Papacharalampous et al.
Progress in Earth and Planetary Science(2023) 10:46
https://doi.org/10.1186/s40645-023-00574-y

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open AccessFeatures of the Earth’s seasonalhydroclimate: characterizations
and comparisons across the Köppen–Geiger
climates and across continents
Georgia Papacharalampous1* , Hristos Tyralis2,3 , Yannis Markonis1 , Petr Máca1   and Martin Hanel1   

Abstract
Detailed investigations of time series features across climates, continents and variable types can progress our understanding and modelling ability of the Earth’s hydroclimate and its dynamics. They can also improve our comprehension of the climate classification systems appearing in their core. Still, such investigations for seasonal hydroclimatic
temporal dependence, variability and change are currently missing from the literature. Herein, we propose and apply
at the global scale a methodological framework for filling this specific gap. We analyse over 13,000 earth-observed
quarterly temperature, precipitation and river flow time series. We adopt the Köppen–Geiger climate classification
system and define continental-scale geographical regions for conducting upon them seasonal hydroclimatic feature summaries. The analyses rely on three sample autocorrelation features, a temporal variation feature, a spectral
entropy feature, a Hurst feature, a trend strength feature and a seasonality strength feature. We find notable differences to characterize the magnitudes of these features across the various Köppen–Geiger climate classes, as well
as between continental-scale geographical regions. We, therefore, deem that the consideration of the comparative
summaries could be beneficial in water resources engineering contexts. Lastly, we apply explainable machine learning to compare the investigated features with respect to how informative they are in distinguishing either the main
Köppen–Geiger climates or the continental-scale regions. In this regard, the sample autocorrelation, temporal variation and seasonality strength features are found to be more informative than the spectral entropy, Hurst and trend
strength features at the seasonal time scale.
Keywords Comparative hydrology, Explainable machine learning, Hydroclimatic features, Köppen–Geiger climateclassification, Precipitation, Seasonality, Streamflow, Temperature, Temporal dependence, Trends*Correspondence:
Georgia Papacharalampous
papacharalampous.georgia@gmail.com
Full list of author information is available at the end of the article© The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/.

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

1 Introduction
The study of temporal and spatial aspects of the varioushydroclimatic phenomena (e.g. the ones linked to temperature, precipitation or streamflow variables) holds
a prominent position in Earth system science and engineering (see, for example, the detailed lists of research
topics compiled by Montanari et al. 2013 and Blöschl
et al. 2019), with a large variety of hydroclimatic features
being investigated with increasing frequency. Such investigations, as well as their underlying methodologies, areindeed necessary either when referring to high-impact
case studies (i.e. case studies conducted for areas withlarge engineering interest; see, for example, Montanari2012), or when based on large-sample datasets (see, forexample, Archfield et al. 2014; Ledvinka and Lamacova
2015; Fischer and Schumann 2018; Hall and Blöschl 2018;
Hanel et al. 2018; Markonis et al. 2018; Tyralis et al. 2018;
Jehn et al. 2020; Messager et al. 2021; Papacharalampous
et al. 2021; Slater et al. 2021), and often focus on hydroclimatic temporal dependence (which can be characterized
by estimating the autocorrelation of hydroclimatic timeseries), variability and change. An overview of the related
literature, summarizing information on both mean- andextreme-value hydroclimatic time series analyses, can befound in Papacharalampous et al. (2021).
Detailed comparisons of hydroclimatic features acrossdifferent climate classes and geographical regions havetheir own key role towards improving our understanding
and modelling ability of the Earth’s hydroclimate and its
dynamics (through the identification of climates and/or
regions with similar hydroclimatic characteristics) and,at the same time, facilitate a direct connection with theclimate literature. From a different point of view, they canalso progress our comprehension of the climate classification systems appearing in their core, especially when
conducted at the global scale (see, for example, Beck et al.
2005; Markonis et al. 2018; Tyralis et al. 2018; Messager
et al. 2021; Slater et al. 2021; Papacharalampous et al.
2022). Nonetheless, such comparisons in terms of hydroclimatic temporal dependence, variability and change are
currently missing from the literature for time series withseasonality, although the scientific interest in the moregeneral topic of investigating hydroclimatic features atthe seasonal and monthly time scales at different partsof the world (see, for example, the analyses by Nigam
and Ruiz-Barradas 2006; Ljungqvist et al. 2016; PAGES
Hydro2k Consortium 2017; Thomas and Nigam 2018;
Papacharalampous et al. 2021, and the review by Koster
et al. 2017) is undoubtedly large.
Herein, we fill this specific knowledge gap. More precisely, our aims are to:(i) Devise a methodological framework for (a) thecomprehensive characterization of the Earth’s sea-

Page 2 of 20

sonal hydroclimate and its dynamics, and (b) the
improved understanding of climate classification
systems in terms of their seasonal hydroclimatic
properties, through detailed feature investigations
and comparisons across climate classes and continental-scale regions.
(ii) Apply the new framework to global temperature,
precipitation and river flow time series datasets,
thereby providing the first scientific insights on thetargeted topic.
The remainder of the paper is structured as follows:
Sect. 2.1 presents information on the investigated global
datasets and their attentive use towards reaching oursecond aim, while Sect. 2.2 covers the feature estimation
methodology, and the methodology followed for comparing the features across climates and continental-scaleregions. Furthermore, Sect. 2.3 describes some additional methodological steps taken for ranking the investigated features according to how indicative they are in
explaining roughly summarized climate or geographicalinformation. These latter methodological steps are basedon explainable machine learning, the role of which indelivering scientific insights and discoveries in naturalsciences has been extensively discussed by Roscher et al.
(2020). The results are presented in Sects. 3.1, 3.2, 3.3 and
3.4, which are devoted to the global summaries, the summaries across climates, the summaries across continents
and the comparisons enabled by explainable machinelearning, respectively. The most important findings arefurther elaborated and discussed with respect to their
theoretical and practical implications, as well as theirlinks with the climate literature, in Sect. 4. In the same
section, the strengths and limitations of the work are outlined. The paper concludes with Sect. 5, where the findings are summarized in the form of take-home messages.

2 Data and methods
2.1 Seasonal hydroclimatic time series, geographicaldivisions and climate classes

Peterson and Vose (1997), Do et al. (2018) and Menne
et al. (2018) have compiled and made publicly available
high-quality global time series datasets that summarize
earth-observed hydroclimatic quantities. Starting from
13,104 mean monthly temperature, total monthly precipitation and mean monthly river flow time series that(i) originate from the aforementioned open time series
datasets (see the information on their availability in the“Availability of data materials” section) and (ii) satisfy aseries of specific length and quality conditions, we compute 13,104 39-year-long quarterly time series of 3-monthmeans. These latter time series are the ones analysedherein in terms of their features (according to Sect. 2.2),

