Atmospheric Research 137 (2014) 228–244
Contents lists available at ScienceDirect
Atmospheric Research
journal homepage: www.elsevier.com/locate/atmos
Simulation of the PDO effect on the North America summer
climate with emphasis on Mexico
Víctor M. Mendoza a,⁎, Berta Oda a, René Garduño a, Elba E. Villanueva a, Julián Adem a,b
a
b
Centro de Ciencias de la Atmósfera, UNAM, Ciudad Universitaria, 04510 México DF, Mexico
Member of El Colegio Nacional, Mexico
a r t i c l e
i n f o
Article history:
Received 3 April 2013
Received in revised form 7 October 2013
Accepted 8 October 2013
Keywords:
Energy balance model
Simulation
PDO phases
Summer temperature
Precipitation
Circulation
a b s t r a c t
Five composite anomaly fields (CAF) are built for the summer of each Pacific decadal oscillation
(PDO) phase: skin temperature; air temperature (T7), zonal (u7) and meridional (v7) wind at the
700 mb level; and precipitation (R).
An energy balance model, named thermodynamic climate model (TCM), is integrated on the
NH to compute the summer anomalies (sub-index A) of the land surface temperature (LST),T7,
u7, v7, R and cloudiness (ε). To study the effect of the PDO phases on Mexico's climate, the CAF
of the sea surface temperature (SST) is used in the TCM as an input. The output fields are
objectively compared with their respective CAF (except SSTA) using an index of agreement, and
the six variables are mainly discussed on the north Pacific and adjacent continents (NPAC),
with emphasis on Mexico.
The TCM generates a kind of atmospheric bridge by which the SSTA produces a T7A, the consequent
condensation of water vapour anomaly and the corresponding εA over the continent, affecting the
planetary albedo and therefore the LST.
The u7A forms a large meridional wave train over the NPAC centre, which is part of the Pacific/North
American pattern in both PDO phases and is more intense in winter than in summer. In the PDO
warm phase and over the eastern half of the NPAC, the v7A is positive, so that the moisture flux from
the Pacific Ocean toward North America (NA) increases the precipitation during NA monsoons.
These results have an acceptable agreement with the CAF.
We also analysed the combined effect of cloudiness and evaporation according to the soil moisture,
over the eastern NA and the Gobi Desert for both PDO phases, showing its thermal moderator effect.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Pacific decadal oscillation (PDO) is one of most conspicuous
modes of interdecadal planetary oscillations (Enfield and
Mestas-Nuñez, 2001). It is characterized by spatial contrast of
temperature or pressure anomalies with two phases. In the
positive or warm PDO phase (PDO+), the sea surface temperature anomaly (SSTA) is negative in the central region of the
North Pacific Ocean (NPO) and positive in its eastern region; in
the cool PDO phase (PDO−) the situation is the opposite.
⁎ Corresponding author at: Centro de Ciencias de la Atmósfera, Universidad
Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, C.P.
04510 México D.F., Mexico. Tel.: +52 55 56 22 40 44.
E-mail address: victor@atmosfera.unam.mx (V.M. Mendoza).
0169-8095/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.atmosres.2013.10.010
According to Mantua et al. (1997), the intensity of this oscillation
is assessed using a PDO index, based on the standardised SSTA or
alternatively the sea level pressure anomaly (SLPA). However the
PDO is not alone and shows some phase relationship with
El Niño/southern oscillation (ENSO): in the PDO+ (PDO−)
phase, more El Niño (La Niña) events occur.
The atmospheric response to the prescribed SSTA in the
middle and polar latitudes of the Pacific Ocean, significantly
smaller than when it is prescribed in the tropical and equatorial
latitudes (Webster, 1981), is difficult to detect using general
circulation models (GCMs). This is partly due to the weak
signal-to-noise ratio resulting from the nonlinearity of the
coupled hydrodynamic equations in the GCMs (Barnett et al.,
1997; Miyakoda and Jin-Ping, 1982; Sang-Wook and Kirtman,
2006). In energy balance models, such as the one of the Group
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
of Long-Range Numerical Weather Forecasting (1977, 1979) in
Peking and the thermodynamic climate model (TCM) (Adem,
1964a; Adem et al., 2000), the atmospheric anomaly adjusts to
the ocean thermal forcing (a persistent SSTA), resulting in a
large signal-to-noise ratio; as suggested by Barnett et al. (1997)
this effect justifies the use of the kind of models like ours
instead of a GCM.
Low-frequency thermal oscillations, such as the PDO and the
Atlantic multidecadal oscillation (AMO), can be simulated with
climate models that include the interaction of the ocean and
continent with the atmosphere, in which the dominant modes
are governed by the huge thermal and dynamic inertia of the
ocean through intrinsic mid-latitude or tropical–extratropical
processes (Schneider et al., 2002; Zhong and Zhengyu, 2009).
Several authors have statistically analysed the combined
effect of PDO and AMO on the climate. McCabe et al. (2004)
found that the combination of PDO and AMO may explain the
spatial and temporal variance of decadal drought variability
over NA (including Mexico). Méndez and Magaña (2010)
studied the effect in summer of these same combinations on
prolonged droughts over a region that includes the U.S., Mexico
and Central America. McCabe et al. (2008) show that the
interaction between the ENSO and the AMO explain a great
part of the drought variability during the 20th century in the
conterminous U.S., and Sanchez-Rubio et al. (2011) found that
the combination of PDO, AMO and interdecadal North Atlantic
oscillation (NAO) determine long-term Mississippi River flow
regimes.
Higgins and Shi (2000) found that the NA summer
monsoon and its precipitation are modulated by the PDO
phases. Pavia et al. (2006) investigated the joint role of PDO
and ENSO on the temperature and precipitation over Mexico
during winter and summer; they explicitly combine the PDO
and ENSO phases of the same sign for doing the statistics of
their effects on Mexico's climate. Nigam et al. (1999) studied
the PDO effect (during both phases) from October to March
on the surface air temperature and precipitation anomalies
over the U.S. and northern Mexico.
Our objective in this work is to study the impact of the
PDO on the summer climate of NA, particularly over Mexico.
For this purpose, the TCM will be forced with SSTA of the PDO
phases; of particular interest is the analysis of circulation
anomalies associated with regional pluvial and drought
events. The TCM is integrated monthly over the Northern
Hemisphere (NH).
Our study of the PDO and Mexico's climate, subject matter
of this work, is divided into: Section 2 which describes the data,
Section 3 which explains the physical bases of the TCM and
includes appendices about the major model parameterisations,
Section 4 which the CAF analysis, and Section 5 which presents
and discusses the model simulations and Section 6 contains
final remarks.
2. The data
As usual, the normal (or climatological) value is the
long-term monthly average, and the anomaly (denoted by a
sub-index A) is the departure from the normal; thus, a positive
(negative) anomaly means a value above (below) the normal.
