International Journal of Climatology - For peer review only. On the reliability of Brazilian rainfall data for climate studies

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1 International Journal of Climatology - For peer review only On the reliability of Brazilian rainfall data for climate studies Journal: International Journal of Climatology Manuscript ID: JOC-0-00 Wiley - Manuscript type: Research Article Date Submitted by the Author: -Feb-00 Complete List of Authors: Sugahara, Shigetoshi; UNESP, Instituto de Pesquisas Meteorológicas da Rocha, Rosmeri; Universidade de São Paulo, de Ciências Atmosféricas Silveira, Reinaldo; Instituto Tecnológico SIMEPAR Keywords: daily rainfall series, inhomogeneity, change-point, climate change problem, remote climate influence, multiple-breaks linear regression model, Brazil

2 Page of International Journal of Climatology - For peer review only On the reliability of Brazilian rainfall data for climate studies Shigetoshi Sugahara * Instituto de Pesquisas Meteorológicas e Programa de Pós-Graduação da Faculdade de Ciências, UNESP/Bauru, São Paulo, Brazil. Rosmeri Porfirio da Rocha Departamento de Ciências Atmosféricas, Universidade de São Paulo, São Paulo, Brazil Reinaldo Silveira Instituto Tecnológico SIMEPAR Centro Politécnico da UFPR, Curitiba, Brazil * Corresponding author address: Shigetoshi Sugahara, Instituto de Pesquisas Meteorológicas, UNESP/Bauru, Av. Luis Edmundo Carrijo Coube -0, Bauru, SP, -0 Brazil Telephone: +()-00 Fax number: +() 0- shige@ipmet.unesp.br

3 International Journal of Climatology - For peer review only Page of ABSTRACT A set of historical daily rainfall series of Brazil from different climates were assessed for inhomogeneity. These series have at least 0 years in length. The work was undertaken assuming that all stations are potentially inhomogeneous, regarding raw data. Various statistical techniques were applied to track down inhomogeneity including multiple breaks linear regression model with supf test, the Anderson-Darling distribution test, the proportion test, and the Mann-Kendall trend test, among others. The examined quantities in the annual time scale were number of dry days, median of daily amounts, and total annual. The outcomes of these tests indicated the presence of various types of homogeneity problem in the majority of series. Many of them can be attributed to bad observing routine, among which are the reporting of only significant amount or zero neglecting small amounts, during one or more sub-periods of record, the reporting of missing observations as zero, and multi-day accumulation. These homogeneity problems might be observed all across the country, regardless source of data. The number of series classified as homogeneous is disappointingly small, only out of the total number (or.%), when % significance level is adopted as critical level in all homogeneity tests. This number certainly could hinder achievement of many climate studies, particularly those in which the involved climate signal is weak and spatially complex, as that associated with El Niño-Southern Oscillation (ENSO) and long-term climatic trend. Key words: daily rainfall series; rain-gauge; inhomogeneity; change-point, climate change problem; remote climate influence; multiple-breaks linear regression model; Brazil.

