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1
Trend analysis by a piecewise linear regression model
1
applied to surface air temperatures in Southeastern Spain
2
(19732014)
3
4
Pablo Campra
1
, Maria Morales
2
5
1
Engineering School D2.36, University of Almeria, Almeria 04120, Spain
6
Correspondence to: Pablo Campra, pcampra@ual.es
7
2
Mathematics Department. University of Almeria, Almeria 04120, Spain
8
9
Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
Manuscript under review for journal Nonlin. Processes Geophys.
Published: 30 May 2016
c
Author(s) 2016. CCBY 3.0 License.
2
Abstract: The magnitude of the trends of environmental and climatic changes is mostly derived from the
1
slopes of the linear trends using ordinary leastsquare fitting. An alternative flexible fitting model,
2
piecewise regression, has been applied here to surface air temperature records in southeastern Spain for
3
the recent warming period (19732014) to gain accuracy in the description of the inner structure of
4
change, dividing the time series into linear segments with different slopes. Breakpoint years, with
5
confidence intervals (CIs), were estimated and separated periods of significant trend change were
6
determined. First, simple linear trends for mean, maximum and minimum surface air temperatures and
7
diurnal temperature range (DTR) from the four longest and most reliable historic records in SE Spain
8
were estimated. All series in the region showed intense linear warming signs during the period 1973
9
2014. However, updated warming trends were lower than those previously cited for the region and Spain
10
from the 1970s onwards. Piecewise regression model allowed us to detect breakpoints in the series, and
11
the absence of significant trends in the most recent period of the segmented fits for two stations. In
12
general, piecewise regression model showed better fit than simple linear regression model, and thus,
13
showed a better description of temperature variability.
14
15
Keywords: temperature trends; piecewise regression; segmented regression; Southeastern Spain; regional
16
climate change; warming slowdown;
17
18
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Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
Manuscript under review for journal Nonlin. Processes Geophys.
Published: 30 May 2016
c
Author(s) 2016. CCBY 3.0 License.
3
1. Introduction
1
2
Trend analysis is useful for a better understanding of climate change and variability. The estimation of
3
simple linear trends is the most straightforward assessment of the longterm behavior of a time series in
4
climate change studies. However, due to changes in the trends, realworld time series do not generally fit
5
in a straight line. Thus, simple linear regression may be misleading, as it does not describe the inner
6
structure of change in the series, ignoring the existence of significant changes in the slope of the linear fit,
7
called breakpoints. Such simple linear trends may be illogical and physically meaningless for climatic
8
data analyses, where the linearly fitted trend makes little sense, for the underlying mechanisms of global
9
climate change are likely to be nonlinear and nonstationary, so other methods of time series analysis
10
might be advisable (Seidel and Lanzante, 2004; Wu et al, 2007; Sefidmadgi et al, 2014). In particular,
11
linear trend does not adequately describe lowfrequency behavior of temperature time series (Karl et al.,
12
2000). Piecewise regression model fits a nonlinear function with a non constant rate of change, and has
13
been applied to analyze time series of different climatic variables to detect breakpoints in linear trends.
14
Karl et al, (2000), identified the timing of change points in global temperature time series by minimizing
15
the residual sum of squares of all possible combinations of four line segments representing time intervals
16
of 15 years or more. Tome and Miranda (2004) adapted that fitting method to develope an algorithm for
17
fitting a continuous regression model with several break points to data and then it was applied local
18
changes in temperature, precipitations and the NAO index in Portugal. Liu et al. (2010) used the same
19
method to find partial trends of wind variability in the mesosphere and the lower thermosphere over a
20
local observatory at Collm, Germany.
21
22
Piecewise regression is a method of regression analysis where the response variable is split in two or
23
more intervals, and a line segment is fitted to each interval, with the constraint that the regression function
24
will be continuous. Each line is connected at an unknown value called breakpoint. Piecewise regression is
25
suitable for situations where the response variable shows abrupt changes within a few values of the
26
explanatory variable, (Toms and Lesperance, 2003). This flexible regression method is scarcely used in
27
the analysis of long term trends of climatic variables, though in many cases it offers a better fit to the
28
records, and shows better compliment with the assumptions of regression analysis.
