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Modelling low-frequency rainfall events using airflow indices, weather patterns and frontal frequencies
HYDROL 3636
Journal of Hydrology 212–213 (1998) 380–392
Modelling low-frequency rainfall events using airflow indices, weather patterns and frontal frequencies R.L. Wilby Department of Geography, University of Derby, Kedleston Road, Derby DE22 1GB, UK Received 18 October 1995; accepted 11 July 1996
Abstract Low-frequency, high-magnitude daily rainfall amounts recorded at several sites in central and southern England were related to the prevailing Lamb Weather Types (LWTs), daily weather front and airflow data. Three statistically distinct weather-type clusters were indentified and used to construct a simplified frontal model of daily precipitation occurrence/amount. The model was calibrated against station data for the period 1970–1990 and used to reconstruct observed daily precipitation between 1875 and 1969 given the historic sequence of LWTs. Although the model reproduced the incidence of low-frequency, high-magnitude events, it failed to capture variations in mean wet day probabilities and wet/dry spell persistence. This inability was attributed to the general limitations of the weather classification methodology, which did not capture all aspects of the precipitation regime with equal levels of proficiency. Therefore, the prospects for downscaling high-resolution precipitation series directly from indices of mean sea-level pressure rather than via weather patterns was discussed. Preliminary results indicate that relationships can be established between mean daily precipitation occurrence and airflow indices such as vorticity and strength of air flow. However, further research is required to establish the value of such indices for modelling lowfrequency, high-magnitude precipitation events. 䉷 1998 Published by Elsevier Science B.V. All rights reserved. Keywords: Low-frequency rainfall events; Downscaling; Weather classification; Airflow indices
1. Introduction Downscaling techniques are firmly established as a means of relating mesoscale atmospheric circulation patterns to regional scale surface climate variables (Bardossy, 1998, this issue). This involves correlating observed daily weather patterns with measured data, such as precipitation or temperature series. Using the surface pressure information from a perturbed General Circulation Model (GCM), it is then possible to derive a sequence of weather patterns and thence a regional climate change scenario at the GCM sub-grid scale resolutions required for water resource studies (Hay et al., 1991; 1992). To date, downscaling has been applied to precipitation modelling in a number
of regions, including Germany (Bardossy and Plate, 1991, 1992; Schubert, 1994), the British Isles (Wilby et al., 1994) and North America (Matyasovszky et al., 1993; Hughes and Guttorp, 1994). These models provide good representations of seasonal and longterm mean precipitation occurrence and amounts, but are less proficient at simulating extreme events and the persistence of long wet or dry spells. This has been attributed to the subjectivity involved in weather-type classifications and to the constraints imposed by limited data sets (Wilby, 1994). Nonetheless, circulation pattern data have been used extensively to forecast a range of hydrological phenomena and to account for spatial–temporal trends in extreme events (e.g., Roy and Fox, 1995;
0022-1694/98/$ - see front matter 䉷 1998 Published by Elsevier Science B.V. All rights reserved. PII: S0022-169 4(98)00218-2
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Fig. 1. Location of observed precipitation sites.
Grew and Werrity, 1995). Furthermore, reliable estimates of high-magnitude precipitation events are also essential for a variety of climate change impact analyses, such as assessments of future flood hazards (Beven, 1993), engineering design (Cowpertwait, 1994), rates of soil erosion (Favis-Mortlock and Boardman, 1995) and water quality changes (Wilby, 1993). The downscaling approach described by Wilby (1995) was based on the Lamb Weather Type (LWT) classification of daily circulation patterns across the British Isles since 1861 (Lamb, 1972), a scheme which has been thoroughly documented and critiqued elsewhere (O’Hare and Sweeney, 1992). The classification system incorporates seven major circulation types, 19 hybrid categories and one unclassifiable group, and has been studied extensively in relation to many aspects of climatological and environmental change (e.g., El-Kadi and Smithson, 1992;
Yarnal, 1993). Wilby et al. (1995) subsequently examined rainfall variability across the UK in relation to the most common LWTs and the occurrence of weather fronts between 1970 and 1990. These mesoscale synoptic features were shown to account for much intra-weather pattern rainfall variability at regional and, to a lesser extent, station scales. Furthermore, variations in annual weather front frequencies explain a significant proportion of the non-stationarity in historic rainfall circulation pattern statistics. Thus, the incorporation of frontal information within downscaling procedures has distinct advantages over schemes based upon configurations of surface pressure patterns alone. This conclusion was subsequently endorsed by results obtained from a frontal rainfall model for sites in the British Isles, which produced improved estimates of low-frequency, high-magnitude (⬎20 mm) events when compared with a conventional weather generator (Wilby, 1995). The
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Fig. 2. Analysis of daily rainfall statistics at Cambridge (1970–1990), using Lamb Weather Types and the occurrence of weather fronts.
model used sequences of daily LWTs to determine the number of weather fronts on any given day, and hence the probability and volume of precipitation at a site. Recognized limitations of the frontal model were the higher data requirements and level of parameterization. Furthermore, it was suggested that the statistical integrity and distinctiveness of the conditional probability distributions might be improved by collapsing the existing 16 rainfall distributions (eight LWT
classes divided into frontal and non-frontal sub-sets) into fewer, more physically meaningful categories. This task involves the amalgamation of statistically indistinguishable wet day size distributions into discrete hybrid groups. Not only are the number of model parameters reduced, but also each distribution has a greater number of data for improved representation of the size distribution, in particular, rare, highmagnitude events.
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Table 1 The largest 20 daily precipitation amounts by site and Lamb Weather Type (1970–1990) Lamb Weather Type
Cyclonic
Directional
Anticyclonic
Site
C
CN
CNE
CE
CSE
CS
CSW
CW
N
NE
E
SE
S
SW
W
NW
U
A
AN
ANE
Andover Cambridge Chatsworth Coventry Hatton Grange Kempsford Sandringham Spalding Winborne
9 5 8 7 11 9 7 9 6
— 1 — — — — — — —
2 2 — 1 1 2 1 — 2
— — 3 1 — 1 1 — 1
1 — — — 1 1 — — —
2 — — — — — — — 1
2 — — — 1 1 — — 1
— 1 1 1 — — 2 1 —
1 1 1 — — 1 1 — 2
— 1 — 1 — — — 1 —
— — 1 3 4 — 1 2 1
— — — — 1 — 1 — 1
1 — — — — — 1 2 1
— 4 — — — 1 2 2 1
— 1 3 — — 2 1 2 2
— — — 1 1 — — 1 —
1 2 1 1 — 1 1 — —
1 2 1 3 — 1 1 — 1
— — 1 — — — — — —
— — — 1 — — — — —
Totals
71
1
11
7
3
3
5
6
7
3
12
3
5
10
11
3
7
10
1
1
This paper will determine the usefulness of a subjective weather classification scheme as a means of categorizing low-frequency historic precipitation events with a view to downscaling such information from GCM output. The approach involves disaggregating daily precipitation data for several sites in central and southern England by LWTs (Lamb, 1972) and stratifying wet days according to the presence or absence of weather fronts. The technique thus enables the interpretation of precipitation events in terms of the dominant air mass and causal mechanism (whether of convective or stratiform origin). This procedure forms the basis of a weather generator described previously by Wilby (1995) and simplified below. Finally, and in the light of the results obtained from this model, suggestions are made for the development of a downscaling technique which does not involve the use of subjective weather classification, but instead employs continuous airflow indices.
