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WEATHER AND FORECASTING
VOLUME 30
Extended-Range Forecasts of Areal-Averaged Rainfall over Saudi Arabia
MICHAEL K. TIPPETT
Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York, and
Center of Excellence for Climate Change Research, Department of Meteorology, King Abdulaziz University,
Jeddah, Saudi Arabia
MANSOUR ALMAZROUI
Center of Excellence for Climate Change Research, Department of Meteorology, King Abdulaziz University,
Jeddah, Saudi Arabia
IN-SIK KANG
School of Earth and Environmental Sciences, Seoul National University, Seoul, South Korea, and Center of
Excellence for Climate Change Research, Department of Meteorology, King Abdulaziz University, Jeddah,
Saudi Arabia
(Manuscript received 14 January 2015, in final form 19 April 2015)
ABSTRACT
The climate of Saudi Arabia is arid–semiarid with infrequent but sometimes intense rainfall, which can
cause flooding. Interannual and intraseasonal precipitation variability in the region is related to ENSO and
MJO tropical convection. The predictability of these tropical signals gives some expectation of skillful
extended-range rainfall forecasts in the region. Here, the extent to which this predictability is realizable in the
Climate Forecast System (CFS), version 2, a state-of-the-art coupled global ocean–atmosphere model, is
assessed. While there are deficiencies in the forecast climatology likely related to orography and resolution, as
well as lead-dependent biases, CFS represents the climatology of the region reasonably well. Forecasts of the
areal average of rainfall over Saudi Arabia show that the CFS captures some features of a spring 2013 heavy
rainfall event up to 10 days in advance and a transition from dry to wet conditions up to 20 days in advance.
Analysis of a 12-yr (1999–2010) reforecast dataset shows that the CFS can skillfully predict the rainfall
amount, the number of days exceeding a threshold, and the probability of heavy rainfall occurrence for
forecast windows ranging from 1 to 30 days. While the probability forecasts show good discrimination, they
are overconfident. Logistic regression based on the ensemble mean value improves forecast skill and reliability. Forecast probabilities have a clear relation with the MJO phase in the wet season, providing a
physical basis for the observed forecast skill.
1. Introduction
In early May 2013, widespread heavy rains and subsequent flooding in Saudi Arabia resulted in 25 deaths
(http://reliefweb.int/report/saudi-arabia/25-saudis-killedheavy-rain-floods). The overall climate of Saudi Arabia is
Denotes Open Access content.
Corresponding author address: M. K. Tippett, Dept. of Applied
Physics and Applied Mathematics, Columbia University, Mail
Code 4701, New York, NY 10027.
E-mail: [email protected]
DOI: 10.1175/WAF-D-15-0011.1
Ó 2015 American Meteorological Society
arid–semiarid, and rainfall in most regions is scant and
irregular. However, episodes of heavy rainfall during the
wet season (November–April) are not uncommon, and
when combined with the topography and hydrology of
the region, intense rainfall can result in substantial flood
risk. In fact, floods constitute 8 of the top 10 natural disasters in Saudi Arabia when ranked by the total number
of affected people during the period 1900–2013 [the
Emergency Events Database (EM-DAT), which is hosted by the Office of U.S. Foreign Disaster Assistance/
Centre for Research on the Epidemiology of Disasters
(OFDA/CRED), online at http://www.emdat.be; Université catholique de Louvain, Brussels, Belgium]. The
substantial impact of such rainfall events on society raises
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TIPPETT ET AL.
the following questions regarding their predictability. To
what extent was the May 2013 event predictable? More
generally, what is the skill of rainfall forecasts for the
region as a function of lead time and season? Can reliable
probabilistic predictions of high-impact rainfall for the
region be constructed?
Extended-range (beyond 5 days) forecasts are considered challenging because they stretch toward the limit of
our deterministic predictability, as provided by initial
conditions (Palmer 1993), but provide limited opportunity for boundary forcing such as sea surface temperature
to play a major role (Shukla 1981, 1998). The Madden–
Julian oscillation (MJO) is a mode of intraseasonal variability whose predictability and climate impacts provide a
scientific basis for extended-range prediction (Waliser
et al. 2003). Although a tropical phenomenon, the MJO
influences precipitation around the globe (Jones et al.
2004). In particular, as reviewed in Barlow (2012), the
MJO and other tropical forcings play an important role in
the precipitation of the Arabian Peninsula (AP) region,
and OLR-based estimates indicate that upward of 80% of
the November–April precipitation across the region
might be related to the MJO. The strength and location of
the MJO and its associated tropical convection can be
characterized using the phases (1–8) of the Real-Time
Multivariate MJO (RMM) indices (Wheeler and Hendon
2004). The impact of the MJO on the AP region varies by
phase. Using November–April daily station data for
Riyadh, Saudi Arabia, Barlow (2012) found a statistically
significant increase in the frequency of wet conditions
during phase 1 and a statistically significant increase in dry
conditions during phases 3–6, which correspond to positive values of RMM, series 1 (RMM1), and enhanced
equatorial convection over the Indian Ocean (IO) and the
Maritime Continent from about 708E to the date line.
