1 Introduction

Climate change effects are a major concern, with frequent abnormal climate occurrences (Sivakumar 2011). These events have greatly influenced the hydrological cycle and changes in specific hydroclimate variables, including rainfall, temperature, and streamflow (Getahun et al. 2021; Portela et al. 2009). It is essential to comprehend the variability of the hydroclimate, encompassing the fluctuation of extremes and means at various spatial and temporal scales. The inter-annual hydroclimate can vary significantly, making it difficult to detect statistically significant changes in the climate (Rashid et al. 2015b; Swain et al. 2021; Tolika 2018). Australia’s rainfall and streamflow patterns are highly variable both spatially and temporally (Franks 2004; Rashid et al. 2015a).

Time series analysis is vital for comprehending the characteristics of events, which can be instrumental in the strategic planning of infrastructure and early warning systems (Shumway and Stoffer 2006). Hydroclimatic time series can reveal trends (either increasing or decreasing) and change points that could be attributed to climate change factors such as increased greenhouse gas concentrations, land use changes, and management techniques (Almazroui and Şen 2020; Machiwal and Jha 2012; Şen 2017a, b). Trends and variability studies of hydroclimate variables are essential for gaining a better understanding of the time series and making informed decisions when considering adaptation and mitigation options to address the impacts of climate change (Phuong et al. 2022). Homogeneity tests aid in the detection of changes in the hydrologic regime by assessing the consistency of a time series between two distinct periods, taking into account alterations in distribution, mean, or the presence of a trend (Daba et al. 2020; Malede et al. 2022; Queen et al. 2023; Zhang et al. 2016). Various techniques including Pettitt’s test (Pettitt 1979), Von Neumann ratio test (Von Neumann 1941), standard normal homogeneity test (SNHT) (Alexandersson 1986), and the Buishand range test (Buishand 1982) have been utilized in evaluating the homogeneity of hydro-climatic time series. However, the analysis of homogeneity tests depends on the selected significance level, test algorithm, and test variable. Consequently, it is essential to employ a comprehensive approach that incorporates multiple statistical methods (Bickici Arikan and Kahya 2019; Daba et al. 2020; Wijngaard et al. 2003) that helps in addressing the possible uncertainties that may arise from solely relying on the results of a single methodology.

The parametric (e.g. linear regression) and non-parametric (e.g. Mann–Kendall, Spearman’s rho tests) tests are used to assess the trend of hydrometeorological variables (Chowdhury et al. 2015; Swain et al. 2021; Tenagashaw et al. 2023). The Mann–Kendall test is frequently used for trend analysis (Farooq et al. 2021; Hamadalnel et al. 2021; Imam et al. 2022); nevertheless, its efficacy is constrained in cases involving serial correlation and nonmonotonic trends. The presence of serial correlation has a significant impact on the probability of rejecting the null hypothesis, which asserts that there is no trend in the time series (Douglas et al. 2000; Yue et al. 2003). To tackle this issue, pre-whitening techniques are employed to eliminate autocorrelation before performing the Mann–Kendall test (Bayazit and Önöz, 2007; Gupta et al. 2021; Yue and Wang 2002). However, these methods decrease the statistical power and distort the true trend (Şen 2017a, b; Yue and Wang 2002). Nowadays, a Trend-Free Pre-Whitening Mann–Kendall (TFPW-MK) test (Yue et al. 2002a, b) is utilized to eliminate autocorrelation while minimizing its impact on the underlying trend. This approach provides a more reliable method for analyzing trends in time series datasets, as it safeguards the integrity of the trend while addressing serial correlation. Recently, Sen’s Innovative Trend Analysis (ITA) (Şen 2012), has been used as an alternative approach allowing the identification of trend direction and magnitude of change, enabling the graphical representation of low, medium, and high values (Phuong et al. 2022). To avoid limitations in each technique, recently several studies employed various approaches for analyzing the trends in the time series (Alashan 2020; Caloiero et al. 2018; Gedefaw et al. 2018; Harka et al. 2021; Kişi et al. 2018). To obtain a comprehensive understanding of time series data and assess the effectiveness of different techniques in detecting underlying trends, various statistical methods can be utilized in combination.

The variability of hydroclimate time series, including streamflow, rainfall, and temperature, is extensively studied using the coefficient of variation (Bari et al. 2016; Berihun et al. 2023; Fenta et al. 2017). Scholars have also utilized the Precipitation Concentration Index (PCI) (Berihun et al. 2023; Fenta et al. 2017; Gocic et al. 2016; Tolika 2018) and seasonality indices (Imteaz and Hossain 2022; Walsh and Lawler 1981) to analyze the temporal and seasonal distribution of rainfall and assess the impact of precipitation concentration on the hydrological cycle, flood and drought risk, agriculture, water allocation and land use strategies. PCI was proposed by Oliver (1980) to estimate the temporal distribution of rainfall and evaluate its variability and seasonality. Accurate and up-to-date information about hydroclimate variability is essential for understanding its pattern, developing effective hydrological models, predicting, and mitigating floods, and ensuring sustainable water management.

A comprehensive study of trends and variabilities in rainfall and streamflow in large-scale Australian catchments has been undertaken and found different trends and variations spatially (Chiew and McMahon 1993; Zhang et al. 2016). Small-scale catchment studies are required to minimize natural and anthropogenic variability that avoids the effects of averaging across larger areas (Willems et al. 2019). Moreover, in South Australia, there have been few studies on hydroclimate trends and variability (Chowdhury et al. 2015; Kamruzzaman et al. 2020; Rashid et al. 2015a). Small, urbanized catchments like Dry Creek are highly susceptible to sudden changes, especially during extreme weather events. However, there is a lack of research on the hydroclimatic elements of rainfall, temperature, and streamflow in the Dry Creek catchment, South Australia. Therefore, it is of utmost importance to thoroughly assess the pattern and fluctuations of hydroclimate time series through a combination of methodologies, such as TFPW-MK and ITA techniques. This multi-method approach can enhance the robustness of the analysis and provide a more holistic understanding of the hydroclimatic shifts. This study aimed to investigate the trend and variability in hydroclimatic variables such as rainfall, minimum and maximum temperatures, and streamflow within the Dry Creek catchment. The specific objectives were to explore (1) the variability of rainfall, temperature, and streamflow patterns; (2) hydroclimatic time series data trends; (3) the seasonality and distribution of rainfall; and (4) the potential relationship between rainfall and streamflow. Consequently, using an integrated approach can offer more reliable information about trends and variability. This can help to illustrate how different approaches depict the time series and aid in making informed decisions about water and environmental resource management.