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

after being standardized, and are referred to hereafter
as “seasonal” time series. Each of them starts from winter and ends to fall, with winter, spring, summer and fallbeing represented by the month sets {December, January,
February}, {March, April, May}, {June, July, August} and{September, October, November}, respectively. This specific seasonal representation scheme is adopted both inhydrology and hydroclimatology for conducting investigations at the global scale (see, for example, Angell 1988;
Dai and Wigley 2000; Arnal et al. 2018); therefore, it isconsidered appropriate for reaching the aims of the present work. Also notably, the length and quality conditions imposed for time series selection are the same withthose outlined in the data sections of the earlier works by
Papacharalampous et al. (2021, 2022). In summary, all themonthly hydroclimatic time series of these earlier works(that are used to compute the seasonal hydroclimatictime series of this work) had to be complete and with thesame length, and a good compromise between their number and their length had to be made. Indeed, the available
longer complete time series are much fewer. As regards
the quality conditions, the monthly temperature and precipitation time series did not require additional testingother than that already applied during their original formation (Peterson and Vose 1997; Menne et al. 2018). On
the other hand, the monthly river flow time series had tobe filtered through visual quality inspections for identifying irregularities (e.g. abrupt changes in their mean andvariance) that could be due to human activities (Papacharalampous et al. 2021).
In greater detail, the herein analysed temperature,
precipitation and river flow time series originate from
2432, 5071 and 5601 geographical locations, respectively.
These geographical locations are presented in Fig. 1. In
the same figure, climate classification information forthese geographical locations is provided in terms of percentages both at the global and at continental scales,
and regional groups of stations that are characterized bylarge or medium densities of observational stations aredefined. The climate classification information is basedon the well-established and interpretable system by Kottek et al. (2006), an updated version of the Köppen–Geiger climate classification system. The latter is the firstquantitative system of its kind, as well as the most frequently used one (Kottek et al. 2006; Belda et al. 2014). It
has been introduced by Wladimir Köppen and has later
been made available as a world map updated by Rudolf
Geiger (see Köppen 1936), while other historical information on its formation can be found in Thornthwaite(1943). The exact numbers of temperature, precipitation
and river flow stations representing the various climateclasses in our global hydroclimatic time series datasets(see also Kottek et al. 2006 for the statistical criteria

Page 3 of 20

underlying their definition) are presented in Fig. S1 ofthe supplementary material (see Additional file 1), while
the respective counts of stations representing the main
climate divisions (else referred to in the literature and inwhat follows as “climate zones”) can be found in Fig. S2 ofthe same material. These climate zones are the equatorial(A), arid (B), warm temperate (C), snow (D) and polar (E)ones, and are defined by specific temperature or precipitation conditions that allow the growth of different vegetation groups.
2.2 Feature computation, summaries and comparisons

We separately characterize each quarterly hydroclimatictime series (see Sect. 2.1) by estimating eight interpretable features (see Table 1). Three of these features belong
to the large family of the sample autocorrelation features(see, for example, Wei 2006), thereby being appropriate
for investigating the temporal dependence structure. The
first of them is the lag-1 sample autocorrelation of thetime series (hereafter referred to simply as “lag-1 autocorrelation”). This feature characterizes both the magnitude
and the sign of the correlation between two subsequent
points in the time series and, thus, between the hydroclimatic means corresponding to two subsequent seasons for the analyses herein. The second autocorrelation
feature is the sum of the squared sample autocorrelation
values of the time series at the lags equal from 1 to 10
seasons. This specific feature is hereafter referred to simply as “autocorrelation summary”, as it summarizes multiple autocorrelation features. The third autocorrelation
feature supporting the investigations of this work is thelag-4 sample autocorrelation of a time series, a feature
particularly relevant to characterizing the magnitude of
the relationship between time series values corresponding to the same season (i.e. the annual-scale dependence)in a quarterly time series and, thus, hereafter referred tosimply as “seasonal autocorrelation”.
Another feature supporting our investigations hereinis called “temporal variation”. This feature is the standard deviation of the first-order differenced standardized
time series and is similar to the coefficient of variation.
For detailed information on time series differencing andits usefulness in reducing seasonality and trend features
before conducting further analyses, the reader is referred
to Hyndman and Athanasopoulos (2021). Moreover, we
compute the “spectral entropy” of the time series by following the method by Jung and Gibson (2006). This feature is usually perceived to be measuring the random (ornoisy) component of the time series (see, for example,
Hyndman and Athanasopoulos 2021) and, therefore, itfacilitates characterizations and comparisons in terms ofpredictability. The sixth feature investigated in this workis the Hurst parameter of the fractional Gaussian noisePapacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Page 4 of 20

Fig. 1 Geographical locations of the a temperature, b precipitation and c river flow stations exploited in the present work, climate classification
information following the system by Kottek et al. (2006) and definition of regional groups of stations

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Page 5 of 20

Table 1 Features computed for characterizing each quarterly hydroclimatic time series
S/n

Name

Brief description1

Lag-1 autocorrelation

Lag-1 sample autocorrelation of the time series

2

Autocorrelation summary

Sum of the squared sample autocorrelation values of the time series at the lags equal from 1 to 10 seasons

3

Seasonal autocorrelation

Lag-4 sample autocorrelation of the time series

4

Temporal variation

Standard deviation of the first-order differenced standardized time series

5

Spectral entropy

Spectral entropy of the time series estimated by applying the method by Jung and Gibson (2006)

6

Hurst exponent

Hurst parameter of the fractional Gaussian noise process estimated by applying the method by Tyralis
and Koutsoyiannis (2011) on the deseasonalized time series

7

Trend strength

Strength of trends in the time series estimated according to Kang et al. (2017)8

Seasonality strength

Strength of seasonality in the time series estimated according to Kang et al. (2017)

process, an analogous of the autoregressive fractionallyintegrated moving average process (see, for example, Wei
2006). This feature is computed by applying the method
by Tyralis and Koutsoyiannis (2011) to time series thathave been previously deseasonalized according to theadditive classical model for time series decomposition(see, for example, Hyndman and Athanasopoulos 2021)
and by assuming four seasons. It is herein referred toas “Hurst exponent” and is broadly known to support
long-range temporal dependence (or “Hurst phenomenon”) investigations. While the term “autocorrelation
feature” could also be used to refer to Hurst features, inwhat follows we will be using it to refer only to the lag-1
autocorrelation, autocorrelation summary and seasonalautocorrelation features.
The computation of the last two time series features ofthis work involves seasonal and trend time series decomposition using Loess (STL decomposition; see, for example, Hyndman and Athanasopoulos 2021, Chapter 3.6).
The exact procedures followed for obtaining the seasonal,smoothed trend and remainder components of each timeseries can be found in Hyndman and Khandakar (2008).
Once these procedures have been completed, the “trend
strength” and “seasonality strength” of the time series arecomputed according to Kang et al. (2017). Then, the former of these features is equal to 1 minus the quotient of
the remainder component’s variance and the variance ofthe deseasonalized time series, while the latter of them isequal to 1 minus the quotient of the remainder component’s variance and the variance of the time series with its
smoothed trend component removed.
We characterize the Earth’s seasonal hydroclimate
by providing global summaries, in the forms of histograms and means, of the previously computed features(see above) of the seasonal temperature, precipitation
and river flow time series. Most importantly, we provide feature summaries and comparisons across climatesand continents. The latter investigations are enabled byside-be-side boxplots and mean value computation andare conducted conditional upon the information summarized in Fig. 1. More precisely, we summarize the results
per climate class, per main climate division and per featured group of stations, with each of these groups representing a different pair {time series type, geographicaldivision}. While all the geographical locations are taken
into consideration in the computation of the global andregional summaries, the climate classes and main climate divisions represented by less than 30 stations are
not studied and compared with the remaining ones for
ensuring the sufficient representativeness of our results.
2.3 Feature importance comparisons

