET and its related ecosystem services. In future

applications, urban ET maps can be made publicly available to support

initiatives aiming for sustainable irrigation management of urban

green spaces and heat risk mitigation for urban residents. The presented

approach can also be applied to accurately gap-ﬁll urban EC ﬂux data

and produce long-term ET time series, which can be used to better un-

derstand ET seasonality and trends (Foltýnová et al., 2020).

Generating spatial predictions of ET simply requires predicting with

trained models on a GIS database of all predictors, as has previously

been applied for urban air temperature (Vulova et al., 2020). However,

some challenges need to be resolved before upscaling. Extracted GIS

data by footprint modeling is averaged over different spatial scales

(Kotthaus and Grimmond, 2014). Upscaling spatially would thus re-

quire spatial aggregation of GIS data corresponding to an average

footprint.

The ET dynamics of the less vegetated site (TUCC) need to be further

investigated, particularly in relation to the inﬂuence of land cover. A

study modeling LE from EC data at an hourly resolution with SUEWS

also showed lower accuracy (higher RMSE and lower R

) in modeling

LE in a dense urban site compared to a suburban site surrounded by

more vegetation (Ward et al., 2016). The lower range of ET values and

therefore lower R

is expected in a site with less vegetation (Ward

et al., 2016). Furthermore, at the more vegetated site (ROTH), footprint

modeling revealed the expected positive correlation of vegetation cover

and ET (Appendix; Fig. 11). At the less vegetated site, however, the cor-

relations were counter-intuitive, showing a negative relationship be-

tween ET and indicators of vegetation presence (vegetation fraction

and vegetation height) (Appendix; Fig. 11). As the TUCC tower is an

inner-city tower situated on a building roof, it may be more affected

by water vapor released through anthropogenic activities, which can

confound the contribution of surrounding vegetation to ET (Karsisto

et al., 2016;Kotthaus and Grimmond, 2012;Nordbo et al., 2012;Ward

et al., 2013). In addition, observed ET from EC towers is not reliable dur-

ing rain. In this study, four hours of data after precipitation were re-

moved; however, the effect of increased ET by wet surfaces after

rainfall may persist for more than 12 h (Kotthaus and Grimmond,

2014). Advection effects, which are more common in a patchy urban

landscape, may also affect EC ﬂuxes (Kotthaus and Grimmond, 2014;

Vesala et al., 2008). Kotthaus and Grimmond (2014) also found that tur-

bulent ﬂuxes in the center of London, UK could not be explained by sur-

face cover types and suggested that other effects besides impervious

surface cover fractions need to be considered to interpret urban ﬂuxes.

The presented approach can be integrated with any remote sensing

and GIS layers that may be relevant to modeling an EC ﬂux, such as

urban morphology and Leaf Area Index (LAI). The integration of foot-

print models with ML and DL is also relevant for other urban ﬂuxes,

such as CO

(Crawford and Christen, 2015;Järvi et al., 2012;Kotthaus

and Grimmond, 2014;Menzer et al., 2015). Future studies can apply

this approach to other cities and ﬂuxes.

6. Conclusions

Urban ET is a key aspect of urban greening efforts worldwide and

therefore requires innovative methods to be accurately quantiﬁed. We

presented a novel approach fusing ﬂux footprint modeling, remote

sensing and GIS data, and ML and DL to model urban ET at a half-

hourly scale. Flux footprints allow forland cover characteristics to be in-

corporated into ML and DL algorithms, which is essential to estimating

ET in heterogeneous urban terrain. We compared two DL and ML algo-

rithms (1D convolutional neural networks (CNNs) and random forest

(RF)). Although RF showed a slightly higher accuracy, the performance

of CNNs was also promising and warrants further exploration with

other model architectures.

Four predictor scenarios were tested to assess the contribution of re-

mote sensing and GIS data to model performance. We found incorporat-

ing remote sensing, GIS, and meteorological predictors to be the best-

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

performing scenario to estimate urban ET. This predictor scenario with

RF showed an RMSE of 0.024 mm/h and R

of 0.84 and an RMSE of

0.017 mm/h and R

of 0.54 for the more vegetated and less vegetated

site, respectively. NDVI and impervious surface fraction emerged as

the most important GIS predictors, while solar zenith angle, shortwave

downward radiation, wind speed, and air pressure were the most im-

portant meteorological predictors.

