Examensarbete vid Institutionen för geovetenskaper ISSN 1650-6553 Nr 127

Downscaling of Wind Fields Using NCEP-NCAR-Reanalysis Data and

the Mesoscale MIUU-Model

Mattias Larsson

ABSTRACT

The profitability from the production wind power energy is related to the quality of the wind speed forecasts. All wind predicting methods needs meteorological data, for the prevailing synoptic situation, as input. High quality input is wanted for a better result. In this study a new idea of a method for estimation of high resolution wind fields is examined. The idea is to use an existing database, containing simulations of high resolution wind fields, to estimate the actual wind by combining the simulations in a way fitting actual synoptic data. The simulations in the database have been produced by the mesoscale MIUU-model, which has been developed by Leif Enger at Uppsala University. The database contains simulations characterized by different geostrophic wind speeds and directions. There is also a separation into four seasons, where values which are typical for each season is put on meteorological parameters. Reanalysis data from NCEP-NCAR, containing 850 hPa geopotential heights describing actual synoptic situations, is used to calculate geostrophic wind speeds and directions. Three different geostrophic wind calculation methods, the triangle method, the small cross-method and the large cross-method, are tested. The calculated geostrophic wind is compared between the methods. The small cross-method is chosen and the main reason for that is the large amount of reanalysis information considered by this method and the use of a small calculation area. Measurements of the wind speed and direction are available from the tower at Utgrunden. The geostrophic wind speeds and directions are therefore calculated especially for the position of Utgrunden. This is done by a linear weighting of data, from several grid points close to Utgrunden, with respect to the distance to Utgrunden. Linear weighting is also used when estimating the wind speed for Utgrunden. The wind speed is estimated by weighting together MIUU-model simulations, for different geostrophic wind speeds and directions, so that they fit the geostrophic wind values calculated for Utgrunden. The calculated wind speed, measured wind speed and calculated geostrophic wind speed, for Utgrunden, are compared. The correspondence, between the calculated and measured wind speed, turns out to be quite good for many time periods. The diurnal variations in the measured wind speed are partly captured by calculated wind speed, but the diurnal variations tend to be larger in the measured wind speed then in the calculated. There are also cases where there are large differences between the measured and estimated wind speed. Many of these cases are probably cased by unusual weather situations. By considering additional parameters, as the temperature field, it is likely that these wind estimations can be improved. With more research it may be possible to produce high resolution wind fields with enough accuracy to be useful as inputs in wind prognostic systems. The advantage with such a method would be that accurate high resolution wind fields could be produced without the use of a time consuming numerical high resolution model.

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SAMMANFATTNING AV ”NEDSKALNING AV STORSKALIGA VINDFÄLT GENOM ANVÄNDANDE AV ÅTERANALYS DATA FRÅN NCEP-NCAR OCH DEN MESOSKALIGA MIUU-MODELLEN” Lönsamheten för produktion av vindkraft elektricitet bestäms delvis av förmågan att göra bra vindprognoser för nästkommande dygn. Alla metoder för vindprognostisering behöver meteorologisk indata som beskriver den rådande synoptiska situationen. Kvaliteten och upplösningen på dessa indata har stor betydelse för metodens resultat. I denna studie undersöks en alternativ metod för bestämning av högupplösta vind fält. Idén är att man ska försöka utnyttja en tillgänglig databas av högupplösta vindfält, producerade av den mesoskaliga MIUU – modellen som är utvecklad av Leif Enger på meteorologiska institutionen vid Uppsala Universitet. Tanken är att dessa vindfält ska kunna kombineras på ett sådant sätt att de överensstämmer med en given synoptisk situation. MIUU – modell körningarna, i databasen, är indelade i situationer karaktäriserade av olika värden på den geostrofiska vindstyrkan och vindriktningen. Körningarna är gjorda för fyra säsonger, för vilka typiska värden för säsongen är satta på styrande parametrar. För att kunna kombinera MIUU - modell körningarna beräknas den geostrofiska vinden från 850 hPa geopotential höjd återanalys data tillgänglig från NCEP-NCAR. Tre olika beräkningsmetoder för geostrofisk vind testas och jämförs. Den ”lilla korsmetoden” väljs för uppgiften beroende på att den utnyttjar en förhållandevis stor mängd återanalys data, för beräkning av geostrofisk vind, samt använder litet beräkningsområde. Automatiskt uppmätta värden över vindhastighet och vindriktning finns tillgängliga från en mast positionerad vid Utgrunden i Kalmar sund. Den geostrofiska vinden beräknas därför i Utgrundens position. Beräkningen utförs genom linjär viktning av data från de från Utgrunden sett fem närmaste gridpunkterna (i lilla korsmetodens gridfält). En linjär viktning används sedan även för att vikta ihop de MIUU – modell simulerade vindfälten så att de passar de beräknade värdena på geostrofisk vindhastighet och vindriktning. Jämförelser görs mellan den beräknade vinden, den uppmätta vinden samt den geostrofiska vinden, för Utgrunden. Korrelationen, mellan uppmätt och beräknad vind, visar sig vara ganska god periodvis. Den dagliga variationen i den uppmätta vindhastigheten fångas delvis av beräkningsmetoden, men dygnsvariationen är betydligt större i den uppmätta vinden än i den beräknade. Det noteras även att det finns situationer då det är stora skillnader mellan beräknad och uppmätt vind. Dessa situationer beror i många fall troligen på onormala vädersituationer. Studium av ytterliggare parametrar, som t.ex. temperaturfältet, skulle troligen leda till betydande förbättringar i vinduppskattningen. Ytterligare forskning och förbättring av metoden skulle kunna leda till produktion av högupplösta vindfält med tillräcklig kvalitet för användning i vindprognostiseringsmodeller. Fördelen skulle i så fall vara möjligheten att kunna producera högupplösta vindfält utan användning av tidskrävande numerisk modeller.

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CONTENTS

1. INTRODUCTION 5 2. REANALYSIS DATA FROM NCEP-NCAR 7 3. THE MIUU-MODEL DATABASE 8 4. CALCULATION OF GEOSTROPHIC WIND 10

4.1 The Triangle-Method 11 4.2 The Cross-Method 13 4.3 Comparison of Ug between methods 14 4.3.1 Mean statistics 15 4.3.2 Computation of geostrophic wind speed 17 4.3.3 Computation of geostrophic wind direction 19 4.4 Elimination of bias 21 4.5 Discussion considering the determination of geostrophic wind 24 5. METHOD OF SELECTION 24 5.1 Simplifications 25 5.2 Method for estimation of the actual wind 25 5.3 Results and Comparisons 28 6. SUMMARY AND CONCLUSIONS 33 ACKNOWLEDGEMENTS 36 REFERENCES 36 APPENDIX A 37 APPENDIX B 40

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1. INTRODUCTION Now as oil is getting expensive, renewable energy sources gets more and more popular. One of these renewable energy sources is wind power. Energy companies around the world are investing money in wind power plants. For electricity producers, the percentage of the energy producing capacity produced by wind power technology is growing. On the “electricity market” the price for wind energy electricity is changing all the time. The economical winning is closely related to the quality of the predictions of energy production for the nearest future (nearest 24 hours or so). In Scandinavia, the electricity market is called, NordPool (www.nordpool.com). A little bit of how the market works is as follows. As a producer of wind power electricity you are closing deals with customers to produce a certain amount of electricity under a certain time period. If the company then can’t produce that amount of electricity they must buy extra electricity from other energy producers at a high price, or pay a fine. Sometimes more energy than expected is produced. To get rid of the excess energy, the companies have to sell it sheap with no or only small economical winning, Elmqvist (2003). In addition to good market prices, good wind predictions can also be used as guidence when planning for reparations and maintenance work. Predicting wind energy production is difficult compared to predicting energy production from many other energy resources. As a comparison, take energy sources such as nuclear power and water power, the amount of energy produced from these are a lot easier to predict. Nuclear power is not affected by different seasons or the weather. Water Power is affected by the weather, but at a far longer basis than wind power. The time lag between sudden changes in the whether and their effects on the water power energy production make it possible to do predictions weeks and months in to the future rather then days. Wind power production is very much ruled by the wind speed so predicting wind speed is a large step against predicting energy production. The drawback is that it is difficult to make good wind forecasts for wind power plants. On small scales effects from local topography and meso - scale circulations, like sea breezes and low level jets, are of a great importance. Wind power plants are rather local and greatly affected by these effects. There is also a need to consider effects from the wakes that are produced behind each wind power turbine. They will affect the local wind field and therefore the wind energy production from the nearby turbines in the wind power park. Therefore there is a need for models producing high resolution wind fields (called physical models) or models using statistical methods. Combinations of those are used in many of the existing systems. The physical models uses wind field predictions from numerical weather prediction models, often available from the national weather center, as start data to a local numerical high resolution model. This model produces much more details to the local wind field. Also the statistical methods uses wind field predictions as start data. Then they can use a simple statistical relationship between the wind speed and the energy production of the