4 Page of International Journal of Climatology - For peer review only Introduction The need for reliable climate series is growing rapidly. In fact, they are essential to any climate studies and many recent studies of quality assessment of instrumental climate records have been motivated by IPCC report (00), which calls attention to the need for quantitative reconstruction of past climate change. It is well known that a climate time series could only be regarded reliable if it is homogeneous, i.e., if their variations were caused only by variation of weather and climate (Conrad and Pollak, ). Unfortunately, most long-term climate series are contaminated by spurious variations due to nonclimatic factors, among which are changes in instruments, observing routines, local environment, instrument exposure, and station relocation (e.g. Karl and Williams, ; Peterson et al., ; Alexandersson, ; Alexandersson and Moberg, ; Hansen-Bauer and Førland, ; DeGaetano, 00; Easterling and Peterson, ; Vincent, ; Wijngaard et al., 00; Auer et al., 00; Davey and Pielke, 00; Klok and Klein Tank, 00). All these factors can introduce bias into the climate statistics in some degree, which in turn might lead to misinterpretations or doubtful conclusions about the evolution of climate and of the climate itself (e.g. Hansen-Bauer and Førland, ; Peterson et al., ; Tuomenvirta, 00; Caussinus and Mestre, 00; Wijngaard et al., 00; Davey and Pielke, 00; Rust et al., 00; Sherhood et al., 00). The homogeneity assessment is by no means a trivial exercise. In general, various statistical tools need to be considered (e.g. Tuomenvirta, 00; Auer et al., 00) due to a variety of homogeneity problems that have to be addressed. Moreover, in the homogeneity work it is necessary to consider that the effectiveness of a particular tool may depend on the testing variable, climate, stations density, etc. (e.g. Lavery et al., ; Hansen-Bauer and Førland, ; Peterson et al., ; Tuomenvirta, 00; Wijngaard et al., 00; Klok and Klein Tank, 00). A station history metadata would be useful for this task if it brings information that can help identify potential inhomogeneities, though it rarely occurs, as reported by many authors of various nations (e.g. Klein Tank, 00; Auer et al., 00; Wijngaard et

5 International Journal of Climatology - For peer review only Page of al., 00). An important aspect of inhomogeneity assessment is that no homogeneity work is definitive. A good example of it is given by Viney and Bates (00), for the Australian daily rainfall dataset, in which an error caused by multi-day accumulation, particularly that involving weekends (Saturday- Sunday), was found even within a data set deemed to be highly reliable after Lavery et al. () and Haylock and Nicholls (000). The sudden jump also called change- or break- point is one of the most common type of inhomogeneity encountered in the climatic series. This can be caused for example by the relocation of the station or change in observing practices (e.g. Alexandersson, ; Peterson et al., ; Wijngaard et al., 00; Klok and Klein Tank, 00). Statistically, such series is broken down into segments with observations following the same statistical properties within each segment. To the knowledge of present authors, in the works involving rainfall over Brazil this problem has not received due attention, with rare exceptions as in Xavier et al. (), and Sugahara et al. (00). But these works are restricted to few stations of Sao Paulo state, in the Southeastern portion of Brazil. In other works, a possible presence of it has been disregarded tacit or explicitly, even those in which only homogeneous data should be used, such as climate variability studies. Not always the inhomoneity appears as abrupt variations. Instead, in some cases it appears as slow variations as an effect of the environmental change around the station (e.g. Peterson et al. ). But regardless of type of homogeneity, what is important to consider is that, as stated by Auer et al. (00), in general all climate series exceeding a few decades are contaminated by non-climatic information. When the testing variable is precipitation, an additional problem that can emerge is related to the reporting of missing day as day of no precipitation (see e.g. Lavery et al., ; Viney and Bates,

6 Page of International Journal of Climatology - For peer review only ; Liebmann and Allured, 00; Higgins et al., 00). Particularly, with respect to the South American daily rainfall dataset, Liebmann and Allured (00) have called attention to this problem. An obvious effect of this is that it leads to biased estimates of both dry and wet spell length, which are an important local climatic characteristic for agricultural and water resources purpose, and recently has been regarded in the climate change analysis. The present work aims to perform homogeneity analysis of long-term daily observations of rainfall across Brazil territory. Following Auer et al. (00), the work is carried out under the assumption that all series are potentially inhomogeneous, even those which were used in many previous works. The remaining of this work is organized as follows. Section describes the dataset gathered for this work. The possible types of inhomogeneity that are expected to be encountered are discussed in Section. In Section we describe methods for detection of inhomogeneity. In Section we present the results, and considering that some regions have attracted more attention than other, we seek to present the results for each state separately, with the hope that they may be useful for future research. Section presents the concluding remarks.. Data The raw data daily rainfall series checked on this work are from rain-gauges stations which began reporting daily amount since or before and extended at least up to. The minimum length of 0 years and completeness of records were required in the selection process. One record having more than four consecutive missing years was discarded. A year with more than missing days, which may also include negative amount, was considered as missing.

