Prediction of monthly-mean hourly relative humidity, ambient temperature, and wind velocity for India

Renewable Energy, Vol. 13, No. 3, pp. 363-380, 1998

~ Pergamon

© 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain (98)00010-X 0960-1481/98 $ ! 9.00 + 0.00

PII : S0960-1481

DATA

BANK

Prediction of monthly-mean hourly relative humidity, ambient temperature, and wind velocity for India G. V. PARISHWAD,* R. K. BHARDWAJ and V. K. N E M A Department of Mechanical Engineering, Motilal Nehru Regional Engineering College, Allahabad--211 004, India (Received 10 November 1997 ; accepted 2 January 1998) Abstract--This paper presents a procedure to predict monthly-mean hourly values of relative humidity, ambient temperature and wind velocity for an Indian location. Three maps, showing distribution of annual-average hourly values of humidity, temperature and wind velocities, are prepared from the analysis of available meteorological data of 205 Indian cities. An equation is obtained for annual-average temperature as a function of altitude of the location. Sets of equations are then developed to predict the said weather parameters by the least square regression analysis of the data of 14 cities, taken from different regions, out of 19 cities for which detailed weather data was available. A ratio of monthly-mean to the yearly-mean value of variable is correlated with month and then hourly to the monthly-mean value is correlated with day-hours. On comparison of the computed results with the measured data of the remaining 5 cities, yearly-average relative standard deviations are 14.6, 10.5 and 26.7% for monthly-mean hourly relative humidity, ambient temperature and wind velocities, respectively. © 1998 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION Information on monthly-mean hourly values of relative humidity, ambient temperature and wind velocity is useful in the thermal analysis of building, beating and cooling load calculations to decide the correct sizing of an air-conditioning system for thermal comfort and in the performance evaluation and optimum design of many solar energy systems. Hittle and Pendersen [1] analyzed actual weather data for the calculation of heat conduction through multi-layer building walls. Hokoi et al. [2] developed stochastic models for estimating solar radiation ( A R M A model) and outdoor temperature time series ( A R M A X model) considering the cross correlation between the two. They used weather data of Japan. Average weather data from observations of meteorological department of India are available in the form of compiled books [3-6]. Mani [3] presented detailed data on monthly-mean hourly solar radiation, monthly-mean hourly humidity, rainfall, temperature and wind velocities for 18 cities averaged over 21 years. Mani and Rangarajan [4] have included the derived solar radiation data for 127 cities and the measured data on monthly-mean hourly weather parameters such as temperature, humidity and rainfall for 30 cities. It also includes monthly-mean daily values with hourly values for a few specific hours of these parameters for 76 cities. Mani and Mooley [5] have compiled measured data on monthly-mean hourly values of wind velocity and other data related to wind energy for 25

* Author to whom correspondence should be addressed. 363

364

Data Bank

cities. It also contains monthly-mean daily values from the measured wind velocities for a few specific hours based on the observations of 10 years for 300 stations. Seshadri et al. [6] have given average of daily minimum, maximum and mean values for temperature, humidity and wind velocity for 155 cities. Many cities are common in the Refs. [3-6]. However, there is a need to develop a mathematical procedure using the above data which would help to predict the weather information for places for which measured data is not available. It is observed from the available meteorological data [3-6] on monthly-mean hourly relative humidity, ambient temperature and wind velocity for different Indian locations that they follow a certain pattern with respect to time at any location. This work presents a procedure to predict monthly-mean hourly values of these weather parameters for any Indian location based on the least square regression analysis of the available measured data. 2. ANALYSIS 2.1. Determination of annual-mean values of weather parameters From the available weather data [3-6] it is observed that variation of the monthly-mean hourly values of humidity, temperature and wind velocity, non-dimensionalised with the corresponding monthly-mean value, with day hours has a particular pattern. Monthly-mean values non-dirnensionalised with the corresponding yearly-mean value also follow a particular pattern over various months of a year. Therefore, initially the monthly-mean hourly weather data of 205 cities is used to estimate annual-mean values of humidity, temperature and wind velocities. Using these values three maps are prepared showing distribution of annual-mean relative humidity (Fig. 1), ambient temperature (Fig. 2) and wind velocity (Fig. 3). These 205 cities, distributed over India, are shown by small dots in the figures. Nineteen cities out of these 205 cities for which monthly-mean hourly data of humidity, temperature and wind velocity is available [3-6], are selected for detailed analysis. Geographical data and annual average weather data of these 19 cities is given in Table 1. These 19 cities are shown by bigger dots in the three maps. Annual-mean of these parameters can be obtained from these three maps. Annual-mean of ambient temperatures of 35 locations in India having altitude higher than 500 m is plotted against the height above mean sea level (HAMSL) in (Fig. 4). It is found that a simple linear equation provides a fairly accurate fit. The equation thus obtained is