2. Analysis of high-magnitude precipitation events Daily precipitation data were drawn from a network of nine stations across central and southern England (Fig. 1). These sites were chosen on the basis of their disparate geographical locations, length and
completeness of the rainfall records. Fig. 2a shows the 27 LWT classes grouped according to their relative wetness (percentage total precipitation/percentage frequency of occurrence) and proportion of wet days (frequency of days with precipitation ⬎ 0.1 mm/frequency LWT days) at the Cambridge site. Three distinct clusters emerged: a low yield/low wet day group, comprising the anticyclonic hybrids (A, AN, ANE, AE, ASE, AS, ASW, AW and ANW); an intermediate group composed predominantly of the directional LWTs (N, NE, E, SE, S, SW, W, NW and U); and the high yield/high frequency of rain days group, incorporating the cyclonic hybrids (C, CN, CNE, CE, CSE, CS, CSW, CW and CNW). These groups were defined from cluster analyses of the relative wetness and wet day probabilities at selected sites. In general, the three clusters were found to characterize the precipitation statistics at each location, although individual LWTs displayed some variation between sites. For example, at Cambridge the outliers, NE and CNE, reflect the proximity of the site to wet air masses originating from the North Sea. Fig. 2b indicates that there was also a relationship between the relative frequency of fronts (percentage of days with fronts/percentage of LWT days) and the relative wetness of each LWT, with the wettest LWTs
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Fig. 3. Probabilities of 24-h wet day precipitation amounts at Kempsford (1970–1990) for (a) days without weather fronts, or (b) days with weather fronts.
tending to have the highest frequency of days with fronts. Fig. 2 deals with the average precipitation characteristics of each of the LWT classes. By comparison, Table 1 categorizes the 20 largest daily precipitation amounts at each site between 1970 and 1990 by the prevailing LWT. In common with previous studies (e.g., Roy and Fox, 1995), the results display a degree
of site specificity that reflects regional differences in precipitation associated with any given LWT (Mayes, 1991). These differences may be attributed to the geographical location of each site in relation to dominant airstreams and orography. Overall, however, the cyclonic cluster accounted for 61% of the events, the directional cluster 32% and the anticyclonic cluster just 7%. This allocation was also evident in the 20
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Table 2 Frontal model parameters for Kempsford Cluster
P(F ⬎ 0)
Pwet
rwet
Anticyclonic
0.584
0.102 (F 0) 0.150 (F ⬎ 0)
2.579x 2 ⫺ 4.778x (F 0) 4.169x 2 ⫺ 4.400x (F ⬎ 0)
Directional
0.697
0.398 (F 0) 0.534 (F ⬎ 0)
1.459x 2 ⫺ 7.240x (F 0) 1.397x 2 ⫺ 8.048x (F ⬎ 0)
Cyclonic
0.751
0.652 (F 0) 0.738 (F ⬎ 0)
5.499x 2 ⫺ 4.073x (F 0) 2.024x 2 ⫺ 10.16x (F ⬎ 0)
Note: P(F ⬎ 0) is the probability of frontal weather, F is the number of fronts, Pwet is the probability of a wet day, rwet is the wet day precipitation amount (mm) and x log10 R, where 0 ⬍ R ⱕ 1.
largest areal average rainfalls derived from the England, Scotland, Wales and Ireland (ESWIR) network since 1970 (Sweeney and O’Hare, 1992). The corresponding proportions were 60% (cyclonic), 40% (directional) and 0% (anticyclonic). Furthermore, these high-magnitude events appear to be biased towards frontal origin, since weather fronts were found to occur on 85% of the days (compared with the 1970–1990 average of 67% of days). Fig. 3 compares the daily wet day amount exceedences at Kempsford (1970–1990) for each of the six distributions. These distributions were represented using a second order polynomial regression, which yielded a significant (P ⬍ 0.0001) fit in each case. The significance of the differences between the six clusters was then tested by comparing their relative size distributions using the Mann–Whitney statistic. This exercise revealed that all the groups, with the exception of the non-frontal directional cluster and
the frontal anticyclonic cluster, were statistically different (P ⬍ 0.0001) to one another. 3. The model The above results suggested that, in terms of modelling extreme precipitation events, the 16 classes originally employed by Wilby (1995) could be legitimately reduced to three composite clusters of LWTs (cyclonic, directional, anticyclonic), with each incorporating a frontal and non-frontal sub-category. These three weather pattern clusters were then used to condition daily precipitation series at selected sites. The modelling sequence involved four principal steps: (1) input a series of daily LWTs and reclassify each day into one of the three clusters; (2) given the prevailing cluster type, determine the probable precipitation mechanism (i.e. frontal or convective); (3) given the precipitation mechanism, determine the
Fig. 4. Daily probability of frontal weather across the British Isles by Lamb Weather Type cluster and month (1970–1990).
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Table 3 Summary of frontal model results Period
1875–1889 1890–1909 1910–1929 1930–1949 1950–1969 1970–1990*
Cluster
Pwet
Mean (mm)
Variance (mm)
⬎ 20 mm
Dry-spell (d)
Wet-spell (d)
A
D
C
Obs.
Sim.
Obs.
Sim.
Obs.
Sim.
Obs.
Sim.
Obs.
Sim.
Obs.
Sim.
0.33 0.35 0.31 0.33 0.32 0.34
0.42 0.43 0.45 0.46 0.45 0.43
0.25 0.22 0.24 0.21 0.23 0.23
0.43 0.46 0.51 0.42 0.42 0.43
0.43 0.41 0.43 0.42 0.42 0.42
4.6 3.6 4.0 4.2 4.8 4.1
4.4 4.1 4.2 4.1 4.3 4.2
28 22 24 25 30 25
29 23 25 23 29 27
55 56 66 44 53 63
44 58 62 51 64 62
3.5 3.2 3.1 3.5 3.3 3.6
2.7 2.7 2.6 2.6 2.6 2.7
2.7 2.8 3.2 2.9 2.4 2.7
2.0 1.9 2.0 1.9 2.0 1.9
Key: Clusters Anticyclonic (A), Directional (D), Cyclonic (C); Pwet mean daily probability of precipitation; Mean average wet day precipitation amount (mm); Variance variance in wet day precipitation amount (mm); ⬎ 20 mm number of days exceeding 20 mm precipitation in a day; Dry mean dry spell duration (days); Wet mean wet spell duration (days); *period used for model calibration.
