The relationship between orographic precipitation, low-level thermodynamic stability, and the synoptic meteorology is explored for the Snowy Mountains of southeast Australia. A 21-yr dataset (May–October, 1995–2015) of upper-air soundings from an upwind site is used to define synoptic indicators and the low-level stability. A K-means clustering algorithm was employed to classify the daily meteorology into four synoptic classes. The initial classification, based only on six synoptic indicators, distinctly defines both the surface precipitation and the low-level stability by class. Consistent with theory, the wet classes are found to have weak low-level stability, and the dry classes have strong low-level stability. By including low-level stability as an additional input variable to the clustering method, statistically significant correlations were found between the precipitation and the low-level stability within each of the four classes. An examination of the joint PDF reveals a highly nonlinear relationship; heavy rain was associated with very weak low-level stability, and conversely, strong low-level stability was associated with very little precipitation. Building on these historical relationships, model output statistics (MOS) from a moderate resolution (12-km spatial resolution) operational forecast were used to develop stepwise regression models designed to improve the 24-h forecast of precipitation over the Snowy Mountains. A single regression model for all days was found to reduce the RMSE by 7% and the bias by 75%. A class-based regression model was found to reduce the overall RMSE by 30% and the bias by 85%.
The Snowy Mountains, with peaks in excess of 2000 m, are the tallest mountains in Australia and are part of a continental divide along the eastern seaboard, known as the Great Dividing Range. Precipitation to the west and north of these mountains naturally flows inland into the Murray and Murrumbidgee Rivers, ultimately reaching the Great Australian Bight, while precipitation to the east naturally flows into the Snowy River reaching the Tasman Sea (Fig. 1a). This water is of immediate economic value for the generation of hydroelectric power and is of further value for downstream consumption, particularly for agriculture across the semiarid Murray–Darling basin. For this reason, water is routinely diverted through a series of tunnels, aqueducts, and pumps from the Snowy River basin across the divide into the inland catchments. The day-to-day management of this water resource requires accurate quantitative precipitation estimates and forecasts over the mountains.
Distinct from daily forecasts and estimates, the climatology of precipitation has been of great interest, particularly over the last decade. For instance, Landvogt et al. (2008) produced a climatology of wintertime precipitation in the Australian Alpine regions, in which daily precipitation was categorized into synoptic clusters consisting of “prefrontal,” “postfrontal,” and “cutoff” classes. Chubb et al. (2011) studied a 20-yr period beginning in 1990, which included most of the “millennium drought,” one of the most severe droughts in the past century (Timbal 2009). Through this period, a 43% decline in wintertime precipitation at high elevations (greater than 1000 m) was observed. Local weather systems were classified into three major synoptic types (embedded lows, cutoff lows, and other) based on the synoptic mean sea level pressure (MSLP) and the 500-hPa geopotential height. Dai et al. (2014, hereafter D14) assigned the daily synoptic meteorology into one of four classes using a K-means clustering algorithm with the upwind upper-air sounding. They found that the two wet clusters accounted for 30% of all days and 70% of the total wintertime precipitation. These two wet classes were associated with fronts (both embedded and cutoff) and postfrontal conditions, respectively. Fiddes et al. (2015) employed a set of circulation dynamics indices to show that there has been a continuing decline in western high-elevation wintertime precipitation of the Australian Alps and a relatively stable rainfall trend in eastern parts of this region. These distinct phenomena are hypothesized to be caused by the likely presence of complex relationships between the amount of precipitation and large-scale climate patterns over this region, especially for extreme events (Theobald et al. 2015).
Orographic precipitation is commonly defined as precipitation arising from the lifting of moist air in response to the presence of mountains. Fundamentally, orographic precipitation depends on the local upwind lower atmospheric stability, commonly referred to as the nondimensional mountain height , or the inverse Froude number (Pierrehumbert and Wyman 1985). Smith (1989) developed a regime diagram for hydrostatic flow over a mountain to illustrate the stagnation onset as a function of the spanwise-to-streamwise horizontal aspect ratio of the topography and . Orographic precipitation is also known to be sensitive to small variations in ambient conditions, the evolution of the moisture fields, and the geometry of the barrier (e.g., Colle 2004; Watson and Lane 2014). These variations give rise to a variety of distinct dynamical and microphysical mechanisms that are classified as orographic mechanisms (Houze 2012).
Forecasting orographic precipitation with a numerical weather predication (NWP) model is challenging due not only to the difficulties of representing the variety of complex physical mechanisms, but also to the limited resolution of a simulation to resolve the complex surface geometry (e.g., Panziera 2010). The evaluation of precipitation forecasts is a further challenge given the high spatial variability of precipitation across a complex terrain and the limited number of surface sites available that can be used to rigorously evaluate the simulations.