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wind power park as whole. There is also possible to use a neural network which is a little more sophisticated. A neural network gives the possibility to account for meteorological parameters as the temperature and humidity. The different parameters, categorizing the current situation, are then weighted together in order to predict the energy production. Neural networks can give quite good results but need to be trained on a large amount of earlier and current measurements before they can get useful. Because of the local differences between different wind energy parks, the systems need to be trained individually at those places. Implementation and training of neural networks are expensive and therefore those methods are most useful for large wind power parks. For the interested person more information on neural networks can be found at (www.statsoftinc.com/textbook/stneunet.html) and at (www.phil.gu.se/ann/annintr.html). Wind predictions may produce two kinds of errors of particular interest for the wind energy producers, “level errors” and “phase errors”. See Figure 1.1 below. Level errors is categorized by that for specific events the production of energy is larger or less than predicted. Phase error is a miscalculation in time. As an example a misscalculation of the time of arrival for of a fast rise in wind speed, which may occur in case of a frontal passage, can create a large deficit or surplus of energy during short periods.

Level error

Phase error

Wind speed

Time

Wind speed

Time

a)

b)

Estimated wind speed

True wind speed

Estimated wind speed

True wind speed

Figure 1.1: Figure a) shows a phase error, i.e. a displacement in time between the prediction and the reality. Figure b) shows a phase error, i.e. a difference in magnitude between the predicted wind speed and the real wind speed. There exist a number of methods that is already in use or is under development in countries around the world. Some basic information on wind energy prediction systems and a good review of systems that are in use, or under evolution, can be found in Källstrand, (2004).

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A higher order closure mesoscale numerical model with 1 km horizontal resolution, called the MIUU-model, has been developed by Leif Enger at the Meteorological Department at Uppsala University, (www.met.uu.se). The MIUU-model is described shortly in section 3 and in more technical detail in Enger, 1990. At the Department of Earth Sciences at Uppsala University there has also been a project going on since 2002, in purpose to make a wind resource estimation over Sweden using the MIUU-model. The mapping of the wind potential is useful as a guide for the companies planning to build new wind power parks. During the wind resource program a database of high resolution MIUU-model simulations was created. The idea is to use this already existing database in order to create high resolution wind fields, that satisfies any given weather situation described by reanalysis data. The use of geostrophic wind, calculated from reanalysis 850 hPa geopotential height data, could be a good start when describing atmospheric weather situations. The purpose of this work is to see if it is possible to create good high resolution MIUU-model wind fields, using reanalysis data as input. If possible, they can be used as input in a prognostic wind model. The result from the using of a higher resolution on the input wind fields will likely be an improved wind prediction and therefore also an improved prediction of the energy production.

2. REANALYSIS DATA FROM NCEP – NCAR The reanalysis concept is to collect data from all around the world and then by a modern numerical model create analysis of the weather situation. There are two aspects of reanalysis. One is to create a large database containing analysis of the past weather and one is to continuously make reanalyse updates of the present situation. For the historical reanalysis, sophisticated quality control of large amounts of collected data from the world has been done. The same modern assimilation method has been used during the whole reanalysis period. This has been done to eliminate strange behaviour due to changes in operational assimilation systems during history (because of technical development). There are two large sets of reanalysis data. One produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) called ERA-40, (http://www.ecmwf.int/research/era/) and one produced by National Centre for Environmental Prediction (NCEP) and National Centre for Atmospheric Research (NCAR), (http://www.cpc.ncep.noaa.gov/products/wesley/reanalysis.html). The ERA-40 data set covers the period 1958 – 2001 and NCEP-NCAR reanalysis data is available from 1948 and forward. The NCEP-NCAR reanalysis is continuously updated which will make it useful in an eventual future implementation of the method. Therefore the NCEP-

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NCAR reanalysis has been chosen prior to the ERA-40 in this work, and NCEP-NCAR reanalysis data from the period 1958-2005 has been used. The NCEP-NCAR reanalysis data is available for the whole world four times a day, 00, 06, 12 and 18 UTC. Data is calculated in a grid system with grid-points every 2.5° longitude (0°E, 2.5°E, 5°E, …, 357.5°E) and 2.5° latitude (90°S, 87.5°S, …,2.5°S, 0°, 2.5°N, …, 87.5°N, 90°N). The area considered in this work is the one bounded by grid points from 0°E to 35°E and 50°N to 75°N. This area contains Scandinavia and will be referenced to as the Scandinavian area. The 850 hPa geopotential height is the primary considered reanalysis variable in this paper, even though a lot of other meteorological variables are available and likely will be of interest later on. Geopotential height is classified as a type A variable in the NCEP-NCAR reanalysis system. This means that it is strongly influenced by observational dataset and not much by the NCEP-NCAR reanalysis model itself. Type A variables are considered as the most reliable variables in the reanalysis. On the other hand there are C-variables, such as precipitation, which are totally determined by the model and therefore insecure. This and much more information about NCEP-NCAR reanalysis can be found in Kalnay et al. (2001) and Kalnay et al. (1996). The 850 hPa geopotential heights can be used to calculate the geostrophic wind field. The geostrophic wind is then used as input data for a method that calculates the wind field using a database of MIUU-model simulations (section 3). Some methods for the calculation of geostrophic wind are described in section 4.1 – 4.2. Comparisons of the methods are carried out in section 4.3 and the small cross-method (section 4.2) is finally chosen.

3. THE MIUU – MODEL DATABASE The MIUU-model is a three dimensional hydrostatic model developed by Leif Enger at the Meteorological Department at Uppsala University. It has a coordinate system that follows the topography near the ground and that gradually transforms to a terrain independent system higher up. The MIUU-model has height levels from z0 up to about 10000 m. The calculation levels are logarithmically spaced near the ground and linearly spaced higher up giving a higher concentration of levels near the ground than at high altitude. The model has a telescopic horizontal grid with a high resolution of 1 km over much of the model area. The distances between the grid points are increased in the outskirts of the model area. In the MIUU-model, turbulence is parameterized by a 2.5 scheme according to the definition by Mellor and Yamada (1974). Detailed technical information about the MIUU-model can be found in Enger (1990). During a wind resource program, a database of simulated MIUU-model wind fields was created. The database covers a broad spectrum of atmospheric situations by modeling of a number of chosen weather situations. The simulated wind-fields has been produced for 3

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different geostrophic wind speeds (4, 9 and 14 m/s), 16 different geostrophic wind directions (0°, 22.5°, 45°, …, 315°, 337.5°) giving 48 different simulations. These simulations are carried out for four different seasons giving a total number of 192 simulations. Each model run starts at midnight and runs for a 36 hour period finishing at 12:00 the day after. The first 12 hours is an initialization period and are not stored as results. The results start instead at 13:00 and runs for 24 hours finishing at 12:00 the day after. Outputs for the model are produced for each hour resulting in 24 values for each grid point and each model run. The MIUU-model is rather computer demanding, therefore the model area is split into 14 smaller areas. The model simulations of the chosen atmospheric situations are carried out in each of these smaller model areas and added together they cover whole Sweden. The area covering the south-east part of Götaland is considered in this paper, this area will referenced to as the SE-Götaland area. About half this area is covered by the Baltic Sea and that part includes the islands of Gotland and Öland; see Figure 3.1 and Bergström (2004). The model area has a grid resolution of 1 km and contains 301*291 grid points, 301 grid points in latitude and 291 grid points in longitude. January, April, July and October are chosen to represent the different seasons. In simulations belonging to different seasons there are typical values set on parameters as for example, the difference in temperature between land and ocean. In reality parameters like those are changing all the time and may differ a lot from the mean value of the season. This is why other parameters, than the geostrophic wind speed and direction, also must be considered later on. If this is done, the accuracy can probably be improved for the resulting computed wind fields, especially for the non typical weather situations.