In this paper we use the PDO index based on SSTA, which
by definition is positive in the PDO+ and negative in the PDO−.
229
The data corresponding to summer were taken from the
website ftp://ftp.atmos.washington.edu/mantua/pnw_impacts/
INDICES/PDO (last accessed: March, 2012) and is shown in Fig. 1
for the period 1900–2004. Here we can see that during 1923–47,
the PDO+ dominated; in 1948–75 the PDO− did; and in 1976–
2004, the PDO+ dominated again.
Five composite anomaly fields (CAF) are built for the
summer of each PDO phase: skin temperature (ST), which
complementarily consists of the SST and land surface
temperature (LST); air temperature (T7), zonal (u7) and
meridional (v7) wind at 700 mb (which is the representative
level for the troposphere); and precipitation (R).
In order to characterise the temperature, circulation and
precipitation patterns, and to compare our model results, we
formed for summer (June, July and August) the CAF of ST (SST
and LST), T7, u7, v7 and R, in the NH for both PDO phases. These
fields were constructed from the interactive Reanalysed Data
Set NCEP/NCAR1 for 1948–2004 (http://www.cdc.noaa.gov/
cgi-bin/Composites/printpage.pl; last accessed: November,
2011), and their normal reference is the 30-year climatology
of 1981–2010 (Kalnay et al., 1996).
The CAF are based on the average of eight summers
with PDO+ index ≥ +0.8 and another eight with PDO−
index ≤ −0.8 drawn from the period of 57 years from January
1948 to December 2004, which contains the last two PDO
phases (Fig. 1). For the PDO+, the selected summers are from
the years 1981, 1983, 1986, 1987, 1992, 1993, 1995 and 1997,
whereas the summers for the PDO− are 1950, 1952, 1955,
1956, 1961, 1962, 1967 and 1971.
Data needed for parameterizations in the TCM are from
several sources. Clapp et al. (1965) prepared a set of seasonal
fields for the TCM with the available observations in the mid
20th century and are an unorthodox climatology with a
period of years not well defined. These are normal values
(subindex Nob) of sensible (G2) and latent (G3) heat fluxes
from the surface to the atmosphere, heat released by
condensation in the clouds (G5), surface wind speed (|V|),
relative humidity at the surface (U) and fractional cloud
cover (ε), that form the reference climatology which the TCM
has operated with (Adem, 1964b); these are input fields in
any model run, besides the initial conditions or external
forcing specific for every application.
The parameterisation for the advection in the TCM (Eq. (C9))
requires the observed normal value of geopotential height at
300 mb (H3Nob in Eq. (C12)); this monthly climatology for the
period 1961–1990 (established by WMO and adopted by IPCC in
2007) is from the Reanalysis NCEP/NCAR1.
3. Physical bases of the thermodynamic model
The TCM consists of an atmospheric layer of 9 km height
including a cloud layer, an upper oceanic layer of 60 m depth,
and a continental layer of negligible depth. The model also has
an ice and snow layer (the cryosphere) over continents and
oceans. The basic equation is the thermodynamic energy
equation applied to the components of the climatic system:
atmosphere, ocean and continent. The hydrostatic equilibrium,
perfect gas, continuity and geostrophic balance equations are
used diagnostically. Provided that the model is run month by
month, we assume that the equations are valid for the monthly
averaged variables. The basic variable is the mid-troposphere
230
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
Fig. 1. PDO index for the summers (average of June, July and August) based on the CAF for SST over the North Pacific region during a period of 105 years, from
1900 to 2004 (ftp://ftp.atmos.washington.edu/mantua/pnw_impacts/INDICES/PDO). The global warming signal has been removed from the data. The upward
bars indicate years with positive index, and the downward bars indicate years with negative index.
temperature (Tm). The initial conditions are the anomalies of
the climate variables: SST, T7 and the cryosphere's albedo (α) of
the previous month; and the output fields are the computed
anomalies (Adem, 1964a, 1970b). The TCM is integrated using
the Liebmann relaxation method over almost all the NH (from
~12° to 90° N latitude) using the National Meteorological
Center (NMC) grid with 1977 points and a resolution of
408.5 km.
The TCM has the following heating functions: the radiation
(short and long wave) balance in the atmosphere and at the
surface, the sensible and latent heat fluxes at the surface–
atmosphere interface and the water vapour condensation in
the clouds (whose anomaly is assumed to be proportional to
the cloudiness one). It also has the following horizontal heat
transports: due to mean wind and ocean currents, and due to
the atmospheric and oceanic phenomena considered turbulent
on this spatio-temporal scale. These turbulences are parameterised using two exchange coefficients (austausch) that for
the atmosphere (K) is two orders of magnitude greater than
that for the ocean (Ks). Due to the high value of K, the TCM has a
large diffusivity, which increases the signal-to-noise ratio, and
therefore, the computed anomaly does not critically depend on
the initial conditions (Barnett et al., 1997).
In this way, the TCM is used for simulation experiments
(e.g., Adem, 1991), by prescribing the anomaly of a variable
(such as SST) and then computing the atmospheric
response to assess the impact of the prescribed anomaly.
In this paper the NA climate is simulated according to the
PDO phases, prescribing the respective SSTA as the input
anomaly. The simulations are stationary solutions of Eq. (A1),
taking ∂T ′ m =∂t ¼ 0.
The TCM equations are described in Appendix A;
Appendices B, C and D contain the parameterisations of the
heating functions, advection by mean wind and precipitation,
respectively; Appendix E is the list of abbreviations used.
4. Analysis of the observed CAF
The value of ±0.8 for the PDO index, selected in Section 2,
is an adequate level because it gives enough cases (eight
summers) for CAF to be representative of each phase, and
this level is sufficiently big for the PDO signal to be
significant. This significance of the CAF is confirmed by the
similarity between these fields and the fields of seasonal
correlation of the corresponding variables with the PDO
index, obtained from the NCEP/NCAR Reanalysis. At the same
time, the eight summers, that span more than 20 years
in each phase, do not present a clear AMO signal (http://
www.esrl.noaa.gov/psd/data/timeseries/AMO/, last accessed:
October, 2012). This way to build the CAF of SST emphasizes
the PDO signal in the NPO region; for the oceans outside this
region, the selected years' results are fortuitous and thus the
net signal is small, so that SST is almost normal.
Although the model is integrated in the NH, we assume
that the PDO has a greater impact on the continental regions
adjacent to the NPO. For this reason, on the following figures,
the CAF and the corresponding simulated anomalies are
shown in a limited region called north Pacific and adjacent
continents (NPAC), which comprises the NPO, NA and
eastern Asia, from 60° W to 100° E longitude and from 10°
to 80° N latitude, shown in Fig. 2. The CAFs are shown in Part
a of Figs. 3–12, with the PDO+ on the odd-numbered figures
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
and the PDO− on the even ones; the corresponding simulated
anomalies are shown in Part b.