Ta = 28.87-- (7.412 x H)

for H >t 0.5

(1)

where T~ is annual-mean ambient temperature in °C and H is the H A M S L of the location in kin. Coefficient of correlation, r, is found to be 0.9658 for the equation. The equation obtained (eqn. (1)) is found similar to the theoretical one given by Schlichting et al. [7]. 2.2. Determination of monthly-mean values of weather parameters In order to find the variation of monthly-mean values of humidity, temperature and wind velocity with respect to the yearly-mean value 14 cities, namely, Calcutta, Chennai, Indore, Jagadalpur, Jaipur, Jodhpur, Kodaikanal, Leh, Mumbai, Nagpur, Pune, Shilong, Thiruvananthapuram, and Vishakhapatnam are taken out of the initially selected 19 cities. From the available [3~] monthlymean hourly values of the three parameters monthly-average and then yearly-average values from monthly-mean values for these 14 cities are calculated. The monthly-mean hourly values, (H, T and W), are then non-dimensionalised with respect to monthly-mean values for each month (Hm, Tm and Win), and the monthly-mean values with respect to yearly-mean values (Ha, Ta and Wa). 2.2.1. Relative Humidity. It is observed that the variation of the humidity ratio, (Hm/H~), over the year for a location depends upon the annual-average humidity, (Ha), of the city. Accordingly the cities can be divided into 4 groups of annual average relative humidity (%), such as, 40 < Ha ~< 50, 50 < H~ ~< 60, 60 < Ha ~< 70 and H, > 70. The pattern of (Hm/Ha) over the year for different cities for these four groups are shown in Fig. 5(a~t). It is observed that the fluctuation of humidity ratio is more in case of lower H,. Annual-mean humidity (Ha) for Indian cities ranges between 40-80%. The scatter of different cities according to their annual-mean humidity is found to be best fitted into two different third order polynomials into two half-yearly parts. The humidity ratio can be obtained from the equation

Data Bank 1

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Fig. 1. Distribution of annual-average of hourly relative humidity (%).

366

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Fig. 3. Distribution of annual-average of hourly wind velocities in kmph.

368

Data Bank Table 1. Geographical data of the 19 Indian locations of the study Annual-average-hourly

S.N.

City

Latitude

1 2 3 4 5 6 7 8 9 I0 11 12 13 14 15 16 17 18 19

Ahmedabad Bangalore Calcutta Chennai Gaya Indore Jagadalpur Jaipur Jodhpur Kodaikanal Leh Mangalore Mumbai Nagpur New Delhi Pune Shillong Thiruvananthapuram Vishakhapatnam

23.07N 12.95N 22.65 N 13.00N 24,82N 22.72N 19.80N 26.82N 26.30N 10.23N 34.15N 12.92N 19.12N 21.10N 28.58N 18.53N 25.57N 08.48N 17.72N

(o)

Wind Longitude HAMSL* Humidity Temperature Velocity (°) (m) (%) (°C) (kmph) 72.63E 77.63E 88.45 E 80.18E 85.02E 75.80E 82.03E 75.80E 73.02E 77.47E 77.57E 74.88E 72.85E 79.50E 77.20E 73.85E 91.88E 76.95E 83.23E

