AMERICAN METEOROLOGICAL SOCIETY Journal of Climate
EARLY ONLINE RELEASE This is a preliminary PDF of the author-produced manuscript that has been peer-reviewed and accepted for publication. Since it is being posted so soon after acceptance, it has not yet been copyedited, formatted, or processed by AMS Publications. This preliminary version of the manuscript may be downloaded, distributed, and cited, but please be aware that there will be visual differences and possibly some content differences between this version and the final published version. The DOI for this manuscript is doi: 10.1175/JCLI-D-17-0115.1 The final published version of this manuscript will replace the preliminary version at the above DOI once it is available. If you would like to cite this EOR in a separate work, please use the following full citation: Munoz, A., X. Yang, G. Vecchi, A. Robertson, and W. Cooke, 2017: A Weathertype based Cross-Timescale Diagnostic Framework for Coupled Circulation Models. J. Climate. doi:10.1175/JCLI-D-17-0115.1, in press. © 2017 American Meteorological Society
LaTeX File (.tex, .sty, .cls, .bst, .bib)
Click here to download LaTeX File (.tex, .sty, .cls, .bst, .bib) Munozetal17_CrossTimescaleDiagnostics_final.tex
1
A Weather-type based Cross-Timescale Diagnostic Framework for Coupled
2
Circulation Models
3
Ángel G. Muñoz ∗
4
Atmospheric and Oceanic Sciences (AOS). Princeton University. Princeton, NJ 08540-6649. USA
5
NOAA. Geophysical Fluid Dynamics Laboratory. Princeton University. Princeton, NJ
6
08540-6649. USA
7
International Research Institute for Climate and Society (IRI). The Earth Institute. Columbia
8
University. Palisades, NY. 10964-1000
9
Xiaosong Yang
10
NOAA. Geophysical Fluid Dynamics Laboratory. Princeton University. Princeton, NJ
11
08540-6649. USA
12
Cooperative Programs for the Advancement of Earth System Science (CPAESS), University
13
Corporation for Atmospheric Research (UCAR), Boulder, Colorado, USA.
14
Gabriel A. Vecchi
15
Department of Geosciences, Princeton University. Princeton, NJ 08540-6649. USA
16
Princeton Environmental Institute, Princeton University. Princeton, NJ 08540-6649. USA
17
Atmospheric and Oceanic Sciences (AOS). Princeton University. Princeton, NJ 08540-6649. USA
18
Andrew W. Robertson
Generated using v4.3.2 of the AMS LATEX template
1
19
International Research Institute for Climate and Society (IRI). The Earth Institute. Columbia
20
University. Palisades, NY. 10964-1000
21
William F. Cooke
22
Cooperative Programs for the Advancement of Earth System Science (CPAESS), University
23
Corporation for Atmospheric Research (UCAR), Boulder, Colorado, USA.
24
NOAA. Geophysical Fluid Dynamics Laboratory. Princeton University. Princeton, NJ
25
08540-6649. USA
26
∗ Corresponding
author address: Á. G. Muñoz, Atmospheric and Oceanic Sciences (AOS). Prince-
27
ton University. Princeton, NJ 08540-6649. USA
28
E-mail:
[email protected] 2
ABSTRACT 29
This study proposes an integrated diagnostic framework based on atmo-
30
spheric circulation regime spatial patterns and frequencies of occurrence
31
to facilitate the identification of model systematic errors across multiple
32
timescales. To illustrate the approach, three sets of 32-year-long simulations
33
are analyzed for northeastern North America and for the March-May season
34
using the Geophysical Fluid Dynamics Laboratory’s Low Ocean-Atmosphere
35
Resolution (LOAR) and Forecast-oriented Low Ocean Resolution (FLOR)
36
coupled models; the main difference between these two models is the hori-
37
zontal resolution of the atmospheric model used. Regime-dependent biases
38
are explored in the light of different atmospheric horizontal resolutions and
39
under different nudging approaches. It is found that both models exhibit a
40
fair representation of the observed circulation regime spatial patterns and fre-
41
quencies of occurrence, although some biases are present independently of the
42
horizontal resolution or the nudging approach, and are associated with a mis-
43
representation of troughs centered north of the Great Lakes, and deep coastal
44
troughs. Moreover, the intra-seasonal occurrence of certain model regimes
45
is delayed with respect to observations. On the other hand, inter-experiment
46
differences in the mean frequencies of occurrence of the simulated weather
47
types, and their variability across multiple timescales, tend to be negligible.
48
This result suggests that low-resolution models could be of potential use to
49
diagnose and predict physical variables via their simulated weather type char-
50
acteristics.
3
51
1. Introduction
52
Global Circulation Models (GCMs) are essential tools for both scientific research (e.g., Delworth
53
et al. (2012); Taylor et al. (2012)) and the development of climate services (Vaughan and Dessai
54
2014) at different timescales. Since, by definition1 , models are not a perfect representation of
55
reality, different types of errors must be accounted for before GCMs can be used as a fair depiction
56
of the real world.
57
Common approaches to diagnose systematic errors involve the computation of metrics aimed
58
at providing an overall summary of the performance of the model in reproducing the particular
59
variables of interest in the study, normally tied to specific spatial and temporal scales. For exam-
60
ple, Gleckler et al. (2008) used different metrics to assess the climatological behavior of GCMs,
61
Covey et al. (2016) focused on model evaluation of the rainfall diurnal cycle, and several studies
62
have analyzed the present-time rainfall characteristics in state-of-the-art climate change simula-
63
tions (see, for example Reichler and Kim (2008); Delworth et al. (2012); Ryu and Hayhoe (2014);
64
van der Wiel et al. (2016)). Moreover, the number of open source packages to evaluate the fidelity
65
of GCMs compared to observations (e.g., Phillips et al. (2014); Mason and Tippet (2016); Gleck-
66
ler et al. (2016)) is rapidly increasing. Nonetheless, the evaluation of the goodness of a model
67
is not always tied to the understanding of the physical processes that are correctly represented,
68
distorted or even absent in the model world. As the physical mechanisms are more often than
69
not related to interactions taking place at multiple time and spatial scales (e.g., Nakamura et al.
70
(2012); Robertson et al. (2015); Muñoz et al. (2015, 2016)), cross-scale model diagnostic tools are
71
not only desirable but required.
1 The
word “model” is derived from Latin “modulus”, a “measure” or “standard” of something, which evolved to today’s idea of “likeness made
to scale”, for example in clay, wax or via mathematical or numerical expressions.
4
72
A complementary alternative to the common diagnostic approach mentioned above can be
73
achieved via a non-linear dynamical system perspective (Lorenz 1963; Palmer 1999). Thus, typ-
74
ical questions like “How well does this model represent the observed seasonal rainfall patterns?”
75
are framed as part of the more general question “Can the model adequately represent the available
76
states of the system?” (in a suitably coarse-grained phase space; see Ghil and Robertson (2002)).
77
Since only certain physical states can be accessed by the real-world system under study, as in sta-
78
tistical or quantum mechanics, the rationale is that models that cannot faithfully reproduce those
79
states should not be expected to provide, for example, the right rainfall or temperature patterns for
80
the correct reasons.
81
How to identify the available states? Theoretically, they are related to the concept of multiple
82
flow equilibria (Lorenz 1969; Charney and DeVore 1979; Reinhold and Pierrehumbert 1982) and
83
quasi-stationary regimes or metastable fixed points capable of attracting the chaotic trajectory of
84
the system; they can be recognized in a state (or phase) space as regions that are visited more
85
frequently – or, equivalently, regions surrounding a local density maximum. The identification
86
of these clusters in the state space poses a non-trivial statistical problem (Stephenson et al. 2004;
87
Christensen et al. 2015), and in general they correspond to proxies of the available states of the
88
system, and not the states themselves. From a practical perspective, in the atmosphere those clus-
89
ters are typically associated with recurrent daily circulation types or “weather types” (WTs), which
90
have been widely studied in the literature (Lorenz 1969; Charney and DeVore 1979; Reinhold and
91
Pierrehumbert 1982; Lorenz 2006; Vautard 1990; Michelangeli et al. 1995; Robertson and Ghil
92
1999; Moron et al. 2008; Johnson and Feldstein 2010; Riddle et al. 2013), as they can lead to both
93
important positive and negative socio-economic impacts.
94
Formally speaking, weather types are statistical constructs associated with recurrent circulation
95
configurations which can be used to study weather regimes, a more physical concept that often 5
96
requires additional conditions (e.g., the average time spent on each regime must be long compared
97
to other oscillations in the system, as in Lorenz (2006)). Having stated that formal difference,
98
for the purposes of this work both concepts are considered largely interchangeable. If correctly
99
defined, these weather types can be understood as “building blocks” or some sort of “alphabet”
100
that can be used to describe all the physically acceptable events of the system (Muñoz et al. 2015,
101
2016). This is shown schematically in Figure 1; the events, e.g., rainy days, can be explained by the
102
occurrence of individual weather types (letters) or particular WT sequences/transitions (words).
103
The underlying hypothesis used here is that climate variability across timescales can be de-
104
scribed in terms of the frequency of occurrence of weather types at the different scales, with
105
external (or internal) forcings taking the form of shifts in the residence time of the system in the
106
different basins of attractions of the state space. This idea is related to the Fluctuation-Dissipation
107
Theorem in climate (Leith 1975), that relates the mean response to small perturbations of a non-
108
linear dynamical system to fluctuations in the unforced system. As indicated by Leith (1975), the
109
nonlinear transfer of energy and enstrophy in the climate system implies sources of these variables
110
in some scales of motion and dissipation in others; hence, considering the present cross-timescale
111
diagnostics approach can help to understand better the problem.
112
Beyond the theoretical interest of associating weather types with physically acceptable states
113
of the system, the present approach is useful in those cases in which it is possible to identify
114
circulation-dependent systematic errors in climate models; a weather-type rectification (correc-
115
tion) has the potential to improve the related physical fields and events in the simulations.
116
A regime approach has been explored to study general biases and uncertanty in climate models
117
at specific timescales (e.g., Palmer and Weisheimer (2011); Perez et al. (2014); Christensen et al.
118
(2015)). Since it is possible to analyze the behaviour of the circulation regimes over a wide range
119
of different timescales –for example, by aggregating their frequency of occurrence at sub-seasonal, 6
120
seasonal, inter-annual and longer timescales–, and since they can be associated with physical pro-
121
cesses occurring across timescales (Moron et al. 2015; Muñoz et al. 2015, 2016), it is proposed
122
here that the weather-typing approach provides a natural and unified framework for cross-timescale
123
diagnostics of GCMs. Although the scheme is deemed especially useful when considering seam-
124
less prediction systems (Hoskins 2013), it can be also employed to analyze causes of bias at any
125
particular timescale. Furthermore, the same set of weather types can be used to diagnose a wide
126
range of variables in a physically consistent way, thus shedding light on the causes of biases rather
127
than focusing on the bias itself.
128
The goal of the present study is to illustrate the proposed approach using simulations produced
129
by two coupled GCMs developed by the Geophysical Fluid Dynamics Laboratory (GFDL), with
130
physical configurations designed to reproduce key aspects of the observed climate variability. For
131
the sake of the illustration, the study is only focused on rainfall during the March-April-May
132
(MAM) season for Northeastern North America (NENA). The MAM atmospheric circulation
133
regimes in this region are relatively well understood, especially in relation to flood events in the
134
Ohio and Mississipi river basins (Nakamura et al. 2012; Robertson et al. 2015).
135
The rest of the paper is organized as follows. After introducing the datasets and sumarizing the
136
methods in the next section, observed and modeled rainfall climatologies are analyzed in section
137
4. The weather-type diagnostics are presented in section 5 for daily, sub-seasonal, inter-annual and
138
“decadal” timescales, while section 6 deals with possible sources of bias and an overall discussion
139
of the results. Finally, the concluding remarks are presented in section 7.
140
2. Data
141
142
Both observations and model outputs were used in the present study. These are described in the following subsections. The time period considered in all datasets is MAM 1981-2012. 7
143
a. Observations
144
Observed rainfall fields were obtained from the gauge-based NOAA-NCEP-CPC Unified Pre-
145
cipitation gridded dataset (Chen et al. 2008). This product has daily temporal resolution and a
146
spatial resolution of 1◦ x 1◦ .
147
The analysis of the observed daily circulation over NENA was derived from the NCEP-NCAR
148
Reanalysis Project (version 2, or NNRPv2) 500 hPa geopotential data on a 2.5◦ x 2.5◦ grid (Kalnay
149
et al. 1996; Kistler et al. 2001), and also from the Modern-Era Retrospective Analysis for Research
150
and Applications (MERRA) for the same variable on a 0.5◦ x 0.5◦ grid (Rienecker et al. 2011).
