Spatial variability of annual precipitation using globally gridded data sets from 1951 to 2000

Authors

  • Renata Sokol Jurković,

    Corresponding author
    1. Department for Climatological Research and Applied Climatology, Meteorological and Hydrological Service, Grič 3, Zagreb, Croatia
    • Department for Climatological Research and Applied Climatology, Meteorological and Hydrological Service Grič 3, 10000 Zagreb, Croatia.
    Search for more papers by this author
  • Zoran Pasarić

    1. Department of Geophysics, Faculty of Science, University of Zagreb, Zagreb, Croatia
    Search for more papers by this author

Abstract

This study assesses the variability of the amounts of annual precipitation in global land areas (excluding Greenland and Antarctica) from 1951 to 2000. The analysis is based on 0.5° longitude/latitude gridded data. Three different data sets were analysed (University of East Anglia Climate Research Unit's (UEA CRU) TS 2.1 data set, the Global Precipitation Climatology Centre's (GPCC) Full Data Reanalysis version 5 data set, Variability Analysis of Surface Climate Observations (VASClimO) version 1.1 data set), and all led to very similar results. The results included here correspond to the VasClimO project data. Precipitation variability is examined through the anomaly of the coefficient of variation, which is shown to be a robust concept. It is defined as the departure of the actual coefficient of variation from the value that could be expected ‘on average’, conditioned on the total annual amount of precipitation. A brief discussion of the so-called Jackknife error is included. The analysis revealed diverse areas of larger-than-normal, smaller-than-normal and close-to-normal variability. Negative anomalies occur more often but have, on an average, lower values than do positive anomalies. Large areas of slightly negative anomalies were found inland for all continents except Australia. A zonal pattern in the distribution of the anomalies was clearly seen at subtropical latitudes, which generally showed positive anomalies. This general picture is modified by various local factors, such as cold ocean currents, monsoon activity and cyclone formation areas. Global modes of climate variability, such as the El Niño-Southern Oscillation (ENSO) and the Madden-Julian Oscillation (MJO), affect the variability of precipitation either directly or by modifying other relevant atmospheric and oceanic processes. Their influence is seen in many areas with higher-than-normal variability and is especially true if the high variability is accompanied by large amounts of mean annual precipitation. The authors believe that the present methodology may be useful in assessing the quality of future global data sets. It is, however, very desirable that such data sets include interpolation error estimates. Copyright © 2012 Royal Meteorological Society

1. Introduction

The precipitation regime of a given area is essential for all of its human activities, particularly agriculture. Total precipitation is not the only factor that determines the hydrological characteristics of a given area, as the variability of precipitation is of comparable importance. For example, in arid areas, ‘low values of total precipitation do not lead necessarily to drought and drought is not necessarily associated with low precipitation totals’ (Gommes and Petrassi, 1994). Furthermore, precipitation is known to be one of the most variable meteorological elements both in space and over time. This variability poses considerable difficulties for precipitation measurements and can strongly influence any subsequent analyses.

The amount of total precipitation over a certain period generally depends on the number of days with precipitation during that period and the amount of daily precipitation. It is possible to describe the variability of precipitation by utilizing statistics of daily data (Karl and Knight, 1998; Katz and Parlange, 1998). However, detailed, long-term information on daily precipitation does not exist globally (satellite-based data with their own limitations only became available after 1970); therefore, in global studies dealing with longer time intervals, one must use monthly or annual sums.

A basic statistical description of any quantity consists of some measure of location and some measure of variability. In the case of precipitation, measures of (absolute) variability, such as standard deviation, do not appear to be very useful. It is well known and intuitive that higher precipitation amounts are normally associated with a higher variability of precipitation. When total annual precipitation over a certain region is analysed using the available rain station data, one typically finds a fairly strong linear relationship between the standard deviations and mean values of the measuring stations. The spatial distribution of these two quantities carries essentially the same information, which stresses the need to use a measure of variability that is less dependent on the total precipitation amount. For this reason, the coefficient of variation is typically used. Longley (1952) compared four measures of precipitation variability (coefficient of variation, relative variability, interquartile variability and range divided by median) and concluded that the coefficient of variation was best for this purpose. In global studies, however, it appears that further ‘relativization’ is beneficial. A significant amount of additional information can be extracted by considering not the coefficient of variation itself but rather its departure from ‘typical’ values that would be expected on an average. This concept was first employed by Conrad (1941), who based his work on another measure of relative variability.