The CAF for SST (Figs. 3a and 4a) shows the characteristic
PDO pattern. During the PDO+, the SSTA reaches ~ − 1 °C in a
great extension of the central NPO and ~ 0.5 °C in the Pacific
adjacent to NA. In the central and southern regions of Mexico,
the positive LSTA (b0.5 °C) in the PDO+ and the negative
(~ − 0.5 °C) in the PDO− suggest a certain influence from the
Pacific Ocean adjacent to Mexico during both phases of the
PDO. Throughout the PDO+, a negative anomaly (~ − 0.5 °C)
extends over the northeastern U.S., eastern Canada and the
Gobi Desert (GD) in eastern Asia (~ 44° N, 110° E); in the
PDO−, the situation is reversed.
During the PDO+, a huge negative T7A is located on the
NPO and over eastern Asia (Fig. 5a). This anomaly could be
forced by the negative SSTA of the central NPO (Fig. 3a) and
could spread from there to the GD by thermal energy
advection. The PDO− (Fig. 6a) shows the opposite situation.
The temperature anomalies at the 500 and 250 mb levels
(whose CAFs are not shown) have a similar pattern, but it is
more extended, ranging from the Bering Sea across Asia and
up to the Sahara Desert and the adjacent Atlantic Ocean.
In fact, the relationship between the PDO phases and
atmospheric circulation can reach levels above 250 mb;
Jadin et al. (2010) found that the interannual variations of
the polar jet in the lower stratosphere are strongly associated
with the SSTA at the Aleutian Low region in December for
PDO+ years.
With regard to the summer u7A, a great wave pattern
(shown only in the NPAC region) is seen, formed of meridionally
alternating positive and negative anomalies, from the NPO
throughout the Arctic until the north Atlantic Ocean, beginning
with a positive anomaly at approximately 30° N for the PDO+
(Fig. 7a) and negative for the PDO− (Fig. 8a). A similar situation
occurs at 500 and 250 mb (not shown). In contrast, during
winter these patterns (not shown) are clearer and similar to the
Pacific/North America (P/NA) pattern (Wallace and Gutzler,
1981), especially during El Niño events. The v7A during the
PDO+ (Fig. 9a) is positive over western and northwestern
Mexico and the southwestern U.S., and favours the humidity
flux from the Pacific Ocean toward NA. This pattern is more
significant at 850 and 950 mb (not shown), suggesting that the
NA monsoon precipitation can be intensified in summer.
The CAF of RA has a positive pattern during the PDO+
(Fig. 11a) that enters from the east Pacific toward northwest
231
Mexico and the U.S., with a maximum in the eastern U.S. Over
the central region of NPO, below 35° N latitude, RA is negative
and strong, possibly due to the deficit of convective systems
by the negative SSTA of the PDO+ (Fig. 3a). The opposite
situation occurs during the PDO− (Fig. 12a).
5. Results and discussion
In order to simulate the effect of the PDO on the NA climate
during summer, the TCM is run taking as a prescribed input field
the CAF of SST in the NH for each PDO phase (Figs. 3a and 4a).
The other initial conditions, that would be the anomalies of T7
and the cryosphere albedo, are not taken because our purpose is
to assess the isolated effect of the SSTA, which includes the PDO
signal. As shown in a former experiment (Adem et al., 2000), the
thermal energy storage in the atmosphere (determined by the
T7 anomaly of the previous month) is negligible; therefore,
include it practically does not improve the simulation. Adem et
al. (2000) also argued that the cryosphere albedo anomalies
have little effect at low latitudes as Mexico, where we emphasize
in the present paper.
The output fields are LSTA, T7A, u7A, v7A and RA, computed
on the NH. These are the target fields to be compared with
the CAF.
The horizontal transport of humidity by anomalies of
thermal wind and of cloudiness (ε), both internally generated
by the model (Eqs. (B6) and (B7)), forms an atmospheric bridge,
through which the SSTA generates a significant anomaly of land
surface temperature (LSTA), in accordance with the findings of
Alexander et al. (2004). This physical process occurs as follows:
the SSTA, prescribed in the model, induces a mid-troposphere
temperature anomaly (TmA) through the F4 term in Eq. (A3); so,
the TmA generates anomalies of latent heat flux (G3A), of heat
released by condensation in the cloud (G5A) and of fractional
cloud cover (εA), via parametric Eqs. (B5), (B6) and (B7); thus,
εA generates a LSTA by an anomaly of cloud albedo, and this
same LSTA in turn generates a new TmA, mainly of a local scale,
corresponding to the same one of the LSTA, establishing an
internal feedback process in the model. Over the NPAC the
atmospheric bridge takes place since the NPO centre toward
two regions: eastern NA (ENA: southwestern U.S. and
northwestern Mexico) or the GD.
At the continental sides of the bridge we analyse the effect
of εA, (α1I)A, G3A and LSTA, selecting from the Figs. 3b and c
and 4b and c the polygonal areas ENA and GD, indicated in
Fig. 2. North Pacific Ocean and adjacent continental (NPAC) region. Polygonal areas east North America (ENA) and Gobi Desert (GD).
232
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
Fig. 3. Part a is the CAF of ST (in °C) in summer, and Part b is the corresponding simulated STA (in °C), both during the PDO+. Part c is the simulated εA (in %), also
in the PDO+.
the Fig. 2; (α1I)A and G3A are not shown in any figure. As can
be seen in Appendix B, (α1I)A is the anomaly of the solar
radiation absorbed by the surface and G3A (anomaly of latent
heat flux by soil evaporation) is proportional to ESA according
to the formula (B5). In order to contrast the temperature
anomaly due to evaporation, we use different values of d7
(soil moisture deficit). In Tables 1a and 1b we present the
geographic average of εA, (α1I)A, G3A and LSTA, for both
regions, ENA (part a) and GD (part b) and for both PDO
phases, computing each anomaly for three values of d7. Its
climatological normal value for summer is coincidently the
same for ENA and GD, namely 0.65, because they are about
the latitude belt ~ 22–40°N; besides this actual value, we
compute the above anomalies for two hypothetical extreme
values of soil moisture deficit: d7 = 0.0 (saturated soil) and
d7 = 1.0 (absolutely dry soil). The last column shows the CAF
of ST for comparing it with LSTA.
During the PDO+ (PDO−) the increase (decrease) of ε is
greater in dry than in saturated soil, so that the decrease
(increase) of α1I is greater in dry than in saturated soil,
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
233
Fig. 4. Same as Fig. 3 but for the PDO−.
whereas the decrease (increase) of G3 is greater in saturated
than in dry soil, where G3A = 0. The cooling (heating) of the
surface in both regions is greater in dry than in saturated soil,
i.e. the soil moisture is a thermal regulator of the land surface.
Furthermore, LSTA is closer to the CAF of skin temperature (ST)
when the soil is saturated. According to the values of (α1I)A and
G3A, both terms contribute to cool or heat the surface; however,
in both phases the absolute value of (α1I)A is always greater
than of G3A one; so that the cooling (heating) of the continental
surface by the increase (decrease) of ε is due primarily to the
decrease of α1I and secondly to the decrease of G3.
