As a result of technological advances in monitoring atmosphere, hydrosphere, cryosphere and biosphere, as well as in data management and processing, several databases have become freely available. These can be exploited in revisiting the global hydrological cycle with the aim, on the one hand, to better quantify it and, on the other hand, to test the established climatological hypotheses according to which the hydrological cycle should be intensifying because of global warming. By processing the information from gridded ground observations, satellite data and reanalyses, it turns out that the established hypotheses are not confirmed. Instead of monotonic trends, there appear fluctuations from intensification to deintensification, and vice versa, with deintensification prevailing in the 21st century. The water balance on land and in the sea appears to be lower than the standard figures of literature, but with greater variability on climatic timescales, which is in accordance with Hurst–Kolmogorov stochastic dynamics. The most obvious anthropogenic signal in the hydrological cycle appears to be the over-exploitation of groundwater, which has a visible effect on the rise in sea level. Melting of glaciers has an equal effect, but in this case it is not known which part is anthropogenic, as studies on polar regions attribute mass loss mostly to ice dynamics.
If the dark side of concerns about Earth's climate is
The availability of different types of data allows revisiting the global
hydrological cycle and improving its quantified knowledge. It can also
be useful in testing the climatological hypotheses that are relevant to
hydrology. Among them, most crucial is the conjecture that, in a warming climate,
atmospheric moisture is changing in a manner in which the relative humidity
remains constant but specific humidity increases, according to the
Clausius–Clapeyron relationship. As a result, the established view is that
the global atmospheric water vapour should increase by about 6 %–7 %
Hence, the purpose of this study is to revisit the hydrological cycle in an
era of climate change concerns and rich data availability, with an emphasis
on the following points:
providing an overview of and retrieving a great number of global hydroclimatic data sets;
improving the quantification of the global hydrological cycle, its
variability and its uncertainties through the surge of newly available data
sets; testing established climatological hypotheses according to which the
hydrological cycle should be intensifying because of global warming; outlining a stochastic view of hydroclimate which provides reliable means to
deal with its variability.
These points are reflected in the structure of the paper in the following
manner. The material related to point 1 is detailed in Sect. 2. Sections 3–5 are aligned according to point 2, namely the quantification of the global
hydrological cycle. On the other hand, point 3 elevates the significance of
atmospheric water and, thus, Sect. 3 is devoted to this topic. Precipitation and
evaporation are the key components of the hydrological cycle, as their imbalance
in the land part of Earth drives all other hydrological processes.
Quantification and changes in these drivers are examined in Sect. 4. Based
on the results in Sect. 4, the water balance per se is studied in Sect. 5. Moreover, to quantify storage changes within water balance, and in
particular the groundwater and cryosphere storage changes, Sect. 5
includes an extended review of related literature.
Point 3 is dealt with, together with point 2, in Sects. 3 and 4, which is devoted to the atmospheric water, precipitation and evaporation, and in two Appendices, which provide additional information on testing established climatological hypotheses. Point 4 is contained in Sect. 6, in which the scope is the future hydroclimatic variability. The necessity of proposing a stochastic approach to hydroclimate becomes obvious after examining whether climate models (and other more empirical techniques commonly used) are consistent with the reality (tracked in the earlier sections) and skilful, so as to be usable for future hydrological projections. It turns out that the state of affairs with current common methodologies is not satisfactory, and hence the need for an alternative approach emerges. This has to be stochastic and consistent with observed natural behaviours, as outlined in Sect. 6. Finally, Sect. 7 concludes the study with relevant remarks.
This study tries to use a wide range of available data sets reflecting the real-world hydrological cycle at the global level, either directly (by accessing the data per se) or indirectly (by using processed data and results from other studies). In particular, the information used comprises the following: (a) gridded ground observations, (b) satellite data and (c) reanalysis data. Gridded ground observations are available for precipitation over land. Gridded satellite data exist for several variables of hydrologic importance, including air temperature, water vapour amount, cloud water amount, precipitation and snow cover, as detailed in the next subsections. Information from reanalyses is far richer, as this provides a numerical description of the weather system, in terms of a great deal of atmospheric variables, by combining numerical weather prediction models with observations. Here we use the Reanalysis 1 by the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR), collectively NCEP–NCAR, and the ERA5 reanalysis, which are publicly available.
The temporal coverage of the NCEP–NCAR Reanalysis 1 (Kalnay et al., 1996) includes data collected four times daily to provide daily and monthly values from 1948 to the present at a horizontal
resolution of 1.88
The ERA5 (Copernicus Climate Change Service, 2017) is the fifth-generation atmospheric reanalysis of the European Centre for Medium-Range Weather Forecasts (ECMWF), where the name ERA refers to ECMWF reanalysis. It spans the modern observational period, from 1979 onwards, with daily updates continuing forward in time, and fields available at a horizontal resolution of 31 km on 139 levels from the surface up to 0.01 hPa (around 80 km). It has been produced as an operational service, and its fields compare well with the ECMWF operational analyses (Hersbach and Dee, 2016).
We did not use the longer-term reanalyses that appeared recently to serve climate change studies, as these have lower reliability. Specifically, the ERA-20C reanalysis, which covers the period 1900–2010, compares poorly even to the ERA5 reanalysis, developed by the same institution (ECMWF), while the 20th century reanalysis V3 (20CR V3 by the National Oceanic and Atmospheric Association (NOAA), the Cooperative Institute for Research in Environmental Sciences (CIRES) and the Department of Energy (DOE), collectively NOAA–CIRES–DOE), which covers the period 1836–2015 has, in addition, huge departures of the precipitation from the evaporation quantities over the globe, with the global imbalance being more than half of the precipitation over land or almost twice the runoff. Therefore, here they are judged as not hydrologically useful.