Previous studies on precipitation variability were typically based on data obtained from weather stations. Conrad (1941) examined global variability using data from 384 weather stations all over the world. Necessarily, the spatial distribution of the stations was very irregular and heavily biased towards more populated areas (e.g. northern hemisphere, coastal regions). Nicholls and Wong (1990) refined Conrad's results in connection with the Southern Oscillation by using approximately three times as many stations, but the spatial coverage, although improved in certain areas, did not change substantially. Peel et al. (2002) reassessed this work with a larger data set and a different methodology.

Recently, constructed gridded data sets have created new possibilities for analysing precipitation. This paper aims to globally analyse the variability of annual precipitation sums over land areas. To that end, three recently available gridded data sets are used. The analysis relies on the anomaly of the coefficient of variation and shows that the spatial distribution of the anomalies offers significant climatological information. The anomaly is used to distinguish diverse areas that are subsequently shown to be under the influence of various climatic factors. Of particular interest are regions where both the amount of annual precipitation and the variability are (relatively) high. Typically, this phenomenon could be related to one or more dominant patterns of climate variability, such as the El Niño-Southern Oscillation (ENSO) (Nicholls, 1988).

In Section 2, the data are described in some detail, followed by a brief description of the anomaly of the coefficient of variation. Section 3 begins with a statistical analysis of the anomalies and continues with a detailed spatial analysis. The conclusions of the study are presented in Section 4.

2. Data and methods

This paper focuses on globally gridded precipitation data sets of sufficiently high spatial resolution and sufficiently long temporal duration. Among several candidate data sets (see The International Research Institute for Climate and Society, 2011; Deutscher Wetterdienst, 2011), the following three globally gridded, monthly data sets with spatial resolutions of 0.5° longitude/latitude that span at least 50 years were selected: the University of East Anglia Climate Research Unit's (UEA CRU) TS 2.1 data set (Mitchell and Jones, 2005), the Global Precipitation Climatology Centre's (GPCC) Full Data Reanalysis version 5 (Rudolf et al., 2010) data set and the VASClimO version 1.1 (Beck et al., 2004) data set. All three data sets are interpolated from station data, the first two by using weighted averaging and the third by a variant of kriging. The TS 2.1 and the Full Data Reanalysis data sets attempt to provide the best estimates of instantaneous spatial patterns; therefore, the spatial density of stations varies in time. The VASClimO data set emphasizes homogeneity in time, relying on stations with a sufficiently complete record or those that could be reasonably completed. In all three data sets, it is the anomalies, i.e. the departures from the long-term means that are actually interpolated. As expected, the same sparsely gauged regions (e.g. central Africa, Arabian Peninsula, Sahara region, Siberia, Tibet Plateau, Amazon Basin and central Australia) are common to all three data sets. However, it appears that our main results are nearly the same for all three data sets, indicating that the anomaly of the coefficient of variation (see below) as calculated in this paper is robust. For this reason and because all statistics that is being used here are time-based, we report primarily on the results corresponding to the VASClimO data.

For the reader's convenience, we will present a brief description of all three data sets. The VASClimO data set contains monthly precipitation sums during the period 1951–2000 for global land areas (not including Greenland and Antarctic) with a spatial resolution of 0.5°, 1.0° and 2.5° longitude/latitude. It is based on data that were observed in situ from rain gauge networks originating from several sources. The study used historical data sets from the Food and Agriculture Organization of the UN (FAO—13 500 stations), the Climate Research Unit (CRU—9500 stations) and the Global Historical Climatology Network (GHCN—22 600 stations) and data obtained directly from national meteorological and hydrological services and regional research projects. Approximately 2000 stations from CLIMAT reports were also used. When necessary, the GPCC and CRU SYNOP data were used to fill in the gaps in station time series, but their usage was minimized. To minimize eventual temporal inhomogeneities, care was taken to use as few data sources as possible and made certain that all sources corresponded well with each other. This procedure resulted in 9343 station data series with a minimum of 90% data availability from 1951 to 2000. It should be noted, however, that the station density was very irregular, being very high over Germany and France and rather low in areas such as the Sahara Desert, central Africa, the Arabian Peninsula or central Australia (see Figure 3 in Beck et al., 2004). The compiled station data were subsequently submitted to quality control to identify outliers and temporal inhomogeneities. Finally, kriging was used to interpolate the station data onto a regular 0.5° latitude/longitude grid over the given land areas.