151
These two datasets were used to investigate the impact of horizontal resolution and reanalysis
152
methods in the identification of the weather types.
153
b. Model data and Experimental design
154
This study explores the impact of (a) horizontal resolution and (b) Newtonian relaxation towards
155
observed fields on model biases associated with the variability of circulation regimes at multiple
156
timescales.
157
The three sets of climate simulations used are 32-year long, with 5 members each, produced by
158
two kindred coupled GCMs developed by the Geophysical Fluid Dynamics Laboratory (GFDL).
159
They share the same ocean, land and ice model components inherited from the GFDL Coupled
160
Models version 2.1, CM2.1 (Delworth et al. 2006), and version 2.5, CM2.5 (Delworth et al. 2012).
161
The models used in this study are the Low Ocean-Atmosphere Resolution, or LOAR (van der
162
Wiel et al. 2016), and the Forecast-oriented Low Ocean Resolution, or FLOR (Vecchi et al. 2014).
163
Unlike CM2.1 and CM2.5, LOAR and FLOR use essentially the same atmospheric model compo-
164
nent, based on a finite volume dynamical core on a cubed sphere (Putman and Lin 2007), integrat-
165
ing along 32 vertical levels and with horizontal resolutions of 2◦ x 2◦ (C48) for LOAR and 0.5◦ 8
166
x 0.5◦ (C180) for FLOR. The dynamical time step is modified to match the individual model’s
167
atmospheric resolution, and the atmospheric physics for both models is similar to that in CM2.5
168
(Delworth et al. 2012; Vecchi et al. 2014). The ocean model component is the Modular Ocean
169
Model (MOM) version 5 (Griffies 2012), at 1◦ x 1◦ and configured as reported in Vecchi et al.
170
(2014). The land surface model is the Land Model version 3 (LM3, (Milly et al. 2014)), with the
171
same horizontal resolution as the atmospheric model component. The sea ice model component is
172
the Sea Ice Simulator (SIS), having three vertical layers, one snow and two ice, and five thickness
173
categories, as reported in Delworth et al. (2006) and references therein. The time resolution for all
174
model output is daily.
175
A typical way to explore how well uncoupled GCMs reproduce the observed natural variability
176
is to force them with observed SSTs (e.g., à la Atmospheric Model Intercomparison Project, AMIP
177
(Gates et al. 1999)). Although this approach is, by definition, not possible for coupled GCMs, a
178
common alternative is to use a Newtonian nudging to relax certain model fields, such as SSTs,
179
towards observations (e.g., Rosati et al. (1997)), like SSTs. This method has been shown useful
180
to reproduce key aspects of the natural variability of the climate system and to decrease model
181
biases (e.g., Luo et al. 2008 and references therein). Thus, all 3 experiments used in the study
182
were nudged to observed fields as follows.
183
In two sets of numerical experiments, LOARsst and FLORsst , the models’ SSTs were relaxed
184
to daily-interpolated observed HadISST product (Rayner et al. 2003), SSTO , using a restoring
185
timescale τ = 5 days, such that
d + 1 (SSTO − SST ) ∂t SST = SST τ 9
(1)
186
b the coupled model tendency where ∂t represents the partial time-derivative of the field, and
187
of the field. These two experiments were used to analyze the impact of horizontal resolution on
188
model biases.
189
Since nudging only SSTs is often inadequate (Fujii et al. 2009), as the variability in the climate
190
system is not only controlled by sea-surface temperatures, for the third set of numerical experi-
191
ments, called FLORsst+strat , MERRA’s 6-hourly stratospheric temperatures and winds above 100
192
hPa were nudged in addition to the SST-nudging described above, using the same ansatz presented
193
in equation (1), but with a relaxation time τ = 6 hours, and a tapering factor γ such that it is one
194
for model layers above 50 hPa (i.e., 1, 4, 8, 14, 21, 30 and 41 hPa), and it is zero for layers below
195
100 hPa; from 50 hPa to 100 hPa, γ varies linearly from one to zero, thus transitioning in a smooth
196
way from the stratosphere to the troposphere. This same stratospheric nudging approach has been
197
used recently by Jia et al. (2017) to show the role of the extra-tropical stratosphere as an important
198
source of predictability at interannual scale. Both FLORsst and FLORsst+strat were used in this
199
study to explore the role of nudging in model biases.
200
3. Methods
201
Here the general methodology is described. The diagnostic approach per se is described in
202
section 5.
203
a. Cluster analysis
204
In order to identify the proxies of the available states of the system, daily circulation regimes
205
were determined performing a k-means analysis (e.g. Robertson and Ghil (1999)) on observed
206
and modeled 500 hPa geopotential height anomalies, each at its own spatial resolution to avoid the
207
possibility of spurious results induced by the spatial interpolation process. 10
208
The k-means technique is a partitioning method that classifies all days into a predefined number
209
of clusters, minimizing the intracluster sum of variance, W , for a partition P (the Voronoi diagram
210
generated by the classification process):
k
W (P) =
∑ ∑ ds2(X, p¯i)
(2)
i X∈pi
211
where i = 1...k, k is the total number of clusters in the solution, pi denotes the different clusters in
212
the partition and ds2 (X, p¯i ) represents the Euclidean line element (distance) between the cluster’s
213
maps X and centroid p¯i . In this work, no areal weighting was necessary, as the selected domain is
214
relatively small and it does not extend into high latitudes (30◦ N-50◦ N, more details below).
215
This procedure assigns only one cluster to each day on record. Daily geopotential data was first
216
projected onto its six leading empirical orthogonal functions (same number for all datasets), ac-
217
counting for at least 95% of the total observed variance. No additional time filtering was applied
218
to the data before clustering, thus retaining the annual seasonal cycle, inter-annual, sub-seasonal
219
and synoptic weather time scales for diagnosis. No projection between the modeled and observed
220
leading empirical orthogonal functions was performed, i.e., the modeled WTs were directly ob-
221
tained using exactly the same procedure as for the observed ones. As with the avoidance of any
222
kind of spatial interpolation before the k-means analysis, this was done in order to evaluate each
223
model’s weather types in an unbiased way.
224
Two approaches were tested to define the 500 hPa geopotential anomalies (departure from the
225
long-term mean) that characterizes each weather type. In one, the anomalies of all members were
226
concatenated along the time coordinate before the k-means process was performed, as in Muñoz
227
et al. (2016). In the second approach, the classification of the 500 hPa geopotential anomalies
228
was performed for each member independently, then computing the ensemble mean of the same 11
229
weather type across members. The latter method was used in the present study as it respects the
230
chronology and transition probabilities of the weather types in the presence of non-stationary data.
231
The classifiability index (Michelangeli et al. 1995), CI, measures the similarity of partitions of
232
the data, and permits the identification of the minimum number of clusters required to achieve a
233
good classification. Classification performance is measured via the pattern (or anomaly) correla-
234
tion coefficient ρi j between pairs of cluster centroids p¯i and q¯ j in partitions P and Q, respectively,
235
which allows the matrix ρ(P(k), Q(k)) to be computed, with elements given by M
∑ p0imq0 jm m
ρ( p¯i , q¯ j ) ≡ s
M
∀i, j = 1...k
M
(3)
∑ p02im ∑q02jm m
m
236
where the sums consider all the M grid points in the domain, and the grid point deviations are
237
computed as usual p0im
1 = p¯im − k
k
∑ p¯rm
(4)
r
238
q0jm
1 = q¯ jm − k
k
∑q¯rm
(5)
r
239
where m = 1...M. The maximal value of the i−th row of the k × k matrix ρ (3) represents the
240
cluster in Q that best fits the i−th cluster in P. If the two partitions are identical, of course,
241
ρ = 1.
242
In this study, a total of N = 100 partitions are used, obtained from 100 different initial random
243
seeds of the algorithm; the single partition that matches most closely the remaining ones is then
244
selected. This similarity is computed by averaging the values of ρ(Pn , Pn0 ) ∀n, n0 = 1...N, and,
245
following Michelangeli et al. (1995), CI(k) ≡
1 N(N − 1)
∑
1≤n6=n0 ≤N
12
ρ(P(k)n , P(k)n0 ))
(6)
246
Clustering solutions within the range of k = 2 − 10 were explored for the NENA geographical
247
domain, bounded by 30◦ N-50◦ N and 105◦W -69◦W . A k-means 7-cluster solution was found to
248
yield a statistically significant value of the classifiability index (p < 0.1), compared to a red-noise
249
background modeled as a first-order Markov process having the same covariance at lag 0 and 1
250
days as the atmospheric data (Michelangeli et al. 1995); therefore the solution, which is the same
251
one reported by Robertson et al. (2015), was selected for further analysis.
252
This set of clusters, or weather types, can be interpreted as a set of geopotential regimes that
253
typify the daily variability, and are considered to be the “building blocks” or “letters” mentioned
254
at the Introduction. Other cluster solutions were explored, verifying that the general features of
255
the circulation regimes presented below are robust and sufficient for the purposes of this study.
256
b. Similarity metrics
257
There are multiple metrics to evaluate how well a model reproduces observations (e.g., Mason
258
and Stephenson (2008); Jolliffe et al. (2012)); selection among them depend on the attribute or
259
type of question to be addressed. For the sake of simplicity, this work focuses on the similarity
260
of spatial patterns and temporal behavior between the simulated and observed weather types. Two
261
metrics are chosen for that purpose: pattern correlation and the scatter index. As indicated before,
262
the k-means analysis is performed on the native grid of the models and the observations; however,
263
when comparing results, all calculations were always carried out in a common low resolution grid
264
of 2◦ x 2◦ (the one of the NNRPv2 dataset).
265
266
The pattern correlation ρ is computed following equation (3), but considering the fact that the partitions now correspond to those modeled and observed.
267
The scatter index ξ is defined here as the root mean square error operator of the simulated and
268
observed frequencies of occurrence of the weather types, normalized by the weather type mean 13
269
frequency (e.g., Perez et al. (2014)). The frequency of occurrence is defined as the proportion of
270
time that each weather type occurs at each timescale window of interest, averaged across ensemble
271
members for the case of model simulations (see an example below). Two versions of the scatter
272
273
index are used in this work, one to evaluate the mean frequency state, ξ¯ |ts , and another for the temporal variability at different timescale windows ts , ξσ |ts :
s
k
k ∑ fiS − fiO
ξ¯ ≡
i
k
ts
∑ fiO i
s ξσ ≡
2
ts
k 2 k ∑ σ ( fiS ) − σ ( fiO ) i
ts
k
∑σ ( fiO) i
(7)
(8)
ts
274
where fiS and fiO denote the simulated and observed frequencies of the i = 1..k weather types, and
275
σ denotes the corresponding sample standard deviation. The different timescales (or timescale
276
windws) are presented in Section 5. A model with a perfect represetation of the observed frequency
277
of occurrence satisfies ξ¯ |ts = 0, and in consequence its representation of the variability in the
278
frequency of occurrence is also perfect (ξσ |ts = 0). In general that is not the case, and each index
279
provides information on these two statistics.
280
To evaluate the scatter index at a particular timescale implies to perform the corresponding
281
calculations on the time window defined for that purpose. To illustrate this idea, consider as an
282
example the overall evaluation of a model representation of the observed weather types frequencies
283
during the window defined as May 16-31, for all seasons in the period 1981-2012. The scatter
284
indices are then computed considering the observed and simulated frequencies of occurrence of 14
285
weather types for those thirty one 16-day-long windows, using equations (7) and (8), where the
286
vertical bars indicate that the indices are to be evaluated for the particular timescale (window) ts .
287
Once the scatter indices have been computed for the different timescales of interest, they can be
288
presented using boxplots to also convey information about their uncertainties in the models; for
289
example, if all members in a model perfectly agree of the value of a scatter index for a particular
290
timescale, the corresponding box in the boxplot will collapse to an horizontal line. More details
291
about these boxplots are discussed in section 5.
292
To analyze persistence of the weather types, the empirical probability density functions were
293
computed for each dataset and regime. In order to compare between the different numerical exper-
294
iments and the reanalysis, the Euclidean distance between each pair of the corresponding Weibull
295
distribution parameters, α (scale) and β (shape), was used to assess similarity. The Weibull distri-
296
bution f (x|α, β ) =
x β β x β −1 exp − α α α
(9)
297
is commonly used in survival or duration analysis, and provided better fit than other less flexible
298
distributions, like the Exponential one (which corresponds to the special case of β = 1).
299
4. Northeastern North America’s rainfall climatology
300
It is a common practice to evaluate the fidelity of a model compared to observations through
301
the analysis of the climatological behaviour of the variable of interest. This section uses the
302
MAM rainfall climatology of the region under study (30◦ N-50◦ N and 105◦W -69◦W , see Fig. 2)
303
to illustrate some key ideas of the present diagnostic approach.
