Introduction
The lack of sufficient information about spatial distribution of short-term
rainfall has always been one of the most important sources of errors in urban
runoff estimation . In the last decades
considerable advances in quantitative estimation of distributed rainfall have
been made, thanks to new technologies, in particular weather radars
. These developments have been
applied in urban hydrology researches; see and
for a review. The hydrological response is sensitive to
small-scale rainfall variability in both space and time , due to a typically high
degree of imperviousness and to a high spatial variability of urban land use.
Progress in rainfall estimation is accompanied by increasing availability of
high-resolution topographical data, especially digital terrain models and
land use distribution maps .
High-resolution topographical datasets have promoted development of more
detailed and more complex numerical models for predicting flows
. However, model complexity and resolution
need to be balanced with the availability and quality of rainfall input data
and datasets for catchment representation . This is
particularly critical in small catchments, where flows are sensitive to
variations at small space and timescales as a result of the fast
hydrological response and the high catchment variability . Alterations of natural flows introduced by human interventions,
especially artificial drainage networks, sewer pipe networks, detention and
control facilities, such as reservoirs, pumps, and weirs, are additional
elements to take into account for flow predictions. Recently, various authors
investigated the sensitivity of spatial and temporal rainfall variability on
the hydrological response for urban areas . Despite these efforts, many aspects
of hydrological processes in urban areas remain poorly understood, especially
in the interaction between rainfall and runoff.
It is timely to review recent progress in understanding of interactions
between rainfall spatial and temporal resolution, variability of catchment
properties and their representation in hydrological models. Section 2 of this
paper is dedicated to definitions of spatial and temporal scales and
catchments in hydrology and methods to characterize these. Section 3 focuses
on rainfall, analysing the most used rainfall measurement techniques, their
capability to accurately measure small-scale spatial and temporal
variability, with particular attention to applications in urban areas.
Hydrological processes are described in Sect. 4, highlighting their variability and
characteristics in urban areas. Thereafter, the state of the art of
hydrological models, as well as their strengths and limitations to account
for spatial and temporal variability, are discussed. Section 6 presents
recent approaches to understand the effect of rainfall variability in space
and time on hydrological response. In Sect. 7, main knowledge gaps are
identified with respect to accurate prediction of urban hydrological response
in relation to spatial and temporal variability of rainfall and catchment
properties in urban areas.
Spatial and temporal scale variability of hydrological processes,
adapted from , ,
, and . Colours represent different
groups of physical processes: blue for processes related to the atmosphere,
yellow for surface processes, green for underground processes, red highlights
typical urban processes, and grey indicates problems hydrological processes
can pose to society.
Scales in urban hydrology
Spatial and temporal scale definitions
Hydrological processes occur over a wide range of scales in space and time, varying
from 1 mm to 10000 km in space and from seconds up to 100 years in
time. A scale is defined here as the characteristic region in space or period
in time at which processes take place or the resolution in space or time at
which processes are best measured .
Several authors have classified hydrological process scales and variability,
focusing in particular on the interaction between rainfall and the other
hydrological processes .
presented a graphical representation of spatial and
temporal variability of the main hydrological processes on a logarithmic
plane. The plot has been updated by other authors, each focusing on specific
aspects. For example, analysed phenomena related to
urban processes, focusing on small spatial scale, while ,
added scales of some hydrological problems, such as flood and drought.
Figure presents an updated version of the plot that integrates the
information contributed by , ,
, and . Figure shows
that in urban hydrology attention is mainly focused on small scales.
Characteristic processes, such as storm drainage, infiltration, and
evaporation, vary at a small temporal and spatial scale, from seconds to hours
and from centimetres to hundreds of metres. Many processes are driven by
rainfall, that varies over a wide range of scales.
Downscaling and upscaling processes (modified from
).
highlighted the importance of making a distinction
between two types of scales: the “process scale”, i.e. the proper scale of
the considered phenomenon, and the “observation scale”, related to the
measurement and depending on techniques and instruments used. Under the best
scenario, process and observation scale should match, but this is not always
the case, and transformations based on downscaling and upscaling techniques
(Fig. ) might be necessary to obtain the required match
between scales. These techniques are discussed in Sect. 2.2.
Rainfall downscaling
The term downscaling usually refers to methods used to take information known
at large scale and make predictions at small scale. There are two main
downscaling approaches: dynamic or physically based and statistical methods
. Dynamic downscaling approaches solve the process-based
physics dynamics of the system. In statistical downscaling, a statistical
relationship is defined between local variables and large-scale prediction
and this relationship is applied to simulate local variables .
Dynamical downscaling is widely used in climate modelling and numerical
weather prediction, while statistical models are often used in
hydrometeorology, for example rainfall downscaling. Dynamic downscaling
models have the advantage of being physically based, but they require a lot
of computational power compared to statistical downscaling models.
Statistical approaches require historical data and knowledge of local
conditions .
presented a review of three common stochastic
downscaling models, mainly used for spatial rainfall downscaling:
multifractal cascades, autoregressive processes, and point-process models
based on the presence of individual cells. The first were introduced in the
1970s and are widely used to reproduce the spatial and temporal variability
(see for a review). Autoregressive methods, also
nowadays often referred to as “rainfall generator models”, are used to
generate multidimensional random fields while preserving the rainfall spatial
autocorrelation, for natural
and urban areas. Point-process models are used when the
spatial structure of intense rainfall is defined by convective rainfall cells
(see for an example). It incorporates local information
and requires a more detailed storm cell identification.
Statistical downscaling and upscaling approaches are reported in the
literature for a wide variety of variables and
techniques such as regression methods, weather pattern-based approaches and
stochastic rainfall generators (see for a
review). Some recent studies about downscaling and upscaling focus mainly on
urban areas :
, for example, presented a gauge-based radar-rainfall
adjustment method sensitive to singularities, characteristic of small scale.
The importance of using downscaling methods was discussed by
, in a work where they investigated what can be learned
from downscaling method comparison studies, what new methods can be used
together with downscaling to assess uncertainties in hydrological response
and how downscaling methods can be better utilized within the hydrological
community. They highlighted that the importance given to the applied research
is still too little, and manager and stakeholders should be more aware of
uncertainties within the modelling system.
Methods to characterize hydrological process scales
Spatial variability of basin characteristics
Slope, degree of imperviousness, soil properties, and many other catchment
characteristics are variable in space and time and this variability affects
the hydrological response . This is especially the case of
urban areas, where spatial variability and temporal changes in land use are
typically high.
gave a first definition of the catchment length scale
Ls as part of a theoretical framework applied to a natural catchment,
where they analysed 8400 dimensionless hydrographs obtained from
one-dimensional finite element models under spatially varied input. Length
scale was presented as a function of rainfall duration d, spatially averaged
rainfall intensity i, average slope s0, and average roughness n:
Ls=d56s012i23n.
