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\begin{document}

\title{Disentangling climate change trends in Australian streamflow}



\author[1]{Rutger Vervoort}%
\author[2]{Michaela Dolk}%
\author[1]{Floris van Ogtrop}%
\affil[1]{The University of Sydney}%
\affil[2]{Swiss Re Management (US) Corporation}%


\vspace{-1em}



  
  \date{May 23, 2024}


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\selectlanguage{english}
\begin{abstract}
The effect of climate change on water resources has been an area of
continued research, especially in Australia. Previous studies have
suggested significant trends in rainfall, and these are amplified
causing larger changes in streamflow. However, most of the previous
analysis was based on annual time scales or modelled data and did not
account for changes in land cover, which could interact with changes in
climate. Climate data and streamflow data sourced from 13 fully forested
small catchments (\textless{}250 km2) was analysed for trends.
Non-parametric Mann-Kendall trend analysis, generalised additive mixed
modelling and rainfall-runoff modelling were combined for the analysis.
This indicates consistent increases in maximum temperature and varied
decreases in rainfall. Limited to a small number of catchments in south
eastern Australia there were small, but significantly amplified,
decreases in streamflow. In general, overall decreases are much smaller
than predicted in earlier research.%
\end{abstract}%



\sloppy


\section*{Introduction}

{\label{introduction}}

The effects of climate change will influence water resource availability
in the future (Huntington, 2006; Trenberth et al., 2014). This is
particularly of importance in Australia where major droughts have
drastically increased public concerns about water availability (Leblanc,
Tweed, Van Dijk, \& Timbal, 2012). As a result, there have been several
studies focussing on climate change impacts on water resources (Betts et
al., 2007; Chien, Yeh, \& Knouft, 2013; Chiew \& McMahon, 2002; Chiew et
al., 2009).

Most of the earlier studies on future water availability have used
rainfall-runoff models with climate data from downscaled global
circulation models to highlight future scenarios (e.g. Chien et al.,
2013; Chiew et al., 2009; Leblanc et al., 2012; Vaze, Davidson, Teng, \&
Podger, 2011). For Australia, most of these studies indicate a more
variable future and a decreased water availability (van Dijk et al.,
2013). The main explanation is decreased rainfall and increased
evaporation and therefore decreased streamflow. A drawback of such
studies is that they introduce at least two types of errors: the
calibration uncertainty of the rainfall-runoff model and the associated
uncertainty in the prediction; and uncertainty in future climate data,
either from downscaling global models (Leblanc et al., 2012), or from
scaling of historical data (Chiew, 2006; Fu, Charles, \& Chiew, 2007).

Reductions in streamflow in Australia have also been attributed to
increased CO\textsubscript{2} fertilisation of the vegetation due to
changes in the atmospheric CO\textsubscript{2} concentrations (Trancoso,
Larsen, McVicar, Phinn, \& McAlpine, 2017; Ukkola et al., 2015).
However, as Ajami et al. (2017) highlight, this effect varies along
aridity gradients and depends on other factors such as nutrient
availability. Biological work (Franks et al., 2013) suggests that tree
stomata adapt to changes in climate, i.e. there is a certain level of
bio-plasticity to reduce how water is transpired as a function of
temperature. This highlights further other, possibly interacting and
counteracting, factors that could influence future changes in
streamflow, well beyond the traditional forcing variables.

Another issue with the earlier work, including some of the latest work
on the changes in catchment responses with drought (Ajami et al., 2017;
Booij, Schipper, \& Marhaento, 2019; Saft, Western, Zhang, Peel, \&
Potter, 2015), is that very few of the studies have controlled for land
cover and therefore might have stationarity issues (Montanari et al.,
2013; Navas, Alonso, Gorgoglione, \& Vervoort, 2019). Ajami et al.
(2017) analysed vegetation cover and found that runoff sensitivity to
precipitation varied with fractional vegetation cover. Moreover, they
confirmed that increased vegetation cover decreases runoff sensitivity,
confirming earlier work (Chiew, 2006). However, Ajami et al. (2017) also
point out that fractional vegetation cover covaries with precipitation,
therefore making the comparison difficult.

An alternative approach to biophysical modelling with future climate
scenarios to understand changes in future water yield, would be to
analyse historical data sets, as several older studies in Australia have
done (Booij et al., 2019; Cai \& Cowan, 2008; Chiew, Whetton, McMahon,
\& Pittock, 1995; Petrone, Hughes, Van Niel, \& Silberstein, 2010;
Potter, Petheram, \& Zhang, 2011; Trancoso et al., 2017). However, there
are several reasons why the issue of trends in streamflow might need
revisiting. Many of the older studies were based on annual data, a
limited geographical area (Petrone et al., 2010) and varied in terms
data periods and data aggregation in space and time. Some studies
focused on a few rivers (Petrone et al., 2010; Potter \& Chiew, 2011),
some focussing on the whole Murray Darling water balance (Cai \& Cowan,
2008) and some focussing on a large data base of catchments (Booij et
al., 2019; Chiew, 2006; Trancoso et al., 2017).

Finally, the models and types of analyses varied across the studies,
including simple linear regression on un-transformed and transformed
data (Cai \& Cowan, 2008; Chiew, 2006; Chiew et al., 2014; Potter et
al., 2011), non-parametric Mann-Kendall and step change methods (Petrone
et al., 2010; Potter \& Chiew, 2011), statistical analyses and using
rainfall runoff models (Chiew, 2006; Potter, Chiew, \& Frost, 2010) and
applying an energy framework (Booij et al., 2019) and focussing on
baseflow (Trancoso et al., 2017). As a result, despite a consistent view
of a sharply declining streamflow in response to changing rainfall, it
is difficult to compare across studies.

Rather than using conceptual or deterministic modelling approaches, data
based statistical models allow quick identification of the main
variables explaining variations in streamflow. If the variables in the
statistical model represent real physical processes (Fu et al., 2007),
the model removes all variance based on the physical processes and the
remaining unexplained trend in the residuals can be analysed. Modern
regression approaches also allow non-linearity and the identification of
uncertainties (Wood, 2006), rather than being limited to linear
relationships. The disadvantage of statistical models is that they are
essentially a ``black box'' as they do not explicitly include any
physical processes. This means that, while the model can show
correlation, it does not necessarily prove causation, and a lack of
understanding of processes within a system may lead to an incorrect
interpretation of statistical relationships.

The above review highlights that it is therefore important to have
consistent methodology that includes several different statistical
analyses to cross check the trend results, as each analysis included
methodological and data uncertainty.

Given the range of approaches, the aim of this paper is 1) to offer a
combination of statistical approaches to analyse climate change trends
in streamflow data in forested catchments; 2) to use the increased
observed data length to revisit the work by Chiew (2006) and other past
research to investigate climate change trends on a subset of the
Australian hydrological reference stations across the continent; and 3)
to highlight the spatial and temporal variation in these rainfall and
temperature effects on streamflow across the Australian continent.

While the data in this paper focuses on Australia, the outcomes and
methodology are relevant for other regions that are experiencing changes
in rainfall and temperature and have predicted changes in streamflow.

