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Characteristics of Wintertime Daily Precipitation over the Australian

FAHIMEH SARMADI,YI HUANG, AND STEVEN T. SIEMS School of Earth, Atmosphere and Environment, and Australian Research Council Centre of Excellence for Climate System Science, Monash University, Victoria,

MICHAEL J. MANTON School of Earth, Atmosphere and Environment, Monash University, Victoria, Australia

(Manuscript received 20 April 2017, in final form 30 August 2017)

ABSTRACT

The relationship between orographic precipitation, low-level thermodynamic stability, and the synoptic me- teorology 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 as- sociated 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 re- gression 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%.

1. Introduction inland catchments. The day-to-day management of this water resource requires accurate quantitative pre- The Snowy Mountains, with peaks in excess of 2000 m, cipitation estimates and forecasts over the mountains. are the tallest mountains in Australia and are part of a Distinct from daily forecasts and estimates, the cli- continental divide along the eastern seaboard, known as matology of precipitation has been of great interest, the Great Dividing Range. Precipitation to the west and particularly over the last decade. For instance, Landvogt north of these mountains naturally flows inland into the et al. (2008) produced a climatology of wintertime pre- Murray and Murrumbidgee Rivers, ultimately reaching cipitation in the Australian Alpine regions, in which the Great Australian Bight, while precipitation to the daily precipitation was categorized into synoptic clusters east naturally flows into the reaching the consisting of ‘‘prefrontal,’’ ‘‘postfrontal,’’ and ‘‘cutoff’’ Tasman Sea (Fig. 1a). This water is of immediate eco- classes. Chubb et al. (2011) studied a 20-yr period be- nomic value for the generation of hydroelectric power ginning in 1990, which included most of the ‘‘millennium and is of further value for downstream consumption, drought,’’ one of the most severe droughts in the past particularly for agriculture across the semiarid Murray– century (Timbal 2009). Through this period, a 43% de- Darling basin. For this reason, water is routinely di- cline in wintertime precipitation at high elevations verted through a series of tunnels, aqueducts, and pumps (greater than 1000 m) was observed. Local weather from the Snowy River basin across the divide into the systems were classified into three major synoptic types (embedded lows, cutoff lows, and other) based on the Corresponding author: Fahimeh Sarmadi, fahimeh.sarmadi@ synoptic mean sea level pressure (MSLP) and the 500-hPa monash.edu geopotential height. Dai et al. (2014, hereafter D14)

DOI: 10.1175/JHM-D-17-0072.1 Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 09/26/21 07:52 PM UTC 2850 JOURNAL OF HYDROMETEOROLOGY VOLUME 18

FIG. 1. (a) Map of the Snowy Mountains analysis region (red box) in southeastern Australia showing the closest upper-wind site of the BoM to the Snowy Mountains (). (b) Location of the seven alpine rain gauges used in this study [enlarged from the red box in (a)]. assigned the daily synoptic meteorology into one of four moisture fields, and the geometry of the barrier (e.g., classes using a K-means clustering algorithm with the Colle 2004; Watson and Lane 2014). These variations upwind upper-air sounding. They found that the two wet give rise to a variety of distinct dynamical and micro- clusters accounted for 30% of all days and 70% of the physical mechanisms that are classified as orographic total wintertime precipitation. These two wet classes mechanisms (Houze 2012). were associated with fronts (both embedded and cutoff) Forecasting orographic precipitation with a numerical and postfrontal conditions, respectively. Fiddes et al. weather predication (NWP) model is challenging due (2015) employed a set of circulation dynamics indices not only to the difficulties of representing the variety of to show that there has been a continuing decline in complex physical mechanisms, but also to the limited western high-elevation wintertime precipitation of the resolution of a simulation to resolve the complex surface Australian Alps and a relatively stable rainfall trend in geometry (e.g., Panziera 2010). The evaluation of pre- eastern parts of this region. These distinct phenomena are cipitation forecasts is a further challenge given the high hypothesized to be caused by the likely presence of spatial variability of precipitation across a complex ter- complex relationships between the amount of precipita- rain and the limited number of surface sites available tion and large-scale climate patterns over this region, es- that can be used to rigorously evaluate the simulations. pecially for extreme events (Theobald et al. 2015). Another challenge for local forecasts lies in the Orographic precipitation is commonly defined as unique environment of the Snowy Mountains, which precipitation arising from the lifting of moist air in distinguishes itself from other mountainous regions of response to the presence of mountains. Fundamentally, the world (e.g., the Sierra Nevada in the western United orographic precipitation depends on the local upwind States) by the frequent presence of clouds composed of lower atmospheric stability, commonly referred to as the supercooled liquid water (SLW; Morrison et al. 2013). nondimensional mountain height H^, or the inverse The development of precipitation in mixed-phase clouds Froude number (Pierrehumbert and Wyman 1985). remains poorly understood and difficult to model (e.g., Smith (1989) developed a regime diagram for hydro- Furtado et al. 2016). Osburn et al. (2016) reported a high static flow over a mountain to illustrate the stagnation frequency of occurrence of SLW (53% of the time be- onset as a function of the spanwise-to-streamwise hori- tween April and September) over the Snowy Mountains zontal aspect ratio of the topography and H^. Orographic from a surface-based radiometer located on the upwind precipitation is also known to be sensitive to small slope. These observations were qualitatively consistent variations in ambient conditions, the evolution of the with those from the Moderate Resolution Imaging

