The determination of regionalised wind roses for the UK, for use with the HARM acid depositional model. Kevin H. Jones 2002 Statement of Originality I declare that this dissertation represents my own work, and that where the work of others has been used it has been duly accredited. I further declare that the length of the components of this dissertation is 5500 words for the Research paper and 10000 words for the Technical Report. Kevin H. Jones 11th September 2002 Acknowledgements Many thanks for helpful discussions and advice during the work for this dissertation are due to: Prof. Sarah Metcalfe Dr. Claire Jarvis & Dr. Jim Nicholson Abstract- The Hull acid rain (HARM) depositional model currently uses a single, representative wind rose for the UK (valid for 400 metres height above ground level) to scale the contributions from different wind directions to total deposition at any selected receptor site. Geostrophic wind data and surface roughness have been used to develop two models that together can estimate a 400 metre elevation wind rose at any location in the UK. The first model uses a least-squares interpolation technique to estimate a geostrophic wind rose at a location. The second model is an atmospheric boundary layer model based on the Ekman spiral, which ‘downconverts’ the geostrophic wind data to provide a wind rose for 400 metres above surface level. The consequence of this wind rose model for receptor sites in the HARM model is that a given site will be able to make use of a local wind rose to determine deposition contributions. Both models worked as expected, but only provided a marginal advantage over an all UK wind rose. In addition a mean UK wind rose for the geostrophic level was calculated covering the years 1990-96. HARM model runs conducted with this new rose showed significant differences compared with runs using the popular Jones (1981) wind rose. Key Words. HARM, wind rose, geostrophic, radiosonde, Ekman, Ekman-Taylor, surface roughness, Zo, least squares, planetary boundary layer. Copyright of this dissertation is retained by the author and The University of Edinburgh. Ideas contained in this dissertation remain the intellectual property of the author and their supervisors, except where explicitly otherwise referenced. All rights reserved. The use of any part of this dissertation reproduced, transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in a retrieval system without the prior written consent of the author and The University of Edinburgh (Department of Geography) is not permitted. INTRODUCTION The Hull acid rain (HARM) Lagrangian receptor depositional model (Metcalfe et al, 2001) currently uses a single, representative wind rose for the UK (Jones, 1981, p10) (valid for 400 metres height above ground level, and for wind speeds of 5 to 10 m/s (Metcalfe, 2002, pers comm)) to scale the contributions from different wind directions to total deposition at any selected receptor site. HARM uses a simplified 800 metre thick atmospheric mixing/boundary layer (Jones, 2002, p1 & 6). Other acid rain models that use the Lagrangian receptor technique such as the original EMEP model (NEGTAP, 2001 and RGAR, 1997) and FRAME (NEGTAP, 2001 and RGAR, 1997) also use a single wind rose. It is possible that the representative wind rose may vary from region to region across the UK, so affecting regional pollution deposition. This paper adopts a top-down approach to the modelling of local UK wind roses. Local wind roses could be used by the HARM model for a particular region or receptor site. METHODOLOGY The modelling technique developed in this paper uses two distinct models. A spatial model to interpolate geostrophic wind information to locations between observation points (radiosonde stations), and an atmospheric boundary layer model to transform the interpolated wind information from the geostrophic level to a height in the boundary layer (400 metres above ground level). Using radiosonde observations from several stations for the years 1990-96, results derived from the models were compared to observations at Hemsby in East Anglia. Hemsby has synoptic radiosonde data available for 1990-96, which have been used to generate an observed geostrophic and 400 metre level wind rose for comparison with the modelled ones. The wind data object (WDO) In order to pass the radiosonde wind data through the boundary layer model, and to enable the spatial interpolation of wind information between radiosonde station sites this paper develops the concept of the wind data object (WDO). The WDO is essentially a high definition wind rose consisting of 30 wind speed bands (between just above zero and 30 m/s), and 72 direction sectors from 5 to 360 degrees clockwise from north. The WDO can be visualised as 1 an array of 72 by 30 cells, each of the 2160 cells containing a percentage value for a given speed band and direction. Figure 1 shows the WDO resulting from seven years (1990-96) of geostrophic radiosonde observations (represented by synoptic wind observations between 1457 and 3000 metres above sea level (see technical report)) for Hemsby. Figure 1: Hemsby, 1457-3000m asl wind data object (WDO) for 1990-96, using 34671 synoptic observations. The 72 direction bins along the x-axis correspond to the angles 5-360 degrees in 5 degree increments (raw radiosonde angles are given to the nearest 5 degrees). The 30 speed bands along the y-axis have widths of 1m/s, with central values of 0.5 to 29.5 m/s. The z-axis shows the percentage value in each cell. Table 1: A seven year (1990-96) geostrophic wind rose for Hemsby, calculated for wind observations between 1457 and 3000 m above sea level. 2 This WDO can be used to create a geostrophic wind rose for Hemsby (see table 1) in the same format as the wind rose provided by Jones (1981) (see also Jones, 2002, p31). The four wind speed bands in table 1 can be plotted as individual wind roses as shown in figure 2. Comparing the wind rose given for speed band 2 (5-10m/s) in figure 2, with the corresponding speed band from Jones (1981), it can be seen that the predominant northerly component is missing from Hemsby data. Figure 2: Speed bands 1 to 4 from table 1, for Hemsby 1990-96 (1457-3000m asl), plotted as individual wind roses. (North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) 3 The spatial interpolation method In order to provide a geostrophic wind rose for any point in the UK, a process of spatial interpolation needs to be applied to the WDOs derived for the radiosonde stations. Figure 3, shows a map of the locations of the five radiosonde stations (Camborne, Herstmonceux, Hemsby, Hillsborough and Lerwick) used in this study. Since no a priori information was available as to the desirable shape of trend surfaces relating to the spatial distribution of the WDO contents, it was decided to create a spatial model for the WDOs using linear trend surfaces (i.e. ‘Ocham’s Razor’ determined simplest surface shape was used ) . Only four of the five stations were used in spatially interpolating the WDOs; the remaining station being used as an independent check on the model. For each of the 2160 (72 x 30) percentage values at the four stations a linear trend surface was constructed, using the least-squares method described by Harbaugh (1964, p7-32). This resulted in an ensemble of 2160 least-squares fitted linear surfaces from which a WDO could be synthesised at any location within the UK. Linearly spatially interpolated geostrophic models were created for radiosonde stations Camborne, Hemsby, Hillsborough and Lerwick (model #1), and stations Camborne, Herstmonceux, Hillsborough and Lerwick (model #2). These two models can estimate a geostrophic WDO at any position in the UK. Figure 4, shows wind roses constructed from estimated geostrophic WDOs using model #1, for all stored wind speeds (just above zero to 30 m/s) and 12 wind sectors of 30 degrees width (following, Jones, 1981). The wind roses shown in figure 4 demonstrate that the least-squares linear trend surface method can spatially interpolate WDOs without any obvious artefacts being created, and also seems to show a decrease in the westerly wind component between Camborne and Lerwick. 4 Figure 3: Location of the five synoptic radiosonde stations used to provide wind information. 5 Figure 4: Geostrophic wind roses for each 100km O/S square, derived from ‘geostrophic model #1’, showing 12 direction sectors for wind speeds greater than zero and less than or equal to 30 m/s. (Figure 4, covers the same area on the ground as figure 3, and the scale on each wind rose is 20%) 6 The boundary layer model Once a geostrophic WDO has been created for a desired location in the UK, it is passed through an Ekman spiral model (Ekman, 1905) to obtain a WDO modelled for 400 metres above ground level (agl). The Ekman model used is described in Jones (2002, p39-41), and shown conceptually in figure 5. Figure 5: The surface roughness coupled Ekman spiral model used represent the upper 90% of the boundary layer. The novel aspect of the modelling procedure is the way in which the WDO is ’presented’ to the model. Each of the 2160 percentage cells contained in the geostrophic WDO is labelled with a wind speed (0.5 to 29.5 m/s) and wind azimuth value (5 to 360 degrees). Given a surface roughness length, z0, appropriate for the location, and an inner layer height, h, of the 7 order of say 80 metres (see Jones 2002, p8), the model uses the WDO wind speed and azimuth label values as geostrophic wind speeds and directions. These 2160 geostrophic wind speed values are used to obtain 2160 sets of perpendicular wind components (u’ and v’) from which new wind speed and azimuth values are calculated. These ‘400 metre’ wind speed and azimuth values are used to re-label the percentage cells within the WDO. This re-labelled WDO now becomes a ‘400m agl’ WDO. The percentage values of such a 400m WDO can be straightforwardly re-binned on the basis of wind speed and azimuth to obtain a modelled 400m wind rose with 12-sectors and 4 speed bands. In addition to wind speed and azimuth values, important meta-data is created during the Ekman modelling process. Such data consists of individual friction velocity, u*, eddy viscosity, K, and planetary boundary layer (PBL) depth estimates, DE. These values are stored in the 400m WDO and maintain their association with the individual cells, to enable subsequent minimum, maximum and mean values to be calculated. Figure 6, shows the set of modelled 400m agl wind roses that result from the Ekman spiral model being applied to the observed geostrophic WDO for Hemsby shown in figure 1. The h value used is 80 metres, and the z0 used is 0.13 metres (which is typical for the landcover around Hemsby (Jones, 2002, p44)). Table 2, contains the modelled 400m agl wind rose data used to create figure 6. 8 Figure 6: Speed bands 1 to 4 modelled for Hemsby at 400m agl, using h = 80m, z0 = 0.133m, plotted as individual wind roses. (The Ekman model input data was the observed geostrophic WDO for Hemsby 1990-96, shown in figure 1. Also north is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Figures 2 and 6 clearly show that the Ekman model has caused the direction of the most prominent wind sectors for wind speed bands 2 and 3 (5-10 m/s and 10-15 m/s) to rotate anticlockwise from 250-280 degrees to 220-250 degrees. The mean wind speed has been reduced from a value of 11.2 m/s for the geostrophic WDO, to a value of 8.1 m/s derived from the modelled 400m WDO. Figure 7 shows wind speed histograms for both the observed geostrophic Hemsby WDO, and the Ekman modelled 400m WDO. 9 Figure 7: Total wind speed histograms for all wind directions, derived from the Hemsby 1990-96 (1457-3000m asl) observed geostrophic WDO, and from the WDO for 400m agl modelled from it using h = 80m, z0 = 0.133m. Figure 7, demonstrates that the wind speed reduction caused by the model is most pronounced at the higher end of the wind speed distribution, especially in the ‘tail’ of the distribution above 15 m/s. This explains why wind speed band 4 (15 m/s upwards) in figure 6 has been so severely attenuated compared with band 4 in figure 2. Such wind speed attenuation and anticlockwise sector rotation are expected from the theory of the Ekman spiral (see Haltner and Williams, 1980, p276). However, as shall be discussed in the RESULTS section the magnitude of the rotation and attenuation shown by the model in figures 6 and 7 are somewhat greater than that actually observed. 10 Table 2: A seven year (1990-96) Ekman modelled wind rose for Hemsby at 400m agl, using h = 80m, z0 = 0.133m. Calculated from the Hemsby 1990-96 (1457-3000m) observed geostrophic WDO. 11 RESULTS THE SPATIAL LINEAR INTERPOLATION MODEL In order to validate the ability of the least-squares linear trend surface method of spatial interpolation to produce an estimated WDO at a given location within the UK; geostrophic model #2 (which uses observed 1457-3000m WDOs from Camborne, Herstmonceux, Hillsborough and Lerwick) was run to produce an estimated 1457-3000m WDO for the 52.48oN 1.68oE co-ordinates of the Hemsby station. The resulting wind roses for the four wind speed bands (under 5 m/s, 5-10 m/s, 10-15 m/s, 15 m/s upwards) are shown in figure 8. Figure 8: 1457-3000m asl speed bands 1 to 4, estimated for Hemsby’s location 52.48oN 1.68oE from the geostrophic least-squares model #2, plotted as individual wind roses. (North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) 12 Table 3, contains the modelled 1457-3000m asl wind rose data used to create figure 8. For comparison geostrophic model #1 (using 1457-3000m WDOs from Camborne, Hemsby, Hillsborough and Lerwick) was used to create wind roses for the same location (52.48oN 1.68oE) which are shown in figure 9 and Table 4. The ‘goodness of fit’ statistics for the 2160 least squares linear trend surfaces used to create models #1 and #2 are shown in table 5, and give a percentage sum of squares (Harbaugh, 1964, p32) fit of around 75% for each model with a standard deviation of about 30%, which is a fair to good fit. Table 3: A geostrophic (1457-3000m asl) wind rose estimated for Hemsby’s location 52.48oN 1.68oE from the geostrophic least-squares model #2. In order to evaluate the geostrophic least squares model, comparisons must be made between the modelled 1457-3000m wind roses shown in figures 8 and 9 and the observed 1457-3000m wind rose shown in figure 2 (see also tables 1, 3 and 4). It can be seen that the results for model #1 give a very close fit to the observed Hemsby wind rose. This is to be expected since model #1 uses the Hemsby WDO as part of its input dataset. Nevertheless, this result is not trivial in that it verifies that the least-squares technique does not in itself introduce artifactual errors into the WDO data, and it should remembered that least-squares plane solutions are not constrained to agree with their data points. The results for model #2 as shown in figure 8 and table 3, show fairly good agreement with the observed Hemsby wind roses in figure 2 and 13 table 1, with the prominent 250 to 280 degree rose sector in the HARM relevant 5-10 m/s speed band having similar values of 4.88% observed, against 4.69% for model #2. Mean wind speeds and directions for the observed Hemsby WDO and the model #1 and #2 WDOs are respectively, 11.2m/s and 270o, 11.2m/s and 270o, 11.0m/s and 265o, for the 1457-3000m geostrophic level. However, in order to judge if use of the spatial least-squares linear trend surface model is justified a quantitative comparison must be made between the differences or ‘error’ between the observed and modelled Hemsby windrose, and similar differences between the observed Hemsby rose and observed wind roses of radiosonde stations at the opposite periphery of the UK. Figure 9: 1457-3000m asl speed bands 1 to 4, estimated for Hemsby’s location 52.48oN 1.68oE from the geostrophic least-squares model #1, plotted as individual wind roses. (North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) 14 Residual modulus differences between the relevant wind roses for the 5-10m/s wind speed band used by the HARM model, are displayed in table 6. The 5-10 m/s wind roses used as inputs to table 6 are shown in figure 10. It is justified to use the 5-10 m/s band sectors for comparisons at the 1457-3000m level since Jones (1981, p10) regards them as being similar to those observed at 400 metres as required for the HARM model. Table 4: A geostrophic (1457-3000m asl) wind rose estimated for Hemsby’s location 52.48oN 1.68oE from the geostrophic least-squares model #1. Table 4: A geostrophic (1457-3000m asl) wind rose estimated for Hemsby’s location 15 Table 5: Least squares linear trend surface statistics resulting from the creation of geostrophic least-squares models #1 and #2. 