55 897 6 16 111 567 533 390 224 2345 3514 102 14 310 216 559 1600 64 3

52.51 71.44 75.29 74.24 62.51 47.82 67.53 47.77 41.99 78.47 44.08 79.3 70.72 56.65 56.34 60.65 74,86 81,02 74.67

27.12 23.23 25.75 27.92 25.83 24.68 24.62 25.22 26.91 13.69 5.56 26.55 26.75 26.31 24.87 24.96 16.29 26.66 27.46

11.57 9.12 8.08 11.57 7.51 14.4 3.48 6.73 9.27 13.2 5.6 4.79 11.08 6.93 10.15 9.63 3.26 6.88 8.89

* HAMSL-Height Above Mean Sea Level.

Hm/H~ = a + b m + c m z + d m 3

(2)

2.2.2. Ambient Temperature. It is observed that the variation of the ambient temperature ratio, (Tm/Ta), for different cities also depends upon the annual-average humidity, (Ha), of the city. This variation can be divided into two groups of annual average relative humidity (%), such as, H, < 60 and Ha > 60. It is observed that the fluctuation of temperature ratio is more in case of lower Ha. The pattern of (Tm/Ta) over the year for different cities for these two groups are shown in Fig. 6(a,b). The temperature ratio can be obtained from the equation

T~/T~ = a + b m + c m z + d m 3

(3)

2.2.3. Wind Velocity. For all the cities variation of wind velocity ratio, (Wm/Wa), over the year is found similar as shown in Fig. 7. Though the scatter is slightly wide, wind velocity ratio can be obtained from the equation Wrn/Wa =

a + b m + c m 2+ d m 3

(4)

In eqns (2)-(4), m is a month number and values of constants a, b, c and d can be taken from the Table 2. 2.3. Determination of monthly-mean hourly values of weather parameters On the same line as above, non-dimensionalmonthly-mean hourly values (H/Hm, T/Tm and W/Wm) for the three parameters are correlated with day-hours. 2.3.1. Relative Humidity. It is observed that the pattern of variation of humidity ratio (H/H~) for the cities over the year vary in a particular manner. The amplitude of the fluctuation is large in the

Data Bank

369

30 +

g:0

............................

gl5

Measured

............................................................................................... *

+'¢'

....

0l

Or-, 0

, 1

. 2 HAMSL,

.

.

. 3

. 4

kin

Fig. 4. The scatter of annual-average ambient temperature with height of the Indian location above mean sea level.

month of January. This amplitude slowly goes on decreasing in the following months. This fluctuation is minimum during rainy season i.e. June-August. The amplitude again goes on increasing from September to December. However, this pattern for different cities can be divided into two groups based on annual-average humidity, (Ha), of the city, such as, Ha ~< 70% and Ha > 70%. Overall fluctuation of humidity ratio, (H/Hm), for former is more as compared to that with other. The representative scatter of humidity ratio (H/Hm) with day-hours for cities having annual-mean humidity, (Ha), less than 70% is shown in Fig. 8(a) for the month of February when the variation is quite large over the day. Equations are developed in two parts of 12 h for each month using regression analysis for both the groups of the cities. In order to reduce the number of equations, variation of constants A, B, C and D in each equation are further fitted into polynomial equation as a function of month. Thus humidity ratio, (H/H,,), with respect to day-hour can be calculated by the equation H/Hm = A + Bh + Ch z + Dh 3

where A = ( a + b m + c m 2 +dm3)/10 B = ( a + b m + c m 2 +din3)/100 C = ( a + b m + c m 2 +dm3)/1000 D = (a+ b m + c m 2 + din3)/10,000 m is the month number and h is the hour number defined as h=hours

for hours~<12

h = h o u r s - 12

hours > 12,

(5)

370

DataBank 2.0

(a) + --

Measured By Eqn.(2)

4-

~,~:

1.5

+

/

,o=, +

1.0

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.m °l,q

0"5I tlumidity 0.0

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0

,

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,.