In both ENA and GD, there is a positive εA (Fig. 3c) that
increases the planetary albedo, which induces a negative
LSTA during the PDO+ (Fig. 3b). In contrast, during the PDO−,
the negative εA (Fig. 4c) reduces the cloud albedo, which
induces positive LSTA (Fig. 4b).
An objective comparison of the computed anomalies and
the CAF is carried out by the index of agreement (IOA), which
measures the ability of the model in computing the size and
distribution of a variable, regardless of its units. The IOA
ranged from 0.0 for a complete disagreement to 1.0 for a
perfect agreement between the computed and the observed
234
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
Fig. 5. Part a is the CAF for T7 (in °C) in the summer, and Part b is the corresponding simulated T7A (in °C), both for the PDO+. Part c is similar to Part b but without
air pressure anomaly at the top of the layer model.
(in this case, the CAF) variables. Willmott (1981) expressed
the IOA as follows:
N
X
IOA ¼ 1−
2
ðC i −Oi Þ
i¼1
N h
X
i
C −O þ O −O 2
i
i
;
i¼1
where Ci is the i-value of the computed variable, Oi is the
i-value of the observed one, O is the average value of the
observed variable and N is the number of values taken by each
variable. The IOA should be assessed taking into account
the studied phenomenon, the observational accuracy and the
model employed. This index becomes intuitively meaningful
after repeated use in a variety of problems (Willmott, 1981,
1982; Willmott et al., 1985). From numerous applications of
the IOA to compare modelled and observed climatic fields, such
as those presented in this paper, we estimate that an IOA N 0.4
indicates acceptable agreement between the fields. Table 2
shows the IOA between the simulated anomalies and the CAF
for the NH, NPO, CA and Mexico (MEX) for each PDO phase.
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
235
Fig. 6. Same as Fig. 5 but for PDO−.
The simulated LSTA shows some agreement with the
corresponding CAF (Figs. 3 and 4, Parts a and b), with an IOA
of 0.42 for the PDO+, of 0.45 for the PDO− over the CA and of
0.51 for MEX and PDO+, and 0.32 for PDO− (Table 2).
The simulated 700 mb temperature anomaly (T7A) is shown
in Part b of Figs. 5 and 6 for PDO+ and PDO−, respectively. In
the PDO+ (PDO−), a negative (positive) large-scale anomaly is
seen, which is extended from the central NPO to the GD, in
agreement with the CAF (Part a of Figs. 5 and 6); we assume
that this anomaly is in part due to the horizontal transport of
thermal energy by an anomaly of zonal wind at 700 mb (u7A).
This effect is verified by recalculating the T7A while excluding
from the model the horizontal transport anomaly due to wind,
which is obtained with A = 0 in Eq. (C12); the resulting T7A is
shown in Part c of Figs. 5 and 6 for the warm and cold phases,
respectively. On comparing these parts with their respective
Part b (case A ≠ 0), the assumption is verified. The IOA for T7A
over the whole NH is 0.67 and 0.41 in the PDO+ and PDO−,
respectively. In the NPO, the agreement is substantially
increased to 0.77 and 0.60, respectively.
A comparison between Fig. 7a and b for the PDO+, and
between Fig. 8a and b for the PDO−, indicates that the main
236
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
Fig. 7. Part a is the CAF for u7 in the summer, and Part b is the corresponding simulated u7A, both in m s−1 for the PDO+.
characteristic of the pattern for the u7A (similar to the PNA
pattern) is well simulated by the model in the NPO, where
the IOA is 0.67 for the PDO+ and 0.73 for the PDO−. The
IOA decreases for the NH to 0.58 in the PDO+ and 0.55 in the
PDO−; for the CA, the corresponding value is 0.43 in the
PDO+ and 0.41 in the PDO− (Table 2). Like u7A, the anomaly
of meridional wind at 700 mb (v7A) (Figs. 9 and 10) also
shows better agreement with the CAF for the central region
of NPO (0.44 for the PDO+ and 0.49 for the PDO−) than
the NH and CA. In the NH, the agreement is smaller (0.40
for the PDO+ and 0.36 for the PDO−), and over CA, the agreement is poor (0.35 for the PDO+ and 0.29 for the PDO−).
Nevertheless, the positive v7A from the Pacific Ocean that
crosses Mexico, the U.S. and Canada toward the northeast
during the PDO+ (Fig. 9a) is partially well simulated by the
model (Fig. 9b). The positive v7A contributes such that the
simulated precipitation (R) over these regions has values
above the normal (intensifying the NA monsoon) during the
PDO+ (Fig. 11b), which agrees with the CAF (Fig. 11a). During
the PDO− the simulated v7A (Fig. 10b) in the mentioned
regions is positive but has very small values (almost the
normal), which is in agreement with the CAF (Fig. 10a). In this
case, the simulated R (Fig. 12b) has values below the normal
over northern Mexico and the southern U.S., which partially
agrees with the CAF (Fig. 12a).
In the case of precipitation, which is a difficult process to
simulate or forecast, the agreement between the simulated
anomaly and its CAF is lower than that obtained for the other
variables (Table 2). Despite that finding, on the NPO the
agreement is acceptable during the PDO+, when the IOA is 0.45;
and still better on MEX with 0.63 (0.41) for PDO+ (PDO−).
The simulated anomalies of ST, ε and R and the CAF for the
ST and R in Mexico during the PDO phases are summarised in
Table 3. Several interesting features can be seen there, such as
the effect of planetary albedo on the temperature, i.e., positive
εA is associated to temperatures below normal, and vice versa,
for both phases. Positive anomaly RA predominates during the
PDO+, and the opposite occurs during the PDO−.
6. Final remarks
We have simulated the effect of the PDO on the NA
summer climate, by means of the TCM prescribing the SSTA of
each phase. Provided that the PDO signal is settled in the NPO
and around it, we put emphasis on the NPAC region.
The horizontal transport of humidity by anomalies of
thermal wind and cloudiness, both internally generated by
the TCM, forms an atmospheric bridge, through which the SSTA
generates a significant LSTA. The simulated εA has an important
role in the LSTA that appears on both sides of NPAC (ENA and
the GD), where a positive εA increases the planetary albedo,
inducing negative LSTA, during the PDO+; by contrast, in the
PDO− a negative εA reduces the planetary albedo, which
induces positive LSTA. The simulated LSTA shows a partial
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
237
Fig. 8. Same as Fig. 7 but for the PDO−.
agreement with the corresponding CAF during both PDO
phases, with an IOA of 0.42 (0.45) for the PDO+ (PDO−) over
the continental areas (CA), and 0.51 (0.32) for the PDO+
(PDO−) over MEX.
