Estimation of Gusty Winds in RCA

Examensarbete vid institutionen för geovetenskaper ISSN 1650-6553 Nr 101

Estimation of gusty winds in RCA

Maria Nordström

Abstract

In this study a new wind gust estimate (WGE) method proposed by Brasseur (2001) is implemented in a limited area climate model (RCA, Rossby Centre regional Atmospheric model). The WGE method assumes that wind gusts develop when air parcels higher up in the boundary layer deflect down to the surface by turbulent eddies. The method also gives an interval of possible gusts by estimating an upper and lower bound of a bounding interval.

Two separate storms (December 3-4, 1999 and January 8-9, 2005) and a three month period (November 1, 2004 - January 31, 2005) are simulated with RCA. The results are compared to direct observations and to gridded analysis (MESAN). The result is highly dependent on how well the meteorological fields are represented in RCA. Since the storm of December 1999 was not well captured by RCA, the wind gusts were consequently not correctly estimated. The storm of January 2005 was well captured by the RCA and the wind gusts relatively well described. Both the storm of January 2005 and the simulation over a three month period give rather good estimated gusts over sea areas, while over land there is an obvious overestimation of the calculated gusts.

A correction to the estimated gust is necessary in order to make the parameterisation useful. Such a correction is tested in this study. It shows significant improvement over most land areas and also gives a certain underestimation in other areas.

Sammanfattning av ”Beräkning av byiga vindar i RCA”

En ny metod (WGE-metoden) för att bestämma byvindar har i den här studien implementerats i en regional klimatmodell (RCA, Rossby Centre regional Atmospheric model). WGE-metoden utgår från att vindbyar genereras när luftpaket högre upp i gränsskiktet förs ner till marken av stora turbulenta virvlar. Ett intervall av möjliga byvindar erhålls genom att en övre och undre gräns för detta intervall beräknas.

Två stormar (3-4 december 1999 och 8-9 januari 2005) och en tremånaders period (1 november 2004 – 31 januari 2005) har simulerats, och resultaten har jämförts med mätdata och MESAN. Resultatet är till stor del beroende av hur väl de meteorologiska fälten representeras av RCA. Stormen i december 1999 simulerades dåligt av RCA, vilket medförde att byvinden inte heller simulerades korrekt. Både stormen januari 2005 och simuleringen över tre månader ger en tämligen korrekt byvind över hav, samtidigt som man över land får kraftiga överskattningar av den beräknade byvinden.

För att byvind-parametriseringen ska vara användbar krävs korrigeringar för att komma till rätta med överskattningen över land. En korrigering testades i den här studien med resultatet att ett förbättrat resultat över land samtidigt leder till en viss underskattning av byvinden i andra områden.

2 Table of contents

1. Introduction...... 4 2. Theory ...... 5 2.1 Wind gusts ...... 5 2.2 Wind gust estimate method...... 5 2.2.1 Gust estimate...... 6 2.2.2 Upper and lower bound of the bounding interval ...... 7 3. Method ...... 9 3.1 RCA ...... 9 3.1.1 A regional climate model...... 9 3.1.2 Physical parameterisations...... 9 3.1.3 Implementation and testing of the WGE method in RCA ...... 10 3.2 MESAN...... 10 3.3 Observational data ...... 11 4. Results ...... 12 4.1 The storm of December 3-4, 1999 ...... 12 4.2 The storm of January 8-9, 2005 ...... 16 4.3 Simulation over a three month period...... 24 4.4 Correction to the estimated wind gust ...... 28 5. Summary and conclusions...... 33 Acknowledgments ...... 34 References...... 35 Appendix...... 37

The photographer of the front page picture is Eva Melakari

3 1. Introduction

Severe storms can cause extensive damage due to the high wind speeds. The strongest wind intensities are caused by wind gusts, which can give a magnitude of 10-15 m/s higher than the mean wind. One example is the storm of January 2005 in southern Sweden where 70 million cubic metres of wood was damaged. The storm caused the death of 9 people and 415,000 household were affected by power failure. During this storm the highest measured gust over land was 33 m/s (in Växjö), while the maximum mean wind speed measured at the same synoptic station was 17 m/s. Warnings may to a certain extent reduce the damages, and it is therefore important to correctly estimate severe wind gusts. Estimating wind gusts is also necessary in mapping the potential use of wind energy as well as for biological processes in the oceans, where the wind causes water mixing.

Brasseur (2001) suggests a new method for estimating wind gusts. Unlike statistical or empirical methods, this method gives an explanation to the physics behind the gusts. This new method of wind gust estimate (WGE) also gives a confidence interval on the predicted value by giving a range of possible gust speeds. The WGE method assumes that wind gusts develop when air parcels higher up in the boundary layer deflects down to the surface by turbulent eddies. This requires that the turbulence kinetic energy is greater than the buoyancy forcing.

The method has been applied by Goyette et al. (2003) to the Canadian regional climate model. Two storms were studied with different model resolutions. The result was fairly realistic and depended on the model resolution. The magnitude and variability of the gusts were not always exactly reproduced, however most of the strengthening and weakening phases were correctly simulated.

In the Rossby Centre regional Atmospheric model (RCA) severe winds are often underestimated, and the mean wind speed over a longer period of time is also underestimated. RCA is a regional climate model developed from the Swedish operational model, HIRLAM (High Resolution Limited Area Model). In this study the WGE method is applied to RCA while studying the storms of December 3-4, 1999 and January 8-9, 2005. The results are compared to MESAN (an Operational Mesoscale Analysis System) and to measured data from synop stations in southern Sweden and one buoy outside of the Swedish west coast. A simulation over a three month period is also analysed and compared to station data and MESAN. Additionally, a test where the parameterisation is tuned to achieve better agreement between estimated wind gusts and observed wind gusts has been performed.

4 2. Theory

2.1 Wind gusts

Wind gusts are defined as sudden, brief increases of the mean wind. The wind gusts have a great variability of intensity and are therefore not easily predicted. Most models use an empirical or statistical method to determine gusts. In one method a constant ratio of maximum gusts to the surface wind speed is being used. This ratio depends mainly on surface roughness, and is smaller over open sea and larger over big cities. Generally, the wind is more gusty over rough land than over open water.

2.2 Wind gust estimate method

A new method for estimating wind gusts is proposed by Brasseur (2001). Unlike empirical and statistical methods this wind gust estimate method gives an explanation to the physics behind the gusts. The WGE method takes under consideration the turbulence kinetic energy, the mean wind and the stability of the boundary layer.

It is assumed that turbulent eddies higher up in the boundary layer cause air parcels to deflect down to the surface as shown in Figure 2.1. When these air parcels with a higher wind speed reach the surface they become gusty winds. The deflection of air parcels is strongly connected to the stability of layers. The vertical component of the turbulent kinetic energy for a given air parcel must be strong enough to counteract the buoyancy forces. This implies that stable layers prevent deflection of air down to the surface while less stable or unstable layers allow deflection of air to the surface.

Figure 2.1 Air at high levels in the boundary layer is deflected down to the surface by large turbulent eddies. (Brasseur, 2001)

WGE also gives a range of possible wind gusts by estimating upper and lower bounds as a possible interval for the estimation. This interval gives an idea about the uncertainty of the estimated gust. The uncertainty can be due to different reasons; If the three-

5 dimensional meteorological fields are not correctly represented it will affect the determination of wind gusts. Furthermore, local variability and the environment near the observational station have a significant impact when comparing estimated gusts with the observed gusts. It is therefore at least as important to determine the bounding interval as it is to accurately estimate the wind gusts.

