METEOROLOGICAL PRODUCTS EXTRACTION FACILITY (MPEF)

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CHAPTER 3 EVALUATION OF GLOBAL AND REGIONAL INSTABILITY INDICES OVER SOUTH AFRICA

BACKGROUND

In this chapter the accuracy of the GII and RII is assessed for South African circumstances. Since convection is mostly a summer phenomenon in South Africa, fifty cases from the summer seasons of 2007 to 2008 and 2008 to 2009 were selected. The first part of this chapter lists the cases and data used for the case studies, which are used in the following chapters.
The most obvious way of comparing the RII to another field, is to use the Unified Model fields for the same indices. Although the model fields are not seen as the ultimate truth, the differences between the RII and model fields provide a useful indication of the benefit of the satellite based fields. As mentioned in Chapter 2, it does happen that the model fields are already very good and the fields do not differ greatly, but on occasion the RII provide more detail in areas where convection occurs. Some examples of this principle will be the shown in this chapter. Finally the RII are compared to the occurrence of lightning. The methodology for this is discussed in detail, as this forms the basis for the development of the new index, which will be described in Chapter 4.

DATA

Case studies

For the purposes of this study, 24 cases were selected from the 2007/8 summer season when convection occurred from November 2007 to March 2008. A further 26 cases were selected from October 2008 to March 2009. Although thundershowers occurred on all of these days, not all of the cases were associated with structural or other damage or loss of life. Table 3.1 lists the events with their dates and location, together with possible information of injury, loss of life or damage to property according to the SAWS Climate Data Base.

Lightning data

Lightning data based on the 19 sensors installed over South Africa (see Chapter 1) was used for the 50 cases. An in depth study on the accuracy of the lightning data falls outside the scope of this study and the reader is referred to Gill (2008b) for more detail. Suffice it to say that the projected detection efficiency for the SAWS LDN is 90% over most of the country while the projected location accuracy is 0.5 – 1 km (Figure 3.1).
In order to evaluate the RII, one would need to confirm that convection did in fact take place when the indicators exceeded specific thresholds. The question could be asked: what would be confirmation of convection? Of course, the occurrence of a thunderstorm means that there is convection, but what would be a quantifiable measure of this? Using precipitation measurements is the first option. However, considering their spatial distribution, it is evident that rain gauges can provide only a limited picture of the precipitation. Radar measurements of precipitation can be considered, but the South African radars do not cover the entire country, so there would be no observations over some parts.
Satellite estimates of precipitation are another option and will be discussed in Chapter 6. A useful alternative is to use lightning detection as a confirmation of convective activity since most lightning is produced by convective clouds (Krider, 1986). Levin and Tzur (1986) reported on models of the development of the electrical structure in clouds and mention that lightning activity follows strong vertical air currents and precipitation. They state that the consequence of this correlation is that lightning is most frequently observed in cumulus clouds, rarely in stratus clouds and never in isolated cirrus clouds. Piepgrass et al. (1982) said, “when the meteorological conditions are favourable for the production of lightning, there is almost a direct proportionality between the total rainfall volume and the total number of flashes”. Since the lightning sensors in South Africa measure only cloud-to-ground lightning, it can be assumed that by the time we observe lightning on the ground, the thunderstorms are already in a mature phase (Figure 3.2, from Price, 2008). Acknowledging the fact that not all convection leads to lightning (Mecikalski, 2009) and that cloud-to-ground lightning by no means accounts for all the lightning, in this study the presence of lightning will be regarded as a confirmation of convective activity.
Convection is often heat driven in South Africa and thus usually occurs from the early afternoon to late evening. According to analysis of the 2007 and 2008 lightning data set the occurrence of lightning starts at around 1200 UTC (2 pm SAST) and continues until late at night, with a peak occurrence in the late afternoon (around 4 pm SAST). For the purposes of this study observations of lightning occurring between 1200 and 2100 UTC were used. For each of the case study days the total number of lightning strokes which occurred within this time interval was calculated and plots showing the spatial distribution of lightning for each day were produced. A mask was also used to restrict the use of the data to within the borders of South Africa to ensure maximum detection efficiency and accuracy (Figure 3.3). As a consequence of the use of this mask, distinct lines will be seen in lightning occurrence maps later in this study.