In addition, this study uses results from several other studies which are based on different data sets, such as the Gravity Recovery and Climate Experiment (GRACE; Syed et al., 2009; Eicker et al., 2016; Schellekens et al., 2017); NASA's Global Land Data Assimilation System (GLDAS; Zhou et al., 2019); and hydrological models such as the global gridded monthly reconstruction of runoff (GRUN; 1902–2014; Ghiggi et al., 2019) or the PCRaster Global Water Balance (PCR-GLOBWB; Wada et al., 2010). Archfield et al. (2015) provide additional links to other useful data sources.
In the next subsections we describe each data set used, while in Table 1 we
summarize all the details and provide all necessary links to the retrieved
information so that the reader can easily reproduce the results of this
study. In general, we use actual values of time series, disfavouring the
popular notion of “anomalies”, i.e. for differences from a certain
mean
List and details of variables and data sets used in the study (unless otherwise stated in a particular entry, all data were last accessed in February 2020).
Continued.
The satellite temperature data set, developed at the University of Alabama in
Huntsville (UAH), infers the temperature,
For the more recent years, monthly land surface temperature and emissivity
are also available from the Moderate Resolution Imaging Spectroradiometer
(MODIS), a key instrument aboard two satellites, namely the Terra (originally known
as EOS AM-1) and the Aqua (originally known as EOS PM-1), providing
observations since 2000 and 2002, respectively. The MOD11C3 Version 6
product provides temperature values on a 0.05
The NCEP–NCAR and ERA5 reanalyses provide more detailed information for
For the same levels, data for relative humidity,
As already mentioned, the relative humidity, The adjective “precipitable” for the water vapour amount is a misnomer; if the
total water vapour amount in the atmosphere was indeed to precipitate in its
entirety, this would violate the laws of thermodynamics.
In addition,
Gridded ground data for precipitation rate,
Another gridded precipitation data set, this time also extending over the
sea, is the data set of the Global Precipitation Climatology Project (GPCP),
which combines gauge and satellite precipitation data over a global grid.
The general approach is to combine the precipitation information available
from each of several satellites and in situ sources into a final merged
product, taking advantage of the strengths of each data type. Passive
microwave estimates are based on Special Sensor Microwave Imager/Special
Sensor Microwave Imager Sounder (SSMI–SSMIS) data; infrared precipitation
estimates are included using Geostationary Operational Environmental
Satellite (GOES) data and Polar-orbiting Operational Environmental Satellite
(POES) data and other low Earth-orbit data and in situ observations
(Adler et al., 2016). Monthly data are provided on a 2.5
The NCEP–NCAR and ERA5 reanalyses also provide gridded daily and monthly precipitation data.
Information about snow is provided by satellite data. The most complete data
set of this type is the snow cover extent for the Northern Hemisphere (NH),
monitored via satellites by the US National Oceanic and Atmospheric
Administration (NOAA) from 1966 to the present, updated monthly. Data prior to
June 1999 are based on satellite-derived maps of the NH snow cover extent
produced weekly by trained NOAA meteorologists; after that date, they have
been produced by daily output from the Interactive Multisensor Snow and Ice
Mapping System (IMS). The data are provided on a Cartesian grid with
At present, the evaporation rate,
There are lots of software applications to analyse and process gridded data. Here we are using free web platforms that are easy to use and allow direct reproducibility of the results by the interested reader; the links to these platforms are given in Table 1.
Most of the processing in this study has been made via the Climate Explorer
(Climexp) system of the Royal Netherlands Meteorological Institute
(Koninklijk Nederlands Meteorologisch Instituut – KNMI). This very powerful
system combines access to many sources of data, including most of the data
sets used here, but also data from individual stations and multiple
processing options. The data access includes, among other options, daily
fields of observations and reanalyses, monthly observations and monthly
reanalysis fields. The processing options include averaging over
geographical areas (including prespecified or user-defined “masks”,
i.e. polygons defined by a set of connected (
NASA's Giovanni online web environment is another useful tool for the access, display and analysis of NASA's geophysical data (Acker and Leptoukh, 2007). A similar system for NOAA's data, which also incorporates data for fields of additional sources, is the Web-based Reanalyses Intercomparison Tools (WRITs; Earth System Research Laboratory's Physical Sciences Division; see Smith et al., 2014).
Access to some of the data which are not contained in the above three systems is provided by other platforms, as specified in Table 1.
For the study of atmospheric water, air temperature is an important variable and thus we start with this. Figure 1a shows the evolution of global average temperature at the level of 2 m above ground at the monthly and annual scale, according to both reanalyses data, NCEP–NCAR and ERA5. In addition, Fig. 1b depicts satellite data in comparison to reanalysis ones but at a higher altitude. Specifically, the UAH satellite time series is used, which refers to the lower troposphere. Comparing this to reanalysis data at several pressure levels, we found that it roughly corresponds to the weighted averages of those at the levels of 500 and 700 hPa, with weights of 0.62 and 0.38, respectively. Figure 1 shows a good agreement of all three information sources at both pressure levels. At the same time, they show a gradual increase in temperature, with about the same rate of increase. All three sources provide complete information for the last 40 years, while one of them, NCEP–NCAR, has a longer span, namely 68 years.
