International Journal of Science, Technology, Engineering and Management- A VTU Publication 2020; Vol: 2, Issue: 2, pp: 27 - 36 ISSN: 2582-5844 (Online)

SPATIAL DISTRIBUTION OF DAILY RAINFALL IN - DEVIATIONS FROM THE WORLD TROPICAL PATTERNS

N.M.Thipperudrappa, a*

a Professor, Department of Civil Engineering, Siddaganga Institute of Technology, Tumkur,

Abstract: The dependence of monthly rainfall on the number of rainy days and the mean daily intensity is studied in the case of two geographical regions of Karnataka, situated in the tropics. The pattern of rainfall distribution in the state, represented by the relationships, is A R T I C L E H I S T O R Y compared with that commonly found in tropical regions, situated elsewhere in the world. The study reveals that the pattern in the plains of Karnataka is somewhat comparable to that Received: 2020-06-14 generally found over the globe, while that in the case of mountainous Western Ghat region Revised: 2020-06-26 deviates much. The deviations are attributed to local factors, including the source of moisture Accepted: 2020-06-26 and the mechanism of precipitation. It is concluded that generalizations concerning rainfall pattern, based on geographical location, alone are dangerous and that general guidelines for hydrological designs must be adopted only after a study of the locally available rainfall records. Keywords: daily rainfall, tropical region, world patterns, Southwest monsoon, local factors, deviations from the general pattern.

1. INTRODUCTION in the state can be expected to furnish important information Studies on spatial and temporal distribution of rainfall, both on local factors such as location and topography in The study on regional and on global scales, have been of research is also expected to bring to light the deviations that exist in interest in hydrology for a very long time. They continue to the pattern of rainfall in this region from the general pattern be so, since generalization regarding the pattern of rainfall that is often believed to characterize the tropical rainfall distribution, even within similar climatic zones is ever (Jackson, 1977). elusive. Among all the climatic zones into which the globe is often divided (Strahler and Strahler, 1992, WMO, 1983 and 2. STUDY AREA AND THE DATA USED Jackson, 1977), the tropics are the most widely studied. The reasons are obvious - tropics experience much higher and Karnataka (Figure 1), with a total geographical area of much more intense rainfall than other areas and host a very 191,757 km2, is situated in the tropics between north large part of the world’s population. The work being latitudes 11○50’ and 18○05’ and east longitudes 74○00’and presented in this paper concerns the rainfall distribution over 78○05’. It is characterized by a coast line of length the state of Karnataka in South India, situated in the tropics exceeding 260 km, the (locally called and influenced by all the rainfall types. Karnataka forms an Sahyadri range of hills) running parallel to the coast and exceptional example of a case, where all the different extensive areas of plains situated in the plateau of South mechanisms of adiabatic precipitation (Strahler and Strahler, India. The coast line and the Sahyadri range of hills are 1992, Putty, 2009) are active and the range of rainfall oriented almost normal to the direction of Southwest magnitude is very wide – normal annual rainfall in the state monsoon winds and hence the state is bestowed with ranges between 450 mm and 7800 mm, within an area less bountiful rainfall, amounting to an average of about 135 cm than 200,000 km2. Hence, the studies on rainfall distribution per annum. However, the distribution of rainfall over the state is highly uneven (Figure 2), the rainfall magnitudes being markedly influenced by location with respect to the **Professor, Department of Civil Engineering, coast and the Sahyadri range of hills. The region influenced Siddaganga Institute of Technology, Tumkur, India by the orography of the Sahyadri range of hills receives exceptionally high rainfall, while the plains, beyond these ([email protected]) ranges, are characterized by low to moderate amounts of rainfall. The chief mechanism of rainfall in the coastal and

© 2020 VTU Page No. 27 28 IJSTEM – VTU, 2020, Vol. 2, Issue. 2, pp. 27 – 36 Thipperudrappa et al. hilly region is orographic, while it is convective in the plains. rainfall. However, the state of Karnataka, despite being The tropical cyclones originating off the eastern coast of located well within the tropics, has two clearly distinct South India also influence rainfall in southern part of the divisions, influenced by different rain state, although to a small extent only.

