FORECAST MODELS OF WIND CHARACTERISTICS IN SOUTH AREA OF TAIWAN

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1 FORECAST MODELS OF WIND CHARACTERISTICS IN SOTH AREA OF TAIWAN YANG H. Y. Air Force Aeronautical & Technical School, No., Cheh-Sou W. Road, Kang-Shan, Kaohsiung county, Taiwan, R.O.C. The prediction of wind characteristics is very important for meteorology of air pollution. The wind characteristics include wind speed, wind direction and wind gust. In this study, the time series forecast models are developed. The correlation between wind characteristics at different time steps is investigated. This correlation study suggests the significant predictors of individual wind characteristics for required forecast time. The single variable and multivariable autoregression models are built and the forecast abilities are evaluated utilizing real data. To improve the prediction of the trend, the time series are normalized using their means and standard deviations. The wind characteristics in Taiwan are strongly influenced by monsoon and sea breeze. The monsoon is very insistent in winter and summer. The sea breeze is more obvious in summer time. Considering these two main mechanisms, the wind velocity is decomposed into two components. One is perpendicular to coastal line, and the other is along the coastal line or along the monsoon direction. The models include fixed time and arbitrary time forecast models. The former is the forecast for a fixed hour in each day and therefore has 4 forecast models in each season. The modeling results will be evaluated using real data, and recommendations for further studies are also suggested. INTRODCTION Taiwan is surrounded by sea and affected by monsoon and sea-land wind in the whole year. This report divides into two types of timing and non-timing, discussing the change of wind speed vector of seaside surface with auto regression models. Cases study in report comes from the data proceeded in summer and winter of Taiwan Power Company stations set up in Sin-Da and Yun-An of Kaohsiung Hsien. RESEARCH METHOD Auto Regression models can be written as below type: ~ ~ ~ ~ Z t = Zt + Zt nzt p + at, here, Z ~ t = Z t µ. µ is the average value of observational physical quantity. µ = E(Z), E ( Z) = ZP( Z) Z E(Z) is µ, showing expecting value (ensemble mean), Z is non-serial physical value, P(Z) is the appearance percentage of observational value. Generally, doing research never trying the average of population but samples of population only. So showing the evaluating value of µwith samples average value Z. Zi i= Z = µ = N N is non-serial observational physical number (means data number), Z i is non-serial physical value.ψ,ψ,ψ 3,...,ψ P is the parameters of auto regression type AR(P), { a t }series is shocks, hypothesis of such shocks is normal distribution, whose expecting value is zero. ariance is a t, a t-,,a t-p, which is so-called white noise. If identify function(b) is (-ψ B-ψ B -...-ψ P B P ), B is back-shift operator, thus B m Z t means Z t-m,so AR(P) can Z ~ = a t. The above type is the general type of auto regression model. be written ψ(b) t The data of observational stations are wind vector (eight-position), can be divided into two independent component,, for establishing models separately. () Timing Prediction: Doing auto regression model AR(P) on firm time everyday. Setting one model each hour, there are 4 hours of time serial models. But this content only shows case study with time of 3:00 p.m. IAPPA Praha Section: B

2 () Non-Timing Prediction: Doing each hour wind field auto regression model AR(P) by season (3 months data), different season shows different model. (3) Best Forecasting Component Angle: The best component standard on deleting or not, is to find out two sets of best effect from different shadow component. Which can forecast the size and direction of wind field. RESLTS & DISCSSION The aim of this report is wind field, weather data from the surface wind data of Taiwan Power company observational stations in Sin-Da and Yun-An(based on the summer of 983, June 5 to Sep. 5 and the winter of 983, Dec. to Feb. of 984 ). Generally, we separates wind direction into 6 positions to get a more accurate data than that wind direction is divided by eight positions. The data acquired in this paper is the angle of average wind direction of each hour (position product 45 ). Wind speed adopts the average of wind speed of each hour, showing by m/sec. Best Choice of Component Direction: α is the projected holding-angle between component and north direction, which can be divided into eight individual cases from precise north with clockwise direction as 0,.5, 45, 67.5, 90,.5, 35, The α can be got through wind speed and wind direction θ: W = -cos(θ-α) Doing projected component on different α can be set up on the auto regression models AR(), AR(4), AR(6) of Sin-Da station. The orders of M to M8 are α=0 toα= 57.5 (the range is.5 ), the stable standards of seeking ψ and ψ of AR() are: ψ + ψ <, ψ - ψ <, - <ψ <. The all models ψ and ψ of M to M8 from winter wind field of Sin-Da station are satisfied with the above stable condition. Average Observations, Standard Deviation of Observations σ o and Standard Deviation of Forecasts σ c on auto regression Models are listed. For testing model precision, it needs to omit standard deviation of forecasts from standard deviation of observations. Then, uses the difference to divide standard deviation of observations. At last, products percentage for getting Forecast Efficiency. The percentage of forecast efficiency is bigger, the standard of forecasts is higher; on the other hand, the standard is lower (William, 980), means: ( ) 0 = Z Z σ N σ c = ( Z Z ) N P σ 0 σ c = σ 0 00% The Z in models shows observing value, Z shows evaluating value of µmeaning sample mean of observing value; N is time number, Z shows prediction value;σ c is standard deviation of prediction meaning value to observing value; P is the parameter of auto regression model; is forecast efficiency. The relationship of σ 0,σ c and can be described in different conditions as below: If σ c > σ 0, <0 then the model meaningless () If σ c =σ 0, =0, then the value is average value (3) If σ c =0, =l, then the is precise (means value is observed value ) (4) If σ c < σ 0, 0, then the models has its own meaning.the three models σ 0,σ c and are shown in table. The forecast efficiency in model M to M8 are 36.0% %, the biggest value is on M or M3 with 53.6% or 53.5%. The majority of north-east monsoon in winter of Taiwan, and the wind directions are most between 0 and 67.5.The projected component value of direction α =.5 or α 3 = 45 are bigger, its observing value are IAPPA Section: B

