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  • View in gallery

    The locations of rain gauge stations (black dots) in India. Overlaid is the topography obtained from U.S. Geological Survey data center (http://eros.usgs.gov/). The global 30 arc second elevation dataset (GTOPO30) is a global raster digital elevation model (DEM) with a horizontal grid spacing of 30 arc seconds (~1 km).

  • View in gallery

    A typical example showing the construction of coherent rainfall zones around two nearby seed points (i.e., rainfall at each station within the zone shows significant correlation with the seed point). The biggest solid symbols (square and circle) are seed points and the size of the symbol indicates the correlation coefficient for rainfall between the seed point and corresponding station.

  • View in gallery

    Delineated homogeneous rainfall regions when (a) annual, (b) southwest, and (c) northeast monsoon rainfall are used for the correlation analysis.

  • View in gallery

    Comparison of rainfall interseries correlations between stations within the coherent zones as identified by different studies (correlation = present study, IMD = Parthasarathy et al. 1993, PCA = Iyengar and Basak 1994, and cluster = Satyanarayana and Srinivas 2008).

  • View in gallery

    Histograms of correlation coefficients for (a) annual, (b) SWM, and (c) NEM rainfall. The correlation analysis is carried out between rainfall series at each station and corresponding regional averaged rainfall series.

  • View in gallery

    Coefficient of variation of (a) rain amount and (b) rain frequency for each zone corresponding to annual, SWM, and NEM rainfall. Zones with rain frequency <10 are excluded from the analysis. Note that the same zone number does not necessarily correspond to the same region in different seasons.

  • View in gallery

    Spatial variability of (a) the occurrence percentage and (b) rain fractions for stratiform, convective, and shallow rain, depicting the rain type homogeneity over delineated zones.

  • View in gallery

    (a) Rainfall variation at each station (thin lines) within zone 16 in year 1951 along with regional averaged rainfall variation (thick line) and rainfall variation at one station (dashed line) at which correlation is estimated. (b) Spatial variation of the correlation coefficient for the year 1951, showing the coherency in rainfall variations occurring within the season (i.e., the correlation analysis is carried out between daily rainfall at each station with its regional mean daily rainfall).

  • View in gallery

    (a) As in Fig. 8b, but for the mean correlation coefficient value. The correlation analysis is carried out on intraseasonal rainfall variations for each year. The mean correlation coefficient and standard deviation (Fig. 9b) are estimated using 51 years of rainfall data.

  • View in gallery

    As in Fig. 9, but for (a) excess rainfall and (b) deficit rainfall years. (c) Cumulative distribution curves for rxy corresponding to excess and deficit rainfall years.

  • View in gallery

    Spatial variation of the correlation coefficient, when the analysis is made using the annual rainfall during the periods (a) 1951–75 and (b) 1976–2001. (c) Cumulative distribution curves for rxy corresponding to two halves of the data.

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Identification and Validation of Homogeneous Rainfall Zones in India Using Correlation Analysis

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  • 1 National Atmospheric Research Laboratory, Gadanki, India
  • 2 Sri Venkateswara University, Tirupati, India
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Abstract

Daily rainfall data obtained from 1025 rain gauges spread across the country over 51 years (1951–2001) are subjected to correlation analysis to identify homogeneous rainfall zones over India. In contrast to earlier studies, which were based on seasonal/annual rainfall, the present study identifies homogeneous rainfall regions with the help of seasonal [southwest monsoon (SWM) and northeast monsoon (NEM)] and annual rainfall. India is divided into 26 (20) homogeneous rainfall zones using annual and SWM (NEM) rainfall. The delineated homogeneous regions are compared and contrasted with those defined by earlier studies, employing a variety of schemes. The interseries correlations of rainfall within each zone are found to be better when the zones are identified by the present study than by other studies. The tests that are performed to evaluate coherency of zones reveal that the zones are homogeneous not only at different temporal scales (interannual and intraseasonal) but also in terms of rain amount, rain frequency, and rain type. Although the delineation of coherent zones is done using interannual/seasonal rainfall data, these zones exhibit coherency in rainfall variations at intraseasonal scale. Nevertheless, the degree of homogeneity is different for rainfall variations occurring at different temporal scales. Further, the zones show better coherency in excess rainfall years than in deficit rainfall years. Longer-term utility of the delineated zones is studied by examining delineated zones and their coherency in the first and second half of the total data period. Although the regions remain the same in both the periods, the coherency is reduced in the second half, suggesting that the homogeneity of regions may vary in the future.