The leading pattern of November–April monthly
precipitation anomalies for the IO precipitation variability on intraseasonal time scales includes the equatorial region from ;808 to 1108E (Hoell et al. 2012).
Observational analysis shows that enhanced convection
in this region on intraseasonal time scales is associated
with suppressed convection over much of the AP region
and an upper-level anticyclone centered across South
Asia. Analysis of the thermodynamic balance shows
cold temperature advection in the AP region to be
mostly balanced by downward motion consistent with
dry conditions. This pattern of IO precipitation variability has hemispheric impacts, and Hoell et al. (2013)
used barotropic Rossby wave ray tracing to show that IO
convection can force stationary Rossby waves that
propagate through the Northern Hemisphere and reach
the Middle East from the west in 15 days. In addition,
the MJO also influences low-level circulation and local
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moisture transport in the AP region (Nazemosadat and
Ghaedamini 2010). Nazemosadat and Ghaedamini
(2010) characterized the MJO using an index based on
principle components of filtered low-level zonal winds
(Maloney and Hartmann 1998), which corresponds to
IO convection in the equatorial region from ;808 to
1408E, slightly to the east of the region identified by
Hoell et al. (2012). Suppressed IO convection in this
region is associated with positive anomalies of precipitable water, consistent with the transport of moisture
to the region by enhanced low-level southerly winds.
This negative association between AP rainfall and IO
convection tends to be weaker when analyzed on interannual time scales, in part because of the additional
effect of El Niño––Southern Oscillation (ENSO). Athar
(2015) examined correlations of seasonal (3-month averages) Saudi station rainfall data with the Indian Ocean
dipole (IOD) and ENSO over the period 1978–2010 and
found generally positive correlations, consistent with the
observed southward shift of the upper-level subtropical
jet stream and enhanced moisture transport to the region
during positive IOD and ENSO events (Chakraborty
et al. 2006). The positive phase of the IOD is associated
with negative SST anomalies in the eastern tropical IO
and positive SST anomalies in the west.
The potentially competing roles of IO and ENSO SST
on the climate of the AP region was highlighted in the
analysis of Hoell et al. (2014) of climate responses to
different La Niña ‘‘flavors’’ (Johnson 2013). When La
Niña conditions are accompanied by negative IO SST
anomalies, there is little robust precipitation response in
the AP region in the observations or model experiments,
reflecting the opposing IO and ENSO factors. However,
when La Niña is accompanied by small or positive IO
SST anomalies, the AP region shows a strong decrease
in rainfall in the observations and model experiments.
Interestingly, these two La Niña types correspond roughly
to the pre- (cool IO SST anomalies) and post-1980 (warm
or no IO SST anomalies) periods. Kang et al. (2015) correlated the November–April average of Arabian Peninsula rainfall with concurrent values of the Niño-3.4 index
and found the correlation to be insignificant (0.1) over the
60-yr period of 1950–2010, but positive and significant
(0.51) over the recent 30-yr period of 1980–2010. This
changing relation between AP rainfall and the Niño-3.4
index can be attributed to changes in the extent to which
IO SST anomalies accompany those of the Niño-3.4 index.
Modeling experiments show that in isolation AP precipitation is negatively correlated with IO SST anomalies
and positively correlated with ENSO (Kang et al. 2015).
In the synoptic context, de Vries et al. (2013) examined the dynamical characteristics associated with the
so-called active Red Sea trough (ARST) and extreme
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rainfall events in the Middle East, including flooding in
Jeddah, Saudi Arabia. The Red Sea trough (RST), a
surface trough extending from East Africa through the
Red Sea, is an increasingly common climatological feature of the region present in autumn, and to a lesser
extent in winter and spring, that is related to the local
topography and thermal forcing (Krichak et al. 1997a,b;
Alpert et al. 2004). The RST is usually associated with
dry warm weather in the region, but when the RST is
accompanied by an upper-tropospheric trough, instability
may result and lead to severe precipitation. Such ARST
events are characterized by tropical–extratropical interactions, and de Vries et al. (2013) found that most
extreme rainfall events were associated with an amplification of a stationary wave that interacts with the lowlevel circulation. This feature of the ARST is highly
reminiscent of the tropically forced stationary Rossby
waves described by Hoell et al. (2013), and suggests that
the midlatitude Rossby wave amplification and forcing
described by de Vries et al. (2013) may potentially have a
tropical origin. Other aspects of ARST events are moisture transport, primarily from the Arabian and Red Seas,
and pronounced midtropospheric ascent, both features
present in the intraseasonal time-scale analysis as well.