Another challenge for local forecasts lies in the unique environment of the Snowy Mountains, which distinguishes itself from other mountainous regions of the world (e.g., the Sierra Nevada in the western United States) by the frequent presence of clouds composed of supercooled liquid water (SLW; Morrison et al. 2013). The development of precipitation in mixed-phase clouds remains poorly understood and difficult to model (e.g., Furtado et al. 2016). Osburn et al. (2016) reported a high frequency of occurrence of SLW (53% of the time between April and September) over the Snowy Mountains from a surface-based radiometer located on the upwind slope. These observations were qualitatively consistent with those from the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite product. As a further challenge, Chubb et al. (2015) found a high catch-ratio loss in the winter precipitation over the high-elevation sites in the Snowy Mountains due to the lack of heated tipping-bucket gauges and wind fences.
Given the many challenges in numerically simulating orographic precipitation, a common practice has been to develop statistically based models to forecast precipitation as a function of some independent predictors (i.e., a regression between synoptic and/or local indicators to forecast precipitation). Statistical models are relatively simpler than NWP models; however, they do not consider the various physical processes of precipitation. Therefore, a combination of current NWP and statistical models seems to be an appropriate solution to address the abovementioned limitations. Model output statistics (MOS) is a commonly used, postprocessing technique to improve the skill of NWP forecasts, employing a statistical method to relate model output to observations (Glahn and Lowry 1972). Examining an ensemble NWP precipitation forecast, D14 found a significant underestimation of precipitation intensity over the high-elevation terrain of the Snowy Mountains. Using their synoptic clustering, they applied a linear regression algorithm to improve the performance of ensemble precipitation forecasts, reducing the root-mean-square error (RMSE) by over 20% for their two wet clusters. The ensemble model, known as the Poor Man’s Ensemble (Ebert 2001), combined the output of seven independent large-scale NWP models to forecast precipitation at a coarse spatial scale of 1° × 1° resolution.
One of the broader aims of the current research is to evaluate the performance of the high-resolution Australian Community Climate and Earth-System Simulator (ACCESS) NWP system (Puri et al. 2013) in forecasting wintertime precipitation across the high-elevation terrain of the Snowy Mountains. A further aim is to test whether the method developed in D14 (based on building a statistical relationship between the variables from synoptic classification and the ensemble forecast of rain to enhance the skill of the model in precipitation intensity prediction) is applicable to an operational, high-resolution precipitation forecast provided by the ACCESS model. Finally, we seek to improve this clustering-based MOS methodology by extending the analysis to explicitly consider the lower atmosphere stability. Limiting our analysis to the cold seasons (May–October), the main outcomes of this study are 1) the categorization of the low-level atmospheric stability for the Snowy Mountains, 2) the investigation of interdependences between the low-level atmospheric stability and the daily precipitation, and 3) the improvement in the accuracy of the daily NWP precipitation forecasts over the Snowy Mountains via stepwise regressions coupled with the results of synoptic categorization.
a. Ground-based wintertime precipitation dataset
Half-hourly precipitation is obtained from seven weather stations above 1100 m across the Snowy Mountains for a 21-yr period from 1995 to 2015. These high-elevation gauges, operated by Snowy Hydro Ltd. (SHL), utilize well-maintained heated tipping buckets for precipitation measurements. For consistency with the soundings, daily precipitation is obtained by aggregating the half-hourly precipitation from 1000 local time (0000 UTC) to the same time of the next day. Chubb et al. (2011, 2016) have evaluated the quality of the precipitation gauge data, finding appropriate accuracy and reliability of these measurements for climatological studies. The locations of the gauges and their long-term mean wintertime precipitation (May–October) are shown in Fig. 1b and Table 1, respectively. For the 21-yr period considered, a full daily record (no missing data) of all stations was available for approximately 60% of the time. When data from one or more sites was either completely missing or its quality was flagged, the area-average daily precipitation was taken to be the mean of the remaining valid observations. No systematic bias in missing or flagged data has previously been noted. For the winter period 2014–15, 92% of all days have at least five stations that had valid data contributing to the mean value.
b. ACCESS model dataset
The model data examined in this study are taken from the current operational ACCESS NWP system. The atmospheric component of ACCESS is the Met Office Unified Model (MetUM), which is a nonhydrostatic model using a semi-implicit, semi-Lagrangian numerical scheme (Davies et al. 2005) to solve deep-atmosphere dynamics. This version of the ACCESS NWP system is referred to as the “Australian Parallel Suite 1” (APS1), which represents the first major upgrade to the system since operational running commenced in August 2010. The ACCESS-R forecasts used in our study for the two years (2014–15) of cold months (May–October) is the Australian-wide regional domain model that covers an area of 65°S–16.95°N and 65°–184.57°E. This model has a horizontal resolution of ~12 km (0.11°) and a vertical resolution of 50 levels, with the highest level at 37.5 km. Benefiting from the 4D data assimilation, the ACCESS-R forecasts are initialized at 0000, 0600, 1200, and 1800 UTC each day and provide hourly precipitation forecasts up to 72 h ahead. The forecast precipitation is the sum of two components that are computed separately in the model using the convective and large-scale (i.e., microphysics) parameterization schemes, respectively. More detailed information on ACCESS-R can be found in Puri et al. (2013). For this study, the mean value of 10 grid boxes covering the Snowy Mountains rain gauges, bounded by latitudes 35.85°–36.40°S and longitudes 148.27°–148.49°E, is employed to represent the ACCESS-R precipitation forecast over the high elevations of the Snowy Mountains.
c. Wagga Wagga sounding dataset
The nearest upwind sounding site to the Snowy Mountains is at Wagga Wagga, located about 180 km to the northwest (Fig. 1a). Both Chubb et al. (2011) and D14 successfully employed these soundings to define the synoptic meteorology during the cold seasons. For the winter period of 1995–2015, the 0000 UTC sounding data were obtained from the database of University of Wyoming (http://weather.uwyo.edu/upperair/sounding.html). Soundings were available for 75% of the days (2897 out of 3843).