Fig. 5. Comparison of observed and simulated maximum daily rainfall total (a) and mean annual precipitation total (b) at Kempsford (1875– 1990).
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probability of a wet day; (4) finally, if a wet day occurs, determine the 24-h precipitation total. The conditional precipitation mechanisms, wet day probabilites and amounts were all derived from observed daily rainfall series. Table 2 provides example model parameters for the period 1970–1990 at Kempsford. The probability of precipitation on any given day is conditional on the probability of frontal (Fr ⬎ 0) or non-frontal (Fr 0) weather, which is in turn conditioned by the prevailing weather-type cluster. Fig. 4 reveals that the probability of Fr ⬎ 0 is greatest during late summer and early autumn, and at its least in winter. However, this apparent seasonality was found to be within the 95% confidence limits of the mean and therefore statistically insignificant. Similarly, wet day probabilities (Pwet) for each cluster also exhibited seasonal cycles which were within the 95% confidence limits. Both these results suggest that the probability of Fr ⬎ 0 and Pwet ⬎ 0 are adequately represented by an annual mean statistic. Table 2 indicates that the daily probability of frontal precipitation was least for the anticyclonic cluster (P(Fr ⬎ 0) 0.584, Pwet 0.150) and greatest for the cyclonic cluster (P(Fr ⬎ 0) 0.751, Pwet 0.738). Wet day precipitation amounts were modelled by fitting polynomial regressions to each of the six probabilities of exceedence size distributions shown in Fig. 3. By entering the logarithm of a linear random number R (where 0 ⬍ R ⱕ 1), it was then possible to determine the 24-h precipitation amount on wet days. This approach differs from that originally employed by Wilby (1995), in which wet day amounts were represented by an exponential distribution rather than an empirical relationship. Given the conditional statistics in Table 2, either historic or GCM-derived series of LWTs may then be used to determine the probability of frontal (P(Fr ⬎ 0)) or non-frontal weather (1 ⫺ P(Fr ⬎ 0)), the likelihood of a wet day (Pwet) and hence the daily wet day amount (rwet). In order to test the validity of the calibrated model, the parameters shown in Table 2 were used to reconstruct the daily precipitation statistics at Kempsford for the period 1875–1969 given only the catalogued LWT series for the same period (Lamb, 1972). This was considered a rigorous test of the revised frontal model, since the calibration period was one of the driest 20-year periods in the record. The model performance was then compared with the
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observed precipitation statistics for five 20-year subperiods since 1875.
4. Model evaluation Table 3 compares simulated and observed precipitation data at Kempsford for six periods since 1875. The model performance was evaluated using the wet day probabilities, means, variances, maximum daily amounts and number of days with precipitation ⬎ 20 mm for each 20-year period. Table 3 also shows the percentage of days allocated to each of the three weather-type clusters in each period. Given the limited amount of data used to conduct the simulations, the results presented in Table 3 were considered satisfactory. In general, the model reproduced the variance and frequency of events ⬎ 20 mm very well, but gave a relatively poor representation of the wet day probabilities and mean wet day amounts. Fig. 5a shows that the model gave a good approximation of the maximum daily amounts (r 0.94) and, as Fig. 5b indicates, successfully captured the observed pattern but not the variance in the 20-year mean annual rainfall amounts (r 0.92). The lower variance in simulated annual means was attributed to the stable proportions of the three weather-type clusters and to the fact that the model was calibrated using a relatively dry period (Table 3). The cluster proportions conceal significant inter-annual variations which are known to have occurred in the frequencies of pure LWTs, such as the cyclonic and anticyclonic types. By grouping pure LWTs with hybrid LWTs, improved estimates of low-frequency wet day occurrence were obtained, but mean statistics were poorly estimated due to the compensatory effects of unstable LWT frequencies within each of the three clusters. The results in Table 3 also show a consistent underestimation of wet and dry spell persistence by the model. This deficiency was attributed to the fact that wet days were generated independently of previous wet/dry days, yet autocorrelation was known to exist between wet-to-wet and dry-to-dry day transitions. It had been assumed that, by using actual series of LWTs, the persistence would have been implicit to the day to day LWT transitions. For example, a series of anticyclonic days should imply a high likelihood of zero rainfall and hence dry spell persistence.
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However, the results indicate that a persistence parameter is required within the model to increase autocorrelation and that this parameter should be independent of the prevailing LWT. Given the severity of the model validation and the limited number of parameters compared with previous algorithms (cf. Wilby, 1995), the results were considered promising. However, in common with the results obtained from generically similar downscaling models (Hughes and Guttorp, 1994), the present model did not capture all aspects of the precipitation regime with equal proficiency. The model construction and calibration were orientated towards the reproduction of low-frequency wet day precipitation amounts and probabilities. Consequently, variations in mean precipitation statistics were not well described beyond the calibration period. These limitations aside, and in addition to low-frequency precipitation simulation, the present frontal model potentially has three further applications. Firstly, the model provides the basis for identifying and modelling the spatial patterns of rainfall fields arising from contrasting air masses and precipitation processes. Secondly, the methodology provides a robust means of validating the precipitation partitioning of the most recent generation of GCMs, such as the Hadley Centre HadCM2 (Mitchell et al., 1995). Thirdly, the incorporation of frontal information within precipitation downscaling models provides a means of reproducing a component of the observed non-stationarity in precipitation–circulation pattern conditional statistics (see Wilby et al., 1995). In the meantime, the low sensitivity of the modelled annual means, daily wet day probabilities and rainfall amounts to different LWT scenarios or periods suggests that the three LWT clusters conceal too much temporal variation in the constituent LWTs. Significant changes in the frequency of pure LWTs such as the C or A types (see Fig. 2) may be concealed by compensatory reductions in the frequency of other cluster members, such as the CNW or AE types. Whilst grouping LWTs has the advantage of increasing the size and integrity of the calibration data for low-frequency events, it may, on the other hand, dilute the effect of subtle changes in the role of critical LWTs. The dichotomy of statistically significant numbers of calibration data versus sensitivity to the uniqueness of minority classes brings into question
the use of discrete categorization within downscaling models. Given the degree of overlap between the mean precipitation statistics of even contrasting LWTs, such as cyclonic or anticyclonic circulations, the definition of boundaries and the implied discontinuities between one weather state and the next is a largely arbitrary (albeit statistically justifiable) exercise. Even objective classification systems must ultimately place a given pressure pattern or rain day within one statistically coherent group or another according to a set of formalized criteria.