Future applications of this methodology include gap-ﬁlling ET in

order to analyze long-term trends, simulating the inﬂuence of altering

urban land cover on ET, and spatially upscaling ET to the city scale

with a high spatial resolution. The presented method can support sus-

tainable urban planning efforts in the face of climate change, including

initiatives to manage blue and green water resources and to mitigate

the urban heat island effect.

CRediT authorship contribution statement

Stenka Vulova: Conceptualization, Methodology, Software, Formal

analysis, Investigation, Writing –original draft, Visualization. Fred

Meier: Resources, Data curation, Writing –review & editing, Funding

acquisition. Alby Duarte Rocha: Software, Writing –review & editing.

Justus Quanz: Software, Writing –review & editing. Hamideh Nouri:

Writing –review & editing. Birgit Kleinschmit: Resources, Writing –re-

view & editing, Supervision, Project administration, Fundingacquisition.

Declaration of competing interest

The authors declare that they have no known competing ﬁnancial

interests or personal relationships that could have appeared to inﬂu-

ence the work reported in this paper.

Acknowledgements

This work was supported by the German Research Foundation

(DFG) within the Research Training Group ‘Urban Water Interfaces’

(GRK 2032-2). Fred Meier acknowledges funding for instrumentation

of the Urban Climate Observatory (UCO) Berlin from DFG grant SCHE

750/8 and SCHE 750/9 within Research Unit 1736 “Urban Climate and

Heat Stress in Mid Latitude Cities in View of Climate Change (UCaHS)”

and the research program “Urban Climate Under Change ([UC]2)”,

funded by the German Federal Ministry of Education and Research

(BMBF) (FKZ 01LP1602A). The authors would like to thank the DWD,

the Chair of Climatology at the Technische Universität Berlin, NASA,

the European Commission, and the Berlin Senate Department for Urban

Development and Housing for providing data used in this paper. They

are also grateful to the three anonymous reviewers for their valuable

comments that improved the quality of the manuscript.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.

org/10.1016/j.scitotenv.2021.147293.

References

Allaire, J.J., Chollet, F., 2020. keras: R Interface to “Keras”(R Package Version 2.3.0.0.9000)

[WWW Document]. URL. https://keras.rstudio.com.

Allen, Richard G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration: Guide-

lines for computing crop requirements. FAO Irrigation and drainage paper 56. FAO -

Food and Agriculture Organization of the United Nations, Rome, Italy.

Allen, R.G., Walter, I.A., Elliott, R.L., Howell, T.A., Itenﬁsu, D., Jensen, M.E., Snyder, R.L.,

2005. The ASCE Standardized Reference Evapotranspiration Equation. American Soci-

ety of Civil Engineers https://doi.org/10.1061/9780784408056.

Bastiaanssen, W.G.M., Pelgrum, H., Wang, J., Ma, Y., Moreno, J.F., Roerink, G.J., Van Der

Wal, T., 1998. A remote sensing surface energy balance algorithm for land (SEBAL):

2. Validation. J. Hydrol. 212–213, 213–229. https://doi.org/10.1016/S0022-1694(98)

00254-6.

Berlin Senate Department for Urban Development and Housing, 2014. Building and Veg-

etation Heights (Edition 2014) [WWW Document]. Berlin Environ. Atlas URL. https://

www.stadtentwicklung.berlin.de/umwelt/umweltatlas/ed610_05.htm.(Accessed14

August 2019).

Besir, A.B., Cuce, E., 2018. Green roofs and facades: a comprehensive review. Renew. Sust.

Energ. Rev. 82, 915–939. https://doi.org/10.1016/j.rser.2017.09.106.

Boegh, E., Thorsen, M., Butts, M.B., Hansen, S., Christiansen, J.S., Abrahamsen, P., Hasager,

C.B., Jensen, N.O., Van Der Keur, P., Refsgaard, J.C., Schelde, K., Soegaard, H., Thomsen,

A., 2004. Incorporating remote sensing data in physically based distributed agro-

hydrological modelling. J. Hydrol. 287, 279–299. https://doi.org/10.1016/j.

jhydrol.2003.10.018.