The UEA CRU TS 2.1 data set (Mitchell and Jones, 2005) contains monthly data for nine climate variables (temperature, diurnal temperature range, daily minimum and maximum temperatures, precipitation, wet-day frequency, frost-day frequency, vapour pressure and cloud cover) for the period 1901–2002 at 0.5° resolution covering the global land surface (excluding Antarctica). It is based on anomalies relative to the 1961–1990 mean. Station normals for the period 1961–1990 originate from a number of sources, such as National Meteorological Agencies (NMA), the World Meteorological Organisation (WMO), the CRU, the Centro Internacional de Agricultura Tropical (CIAT) and few other ones (New et al., 1999; New et al., 2000). Anomalies of the primary variables were obtained from global data sets compiled by CRU for the period 1901–2002. Finally, the data set was updated from seven different sources (Table I in Mitchell and Jones, 2005). Prior to interpolation, the data set was checked for inhomogeneities using an automated procedure developed from the Global Historical Climatology Network (GHCN) method (Peterson and Easterling, 1994; Easterling and Peterson, 1995). Angular distance-weighted interpolation was used to interpolate anomalies relative to the 1961–1990 mean. Although the data set contains variables for the period 1901–2002, only the monthly precipitation for the period 1951–2000 was used in the present analysis.

The GPCC Full Data Reanalysis Version 5 data set (Schneider et al., 2011) contains monthly precipitation sums at 0.5° resolution (excluding Antarctica) and covers the period 1901–2009. Product version 5 uses a data set of around 65 000 stations with at least 10 years of data. The data coverage per month varies from some 10 000 to more than 47 000 stations; consequently, the data set does not comply with requirements for temporal data homogeneity. Data sources for the GPCC Full Data Reanalysis are the same as those for the VASClimO data set. All station data were submitted to quality control and corrected as necessary. The anomalies from the climatological normals at the stations are spatially interpolated onto a regular 0.5° latitude/longitude grid using a modified version of the interpolation method SPHEREMAP, which represents a spherical adaptation (Willmott et al., 1985) of Shepard's empirical weighting scheme (Shepard, 1968). The same period used in the other two data sets was used in this analysis.

The anomaly of the coefficient of variation is derived analogously to the work of Conrad (1941). By and σ, we denote the long-term mean and the standard deviation of the amount of annual precipitation, respectively, which are calculated separately for each grid point. As will be shown, there is a strong linear relationship between the two quantities:

equation image(1)

where the regression coefficients A and B are found by the least-squares method.

By inserting the modelled standard deviation as shown in Equation (1) into the definition of the coefficient of variation, a hyperbolic relationship is obtained:

equation image(2)

where µ denotes the long-term mean. For large amounts of precipitation, the changes of the hyperbola are small; however, the changes are extreme for small amounts of precipitation. Moreover, cv in Equation (2) increases to infinity as decreases to 0, which is not physically reasonable. Therefore, the mathematical equation must be corrected to fit the observed data at low annual precipitations. Following Conrad (1941), the coefficient of variation is modelled as

equation image(3)

where the coefficient C is used to eliminate the undesired increase of to cv infinity. The coefficients A, B and C are computed using nonlinear least squares (Björck, 1996). The modified hyperbola (Equation (3)) represents the ‘theoretical’ value of the coefficient of variation that could be expected on an average for certain annual amounts of precipitation. Further justification is given in Section 3 below.