7 International Journal of Climatology - For peer review only Page of The elected stations cover a substantial portion of Brazil with different climates. The sources of data are: DAEE (Departamento de Águas e Energia Elétrica do Estado de São Paulo), ANA (Agência Nacional de Águas), ANEEL (Agência Nacional de Energia Elétrica), FUNCEME (Fundação Cearense de Meteorologia e Recursos Hídricos), SUDENE (Superintendência do Desenvolvimento do Nordeste), DNOCS (Departamento de Obras contra Secas). The dataset of DAEE are only for São Paulo State and available to the public and it can be downloaded from The dataset for other regions of Brazil are also public available from The list of stations is presented in Appendix, where for the sake of economy of space only station identity (ID) code is shown, but it is sufficient to access the data from aforementioned Web sites, including geographic position, name, and altitude. From this list the readers or users may see which stations were assessed for homogeneity and also perform their own homogeneity analysis. We are conscious that no homogeneity assessment is definite. The elected stations are distributed across states as shown in Figure a. The map with geographic location of each station is depicted in Figure b. As one may see both the density and the number of stations are highly variable. The São Paulo state, in Southeast (SEB), is favored by a high density network with stations of DAEE, but some areas as of the Northeast are poorly covered, and for Amazon Basin no station was elected, since unfortunately many stations in those regions stopped to collect rainfall data before or their data had not been updated in the time of this work. The rainfall series from the institutions which impose data policy restriction or those not easily available for public accessibility are not regarded in this work. The gauge-only precipitation gridded analyses of daily rainfall data covering South America, for horizontal resolution of o and. o, are now provided by NOAA-CIRES Climate Diagnostic Center (CDC) (Liebmann and Allured, 00), benefiting scientific community worldwide. Specifically for

8 Page of International Journal of Climatology - For peer review only Brazil, a new version of the NOAA-Climate Prediction Center historical gauge-only precipitation gridded daily precipitation analysis, for the horizontal resolution of o x o, with improved rain-gauge station coverage was recently presented by Silva et al. (00). Because of our screening process, stations used here are considerably smaller in number and density than considered in those analyses.. Some possible types of inhomogeneity expected to be encountered in rainfall data of Brazil The reporting of missing observation as zero is recognized as one of the most serious problems to be dealt with in the homogeneity analysis of the daily rainfall series (Higgins et al., 000, Liebmann and Allured, 00). This flaw handling of missing observations has been identified even in the other places of the globe like Australia (Lavery et al., ; Viney and Bates, 00) and United States (Higgins et al., 000), where good observing practice is better established than in the countries like Brazil. According to the undocumented historical information kindly provided by the DAEE hydrologist Dr. Sergio de Toledo (00, personnel communication), this practice has been quite common over time, particularly in some DAEE stations and even more on weekends, at least for the periods before - and after mid-0s. This implies that for some stations the data would be reliable only for the period between and before mid-0s. We are also told about the existence of multi-day accumulation problem for some stations, either for not having observer at the station, especially at the weekends, or forgetting the reading of the instrument by the observer. Even though this historical information is not as precise as we wanted, it suggests what types of homogeneity problem might be addressed. Therefore, it would not be surprising to find, for the DAEE rainfall series, discontinuity in number of dry days, larger proportion of zero precipitation for weekends, and distribution of daily amount varying with days of week, in addition to most commonly identified problems of homogeneity, as those related for instance to the station relocation and changes of