Variation of the global average temperature
If we split the common 40-year period into two parts, we may compare the
climatic values on a 20-year climatic scale and calculate the temperature
increase. This is done in Table 2, where an increase of 0.38
Average air temperature (
In addition, Table 2 provides similar information for the land and sea parts of the Earth, in terms of average temperatures and dew points. The dew point, defined as the temperature at which the air must be cooled to become saturated with water vapour, is a more useful variable than temperature for the study of atmospheric water. The time evolution of both variables on Earth, land and sea, can be seen in Fig. 2. All these are based on ERA5 reanalysis information, as this is the only one readily provided for further processing through the Climexp platform, both for temperature and dew point at the surface level. As a means of verification, the MODIS surface temperature over land is also plotted in Fig. 2, which compares well (albeit with a little bias) with the ERA5 temperature over land. It can be seen in Fig. 2 and Table 2 that the evolution of the dew point is also increasing in the recent period, but the increase is lower than that of temperature.
A practical way to express what the increasing rates represent can be
obtained by calculating an offset distance on Earth, which, moving poleward
in the temperate zone, would offset the average decadal increase in
temperature or dew point. This is given in the last column of Table 2 and is
31 km per decade for the surface global temperature and 21 km per decade for
the lower troposphere temperature and the surface dew point. This conversion
was based on the zonal temperature and dew point profiles shown in Fig. 2b; for the temperate zone (
It is quite interesting to assess the zonal variation of the increase in temperature and dew point. This information is provided by Fig. 3 where we plot the difference of the Earth temperature and dew point (according to the ERA5 reanalysis) from their averages in the period 1980–1999. A positive difference corresponds to an increase after 1999. It is important to note that the greater increases are located in the northern polar area. In the tropical zone, which is hydrologically most important as the main source of evaporated water, the increase in temperature is half the global average, while there is no increase at all in the dew point. The latter point is of the highest hydrological significance.
Zonal distribution of the difference of the Earth temperature and dew point from their averages in the period 1980–1999. Source of the data set is ERA5 reanalysis, as detailed in Table 1. The data for the plot were constructed via Climexp by first computing “anomalies” for the period 1980–1999, then by computing zonal mean and finally by applying the option to “Compute mean, standard deviation, or extremes” and specifying “averaging over 12 months”. Note that the graph represents averages for the entire period of over 40 years, rather than differences between two periods (the latter are about twice the former).
The transition from a temperature-based description of atmospheric processes
to a more hydrologically meaningful one is provided by the
Clausius–Clapeyron equation, i.e. the law determining the equilibrium of the liquid and gaseous phase of water, which maps temperatures to saturation
vapour pressures. Koutsoyiannis (2014b) has highlighted the probabilistic
nature of the law by deriving it purely by maximizing probabilistic entropy,
i.e. uncertainty. In particular, the law was derived by studying a single
molecule and maximizing the combined uncertainty of its state related to the following:
its phase (whether gaseous, denoted as A, or liquid, denoted as B); its position in space; and its kinetic state, i.e. its velocity and other coordinates corresponding to
its degrees of freedom and making up its thermal energy.
Denoting the saturation vapour pressure as
This form is both convenient and accurate (more accurate than other customary forms, theoretical or empirical, as illustrated in Koutsoyiannis, 2012).
A state in which the actual vapour pressure
Average vapour pressures,
Variation of the saturation water vapour pressure
Variation of specific humidity at the levels of
It is important to note that all the above quantities and derivations do not
depend on the presence of other atmospheric gases and, hence, on the
air pressure
Specific humidity at 850 hPa (
To connect specific humidity to pressures, we use the law of ideal gases,
which can again be derived by maximizing probabilistic entropy
(Koutsoyiannis, 2014b) and takes the following form:
It has been a common assumption, based on the Clausius–Clapeyron
relationship, that the global atmospheric water vapour should increase by
about 6 %–7 %
It is then easy to verify that for a certain atmospheric level (
Under the assumption that
However, despite the conjecture d
By combining the time series of relative humidity with those of temperature
(entries 3 and 4 in Table 1) and using Eqs. (3) and (4), we constructed
in Fig. 6 the vertical profile of the difference of average water vapour
pressure
Vertical profile of the difference between two climatic periods of
average water vapour pressure
We may try to roughly approximate Eq. (9) by the following:
By integrating the specific humidity over a vertical column of air from a
low altitude
The study of the temporal variation of
Water vapour amount (
Variation of water vapour amount. Thin and thick lines of the same colour represent monthly values and running annual averages (right aligned), respectively. Sources of the data are indicated in the legend and detailed in Table 1. The plotted values for MODIS represent the averages from the Terra and Aqua platforms.
For completeness of the discussion about atmospheric water, Fig. 9 depicts the variation of the cloud water amount in ice and liquid phase according to MODIS satellite data. Again, no monotonic trend is seen. Compared to the water vapour amount (Fig. 8), the cloud water is a very small quantity (2 orders of magnitude smaller).
Variation of water vapour amount, as in Fig. 7, but only for the
MODIS data set and separately for the Terra and Aqua platforms:
Variation of cloud water amount (in ice and the liquid phase). Thin and thick lines of the same colour represent monthly values and running annual averages (right aligned), respectively. Sources of the data are indicated in the legend and detailed in Table 1.
While the analysis of atmospheric water in the previous section signifies
It is virtually certain that, in the long term, global precipitation will increase with increased GMST [global mean surface temperature]. Global mean precipitation will increase at a rate per
Indeed, Fig. 10, which depicts the evolution of the precipitation rate on Earth and its land and sea parts, based on gauged, satellite and reanalysis information, suggests that precipitation fluctuates through the seasons and also through the years but without a monotonic trend. The marked differences among the various sources of information are also indicative of substantial uncertainty in the estimation of precipitation.