29
30
Here we have applied to regional temperature records from SE Spain an alternative fitting approach for
31
long term climatic series, piecewise or segmented regression. SE Spain includes some of the most semi
32
arid areas in the Northern Mediterranean, with increased vulnerability to projected shifts in global
33
circulation and pressure patterns, so it is of great interest the characterization and update of longterm
34
trends in this area. Climate change projections for the Mediterranean region show that hightemperature
35
conditions are generally expected to increase in the future (Giorgi and Lionello, 2008; Jacobeit et al.,
36
2014). Over the Iberian Peninsula, significant high rates of surface air temperature warming have been
37
recorded by the Spanish Meteorological Agency (AEMET) from the early 1970s onward, in accordance
38
with the last period of accelerated global warming (Hartmann et al., 2013). For instance, Brunet et al.
39
Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
Manuscript under review for journal Nonlin. Processes Geophys.
Published: 30 May 2016
c
Author(s) 2016. CCBY 3.0 License.
4
(2007) estimated recent average rates of warming for Spain during 19732005 of 0.48 ºC decade
1
for
1
mean temperatures (T
mean
), with 0.51 and 0.47 ºC decade
1
for maximum (T
max
), minimum (T
min
)
2
temperatures respectively. Del Rio et al. (2012) reported rates of around 0.3 °C decade
1
in over 90% of
3
Spanish weather stations for the period 19612006. However, most studies just have a limited spatial or
4
temporal coverage, and a scarce number of studies have estimated recent changes in longterm mean
5
annual temperature trends in Spain from the early 1970s into the 2010s (El Kenawy et al., 2012; Turco et
6
al., 2014; GonzalezHidalgo et al., 2015). In particular, assessments of observed changes in SE Spain are
7
scarce. FernándezMontes and Rodrigo (2015) have recently reported temperature trends in SE Spain for
8
the period 19702007, estimating increases in T
min
and T
max
in most of the region of 1.2 and 0.5 ºC
9
decade
1
respectively. However, no update of SE Spain temperature trends including recent 2010s years
10
has been reported to date.
11
12
Longterm global warming has been unequivocal from mid 1970s to 2013, with an average global trend
13
of 0.2 ºC decade
1
(Hansen et al., 2010; Lawrimore et al., 2011; Jones et al., 2012; Rohde et al., 2013;
14
Turco et al., 2015). However, recent warming trends throughout the planet have either decreased or lost
15
statistical significance in many regional series in the planet from around 1997 (Easterling and Wehner,
16
2009; Kaufmann et al., 2011), though temperatures still remain well above the longterm average. Recent
17
observations and global averages show a significant decrease in the warming trend from 0.12 °C decade
1
18
in the period 19512012 to 0.05 °C decade
1
in 19982012 (Hartmann et al., 2013). Nevertheless, such
19
slowing for a decade or so has been seen in past observations and has been properly simulated in climate
20
models (Met Office, 2013). Surface air temperatures are characterized by wide spatial and temporal
21
variability (Lovejoy, 2014; Steinmann et al., 2015, Turco et al., 2015), and there is a need to determine
22
local and subregional trends and variability to gain knowledge of global climate change patterns.
23
24
A simple eye inspection of the main temperature records in SE Spain suggest a possible breakpoint year
25
at every series from the early 1990s (Fig. 1), showing decreased rates of warming since then. In order to
26
detect these breakpoints we have used a piecewise regression approach, estimating the continuous set of
27
straight lines that better fits every time series of annual T
mean
, T
max,
T
min
, and diurnal temperature range
28
(DTR), deriving confidence intervals (CIs) for the breakpoint estimates. The main goals of this work
29
were: first use a simple linear regression model to update the longterm warming trends of air surface
30
temperatures at AEMET first order stations in SE Spain from the year 1973 to 2014; and second, to test
31
the goodness of fit and prediction skills of a piecewise regression model compared to simple linear
32
regression applied to the same period. Our main interest in this work is to discuss if there is a recent
33
significant breakpoint in longterm warming trends in SE Spain, and whether it is statistically consistent
34
with the long term warming, likely to happen superimposed on the longerterm warming trend, or whether
35
the last records might represent a key emerging changepoint in long term trends at the area.