From the analysis of the soil moisture effect on the ENA
and GD, we find that it weakens the soil thermal changes,
particularly when these are caused by cloudiness changes; so
that the cooling (heating) of the continental surface by the
increase (decrease) of ε is due primarily to the decrease of α1I
and secondly to the decrease of latent heat flux (G3). These
thermal changes of the surface are stronger in dry than in
saturated soil, i.e. this moisture is a thermal moderator of the
land surface.
An important observation in the CAF is a great wave pattern
in the u7A over the NPO, formed by alternating negative and
positive regions, passing through the North Pole and ending at
the central north Atlantic Ocean. According to IOA, this great
wave pattern is partially simulated by the model for the central
NPO. We find that during the PDO+, a positive pattern in the
v7A suggests a humid air flux from the Pacific Ocean to Mexico
and that the North American monsoon precipitation can
intensify in summer, with positive RA in northern Mexico and
the southeastern U. S.
Regarding the precipitation, the CAF exhibits a great
positive anomaly pattern in the central NPO; this result
indicates that R is increased by the greater convective
activity that occurs when the SSTA in this region is positive
during the PDO−; the opposite process happens during the
PDO+. The model acceptably simulates this anomaly pattern
in the NPO.
Benson et al. (2007) find that some intense and persistent
droughts impacted some Native American cultures in the
west central part of the U.S.; these droughts also reached the
north of Mexico. Tree-ring time series of precipitation and
temperature indicate that the warm and dry periods, that
impacted these cultures, occurred in AD 990–1060, 1135–
1170 and 1276–1297, when PDO− and positive AMO were
present.
Méndez and Magaña (2010) find that when the PDO− and
the positive AMO phase coincide, a lasting drought occurs in
northern Mexico; this result suggests that during the period
1948–61, more of such events would be present there; on the
other hand, in central and southern Mexico, drought is
associated with the opposite combination, i.e. PDO+ and
negative AMO phases. Considering only the PDO phases,
these results are in agreement with the computed RA by the
TCM (Figs. 11 and 12, and Table 3).
In a previous work, we have used the TCM to forecast at
monthly and seasonal resolutions in the NH with emphasis
on Mexico's climate (Adem et al., 2000). The present work
allows us to identify seasonal SST patterns, associated with the
PDO, that influence Mexico's temperature and precipitation. In
this research line, our future work will be oriented to climate
forecasting by sorting the antecedent observed SSTA that
238
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
Fig. 9. Part a is the CAF for v7 in summer, and Part b is the corresponding simulated v7A, both in m s−1 for the PDO+.
presents a clear PDO signal that the SSTA is introducing in
the model; so the input SSTA is the real signal observed in
the previous month of the prediction. Regarding that the
combination of PDO and AMO phases have an important
influence on Mexico's precipitation, we propose to include also
the AMO in the forecast.
Acknowledgements
The authors acknowledge the Climate Diagnostics Center
in Boulder, Colorado, for the use of the images provided by
NOAA-CIRES, from their interactive pages of NCEP/NCAR1
Reanalysis. We are also grateful to Rodolfo Meza and
Alejandro Aguilar for their technical support.
Appendix A. The model equations
The thermodynamic energy equation vertically integrated
and applied to the atmospheric layer (Adem et al., 2000) can
be expressed as follows:
ρm c v H
∂T ′ m
′
2 ′
þ Vm ∇T m −K∇ T m
∂t
!
¼ ET þ G5 þ G2 ;
ðA1Þ
where the sub-index m means the mid-tropospheric value,
ρm is the air density, cv is the specific heat of air at a constant
volume, H is the constant thickness of the atmospheric layer;
′
T m is a small departure of the temperature from a constant
value Tm0, where T m ¼ T m0 þ T ′ m and T m0 ≫T ′ m ; Vm is the
horizontal velocity of the wind and ∇ is the two-dimensional
horizontal gradient operator. K is the exchange coefficient of
the turbulent horizontal transport, equal to 3.5 × 106 m2 s −
1
; for the troposphere, this value corresponds to the scale of
the migratory cyclones and anticyclones at middle latitudes,
which transport heat in the atmosphere from the equator to
the poles.
On the right hand side of Eq. (A1), three heating rates
appear: ET is by short and long wave radiation, G5 is due to
the water vapour condensation in the clouds, and G2 is
produced by sensible heat flux from the surface.
The thermodynamic energy equation for the upper ocean
layer (Adem, 1970a) is given as follows:
ρs c s h
∂T ′ s
′
2 ′
þ Vs ∇T s −K s ∇ T s
∂t
!
¼ Es −G2 −G3 ;
ðA2Þ
where the sub-index s indicates this layer, ρS is the constant
water density, cS is the specific heat of water, h is the layer
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
239
Fig. 10. Same as Fig. 9 but for the PDO−.
′
depth, and T S is a small departure of the Ts (equal to SST)
from a constant value Ts0, where T S ¼ T S0 þ T ′ S and T S0 ≫T ′ S ;
VS is the ocean current velocity (vertically averaged) in the
layer, Ks is the exchange coefficient of the turbulent
horizontal transport equal to 3.5 × 104 m2 s −1, Es is the
heating rate due to short- and long-wave radiation and G3 is
the rate at which heat is given to the atmosphere by latent
heat flux from the surface.
On the continents, Eq. (A2) is reduced to the following
form:
0 ¼ ES −G2 −G3
ðA2′Þ
To numerically solve Eq. (A1),
we use an
implicit method,
replacing the term ∂T ′ m =∂t with T ′ m −T ′ mp =Δt, where T ′ mp is
the T ′ m value in the previous month, and Δt is the time
interval, defined here as one month. Upon substituting the
linear parameterisation of the heating functions (Appendix B) in
Eqs. (A1) and (A2′), and the parameterisation for the advection
term AD ¼ ρm cv H Vm ∇T ′ m (Appendix C) in Eq. (A1), we obtain
two equations to compute T ′ m and T ′ S. Due to the linearity of the
heating functions, Eq. (A2′) becomes an algebraic equation, in
which the surface temperature in the continents is expressed as
a linear function of T ′ m . Eq. (A1) results in an elliptic differential
equation in x and y, which are the Cartesian local coordinates
toward the east and north, respectively:
2 ′
K∇ T
m
þ F1
∂T ′ m
∂T ′ m
′
þ F2
þ F3T m ¼ F4;
∂x
∂y
ðA3Þ
where F1, F2, F3 and F4 are known functions of x and y; F1 and F2
are functions of the pressure p at z = H, and F4 is a function of
T ′ mp and the surface albedo (α).