2.2.1 Gust estimate For an air parcel to deflect down to the surface the mean turbulent kinetic energy (TKE) at a given height must be larger than the buoyant energy between the surface and the height of the air parcel (see Figure 2.2). According to Brasseur (2001) and Burk et al. (2001) this can be described with the following relation:

z z 1 pp∆θ (z) ∫∫E(z)dz ≥ g v dz , (1) z p z′′z Θv (z)

where zp is the height of the air parcel, z´ is a height in the boundary layer below zp (in this study z´ is always 10 meters height), g is gravity, Θv is the virtual potential temperature and ∆θv is the difference of virtual potential temperature over a given layer. The right hand side of (1) is the buoyant energy while E(z) is the turbulent kinetic energy at height z.

Figure 2.2 If the mean TKE at a certain height is stronger then the buoyancy force between the surface and that level the air will deflect down to the surface and create wind gusts. (Brasseur, 2001)

The condition (1) can be fulfilled at several layers in the boundary layer. Therefore the estimated wind gust is the maximum wind speed of all layers satisfying (1):

2 2 Wgestimate = max U (z p ) +V (z p ) , (2)

where zp is every height in the boundary layer satisfying (1). U and V are the two wind components.

Burk et al. (2001) suggests that certain considerations should be taken when computing buoyancy within cloud layers. A modification to equation (1) was proposed for cases with decoupled cloud layers, where there is a stable layer at the cloud base. Brasseur et al.

6 (2002) acknowledge that these modifications give a better description of the physics, although there are no obvious improvements of the result. Therefore these modifications to the WGE method have not been included in this study.

2.2.2 Upper and lower bound of the bounding interval When estimating the lower bound it is assumed that the variance of vertical velocity is the mechanism that cause air parcels to deflect down to the surface as shown in Figure 2.3. In this case air parcels that satisfy the following relation will be deflected down to the surface:

z w′w′(z) plow ∆θ (z) ≥ g ∫ v dz , (3) 2 z′ Θv (z) where w′w′ is the variance of the vertical wind component. Since the vertical variance is not computed when using 1.5 order closure, it can be determined by the diagnostic equation (Stull, 1988):

w′w′ 2.5 = E(z) (4) 2 11

The lower bound is determined by the maximum wind speed among layers where air parcels satisfy (3):

Wg = max U 2 (z ) +V 2 (z ) , (5) lower plow plow where z is every height in the boundary layer satisfying (3). plow

Figure 2.3 The mechanism of the lower bound. The variance of vertical wind velocity causes air to deflect down to the surface. (Brasseur, 2001)

The estimated gust is always greater than the lower bound, i.e. the mean turbulent energy below a given layer is higher than the local vertical turbulent energy at this layer. When the boundary layer is nearly neutral or stable, the shear is the main production term of turbulence, and the turbulent kinetic energy decreases nearly linearly with height

7 (Brasseur, 1998). This mechanism makes certain that the local turbulent energy is always less than the mean turbulent energy below a certain level. When the boundary layer is unstable, there is a maximum of turbulent kinetic energy in the lowest part of the boundary layer (Brasseur, 1998). It is unlikely that the lower bound is larger than the estimated gust below the maximum of turbulent kinetic energy. Furthermore, according to the principles of the WGE method, air parcels responsible for stronger gust in an unstable atmosphere are deflected from nearly the top of the boundary layer. Because it is mainly the upper boundary layer that is concerned in this case, the estimated gust must be larger than the lower bound.

The boundary layer is the only part in the atmosphere where air parcels can be deflected down to the ground by turbulent eddies. The free atmosphere above the boundary layer has very weak turbulent motions. Therefore the upper bound, Wgupper, is the maximum wind speed in the boundary layer:

Wg = max U 2 (z ) +V 2 (z ) , (6) upper pup pup

where z ≤ z and ztop is the boundary layer height. pup top

Because the upper bound is the maximum wind speed in the boundary layer, the upper bound is naturally always larger than or equal to the estimated gust.

8 3. Method

In this study the equations for the WGE method, as described in the previous section, has been implemented and simulated in RCA. The result from the simulation has been evaluated and compared to MESAN and measured data from eight synoptic stations and one buoy. This chapter will give a brief description of RCA, MESAN and observational data.

3.1 RCA

3.1.1 A regional climate model Global climate scenarios are generated by general circulation models (GCMs). Only a coarse spatial resolution is used in the GCMs due to the global scale and long time integrations. The coarse resolution causes significant limitations in the interpretation of the effect on regional and local scales. Regionalization techniques are used to add important details to the large-scale global climate results. One of these techniques is dynamic downscaling (Rummukainen et al., 2001). Dynamic downscaling involves the use of regional climate models (RCM) with time dependent boundary conditions taken from GCM results.

The Rossby Centre regional Atmospheric Model (RCA) is a regional climate model developed for climate studies with focus on northern Europe. RCA was a key tool in the Swedish regional Climate Modelling programme, SWECLIM, whose purpose was to provide regional interpretation of global climate or climate change (Rummukainen et al., 2001). The work initiated in SWECLIM does now continue at Rossby Centre, SMHI. RCA is developed from the Swedish operational model, HIRLAM (High Resolution Limited Area Model). Changes in the HIRLAM parameterizations have been done as this is necessary for climate integrations (Rummukainen et al., 2001; Jones et al., 2004).

3.1.2 Physical parameterisations In all atmospheric models physical parameterisations are used to describe processes not included in the governing equations resolved by the model. The parameterisations are necessary in order to describe sub-grid processes such as radiation, rain, clouds and surface processes.

Parameterisations are required to realistically describe the planetary boundary layer (PBL). Formation of air masses, profiles of the wind, temperature and humidity in the lower atmosphere, boundary layer clouds, forecast of 2 meter parameters, fog and dew/frost formation depend on a proper formulation of the PBL scheme. The turbulence scheme used in RCA is a 1.5 order closure and based on the CBR scheme (Cuxart et al., 2000) which gives a prognostic turbulent kinetic energy (TKE) combined with a length scale. The scheme is therefore called a TKE-l scheme (Undén et al. 2002). Turbulent fluxes are computed with the turbulence scheme. This gives an eddy diffusion term for

9 the tendencies. This diffusion term is a combination of turbulent kinetic energy and a diagnostic length scale. The length scale combines length scales for stable and unstable conditions. Additionally, the length scale includes a term to enable a smooth transition between stable and unstable conditions (Undén et al., 2002).

The boundary layer height is expressed in terms of a bulk Richardson number, which is modified to include the influence of mixing generated both by shear and surface heating (Troen et al., 1986). The daytime mixed layer, as well as cases of weak surface heat flux and transitions between stable and unstable cases are approximated with this scheme. The scheme does not require a high resolution in the boundary layer, and the capping inversions, when it exists, do not have to be captured by the model.

3.1.3 Implementation and testing of the WGE method in RCA

The model version of RCA used in this study is RCA3. There are 24 vertical levels, with the lowest model level at about 90 meters height, and the horizontal resolution is 22 km.

The WGE method has been included into RCA3 as a new subroutine. The 10 meter mean wind, as calculated in the surface flux subroutines of RCA has been used as a lower limit for the estimated gusts and the lower bound. Consequently the 10 meter mean wind is used when the equations (1) and (3) are not fulfilled at any model level. All simulations are performed with European Centre for Medium Range Weather Forecasting (ECMWF) 40 years reanalysis data (ERA40) on the lateral boundaries of RCA.