36
37
2. Data temperature series
38
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Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
Manuscript under review for journal Nonlin. Processes Geophys.
Published: 30 May 2016
c
Author(s) 2016. CCBY 3.0 License.
5
We have selected four meteorological stations with the longest, continuous and most reliable records in
1
SE Spain (Table 1): Almeria (AL), Granada (GR), Malaga (MA), and MurciaSan Javier (MU). These
2
stations are wellspaced across SE Spain (Fig. S1), with a minimum linear distance of 90 Km (between
3
GR and MA), and maximum of 340 km between MA and MU, below the threshold of 400 km that has
4
been suggested as optimal for building a representative meteorological network in Spain (PeñaAngulo et
5
al., 2014). AL, MA and MU are representative of coastal Mediterranean climate, while GR shows a
6
“continentalized” inland Mediterranean climate, with higher extremes of warm and cold days in summer
7
and winter, respectively. Their records cover at least from 1973 to 2014, including the recent period of
8
accelerated global warming from the 1970s that we intended to analyze in our area of study. These
9
stations are located within international airports, and belong to the first order (synoptic) network of the
10
Spanish official meteorological agency (AEMET). This selection was based on potential data quality
11
from highly monitored sites and goodquality records controlled by the Servicio de Desarrollos
12
Climatológicos (SDC, Climatological Branch) of AEMET. Raw data of daily T
max
and T
min
have
13
undergone quality control checks to avoid syntax, internal consistency and temporal coherence errors, and
14
controls of extreme thresholds and spatial coherency. Additionally, these records have been extensively
15
analyzed for artificial inhomogeneities in previous studies (Brunet et al., 2008; Staudt et al., 2007).
16
17
3. Regression methods
18
19
3.1. Simple linear regression
20
21
As a first conventional approach to detect temperature change, simple linear regression was applied to the
22
series. Trends and their 95% CIs were estimated by least squares linear regression. Linear trends were
23
estimated in every series from the slopes of the fit using values of annual averages of T
max
, T
min
,
T
mean
and
24
DTR, calculated from monthly means provided by AEMET.
25
26
3.2. Piecewise regression
27
28
However, when the residuals of simple linear fits for each T
mean
series were tested for the assumptions of
29
normality, independence, homoscedasticity and linearity, it turned out that: a) homoscedasticity was is not
30
met by GR station; b) the linear assumption was not verified by AL and MU residuals; c) the
31
independence assumption was rejected by LjunBox in AL. The violation of the homogeneous variance
32
assumption could result in unreliable estimates of the standard errors that might turn out in mistaken
33
conclusions over the slope. In these cases, heteroscedasticityconsistent (MacKinnon and White, 1985),
34
and autocorrelationconsistent estimators have been used (Newey and West, 1987). To solve these
35
problems, here we have tested and alternative regression model, piecewise regression. We have used a
36
segmented model between the mean response E(Y) and the explanatory variable Z, modeled by adding in
37
the linear predictor the terms. Eq. (1):
38
39
Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
Manuscript under review for journal Nonlin. Processes Geophys.
Published: 30 May 2016
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Author(s) 2016. CCBY 3.0 License.