304
The observed rainfall climatology (Fig. 2a) exhibits a clear precipitation gradient with higher
305
amounts (≈ 3 − 4 mm day−1 ) in a wide region covering approximately 30◦ N-40◦ N and 97◦W -
306
84◦W (most parts of the United States’ Alabama, Mississippi, Louisiana, Arkansas, Tennessee, 15
307
southern Missouri and southwestern Kentucky), with basically no precipitation along the western
308
border of NENA (Texas, Oklahoma, Kansas, Nebraska, the Dakotas, and Canada’s southern On-
309
tario), 0.5 − 1 mm day−1 to the north (southern Ontario and Québec) and 2 − 3.5 mm day−1 along
310
the Eastern Coast (from northern Florida to Maine).
311
A visual inspection of the models’ climatology (Fig. 2b-Fig. 2d) clearly shows some important
312
biases in both magnitudes and spatial distribution of rainfall, with simulations at higher resolution
313
(Fig. 2c - Fig. 2d) exhibiting some improvement with respect to the low-resolution one (Fig. 2b).
314
What are the causes of such biases? Typically, issues involving model resolution or physical pa-
315
rameterizations (specially for rainfall) are frequently identified as the sources of bias –and indeed
316
higher horizontal and vertical resolution, as well as better physics, tend to improve the representa-
317
tion of the observed fields. Nonetheless, it is also possible that the resolution and parameterizations
318
are fit for purpose, and something else is failing. Whatever the causes, a complementary approach
319
consisting of the diagnosis of the physical mechanisms conducive to precipitation –rather than how
320
well the precipitation itself is represented in the model– is also useful and most often required.
321
Rainfall variability in NENA is dominated by synoptic-scale circulation patterns (Archambault
322
et al. 2008; Nakamura et al. 2012; Robertson et al. 2015; Roller et al. 2016) that are, in turn,
323
modulated by well known climate modes at multiple timescales like El Niño-Southern Oscillation
324
(ENSO), the North Atlantic Oscillation (NAO), the Pacific-North American pattern (PNA), or the
325
Madden-Julian Oscillation, (MJO; e.g., Ropelewski and Halpert 1986, 1987; Barnston and Livezey
326
1987; Wheeler and Hendon 2004).
327
Although some studies have found an inconclusive link between ENSO and NENA’s climate
328
(e.g., Ropelewski and Halpert (1986)) others indicate that this mode can modulate the frequency
329
of low-pressure systems and storms in the region (Trenberth and Caron 2000; Frankoski and De-
330
Gaetano 2011). Similarly, pressure and geopotential height anomalies associated with the NAO 16
331
modify the frequency of occurrence of nor’easters, as well as storm track locations over the North
332
Atlantic basin via changes to the position and orientation of the North Atlantic jet stream (Jones
333
and Davis 1995; Archambault et al. 2008). There is also evidence of links between PNA and
334
NENA’s rainfall anomalies (Leathers et al. 1991; Notaro et al. 2006), and between MJO’s phases
335
5-7 and precipitation rate in the region (Becker et al. 2011; Zhou et al. 2012).
336
The effect of these and other climate modes conducive to rainfall in NENA can be studied
337
through their influence in the occurrence, persistence and evolution of daily weather types. For
338
example, Roller et al. (2016) analyzed NENA’s wintertime mean and extreme precipitation, storm
339
tracks and teleconnections using a set of five WTs defined in terms of 850 hPa winds; similar
340
studies have been conducted in other parts of the world for different seasons (Moron et al. 2008,
341
2011, 2015; Muñoz et al. 2015, 2016).
342
The rainfall climatology (Fig. 2) discussed in this section can thus be understood in terms of the
343
(non-)linear contribution of the different mechanisms represented by persistence and transitions
344
of the region’s daily circulation regimes (WTs, or atmospheric states). A misrepresentation of the
345
physical interactions involved, even with perfect rainfall parameterizations, can generate bias not
346
only in the climatological precipitation field, but in higher-order statistics of the rainfall variability
347
at different timescales. The same can be said about other variables physically associated with the
348
behavior of those WTs.
349
Hence, the next section focuses on diagnosing how well the models represent the observed
350
behavior of the WTs for different timescales.
351
5. Cross-timescale diagnostics
352
This section first discusses the circulation regimes obtained for the observations and experi-
353
ments, before turning its attention to different tools to diagnose the weather types evolution at 17
354
daily to decadal scales. Although the method is general and can be used for longer timescales, this
355
study is constrained by the availability of longer observed rainfall records.
356
The computed set of seven NENA WTs found to best typify the daily circulation regimes for
357
MAM is presented in Fig 3 plotted over the entire hemisphere to better identify wave-like patterns,
358
and in Fig 4 for a more regional analysis of the weather types. The regimes with the highest ob-
359
served frequency of occurrence are located to the left and the less frequently occurring to the right
360
(see top row in those figures; the model regimes were ordered to follow each observed pattern).
361
Equation (3) was used to identify the “model-equivalent WT”, and physical interpretation of the
362
hemispheric patterns (Fig 3) was used in those cases in which the pattern correlation coefficients
363
provided too similar values for two given regimes.
364
Two different reanalysis products were used to analyze the robustness of the method identify-
365
ing the observed WTs, and the dependence on horizontal resolution (NNRPv2 at ∼ 2.5◦ versus
366
MERRA at ∼ 0.5◦ ). Table 1 and Table 2 show a comparison of the anomaly correlation coeffi-
367
cient between WTs using NNRPv2 and MERRA as reference, respectively. The results are indeed
368
consistent across reanalyses and resolutions.
369
The observed weather types (top two rows of Fig 3 and Fig 4) exhibit synoptic-scale merid-
370
ionally elongated dipolar wave patterns (WT1, WT3, WT5, WT6), and monopole/dipole patterns
371
zonally elongated (WT2, WT4, WT7). Weather regimes that are predominantly associated with
372
positive geopotential anomalies (WT1 and WT2) tend to be more frequent –and more persistent,
373
as it will be shown later– than the more transient regimes (WT4-WT7), which show spatial struc-
374
tures with dominant negative geopotential anomalies (see Fig 3 and Fig 4). Although this general
375
separation between more persistent and more transient circulation regimes is present in the simu-
376
lations, the ordering in those cases –which reflects their mean frequencies– is not exactly the same
377
as in the observations. 18
378
As it will be shown in sub-section 5b, there are preferred sequences of states whose pattern evo-
379
lution and typical timescales suggest eastward propagation of baroclinic waves (e.g., state transi-
380
tions 3 → 1 → 3, top rows in Fig 3). Generally speaking, in NENA the MAM daily circulation
381
regimes tend to be associated with continental ridges west of the Great Lakes (WT1, top rows
382
in Fig 4), continental ridges over the Great Lakes (WT2), northeastern seaboard ridges (WT3),
383
troughs centered north of the Great Lakes (WT4), deep coastal land troughs (WT5), southeastern
384
seaboard ridges (WT6), and deep northeastern troughs (WT7). The seaboard ridges (WT3 and
385
WT6) have been shown to be associated with extreme rainfall events in the Ohio river basin; these
386
two circulation types tend to occur more often during La Niña years, and phase 5 of the MJO also
387
modulates their seasonal frequency, with lower occurrence for WT3 and higher presence for WT6
388
(for additional details see Robertson et al. (2015)).
389
There is no simple answer to the question of what set of experiments best represents the observed
390
weather types, as the answer depends on the basis for the comparison. The shapes, magnitudes,
391
locations, tilt and frequencies of the weather types are characteristics to consider. On average, both
392
LOAR and FLOR models do a good job reproducing the observed circulation regimes, although
393
some important biases are present (Fig 3 and Fig 4, Table 1 and Table 2). For example, the spatial
394
features of WT1, the most frequently observed, are well represented in all experiments, but the
395
ensemble-mean frequency of occurrence is about 30% too low in FLORsst . The observed dipo-
396
lar configuration in WT3 is basically absent in the FLORsst+strat ensemble mean for that regime,
397
and for WT4 all experiments exhibit southwardly shifted and widely enhanced negative geopo-
398
tential anomalies with respect to the observations. WT5 appears severely tilted (about +45◦ ) in
399
the simulations, arguably due to a misrepresentation and location of the weak positive geopo-
400
tential anomaly observed north of 50◦ N near and over the Great Lakes (Fig 4). FLOR tends to
401
show positive geopotential anomalies along the eastern coast of the US in WT6, especially in the 19
402
FLORsst+strat experiment, which also exhibits important frequency biases for that regime. Finally,
403
although the simulated WT7 spatial patterns are very well represented (see high correlations in
404
Tables 1 and 2), all experiments overestimate its frequency of occurrence.
405
Since there are no striking differences in the weather type representations in terms of the resolu-
406
tion of the reanalyses, the NNRPv2 product is selected as the reference in all following discussions
407
about circulation regimes characteristics, unless otherwise indicated.
408
The persistence of these circulation patterns and their transitions control, both in the real world
409
and in the simulations, aspects like the moisture that is advected into NENA, and thus this weather-
410
within-climate approach is normally used to better understand the physical mechanisms behind
411
the ocurrence or not of (extremely) rainy days in a region (Robertson and Ghil 1999; Moron et al.
412
2008, 2013, 2015; Muñoz et al. 2015, 2016). As discussed in Section 4, the systematic errors in
413
the simulated weather regimes can help to explain the biases in other variables, as for example in
414
the rainfall field and its climatological behavior. To illustrate this idea, Figure 5 shows the average
415
daily rainfall regimes (RR), defined by compositing rainfall values associated with each weather
416
type.
417
As expected, FLOR tends to simulate better the rainfall field than LOAR at a local level; how-
418
ever, at a regional scale, there are not statistically significant differences (p < 0.05, two-sample
419
t-Student test) in the spatial correlation coefficients between the three experiments. Table 3 shows
420
the anomaly correlation coefficients between the rainfall regimes in the models and observations.
421
Overall, the most significant biases appear in the daily rainfall regimes associated with the weather
422
types showing greater bias over NENA (Fig. 5), i.e., WT4 and WT5. Errors in magnitude and spa-
423
tial distribution of the rainfall anomalies are related to misrepresented atmospheric circulations
424
and moisture fluxes in WT4 in all experiments (not shown), exhibiting positive rainfall anomalies
425
along the coast as a result of the deformed and displaced trough discussed above (Fig. 4). In spite 20
426
of the tilt that WT5 exhibits in the simulations, the associated daily rainfall patterns for NENA are
427
not too biased, except along the northeastern coast where the anomalies should have opposite sign;
428
this is attributed in part to the fact that the circulation and moisture fluxes over NENA are similar
429
to the observed one, even when that is not the case at a larger scale. Likewise, although WT3 is
430
the circulation regime with the worst large-scale anomaly correlation coefficients (e.g., Table 1),
431
its representation of the associated physical mechanisms controling rainfall over NENA provides
432
a very good depiction of the observed rainfall regime RR3. Having this regime well represented
433
in the simulations is important to adequately represent extreme rainfall events over the Ohio river
434
basin (Robertson et al. 2015).
435
Biases both in the spatial patterns (involving shape, magnitudes, tilt, location) and the frequency
436
of occurrence of the simulated weather types contribute to biases in rainfall and other variables at
437
different timescales. In studies involving a large number of years, e.g., 100 years, two different k-
438
means solutions should be computed to analyze, for example, whether the climate change signal is
439
modifying the weather types’ spatial patterns or the dimensionality of the phase space. For studies
440
like the present one, however, which involves just 3 decades, the spatial patterns are normally
441
assumed to be constant. This allows for the analysis of the weather types’ temporal variability at
442
different timescales in terms of changes in their frequency of occurrence at those timescales.
443
A possible way to summarize how well the simulations reproduce both the mean frequency of
444
occurrence and its variability across multiple timescales is through the use of the corresponding
445
scatter indices (see equations (7) and (8)), presented in Fig. 6 for two particular sub-seasonal win-
446
dows (March 20th-30th and May 4th-14th; further discussed in section 5c), for the inter-annual
447
variability considering all MAM seasons in the 1981-2012 period (section 5d), and for the first and
448
last decades in the same period of years (section 5e). As with the case of the spatial patterns (e.g.,
449
Table 1), the analysis of the frequencies of occurrence indicates that no particular model or exper21
450
iment can be – overall – considered the best one across all the timescales in study. Certainly, there
451
are differences in terms of the median and dispersion values at particular scales, with higher errors
452
and uncertainties in the sub-seasonal case; nonetheless, within-scale differences in the medians
453
are normally negligible. Furthermore, compared to LOARsst , FLORsst tends to have the same or a
454
lower dispersion for both scatter indices (Fig. 6).