The Fortran code of the wind gust subroutine is included in the appendix.

3.2 MESAN

MESAN is an operational mesoscale analysis system developed at SMHI (Häggmark et al., 2000). MESAN uses all available data (Synop stations, radar data and satellites) together with a numerical model as a background field to generate the best possible gridded data, based on meteorological information. The interpolation method used in MESAN is an optimal interpolation technique, (Häggmark et al., 2000). The background field is also called the first guess and is for MESAN a three or six hour forecast from the Swedish operational model, HIRLAM.

Examples of parameters produced by MESAN are the 2-meters temperature and humidity, precipitation, visibility, clouds and wind at 10 meters. For analysis of the wind, observations together with the 10 m wind from Hirlam are used. The measured wind is from automatic stations and manual observations at 10 meters or reduced to the 10 meters level (Häggmark et al., 2000).

In this study data from MESAN with a horizontal resolution of 22 km is used to compare with the results from the simulations in RCA.

10 3.3 Observational data

The observational data used in this study are eight Swedish synoptic stations and one buoy. The location of the stations can be seen in Figure 3.1.

59.5

59 Landsort Norrköping 58.5 Gotska Måseskär Sandön 58 Fårösund 57.5 Läsö 57 Växjö Latitude 56.5 Helsingborg 56 Hanö 55.5

54.5

8 10 12 14 16 18 20 Longitude

Figure 3.1 Locations of the observational stations

The buoy, Läsö, gives hourly wind data measured at 4 meters height. The measured mean wind is the mean wind over the last 10 minute period, and the measured wind gust is the maximum 2 second mean wind over the last 10 minute period.

The synop stations give wind data at 10-meters. The measured mean wind is the maximum 10 minute mean wind over the last 3 hours, and the measured wind gust is the maximum 2 second mean wind over the last 10 minute period.

11 4. Results

Two storms over southern Scandinavia, one in December 1999 and one in January 2005 have been studied using the wind gust estimate method. The storm in January 2005 has been evaluated and compared to both MESAN and data from separate synoptic stations. For the storm in December 1999 only MESAN has been compared to the result from the simulation. A simulation over a three month period has also been evaluated stretching from November 2004 to January 2005, and the result was compared to MESAN and observational data.

4.1 The storm of December 3-4, 1999

The storm of December 3-4, 1999 passed over Denmark and southern Sweden. Even though the location of the storm was fairly correct, the magnitude was not satisfyingly simulated by RCA. According to MESAN the pressure during the culmination of the storm was as low as 952 hPa while in RCA the pressure was not lower than 973 hPa. The pressure field for MESAN and RCA 18Z December 3 can be seen in Figure 4.1. Since the pressure gradient was not correctly represented in RCA the maximum 10 meter mean wind during the storm was also underestimated by RCA, in some areas by as much as 10 m/s (See Figure 4.2).

The reason why the storm December 3-4, 1999 is not easy to simulate is because of its very small horizontal scale. A realistic simulation of the storm is therefore highly dependent on correct initial data. Because the storm was not well captured by RCA, the estimated wind gust can not be expected to be accurate. Figure 4.3 illustrates the maximum wind gust for each grid point during the storm, from 12Z December 3 to 12Z December 4. The wind gusts in RCA did not reach the magnitude of the strongest wind gusts in MESAN during this period. Not only are RCA unable to reproduce the high wind speeds during the storm, the location for maximum wind speed is also inaccurate. Looking at the upper bound, it is obvious that the maximum wind speeds of MESAN are not reached at any height in the boundary layer in RCA due to the poor simulation of the storm.

In Figure 4.4 the difference of the maximum wind gusts between RCA and MESAN are illustrated. The wind gusts in RCA are, as expected, underestimated where MESAN has the strongest winds over northern Denmark. The difference between RCA and MESAN in this area is almost 30 m/s. Looking at Figure 4.4 it is evident that RCA overestimates wind gusts somewhat over land areas in northern Germany and Poland.

Figure 4.5 illustrates time series for Måseskär and Norrköping, whose locations can be seen in Figure 3.1. Måseskär is located near the centre of the storm on the west coast of Sweden. RCA seriously underestimates the wind gust here, and MESAN gusts are higher than the upper bound almost during the entire period. The 10 meter mean wind is also strongly underestimated by RCA. Norrköping is situated further east outside the centre of the storm. Here the estimated wind gust is simulated quite well, and the MESAN gusts

12 mostly fall within the bounding interval. Also the 10 meter mean wind is mostly correct simulated. Even though the wind gust is correctly estimated at Norrköping, this is of less importance since the intensities of wind speed is weak. It is mainly the strong intensities of wind speed that is of interest when estimating gusts.

First of all this case illustrate the importance of well captured synoptic situation by the model to be successful in gust estimations as also concluded by Ágústsson and Ólafsson (2005).

Mesan RCA

1020 1010 1000 990 980 970 960

Figure 4.1 Pressure field 18Z December 3, 1999 in MESAN and RCA. Unit is hPa.

MESAN 10 m mean wind RCA 10 m mean wind

Figure 4.2 The maximum 10 meter mean wind for each grid point during the period 12Z December 3 – 12Z December 4, 1999. Unit is m/s.

13 MESAN wind gust RCA gust estimate

RCA lower bound RCA upper bound

Figure 4.3 Maximum values of MESAN wind gust, RCA gust estimate, lower and upper bound for each grid point during the period 12Z December 3 – 12Z December 4, 1999. Unit is m/s.

14 RCA gust estimate − Mesan gust RCA lower bound − Mesan gust 40

−20

−40

RCA upper bound − Mesan gust

Figure 4.4 The difference (RCA minus MESAN) between the maximum values of wind gust in RCA and MESAN during the period 12Z December 3 – 12Z December 4, 1999. Unit is m/s.

15 Måseskär Norrköping 40 40

35 35

30 30

25 25

20 20

wind gust (m/s) 15 15

10 10

5 5

0 0 12:00 18:00 00:00 06:00 12:00 12:00 18:00 00:00 06:00 12:00

Måseskär Norrköping 18 18

16 16

14 14

12 12

10 10

8 8

6 6 10 m mean wind (m/s)

4 4

2 2

0 0 12:00 18:00 00:00 06:00 12:00 12:00 18:00 00:00 06:00 12:00

Figure 4.5 Time series of wind speeds at Måseskär and Norrköping during the storm (12Z December 3 – 12Z December 4). The upper figures show wind gust estimate (plus signs), MESAN gust (asterisk), the bounding interval (shaded area), upper and lower bound (solid lines). The lower figures show the 10 m mean wind of RCA (solid line) and MESAN (dotted line). The location of the stations can be seen in Figure 3.1.

4.2 The storm of January 8-9, 2005

The storm of January 8-9, 2005 was quite accurately simulated by the RCA. The centre of the storm was located in the middle of Scandinavia. Denmark and southern Sweden was strongest affected by the storm. The strongest wind gust of 42 m/s was measured at Hanö, and the maximum 10 meter mean wind at the same synoptic station was 33 m/s.

The pressure field 21Z January 8, 2005 for RCA and MESAN can be seen in Figure 4.6. In MESAN the lowest pressure at this time was 961 hPa and in RCA it was 962 hPa. The magnitude as well as the location of the low pressure was well simulated. The agreement in pressure fields between MESAN and RCA makes this case a good one for validation of the WGE method, in contrast to the 1999 storm. Furthermore, the 10 meter mean wind was well represented in RCA compared to MESAN as illustrated in Figure 4.7, even though the highest magnitudes was not accurately captured by RCA.