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Spectroradiometer (MODIS) satellite product. As a precipitation forecasts over the Snowy Mountains via further challenge, Chubb et al. (2015) found a high stepwise regressions coupled with the results of synoptic catch-ratio loss in the winter precipitation over the high- categorization. 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 2. Datasets orographic precipitation, a common practice has been to a. Ground-based wintertime precipitation dataset develop statistically based models to forecast precipita- tion as a function of some independent predictors (i.e., a Half-hourly precipitation is obtained from seven regression between synoptic and/or local indicators to weather stations above 1100 m across the Snowy Moun- forecast precipitation). Statistical models are relatively tains for a 21-yr period from 1995 to 2015. These high- simpler than NWP models; however, they do not con- elevation gauges, operated by Ltd. (SHL), sider the various physical processes of precipitation. utilize well-maintained heated tipping buckets for pre- Therefore, a combination of current NWP and statistical cipitation measurements. For consistency with the models seems to be an appropriate solution to address soundings, daily precipitation is obtained by aggregating the abovementioned limitations. Model output statistics the half-hourly precipitation from 1000 local time (0000 (MOS) is a commonly used, postprocessing technique to UTC) to the same time of the next day. Chubb et al. improve the skill of NWP forecasts, employing a statis- (2011, 2016) have evaluated the quality of the pre- tical method to relate model output to observations cipitation gauge data, finding appropriate accuracy and (Glahn and Lowry 1972). Examining an ensemble NWP reliability of these measurements for climatological precipitation forecast, D14 found a significant underes- studies. The locations of the gauges and their long-term timation of precipitation intensity over the high-elevation mean wintertime precipitation (May–October) are terrain of the Snowy Mountains. Using their synoptic shown in Fig. 1b and Table 1, respectively. For the 21-yr clustering, they applied a linear regression algorithm to period considered, a full daily record (no missing data) of improve the performance of ensemble precipitation all stations was available for approximately 60% of the forecasts, reducing the root-mean-square error (RMSE) time. When data from one or more sites was either by over 20% for their two wet clusters. The ensemble completely missing or its quality was flagged, the area- model, known as the Poor Man’s Ensemble (Ebert 2001), average daily precipitation was taken to be the mean of combined the output of seven independent large-scale the remaining valid observations. No systematic bias in NWP models to forecast precipitation at a coarse spatial missing or flagged data has previously been noted. For scale of 18318 resolution. the winter period 2014–15, 92% of all days have at least One of the broader aims of the current research is five stations that had valid data contributing to the to evaluate the performance of the high-resolution mean value. Australian Community Climate and Earth-System b. ACCESS model dataset Simulator (ACCESS) NWP system (Puri et al. 2013)in forecasting wintertime precipitation across the high- The model data examined in this study are taken from elevation terrain of the Snowy Mountains. A further the current operational ACCESS NWP system. The at- aim is to test whether the method developed in D14 mospheric component of ACCESS is the Met Office (based on building a statistical relationship between the Unified Model (MetUM), which is a nonhydrostatic model variables from synoptic classification and the ensemble using a semi-implicit, semi-Lagrangian numerical scheme forecast of rain to enhance the skill of the model in (Davies et al. 2005) to solve deep-atmosphere dynamics. precipitation intensity prediction) is applicable to an This version of the ACCESS NWP system is referred to as operational, high-resolution precipitation forecast the ‘‘Australian Parallel Suite 1’’ (APS1), which represents provided by the ACCESS model. Finally, we seek to the first major upgrade to the system since operational improve this clustering-based MOS methodology by running commenced in August 2010. The ACCESS-R extending the analysis to explicitly consider the lower forecasts used in our study for the two years (2014–15) of atmosphere stability. Limiting our analysis to the cold cold months (May–October) is the Australian-wide re- seasons (May–October), the main outcomes of this gional domain model that covers an area of 658S–16.958N study are 1) the categorization of the low-level atmo- and 658–184.578E. This model has a horizontal resolution spheric stability H^ for the Snowy Mountains, 2) the in- of ;12 km (0.118) and a vertical resolution of 50 levels, vestigation of interdependences between the low-level with the highest level at 37.5 km. Benefiting from the 4D atmospheric stability and the daily precipitation, and 3) data assimilation, the ACCESS-R forecasts are initialized the improvement in the accuracy of the daily NWP at 0000, 0600, 1200, and 1800 UTC each day and provide

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TABLE 1. Properties of precipitation gauges sites at high altitudes in the Snowy Mountains. The mean winter precipitation values are calculated over the period 1995–2015.

Site Start year Longitude (8) Latitude (8) Elevation (m) Mean winter precipitation (mm) Tooma 1992 148.28 236.05 1221 1156.96 1992 148.31 236.30 1175 1054.92 Jagungal 1990 148.39 236.14 1659 1104.37 The Kerries 1995 148.38 236.26 1740 1027.27 1992 148.37 236.38 1175 881.84 Guthega 1994 148.41 236.35 1320 963.30 Cabramurra 1955 148.38 235.94 1482 857.69

hourly precipitation forecasts up to 72 h ahead. The large-scale environment and daily winter precipitation forecast precipitation is the sum of two components that across the Snowy Mountains. The synoptic indicators are computed separately in the model using the convec- chosen are 1) surface pressure at Wagga Wagga (GP), 2) tive and large-scale (i.e., microphysics) parameterization southerly moisture flux up to 250 hPa (QV), 3) westerly schemes, respectively. More detailed information on moisture flux up to 250 hPa (QU), 4) total moisture up to ACCESS-R can be found in Puri et al. (2013).Forthis 250 hPa (TW), 5) root-mean-square wind shear between study, the mean value of 10 grid boxes covering the Snowy 850 and 500 hPa (SH), and 6) total totals index (TT). Mountains rain gauges, bounded by latitudes 35.858– More details regarding these indicators can be found in 36.408S and longitudes 148.278–148.498E, is employed to Table 2. Briefly, the three indicators TW, QV, and QU represent the ACCESS-R precipitation forecast over the represent the available amount of water for the formation high elevations of the Snowy Mountains. of precipitation, while TT and SH are considered to be simple estimates of the static stability of the atmosphere c. Wagga Wagga sounding dataset (Henry 2000). Expanding on the framework of D14, the low-level The nearest upwind sounding site to the Snowy atmospheric stability, that is, the nondimensional Mountains is at Wagga Wagga, located about 180 km to mountain height H^, is added as a seventh predictor. TT the northwest (Fig. 1a). Both Chubb et al. (2011) and and SH are defined between the levels of 850 and D14 successfully employed these soundings to define the 500 hPa, whereas H^2 is defined to a height of 1000 m. The synoptic meteorology during the cold seasons. For the mathematical expression of the nondimensional moun- winter period of 1995–2015, the 0000 UTC sounding tain height is data were obtained from the database of University of Wyoming (http://weather.uwyo.edu/upperair/sounding.html). 1 Nh H^ 5 5 , (1) Soundings were available for 75% of the days (2897 out Fr U of 3843). 2 Following D14, as a first step we employ a cluster anal- where U is the cross-mountain wind speed (m s 1)andh ysis with six synoptic indicators calculated from the Wagga is the mountain height (h 5 1 km) representing the mean Wagga soundings to investigate interactions between the elevation of the region (e.g., Reinecke and Durran 2008).

TABLE 2. Summary of six synoptic indicators used to represent the large-scale environment.