In simulation experiments, such as those in this paper, the
ocean temperature T ′ S is prescribed in the heating functions
of Eq. (A1) using observed values for T ′ S . In this case F4 is a
function of it and Eq. (A2) is not used at all. To compute the
atmospheric pressure p at z = H, we first computed T ′ m from
Eq. (A3) assuming normal pressure, which is obtained using
A = 0 in Eq. (C12). The T ′ m computed in the first step is then
incorporated in Eq. (C12) with A ≠ 0 to compute the
pressure anomaly from Eq. (C11), which is then used in
Eq. (A3) to compute the temperature in a second step. The
adjustment process between temperature and pressure is
repeated until the computed temperature differs 0.1 °C from
the computed temperature in the previous step; at this
moment, we assume that the geostrophic wind has been
coupled to the computed temperature.
240
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
Fig. 11. Part a is the CAF for R in summer, and Part b is the corresponding simulated RA, both in mm day−1 for the PDO+.
At the lateral boundary, the solution is obtained assuming
that all the horizontal transports of heat are zero, and in this
way the solution is computed using the following relation:
T
′
m
¼ F 4 =F 3 :
ðA4Þ
This solution is also used as the first guess in the relaxation
method to obtain the solution in the interior. The relaxation
finishes when the numerical solutions in two consecutive
iterations have a difference of approximately 0.001 °C, which
indicates that the model has a truncation error of this magnitude
in all the points of the integration region.
Given that the TCM is a dissipative model (unlike GCMs)
due to the exchange-coefficient value for the atmosphere,
the noise level is not significant with respect to the signal of
interest produced by SSTA. This means that the model can be
run with slightly different initial conditions and still
produce, in the steady state, the same solution that depends
on SSTA.
Appendix B. The parameterisation of the heating functions
The heating functions by radiation in the atmosphere and
the surface are parameterised assuming that the cloud layer
and the surface of the Earth absorb and emit long-wave
radiation as black bodies; and assuming that the atmospheric
layer absorbs and emits as a black body between 0 and 8 μm;
absorbs and emits a small fraction of the black body between 8
and 12 μm; and between 12 and 19 μm, in the shared band of
H2O and CO2, it absorbs and emits a fraction of the black body
that depends on the content of precipitable water and of CO2 in
the atmosphere, which can be computed using a logarithmic
formula (Garduño and Adem, 1988). The resultant formulae,
linearised with respect to T ′ m and T ′ S , are the following:
ET ¼ F 30 þ ε F
′
30
þ F 31 T
′
m
′
′
þ F 32 þ εNob F 32 T S
þ ða2 þ εb3 ÞI;
′
ES ¼ F 34 þ ε F 34 þ F 35 T
ð1−α Þ;
ðB1Þ
′
′
m
þ F 36 T S þ ðQ þ qÞ0 ½1−ð1−kÞε
ðB2Þ
where F 30 ; F ′ 30 ; F 31 ; F 32 ; F ′ 32 ; F 34 ; F ′ 34 ; F 35 and F 36 are constants; εNob is the observed normal cloudiness value (in
the following the sub-indexes N and ob indicate normal and
observed values, respectively), a2 and b3 are functions of the
latitude and the season. I represents the insolation; (Q + q)0 is
the total solar radiation (direct plus diffuse) received by the
surface under a clear sky; and k is a function of the latitude; and
a2I, εb3I and α1I = (Q + q)0[1 − (1 − k)ε](1 − α) are the
fraction of the short wave absorbed in the atmosphere, the cloud
layer and the surface, respectively.
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
241
Fig. 12. Same as Fig. 10 but for the PDO−.
For G2 and G3, we use over the ocean the linearised
approximate equations deduced by Clapp et al. (1965):
′
′
G2 ¼ G2Nob þ K 3 jVaNob j T SA −T mA
ðB3Þ
′
′
′
G3 ¼ G3Nob þ K 4 jVaNob j 0:981T SA −U Nob T mA :
x and y, that varies between 0.0 and 1.0, the first value
corresponds to a saturated soil and the second one to an soil
absolutely dry.
For G5, we use the empirical equation, also deduced by
Clapp et al. (1965):
ðB4Þ
′
K3 and K 4 are constants; U is the surface relative humidity;
and |Va| is the surface wind speed.
Over the continents, we use for G2 a similar equation to
that used over the oceans, and for G3, the equation:
G3 ¼ G3Nob þ ð1−d7 ÞESA ;
ðB5Þ
where d7 is the soil moisture deficit normalized to its
maximum value, which is an empirical seasonal function of
′ ′
G5 ¼ G5Nob þ b T
mA
″
þd
′
′
∂T mA
″ ∂T mA
þc
;
∂x
∂y
ðB6Þ
where b′, d″ and c″ are functions of x and y, and depend on the
season. The second term in the right side of Eq. (B6) represents
the heating rate due to local water vapour condensation, and
the last two terms represent the contribution to the heating
due to horizontal transport of humidity by thermal wind
anomalies in the layer.
Table 1a
Increase (decrease) of cloudiness, εA, and subsequent cooling (heating) of land surface (LSTA), due to decrease (increase) of solar radiation absorbed by the
surface (α1I)A, and of latent heat flux by evaporation (G3A), for a soil with moisture deficit d7 = 0.0 (saturated), 0.65 (actual normal and climatological value) and
1.0 (dry soil), during PDO+ (PDO−) in the geographically averaged region ENA.
εA = d2G5A
(%)
d7
PDO+
PDO−
0.0
0.76
−1.21
0.65
1.10
−1.85
1.0
1.13
−1.94
(α1I)A = ‐ (Q + q)0(1 − k) (1 − α) εA
(W m−2)
G3A = (1 − d7)ESA
(W m−2)
0.0
−1.68
2.64
0.0
−1.55
2.48
0.65
−2.42
4.07
1.0
−2.50
4.27
0.65
−0.12
0.22
LSTA
°C
1.0
0.0
0.0
0.0
−0.1
0.1
CAF
of ST
°C
0.65
−0.4
0.7
1.0
−0.5
0.8
−0.2
0.1
242
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
Table 1b
Same as Table 1a but in GD.
εA = d2G5A
(%)
d7
PDO+
PDO−
0.0
1.05
−0.89
0.65
1.27
−1.06
1.0
1.31
−1.08
(α1I)A = ‐ (Q + q)0(1 − k) (1 − α) εA
(W m−2)
G3A = (1 − d7)ESA
(W m−2)
0.0
−2.29
1.94
0.0
−1.93
1.71
0.65
−2.71
2.21
1.0
−2.78
2.23
The cloud cover is given by the following relation:
ε ¼ ε Nob þ d2 G5A ;
ðB7Þ
where d2 is an empirical constant.
Appendix C. The parameterisation of the advection by the
mean wind
The advection of thermal energy by the mean wind,
denoted AD, is parameterised as follows:
AD ¼ C v ∇T
Z
′
m
H
0
ρ V dz ¼ ρm cv HV m ∇T
′
m;
ðC1Þ
where ρ* is the density field, V* is the horizontal wind
velocity, and u* and v* are the x and y components of V*,
which are computed using the following geostrophic wind
equations:
1 ∂p
u ¼− f ρ ∂y
υ ¼
ðC2Þ
1 ∂p
;
f ρ ∂x
ðC3Þ
where f is the Coriolis parameter, p* is the pressure, and the
asterisk (*) means the value of a variable at the height z.