Pressure field MESAN Pressure field RCA

1030 1020 1010 1000 990 980 970

Figure 4.6 Pressure field 21Z January 8 in MESAN and RCA. Unit is hPa.

MESAN 10m mean wind RCA 10m mean wind

Figure 4.7 The maximum 10 meter mean wind for each grid point during the period 12Z January 8 – 12Z January 9, 2005. Unit is m/s.

Figure 4.8 illustrates the same parameters as Figure 4.3 but for the storm of January 8-9, 2005. The highest gust speeds in MESAN are here captured well by RCA even though the locations of the maximum gusts are not completely accurate. The difference between the maximum wind gust in RCA and MESAN can be seen in Figure 4.9. It is obvious that there is a very large difference between MESAN and RCA over land, where RCA overestimates the estimated gusts by as much as 25 m/s in some areas. This problem will be further discussed in section 4.4.

17 MESAN wind gust RCA wind gust estimate

RCA lower bound RCA upper bound

Figure 4.8 Maximum values of MESAN wind gust, RCA gust estimate, lower and upper bound for each grid point during the period 12Z January 8 – 12Z January 9, 2005. Unit is m/s.

Figure 4.10 illustrates time series of wind speed for four synoptic stations. For Hanö the 10 meter mean wind during the storm was underestimated compared to observations and the MESAN analysis. At 21Z on January 8 the difference between RCA and the observed value was 20 m/s, and between RCA and MESAN almost 10 m/s. Although the 10 meter mean wind was not well represented in RCA, the estimated gust was rather well simulated. The strongest wind gusts were not quite captured though. For Måseskär the 10 meter mean wind was somewhat better represented, but still significantly underestimated. The wind gust is also more accurately estimated for Måseskär.

It is interesting to look at the difference between Norrköping and Gotska Sandön (Figure 4.10). For both Norrköping and Gotska Sandön the 10 meter mean wind is very well represented in RCA, but the two stations differ in how good the estimated wind gusts are simulated. The wind gusts are strongly overestimated in Norrköping during the storm. This is obvious at 21Z on January 8 when the estimated wind gust is 40 m/s while the

18 observed and MESAN gust is about 18 m/s. Norrköping is an example of the overestimation of wind gusts in RCA over land areas seen in Figure 4.9. The agreement between simulated wind gusts by RCA and measurement at the synoptic station Gotska Sandön, located over sea, is very good.

For the estimated gusts there is a slight displacement in time at all of the four stations in Figure 4.10. The maximum gusts during the storm are reached somewhat earlier in RCA than in MESAN. This is most obvious for Norrköping. A time difference between the simulated and the observed pressure field, or a too fast growth of the simulated boundary layer depth can be the cause of the displacement in time (Brasseur, 2001). Since the pressure in this case was fairly well simulated in time, shortage in estimation of the boundary layer growth should be the reason of the time displacement.

RCA gust estimate − MESAN gust RCA lower bound − Mesan gust

−10

−20

RCA upper bound − Mesan gust

Figure 4.9 The difference (RCA minus MESAN) between the maximum values of wind gust in RCA and MESAN during the period 12Z January 8 – 12Z January 9, 2005. Unit is m/s.

19 Hanö Måseskär 45 45

40 40

35 35

30 30

25 25

Wind gust (m/s) 20 20

15 15

10 10 (a) (b) 5 5 12:00 18:00 00:00 06:00 12:00 12:00 18:00 00:00 06:00 12:00

Hanö Måseskär 35 35

30 30

25 25

20 20

15 15 10 m mean wind (m/s) 10 10

5 5 (c) (d) 0 0 12:00 18:00 00:00 06:00 12:00 12:00 18:00 00:00 06:00 12:00

Måseskär Gotska Sandön 45 45

40 40

35 35

30 30

25 25

Wind gust (m/s) 20 20

15 15

10 10 (b) (f) 5 5 12:00 18:00 00:00 06:00 12:00 12:00 18:00 00:00 06:00 12:00

20 Norrköping Gotska Sandön 35 35

30 30

25 25

20 20

15 15 10 m mean wind (m/s) 10 10

5 5

(g) (h) 0 0 12:00 18:00 00:00 06:00 12:00 12:00 18:00 00:00 06:00 12:00

Figure 4.10 Time series of Måseskär and Norrköping during the storm (12Z January 8 – 12Z January 9). The figures (a), (b), (e) and (f) show wind gust estimate (plus signs), observed gust (dots), MESAN gust (asterisk), the bounding interval (shaded area), upper and lower bound (solid lines). The figures (c), (d), (g) and (h) show the 10 m mean wind of RCA (solid line), observations (dash-dotted line) and MESAN (dotted line). The location of the stations can be seen in Figure 3.1.

Table I shows maximum values of wind gust estimate, upper and lower bound, observational data and MESAN wind gust during the storm for 9 synoptic stations. The root mean square (RMS) error and the correlation coefficients (r0) for the storm are also shown. The stations with the largest RMS error, when estimated wind gusts are compared to observations and MESAN, are those located over land, i.e. Växjö, Norrköping and Helsingborg. The correlation coefficients are rather high, except for Norrköping where the coefficients are 0.70 and 0.76 when the estimated gust is compared to observations and MESAN respectively. The poor correlation coefficient at Norrköping can be explained by the displacement in time as seen in Figure 4.10e. For synoptic stations located over sea the RMS error are lower and the correlation coefficients are generally higher. For these stations located over sea the RMS errors are about 3-5 m/s and the correlations coefficients about 0.90.

Table II illustrates the same as table I but for the mean 10 meter wind. It is clear that the RMS errors for the 10 meter mean wind are lower and the correlation coefficients are generally higher when RCA are compared with MESAN than compared with observations. Växjö, Norrköping and Helsingborg have the lowest RMS errors for the 10 meter mean wind.

It may be misleading for a validation of the WGE method to study individual stations if the path of the storm is not correctly represented in RCA, which is probably an important reason why the wind gusts are under- or overestimated. A displacement in time will also cause incorrect results. Studying frequency plots over a given area, which includes maximum wind speeds in both RCA and MESAN, gives a more correct illustration when comparing the magnitudes of gusts. The frequency plots show the percentage of occasions of wind speeds in certain wind speed intervals for a period of time over a given area with respect to the total number of wind samples.

