Daily precipitation extremes and annual totals have increased in large parts
of the global land area over the past decades. These observations are
consistent with theoretical considerations of a warming climate. However,
until recently these trends have not been shown to consistently affect dry
regions over land. A recent study, published by

Daily precipitation extremes are expected to increase over large parts of the
global land area roughly by 6–7 % per

The question whether precipitation extremes increase in dry regions is highly
relevant in the context of climate change adaptation, as generally dry areas
may be less prepared to deal with precipitation extremes

However, scrutinizing the findings by

Conceptual example of biases in the mean induced by normalization
based on a fixed reference period.

As a first step in the analysis of

Normalization-induced biases on time series and trend estimates.

Different mask of the world's dry and wet regions.

Statistical pre-processing uncertainties and biases in period increments and trend slopes.

An additional statistical bias stems from the choice of the world's 30 %
wettest and 30 % driest regions based on the climatology of PRCPTOT and Rx1d
in the reference period (1951–1980). Because 30 years is fairly short to
derive a robust climatology of the tails of the precipitation distribution,
the computed changes in wet and dry regions are distorted by the “regression
to the mean” phenomenon

The chosen normalization approach combined with the spatial point selection
method results in a bias toward PRCPTOT and Rx1d increasing at a faster rate
in dry regions compared to wet regions. Over dry regions, both effects lead
to an overestimation of the trends in precipitation totals and extremes by

Climatological dryness is typically not determined by water supply alone but
also depends on atmospheric water demand, i.e. the ability to evaporate
water from the land surface

To clarify this issue, we test the sensitivity of the reported increases in
Rx1d and PRCPTOT to the choice of dryness definition by using a variety of
different dryness definitions (Fig.

regions that fall below the global 30 % quantile in HadEX2 in the
respective diagnostic (Rx1d or PRCPTOT), following

dry regions (“B-climates”) from a traditional climate classification
based on temperature and precipitation

dry regions as identified from an aridity-based definition of dryness

dry and transitional regions combined from the latter definition

Our results show that, if dry regions are defined based on water availability
(i.e. dry regions following either

Uncertainties regarding the definition of a “dry region”, Rx1d.

Uncertainties regarding the definition of a “dry region”, PRCPTOT.

Monitoring and an accurate quantification of trends in meteorological risks
in a rapidly changing Earth system is a prerequisite to well-informed
decision-making in the context of climate change adaptation

Furthermore, the definition of a “dry region” induces considerable
uncertainty in quantifying changes in Rx1d and PRCPTOT in such areas. If
dryness is defined based on water supply and demand (i.e. aridity), we find
much smaller trends and period increments in Rx1d and PRCPTOT, which are
almost exclusively positive but in many cases insignificant
(Tables

In summary, understanding and disentangling ongoing changes in precipitation characteristics in the world's dry regions remains a research priority of high relevance. In this context, our paper demonstrates that (1) data pre-processing can introduce substantial bias, and (2) trends and period changes can be sensitive to the specific choice of dryness definition that is used; therefore, we urge authors to be considerate and specific regarding both choices and to consider associated uncertainties.

The gridded HadEX2 and GHCNDEX datasets that contain Rx1d and PRCPTOT data used
in this study are available for download under the following URLs:

HadEX2:

GHCNDEX:

Assumptions and notation:

Assume independent and identically distributed (i.e. stationary) variables

Let

Let

Our objective is to find an analytical approximation of the expected value
for the artificially induced relative change (

normalization with a “reference period sample mean” leads to an
artificial increase of spatial averages in the out-of-base period, i.e. the
bias is always positive in the out-of-base period,

that

a Gaussian distribution;

a GEV distribution with two different choices
for the shape parameter (

Assume

A comparison of Eq. (A10) (i.e. the first three terms in the Taylor
approximation) to numerical simulations shows that the analytical
approximation works well (Fig.

However, one important caveat is that Eq. (A3) and the subsequent approximation
only works as long as

We investigate whether in Eq. (A7) the higher-order terms in the Taylor
approximation can be ignored in practical applications, where an assumption
of Gaussianity might not hold. Here, we test this for the GEV distribution as an appropriate model for annual maxima as investigated
in the main paper with two different choices for the distribution's
shape parameter (

We first assume, in analogy to the paragraph above, independent and
identically distributed (i.e. stationary) random variables drawn from a
GEV distribution with zero shape parameter

Following Eq. (A7), we can readily derive an analytical expression for the
expected value of the normalization-induced bias:

Here, we test whether the analytical argument from above can be extended to
GEV distributions with

Hence, the (dominant) quadratic term in the Taylor approximation in Eq. (A7) reads

The approximation works again very well in numerical simulations
(Fig.

Many real-world precipitation time series show non-stationarities due to
climatic variations

Let

Relationship between annual-maximum daily rainfall (Rx1d from
HadEX2–GHCNDEX-merged dataset) and aridity

Available data in the HadEX2 dataset

Sebastian Sippel and Jakob Zscheischler conceived the study. All authors contributed to writing the paper.

The authors declare no conflict of interest.

Sebastian Sippel and Miguel D. Mahecha are grateful to the European Commission for funding the BACI project (grant agreement no. 640176) and to the European Space agency for funding the STSE project CAB-LAB. We thank M. Donat for discussions and four anonymous reviewers for comments on an earlier form of the manuscript. Discussions with Holger Metzler and Fabian Gans on the analytical approximation presented in the Appendix are gratefully acknowledged. The article processing charges for this open-access publication were covered by the Max Planck Society. Edited by: V. Andréassian Reviewed by: D. Stone and three anonymous referees