Variation of
The snow part of precipitation is also interesting to examine, as snow is more directly related to temperature. Figure 11 depicts the evolution of the snow cover in the Northern Hemisphere. Despite temperature increases, no noticeable change appears on an annual basis. However, there are perceptible changes in the seasonal variation, namely in the most recent period where the snow cover has decreased during the summer months and increased during the autumn and winter months.
As already mentioned, the evaporation rate is difficult to estimate and even more difficult to measure. The available gridded data come from reanalyses. Their plots in Fig. 10 again show fluctuations through the seasons and through the years and there are no monotonic trends.
Overall, the preceding data and analyses, particularly those of atmospheric water, can hardly support the intensification of the global hydrological cycle. Certainly, they reveal changes but the changes appear as multi-year fluctuations and not as consistent trends. These fluctuations do not correspond to popular hypotheses attributing changes to global warming. The above results are not exceptionally new. Indeed, Sun et al. (2012) reported a near-zero temporal trend in global mean precipitation for the period 1940–2009. Nonetheless, our results are dissimilar (or opposite) to the vast majority of studies reporting intensification. The reasons for the dissimilarities are explained in Appendix A. Additional analyses, which show the absence of intensification and, more recently, deintensification, in terms of precipitation extremes, are given in Appendix B.
The reasons for the failure of the popular hypothesis of intensification
include these two: (a) the unsupported (and eventually falsified) conjecture
that the relative humidity should be constant, and (b) the oversimplification
of the representation of natural process, which neglects or underrates
important mechanisms that affect the atmospheric water more than those
related to the greenhouse effect. Among these, mostly unpredictable or
unaccounted for, mechanisms are the following: (a) the tropospheric aerosols (Wu et al.,
2013) affecting radiation while enabling the condensation of water vapour and
formation of cloud droplets; (b) the vapour buoyancy feedback, which
stabilizes the tropical climate by increasing the outgoing longwave radiation
(Seidel and Yang, 2020) Perhaps this could explain the zonal
distribution of the difference in the Earth temperature and dew point shown
in Fig. 3, but this needs a great deal of
additional work to investigate.
The analyses of atmospheric water, and those of precipitation and evaporation, reveal the following two important points: (a) all processes fluctuate in time at all timescales, and (b) no monotonic trends that would be attributed to temperature increase appear in any type of data. In some cases (e.g. satellite observations of water vapour amount) there appear to be some trends, which, however, are opposite to established expectations. Here we treat them as irregular fluctuations, which appear as monotonic trends because of the limited time window of the observation. Consequently, in subsequent analyses we make all estimations on the basis of stationarity. It must be stressed that stationarity does not mean the absence of change. It simply means that the change, however large, resists a deterministic description, and hence a stochastic description becomes more appropriate and powerful (Montanari and Koutsoyiannis, 2014; Koutsoyiannis and Montanari, 2015). Additional information on this choice is provided in Sect. 6.2 and 6.3.
A rather impressive result, shown in Fig. 10, is that the
precipitation and evaporation over the entire Earth in the NCEP–NCAR
reanalysis agree very well with each other, indicating the conservation of mass, a
property that is not granted in reanalyses. Indeed, on the annual timescale,
the differences between the global precipitation and evaporation are small,
ranging between
Global water balance derived from the difference of precipitation
and evaporation at land and sea from
Before proceeding to water balance estimation, we stress the importance of that balance in quantifying the availability of water resources. Contrary to most other common goods (e.g. fossil fuels and metals) that are subject to depletion, water resources are renewable, not reserves. In this respect, hydrology should fight the common misrepresentation (or even misconception in reports from media and information provided to the wider public and decision makers) implied by the popular use of graphs such as Fig. 13. It is not the purpose of this study to examine or question the correctness of the information in the graph, which shows where on Earth water is stored. However, the graph gives wrong impressions or messages. As an example, it suggests that the vast majority of liquid freshwater on Earth is groundwater, while river water is almost negligible. However, considering the renewable character of water resources, the truth is just the opposite; the vast majority is river water, while groundwater is almost negligible, as will be detailed below. For that reason, a caution stamp is added to Fig. 13.
Typical depiction of water on Earth (source of the background image without the stamp: USGS;
We now proceed to calculations, noting that their precision will be of the
order of 100 km
Proposed quantification of water balance.
Changes in land and seawater storage are small but not negligible. With
reference to Fig. 13, the land storage can be decomposed into five
compartments, namely ice,
For the ice loss, Syed et al. (2009), on the basis of the average of two
earlier studies, estimated a quantity of Some of the reviewed studies provide estimates in
terms of volume (km
For the snow storage, the snow data analysed in Sect. 4 allow the
assumption of a zero mean change at the annual and overyear scales, even
though at seasonal scales it is certainly not negligible (see Fig. 11).
