Impact of atmospheric circulation on the rainfall-temperature relationship in Australia

Moron et al [46] classified 6 hourly low-level winds from 37 wet seasons (November to March) from 1979 to 2016 into six distinct WTs. The WTs were computed using cluster analysis (k-means) of 6 hourly ERA-Interim winds at 850 hPa and were found to be a varying combination of different phenomena operating at various time scales including the diurnal and the annual cycles, interannual variations such as El Niño-Southern Oscillation (ENSO), intra-seasonal Madden Julian Oscillation (MJO), as well as faster transient phenomena such as low pressure travelling across Northern Australia. The WTs may be clustered into two broad systems, 'trade wind' and 'monsoonal' and are summarised in table 1.

WT1 and WT6 are characterized by trade winds over tropical Australia, where winds extend over Indonesia in WT1 and weak westerly flows are established north of 5°S in WT6. WT1 is almost restricted to pre-monsoon and post-monsoon seasons, while WT6 frequency is less seasonal, occurring either during (and then mostly corresponding to 'breaks') or after the monsoon. Comparatively, the least seasonal WT, monsoonal WT3, is associated with a zonal monsoon trough centred around 12°S and extending till 135°E, corresponding to the 'moist East Regime' in Darwin [56]. The remaining monsoonal systems WT4 and WT5 occur mostly from mid-December to early March. WT4, the most active phase of the monsoon, is primarily associated with a low pressure system, centred around 18°S and 120°E and with a strong westerly wind regime over most of Northern Australia (not inclusive of the Eastern coast of Queensland), corresponding to the 'deep west regime' [56]. WT5 however is better associated to the 'shallow west regime' [56], showing correspondence to fast westerlies NE of Cape York. Lastly, WT2, which lies in a phase between trade-winds and monsoonal activity known as 'transitional', is characterised by weak synoptic winds and a seasonal peak from mid-November to mid-December during the pre-monsoon season [54]. Further details on the WTs can be found in Moron, et al [46].

Less rainfall occurs for trade-wind WTs and more for monsoonal ones (table 1). Average air temperature is relatively consistent between the WTs unlike dew point temperatures which are higher for monsoonal ones. The frequency of WTs during the wet season also varies, with trade wind WTs occurring more frequently than monsoonal WTs on average, especially on either end of the wet season (not shown, see figure 3(g) of Moron, et al [46]).

For this study, Australian Bureau of Meteorology (BoM) weather station data consisting of daily rainfall, daily mean dry bulb temperature and daily mean dew point temperature, used extensively in previous studies [31, 36], were matched with the 6 hourly sub-daily WT dataset. The 6 hourly WTs were aggregated to daily values, with the most prevalent WT chosen as the daily WT, though it should be noted that most WTs persist for several days [46]. A total of 308 weather stations were used with only wet days (>1 mm) considered for analysis.

To analyse the rainfall-temperature scaling relationship for each WT pairs of rainfall and corresponding temperature are needed. Often studies use all non-zero rainfall observations [27], whilst some use the maximum intensity within a storm [41, 57]. Here we use wet days (>1 mm) paired with both mean daily dry bulb temperature and mean daily dew point temperature, which are then analysed using quantile regression to estimate the scaling coefficient for the temperature-rainfall relationship [57]. To ensure reliability in our quantile analysis, scaling is only calculated where there are more than 50 pairs of rainfall and corresponding temperature observations conditioned on WT.

Conventionally, most studies bin pairs of precipitation and temperature data into equal width or equal sample temperature bins, for which the extreme precipitation percentiles for each bin are calculated or fitted from a distribution. The trend in the precipitation percentiles are then either visually inspected [27] or analysed through linear regression techniques [26], to determine the scaling of extreme precipitation with temperature. This method results in smaller sample sizes to analyse, possibly reducing the accuracy of the investigation. Furthermore, the binning methodology relies on the assumption that widths of the temperature bins are appropriately determined, as well as what outlier data is excluded to ensure the result is not biased [57]. The use of quantile regression has been presented as an alternative to the binning approach, whereby it has been shown to provide a more flexible and unbiased framework for determining the scaling of extreme precipitation events with temperature, thereby negating the need to assume bin sizes or exclude outlier data [57].

