Intensity–duration–frequency (IDF) curves are widely used to quantify the
probability of occurrence of rainfall extremes. The usual rain gauge-based
approach provides accurate curves for a specific location, but uncertainties
arise when ungauged regions are examined or catchment-scale information is
required. Remote sensing rainfall records, e.g. from weather radars and
satellites, are recently becoming available, providing high-resolution
estimates at regional or even global scales; their uncertainty and
implications on water resources applications urge to be investigated. This
study compares IDF curves from radar and satellite (CMORPH) estimates over
the eastern Mediterranean (covering Mediterranean, semiarid, and arid
climates) and quantifies the uncertainty related to their limited record on
varying climates. We show that radar identifies thicker-tailed distributions
than satellite, in particular for short durations, and that the tail of the
distributions depends on the spatial and temporal aggregation scales. The
spatial correlation between radar IDF and satellite IDF is as high as 0.7 for
2–5-year return period and decreases with longer return periods, especially
for short durations. The uncertainty related to the use of short records is
important when the record length is comparable to the return period
(
Intensity–duration–frequency (IDF) curves are widely used in
hydrological design and as decision support information in flood risk and
water management
In the last decades a body of research has been devoted to these issues.
Areal reduction factors and design storms assume homogeneity of rainfall
extreme climatology to adapt the point-IDF values estimated by rain gauges
to wider areas, such as catchments, based either on the climatology of the
region
Remote sensing instruments, such as weather radars or satellites, provide
high spatio-temporal resolution (i.e. 1–10
Since quantitatively accurate information is essential for design
applications and the derivation of IDF curves based on historical records
does not require short latency in the data, these studies made use of
gauge-adjusted products and assessed the accuracy of the IDF curves derived
from remote sensing datasets, using rain gauge curves as a reference. However,
this approach neglected two important aspects. First, early warning systems,
e.g. for flash floods
The aim of this study is to advance knowledge on the use of remote sensing
precipitation estimates for rainfall frequency analysis. IDF curves computed
from different datasets, namely the National Oceanic and Atmospheric
Administration (NOAA) Climate Prediction Center morphing (CMORPH) technique
The study area and the rainfall datasets are presented in Sect. 2. Section 3 describes the methods used for computing and comparing satellite and radar IDF curves and for estimating the uncertainty related to the record length. In Sect. 4 the results of the study are presented and discussed. Section 5 provides the conclusions and suggestions for the future use of remote sensing datasets for rainfall frequency analysis.
The present study is focused on the eastern Mediterranean, in particular on
the area covered by the Shacham weather radar, shown in Fig. 1. The orography
presents a longitudinal organization that, going east from the Mediterranean
Sea, encounters a coastal plain, a hilly region (up to
Map of the study area showing terrain elevation, climatic
classification from
Köppen–Geiger classification (
Three climatic regions, the Mediterranean, semiarid, and arid, can be identified
in the area, corresponding to the Csa, BSh, and BWh Köppen–Geiger
definitions, respectively
The Shacham weather radar is a C-Band (5.35 cm wavelength), non-Doppler
instrument, operational since the late 1980s. Observations from this radar
have been archived from October 1990 to March 2014, providing a unique
23-year record and have been extensively used for climatologic and
hydrological studies
The Shacham radar record has recently been reanalysed for rainfall frequency
analysis
This study is based on the hourly radar archive. Each hourly radar product is
created when at least 60 % of radar scans are available during the 1 h
time interval. This quality check on the data availability ensures a good
coverage of the examined time interval and allows for exploring durations longer
than the ones analysed by
The satellite precipitation products selected for this study are the high-resolution CMORPH (HRC)
and its gauge-adjusted version (CHRC) available from
NOAA CPC. The two products, with
The small-scale representativeness of rain gauge measurements makes them not
suitable for a large-scale quantitative assessment of remote sensing products
We identified 11 rain gauges, operated by the Israeli Meteorological Service,
among the ones already used by
In this study, the generalized extreme value (GEV) distribution (Appendix A)
is used to fit the annual maxima series (AMS) of average rain intensities
observed over 1, 3, 6, 12, and 24 h durations. The use of AMS ensures
independency of the elements of the series and, rather than peak over
threshold series, is suitable for this study because it does not require the
definition of thresholds, problematic operation on highly variable climatic
conditions, and potentially undermining the interpretation of the comparison
between different datasets. The GEV distribution is a three-parameter
extreme values distribution used worldwide to model rainfall extremes
In order to have radar and satellite data on a common grid suitable for the
comparison, the full archive of hourly radar data was remapped by spatially
averaging the 1 km
The effect of spatial and temporal aggregation of rainfall estimates, key
issue when dealing with remote sensing instruments, is analysed spatially
aggregating the original radar record (23 years, 1 km
IDF maps obtained from the satellite precipitation datasets (HRC and CHRC)
are compared to the ones obtained from the radar archive during corresponding
years (16 years: 1998–2013). The comparison is extended over an analysis
domain defined excluding the pixels that are known to be not reliable. In
particular, pixels located closer than 27
Three widely used non-dimensional, normalized metrics are selected to compare radar-IDF and satellite-IDF maps: correlation coefficient (CC), measuring the spatial correlation of the maps; multiplicative bias (bias), measuring the mean quantitative agreement of the maps; and normalized standard difference (NSD), measuring the variability of the residuals of the normalized maps. Additional information on the metrics is provided in Appendix B.