The predictability of the MJO combined with its
substantial precipitation impacts in the region provide a
conceptual basis for skillful extended-range forecasts,
and Barlow et al. (2005) suggested that there was potential for 3-week forecasts. Realization of this potential
for skillful extended-range forecasts in the AP region by
dynamical prediction models requires that the model
both predict the MJO skillfully and represent the regional MJO response (teleconnection) with adequate
fidelity. The complexity of the observed synoptic
tropical–extratropical interactions discussed above
means that despite the apparent importance of tropical
forcing and the predictability it provides, forecast skill
for the region is not assured. Assessment of MJO forecast skill requires a substantial archive of forecasts, and
the Climate Forecast System (CFS), version 2, provides
such a reforecast archive (Saha et al. 2014), which has
been used to document the considerable improvement
of MJO forecasts in CFS, version 2, compared to those
of the previous version of CFS; MJO forecast skill in
CFS, version 2, now extends out to 2–3 weeks (Zhang
and van den Dool 2012; Wang et al. 2014). Here, we use
the CFS, version 2, reforecast archive to assess regional
precipitation forecast skill.
The paper is organized as follows. In section 2 we
describe the observational and forecast data, as well as
the verification metrics. The observed and forecast climatologies of the region are described in section 3.
Section 4 describes forecasts of the 2013 flooding event
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mentioned in the introduction. A 12-yr reforecast dataset is analyzed in section 5. Finally, a summary and
conclusions are given in section 6.
2. Data and methods
We consider forecasts and observation-based estimates of rainfall over the Arabian Peninsula region. We
restrict most of our analysis, in particular forecast skill
verification, to the areal average of rainfall over Saudi
Arabia, and we refer to this quantity as the SA rainfall
index. The SA rainfall index, while not capturing rainfall
variability at smaller scales, does provide a concise
summary of rainfall variability affecting large regions of
the country. Intense localized rainfall events are not well
resolved by the index because of the areal averaging. For
instance, the rainfall amounts associated with the
25 November 2009 flooding event in Jeddah were locally
extreme (Almazroui 2011b), but the corresponding
values of the SA rainfall index, while above normal,
were not so extreme. We use the SA rainfall index as a
tool to identify widespread rainfall situations of interest
whose spatial features can then be further investigated.
a. Observations
The observation-based rainfall estimate used here is
the 3B42 product from the TRMM Multisatellite Precipitation Analysis, version 7 (hereafter referred to as
simply TRMM; Huffman et al. 2007, 2010). This product
combines precipitation estimates from various satellite
systems (both infrared and radar) as well as surface
gauge analysis on a 0.258 3 0.258 spatial grid with 3hourly resolution. Here, we use the daily resolution of
the research version of the TRMM product for the period from 1 January 1999 to 14 February 2011, a total of
4428 days. TRMM, version 6, was previously compared
to rainfall data from 30 Saudi stations over the period
1998–2009 (Almazroui 2011a) and was found to match
well with daily station data on a countrywide basis. The
TRMM data matched less well with individual station
data on a daily basis. Monthly averaging improved the
relation between station and TRMM data. Our focus
here is on widespread rainfall events, and we expect that
the spatial averaging of the SA rainfall index will serve
to reduce the impact of small-scale discrepancies between the TRMM data and actual rainfall amounts.
b. Forecasts
We analyze Climate Forecast System (CFS), version
2, reforecasts for the period 1999–2010 and real-time
forecasts around the April–May 2013 flooding event
(Saha et al. 2014). The CFS atmospheric model has a
spectral resolution of T126 (18 3 18) in the horizontal
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and 64 sigma-pressure hybrid layers in the vertical. CFS
reforecasts are initialized four times daily at 6-hourly
intervals using the Climate Forecast System Reanalysis
(CFSR; Saha et al. 2010), and one ensemble member per
initialization time is integrated for at least 45 days, with
output available at 6-hourly intervals; we use only the
reforecast output out to 45 days. There are 17 532 reforecasts over the 12-yr period. The CFS reforecast dataset is available from the NOAA/National Climate
Date Center (NCDC); forecasts are missing from
25 days (100 starts). We group the four reforecast starts
per day (0000–1800 UTC) together to form a fourmember ensemble. This reforecast ensemble is ‘‘lagged’’ in the sense that each reforecast starts at a different
time, and ensemble reforecasts for a given target contain
forecasts of varying (by up to 18 h) lead times (Hoffman
and Kalnay 1983). Real-time forecasts for the period
around April–May 2013 are likewise initialized four
times daily but with four ensemble members per initialization time as compared to one in the reforecast. For
the real-time forecasts of the 2013 event, we average the
four ensemble members per start time and retain the
6-hourly start and forecast resolution.