Following D14, as a first step we employ a cluster analysis with six synoptic indicators calculated from the Wagga Wagga soundings to investigate interactions between the large-scale environment and daily winter precipitation across the Snowy Mountains. The synoptic indicators chosen are 1) surface pressure at Wagga Wagga (GP), 2) southerly moisture flux up to 250 hPa (QV), 3) westerly moisture flux up to 250 hPa (QU), 4) total moisture up to 250 hPa (TW), 5) root-mean-square wind shear between 850 and 500 hPa (SH), and 6) total totals index (TT). More details regarding these indicators can be found in Table 2. Briefly, the three indicators TW, QV, and QU represent the available amount of water for the formation of precipitation, while TT and SH are considered to be simple estimates of the static stability of the atmosphere (Henry 2000).
Expanding on the framework of D14, the low-level atmospheric stability, that is, the nondimensional mountain height , is added as a seventh predictor. TT and SH are defined between the levels of 850 and 500 hPa, whereas is defined to a height of 1000 m. The mathematical expression of the nondimensional mountain height is
where U is the cross-mountain wind speed (m s−1) and h is the mountain height (h = 1 km) representing the mean elevation of the region (e.g., Reinecke and Durran 2008). Parameter N is the Brunt–Väisälä frequency (s−1). Following Hughes et al. (2009), the moist Brunt–Väisälä frequency (Durran and Klemp 1982) is employed when the relative humidity is greater than 90% (i.e., saturated conditions); otherwise, the dry Brunt–Väisälä frequency is adopted. As the value of N is imaginary when the atmosphere is conditionally unstable, so is the value of . To account for conditionally unstable events, which occur about 11% of the time, we employ the square of the values () for all analyses. Negative values of indicate conditional instability. Hughes et al. (2009) showed that the large square Froude number values have similar behavior as the negative ones (known also as conditionally unstable).
For small values, the low-level atmospheric conditions are generally referred to as being unstable to orographic lifting, implying that the airflow can readily pass over the terrain and mountain waves will be generated. For large values, the flow can be stagnated or diverted laterally around the barrier instead of being lifted over the terrain. In this scenario, stable or blocked conditions (hereafter “blocked days”) are generally observed (e.g., Watson and Lane 2014; Miao and Geerts 2013; Wang et al. 2016). Following the literature, we use equal to 1 as the threshold to distinguish stable and unstable conditions. In practice, however, the transition is not precise, especially as we use only a fixed estimate for the mountain height h. As discussed, the spatial distribution, magnitude, and frequency of orographic precipitation has commonly been found to be sensitive to . When < 1 (unblocked days here), heavier precipitation events can be expected (e.g., Miglietta and Buzzi 2001; Colle 2004; Wang et al. 2016). By inspecting the coastal winds of California, Hughes et al. (2009) showed that the spatial distribution of precipitation became more homogenous for blocked cases, while for unblocked flows local orographic precipitation was strongly dependent on the slope of topography.
d. ERA-Interim reanalysis dataset
Following Theobald et al. (2015), we employ the ERA-Interim reanalysis products (Dee et al. 2011) provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) to derive composite synoptic charts that correspond to the clusters. The ERA-Interim data we employ are from 1995 onward and at a spatial resolution of 0.75° × 0.75°. As the soundings at Wagga Wagga were not available at all times, the six synoptic indicators and values obtained from the ERA-Interim reanalysis dataset are used to fill in missing physical soundings for days in 2014–15. Comparisons of the in situ Wagga Wagga soundings and the corresponding ERA-Interim reanalysis soundings for common days over the 21-yr winter period show strong correlations for all synoptic indicators (GP: 0.99, SH: 0.90, TT: 0.92, TW: 0.97, QV: 0.98, QU: 0.97). Therefore, we consider that using the ERA-Interim reanalysis soundings as a surrogate is appropriate. We note that as the Wagga Wagga soundings are likely employed in the data assimilation for ERA-Interim, the two sets of soundings may not be completely independent. The ERA-Interim soundings may be less skilled when the physical soundings are not available.
a. Cluster analysis
The weather systems in southeastern Australia can be classified using simple clustering methodologies such as the K-means algorithm (Hartigan and Wong 1979). Recent studies by Wilson et al. (2013) and D14 show that winter days in Australia can be categorized into unique synoptic regimes by utilizing six synoptic indicators as independent variables for the clustering procedure, applied in the present study as well. In addition to these six indicators, is also employed to account for the low-level local atmospheric stability.