Corresponding author address: K. Saikranthi, P.O. Box No. 123, National Atmospheric Research Laboratory, S.V.U. Campus, Prakasham Nagar, Tirupati - 517 502 A.P., India. E-mail: saikranthi@narl.gov.in

Abstract

Daily rainfall data obtained from 1025 rain gauges spread across the country over 51 years (1951–2001) are subjected to correlation analysis to identify homogeneous rainfall zones over India. In contrast to earlier studies, which were based on seasonal/annual rainfall, the present study identifies homogeneous rainfall regions with the help of seasonal [southwest monsoon (SWM) and northeast monsoon (NEM)] and annual rainfall. India is divided into 26 (20) homogeneous rainfall zones using annual and SWM (NEM) rainfall. The delineated homogeneous regions are compared and contrasted with those defined by earlier studies, employing a variety of schemes. The interseries correlations of rainfall within each zone are found to be better when the zones are identified by the present study than by other studies. The tests that are performed to evaluate coherency of zones reveal that the zones are homogeneous not only at different temporal scales (interannual and intraseasonal) but also in terms of rain amount, rain frequency, and rain type. Although the delineation of coherent zones is done using interannual/seasonal rainfall data, these zones exhibit coherency in rainfall variations at intraseasonal scale. Nevertheless, the degree of homogeneity is different for rainfall variations occurring at different temporal scales. Further, the zones show better coherency in excess rainfall years than in deficit rainfall years. Longer-term utility of the delineated zones is studied by examining delineated zones and their coherency in the first and second half of the total data period. Although the regions remain the same in both the periods, the coherency is reduced in the second half, suggesting that the homogeneity of regions may vary in the future.

Corresponding author address: K. Saikranthi, P.O. Box No. 123, National Atmospheric Research Laboratory, S.V.U. Campus, Prakasham Nagar, Tirupati - 517 502 A.P., India. E-mail: saikranthi@narl.gov.in

1. Introduction

The Indian monsoon rainfall exhibits large and complex variability in space and time. Several researchers studied this large spatial heterogeneity in the rainfall patterns at different temporal scales (Ramamurthy 1969; De et al. 1998; Krishnamurthy and Shukla 2000; Gadgil et al. 1993; Iyengar and Basak 1994; Gadgil 2003; Goswami 2005; Rao et al. 2009; Malik et al. 2010; Rajeevan et al. 2010; Kulkarni et al. 2011). For example, Gadgil et al. (1993) have shown that pairwise correlations of the time series of the southwest monsoon (SWM; June–September) rainfall at 200 stations range from −0.57 to 0.87, indicating the rainfall does not vary coherently at all stations within India. These studies suggest that all-India average rainfall may not be a meaningful index for various applications and research studies. But, they have shown that the rainfall is coherent and homogeneous over smaller spatial scales (few hundred kilometers) (Gadgil et al. 1993; Iyengar and Basak 1994). These studies also stressed the importance of regionalization based on rainfall for various applications related to agriculture and water management (Walker 1924; Gregory 1989; Shukla 1987; Parthasarathy et al. 1993). To determine spatial and temporal variability of rainfall, it is useful to analyze the spatial average of a homogeneous region over longer time periods, instead of long-term variability of rainfall at all individual stations within that region. The average over a homogeneous region not only reduces the data volume, but also reduces small-scale variability and enhances signal variation at larger spatial scales (Nicholson 1986). Further, understanding the linkages between these homogeneous rainfall zones and global/regional circulation parameters may yield better regional forecasts, which are more useful than all-India forecast as one unit (Parthasarathy et al. 1993).

The first effort of regionalization has been done by Blanford (1886), who divided India into 21 subdivisions based on rainfall collected at different stations spread all over India. Since then, several studies focused on identifying homogeneous rainfall zones in India (Gregory 1989; Gadgil et al. 1993; Parthasarathy et al. 1993; Iyengar and Basak 1994; Singh and Singh 1996; Venkatesh and Jose 2007; Satyanarayana and Srinivas 2008, 2011; Malik et al. 2010; Azad et al. 2010; Ratna 2012). The India Meteorological Department (IMD) divided the country into 36 meteorological subdivisions (or coherent regions) for various applications. But, these subdivisions are primarily meant for generating weather forecasts for political regions like states. The variation of rainfall within those subdivisions is not homogeneous and interseries correlations in those subdivisions are not significant (Gadgil et al. 1988, 1993; Parthasarathy et al. 1993). The principal aim of this paper is, therefore, to delineate homogeneous rainfall regions within India using a large rainfall dataset (51 years of rain gauge data collected at >1000 stations) without the caveats mentioned above.

A variety of techniques are being used to identify homogeneous rainfall regions. They include, among others, correlation analysis (Nicholson 1986; Gadgil et al. 1993), principal component analysis (PCA; Iyengar and Basak 1994; Singh and Singh 1996), spectral analysis (Azad et al. 2010), cluster analysis (Matulla et al. 2003; Venkatesh and Jose 2007; Rao and Srinivas 2008; Malik et al. 2010), and PCA in association with cluster analysis [k-means cluster (Satyanarayana and Srinivas 2008) and fuzzy c-means cluster (Satyanarayana and Srinivas 2011)]. Each method has its own pros and cons. Gadgil et al. (1993) found that the delineation technique for coherent rainfall zone based on correlation analysis is robust and easy to implement. In the present study, correlation analysis, following Gadgil et al. (1993), has been used to delineate coherent rainfall zones in India.

