HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus PublicationsGöttingen, Germany10.5194/hess-22-3685-2018Precipitation downscaling using a probability-matching approach and
geostationary infrared data: an evaluation over six climate
regionsAn evaluation over six climate regionsGuoRuifanghttps://orcid.org/0000-0003-2114-8306LiuYuanboybliu@niglas.ac.cnhttps://orcid.org/0000-0002-8780-927XZhouHanZhuYaqiaoKey Laboratory of Watershed Geographic Sciences, Nanjing Institute
of Geography and Limnology, Chinese Academy of Sciences, No. 73
East Beijing Road, Nanjing 210008, ChinaUniversity of Chinese
Academy of Sciences, No. 19 Yuquan Road, Beijing 100049, ChinaCollege of Urban and Environmental Sciences, Hubei Normal
University, No. 11 Cihu Road, Huangshi 435002, ChinaYuanbo Liu (ybliu@niglas.ac.cn)10July2018227368536992October20178November20178June201825June2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://hess.copernicus.org/articles/22/3685/2018/hess-22-3685-2018.htmlThe full text article is available as a PDF file from https://hess.copernicus.org/articles/22/3685/2018/hess-22-3685-2018.pdf
Precipitation is one of the most important components of the global water
cycle. Precipitation data at high spatial and temporal resolutions are
crucial for basin-scale hydrological and meteorological studies. In this
study, we propose a cumulative distribution of frequency (CDF)-based
downscaling method (DCDF) to obtain hourly
0.05∘× 0.05∘ precipitation data. The main
hypothesis is that a variable with the same resolution of target data should
produce a CDF that is similar to the reference data. The method was
demonstrated using the 3-hourly 0.25∘× 0.25∘
Climate Prediction Center morphing method (CMORPH) dataset and the hourly
0.05∘× 0.05∘ FY2-E geostationary (GEO) infrared
(IR) temperature brightness (Tb) data. Initially, power function
relationships were established between the precipitation rate and Tb
for each 1∘× 1∘ region. Then the CMORPH data were
downscaled to 0.05∘× 0.05∘. The downscaled results
were validated over diverse rainfall regimes in China. Within each rainfall
regime, the fitting functions' coefficients were able to implicitly reflect
the characteristics of precipitation. Quantitatively, the downscaled
estimates not only improved spatio-temporal resolutions, but also performed
better (bias: -7.35–10.35 %; correlation coefficient, CC: 0.48–0.60)
than the CMORPH product (bias: 20.82–94.19 %; CC: 0.31–0.59) over
convective precipitating regions. The downscaled results performed as well as
the CMORPH product over regions dominated with frontal rain systems and
performed relatively poorly over mountainous or hilly areas where orographic
rain systems dominate. Qualitatively, at the daily scale, DCDF and CMORPH had
nearly equivalent performances at the regional scale, and 79 % DCDF may
perform better than or nearly equivalently to CMORPH at the point (rain gauge)
scale. The downscaled estimates were able to capture more details about
rainfall motion and changes under the condition that DCDF performs better
than or nearly equivalently to CMORPH.
Introduction
Precipitation is a critical component in the global water cycle (Barrett and
Martin, 1981; Smith et al., 1998; Tobler, 2004). Precipitation data at
spatio-temporal resolutions are favoured mainly for two reasons. First, the
poor representativeness and uneven distribution of gauge stations make the
data incapable of reflecting the precipitation variation spatially (Hughes,
2006, Collischonn et al., 2008; Javanmard et al., 2010). Second, ground
radar systems can provide full coverage spatial data for most regions, but
RADAR is very weak in view of the precipitation intensity and is subject to
short time series. Moreover, the validation poses a big challenge for
hydrological applications (Krajewski and Smith, 2002).
A number of techniques have been developed to estimate or retrieve
precipitation (Kidd and Levizzani, 2011). Based on these technologies,
precipitation datasets have been produced at various resolutions, including
the Global Precipitation Climatology Project (GPCP) (Huffman et al., 1997,
2001, 2009), the Tropical Rainfall Measuring Mission (TRMM) Multi-Satellite
Precipitation (TMPA) (Huffman et al., 2007), the Climate Prediction Center
morphing method (CMORPH) (Joyce et al., 2004) and the Global Satellite
Mapping of Precipitation (GSMaP) (Ushio et al., 2009), especially over the
last 20 years. The typical spatial resolution of these products is
0.25∘× 0.25∘ (Dinku et al., 2007; Ebert et
al., 2007; Hirpa et al., 2010; Sohn et al., 2010; Bitew and Gebremichael,
2011; Romilly and Gebremichael, 2011; Thiemig et al., 2012; Hu et al.,
2014). This coarse resolution generally impedes the applications of the data
for basin-scale hydrological and meteorological studies (Mekonnen et al.,
2008). A downscaling procedure would therefore be highly necessary to meet
the requirements of small-scale (<10 km) applications.