9 International Journal of Climatology - For peer review only Page of surrounding. For the stations outside Sao Paulo state, for which no information about stations history was available at the time of this work, we assume they are potentially inhomogeneous with all possible problems of homogeneity expected for DAEE stations. ) Method a) testing variables The variables considered in the homogeneity analysis are normalized annual number of dry days (NACZP), annual median of daily amount ( q 0 ), and total annual. The latter is used only in the final stage, after isolating more homogenous series. A dry day is defined as that day with zero precipitation. In the construction of NACZP and q0 series, a missing year was interpolated using bicubic spline. b) Detection of abrupt and gradual change Among various techniques presented in the literature for detection of abrupt change (e.g. Carlstein, ; Guan, 00; Alexandersson, ; Alexandersson and Moberg, ; Wang, 00; Caussinus and Mestre, 00; Perreault et al., 000a) we adopted that proposed by Bai and Perron (, 00), henceforth BP, which has been firmly established in the statistical literature (see e.g. Granger and Hyung, ). The method has the flexibility of fitting multiple breaks linear regression model to a time series, enabling the access of the occurrence of various regime change over time, in terms of mean. The break-points, i.e., where occurs change in the regression coefficients or model structure, are treated explicitly as unknown variables to be estimated from the data as such way that the method is suitable when no metadata information is available about them. The method can be applied for a wide range of conditions. For example, serial correlation, different distributions for the errors across each

10 Page of International Journal of Climatology - For peer review only segment between breaks and heteroskedacity are allowed. The strategy for estimating the change-points is based on ordinary least square (OLS) and the residual sum of squares (RSS). The dynamic programming algorithm, based on principle of optimality (e.g. Belmann, ), is used to evaluate all potential change-points (Bai and Perron, 00). For a series of record length T, this algorithm requires at most least-squares operations of order O(T ) for any number of breaks m, or ( m+ ) regimes, while standard procedure requires least squares operations of order O(T m ). From a computational point of view, this is an important feature mainly when a large number of series have to be analyzed as in the present work. The complete theoretical insights and mathematical formulation of the method are given in the above referred papers, and also in more recent paper by Perron (00). In the meteorological literature, some authors (e.g. Wang 00, 00) have put effort for the development of regression-based method for change-point problem whose central idea is similar to that of BP. Let y be an annual series of some quantity. One change-point at year t c is defined whether the time average of y over a number of years before t c would differ significantly from the time average after the same year. As a way for assessing whether there exist evidence for such a change-point or not, we tested if the data support the hypothesis that there is no structural change, against an alternative that the structure changed over time. In this work, we choose, among various, the supf test which has been deeply discussed by Andrews (), whose performance is well-evaluated, outperforming for example in some situations methods based on information criteria such as Bayesian or Akaike Information Criteria, which had been proposed by Yao (). In the supf test, the F statistic is computed for all potential change points. The null hypothesis of no structural change is hence rejected if some value of F exceed a specified limit corresponding to a particular significance levelα. The p -value for the test can be obtained based on Hansen (). For the present work, because of station sparsely for most regions, the BP method there seems to be more suitable than the widely used approach proposed by Alexanderson () called standard

11 International Journal of Climatology - For peer review only Page of normal homogeneity test (SNHT), a likelihood ratio test which relies on so-called reference series supposedly homogeneous based on neighboring station. In the case of rainfall climate series from Brazilian rain-gauge network another problem for utilizing this approach is that there is practically no information about homogeneity. The ineffectiveness of SNHT, for areas where lack good neighboring stations, has been pointed out by many authors (e.g. Vincent, ; Hansen-Bauer and Forland, ; Peterson et al., ; Wijngaard et al., 00), and it has been one of the reasons for adopting alternative approaches in various countries. In the present work, as in Lavery et al. () and many others, we restrict homogeneity assessment to absolute tests, i.e., focusing on each station without accounting for neighboring stations. This approach has been adopted for example by Trenberth and Paolino (0) for detecting inhomogeneities in the Northern Hemisphere sea-level pressure data. We compared the ability of BP method with that of developed in the Bayesian framework, by means of Monte Carlo simulation study, to ensure that the result of change-point analysis is methodindependent as much as possible. From a number of Bayesian approaches for change-point problem available in the literature (see e.g. Menzefricke, ; Hsu, ; Smith, ; Elliot and Shope, 00), we chose the one that is based on so-called product partition model (PPM) introduced by Hartigan () and Barry and Hartigan (,). Further references for PPM method are Crowley () and Quintana and Iglesias (00). The BP and PPM approaches are completely independent in the sense that there is no theoretical bridge between them. In Meteorology, Bayesian approach and its variations to change-point problem have been used by some authors. Elsner et al. (00) used them for detecting shifts in the annual hurricane rates in North Atlantic and coastal area of the US, Chu and Zhao (00) for identifying change-points in the Tropical cyclone activity. In hydrology, Perreault () and Perreault et al. (000b) used Bayesian method for detecting sudden change in a sequence of energy inflows modeled by normally distributed random variables. Like BP, PPM is suitable for detecting unknown change-points because they are treated as a random variable. Figure illustrates the