The present study differs from earlier studies in several ways. Most of the earlier studies in India utilized either SWM or annual rainfall to delineate coherent rainfall zones (Gadgil et al. 1993; Parthasarathy et al. 1993; Iyengar and Basak 1994; Malik et al. 2010; Azad et al. 2010; Satyanarayana and Srinivas 2008, 2011). Nevertheless, significant amount of rainfall (~35%–50% of the annual rainfall) is observed in southeast peninsular India during the northeast monsoon season (NEM; October–December). The present study, therefore, considers both the seasons (SWM and NEM separately) and annual rainfall for identifying coherent rainfall zones. In earlier studies, evaluation of identified homogeneous regions is done only by pairwise correlation between the stations within the zone. The present study extends the evaluation analysis by testing the homogeneity at different temporal scales (intraseasonal, interannual, and climatological). Earlier studies (Gadgil et al. 1993; Parthasarathy et al. 1993; Iyengar and Basak 1994) utilized time series of individual rain gauge data. Nevertheless, the number of stations that they used for the analysis is limited (few hundred) and these stations are inhomogeneously distributed across the country. Identification of the boundaries between homogeneous regions may be a concern with such a sparse rain gauge network. To reduce this problem, the present study utilizes a large dataset comprising daily rainfall measurements obtained from 1025 stations spread over India (except for few mountain regions as shown in Fig. 1—more discussion in section 2).

Fig. 1.
Fig. 1.

The locations of rain gauge stations (black dots) in India. Overlaid is the topography obtained from U.S. Geological Survey data center (http://eros.usgs.gov/). The global 30 arc second elevation dataset (GTOPO30) is a global raster digital elevation model (DEM) with a horizontal grid spacing of 30 arc seconds (~1 km).

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

Also, it is important to remember that coherent zone identified for one purpose (say, watershed studies) may not be necessarily coherent (agricultural planning or precipitation processes) for other purposes. Earlier studies in India have identified different rainfall coherent zones for watersheds (at country and river level), flood frequency analysis, regional drought analysis, agricultural management, better regional forecast (Parthasarathy et al. 1993), based on rainfall spectral characteristics (Azad et al. 2010), annual or seasonal rainfall (Malik et al. 2010), similar rainfall variations (Gadgil et al. 1993), and similarity in meteorological characteristics (Satyanarayana and Srinivas 2008, 2011). The purpose for which the coherent zones are identified is to understand basic rainfall processes/mechanisms. Accordingly, evaluation of homogeneity within the coherent zone is done from that viewpoint. For example, homogeneity tests were performed to check whether or not all the stations within the zone receive the same amount of rainfall and by the same type of rain (stratiform or convection or shallow) and exhibit similar rainfall variations at intraseasonal scales.

The paper is organized as follows. Section 2 describes the data used in the present study. Methodology for delineating homogeneous regions is illustrated in section 3. The homogeneous regions are evaluated at different temporal scales and the results are compared and contrasted with the existing reports on homogeneous regions in section 4. The results are summarized in section 5.

2. Data

The present analysis utilizes daily rainfall data collected over 51 years (1951–2001) at 1025 stations (Fig. 1) scattered across the country (Rajeevan et al. 2006). The present dataset is a subset of high-resolution (1° × 1°) daily rainfall data prepared by IMD. Although rain measurements at >6000 stations are used to prepare the high-resolution gridded data (Rajeevan et al. 2006), the data were continuous and available for the entire period only at 1025 stations. Also, the rain gauge locations are not uniformly distributed. The rain gauge density is high in southern India, low in the Himalayan mountain range (Kashmir and northeastern states of India), and reasonable in desert (Rajasthan) regions. The regions with few rain gauges (Kashmir and northeastern states of India) were excluded from the present analysis. From the daily rainfall data, seasonal and annual accumulations at each station are estimated for the correlation analysis.

The rain type information is obtained from the spaceborne precipitation radar (PR) on board the Tropical Rainfall Measuring Mission (TRMM). The PR identifies different types of rain based on parameters obtained from the radar and the freezing level height. It categorizes them into three as stratiform, convection, and others (Iguchi et al. 2000; Awaka et al. 2009). The rain category “others” contain mostly noise and information of clouds. Therefore, it is not considered in the present study. Instead, we have segregated shallow rain from the above categories (based on rain top and freezing level height) from 2A25. Later, it will be shown that the occurrence and rain fraction of shallow rain is significant in some coherent zones. The PR data (2A25) during 1998–2010 over India are grouped into 0.5° × 0.5° grids. First, the number (amount) of stratiform, convective, and shallow rain pixels (rain) is estimated in each grid. The rain occurrence (fraction) of a particular type of rain is 100 times the fraction between number of rain pixels (rain amount) by that type of rain and the total number of rain pixels (rain amount). Using the above formulas, the occurrence of different types of rain and their contribution to the total amount of rain are estimated at each grid.

