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Earth Syst. Sci. Data, 11, 1583–1601, 2019
https://doi.org/10.5194/essd-11-1583-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
SM2RAIN–ASCAT (2007–2018): global daily satellite
rainfall data from ASCAT soil moisture observations
Luca Brocca1, Paolo Filippucci1, Sebastian Hahn2, Luca Ciabatta1, Christian Massari1,
Stefania Camici1, Lothar Schüller3, Bojan Bojkov3, and Wolfgang Wagner2
1Research Institute for Geo-Hydrological Protection, National Research Council, Perugia, Italy
2Department of Geodesy and Geoinformation, TU Wien, Vienna, Austria
3European Organisation for the Exploitation of Meteorological Satellites, Darmstadt, Germany
Correspondence: Luca Brocca (luca.brocca@irpi.cnr.it)
Received: 13 March 2019 – Discussion started: 23 April 2019
Revised: 1 August 2019 – Accepted: 19 September 2019 – Published: 22 October 2019
Abstract. Long-term gridded precipitation products are crucial for several applications in hydrology, agricul-
ture and climate sciences. Currently available precipitation products suffer from space and time inconsistency
due to the non-uniform density of ground networks and the difficulties in merging multiple satellite sensors. The
recent “bottom-up” approach that exploits satellite soil moisture observations for estimating rainfall through the
SM2RAIN (Soil Moisture to Rain) algorithm is suited to build a consistent rainfall data record as a single polar
orbiting satellite sensor is used.
Here we exploit the Advanced SCATterometer (ASCAT) on board three Meteorological Operational (MetOp)
satellites, launched in 2006, 2012, and 2018, as part of the European Organisation for the Exploitation of Me-
teorological Satellites (EUMETSAT) Polar System programme. The continuity of the scatterometer sensor is
ensured until the mid-2040s through the MetOp Second Generation Programme. Therefore, by applying the
SM2RAIN algorithm to ASCAT soil moisture observations, a long-term rainfall data record will be obtained,
starting in 2007 and lasting until the mid-2040s. The paper describes the recent improvements in data pre-
processing, SM2RAIN algorithm formulation, and data post-processing for obtaining the SM2RAIN–ASCAT
quasi-global (only over land) daily rainfall data record at a 12.5 km spatial sampling from 2007 to 2018. The
quality of the SM2RAIN–ASCAT data record is assessed on a regional scale through comparison with high-
quality ground networks in Europe, the United States, India, and Australia. Moreover, an assessment on a global
scale is provided by using the triple-collocation (TC) technique allowing us also to compare these data with the
latest, fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5), the
Early Run version of the Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG),
and the gauge-based Global Precipitation Climatology Centre (GPCC) products.
Results show that the SM2RAIN–ASCAT rainfall data record performs relatively well at both a regional and
global scale, mainly in terms of root mean square error (RMSE) when compared to other products. Specifically,
the SM2RAIN–ASCAT data record provides performance better than IMERG and GPCC in data-scarce regions
of the world, such as Africa and South America. In these areas, we expect larger benefits in using SM2RAIN–
ASCAT for hydrological and agricultural applications. The limitations of the SM2RAIN–ASCAT data record
consist of the underestimation of peak rainfall events and the presence of spurious rainfall events due to high-
frequency soil moisture fluctuations that might be corrected in the future with more advanced bias correction
techniques.
The SM2RAIN–ASCAT data record is freely available at https://doi.org/10.5281/zenodo.3405563 (Brocca et
al., 2019) (recently extended to the end of August 2019).
Published by Copernicus Publications.
1584 L. Brocca et al.: SM2RAIN–ASCAT (2007–2018)
1 Introduction
Rainfall is ranked the first among the Essential Climate Vari-
ables by the Global Climate Observing System (GCOS) as it
represents the most important variable in many applications
in the geosciences (Maggioni and Massari, 2018). Long-term
rainfall records are essential for drought monitoring (e.g. Fo-
rootan et al., 2019), water resource management (e.g. Abera
et al., 2017), and climate studies (e.g. Herold et al., 2016;
Pendergrass and Knutti, 2018), while near-real-time rainfall
data are needed for the mitigation of the impacts of natu-
ral disasters such as floods and landslides (e.g. Wang et al.,
2017; Camici et al., 2018; Brunetti et al., 2018; Kirschbaum
and Stanley, 2018). Additional applications in which near-
real-time rainfall plays a crucial role are weather forecast-
ing, agricultural planning, and vector-borne and waterborne
disease monitoring (e.g. Rinaldo et al., 2012; Thaler et al.,
2018).
Three different techniques can be used for estimating
rainfall: ground measurements, meteorological modelling,
and remote sensing. Ground measurements are based on
rain gauges and meteorological radars (Lanza and Vuerich,
2009), but also new approaches such as microwave links are
being developed (e.g. Overeem et al., 2011). These measure-
ments guarantee high accuracy, but they suffer in many re-
gions from limited spatial coverage (Kidd et al., 2017). Al-
ternatively, meteorological models are used to estimate rain-
fall mainly in areas without reliable ground observations
(Ebert et al., 2007), e.g. reanalysis. The uncertainties as-
sociated with these estimates can be large, mainly in ar-
eas where ground observations are scarce (Massari et al.,
2017a). Therefore, to fill the gaps in the spatial coverage
of ground measurements and to improve the estimates ob-
tained by models, different remote-sensing techniques have
been developed in the last 30 years (Hou et al., 2014). The
standard methods for estimating rainfall from space are based
on instantaneous measurements obtained from microwave ra-
diometers, radars, and infrared sensors (Kidd and Levizzani,
2011). These methods are based on inversion techniques
where the upwelling radiation (or backscattered signal for
radars) is related to the surface precipitation rate, i.e. a “top-
down” approach (Brocca et al., 2014).
The most recent and successful example of satellite pre-
cipitation estimates is represented by the Integrated Multi-
Satellite Retrievals for Global Precipitation Measurement
(GPM) (IMERG) of the GPM mission (Hou et al., 2014),
which provide a high spatial (0.1◦) and temporal (30 min)
resolution and quasi-global coverage (±60◦). To obtain such
a resolution and coverage, the IMERG products use a con-
stellation of polar and geostationary satellite sensors operat-
ing in the microwave and infrared bands. However, the use of
multiple sensors has some problems including the inconsis-
tency between rainfall estimates from different sensors (in-
tercalibration problem), the difficulties in collecting observa-
tions from multiple space agencies (i.e. problem of deliver-
ing the products in near-real time), and the high costs for the
operation and the maintenance of the overall constellation.
Moreover, as the top-down approach requires the merging of
instantaneous rainfall measurements from multiple sensors,
the failure of one of them may imply a significant degrada-
tion in the accuracy of the accumulated rainfall estimate due
to the high temporal variability of rainfall (Trenberth and As-
rar, 2014).