455
The following sub-sections provide more details on daily transition statistics using Klee dia-
456
grams (sub-sections 5a and 5b), and further analysis pertinent to the temporal variability of the
457
simulated circulation regimes and to understanding Fig. 6 (sub-sections 5c,d,e).
458
a. Klee diagrams
459
Klee diagrams, shown in Fig. 7, are a way to represent the temporal evolution of the available
460
states of the system (Muñoz et al. 2015). These diagrams consist of a simple matrix plot sketching
461
the daily evolution of weather types for the entire period under study. They are equivalent to
462
the representation of the Viterbi state-sequences, except for the fact that no Viterbi algorithm or
463
Hidden Markov Model (e.g., Robertson et al. (2006)) is involved in the process. A Klee diagram
464
is the basis to analyze daily transitions and temporal variability at sub-seasonal, seasonal, decadal
465
and longer timescales. Moreover, it has been used to define subseasonal-to-seasonal states for
466
forecast purposes, using hybrid dynamical-statistical models (Muñoz et al. 2016).
467
If a simulation has exactly the same Klee diagram as the one computed from the observations,
468
then it has a perfect representation of the observed weather types’ evolution across timescales,
469
independently of how well the model represents their spatial patterns; of course, even if the mod-
470
els were perfect, the Klee diagrams would not be exactly the same due to atmospheric chaos.
471
Nonetheless, the idea is conceptually useful, and helps to define several ways to diagnose similar-
472
ity in the temporal evolution and associated statistics. Moreover, having simulated Klee diagrams 22
473
that exhibit similar characteristics to observations is also of practical use because it is then pos-
474
sible to use a combination of modeled frequencies of occurrence and observed spatial patterns to
475
represent the evolution of the circulation regimes at a given timescale. In such cases, this approach
476
has important implications for prediction, an idea that is briefly discussed in Section 6, and that
477
will be explored in more detail elsewhere.
478
Overall, the observed and simulated Klee diagrams for NENA show high similarity (Fig. 7).
479
Since it is not possible to have an ensemble mean of Klee diagrams because they represent cat-
480
egories and not real numbers, the analysis must be performed on a member-per-member basis.
481
Visual inspection suggests that all experiments exhibit a dominance of WT1 and WT2 toward the
482
end of the season, and of WT6 and WT7 during the first half, all consistent with the observations
483
and consistent with the predominance of negative height anomalies in March and positive ones
484
in May within the MAM season (Fig. 4). However, some biases are apparent, like the presence
485
in LOARsst and FLORsst+strat of too many days with WT3 at the end of the season, which, for
486
example, could provide false alarms in those cases in which WT3 is related to floods in the Ohio
487
river basin.
488
Different statistics can easily be computed from the Klee diagrams to help diagnose and compare
489
dynamical models. Some examples – like daily transition probabilities, mean durations (persis-
490
tence) for each weather type, and other summaries to analyze the evolution of the circulation
491
regimes at different timescales – are discussed in the following sub-sections.
492
b. Daily transitions and typical durations
493
Daily transition matrices are commonly used to characterize persistence and preferred state tran-
494
sitions. Their diagonal sketches the persistence probabilities for each weather type, and the off-
495
diagonal elements represent the conditional probabilities of transition to a particular regime (along 23
496
the horizontal axes of the matrix, “posterior WT”) given that a different weather type (along the
497
vertical axes, “prior WT”) occurred on the previous day.
498
Daily transitions in NENA, presented in Fig. 8, are dominated by persistence, with continental
499
ridges over the Great Lakes (WT2) being the most probable regime to persist, especially during
500
May (Fig 7). The most frequently observed statistically significant transitions (p < 0.1, see Vau-
501
tard et al. (1990)) suggest circuits like 1 → (2, 3) → 1 or 4 → 3 → 1, that can be associated with
502
the propagation of baroclinic waves over NENA, but also transitions leading to highly persistent
503
states, like 6 → 7 → 4, associated with anomalously high moisture fluxes from the Gulf of Mex-
504
ico and the Caribbean conducive to rainy days along the eastern coast, followed by days with a
505
high-pressure system stationed in the northern part of the region, typically conducive to low-level
506
divergence and no rain (see Fig 7, Fig 4 and Fig 5).
507
All simulations for NENA adequately represent the fact that the persistence probabilities are
508
significantly higher than non-self transitions. As expected, some biases exist; for example, the
509
persistence of WT4 in the LOARsst and FLORsst experiments (see Fig 8) is overestimated, and
510
there are consistent biases in all experiments for transitions like 3 → 4, 4 → 3, 4 → 1, 7 → 5 and
511
4 → 7. But in general, all models tend to capture most of the observed transition probabilities, with
512
differences always less than ±15%; moreover, no statistically significant differences (p < 0.05,
513
two-sample t-Student test) exist between the average transition probabilities of the experiments.
514
It is also important to evaluate if the simulations fairly represent the typical persistence of the
515
weather types. Figure 9 shows relative frequency histograms and their corresponding Weibull
516
distribution fit for the most common durations; for comparison, Table 4 presents the values of the
517
Weibull distribution parameters α and β , which measure the scale (or characteristic life) and the
518
shape (or slope) of the distribution, respectively.
24
519
This analysis indicates that WT1-WT3 (predominant in May) tend to persist more than the other
520
weather types (as expected from the visual inspection of the observations’ Klee diagram, Fig 7),
521
WT4 tends to transition faster than the other regimes, and WT5-WT7 exhibit similar duration
522
probability density functions (PDFs), all these facts in agreement with the observations.
523
As with the spatial patterns of the weather types between models and observations, there is not a
524
unique set of experiments that is consistently better than the others (i.e., for which all the regimes
525
adequately represent the observed persistence distributions); nonetheless, FLORsst tends to have
526
better self-transition statistics for WT2, and WT4-WT6 (Table 4; bold numbers indicate experi-
527
ments with best representation of self-transitions –persistence– for each WT). Overall, although
528
the main characteristics of the duration PDFs are captured well by the experiments (e.g., the fact
529
that can be well modeled by a Weibull distribution, higher persistence in WT1-WT3), certain fea-
530
tures are not. It is possible to identify WT5 and WT6 as the regimes with the worse representation
531
in terms of its persistence in all simulations (Table 4); for example, WT5 overestimates the number
532
of “early” transitions by at least a factor of 1.5. As complementary information, Table 5 summa-
533
rizes the average persistence of each WT in the NNRPv2 and the numerical experiments; results
534
are consistent with the discussion presented above and Table 4.
535
c. Sub-seasonal evolution
536
The typical sub-seasonal evolution of the weather types can be analyzed using their “climato-
537
logical” frequency of occurrence as computed by the regime’s appearance for each calendar day,
538
after an 11-day moving average is applied to the frequency of occurrence time series in order to
539
filter out the shortest timescales. This metric, hereafter referred to as “sub-seasonality” to avoid
540
the cacophonic “sub-seasonal seasonality”, is shown in Fig. 10. Clearly, MAM is a transition 25
541
season between boreal winter and summer, that could be characterized by low occurrence of ridge
542
configurations (WT1-WT3) during March, and their dominance during May.
543
Generally speaking, the sketched sub-seasonal evolution of the weather types in the numerical
544
experiments is similar to the observations, although there is an overall delayed sub-seasonality in
545
several weather types (compare the slopes of the curves in Figs. 10b,c,d with the ones in Fig. 10a).
546
Biases are present both in the sub-seasonal frequency of occurrence of some weather types and in
547
their actual evolution. For example, the frequency of WT4 is underestimated in all experiments,
548
especially after calendar day 50 (Fig. 10); the model-equivalent WT5-WT7 tend to have more
549
or less the same relative frequency of occurrence in April than in March, which is inconsistent
550
with observations; WT1 has its peak of occurrence typically between calendar days 65-75 (May
551
4th-May 14th), but this maximum appears about 10 days earlier in FLORsst+strat .
552
Due to the clear differences between the beginning and the end of the season, two periods were
553
considered for further analysis: March 20th-March 30th, and May 4th-May 14th (see black boxes
554
in Fig. 10).
555
Errors in the median values of the simulated frequencies of occurrence of weather types, as
556
measured by the scatter index (Fig. 6a), tend to be similar between the two periods under con-
557
sideration, although with higher dispersion during the second half of the season which is mostly
558
due to the misrepresentation of the sub-seasonality of WT4-WT6. On the other hand, errors in the
559
standard deviations of the occurrences are more clearly discriminated (Fig. 6b), being similar in all
560
three experiments but with higher values for the May 4th-May 14th period. For the end-of-March
561
section under study, the median values for the standard deviations of the simulated frequencies are
562
similar to the other timescales analyzed in this work (inter-annual and decadal), although LOARsst
563
exhibits higher and similar dispersions at sub-seasonal scale than at the other scales.
26
564
d. Inter-annual variability
565
Analysis of the ensemble-mean inter-annual evolution of the frequency of weather types, shown
566
in Figure 11, indicates that the highest root mean squared errors, presented in Table 6, occur for
567
patterns associated with troughs north of the Great Lakes (WT4), especially for LOARsst (∼ 11.7
568
days per season, compared to ∼ 10.0 days and ∼ 9.8 days for FLORsst and FLORsst+strat , respec-
569
tively). On the other hand, WT3 and WT7 – northeastern seaboard ridges and deep troughs – have
570
the best average representation of the inter-annual variability in all experiments, with slightly lower
571
errors for LOARsst and FLORsst+strat (∼ 5.1 days for both WT3 and WT7 in both experiments,
572
compared to ∼ 6 days for the same weather types in FLORsst ). Nonetheless, on average, there
573
are no statistically significant differences (p < 0.05, using a two-sample t-Student test) between
574
the experiments, with an overall median error of 7.3 days, which is lower than 10% of the total
575
days in the season. This result is consistent with the scatter index values for the mean frequency
576
of occurrence at inter-annual scales (Fig. 6a).
577
The variability in the frequencies –measured by the associated standard deviation– is, again,
578
very similar between the experiments. Moreover, the fact that there is relatively low dispersion
579
in the variability scatter index for almost all timescales (Fig. 6b) implies agreement between the
580
different members in each numerical experiment, suggesting low model uncertainty in the reported
581
values of this parameter. Nonetheless, overall, Fig. 11 suggests that the experiments do not seem
582
to capture well the observed inter-annual variability.
583
e. Decadal differences
584
There are not enough years to formally study inter-decadal variability, and thus only the differ-
585
ences in the frequency of occurrence of weather types were analyzed for the first and last decades, 27
586
after smoothing the frequency of occurrence time series using an 11-year moving average, to pick
587
up the long time-scale signals of interest in the present analysis.
588
Differences in medians and dispersions of the mean frequency of occurrence are negligible for
589
the two decades (Fig. 6a), although dispersion in the simulated mean frequencies of occurrence are
590
definitively higher in the FLOR experiments than in LOARsst for the 1981-1990 decade. FLORsst
591
and FLORsst+strat show slightly lower medians for the scatter index of the standard deviations for
592
the 2003-2012 decade, although with higher dispersions than LOARsst . Overall, both decades are
593
showing the same ranges and values for the statistics considered.
594
6. Discussion
595
The approach presented here offers tailored diagnostics to understand possible sources of model
596
biases at multiple timescales. The basic idea is that the inherent biases at the synoptic or low-
597
frequency variability scale in models could be rectified at larger scales, according to how climate
598
drivers excite the observed weather types differentially on longer subseasonal-to-seasonal and
599
seasonal-to-decadal scales. A variety of diagnostic metrics were explored to identify model er-
600
rors at several timescales. Nonetheless, putting together the big picture provided by the different
601
metrics is in general not a trivial task.
602
The analysis performed indicates that, at large scale, the simulations have trouble represent-
603
ing the observed spatial pattern associated with WT3 (Table 2), although at regional scale –over
604
NENA– the spatial configuration of the northeastern seaboard ridges is actually good enough to
605
provide a fair representation of the observed rainfall regimes (Table 3), suggesting that the ob-
606
served physical mechanisms that control rainfall in that case, e.g., moisture and heat transport
607
from the Gulf of Mexico (Fig. 4), are present in the simulations. This has important implications
608
for flood prediction in the Ohio river basin (Nakamura et al. 2012; Robertson et al. 2015). 28
609
In contrast, the lowest rainfall pattern correlations are obtained for the regime associated with
610
troughs north of the Great Lakes (RR4, WT4; see Table 3), attributed earlier to the southward dis-
611
placement of the geopotential anomaly with respect to the observed pattern, and its enhancement
612
over most of North America. This is truly the worst circulation regime simulated in the exper-
613
iments. Not only is the spatial pattern poorly simulated, but also the depiction of the observed
614
temporal variability across all timescales is the worst of all WTs. These issues are hypothesized
615
here to be part of the same pathology, and they could be related to problems in the models’ ren-
616
dition of tropical-extratropical interactions, as the seasonal frequency of occurrence of WT4 is
617
significantly correlated with the Niño3.4 SST index (not shown), a link that will be treated –
618
along with other teleconnection indices and circulation regimes – in a future paper, following the
619
methodology discussed in Muñoz et al. (2015).