Boegh, E., Poulsen, R.N., Butts, M., Abrahamsen, P., Dellwik, E., Hansen, S., Hasager, C.B.,

Ibrom, A., Loerup, J.K., Pilegaard, K., Soegaard, H., 2009. Remote sensing based evapo-

transpiration and runoff modeling of agricultural, forest and urban ﬂux sites in

Denmark: from ﬁeld to macro-scale. J. Hydrol. 377, 300–316. https://doi.org/

10.1016/j.jhydrol.2009.08.029.

Breiman, L., 2001. Random forests. Mach. Learn. 45, 5–32. https://doi.org/10.1023/A:

1010933404324.

Chollet, F., Allaire, J.J., 2018. Deep Learning With R. Manning Publications Co, Shelter Is-

land, NY.

Christen, A., 2016. Gridded Turbulent Source Area [WWW Document]. GitHub URL.

https://github.com/achristen/Gridded-Turbulent-Source-Area. (Accessed 26 October

2020).

Christen, A., Coops, N.C., Crawford, B.R., Kellett, R., Liss, K.N., Olchovski, I., Tooke, T.R., Van

Der Laan, M., Voogt, J.A., 2011. Validation of modeled carbon-dioxide emissions from

an urban neighborhood with direct eddy-covariance measurements. Atmos. Environ.

45, 6057–6069. https://doi.org/10.1016/j.atmosenv.2011.07.040.

Chrysoulakis, N., Grimmond, S., Feigenwinter, C., Lindberg, F., Gastellu-Etchegorry, J.-P.,

Marconcini, M., Mitraka, Z., Stagakis, S., Crawford, B., Olofson, F., Landier, L.,

Morrison, W., Parlow, E., 2018. Urban energy exchanges monitoring from space. Sci.

Rep. 8, 11498. https://doi.org/10.1038/s41598-018-29873-x.

Claverie, M., Ju, J., Masek, J.G., Dungan, J.L., Vermote, E.F., Roger, J.C., Skakun, S.V., Justice, C.,

2018. The harmonized Landsat and Sentinel-2 surface reﬂectance data set. Remote

Sens. Environ. 219, 145–161. https://doi.org/10.1016/j.rse.2018.09.002.

Cong, Z.T., Shen, Q.N., Zhou, L., Sun, T., Liu, J.H., 2017. Evapotranspiration estimation con-

sidering anthropogenic heat based on remote sensing in urban area. Sci. China Earth

Sci. 60, 659–671. https://doi.org/10.1007/s11430-016-0216-3.

Crawford, B., Christen, A., 2015. Spatial source attribution of measured urban eddy covari-

ance CO

ﬂuxes. Theor. Appl. Climatol. 119, 733–755. https://doi.org/10.1007/

s00704-014-1124-0.

Dettmann, Ullrich, Grimma, R., 2019. MeTo: Meteorological Tools (R package version

0.1.0). https://cran.r-project.org/package=MeTo.

Dousset, B., Gourmelon, F., Laaidi, K., Zeghnoun, A., Giraudet, E., Bretin, P., Mauri, E.,

Vandentorren, S., 2011. Satellite monitoring of summer heat waves in the Paris met-

ropolitan area. Int. J. Climatol. 31, 313–323. https://doi.org/10.1002/joc.2222.

Dwarakish, G.S., Ganasri, B.P., De Stefano, L., 2015. Impact of land use change on hydrolog-

ical systems: a review of current modeling approaches. Cogent Geosci. 1, 1115691.

https://doi.org/10.1080/23312041.2015.1115691.

DWD, 2020a. DWD Climate Data Center (CDC) [WWW Document]. URL. http://ftp-cdc.

dwd.de/climate_environment/CDC/. (Accessed 15 June 2020).

DWD, 2020b. Vieljährige Mittelwerte [WWW Document]. URL. https://www.dwd.de/DE/

leistungen/klimadatendeutschland/vielj_mittelwerte.html. (Accessed 4 November

2020).

European Environment Agency, 2018. Urban Atlas [WWW Document]. URL. https://

www.eea.europa.eu/data-and-maps/data/copernicus-land-monitoring-service-

urban-atlas. (Accessed 14 May 2020).

Fenner, D., Holtmann, A., Krug, A., Scherer, D., 2019. Heat waves in Berlin and Potsdam,

Germany –long-term trends and comparison of heat wave deﬁnitions from 1893

to 2017. Int. J. Climatol. 39, 2422–2437. https://doi.org/10.1002/joc.5962.

