SUITMA+20
Water dynamics at the urban soil-atmosphere interface—rainwater
storage in paved surfaces and its dependence on rain
event characteristics
Thomas Nehls
1,2
&Andre Peters
1,3
&Fabian Kraus
1,4
&Yong Nam Rim
1
Received: 6 January 2020 /Accepted: 17 August 2020
#The Author(s) 2020, corrected publication 2020
Abstract
Purpose The surface store governs the rainwater partition, e.g., water storage and evaporation on paved surfaces, especially for
low-intensity and low-sum rain events, which account for the greatest part of the total rainfall in a temperate climate city like
Berlin, Germany. The surface store Sis a fixed value, dependent on surface relief and pore system characteristics. Contrary, in
this study, the surface storage was assumed to depend also on the rain intensity, thus being variable from event to event.
Materials and methods The surface store filling dynamics for dense (DP), porous (PP), and highly infiltrative (IP) paving
materials were studied in a rainfall simulator. Irrigation intensities pranged from 0.016 to 0.1 mm min
−1
which represent the
25 to 88% quantiles of the rain event distribution in Berlin, Germany (1961 to 1990).
Results and discussion Three surface stores can be separated: storage until initial runoff, S
f
, at maximum filling, S
m
, and for
steady-state runoff, S
eq
—all of them can be regarded as effective stores depending on the aim of its use. The equilibrium store
varies from 0.2 to 3 mm for DP, PP, and IP for the investigated rainfall intensities.
Conclusions For all pavers, the surface store depends on rainfall intensity, which was shown experimentally and confirmed by
numerical simulation of the infiltration. We introduce a simple and robust method to describe S
f
,S
m
=f(p) for different pavers.
Pavers can evaporate a multiple of their surface store per day, depending on the rainfall distribution, which implicates the need for
high temporal resolutions in urban hydrology modeling. Pavers can evaporate a multiple of their surface store per day, depending
on the rainfall distribution. That implicates the need for high temporal resolutions in urban hydrology modeling.
Keywords Evaporation .Paved soils .Paving material .Precipitation intensity .Surface store .Water storage
1 Introduction
Urban areas have open soils and sealed and partially sealed
soils, also called paved soils, impervious pavements, or po-
rous pavements. Paved soils, impervious or pervious, account
for large proportions of urban surfaces. In Berlin, they make
two-thirds of the whole overbuild area. The water budget of
these paved soils differs from natural soils; i.e., infiltration and
evaporation are much smaller and thus, surface runoff is
higher (Wessolek and Facklam 1997). The imbalanced water
budget leads to ecological problems in the city. Runoff leads
to the eutrophication of surface waters due to the first flush
effects and combined sewer overflows (Heinzmann 1998).
The relatively small amount of available water for evaporation
is one cause for overheating of city centers (Oke 1982).
Consequently, a paradigm change in urban rainwater man-
agement from fast water removal towards storage leading to
Responsible editor: Kye-Hoon John Kim
*Thomas Nehls
thomas.nehls@tu-berlin.de
1
Chair of Soil Conservation, Technische Universität Berlin,
Ernst-Reuter-Platz 1, 10587 Berlin, Germany
2
Chair of Ecohydrology and Landscape Assessment, Technische
Universität Berlin, Ernst-Reuter-Platz 1, 10587 Berlin, Germany
3
Institute for Geoecology, Division of Soil Science and Soil Physics,
Technische Universität Braunschweig, Langer Kamp 19c,
38106 Braunschweig, Germany
4
Kompetenzzentrum Wasser Berlin gGmbH, Cicerostrasse 24,
10709 Berlin, Germany
Journal of Soils and Sediments
https://doi.org/10.1007/s11368-020-02762-5
infiltration and evaporation was suggested (e.g., Field et al.
1982). Although increasing infiltration through permeable
pavements is currently referred to as the “best practice,”it
cannot be the sole measure for good water management in
urban areas. Many cities already observe rising groundwater
levels due to increased infiltration and decreased water de-
mand per capita. This can cause severe damage to buildings
and infrastructures (Goebel et al. 2007)aswellasincreased
leaching from vadose zone contaminations. An increased in-
filtration would also bear the risk of groundwater contamina-
tion due to recent emissions (Nehls et al. 2008). Furthermore,
the water is needed at the surface rather than in the ground for
other uses such as evaporative cooling. Namely, several cities
need to adapt to climate change and to mitigate heat stress and
the urban heat island. This requires adapted surface water
stores (Nakayama and Fujita 2010;Starkeetal.2010).