Determining the optimal number of clusters using the K-means algorithm is challenging given the opposite relationship between the number of clusters and their variances. Following D14, the optimal number of clusters is determined when the probability distributions of the daily rainfall for different clusters can be separated distinctively. Given that a relationship between orographic precipitation and is expected (Colle 2004), it is also worthwhile to appreciate the probability distributions of for each cluster when only the original six indicators are employed for the cluster analysis. A two-sample Kolmogorov–Smirnov (KS) test is applied to insure the distinctiveness of the distributions.
b. Model output statistics approach in precipitation forecasting
The main aim is to improve the daily ACCESS-R precipitation forecasts (Prec_Acc) by combining the results of the synoptic classification with a stepwise regression. To this end, the averaged high-elevation SHL rain gauge observations are taken as the “ground truth” for this analysis. As the aim is to develop an operational MOS algorithm, the six predictors and are taken from ACCESS-R instead of the physical soundings. Note that, because of operational management issues, the number of daily soundings at the Wagga Wagga station has been reduced to roughly three per week (i.e., available 154 days during the two winter period of interest) in recent years.
To assess the skill of ACCESS-R in representing the synoptic regimes as observed by the physical soundings, the six synoptic indicators derived from the Wagga Wagga and ACCESS-R soundings are compared for the same time window (2014–15). The pairwise Pearson correlations between synoptic indicators showed significant correlations (at the level of 0.05) ranging from 66% (for SH) to 99% (for GP), suggesting a good agreement between the model and the observations. Based on this, the synoptic classification scheme is applied to the ACCESS-R soundings. The results show high consistency, justifying the use of the synoptic classification on the ACCESS-R soundings for deriving the regression equations.
As discussed above, within a forecasting context, all variables are taken from the ACCESS-R outputs, including the definition of a rainy day. Model 1 is a single regression for all 366 winter days, regardless of cluster. Model 2 first classifies each day into one of the four clusters, with each cluster having its own regression.
The seven predictors and the ACCESS-R precipitation data were normalized before the regression models were developed. Model selection/complexity is an obvious problem when a large number of predictors are available. A stepwise approach (from a single constant value to quadratic combinations, including an intercept, linear terms, products, and squared terms) was applied to determine the leading predictors and the optimum regression formulation (degree of complexity within equations). Measures of accuracy (e.g., the RMSE or bias) will automatically improve as more predictors are included, but this comes at the cost of model simplicity. To balance the complexity and accuracy, the number of predictors employed was determined by minimizing the Bayesian information criterion (BIC) as an objective function (Liebscher 2012). The BIC is expressed as
where k is the number of free parameters to be estimated, n is the number of observations, and is the maximized value of the likelihood function of the model. Further, we have considered a stepwise procedure that entails a forward selection and backward elimination algorithm. This process includes an examination of any linear dependency between predictors (called as multicollinearity) with redundant variables removed regardless of the goodness-of-fit criterion value (Curtis and Ghosh 2011).
Both regression models were cross validated via a bootstrapping methodology with 10 000 simulations to ensure that the results were statistically robust. For each simulation, 80% of the data are randomly assigned to the control group (used for deriving the coefficients) and the rest for testing.
a. Winter precipitation characteristics
Following Chubb et al. (2011), a rainy day is defined at a threshold of 0.25 mm day−1 for either the average SHL surface observations or ACCESS-R precipitation. A basic summary of the winter precipitation is provided in Table 3. The frequency of rainy days is seen to follow a seasonal cycle with peaks being present in July and August. The intensity, however, is not found to present such a cycle; an overall mean intensity of 10.4 mm day−1 is observed for rainy days, with a standard deviation of 13 mm day−1. The mean intensity can be broken down into quartiles, which again do not display any strong seasonal cycle over the course of the winter. Average monthly precipitation on rainy days indicates lower values in the transition months of May and October with an overall wintertime mean precipitation of about 167 mm.
Focusing on the 2-yr analysis period (2014–15), the SHL surface observations show a reduction in both the frequency of rainy days and the intensity (not significant at the 5% level) compared with the climatology. The statistics with ACCESS-R show that both the frequency and intensity are greater than the observed values (not significant at the 5% level).
b. Synoptic classification
The K-means clustering technique was applied to the Wagga Wagga soundings data (complemented with ERA-Interim soundings for days when the physical soundings were unavailable) for winter days for the 21-yr period of 1995–2015 using the six indicators. When employing the original six sounding variables (TT, SH, QU, QV, GP, and TW), the new analysis was consistent with that of D14; four clusters were the maximum number found to produce distinct daily rainfall probability distributions (Fig. 2, left), passing the KS test at the 5% significance level. As a major objective of this research is to better understand the nature of the low-level stability over the Snowy Mountains and its value as a predictor of orographic precipitation, daily probability distributions are also produced (Fig. 2, right). As with the daily precipitation, four clusters lead to distinct distributions of , suggesting that the low-level stability is reflected in the broader synoptic meteorology.