In light of the complexity of the topic, and the number of existing
papers with somewhat conflicting results, all the data, explanations and
code for the analyses used in this paper have been stored as
supplementary data in an on-line repository, which can be accessed via:
https://doi.org/10.5281/zenodo.3757041

\section*{Methods}

{\label{methods}}

\subsection*{Site selection and data}

{\label{site-selection-and-data}}

A total of 13 hydrologic reference stations across Australia, focussing
on stations with catchments areas that are less than
250km\textsuperscript{2} were selected from the Bureau of Meteorology
(http://www.bom.gov.au/water/hrs/) (Figure 1 and Table 1). Using a basic
land use data interpretation, we focussed on catchments that are
essentially fully forested to minimise effects of landuse variation. By
focussing on relatively small catchments, we also aimed to control for
catchment size which influences storage and routing.

Rainfall and temperature stations were selected for each streamflow
station based on proximity, data length and data continuity. Data for
the selected rainfall and temperature sites for the period 1970-2010
were obtained from the Bureau of Meteorology. However, since climate
stations were not necessarily close to the catchments, we also extracted
the ANUCLIM 1km gridded rainfall product via the eMast NCI server
(http://dapds00.nci.org.au/thredds/catalog/rr9/ANUClimate/catalog.html)
for each of the catchment outlets.

\subsection*{Analysis of annual trends and elasticities following Chiew
(2006)}

{\label{analysis-of-annual-trends-and-elasticities-following-chiew-2006}}

As a first step annual summaries of the data were analysed, following
Chiew (2006). Both the non-parametric approach for calculating the
rainfall elasticity, \selectlanguage{greek}ε\selectlanguage{english}\textsubscript{P}, (Fu et al., 2007) and the
modelling approach (Chiew, 2006) were used. The non-parametric approach
calculates the elasticity as (Fu et al., 2007):

\(\epsilon_{p}=median\left(\frac{Q_{t}-\overset{\overline{}}{Q}}{P_{t}-\overset{\overline{}}{P}}\frac{\overset{\overline{}}{P}}{\overset{\overline{}}{Q}}\right)\)(1)

For the modelling approach, both GR4J (Perrin, Michel, \& Andr\selectlanguage{ngerman}éassian,
2003) and SimHyd including the Muskingum routing routine (Chiew et al.,
2009) were used on the daily data. The models were all calibrated on the
full 40 year daily dataset (1970 -- 2010). The calibration used shuffled
complex evolution optimisation with 20 complexes, and this was repeated
10 times to capture model uncertainty due to parameter equifinality. The
residuals of the modelling were calculated as the difference between
observed and predicted values.

Following the original work (Chiew, 2006), the daily rainfall series
(\emph{P} ) was scaled by -15\%, -10\%, 0\%, +10\%, while the daily
maximum temperature (\emph{MaxT} ) series, rather than the monthly
Potential Evapotranspiration (PET) as in Chiew (2006), was scaled by
0\%, +5\% and +10\%. The resulting predicted daily flow series (\emph{Q}
) were summarised to annual series and \selectlanguage{greek}ε\selectlanguage{english}\textsubscript{P} and the
elasticity due to \emph{ET} , \selectlanguage{greek}ε\selectlanguage{english}\textsubscript{ET,} were calculated using
regression (Chiew, 2006):

\(\delta Q_{\text{annual}}=\varepsilon_{P}\delta P_{\text{annual}}+\varepsilon_{\text{ET}}\delta\text{MaxT}_{\text{annual}}\)(2)

Where, \emph{MaxT\textsubscript{annual}} is the average annual maximum
daily temperature rather than the maximum annual daily temperature. The
elasticity is a measure of amplification of the rainfall change in the
streamflow, with elasticities greater than unity indicating
amplification of the rainfall and ET signal (Chiew, 2006).

\subsection*{Mann-Kendall non-parametric trend test and linear
trends}

{\label{mann-kendall-non-parametric-trend-test-and-linear-trends}}

The presence of monotonic trends in weekly mean streamflow, rainfall and
maximum temperature were initially assessed using non-parametric
Mann-Kendall tests. The advantages of Mann-Kendall based tests are that
there is no assumption that the data are normally distributed, nor does
it assume that the trend is linear. However, there are two possible
issues with simply using a Mann-Kendall test on the data. The first is
outlined by Westra et al. (2012), which highlights that even in random
data there is a probability of identifying a trend. As a result, we
followed Westra et al. (2012) and ran a bootstrap with 500 samples to
identify this error in the basic Mann-Kendall analysis. The second issue
is outlined by Koutsoyiannis and Montanari (2007): A locally observed
trend is not necessarily a true trend in the data due to scaling
properties. Under the assumption of scaling, the Mann-Kendall trend can
be further tested to identify if the Hurst coefficient is significant
and the Mann-Kendall test can be corrected for this (Hamed, 2008), we
indicate this test as the LTPMK test (long time period Mann-Kendall).

The daily data were de-seasonalised and summarised to weekly before
running the Mann-Kendall and LTPMK tests using the package
``deseasonalize'' (McLeod \& Gweon, 2013). Calculations for the standard
Mann-Kendall and LTPMK tests were performed using the ``Kendall''
package (Mcleod, 2011) and ``HKProcess'' (Tyralis, 2016) in R (R Core
Team, 2013), respectively.

In addition to analysing the data series, the trend in the residuals of
the modelled series from the previous rainfall-runoff modelling step was
also analysed using the same LTPMK test. If the modelled series deviates
from the observed series for the post calibration period with a
consistent trend, then this would be another indication of a trend in
the data series. For this analysis, the residuals were summarised to
weekly data to match the observed data. All analyses were repeated with
both the station rainfall data and the gridded rainfall data.

\subsection*{Generalized additive mixed model
(GAMM)}

{\label{generalized-additive-mixed-model-gamm}}

The basic starting assumption in this analysis is that streamflow
(\emph{Q} ), combining both surface runoff and groundwater inflows, in
relatively small homogeneous catchments can be modelled as a simple
water balance of rainfall (\emph{P} ) and evapotranspiration (\emph{ET}
):

\(Q=P-ET\) (3)

Due to the relatively small size of the catchments, storage effects
based on the weekly data can be considered minor and the majority of the
storage delays can be captured (in other words, residence times of water
moving towards the stream are considered to be smaller than a week for
the majority of the flow).

Generalized additive mixed models (GAMMs) were defined to model the
weekly streamflow at each station as a function of rainfall and weekly
mean maximum temperature. GAMMs may be considered as an extension of
generalized linear mixed models whereby the predictors are additive, but
can also be non-linear (Chen, 2000). The mixed model addition to the
standard Generalized Additive Model (GAM), allows modelling of the
autocorrelation in the residuals. Details of the statistical basis of
GAMMs can be found in Chen (2000) and Lin and Zhang (1999).

Mean weekly streamflow and rainfall are indicated
by\emph{Q\textsubscript{w}} and \emph{P\textsubscript{w}} ,
respectively. A smoothing function, s(), was applied to the rainfall
term to account for non-linear responses in the rainfall-runoff
relationship. Weekly mean streamflow data was used to remove any effects
of filled in missing data by the Bureau of Meteorology, and to remove
most of the stream routing effects.