For the water in the biosphere, there must be a positive change as in the
21st century the Earth has been greening, mostly due to
Surface water storage has been affected by the substantial depletion of several
large natural water bodies in the past, mostly due to overexploitation of
their water, while at the same time it was enhanced by the construction of
artificial reservoirs. The Caspian Sea changes, often associated with the sea
level changes, are large but alternating in sign, i.e. positive or negative (Chen et al., 2017), and
thus there is no reason to assume a balance value other than zero. The Aral
Sea has dramatically shrunk in volume since 1950 (Gaybullaev et al., 2012;
Cretaux et al., 2019) and has thus contributed to a negative water balance
in the land (and positive in the sea, corresponding to the rise in sea level), but its
stabilization is a likely possibility for the present and future. Reservoir
impoundment has also affected the water balance after the construction of
reservoirs (Chao et al., 2008). However, given that the number of new
reservoirs has diminished after 2000, while a reservoir has zero
further effect on the long-term water balance after its first fill, we do
not expect further substantial effects. Chao et al. (2008), in their
estimates, include a seepage effect into the future, which they base on
arbitrary assumptions, among which is the continuation of a seepage loss
into the future at a rate inversely proportional to the square root of time.
Noting that this assumption would lead to losses that diverge to infinity as
time increases, while the water from the loss (as that of reservoir
withdrawal) remains in the land water storage, here we disregard this
assumption.
For the groundwater storage change, which we expect to be significant, Wada
et al. (2010) have estimated a global depletion rate of
In summary, we have assumed the following:
Accordingly, the water storage in land has a total loss of 600 km
The submarine groundwater discharge (or groundwater outflow to the sea) is
the most difficult to estimate. A most recent estimation has been conducted
by Zhou et al. (2019) using a water budget approach at high resolution. They
examined the near-global coastal recharge areas (60
This choice needs some further explanation, as it is substantially (by 4–5
times) lower than the commonly adopted earlier estimates, such as those by
Shiklomanov and Sokolov (1985) and Zekster and Loaiciga (1993; citing
Zektser and Dzhamalov, 1981), which are 2200 and 2400 km
An even earlier, yet frequently cited, estimate by Lvovitch (1970), is
somewhat lower, namely 1600 km
These old guesses, rather than estimates, have been adopted (by citing the
above studies) in most papers and textbooks until now, either in its
percentage version (e.g. 5 % in Dai and Trenberth, 2002, who cite
Lvovitch, 1970) or in absolute values, mostly adopting Shiklomanov and
Sokolov's (1985) values of 2200 and 46 800 km
Values even higher than those have also been published; for example, in
a celebrated paper, Oki and Kanae (2006) assert the following: some part of the water, approximately 10 % of total river discharge (Church, 1996), infiltrates to deep underground and will never appear as surface water but discharge into the ocean directly from groundwater.
The only case of a low estimate, of the order of that used here, is in
Nace's (1970) paper, which appears to be the first quantitative
analysis in history of the groundwater discharge to the sea. Surprisingly, only 3 years after his 5 % arbitrary set guess, Nace (1970) came up with the quantitative
estimate of 7000 m The average total runout [i.e. submarine groundwater discharge] then would be about 7000 m
The fact is that the estimate of 220 km Integrated over the near-global coastline, the total annual volume of fresh SGD [submarine groundwater discharge] is 489 km
The above detailed review and discussion was about small quantities in water
balance. Fortunately, the big quantities, namely precipitation and evaporation over the
land and sea, are estimated more accurately (on a percentage basis), and the
NCEP–NCAR reanalysis provides a good basis for estimation. As already
stated, the error in satisfying Eq. (14) is
To proceed, we assume that the precipitation values are more reliable, as
they are cross-checked with satellite data, and we adjust the evaporation
data so as to precisely satisfy Eq. (14). A sensitivity analysis of the
effect of allocating the error in the resulting water balance is shown in
Table 6. If we allocate the entire error to sea evaporation, the resulting
mean runoff is 30 800 km
Sensitivity analysis of water balance calculations.
If we apply Eq. (19) and drop the expectations, i.e. use the time-varying values, what we will get is not the actual runoff and advection because some storage changes not included in the equation, such as in snow, soil water and atmospheric water, are not identically zero; rather, their mean is zero. On the annual basis it may be expected that the error is negligible, but on the monthly scale it will be present. Nonetheless, such an exercise is useful to conduct to see the temporal variability. This is depicted in Fig. 15, where, for rigour in terminology, we have replaced the terms “runoff” and “advection” with “water balance from land” and “water balance from sea”, respectively. Figure 15b depicts the mean monthly averages, which differ remarkably. The differences are related to the within-year storages not included in the equation and look quite reasonable. As the Northern Hemisphere dominates in land processes, it is reasonable to expect that in the period December–May the storage is increasing, while during July–October it is decreasing.
Compared to the popular estimates by Shiklomanov and Sokolov (1985) and
Zektser and Dzhamalov (1981), which, as already noted, are 46 800 and 38 000 km
Figure 16 provides a comparison of runoff time series (or balances in the land and sea) from the present study with earlier studies. The differences in estimates are apparent and translate to a huge uncertainty about the true value of runoff. What is also apparent is a satisfactory agreement between the present study and that of Syed et al. (2009). Some of the studies provide ensemble values, but in Fig. 16 only the ensemble means are plotted (the upper limits of the ensembles would exceed the plotting area). In view of the high uncertainty, it seems not meaningful to search for trends in runoff. We may notice, though, that in the time series of the present study, there appear higher values in recent years. These values correspond to increased rainfall in NCEP–NCAR reanalysis over land. This, however, is not confirmed by the gauge and satellite observations (Fig. 10), which, as already discussed, indicate falling trends. Therefore, the changes will be interpreted as irregular fluctuations within a frame of very high uncertainty rather than monotonic trends which clearly are not.