The anomaly of the coefficient of variation at each grid point is defined as the difference between the coefficient of variation obtained from the observed data and the theoretical coefficient of variation, which are calculated from Equation (3). All of the calculations were performed for mean annual precipitation sums.

Although the present analysis aims to provide a useful statistical description of global precipitation for one particular period, namely from 1951 to 2000, how analysis is affected by possible nonstationarity of the analysed data records could be debated. A detailed analysis of stationarity is beyond the scope of this study. Moreover, only the VASClimO data set is constructed with homogeneity in mind. However, to address this concern, two sensitivity tests were performed on the VASClimO data. First, the linear trend (Sen, 1968) was calculated for each grid point and subtracted from corresponding time series; all analyses were subsequently performed on the detrended data. Second, all analyses were performed independently for the periods 1951–1975 and 1976–2000. The results obtained were nearly the same as the original results, indicating that nonstationarity, if present, does not noticeably affect our findings.

3. Results and discussion

Figure 1 shows the VASClimO data standard deviation (upper panel), the coefficient of variation (middle panel) and the anomaly of the coefficient of variation (lower panel), all of which are plotted against the mean annual precipitation. The linear relationship between the standard deviation and the mean annual precipitation is more or less obvious (see below). The regression line is given by

equation image(4)

where the correlation coefficient is 0.84, indicating a strong linear relationship. However, a small number of points lie notably above the regression line (Figure 1, upper panel). These data come from the equatorial areas of the Pacific Ocean. Among these points, 81% are located in the coastal area of western South America, 17% are located in Indonesia and 2% are found in the central Pacific islands (Kiribati). These areas, which are almost identical in all three data sets, are characterized by relatively high annual precipitation accompanied by high variability. The physical reasons for this behaviour are discussed later in this section.

Figure 1.

Two-dimensional histogram plots of standard deviation with regression line (upper panel), coefficient of variation with modified hyperbola (middle panel) and anomaly of coefficient of variation (lower panel) versus mean annual precipitation. Shading indicates the number of 0.50 latitude/longitude grid points falling in every bin. The dashed line in the upper panel delimits a small number of equatorial points that notably deviate from the regression line. Those points denoted by circles come from the Eastern Pacific, while the remainder come from the Central Pacific

It is apparent (Figure 1, upper panel) that the data for long-term mean annual precipitation carry a significant amount of information about the long-term standard deviation, which lessens the usefulness of the latter measure. This problem is partially solved by employing the coefficient of variation (Figure 1, middle panel), which measures the variability in terms of the mean value. By computing the coefficients A, B and C from Equation(3), the coefficient of variation is modelled as

equation image(5)

where the respective coefficient of determination is 0.81. This curve, which is plotted in the middle panel of Figure 1, represents the theoretical coefficient of variation. It grows quickly when the mean precipitation moves towards 0 and becomes nearly constant (19–15%) as the mean precipitation increases over 400 mm. The lower panel of Figure 1 shows the anomaly of the coefficient of variation. It is characterized somewhat conspicuously by high absolute values that correspond to low amounts of annual precipitation.

An examination of the distribution of the anomalies over the mean-precipitation range shows a larger share of negative anomalies. The data show that about 65% of all anomalies are negative, but on an average, they reach lower absolute values than do the positive anomalies (Figure 2, lower panel). This behaviour is to be expected because the sum of all anomalies must be close to 0. Overall, only 7% of the negative anomalies are below − 10%, and 32% of the positive anomalies are above 10%. Approximately 84% of all anomalies are between − 10% and + 10%. The weighted mean of all of the positive anomalies is 9.6% and that of the negative anomalies is − 5.3%. On an average, the maximums of the positive anomalies taken over the mean annual precipitation classes are 5 times greater than the respective negative minimums.

Figure 2.

Absolute frequencies (also indicated by numbers, upper panel) and mean values (lower panel) of positive and negative anomalies versus respective classes of the mean annual precipitation

This analysis was also performed without the deviating data (depicted in Figure 1, upper panel). The weighted means (9.2% and − 5.2%) and the relative frequencies of the positive (64%) and negative (36%) anomalies were not significantly changed; however, on an average, the maximums of the positive anomalies were only 2.7 times greater than the respective negative minimums.