Timescale parameters.
Characteristic
Reference
Description
Time of concentration
The time that a drop that falls on the most remote
tc
part of the drainage basin needs to reach the
basin outlet
Time of equilibrium
Minimum time needed for a given stationary
te
uniform rainfall to persist until equilibrium runoff
flow is reached
Lag time
The time difference between the gravity centre
tlag
of the hyetograph of catchment mean rainfall and the
gravity centre of the generated hydrograph
Response timescale
The timescale at which the pattern of time
Ts
averaged radar hyetograph is most similar to the
pattern of the measured hydrograph at the outlet
of the basin
In urban catchments, the concept of catchment length, defined as the squared
root of the (sub)catchment or runoff area, has been used . Additionally, introduced the sewer
length or inter-pipes sewer distance, as the ratio between the catchment area
and the total length of the sewer, to characterize the spatial scale of sewer
networks. used the width function, defined as the number
of channel segments at a specific distance from the outlet, to represent the
spatial variability of the drainage network. This parameter describes the
network geomorphology by counting all stream links located at the same
distance from the outlet, but it does not give an accurate description of the
spatial variability of hydrodynamic parameters.
Timescale characteristics
In this section, we present a brief overview of timescales reported in the
literature and discuss approaches to estimate characteristic timescales that
have been specifically developed for urban areas. A summary of timescale
characteristics is presented in Table .
The first method to investigate the hydrological response is the rational
method, presented more than a century ago by for urban
areas. This method was later adapted for rural areas. The rational method
requires the estimation of the time of concentration in order to define the
runoff volume.
Time of concentration tc is one of the most common hydrological
characteristic timescales and it is defined as the time that a drop that
falls on the most remote part of the basin needs to reach the basin outlet
. Several equations to estimate this parameter
are available in the literature for natural and
urban catchments. The time of concentration is difficult
to measure, because it assumes that initial losses are already satisfied and
the rainfall event intensity is constant for a period at least as long as the
time of concentration. Different theoretical definitions have been developed
in order to estimate the time of concentration as function of basin length,
slope and other characteristics (see for some examples ).
Due to difficulties related to the estimation of time of concentration,
introduced the time of virtual equilibrium tve,
defined as the time until response is 97 % of runoff supply.
When a given rainfall rate persists on a region for enough time to reach the
equilibrium, this time is called time to equilibrium te . Time of equilibrium for a turbulent flow on a
rectangular runoff plane given rainfall intensity i, with given roughness
n, length Lp and slope S can be written as
te=nLpS12i2335.
Another commonly used hydrological characteristic timescale or response time
is the lag time tlag. It represents the delay between rainfall and
runoff generation. tlag is defined as the distance between the
hyetograph and hydrograph centre of mass of , or between
the time of rainfall peak and time of flow peak . tlag can be considered characteristic of a basin, and is
dependent on drainage area, imperviousness and slope . , including the results of
and , defined a relation between the
dimension of the catchment area S (in ha) and the lag time tlag (in
millimetres): tlag=3S0.3 for urban areas. Empirical relations between
tlag and tc are presented in the literature .
Another characteristic timescale is the “response timescale” Ts,
presented for the first time by . It is defined as the timescale
at which the pattern of the time averaged and basin averaged radar-rainfall
hyetograph is most similar to the pattern of the measured hydrograph
at the outlet of the basin. This definition was updated by
, which used an objective and automatic algorithm to analyse
the smoothness of the hyetograph and hydrograph instead of the general
behaviour, and by , who related the number of peaks with
the total duration of the rising and declining limbs of hyetographs and
hydrographs.
In urban areas, where most of the surface is directly connected to the
drainage system, concentration time is given by the time the rainfall needs
to enter the sewer system and the travel time through the sewer system.
Rainfall measurement and variability in urban regions
Rainfall is an important driver for many hydrological processes and
represents one of the main sources of uncertainty in studying hydrological
response .
Urban areas affect the local hydrological system, not only by increasing the
imperviousness degree of the soil but also by changing rainfall generation
and intensity patterns. Several studies show that increase in heat and
pollution produced by human activities and changes in surface roughness
influence rainfall and wind generation . This
phenomenon is not deeply investigated in this paper, but it is an important
aspect to consider.
In this section instruments and technologies for rainfall measurement are
described, pointing out their opportunities and limitations for measuring
spatial and temporal variability in urban environments. Subsequently, methods
to characterize rainfall events according to their space and time variability
are described.
Rainfall estimation
Rain gauges were the first instrument used to measure rainfall and are still
commonly used, because they are relatively low in cost and easy to install
.
Afterwards, weather radars were introduced to estimate the rainfall spatial
distribution. These instruments allow one to get measurements of rainfall
spatially distributed over the area, instead of a point measurement as in the
case of rain gauges. Rainfall data obtained from weather radars are used to
study the hydrological response in natural watersheds and urban catchments
often combined with rainfall
measurement from rain gauge networks , as well as to improve short-term weather
forecasting and nowcasting .
More recently, commercial microwave links have been used to estimate the
spatial and temporal rainfall variability . Rainfall estimates are obtained from the attenuation of the
signal caused by rain along microwave link paths. This approach can be
particularly useful in cities that are not well equipped with rain gauges or
radars, but where the commercial cellular communication network is typically
dense .
Rain gauges networks
Several types of rain gauges have been developed, such as weighing gauges,
tipping bucket gauges and pluviographs . They
are able to constantly register accumulation of rainfall volume over time,
thus providing a measurement of temporal variability of rainfall intensity.
Rain gauge measurements are sensitive to wind exposure and the error caused
by wind field above the rain gauge is 2–10 % for rainfall and up to 50 %
for solid precipitations . Other errors can be due to tipping
bucket losses during the rotation, to wetting losses on the internal walls of
the collector, to evaporation (especially in hot climates), or water splashing
into and out of the collector . The main disadvantage of rain
gauges is that the obtained data are point measurements and, due to the high
spatial variability of rainfall events, measurements from a single rain
gauges are often not representative of a larger area. Rainfall fields,
however, present a spatial organization and, by interpolating data from a
rain gauge networks, it is possible to obtain distributed rainfall fields
. Uncertainty induced by interpolation
strongly depends on the density of the rain gauge network and on homogeneity
of the rainfall field .
In urban areas, rainfall measurements with rain gauges present specific
challenges associated with microclimatic effects introduced by the building
envelope. recommended minimum distances between rain gauges
and obstacles of 1 to 2 times the height of the nearest obstacle, a
condition that is hard to fulfil in densely built areas. A second problem is
introduced by hard surfaces, that may cause water splashing into the gauges,
if it is not placed at an elevation of at least 1.2 m. Rain gauges in cities
are often mounted on roofs for reasons of space availability and safety from
vandalism. This means they are affected by the wind envelope of the building,
unless they are elevated to a sufficient height above the building.