Hence, for the sake of present study, the state of Karnataka can be considered to be made up of two distinct parts (Figure causing factors as discussed in the preceding section. Hence, 3), experiencing different patterns of rainfall - (i) the highly a study of daily rainfall in the state may be expected to help wet coast and the Sahyadri range of hills, characterized by in understanding more about the tropical rainfall and the orographic type of rainfall occurring during Southwest influence of local factors, morphology in particular, on monsoon and (ii) the semi-dry to sub-humid plains, rainfall distribution. The present work is an attempt in this characterized mainly by convective type of rainfall and also direction and is being reported to highlight the differences in by cyclones during the Northeast monsoon. This study on the rainfall distribution pattern that exist in two subdivisions daily rainfall is carried out by analyzing records of 20 and the unique nature of distribution in the Sahyadri range of stations from each of the two regions (Figure 1). The stations hills. have been so chosen that they represent almost the complete range of rainfall magnitude in the two parts of the state. The 4.METHODOLOGY details such as location and the normal annual rainfall, concerning these stations are shown in Table 1. The rainfall The aim of this study is to review the relationships that exist records for a period of twenty years, extending from 1997 to between the total monthly rainfall (TRF) with each of the 2016, made available by the Karnataka Directorate of two variables - the number of rainy days (N) in the month Economics and Statistics, Bengaluru, have been used in the and the mean daily intensity (r), in various cases. The basic present study. data needed for this purpose are the long term averages of TRF, N and r. These parameters are estimated by taking the 3. OBJECTIVE average values from the daily rainfall records for a period of 20 years (1997-2016) for each of the 20 stations. This data According to Jackson (1977), the two relatively simple set is presented in Table 2, in order to provide a general idea parameters that provide a fairly good picture of the tropical regarding the temporal variation of rainfall in the two rainfall characteristics are the number of rainy days and the regions of the study area. The methodology used in involves mean daily intensity. A number of studies concerning the the following steps: distribution pattern of these two parameters, including their relationship with monthly rainfall, have been reported. Developing the best fitting regression equations between Jackson (1977) has carried out studies in Tanzania and found TRF and each of the two parameters N and r, separately for that in this area, the total monthly rainfall is directly the two regions; associated with the number of rainy days rather than mean daily values, and that the relationship is nonlinear. Comparing the form of the best-fit relationships in the two regions mutually and with those derived by investigators Harrison (1983) has carried out similar studies in Eastern elsewhere; and, Orange Free State in the USA. He has found that different kind of relationships exist in different regions - the number Examining the applicability of the relationships derived in of rainy days in a few cases, the mean daily intensity in other regions to the stations in Karnataka and inferring on some, and both the parameters in others, explain well the the deviations. variation in total monthly rainfall. Using data from a large number of stations in tropical areas all over the globe, In step (i) above, various forms of regression equations – Jackson (1986) has shown that the pattern of rainfall in the linear, logarithmic, polynomial, power and the exponential tropics is almost uniform. He has presented what he calls the are validated and the most suitable models are chosen for World equations for the association of these two parameters further analysis. The relationships referred to above in Step with total monthly rainfall. However, in a later study, (i) are developed for each of the rainy months individually, Jackson (1987) has found that the pattern of distribution in and also by combining all the months together. The first set Western Australia deviated from the World pattern and of relationships is called the ‘Monthly relationships’ and the concluded that there are dangers in generalizations. As far as latter are termed the ‘Intra-annual regional relationships’. India is concerned, studies seem to be not many, since only a The results are presented and discussed below. part of the country is in the tropics and even here, a large area is cyclone influenced. Agashe and Padagalwar (2005) 5.RESULTS AND DISCUSSION have discussed the characteristic features of daily rainfall in the central Maharastra region. They find that while the total Monthly Relationships monthly rainfall is influenced to some extent by the number of rainy days; mean daily intensity has little influence on it. A few sample scatter diagrams showing the relationship between the values of TRF and N and between TRF and r are The studies discussed above have been carried out in regions shown in Figure 4 and in Figure 5 for Maidana region. and with no marked spatial variation in factors influencing region respectively. The best fit equations, SPATIAL DISTRIBUTION OF DAILY RAINFALL IN KARNATAKA -DEVIATIONS FROM THE WORLD TROPICAL PATTERNS IJSTEM - VTU, 2020, Vol. 2, Issue.2 29 selected after validating the various models, and the by applying the equations derived in other areas on corresponding R2 values, are presented in Table 3 (a) and Karnataka region. A similar approach has been followed by Table 3(b) for Maidana and Malenadu regions respectively. Jackson (1987) to study the deviations in Australia from the A study of these illustrations reveals the following facts: general trends over the World. In this method, the values of N and r, corresponding to different ranges of values of TRF, i) Maidana region: In this case, the r-TRF relationship is are estimated by local equations, the Australian equations very poor, while the N-TRF relationship is good. This result and the World equations. The Table 6 shows the comparison is nearly similar to the results obtained by other investigators of number of rainy days (N) for different ranges of values of in other tropical areas. TRF by using the various equations, while Table 7 shows the comparison of mean daily intensity values ( r ), ii) Malenadu region: In this case, the N-TRF relationships are reasonably good and also, a non-linear model is They are mutually compared and inferences regarding the appropriate for most of the months, while the r-TRF