5. Airflow indices In order to capture both low-frequency events as well as mean precipitation statistics requires an approach that, on the one hand, maximizes the available data set but, on the other, does not overlook the uniqueness of atmospheric conditions on individual days. A valid line of research might therefore attempt to relate daily precipitation amounts to continuous atmospheric variables, thereby avoiding the issue of classification. This perspective regards the weather as a continuum rather than a series of overlapping classes or states. Furthermore, by relating daily rainfall data directly to an atmospheric index, the downscaling procedure avoids the intermediate step of relating surface pressure to a circulation pattern and thence to rainfall. At the same time, this index must be obtainable from GCM output and historic sources to be of value. Jones et al. (1993) have developed three such indices during the course of research into objective classifications of the Lamb circulation patterns from daily grid point mean sea-level pressure data over the British Isles. The direction (D) and strength of air flow (F), and total shear vorticities (Z) were computed using empirical calculations and daily pressure data extracted from pressure charts or GCM grid points. The corresponding LWTs were then defined from a number of rules depending on the relationship between D, F and Z. The technique has been a useful means of checking the Lamb catalogue for inconsistencies and for validating GCM control simulations (Hulme et al., 1993). However, the same airflow indices may be related directly to station or areal average precipitation series. Indeed, Conway and Jones (1998, this issue), Conway
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Fig. 6. (a) Mean wet-day precipitation amounts, (b) daily wet-day probabilities, and (c) percentage of days with weather fronts at Kempsford and Chatsworth (1970–1990) in relation to the Z and F indices derived for the British Isles by Jones et al. (1993).
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Fig. 7. Distribution of Jones et al. (1993) Z and F indices for the highest and lowest wet day precipitation totals across England, Scotland, Wales and Ireland (1970–1990).
et al. (1996) and Wilby et al. (1996) have made considerable progress in the development of downscaling techniques employing airflow indices. To date, such work has focused on the modelling of mean daily and annual precipitation statistics. For example, Fig. 6a shows the relationship between the mean wet day precipitation amounts at Kempsford and Chatsworth and the Z index. Low values of Z equate approximately to anticyclonic circulations, intermediate values to directional airflows and high values to cyclonic weather. As might be anticipated, the transition through each of these states with increasing Z results in progressively higher rainfall amounts, until a plateau region at Z ⬎ 30 is attained at these two sites. Fig. 6b shows the relationship between the probability of a wet day at the same sites and the F index. Low values of F are indicative of slack pressure, whereas high values are indicative of gale conditions across the UK, conditions often accompanied by heavy rainfall. Once again, the index provides a plausible explanation for the relatively few rain days at low values and for the high rainfall probabilites at the highest F values. Fig. 6c indicates that the percentage of days with weather fronts is also conditioned by the prevailing Z index, attaining a maximum in the region of Z 0 (i.e. directional LWTs). The predictable changes in wet day probabilities, precipitation amounts and weather fronts with F and Z illustrate the potential of these simple indices for modelling mean precipitation statistics, whilst circumventing the need for the intermediate stage of
weather classification. There is also scope for the use of pressure indices in the analysis of extreme events. Fig. 7 shows the distribution of Z and F values in relation to two populations of rainfall data: the 100 greatest areal average precipitation amounts in the ESWIR data set; and all days with zero precipitation for the same network (n 262). The latter set were characterized by negative Z indices (Zmean ⫺ 29.3) and low F values (Fmean 8.1), the former by positive Z values (Zmean 6.1) and a wider range of F indices (Fmean 19). Nonetheless, the days with the greatest areal average precipitation still exhibit considerable heterogeneity in Fig. 7. To specify such events more precisely will clearly require additional information, such as the direction of airflow, atmospheric humidity, precipitation mechanism or precursor airflow condition(s): variables that are all available from gridded GCM output. Similarly, further research is required to determine the value of airflow indices as predictors of extreme precipitation events at individual sites. The development of physically meaningful airflow indices does not necessarily obviate the need for weather classification schemes in the realm of downscaling. Indeed, the non-stationarity evident in circulation pattern–precipitation relations has also been found between the Z and F indices and local rainfall series (Wilby, 1997). Future research should therefore address the causes of temporal and spatial variations in conditional rainfall statistics by adopting a multivariate approach. Analyses of time series of weather fronts, airflow and teleconnection indices may lead to
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explanations of long-term changes in atmosphere– precipitation relations. Furthermore, the inclusion of frontal behaviour within precipitation models enables more realistic representations of the gross causal mechanisms and provides an appropriate basis for disaggregating precipitation data sets (Wilby et al., 1995).
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Acknowledgements I would like to thank Phil Jones and Mike Hulme for providing the daily grid point mean sea-level pressure indices for the British Isles. Thanks to Chris Dawson for the statistical advice offered. The constructive comments of two referees were also greatly appreciated.
6. Conclusion References If the current generation of downscaling techniques are to advance beyond the point of reproducing the statistical properties of their calibration data sets to simulating future precipitation scenarios obtained from GCM output, they must first provide acceptable reconstructions of historic data. The present paper has described a simplified model of low-frequency rainfall events based on physically reasonable aggregations of weather patterns and inferred precipitation mechansims (i.e. frontal or non-frontal). Whilst describing a significant proportion of the total variation in precipitation amounts using a relatively small number of circulation patterns, the research highlighted the constraints imposed by weather classification on model design and performance. A dichotomy was shown between maximizing the available data for accurate estimation of low-frequency precipitation parameters versus minimizing weather class aggregation in order to retain the unique attributes of minority classes. It was suggested that this conflict of interests cannot be reconciled by conventional weather classification-based precipitation models. As a consequence, such models do not simulate all precipitation statistics to equal standards. Improved realizations of historic precipitation data will also require an adequate explanation of nonstationarity and intra-circulation variability. Perhaps the most effective way of describing this variability may be to relax existing methodologies of weather typing, which impose rigid and often artificial boundaries on precipitation data. Future downscaling research should explore the use of complementary data sets, such as temperature, airflow or frontal series as descriptors of low-frequency rainfall events, and perhaps devote less effort to developing the ‘ultimate’ weather classification scheme.