Downscaling approaches were first used to interpolate regional-scale
atmospheric predictor variables to point-scale meteorological series (Karl
et al., 1990; Wigley et al., 1990; Hay et al., 1991, 1992). Currently,
downscaling approaches are well developed and can be categorised into
regression methods, weather pattern approaches, stochastic weather generators
and limited-area climate modelling (Wilby and Wigley, 1997; Cannon, 2008).
Most methods are based on meteorological or climate models, and assume that
relationships can be established between atmospheric parameters at disparate
temporal and/or spatial scales (Giorgi and Mearns, 1999; Willems and Vrac,
2011; Kenabatho et al., 2012). Downscaling approaches can also be
categorised into dynamical methods (using regional climate models to
translate large-scale weather evolution into physically consistent
evolution at a higher resolution) and statistical methods (based on statistical
relationships between the regional climate and large-scale predictor
variables) (Schmidli et al., 2006). At present, these methods are generally
available to downscale data from general circulation models.
Various downscaling techniques have been developed to improve the resolution
of satellite precipitation data. Immerzeel et al. (2009) used an exponential
relationship between the 1 km Normalized Difference Vegetation Index (NDVI) and
precipitation to downscale TRMM 3B43 precipitation data on the Iberian
Peninsula. Jia et al. (2011) used a linear regression relationship between a
combination of NDVI and a digital elevation model and precipitation to downscale TRMM 3B43
precipitation data in the Qaidam Basin of China. Duan and Bastiaanssen
(2013) used a two-degree polynomial regression model between NDVI and
precipitation to downscale TRMM 3B43 precipitation data in the Lake Tana
basin, Ethiopia, and the Caspian Sea region, Iran. These studies manifest the
potential of downscaling methods to obtain fine-resolution precipitation
(<10 km), while mainly focusing on precipitation data with low temporal
resolutions (i.e. annual or monthly).
The main objective of this study is to develop a regression-based downscaling
method to obtain precipitation estimates with a high spatio-temporal
resolution (0.05∘, hourly). Barrett et al. (1991) proposed a
cumulative histogram method to relate precipitation observations to satellite
estimates in an effort to avoid bias problems related to simple regression.
In this study, we propose a cumulative distribution of frequency (CDF)-based
downscaling method (DCDF) and perform preliminary validation using CMORPH
and geostationary (GEO) infrared (IR) temperature brightness (Tb)
data. This new method can (1) lead to a better understanding of satellite
precipitation data and (2) stimulate scientific interests to engender the
development of precipitation data with improved resolutions. The following
section introduces study areas and datasets. Section 3 introduces the principles, framework and procedure of the downscaling
method. Section 4
presents the major findings followed by discussion in Sect. 5. Finally,
Sect. 6 concludes.
Geographic and climate situations of the six regions. The locations
of the rain gauges are superimposed on the map.
Study areas and datasetsStudy areas
Existing studies confirmed that the performances of satellite precipitation
estimates are highly dependent on the rainfall regime (Arkin et al., 2006;
Ebert et al., 2007; Gottschalck et al., 2005), which varies with climate
zone, latitude, longitude and elevation. Thus, six 5∘× 5∘
regions were selected for validation (Fig. 1). Their
corresponding geographic and climatic characteristics are listed in Table 1.
These areas are distributed from south to north and from east to west, and
they incorporate most rainfall regimes.
Geographic and climatic situations of the six regions in
China.
RegionLongitude,ElevationAnnualClimate zone latituderange (m)precipitation (mm)SE110–115∘ E, 23–28∘ N22–14051230Subtropical humidMonsoonCE114–119∘ E, 33–38∘ N6–1533670Warm temperate semi-humidMonsoonNE121–126∘ E, 46–51∘ N147–740460Mid-temperate humidMonsoonCW99–104∘ E, 34–39∘ N1368–850040Warm temperate aridNon-monsoonNW82–87∘ E, 41–46∘ N320–245870–140Mid-temperate aridNon-monsoonTP89–94∘ E, 28–33∘ N3552–8260420Temperature plateauNon-monsoon
Among the six regions, regions SE (south-east), CE (central-east) and NE (north-east) are located in the eastern
monsoon region. It is warm and rainy during the southeast monsoon in
June–August, and cold and dry during the northwest monsoon in
December–February. These three regions feature low-elevation hills
and plains. Regions CW (central-west), NW (north-west) and TP (Tibetan Plateau) are located in the non-monsoon region with
a continental climate. CW and NW belong to arid region, with
60–70 % precipitation occurring in June–August. CW has
a relatively high elevation, mainly covered by plateaus, mountains and
basins. NW is mainly covered by plateaus and basins. TP has a complex
climate, mainly covered by plateaus and mountains. The
seasonal precipitation distribution has two forms: a unimodal distribution
in summer (June–August), and a bimodal distribution in spring (March–May)
and autumn (September–November).
DatasetsMeteorological data
Rain gauge data were obtained from the National Meteorological Information
Centre of the China Meteorological Administration (CMA)
(http://data.cma.cn/, last access: 10 April 2017).