applicability of the equations are drawn. It is evident from relationships are all very good and linear, those for the these tables that the values of N and r estimated by the monsoon months being excellent. Although the best fitting World equations deviate much from those estimated by the equations were non-linear in some cases (N-TRF equations for the Malenadu region and also for Maidan relationship) the significance of the coefficient for the non- region. The N values estimated by the World equations are linear component has been found to be very low and R2 for 10 to 20% higher (between 200 to 2000 mm), the intensities the linear estimated by them are 20 to 30% lower. On the other hand, the estimates of N and r by using the Australian and models were not much different from non-linear models. Malenadu equations seem to match each other to some Hence, the relationships can be considered linear only. extent. However, this match is limited to a small range of Further, it was noted from the results that the relationships total monthly rainfall (TRF) between 50 mm and 400 mm. A for the months of April, May, October, November and careful study of the data and records reveals that this range December, during which the monsoon is not active, are of TRF is confined to only a few stations located near the poorer than those for the monsoon months. All these results border of the two regions of the state. The inference is that go to establish that the pattern of rainfall distribution over even though the daily intensity pattern in the outskirts of the the Malenadu region during the monsoon months is different Malenadu areas resembles that in the tropical areas of from that commonly observed in the tropics. Australia, the pattern in the interiors of the Western Ghats deviates much from those in other areas. Intra - Annual Regional Relationships The presence of such deviations in the case of Malenadu and The association between TRF and N and that between TRF near similarity of the case in Maidana with those in tropics and r obtained by clubbing data of all months together, outside Karnataka is informative. They imply strong separately for each of the two regions - Maidana and influence of the local factors on rainfall distribution. The two Malenadu are illustrated in Figure 6 and Figure 7 important factors to which such dependence can be attributed respectively. The best fitting equations representing the are: (i) the source of moisture causing rainfall and (ii) the relationships obtained in this study are presented in Table 4. mechanism of precipitation. For the Sahyadri range of hills, In order to compare this rainfall regime in Karnataka with which are close to the ocean, the source of moisture is that elsewhere in the tropics, the equations for Northern external, while for many of the tropical areas, the source is Australian areas and the World tropical areas, quoted by local evaporation. Also, while the general mechanism of Jackson (1987), are presented in Table 5. precipitation in the tropics is convection, it is orographic in the Sahyadri range of hills. The source of moisture from the It is seen that in the case of the Maidana region, as is the case oceans is very consistent, lasting very long durations during in regions elsewhere, the N–TRF relationship is quite good summer. But, local evaporation leads to precipitation only (R2=0.70), while the r-TRF association is very poor during the afternoon hours. Further, while the orogrophic (R2=0.20). In the case of the Malenadu region, the N-TRF process results in a gradual ascent of moisture laden air, relationship is asymptotic, reaching values near 31. This convection is a vigorous process. The results from the seems to be so since some stations with very heavy rainfall, present study show that the influence of these factors is very receive rain on all the days of July and August of some much pronounced and that generalizations regarding the years. Further, in this case, the r-TRF relationship is very pattern of rainfall based on geographical locations alone are good and is very nearly linear (R2=0.95), in contrast to the not advisable. areas dealt with by other authors. 6.CONCLUSIONS Suitability of Different Equations for Regional Application This study on the daily intensity pattern over the state of While the discussions above have established that deviations Karnataka in South India leads to the following conclusions. exist in the pattern of rainfall distribution in the Malenadu region, they have not shown the extent to which the There are wide variations in the intra-monthly temporal deviations distinguish the rainfall in different regions. This distribution of rainfall in between the two distinct parts of type of information may be obtained, at least to some extent, 30 IJSTEM – VTU, 2020, Vol. 2, Issue. 2, pp. 27 – 36 Thipperudrappa et al. the state - the Maidana and the mountainous western Ghat 5. 5. Jackson, I.J. (1986). Relationship between rain ranges (Malenadu) days, means daily Intensity and monthly rainfall in the Tropics, J. of Climatology, Vol. 6, pp.117-134. The daily intensity distribution in the Maidana is quite 6. 6. Jackson, I.J. (1987). Daily Rainfall over Northern similar to those found elsewhere in the sub humid tropical Australia, Deviations from the World pattern, J. of areas over the globe, while the patterns in the Malenadu region deviate much. Climatology, Vol. 8, pp.463-476 7. 7. Putty, M.R.Y, (2009).Principles of Hydrology, The total monthly rainfall is found to be related well to the I.K. International Publishers, New Delhi number of rainy days (N) in the Maidana region as in the 8. 8. Strahler, A.H. and Strahler, A.N. (1992). Modern case of most tropical areas. On the other hand in the Physical Geography, John Wiley and Sons, Inc., Malenadu region, contrary to the general pattern found in the NY. tropical areas, over the globe, the monthly rainfall is found to have exceptionally good relationship with mean daily 9. 9. World Meteorological Organization (1983). rainfall (r) and also with N, but to smaller extent. Operational Hydrology in the Humid Tropical Regions, In: Hydrol. of Humid Tropical regions The so called World equations, often believe to be generally with Particular reference to the Hydrological applicable in all tropical areas, fail to estimate the values of effects of Agriculture and Forestry practices, N and r in the Western ghat areas. However, the equations IAHS. Publ., No: 140: 1-25. derived for North Australian regions estimate well these values in some parts of Western ghat areas, where rainfall magnitudes are comparable with North Australian regions. Yet the equations other than those derived from local data fail totally in most parts of Western ghats.