620
621
The other weather regimes have a fair representation of the geopotential anomalies and rainfall patterns over NENA, although this is not necessarily true at continental or hemispheric scale.
622
Altogether, there are not significant differences in the average performance of LOAR and FLOR
623
in terms of the reproduction of the spatial patterns and temporal variability of the observed weather
624
types, although a certain experiment can be better than the others when considering particular
625
characteristics (e.g., mean frequency at inter-annual scale, or the persistence of WT4; see Section
626
5). In this work, the question of which model is better is really a question of what nudging
627
approach performs better and what is the impact of horizontal resolution.
628
Nudging both SST and stratospheric fields did not consistently improve the representation of
629
the weather types in the model, and indeed in some cases provided worse results than the SST-
630
only nudging experiment (FLORsst ). It is possible that some stratosphere-troposphere and ocean-
631
atmosphere interactions are not being well simulated, and that some improvement can be achieved
29
632
if the vertical resolution in the model is increased to adequately account for the stratospheric
633
processes. This is a matter of future research.
634
As indicated earlier, no significant improvement was found when increasing horizontal reso-
635
lution, neither in the reanalysis products nor in the model experiments (LOARsst and FLORsst ).
636
This is attributed to the fact that synoptic-scale 500 hPa geopotential height anomalies do not re-
637
ally require high resolution in order to reproduce the key physical mechanisms associated with, for
638
example, propagation of Rossby waves that perturbs circulation patterns, or the moisture advec-
639
tion conducive to rainfall; in addition, the topography in NENA is not tall or complex enough as
640
to negatively impact the low resolution model. Yet, high horizontal resolution could be important
641
in other regions of the world.
642
Although high spatial resolution does not seem to be necessary to satisfactorily reproduce ob-
643
served weather types, high-resolution models like FLOR have the advantage of providing phys-
644
ically related variables like rainfall or surface temperature at a resolution preferred by decision-
645
makers and for the provision of climate services (Vaughan and Dessai 2014). Nonetheless, it is
646
possible to exploit the fair representation of weather type characteristics by faster coupled models
647
like LOAR to “reconstruct” fields of interest, e.g., the rainfall climatology in NENA.
648
649
Since the rainfall climatology, < p >, can be computed in terms of a linear combination of rainfall regimes, RRi , and the total frequency of occurrence of those regimes, Fi , k
< p >=
∑FiRRi
(10)
i
650
for i = 1..k regimes, if the model has an adequate representation of only one of these fields, then
651
observations could be used to compute the other factor in the linear combination. For example, the
652
rainfall regimes of the experiments analyzed in this work (ModRR) could be used in conjunction
653
with the observed frequencies of occurrences (ObsF) to reconstruct the observed rainfall climatol30
654
ogy, as shown in Fig. 12a,b. For other approaches that can be used for prediction purposes, see
655
Moron et al. (2010).
656
As expected, the experiments with FLOR provide better spatial rainfall patterns than LOARsst ,
657
because of their higher resolution. Although there are biases, the use of the observed frequency of
658
occurrences has improved the original simulated rainfall climatologies (Fig. 2b - Fig. 2d). Further
659
improvement is obtained if the observed rainfall regimes (ObsRR) are used in conjunction with the
660
modeled frequencies (ModF; Fig. 12c). With a satisfactory bias-correction method, this approach
661
has the potential to provide relatively economic – at least from a computational point of view –
662
diagnostic products and forecasts.
663
7. Concluding remarks
664
This work discussed a new diagnostic framework to evaluate the performance of models across
665
multiple timescales, based on their representation of the observed spatial and temporal variability
666
of weather types. Under this non-linear system dynamics perspective, “good” models are those
667
that correctly reproduce the observed characteristics of the weather types at multiple timescales.
668
The framework takes advantage of the weather-typing decomposition, in terms of the spatial
669
patterns of the circulation regimes and their temporal evolution, to analyze model performance at
670
multiple timescales focusing on the evaluation of tailored statistics like daily transition probabil-
671
ities, weather type mean durations and sub-seasonal, inter-annual and longer-term frequencies of
672
occurrence. Furthermore, since the circulation regimes are normally linked to concrete climate
673
modes, they can also be used to diagnose model biases from a physical perspective, like deforma-
674
tions or displacements of particular geopotential height configurations that control the occurrence
675
of rainfall in a region of the world. 31
676
To illustrate how the diagnostic approach works, it was applied to three different sets of numer-
677
ical experiments using Geophysical Fluid Dynamics Laboratory coupled circulation models. The
678
simulations tend to represent well the location, shape and magnitude of daily circulation regimes
679
and associated rainfall patterns, although some important biases were reported and discussed. Fur-
680
ther research is being conducted to perform an in-depth analysis of possible tropical-extratropical
681
interactions that might not be well represented by the models.
682
Finally, the present framework can also be used for model inter-comparison, and can be applied
683
to uncoupled and regional models.
684
Acknowledgments. The authors are grateful to Tony Barnston and Simon Mason (IRI), and
685
Nathaniel Johnson and Ángel Adames (GFDL) for discussions about different aspects of the pa-
686
per. ÁGM was supported by National Oceanic and Atmospheric Administration’s Oceanic and
687
Atmospheric Research, under the auspices of the National Earth System Prediction Capability.
688
AWR was supported by NOAA Next Generation Global Prediction System (NGGPS) project grant
689
NA16NWS4680014. This paper is dedicated to Eneko Muñoz and Cathy Vaughan (ÁGM’s nena).
690
References
691
Archambault, H. M., L. F. Bosart, D. Keyser, and A. R. Aiyyer, 2008: Influence of Large-Scale
692
Flow Regimes on Cool-Season Precipitation in the Northeastern United States. Monthly Weather
693
Review, 136 (8), 2945–2963, doi:10.1175/2007MWR2308.1, URL http://journals.ametsoc.org/
694
doi/abs/10.1175/2007MWR2308.1.
695
Barnston, A. G., and R. E. Livezey, 1987: Classification, Seasonality and Persistence of Low-
696
Frequency Atmospheric Circulation Patterns. URL http://journals.ametsoc.org/doi/abs/10.1175/
697
1520-0493{\%}281987{\%}29115{\%}3C1083{\%}3ACSAPOL{\%}3E2.0.CO{\%}3B2http: 32
698
//journals.ametsoc.org/doi/abs/10.1175/1520-0493(1987)115{\%}3C1083:CSAPOL{\%}3E2.
699
0.CO;2, 1083–1126 pp., doi:10.1175/1520-0493, 9605103.
700
Becker, E. J., E. H. Berbery, and R. W. Higgins, 2011: Modulation of Cold-Season U.S. Daily
701
˘ SJulian Precipitation by the MaddenâA ¸ Oscillation. Journal of Climate, 24 (19), 5157–5166, doi:
702
10.1175/2011JCLI4018.1, URL http://journals.ametsoc.org/doi/abs/10.1175/2011JCLI4018.1.
703
Charney, J. G., and J. G. DeVore, 1979: Multiple Flow Equilibria in the Atmosphere and
704
Blocking.
URL
http://journals.ametsoc.org/doi/abs/10.1175/1520-0469{\%}281979{\%
705
}29036{\%}3C1205{\%}3AMFEITA{\%}3E2.0.CO{\%}3B2http://journals.ametsoc.org/doi/
706
abs/10.1175/1520-0469(1979)036{\%}3C1205:MFEITA{\%}3E2.0.CO;2,
707
doi:10.1175/1520-0469(1979)0362.0.CO;2.
1205–1216 pp.,
708
Chen, M., W. Shi, P. Xie, V. B. S. Silva, V. E. Kousky, R. Wayne Higgins, and J. E. Janowiak,
709
2008: Assessing objective techniques for gauge-based analyses of global daily precipitation.
710
Journal of Geophysical Research, 113 (D4), D04 110, doi:10.1029/2007JD009132, URL http:
711
//doi.wiley.com/10.1029/2007JD009132.
712
Christensen, H. M., I. M. Moroz, and T. N. Palmer, 2015: Simulating weather regimes: impact of
713
stochastic and perturbed parameter schemes in a simple atmospheric model. Climate Dynamics,
714
44 (7-8), 2195–2214, doi:10.1007/s00382-014-2239-9, URL http://link.springer.com/10.1007/
715
s00382-014-2239-9.
716
Covey, C., P. J. Gleckler, C. Doutriaux, D. N. Williams, A. Dai, J. Fasullo, K. Trenberth, and
717
A. Berg, 2016: Metrics for the Diurnal Cycle of Precipitation: Toward Routine Benchmarks
718
for Climate Models. Journal of Climate, 29 (12), 4461–4471, doi:10.1175/JCLI-D-15-0664.1,
719
URL http://journals.ametsoc.org/doi/10.1175/JCLI-D-15-0664.1. 33
720
Delworth, T. L., and Coauthors, 2006: GFDL’s CM2 Global Coupled Climate Models. Part I:
721
Formulation and Simulation Characteristics. Journal of Climate, 19 (5), 643–674, doi:10.1175/
722
JCLI3629.1, URL http://journals.ametsoc.org/doi/abs/10.1175/JCLI3629.1.
723
Delworth, T. L., and Coauthors, 2012:
Simulated Climate and Climate Change in the
724
GFDL CM2.5 High-Resolution Coupled Climate Model. Journal of Climate, 25 (8),
725
2755–2781, doi:10.1175/JCLI-D-11-00316.1, URL http://journals.ametsoc.org/doi/abs/10.
726
1175/JCLI-D-11-00316.1.
727
Frankoski, N. J., and A. T. DeGaetano, 2011:
An East Coast winter storm precipita-
728
tion climatology. International Journal of Climatology, 31 (6), 802–814, doi:10.1002/joc.
729
2121, URL http://journals.ametsoc.org/doi/abs/10.1175/1520-0442{\%}282001{\%}29014{\%
730
}3C0882{\%}3AAECWSC{\%}3E2.0.CO{\%}3B2http://doi.wiley.com/10.1002/joc.2121.
731
Fujii, Y., T. Nakaegawa, S. Matsumoto, T. Yasuda, G. Yamanaka, and M. Kamachi, 2009: Coupled
732
climate simulation by constraining ocean fields in a coupled model with ocean data. Journal of
733
Climate, 22 (20), 5541–5557, doi:10.1175/2009JCLI2814.1, URL http://journals.ametsoc.org/
734
doi/abs/10.1175/2009JCLI2814.1.
735
Gates, W. L., and Coauthors, 1999: An Overview of the Results of the Atmospheric Model Inter-
736
comparison Project (AMIP I). URL http://journals.ametsoc.org/doi/abs/10.1175/1520-0477{\%
737
}281999{\%}29080{\%}3C0029{\%}3AAOOTRO{\%}3E2.0.CO{\%}3B2, 29–55 pp., doi:
738
10.1175/1520-0477(1999)0802.0.CO;2.
739
Ghil, M., and A. W. Robertson, 2002: "Waves" vs. "particles" in the atmosphere’s phase
740
space:
a pathway to long-range forecasting?
741
of Sciences of the United States of America, 99 Suppl 1, 2493–500, doi:10.1073/ 34
Proceedings of the National Academy
742
pnas.012580899, URL http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=128567{\&
743
}tool=pmcentrez{\&}rendertype=abstract.
744
Gleckler, P., C. Doutriaux, P. Durack, K. Taylor, Y. Zhang, D. Williams, E. Mason, and J. Ser-
745
vonnat, 2016: A More Powerful Reality Test for Climate Models. Eos, 97, doi:10.1029/
746
2016EO051663, URL https://eos.org/project-updates/powerful-reality-test-climate-models.
747
Gleckler, P. J., K. E. Taylor, and C. Doutriaux, 2008: Performance metrics for climate models.
748
Journal of Geophysical Research, 113 (D6), D06 104, doi:10.1029/2007JD008972, URL http:
749
//doi.wiley.com/10.1029/2007JD008972.
750
751
Griffies, S., 2012: Elements of the Modular Ocean Model (MOM). Tech. Rep. 7. Tech. rep., NOAA - Geophysical Fluid Dynamics Laboratory, Princeton, USA, 614 pp.