16 Table 6: A selection of observed and modelled wind roses for 5 to 10 m/s wind speeds, and associated modulus differences. The wind rose information shown is for the 14573000m geostrophic level, for the years 1990-96 inclusive (apart from Herstmonceux which only has data for 1992-96). Table 6 shows the initially disappointing result that the total percentage difference between the modelled (model #2) and observed Hemsby wind rose (for 5-10 m/s) of 4.09%, is greater than the percentage difference between Hemsby and the mean 5-10 m/s rose for stations other than Hemsby, of 2.96%. Thus, the mean wind rose gives a better estimate of Hemsby’s 5-10 m/s rose taken over all sectors, than does model #2. However, for the prominent 250o-280o rose sector, model #2 gives substantially better results than the mean (0.19% against 0.82% difference). Model #2 gives a better result for Hemsby’s 250o-280o rose sector than the differences between the observed 250o-280o result for Hemsby and any other station apart from Herstmonceux. Herstmonceux is only 250 km to the SSW of Hemsby, and is being used as the ‘surrogate’ east-coast station to replace Hemsby in model #2, so a small difference between Herstmonceux and Hemsby for the 250o-280o sector is not surprising. Table 6, also shows that Camborne and Lerwick show overall percentage differences substantially greater than model #2 or the mean, indicating that meaningful differences can exist between the geostrophic wind roses across the UK (Camborne and Lerwick are both directly exposed to 17 westerly winds, see figure 3). From table 6 it must be concluded that the case for using the least-squares trend surface technique to model 1457-3000m wind roses instead of a mean wind rose is marginal, and may depend on whether the pollution sources within the HARM model take the form of ‘lumps or points’ or ‘extended objects’. Table 7 shows the same information as table 6, but with the 5-10 m/s band wind roses normalised to unity. The same conclusions can be drawn from table 7 as from table 6, but with the added insight that the model #2 rose is very similar to the Herstmonceux rose for 510 m/s. Thus to some extent the least-squares trend suface model is giving ‘nearest neighbour’ type results (in fact the linear interpolation properties of the model should give results slightly better than nearest neighbour interpolation), see figure 10. 18 Table 7: A normalised to unity selection of observed and modelled wind roses for 5 to 10 m/s wind speeds, and associated modulus differences. The wind rose information shown is for the 1457-3000m geostrophic level, for the years 1990-96 inclusive (apart from Herstmonceux which only has data for 1992-96). 19 Figure 10: A selection of observed and modelled 1457-3000m wind roses for the 5-10 m/s wind speed band relevant to the HARM model. The observed wind roses are valid for the years 1990-96, apart from Herstmonceux, which is for 1992-96. 20 THE EKMAN BOUNDARY LAYER MODEL To test the coupled Ekman spiral boundary layer model, Hemsby radiosonde measurements between 1990-96 were used to create a reference 300-500m above ground level (agl) WDO against which to compare 400m agl WDOs created by the Ekman model. It was necessary to create the observed reference WDO over a 200 metre height range centred on 400m agl, in order to get enough synoptic observations to create reliable wind roses (from experience at least 3000 individual observations are required, which give an average of about 80 observations per wind rose sector, for 12 sectors and 4 speed bands). Figure 11: Speed bands 1 to 4 from table 8, for Hemsby 1990-96 (300-500m agl), plotted as individual wind roses. (North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) 21 Figure 11, shows wind roses for the 300-500m agl level for Hemsby, for the four speed bands, and table 8 shows the corresponding wind rose information. The WDO used to create table 8, was made using 5290 individual observations. Comparing figure 11 with figure 2, which gives similar windroses for the geostrophic (14573000m asl) level, it can immediately be seen that the prominent 350o-380o wind sectors in wind speed bands two and four (5-10 m/s and 15 m/s upwards) have been ‘rotated’ anticlockwise by 30o, between the geostrophic and 300-500 m level. This turning effect indicates that surface roughness considerations are indeed causing an anticlockwise movement of the boundary layer winds similar to that indicated by theory (see Haltner and Williams, 1980, p276). This contradicts the notion of Jones (1981, p10) that the geostrophic windrose for 5-10 m/s wind speeds is functionally the same as that seen at the ‘400 m’ level (as far as pollution modelling is concerned). Figure 12, shows a comparison of wind speed histograms for Hemsby (1990-96), for both the 1457-3000m (geostrophic) and 300-500m levels. Figure 12, seems to show relatively little difference between the wind speed histograms at the two levels, with the exception that some percentage ‘energy’ appears to have migrated from the upper and lower ‘tails’ of the distribution into the central (5-10 m/s and 10-15 m/s) bands, during the drop to the lower level. This behaviour is consistent with Troen and Petersen’s (1989) account of changing appearance of the Weibull wind speed distribution with height. 1990-96 Hemsby mean wind speeds and directions are 11.5 m/s and 268o for the 1457-3000m level, and 10.9 m/s and 254o for the 300-500m level, corresponding to a 5% overall wind speed drop, and 14o overall anticlockwise rotation for all wind vectors. For the 5 to 10 m/s speed bands the 1457-3000m vector mean wind direction is 269o, and for 300-500m is 272o. This small clockwise rotation for the mean vector direction of the 5-10 m/s band between the geostrophic and lower level is surprising, and suggests that a non-trivial relationship may exist between the mean vector wind direction over a time period at a location, and the direction of the predominant wind rose sector. For instance, the anticlockwise rotation for all wind vectors is 14o, but the predominant wind sector in speed bands 2 and 4 has rotated anticlockwise by 30o. 22 Table 8: A seven year (1990-96) 300-500m above ground level (agl) wind rose for Hemsby, calculated from 5290 wind observations. Figure 12: Total wind speed histograms for all wind directions, derived from the Hemsby 1990-96 (1457-3000m asl) observed geostrophic WDO, and from the observed WDO for 300-500m agl. For the Hemsby radiosonde station two values of surface roughness length, z0, are appropriate for coupled Ekman spiral modelling (see Jones, 2002, p44). A value of z0 = 0.133 metres for when the radiosonde balloon is over land, and z0 = 0.0002 metres when it is over the sea. The model also requires an a priori assumption of the depth of the ‘inner layer’, h, which from 23 Jones (1981) and Oke (1987) has been determined to be 80 metres (corresponding to 10% of a representative boundary layer depth of 800m for pollution modelling (Jones, 1981)). Figure 13: Speed bands 1 to 4 modelled for Hemsby at 400m agl, using h = 80m, z0 = 0.0002m, plotted as individual wind roses. (Note: the Ekman model input data was the observed geostrophic WDO for Hemsby 1990-96, shown in figure 1. Also north is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) The results of the Ekman model being run using these z0 and h values on the observed 199096 Hemsby 1457-3000m asl geostrophic WDO are shown in figures 6, 7 and table 2, for z0 = 0.133 m, and figures 13, 14 and table 9, for z0 = 0.0002 m. 24 Figures 13 and 6, of Ekman modelled wind roses (using h = 80m, z0 = 0.0002m and 0.133m) for wind speed band two (5-10 m/s) shows a similar one sector anti-clockwise rotation with respect to the geostrophic direction as that shown by the observed 300-500m agl wind roses (figure 11). However, the ‘percentage amplitudes’ of the speed band two rose sectors are not well modelled, being overestimated by 30 to 90% (see tables 8, 2 and 9). The reason for this mismatch can be seen by looking at the modelled and observed wind speed histograms shown in figures 7, 12 and 14. The model has overestimated the wind speed drop in the upper ‘tail’ of the distribution, leading to too much ‘percentage energy’ being ‘pushed down’ into the 510 m/s speed band. Table 10, shows both observed and modelled wind speed information for Hemsby at the geostrophic and 400m level. It shows that the Ekman modelled results for h = 80 m give estimated mean wind speeds for 400m agl of 9.2 and 8.1 m/s (for z0 = 0.0002m and 0.133m respectively), compared to the observed WDO value for 300-500m agl of 10.8 m/s (the 300500m agl value derived directly from radiosonde data is slightly greater at 10.9 m/s, since its estimation can include wind speed values greater than 30 m/s). These modelled 400m wind speeds have values of between 20 to 30% below the geostrophic values (11.2 m/s from WDO, 11.5 m/s from radiosonde observations), compared to the observed drop below geostrophic speeds of around 5% for 300-500m observations at Hemsby (see table 10). The overall mean vector wind directions for the h = 80m modelled results are 245o and 242o (for z0 = 0.0002m and 0.133m) giving a rotation anticlockwise from geostrophic (269o) of around 25o compared with the observed rotation of 15o. Table 10, shows that although the Ekman models for h = 80m show the ‘correct’ behaviour for the ‘direction’ of their predictions, the magnitudes are overestimated. The magnitudes of these over estimations are greater with z0 = 0.133m than 0.0002m. 25 Figure 14: Total wind speed histograms for all wind directions, derived from the Hemsby 1990-96 (1457-3000m asl) observed geostrophic WDO, and from the WDO for 400m agl modelled from it using h = 80m, z0 = 0.0002m. Table 9: A seven year (1990-96) Ekman modelled wind rose for Hemsby at 400m agl, using h = 80m, z0 = 0.0002m. Calculated from the Hemsby 1990-96 (1457-3000m) observed geostrophic WDO. This is not surprising if we consider the geographic setting of the Hemsby station (Jones, 2002, p44). It can be seen that wind directions pertaining for the majority of the time (see 26 figures 2 and 11) will carry the radiosonde balloon over the sea before reaching the lowest height (300m agl) at which observations are used by this study. Thus, the conclusion can be drawn that a surface roughness best characterising the Hemsby observations is z0 = 0.0002m. This assumption can be used to investigate the cause of the mediocre results the Ekman model has produced using an inner layer height, h, of 80 metres. Taking the z0 value of 0.0002 metres for the Hemsby observations as given, enables an investigation to be made of the effect of varying the depth of the inner layer, h. Trial and error variation of h leads to the interesting result that an h value of 35 metres, gives a mean total planetary boundary layer (PBL) depth of 805 metres (see table 10). This PBL depth is very close to the 800 metre value regarded by Jones (1981) and Metcalfe (2001) as being representative for long distance pollution modelling. 27 Table 10: Measured and Ekman spiral modelled wind information for the Hemsby radiosonde station (52.48oN 1.68oE). Hemsby 1990-96 altitude 14 m above sea level (asl) 1457-3000m asl mean wind speed mean vector direction (degrees) 11.5 m/s 268 using 35127 radiosonde observations 300-500m agl (ground is 14m asl) mean wind speed mean vector direction (degrees) 10.9 m/s 254 5% below geostrophic using 3659 radiosonde observations Note: WDOs cannot contain wind speed values greater than 30 m/s, hence mean wind speeds derived from WDOs are slightly less than those derived directly from radiosonde data. WDO wind speed for 1457-3000m asl mean wind speed mean vector direction (degrees) 11.2 m/s 269 WDO 1457-3000m asl, for winds between 5 and 10 m/s mean wind speed 7.5 m/s mean vector direction (degrees) 269 WDO wind speed for 300-500m agl mean wind speed mean vector direction (degrees) 10.8 m/s 254 WDO 300-500m agl, for winds between 5 and 10 m/s mean wind speed 7.5 m/s mean vector direction (degrees) 272 using the equivalent of 34671 observations using the equivalent of 11520 observations 4 to 6% below geostrophic using the equivalent of 3650 observations using the equivalent of 1284 observations Ekman spiral modelled WDOs WDO 400m model Zo = 0.133, h = 80m mean wind speed mean vector direction (degrees) Model derived variables 8.1 m/s 242 28 to 30% below geostrophic WDO 400m model Zo = 0.133, h = 80m (winds between 5-10 m/s) mean wind speed 7.6 m/s mean vector direction (degrees) 246 WDO 400m model Zo = 0.0002, h = 80m mean wind speed mean vector direction (degrees) 9.2 m/s 245 18 to 20% below geostrophic WDO 400m model Zo = 0.0002, h = 80m (winds between 5-10 m/s) mean wind speed 7.7 m/s mean vector direction (degrees) 252 WDO 400m model Zo = 0.0002, h = 35m mean wind speed mean vector direction (degrees) 10.9 m/s 253 3 to 5% below geostrophic WDO 400m model Zo = 0.0002, h = 35m (winds between 5-10 m/s) mean wind speed 7.9 m/s mean vector direction (degrees) 260 min friction velocity U* max friction velocity U* mean friction velocity U* 0.03 m/s 1.13 m/s 0.46 m/s min eddy viscosity value K max eddy viscosity value K mean eddy viscosity value K 0.9 m^2/sec 36.2 m^2/sec 14.7 m^2/sec min PBL depth De max PBL depth De mean PBL depth De 388 metres 2486 metres 1532 metres min friction velocity U* max friction velocity U* mean friction velocity U* 0.02 m/s 0.73 m/s 0.29 m/s min eddy viscosity value K max eddy viscosity value K mean eddy viscosity value K 0.5 m^2/sec 23.4 m^2/sec 9.3 m^2/sec min PBL depth De max PBL depth De mean PBL depth De 296 metres 2000 metres 1218 metres min friction velocity U* max friction velocity U* mean friction velocity U* 0.02 m/s 0.73 m/s 0.29 m/s min eddy viscosity value K max eddy viscosity value K mean eddy viscosity value K 0.2 m^2/sec 10.3 m^2/sec 4.1 m^2/sec min PBL depth De max PBL depth De mean PBL depth De 196 metres 1323 metres 805 metres 28 The Ekman model for h = 35m yields a corresponding mean eddy viscosity K, of 4.1 m2/sec. This K -value along with the observed WDO geostrophic mean speed of Vg = 11.2 m/s, can be used to generate a ‘mean Ekman’ wind velocity profile with height, for comparison with observed wind speeds measured from radiosondes. Figure 15, shows such a comparison wind speed profile for Hemsby. Figure 15: Shows individually plotted Hemsby radiosonde wind speed measurements against height (asl), for 1990-96. Also shown is a 50 metre height band ‘running mean’ wind speed (rough line), and the Ekman wind speed profile for K = 4.1 m2/sec, Vg = 11.2 m/s (smooth curve). Many of the individual radiosonde measurements have plotted on top of each other resulting in a false impression of the importance of the sparser higher wind speed values (see figure 12 for observed wind speed histograms at the 300-500m and 1457-3000m levels). Between 270 and 740 metres above sea level, figure 15 shows excellent agreement between the observed ‘running average’ wind speed and the modelled Ekman profile. Below about 200m asl the Ekman model appears not to apply well as is discussed in the literature (Oke, 1987 and Troen and Petersen, 1989). Above about 800m the Ekman profile and observed ‘running average’ both seem to trend towards their geostrophic values. Table 10, shows that the Ekman model for h = 35m and z0 = 0.0002m gives an excellent match with observed values for wind speed and direction at the 400m level, apart from the mean wind vector direction for 5-10m/s wind speed band, which shows a 12o discrepancy. 29 The observed 5% wind speed drop below geostrophic values at 400m is well predicted in this model. Figure 16, shows the predicted 400m agl wind roses for the model with h = 35m and z0 = 0.0002m (the corresponding information is given also given in table 11). Comparison of figures 2, 11 and 16 (windroses for geostrophic, 300-500 Table 11: A seven year (1990-96) Ekman modelled wind rose for Hemsby at 400m agl, using h = 35m, z0 = 0.0002m. Calculated from the Hemsby 1990-96 (1457-3000m) observed geostrophic WDO. metres, and modelled 400 metres for Hemsby), shows that a similar half to one rose sector anticlockwise rotation is seen in both the modelled and observed wind roses at the ‘400m level’. The ‘percentage magnitudes’ of the two roses are also similar, as seen in tables 8 and 11, with the 4.14% value of the most prominent 221o to 250o sector in the 5-10 m/s band observed for 300-500m, being similar to the 4.73% value given by the model. Figure 17, shows the wind speed histogram for the h = 35m and z0 = 0.0002m model and indicates that the grossly overestimated wind speed drops seen in the distribution ‘tail’ for h values of 80m are no longer seen. Table 12, shows a quantitative comparison between the Ekman modelled wind rose for 400m agl using h = 35m and z0 = 0.0002m and the observed 300-500m agl wind rose at Hemsby. 