We apply explainable machine learning to compare theeight time series features of this work (see Sect. 2.2) withrespect to their relevance as explanatory variables in two
types of classification settings that differ in their dependent variables. More precisely, the investigated classification settings target at predicting—in the form of a best
guess—and explaining–interpreting either (i) the main
climate division from which a seasonal hydroclimatictime series originates or (ii) the group of stations and,
therefore, the geographical division from which a seasonal hydroclimatic time series originates (only for thosetime series originating from one of the groups of stations
featured in this work; see Fig. 1), given only the values ofthe eight features characterizing this time series. These
classification settings allow objective comparisons of
the magnitude of the relationships between the seasonalhydroclimatic features assessed in this work and other
Earth’s features, and are studied separately for seasonaltemperature, precipitation and river flow; therefore, we
study 2 (number of classification setting types) × 3 (number of time series types) = 6 classification problems.
Each time, we fit random forests (Breiman 2001) for
classification with 500 trees and compute two variable
importance measures, namely the “mean decrease accuracy” and “mean decrease Gini” ones. We do not optimize the parameters of random forests, as according toPapacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

the literature (see, for example, the review by Tyralis et al.
2019): (a) the performance of this algorithm is expected
to increase with increasing the number of trees, and (b)the default values of its remaining parameters have been
empirically proven to be adequate. In summary, the firstvariable importance measure is computed as follows(Liaw 2018): For each tree, the error rate on the out-ofbag portion of the data is computed. The computationis repeated after permuting each predictor variable. The
difference between the two are then averaged over alltrees, and normalized by the standard deviation of thedifferences. If the standard deviation of the differences isequal to 0 for a variable, the division is not done (but the
average is almost always equal to 0 in that case). The second metric is the total decrease in node impurities fromsplitting on the variable, as measured by the Gini index
and averaged over all the trees (Liaw 2018). Once all thevariable importance scores have been computed, thetime series features are ranked based on them. The rankings are made separately for each set {time series type,
dependent variable, variable importance measure}. The
variable importance scores are not compared in terms of
their magnitude, as such comparisons have only limited
reliability (Tyralis et al. 2019).

3 Results
3.1 Overall summary of the Earth’s seasonal hydroclimate

The global summaries of the seasonal temperature, precipitation and river flow features are provided in Fig. 2.
As the strengths of these features vary largely from geographical location to geographical location with few
exceptions (referring to specific temperature features; see
Fig. 2a, b, g, j, m, v), providing characterizations and comparisons across climates and continents becomes evenmore important from both a scientific and a practicalpoint of view. Aside from this important remark, otherinteresting results also stem from Fig. 2. For instance, thelag-1 autocorrelation of the seasonal temperature timeseries is very close to zero, indicating almost uncorrelated variables due to the remarkably strong seasonality
patterns at the quarterly time scale. These patterns seemto be manifesting themselves into pairs of consecutive
values in each time series that are much less correlated
than in other time scales, such as the monthly one. Notably, the same is not observed for the precipitation, andespecially for the river flow, time series. Also notably,
the autocorrelation summary feature takes remarkably
large values for seasonal temperature, while the same
does not apply to the cases of seasonal precipitation andriver flow. Indeed, while lag-1 autocorrelation is almost
zero for seasonal temperature and has absolute values
that are much larger than zero for seasonal precipitation
and river flow, it seems that the autocorrelation values atPage 6 of 20

other lags (among those equal from 2 to 10 seasons) aremuch larger for seasonal temperature than for seasonal
precipitation and river flow.
3.2 Seasonal hydroclimatic feature comparisonsacross climates

Statistical summaries of the features of the seasonal temperature, precipitation and river flow time series acrossthe investigated Köppen–Geiger climate classes are presented in Figs. 3, 4, 5, while the respective summaries
per main climate division are presented in Figs. 6 and7. These summaries offer a new basis for comparing thevarious Köppen–Geiger climates, other than the one
offered by their original definitions (see the related discussions in Sect. 4). Moreover, especially Figs. 5 and 7
offer information that could be exploited for constraining
the uncertainty in the design of seasonal stochastic models. This latter contribution holds particularly for geographical locations with short or no time series records.
In what follows, Figs. 3, 4, 5, 6, 7 are collectively summarized and discussed, as they are interconnected.
In brief, both the Hurst phenomenon and trends arehere found to be more intense for the seasonal temperature time series originating from the equatorial zone(A) than for those originating from other Köppen–Geiger climate zones (Figs. 6f, g and 7a). This climate zone
has minimum monthly temperatures equal or less than
18 °C (Kottek et al. 2006). Notably, seasonal temperaturetime series from this zone are further found to exhibit
comparably large and even larger trends and long-range
dependence, on average, than the seasonal river flow timeseries (Figs. 6f, g and 7a, c). The same also holds (but toa less extent) for the seasonal temperature time series
from the polar zone (E; composed by climates with maximum monthly temperatures less than 10 °C; Kottek et al.
2006). The polar zone is mostly represented in the examined temperature dataset by polar tundra climates (ET)and is here found to exhibit more intense seasonal temperature trends and long-range dependence compared to
the remaining main climate divisions (i.e. the arid, warm
temperate, and snow ones; Figs. 6f, g and 7a, c).
Still, the same does not hold for all the individual Köppen–Geiger climate classes (defined by the main climate
and subsequent precipitation conditions). Indeed, snow
and winter dry climates with warm summer (Dwb) are
here found to have the largest trend strength and Hurst
exponent values among all the examined individual Köppen–Geiger climate classes, including the polar tundra
climates (ET) (Figs. 4b, c and 5a). Comparably large trend
strength and Hurst exponent values have been computed, on average, for the warm temperate and summer
dry climates with warm summer (Csb; Figs. 4b, c and5a). On the other hand, the least pronounced seasonal

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Page 7 of 20

Fig. 2 Global summaries of the seasonal a, d, g, j, m, p, s, v temperature, b, e, h, k, n, q, t, w precipitation and c, f, i, l, o, r, u, x river flow features.
For comparison purposes, the limits of the horizontal axes have been set common for the histograms in the same row. The relationships
between the features can be inspected through Figs. S3 − S5 of the supplementary materialPapacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Page 8 of 20

Fig. 3 Side-by-side boxplots of the values of a lag-1 autocorrelation, b autocorrelation summary, c seasonal autocorrelation and d temporalvariation per climate division (Kottek et al. 2006) for seasonal temperature, precipitation and river flow. The limits of the vertical axes of the blue
rectangles have been set identical to the upper and lower limits of the blue ribbons, thereby allowing comparisons both within and across timeseries types. The corresponding mean values are presented in Fig. 5

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Page 9 of 20

Fig. 4 Side-by-side boxplots of the values of a spectral entropy, b Hurst exponent, c trend strength and d seasonality strength per climate division(Kottek et al. 2006) for seasonal temperature, precipitation and river flow. The limits of the vertical axis of the blue rectangle have been set identicalto the upper and lower limits of the blue ribbon, thereby allowing comparisons both across the various temperature time series and across timeseries types. The corresponding mean values are presented in Fig. 5

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Page 10 of 20

Fig. 5 Mean values of the seasonal a temperature, b precipitation and c river flow features in the various climate classes (Kottek et al. 2006).
The mean values presented in each column have been ranked and coloured from the smallest (white) to the largest (dark green), thereby
highlighting even the smallest differences. The grey areas (i.e. areas lacking statistical summaries) correspond to under-represented climate classes
in the investigated global datasets (see Fig. S1 in the supplementary material). The corresponding boxplots are presented in Figs. 3 and 4

temperature trends and long-range dependence arefound to characterize, again on average, the snow andfully humid climates with either hot (Dfa), warm (Dfb)
or cool (Dfc) summer (Figs. 4b, c and 5a). Apart frombeing characterized by the largest trends and longrange dependence, the seasonal temperature time series
originating from equatorial climates have also the largest spectral entropy, followed by those originating from

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Page 11 of 20

Fig. 6 Side-by-side boxplots of the values of a lag-1 autocorrelation, b autocorrelation summary, c seasonal autocorrelation, d temporal variation,e spectral entropy, f Hurst exponent, g trend strength and h seasonality strength per main climate division (Kottek et al. 2006) for seasonaltemperature, precipitation and river flow. The limits of the vertical axes of the blue rectangles have been set identical to the upper and lower limitsof the blue ribbons, thereby allowing comparisons both within and across time series types. The corresponding mean values are presented in Fig. 7