In recent years, a new “bottom-up” approach has emerged
that uses satellite soil moisture observations to infer, or to
correct, rainfall over land (Brocca et al., 2013a; Crow et al.,
2009; Pellarin et al., 2013; Wanders et al., 2015). The major
difference between the bottom-up and top-down approaches
is in the type of measurement, i.e. accumulated rainfall rates
with the bottom-up method and instantaneous rainfall rates
with the top-down method. This difference makes the two
approaches highly complementary and their integration has
already been successfully tested and demonstrated in several
recent studies (e.g. Brocca et al., 2016; Ciabatta et al., 2017;
Chiaravallotti et al., 2018; Massari et al., 2019). When accu-
mulated rainfall estimates are needed (e.g. daily rainfall), the
bottom-up approach has the advantage of requiring a much
lower number of measurements and, hence, of satellite sen-
sors. The limitations of the bottom-up approach are the pos-
sibility to estimate only terrestrial rainfall and its dependence
on land characteristics (e.g. low accuracy for dense vegeta-
tion coverage and complex topography; Brocca et al., 2014).
The bottom-up approach has been applied over a range of
scales: global (Crow et al., 2011; Brocca et al., 2014; Cia-
batta et al., 2018), continental (Wanders et al., 2015; Brocca
et al., 2016), and local (Massari et al., 2014; Brocca et al.,
2015; Román-Cascón et al., 2017). Moreover, different satel-
lite soil moisture products have been considered including
the SMOS (Soil Moisture Ocean Salinity mission; Brocca et
al., 2016), ASCAT (Advanced SCATterometer; Brocca et al.,
2017), AMSR-E (Advanced Microwave Scanning Radiome-
ter; Crow et al., 2009), and SMAP (Soil Moisture Active and
Passive; Koster et al., 2016; Tarpanelli et al., 2017; Zhang et
al., 2019). The first studies employing satellite rainfall esti-
mates obtained through the bottom-up approach for hydro-
logical and water resources applications have been recently
published (e.g. Ciabatta et al., 2016; Abera et al., 2017;
Brunetti et al., 2018; Camici et al., 2018). These studies have
highlighted the large potential of this technique as a com-
plementary and useful approach for estimating rainfall from
space, and they have also shown its main limitations. Specif-
ically, the temporal resolution and the accuracy of satellite
soil moisture products play a fundamental role in determin-
ing the accuracy of the bottom-up rainfall estimates.
In this study, we describe the newly developed
SM2RAIN–ASCAT (Soil Moisture to Rain) rainfall
Earth Syst. Sci. Data, 11, 1583–1601, 2019 www.earth-syst-sci-data.net/11/1583/2019/
L. Brocca et al.: SM2RAIN–ASCAT (2007–2018) 1585
data record covering the period 2007–2018 and character-
ized by a spatial and temporal sampling of 12.5 km d−1.
The new SM2RAIN–ASCAT data record is obtained from
the application of the SM2RAIN algorithm (Brocca et
al., 2014) to the ASCAT soil moisture data records H113
and H114 provided by the European Organisation for the
Exploitation of Meteorological Satellites (EUMETSAT)
Satellite Application Facility on Support to Operational
Hydrology and Water Management (H SAF). It is the first
SM2RAIN–ASCAT data record available at the same spatial
resolution as the ASCAT soil moisture product (previous
data records have been under-sampled at a 0.5 and 1◦reso-
lution). Moreover, we have included the latest improvements
in the pre- and post-processing of soil moisture and rainfall
data as well as of the SM2RAIN algorithm. The main differ-
ences with the SM2RAIN–CCI (Climate Change Initiative)
rainfall data record (Ciabatta et al., 2018) are the input soil
moisture product (the inputs of SM2RAIN–CCI are from
the European Space Agency Climate Change Initiative Soil
Moisture, ESA CCI soil moisture, product; Dorigo et al.,
2017) and the time coverage (SM2RAIN–CCI spans the
period 1998–2015). Technically, the use of the same satellite
sensor in the SM2RAIN–ASCAT data record is preferable
to ensure consistency between soil moisture estimates over
time to which the SM2RAIN algorithm is highly sensitive.
The purpose of this study is twofold. As a first objective,
we have applied SM2RAIN algorithm at 1009 uniformly
distributed points (with a spacing of 1.5◦) in the United
States, Italy, India, and Australia for testing different con-
figurations of data pre- and post-processing and SM2RAIN
model equation. This analysis has allowed us to select the
best configuration that is implemented on a global scale for
obtaining the SM2RAIN–ASCAT data record. The second
objective is the assessment of the global scale SM2RAIN–
ASCAT data record through the comparison with reference
datasets and by exploiting the triple-collocation (TC) ap-
proach (Massari et al., 2017a). As reference datasets we have
used high-quality local rain gauge networks from 2013 to
2017 in the United States, Italy, India, and Australia for
the assessment at 1009 points and for the regional assess-
ment. Three additional global datasets have been considered:
the latest, fifth-generation reanalysis of the European Cen-
tre for Medium-Range Weather Forecasts (ECMWF), ERA5,
the gauge-based Global Precipitation Climatology Centre
(GPCC), and the GPM IMERG product (Early Run version).
ERA5 has been used for the generation of the quasi-global
SM2RAIN–ASCAT data record; GPCC and GPM IMERG
have been considered for the TC analysis.
We underline that the paper goal is to present and describe
the SM2RAIN–ASCAT quasi-global rainfall data record and
to perform a comparison with state-of-the-art global rainfall
products. We do not want to show a comprehensive assess-
ment of the product. Indeed, we believe that researchers other
than the product developers should perform the validation of
the dataset. Even better, we stress the importance of perform-
ing the validation by using the datasets in hydrological or
agricultural applications (e.g. flood prediction and agricul-
tural water management).
2 Datasets
Nine different datasets have been collected for this study,
which are based on remote sensing, ground observations, and
reanalysis. Refer to Table 1 for a summary of the datasets.
The main input dataset for producing the SM2RAIN–
ASCAT data record is the ASCAT soil moisture data record
provided by the EUMETSAT H SAF (http://hsaf.meteoam.
it/, last access: 11 February 2019). ASCAT, currently on
board the MetOp-A (Meteorological Operational; launched
in October 2006), MetOp-B (September 2012), and MetOp-
C (November 2018) satellites, is a scatterometer operating
on the C-band (5.255 GHz), and by using the TU Wien al-
gorithm (Wagner et al., 2013), the H SAF provides a soil
moisture product characterized by a 12.5 km spatial sam-
pling. The temporal sampling varies as a function of latitude
and the number of satellites: by using MetOp-A only a daily
sampling is obtained; by using MetOp-A and MetOp-B two
observations per day are available at mid-latitudes. Here we
have used the H SAF–ASCAT soil moisture data record (us-
ing MetOp-A and MetOp-B) available through the product
H113 (PUM, 2018) covering the period 2007–2017 and its
extension product H114 for the year 2018.