The surface store or surface storage capacity is the maxi-
mum volume, which can be filled with water at the pavement
surface and which is therefore not contributing to surface run-
off (McGraw-Hill 2002). The surface storage in turn denotes
the actual filling status of that volume and thus is dependent
on the rain events and the general weather conditions.
In urban areas, the total precipitation P(mm) in a given
time span is partitioned into the components surface runoff
(including water flowing into sewer canals) R(mm), evapora-
tion E(mm), infiltration into underlying soil I(mm), and stor-
age in the surface store S
tot
(mm), leading to the following
urban water balance equation:
P¼RþEþIþStot ð1Þ
In order to adequately quantify the different terms of the
water budget, it is necessary to know the quantities of the
different components as well as the transmission rates be-
tween them. To do so, engineering-type maximum approxi-
mations (e.g., maximum storage capacity, maximum removal
by drainage system) based on stormwater events are inappro-
priate. Instead, new process-based model approaches are
needed, which predict all terms of the water budget for storm
events, but also for medium and small rain events. One task to
achieve that goal is to precisely know the quantity of the
surface storage, where the water is retained after precipitation
events for subsequent evaporation. Especially for small rain
events, the runoff generation from pavements strongly de-
pends on the amount of water which can be stored on and
on the surface, as this water can infiltrate or evaporate from
the surface (Mansell and Rollet 2009).
Whether the water stored at the surface may contribute to
infiltration depends on the pavement design (sealed, partially
sealed, pavement joint fraction) and the subsurface characteristics
(Mansell and Rollet 2009). Usually, the surface store is regarded
as a fixed value, dependent on surface relief, and porous material
characteristics. Contrary to that assumption, we show that the
effective storage for water at and near the surface is a process
function dependent on material properties as well as on meteo-
rological conditions, and thus, it is time variable.
In general, the surface store of pavement is built of (i) water
held in its porous system by capillary and adsorptive forces
and (ii) free water on the surface.
The storage of free water can take place in macroscopic sur-
face depressions (puddles), pavement joints, and small depres-
sions in the pavement material (coarse surface roughness). Such
storing is not rate limited; the maximum store is a constant value.
According to Jarvis (2007), water held at tensions greater than −
6 cm water column can be regarded as free water. This corre-
sponds to pores greater than 0.5 mm in diameter. Nehls et al.
(2015) found ~ 1 mm
3
to be the smallest micro-relief feature still
detectable by a terrestrial laser scanning method and regarded a
pore diameter of 1 mm as an operational limit for free water.
According to this, structures smaller than 1 mm in diameter can
be treated as a porous system.
The porous system builds the second part of the surface store.
It comprises the porosity of the paving materials, the joint fillings,
and optionally the subsoil until the groundwater. Obviously, the
surface store depends on the depth which is still considered as
“surface.”As a proposed operational measure, the surface depth
is the thickness of the paving materials, excluding the subsoil.
Although the subsoil can influence the precipitation partitioning
for low-intensity rainfall, in this study, we will focus on the
pavement. That is because the pavement system and subsoil
are mostly hydraulically separated by a coarse-grained sublayer.
Water, which entered the subsoil, will not evaporate from the
paver surface. Also, the soil below the pavement layer can be
described by traditional models.
Different from the depression store of the pavement, the
filling of the porous system is limited by its maximum infil-
tration rate. The maximum infiltration rate depends on the
hydraulic properties of the system, i.e., hydraulic conductivity
and water retention characteristics and on the initial water
content. If the rainfall rate exceeds the maximum infiltration
rate, runoff is generated, although the surface store might still
be filled. Thus, we regard the effective surface store as a time
variable quantity depending on initial and boundary condi-
tions. From this point of view, the total effective surface store
(S
tot
(mm)) can be expressed as:
Stot ¼SdþSps ð2Þ
where S
d
(mm) is the depression store and S
ps
(mm) is the
pore system store. S
ps
can be further sub-divided to S
ps
=S
ps,p
+S
ps,j
+S
ps,s
, where the subscripts p, j, and s indicate the paver
block, the pavement joints, and the subsoil, respectively. In
this study, we focus on S
ps,p
and on S
d
as far as it is a charac-
teristic of the paver itself.
Given its importance for its water balance, the systematic
knowledge on the surface store of pavements is surprisingly
J Soils Sediments
small. Specialist experience and rule of thumb values are
employed in practice but are rarely discussed scientifically
nor measured directly yet.
Ramier et al. (2006) compared the runoff generation of two
asphalt streets for 38 months and derived different runoff
coefficients depending on precipitation and evaporation.
They also estimated the surface stores of the two streets to
be 1 mm and 3 mm by calibration of a model.
Unfortunately, infiltration through cracks could not be
excluded due to the given experimental design. Nehls et al.