Deterministic reforecasts are constructed from the
lagged ensemble for two SA rainfall index quantities:
the rainfall amount in a given forecast window and the
number of days in a given forecast window that the SA
rainfall index exceeds 0.25 mm day21. This threshold
corresponds to about the 75th percentile of the SA
rainfall index during the wet season, and its relatively
low value reflects the rarity of widespread rainfall. The
forecast rainfall amount is computed by taking the ensemble average, and the rainfall exceedance frequency
is computed by counting the number of days that an
ensemble member has an SA rainfall index greater than
0.1 mm day21, which is roughly the 75th percentile of the
forecast values during the wet season; the precise value
of the percentile depends somewhat on lead time as will
be discussed in section 3. The results are not particularly
sensitive to either the choice of observations or forecast
thresholds. We consider forecast windows of differing
lengths and leads. For instance, we consider forecasts of
the 5-day average of the SA rainfall index and forecasts
of the number of days in that 5-day window for which the
SA rainfall index exceeds the 0.25 mm day21 threshold.
Probabilistic forecasts of heavy rainfall occurrence are
also considered. Heavy rainfall is defined as occurring
when the SA rainfall index exceeds 1.0 mm day21 on any
day during the forecast target window. This threshold
corresponds to about the 90th percentile of daily rainfall
during the wet season. Two methods are used to construct probability forecasts. In the first method, the
forecast probability is simply the fraction of the four
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ensemble members exceeding 0.50 mm day21 (the lower
threshold value is used to account for model bias), and in
the second, the forecast probability comes from a logistic regression using the fourth root of the total ensemble mean rainfall during the forecast target window
as a predictor. The two logistic regression coefficients
vary with season (wet or dry) and lead, and there are
roughly 2100 samples for each season and lead.
Our convention with regard to lead time and forecast
target window is illustrated by the following examples.
The shortest lead (first lead) forecast of 2 January 1999
daily rainfall is computed from the lagged ensemble with
forecasts initialized at 0000, 0600, 1200, and 1800 UTC
1 January 1999, and we define such a forecast to have a
lead time of 6 h, the time from the last initialization to
the beginning of the forecast target window. Likewise,
the shortest lead (first lead) forecast of the 2–6 January
1999 average is computed from the same 1 January 1999
forecasts and is also defined to have a lead time of 6 h.
c. Verification measures
Forecasts are verified separately during two 6-month
seasons: wet and dry (May–October). We use a rank
(Spearman) correlation for the verification of the deterministic forecasts. Rank correlation, unlike the usual
Pearson correlation, is invariant to monotonic transformations and not affected by outliers. We verify
probabilistic forecasts using the Brier skill score
(Murphy 1973). The Brier skill score is the squared
difference between forecast probabilities and observed
occurrence, and measures both forecast reliability and
resolution. The Brier skill score compares the Brier
score of a forecast to that of a reference forecast, here
the climatological probability of the events during each
of the 6-month seasons. The Brier skill score is oriented
so that values greater than zero indicate skill greater
than that of a forecast whose prediction probability is
equal to the climatological probability. Reliability diagrams and relative operating characteristic curves
(ROCs) provide additional information about the
quality of the probabilistic forecasts.
3. Climatology
The climate of Saudi Arabia is mostly arid and semiarid, though regions in the southwest do have a steppe
climate and receive considerable rainfall year-round
(Abdullah and Al-Mazroui 1998). Overall, the annual
cycle of the country can be divided into a 6-month wet
and a 6-month dry season (Almazroui 2006, 2011a).
Figures 1a and 1b show TRMM estimates of the
November–April and May–October average rainfall,
respectively, over the 12-yr period 1999–2010. There is
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FIG. 1. TRMM rainfall during the (a) wet and (b) dry seasons during 1999–2010. (c),(d) As in (a),(b), but for CFS
first-lead rainfall.
some precipitation throughout the country on average
during the wet season, with the largest values found
over a broad region in the northeast of the country, and
along a narrow zone in the southwest following the
central (Asir) and the southern (Sarat al Yemen) parts
of the Sarawat mountain range as they parallel the Red
Sea coast, about 100 km inland, to the southernmost tip
of Yemen (Abdullah and Al-Mazroui 1998). Figure 2
shows the topography of the region, highlighted by the
rapid rise in elevation from the Red Sea coast eastward
toward the interior of the country. Annual rainfall
amounts in the southwestern region vary strongly with
elevation, and there is more rainfall on the western side
of the mountain ranges. Annual amounts on the order
of 400 mm are measured at some stations (Abdullah
and Al-Mazroui 1998). Much of the winter rainfall is
the result of tropical–extratropical interactions. Moisture at low levels is supplied via the Sudan low–Red
Sea trough and interacts with upper-level Mediterranean cyclones and Rossby waves associated with the
subtropical jet (Abdullah and Al-Mazroui 1998; de
Vries et al. 2013).