The datasets include daily precipitation records at 137 rain gauge stations
in 2014 (Fig. 1). Strict quality control has been applied to check extreme
values (Ma, 1998). There are 33, 29, 14, 31, 12 and 18 rain gauges in regions
SE, CE, NE, CW, NW and TP, respectively. In the case of more than one station
located within a pixel, the rain gauge values are averaged to represent the
grid value. Statistical analyses were used to evaluate precipitation
estimates at the daily scale. In addition, a disdrometer installed at Xingzi
station (29.45∘ N, 116.05∘ E) in Jiangxi Province
(Fig. 1) provided hourly data in 2014, except June and July when the
instrument was subject to a transmission error. Disdrometer data is used to
evaluate the precipitation estimates.
Satellite data
IR data (10.7 µm) were collected from the Stretched Visible and
Infrared Spin Scan Radiometer (S-VISSR) on board the FY2-E satellite. The data are
available at the National Satellite Meteorology Center
(http://satellite.nsmc.org.cn/portalsite/default.aspx, last access: 12 August 2017).
FY2-E provides hourly coverage of eastern Asia from 75∘ S to
75∘ N. The IR Tb data were corrected for zenith angle
viewing effects.
CMORPH was developed and produced by the Climate Prediction Center (CPC) in
the National Oceanic and Atmospheric Administration (NOAA). CMORPH produces
0.25∘× 0.25∘ 3-hourly global precipitation
data using PMW and IR data. PMW data are from the Microwave Imager (TMI) on
TRMM, the Special Sensor Microwave Imager (SSM/I) on Defense Meteorological
Satellite Program (DMSP) satellites 13–15, the Advanced Microwave Scanning
Radiometer Earth Observing System (AMSR-E) on Aqua and the Advanced Microwave
Sounding Unit-B (AMSU-B) on NOAA satellite 15–18. Precipitation estimates
are generated using the algorithms of Ferraro (1997) for SSM/I, Ferraro et al. (2000)
for AMSU-B and Kummerow et al. (2001) for TMI. IR data are
obtained from the GEO Operational Environmental Satellites (GOES) 8/10,
European Meteorological Satellites (Meteosat) 5/7 and Japanese GEO
Meteorological Satellites (GMS) 5. CMORPH uses motion vectors derived from
GEO satellite IR imagery to propagate the relatively high-quality
precipitation estimates derived from PMW data (Joyce et al., 2004). Hence,
quantitative precipitation estimates are based solely on PMW data. GEO-IR
data are not used to estimate precipitation but rather to interpolate
between two PMW-derived precipitation rate fields.
MethodologyCDF matching
The CDF matching is a probability-based process. It assumes a variable (v)
should produce a similar CDF to the reference variable (t). The frequencies
of t and v are shown in Eqs. (1)–(2), and the cumulative frequencies in
Eqs. (3)–(4).
Pt=f1(t)Pv=f2(v)Ct(t)=∫T1tf1(t)dtCv(v)=∫V1vf2(v)dvCv-1[Ct(t)]⟶f3t,
where Pt and Pv are the probability of t and v, f1(t) and
f2(v) are probability density functions of t and v and Ct(t)
and Cv(v) are the cumulative density functions of t and v,
respectively. f3(v) represents the relationship between t and v.
Schematic of the cumulative distribution of frequency (CDF) matching
method.
The steps for CDF matching are summarised in Fig. 2. First, t and v are
shown in histograms (Fig. 2a, b). The frequency of an arbitrary point
ti (or vi) on the f1(t) [or f2(v)] curve can be expressed
as P(t=ti)=f1(ti) [or P(v=vi)=f2(vi)]. Second, these
histograms are transformed into cumulative histograms (Fig. 2c, d). The
cumulative frequency of an arbitrary point ti (or vi) on the
Ct(t) [or Cv(v)] curve can be expressed as
C(t<ti)=∫T1tif1(t)dt [or
C(v<vi)=∫V1vif2(v)dv]. Third,
these cumulative histograms are matched so that v has a cumulative
histogram similar to t. The matching process is implemented by a one-to-one
mapping CDF of the variable onto that of the reference (Eq. 5). Last, the
v–t relationship is established (Eq. 5) (Fig. 2e). Magnusson et
al. (2015) demonstrated that CDF matching works better than
a histogram-matching method when low values have high frequencies, which is
generally the case for precipitation.
Downscaling
Our method is based on the work of Barrett et al. (1991) and Kidd and
Levizzani (2011). Rainfall can be inferred from IR imagery because heavy
rainfall tends to be associated with large, tall clouds with cold cloud tops.
Therefore, empirical relationships between the precipitation rate and
Tb are derived (Arkin and Meisner, 1987; Greene and Morrissey,
2000; Prigent, 2010). However, these relationships are indirect and exhibit
significant variations during the lifetime of a rainfall event. They also
differ among rain systems and climatological regimes, which causes
large uncertainties in precipitation estimations (Kidd and Levizzani, 2011).
Ba and Gruce (2001) demonstrated that a two-degree polynomial model is more
effective for describing the relationship, and that the coefficients of the
model are region-dependent. Overall, the precipitation–Tb
relationship is highly variable over time and space.