A key difference between quantile regression and linear regression is that the absolute deviation of the errors is minimised with a penalty weighting of p for under-prediction and (1-p) for over-prediction, as opposed to the minimisation of the sum of squared errors used by linear regression techniques. Consider the set of data pairs (x_i, y_i) for i = 1, ..., n. (in this context, x_i is the surface temperature observations and y_i is the rainfall), then the quantile regression can be expressed as [58]:

$$\begin{equation}{y_i} = \beta _0^{(P)} + \beta _1^{(P)}{x_i} + \varepsilon _i^{(P)}\end{equation} \tag{ 1 }$$

where 0 < p < 1 is the quantile and ${\varepsilon _i}$ is an error term with zero expectation. The parameters $\beta _0^{\left( p \right)}$ and $\beta _1^{\left( p \right)}$ are chosen to minimize the cost function D defined as

$$\begin{equation}\eqalign{ D\left( {\beta _0^{\left( p \right)},\beta _1^{\left( p \right)}} \right) = p\sum\limits_{{y_i}\beta _0^{\left( p \right)} + \beta _1^{\left( p \right)}{x_i}} {\left| {{y_i} - \beta _0^{\left( p \right)} - \beta _1^{\left( p \right)}{x_i}} \right|} \\ \,\,\,\,\,\,\,\,\,\,\,{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} + \left( {1 - p} \right)\sum\limits_{{y_i} < \beta _0^{\left( p \right)} + \beta _1^{\left( p \right)}{x_i}} {\left| {{y_i} - \beta _0^{\left( p \right)} - \beta _1^{\left( p \right)}{x_i}} \right|} } \end{equation} \tag{ 2 }$$

The scaling relationship is given by β₁^(p) by taking the log value for the daily rainfall measurements in millimetres and using the transformed equation ${e^{\beta _1^p}} - 1$ to give the scaling rate as a percentage increase/decrease per degree Celsius [31]. Where the scaling relationship is presented as a function of temperature a RLOESS (Robust Locally Weighted Smoothing) second order local polynomial regression is applied to the mean. This non-parametric approach to fitting a smooth curve to noisy data is based on applying a weighting to data surrounding the point of analysis, whereby a lower weighting is assigned to outliers in the regression, such that it reveals the underlying temperature-rainfall scaling of the WTs [58].

To assess the relationship between temperature and rainfall across northern (tropical) Australia, we first pooled data across all stations from wet days (>1 mm) to confirm linearity of the rainfall-temperature relationship and to reduce noise from limited data samples [29, 59]. As dew point temperature has been shown to be a better indicator of atmospheric moisture (than temperature) in calculating scaling relationships [37, 39], the results focus on the relationship of rainfall with dew point temperature, with results for temperature presented in Supplementary Information(available online at stacks.iop.org/ERL/15/094098/mmedia). The average relationship between rainfall and dew point temperature across northern Australia is presented in figure 1.

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For the interested reader the mean daily rainfall and air temperature for each WT are presented in figure S1, with fitted relationships presented in figure S3. There is a negative linear scaling for all WTs (excluding WT1 which shows a unique almost flat linear scaling), highlighting great sensitivity to thermal warming (figure S3). This is unlike the relationship in figure 1 that shows positive scaling with dew point temperature confirming previous findings that dew point temperature is a better indicator of atmospheric moisture and related rainfall intensity [25, 35, 36].

The monsoonal WT3, WT4 and WT5 and trade wind WT6 have very similar scaling and represent the greatest sensitivity to changes in dew point temperature. Close to super C-C scaling is found with the monsoonal (WT3, WT4 and WT5) but also trade wind WTs (WT6). This suggests that scaling in excess C-C is not necessarily an effect of mixing seasons or weather systems. WT1 and WT2 have scaling similar to that of the 7% C-C rate.

For both air and dew point temperature, the scaling is approximately linear and does not display a 'hook' like shape where the scaling reverses at higher temperatures. Whilst all WTs show that rainfall is positively correlated with dew point temperature and negatively correlated with air temperature, the slope of the relationships, and hence degree of association, is different, evidencing the different behavioural patterns of each system. The WTs individually replicate behaviour seen when cumulatively analysed (e.g. positive scaling with dew point temperature). Individually, the WTs appear to respond differently to a change in temperature.

Figure 2 presents the median scaling for each WT, where the scaling has been estimated at each station individually first using dew point temperature and then taking a median across stations. The sensitivity with rainfall (non-exceedance) percentile is presented as this is known to modify the scaling calculated. For the interested reader is repeated using air temperature in figure S4.

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There is a minimal increase in the scaling for air temperature for the most extreme events, but this is not evident with dew point temperatures confirming dew point temperature is a more robust covariate for investigating rainfall-temperature relationships being insensitive to the (non-exceedance) percentile. There is suitable evidence to support the use of dew point temperature response in the tropics [31, 36], and therefore we can consider the positive scaling relationships to have greater reliability as they better match long-term historical extreme rainfall intensity increases in the region [32].