30 Figure 16: Speed bands 1 to 4 modelled for Hemsby at 400m agl, using h = 35m, z0 = 0.0002m, plotted as individual wind roses. (Note: the Ekman model input data was the observed geostrophic WDO for Hemsby 1990-96, shown in figure 1. Also north is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Figure 17: Total wind speed histograms for all wind directions, derived from the Hemsby 1990-96 (1457-3000m asl) observed geostrophic WDO, and from the WDO for 400m agl modelled from it using h = 35m, z0 = 0.0002m. 31 Table 12: A comparison of modulus differences for the 5-10 m/s wind speed band, between an Ekman modelled wind rose for 400m agl (using h = 35m, Z0 = 0.0002m), and observed wind roses for 300-500m agl and 1457-3000m asl, at Hemsby. Wind roses for the 5 to 10 m/s wind speed band (speed band 2) wind rose sector (degrees) h = 35m, Zo = 0.0002m 11 to 40 41 to 70 71 to 100 101 to 130 131 to 160 1.95 1.67 1.57 1.89 1.85 300-500m 3.07 2.80 2.30 2.06 1457-3000m 2.01 1.60 1.69 model & 300-500m 1.12 1.13 model & 1457-3000m 0.06 161 to 190 Total % 191 to 220 221 to 250 251 to 280 281 to 310 311 to 340 341 to 10 2.44 3.30 4.73 4.71 3.58 3.06 2.51 33.27 2.36 2.96 3.13 4.14 3.62 2.94 2.69 3.16 35.23 1.78 1.86 2.28 3.06 4.47 4.88 3.86 3.12 2.67 33.27 0.74 0.16 0.51 0.52 0.17 0.59 1.09 0.65 0.38 0.64 7.70 0.07 0.12 0.12 0.02 0.16 0.23 0.26 0.17 0.27 0.05 0.16 1.70 1.20 0.62 0.28 0.50 0.68 0.06 0.33 1.26 0.92 0.43 0.48 7.82 341 to 10 400m model at Hemsby (%) real observations (%) Modulus Differences (%) Total % difference Between actual observations (%) 300-500m & 1457-3000m 1.06 Normalised Version Wind roses for the 5 to 10 m/s wind speed band (speed band 2) wind rose sector (degrees) h = 35m, Zo = 0.0002m 11 to 40 41 to 70 71 to 100 101 to 130 131 to 160 161 to 190 191 to 220 221 to 250 251 to 280 281 to 310 311 to 340 Total 400m model at Hemsby 0.059 0.050 0.047 0.057 0.055 0.073 0.099 0.142 0.142 0.108 0.092 0.076 1.00 300-500m 0.087 0.079 0.065 0.058 0.067 0.084 0.089 0.118 0.103 0.083 0.076 0.090 1.00 1457-3000m 0.061 0.048 0.051 0.053 0.056 0.068 0.092 0.134 0.147 0.116 0.094 0.080 1.00 model & 300-500m 0.029 0.029 0.018 0.001 0.012 0.011 0.010 0.025 0.039 0.024 0.016 0.014 0.228 model & 1457-3000m 0.002 0.002 0.004 0.004 0.001 0.005 0.007 0.008 0.005 0.008 0.002 0.005 0.051 0.031 0.015 0.005 0.011 0.016 0.003 0.017 0.044 0.033 0.017 0.009 0.228 real observations Modulus Differences Total difference Between actual observations 300-500m & 1457-3000m 0.027 Table 12, shows that overall, the model for h = 35m and z0 = 0.0002m, gives at least as good an estimate of the observed 400m agl wind rose as using the geostrophic 1457-3000m asl wind rose as the 400m agl estimate. 32 DISCUSSION Two models have been produced that operating together have the potential capability to estimate a 400 metre agl wind rose (for the 5 to 10 m/s wind speed band relevant to the HARM model) at any location within the UK. The data inputs are geostrophic (1457-3000m) wind roses derived from at least four radiosonde stations on the periphery of the UK, and knowledge of the surface roughness length, z0, at the location. For the 5 to 10 m/s wind speed band, the least-squares spatial linear interpolation model has demonstrated its ability to estimate a geostrophic wind rose at any location within the UK, at least as well as using the geostrophic wind rose from the nearest radiosonde station. However, the added utility of using the spatial model instead of the mean geostrophic wind rose for the UK, for estimating the 5-10 m/s speed band rose at the geostrophic level, has been shown to be only marginal. The second model, an Ekman spiral boundary layer model, coupled to surface roughness length, z0, has shown that given a geostrophic WDO for a location within the UK, and a reliable estimate of z0 for the area, an estimate of the 5 to 10 m/s speed band wind rose can be made at 400 m agl. The resulting wind rose being at least as good an estimate of the 400m rose for the 5-10 m/s speed band as using the geostrophic rose unaltered. This conclusion for the Ekman model is only valid if the use of an inner layer height, h, of 35 metres for the model is valid for the whole UK. The Hemsby radiosonde station results for the Ekman model with h = 35m and z0 = 0.0002m, are encouraging, but the ‘trial and error’ manner in which the inner layer depth, h, of 35 metres was obtained is open to the criticism of ‘curve-fitting’, or that in modelling terms its validity for other locations other than Hemsby (although suspected) has not yet been demonstrated. Thus, further work would needs to be carried out to see if the h = 35m value gives similar satisfactory results at other radiosonde stations. In the mean time, it is recommended that if one wishes to run the HARM model for a particular site within the UK, the least-squares spatial linear interpolation model be used to estimate the geostrophic (1457-3000m asl) wind rose for the location, and that this wind rose be used as a surrogate for the desired 400m agl rose. This follows the opinion of Jones (1981) 33 that the geostrophic rose for 5-10 m/s wind speeds can be used at 400m, but with a wind speed used for the pollution model (HARM in our case) of 10% below geostrophic. In order to be consistent with Jones (1981) and the wider literature on geostrophic wind speeds (Borresen, 1987 and Troen and Petersen, 1989, p31 & 117) the geostrophic wind speeds should be calculated from radiosonde station winds at the 850mb pressure level (1457m altitude in the 1976 standard atmosphere, see Jacobson, 1999) and linearly interpolated to the site location (see Jones, 2002, p34). For HARM model runs intended to predict annual pollution deposition for the whole UK in the immediate future, it is suggested that the geostrophic wind rose shown in figure 18, and table 13, be used to replace the wind rose of Jones (1981), see Jones, 2002, p31. Jones’s (1981) wind rose has a significant northerly component in the 5-10 m/s wind speed band, that is not seen in geostrophic wind roses derived for the 1990-96 period investigated in this study. Unfortunately, information concerning the years for which Jones’s (1981) rose is valid is not available, other than it probably dates from the 1960s or 1970s from a study called ‘the MESOS program’, which Jones (1981) mentions but does not reference. It is not clear if the northerly component seen on the Jones (1981) rose is the result of a wind climate fluctuation for a particular time period, the use of wind data from a particular location, or a statistical fluctuation caused by small numbers of individual observations being used to construct the rose. The Jones (1981) wind rose has several ‘zero percentage’ sectors in the 15 m/s and over speed band, suggesting that far less observations were used in its construction than for roses in the current study. The new UK wind rose (figure 18, and table 13) is the result of taking the mean WDO for 1457-3000m asl, for Camborne, Hemsby, Hillsborough and Lerwick radiosonde stations (see figure 3) for the years 1990-96 inclusive. The mean geostrophic wind speed measured at 850mb for these four stations from 1990-96 is 11.81 m/s, which results in a pollution modelling wind speed of 10.63 m/s at 400m after Jones’s (1981) 10% speed reduction is applied. The 10.63 m/s value compares well with the 10.44 m/s value currently used in the HARM model (Nicholson, 2002, pers comm). 34 Figure 18: Mean UK geostrophic (1457-3000m asl) wind rose for the years 1990-96, derived from radiosonde measurements at Camborne, Hemsby, Hillsborough and Lerwick. Wind speed bands 1 to 4 (under 5 m/s, 5-10 m/s, 10-15 m/s, 15 m/s upwards) are plotted as individual wind roses. (Note: north is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artefact and should be ignored) Table 13: A seven year (1990-96) mean UK geostrophic, 1457-3000m above ground level (agl) wind rose, calculated from 135966 synoptic wind speed observations at Camborne, Hemsby, Hillsborough and Lerwick. 35 HARM model results using the new mean UK geostrophic wind rose, have been compared with those using the Jones (1981) wind rose (Nicholson, 2002, pers comm). The results are shown in table 14. Table 14: HARM 11.5 annual deposition budgets in kT, using 1997 emissions and rainfall, for the Jones (1981) and mean UK (1990-96) wind rose (Nicholson, 2002, pers comm). Table 14, shows that the new mean UK rose leads an increase in all types of deposition, with the annual UK wet sulphur deposition increasing by almost 5%. The increase in wet sulphur deposition across the UK is shown in figure 19. This map shows increased wet sulphur deposition greater than 1 kg/ha/yr in parts of Northwest Scotland, and generally increased wet sulphur deposition in the North of the UK. This is a consequence of the new mean UK (199096) wind rose not having the large Northerly wind component present on the Jones (1981) rose. Since availability of synoptic radiosonde data is limited, this study was restricted to the years 1990-96. This seven year period is somewhat less than the thirty years normally used to generate climalogical means (WMO, 1989), but it was the longest period available with consistent data sampling. It would be desirable to compare the results of this study with annual (12-month duration) wind roses estimated from the same raw data, at the same radiosonde stations. This would enable the magnitude of year to year variation in the wind roses to be compared to the geographic variations between stations. 36 Figure 19: The annual wet sulphur deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and the new mean UK (1990-96) wind rose (Nicholson, 2002, pers comm). (The differences are calculated as mean UK (1990-96) - Jones (1981), so any positive values indicate an increase in deposition when the new mean wind rose is used. Concentrations are in kg of S per hectare per year and the resolution is 10km.) 37 Although, this study has produced geostrophic wind roses for each radiosonde station (see figure 10), no statistical analysis has been made of the differences between the wind roses other than noting they look fairly similar for the 5-10 m/s wind speed band. An apparent decrease in the prominent 250o-280o sector component of the ‘all wind speed’ wind rose is also seen between Camborne and Lerwick, see figure 4. It would be useful to compare the rose of Jones (1981) with the mean UK rose produced by this study for 1990-96, see figure 18, in order to assess change of UK wind climate between the 1970s and 1990s. However, the provenience and meta-data for the Jones (1981) is problematic making a meaningful comparison difficult. However, it would be possible to compare the current 1990-96 study with another time period by using data for the four radiosonde stations which are available for 1997-2002. However this 1997-2002 data has a somewhat different number of raw observations per year compared with the 1990-96 data (see Jones, 2002, p18). Such a new study would be useful for the kind of HARM scenario analysis that looks at issues of sulphur deposition change in the near future up to 2010, as described in RGAR (1997, p119). 38 Conclusions This paper has developed two models, which if used together can potentially predict a 400 m agl wind rose at any location within the UK. However, tests on the wind roses estimated by the models have shown that the case for using them in the HARM model, instead of an all UK geostrophic wind rose, is marginal. A mean UK geostrophic wind rose (valid for 1990-96) has been calculated, and the effect of using it in the HARM model in place of the Jones (1981) wind rose has been shown to be significant. 39 References Borresen, J. A., 1987. Wind atlas for the North Sea and the Norwegian Sea. Norwegian University Press and Norwegian Meteorological Institute, Oslo, p183 Ekman, V. W., 1905. On the influence of the earth’s rotation on ocean currents. Ark.Mat., Astron. Fys. 2, No.11 Haltner, G. J. and Williams, T. W., 1980. Numerical Prediction and Dynamic Meteorology, second edition. John Wiley & Sons , Inc., New York, Chichester, Brisbane, Toronto, Singapore, p477 Harbaugh, J. W., 1964. A Computer Method for Four-Variable Trend Analysis Illustrated by a Study of Oil-Gravity Variations in Southeastern Kansas. Bulletin 171, State Geological Survey of Kansas, p58 Jacobson, M. Z., 1999. Fundamentals of Atmospheric Modeling. Cambridge University Press, Cambridge, p635 Jones, J. A., 1981. The Estimation of Long Range Dispersion and Deposition of Continuous Releases of Radionuclides to Atmosphere. The Third Report of a Working Group on Atmospheric Dispersion, NRPB, Chilton, Didcot, Oxon, p25 Jones, K. H., 2002. Unpublished technical report. Metcalfe, S. E., Whyatt, J. D., Broughton, R., Derwent, R. G., Finnegan, D., Hall, J., Mineter, M., O'Donoghue, M., Sutton, M. A., 2001. Developing the Hull Acid Rain Model: its validation and implications for policy makers. Environmental Science and Policy, 4, 25-37 NEGTAP, 2001. Transboundary Air Pollution: Acidification, Eutrophication and Ground-Level Ozone in the UK. EPG 1/3/153, CEH, Edinburgh. Oke, T. R., 1987. Boundary Layer Climates. Methuen, London and New York, p435 RIGAR, 1997. Acid Deposition in the United Kingdom 1992-1994. Department of the Environment, Transport and the Regions, London, p176 Troen, I. and Petersen, E. L., 1989. European wind atlas. Roskilde, Denmark : Published for the Commission of the European Communities, Directorate-General for Science, Research, and Development, Brussels, Belgium by Risø National Laboratory, p656 WMO, 1989. Calculation of Monthly and Annual 30-year Standard Normals. WCDP No. 10, WMO-TD/No.341, world Meteorological Organisation, Geneva 40 Technical Report Table of Contents Page Number 1. Introduction 1 2. The HARM acid rain model 1 3. The wind literature and the planetary boundary layer (PBL) 3.1 Techniques for calculating the wind rose at 400 metres above ground level 6 10 4. The synoptic radiosonde data 4.1 The Radiosonde Windfinding Equipment 4.2 The UK radiosonde data files 13 15 15 5. The choice of radiosonde stations used 18 6. Pre-processing of the ASCII data 6.1 Wind Statistics from the Pre-processed Data 19 21 7. Wind rose creation 7.1 The Wind Data Object (WDO) 7.2 The Wind Rose plotting program 23 23 27 8. The mean UK geostrophic wind rose (1990-96) 8.1 HARM output comparisons for the Jones (1981) and mean UK (1990-96) wind roses 29 32 9. The Spatial Least-Squares Linear Interpolation model 9.1 Fitting a plane by least-squares 9.2 Using fitted least squares planar surfaces to interpolate WDOs 33 33 35 10. The Surface Roughness Coupled Ekman Model 10.1 Using the WDO in the coupled Ekman model 10.2 Mean Ekman profiles 39 40 41 11. Surface Roughness of the UK 43 12. The Hemsby Radiosonde Station 44 13. References 46 i Table of Figures Figure 1: The geographical relationship between the 10 km HARM grid and the 100 km EMEP grid (taken from Metcalfe et al, 2001). Figure 2: Representation of the cycle of emission, transport and deposition of pollutants (taken from Metcalfe et al, 2001). Figure 3:An idealised flow chart of HARM’s structure, based on pseudo-code given in Metcalfe et al, 2001. Figure 4: The UK Upper Air Radiosonde Network of twelve stations (taken from the BADC web-site, www.badc.rl.ac.uk/data/radiosonde/network.html ). Figure 5: The beginning of ASCII file hemsby.199001 which shows part of the first radiosonde ascent profile for January 1st 1990, for synoptic hour 00 (12 midnight on the 31st December). Figure 6: The beginning of ASCII file verthemsby9096.dat, which shows several radiosonde ascent profiles for January 1st 1990, for synoptic hours 00, 06, 12 and part of 18. Figure 7: The beginning of binary file hemsbyvertwind9096.dat, which shows several radiosonde ascent profiles up to 3000 m altitude, for January 1st and 2nd 1990. Figure 8: Hemsby, 1457-3000m asl wind data object (WDO) for 1990-96, using 34671 synoptic observations. Figure 9: The geostrophic (1457-3000m asl), 12-sector, 4-speed band wind rose for the Lerwick radiosonde station, for the years 1990-96. Figure 10: Mean UK geostrophic (1457-3000m asl) wind rose for the years 1990-96, derived from radiosonde measurements at Camborne, Hemsby, Hillsborough and Lerwick. Wind speed bands 1 to 4 (under 5 m/s, 5-10 m/s, 10-15 m/s, 15 m/s upwards) are plotted as individual wind roses. Figure 11: The Jones (1981) ‘400 metre’ wind rose displayed as a series of sector plots. Figure 12: Mean geostrophic wind speeds at the 850 mb level (1990-96), interpolated between four radiosonde stations using a planar surface fitted by least squares. Figure 13: Geostrophic (1457-3000m asl) wind roses for each 100km O/S square, derived from WDOs at the four principal radiosonde stations, showing 12 direction sectors for wind speeds greater than zero and less than or equal to 30 m/s. Figure 14: Geostrophic wind roses for each 100km O/S square, superimposed one upon the other, derived from WDOs at the four principal radiosonde stations, showing 12 direction sectors for wind speeds greater than zero and less than or equal to 30 m/s. ii Figure 15: 91 geostrophic wind speed histograms for all wind directions, derived from the WDOs modelled for each O/S 100km grid square, using the least squares planar model for the four principal stations. Figure 16: A conceptual flowchart of the surface roughness coupled Ekman model. Figure 17: A comparison of the measured geostrophic (1457-3000m asl) wind rose at Hemsby, and the 400 m agl rose modelled for Hemsby. Figure 18: Individually plotted Hemsby radiosonde wind speed measurements against height (asl), for 1990-96. Also shown is a 50 metre height band ‘running mean’ wind speed (rough line), and the Ekman wind speed profile for K = 4.1 m2/sec, Vg = 11.2 m/s (smooth curve). Figure 19: Map of the environs of Hemsby radiosonde station, showing 1:50 000 O/S mapping out to a distance from the station of approximately 15 km. iii Table of Tables Table 1: mean wind speed and mean vector direction for the five radiosonde stations for various altitude levels. Table 2: Mean wind speeds and mean vector directions, derived from the WDOs for all five radiosonde stations. Table 3: Mean wind speeds and mean vector directions, for the 5-10 m/s wind speed band derived from the WDOs for all five radiosonde stations. Table 4: The geostrophic (1457-3000m asl), 12-sector, 4-speed band wind rose for the Lerwick radiosonde station, for the years 1990-96. Table 5: A seven year (1990-96) mean UK geostrophic, 1457-3000m above ground level (agl) wind rose, calculated from 135966 synoptic wind speed observations at Camborne, Hemsby, Hillsborough and Lerwick. Table 6: A representative wind rose for use in long-range dispersion calculation (from Jones, 1981, p19). Table 7: HARM 11.5 annual deposition budgets in kT, using 1997 emissions and rainfall, for the Jones (1981) and mean UK (1990-96) wind rose (Nicholson, 2002, pers comm). Table 8: Roughness length estimates, z0, for 22 UK surface meteorological stations, derived from Troen and Petersen 1989. iv 1. INTRODUCTION This report describes the methods used to create wind roses from radiosonde balloon data provided by the British Atmospheric Data Centre (BADC), using ESRI’s Arc Macro Language (AML) and the PV-WAVE programming language produced by Visual Numerics. Also described are two computer models written in PV-WAVE, one used to interpolate the wind rose information spatially (horizontally within the Ordnance Survey co-ordinate system for the UK), and the other an atmospheric boundary layer model based on the Ekman spiral (Haltner and Williams, 1980, p274), which is used to transform geostrophic level wind roses down to a level 400 metres above a ground surface of known aerodynamic surface roughness. The reason for modelling a wind rose at 400 metres elevation at any position within the UK is so it can be used as one of the inputs of the Hull Acid Rain Model (HARM). Background information on the HARM model and Ekman spiral model are thus also given. 