2 Methods

2.1 Description of the Study Area

The Dry Creek catchment is an urbanized catchment located in metropolitan Adelaide, South Australia and drains to Barker inlet. The catchment area is approximately 115 km2, stretching from Mount Lofty to the Barker Sea shore inlet. The topography of the catchment ranges from 0 to 421.8 m above Australian Height Datum (AHD) (Fig. 1). The catchment area presents an array of topographical features, with slopes ranging from almost flat at less than 1% to steep cliffs exceeding 100%. The area is predominantly composed of gentle slopes, with 19.8% classified as very gentle between 1 and 3%, 36.5% as gentle between 3 and 10%, and 23.4% as moderately sloping between 10 and 32%. The climate of the Dry Creek catchment is classed as Mediterranean—hot, dry summers and cool, wet winters (Kamruzzaman et al. 2020). Between 1979 and 2019, the catchment area experienced significant urbanization, with an increase of equivalent impervious area by 60.63% (Andualem et al. 2023). The land use land cover map of 2019 indicates that the catchment area is predominantly characterized by built-up areas, accounting for 51% of the total land cover. The remaining portion is distributed between grass (21.3%), tree plantations (27.1%), and water bodies (0.65%). The long-term mean annual rainfall (MAR) at rain gauges ranges between 438 and 682 mm. The average temperature in South Australia has increased by 1 °C in comparison to the year 1960 (CSIRO and BoM 2022). The annual mean minimum and maximum temperature at Parafield Airport, located at the center of the catchment, is approximately 11.2 and 22.5 ( °C) respectively (http://www.bom.gov.au/climate/averages/tables/cw_023013.shtml).

Fig. 1
figure 1

Location of Dry Creek catchment

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2.2 Source and Availability of Time Series Data

Daily rainfall and temperature time series data were provided by the Bureau of Meteorology (BoM), Australia. The streamflow records at the gauging stations were obtained from the Water Data Services (WDS) information source provided by the Adelaide and Mount Lofty Ranges Natural Resources Management Board. This study analysed time series data from six rainfall stations, one temperature station, and two flow gauging stations. The Thiessen polygon, which includes stations at Parafield Airport, Upper Hermitage, Salisbury Bowling Club, and Hope Valley Reservoir, accounts for approximately 88% of the entire area (Table 1).

Table 1 Rainfall data availability at the selected rain gauge stations
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The analysis of temperature trends and variability was based on data from Parafield Airport station spanning 1973 to 2022. The Adelaide Airport station data was used to estimate the missing temperature records (1%) at Parafield Airport station using linear regression. The trend and variability of flow volume in the catchment was evaluated by using the upstream (Conway Crescent Valley View) and downstream (Bridge Road) gauging stations. This is due to the fact that the other stations lack adequate long-term data, and the flow volume records used in the current study cover the period from 2001 to 2022. Since the difference in normal annual rainfall exceeded ± 10%, the normal ratio method was used to fill in the missing rainfall records.

$$ P_{X} = \mathop \sum \limits_{1}^{m} \frac{{N_{x} }}{{N_{i} }}*P_{i} $$
(1)

where Px is the precipitation at the missing station, Nx is the normal annual rainfall at the missing station, Pi is the rainfall at each of the neighbouring stations, Ni is the normal annual rainfall at the surrounding stations and m is the number of surrounding recording stations.

2.3 Trend Analysis of Time Series Data

A thorough examination of rainfall, temperature, and streamflow trends was conducted at both seasonal and annual time scales, employing a range of statistical methodologies, including the TFPW-MK, simple linear regression (SLR), and innovative trend analysis (ITA) techniques. Multiple approaches were used to address the limitations of each method, as well as the assumptions involved in trend analysis, such as normality, monotonicity, and serial independence.

2.3.1 Trend-Free Pre-Whitening Mann- Kendal Trend Test

Prior to analyzing the trend of the time series data, the data distribution was assessed through plotting and explanatory data analysis. To identify whether a time series displays a statistically significant increasing or decreasing trend over time, the trend-free pre-whitening (TFPW) (Yue et al. 2002a, b) non-parametric Mann–Kendall test (Kendall 1975) was utilized. This test is widely used to evaluate trends or patterns of change over time in time series data, including rainfall, temperature, and streamflow, and does not assume any underlying data distribution. The TFPW-MK procedure followed the method proposed by Yue et al. (2002a, b).

  1. 1.

    The slope \(\beta \) of the of a trend in sample data is estimated using Sen’s method and if the slope is different from zero, TFWP will be followed.

  2. 2.

    The sample data is detrended by: \({X^{\prime}}_{t}= {X}_{t}-\beta t\)

  3. 3.

    The lag-1 serial coefficient r1 of the detrended series \({X^{\prime}}_{t}\) is computed and AR (1) is removed from \({X^{\prime}}_{t}\) by: \({Y^{\prime}}_{t}= {X^{\prime}}_{t}-r1{X^{\prime}}_{t-1}\), the residual series after applying this TFPW should be an independent series.

  4. 4.

    Then, the identified trend Tt and the residual \({Y{\prime}}_{t}\) are blended by: \({Y}_{t}= {Y^{\prime}}_{t}+{T}_{t}\)

  5. 5.

    Finally, the MK test is applied to the blended series to assess the significance of the trend.