Variable Abbreviation Formula Unit Surface pressure at Wagga Wagga GP Not applicable hPa ð​ 1 2 2 Southerly moisture flux up to 250 hPa QV qV dp kg s 1 m 1 g ð​ 1 2 2 Westerly moisture flux up to 250 hPa QU qU dp kg s 1 m 1 g ð​ 1 2 Total moisture up to 250 hPa TW qdp hPa s2 m 1 g sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   2 2 D D 21 Root-mean-square wind shear between 850 and 500 hPa SH U 1 V s Dz Dz 8 Total totals index TT T(850) 2 2T(500) 1 Td(850) C

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2 Parameter N is the Brunt–Väisälä frequency (s 1). Fol- winter period show strong correlations for all synoptic lowing Hughes et al. (2009), the moist Brunt–Väisälä indicators (GP: 0.99, SH: 0.90, TT: 0.92, TW: 0.97, QV: frequency (Durran and Klemp 1982) is employed when 0.98, QU: 0.97). Therefore, we consider that using the the relative humidity is greater than 90% (i.e., saturated ERA-Interim reanalysis soundings as a surrogate is ap- conditions); otherwise, the dry Brunt–Väisälä frequency propriate. We note that as the Wagga Wagga soundings is adopted. As the value of N is imaginary when the at- are likely employed in the data assimilation for ERA- mosphere is conditionally unstable, so is the value of H^. Interim, the two sets of soundings may not be completely To account for conditionally unstable events, which occur independent. The ERA-Interim soundings may be less about 11% of the time, we employ the square of the H^ skilled when the physical soundings are not available. values (H^2) for all analyses. Negative values of H^2 in- dicate conditional instability. Hughes et al. (2009) showed that the large square Froude number values have similar 3. Methodology behavior as the negative ones (known also as condition- a. Cluster analysis ally unstable). For small H^2 values, the low-level atmospheric con- The weather systems in southeastern Australia can be ditions are generally referred to as being unstable to classified using simple clustering methodologies such as orographic lifting, implying that the airflow can readily the K-means algorithm (Hartigan and Wong 1979). pass over the terrain and mountain waves will be gen- Recent studies by Wilson et al. (2013) and D14 show that erated. For large H^2 values, the flow can be stagnated or winter days in Australia can be categorized into unique diverted laterally around the barrier instead of being synoptic regimes by utilizing six synoptic indicators as lifted over the terrain. In this scenario, stable or blocked independent variables for the clustering procedure, ap- conditions (hereafter ‘‘blocked days’’) are generally plied in the present study as well. In addition to these six observed (e.g., Watson and Lane 2014; Miao and Geerts indicators, H^2 is also employed to account for the low- 2013; Wang et al. 2016). Following the literature, we use level local atmospheric stability. H^2 equal to 1 as the threshold to distinguish stable and Determining the optimal number of clusters using the unstable conditions. In practice, however, the transition K-means algorithm is challenging given the opposite is not precise, especially as we use only a fixed estimate relationship between the number of clusters and their for the mountain height h. As discussed, the spatial variances. Following D14, the optimal number of clus- distribution, magnitude, and frequency of orographic ters is determined when the probability distributions of precipitation has commonly been found to be sensitive the daily rainfall for different clusters can be separated to H^2. When H^2 , 1 (unblocked days here), heavier distinctively. Given that a relationship between oro- precipitation events can be expected (e.g., Miglietta and graphic precipitation and H^2 is expected (Colle 2004), it Buzzi 2001; Colle 2004; Wang et al. 2016). By inspecting is also worthwhile to appreciate the probability distri- the coastal winds of California, Hughes et al. (2009) butions of H^2 for each cluster when only the original six showed that the spatial distribution of precipitation indicators are employed for the cluster analysis. A two- became more homogenous for blocked cases, while for sample Kolmogorov–Smirnov (KS) test is applied to unblocked flows local orographic precipitation was insure the distinctiveness of the distributions. strongly dependent on the slope of topography. b. Model output statistics approach in precipitation d. ERA-Interim reanalysis dataset forecasting Following Theobald et al. (2015),weemploytheERA- The main aim is to improve the daily ACCESS-R Interim reanalysis products (Dee et al. 2011) provided by precipitation forecasts (Prec_Acc) by combining the the European Centre for Medium-Range Weather results of the synoptic classification with a stepwise re- Forecasts (ECMWF) to derive composite synoptic charts gression. To this end, the averaged high-elevation SHL that correspond to the clusters. The ERA-Interim data rain gauge observations are taken as the ‘‘ground truth’’ we employ are from 1995 onward and at a spatial reso- for this analysis. As the aim is to develop an operational lution of 0.75830.758. As the soundings at Wagga Wagga MOS algorithm, the six predictors and H^2 are taken were not available at all times, the six synoptic indicators from ACCESS-R instead of the physical soundings. and H^2 values obtained from the ERA-Interim reanalysis Note that, because of operational management issues, dataset are used to fill in missing physical soundings for the number of daily soundings at the Wagga Wagga days in 2014–15. Comparisons of the in situ Wagga station has been reduced to roughly three per week Wagga soundings and the corresponding ERA-Interim (i.e., available 154 days during the two winter period of reanalysis soundings for common days over the 21-yr interest) in recent years.