Microwave (MW) radiation reflects the physical structures of clouds.
Emission from rain droplets increases MW radiation, and scattering by
precipitating ice particles decreases MW radiation. Although MW techniques
are physically more direct than those based on IR radiation, they can both
reflect rainfall events. Therefore, we assume that an IR signal produces a
similar frequency distribution of precipitation rates to a MW signal over a
certain region during a certain period. Barrett et al. (1991) proposed a
cumulative-histogram-matching method to relate rainfall observations to
satellite precipitation data. Kidd et al. (2003) applied the same method to
estimate rainfall using passive microwave (PMW) and IR data over Africa.
Schematic of the CDF-based downscaling method (DCDF) using CMORPH
and FY2-E Tb in this study. R represents the precipitation rate.
The assumptions behind the downscaling method include the following: (1) Tb has
a similar cumulative frequency to the precipitation rate at certain spatial and
temporal scales, and (2) satellite precipitation products provide relatively
accurate estimates with low spatial and temporal resolutions. In contrast,
GEO-IR data have a high spatio-temporal resolution, yet low accuracy.
Illustrated in Fig. 3, the downscaling method explores the advantages of
the satellite precipitation product and GEO-IR data, specifically, (1) to
aggregate Tb (Tbh) from a high resolution to a
low resolution (Tbl) similar to the precipitation data
(Eq. 6), and (2) to apply the CDF matching to the Tbl and
precipitation rate (Rl) to obtain a
Tbl–Rl relationship and a rain–no-rain
threshold (Eq. 7). The downscaled precipitation rates are estimated based on
the Tbl–Rl relationships (Eq. 8).
Tbl=1n∑i=0nTbh(i)Tbl=m×RlpRh=(Tbhm)1/e,
where Tbh denotes high-resolution GEO-IR Tb
data, Tbl denotes upscaled Tb data,
Rl denotes the low-resolution precipitation product, Rh
denotes the derived high-resolution estimates, m and e are coefficients
of the Tb–R relationship and n is the number of
high-resolution pixels within a low-resolution pixel.
Under the assumption that colder clouds are linked to higher rainfall than
warmer clouds, the downscaling method assumes a monotonically increasing
precipitation rate with decreasing Tb. Therefore, cumulative
histograms of the precipitation rate and Tb are matched, so that the
occurrence of the heaviest precipitation is associated with the Tb
values linked to the heaviest rainfall. Decreasing Tb values are
assigned to increasing precipitation rates so that the final distribution of
Tb assigned to the precipitation rates is the same as that
determined using precipitation rate data. Specially, all precipitation rate
(Tb) are sorted in ascending (descending) order. Then both cumulative
probability distributions are obtained. The cumulative probability is
defined as critical probability when the precipitation rate equals zero. The
rain–no-rain threshold is the Tb with a cumulative probability the same
as the critical probability. As shown in Fig. 2c and d (T means precipitation
rate; V represents Tb), the rain–no-rain threshold is set at
about vi, where the cumulative probability equals Ci (critical
probability).
The specific steps used for downscaling with CMORPH and FY2-E IR data are
described as follows.
Aggregate IR–Tb data (Tb0.05) from 0.05 to 0.25∘ by pixel
averaging (Tb0.25).IR–Tb data (Tb0.05) were aggregated
to a 0.25∘ grid (Tb0.25) for each 3 h period
(00:00–03:00, 03:00–06:00, …, 21:00–24:00 UTC), in order to match
the spatial and temporal resolutions of CMORPH.
Generate the histogram database for CDF matching. IR–Tb (Tb0.25) and the CMORPH
precipitation rate (R0.25) were recorded in a database. The sample area
for CDF matching was determined as follows. The horizontal and temporal
scales of stratiform precipitation range from 101 to 103 km and
from hours to days (Orlanski, 1975; Trapp, 2013), while those of cumuliform
precipitation range from a few kilometres to tens of kilometres and from minutes to
hours (Orlanski, 1975; Rickenbach, 2008). In combination with previous
studies (Kidd et al., 2003; Huffman et al., 2007), the downscaling procedure
was conducted at 1∘× 1∘ grids over a 10-day
period. To reduce the heterogeneity among grids, a 3 × 3 window was
used for smoothing purposes.
Build relationships between the precipitation rate and
Tb. The histograms of Tb–precipitation rate were generated and converted to cumulative histograms,
and then matched using the CDF matching. (As shown in Fig. 2, the precipitation
rate is denoted by T; Tb represents V; vi is the rain–no-rain
threshold.) A power function relationship between the precipitation rate
(R0.25) and Tb (Tb0.25) was established for
each 1∘× 1∘ area over a 10-day period. Meanwhile,
various parameters, including coefficients of the Tb–R
relationship, rain–no-rain threshold and R2, were obtained.