Ferreira, L.B., da Cunha, F.F., 2020. New approach to estimate daily reference evapotrans-

piration based on hourly temperature and relative humidity using machine learning

and deep learning. Agric. Water Manag. 234, 106113. https://doi.org/10.1016/j.

agwat.2020.106113.

Foken, T., 2016. Angewandte Meteorologie: Mikrometeorologische Methoden. Springer

Spektrum, New York, United States https://doi.org/10.1007/978-3-642-25525-0.

Foltýnová, L., Fischer, M., McGloin, R.P., 2020. Recommendations for gap-ﬁlling eddy co-

variance latent heat ﬂux measurements using marginal distribution sampling.

Theor. Appl. Climatol. 139, 677–688. https://doi.org/10.1007/s00704-019-02975-w.

Gabriel, K.M.A., Endlicher, W.R., 2011. Urban and rural mortality rates during heat waves

in Berlin and Brandenburg, Germany. Environ. Pollut. 159, 2044–2050. https://doi.

org/10.1016/j.envpol.2011.01.016.

Greenwell, B., Boehmke, B., Gray, B., 2020. vip: Variable Importance Plots (R Package Ver-

sion 0.2.2) [WWW Document]. URL. https://cran.r-project.org/package=vip.

Gunawardena, K.R., Wells, M.J., Kershaw, T., 2017. Utilising green and bluespace to miti-

gate urban heat island intensity. Sci. Total Environ. 584–585, 1040–1055. https://

doi.org/10.1016/j.scitotenv.2017.01.158.

Haidar, A., Verma, B., 2018. Monthly rainfall forecasting using one-dimensional deep

convolutional neural network. IEEE Access 6, 69053–69063. https://doi.org/

10.1109/ACCESS.2018.2880044.

He, B.J., Zhu, J., Zhao, D.X., Gou, Z.H., Qi, J. Da, Wang, J., 2019. Co-beneﬁts approach: oppor-

tunities for implementing sponge city and urban heat island mitigation. Land Use Pol-

icy 86, 147–157. https://doi.org/10.1016/j.landusepol.2019.05.003.

Holl, D., Pfeiffer, E.M., Kutzbach, L., 2020. Comparison of eddy covariance CO

and CH

ﬂuxes from mined and recently rewetted sections in a northwestern German cutover

bog. Biogeosciences 17, 2853–2874. https://doi.org/10.5194/bg-17-2853-2020.

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293

Järvi, L., Grimmond, C.S.B., Christen, A., 2011. The Surface Urban Energy and Water Bal-

ance Scheme (SUEWS): evaluation in Los Angeles and Vancouver. J. Hydrol. 411,

219–237. https://doi.org/10.1016/j.jhydrol.2011.10.001.

Järvi, L., Nordbo, A., Junninen, H., Riikonen, A., Moilanen, J., Nikinmaa, E., Vesala, T., 2012.

Seasonal and annual variation of carbon dioxide surface ﬂuxes in Helsinki, Finland, in

2006–2010. Atmos. Chem. Phys. 12, 8475–8489. https://doi.org/10.5194/acp-12-

8475-2012.

Jiang, Y., Weng, Q., 2017. Estimation of hourly and daily evapotranspiration and soil mois-

ture using downscaled LST over various urban surfaces. GIScience Remote Sens. 54,

95–117. https://doi.org/10.1080/15481603.2016.1258971.

Karsisto, P., Fortelius, C., Demuzere, M., Grimmond, C.S.B., Oleson, K.W., Kouznetsov, R.,

Masson, V., Järvi, L., 2016. Seasonal surface urban energy balance and wintertime sta-

bility simulated using three land-surface models in the high-latitude city Helsinki. Q.

J. R. Meteorol. Soc. 142, 401–417. https://doi.org/10.1002/qj.2659.

Kim, Y., Johnson, M.S., Knox, S.H., Black, T.A., Dalmagro, H.J.,Kang, M., Kim, J., Baldocchi, D.,

2020. Gap-ﬁlling approaches for eddy covariance methane ﬂuxes: a comparison of

three machine learning algorithms and a traditional method with principal compo-

nent analysis. Glob. Chang. Biol. 26, 1499–1518. https://doi.org/10.1111/gcb.14845.