Regardless of the percentile, WT6 produces the strongest positive scaling, consistently greater than 10%/°C. WT4, WT3 and WT1 initially demonstrate scaling greater than 10%/°C, closer to super C-C scaling, but decrease with increasing intensity, falling closer to the 7%/°C C-C rate at the most extreme percentiles. WT2 and WT5 consistently scale below 10%/°C and generally scale at, or just above, the C-C rate.

The overall relationship between temperature and rainfall across WTs is presented in figures 1 and 2, but there is large spatial variation present between sites hence care is needed when interpreting spatially averaged scaling rates. As there is little difference between the scaling for different percentiles for dew point temperature, and lower percentiles exhibited less variability, figure 3 presents the 50th percentile of extreme rainfall event scaling of dew point temperature at 308 weather stations across Tropical Australia. For the interested reader figures S5 and S6 present the scaling with dew point temperature for the 90th and 99th percentile respectively. As the results differ little for higher percentiles the focus remains on the 50th percentile.

Figure 3 shows a distinct spatial variability in scaling across the continent with further variations exhibited among the six WTs. There is greater scaling further south and towards the east coast, particularly for WT3 and WT6. Although the at-site differences in scaling between WTs are predominately not significant, the spatial variation of the scaling highlights that the WTs are each subject to local factors as topography, slope orientation, etc which alter their response to temperature. There is no relationship between the difference in scaling between WTs and the sample size confirming the results are not an artefact related to differing sample size [57].

The greatest differences exist between northern Australia (blue outline) and central tropical Australia (red outline), demarcated by approximately 17.5^°S. While the average scaling for (all) northern Australia stations is positive, a large number of stations exhibit negative scaling. This is very different to the largely positive scaling in the central (inland) tropical region of Australia where the moist air layer is less deep.

The analysis presented in figure 2 is repeated under different geographical regions (on each side of 17.5^°S) to capture the influence of the latitudinal gradient of the rainfall-temperature relationship. Figure 4 presents figure 2 repeated for stations north of 17.5^°S and figure 5 for stations south of 17.5^°S. Here, ANOVA (analysis of variance) tests present that the rainfall scaling between WTs are significantly different from each other except for a few cases for each regions. The details of the ANOVA tests are available in table S1 and figure S10 of Supporting Information. Closer to the tropics (north of 17.5^°S), in a similar fashion to figure 2, trade wind WT6 produces the strongest positive scaling, especially windward of the Great Dividing range, however moving southwards (figure 3), monsoonal WT3 demonstrates significantly more positive scaling. A greater confidence in scaling is captured south of the latitudinal threshold (figure 5), with less variable uncertainty produced for all WTs in this region, suggesting temperature induced changes in weather dynamics may be easier to constrain when moving away from the tropics.

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Unlike the global results in figure 2, both trade wind WT1 and WT2 in scale lower in the northern region of Australia (figure 4), with WT1 scaling closer to the 7%/°C C-C scaling threshold and WT6 consistently below the 14%/°C super C-C scaling threshold at various percentiles.

This region exhibits a unique behaviour, with monsoonal WT5, increasing marginally in scaling at higher percentiles. The remaining WTs evidence a decline with increasing percentile, a similar result to that seen in figure 2. Interestingly, the monsoonal WT3, WT4 and WT5 demonstrate greater negative scaling compared to the trade wind and transitional WTs which produce significant variation in the region. In the north we find many stations with negative scaling rates and increasingly positive scaling as we move further inland (figure S7).

Irrespective of WT, the local scaling in each region demonstrates similarities to scaling over increasing percentile when analysed collectively across tropical Australia as in figure 2, however, the scaling among WTs varies with location as in figure 3. This highlights that local effects can alter the behaviour of weather systems. These effects can range from topographic variation, wind direction (leeward vs windward), moisture availability and surface temperature variability. Locations closer to the tropics demonstrate significantly more variability in scaling for the WTs whereas stations towards central Australia record more consistent scaling (figure S8). This highlights the presence of a latitudinal effect on scaling however, there is also a longitudinal variation, where the Eastern coast of Australia presents significantly more positive scaling—where there is probably a moderate-to-strong interaction with topography. For example, the Great Dividing Range along the Eastern coast of Australia may alter the way WTs interact, with easterly WTs affected by orographic lifting, and longer lasting wet events sustaining higher scaling rates at the daily scale.