Variability of the terrestrial water cycle, i.e. precipitation (

In describing the terrestrial branch of the water cycle, the precipitation
(

However, the long-term mean annual hydrologic fluxes rarely occur in any
given year. Instead, society must (routinely) deal with variability around
the long-term mean. The classic hydro-climate extremes are droughts and
floods but the key point here is that hydrologic variability is expressed on
a full spectrum of time and space scales. To accommodate that perspective,
we need to extend our thinking beyond the long-term mean to ask how the
variability of

Early research on hydrologic variability focussed on extending the Budyko
curve. In particular, Koster and Suarez (1999) used the Budyko curve to
investigate inter-annual variability in the water cycle. In their framework,
the evapotranspiration standard deviation ratio (defined as the ratio of
standard deviation for

Hydrologists have only recently accepted the challenge of developing their
own re-analysis-type products with perhaps the first serious hydrologic
re-analysis being published as recently as a few years ago (Rodell et al.,
2015). More recently, the Princeton University group has extended this early
work by making available a gridded global terrestrial hydrologic re-analysis
product known as the Climate Data Record (CDR) (Zhang et al., 2018).
Briefly, the CDR was constructed by synthesizing multiple in situ
observations, satellite remote sensing products and land surface model
outputs to provide

The paper is structured as follows. We begin in Sect. 2 by describing the
various climate and hydrologic databases used in this study and also
include a further assessment of the suitability of the CDR database for this
initial variability study. In Sect. 3, we examine relationships between
the mean and variability in the four water cycle variables (

The water balance is defined by

We use the CDR database (Zhang et al., 2018), which is
a recently released global land hydrologic re-analysis. This product
includes global precipitation

In general, we anticipate two important factors, i.e. the water storage
capacity and the presence of ice/snow at the surface, which are most likely
to have influence on the partitioning of hydrologic variability. For the
storage, the active range of the monthly water storage variation was used to
approximate the water storage capacity (

The CDR database provides an estimate of the uncertainty (

In the original work, the CDR database was validated by comparison with
independent observations including (i) mean seasonal cycle of

For the comparison to FLUXNET observations (Baldocchi et al., 2001; Agarwal
et al., 2010) we identified 32 flux tower sites (site locations are shown in
Fig. S3 and details are shown in Table S1) with at least 3 years of
continuous (monthly) measurements using the FluxnetLSM R package (v1.0)
(Ukkola et al., 2017). The monthly totals and annual climatology of

The comparison of

We concluded that while the CDR database was unlikely to be perfect, it was nevertheless suitable for an initial exploratory survey of inter-annual variability in the terrestrial branch of the global water cycle.

The global pattern of mean annual

Mean annual (1984–2010)

Relationship of mean annual

We relate the grid-box level ratio of

We use the variance balance equation (Eq. 2) to partition the inter-annual

Water cycle variances (

These results show that the spatial patterns in variability are not simply a
reflection of patterns in the long-term mean state. On the contrary, we find
that of the three primary variance terms, the overall magnitude of
(inter-annual)

Differences in the spatial patterns of the mean (Fig. 1) and inter-annual
variability (Fig. 3) in the global water cycle led us to further investigate
the relation between the mean and the variability for each separate
component. Here we relate the standard deviation (

Relation between inter-annual mean and standard deviation for

In the previous section, we investigated spatial patterns of the mean and
the variability in the global water cycle. In this section, we extend that
by investigating the partitioning of

We first evaluate the classical empirical curve of Koster and Suarez (1999)
by relating ratios

Relationship of inter-annual standard deviation of

Here we examine how the fraction of the total variance in precipitation
accounted for by the three primary variance terms along with the three
covariance terms varies with the aridity index (

Relation between water cycle variances and covariances (see Fig. 3b–g)
as a fraction of the variance of

The covariance ratios are all small in extremely dry (e.g.

Results in the previous section demonstrated that spatial variation in the
partitioning of

We first relate the partitioning of

Relation between water cycle variances and covariances (see Fig. 3b–g)
as a fraction of the variance for

To understand the potential role of snow/ice in modifying the variance
partitioning, we repeat the previous analysis (Fig. 7) but here we use the
mean annual air temperature (

Relation between water cycle variances and covariances (see Fig. 3b–g)
as a fraction of the variance for

The previous results (Sect. 4.3) have demonstrated that the partitioning
of

Locations of three representative grid cells used as case study sites.

Inter-annual time series (

Location of three case study sites in the water cycle variability space. The grey background dots are from Fig. 6.

We show the

To put the data from the three case study sites into a broader variability
context we position the site data onto a backdrop of Fig. 6. As
noted previously, at Site 1, the ratio

The above simple examples demonstrate that aridity

Synthesis of factors controlling variance partitioning. The
arrows denote trends with increasing

Under extremely wet conditions, the largest difference in variance
partitioning is not due to differences in storage capacity but is instead
related to differences in mean air temperature. In wet and hot environments,
we have maximum runoff and find that

However, the most complex patterns to interpret are those for semi-arid to
semi-humid environments (i.e.

Importantly, hydrologists have long been interested in hydrologic
variability, but without readily available databases it has been difficult
to quantify water cycle variability. For example, we are not aware of maps
showing global spatial patterns in variance for any terms of the water
balance (except for

The mean annual

Our initial attempt to develop deeper understanding of variance partitioning
was based on a series of case studies located in extreme environments
(wet/dry vs. hot/cold vs. high/low water storage capacity). The results
offered some further insights about hydrologic variability. For example,
under extremely dry (water-limited) environments, with limited storage
capacity (

In extremely wet/hot environments (i.e. no snow/ice presence) we found

The most complex results were found in mesic biologically productive
environments (

The syntheses of the long-term mean water cycle originated in 1970s (Budyko, 1974), and it took several decades for those general principles to become widely adopted in the hydrologic community. The hydrologic data needed to understand hydrologic variability are only now becoming available. With those data we can begin to develop a process-based understanding of hydrologic variability that can be used for a variety of purposes; e.g. deeper understanding of hydro-climatic behaviour, hydrologic risk analysis, climate change assessments and hydrologic sensitivity studies are just a few applications that spring to mind. The initial results presented here show that a major intellectual effort will be needed to develop a general understanding of hydrologic variability.

The global terrestrial water budget used in this study can be accessed at

The supplement related to this article is available online at:

DY and MLR designed the study and are both responsible for the integrity of the manuscript. DY performed the calculations and analyses, and prepared the original manuscript, and MLR contributed to the interpretation, discussion and writing of the manuscript.

The authors declare that they have no conflict of interest.

We thank Anna Ukkola for help in accessing the FLUXNET database. We thank the reviewers (including René Orth and two anonymous reviewers) for helpful comments that improved the manuscript.

This research has been supported by the Australian Research Council (grant nos. CE11E0098 and CE170100023) and the National Natural Science Foundation of China (grant no. 51609122).

This paper was edited by Anke Hildebrandt and reviewed by Rene Orth and two anonymous referees.