The models were applied in several steps (Table 2). Initially, the
linear trends in both rainfall and temperature were analysed using
generalised least squares using an autoregressive order 1 (AR1)
correlation structure fitted to the errors (\emph{e\textsubscript{t}}\selectlanguage{english} ).
As an added benefit, the AR1 error structure accounts for further
storage effects in the catchment, including the effect of past rainfall.

Subsequently a GAMM with a smooth function of \emph{P\textsubscript{w}}
, a linear trend and autoregressive order 1 (AR1) correlation structure
fitted to the errors (\emph{e\textsubscript{t}}\selectlanguage{english} ) was evaluated.

\(\text{Log}\left(Q_{w}\right)\sim s\left(P_{w}\right)+trend+\varepsilon_{t}\)(4)

Streamflow data were log transformed to stabilise the variance of the
residuals. The trend in equation 3 can be interpreted as a change in the
residual \emph{log} (\emph{Q\textsubscript{w}} ) over time. In order, to
identify \(\selectlanguage{greek}\frac{\text{δQ}}\selectlanguage{greek}\selectlanguage{english}{\text{δt}}\selectlanguage{english}\) as a fractional change the trend needs to be
back transformed using:

\(\selectlanguage{greek}\frac{\text{δQ}}\selectlanguage{greek}\selectlanguage{english}{\text{δt}}\selectlanguage{english}=\left(\exp\left(\text{trend}\right)-1\right)\). (5)

The first model (equation 4) removes the direct effect of weekly
rainfall (\emph{P\textsubscript{w}} ) on the weekly streamflow
(\emph{Q\textsubscript{w}} ). Amplification can be defined
as\(\selectlanguage{greek}\frac{\text{δQ}}\selectlanguage{greek}\selectlanguage{english}{\text{δP}}\selectlanguage{english}>1\), using the annual data. However, the trend in
equation 4 can include other phenomena changing the rainfall-runoff
response over time. As a second step, a GAMM with a smooth function of
\emph{P\textsubscript{w}} and a smooth function of the interaction
between \emph{maxT\textsubscript{w}} and\emph{P\textsubscript{w}} was
fitted:

\(\text{Log}\left(Q_{w}\right)\sim s\left(P_{w}\right)+s\left(\text{maxT}_{w},P_{w}\right)+trend+\varepsilon_{t}\)(6)

The interaction between \emph{maxT\textsubscript{w}}
and\emph{P\textsubscript{w}} is a proxy for the actual
evapotranspiration. Equation 6 identifies the residual trends in the
streamflow data after removal of the effects of rainfall and actual
evapotranspiration. The difference in the trend in the second model
(equation 6) and the first model (equation 4) highlights the impact of
actual evapotranspiration effects on streamflow. The final trend
remaining in the model therefore includes any ``other'' phenomena in the
rainfall-runoff relationship. Examples of these could be changes due to
tree physiology, CO\textsubscript{2} fertilization or geomorphology and
is the degree of amplification, i.e. the change in streamflow after
changes in rainfall and evapotranspiration have been considered.

Using equation 6, a GAMM which removes the linear trend was also fitted,
to test whether the assumption of a linear trend affected the results:

\(\text{Log}\left(Q_{w}\right)\sim s\left(P_{w}\right)+s\left(\text{maxT}_{w},P_{w}\right)+\varepsilon_{t}\)(7)

The residuals (\selectlanguage{greek}\emph{ε\textsubscript{t}}\selectlanguage{english} ) of this final GAMM model
(equation 7) were subsequently analysed for a trend using a LTPMK test.

The GAMM modelling was conducted using the ``mgcv'' package in R (Wood,
2006).

Given the complexity of all the methodology a flow chart of the
different approaches and comparisons is presented in Figure 2.

\section*{Results}

{\label{results}}

\subsection*{Annual data trends following Chiew
(2006)}

{\label{annual-data-trends-following-chiew-2006}}

The relationship between annual rainfall and runoff for the catchments
(Figure 3), generally plots below the 1:1 line. Ignoring storage
variations, the divergence of the 1:1 line is related to the removal of
water due to evapotranspiration. Except for some single points all the
data plot below the 1:1 line for the gridded rainfall data. For the
station data this is not the case for a few of the catchments
(supplementary data on zenodo https://doi.org/10.5281/zenodo.3757041),
but the results generally show similar behaviour. One of the catchments,
where a lot of the data plotted above the 1:1 line using the observed
station rainfall data, is a small catchment (SOUT). Two other catchments
(NIVE and HELL) occur in areas with steep elevation gradients, and as a
result the nearest rainfall station might not be representative. In
contrast the ANUCLIM gridded data appears more representative, as less
of the data plot above the 1:1 line.

Non-parametric elasticities (\selectlanguage{greek}ε\selectlanguage{english}\textsubscript{p}, red triangles in Figure
4), calculated from the streamflow and gridded rainfall data, were in
the same range as those observed by Chiew (2006). All elasticities were
less than 3, with most about 2 or above, and some stations indicating
elasticities very close to 1 (COCH, HELL and SOUT).

In contrast, elasticities calculated from the simulated data based on
the rainfall runoff models were quite different (boxplots and large blue
dots indicating mean values in Figure 4), and in fact almost constant.
The variation between the 10 replications of the rainfall runoff model
calibration was very narrow, particularly for GR4J, so most of the
boxplots look like single straight horizontal lines. Overall the
elasticities calculated from the rainfall runoff modelling results were
close or smaller than 1. This suggest decreases in runoff that are
smaller than the associated decreases in rainfall, considering changes
in evapotranspiration.

The calibration of the rainfall models with the gridded rainfall data
was generally good (NSE \textgreater{} 0.5) considering the 41 year data
period, although the SimHyd performance was lower than the GR4J
performance (Figure 5), and some catchments had low model performance
(Chiew et al., 2009). In addition, the different replications of the
calibration with SimHyd showed considerable variation (wide boxplots),
while the replications in the GR4J calibrations were very consistent
(resulting in the boxplots being plotted as single lines). Comparing the
two rainfall sources. the calibration performance using the observed
station rainfall data (document 6 supplementary data) was slightly worse
for both models and the calculated elasticities were also slightly lower
(document 6 supplementary data).

\subsection*{Mann-Kendall and LTPMK
tests}

{\label{mann-kendall-and-ltpmk-tests}}

The results of the standard Mann-Kendall tests on the de-seasonalised
weekly data indicate that there is a consistent decreasing trend in
streamflow (Table 3), with a significant (p-value \textless{} 0.05)
trend for nine of the 13 sites, which are all located in south of the
continent and Western Australia. At least five and maybe seven of these
sites with significant trends had trends outside the bootstrap
distribution (Figure 6).

There is a matching decreasing trend in most of the gridded rainfall
records, with a significant (p-value \textless{} 0.05) trend for 8
sites. However, only 2 of these are outside the bootstrap distribution
(supplementary material document 2). The station rainfall data had
similar results to the gridded data. Basically, all the 13
de-seasonalised weekly average maximum temperature records have a
significant increasing Mann Kendall trend, even though only 5 of these
are falling outside the bootstrap distribution (supplementary material
document 2), with locations in south eastern Australia.

