A detailed analysis of how intermittency (i.e., the alternation of dry and
rainy periods) modulates the rate at which sub-daily rainfall extremes depend
on temperature is presented. Results show that hourly extremes tend to be
predominantly controlled by peak intensity, increasing at a rate of
approximately 7% per degree in agreement with the Clausius–Clapeyron
equation. However, a rapid increase in intermittency upward of
20–25
Recently, there has been an increased interest in understanding and
predicting changes in precipitation extremes due to global warming
One important yet poorly discussed issue in all these studies concerns the
role played by intermittency (i.e., the alternation of dry and rainy periods)
in controlling the response of rainfall extremes to changing temperatures.
Indeed, beyond a few hours of aggregation timescale, total rainfall amounts
often turn out to be more correlated to storm duration and intermittency
rather than peak rainfall intensity
A recent study by
The present study aims at shedding new light on this important issue by presenting a detailed statistical analysis of how intermittency modulates the rate at which precipitation extremes (in current climate) depend on temperature. Results show that at timescales of 1 h or less, rainfall extremes tend to be predominantly controlled by changes in temperature. However, rapid local increases or decreases in intermittency with temperature can significantly lower or amplify the net scaling rates. In extreme cases, this may lead to (locally) negative scaling rates or, conversely, super-Clausius–Clapeyron scaling. As we move towards rainfall extremes at daily scales and beyond, intermittency rapidly gains in importance, masking most of the thermodynamic effects. To disentangle the two, a more general scaling model that takes into account simultaneous changes in intermittency and maximum intensity with temperature is proposed. Results show the new model greatly improves predictions of rainfall extremes with temperature, producing a more consistent and reliable depiction of observed responses across a wide range of temporal scales.
The rest of this paper is structured as follows: Sect. 2 introduces the
data used for the analysis. Section 3 describes the methods and models used
to detect and analyze rainfall extremes. The main results are provided in
Sect. 4. The first part focuses on how intermittency affects the scaling of
rainfall extremes across temperatures and timescales. The second part
analyzes the goodness of fit of the newly proposed model and the third and
last part investigates the sensitivity of derived scaling rates with respect
to the chosen quantile
Map showing the location of the 99 selected USCRN stations. The red cross denotes station AL-Fairhope-3-NE, which was chosen for illustration purposes.
The data used in the study were taken from the sub-hourly US Climate
Reference Network
Since the goal of this paper is to analyze the properties of rainfall
extremes across different scales, all time series were aggregated from their
original resolution of 5 min to larger timescales of 1, 2, etc., … up to
24 h in regular steps of 1 h. Aggregation was performed over overlapping time
windows (shifted by 5 min), taking the sums of all 5 min rainfall amounts in
each time interval. Air temperature was aggregated using the arithmetic mean, and values were binned into regular classes of 1
The full weather station network consisted of 232 different stations spread
across the US, Canada and Siberia. However, only a small subset of
these stations were kept for the analysis. Specifically, only the time series
with at least 20 valid positive rainfall values in at least 20 different
temperature classes between 5 and 30
Consider a time series of strictly positive rainfall amounts
Highest rainfall accumulations recorded at AL-Fairhope-3-NE for 1, 2, 6 and 24 h aggregation timescales.
Consider an aggregated rainfall amount
Also, note that because of the original sampling resolution of 5 min in the
USCRN (US Climate Reference Network) data, the internal intermittency of a rainfall amount at scale
The way rainfall intermittency varies with spatial and temporal aggregation
scale has already been studied quite extensively
Figure
Similarly to rainfall and temperature, it is possible to represent the
internal intermittency
Logistic regression between intermittency and rainfall quantile at
AL-Fairhope-3-NE for the 1 h timescale and two different temperatures
(10 and 25
The two model parameters
Scaling analyses in this paper are performed by considering the mean air
temperature
Previous studies have shown that rainfall extremes
To address this limitation, another slightly more general scaling model is
proposed in which a multiplicative correction term is added in
Eq. (
95th quantile of rainfall amounts at the hourly timescale as a
function of temperature and intermittency at AL-Fairhope-3-NE. Black dots
denote sample estimates. The black and red lines represent the fitted scaling
models given in Eqs. (
Since the internal intermittency
Figure
The 95th quantile of rainfall amounts at the daily timescale as a
function of temperature and intermittency at AL-Fairhope-3-NE. Black dots
denote sample estimates. The black and red lines represent the fitted scaling
models given in Eqs. (
Box plots of 95th rainfall quantile vs. temperature at 1, 2, 3, 6, 12 and 24 h aggregation timescales.
Figure
Similar analyses of the 95th rainfall quantiles and intermittency for all
99 stations in the dataset in Figs.
Box plots of internal intermittency vs. temperature for 1, 2, 3, 6, 12 and 24 h aggregation timescales.
Box plots of estimated scaling rates of 95th rainfall quantile with temperature as a function of timescale. Each box plot shows the 0, 25, 50, 75 and 90 % quantiles of all 99 stations in the dataset.