Both the positive and negative bars in Figure 2 (lower panel) reach their local minimum somewhere between 1200 and 1800 mm, and a similar behaviour occurs if both the positive and negative anomalies are taken together. Conrad (1941) also noticed this type of behaviour, but the minimum of his curve was between 1800 and 2200 mm.

Before turning to the spatial distribution of the anomalies, it is to be mentioned that Equations (1) and (3) may be replaced with Equations (4) and (5) with general least-square estimates without referring to linearity. As is well known, for any two-dimensional probability distribution, the best least-square estimate of one variable in terms of the other is given by the curve that passes through the means of conditional distributions. This fact corresponds to least-square fitting for a very broad class of all measurable functions (Fisz, 1980). In our case, the resulting general curve, which describes the connection between mean annual precipitation and standard deviation, could be very well approximated with a straight line (the correlation coefficient being greater than 0.98, not shown). Estimating in the same way the relationship between annual precipitation and the coefficient of variation, one obtains a curve that is very similar to Equation (5). The resulting spatial distribution of the anomalies of coefficient of variation is almost identical to that found in Figure 3. For this reason, we preferred to use Conrad's simple, yet insightful, calculations.

Figure 3.

Spatial distribution of the anomaly of coefficient of variation calculated for the total annual precipitation during the period 1951–2000. The colour scale spans 99% of the data. The completely dry area (parts of Egypt and Sudan) where the anomalies are not defined is marked yellow. The capital letters A, B, C and D denote the Californian, Humboldt, Canary and Benguela currents, respectively

We will now discuss the spatial distribution of the anomalies (Figure 3). (For convenience, the global mean precipitation is depicted in Figure 4.) First, there are large areas where the negative anomalies are mostly distributed inland. Here, large land masses decrease the global circulation variability, thereby decreasing the number of rain events. The prevalence of negative anomalies also indicates that most parts of the world have continual annual precipitation regardless of the actual total precipitation amount. Positive anomalies are typically found along coasts where the precipitation regime is influenced by the adjacent ocean. A zonal distribution of the anomalies can also be distinguished. Generally, tropical latitudes have negative anomalies, while subtropical latitudes have very high positive anomalies. The middle and polar latitudes have slightly negative anomalies. The zonal change of variability was discussed by Nicholls and Wong (1990). The inter-tropical convergence zone (ITCZ) is a wider area around the equator that shows the presence of negative anomalies. Because it is characterized by heavy and continuous precipitation, the variability of precipitation is less than normal. However, the ITCZ also has its own variability, which may influence the precipitation variability at some subtropical areas, such as the southern part of Africa and northern Sahel (Grist and Nicholson, 2001).

Figure 4.

Spatial distribution of the mean annual precipitation. The scale covers 99% of the data. Isoline 500 mm is added for convenience

In the northern part of Africa, which comprises the Sahara Desert and the Sahel region below, three belts of precipitation variability stretching in an east–west direction are clearly visible. In the north, there is a belt of moderately positive anomalies that is influenced by moist-air flow that is occasionally advected from the Mediterranean Sea. Another belt of extremely high anomalies lying over the Sahel region may be related to the variability of the ITCZ. Years with notable higher-than-normal precipitation occasionally occur in both areas, thereby increasing the variability. In between, there is a region of extremely low (negative) anomalies that covers the most arid parts of the Sahara Desert. This region is sufficiently separated from the above-mentioned physical processes such that the total annual amounts of a few millimetres of precipitation do not vary much from year to year. In general, low amounts of precipitation are associated with negative anomalies if the continental influence is sufficiently strong. As expected, because the entire region is exceptionally dry, extremely high (positive) anomalies are also found, but they are located closer to the east coast where the moist-air flow is more variable. A high anomaly may be caused by rare precipitation events that originated from the deviating ITCZ or from the moist Mediterranean air flow.