Rain gauge measurement error can be 30 % or more depending on the type of
instrument used for the measurement and local conditions
.
Weather radars
In the last decades, weather radars have been increasingly used to measure
rainfall .
Radars transmit pulses of microwave signals and measure the power of the
signal reflected back by raindrops, snowflakes, and hailstones (backscatter).
Rainfall rate R [L T-1] is estimated using the reflectivity Z
[L6 L-3] measured from the radar through a power law:
R=aZb,
where a and b depend on type of precipitation, raindrop distribution,
climate characteristics and spatial and temporal scales considered
. Weather radars present
different wavelengths λ, frequencies ν and sizes of the antenna
l. Characteristics of commonly used weather radars are reported in Table .
X-band radars can be beneficial for urban
areas; they are low cost and they can be mounted on existing buildings and
measure rainfall closer to ground at higher resolution than national weather
radar networks . Polarimetric weather radars transmit
signals polarized in different directions , enabling it to
distinguish between horizontal and vertical dimension, thus between rain
drops and snowflakes as well as between smaller or larger oblate rain drops.
A specific strength of polarimetric radars is the use of differential phase
Kdp, which allows one to correct signal attenuation thus solving an
important problem generally associated with X-band radars .
Opportunities and limitations of weather radars
presented a comprehensive analysis of the advantages,
limitations and challenges in rainfall estimation using weather radars. One
of the main problems is that an indirect relation is used (Eq. ) to estimate rainfall. Rainfall measurements have to be
adjusted based on rain gauges and disdrometers. Various techniques have been
studied to calibrate radars , to combine radar-rainfall
measurements with rain gauge data for ground truthing and to define the
uncertainty related to radar-rainfall estimation .
These studies show that in most of the cases, radar measurements
underestimate the rainfall compared to rain gauge measurements
.
Weather radar characteristics.
λ
ν
l
cm
GHz
m
S-band
8–15
2–4
6–10
C-band
4–8
4–8
3–5
X-band
2.5–4
8–12
1–2
Another downside of radars is their installation at high locations to have a
clear view without obstacles, while rainfall intensities can change before
reaching the ground . Moreover, radar measurements need to
be combined with a rain drop size distribution to obtain an accurate rainfall
estimation. pointed out additional aspects that have to be
taken into account, e.g., management and storage of the high quantity of
data that are measured, possibility to use the weather radars to estimate
snowfall and the uncertainty related to it, and problems related to rainfall
measurement in mountain areas.
Rain gauge measurements in urban areas tend to be prone to errors due to
microclimatic effects introduced by the building envelope. In this context,
the use of weather radar could represent a big improvement to obtain a more
accurate rainfall information for studying hydrological response.
A promising application of radar is their combination with nowcasting models
to obtain short-term rainfall forecasts. presented a
review of different nowcasting models, which benefit from radar data. This
work focused in particular on a hybrid model, able to merge the benefits of
radar nowcasting and numerical weather prediction models. Radar data can
provide an accurate short-term forecast and recent studies have presented
nowcasting systems able to reduce errors in rainfall estimation (e.g.
).
Characterizing rainfall events according to their spatial and temporal scale
Rainfall events are characterized by several elements, such as duration,
intensity, velocity and their spatial and temporal variability, and many
possible classifications are presented in the literature. Some of the most
used examples of rainfall classification considering the rainfall
variability, are described in this section.
Characterizations and classifications of intense rainfall events have been
proposed by various authors, combining rain gauges and radar-rainfall data.
In particular, weather radars are used as main tools to analyse rainfall
spatial and temporal scale in urban areas. An example of characterization of
rainfall structure was given by , who presented an
empirical analysis of four extreme rainstorms in the Southern Plains (USA),
using data from two networks of more than 200 rain gauges and from a
weather radar. They defined major rainfall event as storms for which
25 mm of rain covered an area larger than 12500 km2.
presented a storm catalogue of heavy rainfall, over a
study area of 73500 km2 in southern Wisconsin, and key elements of storm
evolution that control the scale. The catalogue contains the 50 largest
rainfall events recorded during a 16-year period by WSR-88D radar with
spatial and temporal resolution of 1 km ×1 km and 15 min respectively.
Over the 50 events, there is 0.60 probability that rainfall exceeds 25 mm
of daily accumulation in a 1 km2 pixel and 0.14 probability of
exceeding 100 mm. Results showed that there is a clear relation between the
characteristic length and timescale of the events. The length scale
increased with timescale; a length scale of 35±20 km was found for a
time step of 15 min, up to 160±25 km for a 12 h aggregation
time.
Rainfall variability at the urban scale
Rainfall events are often described and classified considering they
variability in space and time. Spatial variability can be defined, following
, as “the variability derived from having multiple
spatially distributed rainfall fields for a given point in time”.
introduced also the definition of climatological
variability as the variability obtained from multiple climate trajectories
that produce different storm distributions and rainfall intensities in time.
Studying rainfall variability at the urban scale,
classified 24 rain periods, recorded by the weather radar located in
Treillieres (France), with a spatial and temporal resolution of 250 m ×250 m and 5 min respectively.
They classified the events into four groups,
based on variogram analysis: light rain period, shower periods, storms
organized into rain bands and unorganized storms. These groups are defined
considering the decorrelation distance (and decorrelation time), defined as
distance (and time) from which two points show independent statistical
behaviour, and it is obtained as the range of the climatological variogram
. The first group, characterized by light rainfall
events, presented very high decorrelation distance and time (17 km and 15 min)
compared to the second group, with a decorrelation distance and time of
5 km and a decorrelation time of 5 min. The last two groups presented a
double structure, where small and intense clusters, with low decorrelation
distance and time (less than 5 km and 5 min) are located, in a random or
organized way, inside areas with a lower variability (decorrelation of 15 km and 15 min).
presented a study about variability in accumulated
rainfall within a single radar pixel of 500 m ×500 m, comparing it with
9 rain gauges located in the same area. The results showed a variation of
up to 100 % at a maximum distance of about 150 m, due to the rainfall
spatial variability. This study suggested that a huge quantity of rain gauges
is needed to have a powerful rain gauge network capable of representing small-scale
variability. An alternative solution is to consider the variance
reduction factor method, a numerical method to represent the uncertainty from
averaging a number of rain gauges per pixel, taking into account their
spatial distribution and the correlation between them. The variance reduction
factor method was introduced for the first time by
and lately applied in various studies
.
