2.2.1 Gauging stations in the 2020 update

Of the existing 222 gauging stations in the network prior to the service (Zhang et al., 2016), 12 have now been decommissioned by the data-provision agencies, including 5 from the Northern Territory, 2 from Victoria, 2 from Western Australia, 1 from New South Wales and 2 from South Australia. The revised and updated selection guidelines were applied to all 222 gauging stations, and 179 of these stations passed the new guidelines. More information about the rating curves of 43 existing stations became available and suggested that these stations did not pass the selection criteria. Therefore, these 43 stations were removed from the HRS service in 2020 (Table 1).

Table 1Total number of stations.

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2.2.2 New stations included in the service

Australia's instrumental record is relatively sparse before 1940, and few locations have continuous rainfall measurement before 1900. At present, there are approximately 4800 streamflow gauging stations across Australia. Many of these stations previously had insufficient data in the Bureau's system to be considered for the HRS service. Over recent years, more data have become available, and a set of 780 stations identified by Zhang et al. (2013) were selected for further investigation. These 780 unregulated, unimpaired catchments are widely spread across Australia (Fig. 1) and have undergone strict quality assurance/quality control (QA/QC), including quality code checking for daily streamflow records (Zhang et al., 2013). The total number of streamflow gauging stations that met the new guidelines and are now included in the service is 467, which is an increase from 222 stations (Table 1).

Figure 1Map of Australia showing climate zones, drainage divisions and the location of all gauges (new, existing and decommissioned), all scaled to length of record.

2.2.3 Reference period, quality control and catchment description

The HRS service was updated with streamflow data ending in February 2019. This month was chosen to capture the 2018 water year for all stations. Commencement of recording of streamflow data varies across the country. The longest record begins in the 1950s and the shortest begins in the 1980s. Figure 1 shows the location of stations and the duration of the records, including the eight decommissioned stations. Data recorded at stations prior to 1950 were excluded from analysis, as the missing data were more than 5 % before this time in most cases. Stations with the longest records are generally those in the high-value water resource catchments and populated areas along the coastal regions. Upstream catchment area also varied across the country (from 4.5 to 232 846 km²) and in different hydroclimatic regions (Table 2). Most of the catchment areas ranged from 50 to 10 000 km² (Table 2). The number of stations distributed across different drainage divisions varies substantially: the Murray–Darling division has the largest number of stations, whereas the South Western Plateau division has no stations at all. Drainage divisions are defined according to Australian Hydrological Geospatial Fabric (Geofabric) (Atkinson et al., 2008). In a previous update of the HRS service (Zhang et al., 2016), there were no stations in the Pilbara–Gascoyne and North Western Plateau divisions. In the current version, there are 10 and 2 stations in these divisions respectively (Fig. 1, Table 2).

Table 2Metadata for drainage divisions and selected hydrologic reference stations.

^* Calculated from monthly gridded rainfall and potential evapotranspiration (PET) data (5 km × 5 km) from the Australian Water Availability Project – AWAP (Raupach et al., 2009).

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Continental Australia has a wide range of climate zones, as defined by Köppen climate classification (Stern et al., 2000), including a tropical region in the north, temperate regions in the south, and grassland and desert in the vast interior (Fig. 1). In this work, water year is defined in accordance with the Hydrologic Reference Stations' glossary (http://www.bom.gov.au/water/hrs/glossary.shtml, last access: 3 January 2023). It varies across the country – beginning in February–March in the south and in September–October in the north (Table 2). Annual average rainfall for each of the divisions varies from 201 to 1333 mm. Annual average potential evapotranspiration (PET) is generally higher than the annual average rainfall. Therefore, the streamflow generation process in most of the divisions is controlled by water-limited environments (Milly et al., 2005) except for the Tasmanian division (Table 2). Figure 2a shows the relationship between the catchment area and record length. Figure 2b, in contrast, shows the relationship between the catchment area and the distribution of the percentage of catchments: the distribution is reasonably uniformly distributed in the range between 45 and 12 000 km² and is slightly skewed outside of this range. The longest period of record is 69 years for several catchments with an area from 14 to 15 850 km².

Figure 2Catchment area plotted against (a) the length of record and (b) the percentage of catchments.