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S d

Figure 3.1: The left part shows a map over shows a map over the south-east Götaland s

4. CALCULATION O The geostrophic wind speed and direction height data available from the NCEP-NCcalculates the geostrophic wind over the Stested. These methods calculate the georectangles that are formed from grid pgeostrophic winds from all triangles or geostrophic wind fields. In the two following sections two kinds owind are presented, the triangle-method (seComparisons between the methods are thdiscussed. A bias is discovered between

outh - east Götalan

B a

Gotland

Öland

Sweden. The magimulation area.

F GEOSTROP

can be calculateAR reanalysis.

candinavian areastrophic wind oints in the NCrectangles are th

f methods for thction 4.1) and theen carried out (the triangle-met

10

altic Se

nified portion to the right

HIC WIND

d from 850 hPa geopotential A couple of methods that (described in section 2) are

by considering triangles or EP-NCAR reanalysis. The en added together to form

e calculation of geostrophic cross-methods (section 4.2). section 4.3) and results are hod and the cross-methods.

Fortunately the reason to this bias is found and changing to the triangle-method is done (section 4.4). After some discussion it is decided that the small cross-method is to be used for the calculation of geostrophic wind (section 4.5)

h1 h2

(57.5°N, 17.5°E)

(55°N, 22.5°E) (55°N, 17.5°E)

h4 h3

(h1+h3)/2

(h1+h3)/2

(57.5°N, 22.5°E)

(h2+h4)/2

(h3+h4)/2

∆x

∆y(20°E, 56.25°N)

(19.17°E, 56.67°N)

h5

h6

x

y

Figure 4.1: A geometric description of the triangle- and cross-methods. The triangle-method (T) calculates the geostrophic wind by using 850 hPa geopotential height data, h, from the grid points, h1, h2 and h3, in the upper left triangle (ULT). The large cross-method (LC) uses 850 hPa geopotential data from grid points, h1, h2, h3 and h4 in order to calculate the Geostrophic wind. The small cross-method (SC) uses 850 hPa geopotential data from the grid points, h1, h3, h5 and h6, to calculate the geostrophic wind. To each grid point, hi, there belongs, in addition to the latitude and longitude, a pair of coordinates (yi, xi), defined in section 4.1. The filled triangle and rectangle mark the positions for the coordinates of geostrophic wind calculated from (T) and (LC). 4.1 The Triangle - Method Grid-points are chosen in pairs of three to form triangles. There is a possibility to choose different configurations of triangles. Triangles of the shape described by grid points, h1, h2 and h3, in the upper left triangle are used here (Figure 4.1). At the latitude of about 60°N, a distance of 2.5° latitude is about twice as long as a distance of 2.5° longitude.

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Because of this the grid points has been chosen so that the triangle covers 5° in longitude and 2.5° in latitude, meaning that the method is “jumping” over one grid point in longitude when creating triangles. The components of the geostrophic wind speed are according to:

))(())(())(())((

*

))(())(())(())((

*

13121213

12131312

13121213

13121213

yyxxyyxxhhyyhhyy

fgv

yyxxyyxxhhxxhhxx

fgu

g

g

−−−−−−−−−−

=

−−−−−−−−−−

−= (4.1)

where g is the acceleration of gravity, f is the Coriolis parameter, h is the 850 hPa geopotential height, x is the longitudinal distance to the Greenwich meridian in meters and y is the latitudinal distance to the equator in meters. The magnitude of geostrophic wind speed and wind direction is calculated with:

ggg vuU += (4.2)

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

g

gg u

vWD arctan270 (4.3)

Longitude and latitude is transformed to x and y coordinates by the transformations:

3,2,13,2,1

3,2,13,2,13,2,1

*180

)cos(**180

ϕπ

ϕλπ

ry

rx

=

= (4.4)

where λ is longitude and φ the latitude and r is an expression for the earth radius that corrects for the fact that earth isn’t a perfect sphere.

61.237*6378137 meanr ϕ−= (4.5) where φmean is the mean latitude of the considered triangle. The calculated geostrophic wind is given the coordinates

E).E, .E, ..., .E, . (N).N, .N, ... , .N, . (

T

T

°°°°++=°°°°++=

67311729174671 3/)(1774677117545751 3/)(

321

321

λλλλϕϕϕϕ

(4.6)

For the triangle built by h1, h2 and h3 in Figure 4.1, the geostrophic wind will be given the coordinate: 19.17°E 56.67°N.

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From the NCEP-NCAR data it is possible to form triangles for every 2.5° step in both longitude and latitude. Given the fact that each triangle covers 5° in longitude, 130 triangles, 13 triangles in longitude and 10 triangles in latitude, are needed in order to cover the whole Scandinavian area (section 2). The result is then geostrophic wind calculated in 130 grid points. 4.2 The Cross-Method The cross-method uses 4 grid points from the Scandinavian area (section 2), in the form of rectangles, in order to calculate Ug, see Figure 4.1. Two different sizes of rectangles are used. The small size rectangles constitutes of grid points in a similar configuration as h1, h3, h5, h6. The larger size rectangles cover an area twice as large, constituting of grid points in a similar configuration as h1, h2, h3 and h4. The first step in the method is to calculate 850 hPa geopotential heights in points halfway between the grid points. This is done just by calculating the mean values of geopotential height between the grid points, i.e. for the large rectangle, (h1+h2)/2, (h1+h3)/2, (h2+h4)/2, (h3+h4)/2 in Figure 4.1. These points are forming a cross, therefore the name of this method. The components of geostrophic wind are then calculated in terms of the gradients of 850 hPa geopotential height, ∆h/∆y and ∆h/∆x. The equations for the small and large method work in an exactly similar way. The only difference is that h2 and h4 is changed to h5 and h6. The components of geostrophic wind for the large cross-method are given by:

x

hhhh

fgv

y

hhhh

fgu

g

g

∆

+−

+

=

∆

+−

+

−=

22*

22*

3142

4321

(4.7)

The x- and y distances are calculated by:

°=∆

⎟⎠⎞

⎜⎝⎛ +

°=∆

5.2*180

2cos*5*

18031

ry

rx

π

ϕϕπ

(4.8)

where r, the earth radius, is calculated by expression (4.5). Notice that for the small cross-method, the multiplication with 5° in the ∆x – equation must be changed to 2.5°. A rectangle is formed for every 2.5° step in latitude and longitude, leading to a geostrophic wind calculation grid system with a 2.5° step between grid points. The

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calculated geostrophic wind will be given coordinates corresponding to the centre of each rectangle/cross. For the large cross-method coordinates are given by:

)53230552( 2)7573257175532551(2

21

31

E.E, E, ..., E, . )/(N.N, .N, ..., .N, . )/(

LC

LC

°°°°+=°°°°+=

λλλϕϕϕ

(4.9)

For the small cross-method coordinates are given by:

)75332531753251( 2/)()7573257175532551( 2/)(

51

31

E.E, .E, ..., .E, .N.N, .N, ..., .N, .

SC

SC

°°°°+=°°°°+=

λλλϕϕϕ

(4.10)

Where φ is the latitude and λ is the longitude. For the method using small size crosses the geostrophic wind is calculated in 14 x 10 = 140 points. For the large cross version geostrophic wind is calculated in 13 x 10 = 130 points. 4.3 Comparison of Ug between methods A choice of method for the calculation of geostrophic wind fields must be done. There are no true geostrophic wind fields available that can be used for evaluation of the methods. Therefore, an internal comparison between the methods is done. This is done both by calculating mean values of geostrophic wind speed and direction, and by comparing results from the different methods against each other. In order to make life easy the following notation is used below: T=Triangle-method, MT=Modified triangle method (discussed later in section 4.4, see equations (4.16) and (4.17)), SC=Small cross-method, LC=Large cross-method UgT, UgMT, UgSC, UgLC is the geostrophic wind speed calculated with the triangle-, modified triangle-, small cross- and large cross-method. WDgT, WDgMT, WDgSC, WDgLC is the geostrophic wind direction for the triangle-, modified triangle-, small cross- and large cross-method.