(2011) quantified the maximum surface store of a concrete
slab pavement to 1.7 mm from lysimeter studies. Nehls et al.
(2015) used a terrestrial laser scanning-based method to quan-
tify the depression store of ideally constructed pavements to
range from 0.07 to 1.4 mm.
However, the surface store of pavement materials has not
been directly investigated, separately from the pavement de-
sign; thus, it was influenced by depression store, slope, soil
pore system, and infiltration or evaporation.
1.1 Aims of the study
In this study, we analyze the dynamics of the effective surface
store for different pavers depending on typical rainfall inten-
sities. Therefore, the rain events in Berlin (1961–1990) are
analyzed for their event intensity and event sum distribution
functions in order to identify representative rainfall intensities.
The storage dynamics are then recorded for different pavers
and the identified representative rainfall intensities. Three dif-
ferent representative paver types are studied: dense pavers
(DP) without a noteworthy porosity, porous pavers (PP)
which can be expected to store water in their pores, and a
modern paver optimized for infiltration (IP).
2 Materials and methods
2.1 Distribution of precipitation event sums and
intensities
Precipitation data for Berlin—Neukölln, provided in a resolu-
tion of 0.01 mm and 5 min for the years 1961 to 1990 DWD
(online) Deutscher Wetterdienst, have been investigated for
typical precipitation event sums and intensities. Individual
events have been separated by periods of at least 10 min with-
out precipitation (< 0.01 mm in 10 min). Using this minimum
inter-event time, we separated N= 11363 events and calculat-
ed the precipitation event sum (P) and the average precipita-
tion event intensity (p), calculated as the event sum divided by
the event duration, as well as their contribution to the cumu-
lative sum of precipitation in the period (Fig. 1).
2.2 Paving materials
Three different pavers were analyzed in this study: a dense
paver with low porosity (DP), a porous paver with relatively
high porosity (PP), and a porous paver optimized for infiltra-
tion with large pores (IP). The investigated pavers are all made
of concrete but differ in porosity and sizes (Table 1,Fig.2).
They represent typical paving materials which are widely used
in urban areas. The DP slabs are widely used in old inner-city
parts. The PP slabs are recently used for sidewalk construction
and are found in the younger parts of cities. The modern IP
slabs are increasingly used in new single-detached housing
areas and are advertised as “ecologic.”
Cylinders with a cross-sectional area of 2500 mm
2
have been
cut from the pavers for a general characterization of the materials.
The dry bulk density and solid density (helium pycnometry)
were determined. The field capacity (θ
pF = 1.8
) was measured
using the porous plate method, while the saturated hydraulic
conductivity (K
sat
) was measured using the constant head perme-
ability test. The physical properties are listed in Table 1.
2.3 Experimental setup
In order to quantify the dynamic surface store, rainfall simu-
lation experiments were carried out with de-ionized water.
The experimental setup consisted of a plexiglass box in which
the pavers (for dimensions, see Table 1) were irrigated from a
380 × 380 mm needle irrigator with 400 needles (Fig. 3)
connected to Mariott’s bottle, with which the irrigation inten-
sities (p) varying from 0.02 to 0.1 mm min
−1
were adjusted.
The height of the fall for the “raindrops”was 400 mm—
sufficient for bursting drops at the paving slabs. The irrigation
box was sealed against the outer atmosphere in order to pre-
vent evaporation out of the box. Temperature and humidity
have been monitored (hytemod by B+B Thermo Technik,
Donaueschingen, Germany) during the experiment. The loss
of water from the pavers’surface by evaporation did not ex-
ceed 0.005 mm per experiment, which is less than 1% com-
pared with the smallest measured surface store.
Three replicates of oven-dried (333 K until constant
weight) pavers rested horizontally on a digital balance with
0.05-g resolution (Kern 572, Kern & Sohn, Balingen-
Frommern, Germany) and were irrigated from the needle irri-
gator. The time of the first runoff, maximum filling, and the
steady-state runoff rate was identified.