We assumed the records of rain gauge data to be a complete sample of the
climatology of extremes for return periods comparable to the remote sensing
data record length. Synthetic records of rain gauge data were created by
randomly sampling years, without replacement, from the full rain gauge
record, and the corresponding IDF values were calculated. We focused on
synthetic records of 10, 15, 20, and 25 years and bootstrapped the operation
999 times for each rain gauge and for each synthetic record length. The
5–95th quantile interval of the obtained distributions was used to measure
the uncertainty related to the record length
Distribution (median and 25–75th quantiles) of the GEV parameters
derived from satellite (HRC and CHRC) and radar datasets. Note that scale
parameters are normalized over the corresponding location parameters. The
parameters for different products are represented around the corresponding
duration; therefore, the logarithmic scale in the
The distribution of the GEV parameters (25–75th quantile intervals and median over the whole study area) derived from radar and satellite datasets in the three climatic regions and over the Mediterranean Sea (sea, from here on) are presented in Fig. 2. We recall here that the scale, location, and shape parameters provide a measure of the mean, dispersion, and skewness of the underlying distribution, respectively. Location parameters from HRC (CHRC) estimates are smaller (larger) than the ones from radar over Mediterranean climate and over the sea, meaning that extreme values from HRC (CHRC) are in general lower (higher) than radar extreme values while in semiarid and arid climates HRC and CHRC generally identify higher parameters than the radar (i.e. higher extreme values). Differences in the location parameters can be associated to the bias between extreme values in the datasets. The scale parameters are normalized over the corresponding location parameters to appreciate the relative differences. Normalized scale parameters from HRC and CHRC are similar and lower than the ones derived from radar. Normalized scale parameters, together with their variability, tend to increase when moving from sea to Mediterranean, semiarid, and arid climates. The drier climate, the larger the dispersion of the GEV distribution. A slight increase of the normalized scale parameters with duration can be noticed in the HRC/CHRC data.
The shape parameters are mostly greater than zero, suggesting, in line with
previous studies
The location and scale parameters consistently decreased as the spatial and
temporal aggregation scales increased. This is an expected effect, caused by
the smoothing of rainfall fields operated by the spatial averaging;
therefore,
results are not reported in this paper. Conversely, it is interesting to
analyse the shape parameter. The distributions of the shape parameters
derived from the full radar record aggregated on grid sizes increasing from
2 km
Visual comparison of the annual maxima and of the IDF curves derived for the examined 16 years (1998–2013) from HRC (red), CHRC (blue), radar (solid black), and rain gauge (dashed black). The shaded area represents the 95 % confidence interval of the rain gauge IDF. Three example locations in the Mediterranean (En Hahoresh), semiarid (Beer Sheva) and arid (Sedom) climates and for 1, 6, and 24 h durations are shown (see gauge location in Fig. 1).
Example of IDF maps for 3 h duration from HRC, CHRC, and radar for 2-, 10-, and 25-year return periods. Only the pixels included in the analyses are shown.