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Page 12 of 20

Fig. 7 Mean values of the seasonal a temperature, b precipitation and c river flow features in the main climate divisions (Kottek et al. 2006). The
mean values presented in each row have been ranked (separately for temperature, precipitation and streamflow) and coloured from the smallest(white) to the largest (dark green), thereby highlighting even the smallest differences. Polar climates are under-represented in the investigatedprecipitation and river flow datasets (see Fig. S2 in the supplementary material); thus, no statistical summaries are available for them in b and c. The
corresponding boxplots are presented in Fig. 6polar climates (Figs. 6e and 7a). The latter climates are
additionally found to have comparably large spectral
entropy with three snow climate classes (specifically, theCwa, Csa and Csb ones).
Links between seasonal temperature features withsmaller interquartile ranges of values and the features
defining the various Köppen–Geiger climates (Kottek
et al. 2006) also emerge. For instance, it is found that theseasonal temperature time series originating from warm
temperate and summer dry climates with warm summer(Csb) are those with the largest positive lag-1 autocorrelation (i.e. correlation between the mean values of two
subsequent seasons in our investigations) and the smallest autocorrelation summaries, seasonal autocorrelation,
temporal variation and seasonality strength, together
with those originating from warm temperate and fully
humid climates with warm summer (Cfb) and thoseoriginating from polar tundra climates (ET) (Figs. 3a, b,
c, d, 4d and 5a). It is additionally found that the seasonaltemperature time series from warm temperate and winter dry climates with hot summer (Cwa) have the smallest negative lag-1 autocorrelation, followed by thosefrom the snow and winter dry climates with either warm
(Dwb) or cool (Dwc) summer (Figs. 3a and 5a). These latter two climate types exhibit the most intense summary
autocorrelation and seasonality features as regards theirseasonal temperature time series. Furthermore, they
exhibit equally pronounced temporal variation featureswith the Cwa climates (again as regards their seasonaltemperature time series; Figs. 3d and 5a).
The equatorial zone (A) also stands out because of its
seasonal precipitation features. Indeed, the seasonal precipitation time series originating from this zone exhibit
the largest autocorrelation summary, seasonal autocorrelation and seasonality strength values, and at the sametime the smallest spectral entropy values, by far, compared to the seasonal precipitation time series originatingfrom other climate zones (Figs. 6b, c, h and 7b). Amongthe various climatic sub-regimes composing the equatorial zone, autocorrelation, temporal variation and seasonality features are more pronounced for the monsoonal
ones (Am), which are also found to have equally intense
autocorrelation and seasonality features with the warm
temperate and winter dry climates with either hot (Cwa)or warm (Cwb) summer (Figs. 3b, c, 4d and 5b). Again
referring to the strength of the same time series characteristics, the Am, Cwa and Cwb climates are closely followed by the warm temperate and summer dry climateswith either hot (Csa) or warm (Csb) summer and theequatorial climates with either dry summers (As) or winters (Aw) (Figs. 3b, c, 4d and 5b). These latter four climate
types are, in their turn, closely followed by the hot arid
steppes (BSh), which also exhibit somewhat more intense
autocorrelation and seasonality, on average, than the
total of the examined seasonal precipitation time series,
in contrast to the remaining climate classes (BWk, BWh,

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

BSk, Cfa, Cfb, Dfa, Dfb), while those seasonal precipitation time series originating from snow and fully humid
climates with cool summer (Dfc) are, on average, characterized by seasonality and summary autocorrelation features approximately equal to the global means (Figs. 3b,c, 4d and 5b). Largely similar (but not identical) would be
the ordering of the various climate classes regarding the
temporal variation characteristics of the seasonal precipitation time series; however, in the case of these characteristics the magnitude differences are less pronounced(Figs. 3d, 5b, 6d and 7b).
Similar to the summary autocorrelation and seasonality features of the seasonal precipitation time series,
their entropy features are strongly related to the features
defining the various Köppen–Geiger climates (Kottek
et al. 2006), with the cold arid deserts (BWk), as well as
the warm temperate and fully humid climates with hot(Cfa) or warm (Cfb) summer, being those with the largest mean values (Figs. 4a and 5b). The opposite holds
for three equatorial (Am, As and Aw) and four warm
temperate (Csa, Csb, Cwa and Cwb) climates, while
medium-magnitude entropy means characterize the seasonal precipitation time series of the remaining climates(Figs. 4a and 5b). The trend and long-range dependence
features of seasonal precipitation have smaller ranges ofvalues compared to their entropy features; nonetheless,they are also somewhat related to the features defining
the Köppen–Geiger climates (Figs. 4b, c and 5b).
Mostly positive lag-1 autocorrelation is found to characterize the seasonal river flow time series originatingfrom all the examined Köppen–Geiger climates apartfrom the snow and fully humid climates with warm (Dfb)
or cool (Dfc) summer, and the snow and summer dry climates with warm summer (Dsb), for which the means(and the medians) of lag-1 autocorrelation of their seasonal river flow time series are quite close to (and, specifically, a bit larger than) zero (Figs. 3a and 5c). The same
three climate classes (Dfb, Dfc and Dsb) are found toalso stand out for the pronounced autocorrelation summary, seasonal autocorrelation, temporal variation andseasonality strength features of their seasonal river flowtime series, as well as for the smallest spectral entropy
values of the same time series (Figs. 3b, c, d, 4a, d and5c), which also characterize the snow zone (D) in general(Figs. 6b, c, d, e, h and 7c). This latter climate zone has
minimum monthly temperatures less than − 3 °C (Kottek
et al. 2006).

Page 13 of 20

Other Köppen–Geiger climates standing out for the
pronounced autocorrelation summary, seasonal autocorrelation, temporal variation and seasonality strengthfeatures of their seasonal river flow time series are theequatorial savannahs with dry winter (Aw) and the warm
temperate climates with dry winter and hot summer(Cwa), while the equatorial monsoonal climates (Am) andthe equatorial savannahs with dry summer (As) are thosewith the least pronounced autocorrelation summary, seasonal autocorrelation, temporal variation and seasonality
strength features (Figs. 3b, c, d, 4d and 5c). These latter
two climate classes are also characterized by the largest,among all the examined Köppen–Geiger ones, spectral
entropy values of seasonal river flow time series, followedby the snow and fully humid climates with hot summer(Dfa), which also have among the smallest means of the
autocorrelation summary, seasonal autocorrelation, temporal variation and seasonality strength features of theirseasonal river flow time series (Figs. 3b, c, d, 4a, d and5c). Regarding the long-range dependence and trend features of the same time series, these are found to be more
pronounced, by far, for the warm temperate climates withdry winter and hot summer (Cwa), with the equatorialsavannahs with dry winter (Aw) and the warm temperate
climates with dry winter and hot summer (Csa) following(Figs. 4b, c and 5c). On the other hand, the seasonal timeseries from the snow and fully humid climates with coolsummer (Dfc) are found to have the smallest trends andlong-range dependence (Figs. 4b, c and 5c).
3.3 Seasonal hydroclimatic feature comparisonsacross continents