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(b)

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+

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......................................................................................

0.4 Humidity

(50-60)

0.2 .....................................................;c ............Measuredl ........... 0.0

0

,2

, 4

, 6

-'~

' 8

By .Eqn. (2)

10 M o n t h of the Y e a r

12

Fig. 5. The scatter of monthly-average relative humidity over the year for four ranges of annual-

averagerelativehumidity.

Data Bank

1.6

1.4

(C)

37! + --*--

................................................................... ~..-~

Measured By Eqn. (2)

...................................................

+ 1.0 .....................................~.---+ . . . . . . . . . . . . . . . . . . . .~ ~+ +

4-

¢. . 0.6 .............................. +++++ ¥ ............................................................................................. t=

= 0.4 .......................................................................................................................... H u m i d i t y (60-70) 0.2 00

1.4

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2

,

,,

,

,,

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4 6 8 10 Month of the Year

,. 12

Humidity (>

(d)

70)

1.2 .................................................................................................................................... + ~__~t ~- + =

o=

0.8 -L

- ~ 0 . 6 ......................................................................................................................................... =

0 . 4 ................................................................................................................................

+ Measured --0-By Eqn.(2) 0.2 ................................................................................................................................

0"00

2

4

6

8

10

Month of the Year Fig. 5--continued.

1'2

372

Data Bank

1.6](a)

Humidity

(<60)

'

1.41- ...............................................+ ........................................................................ +

1.2

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1.0

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0.8

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0.6

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,..

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4 6 8 10 Month of the Year

.

.

(b)

1.2 ~ qtt

Measured

.

Humidity

.............................

+-..---~

12

.

( > 60) ......................................................................................

|

*

+

•

1.0 f - . . + ~ - . . - +

0.8

..................

....................................................................................................................................

I...

.-. 0.6 ........................................................................................................................................... I~ 0.4 ........................................................................................................................................... o + Measured + By Eqn. (3) 0.2 ........................................................................................................................................................ 0.0 0

' 2

' 4

' 6

,' 8

.' 10

' 12

Month of the Year Fig. 6. The scatter o f m o n t h l y - a v e r a g e a m b i e n t t e m p e r a t u r e over the year for two ranges o f annualaverage relative humidity.

D a t a Bank

.2° I

373

+ 4-

~1.5

_o ;~ + ... 0.5 ........................................................................................................................................................

-

~::

I 0.01 0

+ --e-I 2

, 4

, 6

Measured By Eqn. (4)

,

,

,

8

10

12

Monthof theYear

Fig. 7. The scatter of monthly-average wind velocity over the year.

Table 2. Coefficients a, b, c and d for estimating monthly-average weather parameters (eqns (2-4)) Ha

Month

a

b

1. To obtain monthly-mean relative humidity ratio (HmlHa) (eqn 2) Ha ~< 50 m ~< 6 1.1357 -0.1155 m > 6 1.7273 0.0309 50 < Ha ~< 60 m ~< 6 1.1585 -0.2016 m > 6 1.4228 0.0260 60 < Ha ~< 70 m ~< 6 1.0729 -0.1606 m > 6 1.5236 -0.0124 Ha > 70 m ~< 6 0.9388 -0.0334 m > 6 0.7772 0.0566 2. To obtain monthly-mean temperature ratio (Tm/Ta) (eqn 3) Ha ~< 60 m ~< 6 0.6329 -0.0399 m > 6 0.6216 0.0992 Ha > 60 m ~< 6 0.9142 0.0298 m > 6 0.9108 0.0174 3. To obtain monthly-mean wind velocity ratio (Wm/W..,) (eqn 4) m ~< 6 0.7816 0.0083 m > 6 1.5471 --0.0002

c

d

-0.0671 -0.0028 -0.0128 -0.0013 0.0030 -0.0004 0.0021 0.0012

0.0138 --0.0005 0.0070 -0.0003 0.0038 -0.0002 0.0011 -0.0004

0.0836 0.0010 0.0015 0.0006

-0.0099 -0.0007 -0.0001 -0.0002

0.0061 --0.0031

0.0018 --0.0003

Data Bank

374

2"01 ( a )

+

" ~

'Measured By Eqn.(5)

++ . , . . .~. L/ ........................... *-.......+-5 ÷ + ' ÷ ...................................................................................................