12 Page of International Journal of Climatology - For peer review only outcomes of these methods applied for a simulated Gaussian series of length with mean µ and standard deviation σ, for which five breaks were imposed at t c =,,, 0, 0, with shifts σ, σ, σ, σ, σ, respectively. The series has mean 0. and standard deviation 0.0, resembling a typical NACZP series. For example, at Nova Palmira, in Rio Grande do Sul state, one of the stations considered by Ropelewski and Bell (00), the average and standard deviation of NACZP series are 0.0 and 0.0, respectively. The length corresponds approximately to overall mean for all rainfall series. Note in Figure that all the breaks were correctly identified by BP method, in terms of both number and location. The value of supf is significant at the level. A good dating of the breaks is also given by PPM method, considering that the main peaks in the posterior probability of change-points coincides with location of imposed breaks. Further, a good agreement between OLS linear fitting and posterior mean obtained by PPM method is notable, even though the latter is rather noisy. An inherent difficulty of using PPM is the interpretation of the posterior probability of change point without an overall visual inspection of outcomes, as in Figure. This is a disadvantage of the PPM especially when many series are involved in the work, and it was an important reason for preferring BP method in the present work, despite of the similarity of their outcomes as seen above. It is worth mentioning that the underlying notion of break in homogeneity is better described by segmentation with constant mean level given by BP method than noisy PPM posterior mean. The similarity in the capacity of the break detection and dating of the breaks of the two methods was also observed in Monte Carlo study with 000 simulated series (not shown). We noted in two methods that their capacity of detecting breaks diminish with reduction of shift amplitude and when distance between breaks diminished, as occur with other methods as for example SNHT. An important feature of both methods is that bias toward detecting breaks where actually there is not is satisfactorily small.

13 International Journal of Climatology - For peer review only Page of For detecting gradual change we used Mann-Kendall rank correlation (see e.g. Hipel and McLeod, 00). This analysis was carried out after applying other tests and with those series isolated as being more homogeneous. All the computations were carried out using R software environment for statistical computing and graphics (R Development Core Team 00). c) Distribution test for daily amounts After identifying discontinuity either in NACZP or q 0, we tested for the difference in the distribution of daily amounts between one segment and another determined by the change-points. This is equivalent of verifying whether these segments are stochastically different, i.e., in a broader sense than just testing for difference in the mean or median, and may help see whether, for example, the observer had the habit of reporting only significant amount in some sub-period. The null hypothesis of interest is that the samples of daily amounts for different segments come from the same (unknown) population. Therefore, a series with m breaks involves m ( m+ ) / hypothesis testing, regarding pairwise comparisons. We adopted two statistical methods to carry out this analysis, namely Kolmogorov-Smirnov (KS) test and Anderson-Darling (AD) test, again for ensuring that different methods lead to the same conclusion, as far as possible. The KS and AD tests adopted here are from the recent development by Abadie (00) and Scholz and Stephens (), respectively, with a significant improvement that permits to be used safely even to the samples containing tied values, commonly present in instrumental data due to rounding. The procedure proposed by Abadie (00) is a bootstrap version of classic KS test. In the present work this method was implemented with 00 replications. The KS method is designed for testing two samples at a time, while AD method can be used for testing simultaneously more than two samples. But for a consistent comparison, the latter was also used for