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4.3.1 Mean statistics

The position of Utgrunden: (56.4°N, 16.3°N)

Öland

Gotland

Coordinates for the calculation of mean values of the geostrophic wind: Triangle method: (56.67°N, 19.17°E)

S ) Baltic Sea

Figure 4.2: A map of the south-east GötaUtgrunden and the positions of the grid the comparison between the methods. Mean values of geostrophic wind speed athe whole data set, i.e. the whole time s1958-2005) for each grid point. Data froused, meaning 130 grid points for the tpoints for the small cross-method. Mean values are also calculated from the inside the SE-Götaland area (section 2), Sea south east of the island of Gotlandifferences in grid systems between the mthe same positions in all three methods. Tpresented in Table 4.1 below. It is seen that the mean value of the geomethod than for cross-methods. There ismethods, the small version giving a highelarge version. This is due to differences imethods. Situations with large 850 hPa gbe missed in calculations over large areFigure 4.3 below. In this fictive atmosgradient in the lower part of the figure isareas, bounded by the grid points h1, h5, the large area described by h1, h2, h3, h4. Mohr, (2004). A similar behavior as with geostrophic wi.e. there is small internal difference betwbetween the triangle-method and the

mall cross method: (56.25°N, 18.75°E

m

h

Large cross method: (56.25°N, 20.00°E)

land area including the position of the tower at points, over the Baltic Sea, that’s been used in

nd geostrophic wind direction are calculated for eries consisting of 70128 values (4 times/day, m the whole Scandinavian area (section 2) is riangle- and large cross-method and 140 grid

whole time series at specific grid points situated ore specifically they are found over the Baltic

d in, see Figure 4.2 above. Because of the ethods, the chosen grid points have not exactly he results from the mean value calculations are

strophic wind speed is higher for the triangle- also an internal difference between the cross-r value on the geostrophic wind speed than the n the sizes of the calculation areas between the eopotential height gradients are more likely to

as than in calculations over a small areas, see pheric situation the large geopotential height better captured by calculations over the small 3, h6 or h5, h2, h6, h4, then by calculations over

This subject is also discussed in Bergström and

ind speed is seen in geostrophic wind direction, een the cross-methods and a larger difference

cross-methods. The differences between the

15

methods can also be seen in the mean values taken over the chosen grid points in the Baltic Sea.

Figure 4.3: An illustration of the fact that atmospheric situations with large geopotential height- or pressure gradients are easier to capture when calculations are done over small areas instead of large areas. Table 4.1: This table contains a summary of the mean values of Ug and WDg produced by different geostrophic wind calculation methods. Row 2 and 3 shows mean values produced by considering values from the Scandinavian area (50°N-75°N, 0°E - 35°E) and the whole time period (1958-2005). Row 5 and 6 shows mean values produced by considering the chosen grid points in the SE-Götaland area (Figure 4.2) and the whole time period (1958-2005). *MT, the modified triangle-method is described later in section 4.4; see equations (4.16) and (4.17).

Methods: T MT* SC LC Ug (m/s) 9.43 9.35 9.27 9.15

WDg (°) 215.5 212.6 211.8 212.1

In coordinates (56.67°N,19.17°E) (56.67°N,19.17°E) (56.25°N, 18.75°E) (56,25°N, 20,00°E) Ug (m/s) 9.73 9.69 9.53 9.46

WDg (°) 218.4 214.8 215.5 216.6

L

h2 h1 h5

h4h3 h6

H

16

4.3.2 Computation of geostrophic wind speed In order to make comparisons between the methods easier to handle the amount of data used is restricted. Only data from one grid point in each method is considered. The amount of data considered, from each method, is then 70128 values, corresponding to 4 values/day, during the period 1958-2005. Because of the differences in grid systems between the methods, consider equations (4.6), (4.9) and (4.10), there are small differences between the methods for the positions of the chosen grid points. The grid points studied is situated in the Baltic Sea, south east of the island of Gotland, see Table 4.1 and Figure 4.2 above. Data for the chosen grid points are then compared between the triangle-method, the small cross-method and the large cross-method. A “scatter-plot”, showing a comparison of calculated Ug between the SC and T, is presented in Figure 4.4 below. Pretty good correspondence can be seen between the methods. The slightly higher mean value of the triangle-method can be seen in the linear regression. The comparisons of calculated Ug, between LC and T and between LC and SC, show a similar behavior as the comparison of Ug between SC and T, see Figure 4.4, and are therefore not shown in this paper. It is noticed that the comparison of Ug between LC- and SC data result in a linear regression more equal to unity then the linear regression produced by the other comparisons, see equations (4.11)-(4.13). This behavior is expected because the only difference between the LC and SC is the size of the calculation area. The following equations for linear regressions are produced: SC plotted vs. T: 34309440 .U.U gTgSC += (4.11) LC plotted vs. T: 348.0936.0 += gTgLC UU (4.12) LC plotted vs. SC: 156.0976.0 += gSCgLC UU (4.13) There is a larger scatter in the comparison of calculated Ug between T and SC and between T and LC than in the comparison of data between SC and LC. This scatter can be studied by analyzing the residuals in Ug between the methods, see Figure 4.5. For the difference UgLC - UgSC, the majority of values are found in the interval ±2.5 m/s. This can be compared to the differences UgSC - UgT and UgLC - UgT, where the majority of the values are found in an interval about ±4 m/s.

17

Figure 4.4: Comparison of geostrophic wind speed between T and SC. For T the geostrophic wind speed is calculated in the coordinates (56.67°N, 19.17°E) and for SC in (56.25°N, 18.75°E). All 70128 values during the period (1958-2005) are used.

a) b)

−10 −5 0 5 100

2000

4000

6000

8000

10000

12000

14000

The differens, UgSC

− UgT

(m/s)

Num

ber

of v

alue

s

−10 −5 0 5 100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

4

The differens, UgLC

− UgSC

(m/s)

Num

ber

of v

alue

s

Figure 4.5: Figure a) shows residuals of geostrophic wind speed built by taking the difference between SC-values and T-values. Figure b) to the right shows residuals of geostrophic wind speed built by taking the difference between LC-values and SC-values.

18

Figure 4.6: Comparison of geostrophic wind direction between T and LC. For T the geostrophic wind direction is calculated in coordinates (56.67°N, 19.17°E) and for LC in (56.25°N, 20.0°E). All 70128 values during the period (1958-2005) are used. 4.3.3 Computation of geostrophic wind direction Studying scatter-plots of geostrophic wind direction, three obvious things can be seen:

1. There is a large scatter in a very strange pattern. 2. The magnitude of the scatter is a function of geostrophic wind direction. This

apply primary to the comparisons between small/large cross-method and the triangle-method.

3. There is a “bias” in the data between small/large cross-method and the triangle-method. No “bias” is seen between large- and small cross-method.

Those points are visible in Figure 4.6 above, showing a comparison between WDgLC and WDgT. The gathering of points in the upper left and down right corners of Figure 4.6 - 4.10 is an effect of the illusion of a jump in direction between 0° and 360° degrees that becomes visible in direction plots. The large scatter in Figure 4.6 arises because of the uncertainty in the determination of geostrophic wind direction at low geostrophic wind speeds. Removing all values of geostrophic wind direction associated with Ug < 5 m/s leads to a large improvement; see Figure 4.7 and Figure 4.8. It is important to be aware of this existing uncertainty in the calculated geostrophic wind direction. It may influence the result, making it more unreliable when the pressure field is weak.

19

The comparison of geostrophic wind direction between the small and large cross-method, Figure 4.7, shows a well behaved result. The scatter is almost equally large in all directions but slightly less in the 20° and 200° directions. The data is quite well centered around the 1:1 line, and there is no bias. The comparison between small/large cross-method and triangle-method, Figure 4.8, shows interesting features. The scatter is dependent on wind direction. For the comparison of large cross-method against triangle-method, the “nodes” with a minimum of scatter is in directions about 40° and 220°. For small cross-method against triangle-method they are found in directions 0-10° and 180°-190°. The reason for this pattern is that the equations become more equal for those certain geostrophic wind directions. Moreover a bias is clearly seen in the comparisons of geostrophic wind direction between large/small cross-method and the triangle-method, Figure 4.8. All data is clearly deflected above the 1:1 line. This bias is unfortunate and tells us that there is a problem with at least one of the two kinds of methods used for determination of geostrophic wind. The problem must be found. Otherwise it will be difficult to make a good choice of geostrophic wind calculation method. A description of the problem and how it can be solved is given in the next section.

Figure 4.7: Comparison of geostrophic wind direction between SC and LC. For SC the geostrophic wind direction is calculated in the grid point (56.25°N, 18.75°E) and for LC in (56.25°N, 20.0°E). All values>5m/s and are from the period (1958-2005).