21 Table I. Maximum values during the storm for wind gust estimate, lower bound, upper bound, observed gust (Obs) and analyzed gust in MESAN. The last columns are the RMS error between wind gust estimate and observed gust (Obs)/MESAN gust, and the correlation coefficient. Station Gust Lower Upper Obs MESAN Obs MESAN estimate bound bound RMS r0 RMS r0 error error Läsö 33.8 27.9 38.3 34.2 41.1 4.9 0.89 4.0 0.82 Hanö 37.5 26.4 38.8 42.4 42.2 5.0 0.85 4.9 0.85 Växjö 37.0 25.7 39.6 32.6 31.0 9.9 0.83 8.7 0.87 Norrköping 40.3 30.2 40.7 26.8 28.1 13.0 0.70 11.7 0.76 Helsingborg 38.2 30.4 39.5 34.0 33.1 6.6 0.84 6.4 0.84 Måseskär 38.1 34.4 38.5 37.9 38.5 2.8 0.87 3.0 0.87 Landsort 40.2 27.3 40.7 36.3 35.6 4.1 0.92 5.1 0.90 Fårösund 38.9 28.0 39.8 34.5 36.9 5.8 0.95 4.1 0.94 Gotska 38.8 29.4 40.2 36.0 37.1 4.5 0.80 3.4 0.87 Sandön

Table II. Maximum 10 m mean wind during the storm for RCA, observed value (Obs) and MESAN. The two last columns give the RMS error between RCA and observed (Obs)/MESAN, and the correlation coefficient. Station RCA Obs MESAN Obs MESAN

RMS r0 RMS r0 error error Läsö 20.9 22.1 26.6 3.0 0.74 3.7 0.92 Hanö 15.2 32.9 23.6 14.4 0.78 6.0 0.90 Växjö 11.7 17.1 15.5 3.9 0.74 2.3 0.95 Norrköping 12.3 13.8 14.4 2.2 0.59 1.5 0.91 Helsingborg 14.1 20.2 17.7 4.4 0.86 3.0 0.94 Måseskär 19.5 29.2 27.9 9.0 0.78 6.6 0.98 Landsort 14.3 26.6 21.9 9.4 0.80 5.1 0.94 Fårösund 13.6 24.5 21.1 7.8 0.91 5.1 0.95 Gotska 20.4 23.0 23.7 3.0 0.91 3.9 0.88 Sandön

The selected area for the frequency plots is shown in Figure 4.11. Since the land sea contrast of wind speeds seen in MESAN does not show up in RCA, the frequency distributions are shown separately for land and sea over the chosen area as illustrated in Figures 4.12 and 4.13. Looking at Figure 4.12 it is clear that wind gusts in RCA are overrepresented for higher wind speeds over land. Only a few percentages of the land points during the period have a wind gust of 30 m/s or more in MESAN, while for RCA around 45% reach the same wind speeds. Over sea the wind gust is well simulated compared to MESAN as can be seen in Figure 4.13. Both figures show that MESAN data is mainly within the bounding interval. The 10 meter mean wind is shown to be quite good represented by RCA, but with a slight underestimation.

22 62

58 Latitude

52 5 10 15 20 25 Longitude

Figure 4.11 Selected area for the frequency plots.

frequence (%) 20

0 0−5 5−10 10−15 15−20 20−25 25−30 30−35 35−40 40−45 45−50 wind gust (m/s) RCA gust estimate RCA upper bound RCA lower bound RCA 10m mean wind MESAN wind gust MESAN 10m mean wind

Figure 4.12 Frequency plot of land points for the storm of January 8-9, 2005. The area can be seen in Figure 4.11.

23 40

20 frequence (%)

0 0−5 5−10 10−15 15−20 20−25 25−30 30−35 35−40 40−45 45−50 wind gust (m/s) RCA gust estimate RCA upper bound RCA lower bound RCA 10m mean wind MESAN wind gust MESAN 10m mean wind

Figure 4.13 Frequency plot of sea points for the storm of January 8-9, 2005. The area can be seen in Figure 4.11.

4.3 Simulation over a three month period

A simulation for a three month period has been performed. The period extends from November 1, 2004 to January 31, 2005, thus including the storm of January 8-9. As shown in Figure 4.14 most of MESAN gusts and observed gusts are within, or at least close to, the bounding interval. Figure 4.14 shows daily maximum values of estimated gust, observed gust, MESAN gust and upper and lower bound of the bounding interval. There is a difference of stations situated over land and sea. At Norrköping and Växjö, both situated over land, the gusts are better captured within the bounding interval than Hanö and Måseskär that are situated over sea. However, the estimated gusts have more accurately captured the magnitude of the gusts for the stations over sea.

Figure 4.15 shows scatter plots of estimated gusts and MESAN gusts. According to these figures there is a tendency that the intensity of estimated wind gusts in RCA are underestimated over sea areas, as for the stations Hanö and Måseskär. As in the previous results from the two storms, it is also here clear that the gusts estimated by RCA are overestimated over land (Figure 4.15 c and d). This is especially true for the gusts with high intensity.

Figures 4.16 and 4.17 illustrate frequency plots for the three month period. The figures show that the 10 meter mean wind is rather well represented in RCA compared to MESAN. In Figure 4.16 it is again clear that the estimated wind gusts with a high magnitude is overestimated over land. However, here it is not as obvious as for the storm

24 January 8-9, 2005, which is natural since the time interval is longer and the storm situation not as dominating.

45 (a) Hanö 40

wind gust (m/s) 15

0 01/11/04 16/11/04 01/12/04 16/12/04 31/12/04 15/01/05 30/01/05 45 (b) Måseskär 40

wind gust (m/s) 15

0 01/11/04 16/11/04 01/12/04 16/12/04 31/12/04 15/01/05 30/01/05 45 (c) Norrköping 40

wind gust (m/s) 15

0 01/11/04 16/11/04 01/12/04 16/12/04 31/12/04 15/01/05 30/01/05

25 45 (d) Växjö 40

wind gust (m/s) 15

0 01/11/04 16/11/04 01/12/04 16/12/04 31/12/04 15/01/05 30/01/05

Figure 4.14 Time series of four synoptic stations. The figures show daily max of wind gust estimate (plus signs), observed gust (dots), MESAN gust (asterisk), the bounding interval (shaded area), upper and lower bound (solid lines).

Hanö Måseskär 45 45 (a) (b) 40 40

35 35

30 30

25 25

20 20

15 15 Mesan wind gust (m/s) Mesan wind gust (m/s)

10 10

5 5

0 0 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 RCA wind gust estimate (m/s) RCA wind gust estimate (m/s)

Norrköping Växjö 45 45 (c) (d) 40 40

35 35

30 30

25 25

20 20

15 15 Mesan wind gust (m/s) Mesan wind gust (m/s)

10 10

5 5

0 0 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 RCA wind gust estimate (m/s) RCA wind gust estimate (m/s)

26 Figure 4.15 Scatter plots of the same stations as in Figure 4.14 of the three month simulation. The figures show the estimated gust on the x-axis and MESAN gust on the y-axis.

20 frequence (%)

0 0−5 5−10 10−15 15−20 20−25 25−30 30−35 35−40 40−45 45−50 wind (m/s) RCA gust estimate RCA upper bound RCA lower bound RCA 10m mean wind MESAN wind gust MESAN 10m mean wind

Figure 4.16 Frequency plot for a three month period, Nov 2004 - Jan 2005, of land points. The area can be seen in Figure 4.11

15 frequence (%) 10

0 0−5 5−10 10−15 15−20 20−25 25−30 30−35 35−40 40−45 45−50 wind (m/s) RCA gust estimate RCA upper bound RCA lower bound RCA 10m mean wind MESAN wind gust MESAN 10m mean wind

Figure 4.17 Frequency plot for a three month period, Nov 2004 - Jan 2005, of sea points. The area can be seen in Figure 4.11

27 4.4 Correction to the estimated wind gust

The results in the previous sections show an evident overestimation of wind gusts over land especially during storms. These are also the situations, when the estimated gust is of the largest interest. In order to make the WGE method operational it is necessary to make corrections to overcome this problem. The correction made in this study is not a physical explanation of the damping of wind gusts at high surface roughness, but it is rather an empirical tuning of the simulated results toward the observations.

The idea of the correction tested in this study is that the wind deflected down to the ground from higher levels in the boundary layer is slowed down when approaching the surface layer due to surface roughness. In the WGE method air parcels are deflected down by turbulent eddies from higher levels. The wind speed of those air parcels reach the surface unmodified. With this correction, it is assumed that air parcels are deflected down from higher levels, but are modified between the top of the surface layer and down to the surface. As the air parcel with initial wind speed (u2) reaches the top of the surface layer (z2), its speed is modified to the new wind speed (u1) near the surface, (z1).