2.4 Simulations
In order to theoretically investigate the dynamics of store fill-
ing, a simulation study was conducted. Therefore, the
HYDRUS 1D code was used which solves the Richards equa-
tion numerically (Simunek et al. 2008). These simulations
have been done in order to compare theoretical and
J Soils Sediments
experimental infiltration dynamics qualitatively for the porous
paver as it was the only material showing a dynamic behavior
(Table 2). Its hydraulic characteristics were described using
the Fayer and Simmons (1995) retention model modified by
Peters et al. (2011) combined with the conductivity model of
Mualem (1976). The Fayer and Simmons model explicitly
accounts for absorptive water in the dry range, which is
important for simulation of infiltration into initially dry
materials. The slight modification of Peters et al. (2011)as-
sures the monotonicity of the Fayer and Simmons model. The
complete retention function is given by:
θhðÞ¼ θaχþθm−θaχðÞ1þαhðÞ
n
½
n−1=nfor h<hu
θsfor h≥hu
;ð3Þ
with
χ¼1−ln hðÞ
ln h0
ðÞ
ð4Þ
and
θm¼θaχþθs−θaχ
1þαhu
ðÞ
n
½
n−1=n;ð5Þ
where n(-) and α(cm
−1
) are curve shape parameters, h
0
(cm) is the matric head at a water content of zero here set to −
10
6.8
(cm), which equals oven dryness at typical laboratory
environment, θ
s
(m
3
m
−3
) is the saturated water content, and
θ
m
(m
3
m
−3
) is a fictitious parameter slightly greater than θ
s
,
adopted from the retention model of Vogel et al. (2001). θ
a
(m
3
m
−3
) is the water content of the absorptive part at h=1
and h
u
(cm) is the matric head above which the soil must be
saturated here set to h
u
= 1 cm. The hydraulic conductivity
was predicted from the retention function by numerically solv-
ing the capillary bundle model of Mualem (1976):
KFðÞ¼Ksat F0:5∫F
01
hxðÞdx
∫1
0
1
hxðÞdx
2
43
5
2
ð6Þ
where K
sat
(cm d
−1
) is the saturated conductivity, F(-) is the
saturation, defined here as θ/θ
s
,andxis a dummy variable of
integration.
The free adjusted hydraulic parameters (α,n,andθ
a
)were
chosen in a way that the measured quantities for PP given in
Table 1are met. The shape of the resulting water retention and
conductivity curves resemble the shape of the more recently
published Peters-Durner-Iden models (Peters, 2013,2014;
0
10
20
30
40
50
0.001 0.01 0.1 1
precipitation event intensity [mm min
-1
]
precipitation event sum [mm]
0
25
50
75
100
cumulative precipitation [%]
event
cumulative sum of precipitation
0
0.1
0.2
0.3
0.4
0.5
0.01 0.1 1 10 100
precipitation event sum [mm]
precipitation event intensity [mm min
-1
]
0
25
50
75
100
cumulative precipitation [%]
event
cumulative sum of precipitation
ab
Fig. 1 aPrecipitation events (squares) according to their event sum and
intensity with the cumulative precipitation (solid line) in relation to the
event sum distribution; bprecipitation events (squares) according to their
event intensity and sum with the cumulative precipitation (solid line) in
relation to the event intensity. Precipitation data for the station Berlin-
Marienfelde, Germany (1961–1990, resolution 0.1 mm per 5 min). Event
separation was performed using the minimum inter-event time of 10 min
(N= 11363)
Table 1 Physical characteristics
of the investigated concrete
pavers
Dense paver (DP) Porous paver (PP) Infiltration paver (IP)
Dimensions x, y, z (m) 0.35, 0.35, 0.06 0.3, 0.3, 0.05 0.195, 0.195, 0.025
Particle density (kg m
−3
) 2535 2611 2634
Bulk density (kg m
−3
) 2376 2331 2118
Porosity (m
3
m
-3
) 0.06 0.11 0.20
Θ
pF = 1.8
(m
3
m
-3
) 0.05 0.09 0.08
K
sat
(mm min
−1
) 0.001 0.005 9.9
J Soils Sediments
Iden and Durner, 2014), which explicitly distinguish between
water storage and conductivity in capillaries and films and
corners. As upper boundary condition, flux rates of 0.007 to
0.6 mm min
−1
were chosen, encompassing the irrigation rates
of the experimental study. The ponding depth before the first
runoff occurs was set to 2 mm. The lower boundary was set to
no flux boundary, representing the pore discontinuity between
paver and construction sand respectively an impermeable bot-
tom. The initial condition was set to −10
6
cm (pF 6) in the
complete profile, representing initially air-dry conditions
(50% relative humidity and 20 °C). The simulation depth
was 50 mm. All simulations lasted until complete saturation
of the material.
3 Results and discussion
3.1 Precipitation event sum and event intensity
distributions
Half of the precipitation in Berlin-Marienfelde (1961–1990, N
= 11363) is generated by events with intensities of p<
0.026 mm min
−1
and with precipitation event sums of p<
4.4 mm (Fig. 1). The first quartile was found at p<
0.016 mm min
−1
;p< 1.8 mm and the third quartile was at p
<0.06mmmin
−1
,p< 9.3 mm. These distributions demon-
strate the importance of rather small precipitation events for
the water balance of Berlin, a city in the temperate region.