20

a) b)

Figure 4.8: a) Comparison of geostrophic wind direction between T and LC. For T the geostrophic wind direction is calculated in the grid point (56.67°N, 19.17°E) and for LC in (56.25°N, 20.0°E). All values>5m/s and are from the period (1958-2005). b) Comparison of geostrophic wind direction between T and SC. For T the geostrophic wind direction is calculated in the grid point (56.67°N, 19.17°E) and for SC in (56.25°N, 18.75°E). All values>5m/s and are from the period (1958-2005). 4.4 Elimination of bias Consider equation (4.1) for the triangle-method and equation (4.7) for the large cross-method. These equations can be simplified by inserting the latitude and longitude coordinates from Figure 4.1, the values for gravity g = 9.81m/s2 and the coriolis parameter, fT = 1.21518*10-4 for triangle-method and fC = 1.20929*10-4 for the cross-methods. For the triangle-method the equation is simplified to:

)(270514.0

)(0686935.0)(290694.0

12

1213

hhv

hhhhu

g

g

−=

−−−= (4.14)

and for large cross-method:

[ ][ 4321

4321

131444.0

146052.0

hhhhv

hhhhu

g

g

−+−−=

−−

]+−=

(4.15)

21

Consider now a case of a geostrophic wind from the north, i.e. with 0° direction. This means that there should be no east-west component of geostrophic wind i.e. there should be no north-south gradient of 850 hPa geopotential height. For the triangle-method, a large enough requirement for this should be that

013 =− hh . But according to (4.14) we will still have the term ug= -0.0686935(h2 – h1) left, which is zero only when vg = 0. There is obviously something wrong in the triangle-method! Before going further in the problem solving it is worth to mention that the cross-methods work as they should in the case of a northly wind. Eliminating north-south gradients of 850 hPa geopotential height by putting

01324 =−=− hhhh does make ug = 0 and does not affect the vg component. Now back to the analyzing of the triangle-method. Tracing the leftover term, ug= -0.0686935(h2 – h1), back the basic form of the triangle equation, it can be seen that it evolves from of the term –(x3 – x1) (h2 - h1) in (4.1). This term is separated from zero in northly wind because (x3 – x1) ≠ 0. Now analyzing x1 and x3, from Figure 4.1, it can be see that the coordinates has the same longitude but different latitudes. As a consequence of this they will have different distances to the Greenwich meridian and therefore different x distances! To understand the reason for this mistake it must be stated that equation (4.1) is a generalized equation. This generalized form is supposed to work for all four triangle configurations that are possible to build from h1, h2, h3, h4. Putting (x3 – x1) = 0 is the simplest solution to the problem. This can be done without problem because only one of the four triangle configuration, the upper left triangle, is used in this study. The equation for the modified triangle-method (MT) becomes:

))(())((

*

))(())((

*

1312

1213

1312

1312

yyxxhhyy

fgv

yyxxhhxx

fgu

g

g

−−−−

=

−−−−

−=

(4.16)

Where all parts of (4.1) that becomes zero with use of the current triangle configuration has been removed. The modified version of the simplified triangle equation (4.14) can then be written:

)(270514.0

)(290694.0

12

13

hhv

hhu

g

g

−=

−= (4.17)

22

This equation has a form resembling equation (4.15) but there are still some small differences. Those differences and there consequences are discussed in Appendix A. The mean values of geostrophic wind speed and direction calculated with the modified triangle-method are presented in Table 4.1. These mean values should be compared with the mean values from the original triangle-method. Mean values from the cross-methods shows a greater resemblance with the mean values from the modified triangle-method than with the mean values from the original triangle method. In Figure 4.9 geostrophic wind directions calculated with large cross-method and modified triangle-method is compared. It can be seen that the bias is totally gone and that is really good news. For the geostrophic wind speed comparisons, involving modified triangle-method, the following linear regressions are produced: SC plotted against MT: 167.0967.0 += gMTgSC UU (4.18) LC plotted against MT: 217.0954.0 += gMTgLC UU (4.19)

Figure 4.9: Comparison of geostrophic wind direction between MT and LC. For MT the geostrophic wind direction is calculated in the grid point (56.67°N, 19.17°E) and for LC in (56.25°N, 20.0°E). All values >5m/s, from the period (1958-2005).

23

Figure 4.10: Comparison of geostrophic wind direction between MT and SC. For MT the geostrophic wind direction is calculated in the grid point (56.67°N, 19.17°E) and for SC in (56.25°N, 18.75°E). All values >5m/s, from the period (1958-2005). 4.5 Discussion considering the determination of geostrophic wind All three methods now give results that are quite similar in appearance so the choice of calculation method for the geostrophic wind should not be critical for the continuation of this study. What speaks in favour for the cross-method is the use of information from four grid points instead of three. Probably this will lead to a better description of reality. In order to capture as many large gradient situations as possible, the cross-method with small cross should be used. As discussed earlier in section 4.3.1, see particularly Figure 4.3, and in Bergström and Mohr (2004), small calculation areas lead to higher mean values of geostrophic wind speed than larger areas, and a smaller deviation from reality.

5. METHOD OF SELECTION

We remind ourselves of our goal to create high resolution wind fields. The first step is to use 850 hPa geopotential height data from NCEP-NCAR reanalysis in order to calculate the geostrophic wind. The next step is to use a database of MIUU-model simulated wind fields to create an accurate high resolution wind field. The MIUU-model (described in section 3) is a high resolution numerical model reaching down to 1 km horizontal resolution. The idea is to combine the MIUU-model wind fields in a way that is determined by the geostrophic wind field calculated in the first step. If the task in

24

producing accurate high resolution wind fields is successful, the wind fields can be used in e.g. a wind prediction model or wind energy production model. In section 4 some methods for the calculation of geostrophic wind were discussed and the small cross method was chosen. This section concentrates on the second part of the problem. A methodology used in order to combine MIUU-model simulated wind fields is developed and some first results are presented. A simplified method involving a restriction in space is discussed in section 5.1. The different steps involved, in this method for the calculation of high resolution wind fields, are discussed in section 5.2. After this in section 5.3, follows a presentation of the results. This part includes comparisons between the calculated wind, the geostrophic wind and the measured wind from the tower at Utgrunden, Figure 4.2. 5.1 Simplifications In order to develop a method for the calculation of the wind, which can be tested and evaluated on an early stage, some restrictions are made. Wind speed and wind direction data for comparison is available from a tower at Utgrunden, se below. The wind is therefore calculated for one grid point, having the position of Utgrunden, instead of for the whole area. Utgrunden (56.4°N, 16.3°E) is situated in an area with a wind power park in the south part of the strait between the island of Öland and the Swedish mainland (Figure 4.2). Automatic meteorological measurements are carried out in a tower at Utgrunden, from which wind speed and wind direction data is available. Wind speed data from April, May, September and October 2001 are used for the evaluation of the developed wind calculation method. Utgrunden tower measures wind-speed and direction at the height of 38 m. This height is situated between two wind calculation levels in the MIUU-model. To account for this a logarithmical weighting is made between the levels. 5.2 Method for estimation of the actual wind In order to calculate the geostrophic wind speed- and direction for the position of Utgrunden, a weighting of values from different grid points, in the geostrophic wind grid system described by equation (4.10), is done. Values from the nearest five grid points are linearly weighted according to their distances to Utgrunden. In the MIUU-model database there are high resolution wind field simulations for a number of chosen atmospheric situations.

25

There are, as mentioned in section 3, 192 different MIUU-model simulations, 48 for each of the four defined seasons. Those MIUU-model simulations are combined to fit real atmospheric situations and for those give an estimation of the actual wind. The simulations are combined according to the calculated values on the geostrophic wind speed and direction that are calculated from the NCEP-reanalysis. The method uses linear weighting between the MIUU-model simulations that are close to the actual atmospheric situation. First, the geostrophic wind speed interval is identified. The geostrophic wind speed is included in one of the following intervals: Ug ≤ 4 m/s, 4 m/s < Ug < 9 m/s, 9 m/s ≤ Ug < 14 m/s or 14 m/s ≤ Ug. If Ug ≤ 4 m/s, one of the sixteen 4 m/s-MIUU-model simulations are used when combining the wind fields. The same goes for when 14 m/s ≤ Ug. In this case, one of the sixteen 14 m/s-MIUU-model simulations is used. If 4 m/s < Ug < 9 m/s, both 4 m/s- and 9 m/s simulations must be used. The amount taken from each of the simulations is decided by linear weighting and depends on the exact value of Ug. The same tactic as above is used when 9 m/s ≤ Ug ≤ 14 m/s. The selection through geostrophic wind direction is carried out in a similar way as the selection through geostrophic wind speed. Wind direction is a continuous medium with no start or ending point. A linear weighting is therefore done between MIUU-model simulations for two of the geostrophic wind directions, 0°, 22.5°, 45° … 315°, 337.5°, no matter the value on the calculated geostrophic wind direction. The selections through geostrophic wind speed and direction are combined in a method that is expressed in terms of equations below. The following notation is used. Notation: UgLow = the closest simulation speed in the MIUU-model database that is < UgSC. UgHigh = the closest simulation speed in the MIUU-model database that is > UgSC. WDgLow = the closest simulation direction in the MIUU-model database that is < UgSC. WDgHigh = the closest simulation direction in the MIUU-model database that is > UgSC.