During the dry season, mid- and upper-level subsidence over the region serves to suppress rainfall, and
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FIG. 2. The topography of the region.
rainfall is mostly isolated to the region in the southwest
where the combination of steep elevation, southwesterly
winds, and strong orographic effects produces frequent
rainfall on the western slopes. Figure 1b indicates that
the dry season rainfall in this region actually exceeds
that of the wet season. Little rainfall occurs in the remainder of the country during the dry season. Two exceptionally dry zones are the Rub al Khali, known in
English as the Empty Quarter, in the eastern and the
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northwestern corner of the country including the
Tabuk region.
The first-lead CFS forecast climatology for the region
is represented by the average of 6-h forecasts made
four times daily over the 12-yr reforecast period (1999–
2010). Figures 1c and 1d show the first-lead CFS
precipitation climatology for November–April and
May–October, respectively. The first-lead CFS climatology captures the contrast between the wet and dry
seasons well, and the patterns compare relatively well
with those of the TRMM estimates. The first-lead CFS
climatology underestimates rainfall in the north, especially during the wet season, and does not resolve orographic rainfall in the southwest. Some aspects of this
southwestern orographic rainfall are present in the firstlead CFS forecasts during the wet season, but do not
appear at all in the dry season. The properties of the CFS
first-lead climatologies are constrained by the CFSR
data used to initialize the CFS forecasts, and next we
present lead time–dependent features of the CFS forecast climatology.
The annual cycle of the SA rainfall index computed
from 10 annual harmonics of the TRMM estimates is
shown in Fig. 3. As estimated during this particular period, the SA rainfall index has its maximum values in
April, January, and the beginning of December. The
annual cycle of the CFS SA rainfall index is also shown
for forecast leads varying from 1 to 15 days. Overall, the
CFS forecast SA rainfall index shows the same seasonality, but with generally lower values. However, the
annual cycle of the CFS SA rainfall index forecasts
shows considerable dependence on lead time. In April,
the CFS SA rainfall index becomes wetter as lead time
FIG. 3. Annual cycle (1999–2010) computed from 10 harmonics of the TRMM estimate
(black) of the SA rainfall index and the CFS forecast with leads of 1–5 (brown), 6–10 (blue), and
11–15 days (green).
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FIG. 4. January rainfall from (a) TRMM, (b) CFS lead 1, and (c) CFS lead 15. (d)–(f) As in (a)–(c), but for April rainfall.
increases. In contrast, the CFS SA rainfall index becomes drier in January as lead time increases. During
the July–August period, the shortest lead CFS SA
rainfall index forecasts are too dry while the longerlead examples are too wet. The CFS forecast of the
SA rainfall index during the November–December
period shows relatively little systematic dependence
on lead time.
The spatial expression of the dependence of the CFS
forecast climatology on lead time is shown in Fig. 4 for
January and April. The January climatology of the
initial CFS lead matches the TRMM January climatology well (Fig. 4b). However, for a 15-day lead, the
CFS January climatology is too dry, especially in the
north and west of the country (Fig. 4c). In April,
the initial lead CFS climatology is too dry, especially
along the southwestern coastal region and in the center
of the country (Fig. 4e). At a 15-day lead, the CFS
climatology becomes wetter in the central portion of
the country (Fig. 4f), in contrast to the drying seen with
the increasing lead in January. Figure 5 shows variations in July–August forecast climatology with lead.
The model climatology for the first lead is too dry, especially in the southwest of the AP. However, the climatology based on 15-day forecasts is much wetter,
perhaps overly so, in this region.
There are substantial differences between the observed and forecast daily climatological distributions of
the SA rainfall index. Figure 6 shows the cumulative
distribution functions of the observed and forecast daily
SA rainfall index for the wet and dry seasons separately.
One striking difference between the observed and
forecast daily SA rainfall index climatological distributions is the frequency of zero values. The observed
TRMM SA rainfall index has no zero values while for
the frequency of CFS forecasts with zero SA rainfall
index the value is around 35% during the wet season and
between 40% and 70% during the dry season depending
on lead. This discrepancy is primarily due to the inability
of the CFS to resolve the frequency of sparse orographic
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FIG. 5. Total July–August rainfall from (a) TRMM, (b) CFS lead 1, and (c) CFS lead 15.
rainfall in the southwest. On days when the CFS SA
rainfall index is zero, the TRMM data often indicate
isolated rainfall located along the western side on the
steep orography of the southwest. The forecast climatological statistics depend on lead time in both seasons,
with longer-lead forecasts tending toward more frequent precipitation. The lead time dependence of the
forecast statistics is more pronounced in the dry season
forecasts. In addition to having more zero values, the
forecast SA rainfall index percentiles are smaller than
the corresponding observed SA percentiles, indicating
model bias and that forecast values of the SA rainfall
index should not be directly compared with observed
values.