Analyzing the precipitation distribution functions is crucial
for the understanding of runoff and evaporation processes.
DP
IP a
PP
IP b
Fig. 2 Paving materials
investigated in this study DP)
dense paver; PP) porous paver;
IP. aporous paver optimized for
infiltration seen from above, IP b
macro - pores seen from the bot-
tom side
a
b
e
f
d
c
g
h
Fig. 3 Experimental setup for the irrigation of pavers. (a) Mariott’sbottle,
(b) needle irrigator, (c) T, rH probe, (d) hermetically sealed plexiglass
box, (e) data logger, (f) paver, (g) balance, (h) the pressure difference, can
be adjusted according to the aimed irrigation rate
J Soils Sediments
3.2 Three different stages of surface store
filling—dynamic pavement retention
3.2.1 Measurements
In Fig. 4, the results of three of the lab experiments are
exemplarily shown. In general, S
tot
can be represented
by three different store filling stages, according to the
rainfall duration and paving material: S
f
,S
m
,andS
eq
.
Thefirststore(S
f
) refers to the start of the runoff from
the paver. In the beginning, all the rainwater is retained
on and in the paver, and runoff generation starts after a
certain time (t
f
). However, the filling process is not
finished then but can continue until the maximum water
mass is reached which can be kept on the paver (S
m
).
This second store is reached when the upper pores and
the micro-depressions are filled, often connected with
water held by surface tension (Fig. 4). Therefore, this
maximum storage (S
m
)attimet
m
canbefollowedbya
fast drop in storage, when water drains almost
completely from the surface due to the siphon effect.
Such behavior was observed for all paver types and
all rain intensities. Such draining can lead to different
surface storage levels smaller than S
m
.
After that drop, an equilibrium store (S
eq
) is built which is
reached at t
eq
. This third store (S
eq
) then refers to the full
amount of pores and/or micro-depressions which are water
filled under steady-state runoff conditions.
The dynamics of such surface store filling are highly de-
pendent on material properties but also on infiltration intensi-
ty. Not all of these store fillings could be separated in all
experiments. Depending on the material (pore system, surface
structure) and irrigation intensities, the different stores can be
identical (S
f
=S
m
=S
eq
). This is when the rain intensity is
small enough—compared with the conductivity of the
material—to fill the pore system completely before the first
runoff occurs.
3.2.2 Simulations
Figure 5shows the simulation results for the porous paver
(PP) with an intensity of 0.1 mm min
−1
. After less than 20
min, the infiltration sum does not equal rainfall sum anymore.
At this time, free water is built up on the surface. Until t=60
min, free water is built up on top of the paver and infiltration is
Table 2 Store volume at first runoff S
f
, the maximum store volume S
m
,
and the store volume at steady-state runoff S
eq
as measured in the labo-
ratory experiments for irrigation intensities ranging from 0.015 to
0.15 mm min
−1
. The numbers in brackets show the standard deviation
(N= 6). Note that for PP, the stores can be described as a function; the
same applies for DP for smaller and for IP for higher rainfall intensities
Surface store Dense paver (DP) Porous paver (PP) Infiltration paver (IP)
S
f
(mm) 0.24 (0.08) f(p) = 0.69 p
−0.29
1.74 (0.16)
S
m
(mm) 0.36 (0.13) f(p) = 0.03 p
−1.22
1.92 (0.05)
S
eq
(mm) 0.31 (0.11) f(p) = 0.07 p
−0.86
1.88 (0.04)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
0 50 100 150
time [min]
cumulative water quantity [mm]
rainfall
runoff
infiltration
ponding starts
run-off rate = rainfall rate
p
onding
Fig. 5 Filling dynamic of the surface store of the porous paver (PP) as
numerically simulated with HYDRUS 1D. Infiltration intensity was
0.1 mm min
−1
. See text for further explanation
0.0
0.1
0.2
0.3
0.4
024681012
irrigation duration [min]
water storage [mm]
p=0.03 mm/min
p=0.05 mm/min
p=0.08 mm/min
S
f
S
m
S
eq
Fig. 4 Water storage exemplary shown for dense pavers (DP) for differ-
ent constant irrigation intensities. The stores S
f
storage at the time of first
runoff, S
m
: maximum storage, S
eq
: stored water at steady-state runoff rate
are exemplary shown for very prominent examples. Note, that the stores
could be identified for all three curves
J Soils Sediments
becoming smaller. At t= 60 min, the maximum free water
height of 2 mm is reached and runoff starts. At this time, the
store S
eff
(cumulative infiltrated water + cumulative amount of
water stored on the surface) is approximately 60% of S
eq
,
which is reached at t
eq
≈110 min. Thus, the simulations show
that water storage can neither be simply approximated by one
of the identified stores S
f
,S
m
,orS
eq
nor by a single value
below total porosity because the real storage depends on the
rainfall intensity (and duration, of course). Note, that the sim-
ulations cannot capture the dynamics between S
m
and S
eq
since the siphon effect is not described by the simulation.