Estimate the precipitation rate pixel by pixel at 1 h and 0.05∘. All pixels in the Tb images (Tb0.05)
were divided into two categories, raining ones below the rain–no-rain
threshold and non-raining ones above the threshold. Tb–R
relationships were applied to these “raining” pixels. Finally, CMORPH data were
downscaled to 1 h and 0.05∘× 0.05∘.
Variogram
A variogram describes how data correlate with distance. The variogram
function γ(h) is defined as half of the mean value of the square of
the difference between points separated by a distance h (Matheron, 1963). A
variogram is generally an increasing function of distance h. The
relationship between γ(h) and h is commonly described using the
nugget effect (C0), sill (C0+C) and range (D). C0 denotes
micro-scale variations, equated to of γ(0). C0+C denotes the limit
of the variogram γ (+∞). D denotes the distance at which the
difference of the variogram from the sill becomes negligible. A variogram is
used here to describe the spatial structure of satellite precipitation data.
Examples of fitting of the precipitation rate and Tb for each
region in China during 9–18 July 2014 for subregion SE (115∘35′ E, 27∘28′ N), subregion CE
(115∘39′ E, 36∘14′ N), subregion NE
(124∘20′ E, 51∘42′ N), subregion CW
(101∘38′ E, 37∘31′ N), subregion NW
(85∘43′ E, 46∘47′ N) and subregion TP
(91∘06′ E, 30∘29′ N).
ResultsTb–precipitation rate relationship
Figure 4 shows fitting functions between the precipitation rate and
Tb within each 1∘× 1∘ grid. It was
observed that Tb had a power function relationship with the
precipitation rate. With an increase in the precipitation rate, Tb
decreased, and the rate of change also reduced. The model fitting R2 values were
all higher than 0.90. From the region SE to NE, the precipitation rate
decreases, mainly subject to latitude. The maximum precipitation rate,
rain–no-rain threshold and R2 all showed decreasing trends. The maximum
precipitation rate was 19.9 mm h-1 in region SE, 9.8 mm h-1 in
region CE and 4.3 mm h-1 in region NE. The corresponding Tb
values were 198, 202 and 210 K, respectively, and the rain–no-rain threshold
values were 265, 259 and 249 K. The probability of the precipitation rate
was the largest for a given Tb in region SE, followed by region CE
and then region NE. Regions CW and NW are arid, while TP is humid. The
maximum precipitation rate was 3.5 mm h-1 for both regions CW and NW
and 11 mm h-1 for region TP. The rain–no-rain thresholds for regions
CW and NW were approximately 230 K, while it was 254 K for region TP. The
probability of the precipitation rate was the largest for a given Tb in
region TP because region TP has a complex rain system and high elevation.
Generally, the fitting relationships reflected precipitation characteristics
well.
CMORPH precipitation estimates at a nominal resolution of
0.25∘ and DCDF precipitation maps at a 0.05∘ resolution
for regions SE, NE and TP.
Estimation results
Figure 5 shows a comparison of the spatial distributions of CMORPH and DCDF
precipitation estimates for regions SE, NE and TP. The downscaled precipitation
showed a similar spatial distribution to CMORPH, yet it reflected more
detailed moving and changing processes of rainfall. To demonstrate clouds
captured through DCDF and CMORPH, region SE was exemplified (14:00 to 16:00,
21 June 2014). Three cloud centres were observed in the southeastern and
mid-eastern parts at 14:00. One hour later, two centres in the southeast
moved eastward and joined together, while another centre moved eastward. Two
precipitation centres continued to move eastward at 16:00. In addition, D and
sill values of DCDF (2.796 and 1.070) were higher than those of CMORPH (1.614
and 0.489). Large range and sill values indicate a high spatial dependence
and high spatial variability. Thus, the spatial dependence and variability
for high-resolution data were generally larger than those for low-resolution data.
In region SE, clouds were relatively centralised with a high precipitation
rate and were small in size. In region NE, clouds were discrete with a low
precipitation rate and were widely distributed. In region TP, both
centralised and discrete clouds appeared. Cumuliform cloud is the main type
in region SE, while stratiform cloud is dominant in region NE, and both are dominant in
region TP. Thus, the cloud distributions obtained through satellite data,
especially using the DCDF approach, were consistent with the local
characteristics. Sill for cumuliform clouds was larger than that for
stratiform clouds. A larger sill value was obtained for region SE (DCDF:
1.070; CMORPH: 0.489) than for region NE (DCDF: 0.007; CMORPH: 0.008). These
results indicated that the DCDF method can reflect precipitation
characteristics among rain systems and climatological regimes.
Time series of disdrometer data, original CMORPH and DCDF
precipitation at an hourly scale in 2014.
Validation
Figure 6 shows a comparison among the DCDF, CMORPH and disdrometer at the
hourly scale. The DCDF and CMORPH were able to capture rainfall events,
although they differed in magnitude from the reference data in some cases.