In contrast, all the LTPMK results indicated highly significant Hurst
coefficients and therefore, based on this analysis, the Man Kendall
trends were all not significant for all three variables under the
scaling hypothesis (Hamed, 2008). To check the overall test, we also ran
the monthly and annual summaries of the three variables. The results
(supplementary material document 2A) show that the significance of the
LTPMK trends increases with an increase in the time aggregation. For
example, the LTPMK average maximum temperature was significant and
increasing for six stations at the monthly time scale, and significant
and increasing for eight of the 13 stations at the annual time scale.
Similar results were found with the time integration for the rainfall
and streamflow data, but in this case all significant trends were
decreasing in time.

\subsection*{Generalized additive mixed
modelling}

{\label{generalized-additive-mixed-modelling}}

The results of the generalised least squares (GLS) modelling (model 1 in
Table 2) suggest only four of the studied catchments have significant
linear trends in the streamflow over the last 41 years (Table 4), which
is fewer than in the earlier Mann Kendall results (Table 3 and Figure
6). The negative trends were very small in actual percentage value, in
the order of 10\textsuperscript{-4} \% of the streamflow (Table 4).
Similarly, significant trends in rainfall were also all negative, and
very small in actual percentage. For those stations that have
significant trends in both rainfall and streamflow, ``amplification''
(calculated as the trend in Q/trend in P) between 0.95 and 4.29 occurs.
This is a larger trend then calculated from the original data and the
rainfall-runoff modelling in Figure 3. However, the trend in streamflow
derived in the GLS analysis still incorporates the changes in climate in
the streamflow, such as changes in rainfall and temperature. These need
to be removed to identify the true ``amplification'' effect.

Comparing the streamflow model results without rainfall (model 2, Table
4) with the results of the model that removes the rainfall effect (model
3, Table 5), indicates a small reduction in the negative trend and the
same number of significant stations. Overall the inclusion of rainfall
in the model removes approximately \textless{} 10 to 30\% of the
original trends. In other words, the linear trend is the remaining trend
in the streamflow after removing the trend in the rainfall. In terms of
amplification, this is the additional decrease in streamflow on top of
any reduction in the rainfall. However, some of the remaining trends
could be due to trends in temperature affecting potential ET.

Overall variation explained by the final models that include both
rainfall and evapotranspiration (model 4, Table 2 and Table 6) was low
to medium (-0.03 \textless{} Adj \emph{r} \textsuperscript{2}
\textless{} 0.43, supplementary material document 3C). The worst
performing model was for station NIVE, but more generally these results
suggest that there are other processes causing variation in the runoff
that the statistical model does not include. This is not necessarily an
issue, as the goal of the statistical modelling was to explain the
maximum variation in the streamflow related to rainfall and ET, and not
to find the best predictive model.

After rainfall and evapotranspiration effects are accounted for (model
4), the models identify significant trends in the weekly data in only
six catchments (Table 6). These trends are once again very small and
only in the order of 1.1 -- 5.5 \selectlanguage{ngerman}× 10\textsuperscript{-4} \% change. This
suggests that the overall streamflow is indeed declining over time, even
after accounting for changes in rainfall and evapotranspiration, but
currently the overall change is very small. This remaining trend is the
amplification.

Note that inclusion of the maximum temperature (evaporation) explains
very little of the variation in streamflow, as the improvement in the
performance measure AIC (Aikaike Information Criterium) between model 3
(Table 5) and model 4 (Table 6) is small. As a result, for those
catchments still showing significant trends, the variance explained by
including rainfall and temperature is small, from \textless{} 10\% to
30\%. As with the previous analyses (Chiew et al., 2009; Potter \&
Chiew, 2011), the catchments with significant trends are all located in
the South and West of Australia.

For the Mann-Kendall tests on the remaining residuals, eight catchments
have significant trends (Table 6, Figure 7), again more than with the
regression modelling. However, the bootstrap results in Figure 7 suggest
that even fewer of the sites have true trends, with a minimum of one and
a maximum of three of the residual trends clearly falling outside the
bootstrap distribution, including some on the outer edge. The overlap
between the results from the Mann-Kendall residual analysis and the
trend in the GAMM is clear for most of the locations, except for the
very small YARR, for which the residual analysis suggests there is no
significant trend, but the GAMM suggests the linear trend is
significant. In this case, the actual trend might not be linear, but in
general the assumption of a linear trend is not influencing the results.
Moreover, there is clear overlap between the LTPMK analysis and the
traditional Mann-Kendall analysis, with the same stations showing
significance, despite the Hurst coefficient being significant for all
the stations.

\subsection*{Model non-stationarity over long
periods}

{\label{model-non-stationarity-over-long-periods}}

This part of the analysis tested whether numerical models used for the
analysis of trends and elasticities impact the analysis of the
elasticities presented earlier. This is important as several climate
change studies are based on model output analysis (Chiew et al., 2009;
Potter \& Chiew, 2011; Vaze et al., 2011) rather than observed data. As
calibrated models essentially fit a stationary series, the residuals
(between observed and simulated) should retain any existing trend in the
data. This builds on earlier analyses (Buzacott, Tran, van Ogtrop, \&
Vervoort, 2019; Saft et al., 2015; Vaze et al., 2010), which contrasted
calibration differences in dry and wet periods to investigate
non-stationarity.

The result of the Mann-Kendall non-parametric analysis on the weekly
residuals (observed -- predicted) for the 41 years of the data series
indicates significant slopes for only part of the stations (Figure 8).
While there appears to be no consistent pattern, it indicates that for
SimHyd (at least for some of the stations) there are stronger decreasing
trends than for GR4J. In contrast, the residuals of GR4J had more
significant trends in the standard Mann Kendall analysis, but also
predicted some (very small) positive trends. Overall the identified
catchments with significant slopes, CORA COTT, RUTH, SOUT and MURR,
match the GAMM and earlier Mann-Kendall analysis on the data. Again, the
small YARR catchment is an outlier, indicating a significant slope in
the Mann-Kendall analysis, but positive for the GR4J residuals and
negative for the SimHyd residuals. However, in both cases the actual
slope value is very close to 0. Overall this matches the uncertainty for
this catchment indicated in the earlier analyses.

The LTPMK tests however indicated that none of the identified trends
were significant under this test (supplementary documents, document 6A).
This essentially shows that identified slope in the model residuals
exists locally, but currently the overall variation in the data means we
cannot yet affirm a long-term trend in the residuals under the scaling
hypothesis (Hamed, 2008).

Overall, these results are broadly similar to the earlier analyses,
suggesting trends in only some of the South-eastern Australian stations,
but with many of the trends being very small. All analyses also indicate
the largest negative trend for the RUTH catchment.