In neutral conditions, the wind speed varies with height according to the logarithmic wind law:

u z u = * ln , (7) k z0

where u is the wind speed at height z, u* is the friction velocity, k is von Karman’s constant and z0 is the roughness of the surface.

The assumption made, is that the wind gust follows the logarithmic wind law between the top of the surface layer and the surface. This is not completely true, and thus an empirical constant is also added.

Dividing u1 with u2, using the logarithmic wind law, in order to derive u1:

z ln 1 u1 z0 ⎡ ⎛ z1 ⎞ ⎛ z2 ⎞⎤ = ⇔ u1 = u2 ⎢ln⎜ ⎟ / ln⎜ ⎟⎥ (8) u z ⎜ z ⎟ ⎜ z ⎟ 2 ln 2 ⎣ ⎝ 0 ⎠ ⎝ 0 ⎠⎦ z0

where u1 is the wind speed at 10 meters height, u2 is the wind speed deflected down from a higher level, z1 is 10 meter and z2 is the height of the surface layer estimated as 10% of the simulated diagnostic PBL height.

28 The constant, α, is added to equation (8) to get the wind gust at 10 meters height:

⎡ ⎛ z ⎞ ⎛ z ⎞⎤ ⎜ 1 ⎟ ⎜ 2 ⎟ u1 = u2 ⎢ln⎜ ⎟ / ln⎜ ⎟⎥ ⋅α (9) ⎣ ⎝ z0 ⎠ ⎝ z0 ⎠⎦

When the correction is added to the estimated wind gust, the result is significantly improved over land. Unfortunately, while the result in most land areas is improved, there is an underestimation of gusts in southern Sweden and northern Denmark. For a smaller value of α, the overestimation is smaller and the underestimation is larger. This is illustrated in Figure 4.19 for the storm of January 2005. Figure 4.19 shows the estimated wind gust for different α, and the difference between this new gust estimation and MESAN gust. For comparison with the original wind gust estimate see Figures 4.8 and 4.9.

The best correction to the estimated gusts can be consider to be given by α=1.4 or α=1.3. For the following tests α=1.4 is used. Figures 4.20 and 4.21 illustrate frequency plots for the estimated gusts when applying the correction along with MESAN gusts and the original gust estimate during the storm of January 2005. The correction gives a clear improvement over land areas, as shown in Figure 4.20. For sea areas (Figure 4.21) there is a higher intensity of the estimated wind gusts when the correction is added.

The correction has also been tested for the three month period (Nov 2004-January 2005). Looking at the scatter plots in Figure 4.22 it is again evident that there is an obvious improvement over land areas (Figure 4.22 c and d). For the station Hanö (Figure 4.22a), there is no significant difference when the correction is added, and for Måseskär (Figure 4.22b) there is a slight tendency of more underestimated gusts.

29 RCA gust estimate, alfa=1.5 RCA gust estimate − Mesan gust, alfa=1.5

40 20

30 10

0 20

−10 10 −20

RCA gust estimate, alfa=1.4 RCA gust estimate − Mesan gust, alfa=1.4

40 20

30 10

0 20

−10 10 −20

RCA gust estimate, alfa=1.3 RCA gust estimate − Mesan gust, alfa=1.3

40 20

30 10

0 20

−10 10 −20

Figure 4.19 The left hand figures show estimated maximum wind gust during the storm of January 8-9, 2005 with the correction for different α. The difference from MESAN gust is shown in the right hand side figures. This can be compared to uncorrected estimated gust in Figures 4.8 and 4.9.

30 60

frequence (%) 20

0 0−5 5−10 10−15 15−20 20−25 25−30 30−35 35−40 40−45 45−50 wind (m/s) RCA gust estimate RCA gust estimate, alfa=1.4 MESAN wind gust

Figure 4.20 Frequency plot of land points for the storm of January 8-9, 2005. The area can be seen in Figure 4.11. The figure shows the original wind gust estimated by RCA and the estimated gust with the correction α =1.4. MESAN gust is also illustrated.

20 frequence (%)

0 0−5 5−10 10−15 15−20 20−25 25−30 30−35 35−40 40−45 45−50 wind (m/s) RCA gust estimate RCA gust estimate, alfa=1.4 MESAN wind gust

Figure 4.21 Frequency plot of sea points for the storm of January 8-9, 2005. The area can be seen in Figure 4.11. The figure shows the original wind gust estimated by RCA and the estimated gust with the correction α =1.4. MESAN gust is also illustrated.

31 Hanö Måseskär 45 45 (a) (b) 40 40

35 35

30 30

25 25

20 20

15 15 Mesan wind gust (m/s) Mesan wind gust (m/s)

10 10

5 5

0 0 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 RCA wind gust estimate (m/s) RCA wind gust estimate (m/s)

Norrköping Växjö 45 45 (c) (d) 40 40

35 35

30 30

25 25

20 20

15 15 Mesan wind gust (m/s) Mesan wind gust (m/s)

10 10

5 5

0 0 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 RCA wind gust estimate (m/s) RCA wind gust estimate (m/s) Figure 4.22 Scatter plots of the three month simulation. The figures show the estimated gust on the x-axis and MESAN gust on the y-axis. The wind gust estimated by RCA is corrected with α =1.4. The figure can be compared to Figure 4.15.

32 5. Summary and conclusions

The wind gust estimate (WGE) method proposed by Brasseur (2001) has been used in this study with somewhat varying results. It is clear that the accuracy of the meteorological fields is of crucial importance when estimating wind gusts (Ágústsson and Ólafsson, 2005). This problem is clearly illustrated for the storm of December 3-4, 1999, which was not well simulated in RCA, and hence the extreme wind speeds of 50-60 m/s was not captured by the WGE method. Areas not highly affected by the storm gave quite a good accuracy of estimated wind gusts. These areas have a rather weak intensity of gusts and are of less importance, since it is mainly the higher wind speeds that are of interest when estimating gusts.

The storm of January 8-9, 2005 is more accurately represented in RCA, and is therefore a better storm situation to evaluate when investigating the WGE method. When studying this storm it is obvious that the estimated gusts are clearly overestimated over land areas, but rather well described over the sea. The RMS errors of the hourly gusts during the storm of 2005 are about 3-5 m/s for synop stations located over sea. A similar result can be seen in Brasseur (2001), where the RMS error is about 5 m/s. However, over land areas the RMS errors in this study are about 7-13 m/s.

Also for the three month period there is a good agreement of gusts between RCA and MESAN for stations over sea. Generally, the bounding interval, with upper and lower bound, gives a rather good interval of gusts. For high intensities of gusts there is also here an evident overestimation of gusts over land areas.

The WGE method takes into account the turbulent kinetic energy (TKE), the mean wind and stability of layers. The results in this study, with overestimation of gusts over land areas, imply that the physic behind wind gusts is somewhat more complicated. Because the overestimation is over land areas, it indicates that the roughness should be of importance. According to Brasseur (2001) the roughness length has a very little impact when estimating wind gusts, since it only modifies TKE and the mean wind near the surface. It is instead suggested that overestimations are due to too intense mixing in the boundary layer. However, research by Högström et al. (2002) shows that large scale eddies from higher up in the boundary layer are distorted by local shear when reaching the surface layer. This implies that wind high up in the boundary layer do not reach the surface unmodified as suggested in the WGE method.