Most of the results of study imply that the Western ghat regions, despite being located in the tropics experience a pattern of rainfall much different from that found in similar areas over the globe. This may be attributed to the dominating influence of Western ghat range of hills.

Finally it is not out of place to conclude that generalizations made about rainfall pattern in similarly located areas over the globe may turn out to be non- applicable in some areas, like the Western Ghat regions in South India and it is necessary to take extreme care while making such generalizations.

This being the case local conditions must be looked into and the local data must be analyzed in order to understand the pattern of rainfall, while carrying out hydrological designs for water resources development.

REFERENCES

1. 1. Agashe, P.S. and Padgalwar, K.V. (2005). On some characteristic features of daily rainfall over Madhya Maharastra, Mausam, Vol. 56, No.3, Figure 1: The Study area, showing pp. 571-580. the rain gauging stations 2. 2. Harrison, M.S.J. (1983). Rain day frequency and (Station numbers as per Table 1) mean daily rainfall intensity as determinants of total rainfall over eastern Orange Free State, J. of Climatology, Vol. 3, pp. 35-45 3. 3. Jackson, I.J. (1972). Mean daily rainfall Intensity and number of rainy days over Tanzania, Geografiska Annaler, 54 A, 369 4. 4. Jackson, I.J. (1977). Climate, Water and Agriculture in the tropics, Longman SPATIAL DISTRIBUTION OF DAILY RAINFALL IN KARNATAKA -DEVIATIONS FROM THE WORLD TROPICAL PATTERNS IJSTEM - VTU, 2020, Vol. 2, Issue.2 31 TABLE 1: LOCATION DETAILS OF RAIN GAUGE STATIONS