The water stored in the paver is thus not S
eff
but rather the
cumulative infiltrated water at this time because the free sur-
face water will drain if rainfall does not cease before.
3.2.3 Discussion of the different surface stores
As analyzed in this study, in Berlin, 50% of the cumulative
rainfall (by event sum) is gained by rain events with an aver-
age duration of only < 11.5 min. Measurements and simula-
tions show that S
eq
will rarely be reached in reality. Therefore,
a better predictor for the surface storage must be defined.
Beside of naming one of the identified stores S
f
,S
m
,orS
eq
,
we also suggest to quantify the S=f(t)function(Fig.5)andto
identify S
eff
according to the individual question. Apart from
the siphon effect, the applied model was appropriate to de-
scribe the behavior of water on and in the paver. Having iden-
tified the right S
eff
from the store filling function, one has to
derive the S
eff
=f(p)relationfromsimulation(Fig.6aandb)
or measurement (Fig. 7a) for the corresponding materials and
corresponding range of p.
In this study, S
eff
(p) can be described as a composite func-
tion:
Seff pðÞ¼ Seff ¼Afor p<pcrit
Seff ¼ap−bfor p≥pcrit
ð7Þ
where p
crit
is the critical rainfall intensity, which is a hy-
draulic characteristic of the paver that can be identified from
measurements or simulation.
Both experiment and simulation have been done with con-
stant rain intensities. However, in the real world, the intensi-
ties change during a rain event. This leads to over- and under-
estimation of the paver storage dynamics. The time to reach
S
eff
might be overestimated by the experiment as the high rain
intensities normally occur at the beginning of real rain events.
In turn, the time to reach S
eq
was underestimated for some rain
events. For instance, for cyclonal rain events, the intensities at
the end of rain events are much lower than in the beginning
(Rim, 2011). Summing these effects suggest that the generat-
ed runoff might occur earlier but its sum at the end of the rain
event might be smaller when the rain intensity drops under the
actual maximum infiltration rate of the paver material after
first wetting. However, this remains speculative and should
be evaluated in the following experiments and simulation
studies. In the following, S
eq
is discussed for the different
paving materials, in order to focus on differences between
the three materials.
3.3 Surface stores for three different paver materials
From the field capacity and the paver dimensions (Table 1),
the theoretic pore system stores are calculated: 3.0 for DP, 4.7
for PP, and 1.9 mm for IP. The surface stores experimentally
found are 0.2 mm for DP, 1.2 to 3.0 mm depending on pfor
PP, and 1.8 for IP (Fig. 7a). The reasons for the differences
between the pavers and between theoretical storage and ex-
periment are discussed in the following.
For IP, the paver with the highest porosity, only 8% of the
pore volume can hold water against gravity. Furthermore, IP is
thin, which leads to a smaller store volume per surface com-
pared with the other pavers. Calculated for the same depths of
y = 0.796x
-0.661
R
2
= 0.999
0.0
2.0
4.0
6.0
0.0 0.3 0.5
rainfall intensity [mm min
-1
]
water storage depth [mm] a
porous concrete paver
simulated
fitted power function
b
a
0.0
1.0
2.0
3.0
4.0
5.0
6.0
060120180
rainfall duration [min]
cumulative storage [mm
0.42 mm min
-1
0.056 mm min
-1
0.028 mm min
-1
0.014 mm min
-1
0.007 mm min
-1
0.005 mm min
-1
= K
sat
0.0
1.0
2.0
3.0
4.0
5.0
6.0
060120180
rainfall duration [min]
cumulative storage [mm
0.42 mm min
-1
0.056 mm min
-1
0.028 mm min
-1
0.014 mm min
-1
0.007 mm min
-1
0.005 mm min
-1
= K
sat
]
Fig. 6 aSimulated dynamic surface storage filling behaviors for different rainfall intensities indicated by the numbers and the bderived S
eq
=f(p)
function. Note that a ponding depth of 2 mm was simulated on top of the paver
J Soils Sediments
50 mm, the water retention at pF = 1.8 would be second
highest after the PP (Table 1).