2. THE HARM ACID RAIN MODEL The HARM model is widely utilised in the UK to aid decision-makers formulate policies for the reduction of acidifying air pollutants (Reynolds et al, 2002, p6). The current version of the model, HARM 11.5 (Metcalfe et al, 2001), uses 10 by 10 km by 800 m high grid cells (aligned with the UK OS grid) to represent the atmospheric boundary layer over the UK (a total of 3064 receptor sites). Outside the OS grid area the HARM model uses a grid made up of 100 by 100 km by 800 metre cells to represent the eastern Atlantic Ocean and the whole of Western Europe (the same grid as used by the European Monitoring and Evaluation programmme (EMEP) model, see Reynolds et al, 2002, p6). The relationship of the two grids is shown in figure 1. HARM uses a Lagrangian receptor oriented statistical approach to provide estimates of wet and dry Chloride, Nitrogen (both oxidised and reduced) and Sulphur deposition across the UK. Lagrangian atmospheric pollution models work by taking multiple air parcels from the edge of the model along straight line trajectories to given receptor locations, such that sufficient evenly spaced azimuths from the receptor are covered by the parcel trajectories to allow air pollution pick up/change from each cell in the model. The pollution concentrations at a given receptor are calculated by weighting the pollutant 1 quantities arriving from each direction using a wind rose for wind speeds of 5-10 m/s (Metcalfe, 2002, pers comm), for the middle (400 metres above ground level) of an 800 metre deep mixing/boundary layer. Figure 1: The geographical relationship between the 10 km HARM grid and the 100 km EMEP grid (taken from Metcalfe et al, 2001). For typical HARM runs the receptor sites are at the centre of each 10 by 10 km OS grid square across the UK and the run represents deposition over the period of a year. HARM assumes that pollutant chemicals are mixed instantaneously throughout an 800 metre mixing/boundary layer of constant depth and that individual air parcels remain intact for their journey across the model. 2 Unlike most other European or UK pollution models HARM also incorporates orographic seeder feeder type deposition enhancement in upland areas. The typical pollution transport issues that models such as HARM try to represent are show in figure 2. Figure 2: Representation of the cycle of emission, transport and deposition of pollutants (taken from Metcalfe et al, 2001). The way in which the HARM model makes use of wind rose information is of particular relevance to this study. This is elucidated by figure 3, which shows an idealised flow chart of HARM’s structure. Figure 3, shows that the contribution made by a given air parcel to a receptor cell, depends on the pollution content of the parcel, the azimuth with respect to the receptor of the parcels trajectory, and the wind rose used to provide a weighting for each contributing azimuth at the receptor. Thus, the pollutant contribution to the receptor cell depends on both the distribution of pollution sources on the emissions grid, and the wind rose. The situation of the UK illustrates these two dependencies nicely with the predominant wind direction being from the west (Jones, 1981), but with most non-UK pollution sources being to the east in Europe (see figure 1). Thus, for a receptor location within the UK, the westerly winds will tend to ‘cancel out’ to some extent the easterly preponderance of pollution sources, as far as the European pollution contribution to the receptor site is concerned. Consequently, determination of a reliable wind rose for use at the receptor site is of crucial importance. 3 For each 10 km receptor cell in the UK For each air parcel trajectory. At the starting point of the air parcel trajectory at the edge of the EMEP grid set the pollution concentrations in the parcel to zero. Move the air parcel one step at a time along a straight-line trajectory towards the receptor cell. Pick up a fraction of the pollution from the underlying emissions grids, and mix instantaneously through the mixing layer parcel. Calculate the new parcel chemistry, and remove a fraction of each pollutant using wet and dry deposition. Then move on one step. When the receptor is reached, weight the pollutant concentrations in the air parcel for its trajectory azimuth using the wind rose for 400 metres above ground level. Combine the weighted pollution contributions from all air parcels to provide a concentration estimate for the receptor cell. Repeat for each trajectory. Repeat for each receptor cell in the UK. Figure 3: An idealised flow chart of HARM’s structure, based on pseudo-code given in Metcalfe et al, 2001. 4 For the UK, HARM currently uses a 12-sector wind rose for the 5-10 m/s wind speed band, valid for 400 metres above ground level (agl), provided by Jones (1981). Other wind roses for the UK have been tried with HARM, such as one derived at Heathrow airport, and have resulted in HARM outputs differing significantly from those derived using Jones’s (1981) rose ((Metcalfe, 2002, pers comm). The objective of this study is to, using radiosonde upper air wind data from BADC, model regional 400 m agl wind roses for the 5-10 m/s wind speed band at any desired location within the UK. Such roses could then be used in HARM model runs, and comparisons made with otherwise similar runs using Jones’s (1981) wind rose. 5 3. THE WIND LITERATURE AND THE PLANETARY BOUNDARY LAYER (PBL) One of the principle sources of wind climate information for the UK is the European wind Atlas (Troen and Petersen, 1989). The European wind Atlas is oriented towards the concerns of wind power generation and so the atmospheric models utilised in its compilation neglect the subtle atmospheric conditions associated with the lowest wind speeds, resulting in considerable simplification of the models (Troen and Petersen, 1989, p566). These simplifications result in a planetary boundary layer of about 1km total depth with an inner or Prandtl layer where surface-layer physics apply of about 100 metres thickness. Similarly the HARM model neglects the lowest wind speeds, utilising only the 400metre elevation wind rose information corresponding to wind speeds between 5 and 10 m/s (Metcalfe, 2002, pers comm). Jones (1981, p8-10) discusses how the variations in the depth of the boundary layer combined with likely changes in the atmospheric stability category, mean that for practical purposes a constant boundary layer depth of 800 m and neutral atmospheric stability may be assumed for long-range dispersion models (> 100 km) such as HARM. Jones (1981, p10) has the opinion that the effective wind rose for use with long-range models should be similar to the geostrophic wind rose but with wind speeds reduced by about ten percent. Jones introduces a representative wind rose (shown in table 6) as valid for a height of 400 m above the UK ground surface (the middle of the 800m boundarylayer). However, it is unclear from the description what method was used to create the wind rose, whether it was derived from geostrophic winds, radiosonde ascents through 400 metres altitude, high tower measurements or some combination of techniques. The 5 to 10 m/s speed band taken from the wind rose of Jones (1981) is shown as a sector rose plot in figure 11; from which it can be seen that the two prominent wind directions are south westerlies (5.07% of the time blowing from 221-250 degrees), and northerlies (4.53% of the time from 341 to 10 degrees). The 5 to 10 m/s wind direction distribution shown in figure 11 has frequently been used as the wind input for the HARM model (Metcalfe, 2002, pers comm). It shall be shown later that similar wind roses derived from UK radiosonde stations for 1990-96 do not show this dominant northerly component. 6 The structure of the planetary boundary layer (PBL) is described by Oke (1987, p37-41) as consisting of four conceptual layers. The layer closest to the ground called the laminar boundary layer is a few millimetres in thickness, consisting of only smooth laminar airflow. Next is the roughness layer of a several centimetres to several metres thickness, which is dominated by the effects of surface roughness elements, resulting in complex eddy and vortex types of air motion. This layer is important in that it couples surface roughness to the overlying layers of the atmosphere. The inner layer comes next and occupies roughly the lower 10 percent of the entire planetary boundary layer depth. This layer is also referred to as the Prandtl layer or constant flux layer since ‘vertical fluxes’ within it vary by less than 10 percent with height. Heat, mass and momentum transfer in this layer are the result of turbulent diffusion and are governed by quantities called eddy diffusivities, which are often written as K’s in atmospheric equations. For the inner layer the K values increase with height as the size of the atmospheric eddies increase with height, resulting in the given atmospheric property profile having a logarithmic shape. Haltner and Williams (1980, p273), Troen and Petersen (1989, p566) and Landsberg (1981, p137) give a logarithmic relation for wind speed, u, with height, z, above the ground as: u( z) = u* z ln k z0 (1) which is valid for neutral atmospheric stability conditions in the inner layer. z0 is the roughness length, the height at which the mean wind should go to zero, and represents the aerodynamic roughness of the ground surface. u* is the friction velocity and k is the von Karman constant, usually taken as 0.40 . Stull (1988, p358 & p181) gives typical values of u* for neutral conditions as 0.05 to 0.3 m/s, and states that experimental values of k vary between 0.35 and 0.42, but that 0.40 is the most widely used value. The eddy diffusivity for wind speed is called the eddy viscosity and in the inner layer for neutral conditions is given by: K = kzu* (2) as given by Haltner and Williams (1980, p273). Typical K values for the inner layer vary from 0.00001m2 s-1 for just above the surface to as high as 100 m2 s-1 at the top of the layer 7 (Oke, 1987, p40). Haltner and Williams state that equation (1) is valid for heights of up to the order of 50 metres for neutral stability. The European wind Atlas (Troen and Petersen, 1989, p566) introduces a modified version of equation (1) for use in non-neutral atmospheric conditions which takes thermal buoyancy forces into account by using the similarity theory of Monin and Obukhov (Haltner and Williams, 1980, p277), and can provide usable wind speed estimates at heights of up to 200 metres above the ground, within the inner layer. Above the inner layer is a turbulence dominated domain which extents upwards to the top of the atmospheric boundary layer. This layer is termed the outer layer or Ekman layer and typically has a depth of 90 percent of the total depth of the boundary layer (Oke, 1987, p41). The depth of the Ekman layer can vary from as small as 100 metres on clear winter nights, up to 1-2 km on summer days with light winds and thermal convection (Oke, 1987, p41). As already discussed Jones (1981, p8-10) regards an assumed boundary layer thickness of 800 metres with neutral stability as suitable for long range pollution modelling, which will result in an inner layer depth of about 80 metres, and an Ekman layer depth of 720 metres. In the Ekman layer the friction, pressure and Coriolis forces are of the same order of magnitude with the consequence that wind speed and direction can be modelled using an Ekman spiral (Ekman, 1905, Ryan, 1974, p6, Haltner and Williams, 1980, p274). The Ekman spiral can be described by the following equations taken from Ryan (1974, p6): u ' = V g − V g e − az cos(az ) (3a) v ' = V g e − az sin(az ) (3b) where a is the Ekman parameter and is given by: a= f 2K (3c) In equation 3c, f is the Coriolis parameter, which is dependent on latitude and is given by Landsberg (1981, p136) as: 8 f = 2Ω sin φ (4) where Ω is the angular velocity of the Earth (7.27 x 10-5 radians s-1) and φ is the latitude angle. For the UK equation 4 gives f values of between 1.1 to 1.3 x 10-4s-1. K is the eddy viscosity value for the Ekman layer which has typical values of around 5 m2 s-1 (Allison, 1992), and maximum values of less than 100 m2 s-1 (Oke, 1987, p40). The Ekman spiral model assumes a constant K value for whole outer layer. In equations 3a and 3b, Vg is the geostrophic wind speed, z is the height above the ground, u’ is the wind component +ve in the same direction as the geostrophic wind, and v’ is the wind component +ve in the direction 90 degrees to the left of the geostrophic wind (for the Northern hemisphere). The wind speed at a height z within the Ekman layer can be obtained from the perpendicular components u’ and v’ using Pythagoras’s theorem as follows (Ryan, 1974, p34): Magnitude of resultant wind speed Vres = (u ' ) 2 + (v ' ) 2 (5) Allison (1992) and Landsberg (1981, p137) describe how the angle α between the geostrophic wind vector and the wind vector modelled by the constant-K Ekman spiral varies from zero at the top of the Ekman layer to 45 degrees anti-clockwise of geostrophic direction close to the ground (for the Northern hemisphere. Note also, that the Ekman spiral result is not valid in the inner layer). The top of the Ekman layer is defined as when going upwards from the surface the angle α reaches zero for the first time, with v’ reaching zero in equation 3b, and u’ asymptotically approaching the geostrophic wind speed Vg in equation 3a. Allison (1992) gives the height of the top of the Ekman layer, DE as: 1 DE = π (2 K f ) 2 (6) Allison regards DE as being representative of the total depth of the atmospheric boundary layer. Using equation 6, an eddy viscosity K -value of 4m2 s-1 will result in a total 9 boundary layer depth of approximately 800m. K –values of 50m2 s-1 and 100m2 s-1 result in DE –values of around 3 km and 4 km respectively. Above the atmospheric boundary layer the wind speeds are assumed to be decoupled from the frictional effects of the ground surface and are said to be geostrophic winds, which have the pressure-gradient and Coriolis forces in balance with each other such that the wind flows parallel to the isobars on a pressure chart (Anthes et al, 1978, p115), with low pressure to the left of the wind vector (for the Northern Hemisphere). The geostrophic wind speed may be estimated from the pressure gradient calculated from meteorological pressure charts as described by Landsberg (1981, p136). Geopotential heights derived from pressure charts or direct radiosonde measurements of wind speed above the boundary layer (usually measured at the 850mb pressure level (Ryan, 1977)) may also be used. Pedder, (1981b) describes a multivariate analysis of both types of data. Troen and Petersen (1989, p31) and Borresen (1987) show mean geostrophic wind speeds increasing from 10.4 to 12.4 ms-1 across the UK from the Kent coast to the Outer Hebrides. 