Characterization of rainfall events, spatial and temporal scales, and
rainfall estimation uncertainty. From ,
, and .
Characterization
Spatial
Temporal
Radar
and Intensity
Range
Range
Estimation
Light
1 mm h-1
17 km
15 min
Underestimation rainfall values often
rainfall
below the threshold (0.17 mm h-1)
Convective
short and intense
5 km
5 min
Overestimation
cells
from 25 mm
Organized
up to 17 mm h-1
<5 km
< 5 min
General underestimation, good
stratiform
representation of the hyetograph behaviour
Unorganized
high-intensity core, combined
15 km
15 min
Underestimation of the peaks, good
stratiform
with low-intensity areas
representation of the hyetograph behaviour
focused on the gap between rain gauges and radar spatial
scale, considering that a rain gauge usually collects rainfall over 20 cm
of surface and the spatial resolution of most used radars is of 1 km ×1 km.
They evaluate the impact of small-scale rainfall variability using a
universal multifractal downscaling method. The downscaling process was
validated with a dense rain gauge and disdrometer network, with 16 instruments
located in 1 km ×1 km. They showed two effects of small-scale
rainfall variability that are often not taken into account; high rainfall
variability occurred below 1 km2 spatial scale and the random position
of the point measurement within a pixel influenced measured rainfall events.
Similar results are confirmed by , who studied the spatial
variability of extreme rainfall at radar subpixel scale. Comparing a radar
pixel of 1 km × 1 km with high-resolution rainfall data, obtained by applying the
stochastic rainfall generator STREAP to simulate rain
fields, this study highlights that subpixel variability is high and increases
with increasing of return period and with shorter duration.
In Table four types of rainfall events are presented
with their characterization and typical spatial and temporal decorrelation
lengths, based on , , and
. Considering that the minimal rainfall measurement
resolution required for urban hydrological modelling is 0.4 the decorrelation
length (; ;
), operational radars are not able to satisfy
this requirement.
Hydrological processes
In this section, general characteristics and parametrizations of hydrological
processes are presented, highlighting their spatial and temporal variability
and characteristics specific to urban environments.
Precipitation losses
Infiltration, interception and storage
The term infiltration is usually used to describe the physical processes by
which rain enters the soil . Different equations and
models have been proposed to describe infiltration. The most commonly used is
Richards equation , which represents this phenomenon
using a partial differential equation with non-linear coefficients.
Another possibility to estimate the infiltration capacity is given by the
empirical equation presented by . In Horton's equation
hydraulic conductivity and diffusivity are constant and do not depend on
water content or on depth.
If water cannot infiltrate, as is the case in impervious areas, it can be
stored in local depressions, where it does not contribute to runoff flow.
This is the case of local depressions on streets or flat roofs, where water
accumulates until the storage capacity is reached. Before reaching the
ground, rainfall can be intercepted by vegetation cover or buildings.
Interception can constitute up to 20 % of rainfall at the start of a
rainfall event , and decreases quickly to zero, once
surfaces are wetted.
During the process of transformation of rainfall in runoff, part of the water
is lost due to several phenomena, such as infiltration, storage or
evaporation. presented an experimental study of water
fluxes in a residential area, in which they estimated infiltration and
evaporation in urban areas, showing that the assumption that all rainfall
becomes runoff is not correct and that it leads to an overestimation of
runoff. studied the hydrological behaviour of urban
streets over a 38-month period to estimate runoff losses and to better define
rainfall runoff transformations. They estimated losses due to evaporation and
infiltration inside the road structure between 30 and 40 % of the total
rainfall.
Spatial scale of precipitation losses is strongly influenced by land cover
variation. In urban areas, land cover variability typically occurs at a
spatial scale of 100 to 1000 m. Timescale is associated with local
storage accumulation volume, sorptivity, and hydraulic conductivity, which in
turn depend on soil type and soil compaction.
Groundwater recharge and subsurface processes in urban areas
Groundwater recharge mechanisms change due to human activities and
urbanization, both in terms of volume and quality of the water. The increase
of imperviousness of land cover leads to a decrease in infiltration of
rainfall into soil, reducing direct recharge to groundwater. The presence of
leakage from drinking water and sewer networks can increase infiltration to
groundwater and amount of contaminants that is spread from the sewer system
into the soil .
Although it is well known that not all rainfall turns into runoff
, it is common to consider the losses from
impervious areas so small that they can be assumed negligible compared to the
total runoff volume . tried
to emphasize the importance of accounting for infiltration in the urban water
balance, and found that infiltration through the road surface can constitute
between 6 and 9 % of annual rainfall. Due to high spatial variability of
infiltration, representative measurements are difficult to obtain and require
a large amount of point-scale measurements .
Several types of pervious pavements are used in urban areas. They can
generally be divided into monolithic and modular structures. Monolithic
structures consist of a combination of impermeable blocks of concrete and
open joints or apertures that allow water to infiltrate. In modular
structures, gaps between two blocks are not filled with sand, as with
conventional pavements, but with 2–5 mm of bedding aggregate, that
facilitate infiltration . Following European standards,
minimum infiltration capacity for permeable pavements is 270 L s-1 ha-1, equal to 97.2 mm h-1 .
Pervious areas in cities can effectively act as semi-impervious areas,
because within the soil column there is a shallow layer that presents a low
hydraulic conductivity at saturation, caused by soil compaction during the
building process. studied the influence of this phenomenon
on peak runoff flow by applying 21 storm events on a physically based,
minimally calibrated model of the dead run urban area (USA) with and without
the compacted soil layer. Results showed that the compacted soil layer
reduced infiltration by 70–90 % and increased peak discharge by
6.8 %.
Surface runoff
When rainfall intensity exceeds infiltration capacity of the soil, water
starts to accumulate on the surface and flows following the slope of the
ground. This process is generally called Hortonian runoff
or infiltration capacity excess flow. It is usually contrasted with
saturation excess flow, or Dunne flow , that occurs when
the soil is saturated and rainfall can no longer be stored
.
In urban areas, runoff is generated when the surface is impervious and water
can not infiltrate, or when infiltration capacity is exceeded by rainfall
intensity. Water flows over the surface and can reach natural drainage
channels or be intercepted by the drainage network through gullies and
manholes. If the drainage network capacity is exceeded, the system become
pressurized, and water starts to flow out from gullies, increasing runoff on
the street .
It is important to pay attention to some elements that characterize the
runoff in urban environments: sharp corners or obstacles can, for example,
deviate the flow and introduce additional hydraulic losses. Interactions
between surface flow and subsurface sewer systems through sewer inlets and
gully pots are hydraulically complex and their influence on overland and
in sewer flows remains poorly understood. Runoff flows are often
characterized by very small water depths that are often alternated with dry
surfaces, especially when rainfall intensities vary strongly in space and
time.