Three datasets obtained from the latest reanalysis of the
ECMWF, i.e. ERA5, have been used. The ERA5 reanalysis
is characterized by a spatial resolution of ∼36 km and hourly
temporal resolution. ERA5 is available from the Coperni-
cus Climate Change service, and the datasets cover the pe-
riod 1979 to present. We have extracted hourly observations
for the period 2007–2018 for three variables: evaporation,
soil temperature for the first layer (0–7 cm), and total rainfall
(computed as the difference between total precipitation and
snowfall). Evaporation data are used as an additional input
into the SM2RAIN algorithm, and soil temperature data are
used for masking periods with frozen soils. Total rainfall has
been considered as a benchmark for the calibration of global
SM2RAIN parameter values (see next section).
Ground-based rainfall datasets from regional networks
have been also collected including the Climate Prediction
Center (CPC) Unified Gauge-Based Analysis of Daily Pre-
cipitation in the United States, the gridded rainfall data pro-
vided by ∼3000 stations of the National Department of Civil
Protection in Italy (Ciabatta et al., 2017), the India Mete-
orological Department (IMD, http://www.imd.gov.in/pages/
services_hydromet.php, last access: 11 February 2019) rain-
fall observations in India, and the Australia Water Availabil-
ity Project (AWAP, http://www.bom.gov.au/jsp/awap/rain/
index.jsp, last access: 11 February 2019) gridded rainfall data
in Australia. These datasets have been firstly used for the se-
lection of the optimal configuration of the SM2RAIN imple-
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1586 L. Brocca et al.: SM2RAIN–ASCAT (2007–2018)
Table 1. List of satellite, ground-based, and reanalysis products used in this study (the spatial and temporal sampling used in this study is reported).
Short name Full name and details Data source Spatial and temporal Time period References
sampling
Soil moisture
ASCAT Advanced scatterometer Satellite 12.5 km/daily 2007–present Wagner et al. (2013)
Rainfall
ERA5 ECMWF Reanalysis 0.25◦/daily 1979–present https://cds.climate.copernicus.eu/cdsapp\#!/dataset/
reanalysis-era5-single- levels?tab=overview
(last access: 11 February 2019)
GPCC Global Precipitation Climatology Centre Full Data Reanalysis Gauge 1◦/daily 1988–present Schamm et al. (2015)
IMERG Early Run Global Precipitation Measurement Satellite 0.1◦/daily 2014–present Hou et al. (2014)
CPC Climate Prediction Center – United States Gauge 0.5◦/daily 1948–present https://www.esrl.noaa.gov/psd/data/gridded/data.unified.daily.conus.html
(last access: 11 February 2019)
ITA-DPC National Department of Civil Protection gauge-based rainfall dataset – Italy Gauge 0.1◦/daily 2008–present Ciabatta et al. (2017)
AWAP Australian Water Availability Project – Australia Gauge 0.05◦/daily 1900–present http://www.bom.gov.au/jsp/awap/rain/index.jsp
(last access: 11 February 2019)
IMD India Meteorological Department – India Gauge 0.25◦/daily 1901–present http://www.imd.gov.in/pages/services_hydromet.php
(last access: 11 February 2019)
Soil temperature and evapotransportation
ERA5 ECMWF Reanalysis 0.25◦/daily 1979–present https://cds.climate.copernicus.eu/cdsapp\#!/dataset/
reanalysis-era5-single- levels?tab=overview
(last access: 11 February 2019)
mentation. For that, 1009 uniformly distributed points over
the four regions have been selected. Secondly, the regional
networks have been used for the assessment of the global
SM2RAIN–ASCAT rainfall product at a regional scale.
The ERA5 and local rainfall datasets have been regridded
over the ASCAT grid (12.5 km) through the nearest neigh-
bouring method and resampled at a daily timescale as accu-
mulated rainfall from 00:00 to 23:59 UTC. The ERA5 evap-
oration and soil temperature data are also regridded to the
same grid and aggregated at a daily scale as accumulated and
average values from 00:00 to 23:59UTC, respectively.
For the global assessment of SM2RAIN–ASCAT, two ad-
ditional rainfall datasets have been considered: the Global
Precipitation Climatology Centre Full Data Daily Product
(Schamm et al., 2015) and GPM IMERG Early Run product
(Hou et al., 2014), hereinafter referred to as GPM-ER. Due
to the availability of GPM-ER from April 2014, the global
analysis has been carried out in the 4-year period from Jan-
uary 2014 to December 2018. Moreover, for the global inter-
comparison all the datasets (SM2RAIN–ASCAT, ERA5,
GPCC, and IMERG-ER) have been regridded at a 0.25◦res-
olution by spatially averaging the pixels contained in each
0.25◦cell for SM2RAIN–ASCAT and GPM-ER and by se-
lecting the nearest pixel for ERA5 and GPCC.
3 Methods
In the following, the methodology used for obtaining the
SM2RAIN–ASCAT data record is described. Specifically,
three steps are carried out (see Fig. 1): (1) surface soil mois-
ture data pre-processing, (2) employing the SM2RAIN algo-
rithm, and (3) rainfall data post-processing. Different con-
figurations for the data pre- and post-processing and for the
SM2RAIN model equation are considered; the details are
given in Table 2.
3.1 Soil moisture data pre-processing
The ASCAT surface soil moisture product is provided as rel-
ative soil moisture (between 0 and 1) at the overpass time
of the satellite sensor (see Fig. A1 in the Appendix) for the
mean daily revisit time of ASCAT. The period 2007–2012
only had MetOp-A data, while the period 2013–2018 had
data from both MetOp-A and MetOp-B. For the application
of the SM2RAIN algorithm, data should be equally spaced
in time, and hence, we have linearly interpolated in time soil
moisture observations every 24, 12 and 8h. The interpola-
tion may increase the risk of false rainfall events, but it is a
required step to obtain accumulated rainfall over a fixed du-
ration. In a preliminary test (not shown for brevity), we tested
the three sampling frequencies with the baseline formulation
for SM2RAIN (Eq. 6, see below). The best performance re-
sults were obtained with a 12 h sampling, particularly from
2013 to 2018, in which both MetOp-A and MetOp-B are
available. Therefore, 12 h sampling has been used in the fol-
Earth Syst. Sci. Data, 11, 1583–1601, 2019 www.earth-syst-sci-data.net/11/1583/2019/
L. Brocca et al.: SM2RAIN–ASCAT (2007–2018) 1587
Figure 1. Processing steps for obtaining the SM2RAIN–ASCAT global rainfall data record (2007–2018) from ASCAT surface soil moisture
data: pre-processing, SM2RAIN algorithm, and post-processing. Each bullet represents a possible configuration that has been tested; the
selected configuration is in a red, bold font.