\section*{Discussion}

{\label{discussion}}

Summarising, this study used multiple approaches to confirm that in
general streamflow in south-eastern Australia is declining based on the
41 years of data, and that this decline tends to be greater than the
associated decline in rainfall (Tables 4 and 6). In other words, there
is significant ``amplification'' of the observed rainfall declines.
However, the overall declines, for small forested catchments and
considering 41 years of data, is (still) very small in percentage and mm
year\textsuperscript{-1} terms, once variability of rainfall and
temperature is accounted for. In addition, using the LTPMK approach,
which accounts for the autocorrelation in the data and test for
significance of the Hurst coefficient, most of the approaches indicated
non-significant trends. This indicates that while there is a clear local
trend in the 41 years of some of the data, we cannot (yet) say with
confidence whether this represents a long-term declining trend in
streamflow.

\subsection*{Comparison to other
studies}

{\label{comparison-to-other-studies}}

In comparison, an analysis of Australian streamflow records for the
latter half of the 20\textsuperscript{th} Century using a Mann-Kendall
test by Chiew and McMahon (1993) found significant declines at 7 of the
30 studied stations. That study points out that due to the high
inter-annual variability of Australian streamflow, a greater change
might be required to identify a statistically significant trend (Chiew
\& McMahon, 1993). A similar observation can be made in this study
considering the significance under the LTPMK test. Significant larger
declines in streamflow have been observed by Petrone et al. (2010), for
catchments in southwest Western Australia between 1950-2008. A more
recent paper identified significant trends in 20 of 199 catchments,
concentrated in the South-East of Australia (Ajami et al., 2017). An
analysis of global data (Milly, Dunne, \& Vecchia, 2005) similarly
indicated decreases in streamflow in Australia, but the database from
that study overlaps with the other studies.

In general, decreasing trends in rainfall in the south east of Australia
and increasing trends in temperature have been widely identified (Cai \&
Cowan, 2012; Chowdhury, Beecham, Boland, \& Piantadosi, 2015; Murphy \&
Timbal, 2008). In contrast, positive trends in rainfall were found in
the 20\textsuperscript{th} Century in earlier studies (Collins \&
Della-Marta, 1999; Smith, 2004), although the data period was suggested
to be an issue (Smith, 2004). Some other studies have found much larger
decreases in annual rainfall (Gallant, Hennesy, \& Risbey, 2007; Murphy
\& Timbal, 2008) in the order of 1 mm per year and greater decreases in
streamflow (Petrone et al., 2010). The differences are most likely
related to the difference in aggregation time scale (annual anomalies
versus weekly data). Another complicating factor could have been that
many of these earlier studies had timeseries to 2008, which was at the
end of the millennium drought (van Dijk et al., 2013), while our study
included the drought breaking year 2010. This ``local trend'' phenomena
can also explain why many of our LTPMK tests showed no significant
trends. This highlights once again the need for careful consideration of
the trend tests applied to the data.

The low rainfall elasticities calculated from the rainfall runoff
simulations (Figure 4) differ from earlier research (Chiew, 2006), which
suggested much higher amplifications from their SimHyd modelling. There
are however differences with the original work (Chiew, 2006), which
could explain the outcomes. Our study simulates the streamflow on a
daily scale and scales this to annual data, while the original work
calibrated on monthly data and scaled to annual. As larger time scales
are smoother and show more significant trends than weekly and daily data
(see the monthly and annual Mann Kendall results in the supplementary
documents, document 3) this could have also affected the amplification
calculations.

There could be differences in the magnitude of the analysed trends in
this study compared to other studies, due to the differences in time
scale. A reduction in variance occurs when the data is summarised to
annual and monthly data (Cai \& Cowan, 2008; Petrone et al., 2010). In
addition, there could be differences due to the translation of remotely
sensed (Ukkola et al., 2015), filtered (Trancoso et al., 2017) or
modelled data (Chiew et al., 2009) to streamflow declines. Several other
studies investigated mainly the difference between decades or specific
periods (Chiew et al., 2014; Potter et al., 2010; Saft et al., 2015).

Furthermore, our work concentrates on 13 single land cover (forested)
small catchments, while several older studies did not control for land
cover, but mainly selected ``unimpaired'' catchments (meaning no water
resource development). The data based analyses (triangles in Figure 4),
and the GAMM modelling supports the magnitude of the amplification
(Chiew, 2006) for the few catchments that showed significant trends.
However, the non-parametric rainfall elasticities (grey triangles in
Figure 4) could be biased (Fu et al., 2007) as this does not take into
account the full interaction between rainfall and temperature.

\subsection*{Remaining trends}

{\label{remaining-trends}}

What the remaining trends in the streamflow (after removing rainfall and
temperature effects) exactly represent is still difficult to say.
Amplification has been mainly explained as an additional drying effect
(Chiew, 2006), mostly driven by the increases in temperature. Given that
in most catchments the remaining trend (Table 6) represents up to 80\%
of the original trend in the streamflow (Table 4), this would correspond
to amplifications around 4 (the data suggests 0.98 - 4.5).

There is no indication that streamflow in these forested catchments has
decreased by a large amount (24 - 28\%) due to increases in
evapotranspiration as a result of CO\textsubscript{2} fertilisation
(Ukkola et al., 2015; van Dijk et al., 2013). Because we selected
homogeneous land cover (forestry), the larger declines found in earlier
studies (Ukkola et al., 2015; van Dijk et al., 2013) might be due to
trends in land management and land cover, such as changes in cropping
patterns, introduction of conservation tillage, or terracing and crop
variety effects. Furthermore, changes in the vegetation water use
efficiencies and changes in the tree physiology (Franks et al., 2013;
Ukkola et al., 2015) can also explain part of the remaining trends.
Conceptually, if trees become more water use efficient and produce more
leaf mass, then this could affect evapotranspiration and streamflow. In
addition, larger leaf area could also result in increased interception,
specifically for smaller rainfall events (Stoof et al., 2012). This
clearly highlights that more work in the area of vegetation effects on
streamflow would be useful, given the dominance of transpiration in the
global water balance (Jasechko et al., 2013), to support investigations
into climate change effects.

\subsection*{Distribution changes}

{\label{distribution-changes}}

Changes in the timing and distribution of rainfall could impact the
amplification of the rainfall signal in the streamflow. Shifts in the
main rainfall season from winter towards summer, or changes in the
average storm depth and timing between rainfall events can all affect
the runoff process (Ishak, Rahman, Westra, Sharma, \& Kuczera, 2013;
Westra et al., 2012) and shift the balance between surface runoff and
groundwater flow. For example, Trancoso et al. (2017) recently found
declines of about 1 mm/year focussing on baseflow. We compared
streamflow and rainfall distribution curves across the four decades in
the data (supplementary data, document 4) but found no obvious or clear
patterns. But this analysis was essentially qualitative and a more
detailed analysis of changes in the distribution of flows and rainfall
is warranted.

\subsection*{Limitations}

{\label{limitations}}

However, there are also some limitations to the present study. Small
catchments might have smaller temperature effects on streamflow (as
there is less time for evaporation to work on the catchment storage).
However, the advantages of controlling for routing and land cover in
smaller catchments were important for this study.

Some of the reasons for the low performance of the GAMM models could be
that the weekly data is too coarse to pick up some of the non-linear
rainfall responses, or that the AR1 model is not complex enough to model
the remaining storage delays in the weekly data despite the small
catchments. However, computational difficulties and missing data make
working with daily data in GAMM challenging.