Statistical summaries of the seasonal temperature, precipitation and river flow features across the various
examined continental-scale regions (represented by specific groups of temperature, precipitation and river flow
stations in our global hydroclimatic time series datasets;
see Fig. 1) are presented in Figs. 8 and 9. These summaries could be used for reducing uncertainty in the designof seasonal stochastic models for geographical locations
with short time series records, in a similar way to the previously discussed summaries. Their physical interpretation through Figs. 1, 3, 4 and 5 is also possible to someextent. Rather small differences are found between seasonal temperature in North America, Europe and East
Asia, with the latter continental-scale region having themost pronounced autocorrelation summary, seasonality,(See figure on next page.)
Fig. 8 Side-by-side boxplots of the values of a lag-1 autocorrelation, b autocorrelation summary, c seasonal autocorrelation, d temporal variation, e
spectral entropy, f Hurst exponent, g trend strength and h seasonality strength per featured group of stations (representing a specific geographicaldivision) for seasonal temperature, precipitation and river flow. The limits of the vertical axes of the blue rectangles have been set identicalto the upper and lower limits of the blue ribbons, thereby allowing comparisons both within and across time series types. The corresponding meanvalues are presented in Fig. 9

Papacharalampous et al. Progress in Earth and Planetary ScienceFig. 8 (See legend on previous page.)(2023) 10:46

Page 14 of 20

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Page 15 of 20

Fig. 9 Mean values of the seasonal a temperature, b precipitation and c river flow features in the various featured groups of stations (representing
different geographical divisions). The mean values presented in each row have been ranked (separately for temperature, precipitationand streamflow) and coloured from the smallest (white) to the largest (dark green), thereby highlighting even the smallest differences. The
corresponding boxplots are presented in Fig. 8

temporal variation, spectral entropy, long-range dependence and trend features of seasonal temperature timeseries, and Europe having the least pronounced autocorrelation summary, seasonality and temporal variation
features (Figs. 8 and 9a).
The most notable differences from continent to continent are identified in terms of seasonal precipitation(Figs. 8 and 9). In these terms, the most intense autocorrelation summary and seasonality features are foundto characterize Central Africa. Two other continentalscale regions with comparably pronounced autocorrelation summary and seasonality features are East Asia andIndia, with the latter one having also the most intense
temporal variation features of seasonal precipitation, followed closely by Central Africa and East Asia (Figs. 8b, c,d, h and 9b). The same three geographical divisions also
stand out for the spectral entropy values of their seasonal
precipitation time series. These values are, on average,
the smallest among those computed for the eight examined geographical divisions, while the largest are, by far,those characterizing North America, Europe and Australia (Figs. 8e and 9b). Regarding the long-range dependence and trend features of the seasonal precipitation
time series, these are somewhat more intense for SouthAmerica than they are for the remaining examined geographical divisions, with Australia being next and this latter continent being followed, in its turn, by Central Africa(Figs. 8f, g and 9b).
Among the three geographical divisions compared withrespect to their seasonal river flow characteristics, SouthAmerica is the one standing out. Indeed, the values oflag-1 autocorrelation, autocorrelation summary, seasonalautocorrelation, Hurst exponent, trend strength and seasonality strength of the time series originating from thislatter geographical division are, on average, larger thanthose of the remaining two geographical divisions, while
their temporal variation values are, on average, smaller(Figs. 8 and 9c). Some similarities are additionally identified between the differences in the seasonal precipitation
features of North America, South America and Europe,Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Page 16 of 20

Fig. 10 Rankings of the eight features from the most (1st) to the least (8th) important ones in distinguishing a the main climate divisions or b
the groups of stations (i.e. the T1, T2, T3, P1, P2, P3, P4, P5, P6, P7, P8, R1, R2 or R3 ones) for temperature, precipitation and river flow using two
variable importance methods

and the respective differences in the seasonal river flow
features (Fig. 8), probably because of the strong physicalrelationship between precipitation and river flow.
3.4 Feature importance in distinguishing climatesand continents

Feature comparisons with respect to their importance–
relevance in distinguishing the main climate divisions
or the groups of stations (i.e. the T1, T2 and T3 ones fortemperature, the P1, P2, P3, P4, P5, P6, P7 and P8 ones
for precipitation and the R1, R2 and R3 ones for riverflow) are allowed by Fig. 10. We observe that the spectral
entropy, Hurst exponent and trend strength are ranked
in the first three or four positions fewer times than theremaining features. Notably, differences in the feature
values that are small in absolute terms (but significant
in relative terms across climates and continents; see, forexample, the differences in the side-by-side boxplots inmost of the blue rectangles of Figs. 3, 4, 6 and 8) might
be more relevant to the distinction between the climate
zones or the groups of stations than differences that arelarger in absolute terms (but less significant in relative
terms).

4 Discussion
Our contribution to the literature rotates around eightinterpretable time series features. These have been here
computed, for the first time, for quantifying the differences in the Earth’s seasonal hydroclimate across climates and continents, and even for questioning theexistence of such notable differences. Facilitating directcomparisons in terms of temporal dependence, seasonality, temporal variation, entropy and trends at the global
scale, our methodological framework has succeeded toaddress the aforementioned important targets, thereby
substantially progressing our understanding and knowledge of the Earth’s seasonal hydroclimate, in line withcentral themes, concepts and directions provided by thePanta Rhei initiative for the International Association of
Hydrological Sciences (IAHS) scientific decade 2013–2022 (Montanari et al. 2013). Notable differences havebeen found in the strengths of most of the investigatedPapacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

temperature, precipitation and river flow features acrossthe various Köppen–Geiger climate classes, as well as
between several continental-scale regions. We, therefore, deem that (most of ) the provided feature summaries across climates and continents (Figs. 3, 4, 5, 6, 7, 8, 9)
could lead to a larger reduction of the modelling uncertainties than the respective global summaries (Fig. 2),
and especially of those uncertainties that accompany thestochastic modelling and simulation of precipitation andriver flow (but possibly of temperature as well) in areas
with short or without earth-observed time series records.
Reducing modelling uncertainties is traditionally among
the most important targets in hydrology and hydroclimatology (Montanari et al. 2013; Blöschl et al. 2019). We
also deem that the exploitation of our findings in thisregard could be straightforward, given the direct utilityof the computed statistics. For instance, these statistics
could be used within feature-based time series simulation
methodologies, such as the one proposed by Kang et al.
(2020). In this particular case, each region or climateclass could be represented by a set of features, with eachof the latter taking simply as its value either the mean or
the median of the values that have been computed for all
the seasonal hydroclimatic time series representing thissame region or climate class. Notably, the usefulness of
this modelling approach depends on multiple factors,
including the number of the time series available for eachregion or climate class and the spatial variability of thetime series characteristics within each region or climateclass.
From a different perspective, results of this work facilitate a better understanding of the various Köppen–
Geiger climate classes. Indeed, these classes are here
compared for the first time with respect to their seasonalhydroclimate in different terms than those followed fortheir original definition (see Kottek et al. 2006). Onlya few of the relationships between the various hydroclimatic features defining these classes and the herein
investigated hydroclimatic dependence, variability andchange features could be expected. Yet, even for theircase, additional quantitative and qualitative insights haveemerged from our investigations. For instance, one could
expect—already from existing climate knowledge—large
seasonality strength to characterize the seasonal precipitation time series originating from equatorial monsoonal
climates, a fact indeed confirmed and further quantified
by our investigations. Nonetheless, one could not expect,among others, that seasonality strength of similar magnitude characterizes the seasonal precipitation time series
originating from these latter climates and the warm temperate and winter dry climates with hot summer. Given
the long history of the Köppen–Geiger climate classification system and its significance for the climate literature