Impact of land cover on overland flow in urban areas
In urban areas, the land cover, represented by an alternation of impervious
surfaces, such as roads and roofs, and small pervious areas, such as gardens,
vegetation and parks, shows a high variability in space.
The impact of increase of imperviousness on hydrological response was studied
by , who analysed the effects of urban development in Wu-Tu
(Taiwan's catchment) considering 28 rainfall events (1966–1997). Results
showed that response peak increased by 27 % and the time to peak decreased
from 9.8 to 5.9 h, due to an increase of imperviousness from 4.78 to
11.03 %.
In a similar study, analysed the effects of imperviousness
on flood peak in the Charlotte metropolitan region (USA), analysing a 74-year
discharge record. Results showed that different land covers were
associated with large differences in timing and magnitude of flood peak,
while there were not significant differences in the total runoff volume.
Hortonian runoff was the dominant runoff mechanism. Antecedent soil moisture
played an important role in this watershed, even in the most urbanized
catchment.
The influence of antecedent soil moisture is, however, not always so evident.
showed that in nine watersheds, located in the Baltimore
metropolitan area, the antecedent soil moisture, defined as 5-day antecedent
rainfall, seemed not to affect the hydrological response. Introduction of
storm water management infrastructure played an important role in reducing
flood peaks and increasing runoff ratios. Results showed that rainfall
variability may have important effects on spatial and temporal variation in
flood hazard in this area.
Analysing the effects of a moderate extreme and an extreme rainstorm on the
same area presented by , highlighted the
importance of changes in imperviousness on flood peaks. They found that for
extreme rainfall event, imperviousness had a small impact on runoff volume
and runoff generation efficiency.
Evaporation
Evaporation plays an important role in the hydrological cycle: in forested
catchment around 60–95 % of total annual rainfall evaporates or is absorbed
by the vegetation . In an urban catchment, evaporation
is drastically reduced .
Evaporation is often neglected in analysis of fast and intense rainfall
events ; the order of magnitude of evaporation is very small
compared to the total amount of rainfall. Some studies have shown that
evaporation is not always negligible in urban areas and can constitute up to
40 % of the annual total losses .
In their experimental study, showed that evaporation
represents 21–24 % of annual rainfall, with more evaporation taking place
during summer than winter. It is particularly important to have measurements
with high resolution because a coarse spatial description can hide
heterogeneous land covers and consequently, heterogeneous evaporation losses
.
Evaporation measurements in urban areas are one of the weak points of the
water balance and they present many problems and
challenges . It is quite hard in fact to find a site,
representative of the area, far enough from obstacles and not unduly shaded.
Errors in estimation of annual evaporation in urban areas may still be higher
than 20 % .
Different techniques and approaches have been developed to measure and
estimate the impact of evaporation, from the standard lysimeter to the use of
remote sensing , to the combined used of remote sensing and
ground measurements . Different models to estimate
evaporation in urban areas have been proposed . estimated evaporation in the urban area of
Los Angeles, as combination of empirical models of turfgrass evaporation and
tree transpiration derived from in situ measurements. Evaporation from
non-vegetated areas appears to be negligible compared with the vegetation, and
turfgrass was responsible for 70 % of evaporation from vegetated areas.
Flow in sewer systems
In urban areas, part of the surface runoff enters in the sewer system through
gully inlets, depending on the capacity of these elements, on their
maintenance and the sewer system itself.
Storm water flow in sewer systems is highly non-uniform and unsteady, it can
be considered as one dimensional, assuming that depth and velocity vary only
in the longitudinal direction of the channel. Flow in sewer pipes is usually
free surface, but during intense rainfall events the system can become full
and temporarily behave as a pressurized system, a phenomenon called
surcharge. In particular conditions, as for example in flat catchments,
inversion of the flow direction in pipes can occur during filling and
emptying of the system. The most common form to model flow in sewer pipes is
based on a one-dimensional form of the de Saint-Venant equations.
Sewer system density influences runoff generation : a dense pipe network can, in fact, reduce the runoff generation,
increasing the storage capacity of the system .
presented a study about the importance of drainage density
on flood runoff in urban catchments. Defining the drainage density as channel
length per total catchment area, they studied the hydrological response of
the same basin modelled with drainage density that varied from 0.4 to 3.9 km km-2.
Results showed a significant increase in peak
discharge and runoff volume for drainage density between 0.4 and
0.9 km km-2, while for values higher than 0.9 km km-2, effects were
negligible. When the storage and transport capacity of a system is not
sufficient to prevent flooding, detention basins are effective tools to
reduce peak flows, and they can reduce the superficial runoff up to 11 %
.
Similarly, green roofs can significantly decrease and slow peak discharge and
reduce runoff volume. presented a study on the impact of
green roofs at urban scale using a distributed rainfall model. They showed
that green roofs can reduce runoff generation in terms of peak discharge,
depending on the rainfall event and initial conditions. The reduction can be
up to 80 % for small events, with an intensity lower than 6 mm.
Urban hydrological models
Urban hydrological models were developed since the 1970s to better understand
the behaviour of the components of the water cycle in urban areas
. Since then, many models, with different characteristics,
principles, and complexity have been built. These models are used for several
purposes, such as to study and predict the effects of urbanization increase
on the hydrological cycle, to support flood risk management, to ensure clean
and fresh drinking water for the population, and to support improvement of
waste water networks and treatments (see
for a review). A good summary of the most used urban hydrological models has
been recently proposed by , where a table with the most
used hydrological models is presented and discussed.
Hydrological models have shown to be useful to compensate partially for the
lack of measurements , but all models present errors
and uncertainties of different nature and magnitude
. In this chapter, different classifications and
characterizations of hydrological models are presented.
Urban hydrological model characterization
Hydrological models can be characterized and classified in different ways. A
first distinction can be made according to the representation of spatial
variability of the catchment. A lumped model does not consider spatial
variability of the input, and uses spatial averaging to represent catchment
behaviour. In contrast, distributed models describe spatial variability,
usually using a node-link structure to describe subcatchment components
. The choice of a suitable model depends on
many factors and it is generally related to the applications and final
objective. For example suggested a guideline for choosing
between lumped and distributed modelling considering the representative
surface associated to a single rain gauge Sr. This characteristic, defined
in relation to the rainfall spatial resolution r as Sr=π[r/2]2, is
compared with the surface area of a catchment S. If Sr>S or Sr∼S
a lumped modelling approach is suggested, while for Sr<S, a distributed
model is recommended, as well as collecting measurements at the subcatchment
scale. Different sub-categories are presented to characterize model spatial
variability. Distributed models can be divided into fully distributed and
semi-distributed models. Fully distributed models present a detailed
discretization of the surface, using a grid or a mesh of regular or irregular
elements, and apply the rainfall input to each grid element, generating
grid-point runoff. The flow can be estimated at any location within the basin
and not only at the catchment outlet. This is, however, possible only if the
rainfall is provided with an appropriate spatial resolution. Semi-distributed
models are based on subcatchment units, through which rainfall is applied.