1.0 . . . . . . . . . . . . . . .

~0.5 .

+ \ ................................................... +.~...~.* .... +~=

~

.....................

H u m i d i t y ( < 70) February I

O.C 0

5

1.6

,

,I

I

10 15 H o u r o f the D a y

20

'25

(b)

1.4

iiiiiiiiiiiiiiiiiiiiiiiiii[. . . . . . . .iiiiiiiiiiiill . . . . . iiiiiii¸ 1.2

~1.0

~ 0.8 '-0.6

.......................................................................................................................

m,

0.4

.......................................................................................

+ - ................ M e a s u r e d

.........

H u m i d i t y ( _< 60) --*By Eqn. (6) 0.2 ......................................................................................................................................................... February

0.1

0

, 5

, , 10 15 H o u r o f the D a y

20

25

Fig. 8. The representative scatter of non-dimensionalised monthly-mean hourly ratio of (a) relative humidity, (b) ambient temperature and (c) wind velocity over the day.

Data Bank

2.0

375

+ 4-+ +

(C) 4-

4-

4-~

+++

.~

+4-:t:

+

|

+ ~

00 ! 0

.

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., , 10 15 Hour of the Day

+

Measured B y Eqn. (7) , 20

25

Fig. 8--continued,

hours being the time during the day in decimal notation. Values of constants a, b, c and d are to be taken from Table 3. 2.3.2. Ambient Temperature. The pattern of temperature ratio, (T/Tm), also vary in the same manner over the year as in the case of humidity ratio, (H/Hm). However, variation of temperature ratio for different cities can be divided into three groups. For cities with annual-mean humidity, (HaL less than 70% amplitude of the fluctuation over the day is large irrespective of the altitude. It is smaller for the cities with Ha greater than 70% and altitude less than 500 m. Whereas, it is found in between the two for cities having Ha greater than 70% with altitude more than 500 m. The representative scatter of temperature ratio, (T/Tm), with day-hours for cities having annual-mean humidity, (H,), less than 70% is shown in Fig. 8(b) for the month of February. Set of equations are developed for temperature ratio, (T/Tm). The temperature ratio, (T/Tm), with respect to day-hour can be calculated by the equation

T/Tm = A + B h + C h 2 + D h 3

(6)

similar to the eqn (5). The constants a, b, c and d are to be taken from Table 4. 2.3.3. Wind Velocity. The pattern of wind velocity ratio, (W/Wm), over the day was found to be similar for all cities. The representative scatter of wind velocity ratio, (W/Wm), with day-hours is shown in Fig. 8(c) for the month of February. However, for about 10% of the stations out of 300 stations for which wind velocity data was available, amplitude of fluctuation is observed more than the remaining 90%. In Fig. 8(c) such higher fluctuation is shown for the Chennai city. Such type of large fluctuation is also found in the case of Jagadalpur, Mumbai, Mangalore, Pune and Vishakhapatnam, out of the selected 19 cities. Authors could not attribute any parameter which results in the large fluctuation of wind velocities for these cities. For the majority of cities the wind velocity ratio, (W/Win), with respect to day-hour can be calculated by the equation