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A QA/QC process was applied to observed time series of daily streamflow from each gauging station. This process identified and removed erroneous data values such as negative and extreme values. The process of detection and removal was automated and then checked manually, as detailed on the Hydrologic Reference Stations website (http://www.bom.gov.au/water/hrs/references.shtml, last access: 3 January 2023). The GR4J model (Perrin et al., 2003) was adopted to infill any missing data in accordance with the selection guidelines detailed in Sect. 2.1. The mean and standard deviation of the Nash–Sutcliffe efficiency for all 467 catchments was 0.74 and 0.12 respectively. As part of this process, a simple error correction procedure was used to ensure that the initial and final estimated flows matched adjacent observed values. This was done by linearly interpolating the start and end of the infilled period to the observed flows. Via this process, a continuous quality-checked daily streamflow time series was created for trend analyses.

3.1.1 The Theil–Sen approach

The magnitude of the trend is obtained using the Theil–Sen approach (Theil, 1992; Sen, 1968), where the magnitude of the slope of the trend is estimated as follows:

Here, x_i and x_j are streamflow data (annual and all seasons) at time points i and j respectively. If the time series has n values, there will be $N=n(n-\mathrm{1})/\mathrm{2}$ slope estimates, and the Theil–Sen slope β is taken as the median of these N values.

3.1.2 Independent Mann–Kendall (MK1) test

The Mann–Kendall test statistic (S) for a series x₁, x₂, x₃, …, x_n is given by

where

The test statistic S is approximately normally distributed for n≥8 with zero mean. The variance as given as follows:

where m is the number of tied groups, and t_i is the number of data in the ith tied group. The standardized test statistic Z (standard normal distribution) is given as follows:

To identify and address the short-term and long-term persistence in a streamflow series, we used three modified versions the of Mann–Kendall test for monotonic trend analyses: (i) the variance correction approach, (ii) the block bootstrap approach and (iii) the long-term persistence approach.

3.1.3 Mann–Kendall (MK3) test – variance correction approach

The modified Mann–Kendall variance correction approach, proposed by Hamed and Ramachandra Rao (1998), considers all of the significant autocorrelation structure in a time series. The series x_i was ranked, and an autocorrelation coefficient of rank i of time series was obtained to consider only the significant terms at the 10 % significance level. Autocorrelation becomes insignificant after a lag of 3 (Rao et al., 2003). The effect of all significant autocorrelation coefficients in the dataset was removed using a modified variance of S, described as V(S)^*:

where n^* represents the effective sample size. The $\frac{n}{n^{*}}$ ratio was computed directly from the equation proposed by Hamed and Ramachandra Rao (1998) as follows:

where n is the number of observations, and r_i is the lag-i significant autocorrelation coefficient of rank i of time series. V(S)^* is calculated using Eq. (6) and using V(S) from Eq. (4). Finally, the Mann–Kendall Z was tested for significance of trend by comparing it with threshold levels.

3.1.4 Mann–Kendall (MK3bs) test – block bootstrap (BBS) approach

The block bootstrap (BBS) approach by Önöz and Bayazit (2003) was used to mitigate the effects of serial correlation in datasets by performing bootstrapping (in blocks of data) so that the autocorrelation in the data is replicated. Data are resampled in blocks many times to estimate the significance of the observed Mann–Kendall test statistic S from the data sample while reflecting the serial correlation present in the dataset (Burn et al., 2016). Block length should be chosen so that data points in adjacent block are more or less independent. Khaliq et al. (2009) provide a detailed description of the steps involved in implementing the BBS approach.

In block bootstrapping, the simulation size N_s (the number of bootstrap samples to be generated in each case) and the block length L_b are the parameters whose values are to be chosen. The simulation size (N_s) is related to the level of significance required and the loss of power that can be allowed. Svensson et al. (2005) found that N_s=2000 samples resulted in good stability in significance level estimates. The block length chosen depends on autocorrelation of the data and should be larger than the lag k of the smallest significant autocorrelation coefficient R_i. Svensson et al. (2005) found that blocks with lengths of 5 were generally sufficient for most streamflow series.