3.1 Techniques for calculating the wind rose at 400 metres above ground level The European Wind Atlas (Troen and Petersen, 1989) uses a ground-up method for calculating the wind speeds in an inner layer of up to 200 metres depth. Troen and Petersen (1989, p77) have for the UK used 22 surface wind stations to determine Weibull distribution parameters for each of 12 wind rose sectors associated with each station. The Weibull distribution is a mathematical representation of the wind speed histogram (Weibull, 1951). In the European Wind Atlas the effects of the surface roughness (represented by roughness length, z0) near each station have been taken into account for each 30 degree width sector radiating from the station location, out to a distance of several kilometres. Each 30 degree surface roughness sector corresponds to one of the 12 wind rose sectors. The resulting tables of Weibull parameters for each wind sector represent the wind resource for a given station location at five reference heights above the ground (10, 25, 50, 100 and 200 metres) and four reference z0 values (0.0002, 0.03, 0.10 and 0.40 metres). For the 22 UK Wind Atlas stations the mean value of surface roughness length, z0 was found to be 0.16 metres with a standard deviation of 0.12 metres (see section 11) corresponding to farmland with a closed appearance with many trees and bushes (Troen and Petersen, 1989, p58). The typical spacing for the UK surface wind stations used by the Wind Atlas is between 75 and 200 km (Troen and Petersen, 1989, p38-39), and to estimate 10 the wind at a point between stations one would simply use the Weibull tables for the closest station. The European Wind Atlas model has a number of drawbacks for estimating a representative wind rose at 400 metres height above ground level. Firstly the logarithmic wind profile model used by the atlas is only valid in the inner layer, and for a representative atmospheric boundary layer depth of 800 metres for pollution modelling (Jones, 1981, p8-10), the 400 metre height level is in the Ekman layer. Even without the boundary layer thickness assumptions of Jones (1981) the 400metre level will only spend time either in the Ekman layer or above the PBL in geostrophic winds. Secondly, Jones (1981, p10) specifically states that for long distance pollutant modelling ‘effective windspeed is more easily related to the geostrophic wind-speed than to wind-speed at a defined, low height in the mixing layer’. This statement is strongly suggestive that any attempt to calculate representative regional 400 metre level wind roses for the UK should employ a geostrophic-down approach starting with geostrophic wind data and somehow ‘conditioning’ it with surface roughness information to obtain 400 metre level winds. Such a geostrophic-down model can be achieved by using measurements of the geostrophic winds taken from synoptic radiosonde stations to drive a ‘coupled’ Ekman model to obtain a wind rose at 400 metres. One such model is the Ekman-Taylor model described by Haltner and Williams (1980, p272-277). This is a two-layer model which links a constantflux inner layer with a superimposed constant-K Ekman layer for conditions of neutral atmospheric stability. Given the geostrophic wind speed Vg, the surface roughness length z0, and the height of the inner layer h, the model can predict the perpendicular components of the wind vector at any height z, within the inner or Ekman layers. A drawback of this type of model is that the depth of the inner layer h, must be specified a priori as a model input, when it would be desirable to have it predicted as a model output. However, such a prediction of h would require a far more sophisticated model. Problems were encountered solving the system of non-linear equations needed to implement this model, so a simpler approach was chosen which linked an Ekman model as given in equations 3a and 3b to surface roughness length z0, by means of the eddy viscosity K. Haltner and Williams (1980, p276) provide a relation that gives the value of eddy viscosity, K at the top of an inner layer of thickness h metres in terms of the friction velocity u* : 11 K = ku* h (7) where k is von Karman’s constant (k = 0.4). The values of K at the inner layer, Ekman layer boundary should match, so equation 7 can be used to estimate the constant-K value for the Ekman spiral (equations 3a and 3b). As with the Ekman-Taylor model an a priori estimate of the h value must be made. The value of friction velocity, u* can be estimated from the geostrophic wind speed, Vg and surface roughness length, z0 by means of the geostrophic drag law, originally formulated for neutral stability conditions by Rossby and Montgomery (1935) to describe the balance between the geostrophic pressure gradient force and the frictional force due to surface roughness. Troen and Petersen (1989, p567) give an expression of the geostraphic drag law as: 2 u Vg = * k u ln * − A fz 0 + B2 (8) where f is the Coriolis parameter and A and B are empirical constants which for neutral stability have values of 1.8 and 4.5 respectively. 12 4. THE SYNOPTIC RADIOSONDE DATA The current (2002) upper-air radiosonde network for the UK, consists of twelve stations (BADC web-site, www.badc.rl.ac.uk/data/radiosonde/network.html). The station locations are shown in figure 4. Figure 4: The UK Upper Air Radiosonde Network of twelve stations (taken from the BADC web-site, www.badc.rl.ac.uk/data/radiosonde/network.html ). The ‘range’ stations shown in figure 4 are situated on military ranges, and perform only irregular measurements that are not useful for the creation of wind roses, so they will not be discussed further. 13 The ‘operational’ stations are the ones that provide the synoptic upper air observations required by this study. These stations provide radiosonde balloon ascent atmospheric data profiles at regular six hour intervals, at the synoptic hours of 00, 06, 12, 18 GMT (the term synoptic merely refers to the standard times at which meteorological observations are taken world-wide). There have been a number of changes to the ‘operational’ station network since 1990: • Shanwell (03170) closed on 15/3/92. Synoptic observations were transferred to Boulmer (03240) on 16/3/92. • Crawley (03774) closed on 30/9/92, and was replaced by Herstmonceux (03882) on 1/10/92, for synoptic observations. • Aughton (03322) closed on 31/3/96, and the 6 hourly synoptic routine transferred to Aberporth (03502), on the same day. According to BADC (BADC web-site), the synoptic radiosonde stations are required to report their observations to the UK Met Office in the form of ‘standard resolution data’ files which consist of measurements made at certain pressure levels with the atmosphere. • Standard Pressure Levels Data are always recorded at the ‘standard pressure levels’ on every radiosonde balloon ascent. The standard pressure levels going upwards from the surface are 1000, 925, 850, 700, 500 and 400 mb, corresponding to altitudes of 111, 760, 1457, 3012, 5574, and 7185 metres above sea level, respectively (the altitudes are derived from the 1976 standard atmospheric model, see Jacobson, 1999). Standard pressure levels are in fact measured all the way up to around 30 km altitude, where the balloon will burst. However, only the levels in the lower few kilometres of the atmosphere (i.e. the troposphere) are relevant to this study. It should be noted that in the literature concerning geostrophic winds, which includes Borresen, 1987 and Troen, I. and Petersen, 1989, the 850 mb pressure level is taken to correspond to the altitude (1457m asl) where the winds become geostrophic (i.e. are no longer frictionally coupled to the earth’s surface). 14 • Significant Pressure Levels In addition to the ‘standard pressure levels’ other data readings are taken at intermediate pressure levels termed ‘significant pressure levels’. Observations at these additional levels are added so as to give a clearer picture of the measured atmospheric profile, and are triggered by significant changes in wind speed, temperature or humidity. These ‘significant pressure level’ observations are very important to the current study in that they provide the extra observations needed to create reliable wind roses in the 300-500 metre above ground level (agl) height band, and also provide plentiful extra observations of wind speed and direction for the creation of geostrophic wind roses (1457-3000m asl). 4.1 The Radiosonde Windfinding Equipment According to BADC the UK Met Office has used the RS80 radiosonde, manufactured by Vaisala of Sweden for the past twenty years. The atmospheric profile data used for the current study consist of wind speed and wind direction, for a given altitude above sea level (pressure is also noted if available). The RS80 radiosonde package can return wind speed values to an accuracy of +/- 1 to 2 m/s, height values accurate to +/- 40 metres, and pressure values accurate to +/- 0.5 mb. Temperature and humidity radiosonde measurements were not used in this study, and so are not discussed. 4.2 The UK radiosonde data files The data files containing the UK standard resolution radiosonde data, as discussed above, are available on the BDAC web-site (www.badc.rl.ac.uk) in the subdirectory: /badc/ukmo-rad/data/united_kingdom from which data for individual UK radiosonde stations can be selected (Note: access to the radiosonde data requires a username and password from BADC). Data for individual stations can be downloaded as ‘gzipped’ files for each individual year for which for which they are available (typically 1990-2002 for the ‘operational’ stations). Once a ‘gzipped’ file has been downloaded it must be ‘gunzipped’ using the UNIX command ‘gunzip’, which will yield a ‘tar’ archive for the given year. This ‘tar’ archive must be ‘unpacked’ using the UNIX ‘tar –xvf’ command, resulting in an ASCII text file of data being produced for each month of radiosonde data within the ‘tar’ archive, resulting in typically 12 monthly files of ASCII data being created from each ‘tar’ archive. The size of the ‘gunzipped’ archive for each year for a station is about 1 megabyte. However, once 15 expanded into ASCII form the data for each year takes up roughly 6.5 megabytes, so for the four stations used in this study that covered a period of seven years, the total size of ASCII data files would be 182 megabytes. A sample of part of one of the monthly ASCII data files is shown in figure 5. Figure 5: The beginning of ASCII file hemsby.199001 which shows part of the first radiosonde ascent profile for January 1st 1990, for synoptic hour 00 (12 midnight on the 31st December). The first line of hemsby.199001 is the header that appears at the start of each synoptic ascent profile. It consists of at station identifier ‘03496’ for Hemsby, a year-month-day number ‘19900101’, a synoptic hour number ‘00’, the decimal latitude and longitude in degrees of the station ’52.68 1.68’, and the altitude of the launch point above sea level in 16 metres ‘14’. The next line contains the ascent profile column titles, PP for pressure in 100 x mb, HT for height above sea level in metres, TT and TD are temperatures in degrees Kelvin, DD is the wind direction in degrees from north and FF is the wind speed in m/s. The third line is the start of the ascent profile data itself, and consists of the data described in the column headings going from the height of the balloon launch point, up to about 20 or 30 km. Bad or missing data is signified by the rogue-value –9999999.0 or –9999999 . Immediately after the end of the profile shown in figure 5, will be a header similar to line one except that the synoptic hour code will be ‘06’, signifying the start of the 6am GMT profile. 17 5. THE CHOICE OF RADIOSONDE STATIONS USED In order to complete the study within the time period allocated and to avoid problems with overrunning computer disk quota allocations (only 520 megabytes), the number of radiosonde stations used, and the temporal duration of the study needed to be limited. From figure 4, it was decided to limit the number of stations used to four, plus one ‘surrogate’ station to be used for model testing. The four principle stations chosen where, Camborne in Cornwall, Hemsby in East Anglia, Hillsborough in Northern Ireland, and Lerwick in the Shetland Islands. It was felt that these four stations gave a good ‘spatial coverage’ around the periphery of the UK. The radiosonde station at Herstmonceux in Southeast England was used as the ‘surrogate’ station to replace Hemsby in the models for test purposes. The format of the ASCII data files changed at the end of 1996, and the frequency of ‘significant pressure level’ observations during ascents decreased significantly. So in order to maintain an equal contribution to the wind roses from each year of observation data, and to avoid having to run the data pre-processing AML scripts twice for each station, it was decided to limit the duration of the study to the years 1990 to 1996 inclusive. For all five stations this still represents 210 megabytes of ASCII data (Herstmonceux, data was only available for the last two months of 1992, and for 1993-96 inclusive). 18 6. PRE-PROCESSING OF THE ASCII DATA The ASCII data files containing the raw monthly radiosonde data for a given station, as shown in figure 5, must be reformatted and concatenated into an ASCII file easily read by a PV-WAVE program. This new file must contain the data for the whole period for which it is desired to generate a wind rose for the given station location. This pre-processing was carried using a program written in ESRI’s Arc Macro Language (AML), which can be run using ESRI’s ArcInfo GIS software. The AML program to perform the pre-processing is called ‘vertread9096he.aml’, with ‘9096’ referring to the years covered, and ‘he’ to the particular radiosonde station; Hemsby in this case. A listing of the program is given in Appendix A. Figure 6, shows a section of the reformatted ASCII data file output by ‘vertread9096he.aml’. Figure 6: The beginning of ASCII file verthemsby9096.dat, which shows several radiosonde ascent profiles for January 1st 1990, for synoptic hours 00, 06, 12 and part of 18. Since this study only requires wind speed and direction up to an altitude of 3000 metres, the reformatted data shown in figure 6, has its profiles truncated at 3000 metres. As a result of this truncation, file verthemsby9096.dat which represents seven years of 19 radiosonde data concatenated from 84 individual monthly files, is only 17 megabytes in size. Thus for the four principle radiosonde stations used, this pre-processing has reduced the data volume from 182 megabytes to only 68 megabytes. The file ASCII file verthemsby9096.dat is further compressed by the PV-WAVE program ‘heipvertwind.pro’ (see Appendix A), into a binary data file hemsbyvertwind9096.dat of only 3.3 megabytes in size (around 13 megabytes for all four stations). Figure 7, shows an excerpt from this new binary file. Figure 7: The beginning of binary file hemsbyvertwind9096.dat, which shows several radiosonde ascent profiles up to 3000 m altitude, for January 1st and 2nd 1990. Figure 7, shows how the program ‘heipvertwind.pro’ has removed the latitude and longitude co-ordinates of the station, as well as the station height. More importantly the program has removed any data lines having invalid values of wind speed or direction. 20 Invalid pressure values are still present but have been flagged with the rogue-value minus 1x107. A final pre-processing step is done by the PV-WAVE program ‘hevertdoublesremove.pro’ (see Appendix A) which removes ‘duplicate data lines’ from the data in hemsbyvertwind9096.dat. Occasionally, duplicated lines consisting of the exactly the same wind speed and direction information will be seen in the data. From the context in which these duplicates appear, often associated with an error in the pressure reading, it is clear that they are some sort of error in the radiosonde system. The corrected data, after duplicate removal is placed in the binary file hemsbyvertwindND9096.dat, which still has the same format as shown in figure 7. The size of this new file for seven years worth of data is still about 3.3 megabytes, since the duplicates only make up about 0.3% of the total data. 6.1 The Wind Statistics from the Pre-processed Data pre-processed radiosonde data binary files for each station, such as hemsbyvertwindND9096.dat for Hemsby, can be used directly to obtain mean wind speeds and direction for the study period (1990-96 for the principle stations, 1992-96 for the surrogate station). The PV-WAVE program ‘windND_datastats.pro’ (see Appendix A) determines mean wind speed and vector direction for various altitude levels, using the complex number method for representing 2D vectors as described by Jones (1998). The results of applying this program to the data from the five stations are shown in table 1. The information in table 1 was derived from a more comprehensive table held in the Microsoft Excel document ‘radiosonde_stn_stats.xls’ (see Appendix B). 