Page 17 of 20(see, for example, the introduction sections in Kottek
et al. 2006; Belda et al. 2014), we consider this aspectof our results particularly important. Of course, variants of the proposed methodological framework could
also be applied in the future to better understand, froma seasonal hydroclimatic feature perspective, other climate classification systems (see, for example, those by
Thornthwaite 1948; Trewartha and Horn 1980; Fovell andFovell 1993; Bunkers et al. 1996; Feddema 2005; Peel et al.
2007; Belda et al. 2014; Netzel and Stepinski 2016; Becket al. 2018; Knoben et al. 2018; McCurley et al. 2021, andthe historical landmark discussions on the formation ofsuch systems by Thornthwaite 1943, 1948).
Overall, we consider the utilization of gauge-measured time series data as a strength of our methodological framework, given also the sufficiently large number ofthe investigated time series (i.e. 2432 temperature, 5071
precipitation and 5601 river flow time series), their sufficient length (i.e. 156 values at the quarterly temporalscale) and their high quality. Alternatives would include
the use of general circulation models or gridded (e.g. reanalysis) time series datasets, which offer optimal coverages of the Earth’s surface and are not characterized byspatial heterogeneities. However, these models and datasets are known to contain large errors (see, for example,
the related discussions by Tyralis et al. 2018, as well as
the related literature information provided therein) that
could affect our hydroclimatic feature comparisons. As
an inevitable consequence of the preference to gaugemeasured data, a few Köppen–Geiger climate classes
have been left out from our analyses. The same holds forcontinental-scale regions with low densities of data-richstations. Moreover, comparisons between IPCC climate
reference regions (Iturbide et al. 2020) would be anotherconsiderable way for extending the results of this work.
Still, we believe to have provided extensive characterizations and comparisons leading to a broad overview of the
Earth’s seasonal hydroclimate.

5 Summary and conclusions
We have devised a new methodological framework for(a) the thorough characterization of the Earth’s seasonalhydroclimate in terms of temporal dependence, seasonality, temporal variation, entropy and trends, and (b) the
better understanding of climate classification systems
in terms of their seasonal hydroclimatic properties. We
have extensively applied the new framework by exploiting over 13,000 temperature, precipitation and river flowtime series, in which the seasonal hydroclimatic behaviour is represented by 3-month means of earth-observed
quantities. We have adopted the well-established andinterpretable Köppen–Geiger climate classification system, and have characterized (most of ) its classes basedPapacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

on their seasonal hydroclimatic feature values. We havefurther characterized continental-scale regions with large
or medium density of observational stations, and applied
explainable machine learning to compare the investigatedfeature types with respect to the amount of informationthat they provide for guessing either the main Köppen–
Geiger climate or the continental-scale region. Our findings have both theoretical and practical implications andare summarized with the following points, together witha few key strengths and limitations of the work:• The Hurst phenomenon and trends are more intense
for the seasonal temperature time series originatingfrom the equatorial zone than for those originatingfrom the remaining climate zones. Nonetheless, eachof the various equatorial climate classes is under-represented in the herein examined temperature data, alimitation that has prohibited further investigations
and insights into their temperature environments.
• Between a variety of well-represented climate classes(including several arid, warm temperate and snow
ones, as well as the polar tundras), snow and winter dry climates with warm summer have the largest
seasonal temperature long-range dependence andtrends, followed by the warm temperate and summer
dry climates with warm summer.
• The differences identified in terms of long-range
dependence and trends across the various climateclasses for the seasonal temperature time series could
support the design of better stochastic models. However, the respective differences identified in terms of
autocorrelation, temporal variation and seasonality
are expected to be less informative in engineeringcontexts due to their rather small magnitude.
• Even in terms of long-range dependence and trends,
seasonal temperature does not differ between North
America, Europe and East Asia as largely as it does
between some of the investigated climate classes.
Still, for the latter continental-scale region, the Hurst
phenomenon and trends are somewhat more pronounced.
• Moreover, the equatorial zone in general, and its
monsoonal, summer dry and winter dry climates inparticular, are characterized by the most pronounced
autocorrelation and seasonality features of seasonal
precipitation, as well as the least pronounced entropy
features, together with the warm temperate and winter or summer dry climates with either hot or warm
summer.
• Notable differences in seasonal precipitation arefound between continental-scale regions as well, withby far the most pronounced autocorrelation, temporal variation and seasonality features, as well as the

•

•

•

•

•

Page 18 of 20

least pronounced entropy features, characterizing
Central Africa, East Asia and India. The opposite
holds for Australia, while the seasonal precipitation
time series from this latter continental-scale region,
as well as those from North America, stand out for
their pronounced long-range dependence and trend
features.
The snow and fully humid climates with warm orcool summer, the snow and summer dry climateswith warm summer, the equatorial savannahs withdry winter and the warm temperate climates withdry winter and hot summer are those with the mostpronounced summary autocorrelation, temporalvariation and seasonality features of their seasonalriver flow time series, while the opposite holds forthe equatorial monsoonal climates and the equatorialsavannahs with dry summer.
The warm temperate climates with dry winter andhot summer are by far those with the most intense
Hurst phenomenon and trends. At the same time, theseasonal river flow time series from North America
are characterized by the most pronounced longrange dependence and trends.
These latter time series are further characterized
by larger correlations of their subsequent seasonsand smaller temporal variation than those originating from North America and Europe. The latter two
continental-scale regions exhibit quite similar summaries of seasonal hydroclimatic features, in general.
Entropy, long-range dependence and trend features are found to be (roughly) less indicative of themain Köppen–Geiger climate division or the continent in predictive modelling contexts than theremaining investigated feature types. It should be
noted, however, that this matter requires additional
investigations. Indeed, the coverage of the earth byground-based stations with seasonal hydroclimatictime series that are long enough for our analyses iscurrently largely heterogeneous, with many classes
being under-represented in the formed classification settings. Furthermore, obtaining seasonal timeseries using different 3-month aggregation schemes(in which winter, spring, summer and fall are represented by different month sets) could lead to deviations in the feature importance in the classification
problems.
Aside from progressing our understanding of the
Earth’s seasonal hydroclimate and the Köppen–Geiger climate classification, the feature summaries
across climates and continents provided by the present work could also help in reducing—as much as
possible—modelling uncertainties, especially thosethat accompany the stochastic modelling of precipi-

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

tation and river flow in areas with short or without
time series records, and given the high quality andexpected accuracy of the utilized global datasets.
They could also be used as a metric for the evaluationof the performance of satellite- and reanalysis-based
data products, as well as the performance of climate
model products, deviating from conventional evaluations (global RMSE, correlations, etc.) in the sensethat they benefit more from the newest data science
concepts (e.g. those synthesized by Hyndman et al.
2022).
Overall, we believe that the authentic and comparative
character of the proposed framework has been the key toproviding fresh useful insights into the Earth’s seasonalhydroclimate and its dynamics. We also deem that possible extensions of this framework would be beneficialfrom both a scientific and a practical point of view, given
the high potential characterizing the newest data scienceadvancements and the rare appearance of largely comparative hydroclimatic characterizations at the global
scale.

Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s40645-​023-​00574-y.
Additional file 1. Additional visualizations.
Acknowledgements
The authors are grateful to the Associate Editor and Reviewers for their constructive remarks.
Author contributions
GP and HT conceptualized the work and designed its experiments with input
from YM, PM and MH. GP and HT performed the analyses and visualizations,and wrote the first draft, which was commented and enriched with new text,
interpretations and discussions by YM, PM and MH.
Funding
This work was carried out within the project “Investigation of Terrestrial HydrologicAl Cycle Acceleration (ITHACA)” funded by the Czech Science Foundation(Grant 22-33266M).
Availability of data materials
The gridded climate data (Kottek et al. 2006) can be retrieved through theR package kgc (Bryant et al. 2017), while the original hydrometeorological
data (i.e. the mean and total monthly time series of varying lengths) can be
retrieved through the following links: (a) https://​www.​ncdc.​noaa.​gov/​ghcnm/​
v4.​php (for temperature; Menne et al. 2018); (b) https://​www.​ncdc.​noaa.​gov/​
ghcnm/​v2.​php (for precipitation; Peterson and Vose 1997); and (c) https://​doi.​
org/​10.​1594/​PANGA​EA.​887477 (for river flow; Do et al. 2018).