Table 2. Configurations used in the paper (SWI – soil water index, BCO – Brooks–Corey, VGEN – van Genuchten, MUA – Mualem–
van Genuchten, SWI-Tvar – SWI with Tvarying with soil moisture, WAV – wavelet filtering, CDF – climatological correction with daily
cumulative density function matching, and MON – climatological correction with monthly correction factors).
Short Filtering Losses Evapotranspiration Depth Climatological
name variation correction
REF SWI BCO No No No
SWI-Tvar SWI-Tvar BCO No No No
WAV WAV BCO No No No
VGEN SWI VGEN No No No
MUA MUA VGEN No No No
EVAP SWI BCO Yes No No
ZVAR SWI BCO No Yes No
BC-CDF SWI-Tvar BCO No No CDF
BC-MON SWI-Tvar BCO No No MON
lowing analyses. The 24 h accumulated rainfall is obtained
by summing the two 12 h accumulated rainfall datasets ob-
tained for each day.
One of the major problems in using satellite soil mois-
ture observations for rainfall estimation is related to the
high-frequency fluctuations caused by measurement and re-
trieval errors. If positive, such fluctuations are interpreted er-
roneously as rainfall by the SM2RAIN algorithm. Therefore,
satellite surface soil moisture data need to be filtered before
being used as an input into SM2RAIN. In previous studies,
the exponential filtering has been considered (Wagner et al.,
1999). The exponential filter, also known as the soil water
index (SWI), has been used for filtering surface soil mois-
ture time series as a function of a single parameter, T, i.e.
the characteristic time length. In this study, we have tested
two additional filtering methods. The first one is an exten-
sion of the exponential filter in which the Tparameter is as-
sumed to be varying with soil moisture as proposed in Brocca
et al. (2013b). Specifically, Tdecreases with increasing soil
moisture through a 2-parameter power law. Therefore, the
data are filtered more during dry conditions. The third ap-
proach that we have implemented is a discrete wavelet filter
(similar to Massari et al., 2017b). The discrete wavelet filter
cuts the higher frequencies of the signal, typically character-
ized by noises, over a threshold selected through the princi-
ple of Stein’s unbiased risk at multiple levels. We have found
the Daubechies wavelets to be the most appropriate functions
because their shape and the shape of the soil moisture signal
is similar. Therefore, we have implemented a Daubechies-
based wavelet filter in which the filtering level is optimized.
For all the filtering approaches, the parameter values of the
filters have been optimized point-by-point in order to repro-
duce the reference rainfall observations.
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1588 L. Brocca et al.: SM2RAIN–ASCAT (2007–2018)
3.2 SM2RAIN algorithm and calibration
The SM2RAIN algorithm is based on the inversion of the soil
water balance equation and allows to estimate the amount of
water entering the soil by using soil moisture observations
from in situ or satellite sensors as an input (e.g. Brocca et
al., 2013a, 2014, 2015; Koster et al., 2016; Ciabatta et al.,
2017; Massari et al., 2014). Specifically, the soil water bal-
ance equation can be described by the following equation
(over non-irrigated areas):
nZ dS(t)
dt=p(t)−g(t)−sr(t)−e(t),(1)
where n(–) is the soil porosity, Z(mm) is the soil layer depth,
S(t) (–) is the relative saturation of the soil or relative soil
moisture, t(d) is the time, p(t) (mm d−1) is the rainfall rate,
g(t) (mm d−1) is the drainage (deep percolation plus subsur-
face runoff) rate, sr(t) (mm d−1) is the surface runoff rate,
and e(t) (mm d−1) is the actual evapotranspiration rate.
For estimating the rainfall rate, Eq. (1) is applied only dur-
ing rainfall periods, and, hence, some of the components of
the equation can be considered as negligible. For instance,
the actual evapotranspiration rate during rainfall is quite low
due to the presence of clouds and, hence, the absence of solar
radiation. Similarly, the surface runoff rate, i.e. the water that
does not infiltrate into the soil and flows at the surface to the
watercourses, is much lower than the rainfall rate, mainly if
Eq. (1) is applied at a coarse spatial resolution (20 km), i.e.
with satellite soil moisture data. Indeed, most of the water
becomes runoff flowing in the subsurface, and also the part
that does not infiltrate, due to for instance impervious land
cover or soil, may re-infiltrate downstream within a pixel at
a 20 km scale. We have indirectly tested this hypothesis by
counting the number of days the ASCAT soil moisture prod-
uct is higher than the 99.5 percentile for 2 (or more) consecu-
tive days in the period 2007–2018. We have indirectly tested
this hypothesis by counting the number of days the ASCAT
soil moisture product is higher than the 99.5 percentile for
2 (or more) consecutive days in the period 2007–2018. We
have found that the number of consecutive days in which the
soil is saturated is equal to 4 d (median value on a global
scale) over 12 years, with 90 % of the land pixels with val-
ues lower than 12 d (i.e. 1 d yr−1). The occurrence of higher
values is limited to very few areas in the tropical forests and
over the Himalayas (see Fig. A2).
Following the indications obtained in Brocca et al. (2015),
we have assumed that the surface runoff rate, sr(t), is negli-
gible (i.e. Dunnian runoff), and we have rearranged Eq. (2)
for estimating the rainfall rate.
p(t)=nZ dS(t)
dt+g(t)+e(t)(2)
In this study, we have considered different formulations for
Eq. (2) by varying the drainage rate as
g(t)=KsS(t)m,(3a)
g(t)=KsS(t)λ+11−1−S(t)λ+1
λλ
λ+12
,(3b)
g(t)=KsS(t)τh1−1−S(t)1
mmi2
,(3c)
where Ks(mm d−1) is the saturated hydraulic conductivity,
m(–) and λ(–) are exponents related to the pore size dis-
tribution index, and τis the tortuosity index. Specifically,
the three equations represent the hydraulic conductivity –
soil moisture formulation by Brooks–Corey (Eq. 3a), van
Genuchten (Eq. 3b), and Mualem–van Genuchten (Eq. 3c).
The actual evapotranspiration rate has been considered as
an additional input, together with soil moisture, here obtained
from the ECMWF reanalysis, ERA5.
e(t)=KcETERA5 (t),(4)
where ETERA5(t) (mm d−1) is the actual evapotranspiration
rate obtained from the ERA5 reanalysis and Kc(–) is a cor-
rection factor for taking into account potential bias in the
ERA5 estimates.
Moreover, we have considered an additional formulation
in which Zis a function of soil moisture taking into account
the different penetration depth of satellite sensors as a func-
tion of wetness conditions.
Z=Z0.1+1−S(t)c,(5)
where the cexponent determines the rate of decrease of the
penetration depth with increasing soil moisture.