14 Page of International Journal of Climatology - For peer review only pairwise comparison. Thus, we isolated statistically more significant outcomes from m ( m+ ) / possible tests for each series with m break-points. We also used KS and AD tests for examining the homogeneity problem related to accumulation, i.e., checking for the difference in the distribution of daily amount among different days of week. d) Proportion test The difference in the proportion of zero precipitation among days of week was checked by using Pearson chi-squared test (e.g. Siegel, ). As aforementioned, this difference is expected in some rainfall records, at least for stations located in Sao Paulo state. The null hypothesis of interest is that the proportions of zero precipitation in a daily series are the same for all days of week, such that a series exhibiting a significant difference should be considered inhomogeneous, as physically there is no plausible explanation for it.. Results a) Discontinuity in the NACZP series Table shows, for each state, the number of NACZP series exhibiting one or more discontinuity ( N b ), and those among N series rejected by the supf test, N F ( α ), at the five b significance levels α =0.0, 0., 0., 0.0, 0.0. This kind of homogeneity problem was detected in the majority of stations (0 out of or.% of total) and all across the country, not only for DAEE stations in Sao Paulo state, for which this problem was already expected according to historical information (section ). For some states the percentage of stations exhibiting this problem is impressive. If the significance level 0.0 was taken as a critical level for rejection of null hypothesis that a rainfall sup

15 International Journal of Climatology - For peer review only Page of series is homogeneous, for the states like Mato Grosso, Sao Paulo, Paraná and Rio Grande do Sul, respectively.%,.%, % and % of their rainfall series would be classified as inhomogeneous. The situation is not much better for Ceará, Sergipe, Bahia, Rio de Janeiro and Santa Catarina, with more than 0% of station rejected at this significance level. For some states as Paraíba, which has only two stations, none of them could be considered homogeneous at this significance level. A similar situation is encountered for Pará. In Sao Paulo state, 0 out of (% of total number) stations exhibit at least one discontinuity in NACZP series ( N in Table ). Of these 0, stations exhibit break for the years b, or, and for % of these cases the shift is negative and statistically significant at the level 0.0. This result was expected because the practice of reporting missing days as days of no precipitation was reduced from - in some stations, as aforementioned (section ). Figure reveals this as the first sharp increases in the cumulative sum of annual counts of stations exhibiting break. Other major increase of inhomogeneity series is depicted in this analysis for, which is also in agreement with the historical information about DAEE stations (section ). For Sao Paulo state, Figure shows the spatial distribution of the stations exhibiting changepoint for the years, or (filled circles) and those which do not (open circles). The lack of spatial coherence does not support the speculation exercise by attributing, for instance, the detected change-points as trigger of regional climate change. The spatial coherence is not observed for changepoint in and (not shown). Figure shows examples of NACZP series revealing discontinuity. The calculated supf statistic for all these series trespasses the limit of the 0.0 level. The median of the distribution of daily amounts for each segment (or sub-period) is also shown. Since it is multi-year based median we denote it as