The DCDF effectively reflected the peak of each rainfall event, but could
not exactly identify same starting and ending times of rainy events,
resulting in somewhat delayed or advanced rainfall. The DCDF may detect
non-rainy events as rainy events, especially in dry seasons. CMORPH reported
low-rain events as non-rainy events. Both of the DCDF and CMORPH estimates
coincided with disdrometer data at precipitation rates ranging from 1 to 10 mm h-1,
such as the events from 10:00 to 14:00 on 9 February and from 21:00 on 13 May to 10:00 on 14 May.
Time series of the average precipitation of each region derived from
the gauge, DCDF and CMORPH at the daily scale in June 2014.
To demonstrate the performance of the DCDF method, a comparison of the DCDF and
CMORPH estimates was conducted at the regional scale and at the point (rain
gauge) scale. Figure 7 shows the average precipitation of each region derived
from the rain gauge, DCDF and CMORPH. The daily average precipitation over each
region showed almost identical temporal variations for DCDF and CMORPH. Both
DCDF and CMORPH showed similar temporal patterns to the rain gauge
observations, but they were probably subject to overestimation for regions
CW and NW and underestimation for regions SE and TP. At the point (gauge)
scale, the better fit between DCDF and gauge data than that between CMORPH
and gauge data is 10 %. The nearly equivalent fit is 69 %. The poorer
fit was mainly evident in regions NW, CW and TP. Figure 8 shows that cases of better
fit in the time series of DCDF were generally more consistent with the
rain gauge data than CMORPH, although the DCDF series occasionally
deviated from gauge data or misreported non-rainy events as rainy events.
These results indicated that both DCDF and CMORPH demonstrated nearly
equivalent performances at the regional scale, and 79 % DCDF may perform
better than or nearly equivalent to CMORPH at the point (gauge) scale.
Time series of rain gauge data, original CMORPH and DCDF
precipitation for each randomly selected gauge. (a) Ganzhou station
(SE):
113.1667∘ E, 25.8667∘ N. (b) Jinan station (CE):
117.05∘ E, 36.6∘ N. (c) Tulihe station (NE):
121.6833∘ E, 50.4833∘ N. (d) Lanzhou station (CW):
103.8833∘ E, 36.05∘ N. (e) Shihezi station (NW):
86.05∘ E, 44.3167∘ N. (f) Lasa station (TP):
91.1333∘ E, 29.6667∘ N.
Validation results of the daily precipitation for CMORPH and
DCDF in 2014 in the six study regions.
IndexesTimeTypeSECENECWNWTPBias (%)1 yearCMORPH-29.60-12.82-7.09-5.57120.2226.41DCDF-3.9111.5415.8532.82.145.4352.33SPCMORPH-20.82-3.31-45.5045.44159.0283.32DCDF-7.352.9431.2350.92191.79100.36SUCMORPH-22.123.176.78-43.92143.11-9.49DCDF-10.472.665.9425.91217.047.53FACMORPH-57.75-33.00-16.9010.90114.4443.22DCDF5.9233.9519.8825.78128.5159.77WICMORPH-94.19-32.83-96.201042-73.751655DCDF10.3520.5422.39187454.582106Root mean square error1 yearCMORPH12.206.696.713.852.324.50DCDF7.944.385.164.743.966.08SPCMORPH16.234.793.132.812.412.70DCDF11.817.322.772.803.093.45SUCMORPH16.6110.2512.395.743.387.43DCDF13.8310.9510.646.985.1310.27FACMORPH6.146.903.893.931.943.46DCDF0.196.442.674.513.723.98WICMORPH3.801.590.681.610.652.45DCDF2.862.050.412.471.143.49CC1 yearCMORPH0.520.320.320.170.330.28DCDF0.600.470.420.290.290.33SPCMORPH0.590.340.360.170.070.04DCDF0.660.400.380.170.050.04SUCMORPH0.360.190.250.170.400.23DCDF0.480.260.460.440.440.37FACMORPH0.400.500.360.070.320.11DCDF0.520.530.460.100.210.08WICMORPH0.310.020.000.050.030.06DCDF0.520.170.050.010.020.15Probability of detection1 yearCMORPH0.640.590.510.760.520.80DCDF0.770.740.620.800.690.87SPCMORPH0.680.520.450.820.510.70DCDF0.800.660.600.950.630.72SUCMORPH0.860.690.780.820.800.91DCDF0.990.850.910.870.901.00FACMORPH0.500.670.460.710.800.72DCDF0.650.750.590.840.920.89WICMORPH0.220.190.000.280.590.14DCDF1.001.001.001.001.001.00False alarm rate1 yearCMORPH0.300.630.480.650.760.65DCDF0.350.590.550.720.810.64SPCMORPH0.170.760.630.710.850.78DCDF0.210.700.730.810.920.85SUCMORPH0.310.530.360.330.680.30DCDF0.430.520.410.570.790.38FACMORPH0.460.520.580.690.680.73DCDF0.480.580.660.890.660.91WICMORPH0.540.901.000.960.760.99DCDF0.610.951.001.000.971.00Heidke skill score1 yearCMORPH0.430.250.340.080.140.13DCDF0.390.310.350.140.080.09SPCMORPH0.410.130.230.000.090.01DCDF0.440.210.290.030.110.07SUCMORPH0.380.290.400.250.170.22DCDF0.320.350.370.33-0.080.16FACMORPH0.380.390.27-0.020.170.04DCDF0.390.480.340.01-0.060.01WICMORPH0.140.00-0.01-0.060.16-0.06DCDF0.210.070.03-0.110.29-0.16
Table 2 lists the seasonal statistics for the six regions at the daily
scale. Generally, DCDF performed better than CMORPH in region SE, while
it performed equivalently to CMORPH in regions CE and NE. Both of the DCDF and
CMORPH showed better performances during the rainy season. The DCDF generally
showed the smallest biases between -7.35 and 10.35 % (correlation coefficient, CC: 0.48–0.60)
in region SE, and overestimated precipitation by
2.66–33.95 % (CC: 0.05–0.53) in regions CE and NE.