In the arid southwest of Africa, precipitation is under the direct influence of the cold Benguela Current (D in Figure 3), whose anomalies are similar to those of the cold Humboldt Current and induce an effect similar to El Niño (Shannon et al., 1986). The northwestern African precipitation regime is influenced by the cold Canary Current (C in Figure 3). The variability of these currents enhances the variability of precipitation by allowing for occasional years in which the amount of total precipitation is considerably higher than the long-term mean values. The east coast of Africa, the Arabian Peninsula and parts of Iran and Pakistan also have high positive anomalies. These dry areas experience a high variability of precipitation because of infrequent precipitation events caused by the Indian monsoon activity (Vizy and Cook, 2003) and tropical cyclone formation over the western part of the Indian Ocean. During El Niño, the formation of tropical cyclones shifts westward from 75°E, and during La Niña, it shifts eastward from 75°E (Ho et al., 2006). In addition, during El Niño, the trade winds weaken and outbreaks of moist air from the South Atlantic occur. This phenomenon is often associated with increased precipitation over east Africa (McHugh, 2006). On the other side of the Indian peninsula, the influence of ENSO and the effects of the variability of the Indian monsoon on precipitation are reduced by the Indian Ocean Dipole (IOD) (Ashok et al., 2001; Krishnamurthy and Kirtman, 2003), which leads to decreased precipitation variability in eastern areas of India.

Most areas of Europe are characterized by a slightly negative anomaly, which indicates a lower-than-normal variability and is a consequence of the strong continual westerly flow that brings moist air from the Atlantic Ocean. Relatively high positive anomalies are found over the Iberian Peninsula, and slightly positive anomalies are seen along the west coast of Norway. The positive anomalies over those areas could be connected with the North Atlantic Oscillation (NAO), which is commonly expressed by the NAO index. The index itself is a measure of the difference in pressure between the Island low and the Azores high. If the difference is low, the westerly flow is shifted southward, resulting in a higher amount of moist air reaching the southern part of Europe (Muñoz-Díaz and Rodrigo, 2004). Under these conditions, precipitation over Norway is also below the mean. During the positive NAO phase (high NAO index), the western Scandinavian coast receives higher-than-normal precipitation, whereas the Iberian Peninsula falls under the strong influence of the Azores anticyclone, and the precipitation is lower than normal (Wibig, 1999).

The west coast of South America is characterized by a high positive anomaly. The cold Humboldt Current (B in Figure 3) keeps Peru and Chile relatively dry; however, El Niño is the key factor that increases precipitation variability over the region. During El Niño, the high sea temperature near Ecuador and Peru results in an abundance of rain, while at the same time, the western equatorial Pacific is under drought conditions. La Niña has the opposite effect, causing the west coast of South America to be cold and dry (Trenberth, 1997). Interestingly, the regional anomaly maximum, which is also one of the deviating points depicted in Figure 1, is found in Ecuador. The corresponding mean annual precipitation is 2000 mm. Because Ecuador falls under the influence of the ITCZ, one would expect the anomaly to be slightly negative, but the variability is apparently increased under the influence of the ENSO (Nicholls, 1988). The anomaly minimum is found in the Atacama Desert. Along the coast of northern Chile, the Humboldt Current is strongest, which, combined with the altitude of the desert and the global subtropical subsidence, keeps both the amount and variability of precipitation very low. Precipitation variability in eastern Brazil is affected by the variability of the South Atlantic convergence zone and the Madden-Julian Oscillation (MJO) (Muza et al., 2008). The MJO is characterized by large regions of both enhanced and suppressed tropical precipitation. Its influence on precipitation variability can also be seen in eastern Africa and the Arabian Peninsula (Jones et al., 2004). The northern Venezuelan coast also has a high positive anomaly, which is a consequence of the ITCZ's variability. During La Niña episodes, the ITCZ shifts northward, and the precipitation in the northern part of Venezuela is amplified (Lyon, 2002). The large inland area of South America belonging to the tropics is not directly influenced by the above-mentioned atmospheric and oceanic processes and, therefore, shows low variability.