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To assess the skill of ACCESS-R in representing the simulation, 80% of the data are randomly assigned to synoptic regimes as observed by the physical soundings, the control group (used for deriving the coefficients) and the six synoptic indicators derived from the Wagga the rest for testing. Wagga and ACCESS-R soundings are compared for the same time window (2014–15). The pairwise Pearson correlations between synoptic indicators showed sig- 4. Results nificant correlations (at the level of 0.05) ranging from a. Winter precipitation characteristics 66% (for SH) to 99% (for GP), suggesting a good agreement between the model and the observations. Following Chubb et al. (2011), a rainy day is defined 2 Based on this, the synoptic classification scheme is ap- at a threshold of 0.25 mm day 1 for either the average plied to the ACCESS-R soundings. The results show SHL surface observations or ACCESS-R precipitation. high consistency, justifying the use of the synoptic clas- A basic summary of the winter precipitation is provided sification on the ACCESS-R soundings for deriving the in Table 3. The frequency of rainy days is seen to regression equations. follow a seasonal cycle with peaks being present in July As discussed above, within a forecasting context, all and August. The intensity, however, is not found to variables are taken from the ACCESS-R outputs, in- present such a cycle; an overall mean intensity of 2 cluding the definition of a rainy day. Model 1 is a single 10.4 mm day 1 is observed for rainy days, with a stan- 2 regression for all 366 winter days, regardless of cluster. dard deviation of 13 mm day 1. The mean intensity can Model 2 first classifies each day into one of the four be broken down into quartiles, which again do not dis- clusters, with each cluster having its own regression. play any strong seasonal cycle over the course of the The seven predictors and the ACCESS-R pre- winter. Average monthly precipitation on rainy days cipitation data were normalized before the regression indicates lower values in the transition months of May models were developed. Model selection/complexity is and October with an overall wintertime mean pre- an obvious problem when a large number of predictors cipitation of about 167 mm. are available. A stepwise approach (from a single con- Focusing on the 2-yr analysis period (2014–15), the stant value to quadratic combinations, including an in- SHL surface observations show a reduction in both the tercept, linear terms, products, and squared terms) was frequency of rainy days and the intensity (not significant applied to determine the leading predictors and the at the 5% level) compared with the climatology. The optimum regression formulation (degree of complexity statistics with ACCESS-R show that both the frequency within equations). Measures of accuracy (e.g., the and intensity are greater than the observed values (not RMSE or bias) will automatically improve as more significant at the 5% level). predictors are included, but this comes at the cost of b. Synoptic classification model simplicity. To balance the complexity and accu- racy, the number of predictors employed was de- The K-means clustering technique was applied to the termined by minimizing the Bayesian information Wagga Wagga soundings data (complemented with criterion (BIC) as an objective function (Liebscher ERA-Interim soundings for days when the physical 2012). The BIC is expressed as soundings were unavailable) for winter days for the 21-yr period of 1995–2015 using the six indicators. When BIC 5 k 3 ln(n) 2 2 3 ln(L^), (2) employing the original six sounding variables (TT, SH, QU, QV, GP, and TW), the new analysis was consistent where k is the number of free parameters to be esti- with that of D14; four clusters were the maximum mated, n is the number of observations, and L^ is the number found to produce distinct daily rainfall proba- maximized value of the likelihood function of the model. bility distributions (Fig. 2, left), passing the KS test at the Further, we have considered a stepwise procedure that 5% significance level. As a major objective of this re- entails a forward selection and backward elimination search is to better understand the nature of the low-level algorithm. This process includes an examination of any stability H^2 over the Snowy Mountains and its value as a linear dependency between predictors (called as multi- predictor of orographic precipitation, daily H^2 proba- collinearity) with redundant variables removed regard- bility distributions are also produced (Fig. 2, right). As less of the goodness-of-fit criterion value (Curtis and with the daily precipitation, four clusters lead to distinct Ghosh 2011). distributions of H^2, suggesting that the low-level stabil- Both regression models were cross validated via a ity is reflected in the broader synoptic meteorology. bootstrapping methodology with 10 000 simulations to A K-means clustering was then undertaken using the ensure that the results were statistically robust. For each original six synoptic variables and H^2 (seven-variable

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TABLE 3. Main statistical characteristics of daily winter precipitation (mm) for rainy days (.0.25 mm). Numbers shown in the parentheses are the ACCESS-R results for a 2-yr period.

Observations Observations (1995–2015) (2014–15) Rainy day Average monthly Mean intensity Rainy day Mean 2 Month frequency (mm) (mm day 1) 1st quartile 2nd quartile 3rd quartile frequency intensity May 41% 122.5 9.5 6.7 9.8 12.8 51% (55%) 8.8 (8.4) June 56% 171.5 10.6 5.7 10.6 14.2 50% (50%) 10.8 (12.0) July 63% 179.6 9.7 8.3 9.5 11.7 58% (64%) 8.8 (9.7) August 60% 193.1 10.9 9.0 10.6 13.4 55% (52%) 6.3 (5.4) September 53% 192.1 11.6 10.0 11.7 13.0 35% (49%) 6.9 (7.4) October 44% 143.3 10.0 6.4 9.1 13.1 23% (40%) 8.2 (10.1) May–Oct 52% 166.7 10.4 7.7 10.2 13 45% (51%) 8.3 (8.8)

clustering results are only elaborated hereinafter). As capture the driest weather. There are fewer days of C1 before, four clusters were found to be necessary to dis- and C2 than C3 and C4. The mean values of H^2 for the tinctly represent the daily precipitation distribution (not four clusters are 20.45, 1.97, 6.24, and 20.20, respectively. shown). C1 and C2 were found to be quite stable to this Higher values of H^2 indicate stronger blocking and, revision with only a handful of days swapping between accordingly, less orographic precipitation. The fractions clusters. The two dry clusters, however, were found to be of unblocked days (H^2 , 1) for the four clusters are more sensitive to this clustering revision. Out of the 63%, 48%, 20% and 5%, respectively. The probability original 1123 days, 1037 days in C3 remain unchanged density functions (PDFs) of H^2 are broken down by (5 days shifted to C1, 50 days to C2, and 31 days to C4), cluster (Figs. 3a–d) for all days. The distribution of H^2 for while 823 of the original 1003 days in C4 remain un- all days is shown in a stacked histogram in Fig. 3e. For changed (35 days shifted to C2 and 145 days to C3). This rainy days only, the PDF will be shifted to lower (less further suggests that, for the wet clusters C1 and C2, the stable) values of H^2, and for no-rain days shifted to low-level stability is reflected in the synoptic meteorol- higher ones (more stable; Fig. 3f). The seasonal vari- ogy. According to Table 4, clusters C1 (frequency of ability of clusters is also found to be consistent with D14; 2 rainy days: 93%, median: 18 mm day 1) and C2 (fre- the relative frequencies of C1 and C2 increase toward the 2 quency of rainy days: 78%, median: 4.54 mm day 1) end of winter. C3 is more frequent in early winter and represent the wettest groups while C3 (frequency of C4 occurs more often in midwinter (not shown). Further, 2 rainy days: 52%, median: 0.32 mm day 1) and C4 (fre- the synoptic meteorology of the wettest cluster C1 is 2 quency of rainy days: 22%, median: 0.03 mm day 1) consistent with the analysis of Chubb et al. (2011),

^ FIG. 2. Probability distribution of (left) daily winter rainfall and (right) H2 for the next 24 h after sounding measurements over the period 1995–2015 based on six large-scale synoptic indicators.

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^ ^ TABLE 4. Main statistical characteristics of daily winter rainfall and H2 across synoptic clusters. Unblocked cases are days with H2 , 1.