In the atmospheric layer, the temperature field is given by
the following equation:
T ¼Γ
H
−z þ T m ;
2
Table 2
IOA between the five CAF and the corresponding computed anomalies by the
model for the PDO+ and the PDO−over the NH, NPO, continental areas (CA)
and Mexico (MEX). The ST is the SST over sea points and the LST over land
points.
Climate anomalies
Phases
NH
NPO
CA
MEX
Skin temperature over continent
PDO+
PDO−
PDO+
PDO−
PDO+
PDO−
PDO+
PDO−
PDO+
PDO−
–
–
0.67
0.41
0.58
0.55
0.40
0.36
0.36
0.25
–
–
0.77
0.60
0.67
0.73
0.44
0.49
0.45
0.26
0.42
0.45
0.54
0.30
0.43
0.41
0.35
0.29
0.34
0.24
0.51
0.32
0.29
0.23
0.16
0.16
0.22
0.27
0.63
0.41
Zonal wind at 700 mb level
Meridional wind at 700 mb level
Precipitation
1.0
0.0
0.0
0.0
−0.1
0.1
CAF
of ST
°C
0.65
−0.4
0.4
1.0
−0.5
0.5
−0.1
0.1
The p* and ρ* values in Eqs. (C2) and (C3) can be determined
using Eq. (C4) and the equations of perfect gas and hydrostatic
equilibrium. The resulting equations are as follows:
g
Γ ðH−zÞ R0 Γ
p ¼p 1þ
T m −ΓH=2
ðC5Þ
g
Γ ðH−zÞ R0 Γ −1
;
ρ ¼ρ 1þ
T m −ΓH=V
ðC6Þ
where p and ρ are the values of p∗ and ρ∗, respectively, at z = H,
g is the gravity acceleration, and R0 is the gas constant.
If we substitute Eqs. (C5) and (C6) in the geostrophic
wind Eqs. (C2) and (C3), we obtain:
u ¼−
v ¼
R0 T ∂p
g ðH−zÞ ∂T ′ m
þ
fp ∂y f ðT m −ΓH=2Þ ∂y
R0 T ∂p
g ðH−zÞ ∂T ′ m
:
−
fp ∂x f ðT m −ΓH=2Þ ∂x
ðC7Þ
ðC8Þ
Substituting Eqs. (C6), (C7) and (C8) in Eq. (C1), results in
the following equation for the advection:
′
AD ¼ ð F 8 Þ0 J T m ; p ;
ðC9Þ
where J is the Jacobian operator and (F8)0 is calculated with:
g !
cv ðT m0 −ΓH=2Þ
T m0 þ ΓH=2 R0 Γ þ1
1−
:
ð F 8 Þ0 ¼
g
T m0 −ΓH=2
þ1
fΓ
R0 Γ
ðC10Þ
ðC4Þ
where Γ is the constant lapse rate for the standard atmosphere
of mid-latitudes.
Air temperature at 700 mb level
0.65
−0.25
0.12
LSTA
°C
The main variables computed by the model are the
temperatures of the atmosphere–ocean–continent system;
therefore, we have formulated a parameterisation in which p
is computed using Tm, also computed by the model. In this way
we apply Eq. (C5) to the isobaric surface of 300 mb with height
H3, which is near H, i.e., H ≫ |H3 − H|. Therefore, we have:
g
Γ ðH3 −HÞ −R0 Γ
:
p ¼ 300 mb 1−
T m −ΓH=2
ðC11Þ
According to Adem (1962), we are assuming a relation of
thermal expansion (compression) of the layer with positive
(negative) T ′ mA , given by:
H 3 ¼ H3Nob þ AT
′
mA :
ðC12Þ
In this equation, H3Nob is the monthly observed normal
value of H3 and was obtained for a period of 30 years from
1961 to 1990 from Reanalysis NCEP/NCAR1. A = BH/
[4(Tm0 − ΓH/2) + ΓH], where B is an empirical parameter.
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
243
Table 3
CAF and computed STA, εA and RA over Mexico for the PDO phases.
Climate
anomalies
PDO−
PDO+
CAF
Simulated anomalies
CAF
Precipitation
Positive in almost all.
Positive in the south and
southeast. Negative in the
center and north.
Negative in the center, south and
southeast. Positive in the north.
Positive in most of the country.
Negative in the southeast, Yucatan
Peninsula and northwest.
All negative, except in the Central Positive in the north. Negative
Pacific Slope.
in the center, south and southeast.
Cloud cover
Positive in all (including the
Baja California Peninsula),
except the northwest.
–
Skin temperature
Adem (1964a) used B = 2; this value does not permit great
horizontal variation in the atmospheric density, making the
advection anomaly of thermal energy almost negligible. To
incorporate a non-negligible advection anomaly, we use
B = 5.4. Furthermore, Eq. (C12) allows one to determine H3
from the computed mean temperature in the troposphere
and therefore the pressure p using Eq. (C11).
Appendix D. The parameterisation of the precipitation
The precipitation anomaly RA is calculated using a multiple
linear regression equation similar to that given by Mendoza et
al. (2001):
′
′
RA ¼ b T SA −T 7A þ cu7A þ dv7A þ eζ 7A ;
ðD1Þ
where ζ7 is the vorticity at 700 mb. The parameters
b, c, d and e are the correlation coefficients, which are functions
of the geographic position. Using z = 3 km (which is the
approximate height of the 700 mb level) in Eqs. (C4), (C7) and
(C8), the values of T7, u7 and v7 are computed, respectively,
and ζ7 is computed with u7 and v7.
Appendix E. Abbreviations list
AMO, Atlantic multidecadal oscillation; CAs, continental
areas; CAF, composite anomaly field; ENA, Eastern North
America; ENSO, El Niño/southern oscillation; GCMs, general
circulation models; GD, Gobi Desert; MEX, Mexico; NA,
North America; NH, Northern Hemisphere; NMC, National
Meteorological Center; NPAC, North Pacific and adjacent
continents; NPO, North Pacific Ocean; PDO, Pacific decadal
oscillation; P/NA, Pacific/North America; PDO+, warm PDO
phase; PDO−, cool PDO phase; TCM, thermodynamic climate
model; IOA, index of agreement; LST, land-surface temperature;
SLP, sea-level pressure; SST, sea-surface temperature, denoted as
Ts in Eqs.; and ST, skin temperature.
References
Adem, J., 1962. On the theory of the general circulation of the atmosphere.
Tellus 4, 102–115.
Adem, J., 1964a. On the physical basis for the numerical prediction of monthly
and seasonal temperatures in the troposphere–ocean–continent system.
Mon. Weather Rev. 92, 91–104.
Adem, J., 1964b. Sobre el estado térmico normal del sistema tropósfera–
océano–continente en el hemisferio norte. Geofis. Int. 4, 3–32.