Data Bank

376

Table 3. Coefficients a, b, c and d for estimating monthly-mean hourly relative humidity over the day (eqn (5)) Hour h

a

b

1. For cities having annual average humidity, H, ~< 70% A 0 < h ~< 12 11.0288 -0.2203 12 < h ~< 24 5.2297 0.4211 B 0 < h ~< 12 --5.2590 10.0936 12 < h ~< 24 7.0890 -6.7220 C 0 < h ~< 12 2.9526 -2.6091 12 < h ~< 24 -0.0043 2.4470 D 0 < h ~< 12 -3.0451 -3.4909 12 < h ~< 24 --2.5206 3.5711 2. For cities having annual average humidity, Ha > 70% A 0 < h <~ 12 11.8640 0.0944 12 < h ~< 24 6.4096 0.0180 B 0 < h ~< 12 4.3569 0.1174 12 < h ~< 24 -6.2726 0.3036 C 0 < h ~< 12 -2.0333 -0.9892 12 < h ~< 24 23.9368 -0.8569 D 0 < h ~< 12 -5.2837 0.8067 12 < h ~< 24 -11.4689 0.0270

W/Wm = A+Bh+Ch2

c

d

0.0147 --0.0014 -1.8539 1.3817 0.4009 -0.5756 0.7821 -0.7559

0.0005 --0.0016 0.0930 -0.0797 -0.0184 0.0355 --0.0435 0.0441

-0.0721 0.0965 -0.1929 0.2298 0.2986 -0.7447 -0.0058 0.4399

0.0055 -0,0083 0,0146 -0.0196 -0.0186 0.0659 -0.0041 -0.0368

+Dh 3

(7)

similar to the eqn (5). The constants a, b, c and d are to be taken from Table 5. Monthly-mean hourly values of these weather parameters are to be calculated by the following equation by substituting values obtained from eqns (1)-(7). H = (n/Hm)

× (H~/H~) × Ha

T = (T/Tm) x (Tm/Ta) x Ta

(8)

W = (W/Wm) X (Wm/Wa) X W a

2.4. Statistical methods used In the present study, two statistical indicators, namely, standard deviation (SD) and relative standard deviation (RSD) for the weather parameters are calculated from the following equations

[8] SD = [(1/n)E(Mi- Ci):] ,/2, and

(9)

RSD = { ( 1 / n ) Z [ ( M , - C , ) / C , ] : } ' / 2 × 100

(10)

where M~ and Ci are measured and computed parameters respectively and n is the number of the data used. 2.5. Calculation Procedure Equations (1)-(8) are then applied to the 5 cities, namely, Ahmedabad, Bangalore, Gaya, Mangalore and New Delhi. These cities belong to different regions of India and are different from those whose meteorological data was used in the development of equations. To start with, the city is located in a map (Fig. 1-3), the range of weather parameter read out, average value of the parameter in the range is taken as annual-average value, e.g. for Gaya H, ranges between 60-65% (Fig. 1), hence

Data Bank

377

Table 4. Coefficients a, b, c a n d d for estimating m o n t h l y - m e a n hourly a m b i e n t t e m p e r a t u r e over the day (eqn (6)) Hour h

a

b

c

1. F o r cities h a v i n g a n n u a l average humidity, Ha 70% -0.1079 0.0548 A 0 < h ~ 12 9.0504 -0.2356 -0.0288 12 < h ~< 24 12.9725 1.3463 -0.0084 B 0 < h ~< 12 -8.5945 12 < h ~< 24 16.0319 - 3.6866 0.0475 0.4943 -0.1432 C 0 < h ~< 12 1.2910 12 < h ~< 24 -41.5535 10.5180 -0.4493 D 0 < h ~< 12 7.1003 - 1.1654 0.0153 12 < h ~< 24 18.8088 -4.3344 0.0695 2. F o r cities h a v i n g a n n u a l average humidity, Ha > 70% A 0 < h ~< 12 8.7912 0.1569 -0.0022 12 < h ~< 24 12.6444 -0.4025 0.0064 B 0 < h ~< 12 -2.2620 0.0586 0.0807 12 < h ~< 24 --2.4422 0.3323 -0.0022 C 0 < h ~< 12 1.3647 0.1504 -0.0754 12 < h ~ 24 -4.0949 1.6919 -0.2219 D 0 < h ~< 12 2.3981 -0.2499 -0.0529 12 < h ~< 24 3.3897 - 1.6685 0.2548 3. F o r cities h a v i n g a n n u a l average humidity, H , > 70% a n d H A M S L > 500 m A 0 < h ~< 12 7.3181 0.2109 0.0294 12 < h ~< 24 14.3705 -0.5621 -0.0028 B 0 < h ~< 12 -0.6697 0.1614 -0.0072 12 < h ~ 24 -0.4341 0.2038 -0.0002 C 0 < h ~< 12 2.8710 -0.4170 0.0058 12 < h ~< 24 -14.7010 0.4735 0.2961 D 0 < h ~< 12 1.8929 -0.2198 -0.0101 12 < h ~< 24 10.0646 -0.4038 -0.2119