The low impact of rainfall and ET on explaining variation in streamflow
contrasts the earlier work in this area using mainly linear regression
and with annual and monthly data (Cai \& Cowan, 2008; Potter \& Chiew,
2011). We believe that this difference has to do with the differences in
aggregation time scale and the non-linearity of the processes.

The value of using observed data to analyse trends is that the model
bias (Figure 5) is not affecting the results. However, finding the right
method of analysis is tricky (Fu et al., 2007). We chose to use
statistical modelling to remove the need to make the assumptions related
to mechanistic rainfall-runoff models. This also removes the need for
water balance closure, which can affect the parameter calibration
(Vervoort, Miechels, van Ogtrop, \& Guillaume, 2014).

This study has concentrated on a relatively small group of Australian
catchments as an example, because we controlled for catchment size and
land cover. We identified about 5 more catchments that could be
included, but these were either very small or would skew the spatial
distribution of the catchments. However, future research could be to
take advantage of other (global) long term databases of unimpaired and
forested catchments, such as the Critical Zone Observatories in the US
(Troch et al., 2015) or the well-publicized French catchment database
(Oudin, Andréassian, Perrin, Michel, \& Le Moine, 2008) and other
European catchments (Euser et al., 2013; Fenicia et al., 2014; Kirchner,
2009). This would identify whether the trends in streamflow are unique
to Australia, or link in with global changes in the hydrological cycle
(Huntington, 2006). Another avenue of future research would be to run
the same analysis on a comparison catchment dataset which is strictly
agricultural. Based on this research, we would hypothesise that these
catchments would demonstrate greater changes in streamflow and larger
elasticities.

\section*{Conclusions}

{\label{conclusions}}

This work highlights that trends in streamflow can be difficult to
detect, even using a range of methods. The analysis is sensitive to the
aggregation scale, the noise in the data and the length of the data
series. In this work, only very small downward trends in the streamflow
for 13 hydrological reference stations in Australia were observed
between 1970 -- 2010, and only four stations indicated consistent
statistically significant trends across the different methods applied.
This is despite evidence of increasing trends in temperature in all
catchments, and declining rainfall in the southern part of the
continent. While the analyses identified trends in the 1970 -- 2010
data, the Mann Kendall analysis under scaling hypothesis did not always
identify significant trends, meaning that we cannot yet draw a definite
conclusion on the long term decline in streamflow, but can be definite
about trends in the 41 years under investigation.

In the catchments where a statistical downward trend was detected, only
a small part of the trend could be directly explained by changes in
rainfall and temperature. As a result, extrapolation of models
calibrated on current datasets might bias future predictions,
specifically if the assumption is that the runoff response to rainfall
remains stationary.

Currently there is no clear biophysical explanation for the remaining
negative trends after accounting for rainfall and temperature changes
(the observed amplification). Given that the catchments were chosen
based on homogeneous landcover, this suggests that possible vegetation
effects impact the observed trends. An alternative explanation is that
timing and distribution of rainfall affects the rainfall runoff
response. Both these areas will require further research.

\section*{Data Availability Statement}

{\label{data-availability-statement}}

The data that support the findings of this study are openly available in
https://doi.org/10.5281/zenodo.3757041.

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doi:http://dx.doi.org/10.1016/j.jhydrol.2010.09.018

Vervoort, R. W., Miechels, S. F., van Ogtrop, F. F., \& Guillaume, J. H.
A. (2014). Remotely sensed evapotranspiration to calibrate a lumped
conceptual model: Pitfalls and opportunities. \emph{Journal of
Hydrology, 519, Part D} (0), 3223-3236.
doi:http://dx.doi.org/10.1016/j.jhydrol.2014.10.034

Westra, S., Alexander, L. V., \& Zwiers, F. W. (2012). Global Increasing
Trends in Annual Maximum Daily Precipitation. \emph{Journal of Climate,
26} (11), 3904-3918. doi:10.1175/JCLI-D-12-00502.1

Wood, S. (2006). \emph{Generalized additive models: an introduction with
R} . Boca Raton, FL: CRC Press.

Tables

Table 1 Overview of hydrologic reference stations and characteristics\selectlanguage{english}
\begin{longtable}[]{@{}llllllllll@{}}
\toprule
\textbf{Abbreviation} & \textbf{Gauge Number} & \textbf{State} &
\textbf{Catchment area (km\textsuperscript{2})} & \textbf{Latitude} &
\textbf{Longitude} & \textbf{Mean annual flow (mm)} & \textbf{Rainfall
Station} & \textbf{Mean annual Rain (mm)} & \textbf{HQ maxT
station}\tabularnewline
\midrule
\endhead
\textbf{COTT} & 410730 & ACT & 130 & -35.592 & 148.821 & 327.5 & 70316 &
931.9 & 70351\tabularnewline
\textbf{RUTH} & 219001 & NSW & 14 & -36.593 & 149.442 & 451.3 & 69003 &
789.8 & 70351\tabularnewline
\textbf{CORA} & 215004 & NSW & 166 & -35.147 & 150.033 & 305.5 & 69049 &
774.8 & 68072\tabularnewline
\textbf{ELIZ} & G8150018 & NT & 96 & -12.606 & 131.074 & 643.1 & 14149 &
1711.4 & 14015\tabularnewline
\textbf{COCH} & 113004A & QLD & 95 & -17.74 & 145.629 & 1854.0 & 31083 &
2763.5 & 34084\tabularnewline
\textbf{COEN} & 922101B & QLD & 170 & -13.956 & 143.175 & 685.2 & 27005
& 1258.2 & 27045\tabularnewline
\textbf{SCOT} & A5030502 & SA & 29 & -35.099 & 138.673 & 125.9 & 23734 &
803.3 & 23373\tabularnewline
\textbf{HELL} & 312061 & TAS & 101 & -41.419 & 145.67 & 1316.7 & 91109 &
1427.0 & 96003\tabularnewline
\textbf{NIVE} & 304497 & TAS & 174 & -42.031 & 146.42 & 1098.1 & 91065 &
1124.4 & 96003\tabularnewline
\textbf{MURR} & 405205 & VIC & 106 & -37.414 & 145.564 & 496.4 & 88028 &
838.4 & 85072\tabularnewline
\textbf{SOUT} & 225020A & VIC & 10 & -37.833 & 146.354 & 1330.7 & 85238
& 1119 & 85072\tabularnewline
\textbf{YARR} & 614044 & WA & 80 & -32.812 & 116.155 & 23.4 & 09538 &
1178.2 & 09021\tabularnewline
\textbf{DOMB} & 607155 & WA & 116 & -34.579 & 115.972 & 309.2 & 09590 &
1219.8 & 90518\tabularnewline
\bottomrule
\end{longtable}