Mod(...) = the MIUU-model simulations from the MIUU-model database, section 3. U = calculated wind speed. The procedure is split into 3 different cases:

1) UgSC ≤ 4 m/s 2) 4 m/s < UgSC < 14m/s 3) 14 m/s ≤ UgSC

1) If UgSC ≤ 4 m/s:

26

4gSCU

A = (5.1)

5.22)( gLowgSC WDWD

a−

= (5.2)

ModgLow

ModHigh

WDsmaA

WDsmaAU

) ,/4(*)1(*

) ,/4(**

−+

+= (5.3)

where A*a + A*(1-a) = 1 (5.4) 2) If 4 m/s < UgSC < 14 m/s:

5)( gLowgSC UU

B−

= (5.5)

5.22)( gLowgSC WDWD

a−

= (5.6)

ModgLowgLow

ModgLow

ModgLowgHigh

ModgHighgHigh

WDUaB

UaBWDUaB

WDUaBU

) ,(*)1(*)1(

) WD,(**)1() ,(*)1(*

) ,(**

gHigh

−−+

+−+

+−+

+=

(5.7)

where B*a + B*(1-a) + (1-B)*a + (1-B)*(1-a) = 1 (5.8) 3) If 14 m/s ≤ UgSC:

14gSCU

C = (5.9)

5.22)( gLowgSC WDWD

a−

= (5.10)

ModgLow

ModgHigh

WDsmaC

WDsmaCU

) ,/14(*)1(*

) ,/14(**

−+

+= (5.11)

where C*a + C*(1-a) = 1 (5.12) An illustrative example of the procedure is presented in Appendix B.

27

5.3 Results and Comparisons The computed wind speed for Utgrunden, the measured wind speed from Utgrunden and the geostrophic wind speed for Utgrunden are compared. Comparisons are carried out during four different time periods, April 2001, May 2001, September 2001 and October 2001, Figure 5.1 – 5.4. From these figures it can be seen that the estimations of the wind speed are pretty good during parts of the time periods e.g. first part of October 2001 where no big differences are seen at all. The diurnal variations in the measured wind speed are partly captured by the estimated wind speed. But the diurnal variations tend to be larger in the measured wind speed than in the estimated wind speed. There are some periods with large differences between the measured and estimated wind speed. Examples of these situations are 13-14 April, 22-23 April, 5-7 May, 9-11 September, 30 September and 24-25 October. Those particularly large differences are in most cases probably caused by bad estimations of the wind fields even though there could be some errors in the reanalysis data. Take the period 22 – 23 April. During this period the measured wind speed is much larger than both the calculated wind speed and the geostrophic wind speed. An examination of the synoptic situation showed that during this period an unusual warm air mass, over the Baltic States and Russia, was advected northwestward out over the colder Baltic sea. This means that the thermal influence during this period could have been large, causing the observed behaviour. This example shows that it’s very important to consider other parameters as well as the geostrophic wind speed and direction when estimating the wind. The temperature field for example is very important for the resulting wind field. The MIUU-model simulations are, as mentioned before, separated into four seasons categorized by the months January, April, July and October. For each season there are standard values, typical for that season, set on meteorological parameters. One example of such a meteorological parameter is the difference between air and sea temperature. There is then impossible to cover unusual synoptic situations, were the actual values on the parameters differ a lot from the typical, just by combining the MIUU-model simulations according to the geostrophic wind. In Table 5.1 there is a summary containing the mean values for the above parameters for the four different time periods. It can be seen that there is a higher mean value on the measured wind speed than on the calculated wind speed. The reason for this is the lack in capture of unusual synoptic situations in the calculated wind. These unusual weather situations include situations where thermal effects are large and greatly affecting the measured wind speed. In Figure 5.5 measured wind speed values from Utgrunden is plotted against calculated wind speed values for Utgrunden. Some organization in the values around 1:1 line can be seen. The higher mean value of the measured wind speed is visible in the linear regression and in the scatter. The behavior of the linear regression is a little bit strange for high wind speed values but the reason for this is the small amount of data used in the figure.

28

a)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

5

10

15

20

Dagar (2001 04 01 − 2001 04 15)

m/s

Beräknad vindhastighetUppmätt vindhastighetGeostrofisk vindhastighet

b)

16 17 18 19 20 21 22 23 24 25 26 27 28 29 300

5

10

15

20

Dagar (2001 04 16 − 2001 04 30)

m/s

Beräknad vindhastighetUppmätt vindhastighetGeostrofisk vindhastighet

c)

−15 −10 −5 0 5 10 150

5

10

15

The differens, UCALCULATED

− UMEASURED

(m/s)

Fre

quen

cy (

num

ber

of v

alue

s)

Figure 5.1: A comparison between the calculated wind speed (with the developed method), the measured wind speed at Utgrunden and the calculated geostrophic wind speed (from the NCEP – NCAR reanalysis). Figure a) shows a comparison for the first half of April 2001, Figure b) shows a comparison for the second part of April 2001. Figure c) shows residuals of wind speed between the calculated- and the measured wind speed at Utgrunden for April 2001.

29

a)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

5

10

15

20

Dagar (2001 05 01 − 2001 05 15)

m/s

Beräknad vindhastighetUppmätt vindhastighetGeostrofisk vindhastighet

b)

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 310

5

10

15

20

Dagar (2001 05 16 − 2001 05 31)

m/s

Beräknad vindhastighetUppmätt vindhastighetGeostrofisk vindhastighet

c)

−15 −10 −5 0 5 10 150

2

4

6

8

10

12

14

The differens, UCALCULATED

− UMEASURED

(m/s)

Fre

quen

cy (

num

ber

of v

alue

s)

Figure 5.2: A comparison between the calculated wind speed (with the developed method), the measured wind speed at Utgrunden and the calculated geostrophic wind speed (from the NCEP – NCAR reanalysis). Figure a) shows a comparison for the first half of May 2001, Figure b) shows a comparison for the second part of May 2001. Figure c) shows residuals of wind speed between the calculated- and the measured wind speed at Utgrunden for May 2001.

30

a)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

5

10

15

Days (2001 09 01 − 2001 09 15)

m/s

Beräknad vindhastighetUppmätt vindhastighetGeostrofisk vindhastighet

b)

16 17 18 19 20 21 22 23 24 25 26 27 28 29 300

5

10

15

Days (2001 09 16 − 2001 09 30)

m/s

Beräknad vindhastighetUppmätt vindhastighetGeostrofisk vindhastighet

c)

−15 −10 −5 0 5 10 150

2

4

6

8

10

12

14

The differens, UCALCULATED

− UMEASURED

(m/s)

Fre

quen

cy (

num

ber

of v

alue

s)

Figure 5.3: A comparison between the calculated wind speed (with the developed method), the measured wind speed at Utgrunden and the calculated geostrophic wind speed (from the NCEP – NCAR reanalysis). Figure a) shows a comparison for the first half of September 2001, Figure b) shows a comparison for the second part of September 2001. Figure c) shows residuals of wind speed between the calculated- and the measured wind speed at Utgrunden for September 2001.