d

-0.0043 0.0040 -0.0066 0.0199 0.0094 -0.0321 0.0052 0.0245 -0.0008 0.0018 -0.0070 -0.0016 0.0054 0.0089 0.0059 -0.0114 -0.0032 0.0016 -0.0013 0.0003 0.0021 -0.0214 0.0023 0.0149

Table 5. Coefficients a, b, c a n d d for estimating m o n t h l y - m e a n h o u r l y wind velocity over the day (eqn (7)) Hour

h A B

C D

0 < h ~< 12 12 < h ~ 24 0 < h ~< 12 12 < h ~< 24 0 < h ~< 12 12 < h ~< 24 0 < h ~< 12 12 < h ~< 24

a

b

c

d

9.1921 15.8867 -8.8998 -16.2001 3.1586 -15.1530 7.8402 18.3062

-0.5703 - 1.0247 1.2918 18.2204 0.0464 -13.9395 - 1.4081 0.3901

-0.0200 0.0510 0.1866 -2.8697 -0.0010 2.1593 0.0275 -0.0119

0.0055 0.0040 -0.0236 0.1206 0.0000 -0.0902 0.0069 -0.0014

378

Data Bank

Table 6. Variation of annual-mean of standard deviation, SD, and relative standard deviation, RSD, for different cities City

Relative Humidity SD RSD (%) (%)

Ahmedabad Bangalore Mangalore Gaya New Delhi Average

8.564 9.303 5.336 9.167 8.878 8.249

17.3 14.0 07.8 15.9 18.1 14.6

Temperature SD RSD (°C) (%) 1.849 2.515 1.923 3.963 2.561 2.562

07.2 11.4 07.2 15.5 11.3 10.5

Wind Velocity SD RSD (kmph) (%) 2.766 2.017 1.830 2.177 2.461 2.246

27.5 23.9 37.4 23.6 21.3 29.5

SD--Standard Deviation, (eqn 9) ; RSD--Relative Standard Deviation, (eqn 10).