Each subcatchment is modelled in a lumped way, with uniform characteristics
and a unique discharge point .
proposed a model classification based on spatial variability with five
categories: lumped, semi-distributed, Hydrological response unit based
(semi-distributed with a specific way to define the subcatchment area), grid-based
spatially distributed, and urban hydrological element based (mainly
focused on the urban fluxes).
Another distinction is between conceptual and physically based (or process
based) models, depending on whether the model is based on physical laws or
not. Recently, presented an overview of the advantages
and limitations of physically based models in hydrology. They defined a
physically based hydrological model as “a set of process descriptions that
are defined depending on the objectives”. The downsides of using a physically
based model are related to over-complexity and over-parametrization:
conceptual models are much easier to manage and they are usually less
affected by numerical instability. Physically based models usually require
high computational power and time and a large number of parameters, but there
are situations in which it is important to keep the complexity to better
understand system mechanisms. They are also necessary to deal with system
variability and allow one to include a stochastic component to represent
uncertainty in parameter and input values .
Spatial and temporal variability in urban hydrological models
Depending on their characteristics, models can be very sensitive to spatial
and temporal rainfall variability or not be able to correctly reproduce
effects of this variability. Spatial variability of land cover and soil
characteristics is an important element in hydrological models. Choosing
between a lumped, semi-distributed, or fully distributed hydrological model
leads to different representation of catchment characteristics and,
consequently, to a different output .
A comparison between semi-distributed and fully distributed urban storm water
models was made by . Two small urban catchments, Cranbrook
(London, UK) and the centre of Coimbra (Portugal), were modelled with a semi-
and a fully distributed model. Flow and depth in the sewer system of the
different models were compared with observations and, in general,
semi-distributed models predicted sewer flow patterns and peak flows more
accurately, while fully distributed models had a tendency to underestimate
flows. This was mainly due to the presence small-scale surface depressions,
building singularities or lack of knowledge about private pipe connections.
Although fully distributed models are more realistic and able to better
represent spatial variability of the land cover, they need a higher
resolution and accuracy to define module connections. Calibration of
detailed, distributed models remains a complex issue that is not yet well
resolved. The authors suggested to use a semi-distributed model approach in
cases of low data resolution and accuracy.
To study the hydrological response presented the Urban
Drainage Topological Model (UDTM), a model that represents subcatchments of a
semi-distributed model with two conceptual linear elements: a reservoir and a
channel. In a more recent study , this model was compared
to the Storm Water Management Model (EPA SWMM model; ),
that allows the user to choose different conceptual models to simulate runoff
and sewer flow. Results showed that model structure and sensitivity to
parameters influence the sensitivity to the rainfall input resolution.
Interaction of spatial and temporal rainfall variability with hydrological response in urban basins
Storm structure and motion play an important role in the variability of the
hydrological response , especially for small
catchments . The characterization and the
influence of spatial and temporal rainfall variability on runoff response is
still not well understood .
Recent studies address the impact of rainfall variability, focusing on urban
catchments . The main results and conclusions are presented in the following
sections. It is discussed how basin characteristics impact the sensitivity of
hydrological response to rainfall variability and how the interaction between
spatial and temporal rainfall variability influences hydrological response.
Interaction between rainfall resolution and urban hydrological processes
Many studies highlight the importance of high-resolution rainfall data
and how their use could
improve runoff estimation, especially in an urban scenario, where drainage
areas are small and spatial variability is high . These studies have shown how catchments act as
filters in space and time for hydrological response to rainfall, delaying
peaks and smoothing the intensity. However, the influence of spatial
variability of rainfall on catchment response in urban areas is complex and
remains an open research subject.
A theoretical study, conducted by , emphasized the
necessity to use rainfall data with a higher resolution for urban catchments
compared to rural areas, and suggested to choose a minimum temporal
resolution of 1–5 min and a spatial resolution of 1 km. The effects of
temporal and spatial rainfall variability below 5 min and 1 km scale were
subsequently studied by . They investigated the urban
catchment of Cranbrook (London, UK), with the aim of quantifying uncertainty
in urban runoff estimation associated with unmeasured small-scale rainfall
variability. Rainfall data were obtained from the national C-band radar with
a resolution of 1 km2 and 5 min and were downscaled with a
multifractal process, to obtain a resolution 9–8 times higher in space and
4–1 in time. Uncertainty in simulated peak flow associated with small-scale
rainfall variability was found to be significant, reaching 25 and 40 %
respectively for frontal and convective events.
To investigate the effects of spatial and climatological variability on urban
hydrological response, used a stochastic rainfall
generator to obtain high-resolution spatially variable rainfall as input for
a calibrated hydrodynamic model. They compared the contributions of
climatological rainfall variability and spatial rainfall variability on peak
flow variability, over a period of 30 years. They found that peak flow
variability is mainly influenced by climatological rainfall, while the
effects of spatial rainfall variability increase for longer return periods.
Required rainfall resolution for urban hydrological modelling strongly
depends on the characteristics of the catchment. Several researchers have
studied the sensitivity of urban hydrological response to different rainfall
resolutions, highlighting correlations between rainfall resolution and
catchment dimensions, such as drained area or catchment scale length .
Influence of spatial and temporal rainfall variability in relation to catchment dimensions
Drainage area dimensions influence hydrological response and their
sensitivities to spatial and temporal rainfall resolution have recently been
investigated.
presented a flood frequency analysis, based on stochastic
storm transposition coupled with high-resolution radar
rainfall measurements, with the aim to examine the effects of rainfall time
and length scale on the flood response. Rainfall data were used as input for
a physics-based hydrological model representative of 4 urbanized
subcatchemnts. This study showed that there is an interaction between
rainfall and basin characteristics, such as drainage area and drainage system
location, that strongly affects the runoff.
studied the hydrological response of six urban catchments
located in the south-east of the French Mediterranean coast. Rainfall data
and runoff measurements were collected using two X-band weather radars, one
vertically pointing radar, and one radar performing vertical plane cuts of the
atmosphere, with a spatial resolution of 7.5 and 250 m and a temporal
resolution of 4 s and 1 min respectively. The minimum temporal
resolution required Δt was defined as Δt=tc/4,
where tc is the characteristic time of a system and the value 4
depends on catchment properties . By considering lag
time tlag equal to the characteristic time tc, it was
possible to write the minimum required temporal resolution as a function of
surface area S, based on the relationship tlag=3S0.3:
Δt=0.75S0.3. Spatial resolution was studied considering rainfall
data collected from the X-band weather radar performing vertical plane cuts
of the atmosphere, combined with measurements of rain gauges. Two spatial
climatological variograms were built with a time resolution of 1 min (from
radar) and 6 min (from a network of 25 rain gauges). Based on variogram
analysis, it was possible to define the relation between range r and time
resolution Δt as (r=4.5Δt). The minimum required
spatial resolution Δs was defined by the authors as Δs=r/3, and it can also be expressed as a function of Δt:
Δs=1.5Δt.
