246 WEATHER AND FORECASTING VOLUME 15

A Static Stability Index for Low-Topped

NORM L. HENRY Meteorological Service of New Zealand Limited, Wellington, New Zealand

3 March 1999 and 8 September 1999

ABSTRACT Static stability indexes provide a simple representation of a complex aspect of the atmosphere and are widely used in operational forecasting. However, their applicability is limited, since most are speci®cally designed to measure deep instability. In particular, they are ineffective at resolving instability that is capped by an inversion below the height of the 500-mb surface. Unstable thermal pro®les that are capped between 700 and 500 mb have been identi®ed as a signi®cant forecasting problem in New Zealand. Referred to here as low-topped instability, these situations are easily overlooked by forecasters, due to a lack of relevant guidance. In this paper, an index capable of resolving low-topped instability is presented. Denoted TQ, it is based on the and dewpoint at 850 mb and the temperature at 700 mb. A dataset of 90 events, displaying varying degrees of low-topped instability, was used to correlate TQ to observed weather. Using an independent dataset for veri®- cation, TQ was found to be effective at resolving unstable events, demonstrating skill that is statistically signi®cant at the 2% level.

1. Introduction shear [e.g., Severe Weather Threat (SWEAT) Bidner (1970)]. Vertically integrated measures of instability Static stability refers to the tendency of the atmo- such as the convective available potential energy sphere to either resist or enhance small-scale vertical (CAPE; Blanchard 1998) provide a more detailed phys- displacements, due to buoyancy forces arising from tem- ical representation of the state of the atmosphere and perature differences between the ambient air and the are commonly used as stability indexes. displaced parcel. Although most commonly considered in relation to convection, stability in¯uences virtually Situated in the middle of a large data-sparse area, all weather phenomena, and its assessment is an integral Meteorological Service of New Zealand (MetService) part of operational forecasting. However, conducting a forecasters place considerable emphasis on NWP model thorough stability analysis over a broad area requires data for stability assessment, with guidance presented consideration of thermal pro®les at many locations, and either in the form of model soundings or as ®eld rep- at different time steps through the forecast period, which resentations of stability indexes. Detailed analyses of is often impractical due to time constraints. model soundings are carried out for areas of interest and To assist forecasters in this process, a number of in- may include, for example, the assessment of convective dexes have been developed that represent stability as a -top , CAPE, , simple numerical ®eld. They rely primarily on temper- etc. Combined with observational data, and an assess- ature differences between two or more levels in the ment of synoptic and mesoscale forcing, these analyses to assess the potential for convection, based form the basis of forecasts of convective weather. In on a set of empirical threshold values (refer to Peppler contrast, stability indexes provide limited information and Lamb 1989 for a comprehensive review). The sim- about the state of the atmosphere at any particular lo- plest indexes consider only the ambient temperature and cation, but offer a concise, broad-scale, representation dewpoint [e.g., total totals, Miller (1967); George's K of stability. They allow forecasters to easily follow index, (George 1960)], while more complex indexes trends in stability and relate these to tropospheric dy- take into account other effects such as parcel lift [e.g., namics, and to quickly identify those areas requiring a Showalter (1953); , Galway (1956)] or more detailed stability assessment. This implies a broad role for stability indexes in the operational environment: they assist forecasters in vi- sualising the state of the atmosphere on the synoptic Corresponding author address: Norm L. Henry, Meteorological scale, as well as providing a rough initial assessment of Service of New Zealand Limited, 30 Salamanca Road, P.O. Box 722, Wellington, New Zealand. the potential for convection. Historically, the develop- E-mail: [email protected] ment of indexes has been directed mainly at forecasting