21 Table 1: mean wind speed and mean vector direction for the five radiosonde stations for various altitude levels. Note: values calculated directly from the pre-processed radiosonde profile time-series data. Camborne 1990-96 altitude 87 m above sea level (asl) 1457-3000m asl mean wind speed 12.2 m/s mean vector direction (degrees) 266 using 34233 observations mean height 2112 metres asl mean pressure 787 mb 850 mb pressure level mean wind speed mean vector direction (degrees) 11.5 m/s 260 using 6489 observations mean height 1471 metres asl variance 42 Standard Deviation 6.5 m/s 300-500m agl (ground is 87m asl) mean wind speed 11.5 m/s variance 36 Standard Deviation 6.0 m/s mean vector direction (degrees) 242 using 4144 observations mean height 473 metres asl mean pressure 958 mb Herstmonceux 1992-96 variance using using 49 Standard Deviation 7.0 m/s 26426 observations 4144 observations altitude 52m above sea level (asl) 1457-3000m asl mean wind speed 11.4 m/s mean vector direction (degrees) 262 using 25667 observations mean height 2118 metres asl mean pressure 785 mb 850 mb pressure level mean wind speed mean vector direction (degrees) 10.8 m/s 260 using 5924 observations mean height 1463 metres asl variance 41 Standard Deviation 6.4 m/s 300-500m agl (ground is 52m asl) mean wind speed 10.3 m/s variance 31 Standard Deviation 5.6 m/s mean vector direction (degrees) 246 using 3413 observations mean height 422 metres asl mean pressure 965 mb Hemsby 1990-96 variance using using 48 Standard Deviation 6.9 m/s 25667 observations 3413 observations altitude 14 m above sea level (asl) 1457-3000m asl mean wind speed 11.5 m/s mean vector direction (degrees) 268 using 35127 observations mean height 2123 metres asl mean pressure 785 mb 850 mb pressure level mean wind speed mean vector direction (degrees) 11.0 m/s 267 using 6759 observations mean height 1461 metres asl variance 44 Standard Deviation 6.6 m/s 300-500m agl (ground is 14m asl) mean wind speed 10.9 m/s variance 32 Standard Deviation 5.6 m/s mean vector direction (degrees) 254 using 3659 observations mean height 392 metres asl mean pressure 968 mb Hillsborough 1990-96 using using 44 Standard Deviation 6.6 m/s 27560 observations 3659 observations altitude 37 m above sea level (asl) 1457-3000m asl mean wind speed 12.8 m/s mean vector direction (degrees) 257 using 35323 observations mean height 2145 metres asl mean pressure 780 mb 850 mb pressure level mean wind speed mean vector direction (degrees) 12.6 m/s 256 using 8229 observations mean height 1439 metres asl 300-500m agl (ground is 37m asl) mean wind speed 11.2 m/s mean vector direction (degrees) 238 using 5298 observations mean height 409 metres asl mean pressure 963 mb Lerwick 1990-96 variance variance using using 55 Standard Deviation 7.4 m/s 32135 observations variance 50 Standard Deviation 7.1 m/s variance 30 Standard Deviation 5.5 m/s 5298 observations altitude 82 m above sea level (asl) 1457-3000m asl mean wind speed 12.3 m/s mean vector direction (degrees) 247 using 31283 observations mean height 2162 metres asl mean pressure 775 mb 850 mb pressure level mean wind speed mean vector direction (degrees) 12.2 m/s 240 using 6278 observations mean height 1407 metres asl variance 42 Standard Deviation 6.5 m/s 300-500m agl (ground is 82m asl) mean wind speed 12.9 m/s variance 43 Standard Deviation 6.5 m/s mean vector direction (degrees) 216 using 3202 observations mean height 481 metres asl mean pressure 949 mb variance using using 45 Standard Deviation 6.7 m/s 23675 observations 3202 observations 22 7. WIND ROSE CREATION Once pre-processing of the radiosonde data for the four principle stations and one surrogate station was complete, the next step towards creating windroses from the data was to create data entities called ‘Wind Data Objects’ (WDOs) for the required altitude levels (300-500 m agl and 1457-3000 m asl). 7.1 The Wind Data Object (WDO) The WDO is essentially a very high resolution wind rose, consisting of an unusually large number of direction sectors and wind speed bands. Whereas, the conventional wind rose of Jones (1981) has twelve direction sectors and four wind speed bands, the WDOs used in this study have 30 wind speed bands (with central speed values of 0.5 to 29.5 m/s), and 72 direction sectors (with central azimuths from north of 5o to 360o). For example, figure 8 shows 1990-96 geostrophic WDO for Hemsby. Figure 8: Hemsby, 1457-3000m asl wind data object (WDO) for 1990-96, using 34671 synoptic observations. Note: The 72 direction bins along the x-axis correspond to the angles 5-360 degrees in 5 degree increments (raw radiosonde angles are given to the nearest 5 degrees). The 30 speed bands along the y-axis have widths of 1m/s, with central values of 0.5 to 29.5 m/s. The z-axis shows the percentage value in each cell. For the years 1990-96, WDOs were created for the geostrophic level (1457 – 3000 m asl) and the 300-500 m agl level for the four principle stations, and just the geostrophic level for Herstmonceux (the surrogate station). WDOs can be conveniently visualised as an 23 array of the percentage of the time for which the wind is blowing from a particular azimuth, at a given speed (see figure 8). The WDO stage in the processing sequence is important because once created the WDOs provide a very compact way to store the radiosonde data, each WDO being only 29 kilobytes in size. Additionally, conventional ‘low resolution’ wind roses of any desired direction sector, or wind speed band format, can easily be created from the WDOs. Also, the WDOs provide a standardised input data format for the spatial interpolation, and atmospheric boundary layer models used later in this study. Finally, mean wind speeds and mean vector directions can be estimated from the WDOs without reference back to the pre-processed radiosonde time-series data. However, it should be noted that geostrophic (1457-3000m) mean wind speeds estimated from WDOs are approximately 0.4 to 0.6 m/s less than those estimated from the time-series data (for 1457-3000m), because the ‘tail’ of the wind speed distribution in the WDO has been truncated at 30 m/s. The 1457-3000m altitude range was chosen to represent the geostrophic winds, since the literature describes the 850 mb pressure level as being reliably geostrophic (Troen and Petersen, 1989 and Borresen, 1987), with the wind speed and direction above this level remaining constant up to the top of the troposphere at ~10 km. The 850 mb level corresponds to 1457 m asl in the 1976 Standard Atmosphere Model given in Jacobson (1999), so the 1457-3000m asl range was chosen to provide plentiful individual wind speed and direction observations to ‘fill out’ the geostrophic WDO. For example, seven years of data for 1457-3000m asl yields about 35000 individual observations, whereas using just the 850 mb level will give only around 7000 (see table 1). The PV-WAVE programs used to create the 1990 to 1996 WDOs for the radiosonde station at Hemsby, are ‘heweibullrose850_72.pro’ for the 1457-3000m asl level, and ‘heweibullrose300500m_72.pro’ for the 300-500m agl level. Both these programs are given in Appendix A. The programs to create WDOs for the other stations are essentially the same. The WDOs created for Hemsby are stored in the binary data files 30band73rose9096hem.dat and 30band73rose300500m9096hem.dat, for the geostrophic and 300-500m levels respectively. Again, the data file naming conventions for the other stations are similar. 24 Table 2: Mean wind speeds and mean vector directions, derived from the WDOs for all five radiosonde stations. Camborne 1990-96 altitude 87 m above sea level (asl) WDO wind speed for 1457-3000m asl mean wind speed mean vector direction (degrees) 11.8 m/s 267 WDO wind speed for 300-500m agl mean wind speed mean vector direction (degrees) 11.4 m/s 244 Herstmonceux 1992-96 altitude 52m above sea level (asl) WDO wind speed for 1457-3000m asl mean wind speed mean vector direction (degrees) Hemsby 1990-96 11.0 m/s 263 altitude 14 m above sea level (asl) WDO wind speed for 1457-3000m asl mean wind speed mean vector direction (degrees) 11.2 m/s 269 WDO wind speed for 300-500m agl mean wind speed mean vector direction (degrees) 10.8 m/s 254 Hillsborough 1990-96 altitude 37 m above sea level (asl) WDO wind speed for 1457-3000m asl mean wind speed mean vector direction (degrees) 12.2 m/s 257 WDO wind speed for 300-500m agl mean wind speed mean vector direction (degrees) 11.2 m/s 238 Lerwick 1990-96 altitude 82 m above sea level (asl) WDO wind speed for 1457-3000m asl mean wind speed mean vector direction (degrees) 11.9 m/s 247 WDO wind speed for 300-500m agl mean wind speed mean vector direction (degrees) 12.8 m/s 216 Mean wind speeds and vector directions for the study period (1990-96) can be obtained from the WDOs using the PV-WAVE program ‘30band73rose9096_WDO_stats.pro’, for the geostrophic WDOs, and ‘30band73rose300500m9096_WDO_stats.pro’ for the 300500m agl level (both listings are given in Appendix A). Both use programs make use of the complex number method for representing 2D vectors as described by Jones (1998). Table 2 shows wind speeds and directions derived from the WDOs for all five radiosonde stations. 25 Table 3: Mean wind speeds and mean vector directions, for the 5-10 m/s wind speed band derived from the WDOs for all five radiosonde stations. Camborne 1990-96 altitude 87 m above sea level (asl) WDO 1457-3000m asl, for winds between 5 and 10 m/s mean wind speed 7.5 m/s mean vector direction (degrees) 276 WDO 300-500m agl, for winds between 5 and 10 m/s mean wind speed 7.6 m/s mean vector direction (degrees) 280 Herstmonceux 1992-96 altitude 52m above sea level (asl) WDO 1457-3000m asl, for winds between 5 and 10 m/s mean wind speed 7.5 m/s mean vector direction (degrees) 282 300-500m agl for winds between 5 and 10 m/s (from time-series data) mean wind speed 7.4 m/s mean vector direction (degrees) 270 Hemsby 1990-96 altitude 14 m above sea level (asl) WDO 1457-3000m asl, for winds between 5 and 10 m/s mean wind speed 7.5 m/s mean vector direction (degrees) 269 WDO 300-500m agl, for winds between 5 and 10 m/s mean wind speed 7.5 m/s mean vector direction (degrees) 272 Hillsborough 1990-96 altitude 37 m above sea level (asl) WDO 1457-3000m asl, for winds between 5 and 10 m/s mean wind speed 7.5 m/s mean vector direction (degrees) 265 WDO 300-500m agl, for winds between 5 and 10 m/s mean wind speed 7.5 m/s mean vector direction (degrees) 259 Lerwick 1990-96 altitude 82 m above sea level (asl) WDO 1457-3000m asl, for winds between 5 and 10 m/s mean wind speed 7.5 m/s mean vector direction (degrees) 259 WDO 300-500m agl, for winds between 5 and 10 m/s mean wind speed 7.6 m/s mean vector direction (degrees) 256 The HARM acid rain model makes use of the wind rose valid for 400m agl, for the 5-10 m/s wind speed band. Table 3 shows wind speeds and direction for this speed band, at the geostrophic level and 300-500m agl (which is used in this study as surrogate for 400m agl). It is clear from table 3 that the magnitude of the anticlockwise rotation of the mean wind vector direction when going from the geostrophic to 300-500m agl level is far less (a 26 few degrees clockwise in some cases) for the 5-10 m/s wind speed band, than the case with all wind speed bands, which gave about 20o of anticlockwise rotation (see table 2). The information in tables 2 and 3 was derived from a more comprehensive table held in the Microsoft Excel document ‘radiosonde_stn_stats.xls’ (see Appendix B). 7.2 The Wind Rose plotting program The wind rose plotting program is called ‘roseplot_from_dataslab_6pc.pro’ (see Appendix A), and transforms a measured WDO in to a 12-sector, 4-speed band, wind rose plot and table, using the same format as the Jones (1981) rose. The program makes use of a series of ‘IF THEN’ tests contained within a ‘FOR NEXT’ loop to reassign the ‘percentage energy’ from an azimuth/wind-speed cell in the WDO, to the appropriate rose sector and speed band within the conventional rose. Figure 9, shows a wind rose plot created by the program from the 1457-3000m asl WDO for Lerwick. The labels ‘speed band 1’ to ‘speed band 4’ in figure 9, refer to the wind speed bands for, less than 5 m/s, 5 to 10 m/s, 10 to 15 m/s, and over 15 m/s. Table 4 shows the Lerwick 1457-3000m rose in tabular form. Appendix C contains similar rose plots for all the radiosonde stations used in this study, for the 1457-3000m asl and 300-500m agl levels. Table 4: The geostrophic (1457-3000m asl), 12-sector, 4-speed band wind rose for the Lerwick radiosonde station, for the years 1990-96. 27 Figure 9: The geostrophic (1457-3000m asl), 12-sector, 4-speed band wind rose for the Lerwick radiosonde station, for the years 1990-96. (Note: north is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) 28 8. THE MEAN UK GEOSTROPHIC WINDROSE (1990-96) The four principal radiosonde stations used in this study (Camborne, Hemsby, Hillsborough, and Lerwick) were used to create a mean geostrophic WDO for the UK, by taking the mean average of the individual 1457-3000m asl WDOs. The PV-WAVE program used to calculate this mean UK WDO is called ‘meangeostrophic.pro’ (see Appendix A). This mean UK WDO has been used to generate the wind rose shown in figure 10, and table 5. Figure 10: Mean UK geostrophic (1457-3000m asl) wind rose for the years 1990-96, derived from radiosonde measurements at Camborne, Hemsby, Hillsborough and Lerwick. Wind speed bands 1 to 4 (under 5 m/s, 5-10 m/s, 10-15 m/s, 15 m/s upwards) are plotted as individual wind roses. (Note: north is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artefact and should be ignored) A total of 135966 individual radiosonde observations of wind speed and direction, over a period of seven years were used to create the mean UK geostrophic WDO. 29 Table 5: A seven year (1990-96) mean UK geostrophic, 1457-3000m above ground level (agl) wind rose, calculated from 135966 synoptic wind speed observations at Camborne, Hemsby, Hillsborough and Lerwick. The mean vector wind direction derived from the mean UK geostrophic WDO (1990-96) is 260o clockwise from North. The mean WDO derived geostrophic (1457-3000m asl) wind speed is 11.77 m/s. The mean vector wind direction for the 5-10 m/s wind speed band, obtained from the geostrophic WDO, is 266o from North. If the HARM model is to be run using the mean UK geostrophic rose for 5-10 m/s (see figure 10, speed band 2) as a surrogate for the ‘400m elevation’ 5-10 m/s rose, using a wind speed 10% less than the geostrophic value (as described by Jones, 1981). It is suggested that the wind speed be measured at the 850mb level, so as to remain consistent with the geostrophic wind literature (Borresen, 1987 and Troen, I. and Petersen, 1989). The mean 850mb level geostrophic wind speed (1990-96) for the four principle stations is 11.81 m/s, with the Jones (1981) 10% reduction giving a ‘400m agl’ value of 10.63 m/s for the wind speed to be used in a pollution model such as HARM. This value of 10.63 m/s is close to the 10.44 m/s wind speed currently used in HARM model runs (Nicholson, 2002, pers comm). The original Jones (1981, p19) wind rose is shown in figure 11, and table 6, to facilitate comparison with the new UK mean rose (figure 10, table 5). 30 Figure 11: The Jones (1981) ‘400 metre’ wind rose displayed as a series of sector plots. (Note: north is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table 6: A representative wind rose for use in long-range dispersion calculation (from Jones, 1981, p19). It is noticeable that the 5-10 m/s wind speed band (that is used by HARM) of the Jones (1981) rose (see figure 11), has a significant northerly component that is missing from the 31 corresponding band on the new UK mean rose (see figure 10). The effects of these differences between the wind roses on the HARM output have been investigated below. 8.1 HARM output comparisons for the Jones (1981) and mean UK (1990-96) wind roses Nicholson has prepared maps showing the differences in HARM modelled deposition across the UK, between HARM 11.5 model runs using the Jones (1981) wind rose, and the new mean UK wind rose shown in figure 10 (Nicholson, 2002, pers comm). These comparison runs used the standard HARM single-layer model with 1997 emissions and rainfall, with a wind speed of 10.44 m/s. Nicholson has provided maps for differences in sulphur deposition, oxidised nitrogen deposition, and reduced nitrogen (ammonia) deposition, for both wet and dry deposition conditions (these are shown in Appendix D, as figures D1, D2 and D3 respectively). The HARM annual deposition budgets (in kT) using the Jones (1981) and new wind rose are shown in table 7. Table 7: HARM 11.5 annual deposition budgets in kT, using 1997 emissions and rainfall, for the Jones (1981) and mean UK (1990-96) wind rose (Nicholson, 2002, pers comm). It can be seen from table 7, that all types of HARM modelled deposition are slightly increased by the use of the new 1990-96 mean UK wind rose. In particular wet sulphur deposition over the UK is increased by almost 5% (see figure D1, in Appendix D, for the corresponding map). Figure D1, shows that the new UK wind rose has led to increased sulphur deposition over some parts of Northwest Scotland of greater than 1kg per hectare per year, due to the decrease in the northerly wind component. 