Autocorrelation in time series varies across different sites, and Politis (2003) recommends that the block length L_b is based on individual time series. To identify the optimal block length (L_b) for individual annual and seasonal streamflow time series, an automatic block length selection procedure, proposed by Politis and White (2004), was used. The optimal block lengths obtained for the annual streamflow time series and for each of the four seasonal streamflow time series for 467 gauging stations are shown in Fig. 3. In general, more than one-third of the stations exhibit significant serial correlation of 2 or more (L_b≥3), and about 15 % of the stations are serially uncorrelated (L_b=1).

Figure 3The optimal block length for the annual streamflow time series and the four seasonal streamflow time series for all 467 stations.

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We estimated the significance of the original Mann–Kendall test statistic S (Eq. 2) of the observed data from the simulated distribution, developed from the resampled distribution of S from the moving block bootstrap procedure. The test statistic is only likely to be significant if the original test statistic lies within the tails of the simulated distribution (Do et al., 2017; Khaliq et al., 2009).

3.1.5 Mann–Kendall (MK4) test – long-term persistence (LTP)

The long-term persistence (LTP) version of the Mann–Kendall method was proposed by Hamed (2008) and described by Kumar et al. (2009), and it considers the Hurst coefficient (Hurst, 1951), H, of a series for LTP. The coefficient H is used as a measure of long-term memory, i.e. autocorrelation of the time series. An H value of 0.5 indicates a true random walk, which implies that the time series has no memory for previous values of observations. An H value between 0.5 (0) and 1 (0.5) indicates a time series with positive (negative) autocorrelation, e.g. an increase (decrease) between observations will probably followed by another increase (decrease).

In this study, the following steps were carried out to apply the MK4 test:

1. The Hurst coefficient (H) is calculated. A new trend-free time series $x_i^{\prime }$ is calculated using

   $$\begin{array}{}\text{(8)}& x_i^{\prime }=x_i-(\mathit{\beta }\times i),\end{array}$$

   where β is the slope of a trend line using the Theil–Sen approach, and x_i is the streamflow data. Using the ranks of trend-free series [$x_i^{\prime }:(i=\mathrm{1}:n)$] designated by R_i, the standardized Z_i variate (the equivalent normal variates of the ranks of detrended time series) is computed as

   $$\begin{array}{}\text{(9)}& Z_i={\mathit{\phi }}^{-\mathrm{1}}\left({\displaystyle \frac{R_i}{n+\mathrm{1}}}\right),\end{array}$$

   where n is the number of streamflow data, and φ⁻¹ is the inverse of the normal distribution function. Considering the hypothesis that the hydrometeorological processes exhibit scale-invariant properties at any scale greater than annual (Koutsoyiannis, 2003), the elements of the Hurst matrix for a given H are computed as

   $$\begin{array}{}\text{(10)}& {\mathbf{C}}_{\mathrm{n}}\left(H\right)=⌊{\mathit{\rho }}_{|j-i|}\left(H\right)⌋\mathrm{for}i=\mathrm{1}:n,j=\mathrm{1}:n.\end{array}$$

   In the above equation, ρ_l(H) is the lag-l autocorrelation coefficient for a given H and is calculated as

   $$\begin{array}{}\text{(11)}& {\mathit{\rho }}_l\left(H\right)={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\left(|l+\mathrm{1}{|}^{\mathrm{2}H}-\mathrm{2}{l}^{\mathrm{2}H}+|l-\mathrm{1}{|}^{\mathrm{2}H}\right)\mathrm{for}l>\mathrm{0}.\end{array}$$

   The log-likelihood function of n normal observations with a scaling coefficient H is given by Eq. (12) (McLeod and Hipel, 1978), where the accurate value of H can be computed by maximizing the function of H as

   $$\begin{array}{}\text{(12)}& \log L\left(H\right)=-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\log \mathrm{|}{\mathbf{C}}_n\left(H\right)\mathrm{|}-{\displaystyle \frac{Z^{\mathrm{T}}\mathrm{|}{\mathbf{C}}_n\left(H\right){\mathrm{|}}^{-\mathrm{1}}\mathit{Z}}{\mathrm{2}{\mathit{\gamma }}_{\mathrm{0}}}}.\end{array}$$

   In the above equation, Z^T is the transpose of vector Z obtained from Eq. (9), γ₀ equates the variance of Z_i, and C_n(H) and C_n(H)⁻¹ are the Hurst matrix and the inverse of the Hurst matrix respectively. These two last matrices can be obtained using Eq. (10). To maximize log L(H), H is assumed to be in the range of 0.5–0.98, and the mentioned function is computed for a given H. The procedure is repeated for other H values with 0.01 steps. The H value producing the maximum value of log L(H) is taken as the answer.