᭧ 2000 American Meteorological Society

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FIG. 1. Tephigram for Invercargill valid 0000 UTC (1200 LST) 16 Mar 1997. and, with few exceptions, they are de- lems to which it is commonly applied include embedded signed to assess the potential for deep, surface-based, convection in synoptic-scale systems, surface-based convection. Within the broad role suggested above, in- convection in cool air masses, and the interaction of the dexes may be applied to situations that differ markedly synoptic ¯ow with the Southern Alps. from that for which they were designed. This is appro- However, as with most conventional indexes, TT is priate provided a reasonable physical link exists be- of limited value in assessing stability below the 500- tween the index and the phenomenon being considered. mb surface, which is of interest in many forecasting However, there are limits to the applicability of con- applications. The common occurrence of low-topped ventional indexes, since they are so narrowly focused convection in southerly ¯ows over New Zealand, typ- on the problem of deep convection. ically associated with an upper trough migrating east of In recent years, total totals (TT) has become the fa- the country, provides an illustrative example. Because vored stability index among MetService forecasters. of the long fetch over the Southern Ocean, air masses Originally developed for severe forecast- of Antarctic origin are highly modi®ed by the time they ing in the United States, TT is de®ned as reach New Zealand, with 850-mb wet-bulb (␪ ) normally above zero degrees Celsius. TT ϭ T ϩϪT 2T (ЊC), w 850 d850 500 They are typically unstable with respect to surface-based convection, with the depth of the instability dictated by whereTd850 is the 850-mb dewpoint and T 850 and T 500 are the 850- and 500-mb temperatures, respectively. upper-air dynamics. Based on forecaster experience in the application of TT In the vicinity of the upper trough, the instability to warm season air masses in New Zealand, values less normally extends above the height of the 500-mb sur- than 45 generally indicate a stable strati®cation with face and is readily apparent in the TT ®eld. Behind the respect to deep convection, while values of 55 or greater trough, an upper-level inversion typically develops in indicate a high likelihood of thunderstorms. Other prob- response to upper-tropospheric subsidence or warm-air

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TABLE 1. Accuracy scores for actual TQ, UKMO Uni®ed Model t ϩ 24 h forecast TQ, and Monte Carlo 2% signi®cance levels for the veri®cation dataset. Actual TQ Model TQ Monte Carlo 2% level CSI 0.57 0.56 0.36 POD 0.73 0.82 0.58 FAR 0.27 0.36 0.40

, gradually building down to lower altitude with increasing distance behind the trough. When the inversion falls below the height of the 500-mb surface the TT index will drop markedly, regardless of how unstable the atmosphere is at lower levels. This leads to a situation where signi®cant convective weather may occur with TT well below 45. For the purpose of this discussion, the term signi®cant convective weather re- fers to the occurrence of either moderate or heavy show- ers, hail, or thundershowers. For example, consider the 0000 UTC 16 March 1997 sounding for Invercargill (Fig. 1), which is located on the southern tip of the South Island (Fig. 2). At the time of this sounding, an upper trough lay to the east of New Zealand, with a west-southwest ¯ow through the depth FIG. 2. Location of upper-air observing stations in New Zealand of the troposphere over the South Island. The strati®- and geographical areas referred to in the text. cation is unstable below the inversion at 520 mb and, despite a TT index of only 38, the Invercargill airport reported heavy showers and hail within the hour fol- lowing the radiosonde release. This limitation in resolving towering cumulus (TCU)

FIG. 3. Distribution of the (a) training dataset and (b) veri®cation dataset. Values in the table indicate the number of events corresponding to each TQ±stability category pair, with TQ rounded to integer values. The dashed line represents the optimum threshold for unstable events at TQ ϭ 12.