Declarations
Competing Interests
The authors declare no conflict of interest.
Author details
1
Department of Water Resources and Environmental Modeling, Facultyof Environmental Sciences, Czech University of Life Sciences, Kamýcá 129,

Page 19 of 20

Praha‑Suchdol, 16500 Prague, Czech Republic. 2 Department of Water
Resources and Environmental Engineering, School of Civil Engineering, National Technical University of Athens, Heroon Polytechneiou 5,15780 Zographou, Greece. 3 Construction Agency, Hellenic Air Force, Mesogion
Avenue 227–231, 15561 Cholargos, Greece.
Received: 12 October 2022 Accepted: 14 July 2023

References
Angell JK (1988) Variations and trends in tropospheric and stratospheric global
temperatures, 1958–87. J Clim 1(12):1296–1313. https://​doi.​org/​10.​1175/​
1520-​0442(1988)​0012.0.​CO;2
Archfield SA, Kennen JG, Carlisle DM, Wolock DM (2014) An objective and parsimonious approach for classifying natural flow regimes at a continental
scale. River Res Appl 30:1085–1095. https://​doi.​org/​10.​1002/​rra.​2710
Arnal L, Cloke HL, Stephens E, Wetterhall F, Prudhomme C, Neumann J, Krzeminski B, Pappenberger F (2018) Skilful seasonal forecasts of streamflow
over Europe? Hydrol Earth Syst Sci 22:2057–2072. https://​doi.​org/​10.​
5194/​hess-​22-​2057-​2018
Beck C, Grieser J, Kottek M, Rubel F, Rudolf B (2005) Characterizing global
climate change by means of Köppen climate classification. Klimastatusbericht 51:139–149
Beck HE, Zimmermann NE, McVicar TR, Vergopolan N, Berg A, Wood EF (2018)
Present and future Köppen–Geiger climate classification maps at 1-km
resolution. Sci Data 5:180214. https://​doi.​org/​10.​1038/​sdata.​2018.​214
Belda M, Holtanová E, Halenka T, Kalvová J (2014) Climate classification revisited: from Köppen to Trewartha. Climate Res 59:1–13. https://​doi.​org/​10.​3354/​cr012​04
Blöschl G, Bierkens MFP, Chambel A, Cudennec C, Destouni G, Fiori A, Kirchner
JW, McDonnell JJ, Savenije HHG, Sivapalan M et al (2019) Twenty-three
Unsolved Problems in Hydrology (UPH)–a community perspective.
Hydrol Sci J 64(10):1141–1158. https://​doi.​org/​10.​1080/​02626​667.​2019.​
16205​07
Breiman L (2001) Random forests. Mach Learn 45(1):5–32. https://​doi.​org/​10.​1023/A:​10109​33404​324
Bryant C, Wheeler NR, Rubel F, French RH (2017) kgc: Köppen–Geiger Climatic
Zones. R package version 1.0.0.2. https://​CRAN.R-​proje​ct.​org/​packa​ge=​kgc
Bunkers MJ, Miller JR, DeGaetano AT (1996) Definition of climate regions in
the northern plains using an objective cluster modification technique. J
Clim 9(1):130–146. https://​doi.​org/​10.​1175/​1520-​0442(1996)​009%​3c0130:​
DOCRIT%​3e2.0.​CO;2
Dai A, Wigley TML (2000) Global patterns of ENSO-induced precipitation. Geophys Res Lett 27(9):1283–1286. https://​doi.​org/​10.​1029/​1999G​L0111​40
Do HX, Gudmundsson L, Leonard M, Westra S (2018) The Global Streamflow
Indices and Metadata Archive (GSIM) – Part 1: the production of a daily
streamflow archive and metadata. Earth Syst Sci Data 10:765–785. https://​doi.​org/​10.​5194/​essd-​10-​765-​2018
Feddema JJ (2005) A revised Thornthwaite-type global climate classification.
Phys Geogr 26(6):442–466. https://​doi.​org/​10.​2747/​0272-​3646.​26.6.​442
Fischer S, Schumann A (2018) A distribution-free ordinal classification of floods
based on moments. Hydrol Sci J 63(11):1605–1618. https://​doi.​org/​10.​
1080/​02626​667.​2018.​15256​14
Fovell RG, Fovell MYC (1993) Climate zones of the conterminous United States
defined using cluster analysis. J Clim 6(11):2103–2135. https://​doi.​org/​10.​
1175/​1520-​0442(1993)​006%​3c2103:​CZOTCU%​3e2.0.​CO;2
Hall J, Blöschl G (2018) Spatial patterns and characteristics of flood seasonality
in Europe. Hydrol Earth Syst Sci 22(7):3883–3901. https://​doi.​org/​10.​5194/​
hess-​22-​3883-​2018
Hanel M, Rakovec O, Markonis Y, Máca P, Samaniego L, Kyselý J, Kumar R (2018)
Revisiting the recent European droughts from a long-term perspective.
Sci Rep 8(1):1–11. https://​doi.​org/​10.​1038/​s41598-​018-​27464-4
Hyndman RJ, Athanasopoulos G (2021) Forecasting: principles and practice.
OTexts: Melbourne, Australia. https://​otexts.​com/​fpp3
Hyndman RJ, Kang Y, Montero-Manso P, Talagala T, Wang E, Yang Y, O’Hara-Wild
M (2022) tsfeatures: Time Series Feature Extraction. R package version 1.1.
https://​CRAN.R-​proje​ct.​org/​packa​ge=​tsfea​tures