6
(1)
1
2
where
1
is the slope of the left line segmented,
2
is the ‘differenceinslopes’, is the breakpoint, and
3
being I(A)=1 if A is true. In order to estimate the breakpoints
4
location, we use the approach suggested by Muggeo (2003) and at the R package ‘segmented’ (Muggeo,
5
2008). Karl et al. (2000) used this approach to obtain a better fit of global temperatures than simple linear
6
regression. Tomé and Miranda (2004) further developed an algorithm to identify best location for
7
breakpoints in climatic series. Here we have applied a piecewise regression model to those series where
8
there is enough statistical evidence to support the existence of breakpoints. Smoothed scatter plots were
9
used to provide the starting values for breakpoints in order to improve the convergence of the algorithm,
10
and we have checked the existence of a significant breakpoint by testing over the difference in slope
11
(Muggeo, 2003). We have employed the R package to estimate the parameters of the piecewise
12
regression in a deterministic way, and to fit linear segments to the data. The analysis of the residuals from
13
piecewise regression fits of our data showed that the assumptions of normality (ShapiroWilks and
14
AndersonDarling tests), independence (LjungBox test) and homocedasticity (BreuschPagan test) were
15
met by all the series, with the exception of GR. In this case, the robust variance estimator proposed by
16
MacKinnon and White (1985) was used. In order to test for a significant slope, we have applied a Wald’s
17
test. As general criteria, we have not estimated the slope of segments when they represented time
18
intervals of less than 5 years. As stated by Tome and Miranda (2005), “, if the first or the last breakpoint
19
happen near the minimum allowed position the result should be looked upon with some suspicion”. These
20
graphs are not shown in the figures at the results section. hh
21
22
3.3. Evaluation of regression models
23
24
We have compared both fitting and predicting performance of piecewise and simple linear models applied
25
to the whole length of data available for every series of T
mean
, T
max
, T
min
and DTR (Table 2). In order to
26
compare the goodnessoffit of the models, we calculated R
2
for each fit, and the residual standard error
27
(RSE) in order to avoid the artificial skill of R
2
. Also, we carried out a crossvalidation analysis (Hastie et
28
al., 2009) to compare the goodnessofforecasting skills among models. Thus, the data were divided into 5
29
roughly equalsized parts, and for the i
th
part, i=1,…,5, the model was fitted using the other 4 parts of the
30
data. The prediction error of the fitted model was estimated when predicting the i
th
part of the data.
31
Finally, the mean square error (MSE
CV
) of the 5 evaluation parts was calculated as forecasting skill
32
indicator. As we can observe in Table 2, piecewise regression showed a superior behavior both fitting and
33
forecasting compared to simple linear regression.
34
35
4. Results and discussion
36
37
Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
Manuscript under review for journal Nonlin. Processes Geophys.
Published: 30 May 2016
c
Author(s) 2016. CCBY 3.0 License.
7
A casual eye inspection of SE Spain temperature series for 19732014 suggests two periods of different
1
change rates (Fig. 1): a first period of intense warming, from 1973 until the early 1990s; and a second
2
period of lower or not significant rates of temperature increase from 1989 to 2014. The sharp drop in
3
1991, associated to Mt. Pinatubo eruption, was transient and widespread throughout the planet. As a first
4
approach, simple linear regression slopes for 19732014 showed average warming trends of T
mean
in the
5
range of 0.250.46 ºC decade
1
(Table 3), below average rates cited in previous studies for this area and
6
for Spain (Brunet et al., 2007; FernandezMontes and Rodrigo, 2015). However, these studies don’t cover
7
the most recent records of the 2010s, and they are difficult to compare with our results because of the
8
different areas, data sets and periods used (Brunet et al., 2007; Del Rio et al., 2012; GonzalezHidalgo et
9
al., 2015). In all stations except GR, mean annual DTR decreased at significant rates, between 0.25 and
10
0.36 ºC decade
1
, due to higher increases of T
min
(0.43/0.58 ºC decade
1
)
than T
max
. This trend in DTR is in
11
agreement with the expected “fingerprint” for global greenhouse warming (Hartmann et al, 2013), but is
12
opposite to the positive trend in annual DTR reported for Spain for the last decades (Galan et al., 2001;
13
Brunet et al., 2007; Del Rio et al., 2012). However, DTR reductions have been cited in Southern parts of
14
Spain (Horcas et al., 2001; Staudt et al., 2005; GonzalezHidalgo et al., 2015) and have been related to
15
T
min
increases driven by landuse changes. The physical interpretation of DTR trends, and the
16
contribution of local forcings due to landuse changes still remain a key uncertainty, and confidence in
17
this indicator has been defined as medium in reported decreases in observed DTR (Hartmann et al., 2013).