Unauthenticated | Downloaded 09/26/21 06:39 AM UTC APRIL 2000 NOTES AND CORRESPONDENCE 249 and low-topped cumulonimbus (CB) convection is a seasonal dependence inherent in TT. To illustrate this, common feature of stability indexes, which typically note that on a tephigram or similar thermodynamic di- have a strong dependence on the 500-mb temperature agram, the wet adiabats become more steeply sloped as and lack sensitivity to thermal structure between 850 ␪w increases, since more latent heat is available through and 500 mb. Braun and Monteverdi (1991) have dis- condensation. This means that a saturated parcel raised cussed this in relation to so-called cold sector thunder- from 850 to 500 mb will experience a greater temper- storms, in which the maximum parcel buoyancy is often ature decrease in a cool air mass than it would in a found near the 700-mb level, and advise caution when warm air mass, which affects the relationship between applying traditional indexes to such cases. The use of stability and the value of the index. CAPE as an index would be more effective in these For example, consider a saturated pro®le that follows situations, since it is not based on speci®c levels; how- a wet adiabat. At ␪w ϭ 20ЊC this corresponds to a TT ever, without knowledge of the integration depth, the index of 43, whereas at ␪w ϭ 5ЊC the TT index is 61. low-topped nature of the instability would not neces- The pro®les are equally unstable in terms of the buoyant sarily be evident. Blanchard (1998) addresses this issue energy available to a parcel lifted from 850 to 500 mb by considering the vertical distribution of CAPE and (zero in both cases), suggesting that the usual interpre- speci®cally mentions the possibility of obtaining un- tation of TT overestimates instability in cool air masses. representative values from conventional indexes for the By taking into account the variation in slope of the wet type of situation depicted in Fig. 1. He proposes a ver- adiabats, an index can be constructed that has approx- sion of CAPE (NCAPE) that is normalized to the depth imately the same value for any wet-adiabatic pro®le, of the free convective layer, as well as vertical parti- within the relevant range of ␪w. Starting with an ex- tioning of CAPE, both of which would be effective in pression of the form resolving low-topped instability. TQ ϭ T ϩϪT xT (ЊC), Synoptic-scale NWP data for operational use at 850 d850 700

MetService is obtained via World Area Forecast System where T700 is the 700-mb temperature, the condition of broadcasts from both the National Weather Service and constant TQ for saturated pro®les can be expressed as the United Kingdom Meteorological Of®ce (UKMO). These data are currently available at standard upper-air 2T 850 ϭ xT700 ϩ constant. levels only, which limits the usefulness of vertically A plot of 2T versus T for wet-adiabatic pro®les integrated measures of instability such as CAPE. This 850 700 with ␪w ranging from 0Њ to 20ЊC is approximately linear, paper describes the development of a simple stability with a best-®t slope of 1.7 obtained by linear regression, index, denoted TQ, that is effective at resolving low- which leads to the following de®nition of TQ: topped instability. The term low topped is used here to refer to instability that is capped at some level between TQ ϭ T 850 ϩϪTd850 1.7T700 (ЊC). 700 and 500 mb. This implies a suf®cient depth of in- stability to produce signi®cant weather, but insuf®cient 3. Statistical analysis depth to be resolved by a conventional stability index. To establish guidelines for interpreting TQ with re- spect to surface-based convection, a training dataset of 2. The TQ index 90 events was developed using soundings taken from From the outset, the form of the TQ index was chosen the three upper-air sites shown in Fig. 2, during the to be similar to TT, dependent only on ambient tem- period 1 January 1995 to 30 January 1997. An inde- perature and dewpoint. In light of our restrictions re- pendent set of 41 events was developed for veri®cation, garding NWP model data availability, and our de®nition using soundings from the period 1 April 1997 to 30 of low-topped instability, the index has been limited to January 1998. To limit the scope of the problem, the data from standard levels below the 500-mb surface. datasets were designed to represent daytime convection The addition of parcel lift, using a form similar to the in the absence of substantial synoptic forcing or cloud lifted index, was considered to be an unnecessary com- cover, where the likelihood of deep convection was plication, given the rather crude nature of indexes as small. All 0000 UTC (local noon) soundings for these indicators of convection. Furthermore, in addition to time periods were considered, with cases screened to providing guidance for convective weather, the TQ in- exclude those with TT greater than 45 or with signi®cant dex is intended to ®ll a more general role as stability frontal or stratiform cloud. All soundings with an un- guidance for the lower troposphere. The use of surface- stable strati®cation that met these criteria were selected, parcel lift would lead to a strong dependence on the along with a number of other cases ranging from stable diurnal cycle, making the index less useful in this re- to marginally unstable. In addition, t ϩ 24 h forecasts spect. Therefore, the index has been restricted to data of the TT and TQ ®elds from the UKMO Uni®ed Model, from the 850- and 700-mb levels. interpolated to the appropriate upper-air site, were ob- While TT was used as a guide in constructing TQ, tained for all cases in the veri®cation dataset. the form of the index has been adjusted to avoid the For each event, the actual weather was assessed as