Papacharalampous et al. Progress in Earth and Planetary Science(2023) 10:46

Hyndman RJ, Khandakar Y (2008) Automatic time series forecasting: theforecast package for R. J Stat Softw 27(3):1–22. https://​doi.​org/​10.​18637/​
jss.​v027.​i03
Iturbide M, Gutiérrez JM, Alves LM, Bedia J, Cerezo-Mota R, Cimadevilla E,
Cofiño AS, Di Luca A, Faria SH, Gorodetskaya IV et al (2020) An updateof IPCC climate reference regions for subcontinental analysis of climate
model data: definition and aggregated datasets. Earth Syst Sci Data
12:2959–2970. https://​doi.​org/​10.​5194/​essd-​12-​2959-​2020
Jehn FU, Bestian K, Breuer L, Kraft P, Houska T (2020) Using hydrological andclimatic catchment clusters to explore drivers of catchment behavior. Hydrol Earth Syst Sci 24(3):1081–1100. https://​doi.​org/​10.​5194/​
hess-​24-​1081-​2020
Jung J, Gibson JD (2006) The interpretation of spectral entropy based uponrate distortion functions. In: 2006 IEEE International Symposium on
Information Theory, Seattle, WA, USA. IEEE, pp 277–281. https://​doi.​org/​
10.​1109/​ISIT.​2006.​261849
Kang Y, Hyndman RJ, Smith-Miles K (2017) Visualising forecasting algorithm
performance using time series instance spaces. Int J Forecast 33(2):345–
358. https://​doi.​org/​10.​1016/j.​ijfor​ecast.​2016.​09.​004
Kang Y, Hyndman RJ, Li F (2020) GRATIS: GeneRAting TIme Series with diverseand controllable characteristics. Stat Anal Data Min ASA Data Sci J
13:354–376. https://​doi.​org/​10.​1002/​sam.​11461
Knoben WJM, Woods RA, Freer JE (2018) A quantitative hydrological climateclassification evaluated with independent streamflow data. Water Resour
Res 54:5088–5109. https://​doi.​org/​10.​1029/​2018W​R0229​13
Köppen W (1936) Das geographische system der klimate. In: Köppen W, Geiger
R (eds) Handbuch der Klimatologie Part C, vol 1. Verlag von Gebrüder
Borntraeger, Berlin
Koster RD, Betts AK, Dirmeyer PA, Bierkens M, Bennett KE, Déry SJ, Evans JP, Fu
R, Hernandez F, Leung LR et al (2017) Hydroclimatic variability and predictability: a survey of recent research. Hydrol Earth Syst Sci 21(7):3777–
3798. https://​doi.​org/​10.​5194/​hess-​21-​3777-​2017
Kottek M, Grieser J, Beck C, Rudolf B, Rubel F (2006) World map of the Köppen–
Geiger climate classification updated. Meteorol Z 15(3):259–263. https://​doi.​org/​10.​1127/​0941-​2948/​2006/​0130
Ledvinka O, Lamacova A (2015) Detection of field significant long-term monotonic trends in spring yields. Stoch Env Res Risk Assess 29(5):1463–1484.
https://​doi.​org/​10.​1007/​s00477-​014-​0969-1
Liaw A (2018) randomForest: Breiman and Cutler’s Random Forests for Classification and Regression. R package version 4.6–14. https://​CRAN.R-​proje​
ct.​org/​packa​ge=​rando​mFore​st
Ljungqvist FC, Krusic PJ, Sundqvist HS, Zorita E, Brattström G, Frank D (2016)
Northern Hemisphere hydroclimate variability over the past twelve centuries. Nature 532(7597):94–98. https://​doi.​org/​10.​1038/​natur​e17418
Markonis Y, Moustakis Y, Nasika C, Sychova P, Dimitriadis P, Hanel M, Máca
P, Papalexiou SM (2018) Global estimation of long-term persistence inannual river runoff. Adv Water Resour 113:1–12. https://​doi.​org/​10.​1016/j.​
advwa​tres.​2018.​01.​003
McCurley Pisarello KL, Jawitz JW (2021) Coherence of global hydroclimateclassification systems. Hydrol Earth Syst Sci 25(12):6173–6183. https://​doi.​
org/​10.​5194/​hess-​25-​6173-​2021
Menne MJ, Williams CN, Gleason BE, Rennie JJ, Lawrimore JH (2018) The global
historical climatology network monthly temperature dataset, version 4. J
Clim 31(24):9835–9854. https://​doi.​org/​10.​1175/​JCLI-D-​18-​0094.1
Messager ML, Lehner B, Cockburn C, Lamouroux N, Pella H, Snelder T, Tockner
K, Trautmann T, Watt C, Datry T (2021) Global prevalence of non-perennial
rivers and streams. Nature 594:391–397. https://​doi.​org/​10.​1038/​
s41586-​021-​03565-5
Montanari A (2012) Hydrology of the Po River: looking for changing patterns
in river discharge. Hydrol Earth Syst Sci 16:3739–3747. https://​doi.​org/​10.​
5194/​hess-​16-​3739-​2012
Montanari A, Young G, Savenije HHG, Hughes D, Wagener T, Ren LL, Koutsoyiannis D, Cudennec C, Toth E, Grimaldi S et al (2013) “Panta Rhei—Everything Flows”: change in hydrology and society—The IAHS Scientific
Decade 2013–2022. Hydrol Sci J 58(6):1256–1275. https://​doi.​org/​10.​
1080/​02626​667.​2013.​809088
Netzel P, Stepinski T (2016) On using a clustering approach for global
climate classification. J Clim 29(9):3387–3401. https://​doi.​org/​10.​1175/​
JCLI-D-​15-​0640.1

Page 20 of 20

Nigam S, Ruiz-Barradas A (2006) Seasonal hydroclimate variability over North
America in global and regional reanalyses and AMIP simulations: varied
representation. J Clim 19(5):815–837. https://​doi.​org/​10.​1175/​JCLI3​635.1
PAGES Hydro2k Consortium (2017) Comparing proxy and model estimatesof hydroclimate variability and change over the Common Era. Clim Past
13(12):1851–1900. https://​doi.​org/​10.​5194/​cp-​13-​1851-​2017
Papacharalampous GA, Tyralis H, Papalexiou SM, Langousis A, Khatami S, Volpi
E, Grimaldi S (2021) Global-scale massive feature extraction from monthlyhydroclimatic time series: statistical characterizations, spatial patterns andhydrological similarity. Sci Total Environ 767:144612. https://​doi.​org/​10.​1016/j.​scito​tenv.​2020.​144612
Papacharalampous GA, Tyralis H, Pechlivanidis I, Grimaldi S, Volpi E (2022)
Massive feature extraction for explaining and foretelling hydroclimatictime series forecastability at the global scale. Geosci Front 13(3):101349.
https://​doi.​org/​10.​1016/j.​gsf.​2022.​101349
Peel MC, Finlayson BL, McMahon TA (2007) Updated world map of the Köppen–Geiger climate classification. Hydrol Earth Syst Sci 11(5):1633–1644.
https://​doi.​org/​10.​5194/​hess-​11-​1633-​2007
Peterson TC, Vose RS (1997) An overview of the Global Historical Climatology
Network Temperature database. Bull Am Meteor Soc 78(12):2837–2850.
https://​doi.​org/​10.​1175/​1520-​0477(1997)​078%​3c2837:​AOOTGH%​3e2.0.​
CO;2Roscher R, Bohn B, Duarte MF, Garcke J (2020) Explainable machine learningfor scientific insights and discoveries. IEEE Access 8:42200–42216. https://​doi.​org/​10.​1109/​ACCESS.​2020.​29761​99
Slater L, Villarini G, Archfield S, Faulkner D, Lamb R, Khouakhi A, Yin J (2021)
Global changes in 20-year, 50-year, and 100-year river floods. Geophys
Res Lett 48:e2020GL091824. https://​doi.​org/​10.​1029/​2020G​L0918​24
Thomas N, Nigam S (2018) Twentieth-century climate change over Africa:seasonal hydroclimate trends and Sahara desert expansion. J Clim
31(9):3349–3370. https://​doi.​org/​10.​1175/​JCLI-D-​17-​0187.1
Thornthwaite CW (1943) Problems in the classification of climates. Am Geogr
Soc 33(2):233–255. https://​doi.​org/​10.​2307/​209776
Thornthwaite CW (1948) An approach toward a rational classification ofclimate. Geogr Rev 38(1):55–94. https://​doi.​org/​10.​2307/​210739
Trewartha GT, Horn LH (1980) An introduction to climate. McGraw-Hill, NewYork
Tyralis H, Koutsoyiannis D (2011) Simultaneous estimation of the parametersof the Hurst–Kolmogorov stochastic process. Stoch Env Res Risk Assess25(1):21–33. https://​doi.​org/​10.​1007/​s00477-​010-​0408-x
Tyralis H, Dimitriadis P, Koutsoyiannis D, O’Connell PE, Tzouka K, Iliopoulou T(2018) On the long-range dependence properties of annual precipitation
using a global network of instrumental measurements. Adv Water Resour
111:301–318. https://​doi.​org/​10.​1016/j.​advwa​tres.​2017.​11.​010
Tyralis H, Papacharalampous GA, Langousis A (2019) A brief review of random
forests for water scientists and practitioners and their recent history inwater resources. Water 11(5):910. https://​doi.​org/​10.​3390/​w1105​0910
Wei WWS (2006) Time series analysis, univariate and multivariate methods, 2ndedn. Pearson Addison Wesley

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.