3. Methodology

Delineation of homogeneous rainfall regions is difficult in countries like India, where the rainfall exhibits complex large spatiotemporal variation governed by a variety of processes. As discussed in section 1, earlier studies have found that the correlation analysis is robust and easy to implement (Gadgil et al. 1993). We, therefore, opted for the correlation analysis, following Gadgil et al. (1993). The Pearson correlation coefficients are used for examining the goodness of the correlation between the rainfall data at two stations. Let us consider a series of n measurements of X and Y written as xi and yi where i = 1, 2 … , n, then the Pearson’s correlation coefficient rxy between X and Y can be written as
e1

Correlation analysis first identifies two seed points (stations) that are uncorrelated with each other. The technique to identify the seed points is clearly demonstrated in Gadgil et al. (1993). First, the most uncorrelated data points are identified and then the third point is identified, which is highly uncorrelated with the first two, and so on. In the present study for the identification of first two seed points, we estimated the correlation coefficients from rainfall variations at each station with the rainfall variations at all other stations over the Indian region and identified the stations with weakest correlation out of all these correlations. As discussed in section 1, the annual and seasonal (SWM and NEM separately) rainfall are used for correlation analysis.

For annual rainfall, the first two seed points obtained are located at (13.65°N, 77.2°E) and (23.13°N, 84.23°E) and the correlation coefficient between them is −0.63. When we considered SWM and NEM rainfall, the weakest correlation is found between (13.16°N, 76.66°E) and (23.13°N, 84.23°E) for SWM and (13.6°N, 80.03°E) and (22.28°N, 86.70°E) for NEM, with correlation coefficients of −0.68 and −0.61, respectively. The third seed point (station) should be uncorrelated with the first two stations. It is identified as a station that satisfies the following conditions:

  1. the average correlation coefficient between that station and the first two seed points should be minimum, and
  2. it should not have significant correlation (rxy should be <0.3) with the first two seed points.
The automated program for identifying seed points stops when the above conditions do not satisfy. To identify a coherent rainfall zone around the seed point, all the stations, which show similar rainfall variations (correlation coefficient should be significant; i.e., rxy > 0.3, 95% confidence level) with the seed point are considered.

A typical example of the correlation coefficients for annual rainfall around two nearby seed points are shown in Fig. 2. It is apparent from the figure that the correlations at some stations, which are far from the seed point, are significant (e.g., the station at 14.61°N, 74.83°E). Although the variation of rainfall at those stations is similar to that of at the seed point, those isolated stations are not included in the coherent zone for that particular seed point. The interseries correlations between the stations in the coherent rainfall zone are then examined. The stations are removed from the coherent zone if the correlation between any pair of the stations shows negative correlation. In this way, the coherent zones are constructed around all the seed points. Further, a condition is imposed to avoid a few stations or small areas to form a coherent zone. The coherent zone should contain a minimum of 6 stations or 40 000 km2 contiguous grid points.

Fig. 2.
Fig. 2.

A typical example showing the construction of coherent rainfall zones around two nearby seed points (i.e., rainfall at each station within the zone shows significant correlation with the seed point). The biggest solid symbols (square and circle) are seed points and the size of the symbol indicates the correlation coefficient for rainfall between the seed point and corresponding station.

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

Although identification of seed points and coherent rainfall regions around the seed points are done objectively without manual intervention, the decision on a few stations is made subjectively. These stations are of three types: 1) A few stations lying close to the boundary between coherent zones show good correlation with more than one seed point (see stations at around 22.5°N, 73°E in Fig. 2). These stations are placed in the zone that has high interseries correlation and also high correlation with the corresponding seed point. 2) On some occasions, isolated stations located within the zone and not having significant correlation with the seed point are noticed. They are considered as stations of the same zone, because those stations alone cannot form a separate zone. 3) Although the above procedure accommodated ~97% of stations in some zone or other, a few stations were left out without showing any significant correlation with any of the seed points. They are mostly observed between some coherent zones. If the left-out points are contiguous and sufficient to form a zone (i.e., contiguous stations are more than six occupying an area of at least 40 000 km2) then we grouped them as a separate zone. If the interseries correlations of rainfall between the stations of that zone are positive, then it is considered as a coherent zone. Otherwise these stations are assigned to the nearest zone in which the correlation is relatively more with respect to the seed point as well as stations within that zone.

4. Results and discussion

The homogeneous coherent rainfall zones for annual, SWM, and NEM rainfall, obtained following the procedure outlined in section 3, are shown in Fig. 3. Clearly, correlation analysis with different seasonal rainfall provides different structures of coherent rainfall zones. The correlation analysis yields 26, 26, and 20 homogeneous rainfall zones for annual, SWM, and NEM rainfall, respectively. Coherent zones obtained with annual (Fig. 3a) and SWM seasonal (Fig. 3b) rainfall look strikingly similar and they are different from those for NEM (Fig. 3c). It is not surprising, because the SWM is the main rainy season for most parts of India. The influence of synoptic-scale weather systems, geographical features (topography and land–sea contrast), and local-scale atmospheric disturbances on delineated coherent zones is clearly evident. The southwest monsoon flow and topography along the west coast of India produce two coherent zones along the west coast with good amount of rainfall. Also, several coherent zones are formed along the east coast that are controlled significantly by the land–sea breeze circulations. The rainfall over central India and north India is known to depend heavily on the passage of low pressure systems/depressions that form over the Bay of Bengal during the SWM. The coherent zones, which are under the influence of these large-scale systems, seem to be larger in area. Clearly more coherent zones, albeit small in size, are formed in the vicinity of major hills (near the foothills of Himalayas and on the lee side of the Western Ghats) than in the plains of central and north India.