The Kendall Tau (τ) measures the monotony of the trend and ranges from  – 1 to 1. The magnitude of Kendall’s Tau reflects the strength of the trend with τ > 0 implying an increasing trend, τ < 0 a decreasing trend and τ = 0 no trend (Helsel and Hirsch 2002). The test statistic Z and τ are closely related to S statistic and were computed using Eqs. 3 and 5, respectively.

$$ \begin{aligned}& S = \mathop \sum \limits_{i = 1}^{n - 1} \mathop \sum \limits_{j = i + 1}^{n} sgn \left( {x_{j} - x_{i} } \right)\\&\quad {\text{where sign}} \; \left( {x_{j} - x_{i} } \right) = \left\{ {\begin{array}{*{20}c} 1 \\ 0 \\ { - 1} \\ \end{array} \;} \right. if \left[ {\begin{array}{*{20}c} {x_{j} - x_{i} > 0} \\ {x_{j} - x_{i} = 0} \\ {x_{j} - x_{i} < 0} \\ \end{array} } \right]\end{aligned} $$
(2)
$$ Z = \left\{ {\begin{array}{*{20}c} {\frac{S - 1}{{\sqrt {Var\left( S \right)} }}} \\ 0 \\ {\frac{S + 1}{{\sqrt {Var\left( S \right)} }}} \\ \end{array} } \right.\quad \;\;if\left[ {\begin{array}{*{20}c} {S > 0} \\ {S = 0} \\ {S < 0} \\ \end{array} } \right] $$
(3)
$$ {\text{Var}}\left( S \right) = \frac{{n\left( {n - 1} \right)\left( {2n + 5} \right)}}{18} $$
(4)
$$ \tau = \frac{S}{D} $$
(5)
$$ D = \left[ {\frac{1}{2}n\left( {n - 1} \right) - \frac{1}{2}\mathop \sum \limits_{j = 1}^{p} t_{j} \left( {t_{j} - 1} \right)} \right]^{1/2} \left[ {\frac{1}{2}n\left( {n - 1} \right)} \right]^{1/2} $$
(6)

where \({x}_{j}\) and \({x}_{i}\) are the data values at times \({\text{j}}\) and \(i\), respectively \({\text{j}}\) > \(i\); n is the data length; p is the number of the tied groups in the data set and tj is the number of values tied at the j-th set of tied values; Z and Var(S) are the Mann–Kendall and the variance statistics test respectively. The time series trends were assessed at a significance level of 5% by calculating a p-value (Gilbert 1987; Kendall 1975).

To evaluate the magnitude and direction (upward or downward) of the trend the Sen’s slope (β) (Sen 1968) was computed using Eq. 7. Sen’s slope estimator is unbiased and insensitive to outliers but not suitable for capturing seasonal patterns.

$$ \beta = {\text{median}}\left\{ {\frac{{X_{j} - X_{k} }}{j - k}: {\text{j }} < {\text{ k}}} \right\} $$
(7)

where \({x}_{j}\) and \({x}_{k}\) are data values at time j and k, β > 0 indicates an increasing trend, β < 0 indicates a decreasing trend and β = 0 represents no trend.

2.3.2 Innovative Trend Analysis (ITA)

ITA proposed by Şen (2012) involves comparing two halves of a time series, each sorted in ascending order, and computing the trend’s slope and intercept using Eqs. 8, 9. This approach uses a 1:1 (45°) straight line as a reference (representing no trend), and points above or below the line indicate increasing or decreasing trends, respectively. ITA is a more effective technique for analysing trends in nonmonotonic conditions as it allows for a graphical comparison of low, medium, and high-value trends. The ITA method does not make assumptions about normality, monotonicity, or linearity. Moreover, it can be effectively applied to time series data that exhibits serial correlation (Şen 2017a, b). Assessing the degree of change or trend in ITA can be achieved by computing the slope of the trend (Alashan 2020; Şen 2017a, b). The null hypothesis (no trend) and the alternative hypothesis (trend exists) are evaluated at a significance level of alpha = 5% and a standard normal variate, Z-value of ± 1.96. If -CL < bITA < CL, this indicates the absence of a trend. Conversely, if |bITA|< CL, it suggests a decreasing trend, while |bITA|> CL implies an increasing trend (Şen 2017a, b).

$$ Y = a + bt $$
(8)
$$ b_{ITA} = \frac{{\left( {Y_{2} - Y_{1} } \right)}}{n/2} $$
(9)
$$ a_{ITA} = Y_{m} - bt $$
(10)
$$ re = \frac{{a_{st} - a_{ITA} }}{{a_{st} }}*100 $$
(11)
$$ Sv = \frac{{\left( {\sigma_{2} - \sigma_{1} } \right)}}{n/2} $$
(12)
$$ CL \left( {1 - \alpha } \right) = 0 \pm Scri*\sigma_{b} $$
(13)
$$ \sigma_{b} = \frac{2\sqrt 2 }{{n\sqrt n }}\sigma \sqrt {(1 - \rho y_{1} y_{2} } $$
(14)

where bITA is the ITA slope, aITA is the ITA intercept, ast is the stochastic process intercept, t is the time, n is number of records in the time series, re is relative error in percent, Sv is slope of variability, σ1 and σ2 are first and second half standard deviation, CL is the confidence limit at 5% significance level, Scri is the critical limits of the standard deviation, σ is standard deviation of the time series, σb is standard deviation of the slope, Ym is the time series average, \(\rho {y}_{1}{y}_{2}\) is the correlation of the two means, Y1 and Y2 are the first and second half average values, respectively.

2.4 Change Point Detection

Identifying change points in time-series analysis is crucial as they provide insights into the underlying dynamics of the data, indicating a significant change in either the distribution or trend (Gourgouletis and Baltas 2023; Malede et al. 2022). The descriptions of each statistical method and computational equation are specified in Eqs. 15, 16, 17, 18, 19, 20, 21, 22, 23. Xi is the time series to be tested (i is the year from 1 to n), \(\overline{X}\) is the mean and σ is the standard deviation.