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Unauthenticated | Downloaded 09/26/21 06:39 AM UTC APRIL 2000 NOTES AND CORRESPONDENCE 251 either stable or unstable based on a representative set level is represented by the 20th largest value; for the of manned and automated surface observations taken FAR, where smaller is better, the 20th smallest value is between 0000 and 0400 UTC, including observations used. We estimate the probability of obtaining a better from the sounding site itself. A subjective assessment score by random chance to be less than 2%, and any of satellite imagery was also carried out to substantiate result that achieves this is considered to represent a CB reports from manned observations. Unstable events statistically signi®cant correlation. were identi®ed using the following criteria: Scattered or frequent CB reports in manned observations with 4. Results and discussion supporting evidence from satellite imagery; or heavy showers reported at any station; or hail or Applying our analysis procedure to the training da- reported at any station. taset, the best threshold for unstable events was found Based on our weather assessment, the training dataset to be TQ ϭ 12. For comparison, the sounding in Fig. consists of 72 stable events and 18 unstable events, with 1 has a TQ index of 14, while the wet-adiabatic pro®les TQ ranging from Ϫ4 to 18 (Fig. 3a), while the veri®- discussed in section 2 correspond to TQ ഠ 17. The cation set consists of 30 stable events and 11 unstable accuracy scores obtained from the veri®cation dataset events, with TQ ranging from Ϫ4 to 16 (Fig. 3b). The are presented in Table 1, along with their 2% signi®- unstable events are distributed fairly evenly among the cance levels. All scores are statistically signi®cant, in- three upper-air sites, and throughout the year, with cases dicating that TQ is able to effectively resolve unstable occurring in all months. These were mainly associated events in both nowcasting and forecasting modes. Com- with ¯ows from the southwest quadrant with 850-mb paring the scores for actual TQ with those achieved by

␪w between 1Њ and 10ЊC, indicating that pronounced the model, we ®nd they are similar for the CSI, but the low-topped instability occurs primarily in modi®ed air model scores a higher POD with more false alarms. masses of Antarctic origin. For the veri®cation dataset, model TQ was found to Assigning a threshold TQ value, or breakpoint, for have a root-mean-square error (rmse) of 4.9 and a bias unstable events allows the data to be represented by a of 2.0, while model TT has an rmse of 5.2 and a bias 2 ϫ 2 contingency table. The best choice of breakpoint of 2.1. The positive bias in TQ is re¯ected in the higher optimizes some measure of correlation between TQ and POD and FAR scores achieved by the model. Although the stability category, and we have chosen to maximize the errors for the two indexes are nearly equal, TT is the critical success index (CSI) (see, e.g., Wilks 1995). typically three to four times larger, making the relative To assess the performance of TQ using the optimum error and bias that much greater in TQ. Note that the breakpoint, the CSI, probability of detection (POD), and 850-mb dewpoint contributes equally to the two index- false alarm ratio (FAR) were calculated using the ver- es, which makes TQ more sensitive to this term, again i®cation dataset, for both actual TQ and t ϩ 24 h forecast typically by a factor of 3±4. It is generally acknowl- TQ from the UKMO Uni®ed Model. edged that 850-mb is one of the less reliable These results were tested for statistical signi®cance NWP ®elds, and we suspect it is the principal source at the 2% level using a Monte Carlo simulation. This of the error and bias in the model representations of procedure uses a pseudorandom number generator to both indexes. produce a set of 1000 independent contingency tables, The TQ index has been in use operationally at each containing the same number of events as the da- MetService since mid-1998, and while the principal ap- taset. The random forecasts and observations are plication presented here is forecasting surface-based weighted according to the sample climatology of the convective events, it has also proven valuable as a original dataset. This means that, averaged over a large broad-scale measure of stability, regardless of its value. number of contingency tables, the distribution of fore- The TQ ®eld often displays stabilizing or destabilizing casts and observations in the Monte Carlo simulation trends in the lower troposphere that are not clearly cap- will be the same as the distribution of observations in tured in the TT ®eld. In practice, both ®elds are usually the veri®cation dataset. considered at the same time, giving forecasters a more For each contingency table in the simulation, the sta- detailed picture of stability through the depth of the tistical scores are calculated and sorted by value, which troposphere. provides an estimate of the sampling distribution for Operational experience also suggests that the indis- each statistic under the null hypothesis of no predictor± criminant application of the TQ ϭ 12 threshold would predictand correlation. For a statistic such as the POD, lead to many false alarms, particularly when stratiform where a larger value is favorable, the 2% signi®cance cloud is present. Because we have considered only low-