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precipitation yields and circulation types in Britain and Ireland. Trans. Inst. Br. Geogr. 17, 448–463. Wilby, R.L., 1993. The influence of variable weather patterns on river water quantity and quality regimes. J. Climatol. 13, 447–459. Wilby, R.L., 1994. Stochastic weather type simulation for regional climate change impact assessment. Water Resour. Res. 30, 3395–3403. Wilby, R.L., 1995. Simulation of precipitation by weather pattern and frontal analysis. J. Hydrol. 173, 91–109. Wilby, R.L., 1997. Nonstationarity in daily precipitation series: implications for GCM downscaling using atmospheric circulation indices. Int. J. Climatol. 17, 439–454. Wilby, R.L., Greenfield, B., Glenny, C., 1994. A coupled synoptic– hydrological model for climate change impact assessment. J. Hydrol. 153, 265–290. Wilby, R.L., Barnsley, N., O’Hare, G., 1995. Rainfall variability associated with Lamb weather types: the case for incorporating weather fronts. Int. J. Climatol. 15, 1241–1252. Wilby, R.L., Conway, D., Jones, P.D., 1996. GCM downscaling using air flow indices. In: Proceedings of the International Conference on Water Resources and Environment Research: Towards the 21st Century, 29–31 October, Kyoto, Japan. Yarnal, B., 1993. Synoptic Climatology in Environmental Analysis: A Primer. Belhaven Press.
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Modelling low-frequency rainfall events using airflow indices, weather patterns and frontal frequencies R.L. Wilby Department of Geography, University of Derby, Kedleston Road, Derby DE22 1GB, UK Received 18 October 1995; accepted 11 July 1996
Abstract Low-frequency, high-magnitude daily rainfall amounts recorded at several sites in central and southern England were related to the prevailing Lamb Weather Types (LWTs), daily weather front and airflow data. Three statistically distinct weather-type clusters were indentified and used to construct a simplified frontal model of daily precipitation occurrence/amount. The model was calibrated against station data for the period 1970–1990 and used to reconstruct observed daily precipitation between 1875 and 1969 given the historic sequence of LWTs. Although the model reproduced the incidence of low-frequency, high-magnitude events, it failed to capture variations in mean wet day probabilities and wet/dry spell persistence. This inability was attributed to the general limitations of the weather classification methodology, which did not capture all aspects of the precipitation regime with equal levels of proficiency. Therefore, the prospects for downscaling high-resolution precipitation series directly from indices of mean sea-level pressure rather than via weather patterns was discussed. Preliminary results indicate that relationships can be established between mean daily precipitation occurrence and airflow indices such as vorticity and strength of air flow. However, further research is required to establish the value of such indices for modelling lowfrequency, high-magnitude precipitation events. 䉷 1998 Published by Elsevier Science B.V. All rights reserved. Keywords: Low-frequency rainfall events; Downscaling; Weather classification; Airflow indices
1. Introduction Downscaling techniques are firmly established as a means of relating mesoscale atmospheric circulation patterns to regional scale surface climate variables (Bardossy, 1998, this issue). This involves correlating observed daily weather patterns with measured data, such as precipitation or temperature series. Using the surface pressure information from a perturbed General Circulation Model (GCM), it is then possible to derive a sequence of weather patterns and thence a regional climate change scenario at the GCM sub-grid scale resolutions required for water resource studies (Hay et al., 1991; 1992). To date, downscaling has been applied to precipitation modelling in a number
of regions, including Germany (Bardossy and Plate, 1991, 1992; Schubert, 1994), the British Isles (Wilby et al., 1994) and North America (Matyasovszky et al., 1993; Hughes and Guttorp, 1994). These models provide good representations of seasonal and longterm mean precipitation occurrence and amounts, but are less proficient at simulating extreme events and the persistence of long wet or dry spells. This has been attributed to the subjectivity involved in weather-type classifications and to the constraints imposed by limited data sets (Wilby, 1994). Nonetheless, circulation pattern data have been used extensively to forecast a range of hydrological phenomena and to account for spatial–temporal trends in extreme events (e.g., Roy and Fox, 1995;
0022-1694/98/$ - see front matter 䉷 1998 Published by Elsevier Science B.V. All rights reserved. PII: S0022-169 4(98)00218-2
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Fig. 1. Location of observed precipitation sites.
Grew and Werrity, 1995). Furthermore, reliable estimates of high-magnitude precipitation events are also essential for a variety of climate change impact analyses, such as assessments of future flood hazards (Beven, 1993), engineering design (Cowpertwait, 1994), rates of soil erosion (Favis-Mortlock and Boardman, 1995) and water quality changes (Wilby, 1993). The downscaling approach described by Wilby (1995) was based on the Lamb Weather Type (LWT) classification of daily circulation patterns across the British Isles since 1861 (Lamb, 1972), a scheme which has been thoroughly documented and critiqued elsewhere (O’Hare and Sweeney, 1992). The classification system incorporates seven major circulation types, 19 hybrid categories and one unclassifiable group, and has been studied extensively in relation to many aspects of climatological and environmental change (e.g., El-Kadi and Smithson, 1992;
Yarnal, 1993). Wilby et al. (1995) subsequently examined rainfall variability across the UK in relation to the most common LWTs and the occurrence of weather fronts between 1970 and 1990. These mesoscale synoptic features were shown to account for much intra-weather pattern rainfall variability at regional and, to a lesser extent, station scales. Furthermore, variations in annual weather front frequencies explain a significant proportion of the non-stationarity in historic rainfall circulation pattern statistics. Thus, the incorporation of frontal information within downscaling procedures has distinct advantages over schemes based upon configurations of surface pressure patterns alone. This conclusion was subsequently endorsed by results obtained from a frontal rainfall model for sites in the British Isles, which produced improved estimates of low-frequency, high-magnitude (⬎20 mm) events when compared with a conventional weather generator (Wilby, 1995). The
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Fig. 2. Analysis of daily rainfall statistics at Cambridge (1970–1990), using Lamb Weather Types and the occurrence of weather fronts.
model used sequences of daily LWTs to determine the number of weather fronts on any given day, and hence the probability and volume of precipitation at a site. Recognized limitations of the frontal model were the higher data requirements and level of parameterization. Furthermore, it was suggested that the statistical integrity and distinctiveness of the conditional probability distributions might be improved by collapsing the existing 16 rainfall distributions (eight LWT
classes divided into frontal and non-frontal sub-sets) into fewer, more physically meaningful categories. This task involves the amalgamation of statistically indistinguishable wet day size distributions into discrete hybrid groups. Not only are the number of model parameters reduced, but also each distribution has a greater number of data for improved representation of the size distribution, in particular, rare, highmagnitude events.