A K-means clustering was then undertaken using the original six synoptic variables and (seven-variable clustering results are only elaborated hereinafter). As before, four clusters were found to be necessary to distinctly represent the daily precipitation distribution (not shown). C1 and C2 were found to be quite stable to this revision with only a handful of days swapping between clusters. The two dry clusters, however, were found to be more sensitive to this clustering revision. Out of the original 1123 days, 1037 days in C3 remain unchanged (5 days shifted to C1, 50 days to C2, and 31 days to C4), while 823 of the original 1003 days in C4 remain unchanged (35 days shifted to C2 and 145 days to C3). This further suggests that, for the wet clusters C1 and C2, the low-level stability is reflected in the synoptic meteorology. According to Table 4, clusters C1 (frequency of rainy days: 93%, median: 18 mm day−1) and C2 (frequency of rainy days: 78%, median: 4.54 mm day−1) represent the wettest groups while C3 (frequency of rainy days: 52%, median: 0.32 mm day−1) and C4 (frequency of rainy days: 22%, median: 0.03 mm day−1) capture the driest weather. There are fewer days of C1 and C2 than C3 and C4. The mean values of for the four clusters are −0.45, 1.97, 6.24, and 20.20, respectively. Higher values of indicate stronger blocking and, accordingly, less orographic precipitation. The fractions of unblocked days ( < 1) for the four clusters are 63%, 48%, 20% and 5%, respectively. The probability density functions (PDFs) of are broken down by cluster (Figs. 3a–d) for all days. The distribution of for all days is shown in a stacked histogram in Fig. 3e. For rainy days only, the PDF will be shifted to lower (less stable) values of , and for no-rain days shifted to higher ones (more stable; Fig. 3f). The seasonal variability of clusters is also found to be consistent with D14; the relative frequencies of C1 and C2 increase toward the end of winter. C3 is more frequent in early winter and C4 occurs more often in midwinter (not shown). Further, the synoptic meteorology of the wettest cluster C1 is consistent with the analysis of Chubb et al. (2011), indicating a strong northwesterly moisture flux and low surface pressure are commonly present.
To better appreciate the synoptic meteorology of these four clusters (based on seven-variable clustering), ERA-Interim data are used to construct composite maps of the large-scale synoptic indicators for each cluster (Figs. 4–6). Following Theobald et al. (2015), the map domain is 20°–46°S and 120°–140°E in order to capture the dominant synoptic meteorology. For these maps, only the top 25% of days of each cluster are employed. Specifically, these are the days that have the shortest Euclidean distance to the cluster center. While this approach is commonly used when employing daily observations (e.g., Pook et al. 2006; Theobald et al. 2015), it has been noted that the daily resolution of composite maps may mask some unresolved features within daily systems (e.g., a diurnal cycle), as well as overrepresent slow-moving synoptic systems (Gallant et al. 2012).
Starting first with the MSLP and total water (Fig. 4), general synoptic states can be assigned to the four clusters. The MSLP for C1 suggests that the cluster is associated with a frontal passage. It is not possible to distinguish between a cutoff low and an embedded low due to the compositing technique and the low number of clusters. Further, C1 is associated with a maximum in total water over the mountains, which is seen to extend up the Great Dividing Range through New South Wales and Queensland. Chubb et al. (2011) employed a back-trajectory analysis to define a “moisture corridor” across this region for heavy precipitation events. C2, while less well resolved, suggests that the frontal system has passed over the mountains. Chubb et al. (2012) detailed a case study of a frontal passage over the nearby Brindabella ranges, where orographic precipitation was recorded over the 24-h period after the passage of a front. Here, air originating from the Southern Ocean brings limited moisture and modest precipitation. Skipping to the dry cluster C4, a strong high pressure system is evident over the region with very little moisture available. Cluster C3 is less easy to classify, most likely including a variety of synoptic settings that ultimately lead to little precipitation. A high pressure ridge is present across central Australia in the composite map, although it is much weaker than that of C4.
Turning to the moisture fluxes (Fig. 5), the strong northerly and westerly moisture fluxes of C1 stand out, consistent with a frontal passage. There is virtually no northerly moisture flux over the Snowy Mountains for C2. It is strictly a westerly flux that is bringing the moisture for precipitation, again suggesting a postfrontal environment (Chubb et al. 2012). Spatially, C3 and C4 are quite similar, with weak fluxes evident over the mountains. C4 is drier and has weaker fluxes of the two.
The synoptic stability composites (TT and SH, Fig. 6) further complete the general classifications of clusters C1 (frontal), C2 (postfrontal), and C4 (high pressure system). Over the mountains, the atmosphere is most unstable during a frontal passage and most stable under a high pressure system. Unlike the other composite maps, however, these maps for C3 are now quite distinct, especially for the midlevel shear (SH). Very weak shear is evident just to the south of the Snowy Mountains, over Bass Straight and extending into the Tasman Sea. This perhaps suggests that the upper free troposphere may be important in defining the synoptic meteorology of this cluster. A more thorough analysis of C3 revealed that a number of the days included in the composite included “east coast lows” (e.g., 2 October 2004 and 18 September 2015; Bureau of Meteorology 2017).