Pettit test (Pettitt 1979) is a non-parametric rank test that does not consider the distribution of the data. The change point test statistic XK is computed as:

$$ K_{T} = \max \left| {U_{t,T} } \right|\, where \, 1 \le t < T $$
(15)
$$ X_{K} = 2\mathop \sum \limits_{i = 1}^{k} r_{i} - k\left( {n + 1} \right),k \, = \, 1 \ldots n \, {\text{ and }}\, r_{1} \ldots r_{n} {\text{ are ranks}} $$
(16)
$$ X_{K} = \max \left| {X_{K} } \right|, 1 \le k < n $$
(17)

Standard normal homogeneity test (SNHT) (Alexandersson 1986): This test is commonly utilized to analyze a series of ratios that compare the observations with an average, with the ratios subsequently being standardized. If the break is found at point K, the statistic, T(k) reaches its maximum value at k = K. The test statistic, \({T}_{0}\) computed using Eq. 20.

$$ T(k) = k\overline{z}_{1}^{2} + (n - k)\overline{z}_{2}^{2} \quad k = 1, \, \ldots n $$
(18)
$$ \overline{z}_{1} = \frac{1}{k}\mathop \sum \limits_{i = 1}^{k} \left( {X_{i} - \overline{X}} \right)/\sigma\, {\text{and }} \overline{z}_{2} = \frac{1}{k}\mathop \sum \limits_{i = k + 1}^{n} \left( {X_{i} - \overline{X}} \right)/\sigma $$
(19)
$$ T_{0} = \max T\left( k \right), 1 \le k < n $$
(20)

Buishand range test (Buishand 1982) is used for variables that follow any distribution type. When a series is homogeneous, the \({S}_{k}^{*}\) values will fluctuate around zero due to the absence of any systematic deviations of the Yi values from their mean. In the presence of a break in year K, \({S}_{k}^{*}\) will reach a maximum (negative shift) or minimum (positive shift) near the year k = K. The significance of the shift can be assessed by conducting a test using the "rescaled adjusted range" R. The adjusted partial sums, \({S}_{0}^{*}\) and rescaled adjusted range, R computed using Eqs. 21 and 22.

$$ S_{0}^{*} = 0;\, S_{K}^{*} = \mathop \sum \limits_{i = 1}^{k} \left( {X_{i} - \overline{X}} \right),k \, = \, 1, \, 2, \, \ldots n $$
(21)
$$ R = (\max S_{K}^{*} - \min S_{K}^{*} )/\sigma ,0 \le k \le n $$
(22)

Von Neumann ratio test (Von Neumann 1941): Von Neumann ratio, N, is calculated by dividing the sum of squared differences between each pair of consecutive time measurements by the variance. The von Neumann ratio test is effective but does not provide a means to identify the timing of the change.

$$ N = \mathop \sum \limits_{i = 1}^{n - 1} \left( {X_{i} - X_{i + 1} } \right)^{2} /\mathop \sum \limits_{i = 1}^{n} \left( {X_{i} - \overline{X}} \right)^{2} $$
(23)

The null hypothesis (H0): the data are homogeneous (no change points in the time series) and an alternative hypothesis (H1): there is a date at which there is a change in the data were evaluated at a 5% significance level. Furthermore, the results obtained from these four methods were grouped into different classes (Class 1, Class 2, and Class 3) (Schönwiese and Rapp 2013; Wijngaard et al. 2003). Class 1 is characterized by a homogeneous outcome, where either one or zero tests support the null hypothesis. Class 2 represents an uncertain or doubtful outcome when two tests reject the null hypothesis. Lastly, Class 3 signifies a strong rejection of the null hypothesis when three or four tests reject it.

2.5 Analysis of Rainfall Variability

Changes in a time series can occur gradually (a trend), abruptly (a step-change), or in a more sophisticated manner that influences the mean, median, variance, or another characteristic of the time series data. Given the variations in topography, the Empirical Bayesian Kriging (EBK) regression method was utilized to assess the spatial variability of the MAR. This geostatistical interpolation technique estimates values at unsampled locations within a spatial dataset by incorporating kriging and regression analysis, utilizing MAR measurements from rain gauge stations and topographical data. Due to the limited number of stations within the catchment, a total of 17 additional stations in the region were used to perform EBK regression. The best semi-variogram model was selected based on the lower root mean square error value.

To evaluate the temporal variability and distribution of rainfall we utilized the coefficient of variation (CV) and precipitation concentration index (PCI), respectively. During this study, CV was also used to assess the temporal variability in temperature and streamflow time series. PCI was computed to assess the distribution pattern of seasonal and annual rainfall in the time series. The PCI values are computed using Eqs. 25 and 26 at annual and seasonal timescales, respectively (Bari et al. 2016; Fenta et al. 2017). A seasonality index was calculated to analyse the patterns of rainfall in relation to different months or seasons. To achieve this, a multiplicative time series decomposition was conducted (Shumway and Stoffer 2006) using Minitab 21.4.

$$ CV = \frac{\sigma }{\mu }*100 $$
(24)
$$ PCI_{annual} = \frac{{\mathop \sum \nolimits_{{{\text{i}} = 1}}^{12} {\text{P}}_{{\text{i}}}^{2} }}{{\left( {\mathop \sum \nolimits_{{{\text{i}} = 1}}^{12} {\text{P}}_{{\text{i}}} } \right)^{2} }}*100 $$
(25)
$$ PCI_{seasonal} = \frac{{\mathop \sum \nolimits_{i = 1}^{12} {\text{P}}_{{\text{i}}}^{2} }}{{\left( {\mathop \sum \nolimits_{i = 1}^{3} {\text{P}}_{{\text{i}}} } \right)^{2} }}*25 $$
(26)

where µ is the mean, σ is the standard deviation, Pi is the monthly rainfall (mm) during the ith month, and Pan is the annual rainfall (mm). The mean seasonality index was computed from the individual seasonality indices. We have used the precipitation distribution classification proposed by Oliver (1980), which has four categories: uniform (PCI < 10), moderate (11 < PCI < 15), irregular (16 < PCI < 20), and strong irregularity (PCI > 20) (Gocic et al. 2016). During this study period, the calendar months were divided into four seasons: summer (December, January, and February), autumn (March, April, and May), winter (June, July, and August), and spring (September, October, and November) (http://www.bom.gov.au/climate/glossary/seasons.shtml).