32 9. THE SPATIAL LEAST-SQUARES LINEAR INTERPOLATION MODEL This section describes a model that has been developed to spatially interpolate the geostrophic (1457-3000m asl) WDOs measured at the radiosonde stations, to any intervening point in the UK Ordnance Survey grid. 9.1 Fitting a plane surface by least-squares The fitting of a planar surface to four or more data points by least squares is described by Pedder (1981, p58) and in matrix algebra form by Harbaugh (1964, p7 & p29-30). Harbaugh’s technique was used as PV-WAVE supports matrix algebra. For example, if Easting (x) and Northing (y) co-ordinates of a number (greater than three) of observation stations are known, along with the observed quantity to be interpolated, z (say, geostrophic wind speed at 850 mb). Then the least squares planar trend surface: (9) z trend = A + Bx + Cy can be found by evaluating the following matrix system to solve the normal equations: k x x y y 2 xy xy 2 x y −1 z ⋅ A zx = B zy (10) C given that: x = x1 + x 2 + x3 ... + x k y = y1 + y 2 + y 3 ... + y k z = z1 + z 2 + z 3 ... + z k where k is the number of stations. Figure 12, shows the example where geostrophic wind speeds (850 mb) measured at the four principal radiosonde stations, have been subjected to least squares planar interpolation across the UK. The least squares planar demonstration PV-WAVE program used to create figure 12, is called ‘ukgeosmap3.pro’ and is listed in Appendix A. Interestingly, the contours of geostrophic wind speed shown on figure 12, compare fairly well (despite the limitations of the planar surface) with a similar map on page 31 of Troen and Petersen (1989). The main difference being that the 850 mb wind speeds in figure 12 are uniformly 0.4 to 0.5 m/s greater across the UK than those on Troen and Petersen’s (1989) map. 33 Figure 12: Mean geostrophic wind speeds at the 850 mb level (1990-96), interpolated between four radiosonde stations using a planar surface fitted by least squares. (Note: the measured 850mb wind speed values at the stations where, Camborne 11.5 m/s, Hemsby 11.0 m/s, Hillsborough 12.6 m/s, Lerwick 12.2 m/s (see table 1)) Since a planar surface cannot be an exact fit to the contributing data points, some goodness of fit statistic is required to show how well the fitted surface represents the data. Harbaugh (1964, p32) introduces some useful statistical measures, namely Error Measure (EM) which is the sum of the squared residuals, divided by one minus the number of data points (k): EM = (z obs − z trend )2 k −1 (11) 34 (an error measure of zero indicates a perfect fit to the observed data values) and Percent of total sum of squares (PTSOS) which is a measure of how well the fitted surface fits the observed data. PTSOS is calculated using the following equation: z 2 trend − PTSOS = 2 z obs − ( z trend ) 2 k ( z obs ) 2 (12) k A PTSOS value of 100% indicates a perfect fit between the trend surface and the observed data. For the 850 mb level winds example given in figure 12, the calculated EM value was 0.034, and the PTSOS value 90%. 9.2 Using fitted least squares planar surfaces to interpolate WDOs The Wind Data Object (WDO) contains percentages for 72 wind direction sectors and 30 wind speed bands, contained in 2160 data bins or cells, taking the form of a 72 by 30 element data array (see figure 8). In order to create an interpolated WDO at a location between the observation stations, an estimate needs to made of every one of the 2160 cells at the new location. This is done by taking cells with the same speed band value and wind direction, at each of the observation stations, and fitting a planar surface to their percentage values. Thus, the resulting fitted surface can be used to generate the equivalent cell percentage value at the new location. Since the WDO contains 2160 cells, this means that 2160 independent least squares planar surfaces need to be determined. Once, the A, B and C coefficients (see equation 9) have been found for all 2160 surfaces, these can be used to generate an interpolated WDO at any location with the UK Ordnance Survey grid. It should be remembered that WDOs determined by this model, for locations outside the bounding rhomboid defined by the radiosonde station positions are extrapolated rather than interpolated results. The PV-WAVE program ‘geostrophictrendslab.pro’ (see Appendix A) has implemented the WDO spatial least squares model described above. It can take data in the forms of WDOs and station locations (O/S Eastings and Northings in metres) for four individual radiosonde stations, and creates interpolated WDOs for each Ordnance Survey 100 km 35 grid square within the UK. Figure 13, shows wind roses representing all non-zero wind speeds under 30 m/s, derived from the WDOs produced for each O/S 100km square, using ‘geostrophictrendslab.pro’. The wind roses themselves were made by a program called ‘geoswindplot.pro’,that uses the file geostrophicmodel9096uk.dat containing the modelled WDOs output from ‘geostrophictrendslab.pro’. Figure 13: Geostrophic (1457-3000m asl) wind roses for each 100km O/S square, derived from WDOs at the four principal radiosonde stations, showing 12 direction sectors for wind speeds greater than zero and less than or equal to 30 m/s. (Note: figure 13, covers the same area on the ground as figure 12, and the scale on each wind rose is 20%. The principal stations are, Camborne, Hemsby, Hillsborough and Lerwick) 36 Figure 13 demonstrates that the least squares planar trend surface approach to interpolating WDOs can interpolate them smoothly across the UK without any obvious artefacts being introduced. Figure 14, shows the same wind roses as given in figure 13, but superimposed upon each other. Figure 14: Geostrophic wind roses for each 100km O/S square, superimposed one upon the other, derived from WDOs at the four principal radiosonde stations, showing 12 direction sectors for wind speeds greater than zero and less than or equal to 30 m/s. (Note: the scale on each wind rose is 20%) From figures 13 and 14 it can be seen that the most prominent feature is the reduction of the percent of the time that geostrophic winds are blowing from the West, dropping from about 18% to 13% between Camborne and Lerwick. Figure 15, shows superimposed wind speed histograms for all the 91 WDOs represented as wind roses in figure 14, and demonstrates that variations of up to about 2% for each 1 m/s histogram ‘wind speed bin’ can occur across the UK. Also note that the superimposed histograms differ the least at 8.5 m/s wind speed. In addition to providing WDO estimates for each O/S grid square the least squares planar trend surface model can also ‘be run to a given location’ to give an estimated geostrophic (1457-3000m asl) WDO for given O/S co-ordinates within the UK. The PV-WAVE program ‘geostrophictrendslab_locationWDO_he.pro’ runs the model in this mode, see Appendix A. The goodness of fit statistics for the least squares planar trend surface model are calculated by the PV-WAVE program ‘geostrophictrendslab_with_stats.pro’. This derives EM and PTSOS values for each of the 2160 fitted trend surfaces created by the model, and records their minimum, mean and maximum values, and works out the PTSOS standard deviation. 37 For the model run with the four principal stations, or the model run with Hemsby replaced by Herstmonceux (the surrogate station) for test purposes, the mean EM value was around 6x10-5 and the PTSOS value 75%, with PTSOS having a standard deviation of 28% over all 2160 values. Thus demonstrating that the fitted surfaces are giving a fairly good representation of the observed data. Figure 15: 91 geostrophic wind speed histograms for all wind directions, derived from the WDOs modelled for each O/S 100km grid square, using the least squares planar model for the four principal stations. (Note: the wind speed bands are 1 m/s wide) 38 10. THE SURFACE ROUGHNESS COUPLED EKMAN MODEL The simple Ekman type model described at the end of section 3 was implemented as a PVWAVE program ‘ekman_geodrag.pro’, see Appendix A. This model uses the simple Ekman spiral equations (3a and 3b in section 3) and links them to surface roughness via an eddy viscosity, K, estimate. Given values of surface roughness length, z0 and geostrophic wind speed, Vg, the geostrophic drag law (equation 8) can be used to estimate the friction velocity, u* which can be inserted into equation 7 to obtain a value of eddy viscosity, K. This K value can be used to obtain perpendicular wind vector components (u’ and v’) from the Ekman spiral equations (3a and 3b) for any desired height z, within the Ekman layer (see figure 16). Given: Surface roughness length, z0 Geostrophic wind speed, Vg Use: Geostrophic Drag Law to determine the friction velocity, u* Given: A fixed a priori value of the ‘inner layer’ height, h Use: K = ku* h where k = von Karman’s constant, to find the eddy viscosity, K Use the eddy viscosity value, K, in the EKMAN SPIRAL EQUATIONS: u ' = V g − V g e − az cos(az ) v ' = V g e − az sin(az ) where a is a known function of K, to find the perpendicular wind components u’ and v’ at a height, z of 400 metres above ground level. Figure 16: A conceptual flowchart of the surface roughness coupled Ekman model. 39 10.1 Using the WDO in the coupled Ekman model Although, the coupled Ekman model is mathematically simple, the novel aspect of its use in this project, is the way in which it has been applied to the geostrophic WDO to provide a modelled WDO representing winds at 400 m agl. Each of the 2160 individual cells within the WDO contains a value for the percent of the time that the wind blows from a particular azimuth, for a particular wind speed. Each geostrophic WDO cell is thus labelled with a representative direction (5 to 360 degrees) and wind speed value (0.5 to 29.5 m/s), see section 7. In order to ‘present’ the WDO to the coupled Ekman model, each WDO cell is taken one at a time. The wind speed label of the cell is used as the geostrophic wind speed, Vg in the Ekman spiral equations (3a and 3b), from which the perpendicular wind components (u’ and v’) at 400 m above ground level can be determined. The magnitude of the resultant wind speed can be found using Pythagoras’s theorem (see equation 5), and is used to re label the WDO cell with a new wind speed valid for 400 m agl. The u’ and v’ values for 400 m agl define a wind direction (-180o to +180o) relative to the geostrophic direction, which must be corrected to a wind direction clockwise from North by adding the original labelled cell direction at geostrophic height. The wind speed and wind direction from North, thus calculated for 400m agl by the model, become new wind speed and direction labels for the cell. This process is repeated for all 2160 cells in the WDO. When the modelling process is complete all 2160 cells in the WDO have new azimuth and wind speed labels, but retain their original percentage values. So in essence the modelling of the WDO from geostrophic (1457-3000m asl) to 400m agl level is a re-labelling process. The values of the quantities friction velocity, u* eddy viscosity, K and planetary boundary layer depth, DE, that are generated for each WDO cell during the modelling process are stored as meta-data labels attached to each cell in the new WDO. Wind speed and direction and meta-data values can be recovered from the modelled 400 m agl WDO using the PV-WAVE program “30band73rose9096hem_400model_Zo_0_0002_h35_WDO_stats.pro”. Conventional 12sector, 4 wind speed band wind roses can be generated from the Ekman modelled WDOs, using the PV-WAVE program ‘roseplot_from_dataslab_400m.pro’. Figure 17, shows a 5-10 m/s wind speed band wind rose modelled using the coupled Ekman model (using h = 35 m, z0 = 0.0002 m), compared with the observed 5-10 m/s wind rose for geostrophic height. The modelled rose shows the modest anticlockwise ‘rotation’ expected from theory, see section 3. 40 Figure 17: A comparison of the measured geostrophic (1457-3000m asl) wind rose at Hemsby, and the 400 m agl rose modelled for Hemsby. (The Ekman model has been run using z0 = 0.0002 metres, and h = 35 metres. Both roses show the 5-10 m/s wind speed band used by HARM, and are valid for the period 1990-96) 10.2 Mean Ekman profiles The mean values of eddy viscosity, K and geostrophic wind speeds, Vg derived from the coupled Ekman modelling process, can be used in the Ekman spiral equations (3a & 3b), can be used to derive a ‘mean’ Ekman wind speed profile for comparison with the raw radiosonde wind speed observations. Figure 18, shows such a ‘mean’ Ekman curve, laid over the original radiosonde observations. Figure 18:Individually plotted Hemsby radiosonde wind speed measurements against height (asl), for 1990-96. Also shown is a 50 metre height band ‘running mean’ wind speed (rough line), and the Ekman wind speed profile for K = 4.1 m2/sec, Vg = 11.2 m/s (smooth curve). 41 The PV-WAVE programs used to create figure 18, are ‘ekman_profile2.pro’ and ‘windprofileplot.pro’. The coupled Ekman model was also run for h = 80 metres, and z0 = 0.0002 metres (Troen and Petersen (1989, p18) assign a z0 of 0.0002 metres for the sea), using the Hemsby 1457-3000m WDO as the input. The 5-10 m/s wind rose at 400m agl resulting from this modelling was used to perform HARM runs. Comparison plots for these runs and HARM runs done using the Jones (1981) rose are shown in Appendix D (figures D4 to D6). Wind rose plots and tables (valid for 400 m agl) for coupled Ekman model runs using the measured 1990-96 geostrophic (1457-3000m asl) wind rose for Hemsby, for: h = 80 metres, and z0 = 0.0002 metres h = 80 metres, and z0 = 0.133 metres and h = 35 metres, and z0 = 0.0002 metres are shown in Appendix E. 42 12. SURFACE ROUGHNESS OF THE UK The mean surface roughness length, z0 for the UK has been estimated using values taken from Troen and Petersen (1989). Troen and Petersen provide ‘roughness roses’ for 22 surface meteorological stations within the UK, consisting of 12 azimuth sectors and a variable number of distance from station bands, out to a maximum of 10 to 15 km out from the station. For this study the mean roughness length for the area around each station was estimated by taking the mean value of the outermost distance band as shown in table 8. Table 8: Roughness length estimates, z0, for 22 UK surface meteorological stations, derived from Troen and Petersen 1989. Table 8, shows that the mean z0 value for the UK is 0.16 metres with a standard deviation of 0.12 metres. This value of 0.16 metres for z0 is close to the European and North American average (Stull, 1988, p380), and corresponds to ‘farmland with a closed appearance’ (Troen and Petersen, 1989, p58). Both Stull (1988, p380) and Troen and Petersen (1985, p58) provide figures which relate land cover type to z0 value. 43 14. THE HEMSBY RADIOSONDE STATION Synoptic wind observations for the period 1990-96 from the radiosonde station situated at Hemsby (52.48oN 1.68oE) in Norfolk have been used as a reference against which to compare the outputs of spatial linear interpolation and Ekman spiral WDO models. Figure 19: Map of the environs of Hemsby radiosonde station, showing 1:50 000 O/S mapping out to a distance from the station of approximately 15 km. (produced using Ordnance Survey 1:50 000 scale colour raster data from EDINA Digimap; http://digimap.edina.ac.uk, crown copyright reserved.) 44 A radiosonde balloon will attain geostrophic altitudes (~1500m and above) approximately one hour after release (Oke, 1987, p317). The time to reach 500 metres altitude will thus be roughly 20 minutes. In this study radiosonde observations between 300 and 500 metres agl have been used as a reference against which to compare the modelled 400m agl wind roses. Assuming typical 300-500m wind speeds in the range 9 to 12 m/s, the area contributing surface roughness to the observations will take the form of an annulus of inner radius 7 km and outer radius 15 km centred on the Hemsby station. Figure 19 shows a map of the Hemsby area out to a distance of 15km. For the onshore areas of the annulus a roughness length of z0 = 0.133 metres has been used, derived from observations made at RAF Coltishall (52.75oN 1.35oE) which lies about 24 km WNW of Hemsby (see Troen and Petersen, 1989, p498). This roughness length of 0.133 metres corresponds to ‘predominantly arable farmland, though with some parts well wooded’ (Troen and Petersen, 1989, p498). The parts of the annulus that lie over the sea have been assigned a z0 of 0.0002 metres (Troen and Petersen, 1989, p18). The roughness effects of the Great Yarmouth urban area have been ignored. 