Maidana Malenadu Sl. Sl. No Station Lat. Long. Alt. No Station Lat. Long. Alt. NRF NRF 1 Bidar 16.71 75.15 710.0 1 Agumbe 13.31 75.06 897.8 7285. 643. 2 Gulbarga 16.71 75.05 454.0 2 Hulikal 13.47 75.05 688.6 7830. 644. 3 Indi 16.55 76.50 606.6 3 Sagar 13.50 75.15 625.3 1952. 579. 4 Talikote 16.70 76.55 509.0 4 Bhagama 12.22 75.31 604.0 5880. 898 5 Mamadapu 16.75 76.60 629.5 5 Somvarp 12.36 75.57 464.0 2173. 1130 6 Athani 16.71 75.05 554.0 6 Nagarhol 13.45 75.05 564.0 1609. 960. 7 Belgaum 16.51 76.51 784.7 7 Napoklu 12.15 75.05 876.0 2946. 120 8 Bellary 14.05 77.05 485.1 8 Ponnamp 13.25 75.15 497.3 2035. 851. 9 Hadagali 14.05 76.75 561.6 9 Sringeri 13.25 75.15 572.3 3160. 672.. 10 Badami 16.40 76.70 586.0 10 Mudeger 14.40 74.10 587.2 2452. 970. 11 S.belogala 12.40 76.80 871.0 11 N R Pura 12.80 74.30 744.7 1509. 697. 12 S.R.Pattana 12.50 76.90 679.8 12 Yellapur 12.24 75.45 653.3 2336. 541. 13 Maddur 12.30 76.50 662.0 13 Bhatkal 12.25 75.60 755.9 4576. 3.0 14 Nanjanagu 12.10 76.90 1025. 14 Supa 12.25 75.45 711.4 2301. 254. 15 Bhadravath 15.15 77.45 597.0 15 Karwar 14.40 74.15 896.5 3158. 4.0 16 Challakere 15.01 76.50 585.0 16 Siddapur 14.25 75.25 472.3 2616. 564. 17 Hosadurga 15.10 77.50 739.0 17 Puttur 12.30 75.30 714.8 3464. 87.0 18 C N Halli 13.25 77.10 804.0 18 Mangalor 12.80 74.30 740.2 3502. 22.0 19 Tumkur 13.20 77.06 822.5 19 Belthang 12.50 76.95 836.9 3292. 685. 20 Pavgada 13.10 77.05 646.1 20 Sakleshp 12.57 75.47 560.3 2273. 956. 14.05

L E G E N D 18°N

N Plains Malnad Rain gauge station 17

2

16

1 15 3 7

13 14 4

10 9

12 13 6 8 15

11 12 5 14

11°N 75°E 76°E 77°E

Fig.2: Spatial variation of rainfall in Karnataka, Fig. 3: Rainfall zones of Karnataka

32 IJSTEM – VTU, 2020, Vol. 2, Issue. 2, pp. 27 – 36 Thipperudrappa et al.

June NRF: Normal rainfall in mm, Lat: 28 Latitude, Long: Longitude, Alt: Altitude in m 26 24 22

20 N June 18 20 16 18 14 2 16 y = -8E-06x + 0.0194x + 14.547 12 2 14 R = 0.778 10 12 0 500 1000 1500 2000 10N 8 TRF 6 4 y = 0.0823x + 2.1178 July 34.0 2 R2 = 0.6412 0 32.0 25.0 75.0 125.0 175.0 TRF 30.0 28.0

N 26.0 June 24.0 2 16.0 22.0 y = -4E-06x + 0.0135x + 19.887 2 14.0 20.0 R = 0.6052 12.0 18.0 10.0 0 500 1000 1500 2000 2500 3000 TRF

r 8.0 6.0 4.0 June y = 0.0095x + 8.9089 80 2.0 2 R = 0.0174 70 0.0 60 25.0 75.0 125.0 175.0 50 TRF r 40 30 July 20 16 y = 0.0368x + 3.6478 10 R2 = 0.9871 14 0 12 0 500 1000 1500 2000 TRF 10

r 8 July 100 6 90 80 4 y = 0.0267x + 5.4154 70 2 R2 = 0.4878 60

r 50 0 40 0 50 100 150 200 250 300 350 30 TRF 20 y = 0.0316x + 2.8216 10 R2 = 0.9952 Figure 4: Monthly relationship between 0 0 500 1000 1500 2000 2500 3000 TRF TRF, N and r (Maidana) Figure 5: Monthly relationship between TRF, N and r (Malenadu)

SPATIAL DISTRIBUTION OF DAILY RAINFALL IN KARNATAKA -DEVIATIONS FROM THE WORLD TROPICAL PATTERNS IJSTEM - VTU, 2020, Vol. 2, Issue.2 33

30 35

25 30

20 25

N 15 20 10 N y = 0.0765x + 1.3345 15 5 R2 = 0.7047 10 y = 5.6255Ln(x) - 13.968 0 5 R2 = 0.8188 0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 0 TRF 0 500 1000 1500 2000 2500 TRF 30 100 25 90 80 20 70

r 15 60

r 50 10 40 5 y = 1.4099Ln(x) + 5.2335 30 2 20 R = 0.202 y = 0.0283x + 9.2142 0 10 R2 = 0.9202 0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 0 TRF 0 500 1000 1500 2000 2500 TRF Figure 6: Region-wise relationship between TRF, N and r (Maidana) Figure 7: Region-wise relationship between TRF, N and r (Malenadu)