2.6 Analysis of Flow Variability

River flow regimes are important hydrological parameters that can be characterised using the observed flow data at the gauging station within the catchment, such as flow variability including coefficient of variation (Moliere et al. 2009) and Richards-Barker flashiness index (R-B Index) (Baker et al. 2004), and extent of intermittency as number of mean zero flow days ratio (ZFI) (Poff 1996). The R-B index and ZFI were computed using Eqs. 27 and 28, respectively (Baker et al. 2004; Berhanu et al. 2015)

$$ R - B \, Index = \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left| {q_{i} - q_{i - 1} } \right|}}{{\mathop \sum \nolimits_{i = 1}^{n} q_{i} }} $$
(27)
$$ ZFI = \frac{{N_{z} }}{365} $$
(28)

where qi and qi-1 are the average daily discharges (m3/s) on day i and day i-1, respectively and Nz is the mean annual number of days with zero flow. The index is dimensionless and can be obtained by replacing the discharge with the total daily discharge volume (m3). Intermittent rivers can be characterised by the mean zero flow days of greater than 10 days/year (Poff 1996) or 15 days/year (Eng et al. 2016).

2.7 Dynamics of Rainfall-RUNOFF RELAtionships

The rainfall-runoff relationship was evaluated using SLR and Tanh curves. The Tanh curve is frequently employed for filling in missing monthly or annual runoff values based on measured rainfall. It establishes a robust site-specific relationship and can be expressed using Eq. 29, which was first presented by Boughton (1966). The Tanh relationship, which has a hyperbolic shape, suggests that there is no direct proportionality between rainfall and runoff. Rather, there must be a certain threshold of rainfall that needs to be reached before runoff can occur.

$$ Q = P - L - F*\tanh \frac{{\left( {P - L} \right)}}{F} $$
(29)

where, Q is runoff (mm), P is the areal rainfall (mm), L is the notional loss (mm) below which there is little or no runoff, and F is the continuing loss or infiltration (mm). To eliminate catchment size influence, we computed Q (mm) by dividing the flow volume by the catchment area. To accurately represent the relationship between the variables, the Tanh curve parameters, specifically L and F, were computed using a searching and optimization technique through minimizing the residual sum of squares error.

3 Results

3.1 Spatiotemporal Variability and Trends of Rainfall

Except for the Bolivar Treatment Work rain gauge station, the annual rainfall data in the catchment region follows a normal distribution. The mean and median of Bolivar Treatment Work’s annual rainfall exhibit minimal differences, indicating that the data from this station is marginally normally distributed. On the other hand, most of the stations exhibit non-uniform distribution in seasonal rainfall. Given this observation, the TFPW-MK trend test was used in addition to simple linear regression. The minimum and maximum annual rainfall at the rain gauge stations within the study catchment was determined to be 246 mm and 1039 mm, respectively. The long-term MAR at the gauging stations ranged from 438 to 682 mm (Fig. 2). These highlights the presence of diverse rainfall patterns throughout the catchment area.

Fig. 2
figure 2

Graphical summary of annual rainfall time series in the study catchment

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Analysis of annual rainfall data showed the presence of both decreasing and increasing trends, but they are not statistically significant (p-value ≥ 0.05). However, the p-values for Pooraka in both TFPW-MK and SLR are approximately 0.05, suggesting a modestly significant upward trend in annual rainfall. At all-time scales, ITA, SLR, and TFPW-MK identified rainfall trends at 83%, 20%, and 7% of the stations, respectively. Both TFPW-MK test and SLR showed a statistically significant increasing rainfall trend during winter at Salisbury Bowling Club and Pooraka stations. Due to the non-monotonic pattern observed at the Hope Valley Reservoir station, the trends exhibited by the TFPW-MK and SLR variations. While MK did not display any significant trends, SLR indicated a statistically significant increase in summer rainfall, as well as a decrease in spring and annual rainfall (Table 2). When comparing the data from the Hope Valley Reservoir with ITA, it is important to note that the ITA graph showed a decreasing trend in both the spring season and annually. These findings suggest that SLR performed better than TFPW-MK at this specific station.

Table 2 Seasonal and annual rainfall Mann–Kendall, SLR and Pettitt test results
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The relative error between the ITA and stochastic intercepts was < 5% for yearly records and < 10% for most seasons, except for Bolivar Treatment Work rainfall and Bridge Road flow volume in winter and autumn respectively, where it was > 10% (Table 3). In contrast to TFPW-MK and SLR, ITA exhibited trends in the majority of the stations as a result of the presence of nonmonotonic trends in the hydroclimatic variables. The analysis using ITA showed an increasing trend in annual rainfall at Salisbury Bowling Club, Pooraka, and Upper Hermitage stations, while a decreasing trend was observed at Bolívar Treatment Works, Hope Valley Reservoir, and Parafield Airport stations. Most of the stations showed both decreasing and increasing trends seasonally. However, during autumn, Salisbury Bowling Club, Bolívar Treatment Works, Hope Valley Reservoir, and Upper Hermitage stations did not show a statistically significant trend due to the presence of nonmonotonicity (Table 3 and Fig. 3). This indicates that conventional linear trend analysis techniques may not be sufficient in capturing the intricate temporal dynamics that exist in rainfall patterns. Hence, it is crucial to leverage advanced techniques such as ITA to identify and comprehend such non-linear trends. Furthermore, it is essential to thoroughly investigate potential factors that may influence non-monotonic trends by examining their correlations with pertinent environmental or anthropogenic factors.

Table 3 Seasonal and annual ITA analysis results of rainfall, temperature, and flow volume
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Fig. 3
figure 3

Seasonal and annual rainfall ITA trend analysis result of a Parafield Airport, b Salisbury Bowling Club, c Pooraka, d Bolivar Treatment Work, e Hope Valley Reservoir, and f Upper Hermitage stations

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In the first and second halves of the time series, Bolivar Treatment Works, Parafield Airport, and Hope Valley Reservoir stations all witnessed a decline in average annual rainfall, with reductions of 58.1 mm, 27.6 mm, and 26.8 mm, respectively. Conversely, the Salisbury Bowling Club, Pooraka, and Upper Hermitage stations demonstrated an increase in rainfall, with rises of 42.6 mm, 31.8 mm, and 30.8 mm, respectively.

The analysis of rainfall data in the area displays inherent annual and seasonal variations, unaffected by long-term climate patterns. Long-term annual rainfall variability is minor compared to seasonal and monthly fluctuations, with a CV ranging from 18 to 24%. Seasonally, winter and autumn have low variability, but summer has high variability. Monthly, February and March have more variability, with the CV values above 100%, signifying considerable variations in rainfall levels compared to other months (Fig. 4). This reflects the sporadic and less predictable nature of summer rainfall in the area. The ITA variability slope showed a decreasing trend in most seasons and annually, while the spring season revealed an increasing trend in variability. Spatially, the annual coefficient of variation showed a decreasing pattern as it moved towards the east.

