Improving Accuracy of Mapping Cyclone Numbers and Frequencies
Total Page：16
File Type：pdf, Size：1020Kb
748 MONTHLY WEATHER REVIEW VOLUME 130 NOTES AND CORRESPONDENCE Improving the Accuracy of Mapping Cyclone Numbers and Frequencies OLGA ZOLINA AND SERGEY K. GULEV P. P. Shirshov Institute of Oceanology, Moscow, Russia 20 October 2000 and 1 August 2001 ABSTRACT The uncertainties associated with the mapping of cyclone numbers and frequencies are analyzed using the 42-yr winter climatology of cyclone tracks derived from 6-hourly NCEP±NCAR reanalysis. Tracking is performed using an automated procedure, based on computer animation of the sea level pressure ®elds. Uncertainties in the mapping result from an incomplete catchment of cyclones by the grid cells: the coarse temporal resolution of data causes fast-moving storms to skip grid boxes. This introduces error into estimates of cyclone frequency, with cyclone counts systematically underestimated. To minimize these biases, it is possible to simulate higher temporal resolution of the storm tracks by linear interpolation applied to the original tracks. This simple procedure reduces bias in estimates of both cyclone frequencies and numbers and enables quantitative estimation of errors. Errors in cyclone counts are estimated over the Northern Hemisphere for different time resolutions and different grids. Standard errors in cyclone frequencies increase from 5%±15% to as much as 50% as the original temporal resolution of the storm tracks decreases from 6 to 24 h. Mapping the results on circular grids reduces these errors. Appropriate grid sizes for different temporal resolutions of the storm tracks are recommended to minimize the uncertainties in storm occurrence mapping. 1. Introduction found that normalization by latitude results in biases in cyclone occurrence and recommended the mapping of Cyclone activity is usually characterized by cyclone raw frequencies or use of equal-area grids (e.g., Bal- frequency maps derived from sea level pressure (SLP) lenzwieg 1959). However, Hayden (1981a,b) only con- data using automated storm tracking algorithms (e.g., sidered the latitudes from 258 to 458N, for which the Alpert et al. 1990; Le Treut and Kalnay 1990; Murray area change of a latitude±longitude box is less than 25%. and Simmonds 1991; Koenig et al. 1993; Hodges 1994; Sinclair 1994, 1997; Serreze 1995; Serreze et al. 1997; In the high latitudes, mapping becomes very sensitive Blender et al. 1997; Sinclair and Watterson 1999). to the cell size. In Arctic cyclone climatologies (Serreze Blender and Schubert (2000) recently studied the impact and Barry 1988; Serreze et al. 1993, 1997; Serreze of different space±time resolutions on the results of cy- 1995), it is a common practice to use an equal-area grid clone tracking and found that a coarser temporal reso- based on the Lambert polar stereographic projection, lution may result in 10%±50% biases in cyclone counts when the grid cells are referenced to the Cartesian co- (when the resolution decreases from 2-hourly to 24- ordinate system (Thorndike and Colony 1980). How- hourly). Decreasing spatial resolution from T106 to T42 ever, in the midlatitudes and subtropics the actual con- introduces approximately 30% bias in the number of ®guration of cells of such grids becomes very different cyclones. However, accuracy of storm tracking is not from that for the high latitudes and may not necessarily the only source of uncertainty in the analysis of cyclone provide an effective catchment of cyclones. This is the activity. The procedures involved with mapping cyclone second mapping problem, ®rst quoted by Taylor (1986). occurrences can also introduce error. To account for the varying density of the cyclone tracks For latitude±longitude grids, there has been much de- of different directions, Taylor (1986) introduced the so- bate on the choice between the so-called equal-area grids called effective cross sections, which require the use of and scaling the results with latitude. Hayden (1981b) gerrymander-type grids, which are impractical. An al- ternative approach is to use circular cells, ®rst recom- mended by Kelsey (1925) and used for mapping cyclone Corresponding author address: Sergey Gulev, P. P. Shirshov In- frequencies in the Southern Hemisphere by Sinclair stitute of Oceanology, RAS, 36 Nakhimovsky Ave., 117851 Moscow, Russia. (1994). Circular networks are very effective for the con- E-mail: [email protected] sideration of regional climatologies. However, on a q 2002 American Meteorological Society MARCH 2002 NOTES AND CORRESPONDENCE 749 FIG. 1. An idealized example of estimating storm frequencies (n and ni) and numbers (nc and nci) for the 10 idealized boxes from the