North America is characterized by two distinct areas. The eastern and northern parts of the North American continent have negative anomalies, whereas the western and central parts have positive anomalies. Although the eastern coast of North America is under the influence of tropical cyclones (hurricanes), variability of precipitation is negative or slightly positive, indicating low precipitation variability, which may be caused by continual inflow of moist air from the Atlantic Ocean, while only a relatively small portion of precipitation comes from tropical cyclones. Along the western coast, the variability of precipitation is affected by the cold Californian Current (A in Figure 3), whose weakening (i.e. from the intrusion of anomalous warm water from the south) creates conditions that enhance precipitation (Cayan et al., 1998). A weaker positive anomaly associated with the North American monsoon occurs over the southwestern United States and Mexico. The variability of the North American monsoon, which is active from July to September, may be related to La Niña and El Niño conditions. During La Niña, the total amount of precipitation over the region decreases, and during El Niño, it increases, which enhances the precipitation variability (Castro et al., 2001). The eastern parts of North America have relatively high mean annual precipitation with low variability. The continual flow of moist air from the south keeps precipitation in the area stable. The higher variability that occurs in Alaska may be associated with the Pacific Decadal Oscillation (PDO), which, in the Northern Pacific Ocean, is analogous to the ENSO; however, the PDO is associated with interdecadal variability, while the ENSO's variability is interannual. During a positive (warm) PDO, the sea surface temperature over the eastern parts of the Northern Pacific increases (Zhang et al., 1997). Consequently, precipitation amounts over the Gulf of Alaska increase, whereas over inland Alaska, anomalously dry periods occur (Mantua and Hare, 2002).

Uncharacteristic of other continents, nearly all of Australia has high precipitation variability. Being the world's smallest and flattest continent, it seems that Australia's topography does not suppress the influence of the surrounding ocean. Furthermore, because it is located at a subtropical latitude, it is a primarily arid area where high variability is generally more likely to occur. The precipitation regime over Australia is greatly influenced by, among other factors, the ENSO and even more by the IOD, which is a phenomenon similar to the ENSO (Ummenhofer et al., 2009). During the positive IOD, a lower-than-normal sea surface temperature occurs over the eastern Indian Ocean, resulting in severe drought across all of Australia. A lower-than-normal variability of precipitation is found along the southern coast of Australia and over New Zealand, which are located in the mid-latitudes and experience a continual flow of moist air.

Parts of Oceania with relatively large amounts of annual precipitation have high variability. Similar to South America and the eastern Pacific, it is also an area under El Niño's direct influence. During El Niño, the rain remains on the east side of the Pacific Ocean, whereas the west side faces drought conditions.

Most areas of Asia have a slightly negative anomaly due to the wide continental mass that dampens moist-air flow. However, northern China is an area of increased variability. The interannual variability of the East Asian monsoon causes droughts or floods in northern China (Huang et al., 2003). Inland China, although arid, has a negative anomaly. Extremely low variability is found in the Taklamakan Desert. The Himalayas separate this extremely dry area from the influence of the Indian monsoon, which comes from the south.

Although the notion of the anomaly of coefficient of variation employed here seems to be rather robust, it is nevertheless clear that the present analysis relies on reliable estimates of the coefficient of variation and the mean annual sums. These estimates are certainly affected by interpolation errors, which are inevitably present in the gridded data. Of particular concern are the sparsely gauged areas, such as central Africa, the Sahara Desert, the Arabian Peninsula and central Australia (see Figure 3 in Beck et al., 2004). To address these questions, one should have the interpolation error estimates, which, to the best of our knowledge, are not presently available. For the VASClimO data, there are monthly fields of the so-called Jackknife errors that we used to calculate annual Jackknife errors and corresponding 50 year means and standard deviations. Almost all errors are small outside the equatorial region, which encompasses many of the sparsely gauged areas. Small errors indicate that the station density may be sufficient compared to the inherent precipitation variability over those regions and that the interpolation error itself may be low. Enhanced Jackknife errors are found over the western Amazon Basin (Peru) and the Amazon River delta, New Guinea, Indonesia and several other areas. However, large Jackknife errors do not have a unique interpretation, which is particularly true for the sparsely gauged areas. Thus, while containing valuable information, the Jackknife errors cannot completely substitute the ‘true’ interpolation errors. Also, we recalculated the theoretical coefficient of variation (Equation (3)) by using only those grid elements that contain at least one station. The results obtained were nearly identical to those obtained by using all grid elements; therefore, the mean coefficient of variation (Equation (5)) is likely not strongly affected by the lack of station data.