34 IJSTEM – VTU, 2020, Vol. 2, Issue. 2, pp. 27 – 36 Thipperudrappa et al.

TABLE 2: STATISTICAL PARAMETERS (AVERAGE VALUES) OF THE RAINFALL SERIES ANALYZED Belgaum Bellary Month Indi (Maidana) (Maidana) (Maidana) r r TRF TRF TRF N (mm/ N r N (mm/ (mm) (mm) (mm) d) d) April 12..8 2.1 6.1 41.7 4.2 9.9 19.1 1.7 11.4 May 30..3 3.3 9.2 61.1 6.6 9.2 71.5 4.9 14.7 June 70.0 7.6 9.2 192.8 17.2 11.2 50.6 5.6 9.0 July 83.8 8.2 10.2 334.1 24.3 13.7 46.4 6.6 7.1 August 100.5 10.4 9.7 210.7 20.7 10.1 52.4 7.6 6.9 September 137.2 10.4 13..2 129.9 12.4 10.4 110.8 7.8 14.8 October 91.1 5.3 17..2 99.7 7.2 13.8 86.5 7.7 11.2 November 11.3 1.3 8.7 23.5 2.3 10.2 26.5 3.2 8.3 December 0.4 0.2 2.0 3.7 0.3 12.3 1.1 0.4 2.8 Sakleshpur Siddapur Challakere (Malenadu) (Maidana) (Malenadu)

April 35.8 2.1 16.8 39.1 3.7 10.6 80.7 6.8 11.7 May 67.4 3.9 17.4 84.0 7.4 11.4 106.2 9.7 10.8 June 38.8 3.1 12.4 605.3 23.3 25.9 419.3 21.7 19.2 July 33.5 5.4 6.2 1011.0 30.0 33.7 647.0 28.4 22.7 August 73.8 5.8 12.6 670.9 28.2 23.8 453.8 26.9 16.8 September 95.9 5.8 16.5 267.0 21.0 12.7 229.7 19.8 11.5 October 95.6 6.6 14.5 132.6 11.5 11.5 167.8 14.0 11.9 November 28.8 2.6 11.1 36.5 3.7 9.9 58.0 4.7 12.2 December 1.0 0.2 5.0 6.5 0.6 11.2 10.8 0.9 11.3

Somvarpet Nagarahole (Malenadu) (Malenadu) (Malenadu) April 69.2 7.0 9.7 110.5 8.8 12.6 79.5 6.2 12.8 May 122.4 8.1 15.1 318.3 12.6 25.2 102.6 6.2 15.1 June 328.8 21.1 15.8 1043.8 25.4 41.1 218.1 13.7 16.1 July 653.1 27.6 24.7 1571.4 29.8 52.7 320.1 18.5 17.4 August 459.3 24.9 18.4 1028.5 28.6 36.2 195.8 14.9 13.1 September 181.3 17.1 10.6 478.1 21.4 22.3 100.8 9.7 10.4 October 149.9 12.7 11.8 299.4 17.5 17.0 111.7 7.8 14.3 November 59.8 5.5 11.1 82.4 6.7 12.3 50.1 3.0 16.7 December 9.8 1.3 7.6 18.4 1.4 13.2 17.1 0.8 22.3

SPATIAL DISTRIBUTION OF DAILY RAINFALL IN KARNATAKA -DEVIATIONS FROM THE WORLD TROPICAL PATTERNS IJSTEM - VTU, 2020, Vol. 2, Issue.2 35 TABLE 3(a): MONTHLY RELATIONSHIP

BETWEEN TRF, N & r FOR MAIDANA

Maidana Month Relationship between R2 Relationship between TRF & r R2 TRF & N Value Valu April N= 0.06 TRF + 1.0 0.80 r = 0.09 TRF + 7.3 0.35 May N= 0.05 TRF + 1.6 0.70 r = 0.06 TRF+ 7.9 0.32 June N= 0.08 TRF + 2.1 0.60 r = 0.009 TRF + 8.9 0.01 July N= 0.05 TRF + 6.1 0.60 r = 0.02 TRF + 5.4 0.48 August N= 0.06 TRF + 4.4 0.40 r = 1.5 ( TRF ) ^ 0.38 0.17 September N= 0.03TRF + 6.2 0.10 r = 0.04 TRF + 7.3 0.17 October N= 0.05 TRF + 1.4 0.50 r= 0.02 TRF +12.2 0.05 November N= 0.08TRF + 0.30 0.90 r=0.002(TRF) ^ 2 +0.24 TRF+6. 0.22 December N= 0.11 TRF + 0.1 0.60 r=4 (TRF)^0.4 0.42