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383
Table 1 The largest 20 daily precipitation amounts by site and Lamb Weather Type (1970–1990) Lamb Weather Type
Cyclonic
Directional
Anticyclonic
Site
C
CN
CNE
CE
CSE
CS
CSW
CW
N
NE
E
SE
S
SW
W
NW
U
A
AN
ANE
Andover Cambridge Chatsworth Coventry Hatton Grange Kempsford Sandringham Spalding Winborne
9 5 8 7 11 9 7 9 6
— 1 — — — — — — —
2 2 — 1 1 2 1 — 2
— — 3 1 — 1 1 — 1
1 — — — 1 1 — — —
2 — — — — — — — 1
2 — — — 1 1 — — 1
— 1 1 1 — — 2 1 —
1 1 1 — — 1 1 — 2
— 1 — 1 — — — 1 —
— — 1 3 4 — 1 2 1
— — — — 1 — 1 — 1
1 — — — — — 1 2 1
— 4 — — — 1 2 2 1
— 1 3 — — 2 1 2 2
— — — 1 1 — — 1 —
1 2 1 1 — 1 1 — —
1 2 1 3 — 1 1 — 1
— — 1 — — — — — —
— — — 1 — — — — —
Totals
71
1
11
7
3
3
5
6
7
3
12
3
5
10
11
3
7
10
1
1
This paper will determine the usefulness of a subjective weather classification scheme as a means of categorizing low-frequency historic precipitation events with a view to downscaling such information from GCM output. The approach involves disaggregating daily precipitation data for several sites in central and southern England by LWTs (Lamb, 1972) and stratifying wet days according to the presence or absence of weather fronts. The technique thus enables the interpretation of precipitation events in terms of the dominant air mass and causal mechanism (whether of convective or stratiform origin). This procedure forms the basis of a weather generator described previously by Wilby (1995) and simplified below. Finally, and in the light of the results obtained from this model, suggestions are made for the development of a downscaling technique which does not involve the use of subjective weather classification, but instead employs continuous airflow indices.
2. Analysis of high-magnitude precipitation events Daily precipitation data were drawn from a network of nine stations across central and southern England (Fig. 1). These sites were chosen on the basis of their disparate geographical locations, length and
completeness of the rainfall records. Fig. 2a shows the 27 LWT classes grouped according to their relative wetness (percentage total precipitation/percentage frequency of occurrence) and proportion of wet days (frequency of days with precipitation ⬎ 0.1 mm/frequency LWT days) at the Cambridge site. Three distinct clusters emerged: a low yield/low wet day group, comprising the anticyclonic hybrids (A, AN, ANE, AE, ASE, AS, ASW, AW and ANW); an intermediate group composed predominantly of the directional LWTs (N, NE, E, SE, S, SW, W, NW and U); and the high yield/high frequency of rain days group, incorporating the cyclonic hybrids (C, CN, CNE, CE, CSE, CS, CSW, CW and CNW). These groups were defined from cluster analyses of the relative wetness and wet day probabilities at selected sites. In general, the three clusters were found to characterize the precipitation statistics at each location, although individual LWTs displayed some variation between sites. For example, at Cambridge the outliers, NE and CNE, reflect the proximity of the site to wet air masses originating from the North Sea. Fig. 2b indicates that there was also a relationship between the relative frequency of fronts (percentage of days with fronts/percentage of LWT days) and the relative wetness of each LWT, with the wettest LWTs
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Fig. 3. Probabilities of 24-h wet day precipitation amounts at Kempsford (1970–1990) for (a) days without weather fronts, or (b) days with weather fronts.
tending to have the highest frequency of days with fronts. Fig. 2 deals with the average precipitation characteristics of each of the LWT classes. By comparison, Table 1 categorizes the 20 largest daily precipitation amounts at each site between 1970 and 1990 by the prevailing LWT. In common with previous studies (e.g., Roy and Fox, 1995), the results display a degree
of site specificity that reflects regional differences in precipitation associated with any given LWT (Mayes, 1991). These differences may be attributed to the geographical location of each site in relation to dominant airstreams and orography. Overall, however, the cyclonic cluster accounted for 61% of the events, the directional cluster 32% and the anticyclonic cluster just 7%. This allocation was also evident in the 20
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385
Table 2 Frontal model parameters for Kempsford Cluster
P(F ⬎ 0)
Pwet
rwet
Anticyclonic
0.584
0.102 (F 0) 0.150 (F ⬎ 0)
2.579x 2 ⫺ 4.778x (F 0) 4.169x 2 ⫺ 4.400x (F ⬎ 0)
Directional
0.697
0.398 (F 0) 0.534 (F ⬎ 0)
1.459x 2 ⫺ 7.240x (F 0) 1.397x 2 ⫺ 8.048x (F ⬎ 0)
Cyclonic
0.751
0.652 (F 0) 0.738 (F ⬎ 0)
5.499x 2 ⫺ 4.073x (F 0) 2.024x 2 ⫺ 10.16x (F ⬎ 0)
Note: P(F ⬎ 0) is the probability of frontal weather, F is the number of fronts, Pwet is the probability of a wet day, rwet is the wet day precipitation amount (mm) and x log10 R, where 0 ⬍ R ⱕ 1.
largest areal average rainfalls derived from the England, Scotland, Wales and Ireland (ESWIR) network since 1970 (Sweeney and O’Hare, 1992). The corresponding proportions were 60% (cyclonic), 40% (directional) and 0% (anticyclonic). Furthermore, these high-magnitude events appear to be biased towards frontal origin, since weather fronts were found to occur on 85% of the days (compared with the 1970–1990 average of 67% of days). Fig. 3 compares the daily wet day amount exceedences at Kempsford (1970–1990) for each of the six distributions. These distributions were represented using a second order polynomial regression, which yielded a significant (P ⬍ 0.0001) fit in each case. The significance of the differences between the six clusters was then tested by comparing their relative size distributions using the Mann–Whitney statistic. This exercise revealed that all the groups, with the exception of the non-frontal directional cluster and
the frontal anticyclonic cluster, were statistically different (P ⬍ 0.0001) to one another. 3. The model The above results suggested that, in terms of modelling extreme precipitation events, the 16 classes originally employed by Wilby (1995) could be legitimately reduced to three composite clusters of LWTs (cyclonic, directional, anticyclonic), with each incorporating a frontal and non-frontal sub-category. These three weather pattern clusters were then used to condition daily precipitation series at selected sites. The modelling sequence involved four principal steps: (1) input a series of daily LWTs and reclassify each day into one of the three clusters; (2) given the prevailing cluster type, determine the probable precipitation mechanism (i.e. frontal or convective); (3) given the precipitation mechanism, determine the
Fig. 4. Daily probability of frontal weather across the British Isles by Lamb Weather Type cluster and month (1970–1990).
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Table 3 Summary of frontal model results Period
1875–1889 1890–1909 1910–1929 1930–1949 1950–1969 1970–1990*
Cluster
Pwet
Mean (mm)
Variance (mm)
⬎ 20 mm
Dry-spell (d)
Wet-spell (d)
A
D
C
Obs.
Sim.
Obs.
Sim.
Obs.
Sim.
Obs.
Sim.
Obs.
Sim.
Obs.
Sim.