2. The mean and standard deviation of H are calculated. According to Hamed (2008), the respective mean and standard deviation of H are expressed as a function of n as

   $$\begin{array}{}\text{(13)}& {\displaystyle }& {\displaystyle }{\mathit{\mu }}_{\mathrm{H}}=\mathrm{0.5}-\mathrm{2.87}{n}^{-\mathrm{0.9067}},\text{and}\text{(14)}& {\displaystyle }& {\displaystyle }{\mathit{\sigma }}_{\mathrm{H}}=\mathrm{0.77654}{n}^{-\mathrm{0.5}}-\mathrm{0.0062}.\end{array}$$

   Z_cal is then calculated as

   $$\begin{array}{}\text{(15)}& Z_{\mathrm{cal}}={\displaystyle \frac{H-{\mathit{\mu }}_{\mathrm{H}}}{{\mathit{\sigma }}_{\mathrm{H}}}}.\end{array}$$

   This Z_cal, obtained from Eq. (15), was tested for significance of trend at the 10 % significance level. The MK4 procedure was continued if Z_cal was greater than the critical normal value (1.645); otherwise, the procedure for an independent Mann–Kendall (MK1) test was adapted as the LTP was not significant.

3. Significant H values are computed (LTP is significant). The modified variance for the S statistic was computed as recommended by Kumar et al. (2009) and Hamed (2009). This took the form of

   $$\begin{array}{}\text{(16)}& \begin{array}{rl}V(S{)}^{H^{\prime }}=& \sum _{i=\mathrm{1}}^{n-\mathrm{1}}\sum _{j=i+\mathrm{1}}^n\sum _{k=\mathrm{1}}^{n-\mathrm{1}}\sum _{l=k+\mathrm{1}}^n{\displaystyle \frac{\mathrm{2}}{\mathit{\pi }}}{\sin }^{-\mathrm{1}}\\ & \left({\displaystyle \frac{\mathit{\rho }|j-l|-\mathit{\rho }|i-l|-\mathit{\rho }|j-k|+\mathit{\rho }|i-k|}{\sqrt{(\mathrm{2}-\mathrm{2}\mathit{\rho }|i-j\left|\right)(\mathrm{2}-\mathrm{2}\mathit{\rho }|k-l\left|\right)}}}\right).\end{array}\end{array}$$

   In the above equation, ρ_l is calculated using Eq. (11) for a given value of H. As $V(S{)}^{H^{\prime }}$ is a biased estimator, we have corrected it for bias using

   $$\begin{array}{}\text{(17)}& V(S{)}^H=V(S{)}^{H^{\prime }}\times B,\end{array}$$

   where B is expressed as a function of sample size, n (Hamed, 2008; Kumar et al., 2009).

   $$\begin{array}{}\text{(18)}& B=a_{\mathrm{0}}+a_{\mathrm{1}}H+a_{\mathrm{2}}{H}^{\mathrm{2}}+a_{\mathrm{3}}{H}^{\mathrm{3}}+a_{\mathrm{4}}{H}^{\mathrm{4}}\end{array}$$
   $$\begin{array}{}\text{(19a)}& {\displaystyle }& {\displaystyle }{a}_{\mathrm{0}}={\displaystyle \frac{\mathrm{1.0024}n-\mathrm{2.5681}}{n+\mathrm{18.6693}}}\text{(19b)}& {\displaystyle }& {\displaystyle }{a}_{\mathrm{1}}={\displaystyle \frac{-\mathrm{2.2510}n+\mathrm{157.2075}}{n+\mathrm{9.2245}}}\text{(19c)}& {\displaystyle }& {\displaystyle }{a}_{\mathrm{2}}={\displaystyle \frac{\mathrm{15.3402}n-\mathrm{188.6140}}{n+\mathrm{5.8917}}}\text{(19d)}& {\displaystyle }& {\displaystyle }{a}_{\mathrm{3}}={\displaystyle \frac{-\mathrm{31.4258}n+\mathrm{549.8599}}{n-\mathrm{1.1040}}}\text{(19e)}& {\displaystyle }& {\displaystyle }{a}_{\mathrm{4}}={\displaystyle \frac{\mathrm{20.7988}n-\mathrm{419.0402}}{n-\mathrm{1.9248}}}\end{array}$$