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FIG. 4. UKMO Uni®ed Model guidance. (a)±(c) The t ϩ 12 h forecast ®elds valid 1200 UTC 9 Jan 1998; (d)±(f) the t ϩ 24 h forecast ®elds valid 0000 UTC 10 Jan 1998. (a), (d) The 500-mb height (dam) and 850-mb wind (kt); (b), (e) total totals index (ЊC) shaded above 45; (c), (f) TQ index (ЊC) shaded above 12.

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FIG. 5. Tephigrams for Paraparaumu valid (a) 1200 UTC 9 Jan 1998 and (b) 0000 UTC 10 Jan 1998. topped daytime convective events, our analysis implic- 500-mb trough over the eastern North Island, with a itly includes surface diabatic heating and boundary layer strong low-level southerly ¯ow. Deep instability asso- moisture, both of which would have less in¯uence in ciated with the upper trough is indicated in the TT ®eld the presence of stratiform cloud. Furthermore, in satu- (Fig. 4b), with a maximum in excess of 55 over the rated pro®les, TQ tends to be exaggerated by the con- Wairarapa region. Both the TT ϭ 45 and TQ ϭ 12 tribution from the 850-mb dewpoint. As a result, areas contours (Fig. 4c) cover most of the North Island and of deep moisture associated with synoptic-scale systems part of the upper South Island. often show up as maxima in the TQ ®eld with values By 0000 UTC 10 January, the model has moved the above 12; however, this does not necessarily imply in- 500-mb trough well offshore (Fig. 4d), with an upper stability. For embedded convection, the value of TQ ϭ ridge building over the South Island. The TT ®eld de- 17 obtained from the wet-adiabatic pro®les discussed in picts rapid stabilizing behind the upper trough (Fig. 4e), section 2 provides a useful guide. Values greater than with values above 45 affecting only the Gisborne region. this in any saturated pro®le imply positive buoyant en- However, the corresponding decrease in TQ lags by a ergy for a parcel lifted from 850 to 700 mb, indicating signi®cant margin, with the TQ ϭ 12 contour covering the potential for signi®cant embedded low-topped con- most of the eastern and central North Island (Fig. 4f). vection. The soundings taken at Paraparaumu during this pe- riod illustrate the trend of stabilizing from aloft behind the upper trough. The 1200 UTC 9 January sounding 5. Case study: 10 January 1998 (Fig. 5a) shows a deep layer of cold air associated with During the period 9±10 January 1998, a synoptic- the upper trough, extending up to the tropopause at 400 scale upper trough migrated eastward across New Zea- mb. With a TT index of 46 and TQ of 12, the strati®- land. The t ϩ 12 h guidance from the UKMO Uni®ed cation is not as unstable as the t ϩ 12 h model guidance Model valid 1200 UTC 9 January (Fig. 4a) shows the suggests; however, it is conditionally unstable below the