4. Summary and conclusions

This study assessed the variability of precipitation for the period 1951–2000 on a global scale by analysing gridded data sets. The analysis is based on annual precipitation sums with a spatial resolution of 0.5° longitude/latitude. Because of the large spatial scales involved and the high variability that is inherent to precipitation, variability was quantified by the anomaly of the coefficient of variation. The anomaly is defined as the departure of the actual coefficient of variation from the value that could be expected ‘on average’, conditioned on the total annual precipitation amount. The anomaly is a measure of the relative variability that shows no apparent connection with the total annual sums. This method gives large contiguous areas of greater-than-normal, lower-than-normal or close-to-normal variability, thereby revealing significant climatological information.

Negative anomalies occur more often but have, on an average, lower values than do positive anomalies. Large areas of slightly negative anomalies are found inland on almost all continents. Land masses dampen the moist-air flow coming from adjacent oceans and decrease the overall variability of global atmospheric circulation. The continental climate is characterized by a lower-than-normal variability of precipitation. A zonal pattern in the distribution of the anomalies is also clear. In general, tropical latitudes are marked by a low variability of precipitation due to the permanent existence of the ITCZ. On the contrary, subtropical latitudes, which are affected by the variability of the ITCZ, are often marked by positive anomalies. In the northern hemisphere, the middle and polar latitudes are characterized by large areas of slightly negative anomalies.

This general picture is further modified by various factors that are more local in nature. Therefore, a high positive anomaly indicating high variability occurs in arid and semiarid coastal regions with cold ocean currents (e.g. California, Peru, Chile, Namibia and northwestern Africa). Even a small change in the position or temperature of these currents can induce significant changes in precipitation. Some arid and semiarid areas that are not directly influenced by ocean currents also experience high variability. East Africa, the Arabian Peninsula and Pakistan are influenced by the variability of the Indian monsoon and by tropical cyclone formation over the western part of the Indian Ocean. The higher-than-normal precipitation variability of Australia is strongly influenced by the IOD. Enhanced anomalies over eastern Brazil are caused by both the variability of the South Atlantic convergence zone and the MJO. A relatively high positive anomaly in the middle latitudes (e.g. Iberian Peninsula, southwestern United States, Mexico and China) is a consequence of diverse processes that control the moist-air inflow.

Global modes of climate variability, such as the ENSO and the MJO, affect the variability of precipitation either directly or by modifying other relevant atmospheric and oceanic processes. The importance of the ENSO and the MJO is seen in many areas with higher-than-normal variability and is particularly true if the high variability is accompanied by large mean annual precipitation amounts.

In summary, this study confirmed that the precipitation regime throughout the world largely depends on global atmospheric circulation, but the strong influences of various local climatological factors are also clearly visible. High variability occurs where precipitation depends on factors that are variable themselves (e.g. cold ocean currents). On the contrary, a low variability of precipitation is found in areas where the relevant climatic factors are permanent (e.g. land masses) or highly persistent (e.g. the processes of the ITCZ). Following Conrad (1941), this study reaffirms that the anomaly of the coefficient of variation is useful in characterizing global annual precipitation, which is a highly variable climatological element both temporally and spatially.

The authors believe that the present methodology may also be useful in assessing the quality of future global data sets that may possibly be constructed using new interpolation techniques and/or new station data. It is highly desirable that these new data sets incorporate interpolation error estimates.

Acknowledgements

We are grateful to Josip Juras who pointed us to the work of Conrad and shared his thoughts and opinions with us. We thank the two anonymous referees for their constructive comments and suggestions. This research was supported by the Croatian Ministry of Science, Education and Sports (Grants 119-1193086-3085, 119-1193086-1323 and 004-1193086-3035).

Ancillary