Fig. 3.
Fig. 3.

Delineated homogeneous rainfall regions when (a) annual, (b) southwest, and (c) northeast monsoon rainfall are used for the correlation analysis.

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

The delineated 26 homogeneous regions (for both annual and southwest monsoon rainfall) in our study are different from the homogeneous regions identified by earlier studies (Blanford 1886; Gregory 1989; Parthasarathy et al. 1993; Iyengar and Basak 1994). Gadgil et al. (1993), by applying correlation analysis on SWM rainfall, divided India into 31 homogeneous rainfall regions, many of which are similar to the zones identified by the present analysis. The delineated zones also have some similarities with those identified by the cluster analysis (Satyanarayana and Srinivas 2011). On the other hand, the PCA by Iyengar and Basak (1994) and spectral analysis of rainfall by Azad et al. (2010) segregated India into 10 homogeneous rainfall zones that are different from the present study. The regions numbered 6, 10, 11, and 13 in our analysis have similarities with the regions delineated by both Gadgil et al. (1993) and Satyanarayana and Srinivas (2011). The regions 2, 3, 18, and 25 (1, 5, 7, 12, 15, and 19) are similar to those identified by Satyanarayana and Srinivas (2011) (Gadgil et al. 1993). As seen above, in spite of using different methodologies and different datasets, some of the homogeneous regions are common in all the analyses, and some of them differ very much from one study to another.

To demonstrate the effectiveness of the delineated zones in comparison with the above studies, the rainfall interseries correlations between stations within the coherent zones as identified by different studies are compared. Figure 4 shows the cumulative frequency plot of interseries correlation, when the coherent zones are identified by the correlation analysis (present study), cluster analysis (Satyanarayana and Srinivas 2008), PCA (Iyengar and Basak 1994), and IMD. The clusters given in Satyanarayana and Srinivas (2008) are used here, as it is relatively easy to identify the boundary between coherent zones in the case of hard clusters, as opposed to the soft clusters (Satyanarayana and Srinivas 2011). It is clearly apparent from Fig. 4 that the interseries correlations within the coherent zones are good in the present study compared to other studies. For example, it is found from the distribution of interseries correlation coefficient that 35%, 51%, and 62% of rxy is <0.3 when the homogeneous zones are identified by IMD, cluster analysis, and PCA, respectively, whereas the present study shows only 16% of the distribution is below that threshold.

Fig. 4.
Fig. 4.

Comparison of rainfall interseries correlations between stations within the coherent zones as identified by different studies (correlation = present study, IMD = Parthasarathy et al. 1993, PCA = Iyengar and Basak 1994, and cluster = Satyanarayana and Srinivas 2008).

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

Let us now examine how good the coherent rainfall zones are. To evaluate the validity of the identified coherent zones quantitatively, several tests are performed: 1) Following Nicholson (1980), correlations for annual (and also seasonal) rainfall variations at each station with the regional average rainfall are estimated. 2) The homogeneity in terms of absolute rainfall is studied by examining the annual and seasonal rainfall and rain frequency. 3) To study whether or not the identified regions receive similar type of rainfall, the occurrence and rain fraction of stratiform and convective rains are estimated. 4) To assess the appropriateness of coherent zones at a smaller temporal scale (intraseasonal), the correlation of daily rainfall at each station with the regional average daily rainfall is performed.

a. Representativeness of delineated coherent zones for annual (and seasonal) rainfall variations

To test the representativeness of the homogeneous rainfall zone for annual and seasonal rainfall variations, the correlation coefficient for each station is estimated between the annual (and seasonal) rainfall at that station with the average annual (seasonal) rainfall of the corresponding coherent zone (arithmetic average of all stations, excluding the station with which correlation coefficients are estimated). The mean, maximum, and minimum correlation values for each zone corresponding to annual, SWM, and NEM rainfall are shown in Table 1, depicting the spatial variability. Large mean correlation values (≥0.6) are noted at each station for annual and seasonal rainfall, irrespective of size of the zone and geography (orography, coast, plain, etc.), which suggests that the identified rainfall zones are, indeed, homogeneous. Although most (90%–99%) of the stations within each zone show good coherency, some regions have discordant stations, which are found near the boundary between some zones. Even in this case, the correlations are weaker but statistically significant (the minimum correlation values for each zone are always >0.3).

Table 1.

The maximum, minimum, and mean correlation coefficients for each zone, depicting the spatial variability. The correlation analysis is carried out between rainfall series at each station and corresponding regional averaged rainfall series.

Table 1.

Histograms for correlation coefficients corresponding to annual, SWM, and NEM are shown in Figs. 5a–c for a quantitative assessment. The correlation coefficient values are larger than 0.7 (explaining nearly 50% variance) at nearly half of the stations (61% for northeast monsoon). The mean rxy at all stations for annual, SWM, and NEM are 0.67, 0.67, and 0.72, respectively, indicating that the rainfall variations are similar within the zone. Comparison of rxy distributions and mean values for annual and seasonal rainfall indicate that the NEM (SWM) rainfall variations are, relatively, more (less) coherent within the zone [with 97% (61%) of rxy population exceeding 0.5% (0.7%) with a mean rxy of 0.72].