value of Ha is taken as 62.5%. For the cities on the border of the range, e.g. New Delhi is on the border of humidity range of 5 ~ 5 5 % and 55 60% (Fig. 1) hence for New Delhi H~ is taken as 55%. This theory is applied for deciding annual-average values of all the three weather parameters. However, Bangalore is the only city among the five with altitude 897 m, which is higher than 500 m, Td for Bangalore is estimated from eqn (1) as 22.22°C. Thereupon, monthly-mean of the hourly values of each of the humidity, temperature and wind velocity are calculated for January to December separately using eqns (1)-(8) and sets of constants from Tables (2-5). The computed values and the measured monthly-mean hourly values of a weather parameter are compared on the basis of standard deviation, (SD), and relative standard deviation, (RSD), (eqns (9) and (10)). The annual-average values of SD and RSD for each city are given in Table 6 and the variation of RSD over the year for the five cities is plotted in Fig. 9. 3. RESULTS AND DISCUSSION Figures (1-3) show that the distributions of temperature and humidity are smooth over India, whereas, at a few regions in India annual-average wind velocities are higher than 10 kmph and over most of the Indian regions average wind velocities are less than 10 kmph. Figure 4 shows that the annual-mean temperature varies linearly with the altitude of the location and is in accordance with Ref. [7]. Scatter of the weather parameters over the year is seen in Figs 5 7 and that over the day can be observed from representative Fig. 8. These figures show that scatter of variation for different cities is very close for temperature variation and it widens slightly for humidity and more for wind velocity. The same observation is supported by the statistical indicators, standard deviation, (SD), and relative standard deviation, (RSD), (Fig. 9). The SD and RSD values for all the three weather parameters were observed low during May-September during which overall humidity is high. Annual-average of SD is found as 8.249%, 2.56°C and 2.249 kmph, and RSD as 14.6, 10.5 and 26.7% for relative humidity, ambient temperature and wind velocity respectively for the five cities. The RSD value for wind velocity was found more than those for temperature and humidity. It is due to the inclusion of data for Mangalore city (Table 6) where annual-average wind velocity, W,, is low, i.e. 4.79 kmph with abnormally large fluctuations about this value as reported earlier in section 2.3.3. Similarly high SD and RSD values for ambient temperature are observed for Gaya city due to extreme weather conditions in summer and winter. 4. CONCLUSIONS With the knowledge of annual-mean values of the weather parameters, namely, relative humidity, ambient temperature and wind velocity of the location using the maps containing their distributions, detailed monthly-mean hourly values of these weather parameters can be estimated from the

Data Bank

379

35 30 •,= 25 .~. ~ 20 t_

,-,15 r~

~10 "~

5

- 4 ~ Ambient T e m p e r a t u r e --+-- Relative llumidity - G - Wind Velocity i

CO

2

...............................

i

z~

;

8

i

1'0

12

Month of the Year Fig. 9. Variation of relative standard deviation for relative humidity, ambient temperature and wind velocity for Ahmedabad, Bangalore, Gaya, Mangalore and New Delhi over the year.

developed correlations. The annual-mean relative standard deviation are 14.6, 10.5, and 26.7% for monthly-mean hourly relative humidity, ambient temperature and wind velocity respectively. Since the method is simple it will be useful, in general, for engineers, researchers, architects and solar system designers. The results of this study can be used to estimate weather parameters for any location in India as the places selected for evaluation of constants and prediction thereof are obtained using the data for cities fairly distributed over the whole of India.

Acknowledgments-- One of the authors, Mr G. V. Parishwad, is grateful to the Department of Education, Ministry of H u m a n Resource Development, and Mechanical Engineering Department, Motilal Nehru Regional Engineering College, Allahabad, for providing facilities for conducting research towards a doctoral degree under the Quality I m p r o v e m e n t Programme.

REFERENCES 1. Hittle, D. C. and Pendersen, C. O., Periodic and stochastic behaviour of weather data, A S H R A E Trans., 1981, 87(2), 173. 2. Hokoi, S., Matsumoto, M. and Kagawa, M., Stochastic models of solar radiation and outdoor temperature, A S H R A E Trans., Paper No. 3409, 1990, 96(2), 245. 3. Mani, A., Handbook of Solar Radiation Data for India., Allied Publishers, New Delhi, India, 1980.

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Data Bank

4. Mani, A. and Rangarajan, S., Solar Radiation Data Over India., Allied Publishers, New Delhi, India, 1982. 5. Mani, A. and Mooley, D. A., Wind Energy Data for India., Allied Publishers, New Delhi, India, 1983. 6. Seshadri, T. N., Rao, K. R., Sharma, M. R., Sarma, G. N. and Ali, Sharafat, Climatological and Solar Data for India, Sarita Prakashan, Meerut, India, 1969. 7. Schlichting, H., Truckenbrodt, E. and Ramm, H. J., Aerodynamics of Airplane, McGrawHill Int. Book Co., New York, 1979. 8. Chandrasekaran, J. and Kumar, S., Hourly diffuse fraction correlation at a tropical location. Solar Energy, 1994, fi3(6), 505.