752
Hoskins, B. J., 2013: The potential for skill across the range of the seamless weather-climate
753
prediction problem: a stimulus for our science. Quarterly Journal of the Royal Meteorological
754
Society, 139 (672), 573–584, doi:10.1002/qj.1991, URL http://doi.wiley.com/10.1002/qj.1991.
755
756
Jia, L., and Coauthors, 2017: Seasonal Prediction Skill of Northern Extratropical Surface Temperature Driven by the Stratosphere. Journal of Climate.
757
Johnson, N. C., and S. B. Feldstein, 2010: The continuum of North Pacific sea level pres-
758
sure patterns: Intraseasonal, interannual, and interdecadal variability. Journal of Climate,
759
23 (4), 851–867, doi:10.1175/2009JCLI3099.1, URL http://journals.ametsoc.org/doi/abs/10.
760
1175/2009JCLI3099.1.
761
762
Jolliffe, I., D. Stephenson, and (Eds), 2012: Forecast Verification: a practicioner’s guide in atmospheric science. 2nd ed., Wiley and Sons, Chichester, 292 pp. 35
763
764
Jones, G. V., and R. E. Davis, 1995: Climatology of nor’easters and the 30 kPa jet. Journal of Coastal Research, 11 (4), 1210–1220.
765
Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bulletin of the
766
American Meteorological Society, 77 (3), 437–471, doi:10.1175/1520-0477(1996)0772.0.CO;2, URL http://journals.ametsoc.org/doi/abs/10.1175/1520-0477(1996)077{\%
768
}3C0437:TNYRP{\%}3E2.0.CO;2.
769
Kistler, R., and Coauthors, 2001: The NCEP-NCAR 50-Year Reanalysis: Monthly Means
770
CD-ROM and Documentation. Bulletin of the American Meteorological Society, 82 (2),
771
247–267, doi:10.1175/1520-0477(2001)0822.3.CO;2, URL http://journals.
772
ametsoc.org/doi/abs/10.1175/1520-0477(2001)082{\%}3C0247:TNNYRM{\%}3E2.3.CO;2.
773
Leathers, D. J., B. Yarnal, and M. A. Palecki, 1991: The Pacific North-American teleconnec-
774
tion pattern and United States climate. Part I. Regional temperature and precipitation associa-
775
tions. Journal of Climate, 4 (5), 517–528, doi:10.1175/1520-0442(1991)0042.0.
776
co;2, URL http://journals.ametsoc.org/doi/abs/10.1175/1520-0442{\%}281991{\%}29004{\%
777
}3C0517{\%}3ATPATPA{\%}3E2.0.CO{\%}3B2.
778
Leith, C. E., 1975: Climate Response and Fluctuation Dissipation. Journal of the Atmospheric
779
Sciences, 32 (10), 2022–2026, doi:10.1175/1520-0469(1975)0322.0.CO;2,
780
URL
781
}3C2022{\%}3ACRAFD{\%}3E2.0.CO{\%}3B2.
782
http://journals.ametsoc.org/doi/abs/10.1175/1520-0469{\%}281975{\%}29032{\%
Lorenz, E. N., 1963: (2),
Deterministic Nonperiodic Flow. Journal of the Atmospheric
783
Sciences,
20
784
URL
http://journals.ametsoc.org/doi/abs/10.1175/1520-0469{\%}281963{\%}29020{\%
785
}3C0130{\%}3ADNF{\%}3E2.0.CO{\%}3B2.
130–141,
doi:10.1175/1520-0469(1963)0202.0.CO;2,
36
786
Lorenz, E. N., 1969:
Atmospheric Predictability as Revealed by Naturally Occur-
787
ring Analogues. Journal of the Atmospheric Sciences, 26 (4), 636–646, doi:10.1175/
788
1520-0469(1969)262.0.CO;2, URL http://journals.ametsoc.org/doi/abs/10.
789
1175/1520-0469(1969)26{\%}3C636{\%}3AAPARBN{\%}3E2.0.CO{\%}3B2.
790
Lorenz, E. N., 2006: Regimes in Simple Systems. Journal of the Atmospheric Sciences,
791
63 (8), 2056–2073, doi:10.1175/JAS3727.1, URL http://journals.ametsoc.org/doi/abs/10.1175/
792
JAS3727.1.
793
Luo, J.-J., S. Masson, S. K. Behera, and T. Yamagata, 2008: Extended ENSO Predictions Using a
794
˘ SAtmosphere Fully Coupled OceanâA ¸ Model. Journal of Climate, 21 (1), 84–93, doi:10.1175/
795
2007JCLI1412.1, URL http://journals.ametsoc.org/doi/abs/10.1175/2007JCLI1412.1.
796
Mason, S. J., and D. Stephenson, 2008: How Do We Know Whether Seasonal Climate Forecasts
797
are Any Good? Seasonal Climate: Forecasting and Managing Risk, A. Troccoli, M. Harrison,
798
D. Anderson, and S. Mason, Eds., earth and ed., Springer Netherlands, Netherlands, Dordrecht.,
799
259–289.
800
801
Mason, S. J., and M. K. Tippet, 2016: Climate Predictability Tool version 15.3. doi:10.7916/ D8NS0TQ6, URL http://academiccommons.columbia.edu/catalog/ac:194358.
802
Michelangeli, P.-A., R. Vautard, and B. Legras, 1995: Weather Regimes: Recurrence and
803
Quasi Stationarity. Journal of the Atmospheric Sciences, 52 (8), 1237–1256, doi:10.1175/
804
1520-0469(1995)0522.0.CO;2, URL http://journals.ametsoc.org/doi/abs/10.
805
1175/1520-0469(1995)052{\%}3C1237:WRRAQS{\%}3E2.0.CO;2.
806
Milly, P. C. D., and Coauthors, 2014: An Enhanced Model of Land Water and Energy
807
for Global Hydrologic and Earth-System Studies. Journal of Hydrometeorology, 15 (5), 37
808
1739–1761, doi:10.1175/JHM-D-13-0162.1, URL http://journals.ametsoc.org/doi/abs/10.1175/
809
JHM-D-13-0162.1http://journals.ametsoc.org/doi/abs/10.1175/JHM-D-13-0162.1?af=R{\&}.
810
Moron, V., P. Camberlin, and A. W. Robertson, 2013: Extracting Subseasonal Scenarios: An Alter-
811
native Method to Analyze Seasonal Predictability of Regional-Scale Tropical Rainfall. Journal
812
of Climate, 26 (8), 2580–2600, doi:10.1175/JCLI-D-12-00357.1, URL http://journals.ametsoc.
813
org/doi/abs/10.1175/JCLI-D-12-00357.1.
814
Moron, V., A. W. Robertson, and M. Ghil, 2011: Impact of the modulated annual cycle and
815
intraseasonal oscillation on daily-to-interannual rainfall variability across monsoonal India.
816
Climate Dynamics, 38 (11-12), 2409–2435, doi:10.1007/s00382-011-1253-4, URL http://link.
817
springer.com/10.1007/s00382-011-1253-4.
818
Moron, V., A. W. Robertson, J.-H. Qian, and M. Ghil, 2015: Weather types across the Mar-
819
itime Continent: from the diurnal cycle to interannual variations. Frontiers in Environmental
820
Science, 2, doi:10.3389/fenvs.2014.00065, URL http://journal.frontiersin.org/article/10.3389/
821
fenvs.2014.00065/abstract.
822
Moron, V., A. W. Robertson, M. N. Ward, and O. Ndiaye, 2008: Weather Types and Rainfall
823
over Senegal. Part I: Observational Analysis. Journal of Climate, 21 (2), 266–287, doi:10.1175/
824
2007JCLI1601.1, URL http://journals.ametsoc.org/doi/abs/10.1175/2007JCLI1601.1.
825
Moron, V., A. W. Robertson, M. N. Ward, and O. Ndiaye, 2010: Weather Types and Rainfall over
826
Senegal. Part II: Downscaling of GCM Simulations. URL http://journals.ametsoc.org/doi/abs/
827
10.1175/2007JCLI1624.1.
828
Muñoz, A., L. Goddard, A. W. Robertson, Y. Kushnir, and W. Baethgen, 2015: Cross-Time
829
Scale Interactions and Rainfall Extreme Events in Southeastern South America for the Aus38
830
tral Summer. Part I: Potential Predictors. Journal of Climate, 28 (19), 7894–7913, doi:10.1175/
831
JCLI-D-14-00693.1, URL http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-14-00693.1.
832
˘ STime Muñoz, Á. G., L. Goddard, S. J. Mason, and A. W. Robertson, 2016: CrossâA ¸ Scale Interac-
833
tions and Rainfall Extreme Events in Southeastern South America for the Austral Summer. Part
834
II: Predictive Skill. Journal of Climate, 29 (16), 5915–5934, doi:10.1175/JCLI-D-15-0699.1,
835
URL http://journals.ametsoc.org/doi/10.1175/JCLI-D-15-0699.1.
836
Nakamura, J., U. Lall, Y. Kushnir, A. W. Robertson, and R. Seager, 2012: Dynamical struc-
837
ture of extreme floods in the U.S. Midwest and the UK. Journal of Hydrometeorology,
838
14 (2), 485–504, doi:10.1175/JHM-D-12-059.1, URL http://journals.ametsoc.org/doi/abs/10.
839
1175/JHM-D-12-059.1http://dx.doi.org/10.1175/JHM-D-12-059.1.
840
Notaro, M., W.-C. Wang, and W. Gong, 2006: Model and Observational Analysis of the Northeast
841
U.S. Regional Climate and Its Relationship to the PNA and NAO Patterns during Early Winter.
842
Monthly Weather Review, 134 (11), 3479–3505, doi:10.1175/MWR3234.1, URL http://journals.
843
ametsoc.org/doi/abs/10.1175/MWR3234.1.
844
Palmer, T., 1999:
A Nonlinear Dynamical Perspective on Climate Prediction. Jour-
845
nal of Climate, 12 (2), 575–591, doi:10.1175/1520-0442(1999)0122.0.
846
CO;2, URL http://journals.ametsoc.org/doi/abs/10.1175/1520-0442(1999)012{\%}3C0575{\%
847
}3AANDPOC{\%}3E2.0.CO{\%}3B2.
848
Palmer, T. N., and A. Weisheimer, 2011: Diagnosing the causes of bias in climate models
849
˘ S¸ why is it so hard? Geophysical & Astrophysical Fluid Dynamics, 105 (2-3), 351– âA
850
365, doi:10.1080/03091929.2010.547194, URL http://www.tandfonline.com/doi/abs/10.1080/
851
03091929.2010.547194. 39
852
Perez, J., M. Menendez, F. J. Mendez, and I. J. Losada, 2014: Evaluating the performance of
853
CMIP3 and CMIP5 global climate models over the north-east Atlantic region. Climate Dynam-
854
ics, 43 (9-10), 2663–2680, doi:10.1007/s00382-014-2078-8, URL http://link.springer.com/10.
855
1007/s00382-014-2078-8.
856
Phillips, A. S., C. Deser, and J. Fasullo, 2014: Evaluating modes of variability in climate mod-
857
els. Eos, 95 (49), 453–455, doi:10.1002/2014EO490002, URL http://doi.wiley.com/10.1002/
858
2014EO490002.
859
Putman, W. M., and S.-J. Lin, 2007: Finite-volume transport on various cubed-sphere grids.
860
Journal of Computational Physics, 227 (1), 55–78, doi:10.1016/j.jcp.2007.07.022, URL http:
861
//linkinghub.elsevier.com/retrieve/pii/S0021999107003105.
862
Rayner, N. A., D. Parker, E. Horton, C. Folland, L. Alexander, D. Rowell, E. Kent, and A. Kaplan,
863
2003: Global analyses of sea surface temperature, sea ice, and night marine air temperature
864
since the late nineteenth century. Journal of Geophysical Research, 108 (D14), 4407, doi:
865
10.1029/2002JD002670, URL http://doi.wiley.com/10.1029/2002JD002670http://dx.doi.org/
866
10.1029/2002JD002670{\%}5Cnhttp://doi.wiley.com/10.1029/2002JD002670{\%}5Cnhttp:
867
//linkinghub.elsevier.com/retrieve/pii/S1381116906013641.
868
Reichler, T., and J. Kim, 2008: How Well Do Coupled Models Simulate Today’s Climate? Bulletin
869
of the American Meteorological Society, 89 (3), 303–311, doi:10.1175/BAMS-89-3-303, URL
870
http://journals.ametsoc.org/doi/abs/10.1175/BAMS-89-3-303.
871
Reinhold, B. B., and R. T. Pierrehumbert, 1982: Dynamics of Weather Regimes: Quasi-Stationary
872
Waves
and
Blocking.