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FIG.5.(Continued) weak inversion near 650 mb. By 0000 UTC 10 January 6. Conclusions (Fig. 5b), the air has warmed in the middle and upper levels but remains conditionally unstable below the in- Operational forecasters are routinely required to as- version at 700 mb. During this period, TT fell to 24, sess a large amount of information from observing net- while TQ increased to 13. Although the model has some- works and NWP models, often under tight time con- what overestimated TT and underestimated TQ at t ϩ straints. Stability indexes have proven valuable in sim- 24 h, it clearly captures the trend of stabilizing with plifying this process and are a staple component of the respect to deep convection, while maintaining low- NWP guidance suites used at MetService, and else- topped instability in the cold air. where. However, since the indexes presently available Note that, while the depth of instability in the 0000 to forecasters are designed principally to assess deep UTC sounding is not alarming, the height of the capping instability, it is unlikely that the stability index concept inversion slopes upward to the northeast. The model TT is being used to its full potential. The problem of fore- ®eld suggests that at 0000 UTC the cold air extends up casting low-topped convection in New Zealand illus- through the 500-mb surface over the Gisborne region. trates one of the limitations of conventional indexes. Over the Hawke's Bay region, we estimate that the in- We have addressed this issue by presenting an index version lies somewhere between 600 and 500 mb, which capable of resolving instability that is capped between would allow convective cloud-top temperatures of less 700 and 500 mb. The principal application of the TQ than Ϫ20ЊC. Satellite imagery and surface observations index outlined here is forecasting surface-based con- indicate that signi®cant TCU and low-topped CB con- vective events, using TQ ϭ 12 as the threshold. Applied vection occurred during the afternoon over the Wair- as a nowcasting tool using actual radiosonde data, and arapa and Hawke's Bay regions, and about the central as a forecasting tool using NWP model data, TQ has North Island, which coincides reasonably well with the demonstrated skill in resolving unstable events that is TQ ϭ 12 contour on the 0000 UTC model guidance. statistically signi®cant at the 2% level. In addition, TQ

Unauthenticated | Downloaded 09/26/21 06:39 AM UTC 254 WEATHER AND FORECASTING VOLUME 15 has proven to be a valuable operational tool for assessing REFERENCES stability trends below the 500-mb surface, which are not adequately resolved by conventional indexes. Bidner, A., 1970: The Air Force Global Weather Central severe weath- er threat (SWEAT) indexÐA preliminary report. Air Weather However, forecasters need to remain aware of the Service Aerospace Sciences Review, AWS RP 105-2, No. 70-3, strong dependence of TQ on the 850-mb dewpoint, 2-5. [Available from Headquarters, AWS, Scott AFB, IL 62225.] which may not be well represented in NWP models. Blanchard, D. O., 1998: Assessing the vertical distribution of con- vective available potential energy. Wea. Forecasting, 13, 870± Furthermore, application of the TQ ϭ 12 threshold to 877. situations that lie outside of the limits of our analysis, Braun, S. A., and J. P. Monteverdi, 1991: An analysis of a meso- such as embedded convection, may lead to a high rate cyclone-induced tornado occurrence in northern California. Wea. of false alarms. Despite these concerns, the index itself Forecasting, 6, 13±31. Galway, J. G., 1956: The lifted index as a predictor of latent insta- remains a valid representation of static stability under bility. Bull. Amer. Meteor. Soc., 37, 528±529. any circumstance and can be used to follow trends in George, J. J., 1960: for Aeronautics. Academic stability and to highlight areas with the potential for Press, 673 pp. signi®cant low-topped convection. Miller, R. C., 1967: Notes on analysis and severe storm forecasting procedures of the Military Weather Warning Center. AWS Tech. Rep. 200 (revised), 170 pp. [Available from Headquarters, Air Force Weather Agency, Scott AFB, IL 62225.] Acknowledgments. The author gratefully acknowl- Peppler, R. A., and P. J. Lamb, 1989: Tropospheric static stability edges the assistance of Augie Auer, Erick Brenstrum, and central North American growing season rainfall. Mon. Wea. Paul Mallinson, and James Travers of MetService, and Rev., 117, 1156±1180. James Renwick of the National Institute of Water and Showalter, A. K., 1953: A stability index for thunderstorm forecast- ing. Bull. Amer. Meteor. Soc., 34, 250±252. Atmospheric Research. The author would also like to Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. thank three reviewers for their helpful suggestions. Academic Press, 467 pp.

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