Fig. 5.
Fig. 5.

Histograms of correlation coefficients for (a) annual, (b) SWM, and (c) NEM rainfall. The correlation analysis is carried out between rainfall series at each station and corresponding regional averaged rainfall series.

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

b. Representativeness of coherent zones in terms of rain amount and rain frequency

The correlation analysis employed in the present study ensures similar rainfall variations within the zone, but not the equal rain amount and rain frequency. To check how good the homogeneity of the delineated zones in terms of rain amount and rain frequency, they are plotted in Figs. 6a and 6b, respectively. As mentioned in section 1, the rainfall shows complex spatiotemporal variability in India. Therefore, the means and standard deviations (a measure of dispersion from the mean) for different zones are found to be different. We, therefore, used coefficient of variation (standard deviation/mean) to depict the variability of rain amount and rain frequency within each zone in Fig. 6. Figure 6 illustrates that, in general, all stations within the zone receive a nearly equal amount of annual and seasonal rainfall, irrespective of whether or not that zone is in a rainy or arid or semiarid region. Quantitatively, except for two regions (numbered 5 and 13 for annual rainfall and 6 and 14 for SWM), the coefficient of variation for rain amount for each zone is always less than 0.5, indicating that these zones are homogeneous in terms of rain amount. In fact, the majority of the zones shows a coefficient of variation <0.2. It is interesting to note that the region 13 (for annual rainfall), which includes Gujarat and the north coast of Maharashtra, was identified as a coherent zone by earlier studies also (Gadgil 1993). While this region shows very good coherency in interannual variability of rainfall (Fig. 5), the coherency is weak in rain amount, since the mean annual rainfall decreases sharply from south to north.

Fig. 6.
Fig. 6.

Coefficient of variation of (a) rain amount and (b) rain frequency for each zone corresponding to annual, SWM, and NEM rainfall. Zones with rain frequency <10 are excluded from the analysis. Note that the same zone number does not necessarily correspond to the same region in different seasons.

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

Similar to the spatial and seasonal variation of rain amount, the coefficient of variation for rain frequency (number of rainy days − rainfall > 0.1 mm day−1) also shows large variability across India. The stations along the west coast of India (southeast coast of southern peninsular India) have more rainy days during SWM (NEM) (not shown). Irrespective of the season and region, the coefficient of variation for rain frequency is always <0.4, indicating that number of rainy days in a year (season) at all stations within each zone is nearly equal. This homogeneity in rain frequency is observed in all seasons.

c. Homogeneity in rain type

The homogeneity of coherent zones is tested for rain type in this section by partitioning the rain into stratiform, convective, and shallow rain. The 2A25 data product from TRMM PR has been utilized for this purpose. The rain occurrence and fractions for each type of rain are estimated from annual rainfall (Figs. 7a and 7b, respectively) using the formulas given in section 2. The occurrence percentage of stratiform rain is high (60%–80%) over most of the zones. The notable exceptions are the zones in the west coast of India, where considerable rain (40%–50%) occurs in the form of shallow rain. Note that these zones receive maximum rain amount (Fig. 6) in all the zones considered in the study region. It clearly indicates the regions that receive copious rainfall need not necessarily of convective type.

Fig. 7.
Fig. 7.

Spatial variability of (a) the occurrence percentage and (b) rain fractions for stratiform, convective, and shallow rain, depicting the rain type homogeneity over delineated zones.

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

The convective rain fraction dominates in the zones present in the northwestern parts of India, near the foothills of the Himalayas, and in the southeastern peninsular India. While the stratiform rain dominates (50%–60%) in central India, the shallow rain contributes considerably (~30%) to the annual rainfall in zones along the west coast (and also over the Arabian Sea). From rain occurrence and rain fraction plots, it is clear that each zone is not different from another in terms of rain type; rather, a group of zones receive rain predominantly by one of the three types discussed above. Nevertheless, this rain type analysis provides some clues to the origin of precipitation affecting each zone. For example, the zones in central India are influenced by the depressions and low pressure systems that originate in the Bay of Bengal and move over these regions. By the time these systems reach these zones, they weaken and form as mesoscale convective systems with widespread stratiform rainfall (Houze et al. 2007; Romatschke and Houze 2011).

d. Representativeness of delineated coherent zones for rainfall variations within the SWM

In this section, we have examined whether or not the identified coherent rainfall zones are valid for short-term variations of rainfall (i.e., intraseasonal variations). For this analysis, first, the correlation of daily rainfall at each station with the regional average (average of all stations) daily rainfall is estimated. Figure 8a depicts a typical example showing the variation of daily rainfall at each station (thin lines) in zone 16 (for SWM) during the year 1951 (starting year of our time series) along with regional average daily rainfall (thick line) and daily rainfall at one station (thick dashed line) at which the correlation is estimated. The intraseasonal rainfall variation at each station is strikingly similar to the variation of regional average daily rainfall. The correlation of rainfall at each station with the regional average rainfall is also found to be good. The rxy is found to be >0.5 at 65% of stations within the zone 16 with a mean rxy of 0.55.