31

a)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

5

10

15

20

25

Days (2001 10 01 − 2001 10 15)

m/s

Beräknad vindhastighetUppmätt vindhastighetGeostrofisk vindhastighet

b)

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 310

5

10

15

20

25

Days (2001 10 16 − 2001 10 31)

m/s

Beräknad vindhastighetUppmätt vindhastighetGeostrofisk vindhastighet

c)

−15 −10 −5 0 5 10 150

2

4

6

8

10

12

14

16

The differens, UCALCULATED

− UMEASURED

(m/s)

Fre

quen

cy (

num

ber

of v

alue

s)

Figure 5.4: A comparison between the calculated wind speed (with the developed method), the measured wind speed at Utgrunden and the calculated geostrophic wind speed (from the NCEP – NCAR reanalysis). Figure a) shows a comparison for the first half of October 2001, Figure b) shows a comparison for the second part of October 2001. Figure c) shows residuals of wind speed between the calculated- and the measured wind speed at Utgrunden for October 2001.

32

0 5 10 15 20 250

5

10

15

20

25

Estimated wind speed (m/s)

Mea

sure

d w

ind

spee

d (m

/s)

Windspeed

1:1

0.84078x+1.9868

Figure 5.5: Comparison between the measured wind speed at Utgrunden and the estimated wind speed at Utgrunden, calculated with the developed method. Table 5.1: A summary of the mean values of the calculated wind speed at Utgrunden U(calculated)Utgrunden, the measured wind speed at Utgrunden U(measured)Utgrunden and the calculated geostrophic wind speed at Utgrunden UgUtgrunden for the four time periods, April 2001, May 2001, September 2001 and October 2001. U(calculated)Utgrunden m/s U(measured)Utgrunden m/s UgUtgrunden m/s April 2001 6,32 7,12 8,34May 2001 6,31 7,32 8,69September 2001 5,53 6,64 7,84October 2001 6,79 7,83 10,51

6. SUMMARY AND CONCLUSIONS There is a rising interest in renewable energy sources these days. The amount of energy produced by sources as wind power is rising. The profitability in wind power energy depends partly on the position of the turbines but also on the predictability of the next day’s energy production. Many wind energy producers are interested in wind prediction methods. There are already a bunch of methods in use or under development in Europe and North America. Those methods involve both numerical modeling of wind fields, with high resolution, and statistical methods. All models need meteorological data, describing the prevailing synoptic situation, as input. The quality of this synoptic data is important for the wind

33

predictions. Normally the synoptic data is available through the national weather service and may be of routine forecast type, e.g. the synoptic wind field available may be of a large scale type with low resolution. The purpose of this work was to examine if an already existing database, containing high resolution wind fields simulated by the MIUU-model (section 3), could be used to create high resolution fields fitting any wanted synoptic situation. The idea was to use reanalysis data (section 2) to categorize this synoptic situation. The synoptic situations simulated by the MIUU-model are separated into four different seasons containing typical values on meteorological parameters for each season. The only thing separating the simulations, within a season, is the geostrophic wind situation. Simulations are characterized by 3 different values on the geostrophic wind speed and 16 different values on geostrophic wind direction. The idea was then to calculate the geostrophic wind, from reanalysis data, and use it to combine the MIUU-model simulations, by this making a first estimation of the actual wind. The first problem that needed some attention was the calculation of geostrophic wind. The NCEP-NCAR reanalysis data was chosen for this in competition with the ECMWF produced ERA-40 data set. The reason for this choice was the frequent updates in the NCEP-NCAR reanalysis. The geostrophic wind is not available directly from the reanalysis data set but it can be calculated from reanalysis parameters. There are several different reanalysis parameters that could be used to calculate the geostrophic wind. The parameter chosen here was the 850 hPa geopotential height. Some different geostrophic wind calculation methods were examined. All of them try to calculate the geostrophic wind by calculating horizontal gradients of 850 hPa geopotential height. The difference lays in how these gradients are calculated. Methods using data from grid points in the form of triangles (the triangle-method, section 4.1) or rectangles (the small and large cross-methods, section 4.2) were examined. The methods were compared against each other and some problems with the triangle-method were revealed and corrected. It was discovered that the estimation of geostrophic wind direction was insecure for situations with very low geostrophic wind speed. After the corrections, in the triangle-method, there were no large differences left between the results from the different geostrophic wind calculation methods. The choice of method shouldn’t then be critical. The conclusion arrived at was that the small cross-method probably is the method with the best capacity, mainly because it has two advantages. It uses reanalysis data from four grid points instead of three, which is the case for the triangle-method, and it uses a smaller calculation area, than the large cross-method, which should result in a capture of more large 850 hPa geopotential gradient situations. The chosen method seems to work well but there is a lack of actual geostrophic wind fields to test it on. This lack of real testing must be remembered when looking for error sources. It also can not be out ruled that there may exist some errors in the reanalysis data fields. The second important step that needs a lot of attention is the evolution of a method for the fitting of MIUU-model simulations to the synoptic situation, described by calculated

34

geostrophic wind speed and direction values. There is not a total correlation between the geostrophic wind speed and actual wind speed so these first estimations can’t be expected to capture all synoptic situations well. But it still worth some effort to make this first estimation method as good as possible, creating a stable ground to stand on for continuation work. In order to make evaluation simple it was decided to evolve a “local method” that calculates the wind speed for the coordinates of Utgrunden (figure 4.2). At Utgrunden there is a tower from which automatically measured values of the wind speed and wind direction are available. A linear weighting, between geostrophic wind values, have been used to calculate the geostrophic wind for Utgrunden. This weighting is done with respect to the distances between Utgrunden and the closest grid points in the small cross-method grid system. A linear weighting has also been used to fit the MIUU-model simulations to calculated values on the geostrophic wind speed and geostrophic wind direction. There is nothing that says that a linear weighting must be best, but it seemed as the most natural weighting method to start with. Comparisons between the estimated wind at Utgrunden, the measured wind at Utgrunden and the calculated geostrophic wind at Utgrunden are carried out for April, May, September and October 2001. The values on the calculated and measured wind speed show quite good correspondence during some parts of these periods, e.g. the first part of October 2001 shown in Figure 5.4c), but they also differ considerably sometimes e.g. 22 – 23 of April 2001 shown in Figure 5.1b). The reason for many of the cases, with large differences between calculated and measured wind speed, is suspected to be the occurrence of an unusual weather situation. Such a situation could produce values on the meteorological parameters that are very different from the typical of the season. Remember that the MIUU-model database is divided into four different seasons (represented by January, April, July and October), during which typical values is set on meteorological parameters. If the temperature field is considered, it will probably lead to improvements in the resulting wind during many periods; see e.g. the situation during 22 – 23 April 2001 shown in Figure 5.1c). During this period an unusually hot air mass was advected, out over the Baltic Sea against Sweden, from Russia and the Baltic states. Also other parameters than the temperature may have to be studied in order to improve the results. The results arrived at here are produced by a very simple method and they point in the right direction. The conclusion is that it may be possible to produce accurate high resolution wind fields with a method of this kind, given time and research. Accurate high resolution wind fields could possibly be used as input data in wind prognostic models, the high resolution of the data would then be of an advantage. A method of this type, for the calculation of high resolution wind fields, would work as a “short cut”, giving an opportunity to produce high resolution wind fields without the use of any time consuming high resolution model.

35

ACKNOWLEDGEMENTS I want to thank my supervisors Cecilia Johansson and Hans Bergström for all their help and support during this project. Ann-Sofi Smedman and Sven Israelsson for all their time and advises. I also want to thank my fellow students Alexandra and Susanna for their company during this semester. I want to send a great thank you to all my fantastic neighbors in my student corridor in Flogsta, I must have been really lucky turning up living in such a great place. Finally I want to thank my family who supports me in all occasions.