Comparison of the results of the current study for surface runoff
with those of
The latter interpretation is consistent with the results of a large-scale
study of trends in the flow of 916 of the world's largest rivers by Su et al. (2018). The results, and specifically those in their Table 1 that take into
account the long-term persistence, show some trends that are either positive
(3.7 % of the rivers) or negative (8.2 % of the rivers). While negative
trends are more frequent than positive, they have slightly lower
slopes, so that, overall, the positive slopes slightly surpass the negative
ones in magnitude (9.1 vs.
According to Fig. 14, the total evaporation on Earth (precisely equal to
the total precipitation according to Eq. 14) is 522 700 km
Compared to the human energy production, which in the past decade was about
170 000 TWh yr
While most climate impact studies have been based on the assumption that climate models provide plausible predictions (usually termed “projections”) of future hydroclimate, there are a number of studies that claimed that this cannot be true as, when compared with real data of the recent past (after the predictions were cast) or even earlier data (already known at the time of casting the prediction), they prove to be irrelevant with reality (Koutsoyiannis et al., 2008, 2011; Anagnostopoulos et al., 2010). This becomes even worse if we focus on extremes (Tsaknias et al., 2016). Tyralis and Koutsoyiannis (2017) developed a theoretically consistent (Bayesian) methodology to incorporate climate model information within a stochastic framework to improve predictions. However, because of the bad performance of the climate models, application of this methodology leads to increased uncertainty or, in the best case, to results that are indifferent with respect to the case where the climate model information is not used at all. In summary, as implied by Kundzewicz and Stakhiv (2010), climate models may be less “ready for prime time” and more ready for “further research”.
To test if this is also the case on a global setting, here we use climate
model outputs for monthly precipitation simulations for scenario runs for
the period 1860–2100, from the Coupled Model Intercomparison Project
(CMIP5), a standard experimental protocol for studying the output of coupled
atmosphere–ocean general circulation models (AOGCMs). CMIP5 includes the
models for the IPCC Fifth Assessment Report (
A comparison of model outputs with reality, as the latter is quantified by the satellite (GPCP) observations, is provided in Fig. 17. As expected by the assumptions and speculations mentioned in Sect. 3, climate models predict an increase in precipitation after 1990–2000. This hypothetical increase is visible in Fig. 17. However, real-world data do not confirm the increase. What is also noticeable is the large departure from reality of model outputs in terms of the average global precipitation. All these observations support the claim that climate models dissent from the hydrological reality and they further illustrate the fact that the real-world precipitation has not been intensified according to the IPCC expectations.
Comparison of climate model outputs (for the specification of which, see the text) with reality, as quantified by GPCP satellite observations. “Multimodel” refers to CMIP5 scenario runs and entries, namely CMIP5 mean – RCP8.5. “Single model” refers to the ensemble member 0 of the Community Climate System Model version 4 (CCSM4) – RCP8.5 released by NCAR. Thin and thick lines of the same colour represent monthly values and running annual averages (right aligned), respectively.
The statistical counterpart of the endeavour to predict the future, namely the fitting of trends everywhere, based on real data, and projecting them to the future, has been quite popular among hydrologists in the 21st century, as seen in a surge of related articles. Specifically, this has been quantified by a bibliometric investigation by Iliopoulou and Koutsoyiannis (2020), who show that in the last decade almost 90 % of the scientific articles related to precipitation, hydrology and extremes contain the word “trends”.
The comprehensive study by Iliopoulou and Koutsoyiannis (2020) assessed the
“trends everywhere” approach using long precipitation series (
The failure of climate models and trends to describe reality does not imply
that in reality there is no change. On the contrary, all data sets examined
suggest change, but the simplistic assumption that there is virtually a
single cause (i.e.
Assuming that a real-world process
For small
Now, Fig. 18 shows the climacograms of the different types of processes
examined in this study and the different sources of information. It is
evident that all processes are consistent with the HK dynamics. Seasonality
also has a significant effect in some (but not all) of the processes. In
most of the processes
Climacograms of the indicated processes calculated from the monthly
time series; for some series with prominent seasonality the climacograms
from the annual time series are also plotted with thicker lines of the same colour.
For timescales greater than the annual, all slopes in the double logarithmic
plots are close to
High
For
Arguably, climate has been changing for the entire 4.5-billion-year history of the Earth; this has already been confirmed and roughly quantified for the last 0.5–0.75 billion years in aforementioned studies (Markonis and Koutsoyiannis, 2013; van der Meer et al., 2017). A changing climate can hardly be described by a mean value; variability also needs to be specified. For this specification we certainly need a measure of variation, which could be one of the standard measures (variance, standard deviation or coefficient of variation). But we also need to define how this variability decreases as the timescale increases. A parsimonious way of doing the latter task is through the Hurst parameter, which, based on the data sets used, turns out to be very high, implying that the difference between weather and climate is not as dramatic as the common perception. In this respect, even if the established climatic hypotheses of an intensifying hydrological cycle, with rates of the order of 1 %, were validated, hydroclimatic concerns would not be justified. In older times such rates of change would not be discussed at all, as the logical framework about precision was already formed in ancient times (see the motto in the beginning of the article).
In fact, the established climatic hypotheses on the hydrological cycle are not validated by the data analysed. Relative humidity is decreasing in the entire atmosphere instead of being constant. Specific humidity is increasing at a rate of about one-third of that implied by established hypotheses, which results from comparing two recent periods of the climatic timescale. When integrated over the entire troposphere and viewed in continuous time, the water vapour amount is fluctuating without a monotonic trend, while there are differences even in the sign of local trends for different data sets. Precipitation and evaporation again fluctuate. The precipitation extremes and their frequencies also fluctuate (Appendix B). Fluctuations are successions of intensification and deintensification, with deintensification prevailing in the 21st century.