Kingma, D.P., Ba, J.L., 2015. Adam: a method for stochastic optimization. 3rd International

Conference on Learning Representations, ICLR 2015 - Conference Track Proceedings.

San Diego, California, United States, pp. 1–15.

Kljun, N., Rotach, M.W., Schmid, H.P., 2002. A three-dimensional backward lagrangian

footprint. Boundary-Layer Meteorol. 103, 205–226.

Kordowski, K., Kuttler, W., 2010. Carbon dioxide ﬂuxes over an urban park area. Atmos.

Environ. 44, 2722–2730. https://doi.org/10.1016/j.atmosenv.2010.04.039.

Kormann, R., Meixner, F.X., 2001. An analytical footprint model for non-neutral stratiﬁca-

tion. Boundary-Layer Meteorol. 99, 207–224. https://doi.org/10.1023/A:

1018991015119.

Kottek, M., Grieser, J., Beck, C., Rudolf, B., Rubel, F., 2006. World map of the Köppen-Geiger

climate classiﬁcation updated. Meteorol. Z. 15, 259–263. https://doi.org/10.1127/

0941-2948/2006/0130.

Kotthaus, S., Grimmond, C.S.B., 2012. Identiﬁcation of micro-scale anthropogenic CO

heat and moisture sources - processing eddy covariance ﬂuxes for a dense urban en-

vironment. Atmos. Environ. 57, 301–316. https://doi.org/10.1016/j.

atmosenv.2012.04.024.

Kotthaus, S., Grimmond, C.S.B., 2014. Energy exchange in a dense urban environment -

part II: impact of spatial heterogeneity of the surface. Urban Clim. 10, 281–307.

https://doi.org/10.1016/j.uclim.2013.10.001.

Kuhn, M., 2008. Building predictive models in R using the caret package. J. Stat. Softw. 28,

1–26. https://doi.org/10.18637/jss.v028.i05.

Kuhn, M., Johnson, K., 2013. Applied Predictive Modeling. 1st ed. Springer, New York

https://doi.org/10.1007/978-1-4614-6849-3.

Litvak, E., McCarthy, H.R., Pataki, D.E., 2017. A method for estimating transpiration of irri-

gated urban trees in California. Landsc. Urban Plan. 158, 48–61. https://doi.org/

10.1016/j.landurbplan.2016.09.021.

Liu, L., Jensen, M.B., 2018. Green infrastructure for sustainable urban water management:

practices of ﬁve forerunner cities. Cities 74, 126–133. https://doi.org/10.1016/j.

cities.2017.11.013.

Meehl, G.A., Tebaldi, C., 2004. More intense, more frequent, and longer lasting heat waves

in the 21st century. Science 305, 994–997. https://doi.org/10.1126/science.1098704

(80-. ).

Menzer, O., Meiring, W., Kyriakidis, P.C., McFadden, J.P., 2015. Annual sums of carbon di-

oxide exchange over a heterogeneous urban landscape through machine learning

based gap-ﬁlling. Atmos. Environ. 101, 312–327. https://doi.org/10.1016/j.

atmosenv.2014.11.006.

Microsoft Corporation, Weston, S., 2019. doSNOW: Foreach Parallel Adaptor for the

“Snow”Package (R Package Version 1.0.18) [WWW Document]. URL. https://cran.r-

project.org/package=doSNOW.

Moffat, A.M., Papale, D., Reichstein, M., Hollinger, D.Y., Richardson, A.D., Barr, A.G.,

Beckstein, C., Braswell, B.H., Churkina, G., Desai, A.R., Falge, E., Gove, J.H., Heimann,

M., Hui, D., Jarvis, A.J., Kattge, J., Noormets, A., Stauch, V.J., 2007. Comprehensive com-

parison of gap-ﬁlling techniques for eddy covariance net carbon ﬂuxes. Agric. For.

Meteorol. 147, 209–232. https://doi.org/10.1016/j.agrformet.2007.08.011.

Moncrieff, J.B., Massheder, J.M., De Bruin, H., Elbers, J., Friborg, T., Heusinkveld, B., Kabat,

P., Scott, S., Soegaard, H., Verhoef, A., 1997. A system to measure surface ﬂuxes of mo-

mentum, sensible heat, water vapour and carbon dioxide. J. Hydrol. 188–189,

589–611. https://doi.org/10.1016/S0022-1694(96)03194-0.