Frequency Mean First quartile Second quartile Third quartile Rainfall All Rainy Unblocked (rainy days; Rainfall Rainfall Rainfall Clusters days days all days (rainy days) mm) (mm) H^2 (mm) H^2 (mm) H^2 C1 9.9% 93% 63% (66%) 22.94 5.74 0.05 17.48 0.7 29.04 1.7 C2 22.2% 78% 48% (53%) 10.83 0.63 0.03 4.54 1.11 12.87 3.01 C3 39.2% 52% 20% (30%) 6.12 0 1.35 0.32 3.33 8.7 3.66 C4 28.6% 22% 5% (12%) 3.32 0 4.59 0.03 11.1 0.17 27.88 indicating a strong northwesterly moisture flux and low ERA-Interim data are used to construct composite surface pressure are commonly present. maps of the large-scale synoptic indicators for each To better appreciate the synoptic meteorology of cluster (Figs. 4–6). Following Theobald et al. (2015), the these four clusters (based on seven-variable clustering), map domain is 208–468S and 1208–1408E in order to

^ ^ FIG. 3. (a)–(d) Distribution of H2 for each cluster, (e) stacked histograms of the H2 variable for different clusters, and (f) the H^2 distribution for no-rain days and rain days. (H^2 . 25, occurring ;7% of the time and mostly in C4, are not shown.) Note the different axes in (e) and (f) compared with (a)–(d)

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2 21 FIG. 4. Composite charts of (top) MSLP (hPa) and (bottom) TW (hPa s m ) showing total moisture up to 250 hPa for the four classes. ERA-Interim data (0000 UTC, May–October, 1995–2015) at a spatial resolution of 0.75830.758 were used to construct composite maps of only the top 25% of days of each cluster with the shortest Euclidean distance to the cluster center. The corresponding maximum and minimum values of the examined variables are shown on top of the individual panels. capture the dominant synoptic meteorology. For these this approach is commonly used when employing daily maps, only the top 25% of days of each cluster are em- observations (e.g., Pook et al. 2006; Theobald et al. ployed. Specifically, these are the days that have the 2015), it has been noted that the daily resolution of shortest Euclidean distance to the cluster center. While composite maps may mask some unresolved features

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FIG.5.AsinFig. 4, but for QV and QU (westerlypffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi and southerly moisture flux up to 250 hPa) for the four classes. Color-filled contours show 2 2 the magnitude of the moisture fluxes ( QU2 1 QV2;kgs 1 m 1) and arrows of the same length represent the moisture flux direction. within daily systems (e.g., a diurnal cycle), as well as is present across central Australia in the composite map, overrepresent slow-moving synoptic systems (Gallant although it is much weaker than that of C4. et al. 2012). Turning to the moisture fluxes (Fig. 5), the strong Starting first with the MSLP and total water (Fig. 4), northerly and westerly moisture fluxes of C1 stand out, general synoptic states can be assigned to the four consistent with a frontal passage. There is virtually no clusters. The MSLP for C1 suggests that the cluster is northerly moisture flux over the Snowy Mountains for associated with a frontal passage. It is not possible to C2. It is strictly a westerly flux that is bringing the mois- distinguish between a cutoff low and an embedded low ture for precipitation, again suggesting a postfrontal en- due to the compositing technique and the low number of vironment (Chubb et al. 2012). Spatially, C3 and C4 are clusters. Further, C1 is associated with a maximum in quite similar, with weak fluxes evident over the moun- total water over the mountains, which is seen to extend tains. C4 is drier and has weaker fluxes of the two. up the Great Dividing Range through The synoptic stability composites (TT and SH, Fig. 6) and Queensland. Chubb et al. (2011) employed a back- further complete the general classifications of clusters C1 trajectory analysis to define a ‘‘moisture corridor’’ (frontal), C2 (postfrontal), and C4 (high pressure system). across this region for heavy precipitation events. C2, Over the mountains, the atmosphere is most unstable while less well resolved, suggests that the frontal system during a frontal passage and most stable under a high has passed over the mountains. Chubb et al. (2012) pressure system. Unlike the other composite maps, detailed a case study of a frontal passage over the nearby however, these maps for C3 are now quite distinct, es- Brindabella ranges, where orographic precipitation was pecially for the midlevel shear (SH). Very weak shear is recorded over the 24-h period after the passage of a evident just to the south of the Snowy Mountains, over front. Here, air originating from the Southern Ocean Bass Straight and extending into the Tasman Sea. This brings limited moisture and modest precipitation. perhaps suggests that the upper free troposphere may be Skipping to the dry cluster C4, a strong high pressure important in defining the synoptic meteorology of this system is evident over the region with very little mois- cluster. A more thorough analysis of C3 revealed that a ture available. Cluster C3 is less easy to classify, most number of the days included in the composite included likely including a variety of synoptic settings that ulti- ‘‘east coast lows’’ (e.g., 2 October 2004 and 18 September mately lead to little precipitation. A high pressure ridge 2015; Bureau of Meteorology 2017).

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21 FIG.6.AsinFig. 4, but for TT (8C) and SH (s ).

A number of studies have diagnosed the principal syn- depth of the troposphere across the Snowy Mountains. It optic types in southeastern Australia (e.g., Chubb et al. is interesting to compare and contrast our four wintertime 2011; Pook et al. 2006). Specifically, Theobald et al. (2015) clusters with their 11 synoptic types. Only a limited com- applied an automated approach to generate synoptic types parison is possible as Theobald et al. (2015) considered 2 by combining meteorological variables throughout the only heavy precipitation days (threshold of 10 mm day 1)

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TABLE 5. Cross-correlation coefficients between seven synoptic the precipitation. It has also the strongest low-level indicators. Bold numbers are significant correlations at a sig- stability (i.e., highest H^2 values). nificance level of 1%. c. Relationships between independent variables and GP SH TT TW QV QU H^2 observed precipitation GP 20.283 20.361 20.379 0.223 20.530 0.338 SH 20.136 20.030 20.019 0.334 20.154 Given that an aim of this research is to improve oro- TT 0.516 20.224 0.149 20.269 graphic forecasts of precipitation through model output 2 2 TW 0.554 0.388 0.237 statistics, it is worthwhile to examine the correlation of QV 20.297 0.155 QU 20.249 these predictors with the precipitation. Working with H^2 the historic data (1995–2015), QV (20.51), QU (0.46), GP (0.46), and TW (0.43) are highly correlated with precipitation, while the stability measures H^2 (20.24), TT (0.23), and SH (0.16) are less strongly correlated. All for the full year. Further, instead of employing physical correlations are statistically significant, confirming our observations from a sounding site, they employed 13 underlying premise that these variables can be of use in variables provided from the ERA-Interim reanalysis. In forecasting orographic precipitation. Table 5 also illus- spite of these substantial differences, it is evident from the trates the cross correlations between these variables at composite maps that C1 and C2 correspond to Theobald the 0.01 significant level. The highest significant corre- clusters T5 (prefrontal troughs, approaching cold fronts) lation is between GP and QU (20.53), while, the lowest and T1 (embedded cold fronts). Not surprisingly, dry significance is for SH–TT (20.136). SH–TW and clusters C3 and C4 (occurring ;70% of the time during SH–QV did not indicate significant linear correlations. the cold seasons and most frequently at the start and Returning to the correlation between precipitation middle of winter) were not represented by any of the and the seven predictors, it is worthwhile to break down Theobald clusters, since their analysis was limited to wet the analysis to the four clusters (Table 6). Not surpris- conditions throughout the year. ingly, the correlation between the precipitation and any In summary, C1 includes the heaviest precipitation predictor is reduced within an individual cluster defined days and the lowest H^2 values (and the highest fre- by these predictors. While greatly reduced, the corre- quency of unblocked cases). It occurs for 10% of the lations of QV, QU, GP, and H^2 remain statistically winter days, but accounts for 39% of the precipitation. It significant within each of the four clusters. TW remains is associated with frontal passages. C2 is associated with significantly correlated within C1, C2, and C3. SH is only postfrontal conditions. It occurs 22% of the time and significantly correlated with precipitation in C4. Table 6 accounts for 33% of the precipitation. C3 is associated also details the rank correlation of these predictors with a variety of synoptic conditions. It is a dry cluster, against the precipitation. For the three stability pre- occurring 40% of the time and accounts for 23% of the dictors (SH, TT, and H^2), the rank correlation (which total precipitation. Finally, C4 is the driest cluster measures the degree of similarity between two rankings associated with high pressure systems dominating the assigned to two members of a set) is greater in magni- region over the Snowy Mountains and to its north. This tude than the linear correlation, suggesting a nonlinear occurs ;30% of the time and accounts for only 5% of relationship exists between precipitation and stability.