A number of studies have diagnosed the principal synoptic types in southeastern Australia (e.g., Chubb et al. 2011; Pook et al. 2006). Specifically, Theobald et al. (2015) applied an automated approach to generate synoptic types by combining meteorological variables throughout the depth of the troposphere across the Snowy Mountains. It is interesting to compare and contrast our four wintertime clusters with their 11 synoptic types. Only a limited comparison is possible as Theobald et al. (2015) considered only heavy precipitation days (threshold of 10 mm day−1) for the full year. Further, instead of employing physical observations from a sounding site, they employed 13 variables provided from the ERA-Interim reanalysis. In spite of these substantial differences, it is evident from the composite maps that C1 and C2 correspond to Theobald clusters T5 (prefrontal troughs, approaching cold fronts) and T1 (embedded cold fronts). Not surprisingly, dry clusters C3 and C4 (occurring ~70% of the time during the cold seasons and most frequently at the start and middle of winter) were not represented by any of the Theobald clusters, since their analysis was limited to wet conditions throughout the year.
In summary, C1 includes the heaviest precipitation days and the lowest values (and the highest frequency of unblocked cases). It occurs for 10% of the winter days, but accounts for 39% of the precipitation. It is associated with frontal passages. C2 is associated with postfrontal conditions. It occurs 22% of the time and accounts for 33% of the precipitation. C3 is associated with a variety of synoptic conditions. It is a dry cluster, occurring 40% of the time and accounts for 23% of the total precipitation. Finally, C4 is the driest cluster associated with high pressure systems dominating the region over the Snowy Mountains and to its north. This occurs ~30% of the time and accounts for only 5% of the precipitation. It has also the strongest low-level stability (i.e., highest values).
c. Relationships between independent variables and observed precipitation
Given that an aim of this research is to improve orographic forecasts of precipitation through model output statistics, it is worthwhile to examine the correlation of these predictors with the precipitation. Working with the historic data (1995–2015), QV (−0.51), QU (0.46), GP (0.46), and TW (0.43) are highly correlated with precipitation, while the stability measures (−0.24), TT (0.23), and SH (0.16) are less strongly correlated. All correlations are statistically significant, confirming our underlying premise that these variables can be of use in forecasting orographic precipitation. Table 5 also illustrates the cross correlations between these variables at the 0.01 significant level. The highest significant correlation is between GP and QU (−0.53), while, the lowest significance is for SH–TT (−0.136). SH–TW and SH–QV did not indicate significant linear correlations.
Returning to the correlation between precipitation and the seven predictors, it is worthwhile to break down the analysis to the four clusters (Table 6). Not surprisingly, the correlation between the precipitation and any predictor is reduced within an individual cluster defined by these predictors. While greatly reduced, the correlations of QV, QU, GP, and remain statistically significant within each of the four clusters. TW remains significantly correlated within C1, C2, and C3. SH is only significantly correlated with precipitation in C4. Table 6 also details the rank correlation of these predictors against the precipitation. For the three stability predictors (SH, TT, and ), the rank correlation (which measures the degree of similarity between two rankings assigned to two members of a set) is greater in magnitude than the linear correlation, suggesting a nonlinear relationship exists between precipitation and stability. The rank correlation for is nearly as great in magnitude as that for GP, both of which are negative.
To better appreciate the interdependencies between and precipitation, their joint probabilities are explored with the use of a copula function (Sklar 1959). Copula functions have been widely used (e.g., Drouet-Mari and Kotz 2001; Genest and Plante 2003; Nicoloutsopoulos 2005) to detect the probabilistic relationships between variables and to show that a set of variables with low correlations (even zero) may still retain complicated “tail” dependence structures. Unlike the commonly used correlation measures, copulas are invariant under strictly increasing transformations of random variables that are used for comprehensively exploring nonparametric measures of interdependence (Schweizer and Wolff 1981). Copulas are not restricted to any particular type of parametric functions (e.g., Gumbel distribution) for the marginal or the joint probability distributions (Madadgar and Moradkhani 2014). According to Fig. 7a, the scatterplot and marginal histograms illustrate the relationship between precipitation and in which, overall, large values of precipitation are associated with low values of and high values of are associated with weak precipitation. The marginal histograms further indicate that the vast majority of data are located in the range of 0.25–10 mm for precipitation and from −1 to 5 for , overwhelming the tail observations outside this range.
Figures 7b and 7c illustrate the marginal CDF distributions of (ranging from −5 to 25) and precipitation (ranging from 0 up to 100 mm) for rainy days based on the data from 1995 to 2015. A steep slope implies a higher density of data within a considered range; precipitation values less than 10 mm and −1 < < 5 have the highest frequency of occurrences (similar to what is concluded from the marginal histograms). Figures 7b and 7c are the main input elements used in calculating the joint probability values and forming the copula function. The Frank copula (Frank 1979), selected as the best-fitting copula in this study, suggests that values greater than 7.8 correspond to precipitation events less than 0.6 mm, and values less than −0.3 correspond to precipitation events greater than 28.4 mm (Fig. 7d). Conversely, low frequencies are given to pairwise events when and precipitation values are either both low ( < −0.3 and precipitation < 0.6 mm) or high ( > 7.8 and precipitation > 28.4 mm) (Fig. 7d). In summary, the copula identifies and quantifies the tail-end relationship (as previously highlighted by AghaKouchak et al. 2010) between and precipitation that was not evident in the simple correlation coefficient. An inverse, nonlinear relationship between and precipitation was also suggested by the individual probability distributions of Fig. 2.
