Results
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 (εp, 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 > 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).
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 < 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 < 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.
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 10-4 % 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 < 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 < Adj r 2 <
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 × 10-4 % 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 < 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.
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.