Fig. 8.
Fig. 8.

(a) Rainfall variation at each station (thin lines) within zone 16 in year 1951 along with regional averaged rainfall variation (thick line) and rainfall variation at one station (dashed line) at which correlation is estimated. (b) Spatial variation of the correlation coefficient for the year 1951, showing the coherency in rainfall variations occurring within the season (i.e., the correlation analysis is carried out between daily rainfall at each station with its regional mean daily rainfall).

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

The above analysis to check the validity of coherent zones for intraseasonal variations has been carried out for all the zones. Figure 8b shows a typical example of the correlation of daily rainfall at each station with regional average daily rainfall at all stations within India during the year 1951. Except for a few stations, near the boundary of zones in the driest regions (southeastern peninsular India and northwestern parts), the correlation is moderate to high at all stations. This clearly suggests that within the identified coherent zones the rainfall is homogeneous even at intraseasonal scales.

To examine whether or not the same is true in other years, we have carried out similar analysis for all years (from 1951 to 2001) and the average correlation coefficient (and standard deviation) at each station is plotted in Fig. 9. Similar to the spatial variation of the correlation coefficients for 1951, the average correlation values are moderate to high in the interior stations and weak to moderate at the stations near the boundary of some coherent zones. Interestingly, the coherency in rainfall at intraseasonal scale is relatively weak in drier zones (southeast peninsular India and northwest India) and moderate to strong in wet zones (west coast of India and monsoon trough zone). The wet zones not only show good correlation at intraseasonal scale, but also relatively small standard deviations, indicating that the high correlations are observed in most of the years. The wet zones, mentioned above, generally receive a good amount of rainfall in the active phase of the southwest monsoon season mainly because of the large-scale synoptic systems, like depressions and monsoon lows, which produce homogeneous rainfall over a large region (Goswami 2005). Therefore, one would expect high homogeneity in rainfall patterns over wet zones at intraseasonal scale.

Fig. 9.
Fig. 9.

(a) As in Fig. 8b, but for the mean correlation coefficient value. The correlation analysis is carried out on intraseasonal rainfall variations for each year. The mean correlation coefficient and standard deviation (Fig. 9b) are estimated using 51 years of rainfall data.

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

e. Representativeness of homogeneous regions for rainfall variations at intraseasonal scales during excess and deficit rainfall years

We have further examined whether or not the identified coherent rainfall zones are valid in excess and deficit rainfall years by grouping the years into three categories (excess, deficit, and normal rainfall years). For each zone, normalized (by standard deviation) rainfall anomaly for each year is estimated. The year for any zone is considered as excess or deficit or normal based on whether the normalized index is ≥1 or ≤1 or within ±1, respectively. The rxy values (correlation of daily rainfall at each station with the regional average daily rainfall) at each station corresponding to excess rainfall years are averaged. Similarly, average rxy values for deficit and normal rainfall years are also estimated. Figure 10 shows average correlation values at each station along with cumulative distribution curves for rxy for excess and deficit rainfall years. Figure 10 clearly shows that the correlations are significant (>0.2 at 95% confidence level) at all the stations, barring a few discordant stations in northwest India. Significant correlation coefficients at each station in most of the zones indicate that identified regions are homogeneous at intraseasonal scale also in both excess and deficit rainfall years. Nevertheless, the degree of coherence is different in excess and deficit rainfall years. Clearly, correlations are higher during excess rainfall years than in deficit rainfall years. About 70% of rxy values are >0.5 during excess rainfall years, while only 45% values exceed that threshold during deficit rainfall years. The other notable feature is a difference in rxy values in rainy and dry zones, particularly in the deficit rainfall year. High correlations are observed in rainy zones (west coast and monsoon trough zone), whereas the relatively small rxy values are observed in dry zones (northwest and southeastern peninsular India). As discussed above, the large coherency in rainy zones is mainly due to the passage of synoptic-scale systems (low pressure systems and depressions) over those zones. These systems produce rainfall over a wide area in the monsoon trough region because of a favorable synoptic environment for the convergence. Earlier studies have found a positive correlation between the total number of low pressure/depression days and SWM rainfall (or excess rainfall year) (Mooley and Shukla 1973; Kumar and Dash 1999). The observed better correlations in excess rainfall years are also due to these large synoptic-scale systems.

Fig. 10.
Fig. 10.

As in Fig. 9, but for (a) excess rainfall and (b) deficit rainfall years. (c) Cumulative distribution curves for rxy corresponding to excess and deficit rainfall years.

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

f. Validity of delineated zones over a longer period

Recent studies on long-term precipitation trends have demonstrated an intensification of hydrological cycle and an increase in extreme localized events (Huntington 2006; Xie et al. 2010) in response to global warming. Also, contrasting trends in extreme events are seen over central India and northeast India (Goswami et al. 2006, 2010). These studies reiterate the need for regionalization (because there is a spatial variability in extreme rainfall trends) and also raise one important question: how robust are the delineated regions in the face of climate change?