Accordingly, we have used different formulations for
Eq. (2) that are compared with the baseline equation used
in previous studies (e.g. Brocca et al., 2014).
p(t)=Zn dS(t)
dt+KsS(t)m(6)
In synthesis, we have investigated three different configura-
tions (for a total of five options) for (1) selecting the best
equation for the drainage rate (Eq. 3), (2) testing the possibil-
ity to include the evapotranspiration component (Eq. 4), and
(3) testing the use of a variable penetration depth with soil
moisture conditions (Eq. 5). Each new configuration has been
compared with the baseline (Eq. 6) in order to select the best
configuration for the SM2RAIN algorithm (see Fig. 1). For
all configurations, negative rainfall values, that might occur
during some dry-down cycles, have been set equal to zero.
SM2RAIN parameter values are calibrated point-by-point
by using the reference rainfall as the target. As an objective
function, we have used the minimization of the root mean
square error (RMSE) between the SM2RAIN–ASCAT and
reference rainfall.
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L. Brocca et al.: SM2RAIN–ASCAT (2007–2018) 1589
3.3 Rainfall data post-processing
The use of satellite soil moisture observations for obtain-
ing rainfall estimates is affected by errors in the input data
and in the retrieval algorithm SM2RAIN. The correction of
the overall bias in the climatology is a simple and effec-
tive approach for mitigating a part of such errors. Specifi-
cally, we refer here to a static correction procedure, which
once calibrated for a time period can be applied in future
periods and for operational real-time productions. We note
that a climatological correction is performed in several satel-
lite rainfall datasets delivered in near real time (e.g. GPM-
ER). We have implemented two different approaches for
climatological correction: (1) a cumulative density function
(CDF) matching approach at a daily timescale and (2) a
monthly correction approach. Specifically, the implemented
CDF matching approach is a 5th-order polynomial correction
as described in Brocca et al. (2011) for matching the CDF of
estimated rainfall with respect to reference rainfall, in which
the CDF values are computed over the whole calibration pe-
riod at a daily timescale. The monthly correction approach
computes the monthly ratios between the climatology of es-
timated and reference rainfall, i.e. 12 correction factors per
pixel. Then, the SM2RAIN-estimated rainfall is multiplied
for the monthly correction factors to obtain the climatologi-
cally corrected SM2RAIN-estimated rainfall.
3.4 Triple-collocation analysis
For the global assessment of satellite, reanalysis, and gauge-
based rainfall products we have used the triple-collocation
technique. TC can theoretically provide error and correla-
tions of three products (a triplet) given that each of the three
products is afflicted by mutually independent errors. There-
fore, in principle, TC can be used for assessing the quality of
satellite products without using ground observations (Mas-
sari et al., 2017a). In this study, we have implemented the
same procedure as described in Massari et al. (2017a), i.e. by
implementing an additive error model at a daily timescale,
and we refer the reader to this study for the analytical de-
tails. In synthesis, by using the extended TC method firstly
proposed by McColl et al. (2014), it is possible to estimate
the temporal correlation, RTC, of each rainfall product in the
triplets with the true values.
3.5 Performance scores
Several metrics have been used to assess the product perfor-
mance during the validation period. As continuous scores we
have computed the Pearson’s correlation coefficient (R), the
RMSE, the mean error between estimated and reference rain-
fall (BIAS), and the ratio of temporal variability of estimated
and reference rainfall (STDRATIO). Continuous scores have
been computed on a pixel-by-pixel basis by considering 1 d
of accumulated rainfall. Moreover, three categorical scores,
i.e. the probability of detection (POD), false alarm ratio
(FAR), and threat score (TS), have been computed. POD is
the fraction of correctly identified rainfall events (optimal
value POD =1), FAR is the fraction of predicted events that
are non-events (optimal value FAR =0), while TS provides a
combination of the other two scores (optimal value TS =1).
The categorical assessment is carried out by considering a
rainfall threshold of 0.5 mm d−1(instead of 0 mm d−1) in or-
der to exclude spurious events that might be due to rainfall
interpolation or regridding in the reference datasets. For a
complete description of the performance scores, see Table A1
in the Appendix.
4 Results
The results are split in three parts: (1) selection of the op-
timal configuration of SM2RAIN through the assessment
at 1009 points, (2) generation of the global SM2RAIN–
ASCAT rainfall data record, and (3) regional assessment
of the SM2RAIN–ASCAT data with gauge-based rainfall
datasets and global assessments through TC.
4.1 Selection of the best SM2RAIN processing
configuration at 1009 points
As a first step we have collocated satellite soil moisture data
from ASCAT soil moisture H113 and H114, ground-based
rainfall observations, and actual evapotranspiration data from
ERA5 in space and time at 1009 points. We have selected
1009 uniformly distributed points over a regular grid with a
spacing of 1.5◦. Each point is considered representative of a
0.25◦×0.25◦box. The selection is carried out for reducing
the computational time in running the different SM2RAIN
configurations. The number of points for each region de-
pends on the size of the region: 328 points in Australia,
163 in India, 55 in Italy, and 463 in the United States.
Ground observations and GPM-ER and ERA5 data are re-
gridded by spatial averaging measurements contained over
each 0.25◦×0.25◦box. These datasets are freely available
(https://doi.org/10.5281/zenodo.2580285, Brocca, 2019) to
those interested in testing alternative approaches for rain-
fall estimation from ASCAT soil moisture data. Specifically,
we have considered the periods 2013–2016 and 2013–2014
for the calibration and 2015–2016 for the validation; in the
following series only the results in the validation period
are shown. The ground-based high quality rainfall observa-
tions available for the four regions are used as reference
data (ground truth) in this analysis. The reference config-
uration, REF, as used in previous SM2RAIN applications
(e.g. Brocca et al., 2014), uses the SWI for data filtering,
the SM2RAIN formulation as in Eq. (6), and no climatolog-
ical correction. Results in the validation period are shown in
Fig. 2a in terms of temporal Ragainst reference data. As
shown, the median Rfor all points is equal to 0.60, with
better results in Italy (median R=0.67, see boxplots) and
similar results in the other three regions (median R=0.60
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1590 L. Brocca et al.: SM2RAIN–ASCAT (2007–2018)
Figure 2. Performance of two different configurations at 1009 points in terms of Pearson’s correlation, R(–). (a) Rmap with reference
configuration, (b) Rmap with soil water index (SWI) filtering with the variable Tas a function of soil moisture, and (c) Rmap difference
(b–a). The inner box plots show the Rvalues (and Rdifferences) split for different regions.
and 0.59). These results are in line with previous studies
(e.g. Ciabatta et al., 2017; Tarpanelli et al., 2017) carried
out in Italy and India and highlight the potential of ASCAT
soil moisture observations to provide daily rainfall estimates.
Figure 3 (first column) shows the results for the different
performance metrics; in the last two columns the results ob-
tained with GPM-ER and ERA5 are shown for comparison.