A visual comparison between IDF curves derived from rain gauges and from the
co-located radar and satellite pixels is presented in Fig. 4. Corresponding
data periods (16 years, 1 h block) are used over the three climatic regions
(Mediterranean – En Hahoresh, semiarid – Beer Sheva and arid – Sedom;
Fig. 1) for 1, 6, and 24 h durations. The reported cases, discussed in Marra
and Morin (2015), are known to have good radar visibility, with the exception
of Sedom that, being farther from the radar and behind the hilly region, can
be subject to overshooting of the radar beam. Radar reproduces better the
skewness of the IDF curves and radar IDFs are, with the exception of the arid
case, within the rain gauge confidence interval. Note that these results
represent the local scale; while interpreting them, one should take into
account the different scales of rain gauges (point scale) and remote sensing
datasets (
Examples of IDF maps for 3 h duration from HRC, CHRC, and radar products are presented in Fig. 5. It is shown that the spatial variability of IDF values increases with return period, owing to the larger uncertainty associated to longer return periods. Noteworthy, HRC IDFs are lower than the corresponding CHRC and radar IDFs, while the CHRC IDFs seem to be larger than radar IDFs for 2-year return period and comparable for 25-year return period. A quantitative analysis of the differences between HRC/CHRC-IDF maps and radar-IDF maps is provided in the next section.
Comparison of IDF values between HRC and radar (red) and CHRC and radar (blue). The upper row of panels shows the CC for different durations, the middle row the bias and the lower row the NSD.
A comprehensive quantitative comparison between radar-IDF and CMORPH-IDF maps
is presented in Fig. 6. In general, very similar patterns of CC and NSD are
observed for HRC and CHRC while substantially different bias patterns are
observed. This confirms the point made by
The CC, measuring the spatial correlation of the IDF maps, is as high as
Comparison of IDF values between HRC and radar for different climatic regions. Blue lines represent sea areas while green, pink, and orange lines represent the Mediterranean, semiarid, and arid climates respectively. The upper row of panels shows the CC for different durations, the middle row the bias, and the lower row the NSD.
Comparison of IDF values between CHRC and radar for different climatic regions. Blue lines represent sea areas while green, pink, and orange lines represent the Mediterranean, semiarid, and arid climates respectively. The upper row of panels shows the CC for different durations, the middle row the bias, and the lower row the NSD.
Note that the CC between both HRC/CHRC IDFs and radar IDFs is low over the
sea, especially for shorter durations, and that the difference becomes less
important for longer durations. This is not coming as a surprise since no
gauge data are available for the adjustment of satellite or radar data over
the sea. As pointed out above, gauge adjustment is only weakly impacting the
space–time organization of CMORPH extreme estimates, while it is a crucial
step in radar quantitative precipitation estimation. This observation,
together with the increased reliability of satellite-based estimations over
the sea
Uncertainty related to the record length for 1 and 3 h durations for three example cases in the Mediterranean (En Hahoresh), semiarid (Beer Sheva) and arid (Sedom) climates. The dashed lines show the IDF curves from the full records (59, 67, and 51 years, respectively) and the vertical bars show the width of the 5–95th quantile interval of the 999 bootstrap sampling repetitions for record lengths of 10, 15, 20, and 25 years. Width and light of the colour of the bars increase with the record length.
Overestimation of CHRC-IDF maps with respect to radar-IDF maps is more marked
for Mediterranean and semiarid climates, with a factor
In this section, we present the results of the bootstrap sampling of long rain gauge records used to quantify the uncertainty related to the record length of remote sensing datasets. The uncertainty presented here is the component related to the under-sampling of rainfall climatology due to the use of short data records and is quantified as the 5–95th quantile interval of the bootstrap sampling. The uncertainty for two example cases is presented in Fig. 9. The figure reports the 5–95th quantile interval of the bootstrap sampling of 10, 15, 20, and 25 years of data out of the whole record of the three cases shown in Fig. 4. As expected, uncertainties become important when the record length is similar, or smaller, than the estimated return period. Arid climates are characterized by larger uncertainties, especially when short records and short durations are examined; this is probably due to the low number of rain events per year, and to the thicker-tailed characteristic of arid IDF curves. Short records are shown to be more likely overestimating, rather than underestimating, the IDF values.