RII data

The coverage of the RII is restricted to the area 22°S to 36°S and 15°E to 34°E with a 0.1° resolution. Matrices with 174X128 grid points hold MSG data with a 3X3 pixel resolution and model data with a 0.1° (or 12 km) resolution. The RII are available every 15 minutes. The variables used in the study are as described in Chapter 2.

COMPARISON OF RII K INDEX AND LIFTED INDEX FIELDS AGAINST THE UNIFIED MODEL K INDEX AND LIFTED INDEX FIELDS

The RII are the product of both model and satellite data, as explained in the previous chapters. The limitation of the RII is that they cannot be calculated where there are clouds. Unless there are clear skies, the field display of the RII will thus always include pixels with no value. One way of addressing this problem (to some extent) is to use a time averaged field. In this way, pixels which are covered at least some of the time will have a value. In South Africa summer days often start off fairly cloud free over the interior and then convection develops later in the day. It can, of course, happen that the instability changes with time as part of the diurnal cycle, but if there is a constant increase then this will also be reflected in the time average. If there were, however, a temporary change of short duration, it would weigh less in the averaging process. It was decided to use the RII values between 0600 and 0900 UTC to calculate a time averaged field. This should be the most cloud free time of the day and subsequently the RII fields should be filled in a meaningful manner. Not only does this lead to a more complete picture, it also provides more certainty that a positive indication for the development of convection provided by the RII, is consistent with time and not just an outlier. Use of time averages over the period 0600 to 0900 UTC then provides operational forecasters with useful information late in the morning (just after 11 am SAST) to be able to forecast convection for the afternoon. An example of such a time average is shown in Figure 3.4.
Instability fields from the Unified Model and RII may be expected to be rather similar, since model fields form a part of the input to the calculation of the RII (Chapter 2). However, one would hope for sufficient difference to show that adding information from the six MSG channels (Chapter 2) to the model information, does indeed add value. In such cases additional information is provided to the forecaster.
Both model and RII based K Index and Total Totals were averaged over these three hours for all 50 cases. To show all fifty examples here would not serve a useful purpose. In several cases the fields differed very little and emphasized similar areas for possible convective instability. Two examples of where the RII K Index and Total Totals did in fact add value to the model fields will be shown.
In the RII Total Totals graphic (Figure 3.5, top left) cloudy areas are indicated by the grey shade. Although at first glance the Total Totals fields from RII and the Unified Model look rather similar (Figure 3.5 top left and right), some differences are noticeable:
1. Figure 3.5 (bottom left) shows the RII Total Totals minus Model Total Totals. Differences are mostly between +5 to -5°C, which shows that there are differences but that they are small.
2. The Model Total Totals field has its highest values (>54°C) over the western Free State, while for the RII Total Totals there are two areas of high values (>54°C) – one over the western Free State but also one further north over the Northwest Province.
3. Looking at the spatial coverage of lightning (Figure 3.5, bottom right), lightning occurred over the southern Free State, as well as in the Northwest Province. The lightning maxima are slightly more eastwards than the areas of more than 54°C for the Total Totals products of both the Unified Model and the RII. The lightning over the Northwest Province coincides well with the RII Total Totals maxima, which was not evident in the Unified Model Total Totals
In this second example (Figure 3.6), it is clear that, despite the similarities (top left and right), subtle differences are again evident:
4. The difference field (bottom left) shows mostly values of +5 to -5°C, except over the Botswana region where there are values greater than 5°C.
5. The Model K Index field (top right) has the highest values (>40°C) over the Northwest Province and northwestern Free State while the area of high values (>40°C) for the RII K Index (top left) extends further northwestward into Botswana.
6. The RII K Index has no values over the eastern Free State and the surrounding high lying areas, due to the fact that it is dependent on the temperature at 850 hPa and those areas are above 850 hPa. The “normal” K Index could thus NOT be computed there. The Unified Model uses the “normal” K Index and not the Mixed K Index (Chapter 2, Figure 2.5). In order to compare the K Index from the Unified Model to the K Index from the RII, the Mixed K Index was thus NOT used in this comparison.
7. Note that lightning is not accurately detected in northern Botswana and Namibia and can thus not be shown in the lightning data view (bottom right). Lightning occurred over the northern Free State, Northwest Province and into southern Botswana.
8. The RII field of maximum K Index (top left) adds more focus in an area where more lightning (bottom right) was detected.