Very good statistics have been obtained in terms of RMSE
and BIAS, but a tendency exists to underestimate the ob-
served rainfall variability (median STDRATIO =0.60), and
there is a medium-high probability of incorrectly estimat-
ing the false alarm statistic (median FAR =0.53). The other
scores are similar to, or slightly lower than, those obtained
through the GPM-ER and ERA5.
The first test has been dedicated to the filtering of soil
moisture data by using three approaches: (1) SWI, i.e. the
REF configuration, (2) SWI with Tvarying with soil mois-
ture, SWI-Tvar, and (3) the discrete wavelet filtering, WAV.
Figure 3 shows in the first three columns the summary of the
performance scores highlighting that the SWI-Tvar config-
uration is performing the best, even though the differences
with the REF configuration are small. Figure 2b shows the
Rmap for the SWI-Tvar configuration, while in Fig. 2c the
differences in Rvalues with REF are displayed. Improved
performance in terms of Ris visible over most of the pixels
except in central Australia.
The second test has been performed on the SM2RAIN
equation by using different drainage functions (VGEN and
MUA configurations), by adding the evapotranspiration com-
ponent (EVAP) and considering the variability of the sens-
ing depth, Z, with soil moisture (ZVAR). The VGEN, MUA,
and ZVAR configurations are characterized by lower per-
formance than REF (see Fig. 3, columns 4, 5, and 7), even
though MUA and ZVAR incorporate an additional parame-
ter to be calibrated (and, hence, better performance was ex-
pected). The addition of evapotranspiration brings a slight
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L. Brocca et al.: SM2RAIN–ASCAT (2007–2018) 1591
Figure 3. Performance at 1009 points in terms of Pearson’s correlation, R(–), root mean square error, RMSE (mm d−1), the variability ratio,
STDRATIO (–), the mean error between estimated and reference rainfall, BIAS (mm d−1), the false alarm ratio, FAR (–), the probability of
detection, POD (–), and the threat score, TS (–). For details about the different configurations see Table 2 (GPM-ER: GPM IMERG Early
Run product).
improvement with respect to REF (see Fig. 3, column 6),
with results similar to SWI-Tvar. Larger improvements are
obtained over areas in which evapotranspiration is more im-
portant, e.g. in the south-western United States and central
western Australia. In India and Italy, the results are very sim-
ilar to REF. However, EVAP configuration requires actual
evapotranspiration data from ERA5 as an additional input,
and such data might be not available for the implementation
of the processing algorithm in an operational context.
The final test has been done by applying the daily
CDF matching, BC-CDF, and monthly correction factors,
BC-MON, for correcting the climatological bias in the
SM2RAIN-derived rainfall estimates; results are shown in
columns 8 and 9 of Fig. 3. For these two configurations, the
improvements with respect to REF are evident but with dif-
ferent magnitude for the different scores. The BC-CDF sig-
nificantly improves, while STDRATIO, TS, and FAR show
a slight deterioration in Rand RMSE. BC-MON shows the
highest Rvalues among all configurations with the larger
improvements in India, Italy, and the United States. How-
ever, the improvement in terms of STDRATIO, TS, and FAR
is less important than BC-CDF. Therefore, depending on
which score is assumed to be more important, one of the two
configurations can be selected. If compared with GPM-ER,
BC-CDF and BC-MON configurations show similar results
with larger positive differences in terms of RMSE, BIAS,
STDRATIO, and POD; Rvalues are slightly better for GPM-
ER, which is also much better in terms of TS and FAR.
Similar findings can be summarized in the comparison with
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1592 L. Brocca et al.: SM2RAIN–ASCAT (2007–2018)
ERA5, even though ERA5 is performing the best in terms of
R, STDRATIO, FAR, and TS among all configurations.
Figure 4 shows the time series of rainfall averaged over the
four regions as obtained from ground observations and from
the BC-MON configuration. The agreement of spatially aver-
aged rainfall with observations is high with Rvalues greater
than 0.83 and very low BIAS values. Moreover, regional-
scale rainfall events are correctly reproduced both in terms
of timing and magnitude.
4.2 Generation of the SM2RAIN–ASCAT data record
Based on the tests summarized in the previous paragraph, we
have selected the best configuration using the SWI-Tvar for
filtering, Brooks–Corey function for losses, and monthly cor-
rection approach for climatological correction. The addition
of an evapotranspiration component, even though it shows
some improvements, has been not used in view of an opera-
tional implementation of the method. The monthly correction
approach has been selected as Rand RMSE scores have been
considered more important based on previous investigations
on the assessment of satellite rainfall products (e.g. Massari
et al., 20171).
The selected configuration has been applied on a global
scale to 839 826 points over which ASCAT soil moisture ob-
servations are available. As a reference dataset for the cal-
ibration of the parameter values of the pre-processing (fil-
tering) of SM2RAIN and of the post-processing, the ERA5
rainfall has been used mainly because of its higher spatial
resolution compared to the GPCC (36 km versus 100 km).
However, we have also tested the use of the two datasets for
calibration at 20 000 randomly chosen points, which showed
that the estimated rainfall in the two calibration tests is
very similar. For instance, the median Rbetween the two
SM2RAIN–ASCAT data records is higher than 0.90 (not
shown for brevity). This result clearly demonstrates that the
selection of the reference dataset has a small influence on
SM2RAIN-derived rainfall that is mostly driven from soil
moisture temporal fluctuations. Additionally, considering the
improved ASCAT coverage after 2013, the calibration has
been split from 2007 to 2012 (MetOp-A) and from 2013
to 2018 (MetOp-A and MetOp-B). The dual calibration has
solved the issue in terms of a long-term trend that has been
found in previous applications of SM2RAIN to ASCAT soil
moisture data (Beck et al., 2017). Finally, we have flagged
rainfall observations in space and time when the data are sup-
posed to be less reliable. In space (i.e. a fixed spatial mask),
we have used the committed area mask developed for the
ASCAT soil moisture product (i.e. the area in which the AS-
CAT soil moisture retrievals are expected to be good; PVR,
2017), a frozen probability mask, and a topographic com-
plexity mask. In time (i.e. a temporally variable mask), we
have considered the soil temperature data from ERA5 and
flagged the observations with soil temperature values be-
tween 0 and 3 ◦C as temporarily frozen soil and below 3 ◦C
as frozen soil. As many applications require continuous data,
we have preferred to flag the data instead of removing them
with an expected loss of accuracy.