4. Forecasts of the April–May 2013 flooding event
A slow-moving frontal system around the end of April
and beginning of May 2013 caused heavy rain, hail, and
damaging wind, and resulted in widespread flooding
over the Arabian Peninsula. The extreme rainfall
resulted from the interaction of an upper-level trough,
the low-level Red Sea trough, and cross-equatorial
moisture transport (A. J. de Vries et al. 2014, personal
communication). TRMM estimates shown in Fig. 7a for
the period from 27 April to 1 May 2013 indicate heavy
rainfall (.50 mm) over wide areas of Saudi Arabia,
Yemen, and Iran, with rainfall amounts exceeding
70 mm in many regions. A CFS forecast of the total
FIG. 6. Cumulative distribution functions of the observed and forecast SA rainfall index for the (a) wet and (b) dry
seasons. CFS forecast with leads of 1–5 (brown), 6–10 (blue), and 11–15 days (green) are shown.
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FIG. 7. (a) Total TRMM-estimated rainfall from 27 Apr to 1 May 2013. (b) Total CFS forecast rainfall from 27 Apr
to 1 May 2013 for the forecast started at 0000 UTC 23 Apr 2013.
rainfall amount for the 5-day period from 27 April to
1 May 2013 (initialized at 0000 UTC 23 April 2013 and
given as the mean of four ensemble members with lead
times of 4–9 days) is shown in Fig. 7b and indicates
rainfall amounts and a spatial pattern similar to that
seen in the TRMM data.
It is encouraging that a particular CFS forecast run
skillfully indicated extreme rainfall with a lead time of
4 days. However, conclusions about the predictability,
even for a single event, cannot be based on a single
forecast. We compute 6-hourly forecast values of the SA
rainfall index (Fig. 8a) for different forecast times and
leads and compare them with the observed values
(Fig. 8b). Forecast values of the SA rainfall index are
arranged by target day (x axis) and lead time (y axis).
This arrangement of forecast values was used in Tippett
et al. (2012) and Barnston et al. (2012) for ENSO forecasts and permits the visualization of a large number of
forecast runs in a way that emphasizes forecast timing
and consistency from one forecast to another. The earliest forecast start date shown is 27 March 2013. Vertical
features in the figure are an indication of forecast consistency, that is, consistency between forecasts with
different start times but the same forecast target (verification) time. Large values of the observed daily SA
rainfall index are seen beginning around 25 April and
continue through 7 May 2013 with one value reaching
5 mm day21. Forecasts with leads up to 10 days indicated
heavy rainfall (many 6-h periods with rain rates exceeding 4 mm day21), and forecasts with leads up to
20 days indicated a distinct transition from dry to wet
conditions. The largest forecast precipitation rate in any
6-h period exceeded 10 mm day21. The forecasts also
give an indication of the length of the rainfall event and
the transition back to dry conditions. There is a notable
indication of unrealistically extended wet conditions in
the longer-lead (greater than 10 day) forecasts.
A predictable feature of the climate system that may
be relevant to this rainfall event is the MJO, as discussed
in the introduction. ENSO conditions at this time were
neutral. Barlow et al. (2005) related tropical heating in
the Indian Ocean to the MJO to precipitation in the
region and found that negative values of RMM1 favored
precipitation in the region. Figure 9 indicates that the
RMM1 was negative during the April–May flooding
event, consistent with wet conditions in the region. From
about 20 April 2013 until the end of the month, the MJO
was in phase 8, but mostly with weak amplitude. By the
end
of the month, the MJO magnitude, defined as
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
RMM12 1 RMM22 , was ;1. During the period 1–5 May
2013, the MJO remained strongly in phase 1 with a magnitude between 1 and 2.
5. Reforecast skill
We now examine CFS forecasts of the SA rainfall
index over the 12-yr period (1999–2010). Figure 10
shows CFS forecasts for 3 yr (2007–09) of this period,
arranged as in Fig. 8 as a function of lead time and target
date along with the corresponding TRMM SA rainfall
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FIG. 9. Values of the RMM indices from 20 Apr to 15 May 2013.
April (May) dates are shown in black (gray). Corresponding phases
1–8 are indicated.