45 13. References Allison, M., 1992. A preliminary assessment of the Titan planetary boundary layer. In: ESA SP-338: Proceedings Symposium on Titan, Toulouse, France (9-12 September 1991), ESA, Toulouse, France, p113-118 Anthes, R. A., Panofsky, H. A., Cahir, J. J. and Rango, A., 1978. The Atmosphere, second edition. Charles E. Merill Publishing Company, Columbus, Toronto, London, Sydney, p442 Borresen, J. A., 1987. Wind atlas for the North Sea and the Norwegian Sea. Norwegian University Press and Norwegian Meteorological Institute, Oslo, p183 Ekman, V. W., 1905. On the influence of the earth’s rotation on ocean currents. Ark.Mat., Astron. Fys. 2, No.11 Haltner, G. J. and Williams, T. W., 1980. Numerical Prediction and Dynamic Meteorology, second edition. John Wiley & Sons , Inc., New York, Chichester, Brisbane, Toronto, Singapore, p477 Harbaugh, J. W., 1964. A Computer Method for Four-Variable Trend Analysis Illustrated by a Study of Oil-Gravity Variations in Southeastern Kansas. Bulletin 171, State Geological Survey of Kansas. Jacobson, M. Z., 1999. Fundamentals of Atmospheric Modeling. Cambridge University Press, Cambridge, p635 Jones, J. A., 1981. The Estimation of Long Range Dispersion and Deposition of Continuous Releases of Radionuclides to Atmosphere. The Third Report of a Working Group on Atmospheric Dispersion, NRPB, Chilton, Didcot, Oxon, p25 Jones, K. H., 1998. A Comparison of Algorithms used to Compute Hill Slope as a Property of the DEM. Computers & Geosciences, 24, 4, p315-323 Landsberg, H. E., 1981. The Urban Climate (International geophysics series; volume 28). Academic pres, Inc. Ltd, London, p275 Metcalfe, S. E., Whyatt, J. D., Broughton, R., Derwent, R. G., Finnegan, D., Hall, J., Mineter, M., O'Donoghue, M., Sutton, M. A., 2001. Developing the Hull Acid Rain Model: its validation and implications for policy makers. Environmental Science and Policy, 4, 25-37 Oke, T. R., 1987. Boundary Layer Climates. Methuen, London and New York, p435 Pedder, M. A., 1981a. Practical analysis of dynamical and kinematic structure: principles, practice and errors. In Dynamical Meteorology, an introductory selection (ed. B.W. Atkinson), Methuen, London and New York, p55-68 46 Pedder, M. A., 1981b. Practical analysis of dynamical and kinematic structure: more advanced analysis schemes. In Dynamical Meteorology, an introductory selection (ed. B.W. Atkinson), Methuen, London and New York, p87-99 Rossby, C. G. and Montgomery, R. B., 1935. The layer of frictional influence in wind and ocean currents. Papers in Phys. Oceanogr. Meteor., MIT and Woods Hole Oceanogr. Inst., III no.3, p101 Ryan, B. C., 1974. A mathematical model for diagnosis and prediction of surface winds in mountainous terrain. Ph.D. dissertation, University of California, Riverside, p135 Ryan, B. C., 1977. A mathematical model for diagnosis and prediction of surface winds in mountainous terrain. Journal of Applied Meteorology, 16(6), p571-584 Reynolds, B., Cullen, J., Finnegan, D., Fowler, D., Jenkins, A., Jenkins, R., Metcalfe, S. E., Norris, D. A., Ormerod, S. J., and Whyatt, D., 2002. Scoping Study for Acid Waters in Wales Strategy. The Centre for Ecology & Hydrology, Monks Wood, p202 Troen, I. and Petersen, E. L., 1989. European wind atlas. Roskilde, Denmark : Published for the Commission of the European Communities, Directorate-General for Science, Research, and Development, Brussels, Belgium by Risø National Laboratory, p656 Stull, R. B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, Dordrecht, Boston, London, p666 Weibull, W., 1951. A statistical distribution function of wide applicability. Journal of Applied Mechanics, 18, p293-297 47 Appendix A PV-WAVE and AML programs written for this study: The program files are on the enclosed CD-ROM in directory Appendix_A They had been previously in /tsunami14c/msc_stud/msc0220/radiosonde The program files are listed alphabetically as follows: 30band73rose300500m9096hem_WDO_stats.pro 30band73rose9096hem_400model_Zo_0_0002_h35_WDO_stats.pro 30band73rose9096hem_WDO_stats.pro ekman_geodrag.pro ekman_profile2.pro geostrophictrendslab.pro geostrophictrendslab_locationWDO_he.pro geostrophictrendslab_with_stats.pro geoswindplot.pro heipvertwind.pro hevertdoublesremove.pro heweibullrose300500m_72.pro heweibullrose850_72.pro meangeostrophic.pro roseplot_from_dataslab_400m.pro roseplot_from_dataslab_6pc.pro vertread9096he.aml windND_datastats.pro windprofileplot.pro Appendix B The Microsoft Excel document radiosonde_stn_stats.xls This spread-sheet is on the enclosed CD-ROM in directory Appendix_B APPENDIX C Measured Wind Roses at the Radiosonde Stations Wind roses with 12-sectors and four wind speed bands, measured at the five radiosonde stations. Wind roses are presented for two atmospheric levels, 14573000m above sea level (the geostrophic level), and 300-500 above ground level. Contents 03808 Camborne (50.22oN 5.32oW, altitude 87m above sea level) 1990-96 wind rose plots and tables for: 1457-3000m asl (using 33626 observations) 300-500m agl (using 4121 observations) 03882 Herstmonceux (50.90oN 0.32oE, altitude 52m above sea level) 1992-96 wind rose plots and tables for: 1457-3000m asl (using 25269 observations) 03496 Hemsby (52.68oN 1.68oE, altitude 14m above sea level) 1990-96 wind rose plots and tables for: 1457-3000m asl (using 34671 observations) 300-500m agl (using 3650 observations) 03920 Hillsborough (54.48oN 6.10oW, altitude 37m above sea level) 1990-96 wind rose plots and tables for: 1457-3000m asl (using 34349 observations) 300-500m agl (using 5290 observations) 03005 Lerwick (60.13oN 1.18oW, altitude 82m above sea level) 1990-96 wind rose plots and tables for: 1457-3000m asl (using 30813 observations) 300-500m agl (using 3175 observations) Figure C1: Camborne 1990-96 (1457-3000m asl), wind speed bands 1 to 4 plotted as individual wind roses. (Note: the 4 wind speed bands correspond to wind speeds, under 5 m/s, 5-10 m/s, 10-15m/s, and 15 m/s upwards, respectively. North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table C1: The geostrophic (1457-3000m asl), 12-sector, 4-speed band wind rose for the Camborne radiosonde station, for the years 1990-96. Figure C2: Camborne 1990-96 (300-500m agl), wind speed bands 1 to 4 plotted as individual wind roses. (Note: the 4 wind speed bands correspond to wind speeds, under 5 m/s, 5-10 m/s, 10-15m/s, and 15 m/s upwards, respectively. North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table C2: The 300-500m agl, 12-sector, 4-speed band wind rose for the Camborne radiosonde station, for the years 1990-96 (ground level is 87m asl). Figure C3: Herstmonceux 1992-96 (1457-3000m asl), wind speed bands 1 to 4 plotted as individual wind roses. (Note: the 4 wind speed bands correspond to wind speeds, under 5 m/s, 5-10 m/s, 10-15m/s, and 15 m/s upwards, respectively. North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table C3: The geostrophic (1457-3000m asl), 12-sector, 4-speed band wind rose for the Herstmonceux radiosonde station, for the years 1992-96. Figure C4: Hemsby 1990-96 (1457-3000m asl), wind speed bands 1 to 4 plotted as individual wind roses. (Note: the 4 wind speed bands correspond to wind speeds, under 5 m/s, 5-10 m/s, 10-15m/s, and 15 m/s upwards, respectively. North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table C4: The geostrophic (1457-3000m asl), 12-sector, 4-speed band wind rose for the Hemsby radiosonde station, for the years 1990-96. Figure C5: Hemsby 1990-96 (300-500m agl), wind speed bands 1 to 4 plotted as individual wind roses. (Note: the 4 wind speed bands correspond to wind speeds, under 5 m/s, 5-10 m/s, 10-15m/s, and 15 m/s upwards, respectively. North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table C5: The 300-500m agl, 12-sector, 4-speed band wind rose for the Hemsby radiosonde station, for the years 1990-96 (ground level is 14m asl). Figure C6: Hillsborough 1990-96 (1457-3000m asl), wind speed bands 1 to 4 plotted as individual wind roses. (Note: the 4 wind speed bands correspond to wind speeds, under 5 m/s, 5-10 m/s, 10-15m/s, and 15 m/s upwards, respectively. North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table C6: The geostrophic (1457-3000m asl), 12-sector, 4-speed band wind rose for the Hillsborough radiosonde station, for the years 1990-96. Figure C7: Hillsborough 1990-96 (300-500m agl), wind speed bands 1 to 4 plotted as individual wind roses. (Note: the 4 wind speed bands correspond to wind speeds, under 5 m/s, 5-10 m/s, 10-15m/s, and 15 m/s upwards, respectively. North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table C7: The 300-500m agl, 12-sector, 4-speed band wind rose for the Hillsborough radiosonde station, for the years 1990-96 (ground level is 37m asl). Figure C8: Lerwick 1990-96 (1457-3000m asl), wind speed bands 1 to 4 plotted as individual wind roses. (Note: the 4 wind speed bands correspond to wind speeds, under 5 m/s, 5-10 m/s, 10-15m/s, and 15 m/s upwards, respectively. North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table C8: The geostrophic (1457-3000m asl), 12-sector, 4-speed band wind rose for the Lerwick radiosonde station, for the years 1990-96. Figure C9: Lerwick 1990-96 (300-500m agl), wind speed bands 1 to 4 plotted as individual wind roses. (Note: the 4 wind speed bands correspond to wind speeds, under 5 m/s, 5-10 m/s, 10-15m/s, and 15 m/s upwards, respectively. North is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table C9: The 300-500m agl, 12-sector, 4-speed band wind rose for the Lerwick radiosonde station, for the years 1990-96 (ground level is 82m asl). Appendix D Contents Figure D1: The annual sulphur deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and the new mean UK (1990-96) wind rose (Nicholson, 2002, pers comm). Figure D2: The annual nitrogen (oxidised nitrogen) deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and the new mean UK (1990-96) wind rose (Nicholson, 2002, pers comm). Figure D3: The annual ammonia (reduced nitrogen) deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and the new mean UK (1990-96) wind rose (Nicholson, 2002, pers comm). Figure D4: The annual sulphur deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and an Ekman modelled 400 m agl wind rose for Hemsby (Nicholson, 2002, pers comm). The Ekman rose was modelled from the observed 1457-3000m asl WDO at Hemsby (1990-96), using h = 80 metres, z0 = 0.0002 metres. Figure D5: The annual nitrogen (oxidised nitrogen) deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and an Ekman modelled 400 m agl wind rose for Hemsby (Nicholson, 2002, pers comm). The Ekman rose was modelled from the observed 1457-3000m asl WDO at Hemsby (1990-96), using h = 80 metres, z0 = 0.0002 metres. Figure D6: The annual ammonia (reduced nitrogen) deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and an Ekman modelled 400 m agl wind rose for Hemsby (Nicholson, 2002, pers comm). The Ekman rose was modelled from the observed 1457-3000m asl WDO at Hemsby (1990-96), using h = 80 metres, z0 = 0.0002 metres. Figure D1: The annual sulphur deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and the new mean UK (1990-96) wind rose (Nicholson, 2002, pers comm). (Note: The differences are calculated as mean UK (1990-96) - Jones (1981), so any positive values indicate an increase in deposition when the new mean wind rose is used. Concentrations are in kg (of S or N) per hectare per year and the resolution is 10km.) Figure D2: The annual nitrogen (oxidised nitrogen) deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and the new mean UK (1990-96) wind rose (Nicholson, 2002, pers comm). (Note: The differences are calculated as mean UK (1990-96) - Jones (1981), so any positive values indicate an increase in deposition when the new mean wind rose is used. Concentrations are in kg (of S or N) per hectare per year and the resolution is 10km.) Figure D3: The annual ammonia (reduced nitrogen) deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and the new mean UK (1990-96) wind rose (Nicholson, 2002, pers comm). ( The differences are calculated as mean UK (1990-96) - Jones (1981), so any positive values indicate an increase in deposition when the new mean wind rose is used. Concentrations are in kg (of S or N) per hectare per year and the resolution is 10km.) Figure D4: The annual sulphur deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and an Ekman modelled 400 m agl wind rose for Hemsby (Nicholson, 2002, pers comm). The Ekman rose was modelled from the observed 1457-3000m asl WDO at Hemsby (1990-96), using h = 80 metres, z0 = 0.0002 metres. (The differences are calculated as Ekman Hemsby(1990-96) - Jones (1981), so any positive values indicate an increase in deposition when the new mean wind rose is used. Concentrations are in kg (of S or N) per hectare per year and the resolution is 10km.) Figure D5: The annual nitrogen (oxidised nitrogen) deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and an Ekman modelled 400 m agl wind rose for Hemsby (Nicholson, 2002, pers comm). The Ekman rose was modelled from the observed 1457-3000m asl WDO at Hemsby (1990-96), using h = 80 metres, z0 = 0.0002 metres. (The differences are calculated as Ekman Hemsby(1990-96) - Jones (1981), so any positive values indicate an increase in deposition when the new mean wind rose is used. Concentrations are in kg (of S or N) per hectare per year and the resolution is 10km.) Figure D6: The annual ammonia (reduced nitrogen) deposition differences between output from the standard HARM 11.5 single-layer model with 1997 emissions and rainfall, for the Jones (1981) wind rose and an Ekman modelled 400 m agl wind rose for Hemsby (Nicholson, 2002, pers comm). The Ekman rose was modelled from the observed 1457-3000m asl WDO at Hemsby (1990-96), using h = 80 metres, z0 = 0.0002 metres. (The differences are calculated as Ekman Hemsby(1990-96) - Jones (1981), so any positive values indicate an increase in deposition when the new mean wind rose is used. Concentrations are in kg (of S or N) per hectare per year and the resolution is 10km.) Appendix E Wind roses and tables Ekman modelled for 400 m agl Wind roses and tables modelled for 400 m above ground level using the coupled Ekman model with various values of surface roughness length, z0, and ‘inner layer height’, h. The data input to the model was the observed geostrophic (1457-3000m asl) WDO for Hemsby for 1990-96. Contents Figure E1: Speed bands 1 to 4 modelled for Hemsby at 400m agl, using h = 80m, z0 = 0.0002m, plotted as individual wind roses. Table E1: A seven year (1990-96) Ekman modelled wind rose for Hemsby at 400m agl, using h = 80m, z0 = 0.0002m. Calculated from the Hemsby 1990-96 (14573000m) observed geostrophic WDO. Figure E2: Speed bands 1 to 4 modelled for Hemsby at 400m agl, using h = 80m, z0 = 0.133m, plotted as individual wind roses. Table E2: A seven year (1990-96) Ekman modelled wind rose for Hemsby at 400m agl, using h = 80m, z0 = 0.133m. Calculated from the Hemsby 1990-96 (1457-3000m) observed geostrophic WDO. Figure E3: Speed bands 1 to 4 modelled for Hemsby at 400m agl, using h = 35m, z0 = 0.0002m, plotted as individual wind roses. Table E3: A seven year (1990-96) Ekman modelled wind rose for Hemsby at 400m agl, using h = 35m, z0 = 0.0002m. Calculated from the Hemsby 1990-96 (14573000m) observed geostrophic WDO. Figure E1: Speed bands 1 to 4 modelled for Hemsby at 400m agl, using h = 80m, z0 = 0.0002m, plotted as individual wind roses. (Note: the Ekman model input data was the observed geostrophic WDO for Hemsby 1990-96. Also north is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table E1: A seven year (1990-96) Ekman modelled wind rose for Hemsby at 400m agl, using h = 80m, z0 = 0.0002m. Calculated from the Hemsby 1990-96 (14573000m) observed geostrophic WDO. Figure E2: Speed bands 1 to 4 modelled for Hemsby at 400m agl, using h = 80m, z0 = 0.133m, plotted as individual wind roses. (Note: the Ekman model input data was the observed geostrophic WDO for Hemsby 1990-96. Also north is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table E2: A seven year (1990-96) Ekman modelled wind rose for Hemsby at 400m agl, using h = 80m, z0 = 0.133m. Calculated from the Hemsby 1990-96 (1457-3000m) observed geostrophic WDO. Figure E3: Speed bands 1 to 4 modelled for Hemsby at 400m agl, using h = 35m, z0 = 0.0002m, plotted as individual wind roses. (Note: the Ekman model input data was the observed geostrophic WDO for Hemsby 1990-96. Also north is at the top, and the axes are annotated with percentage values. The minus signs are a plotting artifact and should be ignored) Table E3: A seven year (1990-96) Ekman modelled wind rose for Hemsby at 400m agl, using h = 35m, z0 = 0.0002m. Calculated from the Hemsby 1990-96 (14573000m) observed geostrophic WDO.