A correction to the estimated gust is suggested in this study to make it more functional. With this correction, the wind deflected down by large scale eddies is slowed down through the surface layer. The result gives an improvement of wind gusts over most of the land areas, whereas there is an underestimation of gusts in southern Sweden and northern Denmark. Even though this correction does not give fully agreement with observational data it clearly acts to reduce wind gusts over land, which was the desired effect. However, before final implementing the WGE method in RCA more careful investigations of the reason for the presented overestimation over land and more tests with storm situations are required.

33 Acknowledgments

First of all I would like to thank my supervisors Patrick Samuelsson and Anna Rutgersson-Owenius for all the valuable help and support during this time. I would also like to thank Barry Broman and Hans Alexandersson for help with observational data, and Anders Ullerstig for help with MESAN-files. Furthermore, I would like to thank Lars Bärring and Stéphane Goyette for useful comments to the result. I would also like to thank Ulf Högström for interesting point of views. For the nice front page picture, I would like to thank Eva Melakari.

I am especially grateful to Mikael Norman for all the love and support. Thanks also to Lisa Frost and Ulrika Hansson for letting me stay at a very nice “hotel” during my weeks in Norrköping.

Finally, I would like to thank the staff at MIUU and my follow students for a memorable time at Uppsala University.

34 References

Ágústsson, H. and Ólafsson, H., 2005: Wind Gust Forecasting in Iceland with the Method of Brasseur, Geophysical Research Abstracts, 7, 10035.

Brasseur, O., Gallé, H., Schayes, G., Tricot, C. and De Ridder, K., 1998: Impact of turbulent closures on diurnal temperature evolution for clear sky situations over Belgium, Boundary-Layer Meteorology, 87, 163-193.

Brasseur, O., 2001: Development and Application of a Physical Approach to Estimating Wind Gusts, Monthly Weather Review, 129, 5-25

Brasseur, O., Gallée, H., Boyen, H. and Tricot, B., 2002: Reply, Monthly Weather Review, 130, 1936-1942.

Burk, S. D., and Thompson W.T., 2002: Comments on “Development and application of a physical approach to estimating wind gusts”, Monthly weather review, 130, 1933-1935.

Cuxart, J., Bougeault, P. and Redelsperger, J.-L., 2000: A turbulence scheme allowing for Mesoscale and large-eddy simulations, Quarterly Journal of the Royal Meteorological Society, 126, 1-30

Goyette, S., Brasseur, O. and Beniston M., 2003: Application of a new wind gust parameterization: Multiscale case studies performed with the Canadian regional climate model, Journal of Geophysical Research, D-Atmospheres, 108 (13), ACL 1-1 – ACL 1-16.

Häggmark, L., Ivarsson, K., Gollvik, S. and Olofsson, P., 2000: MESAN, an operational mesoscale analysis system, Tellus, 52A, 2-20.

Högström, U., Hunt, J.C.R. and Smedman, A., 2002: Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer, Boundary- Layer Meteorology, 103, 101-124.

Jones, C.G., Willén, U., Ullerstig, A. and Hansson, U., 2004: The Rossby Centre Regional Atmospheric Climate Model Part I: Model Climatology and Performance for the Present Climate over Europe, Ambio, 33, 4-5.

Rummukainen, M., Räisänen, J., Bringfelt, B., Ullerstig, A., Omstedt, A., Willén, U., Hansson, U. and Jones, C., 2001: A regional climate model for northern Europe: model description and results from the downscaling of two GCM control simulations, Climate Dynamics, 17, 339-359.

Stull, R. B., 1988: An Introduction to Boundary Meteorology, Kluwer Academic, 666 pp.

Troen, IB. and Mahrt, L., 1986: A simple model of the atmospheric boundary layer; sensitivity to surface evaporation, Boundary-Layer meteorology, 37, 129-148.

35 Undén, P., et al., 2002: HIRLAM-5 Scientific Documentation, SMHI, 144pp.

36 Appendix

The Fortran code of the wind gust subroutine as implemented in RCA

subroutine wind_gust(nhor,nlev,kstart,kstop, c INPUT $ dtime,yearc,monthc,dayc,hourc,minc,t,q,u,v,cw, $ tke,gpot, $ pf,ph,dpf,dph, $ ts, ps,taux,tauy,senf,latf,ustar, $ pblh,u10,v10,rough, c printing c + along,coslat,kstep, c c OUTPUT $ gustest,gustlow,gustup,wzfwgest) c implicit none integer nhor,nlev,kstart,kstop,kstep,yearc,monthc,dayc,hourc,minc c c ! input variables c real t(nhor,nlev), ! temperature input $ q(nhor,nlev), ! specific humidity input $ cw(nhor,nlev), ! cloud water input $ u(nhor,nlev), ! u wind input $ v(nhor,nlev), ! v wind input $ tke(nhor,nlev), ! TKE input $ gpot(nhor,nlev), ! virtual potential above ground $ ts(nhor), ! surface temperature $ ps(nhor), ! surface pressure $ ustar(nhor), ! surface friction velocity $ taux(nhor), ! x surface stress ((kg/(m s2)) $ tauy(nhor), ! y surface stress ((kg/(m s2)) $ senf(nhor), ! surface heat flux (w/m2) $ latf(nhor), ! surface latent heat flux (w/m2) $ pblh(nhor), ! boundary layer height $ pf(nhor,nlev), ! pressure at model levels $ ph(nhor,nlev+1), ! pressure at model interface $ dpf(nhor,nlev), ! delta-p between model levels $ dph(nhor,nlev+1), ! delta-p at half levels between full leve $ dtime, ! 2 delta-t $ u10(nhor), $ v10(nhor), $ rough(nhor), c $ along(nhor),coslat(nhor) c c ! output variables c real gustest(nhor), ! gust wind speed estimate

37 $ gustlow(nhor), ! lower bound of gust wind speed estimate $ gustup(nhor) ! upper bound of gust wind speed estimate c c ! work space c integer i,k,kk,ii c real wthm(nhor, nlev), ! potential temperature $ wsenf(nhor), ! -senf $ wcflx(nhor), ! -surface moisture flux (kg/m2/s) $ wths(nhor), ! potential surface temperature $ wzh(nhor,nlev+1), ! z half levels $ wzf(nhor,nlev+1), ! z full levels $ wdzf(nhor,nlev), ! delta-z between half levels $ wdzh(nhor,nlev+1), ! delta-z between full levels $ wdzfp(nhor,nlev), $ wdzhp(nhor,nlev+1), $ tpvir(nhor,nlev+1), $ zgbuoy(nhor,nlev+1), $ zgri(nhor,nlev+1), $ fulltke(nhor,nlev), $ totw(nhor,nlev), $ ztke(nhor,nlev+1), $ zfulltke(nhor,nlev+1), $ mv10(nhor), $ wzfwg(nhor), $ wzfwgest(nhor) c real zwork1(nhor,nlev),zwork2(nhor,nlev+1),zwork(nhor), $ zbeta(nhor),zrho(nhor),zi(nhor),buofxs(nhor) c real cwpart, qpart, qsatpart, tpvpart,etheta, emoist, $ wstar, lobukhov, psat, $ zginv,zkappa,zp0,zlati,zlatw,zlatin,zanlev,zdu,zm,zk,vvar, $ inttke,intbuoy,zalat,alfa c logical lprint,lprint2,lprint3,lprint4,lprint5,lprint6,lprint7, + lprint8,lprint9 c c------c#include "CONFYS.inc" c------c real pi,latvap,rair,cpair,ccpq,epsilo,gravit,tmelt,latice, + rhos,rhoh2o,solar,stebol,carman,rearth,omega c common/confys/pi,latvap,rair,cpair,ccpq,epsilo,gravit,tmelt, + latice,rhos,rhoh2o,solar,stebol,carman,rearth,omega c c------c c c Comment from the VCBR-sceme: c C CHANGE 2) TKE defined on half levels ! This increases C numerical precision considerably. C To make the change in code relatively simple, we used C tke(nlev) for the surface. Therefore, the grid index of tke