The SM2RAIN–ASCAT data record so obtained has a spa-
tial sampling of 12.5 km, a daily temporal resolution, and it
covers the 12-year period 2007–2018. Figure 5 shows Rand
RMSE values between SM2RAIN–ASCAT and ERA5 in a
single map. Therefore, Fig. 5 illustrates the consistency be-
tween SM2RAIN–ASCAT and ERA5, and it is not intended
to assess the performance of the data record (even though
we expect better accuracy in areas where the agreement is
higher). Light green indicates very good agreement with high
Rand low RMSE values, colours from orange to red indi-
cate low Rand high RMSE values, and black indicates low
RMSE with Rvalues highlighting areas in which rainfall oc-
currence and variability is very low (e.g. the Sahara and high
latitudes). The data record has been found to be in very good
agreement with ERA5 (high Rand low RMSE values) in the
western United States, Brazil, southern and western South
America, southern Africa, the Sahel, southern central Eura-
sia, and Australia. The areas in which SM2RAIN–ASCAT
is characterized by lower consistency with ERA5 are those
with dense vegetation (Amazon, Congo, and Indonesia), with
complex topography (e.g. the Alps, Himalayas, and Andes),
at high latitudes, and the Sahara and Arabian deserts. In these
areas it is well-known that the ASCAT soil moisture product
has limitations (e.g. Wagner et al., 2013), and generally the
retrieval of soil moisture from remote sensing is more chal-
lenging. The median Rand RMSE values are equal to 0.56
and 3.06 mm d−1, with slightly better scores in the period
2013–2018 (R=0.57, RMSE =2.95) thanks to the avail-
ability of ASCAT on both MetOp-A and MetOp-B.
4.3 Regional and global assessment of the
SM2RAIN–ASCAT data record
By using all the pixels included in the four regions (Italy,
the United States, India, and Australia), for a total of
29 843 points, the new SM2RAIN–ASCAT rainfall data
record has been compared with reference rainfall observa-
tions in Fig. 6 by considering the whole period 2007–2018.
Specifically, the box plots of different performance metrics
(the same of Fig. 3) are shown and compared with the results
obtained through the GPCC, ERA5, and GPM-ER. By focus-
ing on the SM2RAIN–ASCAT data record performance over
the different regions, it shows better performance in Italy
(median R=0.67) and the United States (median R=0.62),
almost comparable with the other datasets; while in Aus-
tralia and India Rvalues are lower (median R=0.61 and
0.59). In the selected regions, the best product is the GPCC
(mainly in Australia) followed by ERA5, while the GPM-ER
and SM2RAIN–ASCAT are performing similarly in terms of
R. The better performance of the GPCC is expected (gauge-
based dataset), and the same is also true for the very good
performance of ERA5 in Italy and Australia thanks to the
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L. Brocca et al.: SM2RAIN–ASCAT (2007–2018) 1593
Figure 4. Time series of mean areal rainfall for the four regions for observed data, OBS, and the SM2RAIN–ASCAT data record, BC-MON
configuration (R(–): Pearson’s correlation, BIAS (mmd−1): mean error).
Figure 5. Pearson’s correlation, R, and root mean square error, RMSE, map of the SM2RAIN–ASCAT data record compared with the ERA5
reanalysis dataset used as a benchmark (period 2007–2018). The analysis is carried out at a 1 d and 12.5 km temporal and spatial resolution.
The map shows that the SM2RAIN–ASCAT data record is performing well in the western United States, Brazil, southern and western South
America, southern Africa, the Sahel, southern central Eurasia, and Australia (green colours).
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1594 L. Brocca et al.: SM2RAIN–ASCAT (2007–2018)
Figure 6. Regional assessment of the SM2RAIN–ASCAT rainfall data record and comparison with GPCC, ERA5 and GPM-ER rainfall
products. As a reference the high-quality ground-based datasets in Italy, the United States, India, and Australia are used. Results in terms
of Pearson’s correlation, R(–), root mean square error, RMSE (mm d−1), the variability ratio, STDRATIO (–), the mean error between
estimated and reference rainfall, BIAS (mm d−1), the false alarm ratio, FAR (–), the probability of detection, POD (–), and the threat score,
TS (–).
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L. Brocca et al.: SM2RAIN–ASCAT (2007–2018) 1595
Figure 7. Global triple-collocation, TC, results. (a) RTC map for SM2RAIN–ASCAT, (b) RTC map for GPM-ER, (c) differences between
(a) and (b), i.e. blue pixels for areas in which SM2RAIN–ASCAT (GPM-ER) is performing better and red for those in which it is performing
worse, and (d) box plot of RTC for SM2RAIN–ASCAT, GPM-ER, and GPCC. SM2RAIN–ASCAT is performing significantly better than
GPM-ER in South America and Africa (excluding desert and tropical-forest areas), elsewhere the two satellite products perform similarly.
Figure 8. Best-performing product based on the results of the triple-collocation data shown in Fig. 7. SM2RAIN–ASCAT is performing the
best among the three products in Africa, South America, the central western United States, and central Asia, while GPCC is performing the
best in the remaining parts of the Northern Hemisphere and in Australia. GPM-ER is the best product in tropical and equatorial regions.
availability of ground observations for the reanalysis. We
also highlight that different than SM2RAIN–ASCAT and the
GPM-ER, the GPCC and ERA5 have a latency of weeks to
months, and, hence, these products cannot be used for near-
real-time applications. When considering the RMSE score,
the results are quite different with respect to R. SM2RAIN–
ASCAT is overall very good and is the best and second best
product in the and United States and India, respectively. The
ranking of the product is the GPCC, SM2RAIN–ASCAT,
ERA5, and GPM-ER, with the latter showing high RMSE
values in the United States and Australia. As shown in pre-
vious studies (Brocca et al., 2016; Ciabatta et al., 2017), the
SM2RAIN approach is very good in obtaining low RMSE
values thanks to its accuracy in the retrieval of accumulated
rainfall. Moreover, the product accuracy is stable over time
as it is not as strongly affected by the availability of satel-
lite overpasses as in the top down approach. As shown also
in Fig. 3, the SM2RAIN–ASCAT data record has limitations
in reproducing the variability of rainfall (low STDRATIO)
mainly due underestimation issues. Moreover, SM2RAIN–
ASCAT FAR values are quite high highlighting the difficul-
ties in removing the problem of high-frequency soil mois-
ture fluctuations wrongly interpreted by SM2RAIN as rain-
fall events.
On a global scale, the TC approach has been imple-
mented by using the triplet SM2RAIN–ASCAT, GPM-ER,
and GPCC by considering the common period 2015–2018
and a daily timescale. In TC analysis we have purposely not
considered ERA5 in order to avoid any dependency between
the products. Theoretically, the extended TC approach pro-
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1596 L. Brocca et al.: SM2RAIN–ASCAT (2007–2018)
vides the correlation, RTC, against the underlying “truth”.