URL
http://journals.ametsoc.org/doi/abs/10.1175/1520-0493{\%
873
}281982{\%}29110{\%}3C1105{\%}3ADOWRQS{\%}3E2.0.CO{\%}3B2, 1105–1145 pp.,
874
doi:10.1175/1520-0493(1982)1102.0.CO;2. 40
875
Riddle, E. E., M. B. Stoner, N. C. Johnson, M. L. L’Heureux, D. C. Collins, and S. B. Feldstein,
876
2013: The impact of the MJO on clusters of wintertime circulation anomalies over the North
877
American region. Climate Dynamics, 40 (7-8), 1749–1766, doi:10.1007/s00382-012-1493-y,
878
URL http://link.springer.com/10.1007/s00382-012-1493-y.
879
Rienecker, M. M., and Coauthors, 2011: MERRA: NASA’s Modern-Era Retrospective Anal-
880
ysis for Research and Applications. Journal of Climate, 24 (14), 3624–3648, doi:10.1175/
881
JCLI-D-11-00015.1, URL http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-11-00015.1.
882
Robertson, A. W., and M. Ghil, 1999: Large-Scale Weather Regimes and Local Climate
883
over the Western United States. Journal of Climate, 12 (6), 1796–1813, doi:10.1175/
884
1520-0442(1999)0122.0.CO;2, URL http://journals.ametsoc.org/doi/full/10.
885
1175/1520-0442(1999)012{\%}3C1796:LSWRAL{\%}3E2.0.CO;2.
886
Robertson, A. W., S. Kirshner, P. Smyth, S. P. Charles, and B. C. Bates, 2006: Subseasonal-to-
887
interdecadal variability of the Australian monsoon over North Queensland. Quarterly Journal
888
of the Royal Meteorological Society, 132 (615), 519–542, doi:10.1256/qj.05.75, URL http://doi.
889
wiley.com/10.1256/qj.05.75.
890
Robertson, A. W., Y. Kushnir, U. Lall, and J. Nakamura, 2015: Weather and Climatic Drivers of
891
Extreme Flooding Events over the Midwest of the United States. Extreme Events: Observations,
892
Modeling, and Economics, John Wiley & Sons, Inc, 113–124, doi:10.1002/9781119157052.
893
ch9, URL http://doi.wiley.com/10.1002/9781119157052.ch9.
894
Roller, C. D., J.-H. Qian, L. Agel, M. Barlow, and V. Moron, 2016: Winter Weather Regimes in the
895
Northeast United States. Journal of Climate, 29 (8), 2963–2980, doi:10.1175/JCLI-D-15-0274.
896
1, URL http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-15-0274.1. 41
897
Ropelewski, C. F., and M. S. Halpert, 1986: North American Precipitation and Temperature
898
Patterns Associated with the El Niño/Southern Oscillation (ENSO). Monthly Weather Re-
899
view, 114 (12), 2352–2362, doi:10.1175/1520-0493(1986)1142.0.CO;2,
900
URL
901
}3C2352{\%}3ANAPATP{\%}3E2.0.CO{\%}3B2.
902
http://journals.ametsoc.org/doi/abs/10.1175/1520-0493{\%}281986{\%}29114{\%
Ropelewski, C. F., and M. S. Halpert, 1987:
Global and Regional Scale Precipita-
903
tion Patterns Associated with the El Niño/Southern Oscillation. Monthly Weather Re-
904
view, 115 (8), 1606–1626, doi:10.1175/1520-0493(1987)1152.0.CO;2,
905
URL
906
}3C1606{\%}3AGARSPP{\%}3E2.0.CO{\%}3B2.
907
http://journals.ametsoc.org/doi/abs/10.1175/1520-0493{\%}281987{\%}29115{\%
Rosati, A., K. Miyakoda, and R. Gudgel, 1997:
The Impact of Ocean Initial Con-
908
ditions on ENSO Forecasting with a Coupled Model. Monthly Weather Review,
909
125
910
http://journals.ametsoc.org/doi/abs/10.1175/1520-0493{\%}281997{\%}29125{\%
911
}3C0754{\%}3ATIOOIC{\%}3E2.0.CO{\%}3B2.
(5),
754–772,
doi:10.1175/1520-0493(1997)1252.0.CO;2,
URL
912
Ryu, J. H., and K. Hayhoe, 2014: Understanding the sources of Caribbean precipitation biases
913
in CMIP3 and CMIP5 simulations. Climate Dynamics, 42 (11-12), 3233–3252, doi:10.1007/
914
s00382-013-1801-1, URL http://link.springer.com/10.1007/s00382-013-1801-1.
915
Stephenson, D. B., A. Hannachi, and A. O’Neill, 2004: On the existence of multiple climate
916
regimes. Quarterly Journal of the Royal Meteorological Society, 130 (597), 583–605, doi:10.
917
1256/qj.02.146, URL http://doi.wiley.com/10.1256/qj.02.146.
918
Taylor, K. E., R. J. Stouffer, and G. A. Meehl, 2012: An Overview of CMIP5 and the Experi-
919
ment Design. Bulletin of the American Meteorological Society, 93 (4), 485–498, doi:10.1175/ 42
920
BAMS-D-11-00094.1, URL http://journals.ametsoc.org/doi/abs/10.1175/BAMS-D-11-00094.
921
1.
922
Trenberth, K. E., and J. M. Caron, 2000: Pressures,
923
Level
924
13
925
URL
926
}3C4358{\%}3ATSORSL{\%}3E2.0.CO{\%}3B2.
(24),
Surface
4358–4365,
Temperatures,
The Southern Oscillation Revisited: and
Precipitation.
Journal
of
Sea
Climate,
doi:10.1175/1520-0442(2000)0132.0.CO;2,
http://journals.ametsoc.org/doi/abs/10.1175/1520-0442{\%}282000{\%}29013{\%
927
van der Wiel, K., and Coauthors, 2016: The resolution dependence of contiguous US precipitation
928
extremes in response to CO 2 forcing. Journal of Climate, JCLI–D–16–0307.1, doi:10.1175/
929
JCLI-D-16-0307.1, URL http://journals.ametsoc.org/doi/10.1175/JCLI-D-16-0307.1.
930
Vaughan, C., and S. Dessai, 2014: Climate services for society: origins, institutional arrangements,
931
and design elements for an evaluation framework. Wiley Interdisciplinary Reviews: Climate
932
Change, n/a–n/a, doi:10.1002/wcc.290, URL http://doi.wiley.com/10.1002/wcc.290.
933
Vautard, R., 1990: Multiple Weather Regimes over the North Atlantic: Analysis of Pre-
934
cursors and Successors. Monthly Weather Review, 118 (10), 2056–2081, doi:10.1175/
935
1520-0493(1990)1182.0.CO;2, URL http://journals.ametsoc.org/doi/abs/
936
10.1175/1520-0493(1990)118{\%}3C2056{\%}3AMWROTN{\%}3E2.0.CO{\%}3B2.
937
Vautard, R., K. C. Mo, and M. Ghil, 1990:
Statistical Significance Test for Transi-
938
tion Matrices of Atmospheric Markov Chains. Journal of the Atmospheric Sciences,
939
47
940
URL
941
}3C1926{\%}3ASSTFTM{\%}3E2.0.CO{\%}3B2.
(15),
1926–1931,
doi:10.1175/1520-0469(1990)0472.0.CO;2,
http://journals.ametsoc.org/doi/abs/10.1175/1520-0469{\%}281990{\%}29047{\%
43
942
Vecchi, G. A., and Coauthors, 2014: On the seasonal forecasting of regional tropical cyclone
943
activity. Journal of Climate, 27 (21), 7994–8016, doi:10.1175/JCLI-D-14-00158.1, URL http:
944
//journals.ametsoc.org/doi/abs/10.1175/JCLI-D-14-00158.1.
945
Wheeler, M. C., and H. H. Hendon, 2004: An All-Season Real-Time Multivariate MJO Index: De-
946
velopment of an Index for Monitoring and Prediction. Monthly Weather Review, 132 (8), 1917–
947
1932, doi:10.1175/1520-0493(2004)1322.0.CO;2, URL http://journals.
948
ametsoc.org/doi/full/10.1175/1520-0493(2004)132{\%}3C1917:AARMMI{\%}3E2.0.CO;2.
949
Zhou, S., M. L’Heureux, S. Weaver, and A. Kumar, 2012: A composite study of the MJO influence
950
on the surface air temperature and precipitation over the Continental United States. Climate Dy-
951
namics, 38 (7-8), 1459–1471, doi:10.1007/s00382-011-1001-9, URL http://link.springer.com/
952
10.1007/s00382-011-1001-9.
44
953
LIST OF TABLES
954
Table 1.
955 956 957 958 959 960
961
Table 2.
962 963 964 965 966 967
968
Table 3.
969 970 971 972 973 974
975
Table 4.
976 977 978
979
Table 5.
980
981 982 983
Table 6.
Anomaly Correlation Coefficient (Spearman) between the model-equivalent ensemble-mean weather types (WTs) in each experiment and the corresponding circulation regime in NNRPv2, computed on the reanalysis grid for the domain sketched in Fig 4. Numbers in bold indicate highest correlations found in the model experiments, all values being statistically significant (t-Student test, p < 0.05). No statistically significant difference was found between the average anomaly correlation coefficients of the experiments. . . . . .
.
. 45
Anomaly Correlation Coefficient (Spearman) between the model-equivalent ensemble-mean weather types (WTs) in each experiment and the corresponding circulation regime in MERRA, computed on the renalaysis grid for the domain sketched in Fig 4. Numbers in bold indicate highest correlations found in the model experiments, all values being statistically significant (t-Student test, p < 0.05). No statistically significant difference was found between the average anomaly correlation coefficients of the experiments. . . . . .
.
. 46
Anomaly Correlation Coefficient (Spearman) between the model-equivalent ensemble-mean rainfall regimes (RRs) in each experiment and the corresponding rainfall pattern in the observations, computed on the observations grid for the domain sketched in Fig 5. Numbers in bold indicate highest correlations found in the model experiments, all values being statistically significant (tStudent test, p < 0.05). No statistically significant difference was found between the average anomaly correlation coefficients of the experiments. . . .
.
47
Best-fit of Weibull parameters (α, β ) for the model-equivalent ensemble-mean weather type durations sketched by the p red curves in Fig 9. Bold pairs indicate minimum Euclidean distance ds = (∆α 2 + ∆β 2 ), where ∆ denotes differences between simulated and observed parameters. . . . . . . . .
.
48
Average persistence (in days) for each WT in the NNRPv2 dataset and the numerical experiments. Values closer to reanalysis are presented in bold. . . Ensemble-mean RMSE (in days per season) for the inter-annual evolution of the frequency of occurrence of the weather types in each experiment, with respect to NNRPv2. . . . . . . . . . . . . . . . . .
45
.
. 49
.
50
984
TABLE 1.
Anomaly Correlation Coefficient (Spearman) between the model-equivalent ensemble-mean
985
weather types (WTs) in each experiment and the corresponding circulation regime in NNRPv2, computed on
986
the reanalysis grid for the domain sketched in Fig 4. Numbers in bold indicate highest correlations found in the
987
model experiments, all values being statistically significant (t-Student test, p < 0.05). No statistically significant
988
difference was found between the average anomaly correlation coefficients of the experiments.
Dataset vs NNRPv2
WT1
WT2
WT3
WT4
WT5
WT6
WT7
Average
MERRA
0.99
0.99
0.97
0.99
0.99
0.99
0.99
0.98
LOARsst
0.93
0.93
0.37
0.54
0.66
0.87
0.91
0.74
FLORsst
0.89
0.96
0.20
0.66
0.72
0.89
0.94
0.75
FLORsst+strat
0.90
0.97
-0.11
0.78
0.66
0.84
0.95
0.71
46
989
TABLE 2.
Anomaly Correlation Coefficient (Spearman) between the model-equivalent ensemble-mean
990
weather types (WTs) in each experiment and the corresponding circulation regime in MERRA, computed on
991
the renalaysis grid for the domain sketched in Fig 4. Numbers in bold indicate highest correlations found in the
992
model experiments, all values being statistically significant (t-Student test, p < 0.05). No statistically significant
993
difference was found between the average anomaly correlation coefficients of the experiments.