Table 2 Overview of different statistical models and trend analysis
related to the models\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
\textbf{No}\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
\textbf{Model}\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
\textbf{Trend}\strut
\end{minipage} & \begin{minipage}[b]{0.22\columnwidth}\raggedright\strut
\textbf{Analysis}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(\text{Log}\left(Q\right)\sim trend+\ \epsilon_{t}\)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
linear\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
40-year trend in streamflow to compare with LTPMK analysis\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(\text{Log}\left(P\right)\sim trend+\ \epsilon_{t}\)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
linear\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
40-year trend in rainfall to compare with LTPMK analysis\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(\text{Log}\left(Q\right)\sim s\left(P\right)+trend+\ \epsilon_{t}\) (equation 4)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
linear\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
The trend in this model relative to model 1 indicates the importance of
``other processes'', while the comparison with model 2 indicates the
``amplification''.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
4\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
\(\text{Log}\left(Q\right)\sim s\left(P\right)+s(maxT,P)+trend+\ \epsilon_{t}\) (equation 6)\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
linear\strut
\end{minipage} & \begin{minipage}[t]{0.24\columnwidth}\raggedright\strut
Difference between model 3 and 4 is the effect of evapotranspiration on
the trend. The remaining trend is related to changes over time in the
rainfall runoff response.\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
\(\text{Log}\left(Q\right)\sim s\left(P\right)+s(maxT,P)+\ \epsilon_{t}\) (equation 7)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Mann Kendall and LTPMK\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Check if linear trend assumption is biased.\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Table 3 Mann-Kendall and Long time period Man Kendall (LTPMK) test
results on de-seasonalised weekly time series.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
& \textbf{Mann Kendall} & \textbf{Mann Kendall} & \textbf{LTPMK}
&\tabularnewline
\midrule
\endhead
\textbf{Catchment} & \textbf{tau} & \textbf{p-value} & \textbf{Hurst
p-value} & \textbf{adj p-value}\tabularnewline
& Stream flow & & &\tabularnewline
COTT & -0.17 & 0.00 & 0.00 & 0.70\tabularnewline
RUTH & -0.25 & 0.00 & 0.00 & 0.39\tabularnewline
CORA & -0.08 & 0.00 & 0.00 & 0.80\tabularnewline
ELIZ & -0.01 & 0.71 & 0.00 & 0.89\tabularnewline
COCH & -0.02 & 0.24 & 0.00 & 0.98\tabularnewline
COEN & -0.02 & 0.18 & 0.00 & 0.98\tabularnewline
SCOT & -0.02 & 0.10 & 0.00 & 0.91\tabularnewline
HELL & -0.10 & 0.00 & 0.00 & 0.88\tabularnewline
NIVE & -0.04 & 0.01 & 0.00 & 0.95\tabularnewline
MURR & -0.22 & 0.00 & 0.00 & 0.63\tabularnewline
SOUT & -0.15 & 0.00 & 0.00 & 0.79\tabularnewline
YARR & -0.15 & 0.00 & 0.00 & 0.69\tabularnewline
DOMB & -0.05 & 0.00 & 0.00 & 0.81\tabularnewline
& Gridded Rainfall & Gridded Rainfall & &\tabularnewline
COTT & -0.05 & 0.00 & 0.00 & 0.04\tabularnewline
RUTH & -0.02 & 0.09 & 0.00 & 0.52\tabularnewline
CORA & -0.02 & 0.22 & 0.00 & 0.58\tabularnewline
ELIZ & 0.01 & 0.59 & 0.00 & 0.98\tabularnewline
COCH & 0.00 & 0.89 & 0.00 & 0.97\tabularnewline
COEN & -0.01 & 0.43 & 0.00 & 0.99\tabularnewline
SCOT & -0.04 & 0.01 & 0.00 & 0.53\tabularnewline
HELL & -0.01 & 0.54 & 0.00 & 0.93\tabularnewline
NIVE & -0.03 & 0.03 & 0.00 & 0.41\tabularnewline
MURR & -0.05 & 0.00 & 0.00 & 0.22\tabularnewline
SOUT & -0.08 & 0.00 & 0.00 & 0.01\tabularnewline
YARR & -0.01 & 0.65 & 0.00 & 0.94\tabularnewline
DOMB & -0.03 & 0.02 & 0.00 & 0.83\tabularnewline
& Maximum Temperature & Maximum Temperature & &\tabularnewline
COTT & 0.14 & 0.00 & 0.00 & 0.90\tabularnewline
RUTH & 0.14 & 0.00 & 0.00 & 0.90\tabularnewline
CORA & 0.07 & 0.00 & 0.00 & 0.93\tabularnewline
ELIZ & 0.07 & 0.00 & 0.00 & 0.85\tabularnewline
COCH & 0.07 & 0.00 & 0.00 & 0.93\tabularnewline
COEN & 0.13 & 0.00 & 0.00 & 0.85\tabularnewline
SCOT & 0.04 & 0.01 & 0.00 & 0.97\tabularnewline
HELL & 0.06 & 0.00 & 0.00 & 0.94\tabularnewline
NIVE & 0.06 & 0.00 & 0.00 & 0.94\tabularnewline
MURR & 0.10 & 0.00 & 0.00 & 0.92\tabularnewline
SOUT & 0.10 & 0.00 & 0.00 & 0.92\tabularnewline
YARR & 0.07 & 0.00 & 0.00 & 0.95\tabularnewline
DOMB & 0.04 & 0.00 & 0.00 & 0.97\tabularnewline
\bottomrule
\end{longtable}