Relative uncertainty (width of the 5–95th quantile interval of the
999 bootstrap sampling repetitions normalized over the rain gauge-IDF value)
plotted against the ratio between the estimated return period and the record
length. The first row of panels shows the results for 1 h duration, the
second row for 3
Figure 10 shows the relative uncertainty (width of the 5–95th quantile
interval of the 999 bootstrap sampling repetitions normalized over the long
record rain gauge-IDF value) as a function of the ratio between return period
and record length. Uncertainties for 1 and 3 h durations are comparable,
with the uncertainty for 3 h duration being smaller. This suggests that time
aggregation potentially decreases part of the issues related to the use of
short records. Uncertainty is larger for return periods longer than the
record length, especially for short durations and drier climates. For the
Mediterranean climate, the uncertainty is generally lower than 50 % when
the return period is shorter than the record length and reaches up to
This study compared the use of rainfall estimates from a ground-based
C-band weather radar and from a high-resolution satellite precipitation
product, CMORPH (HRC), and its gauge-adjusted version (CHRC), for the
identification of intensity–duration–frequency (IDF) curves. IDF curves
were computed using the above products over the eastern Mediterranean
(Mediterranean, semiarid, and arid climates and over the sea) and the
uncertainties due to the limited record length of the remote sensing datasets
were quantified basing on long records of rain gauge measurements. Our
findings can be summarized as follows:
The shape parameters of the generalized extreme values distribution, as
derived from radar, HRC and CHRC, are mostly greater than zero; drier
climates are characterized by higher shape parameters, suggesting that
thicker-tailed distributions better describe rainfall extremes of drier areas.
In general, the shape parameters derived from radar are higher than the ones
from CMORPH, especially for arid climate and over the sea. The shape parameter tends to decrease when rainfall estimates are
aggregated in space and/or time. The effect is related to a non-homogeneity
of spatial and temporal scales of rainfall extremes with return period. This
non-homogeneity depends on the climatic conditions. The spatial correlation coefficient between corresponding radar-IDF and
HRC/CHRC-IDF maps is between 0.70 and 0.76 for short return periods, but
decreases with increase in return period, especially for short durations. In
general, for both HRC and CHRC the correlation is higher in arid climate for
durations up to 3 HRC IDFs and CHRC IDFs are, respectively, lower and higher than radar IDFs.
In both cases the observed bias decreases with return period, especially for
short durations and arid climate. For longer durations and
Mediterranean/semiarid climates, the decreasing trend almost disappears so
that the bias can be considered independent from the return period
( Comparison of HRC IDF and CHRC IDF against radar IDF shows consistent
patterns of correlation and dispersion, and different biases. This means that
gauge adjustment influences the magnitude rather than the space–time
organization of annual extremes and suggests that HRC IDF can potentially be
used to estimate the frequencies of CMORPH estimates in near-real-time early
warning systems. The uncertainty related to the use of short records becomes important
when the record length is shorter or comparable to the examined return
period. This is particularly true for drier climates and shorter durations,
with potential uncertainty of
Rainfall frequency analysis by means of remote sensing rainfall estimates
remains a challenging task, especially when dry climates are explored.
Nevertheless, the agreement between IDF curves derived from different sensors
on Mediterranean and, to a good extent, semiarid climates, demonstrates their
potential for the description of small-scale spatial patterns of IDF curves
and instils confidence on their quantitative use for ungauged areas of the
Earth. Spatial and temporal aggregation of rainfall information represent
viable ways to take advantage of remote sensing datasets and decrease the
uncertainties related to the derived IDF curves. In particular, remote sensing
rainfall archives can provide important information when 2–10-year return
periods and 12–24 h durations are requested, scales that are relevant for
both flood risk management (e.g. issuing of warning) and hydrological design
(e.g. sewer systems design, large-scale drainage planning).
The original and gauge-adjusted CMORPH precipitation
products are downloadable from
The GEV cumulative distribution function can be written as (Coles, 2001):
Correlation coefficient (CC) measures the spatial correlation of the
derived maps. It is calculated as
Multiplicative bias measures the mean quantitative agreement of two maps. It
is calculated as
Normalized standard difference (NSD) measures the standard deviation
of the residuals of the normalized maps and is calculated as
The authors declare that they have no conflict of interest.
Radar data were provided by E.M.S. (Mekorot Company) and rain gauge data were provided by the Israel Meteorological Service. The study was partially funded by the Lady Davis Fellowship Trust [project: RainFreq], by the Israel Science Foundation [grant no. 1007/15], by the PALEX DFG project, and by NSF-BSF grant [BSF 2016953]. This work is a contribution to the HyMeX program. We thank Luca Panziera and two anonymous reviewers for contributions that improved the quality of this paper. Edited by: B. Su Reviewed by: L. Panziera and two anonymous referees