Figure 7a and b show the RTC maps for SM2RAIN–ASCAT
and GPM-ER highlighting similar mean values (0.66 and
0.64 for SM2RAIN–ASCAT and GPM-ER, respectively). It
should be underlined that the RTC values are higher than
those obtained in comparison with ground observations as
theoretically the metric does not contain the error in the refer-
ence (Massari et al., 2017a). The spatial pattern of the perfor-
mance is quite different as demonstrated in Fig. 7c in which
the differences between the two RTC maps is shown. Again,
these results underline the strong complementarity between
bottom-up and top-down approaches (e.g. Ciabatta et al.,
2017; Chiaravallotti et al., 2018). As expected, SM2RAIN–
ASCAT performs worse over desert areas, tropical forests,
and complex mountainous regions. Differently, over plains
and low-vegetated areas SM2RAIN–ASCAT performs better
than GPM-ER, particularly in the Southern Hemisphere. In-
deed, in Africa and South America SM2RAIN–ASCAT per-
forms well (see also Fig. 7a) thanks to the capability of the
bottom-up approach to estimate accumulated rainfall accu-
rately with a limited number of satellite overpasses occurring
in these areas, differently from the top-down approach used
in GPM-ER.
The box plots of RTC shown in Fig. 7d indicate that, over-
all, GPCC performs similarly to the two satellite products
with major differences in the spatial patterns of the per-
formance. SM2RAIN–ASCAT performs the best among the
three products in Africa, South America, the central western
United States, and central Asia, while the GPCC performs
the best in the remaining parts except the tropical region in
which the GPM-ER performs very well (see Fig. 8). If we
consider only the committed area of ASCAT (PVR, 2017),
in which the soil moisture product is supposed to be reli-
able, the mean value of RTC is equal to 0.72, whereas in the
masked area it is equal to 0.59.
5 Data availability
The SM2RAIN–ASCAT data record is freely available at
https://doi.org/10.5281/zenodo.3405563 (recently extended
to the end of August 2019) (Brocca et al., 2019).
6 Conclusions
In this study, we have described the development of the
new SM2RAIN–ASCAT rainfall data record highlighting the
steps carried out for improving the retrieval algorithm and the
pre- and post-processing of the data. The major novelties of
the SM2RAIN–ASCAT rainfall data record developed here
with respect to previous versions are (1) the application of
SM2RAIN at full spatial resolution thus providing a gridded
data record with a spatial sampling of 12.5 km, (2) improved
sampling and filtering of ASCAT soil moisture data, (3) the
application of monthly climatological correction, and (4) the
improved calibration strategy.
The SM2RAIN–ASCAT data record has been preliminary
assessed at regional (Figs. 4 and 6) and global (Figs. 5,
7, and 8) scales in terms of different performance metrics
with a larger emphasis on the temporal correlation, R, and
the root mean square error, RMSE. The overall performance
is good, mainly in terms of RMSE, thanks to the capac-
ity of SM2RAIN to accurately reproduce accumulated rain-
fall consistently over time. Importantly, SM2RAIN–ASCAT
is found to perform even better than ground-based GPCC
products over the Southern Hemisphere in Africa and South
America, the central western United States, and central Asia.
Limitations of SM2RAIN–ASCAT data record consist of
(1) the underestimation of peak rainfall events, (2) the pres-
ence of spurious rainfall events due to high-frequency soil
moisture fluctuations, (3) the estimation of liquid rainfall
only (snowfall cannot be estimated), and (4) the possibility
to estimate rainfall over land only.
In the near future, we are going to develop the near-real-
time version of the SM2RAIN–ASCAT rainfall product that
can be used as an input for applications such as flood pre-
diction (similarly to Camici et al., 2018 and Massari et al.,
2018), landslide prediction (Brunetti et al., 2018), and novel
applications for agriculture and water resource management.
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L. Brocca et al.: SM2RAIN–ASCAT (2007–2018) 1597
Appendix A
Figure A1. Mean daily revisit time (d) of ASCAT soil moisture observations for the period 2007–2012 (only MetOp-A, a) and for the period
2013–2018 (MetOp-A and MetOp-B, b).
Figure A2. Number of days in which ASCAT soil moisture observations are close to saturation (>99.5 percentile, a) for 2 (or more)
consecutive days in the period 2007–2018. Please note that the upper value is set to 20d as in most of the land areas the occurrence is very
low (90 % of the land pixels have values lower than 12 d over 12 years). In the bottom panel the soil moisture values in the 99.5 percentile
(in the period 2007–2018) are shown.
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1598 L. Brocca et al.: SM2RAIN–ASCAT (2007–2018)
Table A1. Equations used for the performance scores. For the continuous scores, Pref is the reference dataset (e.g. ground observations,
ERA5), Pest is the estimated dataset (e.g. SM2RAIN–ASCAT, GPM-ER), cov is the covariance operator, σis the standard deviation operator,
Pis the summation operator, and Nis the sample size. For the categorical scores, His the number of successfully predicted events by a
given rainfall product, Fthe number of non-events erroneously predicted to occur, and Mis the number of actual events that are missed.
Performance score Score symbol Equation
Continuous scores
Pearson’s correlation R R =cov(Pest,Pref )
σ(Pest)σ(Pref )
Root mean square error RMSE RMSE =rP(Pest −Pref)2
N
Temporal variability ratio STDRATIO STDRATIO =σ(Pest )
σ(Pref)
Bias BIAS BIAS =P(Pest−Pref )
N
Categorical scores
False alarm ratio FAR FAR =F
H+F
Probability of detection POD POD =H
H+M
Threat score TS T=H
H+F+M
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L. Brocca et al.: SM2RAIN–ASCAT (2007–2018) 1599
Author contributions. All authors contributed extensively to the
work presented in this paper. LB conceived of and designed the pa-
per, developed the SM2RAIN code, and performed some of the
analysis. PF wrote most of the code and performed most of the
computations. LC, CM, SC, SH, and WW contributed to the pro-
cessing of the input–output datasets, the analysis and exploration of
the data, and the preparation and discussion of the results. LS and
BB contributed extensively to define the concept of the paper and to
define the procedure to be implemented. All co-authors contributed
to the editing of the manuscript and to the discussion and interpre-
tation of the results.
Competing interests. The authors declare that they have no con-
flict of interest.
Acknowledgements. The authors gratefully acknowledge sup-
port from EUMETSAT through the Global SM2RAIN project
(contract no. EUM/CO/17/4600001981/BBo) and the “Satel-
lite Application Facility on Support to Operational Hydrol-
ogy and Water Management (H SAF)” CDOP 3 (grant
no. EUM/C/85/16/DOC/15).
Financial support. This research has been supported
by EUMETSAT (Global SM2RAIN project grant
no. EUM/CO/17/4600001981/BBo and “Satellite Application
Facility on Support to Operational Hydrology and Water Manage-
ment (H SAF)” CDOP 3 grant no. EUM/C/85/16/DOC/15).
Review statement. This paper was edited by Alexander Gelfan
and reviewed by three anonymous referees.
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