Dataset vs MERRA
WT1
WT2
WT3
WT4
WT5
WT6
WT7
Average
NNRPv2
0.99
0.99
0.97
0.99
0.99
0.99
0.99
0.98
LOARsst
0.92
0.93
0.36
0.58
0.73
0.86
0.91
0.75
FLORsst
0.90
0.96
0.18
0.70
0.72
0.89
0.94
0.75
FLORsst+strat
0.91
0.96
-0.10
0.82
0.74
0.85
0.96
0.73
47
994
TABLE 3. Anomaly Correlation Coefficient (Spearman) between the model-equivalent ensemble-mean rain-
995
fall regimes (RRs) in each experiment and the corresponding rainfall pattern in the observations, computed on
996
the observations grid for the domain sketched in Fig 5. Numbers in bold indicate highest correlations found
997
in the model experiments, all values being statistically significant (t-Student test, p < 0.05). No statistically
998
significant difference was found between the average anomaly correlation coefficients of the experiments.
Experiment
RR1
RR2
RR3
RR4
RR5
RR6
RR7
Average
LOARsst
0.80
0.83
0.87
0.51
0.57
0.80
0.87
0.75
FLORsst
0.78
0.81
0.90
0.48
0.64
0.79
0.88
0.75
FLORsst+strat
0.83
0.82
0.88
0.38
0.69
0.62
0.90
0.73
48
1000
TABLE 4. Best-fit of Weibull parameters (α, β ) for the model-equivalent ensemble-mean weather type durap tions sketched by the red curves in Fig 9. Bold pairs indicate minimum Euclidean distance ds = (∆α 2 + ∆β 2 ),
1001
where ∆ denotes differences between simulated and observed parameters.
999
WT1
WT2
WT3
WT4
WT5
WT6
WT7
NNRPv2
(3.52, 1.46) (1.71, 0.55) (2.56, 1.13) (2.53, 1.36) (1.47, 0.76) (1.30, 0.73) (0.83, 0.62)
LOARsst
(2.90, 1.29) (1.13, 0.53)
(2.22,0.83)
(1.89, 0.84) (3.09, 1.48) (3.12, 1.57)
(0.82,0.61)
FLORsst
(2.73, 1.04)
(1.71,0.54)
(2.05, 0.87)
(2.86,1.48)
(1.10, 0.66)
FLORsst+strat
(3.47,1.43)
(1.87, 0.53) (1.82, 0.78) (1.56, 0.82) (2.74, 1.47) (2.95, 1.45) (0.93, 0.63)
49
(1.94,0.95)
(1.21,0.68)
1002
1003
TABLE 5. Average persistence (in days) for each WT in the NNRPv2 dataset and the numerical experiments. Values closer to reanalysis are presented in bold.
WT1
WT2
WT3
WT4
WT5
WT6
WT7
NNRPv2
4.06
3.47
3.36
3.21
2.62
2.48
2.14
LOARsst
3.59
2.94
3.31
2.96
3.66
3.69
2.16
FLORsst
3.59
3.56
3.09
3.46
2.88
2.47
2.40
FLORsst+strat
3.98
3.89
2.95
2.62
3.39
3.57
2.26
50
1004
1005
TABLE 6. Ensemble-mean RMSE (in days per season) for the inter-annual evolution of the frequency of occurrence of the weather types in each experiment, with respect to NNRPv2.
Experiment
WT1
WT2
WT3
WT4
WT5
WT6
WT7
LOARsst
7.4
7.3
5.1
11.7
10.2
7.9
5.2
FLORsst
7.4
6.4
6.2
10.0
7.7
7.1
5.7
FLORsst+strat
6.6
6.9
5.0
9.8
7.1
7.8
5.1
51
1006
LIST OF FIGURES
1007
Fig. 1.
1008 1009 1010
1011
Fig. 2.
1012 1013
1014
Fig. 3.
1015 1016 1017 1018 1019 1020 1021
Schematic showing (left) three available states (A, B, C) and a forbidden or unaccesible state (D). The system transitions between the available states (represented by the arrows). Those transitions define sequences of states (right) that describe events; e.g., ABC could be related to extreme rainfall events, while BBC to heat waves. . . . . . . . . . . .
.
Rainfall climatology (MAM 1981-2012) for Northeastern North America. (a) Observations, (b) LOARsst , (c) FLORsst and (d) FLOARsst+strat . Units are in mm day−1 . Ocean has been masked in (b)-(d). Each dataset is plotted using its native horizontal resolution. . . . .
. 54
Hemispheric view of observed (NNRPv2 and MERRA) and modeled (LOARsst , FLORsst , FLORsst+strat ) weather types –WTs–, using geopotential height anomalies at 500 hPa (contour interval is 20 gpm). Red solid lines indicate positive anomalies, while negative ones correspond to the blue dashed lines. In the model experiments, regions showing statistically significant (p < 0.05) ensemble-mean anomalies are shaded in gray. Relative frequency of occurrence for the entire 32-year period is indicated in parenthesis, with model experiments showing the ensemble mean ± one standard deviation. Each dataset is plotted using its native horizontal resolution. . . . . . . . . . . . . . . . . . .
. 55
53
1022
Fig. 4.
As in Fig. 3, but for most of North America.
.
.
56
1023
Fig. 5.
Observed and modeled (LOARsst , FLORsst , FLORsst+strat ) rainfall regimes, RR, associated with each weather type (units are mm day−1 ). Relative frequency of occurrence for the entire 32-year period is indicated in parenthesis, with model experiments showing the ensemble mean ± one standard deviation. Each dataset is plotted using its native horizontal resolution.
.
57
Boxplots of scatter indices for (a) the mean and (b) standard deviation of the frequency of occurrence of weather types across multiple timescales. Perfect coincidence between simulations and observations correspond to a scatter index value of zero. For each boxplot, the central mark indicates the ensemble median, and the bottom and top edges of the box indicate the ensemble 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers (values > 2.7 standard deviations) are plotted individually using the ’+’ symbol. For additional details see subsections 5c-5e. . . . . . . . . . . . . . . . . . . . . . . .
.
58
1024 1025 1026
1027
Fig. 6.
1028 1029 1030 1031 1032 1033 1034
1035
Fig. 7.
1036 1037 1038
1039
Fig. 8.
1040 1041 1042 1043 1044 1045
1046 1047 1048
Fig. 9.
.
.
.
.
.
.
.
.
.
.
.
.
Klee diagrams for (a) NNRPv2 and numerical experiments (b) LOARsst , (c) FLORsst and (d) FLORsst+strat . Each tile corresponds to a particular day, and the colors represent different weather types (WTs, see color bar). Only one member per experiment is shown (others are similar). . . . . . . . . . . . . . . . . . . . . . . .
. 59
(a) Daily transition probabilities, P, for observed (NNRPv2) weather types (WTs, see label bar). A star indicates statistically significant transitions (p < 0.1, see Vautard et al. (1990)). Vertical and horizontal axes correspond to the prior and posterior WTs, respectively. Differences between the LOARsst , FLORsst and FLORsst+strat ensemble-mean transition probabilities and those presented in (a) are shown in panels (b)-(d), respectively. Average differences between panels (b)-(d) are not statistically significant (p < 0.05, using a two-sample t-Student test). . . . . . . . . . . . . . . . . . . . . .
.
Average durations (in days) for each weather type (WT, see label bar) in NNRPv2, LOARsst , FLORsst and FLORsst+strat . Red curves sketch the corresponding Weibull fit, whose parameters α and β are presented in Table 4. . . . . . . . . . . . . . . .
52
60
. 61
1049 1050 1051
1052 1053
1054 1055 1056 1057 1058 1059
Fig. 10. Ensemble-mean sub-seasonal frequency of occurrence for each weather type (WT), smoothed with an 11-day moving average. Periods in the black boxes were were selected for further analysis (see subsection 5c). . . . . . . . . . . . . . . .
. 62
Fig. 11. Observed (a) and ensemble-mean (b-d) inter-annual frequency of occurrence for each weather type (WT, see label bar), for all MAM seasons. . . . . . . . . . .
.
63
Fig. 12. (a) Observed rainfall climatology (MAM 1981-2012), and reconstruction of the rainfall climatology using, for each numerical experiment, a linear combination of (b) the observed frequencies of occurrence of weather types (ObsF) and the modeled rainfall regimes (ModRR), and (c) the modeled frequencies of occurrence of weather types (ModF) and the observed rainfall regimes (ObsRR). Units in mm day−1 . Ocean has been masked in (b). Each dataset is plotted using its native horizontal resolution. . . . . . . . . . . . .
.
64
53
D ABC ABA BBC CAC …
B
A
C Available physical states and transitions
Events are described in terms of sequences of available states
1060
F IG . 1. Schematic showing (left) three available states (A, B, C) and a forbidden or unaccesible state (D). The
1061
system transitions between the available states (represented by the arrows). Those transitions define sequences
1062
of states (right) that describe events; e.g., ABC could be related to extreme rainfall events, while BBC to heat
1063
waves.
54
1064
F IG . 2. Rainfall climatology (MAM 1981-2012) for Northeastern North America. (a) Observations, (b)
1065
LOARsst , (c) FLORsst and (d) FLOARsst+strat . Units are in mm day−1 . Ocean has been masked in (b)-(d). Each
1066
dataset is plotted using its native horizontal resolution.
55
1067
1068
F IG . 3.
Hemispheric view of observed (NNRPv2 and MERRA) and modeled (LOARsst , FLORsst ,
56
FLORsst+strat ) weather types –WTs–, using geopotential height anomalies at 500 hPa (contour interval is 20
FLORsst
LOARsst 57
FLORsst+strat
MERRA
F IG . 4. As in Fig. 3, but for most of North America.
NNRPv2
FLORsst+strat
LOARsst
FLORsst
NNRPv2 1074
F IG . 5. Observed and modeled (LOARsst , FLORsst , FLORsst+strat ) rainfall regimes, RR, associated with each
1075
weather type (units are mm day−1 ). Relative frequency of occurrence for the entire 32-year period is indicated
1076
in parenthesis, with model experiments showing the ensemble mean ± one standard deviation. Each dataset is
1077
plotted using its native horizontal resolution.
58
a
b
1078
F IG . 6. Boxplots of scatter indices for (a) the mean and (b) standard deviation of the frequency of occur-
1079
rence of weather types across multiple timescales. Perfect coincidence between simulations and observations
1080
correspond to a scatter index value of zero. For each boxplot, the central mark indicates the ensemble median,
1081
and the bottom and top edges of the box indicate the ensemble 25th and 75th percentiles, respectively. The
1082
whiskers extend to the most extreme data points not considered outliers, and the outliers (values > 2.7 standard
1083
deviations) are plotted individually using the ’+’ symbol. For additional details see subsections 5c-5e.
59
WTs
1084
F IG . 7. Klee diagrams for (a) NNRPv2 and numerical experiments (b) LOARsst , (c) FLORsst and (d)
1085
FLORsst+strat . Each tile corresponds to a particular day, and the colors represent different weather types (WTs,
1086
see color bar). Only one member per experiment is shown (others are similar).
60
prior WT
* * * * * * * * * * *
* * *
posterior WT
1087
F IG . 8. (a) Daily transition probabilities, P, for observed (NNRPv2) weather types (WTs, see label bar). A
1088
star indicates statistically significant transitions (p < 0.1, see Vautard et al. (1990)). Vertical and horizontal
1089
axes correspond to the prior and posterior WTs, respectively. Differences between the LOARsst , FLORsst and
1090
FLORsst+strat ensemble-mean transition probabilities and those presented in (a) are shown in panels (b)-(d),
1091
respectively. Average differences between panels (b)-(d) are not statistically significant (p < 0.05, using a two-
1092
sample t-Student test).
61
NNRPv2 LOARsst FLORsst FLORsst+strat 1093
F IG . 9. Average durations (in days) for each weather type (WT, see label bar) in NNRPv2, LOARsst , FLORsst
1094
and FLORsst+strat . Red curves sketch the corresponding Weibull fit, whose parameters α and β are presented in
1095
Table 4.
62
WTs
1096
F IG . 10. Ensemble-mean sub-seasonal frequency of occurrence for each weather type (WT), smoothed with
1097
an 11-day moving average. Periods in the black boxes were were selected for further analysis (see subsection
1098
5c).
63
WTs
1099
1100
F IG . 11. Observed (a) and ensemble-mean (b-d) inter-annual frequency of occurrence for each weather type (WT, see label bar), for all MAM seasons.
64
LOARsst FLORsst FLORsst+strat 1101
F IG . 12. (a) Observed rainfall climatology (MAM 1981-2012), and reconstruction of the rainfall climatology
1102
using, for each numerical experiment, a linear combination of (b) the observed frequencies of occurrence of
1103
weather types (ObsF) and the modeled rainfall regimes (ModRR), and (c) the modeled frequencies of occurrence
1104
of weather types (ModF) and the observed rainfall regimes (ObsRR). Units in mm day−1 . Ocean has been
1105
masked in (b). Each dataset is plotted using its native horizontal resolution.
65