TABLE 6. Linear and rank correlation coefficients between seven synoptic indicators and observed precipitation over the period of 1995–2015 (classification results based on seven-variable clustering). Bold numbers are significant correlations at a significance level of 5%. ‘‘No class’’ means no classification process has been implemented.

GP SH TT TW QV QU H^2 C1 Linear 20.206 0.018 20.039 0.176 20.482 0.194 20.198 Rank 20.261 0.019 0.010 0.063 20.460 0.143 20.296 C2 Linear 20.370 0.032 0.219 0.197 20.181 0.276 20.203 Rank 20.400 20.012 0.311 0.166 20.161 0.308 20.355 C3 Linear 20.288 0.002 0.052 0.119 20.137 0.144 20.180 Rank 20.360 0.010 0.210 0.124 0.002 0.218 20.344 C4 Linear 20.199 0.114 20.061 0.041 20.153 0.194 20.098 Rank 20.150 0.151 20.019 20.073 0.071 0.161 20.215 No class Linear 20.464 0.163 0.232 0.428 20.509 0.465 20.237 Rank 20.555 0.186 0.367 0.376 20.231 0.469 20.533

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The rank correlation for H^2 is nearly as great in mag- d. Daily winter precipitation forecasting nitude as that for GP, both of which are negative. ^ To better appreciate the interdependencies between H2 1) PRECIPITATION ESTIMATIONS BY ACCESS-R and precipitation, their joint probabilities are explored The daily ACCESS-R precipitation forecasts serve as withtheuseofacopulafunction(Sklar 1959). Copula our control forecast for the full two-yr (2014–15) winter functions have been widely used (e.g., Drouet-Mari and (May–October) period. When these precipitation fore- Kotz 2001; Genest and Plante 2003; Nicoloutsopoulos casts were evaluated against SHL’s high-elevation sur- 2005) to detect the probabilistic relationships between face observations, the overall RMSE was 4.20 mm with a variables and to show that a set of variables with low bias of 0.3 mm. On average, ACCESS-R slightly over- correlations (even zero) may still retain complicated estimated the surface observations. Looking at observed ‘‘tail’’ dependence structures. Unlike the commonly used 2 rain days only (0.25 mm day 1 threshold), the hit rate for correlation measures, copulas are invariant under strictly 2 ACCESS-R was 88% with an RMSE of 6.2 mm day 1 increasing transformations of random variables that are 2 and a bias of 0.42 mm day 1. For no-rain days, the false used for comprehensively exploring nonparametric mea- 2 alarm rate was 20.7% with an RMSE of 0.58 mm day 1 sures of interdependence (Schweizer and Wolff 1981). 21 Copulas are not restricted to any particular type of para- and a bias of 0.19 mm day . metric functions (e.g., Gumbel distribution) for the mar- These basic statistics can readily be broken down into ginal or the joint probability distributions (Madadgar and the four clusters (Table 7). As expected, the wet frontal cluster C1 has the highest percentage of rain days, the Moradkhani 2014). According to Fig. 7a, the scatterplot 2 greatest overall RMSE of 10.17 mm day 1, and bias of and marginal histograms illustrate the relationship be- 21 tween precipitation and H^2 in which, overall, large values 0.76 mm day . For rain days only, the hit rate was 97%. of precipitation are associated with low values of H^2 and Over the 2 years of data (no-rain days), the false alarm high values of H^2 are associated with weak precipitation. rate was calculated to be zero for C1. The relatively wet The marginal histograms further indicate that the vast postfrontal cluster C2 shows the next highest overall 21 majority of data are located in the range of 0.25–10 mm for percentage of hits (69%) and RMSE (5.2 mm day ). 21 precipitation and from 21to5forH^2,overwhelmingthe The overall bias for C2 is 0.3 mm day . Most notable for tail observations outside this range. this cluster is the high rate of false alarm (38%) when Figures 7b and 7c illustrate the marginal CDF distri- looking at no-rain days. ACCESS-R produces pre- butions of H^2 (ranging from 25 to 25) and precipitation cipitation too readily in these postfrontal conditions. For (ranging from 0 up to 100 mm) for rainy days based on the dry clusters, C3 and C4, the overall RMSEs are the data from 1995 to 2015. A steep slope implies a small. They are less skilled on rain days (hit rates of 86 higher density of data within a considered range; pre- and 72%, respectively) and relatively skilled on no-rain cipitation values less than 10 mm and 21 , H^2 , 5 have days (false alarm rates of 27 and 13%, respectively). the highest frequency of occurrences (similar to what is More advanced metrics can readily be employed on concluded from the marginal histograms). Figures 7b these observations to assess the skill of deterministic and 7c are the main input elements used in calculating precipitation forecasts, following the World Meteoro- the joint probability values and forming the copula logical Organization Working Group on Numerical function. The Frank copula (Frank 1979), selected as the Experimentation (WWRP/WGNE 2008). For example, best-fitting copula in this study, suggests that H^2 values the frequency bias score (FBS; the ratio of the frequency greater than 7.8 correspond to precipitation events less of forecast precipitation events to that of observed, than 0.6 mm, and H^2 values less than 20.3 correspond to where 1 indicates a perfect score) was calculated to be precipitation events greater than 28.4 mm (Fig. 7d). 1.12, and 0.97, 1.05, 1.24, 1.16 for the overall time period Conversely, low frequencies are given to pairwise events and then broken down by cluster, respectively. An FBS when H^2 and precipitation values are either both low score greater than one suggests that the model generally (H^2 ,20.3 and precipitation , 0.6 mm) or high (H^2 . tends to predict rain days more frequently than they are 7.8 and precipitation . 28.4 mm) (Fig. 7d). In summary, observed. The absence of a false alarm in C1 led to an the copula identifies and quantifies the tail-end re- FBS score of just under unity, indicating the tendency to lationship (as previously highlighted by AghaKouchak less frequently predict precipitation; however, the op- et al. 2010) between H^2 and precipitation that was not posite occurred in the rest of the classes. The equitable evident in the simple correlation coefficient. An inverse, threat score (ETS; the fraction of correctly predicted nonlinear relationship between H^2 and precipitation observed and/or forecast events that has a range was also suggested by the individual probability distri- from 21/3 to 1, where 0 indicates no skill and 1 is a perfect butions of Fig. 2. score.) was calculated to be 0.49, and 0.73, 0.39, 0.41, 0.39