REFERENCES 1. Bergström, H.: 2004, ‘Higher-order closure meso – scale modelling for wind resurse estimates in Sweden’. Proceedings from European Wind Energy Conference EWEC2004, London, 22-25 Nov. 2004 2. Bergström H. and Mohr M.: 2004, ‘Wind Energy Mapping using a Mesoscale Atmospheric Model and a Global Meteorological Database’. Proceedings EWEC2004, London, 22-25 Nov. 2004 3. Elevant K.: 2004, ‘Vindmodellering genom nedskalning av ETA-modellen’, 1 june. 2004, Vindforsk. 4. Elmqvist Å.: 2003, ’Lägesrapport 2003’, Vindforsk 5. Kalnay E., Kistler R., Collins W., Saha S., White G., Woollen J., Chelliah M., Ebisuzaki W., Kanamitsu M., Kousky V., van den Dool H., Jenne R. and Fiorino M.: 2001, ‘The NCEP–NCAR 50–Year Reanalysis: Monthly Means CD–ROM and Documentation’. Bulletin of the American Meteorological Society: Vol. 82, No. 2, pp. 247–267 6. Kalnay E., Kanamitsu M., Kistler R., Collins W., Deaven D., Gandin L., Iredell M., Saha S., White G., Woollen J., Zhu Y., Chelliah M., Ebisuzaki W., Higgins W., Janowiak J., Mo K. C., Popelewski C., Wang J., Leetmaa A., Reynolds R., Jenne R. and Joseph D.: 1996, ‘The NCEP/NCAR 40-year Reanalysis Project’. Bulletin of the American Meteorological Society: Vol. 77, No. 3, March 1996, pp. 437 – 471. 7. Källstrand B.: 2004, ’Inventering av vindenergiprognossystem’. Elforsk rapport 04:14 8. Mellor G. L. and Yamada T.:1974, ’A hierarchy of turbulence closure models for planetary boundary layers’, Journal of the Atmospheric Sciences: Vol. 31, pp. 1791 – 1806. 9. Enger, L.: 1990, ‘Simulation of dispersion in moderately complex terrain. Part A: The fluid dynamic model’, Atmos. Environment, 24A, 2431-2446.

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APPENDIX A: DIFFERENCES BETWEEN TRIANGLE-METHOD AND LARGE CROSS-METHOD AND THEIR CONSEQUENCES

In section 4 different calculation methods for the geostrophic wind was presented and described. When comparisons was done between the triangle-method and the cross-methods a bias was found, i.e. there was a systematic difference in the calculated geostrophic wind between the methods, see Figure 4.8. Examination revealed an error in the triangle-method. Removing this error resulted in elimination of the bias and put the triangle equation on a form resembling the cross-method equation. See the modified triangle equation (A1) and the large cross-method equation (A2) for the situation described by Figure 4.1.

)(270514.0

)(290694.0

12

13

hhv

hhu

g

g

−=

−= (A1)

[ ][ 4321

4321

131444.0

146052.0

hhhhv

hhhhu

g

g

−+−−=

−−

]+−=

(A2)

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

g

g

uv

ionwinddirect arctan270 (A3)

However there still exists differences between the triangle- and the cross-methods, (A1)

and (A2), that reveal them self when studying the quotient g

g

uv

. This quotient decides the

geostrophic wind direction through (A3) and is therefore worth discussion. The large cross-method instead of the small one is used in this comparison because two of the sides in the triangle-method are used by the large cross-method. The difference between the quotients in the two methods arises because Earth is a sphere. Because of this the points h1, h2, h3 and h4 in Figure 4.1 doesn’t make up a real rectangle i.e. the longitudinal distance x4-x3 is larger then the distance x2-x1. The actual situation is better described by schematic Figure A1 below.

37

Figure A1: The distances between two longitudinal circles changes with latitude and therefore an rectangle on Earth’s surface is’t actually a real rectangle. When comparing the methods it can be seen that the longitudinal distances are measured on different latitudes but the latitudinal distances do remain the same, i.e.

( )12 xxx −>∆ and )( 13 yyy −=∆

⇒ 13

12

yyxx

yx

−−

>∆∆ (A4)

where 1.1111xy

∆=

∆ and 2 1

3 1

1.0745x xy y−

=−

for the situation described by Figure 4.1.

In the cases of wind direction in 45°, 135°, 225° or 315°, the components are equal in size. For the triangle-method (A1), we will then have:

0745.1270514.0290694.0

)(270514.0)(290694.0

13

12

1213

==−−

⇒

−=−

hhhh

hhhh (A5)

where h2 - h1 is the longitudinal difference of geopotential height and h3 - h1 is the latitudinal difference. The resulting value of the quotient is the same as the value arrived at in the above study of the quotient between the longitudinal and latitudinal distances The same situation for the large cross-method (A2) gives:

h1 h2

(x1,y1) (x2,y2)

h3 h4

(x3,y3) (x4,y4)

38

[ ] [ ]

1111.1131444.0146052.0

2)(

2)(

2)(

2)(

)()()()(

)(131444.0)(131444.0)(146052.0)(146052.0131444.0146052.0

2413

3412

2413

3412

34122413

43214321

==∆∆

=−

+−

−+

−

=−+−−+−

⇒

−+−=−+−−+−−=−−+−

y

x

hh

hhhh

hhhh

hhhhhhhh

hhhhhhhhhhhhhhhh

(A6)

where ∆hx and ∆hy is the longitudinal- and latitudinal difference in 850 hPa geopotential height. An ideal situation is described by

2 1 4 3

3 1 4 2

( ) ( )

( ) ( )h h h hh h h h− = − ⎫

⎬− = − ⎭ (A7)

This corresponds to a situation where the same amount of iso-lines runs through the contrary sides, see Figure A2. In this case (A6) will be simplified to:

1111.1131444.0146052.0

13

12 ==−−

hhhh (A8)

The above equation should be compared to equation (A5). This result implies that the triangle- and the large cross equations won’t give the same direction.

Figure A2: A figure illustrating the meaning of equation (A7) i.e. that an equal amount of ”iso”-lines runs through the contrary sides

”Iso”- lines for the 850 hPa geopotential height.

39

APPENDIX B: AN ILLUSTRATIVE EXAMPLE SHOWING HOW TO ESTIMATE THE ACTUAL WIND USING THE METHOD DEVELOPED IN SECTION 5.2 Example (B.1): The geostrophic wind is calculated from NCEP-NCAR reanalysis data using the small cross-method. An estimation of the wind, which depends on the calculated geostrophic wind, is then accomplished by a weighting of different MIUU-model wind fields, which are available from a database of MIUU-model simulations. Let’s study a fictive situation with the following values on the geostrophic wind speed and the geostrophic wind direction. Geostrophic wind speed smU gSC / 12=

Geostrophic wind direction °= 50gSCWD The geostrophic wind speed belongs to the interval 4 m/s < UgSC < 14 m/s so this is a case 2, see section 5.2. This means that the weights for geostrophic wind speed and direction should be calculated by equations (5.5) and (5.6). The calculations of the weights are given in equations (B1) and (B2) below.

53

5)/9/12(

5)(

=−

=−

=smsmUU

B gLowgSC (B1)

92

5.22)4550(

5.22)(

=°°−°

=°

−= gLowgSC WDWD

a (B2)

The wind speed is estimated with equation (5.7), see equation below (B3). These weights, a and B above, is combined in four different ways, each combination corresponding to a certain MIUU-model simulated wind field. The resulting calculated wind speed is then created from a weighted combination of the four MIUU-model simulated wind fields that are closest to the synoptic situation in a geostrophic wind sense. In this case the geostrophic wind, UgSC = 12 m/s, is closer to MIUU-model simulations for Ug = 14 m/s, than to MIUU-model simulations for Ug = 9 m/s. The resulting weighting (B1) will then give MIUU-model simulations with Ug = 14 m/s a larger importance, for the resulting calculated wind from (B3), than the simulations with Ug = 9 m/s. The given geostrophic wind direction, WDgSC = 50°, is much closer to 45° than 67.5°. This weighting through (B2) gives the MIUU-model simulations with WDg = 45° much more importance, for the resulting calculated wind, than the simulations with WDg = 67.5°.

40

The (14m/s, 45°)Mod-MIUU-model simulation will then be the simulation that has largest impact on the resulting wind field and the (9m/s, 67.5°)Mod will be the simulation with smallest impact, see the quotients, 21/45, 14/45, 6/45 and 4/45, in equation (B3), that weights the different simulations. Notice that a summation of these weights must give the sum 1. The wind speed for this fictive situation is calculated according to:

=°+°+

+°+°=

=°+°+

+°+°=

=−−+

+−+

+−+

+=

ModMod

Mod

ModMod

Mod

ModgLowgLow

ModgHighgLow

ModgLowgHigh

ModgHighgHigh

smsm

smsm

smsm

smsm

WDUaB

UaBWDUaB

WDUaBU

)45 ,/ 9(*4514)5.67 ,/ 9(*

454

)45 ,/ 14(*4521)5.67 ,/ 14(*

456

)45 ,/ 9(*97*

52)5.67 ,/ 9(*

92*

52

)45 ,/ 14(*97*

53)5.67 ,/ 14(*

92*

53

) ,(*)1(*)1(

) WD,(**)1() ,(*)1(*

) ,(**

Mod

Mod (B3)

where 14514

454

4521

456

=+++

41