18
Spatial variability of trends in T
min
and T
max
was high, as described by with PeñaAngulo et al. (2014),
19
who detected in SE coastal Mediterranean areas the highest variability for mainland Spain, and again
20
suggested an association with the dramatic landuse changes by urbanization and agriculture at this coast
21
in the last decades. However, the two more distant stations, MA and MU, two coastal stations that lie 340
22
km away, showed comparable patterns of change for all variables, different to trends in GR and AL, with
23
higher rates of increase in all variables, and T
min
rates of increase of 0.5 ºC decade
1
. In GR no significant
24
change in longterm DTR was detected, with only slight differences in rates of warming for T
max
and T
min
,
25
in agreement with described patterns from 1970s for Spanish southern plateau (Galan et al., 2001), with a
26
continentalized Mediterranean climate that is more similar to GR climate than to coastal stations. AL
27
showed the lowest rates of warming in the area, probably related to the dramatic landcover change
28
towards greenhouse farming developed from the 1980s, resulting in the widest concentration of high
29
albedo greenhouses in the planet (Fig. S2). The alteration of the local energy balance by widespread
30
reflectivity increase has probably offset in this area the global forcing exerted by the increase of
31
greenhouse gases (Campra et al., 2008; Campra and Millstein, 2013). DTR decrease due to higher rates of
32
warming of T
min
than T
max
has been also associated to urbanization and land cover changes (Mohan and
33
Kandya, 2015). MA is the only station in this study that might have been affected by the rapid growth of
34
urban areas (Malaga city), and the recent growth of low albedo pavements around it by recent
35
development of taxiways and runways from 2005 (Fig. S3) (Fomento Ministry of Spain, 2007). This
36
recent land cover change around the station might have enhanced warming trends in this record,
37
increasing heat retention properties of the surface (McKitrick and Michaels, 2007). In GR and MU, little
38
increase in urbanization has been produced around the stations, located in international airports far from
39
Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
Manuscript under review for journal Nonlin. Processes Geophys.
Published: 30 May 2016
c
Author(s) 2016. CCBY 3.0 License.
8
the growing cities, so trends in temperatures and DTR cannot be clearly associated here to local land
1
cover changes. Besides these local factors, the influence of the Mediterranean is a key forcing of SE
2
Spain temperature records. Observations of Mediterranean surface temperature indicate strong warming
3
from 1973. The average rate of warming at Western Mediterranean was 0.22 ºC decade
1
over 19732008
4
(Skirlis et al., 2012). The Alboran Sea surrounding SE Spain showed an averaged warming trend of 0.31
5
C decade
− 1
on 19822012 (Shaltout and Omstedt, 2014).
6
7
Alternatively, piecewise regression model from the full historic records available at each station offered a
8
better fit to the data in all temperature series (Fig. 2), showing that this model represents the observations
9
more accurately than the simple linear regression model generally used to describe climatic trends. As a
10
general criteria, in figures 2, 3 and 4 we have not represented piecewise regressions where last segment
11
are less than 5 years long. Uncertainty analysis of piecewise regression fits for every series and variable
12
are given in Tables S1S4. This flexible regression model allowed for detection of several trend change
13
points, located in different years for every series and for every variable (Table 4). Recent T
mean
trends
14
were not significant from these breakpoints in AL and GR. In MU, T
mean
increase was less intense since
15
the 1982 breakpoint (Table 5). On the contrary, a breakpoint in 2013 was found in T
mean
in MA driven by
16
the historic T
mean
record in 2014 (Table 4).