Fig. 4
figure 4

Monthly, seasonal, and annual rainfall and flow volume variability

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The seasonal rainfall indices and rainfall variability indicate that there is seasonality in the rainfall patterns within the catchment. The indices show a well-defined wet season from May to September, with less-than-average rainfall occurring between October and April (Fig. 5). The catchment receives moderate annual rainfall distribution, as indicated by the annual PCI values (Table 4). In Dry Creek, there is a clear positive linear relationship between the average annual rainfall and both elevation and longitude, while there is a negative association with latitude. The optimized EBK regression model (Fig. 6) produced a mean error of 0.43 and root mean square error of 69. The spatial distribution of rainfall showed an eastward increasing trend which is consistent with the rises in elevation and tree plantation cover. The downstream parts of the catchment, which are characterized by low elevation levels and intensive urbanization, receive less rainfall. The spatial MAR exhibited spatial fluctuations between 440 and 723 mm, with an average value of 556 mm (Fig. 7).

Fig. 5
figure 5

Rainfall seasonality indices (multiplicative decomposition results)

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Table 4 Rainfall seasonality expressed as a function of PCI
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Fig. 6
figure 6

Optimized EBK semi-variogram model for rainfall prediction in unsampled areas

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Fig. 7
figure 7

Empirical Bayesian kriging regression interpolated spatial distribution of MAR (mm) in the region

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3.2 Temperature Trends

The study station records indicate that the long-term average daily temperature was determined to be 17.02 °C, with the mean minimum and maximum temperatures of 11.2 °C and 22.8 °C, respectively (Fig. 8). The temperature time series follows a normal distribution. The temperature data revealed an upward trend in all seasons except autumn. The TFPW-MK, SLR, and ITA techniques all demonstrated a statistically significant increase in maximum and mean temperatures (Table 5 and Fig. 9). ITA, SLR, and TFPW-MK identified temperature trends in 100%, 60%, and 33% of the station temperature variables, respectively. The three methods exhibited an average trend magnitude difference of zero, with the smallest difference being -0.01 and the largest being 0.02 °C/year. Annually, there is very strong evidence indicating an increase in maximum temperatures at a rate of 0.04 °C/year or 0.4 °C/year/decade. Moreover, during the spring season, there is strong evidence of a temperature rise of 0.06 °C/year or 0.6 °C/decade in maximum temperatures. The ITA slope of variability was determined to be 0 for the minimum, mean, and maximum temperatures, indicating a consistent increase in temperature without any variation.

Fig. 8
figure 8

Annual average Tmin, Tmean, and Tmax trend and change points

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Table 5 Mann-Kendal, SLR and Pettit test analysis results of seasonal and annual mean (Tmean), minimum (Tmin) and maximum (Tmax) temperatures
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Fig. 9
figure 9

Seasonal and annual ITA trend analysis results of a) Tmin, b) Tmean and c) Tmax (°C) of Parafield Airport station

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Furthermore, a comparison of temperature fluctuations between the two halves of the time series reveals that the average minimum, mean, and maximum temperatures have risen by 0.06 °C, 0.57 °C, and 1.09 °C, respectively, on an annual basis. In terms of seasons, the most significant increases have been observed during the spring and summer, with temperature rises of 1.58 °C and 1.25 °C, respectively.

3.3 Trend Analysis and Variability of Streamflow

The normality test shows that the annual streamflow data follows a normal distribution, suggesting a consistent pattern in the flow volume over the study period. The mean annual flow volume were 3868 ML and 5730 ML at the upstream and downstream gauging stations, respectively (Fig. 10).

Fig. 10
figure 10

Annual flow volume (ML) graphical and statistical summary

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However, the magnitude of the trends observed in all three tests is comparable. Both the MK and SLR tests exhibited nonsignificant trends, suggesting that the effectiveness of these tests in analyzing streamflow trends was limited in comparison to ITA, which identified a decreasing trend at 60% of the stations. The ITA at Bridge Road station demonstrated consistent monotonic trends, with an observed annual maximum downward trend of -172.36 ML/year (Table 6). At Conway Crescent Valley View station, ITA exhibited a downward trend during spring and a non-monotonic trend during winter with increases in low flows and decreases in high flows. Additionally, high flows showed increasing trends during summer. However, minimum and medium flows demonstrate trend-free (encircled points in Fig. 11a). There was a decrease in flow volume in the second half at both flow recording stations. The largest reduction was seen at Bridge Road station, with an annual decrease of 1896 ML. Conway Crescent Valley View station also experienced a decrease, with a reduction of 120 ML annually.

Table 6 Mann–Kendall, Pettit test and SLR results of seasonal and annual flow volume
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Fig. 11
figure 11

Seasonal and annual flow volume (ML) ITA trend analysis a Conway Crescent Valley View and b Bridge Road stations

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The annual streamflow variability exhibited moderate variability, with an annual coefficient of variation (CV) of less than 40%. However, the seasonal and monthly variability was observed to be high, with CV values ranging from 50 to 220%. The months of February, March, April, November, and December had the highest variability, with CV values exceeding 100% at both sites. In March, water flow fluctuated greatly, with CV exceeding 200% (Fig. 6). The creek is characterized as flashy, with R-B index values (≥ 0.4), exhibiting rapid increases in flow following precipitation events, followed by quick recession. The ZFI values also indicate a significant occurrence of zero flows, illustrating the ephemeral nature of the creek (Fig. 12). This suggests that the flow experiences rapid fluctuations during rainfall events due to the impermeability of the catchment area and the intermittent nature of the stream. As a result, peak flow events commonly occur during or shortly after rainfall, leading to a decrease in post-peak events.