The water balance on the land and sea appears to be lower than the standard
figures of literature. The total evaporation on Earth, precisely equal to
the total precipitation, is estimated at 522 700 km
The above observations strengthen an earlier (Koutsoyiannis et al., 2009) envisagement of the hydrological community's role. Instead of a passive role in assessing hypothetical hydrological impacts based on doubtful climate model outputs, an active role consistent with its history is possible. Indeed, hydrology has much more to offer to societies than prophesies of future catastrophes (cf. Koutsoyiannis, 2020a). During the 20th century, and particularly after the Second World War, hydrology, by supporting hydrotechnology, water management and risk assessment and reduction, within a strong international collaboration and a strong economy, has substantially contributed to human life as a value and to the quality and length of human life (Appendix B; Fig. B5).
We clarify that here, to detect possible intensification in the hydrological
cycle, we use past information on the global scale. This is similar to the
common practice of detecting global warming, where the temporal evolution of
an observed, globally averaged, temperature is typically used. While the
globally averaged temperature is a statistical quantity with doubtful
physical meaning, the globally (or regionally) averaged precipitation and
evaporation are physically meaningful as they represent fluxes of water mass
or volume. Therefore, it may be puzzling as to why the same method used in
temperature has not been applied to precipitation, yet intensification
claims have been the norm. This methodology of testing the alleged
intensification of the hydrological cycle distinguishes this study from the
plethora of other studies claiming intensification. More specifically, the
differences in the current study with other studies include the following
points.
We do not refer to model projections for the future which predict
intensification (like e.g. Ziegler et al., 2003; Madakumbura et al., 2019).
And, indeed, as evident in Fig. 17, if we used the climate model
simulations and not the actual data, we would “detect” intensification
even for the past years, let alone the future in which the model-projected
increase in rainfall is higher. There are plenty of reasons why one should
avoid that, with these reasons referring both to the past and the future. In general
epistemological terms, according to Bridgman (1966), when a statement
purports to be about the future, it is a pseudo-statement. In more
technical terms, it has been shown that the skill of climate models for
representing hydrological processes (in particular, precipitation), measured
by studying the past performance, is practically zero (Koutsoyiannis, 2008,
2011; Anagnostopoulos et al., 2010; Tsaknias et al., 2016). This situation
is epitomized in the title of the article by Stephens et al. (2010), as being a
“dreary state of precipitation in global models”. We investigate the entire period that each data set allows in order to see
the patterns of changes, i.e. whether there are monotonic trends or
fluctuations. If one focuses on a short period (like in the study of Wild et
al., 2008, which is for 15 years), it is likely that one would obtain a monotonic trend
(even though in Fig. 1 of Wild et al., 2008, consistent increasing appears
for 8 years, and not for the entire 15-year period they examine). We do not refer to specific regions like Canada (Déry et al., 2009;
Creed et al., 2015), the Amazon (Gloor et al., 2013), etc. Certainly, there are
regions where precipitation is currently intensifying, while in earlier
periods in those regions, or in other regions at the same period, are
deintensifying. Even the cited studies speak about trend reversals in
time or give alternating trend signs in different locations. Such temporal
and spatial fluctuations, rather than monotonic trends, are normal
behaviour in natural processes (see Sect. 6.3). Furthermore, we do not
focus on specific seasons of the year. There is no doubt that in certain
areas and in specific seasons one would find intensification or
deintensification. However, as the spatial scale and observation period
increase, the risk of a false claim of intensification decreases. For
example, in their recent study based on 1427 stations across China over the
last 60 years, Wang and Sun (2020) concluded that there is no significant
difference in the annual precipitation between the past 20 years
(1999–2018) and the past 60 years (1959–2018) and suggest utilizing the
historical data of annual precipitation as the basis for water-resources
application. We use a simple and easily reproducible methodology and provide all the
information for the reproducibility of the results. The quantities we use are
observable or estimated quantities, as given in the original data sets,
without making any post-processing or transformation (e.g.
probability-based indices based on fitted distributions or regression on
“signals”, like in Paik et al., 2020), which could involve subjective
choices. We follow Aristotle's advice (to “look for precision in each class of
things just so far as the nature of the subject admits”; see the motto at
the beginning). For example, an alleged 2 % total increase in the
precipitation over land during the entire 20th century (Huntington,
2006, and references therein) is far beyond the precision of estimating
precipitation over land.
Variation of the monthly maximum daily precipitation areally averaged over the continents. Thin and thick lines of the same colour represent monthly values and running annual averages (right aligned), respectively. Dashed lines are for reanalyses and continuous lines for observations. Sources of the data are indicated in the legend and detailed in Table 1.
While, as articulated in Sect. 4, intensification of the global hydrological cycle can hardly be supported on the basis of global precipitation and evaporation fluxes, a large body of literature attempts to re-establish intensification on the basis of extremes. There is no shortage of studies that diagnose such intensification. To refer to just one example, the results of Donat et al. (2016), and specifically those in their Fig. 1 referring to the annual maximum daily precipitation, show some increase in the recent decades, which perhaps inspired their article title, namely “More extreme precipitation in the world's dry and wet regions.” However, when examining their graphs, it is seen that the climatic value of annual maximum daily rainfall of the 30-year period of 1980–2010, compared to that of 1960–1980, is greater by 5 % for dry areas and by 2 % for wet areas. These percentages may perhaps not be meaningful to a hydrologist who deals with real-world planning and design. Also, specifying particular areas such as dry and wet (which are subjectively defined and in the above study represent a small portion of the globe) and neglecting others, may distort the entire global picture.