0.33 0.35 0.31 0.33 0.32 0.34
0.42 0.43 0.45 0.46 0.45 0.43
0.25 0.22 0.24 0.21 0.23 0.23
0.43 0.46 0.51 0.42 0.42 0.43
0.43 0.41 0.43 0.42 0.42 0.42
4.6 3.6 4.0 4.2 4.8 4.1
4.4 4.1 4.2 4.1 4.3 4.2
28 22 24 25 30 25
29 23 25 23 29 27
55 56 66 44 53 63
44 58 62 51 64 62
3.5 3.2 3.1 3.5 3.3 3.6
2.7 2.7 2.6 2.6 2.6 2.7
2.7 2.8 3.2 2.9 2.4 2.7
2.0 1.9 2.0 1.9 2.0 1.9
Key: Clusters Anticyclonic (A), Directional (D), Cyclonic (C); Pwet mean daily probability of precipitation; Mean average wet day precipitation amount (mm); Variance variance in wet day precipitation amount (mm); ⬎ 20 mm number of days exceeding 20 mm precipitation in a day; Dry mean dry spell duration (days); Wet mean wet spell duration (days); *period used for model calibration.
Fig. 5. Comparison of observed and simulated maximum daily rainfall total (a) and mean annual precipitation total (b) at Kempsford (1875– 1990).
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probability of a wet day; (4) finally, if a wet day occurs, determine the 24-h precipitation total. The conditional precipitation mechanisms, wet day probabilites and amounts were all derived from observed daily rainfall series. Table 2 provides example model parameters for the period 1970–1990 at Kempsford. The probability of precipitation on any given day is conditional on the probability of frontal (Fr ⬎ 0) or non-frontal (Fr 0) weather, which is in turn conditioned by the prevailing weather-type cluster. Fig. 4 reveals that the probability of Fr ⬎ 0 is greatest during late summer and early autumn, and at its least in winter. However, this apparent seasonality was found to be within the 95% confidence limits of the mean and therefore statistically insignificant. Similarly, wet day probabilities (Pwet) for each cluster also exhibited seasonal cycles which were within the 95% confidence limits. Both these results suggest that the probability of Fr ⬎ 0 and Pwet ⬎ 0 are adequately represented by an annual mean statistic. Table 2 indicates that the daily probability of frontal precipitation was least for the anticyclonic cluster (P(Fr ⬎ 0) 0.584, Pwet 0.150) and greatest for the cyclonic cluster (P(Fr ⬎ 0) 0.751, Pwet 0.738). Wet day precipitation amounts were modelled by fitting polynomial regressions to each of the six probabilities of exceedence size distributions shown in Fig. 3. By entering the logarithm of a linear random number R (where 0 ⬍ R ⱕ 1), it was then possible to determine the 24-h precipitation amount on wet days. This approach differs from that originally employed by Wilby (1995), in which wet day amounts were represented by an exponential distribution rather than an empirical relationship. Given the conditional statistics in Table 2, either historic or GCM-derived series of LWTs may then be used to determine the probability of frontal (P(Fr ⬎ 0)) or non-frontal weather (1 ⫺ P(Fr ⬎ 0)), the likelihood of a wet day (Pwet) and hence the daily wet day amount (rwet). In order to test the validity of the calibrated model, the parameters shown in Table 2 were used to reconstruct the daily precipitation statistics at Kempsford for the period 1875–1969 given only the catalogued LWT series for the same period (Lamb, 1972). This was considered a rigorous test of the revised frontal model, since the calibration period was one of the driest 20-year periods in the record. The model performance was then compared with the
387
observed precipitation statistics for five 20-year subperiods since 1875.
4. Model evaluation Table 3 compares simulated and observed precipitation data at Kempsford for six periods since 1875. The model performance was evaluated using the wet day probabilities, means, variances, maximum daily amounts and number of days with precipitation ⬎ 20 mm for each 20-year period. Table 3 also shows the percentage of days allocated to each of the three weather-type clusters in each period. Given the limited amount of data used to conduct the simulations, the results presented in Table 3 were considered satisfactory. In general, the model reproduced the variance and frequency of events ⬎ 20 mm very well, but gave a relatively poor representation of the wet day probabilities and mean wet day amounts. Fig. 5a shows that the model gave a good approximation of the maximum daily amounts (r 0.94) and, as Fig. 5b indicates, successfully captured the observed pattern but not the variance in the 20-year mean annual rainfall amounts (r 0.92). The lower variance in simulated annual means was attributed to the stable proportions of the three weather-type clusters and to the fact that the model was calibrated using a relatively dry period (Table 3). The cluster proportions conceal significant inter-annual variations which are known to have occurred in the frequencies of pure LWTs, such as the cyclonic and anticyclonic types. By grouping pure LWTs with hybrid LWTs, improved estimates of low-frequency wet day occurrence were obtained, but mean statistics were poorly estimated due to the compensatory effects of unstable LWT frequencies within each of the three clusters. The results in Table 3 also show a consistent underestimation of wet and dry spell persistence by the model. This deficiency was attributed to the fact that wet days were generated independently of previous wet/dry days, yet autocorrelation was known to exist between wet-to-wet and dry-to-dry day transitions. It had been assumed that, by using actual series of LWTs, the persistence would have been implicit to the day to day LWT transitions. For example, a series of anticyclonic days should imply a high likelihood of zero rainfall and hence dry spell persistence.
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However, the results indicate that a persistence parameter is required within the model to increase autocorrelation and that this parameter should be independent of the prevailing LWT. Given the severity of the model validation and the limited number of parameters compared with previous algorithms (cf. Wilby, 1995), the results were considered promising. However, in common with the results obtained from generically similar downscaling models (Hughes and Guttorp, 1994), the present model did not capture all aspects of the precipitation regime with equal proficiency. The model construction and calibration were orientated towards the reproduction of low-frequency wet day precipitation amounts and probabilities. Consequently, variations in mean precipitation statistics were not well described beyond the calibration period. These limitations aside, and in addition to low-frequency precipitation simulation, the present frontal model potentially has three further applications. Firstly, the model provides the basis for identifying and modelling the spatial patterns of rainfall fields arising from contrasting air masses and precipitation processes. Secondly, the methodology provides a robust means of validating the precipitation partitioning of the most recent generation of GCMs, such as the Hadley Centre HadCM2 (Mitchell et al., 1995). Thirdly, the incorporation of frontal information within precipitation downscaling models provides a means of reproducing a component of the observed non-stationarity in precipitation–circulation pattern conditional statistics (see Wilby et al., 1995). In the meantime, the low sensitivity of the modelled annual means, daily wet day probabilities and rainfall amounts to different LWT scenarios or periods suggests that the three LWT clusters conceal too much temporal variation in the constituent LWTs. Significant changes in the frequency of pure LWTs such as the C or A types (see Fig. 2) may be concealed by compensatory reductions in the frequency of other cluster members, such as the CNW or AE types. Whilst grouping LWTs has the advantage of increasing the size and integrity of the calibration data for low-frequency events, it may, on the other hand, dilute the effect of subtle changes in the role of critical LWTs. The dichotomy of statistically significant numbers of calibration data versus sensitivity to the uniqueness of minority classes brings into question
the use of discrete categorization within downscaling models. Given the degree of overlap between the mean precipitation statistics of even contrasting LWTs, such as cyclonic or anticyclonic circulations, the definition of boundaries and the implied discontinuities between one weather state and the next is a largely arbitrary (albeit statistically justifiable) exercise. Even objective classification systems must ultimately place a given pressure pattern or rain day within one statistically coherent group or another according to a set of formalized criteria.