For PP, the total porosity is smaller than for IP, but also, the
air capacity is smaller, resulting in higher water contents at pF
1.8. Since no macro-pores are present, the saturated conduc-
tivity is also lower than for IP. Due to the small pores, the DP
is almost saturated at pF 1.8 and has by far the lowest saturated
conductivity K
sat
of the tested pavers. This was discussed be-
cause the filling dynamic of the pore system of a paver during
a rainfall event depends on the development of the infiltration
rate i(t) during the rainfall event. The infiltration dynamic i(t)
depends on K
sat
and the absorptivity or sorptivity of the
pavers. The sorptivity is a measure of both the pore character-
istics and the initial moisture and can be determined from
infiltration experiments according to Philips (1957).
For DP, i(t) is lower than the irrigation intensity pduring
our experiments. Thus, the pore system of DP cannot store
substantial amounts of water under realistic conditions. The
filling of the store volume is apparently independent from pin
the investigated range (Fig. 7b). We conclude that for dense
pavers, not the pore system but the depression store was mea-
sured as the apparent surface store. For IP, due to its macro-
pores, i(t) is much higher than pin the investigated range. So
here again, the store filling does not depend on p(Fig. 7b). For
PP in our experiments, the infiltration rates are in the same
order of magnitude as the applied irrigation rates. For low p
the infiltration capacity is higher than p, for the higher p,the
infiltration capacity is not sufficient to catch all irrigation wa-
ter and run-off gets higher. That results in higher store fillings
for low pthan for the higher p(Fig. 7a, b).
Both pavers IP and PP could store more water than DP,
although less than expected from field capacity (at pF 1.8) or
porosity. For IP, we observed, during the experiments, that
most of the irrigation water drained through the macro-pores.
The retained water was stored in depressions at the surface,
film water at the macro-pore surfaces, and water which was
absorbed from meso- and micro-pores in the matrix, around
wetted macro-pores. For the IP pavers, one can expect rising
pore system storage with decreasing rain intensity outside the
experimental range (Fig. 7b).
For PP, the surface store depends strongly on pfor p<
0.06 mm min
−1
(Fig. 7a). With decreasing irrigation intensity,
the porous system can store up to 3 mm (at p= 0.02 mm
min
−1
). For p> 0.06 mm min
−1
, the maximum infiltration
capacity, which depends on hydraulic properties and initial
moisture conditions, is much smaller than the rain intensity.
With 1.2 mm for p>0.06mmmin
−1
, the surface store of PP is
smaller than for IP.
The store of the pore system of pavements is in the same
order of magnitude as the depression store on the surface of
pavements (0.7 to 1.4 mm), directly measured by a terrestrial
laser scanner. The investigated pavements were ideally con-
structed, without puddles and irregularities (Nehls et al. 2015).
Both stores can theoretically add up to about 4.5 mm. Even
then, only stores of ideal pavements are considered; the stores
of real pavements, with depressions, cracks, and puddles, are
not studied yet.
In this study, the irrigated pavers have been horizontally
aligned, even though pavements are often inclined to ≈2° in
practice to prevent ponding waters. We stuck to the simple
y = 0.47x
-0.44
R
2
= 0.73
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.00 0.05 0.10 0.15
irrigation intensity [mm min
-1
]
water storage depth [mm] a
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
00.10.20.30.4
water storage depth [mm
]
PP
IP
DP
experimental
range
rainfall intensity [mm min
-1
]
ab
schematic
IP
DP
PP
Fig. 7 aMeasured dependence of the surface storage from rainfall
intensity for porous concrete slabs (PP), dense concrete slabs (DP), and
infiltration optimized slabs (IP). Error bars indicate the standard error for
the store measurements (N= 3). bSchematic dependencies for rather
porous pavers, rather dense concrete slabs and slabs optimized for
infiltration derived from general theoretical considerations of infiltration
into porous media. Note that the three pavers show different parts of the
generally likewise curves in the range of rainfall intensities tested in the
experiments described in this study.
J Soils Sediments
horizontal setup to focus on the more fundamental question of
how much water the different pavers can store under different
irrigation regimes. Moreover, for the results of our experi-
ments, an inclination of 2° would be of little importance, as
it influences rather S
m
than S
eq
. However, for very high irri-
gation intensities, when p> > infiltration capacity, the slope
might play a role in the effective surface storage. This topic is
beyond our current study but points to a further research
question.