3 easier for. Table shows forecast efficiency of every models of Sin-Da observing station AR(4). The forecast efficiency and the biggest value in models M to M8 all be happened in AR(). All AR(6) models in Sin-Da station its results are familiar as AR(4) except the forecast efficiency of M3 and M7. The value of the forecast efficiency of M to M8 is 39.6% - 54%, M3 has the biggest value 54%( means α= 45 ), as shown in table 3. The comparison of the forecast efficiency of AR(), AR(4) and AR(6) is on table 4, which shows that promoted AR(6) stage can increase forecast efficiency. To discuss that the effect of different wind field to forecast. To proceed different wind field component combinations can seek two wind field components of one better model in order to establish required model. From above models from winter non-timing on different component there are 8 conditions, no matter what the result of AR(), AR(4) or AR(6) showing the better combined condition are α= 45 and α=.5,which have smallest value on biggest error value and standard deviation, meaning the forecast and the observation are closer. The below paragraphs use the wind field component α= 45 as component, and α=.5 as component, for establishing every models in Sin-Da and Yun-An. Wind field models of Sin-Da and Yun-An stations The residual value of Sin-Da and Yun-An non-timing models during the period of winter and summer of the. component less than twice standard deviation. Its χ total inspection also corresponds to requirement (0.95 reliable standard ), which shows that all models are effective. Regarding non-timing, table 5 shows wind direction and speed of time serial model from Sin-Da and Yun-An stations (displaying with. component). The same non-timing process stage, it shows timing component combinations situations the better combinations are also α= 45 and α= ll.5.table 6 shows, models of time serial models from Sin-Da and Yun-An stations. The total comparison on time serial models of Sin-Da and Yun-An stations, timing efficiency is better than non-timing. (as shown in table 7) REFERENCES: [] Box, G.E,P. & Jerkins G.M.,976:Time Series Analysis, Forecasting & Control. Holden Day, San Francisco. 575pp. [] William.G.C.,980:Statislical Methods. The Iowa Stale niversity Press Ames, Iowa,.S.A. 507pp. [3] Yang,H.Y.,985:Multiple Time Series Models for Wind Field Forecasting. Institute of Geography of Chinese Culture niversity. Taipei, Taiwan, R.O.C. 58pp. Forecasting standard M M M M M M M M Tab.. Wind field on auto regression model of winter no-timing AR(), establishing with equal interval by.5 for M to M8 from precise north direction to clockwise direction. standard M M M M M M IAPPA Section: B

4 M M Tab.. Wind field on auto regression model of winter notiming AR(4). standard M M M M M M M M Tab. 3. Wind field on auto regression model of winter no-timing AR(6). Forecasting efficiency AR() AR(4) AR(6) M M M M M M M M Tab. 4. comparison of winter no-timing AR(), AR(4), AR(6), M to M8 reference table 3. Season Component Statistics station γ 4 a Sin-Da Yun-an winter Sin-Da Yun-an Sin-Da Yun-an summer Sin-Da Yun-an Tab. 5. Wind direction and speeds of no-timing model at Sin-Da and Yun-An station. Season Component Statistics station winter summer 0 3 Sin-Da Yun-an Sin-Da Yun-an Sin-Da Yun-an Sin-Da Yun-an IAPPA Section: B γ a

5 Tab. 6. Timing Forecasting Model season winter summer Statistics component stations No-timing efficiency timing efficiency No-timing efficiency timing efficiency Sin-Da Yun-An Tab. 7. Forecasting efficiency comparison of timing and no-timing about and component at Sin-Da and Yun-An stations (per % as unit) IAPPA Section: B