Table 4 log linear trends in streamflow (Q) and rainfall (P), conversion
to \% change and associated p-values (models 1 and 2 in Table 2)\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
\begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{Catchment}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{Linear trend estimate in Q (log scale)
×10\textsuperscript{-4}}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{p- value for trend in Q}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{Trend in Q} \selectlanguage{ngerman}\textbf{(×10\textsuperscript{-4} \%)}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{Linear trend estimate in P ×10\textsuperscript{-4}}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{p-value for trend in P}\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\textbf{Trend in P} \selectlanguage{ngerman}\textbf{(×10\textsuperscript{-4}} \textbf{\%)}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
COTT\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-3.55\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-3.54\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.67\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.67\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
RUTH\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-7.99\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-7.98\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.86\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.86\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
CORA\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-3.23\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-3.23\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.50\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.50\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
ELIZ\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
4.50\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.12\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
8.31\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.44\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
COCH\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.02\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.93\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-0.73\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.40\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
COEN\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
2.59\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.48\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-2.98\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.06\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-2.98\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
SCOT\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-2.85\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.31\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-0.53\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.44\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
HELL\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.68\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.17\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-0.41\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.48\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
NIVE\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-0.63\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.79\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.08\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.04\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.08\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
MURR\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-2.63\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-2.63\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-0.94\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.11\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
SOUT\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.58\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.58\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.67\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.67\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
YARR\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-2.41\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.53\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-0.19\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.83\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
DOMB\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-2.25\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.57\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
-1.05\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
0.24\strut
\end{minipage} & \begin{minipage}[t]{0.12\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Table 5 Results of the GAMM modelling with only P as a smooth term and a
trend (model 3). The results indicate the AIC (Aikaike Information
Criterion) and the estimate of the log transformed trend and the
significance of the trend term, followed by (for those trends that were
significant at p \textless{} 0.05) the trend as \% change in streamflow.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
\textbf{Catchment}\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
\textbf{AIC}\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{Trend estimate (×10\textsuperscript{-4} \%)}\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
\textbf{Trend} \textbf{p-value}\strut
\end{minipage} & \begin{minipage}[b]{0.19\columnwidth}\raggedright\strut
\textbf{Trend} \selectlanguage{ngerman}\textbf{(×10\textsuperscript{-4} \%)}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
COTT\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1347.3\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-2.31\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-2.31\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
RUTH\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1956.8\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-5.37\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-5.37\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
CORA\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
3801.0\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-1.63\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-1.63\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
ELIZ\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2737.1\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-0.30\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.89\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
COCH\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2157.5\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-0.01\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.99\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
COEN\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2790.9\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-0.13\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.95\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
SCOT\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
1561.0\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-0.64\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.45\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
HELL\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2901.6\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-1.37\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.16\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
NIVE\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
3394.7\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-0.61\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.69\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
MURR\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
774.9\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-2.03\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-2.03\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
SOUT\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2239.9\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-1.14\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-1.14\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
YARR\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-512.9\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-1.10\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-1.10\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
DOMB\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
2127.6\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
-1.14\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
0.52\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Table 6 Results of the GAMM modelling with both P and maximum
Temperature as a smooth term (Model 4) including trend analysis. The
first three columns relate to the results of the GAMM model which
includes a trend (model 4), while the second three columns relate to the
GAMM model without a trend (model 5), for which the residuals are
analyzed use a Mann-Kendall test.\selectlanguage{english}
\begin{longtable}[]{@{}llllllllll@{}}
\toprule
\begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\textbf{Catchment}\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\textbf{AIC model 4\textsuperscript{1}}\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\textbf{Trend estimate} \selectlanguage{ngerman}\textbf{(log scale)
×10\textsuperscript{-4}}\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\textbf{Trend p-value}\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\selectlanguage{ngerman}\textbf{Trend\textsuperscript{2} (×10\textsuperscript{-4} \%)}\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\textbf{AIC model 5\textsuperscript{3}}\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\textbf{MK tau residuals}\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\textbf{p-value MK}\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\textbf{p-value Hurst coefficient}\strut
\end{minipage} & \begin{minipage}[b]{0.10\columnwidth}\raggedright\strut
\textbf{Adj p-value}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
COTT\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
997.8\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-2.36\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.06\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-2.36\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1007.8\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.03\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
RUTH\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1746.2\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-5.49\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-5.48\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1777.4\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.12\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.04\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
CORA\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
3803.7\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-1.63\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-1.63\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
3812.3\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.04\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.69\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
ELIZ\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2676.5\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.30\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.89\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2674.7\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.01\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.66\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.15\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.70\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
COCH\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1693.1\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.08\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.94\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1695.2\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.40\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.24\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
COEN\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2780.9\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.16\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.93\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2781.4\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.01\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.34\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.23\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
SCOT\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1555.6\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.66\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.43\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1555.0\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.02\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.28\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.07\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
HELL\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2814.8\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-1.44\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.20\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2824.2\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.02\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.15\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.06\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
NIVE\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
3291.4\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.70\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.69\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
3296.6\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.01\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.49\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.66\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
MURR\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-404.6\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-2.02\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-2.02\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-391.7\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.05\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
SOUT\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1460.1\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-1.25\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.03\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-1.25\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
1468.3\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.03\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.07\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.02\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
YARR\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-514.3\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-1.10\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.02\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-1.10\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-511.7\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-0.01\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.37\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.12\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
DOMB\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2131.5\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
-1.14\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.52\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
2129.8\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.88\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.00\strut
\end{minipage} & \begin{minipage}[t]{0.07\columnwidth}\raggedright\strut
0.85\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\textsuperscript{1}Trend included in the GAMM
model.\textsuperscript{2}Backtransformed trend which is interpreted as a
percentage of the flow. \textsuperscript{3}no trend in the model,
Mann-Kendall trend analysis on the residuals. The Mann-Kendall tau is
similar to a correlation coefficient and varies between -1 to +1

Figure Legends

Figure 1 Location of hydrologic reference stations used in the study
(http://www.bom.gov.au/water/hrs/)

Figure 2 Flowchart of the different approaches and comparisons of trends
and significance used in the methodology

Figure 3 Annual rainfall runoff relationships for all the catchments
based on the available 41 years of streamflow data and associated
gridded rainfall data.

Figure 4 Rainfall elasticities calculated from the original streamflow
and gridded rainfall data using a non-parametric method (Chiew, 2006)
(red triangles). Also plotted are the rainfall elasticities calculated
from the streamflow simulations of the two different rainfall runoff
models (SimHyd and GR4J) using the gridded rainfall data. As the model
calibrations were replicated 10 times to estimate parameter
equifinality, the elasticities from the rainfall-runoff models are
actually distributions. This equifinality is in most cases very small
and the boxplots show up as single horizontal gray lines. Outliers from
the boxplots are shown as light gray dots, median values of the boxplots
are shown as blue points.

Figure 5 Boxplots and median values (black dots) for goodness of fit of
the GR4J and SimHyd calibrations on the 1970 - 2010 daily data using the
gridded rainfall data. The goodness of fit is indicated by the Nash
Sutcliffe Efficiency, which is equal to 1 for a perfect fit, and 0 for a
fit equal to the mean daily streamflow. Because most of the catchments,
and particularly the GR4J model, had very small equifinality
(variability between repeated calibrations), the boxplots are only
visible as horizontal lines.

Figure 6 Mann Kendall trends (tau) for deseasonalised streamflow for the
different catchments, against the distribution of slope results of a
bootstrap analysis. Black points that are located outside the bootstrap
distribution can be confidently seen as highly significant and not
related to possible trends in random data.

Figure 7 Mann-Kendall tau values (Dot points) and tau results of the
bootstrapped residual trend analysis (distribution histograms) for the
residuals of the GAMM analysis.

Figure 8 Analysis of residual trends between modelled and observed data
for the models based on the 1970 -- 2010 data. Red distribution boxes
are significant (p value \textless{} 0.05), while blue boxes are not
significant. The actual p-values can be found in the supplementary
material (document 6A). Boxplots represent the 10 replications of the
calibration. As in Figure 5, the variation between the calibration
replications is very small, especially for GR4J, in some of the
catchments resulting in the boxplots plotting as straight lines.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure1-MapOZMDPaper/Figure1-MapOZMDPaper}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure2-new-FlowChart/Figure2-new-FlowChart}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure3-GriddedRainfallRunoffPlot/Figure3-GriddedRainfallRunoffPlot}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure4-RainfallElasticityPlot/Figure4-RainfallElasticityPlot}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure5-ModelCalStats/Figure5-ModelCalStats}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure6-MKdeseasonalisedStreamflow/Figure6-MKdeseasonalisedStreamflow}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure7-ResidGAM-MDPaper/Figure7-ResidGAM-MDPaper}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure8-ModelResidualTrendPlot/Figure8-ModelResidualTrendPlot}

\end{center}
\end{figure}

\selectlanguage{english}
\FloatBarrier
\end{document}