Comparing the hydraulic properties of pavers with under-
lying urban soils substrates, the following can be stated: field
capacities (at pF 1.8) for soil texture classes vary from 0.1 m
3
m
−3
for heavily compacted sand to 0.5 m
3
m
−3
for a non-
compacted clay (Ad-Hoc-AG Boden, 2005, table 70) not con-
sidering soil organic matter. Thus, for their field capacity, the
pavers are similar to heavily compacted pure sand. The satu-
rated hydraulic conductivity K
sat
for soil texture classes varies
from 0.014 mm min
−1
for heavily compacted clays to more
than 2.6 mm min
−1
for loose sand. Thus, according to their
K
sat
, DP and PP pavers have 14 times respectively 3 times
smaller conductivity compared with soils, while IP pavers,
due to their coarse pores, have a much higher conductivity
than soils.
3.4 Effectiveness of surface storage and evaporation
The surface storage in and on pavers governs the water bal-
ance of paved urban soils to a certain extent. First, for a given
store, only a part of the rain events can be retained completely.
Second, the storage itself depends on the rain event intensity.
Both factors influence the effective store and can be described
by means of the rain event intensity and rain event sum dis-
tribution function for a specific climate in the world (Fig. 8).
Based on that distribution function, the number of intercepted
rain events and their contribution to the cumulative rain event
sum can be calculated for the stores. For the DP, 1.6% of the
cumulative rain event sum can be intercepted (2362 events),
for the IP, it is 25% (8729 events). Considering only the static
storage of 1.2 mm PP can intercept 18% (7779 events) of the
cumulative rain event sum. If the dynamic storage of PP is
considered, that amount doubles (35%, 9418 events).
Obviously, a comparison like given in Fig. 8can only give
a general overview which can be understood as a potential rain
interception. To calculate the actual rainwater storage and the
actual evaporation from that storage, one has to consider a set
of boundary and initial conditions which govern the process
such as temporal rainfall distribution, the antecedent storage
filling (initial moisture), and potential evaporation. Apart from
that, the result of a water balance simulation for the surface is
also very sensitive to the chosen temporal resolution. The
higher the rainfall boundary condition is smoothed as com-
pared with the real rainfall distribution, the higher is the risk to
overestimate the evaporation. An even distribution of rainfall
during the day can lead to a cumulative actual evaporation
higher than the store for potential evaporations higher than
the storage (typical in summer). The more the distribution of
real rainfall events is aggregated for the boundary condition,
the higher is the risk to underestimate the evaporation from
pavements. Both uncertainties sum up for long time series. As
for many applications (e.g., evaporative cooling for heat stress
mitigation) dynamics are of high interest, we encourage sim-
ulating water balance processes in urban areas with the highest
possible temporal resolution and using all available informa-
tion on surface characteristics including pavement materials
and surface micro-morphology.
4 Conclusions
The pore system of paving materials (material characteristics)
contributes to the total surface store of pavements to the same
extent like the storage of free water in depression volumes on
the surface of the pavement system (design characteristics).
Given the water retention function and the saturated conduc-
tivity of the materials, the dependency of the surface store
from the rainfall intensity can be calculated.
Pavement materials can evaporate a multiple of their sur-
face store, depending on the rainfall distribution. This and the
rainfall rate dependence of the surface store of the pavers
suggest modeling of evaporation and rainfall-runoff
partitioning with high temporal resolution. Otherwise, the run-
off is either overestimated and evaporation is underestimated
or vice versa. This must be considered in simulations of urban
heat stress and adaptation strategies.
0
0.1
0.2
0.3
0.4
0.5
0.01 0.1 1 10 100
precipitation event intensity [mm min-1]
precipitation event sum [mm]
event
DP
PP
IP
Fig. 8 Surface store of the three different paver types of porous paver
(PP), dense paver (DP), and infiltration optimized paver (IP) in relation to
rain event’s intensities and rain event sums in Berlin, Germany
J Soils Sediments
Our findings also imply a rainfall intensity dependence of
the runoff coefficient and therefore suggest no longer using
the concept of constant runoff coefficients.
Authors’contributions All authors contributed to the study conception
and design. Material preparation, data collection, and analysis were per-
formed by Thomas Nehls, Fabian Kraus, and Yong Nam Rim; model
setup and simulations were done by Andre Peters and Thomas Nehls.
The manuscript was written by Thomas Nehls and Andre Peters and all
authors commented on previous versions of the manuscript. All authors
read and approved the final manuscript.
Funding information Open Access funding provided by Projekt DEAL.
We cordially thank the German Science Foundation (DFG FOR 1736
“Urban Climate and Heat stress”) and the BMBF (FKZ 033W103G
Blue Green Streets) for funding.
Open Access This article is licensed under a Creative Commons
Attribution 4.0 International License, which permits use, sharing, adap-
tation, distribution and reproduction in any medium or format, as long as
you give appropriate credit to the original author(s) and the source, pro-
vide a link to the Creative Commons licence, and indicate if changes were
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permission directly from the copyright holder. To view a copy of this
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