Extremes are connected to disasters. A shortage of disasters has never been
the case, but our perception of them is driven less by disasters per se and
more by the communication thereof. In this respect, one may notice increasing
trends, both in reporting disasters to the general public and in the production
of research articles on disasters. Such articles typically focus on
particular areas recently hit by disasters. California is a popular example
but not the only one. Evidently, if we choose at random, say, 12 000 sites
on Earth, then every month we will have, on the average, one catastrophic
event of a 1000-year return period in one of the sites. The roots of the
intensification of disaster reporting belong to the domains of psychology
(cf. the notion of “availability bias”) and sociology rather than of hydrology. Thus,
Blöschl and Montanari (2010) note: There may also be a sociological element to the interpretation of flood trends which we term as the hydrologist's paradox: A recent large flood in a catchment will often lead to funding a study on the flood history of that catchment which will find there was a large flood at the end of the record. Simultaneously analysing many catchments in a large region will help reduce the chances of these self-fulfilling prophesies.
As a result of the intensification of disaster reporting, people think that rainfall events have become more intense or frequent recently. However, based on a list of world record point precipitation measurements compiled by Koutsoyiannis and Papalexiou (2017) for various timescales ranging from 1 min to 2 years, the fact is that the highest frequency of record rainfall events occurred in the period 1960–1980; later the frequency was decreased remarkably.
Variation of the areal maximum, over each continent, monthly
maximum daily precipitation. Thin and thick lines of the same colour
represent monthly values and running annual averages (right aligned),
respectively. Dashed lines are for reanalyses and continuous lines for
observations. Sources of the data are indicated in the legend and detailed in
Table 1. Notice that the satellite (GPCP) data do not seem to capture
precipitation rates higher than 100 mm d
Variation of the standard deviation of daily precipitation in each month, areally averaged. Thin and thick lines of the same colour represent monthly values and running annual averages (right aligned), respectively. Sources of the data are indicated in the legend and detailed in Table 1.
Evolution of the frequency of deaths from floods and droughts per decade in the 20th and 21st century. For comparison, deaths from other categories of natural catastrophes are also plotted: “extreme weather” includes storms, extreme temperatures (cold- or heatwave, severe winter conditions) and fog; “earthquake” also includes tsunamis; “other” comprises landslides (wet or dry), rockfalls, volcanic activity (ash fall, lahar, pyroclastic flow and lava flow) and wildfires. For the sources of the data, see entry 23 in Table 1.
A more detailed analysis can be based on the four sources of daily rainfall
information analysed here. This analysis has been performed separately for
each continent, and its results are presented graphically. Figure B1 shows
the temporal evolution of the monthly maximum daily precipitation areally
averaged over the continents. Figure B2 shows similar information but for
the areal maximum, over each continent, monthly maximum daily
precipitation. None of the figures in none of the continents and none of the
sources of data provides support on the intensification allegation. In
particular, the observational data (CPC and GPCP) could support the opposite
hypothesis, namely that of extreme rainfall deintensification. This becomes even
more evident if we examine the temporal evolution of the standard deviation of
daily precipitation in each month averaged over the land. In this respect,
Fig. B3 shows that deintensification, expressed as decreasing standard
deviation, is evident in the 21st century both from CPC and GPCP
observational data. This confirms an earlier result by Sun et al. (2012)
who, using global, land-based (
Even if, on a climatic basis, there was intensification at percentages like 1 % or 5 % mentioned above, casting catastrophic prophesies about the future, would be a misleading approach. The real data on the impacts of disasters of climatic type suggest a spectacular drop in the severest of them since the beginning of the 20th century. Figure B5 summarizes relevant information for victims of natural disasters. The sources of the data are seen in Table 1 (entries 22 and 23). The climate-related victims (particularly those from floods and droughts) have diminished, while other types of disasters, such as earthquakes, still have large numbers of victims. Obviously, the reason behind such diminishing is not that floods and droughts have become less severe or less frequent. Rather it is the fact that in the 20th century, instead of casting pessimistic prophesies about the future, societies improved hydrotechnology, water management and risk assessment and reduction, while strengthening international collaborations and the economy, so that the advances could be actually implemented.
All data used in the study are freely available as described in the article and in particular in Table 1, which provides all the required links.
The author declares that there is no conflict of interest.
I am grateful to the colleagues who have put their huge data sets online, as well as the data processing systems they developed. This has been the most important development in hydrology and geophysics since the time I entered academia several decades ago, to which I too have consistently tried to contribute in my country, with only partial success. I have started this research on the occasion of four invited lectures and seminars during 2017–2019 in Lunz, Palermo, Moscow and Bologna (eventually cancelled). I thank the colleagues who invited me or were involved in any respect with the organization of the talks: Dario Braga, Alexander Gelfan, Tatiana Fyodorova, Elisabet Ejarque Gonzalez, Goffredo La Loggia, Alberto Montanari, Valerio Noto, Dimitri Solomatine and Tz-Ching Yeh. I wish to clarify that my acknowledgement and thanks to them are not meant to imply that they agree with my opinions. I also thank an Austrian professor unknown to me, Rafael Bras and James Kirchner, who by their strongly negative reactions during my lectures in Lunz, Palermo and Moscow, respectively, helped me to strengthen my analyses and results. The Italian newspaper
This paper was edited by Erwin Zehe and reviewed by Zbigniew Kundzewicz and Axel Kleidon.