Figure
The stations with the strongest scaling rates overall (both at the hourly and
daily timescales) were FL-Sebring-23-SSE (12.96 %
Overall, the results confirm that air temperature alone is not systematically a good indicator for understanding extreme rainfall accumulations, and conditions in surrounding regions must be taken into account as well. The correction for intermittency makes it easier to understand and characterize the true sensitivity of heavy rainfall to changes in air temperatures across scales and geographical regions. But significant uncertainty remains, and the corrected model does not tell the full story either. However, it offers new insight into the nature of rainfall extremes, which is helpful in explaining some of the abnormally low/high scaling rates that we see in the observational record.
Box plots of root mean square error (RMSE) and coefficient of
determination (
Repeating the same type of analysis as above, we computed the root mean
square error (RMSE) and coefficient of determination (
Box plots of Spearman rank correlation between the 95th rainfall quantile and intermittency (over temperature) as a function of timescale. Each box plot shows the 10, 25, 50, 75 and 90 % quantiles of all 99 stations in the dataset.
The comparisons above show that while temperature plays an important role in
shaping rainfall extremes at smaller scales, its effects at larger scales are
likely to be masked by changes in storm dynamics, such as increased
intermittency. Additional correlation analyses between the 95th rainfall
quantile and internal intermittency with temperature presented in
Fig.
Box plots of rainfall scaling rates with temperature
(5–30
So far, all results we have shown were for extremes exceeding the
95th quantile of rainfall accumulations. The goal of this last
section is to quantify the sensitivity of the retrieved scaling rates with
respect to the choice of the quantile
Figure
Perhaps one of the most striking features in Fig.
To better understand this phenomenon, it is important to look at how quickly
intermittency levels change when going from one temperature class to another
and how this rate varies with
Figure
From
Intermittency is a key feature controlling the variability in precipitation. Yet its effect is often poorly taken into account. The first main result of this study is that most rainfall extremes above hourly scales are intermittent in nature. For example, it is common for rainfall extremes at daily timescales to exhibit upward of 80 % internal intermittency. For these reasons, peak intensity often turns out to be a rather weak predictor of total amounts compared with storm duration and dynamics.
The second important finding is that the current conceptual framework for studying the relationship between rainfall extremes and temperature based on Clausius–Clapeyron alone is too simplistic. Changes in extreme precipitation with temperature cannot be reduced to a single number. Instead, there appears to be a seamless progression of changes, starting at the sub-hourly scales where rainfall extremes are predominantly controlled by variations in temperature up towards hourly, daily and weekly extremes, which are increasingly dominated by storm dynamics and the organization of convection in larger weather systems. The combination of all these dynamical processes results in changing intermittency, which affects the sensitivity of extremes to temperature. Temperature itself remains a crucial factor across all timescales by controlling evaporation rates and the maximum moisture-holding capacity of the air. But because the rate at which new precipitable water can be brought in from surrounding regions is limited, net effective changes in rainfall totals with increasing temperatures are not necessarily well described by Clausius–Clapeyron scaling alone. New improved scaling models that take into account changes in intermittency, evaporation rates, advection speed and horizontal mass convergence can help to better separate the thermodynamic from the dynamic components, which leads to a more accurate depiction of precipitation extremes across scales. But the insight that these modified scaling laws provide is still limited, as rainfall-producing processes are complex and depend on many other physical factors like shifts in the horizontal and vertical circulations of the atmosphere, instabilities in the thermodynamic profile, aerosol concentrations and cloud microphysics.
Despite decades of development, current numerical weather prediction models
and climate simulations still lack the ability to reproduce realistic
intermittent rainfall patterns, especially at sub-daily timescales where
convective processes are the most important contributors to extremes. As a
result, projections about the future of rainfall extremes are still very
uncertain. Perhaps, future developments might profit from the new scaling
model proposed in this paper, allowing them to make a more in-depth analysis
of how well precipitation extremes are simulated in numerical weather models
and how realistically these vary with scale and temperature. New statistical
metrics and diagnostic tools specifically designed to assess the realism of
simulated intermittency patterns independently of total amounts and peak
intensity might prove useful with regard to this issue
Finally, note that while the present work only focused on temporal
intermittency, the same approach could be used to study the internal
intermittency of extremes aggregated over different spatial scales, for
example by looking at how the fraction of dry pixels within a fixed area
responds to changes in temperature. Also, since intermittency and temperature
are not sufficient to fully predict the response of heavy rainfall
accumulations across scales, additional covariates like wind speed, dew
point, pressure and vertical motion could be used in the analyses to further
refine the models. Similarly, it might be worth looking at alternative
intermittency metrics, like the fraction of the time the rainfall intensity
exceeds a certain threshold or the temporal variability in the rainfall rate
within an extreme. The latter might offer a more detailed picture of internal
storm variability than the simple binary rain/no-rain approach used in this
paper. A more detailed and systematic analysis of the joint probability
distribution of (
All data are freely accessible via anonymous ftp at
The authors declare that they have no conflict of interest.
This article is part of the special issue “Hydro-climate dynamics, analytics and predictability”. It is not associated with a conference.
The author would like to thank the National Oceanic and Atmospheric Administration (NOAA) for collecting and distributing the high-quality datasets used in this study. Edited by: Naresh Devineni Reviewed by: two anonymous referees