   When using the MK4 method, V(S)^H obtained from Eq. (17) was used as V(S) in Eq. (5) of the MK1. The significance of Z was then tested for significance of a trend.

4.1.1 Theil–Sen approach

Box plots of trend slopes estimated by the Theil–Sen approach for annual and seasonal streamflow in the southern and northern divisions that were significant are shown in Fig. 4. For example, the trend slope for a site in the South Esk River in Tasmania is shown in Fig. 5a, where the decrease in annual streamflow is 5.91 GL yr⁻¹r (1.8 mm yr⁻¹ yr⁻¹). For drainage divisions in the south, the medians of slopes for all annual and seasonal streamflows were less than zero. The lowest trend line slope (−2.07 mm yr⁻¹ yr⁻¹) occurred in spring (September–November), and the median of slopes in autumn (March–May) is less negative than the other three seasons in the southern parts of Australia (Fig. 4a). Streamflow in all four seasons showed a downward trend in the southern divisions. Approximately 60 % of the annual streamflow volumes in the southern drainage divisions occur in winter and spring (between June and November). For annual flows in the south, slopes were between −6.5 and −0.07 mm yr⁻¹ yr⁻¹ (Fig. 4a), and the median of slopes was approximately −1.79 mm yr⁻¹ yr⁻¹ .

Figure 5Typical examples of (a) trend and (b) step change in annual streamflow in southern and northern Australia.

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Medians of slopes for annual and seasonal streamflow were located close to or above zero for drainage divisions in the northern part of Australia (Fig. 4b). The highest (+7.13 mm yr⁻¹ yr⁻¹) trend line slope occurred in the summer (December–February). The median of trend line slopes in summer (+1.02 mm yr⁻¹ yr⁻¹) is higher than that in the other three seasons (all <0.01 mm yr⁻¹ yr⁻¹) in the northern divisions. Streamflow in all seasons, except in summer, showed negligible trends in the northern parts of Australia. More than 90 % of the annual streamflow volumes in the northern drainage divisions occur in summer and autumn (December–May). For annual flows, slopes were between +12.1 and −6.0 mm yr⁻¹ yr⁻¹ (Fig. 4b), and the median of slopes was approximately +1.46 mm yr⁻¹ yr⁻¹. Figure 5a shows a typical example of linear trend analysis using the Theil–Sen approach for annual streamflow in southern Australia.

4.1.2 Monotonic trend – short-term persistence (STP) and long-term persistence (LTP)

Streamflow data from stations that are significantly autocorrelated (lag 1 or more) at p<0.10 and H values that are significant at p<0.10 are considered to have short-term persistence (STP) and long-term persistence (LTP) respectively. To analyse the presence of STP and LTP, results from the MK3 and MK4 tests were examined respectively. In the South East Coast (II), South West Coast (VI) and southern Murray–Darling Basin (IV) divisions, most stations showed significant STP, LTP, or both STP and LTP for the water year and for all four seasons (Fig. 6). Across water years and all seasons, the percentage of stations with STP was greater than that with only LTP or that with both STP and LTP. For water years, data from 88 % of stations showed STP and data from 28 % of stations showed LTP across Australia. However, LTP was evident mainly in the southern and south-eastern parts of Australia (divisions II, III, IV, V, VI) and in the north in the Carpentaria Coast (IX) division. Seasonally, autumn had the highest number of stations (221) with LTP persistence.

Figure 6Spatial distribution of stations where streamflow shows persistence, short-term persistence (STP) and long-term persistence (LTP), in (a) autumn (March–May), (b) winter (June–August), (c) spring (September–November), (d) summer (December–February) and (e) annually (water year) at p<0.10.