FIG. 8. (a) The 6-hourly CFS SA rainfall index as a function of
target (x axis) and lead (y axis) time and (b) the daily TRMM SA
rainfall index (mm day21) for target times from 27 Mar to 26 May
2013. In (a), forecast amounts in the intervals 0–0.125, 0.125–1, 1–4,
and .4 mm day21 are shown in light brown, green, purple, and red,
respectively.
estimates. There is a clear visual qualitative correspondence between forecasts and observed values of the SA
rainfall index over the period shown. There are several
cases when the forecasts consistently indicate wet conditions 10 or more days in advance of the occurrence of
wet conditions. Intense rainfall events are captured to
some extent by the forecasts. Transitions between wet
and dry periods are also well represented in the forecasts. There are a number of cases, especially in August,
when longer-lead (greater than 10 days) forecasts indicate substantial rainfall, while little or scant rainfall is
forecast at shorter leads, a feature consistent with the
excess rainfall in the longer-lead forecast climatology
seen earlier in Fig. 3.
Quantitative measures of the skill (rank correlation)
of the deterministic forecasts of rainfall amount and
number of days exceeding 0.25 mm day21 are shown in
Fig. 11 as a function of lead time for forecast target
windows ranging in width from 1 to 30 days. The maximum lead time shown depends on the forecast window,
with forecasts for 30-day windows having a maximum
lead of about 15 days. The correlations for amount and
for number of days exceeding the threshold are qualitatively similar in the wet season. At the shortest leads,
increasing the forecast window width initially increases
skill, but eventually as the forecast window expands to
include increasingly distant target time, skill decreases.
For both quantities, forecasts of 5-day windows have the
highest skill initially (closely followed by forecasts of 10-day
windows), and forecasts of 30-day windows have correlations of nearly 0.6 at the shortest lead. Skill at the
longer leads increases as the forecast window increases
and decreases as lead increases. However, skill for
forecast windows greater than 10 days decreases more
slowly during the wet season than that of short windows
especially for longer leads. This distinction is less evident during the dry season, suggesting different predictability mechanisms. The skill during the wet season
is greater than during the dry season for both quantities,
with the wet season advantage greater in the case of the
forecasts of exceedance days.
Figure 12 shows the Brier skill score for forecasts of
the probability of heavy rainfall occurrence based on
lagged ensemble and logistic regression. This quantity is
challenging to forecast, and even in the wet season when
skill is higher, there is only modest, if any, skill for leads
greater than 10 days. In the dry season, skill drops
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FIG. 10. CFS forecasts (colors) of the SA rainfall index as a function of target (x axis) and lead
(y axis) time for the period 2007–09 as well as TRMM estimates (line plots). Forecast amounts
greater than 0, 0.02, and 0.2 mm are shown in light brown, green, and purple, respectively.
sharply with lead, and there is little skill for windows
greater than 5 days, even with the logistic regression.
Logistic regression increases forecast skill, especially for
leads of less than 10 days during the wet season. The
Brier skill score of the first lead 15-day forecast increases
from 0.2 to more than 0.3 with logistic regression. The
benefit of the logistic regression is limited to the first
couple of leads and the shorter windows (5 days or less)
during the dry season.
We can understand how logistic regression improves
probabilistic forecast quality by considering reliability.
Figure 13 shows reliability and ROCs for the shortest
lead lagged-ensemble and logistic regression probability
forecasts of heavy rainfall during a 15-day window. The
lagged ensemble probability forecasts show substantial
overconfidence in the sense that heavy rainfall occurs
more (less) often in the wet season than low (high)
forecast probability values would indicate. For instance,
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1101
FIG. 11. Rank correlation as a function of lead time (days) for forecasts of the (a),(b) SA rainfall index and
(b),(d) number of days for which the SA rainfall index exceeds the threshold 0.25 mm day21 for the (left) wet and
(right) dry seasons.
when the forecast probability is 0% (80%), heavy rainfall occurs about 20% (65%) of the time. This problem
of overconfidence is more severe in the dry season.
Some of the overconfidence is likely due to the quantization of probabilities by the four-member ensemble,
evident in the forecast issuance frequencies. Despite the
overconfidence, the ROCs indicate that the lagged ensemble probabilities are able to discriminate fairly well
between occurrence and nonoccurrence, with the discrimination (as measured by the area under ROC) being
greater during the wet season. The logistic regression
probabilities are considerably more reliable. Dry season
logistic regression probabilities of heavy rainfall do not
exceed 20%, while in the wet season they nearly cover
the range of possible values. Logistic regression has a
modest impact on the wet season ROC, which suggests
that the primary result of the logistic regression is to
temper the forecast probabilities in a manner that
mostly preserves their ordering. Logistic regression has
the potential to correct for lead-dependent and other
systematic biases in the forecast model output. Greater
improvement from the logistic regression is seen in the
dry season ROC.