5. Airflow indices In order to capture both low-frequency events as well as mean precipitation statistics requires an approach that, on the one hand, maximizes the available data set but, on the other, does not overlook the uniqueness of atmospheric conditions on individual days. A valid line of research might therefore attempt to relate daily precipitation amounts to continuous atmospheric variables, thereby avoiding the issue of classification. This perspective regards the weather as a continuum rather than a series of overlapping classes or states. Furthermore, by relating daily rainfall data directly to an atmospheric index, the downscaling procedure avoids the intermediate step of relating surface pressure to a circulation pattern and thence to rainfall. At the same time, this index must be obtainable from GCM output and historic sources to be of value. Jones et al. (1993) have developed three such indices during the course of research into objective classifications of the Lamb circulation patterns from daily grid point mean sea-level pressure data over the British Isles. The direction (D) and strength of air flow (F), and total shear vorticities (Z) were computed using empirical calculations and daily pressure data extracted from pressure charts or GCM grid points. The corresponding LWTs were then defined from a number of rules depending on the relationship between D, F and Z. The technique has been a useful means of checking the Lamb catalogue for inconsistencies and for validating GCM control simulations (Hulme et al., 1993). However, the same airflow indices may be related directly to station or areal average precipitation series. Indeed, Conway and Jones (1998, this issue), Conway
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Fig. 6. (a) Mean wet-day precipitation amounts, (b) daily wet-day probabilities, and (c) percentage of days with weather fronts at Kempsford and Chatsworth (1970–1990) in relation to the Z and F indices derived for the British Isles by Jones et al. (1993).
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Fig. 7. Distribution of Jones et al. (1993) Z and F indices for the highest and lowest wet day precipitation totals across England, Scotland, Wales and Ireland (1970–1990).
et al. (1996) and Wilby et al. (1996) have made considerable progress in the development of downscaling techniques employing airflow indices. To date, such work has focused on the modelling of mean daily and annual precipitation statistics. For example, Fig. 6a shows the relationship between the mean wet day precipitation amounts at Kempsford and Chatsworth and the Z index. Low values of Z equate approximately to anticyclonic circulations, intermediate values to directional airflows and high values to cyclonic weather. As might be anticipated, the transition through each of these states with increasing Z results in progressively higher rainfall amounts, until a plateau region at Z ⬎ 30 is attained at these two sites. Fig. 6b shows the relationship between the probability of a wet day at the same sites and the F index. Low values of F are indicative of slack pressure, whereas high values are indicative of gale conditions across the UK, conditions often accompanied by heavy rainfall. Once again, the index provides a plausible explanation for the relatively few rain days at low values and for the high rainfall probabilites at the highest F values. Fig. 6c indicates that the percentage of days with weather fronts is also conditioned by the prevailing Z index, attaining a maximum in the region of Z 0 (i.e. directional LWTs). The predictable changes in wet day probabilities, precipitation amounts and weather fronts with F and Z illustrate the potential of these simple indices for modelling mean precipitation statistics, whilst circumventing the need for the intermediate stage of
weather classification. There is also scope for the use of pressure indices in the analysis of extreme events. Fig. 7 shows the distribution of Z and F values in relation to two populations of rainfall data: the 100 greatest areal average precipitation amounts in the ESWIR data set; and all days with zero precipitation for the same network (n 262). The latter set were characterized by negative Z indices (Zmean ⫺ 29.3) and low F values (Fmean 8.1), the former by positive Z values (Zmean 6.1) and a wider range of F indices (Fmean 19). Nonetheless, the days with the greatest areal average precipitation still exhibit considerable heterogeneity in Fig. 7. To specify such events more precisely will clearly require additional information, such as the direction of airflow, atmospheric humidity, precipitation mechanism or precursor airflow condition(s): variables that are all available from gridded GCM output. Similarly, further research is required to determine the value of airflow indices as predictors of extreme precipitation events at individual sites. The development of physically meaningful airflow indices does not necessarily obviate the need for weather classification schemes in the realm of downscaling. Indeed, the non-stationarity evident in circulation pattern–precipitation relations has also been found between the Z and F indices and local rainfall series (Wilby, 1997). Future research should therefore address the causes of temporal and spatial variations in conditional rainfall statistics by adopting a multivariate approach. Analyses of time series of weather fronts, airflow and teleconnection indices may lead to
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explanations of long-term changes in atmosphere– precipitation relations. Furthermore, the inclusion of frontal behaviour within precipitation models enables more realistic representations of the gross causal mechanisms and provides an appropriate basis for disaggregating precipitation data sets (Wilby et al., 1995).
391
Acknowledgements I would like to thank Phil Jones and Mike Hulme for providing the daily grid point mean sea-level pressure indices for the British Isles. Thanks to Chris Dawson for the statistical advice offered. The constructive comments of two referees were also greatly appreciated.
6. Conclusion References If the current generation of downscaling techniques are to advance beyond the point of reproducing the statistical properties of their calibration data sets to simulating future precipitation scenarios obtained from GCM output, they must first provide acceptable reconstructions of historic data. The present paper has described a simplified model of low-frequency rainfall events based on physically reasonable aggregations of weather patterns and inferred precipitation mechansims (i.e. frontal or non-frontal). Whilst describing a significant proportion of the total variation in precipitation amounts using a relatively small number of circulation patterns, the research highlighted the constraints imposed by weather classification on model design and performance. A dichotomy was shown between maximizing the available data for accurate estimation of low-frequency precipitation parameters versus minimizing weather class aggregation in order to retain the unique attributes of minority classes. It was suggested that this conflict of interests cannot be reconciled by conventional weather classification-based precipitation models. As a consequence, such models do not simulate all precipitation statistics to equal standards. Improved realizations of historic precipitation data will also require an adequate explanation of nonstationarity and intra-circulation variability. Perhaps the most effective way of describing this variability may be to relax existing methodologies of weather typing, which impose rigid and often artificial boundaries on precipitation data. Future downscaling research should explore the use of complementary data sets, such as temperature, airflow or frontal series as descriptors of low-frequency rainfall events, and perhaps devote less effort to developing the ‘ultimate’ weather classification scheme.
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