d. Daily winter precipitation forecasting
1) Precipitation estimations by ACCESS-R
The daily ACCESS-R precipitation forecasts serve as our control forecast for the full two-yr (2014–15) winter (May–October) period. When these precipitation forecasts were evaluated against SHL’s high-elevation surface observations, the overall RMSE was 4.20 mm with a bias of 0.3 mm. On average, ACCESS-R slightly overestimated the surface observations. Looking at observed rain days only (0.25 mm day−1 threshold), the hit rate for ACCESS-R was 88% with an RMSE of 6.2 mm day−1 and a bias of 0.42 mm day−1. For no-rain days, the false alarm rate was 20.7% with an RMSE of 0.58 mm day−1 and a bias of 0.19 mm day−1.
These basic statistics can readily be broken down into the four clusters (Table 7). As expected, the wet frontal cluster C1 has the highest percentage of rain days, the greatest overall RMSE of 10.17 mm day−1, and bias of 0.76 mm day−1. For rain days only, the hit rate was 97%. Over the 2 years of data (no-rain days), the false alarm rate was calculated to be zero for C1. The relatively wet postfrontal cluster C2 shows the next highest overall percentage of hits (69%) and RMSE (5.2 mm day−1). The overall bias for C2 is 0.3 mm day−1. Most notable for this cluster is the high rate of false alarm (38%) when looking at no-rain days. ACCESS-R produces precipitation too readily in these postfrontal conditions. For the dry clusters, C3 and C4, the overall RMSEs are small. They are less skilled on rain days (hit rates of 86 and 72%, respectively) and relatively skilled on no-rain days (false alarm rates of 27 and 13%, respectively).
More advanced metrics can readily be employed on these observations to assess the skill of deterministic precipitation forecasts, following the World Meteorological Organization Working Group on Numerical Experimentation (WWRP/WGNE 2008). For example, the frequency bias score (FBS; the ratio of the frequency of forecast precipitation events to that of observed, where 1 indicates a perfect score) was calculated to be 1.12, and 0.97, 1.05, 1.24, 1.16 for the overall time period and then broken down by cluster, respectively. An FBS score greater than one suggests that the model generally tends to predict rain days more frequently than they are observed. The absence of a false alarm in C1 led to an FBS score of just under unity, indicating the tendency to less frequently predict precipitation; however, the opposite occurred in the rest of the classes. The equitable threat score (ETS; the fraction of correctly predicted observed and/or forecast events that has a range from −⅓ to 1, where 0 indicates no skill and 1 is a perfect score.) was calculated to be 0.49, and 0.73, 0.39, 0.41, 0.39 for the overall time period and the four clusters, respectively. The ETS accounts for correct forecasts due to chance when computing an index that combines the hit rate and the false alarm ratio. Ebert (2001) finds an ETS of around 0.4 for the Poor Man’s Ensemble precipitation predictions, suggesting that the present system is especially skillful in identifying heavy-precipitation events. The accuracy score (the fraction of “correct” forecasts) was also calculated to be 0.83, 0.97, 0.84, 0.79, 0.84 for the overall time period and the four clusters, respectively, indicating an encouraging result, with the most accurate forecast in C1.
2) Model 1: Single regression model
The single regression model (model 1) is based on only two predictors, a linear combination of the ACCESS-R precipitation forecast and QU (Table 8), determined by the stepwise approach and the BIC. The ACCESS-R forecast accounts for about 70% of the variance while QU contributed roughly 14%. Four goodness-of-fit criteria [RMSE, the coefficient of determination r2, the hit rate, and bias (for all days)] are calculated to quantify the improvement in using a simple regression formula from the control ACCESS-R forecast precipitation (Table 9).
When limited to forecast precipitation days, the straight ACCESS-R forecast had an RMSE of 6 mm day−1, a bias of 0.68 mm day−1, and a hit rate of 76% for the full 2-yr period (results in Table 9 are different than those previously presented in Table 7 as the selection of a rain day was changed from the surface observations to the ACCESS-R forecast to allow for an operational application). When the single regression model is applied, forecast precipitation had an RMSE of 5.6 mm day−1, a bias of −0.15 mm day−1, a hit rate of 78%, and r2 at 0.83. The single regression produced a 7% reduction in the RMSE. We can examine the forecast rain days by cluster, even when employing a single regression. The single regression model improves the RMSE in all four clusters, most strongly in C4. The bias is also reduced in each of the four clusters, most strongly in C4 and C1. The coefficient of determination remains largely unchanged by cluster. The single regression does not strongly improve one or more clusters at the expense of the remaining clusters. The improvement is largely across all clusters.
3) Model 2: Cluster-based regression model
The cluster-based regression (model 2) produces an RMSE of 4.2 mm day−1, a bias of −0.1 mm day−1, an r2 of 0.89, and a hit rate of 84% when computed over all days. The RMSE was reduced by 30% and the bias was reduced by 7% in comparison to the control ACCESS-R forecast precipitation.