To connect forecast skill with the MJO phase, Fig. 14
shows first-lead logistic regression forecast probabilities for
heavy rainfall during the subsequent 5-day window conditional on the MJO phase. The MJO phase used is the value
from 3 days before the start
of the forecast, andffi only cases
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
with RMM magnitude ( RMM12 1 RMM22 ) . 1 are
considered. During the wet season, average forecast probabilities of heavy rainfall have a strong dependence on MJO
phase. During phases 1, 2, 7, and 8, the average forecast
probabilities for heavy rainfall are significantly greater than
the unconditional average of 22.3%. On the other hand,
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FIG. 12. Brier skill scores for forecasts of the probability of exceeding a threshold. Probability computed from
a (a),(b) lagged ensemble and (c),(d) logistic regression for the (left) wet and (right) dry seasons.
forecasts for heavy rainfall are significantly less than the
unconditional average during phases 3–5. Phase 6 shows no
signal. The results for all cases, as well as other lags, are
qualitatively similar with consistent phase shifts. The same
analysis shows no statistically significant relation between
forecast probabilities and MJO phase during the dry season. While we do not expect the MJO to explain variations
in CFS forecast signals completely, it is reassuring to see
that the forecast signal is modulated by the MJO phase and
that modulation is consistent with previous analyses of the
precipitation variability of the region.
6. Summary
The climate of Saudi Arabia is arid–semiarid, and
rainfall occurrence is infrequent and scattered (Abdullah
and Al-Mazroui 1998). However, when rainfall does occur in the region, it is sometimes intense and causes
flooding, loss of life, and damage to property. The serious
consequences of heavy rainfall in the region make its
prediction important. Several studies have related precipitation in the region to remote forcing, especially
tropical convection related to ENSO and the MJO
(Barlow 2012; Hoell et al. 2012, 2013, 2014; Athar 2015;
Kang et al. 2015). These climate signals are predictable,
and based on the predictability of the MJO, it has been
proposed that rainfall in the region should be predictable
up to 2–3 weeks in advance (Barlow et al. 2005). However, to this point there has been no assessment of the
extent to which this predictability is realizable either in
statistical or dynamical forecasts.
The NOAA Climate Forecast System (CFS), version
2, is a state-of-the-art coupled global ocean–atmosphere
model used to produce forecasts out to 9 months (Saha
et al. 2014). The CFS has good skill in predicting ENSO
and the MJO (Zhang and van den Dool 2012; Barnston
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1103
FIG. 13. Reliability diagrams of (a) lagged ensemble and (b) logistic regression first-lead probability forecasts of
heavy rainfall over the subsequent 15-day window; inset histograms indicate the forecast issuance frequency. Corresponding ROCs for (c) lagged ensemble and (d) logistic regression probability forecasts.
and Tippett 2013; Wang et al. 2014) and therefore has
the potential to forecast the region teleconnections associated with these signals. Here, we have taken advantage of the extensive CFS reforecast dataset with
6-hourly forecast starts over a 12-yr (1999–2010) period
to document the ability of the CFS to forecast arealaveraged Saudi Arabian rainfall (SA rainfall index).
While there are deficiencies in the forecast climatology
likely related to orography and resolution, as well as
lead-dependent biases, CFS represents the climatology
of the region both in terms of spatial patterns and the
annual cycle reasonably well.
A motivation for this work was the heavy rainfall that
occurred between the end of April and the beginning
May 2013, which resulted in widespread flooding over
the Arabian Peninsula. We find that the CFS was able to
predict features of the 2013 event well, although not the
local intensity. Forecasts indicated heavy rainfall up to
10 days in advance of the event and a distinct transition
from dry to wet conditions up to 20 days in advance.
Analysis of the reforecasts shows that the CFS can
skillfully predict rainfall amount, the number of days
exceeding a threshold, and the probability of heavy
rainfall occurrence for varying forecast windows. Heavy
rainfall occurrence is the more difficult quantity to
forecast, and skill is markedly lower in the dry season
(May–October). While the probability forecasts of
heavy rainfall occurrence show good discrimination, the
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FIG. 14. Average first-lead logistic regression forecast probabilities of heavy rainfall during the subsequent 5 days
stratified by the MJO phase 3 days prior to the start of the (a) wet and (b) dry seasons. Heavy and light dashed lines
show the unconditional mean and its 95% confidence intervals, respectively, based on the number of forecasts in
each phase.
probability values indicate overconfident forecasts. We
demonstrate that logistic regression with the ensemble
mean value as a predictor improves forecast skill and
reliability. Forecast probability signals are found to
have a clear relation with MJO phase in the wet season
(November–April) consistent with previous variability
analyses on interseasonal and intraseasonal time scales,
providing a physical basis for observed forecast skill.
Acknowledgments. This study was supported in
part by NOAA Awards NA12OAR4310091 and
NA14OAR4310184 and Office of Naval Research
Award N00014-12-1-091. The views expressed herein
are those of the authors and do not necessarily reflect
the views of NOAA or any of its subagencies.
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