Fig. 12
figure 12

Time series annual ZFI and R-B index values at the two gauging stations

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3.4 Change Point in the Time Series

The analysis revealed that there were no significant abrupt changes or shifts in the annual rainfall time series. However, in terms of seasonal rainfall, the winter rainfall at Salisbury Bowling Club is classified as class 3. This classification suggests compelling evidence of abrupt change points occurring in 1977, with the average winter season rainfall increasing by 46.7 mm following this break point. On the other hand, the winter rainfall at Bolivar Treatment Work falls into class 2 (with a decrease of rainfall by 32.6 mm after 1996), suggesting doubtful/undecided homogeneity, while others fall into class 1. This suggests that while there may be trends of increase or decrease, there are no significant shifts in the data. Moving on to the seasonal and annual maximum temperatures at Parafield Airport station, there is strong evidence of change points, falling under class 3, with breakpoints occurring between 1995 and 2001. The daily average maximum temperature increased by 1.3 °C, 1.1 °C, 0.6 °C, 1.6 °C, and 1.1 °C during the summer, autumn, winter, spring, and annual time periods, respectively, after the breakpoints. The streamflow time series is classified as class 1, except at Bridge Road where it is considered doubtful during autumn and winter due to change points in 2013 and 2014, respectively (Table 7).

Table 7 Homogeneity test results of rainfall, temperature, and streamflow
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3.5 Hydrological Connection Between Rainfall and Streamflow

The SLR analysis revealed that the association between rainfall and flow volume was good, with Pearson correlation, r, more than 0.65 at the daily, monthly, and annual scales (Fig. 13). This suggests that there is a little lag between rainfall and runoff. The remaining correlation percentage that cannot be solely attributed to rainfall can be explained by time lag, spatial heterogeneity in rainfall, single-point streamflow measurement, unique catchment characteristics, and other anthropogenic factors. For a better explanation of the rainfall-runoff relationship, Tanh curves were developed, revealing Pearson correlation of 0.63 and 0.82 for the Bridge Road and Conway Crescent Valley View stations, respectively (Fig. 14). At both stations, the continuing loss (F) was found to be 813 mm and 990 mm, respectively at Bridge Road and Conway Crescent Valley View stations. The notional loss of zero value in Dry Creek corresponds to the high percentage of built-up surfaces in the catchment.

Fig. 13
figure 13

SLR between flow volume (ML) and areal rainfall (mm)

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Fig. 14
figure 14

Rainfall-runoff curves for Dry Creek catchment at Bridge Road and Conway Crescent Valley View gauging stations and other nearby creeks

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4 Discussion

The three approaches employed in this study for trend analysis produced different results, especially in the time series that showed nonmonotonicity. However, the magnitudes of trend were comparable in the hydroclimatic time series that displayed a monotonic trend. The current study reveals that rainfall trends vary across different stations, both seasonally and annually, with a mix of decreasing and increasing patterns. The comparison of trend detection among different methods revealed that ITA, SLR, and TFPW-MK detected trends with success rates of 84%, 28%, and 13% respectively. In terms of upward trends, ITA, SLR, and ITA detected 44%, 24%, and 13%, respectively. The downward trends were only detected by SLR (4%) and ITA (40%). At one station (Hope Valley Reservoir), the TFPW-MK results contradicted those of SLR and ITA. SLR and ITA showed statistically significant increases in rainfall during the summer and decreases during the other seasons (annual, winter, and spring). Studies in various regions of the world have revealed significant patterns and trends in precipitation over time (Abtew et al. 2009; Rashid et al. 2015a). Rashid et al. (2015a) found negative annual rainfall trends, positive winter and monthly rainfall trends, and significant positive trends in specific months in South Australia’s Onkaparinga catchment. Chowdhury et al. (2015) have reported on the rainfall trends in South Australia, that there is an upward trend in Arid Lands, Alinytjara Wilinara, and Adelaide/Mount Lofty Ranges. However, there has been a decline in Murray Darling Basin, Eyre Peninsula, and Southeast regions. According to CSIRO and BoM (2022), rainfall in southeast Australia has decreased by 10% since the 1990s. These findings illustrate the variations in rainfall patterns across different regions and particularly between individual stations. In this study, rainfall showed a higher degree of spatial and temporal variability that has a similar pattern with both elevation and longitude. A study conducted in South Australia by Kamruzzaman et al. (2020) also showed seasonal and spatial differences in rainfall patterns. The study showed a correlation between rainfall and various climate indices, including Southern Oscillation Index (SOI), the Indian Ocean Dipole (IOD), the Southern Annular Mode (SAM), and the Pacific Decadal Oscillation (PDO). According to a study by Montazerolghaem et al. (2016) on southeastern Australia, the fluctuations in rainfall could be attributed to the influence of the lagged SAM, SOI, and IOD, which exhibit a correlation strength that is greatly influenced by the season. Winter season rainfall is uniformly distributed over three months (June, July, and August), with PCI values of less than 10, because of the region’s winter-dominant rainfall (Larkin et al. 2020; Petheram et al. 2008). Rashid et al. (2015b) found a similar result in the Onkaparinga catchment, South Australia, where, except for the winter season, other seasons showed a moderate concentration of rainfall.

Except for autumn and winter minimum temperatures, which showed a downward trend, the temperature at the studied station showed a consistently upward trend in mean and maximum temperature values. In Dry Creek, the built-up covers, which contribute to the urban heat island effect, experienced a rise in coverage from 21.6% to 51% between 1979 and 2019 (Andualem et al. 2023). The observed temperature increases are likely a result of the combined impacts of global warming, which affects global climate patterns, and urbanization, which contributes to localized temperature rises. Xiang et al. (2014) have also demonstrated a 1 °C increase in maximum temperature in Adelaide, South Australia from 2001 to 2010. Another study conducted by Ashcroft et al. (2012) in southeastern Australia also documented a 1.1 °C rise in maximum temperature and a 0.9 °C increase in minimum temperature since 1960. There has been significant climate change in South Australia, characterized by a shift towards drier and warmer conditions, resulting in increased average maximum temperatures and decreased rainfall (Frederiksen & Osbrough 2022). The change point analysis revealed that Class 3 occurred once at one rainfall station during winter and eight times in temperature, providing strong evidence of change point occurrence in the time series. Class 2 was observed twice at flow volume, twice at temperature, and once at rainfall, indicating uncertain change points in the time series. A study by Wijngaard et al. (2003) in Europe showed about 90% of the temperature and 13% of precipitation classified as a doubtful.