Nguyen, T.T., Ngo, H.H., Guo, W., Wang, X.C., Ren, N., Li, G., Ding, J., Liang, H., 2019. Imple-

mentation of a speciﬁc urban water management - Sponge City. Sci. Total Environ.

652, 147–162. https://doi.org/10.1016/j.scitotenv.2018.10.168.

Nordbo, A., Järvi, L., Vesala, T., 2012. Revised eddy covariance ﬂux calculation methodolo-

gies - effect on urban energy balance. Tellus Ser. B Chem. Phys. Meteorol. 64. https://

doi.org/10.3402/tellusb.v64i0.18184.

Norman, J.M., Kustas, W.P., Humes, K.S., 1995. Source approach for estimating soil and

vegetation energy ﬂuxes in observations of directional radiometric surface tempera-

ture. Agric. For. Meteorol. 77, 263–293. https://doi.org/10.1016/0168-1923(95)

02265-Y.

Nouri, H., Beecham, S., Kazemi, F., Hassanli, A.M., 2013. A review of ET measurement tech-

niques for estimating the water requirements of urban landscape vegetation. Urban

Water J. 10, 247–259. https://doi.org/10.1080/1573062X.2012.726360.

Nouri, H., Beecham, S., Anderson, S., Hassanli, A.M., Kazemi, F., 2015. Remote sensingtech-

niques for predicting evapotranspiration from mixed vegetated surfaces. Urban

Water J. 12, 380–393. https://doi.org/10.1080/1573062X.2014.900092.

Nouri, H., Chavoshi Borujeni, S., Hoekstra, A.Y., 2019. The blue water footprint of urban

green spaces: an example for Adelaide, Australia. Landsc. Urban Plan. 190, 103613.

https://doi.org/10.1016/j.landurbplan.2019.103613.

Olmedo, G.F., Ortega-Farías, S., de la Fuente-Sáiz, D., Fonseca-Luengo, D., Fuentes-

Peñailillo, F., 2016. Water: tools and functions to estimate actual evapotranspiration

using land surface energy balance models in R. R J. 8, 352–370. https://doi.org/

10.32614/rj-2016-051.

Papale, D., Valentini, R., 2003. A new assessment of European forests carbon exchanges by

eddy ﬂuxes and artiﬁcial neural network spatialization. Glob. Chang. Biol. 9, 525–535.

https://doi.org/10.1046/j.1365-2486.2003.00609.x.

Pataki, D.E., McCarthy, H.R., Litvak, E., Pincetl, S., 2011. Transpiration of urban forests in

the Los Angeles metropolitan area. Ecol. Appl. 21, 661–677. https://doi.org/10.1890/

09-1717.1.

R Core Team, 2020. R: A Language and Environment for Statistical Computing. [WWW

Document]. R Found. Stat. Comput. https://www.r-project.org/.

Roberts, D.R., Bahn, V., Ciuti, S., Boyce, M.S., Elith, J., Guillera-Arroita, G., Hauenstein, S.,

Lahoz-Monfort, J.J., Schröder, B., Thuiller, W., Warton, D.I., Wintle, B.A., Hartig, F.,

Dormann, C.F., 2017. Cross-validation strategies for data with temporal, spatial, hier-

archical, or phylogenetic structure. Ecography (Cop.) 40, 913–929. https://doi.org/

10.1111/ecog.02881.

Saher, R., Stephen, H., Ahmad, S., 2021. Urban evapotranspiration of green spaces in arid

regions through two established approaches: a review of key drivers, advancements,

limitations, and potential opportunities. Urban Water J. 18, 115–127. https://doi.org/

10.1080/1573062X.2020.1857796.

Scherer, D., Ament, F., Emeis, S., Fehrenbach, U., Leitl, B., Scherber, K., Schneider, C., Vogt,

U., 2019. Three-dimensional observation of atmospheric processes in cities. Meteorol.

Z. 28, 121–138. https://doi.org/10.1127/metz/2019/0911.

Schmid, H.P., Oke, T.R., 1990. A model to estimate the source area contributing to turbu-

lent exchange in the surface layer over patchy terrain. Q. J. R. Meteorol. Soc. 116,

965–988. https://doi.org/10.1002/qj.49711649409.