17
18
In order to identify the components of change of T
mean
, we have carried out additional piecewise
19
regression fits to T
max
and T
min
(Table 6). Breakpoints in both T
max
and T
min
were detected for all series
20
except MA (Fig. 3). DTR showed decreasing trends in the last segments of AL and MU (Fig. 4), but
21
recent breakpoints towards increasing DTR have appeared in MA (2012) and GR (2011), though only
22
significant at 10% (figures not shown) (Table 6). However, we found no signs in our data of the pattern of
23
change in described in global DTR, characterized by a decline and subsequent increase from a breakpoint
24
in mid 1980s, associated to global dimming and subsequent brightening (Wild et al., 2007). (Table 6). In
25
AL, the 1989 breakpoint in T
mean
was driven by a significant fall of T
max
from 1987, further maintained by
26
the later stabilization of T
min
(with no significant trend from 1998). As a consequence of these trends, AL
27
station showed the highest recent rates of DTR reduction in the area (0.61 ºC decade
1
since 1982),
28
probably due to local land cover changes stated before. In GR, the 1997 breakpoint in T
mean
was driven by
29
stabilization of T
min
, with no significant trend from 1997. In MU a breakpoint was located around the
30
early 1980s in both T
max
and T
min
, coincident with T
mean
breakpoint. No significant breakpoints in T
max
and
31
T
min
were detected in MA, showing a continuous warming trend during the period of study, along with the
32
highest simple linear rates in the region (+0.46 ºC decade
1
). MA is the only series that shows no clear
33
signs of warming slowdown in T
min
and T
max
in recent years. Furthermore, a 2013 breakpoint was
34
detected in T
mean
, due to 2014 breaking record, increasing longterm rates of warming. A similar 2013
35
breakpoint was shown by T
max
in GR. Our regression analyses does not allow us to suggest that these
36
recent breakpoints are signs of a future increase in warming trends in these stations, and this might lead to
37
failed conclusions when piecewise segments length is not long enough (Karl et al, 2000).
38
39
Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
Manuscript under review for journal Nonlin. Processes Geophys.
Published: 30 May 2016
c
Author(s) 2016. CCBY 3.0 License.
9
5. Conclusions
1
2
Simple linear trends of temperatures at SE Spain for the period 19732014 reported here are consistent
3
with the magnitude of warming described previously for the region. However, our results show that the
4
generalized use of simple linear regression fits for the estimation of long term trends might not be
5
sufficiently accurate to describe the structure of change of temperatures in longterm series, while flexible
6
models such as piecewise regression provide better fits, and allows the detection of key breakpoints in the
7
trends. Besides, the method is also much simpler and easier to interpret than most nonlinear function
8
fitting. By flexible regression, we have detected a recent slowdown in longterm warming trends in three
9
of the four main records in SE Spain, with no significant trends in T
mean
in the most recent segments of
10
two of them (AL and GR). No matter the uncertainty in the exact location of breakpoints reported here,
11
given by 95% CIs (Table 4), we have shown statistical evidence of the presence of such reduction in
12
warming rates in the area, consistent with previous reports of recent decreasing warming trends in global
13
series. However, and given the limited length of the observations, we cannot suggest by our analysis that
14
the absence of statistically significant warming in the most recent segments of piecewise regression
15
model are necessarily inconsistent with historic variability of the series studied. Furthermore, recent
16
breakpoints observed in MA and GR, might be signing increasing warming trends in the future, enhanced
17
by 2014 global historic record (Jones, 2015), yeartodate global temperatures (up to June 2015) (NOAA,
18
2015a). Spatial differences in longterm trends and breakpoints location might be due to undetermined
19
local dynamics in climate and/or forcings that still remain to be determined in every station, or just simply
20
due to natural variability. To obtain statistical evidence about possible causes of the slowdown in
21
warming rates in the area, future investigations should search for cobreaks and overlapping CIs in the
22
break dates detected at the historic series of key local forcings (Estrada et al, 2013), helping to explain the
23
observed nonlinear trends, and the location of the trend changing points in the temperature series
24
described here. It must also be taken into account that the method of piecewise regression is strongly
25
dependent on the first guesses and imposed parameters such as minimum time distance between
26
breakpoints, and minimum trend change between breakpoints (Tome and Miranda, 2005).
27
Complementary to this search of statistical relationships, recent simulation studies with optimized
28
treatment of global climate forcings have shown better insight to possible causes of a possible slowdown
29
in global warming (Smith et al., 2014).