The limited length of the time series data, as well as the significant random fluctuations observed in the flow volume, prevented the detection of statistically significant trends (Chiew & McMahon 1993) using the MK and SLR tests (Wang et al. 2020; Yue et al. 2002a, b). In this case, the ITA method proved more effective in identifying the underlying trends in the streamflow time series. Chiew and McMahon (1993) found a declining trend, but not statistically significant due to greater interannual variability. According to CSIRO and BoM (2022), 60% of Australian hydrological reference stations show a declining trend in streamflow data series. The findings of this study are consistent with Larkin et al. (2020), who also found a decrease in runoff in South Australia due to lower winter rainfall and rising temperatures. According to Zhang et al. (2016), the majority of South Australian streams are experiencing a declining trend across all four seasons. These streams have limited runoff and undergo significant variations in flow intensity, with notable fluctuations in both maximum and minimum flows. Chiew and McMahon (1993) found that CV values differed depending on location, with lower variability in Tasmania, medium variability in South Australia and larger variability in Queensland, Victoria, and West Australian streams. Furthermore, McMahon (1987) showed that the typical yearly variability for Australian floods is around 35%. Dry Creek is classified as an intermittent stream, with ZFI values of 0.22 and 0.39 estimated at the upstream and downstream gauging stations, respectively (Fig. 12). ZFI values near 0 often suggest perennial rivers that flow all year, whereas values near 1 indicate seasonal to intermittent rivers that flow only during specified seasons (Moliere et al. 2009). Petheram et al. (2008) discovered substantial variability and seasonality in annual streamflow in northern Australia, indicating that a large amount (more than 80%) of total river flow occurred during a three-month peak period. The higher flow variability was attributed to a notable flashiness index, which is expected to occur in small catchments. According to (Baker et al. (2004), the flashiness index tends to increase as the size of the watershed decreases, while larger regions exhibit slower and more stable stormwater responses. Urbanization causes stormwater to enter creeks faster and in higher volume, leading to flashiness that can potentially harm infrastructure and neighbouring lands. According to a study conducted by Andualem et al. (2024), the channels have shifted over the past four decades to accommodate the high flashiness, transportation, and deposition of sediments and floating materials, which necessitate regular monitoring. Therefore, future monitoring practices can be enhanced by taking into account the variability of flow volume and catchment imperviousness in response to the hydrology of the catchment. Furthermore, the correlation between rainfall and streamflow clearly shows that changes in streamflow over time can be explained by changes in rainfall patterns. This correlation has important implications for hydrological modelling and forecasting, as highlighted by Zhang et al. (2016). Comparable Tanh curves have also been established for other catchments located in close proximity in South Australia. In these catchments, such as Little Para Reservoir and Gould Creek, the estimated notional loss (L) value differs from zero for non-urban areas. However, for the South Para catchment, which is partially urbanized, an L value of zero was estimated (Savadamuthu & Teoh 2010).

5 Conclusion

This study provides a thorough examination of the fluctuations and patterns in rainfall, temperature, and streamflow across the Dry Creek Catchment located in South Australia. The present study emphasizes the significance of utilizing advanced analytical methods and adopting multiple approaches to accurately assess variations and trends in hydroclimatic variables, while considering the limitations and assumptions associated with different trend test methods. The analysis of hydroclimatic variable trends using ITA revealed non-monotonic trends in autumn rainfall at most stations, annual minimum temperature, and flow volume at Conway Crescent Valley View at all time scales. ITA proved to be superior compared to SLR and TFPW-MK, with statistically significant trends observed in most hydroclimatic time series. This highlights the need to employ multiple approaches, especially during nonmonotonic trend presence. Seasonal variations were noted, with winter rainfall showing significant increases in certain stations such as Salisbury Bowling Club and Pooraka while most stations exhibited downward trends. Although MK and SLR did not detect statistically significant trends in flow volume due to high variability, ITA identified a decreasing trend in annual flow volume at both of the studied stations. All three methods (TFPW-MK, SLR, and ITA) indicated an upward trend in mean and maximum temperatures across all seasons except autumn, with the most significant increase observed in spring. Temperature changes were attributed to urbanization and global warming, contributing to localized temperature increases and affecting regional climate patterns.

Over the past few decades, urbanization has expanded significantly, with the built-up area increasing from 21 to 51% between 1979 and 2019. This rapid urban expansion is expected to contribute to an increase in temperatures, as shown by the rise in mean daily temperature of 0.23 °C per decade. Additionally, changes in precipitation patterns have been observed, with downstream urbanized areas experiencing a decline in rainfall, while upstream mountainous regions covered with tree plantations have witnessed an increase in rainfall. As a result, these changes in land use and climate have had a notable impact on hydrological processes, resulting in a decrease in flow volume by 172 ML/year at the Bridge Road station. This decline can be primarily attributed to a decrease in rainfall and potential increases in evapotranspiration due to higher temperatures. This indicates the complex and interdependent nature of climate change, urbanization, and local precipitation patterns. The creek’s flow exhibits greater variability in both annual and seasonal patterns due to its ephemeral and seasonal nature, along with the presence of impervious surfaces that cause peak events after rainfall. This effect is particularly pronounced during the dry season, as demonstrated by elevated CV and R-B index values. The application of the Tanh curve and SLR shows a strong association between rainfall and streamflow across different temporal scales. This suggests that flow volume and runoff are closely tied to rainfall, positioning rainfall as a potential predictor of streamflow in the studied catchment.

This study identified limitations that impact the analysis and interpretation of hydroclimate trends. One notable challenge is the absence of consistent data periods for analyzing different variables, which makes direct comparisons difficult. Furthermore, the limited availability of streamflow data poses a challenge in identifying statistically significant trends, underscoring the significance of collecting data over extended periods. Addressing these limitations would enhance the reliability and comprehensiveness of forthcoming hydroclimate research. Ultimately, this study provides valuable insights into the complex dynamics of rainfall, temperature, and streamflow in the study catchment, underscoring the necessity for water resource management in the region, particularly in view of the increasing variability and potential decrease in streamflow. Ongoing monitoring and research are vital to fully comprehend the impacts of urbanization and climate change on the hydrological system. This knowledge is crucial for understanding rainfall-runoff relationship and developing sustainable strategies to mitigate floods and droughts in the studied catchment area.