storm tracks with original temporal resolution (n, nc) and simulated 1/6 temporal resolution (ni, nci). global scale they may result in variable spatial smooth- observer within the box during the chosen time interval ing at different latitudes. Some authors convert the raw (e.g., month, season), the cyclone frequency n. The frequencies into percent frequencies (Keegan 1958; Ser- number of cyclones that pass the box during the same reze et al. 1993). In this case, a given cell is associated time (multiple entries have to be ignored) will be de®ned with a percentage of the total number of lows over the as the number of cyclones nc. These measures corre- hemisphere. However, the use of the percent frequencies spond to the cyclone density and track density, respec- creates dif®culties in studying interannual variability in tively, used by Sinclair (1994). The relationship between the cyclone activity. these two is not trivial. Cyclone frequency is in¯uenced The third problem of cyclone frequency mapping is by both number of transients and their velocities, where- the dependence of the catchment of cyclones on the as number of cyclones is less affected by the propagation temporal resolution of storm tracks. No grid (be it rect- velocity. If we consider a single cyclone tracking, the angular, circular, or other) can account fully for fast- derived cyclone frequency (the so-called partial fre- moving cyclones that pass one or more grid cells during quency) is equal to the time of the cyclone's passing one time step. These biases tend to underestimate storm through the box. It has an accuracy of 62t. counts. Murray and Simmonds (1991), Sinclair (1994), If the typical cyclone migration during one time step and Chandler and Jonas (1999) interpolated 12-hourly is comparable to the box size, both cyclone frequency track points to 6-hourly spacing to account for this prob- and the number of cyclones will be biased. Biases will lem. Nevertheless, a general approach to minimizing increase for fast cyclones (boxes 4 and 9 in Fig. 1) and and understanding this bias has yet to be well developed. for the cyclones ``cutting'' the box corners (box 7). Our study will quantify these biases for different map- Biases can be minimized if we simulate a higher tem- ping geometries and will suggest a simple procedure for poral resolution by linear interpolation between the their minimization. In section 2 we formulate the prob- storm-track points. This procedure has to be applied to lem using an idealized example. Section 3 describes the the results of the tracking and not to the initial SLP data and the method used to perform storm tracking. ®elds; that is, it does not imply any assumptions about Results of the quantitative estimation of the mapping the development of the SLP ®eld during a t-hourly pe- uncertainties associated with the resolution of storm riod and does not change the storm tracks. Linear in- tracks for different grids are presented in section 4. Sec- terpolation results in the same tracks but with t/6 tem- tion 5 summarizes the results and discusses their pos- poral resolution (Fig. 1). The estimates of cyclone fre- sible applications. quencies and numbers from the interpolated data (ni and nci, respectively) are less biased (their accuracy is 6t/3). To compare the frequencies derived from the original 2. Formulation of the problem and interpolated data, partial frequencies have to be An idealized example, summarizing the problem, is scaled with the cyclone lifetime. Table 1 shows the fre- shown in Fig. 1. Two cyclones (I and II) are tracked in quencies derived from the original and interpolated data. the 10 neighboring boxes for the original temporal res- The coarse temporal resolution results in biases of both olution t, which varies in practice from 6 to 24 h for signs, which vary in magnitude from 50% to 100% of different analyses and models. We will term the number the mean values. If we enlarge the box size (holding of the pressure minimum events, counted by an Eulerian the time step constant), the biases reasonably become 750 MONTHLY WEATHER REVIEW VOLUME 130 TABLE 1. Partial and total cyclone frequencies for idealized boxes in Fig. 1. Original temporal Simulated 1/6 Box No. resolution temporal resolution Difference 1 1/6 5 0.16 3/31 5 0.09 0.07 2 1/6 1 1/5 5 0.37 6/31 1 1/25 5 0.23 0.14 3 2/6 5 0.33 10/31 5 0.32 0.01 4 0 4/31 1 1/25 5 0.18 20.18 5 2/6 1 1/5 5 0.54 8/31 1 2/25 5 0.34 0.2 6 1/5 5 0.20 3/25 5 0.12 0.08 7 0 6/25 5 0.24 20.24 8 1/5 5 0.20 5/25 5 0.20 0 9 0 2/25 5 0.08 20.08 10 1/5 5 0.20 5/25 5 0.20 0 1 1 2 1 6 1 7 2/6 1 2/5 5 0.73 9/31 1 10/25 5 0.69 0.04 4 1 5 1 9 1 10 2/6 1 2/5 5 0.73 12/31 1 10/25 5 0.78 20.05 Total 2.00 2.00 0 smaller.