EVALUATION OF RII AGAINST OCCURRENCE OF LIGHTNING

Initial evaluation of the GII

As in studies by Koenig et al. (2007) a more quantitative evaluation method is used in this study to show the accuracy of the RII parameters when compared to the occurrence of lightning over South Africa. Initially a contingency table approach was used to calculate the Probability of Detection (POD) and the False Alarm Ratio (FAR) of the K Index and the Lifted Index from the GII product. The formulas for POD and FAR are listed in Table 3.2. This approach places the events into four categories (Wilks, 2005):
Hit: event was forecast to occur and did occur (A),
Missed: event was not forecast to occur but did occur (C),
False Alarm: event was forecast to occur but did not occur (B) and
Correct Negative: event was forecast not to occur and did not occur (D).
The maximum values of K Index and minimum values of Lifted Index from the 15X15 MSG pixel (corresponding to ~ 50 km X 50 km) over the period 0400 to 0800 UTC were compared to the occurrence of lightning between 1100 and 1800 UTC. The occurrence of lightning was regarded as confirmation of convective activity. If the Lifted Index was less than -5° early in the morning and more than five lightning strokes occurred in the 15X15 pixels block later in the day, the forecast was considered to be a “hit”. Similarly, if the K Index exceeded 35°C early in the morning and more than five strokes occurred in this block later in the day, the forecast was considered a “hit”. Five case studies in the summer of 2006/7 were chosen when convective events took place. The average Probability of detection (POD) for the K Index was 77% and the False Alarm Ratio (FAR) 33% (Table 3.3).
The K Index fields for 0400 to 0800 UTC for 15 January 2007 are given in Figure 3.7 while Figure 3.8 shows the same fields for 16 January 2007. The case of 15 January did not evaluate well as indicated by the scores in Table 3.3. Figure 3.7 shows that the high cloud incidence decreased the number of cloud free blocks which could be used to calculate the GII. The case of 16 January 2007 evaluated much better, coinciding with more cloud free pixels which could be used to calculate the GII. The degree of cloud cover might thus explain the difference in performance to some extent. Based on these few cases the GII product was considered as possibly being a valuable tool for short range forecasting of thunderstorms (de Coning, 2007) and worthy of further investigation.

Evaluation of individual RII against lightning

After the installation of the local version of the GII in South Africa in 2007, the evaluation scheme was adjusted to use a 0.1°X0.1° block, since the resolution of the model input had increased. Instead of using the extreme values of the indices in a six hour period and 15X15 pixel block, the average value of each index over a three hour period from 0600 to 0900 UTC in a 3X3 pixel block was chosen. In this way the spatial resolution was improved and the most cloud free period of the day was selected. Each index was then compared to the occurrence of lightning (one lightning stroke in this smaller block of 0.1°X0.1°). Based on the contingency table approach additional statistical values were calculated for each meaningful value of the index (Table 3.4). For each of the indices, all fifty cases from November 2007 to March 2009, were used to verify against the occurrence of lightning. Instead of using certain thresholds for each index as before, the evaluation was done for every value of the respective index. Two additional scores were also calculated, the Probability of False Detection (POFD), also known as the False Alarm Rate (FAR), as well as the Hanssen-Kuipers Discriminant (HK), also known as the True Skill Statistic (TSS). These scores are defined in Table 3.4.
If all the boxes with K Indices above 20°C are evaluated against the occurrence of lightning, the probability of detection of all the lightning will probably be 100%. At K Index values of more than 25°C, the probability of anticipating all the lightning will be less since areas with K Index values of less than 25°C would also have had lightning. At K Index values of more than 30°C the POD of anticipating all lightning becomes less, and for K Index values of more than 35°C, the probability of being able to capture all the lightning is even less. In essence one is looking to identify the area where it is most likely to see all lightning; the bigger the area (lower threshold for K Index), the higher the POD will be, but the FAR and POFD will be large too. In order to balance these scores, it is necessary to find the area where POD is high and FAR and POFD are low. This approach should not be confused with calculating the POD, FAR or POFD for single values of an index, but rather for an area where the index exceeds a certain value in order to get to a probability map. This is also indicated in the following graphs on the x-axis, with the use of “>”for each value.