CMORPH underestimated precipitation by 20.82–94.19 % (CC: 0.31–0.59) in region SE and showed biases between -93.2
and 6.78 % (CC: 0.00–0.50) in regions CE and NE. DCDF and CMORPH both exhibited poor performances in regions CW, NW and TP,
and showed large biases (-73.75–2106 %), low CC values
(0.01–0.44) and high false alarm rate (FAR) values (0.33–1.00)
during the winter. Further inspection showed that the DCDF overestimation
was due to high probability of detection and FAR, which may be caused by a low rain–no-rain
threshold. The large biases for regions CW, NW and TP were likely due to
the insensitivity of precipitation data to very low precipitation in arid
regions and the inability to estimate precipitation over mountainous or hilly
areas where orographic rain systems dominate.
Discussion
Existing downscaling methods make an assumption that local-scale
patterns are driven by large-scale climatic fluctuations (Wilby and Wigley,
1997; Wilby et al., 2002). Most of these methods rely on meteorological or
climate models and utilise multiple parameters, such as temperature,
humidity, pressure, vorticity and geostrophic airflow. These methods are not
used to downscale satellite precipitation products, possibly due to a
diversity of parameters and complexity of the meteorological and climate
models. In contrast, the DCDF method in this study assumes that the IR retrieval
should produce a frequency distribution of precipitation rates similar to
that produced by MW retrievals over a certain region during a certain
period; that is, IR estimations and MW retrievals from clouds have strong
statistical frequency similarities.
Due to high spatial and temporal variability of precipitation, the DCDF
method must be conducted over a certain region during a certain period. The
area and time period must be large enough for a reasonable sample size, but
small enough to represent local characteristics. In the TMPA algorithm,
a relationship between IR and the precipitation rate is built within a
1∘× 1∘ area by 3 × 3 windows over the
period of a month (Huffman et al. 2007). Kidd et al. (2003) obtained the
relationship within a 1∘× 1∘ area with the use
of a 5∘× 5∘ Gaussian filter over a period of 5
days. Based on the horizontal and temporal scales of stratiform and
cumuliform precipitation (Orlanski, 1975; Rickenbach, 2008, Trapp, 2013) and
previous studies (Kidd et al., 2003; Huffman et al. 2007), the DCDF method
is applied within a 1∘× 1∘ area by 3 × 3
windows over a 10-day period. Nevertheless, the same gridded sample area
is not the optimal selection. The size of sample area is determined
according to local cloud type and varies over space and time. It likely is
our future work to improve the precipitation estimates' algorithm.
It seems that IR data are used twice, one for original CMORPH generation and
the other for downscaling CMORPH. In fact, IR data serve as an intermediate
variable for an interpolation purpose in the first step, while IR data serve
as an ancillary variable in the second step for developing a
precipitation–Tb relationship. The CMORPH product is essentially
derived from MW observations, and therefore the use of IR data is reasonable.
We selected CMORPH as reference precipitation data mainly for the following
reasons. Products with similar resolutions to GEO-IR data (0.05∘) are
not used, such as CMORPH at 0.072∘ and GSMaP at 0.1∘. TRMM
3B42 (RT) and the Naval Research Laboratory blended product (NRLB) (Turk, 2005) algorithm
combine MW-calibrated IR estimates, which would result in IR reuse.
The DCDF method has two main disadvantages. The physical premise of the DCDF
method is that cloud top temperature in the IR imagery is a simple empirical
function of cloud top height, and that heavier rainfall tends to be
associated with larger, taller clouds with colder cloud tops. Unfortunately,
not all cold clouds precipitate, and precipitation does not always fall from
cold clouds only (Barrett, 1970). This phenomenon results in misreporting. In
addition, the rain–no-rain threshold is very critical for final precipitation
estimates. The size of the sample area and the indirect relationship between
IR–Tb and the precipitation rate both affect the rain–no-rain
threshold. However, both of them have uncertainties among rain systems and
climatological regimes, resulting in uncertainties of the rain–no-rain threshold.