Data from stations with a significant correlation at p<0.10 with STP and LTP were tested for trends (Table 3) using the MK3 and MK4 tests respectively. Of the 412 stations with significant STP across water years, 196 stations showed trends from the MK3 test. Of the 130 stations with data showing significant LTP, 14 had significant trends from the MK4 test. In drainage divisions II to VI in the south, nearly half of the stations showed significant trends with STP. However, results vary slightly across different drainage divisions for the four seasons. In autumn, 33 % of the 87 % of stations with significant STP showed trends, whereas 6 % of the 47 % of stations with significant LTP showed trends. Similarly, in winter, 39 % of the 86 % of stations with significant STP showed trends, whereas 3 % of the 27 % of stations with significant LTP showed trends. In spring, 44 % of the 85 % of stations with significant STP showed trends, whereas 2 % of the 24 % of stations with significant LTP showed trends. In summer, 36 % of the 81 % of stations with significant STP showed trends, whereas 3 % of the 19 % of stations with significant LTP showed trends.

Table 3Summary of stations with short-term persistence (STP) and long-term persistence (LTP) of streamflow and of stations that showed trends using the MK3 and MK4 tests across drainage divisions for the water year and the four seasons at p≤0.10. The numbers in each column show the STP or LTP and the trend (as stated in each respective column) separated by a slash.

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4.1.3 Monotonic trends – MK tests

Table 4 summarizes the MK3, MK3bs and MK4 test results. Figure 7 shows the distribution of trends for each drainage division for the water year, autumn, winter, spring and summer for all three MK tests. The MK3 test results are similar to the MK3bs test results for water years and all four seasons, as they both consider the full autocorrelation structure (STP) of the streamflow series. The spatial distribution of trends using all three MK tests in the water year suggests that the annual mean streamflow has increased in the Tanami–Timor Sea Coast division in northern Australia, whereas it has decreased in the south-western and south-eastern parts of the country (Fig. 7). The magnitude trends in streamflow volumes expressed by the Theil–Sen slope show a maximum increase of 2.4 % yr⁻¹ at one station in the Tanami–Timor Sea Coast (VIII) division and a maximum decrease of −3.9 % yr⁻¹ at one station in the Murray–Darling Basin (IV) division over a period of at least 50 years. The MK3 test results are almost like those of the MK3bs test for water years and all four seasons, as they both consider the full autocorrelation structure (STP) of the streamflow series. Therefore, the MK3 test results are initially analysed.

Table 4Results of the three Mann–Kendall (MK) tests, MK3, MK3bs and MK4, for the water year and all four seasons. The numbers in each column represent the number of stations with increasing trends (denoted using “+”) and the number of stations with decreasing trends (denoted using “−”) separated by a slash.

Entries in bold indicate results that are regionally significant at p<0.10.

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Figure 7Maps showing seasonal trends using the (a) MK3, (b) MK3bs and (c) MK4 tests. Results are reported for autumn, winter, spring, summer and annually (water year) (p<0.1). Upward-pointing triangles (green) indicate significant increasing trends, and downward-pointing triangles (red) indicate significant decreasing trends. Grey dots indicate stations with no trends. Drainage divisions with positive and negative trends with regional significance at p<0.10 are coloured blue and yellow respectively.

Although most of the 467 streamflow stations showed trends, only 14 stations had data with increasing trends across water years, and 212 stations showed decreasing trends that were statistically significant (Table 4). With respect to water year, more than 50 % of stations with increasing trends were located in the Tanami–Timor Sea Coast (VIII) drainage division. Streamflows that showed decreasing trends were within the South East Coast (II), Tasmania (III), Murray–Darling Basin (IV), South Australian Gulf (V) and South West Coast (IV) drainage divisions. Most stations in other divisions showed no significant trend (Fig. 7)

For autumn (March–May), streamflows at more than 50 % of stations showed significant trends in the South East Coast (II), Tasmania (III), Murray–Darling Basin (IV), South Australian Gulf (V), South West Coast (IV) and North East Coast (I) divisions. Other divisions showed autumn decreasing trends that were very similar to those found across water years, except for the Tanami–Timor Sea Coast (VIII) in the north, where only one station showed an increasing trend. Data from 173 stations showed significant trends across water years, 4 of which were increasing and 169  of which were decreasing (Table 4). In autumn, the maximum increase in streamflow was 1.3 % yr⁻¹, and the maximum decrease was −5.8 % yr⁻¹. Both trends were at stations in the South West Coast (IV) division.