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^ FIG. 7. (a) Histogram and scatterplot of precipitation and H2; (b),(c) the marginal CDF distributions of precipitation and H^2. (d) Joint frequency using the Frank PDF copula. All the graphs are based on the data from 1995–2015 (for rainy days).

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TABLE 7. Performance of ACCESS-R precipitation estimation of observed precipitation over the period of 2014–15 with a value of 0.25 mm for the rain-day threshold (hit, miss, false alarm, and correct/negative values are in percentages).

All days Rain days only No-rain days only Synoptic classes False Correct/ RMSE Bias RMSE Bias False alarm RMSE Bias (No. of days) Hit Miss alarm negativea (mm) (mm) Hit rate (mm) (mm) rate (mm) (mm) C1 (34) 88 3 0 9 10.2 0.76 97 10.7 0.83 0 0.03 20.01 C2 (51) 69 6 10 16 5.2 0.3 92 6.0 0.15 38 1.50 0.73 C3 (141) 36 6 16 43 2.1 0.1 86 3.2 20.04 27 0.41 0.2 C4 (110) 16 6 10 67 2.0 0.4 72 4.1 1.4 13 0.44 0.10 All days (336)b 40 6 11 43 4.2 0.3 88 6.2 0.42 21 0.58 0.19 a Correct/negative model correctly detects no rain days. b All days without implementing the classification. for the overall time period and the four clusters, re- previously presented in Table 7 as the selection of a rain spectively. The ETS accounts for correct forecasts due day was changed from the surface observations to the to chance when computing an index that combines the ACCESS-R forecast to allow for an operational applica- hit rate and the false alarm ratio. Ebert (2001) finds an tion). When the single regression model is applied, fore- 2 ETS of around 0.4 for the Poor Man’s Ensemble pre- cast precipitation had an RMSE of 5.6 mm day 1,abias 2 cipitation predictions, suggesting that the present system of 20.15 mm day 1,ahitrateof78%,andr2 at 0.83. The is especially skillful in identifying heavy-precipitation single regression produced a 7% reduction in the RMSE. events. The accuracy score (the fraction of ‘‘correct’’ We can examine the forecast rain days by cluster, even forecasts) was also calculated to be 0.83, 0.97, 0.84, 0.79, when employing a single regression. The single regression 0.84 for the overall time period and the four clusters, model improves the RMSE in all four clusters, most respectively, indicating an encouraging result, with the strongly in C4. The bias is also reduced in each of the four most accurate forecast in C1. clusters, most strongly in C4 and C1. The coefficient of determination remains largely unchanged by cluster. The 2) MODEL 1: SINGLE REGRESSION MODEL single regression does not strongly improve one or more The single regression model (model 1) is based on clusters at the expense of the remaining clusters. The only two predictors, a linear combination of the improvement is largely across all clusters. ACCESS-R precipitation forecast and QU (Table 8), 3) MODEL 2: CLUSTER-BASED REGRESSION determined by the stepwise approach and the BIC. The MODEL ACCESS-R forecast accounts for about 70% of the variance while QU contributed roughly 14%. Four The cluster-based regression (model 2) produces an 2 2 goodness-of-fit criteria [RMSE, the coefficient of de- RMSE of 4.2 mm day 1, a bias of 20.1 mm day 1,anr2 termination r2, the hit rate, and bias (for all days)] are of 0.89, and a hit rate of 84% when computed over all calculated to quantify the improvement in using a simple days. The RMSE was reduced by 30% and the bias was regression formula from the control ACCESS-R fore- reduced by 7% in comparison to the control ACCESS-R cast precipitation (Table 9). forecast precipitation. When limited to forecast precipitation days, the straight When breaking this down into the individual clusters, 2 ACCESS-R forecast had an RMSE of 6 mm day 1,abias large improvements are identified in C1 (24% reduction 2 of 0.68 mm day 1, and a hit rate of 76% for the full 2-yr in RMSE) and C4 (42% reduction in RMSE). Further, r2 period (results in Table 9 are different than those increases most for these two clusters. While the gains for

TABLE 8. Leading predictors in regression equations for different models. ‘‘Int.’’ stands for intercept.

Model Leading predictors using the stepwise algorithm coupled with BIC criteria on 8 indicators Regression equation 1 QU, Prec_Acc Y 5 Int. 1 aQU 1 bPrec_Acc 1 gQU 3 Prec_Acc 2 C1 TT, Prec_Acc Y 5 Int. 2 aTT 1 bPrec_Acc 1 gTT 3 Prec_Acc C2 Prec_Acc Y 5 Int. 1 aPrec_Acc C3 QU, Prec_Acc Y 5 Int. 1 aQU 1 b Prec_Acc 1 gQU 3 Prec_Acc C4 QV, Prec_Acc Y 5 Int. 2 aQV 1 bPrec_Acc 1 gQV 3 Prec_Acc

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TABLE 9. Goodness-of-fit criteria for different models for estimating daily winter precipitation over 2014–15 based on ACCESS-R rainy days (results are only for the test groups).