Rain gauge measurements represent a space in a very small area, while satellite
precipitation products have a spatial resolution of several kilometres or
more. Thus, high-resolution data are generally more similar to gauge data
than low-resolution data. Furthermore, the characteristic scale is small for
convective systems and large for frontal rain systems. Convective
precipitation dominates in region SE, while a frontal rain system dominates in
regions CE and NE. Thus, a rain gauge measurement can represent a space in a
smaller area in region SE than in regions CE and NE. Therefore,
discrepancies between rain gauge observations and satellite estimates are
lower in region SE than in regions CE and NE. CMORPH performed poorly in
regions NW and TP, where orographic rain systems dominate (Hirpa et al.,
2010; Romilly and Gebremichael, 2011; Gao and Liu, 2013). Our results are
consistent with these findings.
It is expected that the DCDF method also applied to reanalysis precipitation
data (e.g. ERA-Interim, 0.75∘/6-hourly). First, the assumption that
Tb has a similar cumulative frequency to the precipitation rate at
certain spatial and temporal scales is also applied to reanalysis data.
Second, most average R2 values between Tb and CMORPH are higher
than 0.90, which may infer that the poor performance of the DCDF approach in
winter and in mountainous regions is mainly caused by the low accuracy of CMORPH.
Therefore, using reanalysis data for downscaling may be better than satellite
products.
Conclusions
Precipitation data with high spatial and temporal resolutions are highly
needed in basin-scale hydrological and meteorological studies. Based on the
works by Barrett et al. (1991) and Kidd and Levizzani (2011), this study
proposed a DCDF method to obtain precipitation data at the hourly,
0.05∘ scale. The method was demonstrated using the CMORPH dataset
and FY2-E GEO-IR Tb data for 2014. With the establishment of a power
function relationship, improved precipitation estimates at hourly and
0.05∘ resolution were produced. The DCDF precipitation estimates were
validated using rain gauge data from six 5∘× 5∘
regions in China with different climate and geographical conditions.
There are three key points of the DCDF method. First, it explores the
advantages of satellite precipitation estimates and GEO-IR data. The DCDF
method assumes a monotonically decreasing Tb rate with an increase
of precipitation rate, and it assumes that Tb data have the same cumulative
frequency as that of the precipitation rate for certain spatial and temporal
scales. The matching process is implemented by quantile-mapping the CDF of
Tb onto that of the precipitation rate. Second, the sample area where
the CDF matching was conducted needs to be large enough for a reasonable
sample size, but small enough to represent the local characteristics. In this
study, the size of the sample area was 1∘× 1∘ grid over
a 10-day period, based on the characteristic scale of precipitation clouds.
Third, a power function relationship between the precipitation rate and
Tb was established for each sample area. Meanwhile, a rain–no-rain
threshold was obtained as the Tb value with the same cumulative
frequency as that of the precipitation rate defined at the critical point of
rain–no-rain. Generally, the threshold was the maximum Tb in the
CDF-matching procedure.
The established fitting relationships generally reflected the precipitation
characteristics well in the six validation regions. For the distributions of
precipitation clouds, the DCDF precipitation estimates showed a similar
spatial distribution to that produced by CMORPH, but it reflected more
detailed moving and changing processes of rainfall under the condition that
DCDF performed better than or nearly equivalent to CMORPH. The DCDF method
can effectively reflect the precipitation characteristics among rain systems
and climatological regimes. At the hourly scale, both DCDF and CMORPH
coincided with the disdrometer data at precipitation rates ranging from 1 to
10 mm h-1. The DCDF effectively reflected the peak of each
rainfall event, but could not exactly identify the starting and ending times
of rainy events. The DCDF may detect non-rainy events as rainy events
especially in dry seasons, while CMORPH reported low-rain events as
non-rainy events. At the daily scale, DCDF and CMORPH had nearly equivalent
performances at the regional scale, and 79 % DCDF may perform better than
or nearly equivalent to CMORPH at the point (rain gauge) scale. Generally,
the DCDF performed better (bias: 7.35–10.35 %; CC: 0.48–0.60) than the original CMORPH product (bias:
20.82–94.19 %; CC: 0.31–0.59) over the regions where
convective precipitation dominates. It performed as well as the CMORPH
product over the regions where frontal rain systems dominate and relatively
poorly over mountainous or hilly areas where orographic rain systems
dominate.
The data used to produce the results of this
paper may be obtained by contacting the corresponding
author.
RG and YL developed the method. HZ and YZ were involved in the data processing. RG
prepared the manuscript and all co-authors were asked to review the
manuscript.
The authors declare that they have no conflict of interest.
Acknowledgements
This work was partially supported by the State Key Program of the National
Natural Science Foundation of China under grant 41430855 and by the National High
Technology Research and Development Program under grant 2013AA12A301. The
authors would like to thank Chris Kidd for providing a
report of SSM/I rainfall algorithms, and Pingping Xie for his
guidance at the University of Maryland. The authors would like to thank
research associates Bo Zhong and Shanlong Wu for data collection and
processing at the Institute of Remote Sensing and Digital Earth (RADI),
Chinese Academy of Sciences.
Edited by: Matthias Bernhardt
Reviewed by: two anonymous referees
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