Schmidt, A., Wrzesinsky, T., Klemm, O., 2008. Gap ﬁlling and quality assessment of CO

and water vapour ﬂuxes above an urban area with radial basis function neural net-

works. Boundary-Layer Meteorol. 126, 389–413. https://doi.org/10.1007/s10546-

007-9249-7.

Shaﬁeiyoun, E., Gheysari, M., Khiadani, M., Koupai, J.A., Shojaei, P., Moomkesh, M., 2020.

Assessment of reference evapotranspiration across an arid urban environment hav-

ing poor data monitoring system. Hydrol. Process. 34, 4000–4016. https://doi.org/

10.1002/hyp.13851.

Shojaei, P., Gheysari, M., Nouri, H., Myers, B., Esmaeili, H., 2018. Water requirements of

urban landscape plants in an arid environment: the example of a botanic garden

and a forest park. Ecol. Eng. 123, 43–53. https://doi.org/10.1016/j.

ecoleng.2018.08.021.

Statistical Ofﬁce of Berlin-Brandenburg, 2019. Inhabitants of the State of Berlin on 31 De-

cember 2018. Potsdam.

Su, Z., 2002. The Surface Energy Balance System (SEBS) for estimation of turbulent heat

ﬂuxes. Hydrol. Earth Syst. Sci. 6, 85–99. https://doi.org/10.5194/hess-6-85-2002.

Tucker, C.J., 1979. Red and photographic infrared linear combinations for monitoring veg-

etation. Remote Sens. Environ. 8, 127–150. https://doi.org/10.1016/0034-4257(79)

90013-0.

United Nations, 2019. World Urbanization Prospects: The 2018 Revision. Department of

Economic and Social Affairs, Population Division, New York, United States.

Vesala, T., Järvi, L., Launiainen, S., Sogachev, A., Rannik, Ü., Mammarella, I., Siivola, E.,

Keronen, P., Rinne, J., Riikonen, A., Nikinmaa, E., 2008. Surface-atmosphere interac-

tions over complex urban terrain in Helsinki, Finland. Tellus Ser. B Chem. Phys.

Meteorol. 60 B, 188–199. https://doi.org/10.1111/j.1600-0889.2007.00312.x.

Vickers, D., Mahrt, L., 1997. Quality control and ﬂux sampling problems for tower and air-

craft data. J. Atmos. Ocean. Technol. 14, 512–526. https://doi.org/10.1175/1520-0426

(1997)014<0512:QCAFSP>2.0.CO;2.

Vulova, S., Kleinschmit, B., 2019. Thermal behavior and its seasonal and diurnal variability

of urban green infrastructure in a mid-latitude city - Berlin. 2019 Joint Urban Remote

Sensing Event (JURSE). Vannes, France, pp. 9–12 https://doi.org/10.1109/

JURSE.2019.8809011.

Vulova, S., Meier, F., Fenner, D., Nouri, H., Kleinschmit, B., 2020. Summer nights in Berlin,

Germany: modeling air temperature spatially with remote sensing, crowdsourced

weather data, and machine learning. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.

13, 5074–5087. https://doi.org/10.1109/JSTARS.2020.3019696.

Ward, H.C., Evans, J.G., Grimmond, C.S.B., 2013. Multi-season eddy covariance observa-

tions of energy, water and carbon ﬂuxes over a suburban area in Swindon, UK.

Atmos. Chem. Phys. 13, 4645–4666. https://doi.org/10.5194/acp-13-4645-2013.

Ward, H.C., Kotthaus, S., Järvi, L., Grimmond, C.S.B., 2016. Surface Urban Energy and Water

Balance Scheme (SUEWS): development and evaluation at two UK sites. Urban Clim.

18, 1–32. https://doi.org/10.1016/j.uclim.2016.05.001.

Webb, E.K., Pearman, G.I., Leuning, R., 1980. Correction of ﬂux measurements for density

effects due to heat and water vapour transfer. Q. J. R. Meteorol. Soc. 106, 85–100.

https://doi.org/10.1002/qj.49710644707.

Xenakis, G., 2016. FREddyPro: Post-processing EddyPro Full Output File (R Package Ver-

sion 1.0) [WWW Document]. URL. https://cran.r-project.org/package=FREddyPro.

S. Vulova, F. Meier, A.D. Rocha et al. Science of the Total Environment 786 (2021) 147293