38 c (and tke related variables) is one lower than the usual half c level numbering. Note this carefully !!! c This makes the scheme a bit incompatible with the computations c outside the tke scheme, although probably the errors introduced c are (very) small. c c ------c 1. Preliminary settings c ------c c c define local constants c zginv=1./gravit zkappa=rair/cpair zp0=1.e5 zlati=1./(latvap+latice) zlatw=1./latvap zanlev=10. alfa=0.1 c c geometric height(wzf) at full levels c do i=kstart,kstop gustest(i)=0. gustlow(i)=0. gustup(i)=0. enddo c do k=1,nlev do i=kstart,kstop wzf(i,k)=gpot(i,k)*zginv zwork1(i,k)=t(i,k)* (1.0 + 0.61*q(i,k)) enddo enddo c do i=kstart,kstop wzf(i,nlev+1)=0. enddo c c geometric height (wzh) of the half levels c C zwork2 contains the geopotential of the intermediate levels do i=kstart,kstop zwork2(i,nlev+1)=0. do k=nlev,2,-1 zwork2(i,k)=zwork2(i,k+1)+rair*zwork1(i,k) a *alog(ph(i,k+1)/ph(i,k)) enddo zwork2(i,1)=zwork2(i,2)+(gpot(i,1)-gpot(i,2))/2. enddo c do k=1,nlev+1 do i=kstart,kstop wzh(i,k)=zwork2(i,k)*zginv enddo enddo c

39 c thickness between full and half levels (at half and full resp.) c do k=1,nlev-1 do i=kstart,kstop wdzf(i,k)=wzh(i,k)-wzh(i,k+1) wdzh(i,k+1)=wzf(i,k)-wzf(i,k+1) c wdzfp(i,k) = ( ph(i,k+1) - ph (i,k) ) *zginv wdzhp(i,k+1) = ( pf(i,k+1) - pf (i,k) ) *zginv c enddo enddo c do i=kstart,kstop wdzh(i,1) = 0. wdzf(i,nlev)=wzh(i,nlev)-wzh(i,nlev+1) wdzh(i,nlev+1)=wzf(i,nlev) c wdzfp(i,nlev) = (ph(i,nlev+1)-ph(i,nlev))*zginv wdzhp(i,nlev+1)=(ph(i,nlev+1)-pf(i,nlev))*zginv wdzhp(i,1) = 0. c enddo c ! continuation lines not active to work with dry conservative var. do k=1,nlev do i=kstart,kstop totw(i,k)=q(i,k) wthm(i,k)= t(i,k)*(zp0/pf(i,k))**zkappa enddo enddo c c ------c virtual potential temperature c ------c ! virtual potential temperature at full levels do k=1,nlev do i=kstart,kstop ! rvap/rair=1.61 tpvir(i,k)=wthm(i,k)*(1.+1.61*q(i,k))/(1.+totw(i,k)) enddo enddo c do i=kstart,kstop ! extrapolate tpvir at nlev+1 tpvir(i,nlev+1)= tpvir(i,nlev) * wzf(i,nlev-1) / wdzh(i,nlev) a - tpvir(i,nlev-1)* wzf(i,nlev) / wdzh(i,nlev) enddo c c ------! compute brunt vaisala frequency (stability) zgbuoy from ! virtual potential temperature gradient c ------c do k=1,nlev do i=kstart,kstop zgbuoy(i,k+1) = gravit/tpvir(i,k)*

40 * (tpvir(i,k)-tpvir(i,k+1))/wdzh(i,k+1) ztke(i,k)=tke(i,k) zfulltke(i,k)=0. enddo enddo do i=kstart,kstop zgbuoy(i,1) = zgbuoy(i,2) ztke(i,nlev+1)=tke(i,nlev) zfulltke(i,nlev+1)=0. mv10(i)=sqrt(u10(i)**2+v10(i)**2) enddo c c c ------! add computation Richardson number c ------c do k=1,nlev-1 do i=kstart,kstop zdu = max(0.1, + ((u(i,k)-u(i,k+1))**2 + (v(i,k)-v(i,k+1))**2)) * /(wdzh(i,k+1)**2) ! max as a security for noshear limit; no phys. relevance zgri(i,k+1) = zgbuoy(i,k+1) / zdu enddo enddo do i=kstart,kstop zgri(i,nlev+1) = zgbuoy(i,nlev+1)*(wzf(i,nlev)**2) * / max( u(i,nlev)**2 + v(i,nlev)**2 ,0.1) ! max as a security for noshear limit; no phys. relevance zgri(i,1) = zgri(i,2) enddo c c c ------! wind gust estimate c ------c do i=kstart,kstop gustest(i)=mv10(i) enddo do i=kstart,kstop k=nlev inttke=0. intbuoy=0. do while(pblh(i).ge.wzf(i,k)) zk=(ztke(i,k+1)-ztke(i,k))/(wzh(i,k+1)-wzh(i,k)) zm=ztke(i,k)-wzh(i,k)*zk fulltke(i,k)=wzf(i,k)*zk+zm zfulltke(i,k)=fulltke(i,k) zfulltke(i,nlev+1)=fulltke(i,nlev) inttke=1./(wzf(i,k)-zanlev) + *0.5*(zfulltke(i,k)+zfulltke(i,k+1)) + *wdzh(i,k+1)+inttke intbuoy=0.5*(zgbuoy(i,k)*wdzh(i,k)+zgbuoy(i,k+1) + *wdzh(i,k+1))*wdzh(i,k+1)+intbuoy if(inttke.ge.intbuoy)then gustest(i)=max(sqrt(u(i,k)**2+v(i,k)**2),gustest(i))

41 endif k=k-1 enddo enddo ! for i c c c ------! upper bound c ------c do i=kstart,kstop gustup(i)=mv10(i) enddo do i=kstart,kstop k=nlev do while(pblh(i).ge.wzf(i,k)) gustup(i)=max(sqrt(u(i,k)**2+v(i,k)**2),gustup(i)) k=k-1 enddo enddo c c c ------! lower bound c ------c do i=kstart,kstop gustlow(i)=mv10(i) enddo do i=kstart,kstop k=nlev intbuoy=0. do while(pblh(i).ge.wzf(i,k)) zk=(ztke(i,k+1)-ztke(i,k))/(wzh(i,k+1)-wzh(i,k)) zm=ztke(i,k)-wzh(i,k)*zk fulltke(i,k)=wzf(i,k)*zk+zm vvar=2.5/11.*fulltke(i,k) intbuoy=0.5*(zgbuoy(i,k)*wdzh(i,k)+zgbuoy(i,k+1) + *wdzh(i,k+1))*wdzh(i,k+1)+intbuoy if(vvar.ge.intbuoy)then gustlow(i)=max(sqrt(u(i,k)**2+v(i,k)**2),gustlow(i)) endif k=k-1 enddo enddo c c c return end