Adem, J., 1970a. On the prediction of mean monthly ocean temperatures.
Tellus 22, 410–430.
–
All negative.
Simulated anomalies
Positive in the center, south and
southeast. Negative in the north.
Negative in most of the country.
Positive in the southeast, Yucatan
Peninsula and northwest.
Adem, J., 1970b. Incorporation of advection of heat by mean winds and by
ocean currents in a thermodynamic model for long-range weather
prediction. Mon. Weather Rev. 98, 776–786.
Adem, J., 1991. Review of the development and applications of the Adem
thermodynamic climate model. Clim. Dyn. 5, 145–160.
Adem, J., Mendoza, V.M., Ruiz, A., Villanueva, E.E., Garduño, R., 2000. Recent
numerical experiments on three-months extended and seasonal weather
prediction with a thermodynamic model. Atmosfera 13, 53–83.
Alexander, M.A., Lau, N.-C., Scott, J.D., 2004. Broadening the atmospheric
bridge paradigm: ENSO teleconnections to the tropical west Pacific–
Indian Oceans over the seasonal cycle and to the north Pacific in
summer. In: Wang, C., Xie, S.-P., Carton, J.A. (Eds.), Earth's Climate. The
Ocean–atmosphere Interaction. Amer. Geophys. Union, Washington DC,
pp. 85–103.
Barnett, T.P., Arpe, K., Bengtsson, L., Ji, M., Kumar, A., 1997. Potential
predictability and AMIP implications of midlatitude climate variability in
two general circulation models. J. Clim. 10, 2321–2329.
Benson, L.V., Berry, M.S., Jolie, E.A., Spangler, J.D., Stahle, D.W., Hattori, E.M.,
2007. Possible impacts of early-11th-, middle-12th-, and late-13thcentury droughts on western Native Americans and the Mississippian
Cahokians. Quat. Sci. Rev. 26, 336–350.
Clapp, P.F., Scolnik, S.H., Taubensee, R.E., Winninghoff, F.J., 1965. Parameterization
of certain atmospheric heat sources and sinks for use in a numerical model for
monthly and seasonal forecasting. Unpublished study of Extended Forcast
Division, U.S. Weather Bureau, Washington, D.C., 20235 (Copies available to
interested persons).
Enfield, D.B., Mestas-Nuñez, A.M., 2001. Chapter 2 – interannual to multidecadal
climate variability and its relationship to global sea surface temperatures.
Interhemispheric Climate Linkages. 17–29.
Garduño, R., Adem, J., 1988. Interactive long wave spectrum for the
thermodynamic model. Atmosfera 1, 157–172.
Group of Long-Range Numerical Weather Forecasting, 1977. On the physical
basis of a model of long-range numerical weather forecasting. Sci. Sinica
20, 377–390.
Group of Long-Range Numerical Weather Forecasting, 1979. A filtering
method for long-range numerical weather forecasting. Sci. Sinica 22,
661–674.
Higgins, R.W., Shi, W., 2000. Dominant factors responsible for interannual
variability summer monsoon in the south-western United States. J. Clim.
14, 403–417.
Jadin, E.A., Wei, K., Zyulyaeva, Y.A., Chen, W., Wang, L., 2010. Stratospheric
wave activity and the Pacific decadal oscillation. J. Atmos. Sol. Terr. Phys.
72, 1163–1170.
Kalnay, E., et al., 1996. The NCEP/NCAR 40-year reanalysis project. Bull. Am.
Meteorol. Soc. 77, 437–470.
Mantua, N.J., Hare, S.R., Zhang, V., Wallace, J.M., Francis, R.C., 1997. A Pacific
interdecadal climate oscillation with impacts on salmon production.
Bull. Am. Meteorol. Soc. 78, 1069–1079.
McCabe, G.J., Palecki, M.A., Betancourt, J.L., 2004. Pacific and Atlantic Ocean
influences on multi-decadal drought frequency in the United States.
Proc. Natl. Acad. Sci. U. S. A. 101, 4136–4141.
McCabe, G.J., Betancourt, J.L., Gray, S.T., Palecki, M.A., Hidalgo, H.G., 2008.
Associations of multi-decadal sea-surface temperature variability with
US drought. Quat. Int. 188, 131–140.
Méndez, M., Magaña, V., 2010. Regional aspects of prolonged meteorological
droughts over Mexico and Central America. J. Clim. 23, 1175–1188.
Mendoza, V.M., Oda, B., Adem, J., 2001. An improved parameterization of the mean
monthly precipitation in the Northern Hemisphere. Atmosfera 14, 39–51.
Miyakoda, K., Jin-Ping, C., 1982. Essay on dynamical long-range forecasts of
atmospheric circulation. J. Meteorol. Soc. Jpn. 1, 292–308.
Nigam, S., Barlow, M., Berbery, E.H., 1999. Analysis links Pacific decadal
variability to drought and streamflow in the United States. EOS Trans.
Am. Geophys. Union 51, 621–625.
244
V.M. Mendoza et al. / Atmospheric Research 137 (2014) 228–244
Pavia, E.G., Graef, F., Reyes, J., 2006. PDO-ENSO effects in the climate of
Mexico. J. Clim. 19, 6433–6438.
Sanchez-Rubio, G., Perry, H.M., Biesiot, P.M., Johnson, D.R., Lipcius, R.N., 2011.
Oceanic–atmospheric modes of variability and their influence on riverine
input to coastal Louisiana and Mississippi. J. Hydrol. 396, 72–81.
Sang-Wook, Y., Kirtman, B.P., 2006. The characteristics of signal versus noise SST
variability in the North Pacific and tropical Pacific Ocean. Ocean Sci. J. 41, 1–10.
Schneider, N., Miller, A.J., Pierce, D.W., 2002. Anatomy of North Pacific decadal
variability. J. Clim. 15, 586–605.
Wallace, J.M., Gutzler, D.S., 1981. Teleconnections in the geopotential height
field during the Northern Hemisphere winter. Mon. Weather Rev. 109,
784–812.
Webster, P.J., 1981. Mechanisms determining the atmospheric response
to the sea surface temperature anomalies. J. Atmos. Sci. 38,
554–571.
Willmott, C.J., 1981. On the validation of models. Phys. Geogr. 2, 184–194.
Willmott, C.J., 1982. Some comments on the evaluation of model performance.
Bull. Am. Meteorol. Soc. 63, 1309–1313.
Willmott, C.J., Ackleson, S.G., Davis, R.E., Feddema, J.J., Klink, K.M., Legates,
D.R., O'Donnell, J., Rowe, C.M., 1985. Statistics for the evaluation of
model performance. J. Geophys. Res. 90, 8995–9005.
Zhong, Y., Zhengyu, L., 2009. On the mechanism of Pacific multidecadal
climate variability in CCSM3: the role of the subpolar NPO. J. Phys.
Oceanogr. 39, 2052–2076.