30
31
Author contribution. P. Campra designed the scope of the research, performed the simple linear
32
regressions and wrote the manuscript, and M. Morales carried out all deep statistical analyses, residuals
33
tests and developed the piecewise regression model in R.
34
35
Acknowledgements: We thank the Ministry of Economy and Competitiveness (MINECO) of the Spanish
36
Government, and FEDER Funds from European Union for the Grant CGL201346873R that has
37
supported this work. The authors would like to acknowledge AEMET (Spanish Meteorological Agency)
38
for providing data used in this work.
39
Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
Manuscript under review for journal Nonlin. Processes Geophys.
Published: 30 May 2016
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Author(s) 2016. CCBY 3.0 License.
10
1
Supporting Information
2
3
Map of location of stations in SE Spain, picture of greenhouses land cover around AL station, picture of
4
MA airport new taxiways. Tables of uncertainty estimates of piecewise regression of mean, maximum,
5
minimum and DTR temperature series. This material is available free of charge via the Internet at …
6
7
8
9
Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
Manuscript under review for journal Nonlin. Processes Geophys.
Published: 30 May 2016
c
Author(s) 2016. CCBY 3.0 License.
11
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16
Table 1. First order Spanish Meteorological Agency (AEMET) stations in SE Spain.
*
Length of 2m
1
temperature records available.
2
ALMERIA (AL)
GRANADA
(GR)
MALAGA
(MA)
MURCIA
(MU)
Location
36° 50' 47'' N
2° 21' 25'' W
37° 11' 23'' N
3° 47' 22'' W
36° 39' 58'' N
4° 28' 56'' W
37° 47' 20'' N
0° 48' 12'' W
Altitude (msl.)
21
567
5
4
Length
*
19722015
19732015
19502015
19462015
3
4
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17
Table 2. Goodnessoffit test (R
2
/RSE), and predictive value (MSE
CV
) of the two regression models for T
mean
,
1
T
max
, T
min
y DTR. R
2
= coefficient of determination; RSE= residual standard error; MSE
CV
= mean square
2
error for crossvalidation.
3
PIECEWISE
SIMPLE LINEAR
R
2
RSE
MSE
CV
R
2
RSE
MSE
CV
T
mean
AL
0.60
0.32
0.14
0.40
0.39
0.14
GR
0.42
0.53
0.29
0.36
0.55
0.32
MA
0.76
0.33
0.12
0.74
0.34
0.12
MU
0.67
0.38
0.15
0.59
0.42
0.19
T
max
AL
0.52
0.37
0.17
0.03
0.52
0.27
GR
0.39
0.64
0.32
0.28
0.68
0.33
MU
0.57
0.31
0.10
0.49
0.33
0.12
T
min
AL
0.70
0.36
0.17
0.67
0.38
0.27
GR
0.40
0.58
0.38
0.29
0.62
0.45
MA
0.79
0.38
0.30
0.79
0.37
0.26
MU
0.66
0.53
0.28
0.58
0.58
0.38
DTR
AL
0.73
0.35
0.16
0.46
0.49
0.24
GR
0.21
0.62
0.38
0
0.69
0.47
MA
0.53
0.31
0.11
0.49
0.32
0.11
MU
0.46
0.42
0.18
0.41
0.43
0.20
4
5
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18
Table 3. Change in annual mean (T
mean
), maximum (T
max
), minimum temperatures (T
min
), and diurnal
1
temperature range (DTR), estimated as the slope of a simple linear regression fit (in ºC decade
1
), and
2
associated 95% confidence intervals (CI) for the recent warming period 19732014, at SE Spain first order
3
AEMET stations. Not significant values in italics (p>0.05).