In this way, both spatial and temporal resolution requirements were defined
as a function of surface dimensions of a catchment. Required resolutions for
urban catchments of 100 ha are 3 min and 2 km, but common operational
rain gauge networks are usually less dense, while radars seldom provide data
at this temporal resolution. Results presented are valid for catchments with
characteristics similar to the catchments studied, such as surface area (from
10 to 10000 ha), slope (1 to 10 %), imperviousness degree
(10 to 60 %), and exposed to climatic conditions similar to those of
Mediterranean area.
analysed the impact of spatial and temporal
rainfall resolution on hydrological response in seven urban catchments,
located in areas with different geomorphological characteristics. Using
rainfall data measured by a dual polarimetric X-band weather radar with
spatial resolution of 100 m ×100 m and temporal resolution of 1 min,
they investigated the effects of combinations of different resolutions, with
the aim to identify critical rainfall resolutions. They investigated the
impact of 16 combinations of 4 different spatial resolutions (100 m × 100 m, 500 m × 500 m, 1000 m × 1000 m, and 3000 m ×3000 m) combined with four different
temporal resolutions (1, 3, 5, and 10 min). Resolution combinations
were chosen considering different aspects, such as the operational resolution
of radar and rain gauges networks, characteristics temporal and spatial
scale. A strong relation between drainage area and critical rainfall
resolution and between spatial and temporal resolutions was found.
Sensitivity to different rainfall resolutions decreased when the size of the
subcatchment considered increased, especially for catchment size above 1 km2.
This study highlighted the importance of high-resolution rainfall
data as input. Spatial resolution of 3 km ×3 km is not adequate for urban
catchments and temporal resolution should be lower than 5 min. Most
operational radars present a temporal resolution of 5 min, not sufficient to
correctly represent the effects of temporal rainfall variability.
The sensitivity to rainfall variability on 5 urban catchments of different
sizes, located in the City of Arlington and Grand Prairie (USA), was studied
with a distributed hydrological model (HLRDHM, Hydrology Laboratory Research
Distributed Hydrological Model) by . Rainfall data
were provided by the Collaborative Adaptive Sensing Atmosphere (CASA) X-band
radar with spatial resolution of 250 m ×250 m and temporal resolution of
1 min and upscaled in various steps to 2 km ×2 km and 1 h.
Results showed peak intensity and time to peak error to be sensitive to
spatial rainfall variability. The model was able to represent observed
variability for all catchments except the smallest (3.4 km2) at a
temporal resolution of 15 min or lower, combined with spatial variability
of 250 km ×250 m and capture variability in streamflow.
Resolution required to measure rainfall for small basins is usually high, as
in the case of urban catchments. The influence of slope, imperviousness
degree or soil type were not separately investigated, but the relationships
between catchment area and rainfall resolution are expected to depend on
these characteristics as well.
Sensitivity of hydrological response to different spatial and temporal
rainfall resolutions has been investigated with dimensionless parameters to
represent the length scales of storm events, catchments and of sewer
networks.
identified dimensionless parameters to analyse
correlations between catchment and storm characteristics and to study
sensitivity of runoff models to radar-rainfall resolution. Rainfall data of a
convective storm event, measured by a polarimetric radar with a spatial
resolution of 1 km ×1 km, were applied on two basins. The storm smearing
was defined as the ratio between rainfall data grid size and rainfall
decorrelation length. Storm smearing occurs when rainfall data length is
equal to or longer than the rainfall decorrelation length. The watershed
smearing was described as the ratio between rainfall data grid size and basin
length scale. When infiltration is negligible, watershed smearing is an
important source of hydrological modelling errors, if the watershed ratio
(rainfall measurement length/basin length) is higher than 0.4.
A similar approach, with dimensionless parameters, was recently applied by
to urban catchments. Rainfall data from a X-band dual
polarimetric weather radar were applied to an hydrodynamic model, to
investigate sensitivity of urban model outputs to different rainfall
resolutions. The runoff sampling number was defined as ratio between rainfall
length and runoff area length. Results confirm what was found by
. A third dimensionless parameter, called runoff sampling
number, was identified. Small-scale rainfall variability at the 100 m ×100 m
affects hydrological response and the effect of spatial resolution
coarsening on rainfall values strongly depends on the movement of storm cells
relative to the catchment.
Using dimensionless parameters is a productive approach to study sensitivity
of hydrological response to spatial and temporal rainfall variability.
Effects of other catchment characteristics, such as slope or imperviousness,
were so far neglected, but they need a deeper investigation.
Spatial vs. temporal resolution
As it was already discussed in previous sections, there is a dependency
between spatial and temporal rainfall required resolution and they affect in
a different way the hydrological response .
A first interaction between spatial and temporal rainfall scale was defined
based on the assumption that atmospheric properties are valid also for
rainfall. Following this assumption, Kolgomorov's theory
was combined with the scaling properties of the
Navier–Stokes equation, in order to define a relation between space and time
variability. For large Reynolds numbers, in fact, the Navier–Stokes equation is
invariant under scale transformations , and in this way temporal and spatial “scale changing” operator
can be defined by dividing space and time (s and t) by scaling factors
λs and λt relatively: s↦s/λs and t↦t/λt. For scaling processes, there is a relation between
scaling factors in time and space to take into account, that is represented
the anisotropy coefficient Ht: λt=λs(1-Ht). Ht is
a priori unknown for rainfall, but it can be assumed equal to 1/3, a value
that characterize atmospheric turbulence . estimated Ht=0.5±0.3 for raindrops.
An example of application of this theory in a rainfall downscaling process is
given by : here, the rainfall is measured with a certain
spatial resolution s and temporal resolution t. They hypothesized to
downscale the radar pixels, dividing the length by a scaling factor
λs=3, to obtain nine pixels out of one. In this case, to keep the
relation between spatial and temporal resolution, the duration of the time
step has to be divided by a scaling factor λt=λs1-1/3=22/3≃2.