Evaluation of Mixed K Index (Figure 3.9)

1. POD:
If the area of all Mixed K Index (MK) values above 15°C is considered, a POD of almost 1 will be obtained, i.e. almost all lightning will occur within this area. This value, of course, decreases as one looks at higher and higher values of Mixed K Index, since the area becomes smaller and smaller.
2. POFD:
The POFD starts just above 0.2 (or 20%) and decreases with higher values of Mixed K Index.
3. FAR:
The False Alarm Ratio starts at 70% and decreases to around 50%, after which there are not enough data points to make a calculation possible.
4. HK:
This indicator starts at 0.75 and remains above 0.6 until Mixed K Index becomes more than 30°C, when it decreases steadily.
Evaluation of Mixed Total Totals (Figure 3.10)
5. POD:
If the area of all Mixed Total Totals (MT) values above 35°C is considered, a POD of 1 is noted and all lightning will occur in this area. This value decreases with higher and higher values of MT.
6. POFD:
The POFD starts just above 0.3 (or 30%) and decreases with higher values of MT.
7. FAR:
The False Alarm Ratio starts just below 80% and decreases to just above 50% where Mixed Total Totals is about 51°C.
8. HK:
This indicator starts below 0.70, increases slightly to about 0.75 (where Mixed Total Totals is more than 42°C) and then decreases steadily.
9. POD:
If the area of all Lifted Index (LI) values of >+2°C is considered POD is almost 1 and thus all lightning will occur in such a region.
10. POFD:
The POFD starts high at almost 80% when Lifted Index is positive, which makes physical sense, since then there is no instability. As soon as Lifted Index is less than 0°C, POFD becomes less than 20% and continues to diminish.
11. FAR:
The False Alarm Ratio starts at 90%, drops quickly to just above 60% when Lifted Index is negative and ends at around 50% where Lifted Index is about -6°C.
12. HK:
This indicator only has favourable values when Lifted Index is below zero, where it is above 70% and then it decreases steadily.
13. POD:
If the area of all Precipitable Water (PW) values above 10mm is considered POD is almost 1 and thus all lightning will occur in such a region.
14. POFD:
The POFD starts above 30% and decreases.
15. FAR:
The False Alarm Ratio starts below 80%, drops to below 70% where Precipitable Water is about 22 mm and then increases, contrary to all the other parameters. Evett et al. (2008) in a study on the effect of monsoonal atmospheric moisture on lightning fire ignitions in southwestern North America found that the average number of lightning flashes per day increased with increasing atmospheric moisture and thunderstorm activity, but at higher values of daily minimum relative humidity (more than 50%) there was a slight decrease in the number of lightning flashes. One explanation could be that there is too little data at these higher relative humidity values, but it can also be that high humidity days are often overcast, limiting the necessary convective heating required for thunderstorm development and intensification.
16. HK:
This indicator starts between 60% and 70% and remains high until Precipitable Water exceeds 16 mm and then decreases steadily.

Comparison with similar work done in Poland

Several countries are using the GII product. Only a few have attempted a quantitative evaluation procedure. In Poland Struzik et al. (2006) carried out an evaluation for the GII K Index and Lifted Index against occurrence of lightning in Poland using several cases from April and May 2006. A threshold of 20°C was used for the K Index and Lifted Index was evaluated below 0°C in their contingency table approach. A summary of their results is shown in Table 3.5.
The circumstances as well as weather systems in South Africa and Poland are not exactly the same and for South Africa, the Mixed K Index is shown here but the normal K Index for Poland. In South Africa, a meaningful threshold for the Lifted Index is -2°C and for the K Index 25°C is more relevant. The thresholds used in the Poland study (0° and 20°C) are thus very ‘weak’ compared to the meaningful values in South Africa. This explains the differences in the statistics.