To see whether the regions remain the same or vary in a changing climate, the data were divided into two halves (first half: 1951–75, second half: 1976–2001) and coherent zones were identified for two halves separately. Figure 11 shows correlation maps for first and second halves along with cumulative distribution curves for rxy corresponding to two halves. It is evident from the figure that analysis on both halves resulted in the same homogeneous regions, which are similar to those obtained with the total data. However, the degree of coherence is relatively weak in the second half of the study period. The rxy is >0.5 in 95% of data for the first half, while it is greater than 0.5 in 85% of data for the second half. The high correlations and nearly similar regions in both halves confirm that the identified regions are, indeed, homogeneous (at least for the selected time period).

Fig. 11.
Fig. 11.

Spatial variation of the correlation coefficient, when the analysis is made using the annual rainfall during the periods (a) 1951–75 and (b) 1976–2001. (c) Cumulative distribution curves for rxy corresponding to two halves of the data.

Citation: Journal of Hydrometeorology 14, 1; 10.1175/JHM-D-12-071.1

The weakening of coherence in the later half is intriguing, given the recent reports indicating reduction in large-scale synoptic systems like monsoon depressions and increase in localized precipitation events in response to global warming. A longer dataset (>100 years) may shed more light on this aspect, but certainly it is out of the scope of the present study.

5. Summary and conclusions

A large database, consisting of daily rainfall measurements at 1025 stations across India over 51 years (1951–2001), is used to identify coherent rainfall zones within India. The correlation analysis, following Gadgil et al. (1993), employed here, first identifies seed points, which are highly uncorrelated with respect to each other, and then constructs a correlation zone around the seed points. While constructing a coherent zone several factors are considered like geographical contiguousness of stations, avoiding formation of zones with a few stations/small area, etc. The coherent zones are identified with annual and seasonal (SWM and NEM) rainfall. The influence of several factors, like synoptic-scale weather systems, topography, proximity, etc., on rainfall homogenization is clearly apparent. Many of the coherent rainfall zones identified with the annual rainfall (26) and SWM (26) rainfall look similar. The correlation analysis with NEM rainfall, on the other hand, identifies fewer and different coherent zones (20) than with annual and SWM rainfall. While some delineated zones have similarities with other regionalization studies based on cluster analysis (Satyanarayana and Srinivas 2008, 2011) and correlation analysis (Gadgil et al. 1993), some of them differ very much from earlier studies (Iyengar and Basak 1994). To demonstrate that the zones identified in the present study are effective, interseries correlations of rainfall between different stations within the zone as identified by different studies are compared. The cumulative frequency plot for different regionalization studies suggests that the identified zones by the present study are superior.

The representativeness of the identified coherent zones is tested by examining rainfall variations occurring at different temporal scales (interannual and intraseasonal). The correlation test shows that the correlation of rainfall at each grid point with the regional average rainfall is significant at most of the grid points, as evidenced by large mean correlation coefficient values. High correlation is observed at all stations irrespective of size and geography of the zone, indicating that the interannual variations within the zone are similar. It is found that the correlations are relatively higher when the analysis is done with NEM rainfall than with annual or SWM rainfall. Although the rain amount and frequency is heterogeneous over India with large spatial variability, both exhibit homogeneity within the delineated zones. The zones are also found to be homogeneous in terms of type of rain affecting them. For example, most of the rainfall over the zones in central India is stratiform in nature, whereas the zones in the northwest and southern peninsular India and foothills of Himalayas receive rain mostly in the form of convection. The rain fraction of shallow rain is considerable over the zones along the west coast.

The delineated coherent zones are found to be valid for rainfall variations at intraseasonal scale also, as evidenced by high correlation between the daily rainfall at each station with its regional average daily rainfall. The correlations of rainfall at intraseasonal scale are high in wet zones and relatively weak in dry zones. The above analysis is extended for excess and deficit rainfall years. Better correlations are seen during excess rainfall years than during deficit rainfall years. This is because the wetter zones receive a good amount of rainfall primarily because of synoptic-scale systems, which produce homogeneous rainfall over a large region. Also, it is now known that excess rainfall years will have more monsoon low/depression days than deficit rainfall years. It is interesting to note that though the homogeneous regions are identified using annual/seasonal rainfall variations, the same zones seem to be valid for rainfall variations occurring at intraseasonal scale also.

The data were divided into two halves and correlation analysis is carried out on both halves to examine whether the delineated zones remain the same over time or change in response to the global warming. The analysis resulted in similar coherent zones in both halves, indicating that the delineated zones are valid, at least for the period considered in this study. Nevertheless, the weakening of correlations in the second half of the study period suggests that the homogeneity of the rainfall zones may change in the future.

Summing all the representativeness tests (Figs. 511), it is clear that the identified regions are indeed homogeneous for rainfall variations occurring at different temporal scales (i.e., intraseasonal, interannual, and climatological). Further, the delineated zones are also found to be homogeneous in terms of rain amount, frequency, and type.

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