4
Station
Tª series
Decadal coefficient (ºC)
95% CI
AL
T
mean
0.25
(0.15/0.36)
T
max
0.07
(0.07/0.2)
T
min
0.43
(0.34/0.53)
DTR
0.36
(0.49/0.24)
GR
*
T
mean
0.33
(0.19/0.48)
T
max
0.34
(0.17/0.52)
T
min
0.32
(0.16/0.48)
DTR
0.02
(0.16/0.20)
MA
T
mean
0.40
(0.30/0.51)
T
max
0.26
(0.18/0.35)
T
min
0.55
(0.40/0.70)
DTR
0.29
(0.4/0.18)
MU
T
mean
0.46
(0.37/0.55)
T
max
0.34
(0.24/0.43)
T
min
0.58
(0.48/0.68)
DTR
0.25
(0.34/0.17)
5
6
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19
Table 4. Breakpoint estimates and 95% CIs for annual T
mean
, T
max,
T
min
and DTR series in SE Spain. Values in
1
italics are not significant at 5% level.
+
Significant at 10%
2
3
4
Station
T
mean
T
max
T
min
DTR
AL
1989 + 5.3
1987 + 3.4
1998 + 11.4
1982 + 2.6
GR
1997 + 11.8
2013 + 1.0
1997 + 9.2
2011 + 2.3
MU
1982 + 5.7
1983+ 7.2
1981 + 5.0
1981 + 4.1
+
MA
2013 + 1.2
+

1977 + 10.7
2012 + 3.2
+
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20
Table 5. Trends in ºC decade
1
of annual mean temperature change (T
mean
) from simple linear regression fit
1
(SL) for each station (in bold), compared to the two successive subperiods defined by piecewise (PW)
2
regression. Trend values in italics are not significant at 5% level. *Breakpoint was detected in 2013 and no
3
segmented regression periods are reported.
4
Station
Regression
model
Period
Estimate
95% CI
AL
SL
19732014
0.25
(0.15/0.36)
PW
1
19731989
0.76
(0.51/1.0)
PW
2
19892014
0.07
(0.15/0.14)
GR
SL
19732014
0.33
(0.19/0.48)
PW
1
19731997
0.55
(0.34/0.76)
PW
2
19972014
0.03
(0.57/0.51)
MU
SL
19732014
0.40
(0.30/0.51)
PW
1
19731982
1.28
(0.69/1.87)
PW
2
19822014
0.27
(0.14/0.4)
MA
*
SL
19732014
0.46
(0.37/0.55)
5
6
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21
Table 6. Trends in ºC per decade of annual maximum (T
max
) and minimum (T
min
) temperature anomalies and
1
diurnal temperature range (DTR) for the periods defined by piecewise (PW
13
) regression model. Trend values
2
in italics are not significant at 5% level.
+
Significant at 10%
3
Station
T
max
T
min
DTR
AL
Breakpoint
1987
1998
1982
PW
1
1.08
0.58
1.31
PW
2
0.32
0.16
0.61
GR
Breakpoint
2013
1997
2011
PW
1
0.29
0.63
0.09
PW
2

0.18

MU
Breakpoints
1983
1981
1981
+
PW
1
0.82
1.92
1.01
PW
2
0.16
0.38
0.20
MA
Breakpoint


2012
+
PW
1


0.28
PW
2



4
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22
1
2
Figure 1. Mean annual temperature anomaly series (ºC) from 19732014 at SE Spain First order stations of the
3
Spanish official meteorological network (AEMET). Reference period: 19812010. AL=Almeria; GR=Granada;
4
MA=Malaga; MU=Murcia
5
6
7
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23
1
Figure 2. Piecewise regression fitting of historic records of mean annual temperature anomalies (ºC) in SE
2
Spain. Only those series with last segment > 5 years are shown. AL=Almeria; GR=Granada; MU=Murcia.
3
4
5
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24
1
Figure 3. Piecewise regression fitting of historic records of annual average maximum (Tmax) and minimum
2
(Tmin) temperature anomalies (ºC) in SE Spain stations. Only those series with last segment > 5 years are
3
shown. AL=Almeria; GR=Granada; MU=Murcia.
4
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25
1
2
Figure 4. Piecewise regression fitting of historic records of diurnal temperature range (DTR) in ºC in SE Spain
3
stations. Only those series with last segment > 5 years are shown. AL=Almeria; MU=Murcia. (MA and GR
4
series not shown)
5
6
Nonlin. Processes Geophys. Discuss., doi:10.5194/npg201629, 2016
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