SUMMARY

In this chapter, after a discussion of data used for the study, some verification of results was presented. Fifty cases when convection occurred were listed mentioning where damage to property or loss of life was reported. The handling of lightning data in terms of space and time was described. The initial verification of the GII provided the basis for an evaluation method with a contingency table approach, which was expanded and refined when the RII came into operation. Two of the RII were compared with model fields of the same variables and some examples were shown. Finally, the four modified RII were evaluated against the occurrence of cloud-to-ground lightning over South Africa over two summer seasons by means of four statistics. In general the statistics for the individual RII look like good indicators of the occurrence of convection (or lightning) and could thus be useful for short term forecasts of thunderstorms. Keeping in mind that cloud-ground-lightning does not reflect all lightning, the favourable statistics are especially encouraging. In the next chapter the results obtained so far will be used to develop a new index for the probabilistic forecasting of convection.

Table of Contents
Declaration
Acknowledgements
Abstract
Abbreviations
List of Figures
List of Tables .
CHAPTER 1: BACKGROUND AND ENABLING TECHNOLOGY
1.1 INTRODUCTION
1.2 SOUTH AFRICA’S CLIMATE AND CONVECTIVE ACTIVITY
1.3 ENABLING TECHNOLOGY IN SOUTH AFRICA
1.4 RESEARCH PROBLEM
1.5 HYPOTHESIS
1.6 AIMS AND OBJECTIVES
1.7 LAYOUT OF THE THESIS
CHAPTER 2: MSG APPLICATIONS FOR FORECASTING CONVECTION
2.1 BACKGROUND
2.2 METEOROLOGICAL PRODUCTS EXTRACTION FACILITY (MPEF)
2.3 THE GLOBAL INSTABILITY INDEX (GII)
2.4 THE INITIAL EVALUATION OF GII IN SOUTH AFRICA
2.5 THE REGIONAL INSTABILITY INDICES (RII)
2.6 SUMMARY
CHAPTER 3: EVALUATION OF GLOBAL AND REGIONAL INSTABILITY INDICES OVER SOUTH AFRICA
3.1 BACKGROUND
3.2 DATA
3.3 COMPARISON OF RII K INDEX AND LIFTED INDEX FIELDS AGAINST THE UNIFIED MODEL K INDEX AND LIFTED INDEX FIELDS
3.4 EVALUATION OF RII AGAINST OCCURRENCE OF LIGHTNING
3.5 SUMMARY
CHAPTER 4: PRINCIPLES OF A NEW COMBINED INSTABILITY INDEX
4.1 BACKGROUND
4.2 USING THE FOUR REGIONAL INSTABILITY INDICES IN THE DEVELOPMENT OF A NEW INDEX
4.3 CUMULATIVE FREQUENCY GRAPHS FOR TOPOGRAPHY AND LIGHTNING
4.4 COMBINING THE FOUR RII AND TOPOGRAPHY FOR A NEW INDEX
4.5 EXAMPLES OF THE NEW COMBINED INSTABILITY INDEX (CII) WITH VISUAL VERIFICATION
4.6 SUMMARY
CHAPTER 5: EVALUATION OF THE CII AGAINST THE OCCURRENCE OF LIGHTNING OVER SOUTH AFRICA
5.1 BACKGROUND
5.2 EVALUATION OF THE CII
5.3 CII STATISTICS FOR ALL FIFTY CASES
5.4 CII PERFORMANCE COMPARED TO THE PERFORMANCE OF THE INDIVIDUAL RII
5.5 SUMMARY
CHAPTER 6: EVALUATION OF THE CII AGAINST PRECIPITATION ESTIMATES
6.1 BACKGROUND
6.2 SOUTH AFRICAN RAIN GAUGE NETWORK
6.3 HYDRO ESTIMATOR (HE)
6.4 COMPARING THE CII WITH THE HYDROESTIMATOR RAINFALL
6.5 STATISTICS FOR CII VERSUS HE FOR ALL FIFTY CASES
6.6 VISUAL COMPARISONS OF THE OPERATIONAL CII, LIGHTNING OCCURENCE AND THE HE RAINFALL OVER SOUTHERN AFRICA
6.7 SUMMARY
CHAPTER 7 SUMMARY, RECOMMENDATIONS AND CONCLUSION
7.1 BACKGROUND
7.2 SUMMARY AND DISCUSSION OF RESULTS
7.3 RECOMMENDATIONS
7.4 CONCLUSION
REFERENCES
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