TABLE 3(b): MONTHLY RELATIONSHIP BETWEEN TRF, N & r FOR MALNAD l Malenadu Month Relationship between TRF & N R2 Relationship between TRF & r R2 Value Value April N= 0.07 TRF + 1.0 0.92 r = 0.03 TRF + 9.0 0.37 May N= 0.02 TRF + 5.2 0.52 r = 0.06 TRF + 6.8 0.56 June N= -8E-6 TRF 2+0.01 TRF+14.5 0.77 r = 0.03 TRF +3.6 0.98 July N= -4E-6 TRF 2+0.01 TRF+19.8 0.60 r = 0.03 TRF + 2.8 0.99 August N= -5E-6 TRF 2+0.01 TRF+18.7 0.52 r = 0.03 TRF + 2.9 0.99 September N= -2E-5 TRF 2+0.03 TRF+12.1 0.60 r = 0.04 TRF + 3.1 0.94 October N= 0.02 TRF + 8.3 0.49 r = 0.05 TRF + 5.2 0.76 November N= 0.04 TRF + 1.5 0.67 r= -1E-3 TRF 2+ 0.29 TRF +2. 0.36 December N= 4 ln(TRF) - 4.0 0.66 r= 0.65 TRF + 4.1 0.68

TABLE 4: INTRA-ANNUAL REGIONAL RELATIONSHIPS BETWEEN TRF, N AND r Sl. Maidana R2 Sl. Malenadu R2 No Value No Value 1 N = 0.076 TRF + 1.3 0.70 1 N= 5.6 ln (TRF) - 13.8 0.81 2 r =1.4ln( TRF) + 5.2 0.20 2 r = 0.028 TRF + 9.2 0.95

TABLE 5: WORLD & AUSTRALIAN EQUATIONS Sl. Region Equation R2 No Value 1 World Tropical data N = 7.63 ln (TRF) - 23.8 0.70 (All months with TRF>50 mm r = 6.79 + 0.02 TRF 0.65 2 Northern Australia N = 7.27 ln (TRF) - 25.5 0.91 r = 10.8 + 0.02 TRF 0.61

36 IJSTEM – VTU, 2020, Vol. 2, Issue. 2, pp. 27 – 36 Thipperudrappa et al.

TABLE 6: COMPARISON OF RAIN DAY (N) ESTIMATES FOR WORLD, AUSTRALIA & KARNATAKA EQUATIONS

Sl. Region No. of rainy days (N) for values of TRF (monthly rainfall in mm) exceeding No 50 100 200 300 400 500 750 1000 1500 2000 2500

World 6.0 11.3 16.6 19.7 21.9 23.6 26.7 28.9 32.0 1 34.2 35.9 Australia 2.9 8.9 13.0 16.0 18.1 19.7 22.6 24.7 27.7 2 29.8 31.4 Karnataka (Malenadu) 8.1 11.9 15.8 18.1 19.7 21.0 23.2 24.8 27.1 3 28.7 30.0 Karnataka (Maidana 5.1 8.9 16.5 24.1 31.7 - - - - 4 ) - -

TABLE 7: COMPARISON OF MEAN DAILY INTENSITY (r) ESTIMATES FOR WORLD,

AUSTRALIA & KARNATAKA EQUATIONS Sl. Mean daily intensity (r) for values of TRF (monthly rainfall in mm) exceeding Region N 50 100 200 300 400 500 750 1000 1500 2000 2500 o 1 World 7.7 8.7 10.7 12.7 14.7 16.7 21.7 26.7 36.7 11.8 12.8 14.8 16.8 18.8 20.8 25.8 30.8 40.8 46.7 56.7 2 Australia 50.8 3 Karnataka (Malenadu) 10.6 12.0 14.8 17.6 20.4 23.2 30.2 37.2 51.2 60.8 65.2 79.2 4 Karnataka (Maidana) 10.7 11.6 12.6 13.2 13.6 ------