Improvement of model 1 and 2 in comparison with the ACCESS forecast Goodness-of-fit criteria for each criterion (%) Classes Models RMSE (mm) r2 BIAS (mm) Hit rate RMSE r2 BIAS Hit Overall ACCESS 6.0 0.83 0.68 76 — 1 5.6 0.83 20.15 78 6.7 0.0 77.9 3.1 2 4.2 0.89 20.10 84 30.1 7.2 85.3 10.8 C1 ACCESS 10.8 0.67 1.10 90 — 1 10.3 0.77 21.30 93 4.0 14.9 218.2 3.7 2 8.2 0.81 20.60 100 23.5 20.9 45.5 11.1 C2 ACCESS 5.9 0.82 0.48 90 — 1 5.8 0.84 20.34 93 2.2 2.4 29.2 2.8 2 5.7 0.88 20.19 100 3.9 7.3 60.4 11.1 C3 ACCESS 3.0 0.89 0.23 67 — 1 2.7 0.90 20.17 68 7.4 1.1 26.1 2.0 2 2.6 0.91 20.04 70 13.5 2.2 82.6 4.1 C4 ACCESS 3.9 0.62 1.70 62 — 1 3.4 0.62 1.40 66 12.9 0.0 17.6 5.6 2 2.3 0.69 20.21 79 42.0 11.3 87.6 27.8

cluster C2 were more modest (C2 has the simplest re- It has long been appreciated that orographic pre- gression fit), improvement is evident for all goodness-of- cipitation is sensitive to H^2 with strong stability (large H^2) fit criteria. The cluster-based regressions also reduced suppressing rainfall and, conversely, weak stability en- the false alarm rate (as well as improving the hit rate) in hancing orographic precipitation (e.g., Watson and Lane all clusters, but more strongly in the two wet ones. 2014). An analysis of 21 years of wintertime data con- Histograms of goodness-of-fit criteria for the cluster- firmed this relationship for the Snowy Mountains. Aver- based regression model for C1 (model 2 C1) derived age H^2 was significantly greater for no-rain days (14.5) from cross-validation analysis are illustrated in Fig. 8. than for rain days (3.9). A rain day was defined by a 2 Because of the presence of skewness in histograms of threshold of 0.25 mm day 1. A deeper analysis of these coefficients and goodness-of-fit criteria (Fig. 8), for all data found that the relationship was primarily driven by models, the median of the histograms is considered and extreme values with very large values of H^2 (.7.8) being reported to reduce the influence of outliers. Similar associated with suppressed rainfall and very heavy rainfall 2 histograms are obtained for other classes but not shown. (.28 mm day 1) being associated with low values of H^2. It should be noted that the RMSE and bias histograms Previous research (D14) demonstrated that the pre- are derived from the normalized values of estimations cipitation over these mountains is also sensitive to that are converted to millimeters for the final compari- the large-scale synoptic meteorology. Following this sons between the models. methodology, a K-means clustering algorithm was ap- plied to the precipitation using six synoptic predictors (GP, TW, QU, QV, SH, and TT). As before, four clus- 5. Conclusions ters were identified as the minimum number of clusters A primary aim of this research has been to better necessary to distinguish the precipitation distribution understand the sensitivity of precipitation over the between clusters. Examining these more thoroughly Snowy Mountains of southeast Australia to the low- with the use of ERA-Interim reanalysis data, the wet level stability (as measured by the square of the non- cluster (C1) was associated with frontal passages. C2 was dimensional mountain height H^2) and to understand the also a wet cluster, being associated with postfrontal relationship between the low-level stability and the conditions. C4 was a dry cluster associated with sup- synoptic meteorology, if any. A further aim has been to pressed (stable) conditions, and C3 was a dry cluster exploit any uncovered relationship between the non- constructed from the remaining observations. Distribu- dimensional mountain height and precipitation to im- tions of H^2 were also distinguished by this clustering, prove forecasts of precipitation over these mountains suggesting that H^2 was also strongly defined by the for water management purposes. synoptic meteorology.

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(2014–15 wintertime months) of ACCESS-R precipita- tion 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 addi- tional predictors will improve accuracy, they are only added if they avoid redundancy, collinearity, and com- plexity. It is important to note that all of the tested in- dicators have already been utilized as input variables to the clustering algorithm. Having TT as a leading pre- dictor in C1 suggests that the model systematic error may be mostly associated with the variation of large- scale stability. Following this logic, the model pre- cipitation overestimation in C4 may be rooted in the misrepresentation of the moisture flux. A potential extension of this work could be to con- sider the application of statistical adjustments for fore- casts 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 2 FIG. 8. Histograms of goodness-of-fit criteria (RMSE, r , and ACCESS system continues to improve, the main value bias) based on normalized values for model 2 C1 derived from cross of such statistical analysis may be in the identification of validations with 10 000 simulations. The median of each panel is the source of systematic errors in the system. taken to represent the average values in Table 8. Acknowledgments. This study is supported by Aus- tralian Research Council Linkage Project LP160101494. When repeating the clustering for seven variables (the We are grateful to Snowy Hydro Ltd. for providing the original six predictors plus H^2), only minor changes precipitation data for the Snowy Mountains. In addition, were observed for the two wet clusters, while changes we thank the reviewers for their insightful contributions were observed in the number and composition of dry to this manuscript. clusters, C3 and C4. A further investigation on the re- lationship between the seven predictors and the ob- REFERENCES served precipitation showed that they are all statistically correlated, justifying their application in forecasting AghaKouchak, A., G. Ciach, and E. Habib, 2010: Estimation of tail dependence coefficient in rainfall accumulation fields. Adv. orographic precipitation. Higher values in rank corre- Water Resour., 33, 1142–1149, doi:10.1016/j.advwatres.2010.07.003. lations of the stability indicators (more obviously for Bureau of Meteorology, 2017: About East Coast Lows. Accessed ^ H2) suggested a nonlinear relationship rather than lin- 20 March 2017, http://www.bom.gov.au/nsw/sevwx/facts/ecl.shtml. ear relationship. Chubb, T. H., S. T. Siems, and M. J. Manton, 2011: On the decline D14 noted that over the Snowy Mountains an NWP of wintertime precipitation in the Snowy Mountains of southeastern Australia. J. Hydrometeor., 12, 1483–1497, model demonstrated more skill at predicting the syn- doi:10.1175/JHM-D-10-05021.1. optic meteorology than the precipitation. Thus, MOS of ——, A. E. Morrison, S. Caine, S. T. Siems, and M. J. Manton, 2012: the synoptic variables was used to improve precipitation Case studies of orographic precipitation in the Brindabella forecasts. Two different regression models were de- Ranges: Model evaluation and prospects for cloud seeding. Aust. veloped with the aim of improving the precipitation Meteor. Oceanogr. J., 62, 305–321, doi:10.22499/2.6204.009. ——, M. J. Manton, S. T. Siems, A. D. Peace, and S. P. Bilish, 2015: forecasts of the ACCESS-R model. Specifically, the goal Estimation of wind-induced losses from a precipitation gauge was to reduce the RMSE and bias. First, a single re- network in the Australian Snowy Mountains. J. Hydrometeor., gression model was developed and applied to 2 years 16, 2619–2638, doi:10.1175/JHM-D-14-0216.1.

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