Across winter (June–August), streamflows at over half of the stations showed significant decreasing streamflow trends in the North East Coast (I), Tasmania (III), Murray–Darling Basin (IV), and South West Coast (IV) divisions, whereas they showed significant increasing trends in the Tanami–Timor Sea Coast (VIII) division. However, in the South East Coast (II), Pilbara–Gascoyne (VII), Carpentaria Coast (IX) and the Lake Eyre Basin (X) divisions, fewer than 50 % of stations had flows with significant trends. A total of 189 stations showed significant streamflow trends (for MK3) across Australia, 9 of which were increasing trends and 180 of which were decreasing trends (Table 4). The maximum increase in winter flows was 2.3 % yr⁻¹ (in the Tanami–Timor Sea Coast (VIII) division) and the maximum decrease was −3.4 % yr⁻¹ (in the Murray–Darling Basin (IV) division). For stations in the Murray–Darling Basin (IV) division, significant trends varied between −0.5 % and −3.4 % (median of −1.3 % yr⁻¹).

Spring (September–November) saw more stations with decreasing flow trends compared with water years or the other seasons. Trends in flow were mostly detected at stations in all divisions except for Lake Eyre Basin (X) and North Western Plateau (XI), for which there is very limited flow data. The South East Coast (II) and Murray–Darling Basin (IV) divisions had the highest number of stations with decreasing trends in streamflow, compared with trends in the water year and other seasons (Table 4). There were stations in the South East Coast (II), Tasmania (III), Murray–Darling Basin (IV) and South Australian Gulf (V) that showed significant decreasing trends. For spring (September–November), 235 stations showed significant trends: 8 increasing and 227 decreasing (Table 4). The maximum increase in spring flows was 3.1 % yr⁻¹ (in the Tanami–Timor Sea Coast (VIII) division), and the maximum decrease was −2.8 % yr⁻¹ (in the South West Coast (IV) division).

For summer (December–February), stations in the Tanami–Timor Sea Coast (VIII) division showed significant increasing flow trends, as with trends in other seasons. Stations in the South East Coast (II), Tasmania (III), Murray–Darling Basin (IV), South Australian Gulf (V) and South West Coast (VI) divisions showed significant decreasing trends in flow. In summer, 175 stations showed significant flow trends: 26 increasing and 149 decreasing (Table 4). The maximum increase in summer flows was −2.1 % yr⁻¹ (in the Tanami–Timor Sea Coast (VIII) division) and the maximum decrease was −5.0 % yr⁻¹ (in the South West Coast (IV) division).

While results from the MK3 and MK3bs tests are nearly identical for most cases, MK3 and MK4 do show differences for most annual and seasonal flow statistics. A typical example of the MK3bs statistic obtained from 2000 samples from two locations with (a) decreasing and (b) increasing trends is shown in Fig. 8. It illustrates how the observed values are located below or above the 5th and 95th percentiles respectively. A small number of stations have significant streamflow trends when LTP behaviour (MK4) is considered (Fig. 7, Table 4). This is particularly evident in the South East Coast (II) division for water years and in the Murray–Darling Basin (IV) division for autumn (Fig. 7, Table 4). The MK4 test resulted in more stations with trends in winter and spring, compared with autumn and summer. Across Australia for water years, 14 stations showed significantly increasing trends in flow, and 196 stations showed significantly decreasing trends, slightly less than the MK3 and MK3bs test results (Table 4). Similar results are also evident for the four seasons across Australia (Table 4).

Figure 8Examples of histograms for two stations representing the frequency distribution of the MK statistic (S) obtained from 2000 samples of moving block bootstrap iterations; red triangles are observed values, and dotted lines show the 5th and 95th percentiles for (a) a decreasing trend and (b) an increasing trend in the Tasmania (III) and Carpentaria Coast (IX) divisions respectively.

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