When breaking this down into the individual clusters, large improvements are identified in C1 (24% reduction in RMSE) and C4 (42% reduction in RMSE). Further, r2 increases most for these two clusters. While the gains for cluster C2 were more modest (C2 has the simplest regression fit), improvement is evident for all goodness-of-fit criteria. The cluster-based regressions also reduced the false alarm rate (as well as improving the hit rate) in all clusters, but more strongly in the two wet ones.
Histograms of goodness-of-fit criteria for the cluster-based regression model for C1 (model 2 C1) derived from cross-validation analysis are illustrated in Fig. 8. Because of the presence of skewness in histograms of coefficients and goodness-of-fit criteria (Fig. 8), for all models, the median of the histograms is considered and reported to reduce the influence of outliers. Similar histograms are obtained for other classes but not shown. It should be noted that the RMSE and bias histograms are derived from the normalized values of estimations that are converted to millimeters for the final comparisons between the models.
A primary aim of this research has been to better understand the sensitivity of precipitation over the Snowy Mountains of southeast Australia to the low-level stability (as measured by the square of the nondimensional mountain height ) and to understand the relationship between the low-level stability and the synoptic meteorology, if any. A further aim has been to exploit any uncovered relationship between the nondimensional mountain height and precipitation to improve forecasts of precipitation over these mountains for water management purposes.
It has long been appreciated that orographic precipitation is sensitive to with strong stability (large ) suppressing rainfall and, conversely, weak stability enhancing orographic precipitation (e.g., Watson and Lane 2014). An analysis of 21 years of wintertime data confirmed this relationship for the Snowy Mountains. Average was significantly greater for no-rain days (14.5) than for rain days (3.9). A rain day was defined by a threshold of 0.25 mm day−1. A deeper analysis of these data found that the relationship was primarily driven by extreme values with very large values of (>7.8) being associated with suppressed rainfall and very heavy rainfall (>28 mm day−1) being associated with low values of .
Previous research (D14) demonstrated that the precipitation over these mountains is also sensitive to the large-scale synoptic meteorology. Following this methodology, a K-means clustering algorithm was applied to the precipitation using six synoptic predictors (GP, TW, QU, QV, SH, and TT). As before, four clusters were identified as the minimum number of clusters necessary to distinguish the precipitation distribution between clusters. Examining these more thoroughly with the use of ERA-Interim reanalysis data, the wet cluster (C1) was associated with frontal passages. C2 was also a wet cluster, being associated with postfrontal conditions. C4 was a dry cluster associated with suppressed (stable) conditions, and C3 was a dry cluster constructed from the remaining observations. Distributions of were also distinguished by this clustering, suggesting that was also strongly defined by the synoptic meteorology.
When repeating the clustering for seven variables (the original six predictors plus ), only minor changes were observed for the two wet clusters, while changes were observed in the number and composition of dry clusters, C3 and C4. A further investigation on the relationship between the seven predictors and the observed precipitation showed that they are all statistically correlated, justifying their application in forecasting orographic precipitation. Higher values in rank correlations of the stability indicators (more obviously for ) suggested a nonlinear relationship rather than linear relationship.
D14 noted that over the Snowy Mountains an NWP model demonstrated more skill at predicting the synoptic meteorology than the precipitation. Thus, MOS of the synoptic variables was used to improve precipitation forecasts. Two different regression models were developed with the aim of improving the precipitation forecasts of the ACCESS-R model. Specifically, the goal was to reduce the RMSE and bias. First, a single regression model was developed and applied to 2 years (2014–15 wintertime months) of ACCESS-R precipitation forecasts. This led to a 7% reduction in the RMSE and a 78% reduction in the bias. Then, a cluster-based regression was applied leading to a 30% reduction in the RMSE and an 85% reduction in the bias.
The stepwise-based regression method (Curtis and Ghosh 2011) employed initially seeks a leading predictor that is able to convey a large portion of the dependent variable information (i.e., the ACCESS-R precipitation forecasts). Following on, the regression methodology tries to select another leading predictor to further improve the accuracy of forecasts. While additional predictors will improve accuracy, they are only added if they avoid redundancy, collinearity, and complexity. It is important to note that all of the tested indicators have already been utilized as input variables to the clustering algorithm. Having TT as a leading predictor in C1 suggests that the model systematic error may be mostly associated with the variation of large-scale stability. Following this logic, the model precipitation overestimation in C4 may be rooted in the misrepresentation of the moisture flux.
A potential extension of this work could be to consider the application of statistical adjustments for forecasts at longer lead times. The ACCESS-R model only runs for 36 h, preventing such testing on the immediate observations and simulations. As the accuracy of the ACCESS system continues to improve, the main value of such statistical analysis may be in the identification of the source of systematic errors in the system.
This study is supported by Australian Research Council Linkage Project LP160101494. We are grateful to Snowy Hydro Ltd. for providing the precipitation data for the Snowy Mountains. In addition, we thank the reviewers for their insightful contributions to this manuscript.