Studying the hydrological response of the south-east French Mediterranean
coast, proposed another relationship between spatial
Δs and temporal Δt resolution used to measure rainfall, as
Δs=1.5Δt (see Sect. for the
formula derivation).
derived the theoretically required spatial
rainfall resolution for urban hydrological modelling starting from a
climatological variogram, which characterized average spatial structure of
rainfall fields over the peak storm period, fitted with an exponential
variogram model. They defined characteristic length scale rc of a
storm event as rc=(2π/3)r, where r is the
variogram range. The minimum required spatial resolution for adequate
modelling of urban hydrological response was defined as half characteristic
length scale of the storm: Δs=rc/2≅0.418r. The
theoretically required temporal resolution Δt, was defined based on
the time needed for a storm to move over distance equal to the characteristic
length scale of the storm event rc. It can be written as Δt=rc/v, where v is the magnitude of the mean storm
velocity, obtained from average of the velocity vectors (magnitude and
direction) estimated at each time step.
investigated also the impact of different
combinations of spatial and temporal resolutions as described in
Sect. . One of the criteria used to choose some of the
resolution combination was the already discussed in the literature
, and according to Kolgomorov's scaling theory
. Results showed that hydrodynamic models are more
sensitive to the coarsening of temporal resolution of rainfall inputs than to
the coarsening of spatial resolution, especially for fast moving storms.
In this work, the authors presented also a relation between spatial and
temporal critical rainfall resolutions depending on drainage area (Table ).
For small catchments, with area smaller than 1 ha,
was found to be equal to 100 m ×100 m and 1 min, while for areas between
1 and 100 ha, a spatial resolution of 500 m ×500 m can be sufficient
to estimate the hydrological response. The critical spatial resolution found
is lower than 5 min, for catchment size from about 250 to 900 ha. Results
were confirmed by , that presented an analysis of flash
flooding in two small urban subcatchments of Harry's Brook (Princeton, New
Jersey, USA), focusing on the influence of rainfall variability of storm
events on hydrological response.
Spatial variability seems to influence timing of runoff hydrograph, while
temporal variability mainly influences peak value .
Critical resolutions in relation with the drainage area.
Drainage Area
Critical spatial
Critical temporal
DA
resolution
resolution
(ha)
(m × m)
(min)
DA < 1
100
1
1 < DA < 100
500
1
250 < DA < 900
1000
< 5
investigated the influence of spatial and
temporal scaling factor introduced at the beginning of this section, on
runoff estimation from different input, introducing also a combined
spatio-temporal factor Θst. This factor was defined using the
anisotropy coefficient as Θst=(ΔSrΔS)(ΔtΔtr)(11-Ht), where ΔS and
Δtr are the required spatial and temporal resolutions, ΔS and Δt are the space and time resolutions used as input for
model simulations and Ht is the scaling anisotropy factor. The stronger
relation between drainage area and combined spatio-temporal factor
Θst compared to the relation with singular spatial or temporal
scaling factor suggests that the effects of space and time has to be
considered together. However, the combined effects of spatial and temporal
resolution on the sensitivity to hydrological response requires future works
and deeper investigations.
These studies highlighted the relatively more important role of temporal
variability compared to spatial variability, for extreme rainfall events. The
impact of the spatial variability, seemed to decrease with increase of total
rainfall accumulation.
Summary and future directions
In this article, the state of the art of spatial and temporal variability
impacts of rainfall and catchment characteristics on hydrological response in
urban areas has been presented. The main key points and conclusion of this
study are the following.
A first aspect that has been highlighted is the high variability in space and
time of hydrological processes and phenomena in urban environments.
Measuring, understanding and effectively characterizing temporal and spatial
variability at small-scales is therefore of utmost importance. High-resolution data are essential given the high variability of catchment
characteristics and hydrological processes, such as infiltration, evaporation
and surface runoff. An important role in urban areas is played by drainage
infrastructures that highly affect the hydrological response, while in some
cases the effects of these structures are not perfectly understood. Current
methods and instruments often have insufficient capability to measure the
considered process at their relevant scales.
Several definitions to classify timescale characteristics are available in
the literature, such as time of concentration, lag time, time of equilibrium
and response timescale. However, measurement or estimation of those
parameters is often ambiguous, which implies a high level of uncertainty.
Thus far, no common agreement has emerged on a unique set of parameters able
to characterize small-scale variability of urban catchments in a way that
enhances our understanding of urban hydrological response. Improved rainfall
measurements have also allowed to investigate the relations between temporal
and spatial rainfall scale. Relations have been presented, mostly adapting
the Kolgomorov?s theory to rainfall, to define the interaction between
spatial and temporal scale in atmosphere. A unique relationship has not yet
been found. This highlights the need for methods that can better characterize
spatial and temporal scale parameters of rainfall and urban catchments in an
effective way.
Uncertainty associated with rainfall spatial and temporal variability is one
of the main sources of error in the estimation of hydrological response in
urban areas. New technologies have been developed to measure rainfall spatial
and temporal variability more accurately and at higher resolution. While rain
gauges remain the most common used rainfall measurement instruments, weather
radars are a promising example of recently developed instruments, able to
estimate rainfall variability at high resolution. However, they still need to
be combined with rain gauge networks in order to improve their accuracy. Rain
gauges applied in urban areas present many limitations due to strong
microclimatic variability, complicating identification of suitable locations
for representative rainfall measurements. Polarimetric X-band radars combine
high-resolution and high-accuracy measurement capability with the advantages
of local installation thus avoiding overshooting and resolution loss with
distance associated with large radar network. They constitute a promising
direction for future urban hydrological research and rainfall and flood
forecasting applications.
Many studies are reported in the literature using hydrological models with
different characteristics and different representations of the catchment
spatial variability. Different types of hydrological models have been
developed in order to represent the spatial variability of catchment
properties, such as land cover and imperviousness degree. Models can be
classified based on their ability to represent the spatial variability of the
catchment into lumped, semi-distributed and fully distributed models. These
models have become more and more detailed, reaching high levels of spatial
resolution. However, unless they are driven by similarly high-resolution
rainfall data, increasing model resolution cannot fundamentally improve
understanding of hydrological processes or improve reliability of
hydrological predictions. Infiltration, local storage, interception and
evaporation are quite difficult to measure, especially in urban areas,
because of the strong heterogeneity of urban land use.
The impact of spatial and temporal rainfall variability on the hydrological
response in urban areas and the role of drainage infrastructure and man-made
control structures herein still remains poorly understood. It was found that
sensitivity of hydrological response to spatial and temporal rainfall
variability varies with catchment size, catchment shape, storm scale and
storm velocity. So far, findings are mainly based on sensitivity studies
using theoretical model scenarios. A wider range of conditions and scenarios
based on observational datasets for urban hydrological basins need to be
analysed in order to characterize better the hydrological response and its
sensitivity to different spatial and temporal rainfall resolutions.