16 Page of International Journal of Climatology - For peer review only Q0 to differentiate from the single year median q 0. Our aim to show Q 0 is to call attention to the fact that it is systematically larger (lower) for the sub-period with larger (lower) number of dry days, which is exactly contrary to that would be expected climatologically. This bias is certainly a result of bad observing practice, particularly in that cases in which the observers reported only significant amounts or zero during some period(s). For examining this feature regarding all constructed a scatter diagram as shown in Figure a, where Q0 Nb stations (Table ), we and mean NACZP (mnaczp) correspond to each sub-period. Similar diagrams with respect to higher quantiles, Q (% quantile) and Q (% quantile) are shown in Figures b-c. The Kendall rank correlations between mnaczp and Q 0, Q, and Q are 0., 0. and 0., with p-values practically zero, indicating the presence of a significant bias in the distribution of daily amounts. A high quantile as Q are often regarded as reference value in climate-change problem, in particular, for assessing long-term trend in the frequency and intensity of extreme events (see e.g. Haylock et al., 00; Dufek and Ambrizzi, 00; Sugahara et al., 00). But if this quantile was computed using series as those identified here with homogeneity problem, certainly it will lead to a doubtful result, unless the magnitude of actual change is substantially larger than an artificially introduced change. In the climate series broken down into segments, such as those shown in Figure, it is difficult to discover which one of sub-periods of the data are credible without rely upon other sources of precipitation measurements as satellites and radars (see e.g. Higgins et al., 000). Unfortunately, the satellite data are available only for the period after s, and weather radars data are not a solution for Brazil mainly due to poor spatial and temporal coverage. A sub-period with lower mnaczp not necessarily is the period with reliable data. It may simply be revealing that during this period the improper reporting of zero precipitation was practiced with less frequency. The most important point to be highlighted here, however, is that there is no reasonable explanation for this relation, since, on the

17 International Journal of Climatology - For peer review only Page of average, for a sub-period with lower mnaczp characterizing wetter climate we expect more intense daily amount, and not the contrary as we found here. b) Changes in distribution of daily amount related with change-points in NACZP series. All N b series exhibiting discontinuity in NACZP series were examined if the distribution of daily amounts changed from one segment to another, in a significant manner. As an illustrative example let us consider Figure, which shows, for the station 0000, the changes in empirical cumulative distribution of daily amounts related with three break-points in NACZP series over the period of records -00 (see Figure a), defining four segments -, -, -, and -00. It is important to note that the difference in the distributions of daily amounts between the sub-periods - and -00 is relatively small for lower daily amount as reflected for example in median (see Figure a), but it increases for larger amounts approximately from 0% quantile, making the two sub-periods stochastically different at the 0.0 level, according to both KS and AD tests. It well illustrates how important is the comparison of the distributions of different segments for further ascertaining on the inhomogeneity. By comparing only the median, for instance, the presence of this inhomogeneity would not have been detected, since as stated above the difference in the distributions is manifested only in higher quantile. Figure shows the result of the KS and AD tests for Nb stations. The plotted p-values show that both tests lead to the same conclusion in practically all the cases. It can be noted that for majority of Nb stations, a break in NACZP series is related to highly significant change (small p-value) in the distribution of daily amounts. An important practical implication of it is that when homogeneity adjustment is performed these changes have to be inevitably taken into account, which seems to be an

18 Page of International Journal of Climatology - For peer review only extremely complex task. Table shows for each state the results of the AD test. As result for KS test is practically the same, it is not shown. The summary regarding all stations are also presented. c) Different counts of zero precipitation for different days of week The missing of observations at the weekend as previously mentioned was relatively common by the observers of the DAEE stations in Sao Paulo State, at least during some period of records. In such case, the accumulated Monday s readings comprised - days accumulation and Saturday and Sunday were simply reported as days of no precipitation. Even though the information about possible presence of similar problem is restricted only to the rainfall series of Sao Paulo State, we attempted to ascertain the inhomogeneity in which the count of zero varies as function of day of week regarding all stations. The result shows the presence of this physically inconceivable inhomogeneity in many stations all across country. In fact, we expect the same proportion of zero precipitation for every day of the week, except by some difference due to sampling fluctuation. The stations exhibiting larger number of zero particularly for weekend are highlighted in Figure a. Note that in some regions the proportion of stations presenting such feature is quite impressive, such as for states of Sao Paulo (%), Ceará (%), Pernambuco (%), Paraná (%), Santa Catarina (%), and Rio Grande do Sul (%). For some stations we found larger proportion of zero precipitation for the days of week but not for weekend, for example Thursday, as in the case of station 0000 discussed before. The counts of stations exhibiting the largest number of zero daily precipitation apportioned by day of week is shown in Figure b, regarding all the stations. The feature captured in this figure is more than sufficient for showing that the Brazilian historical rainfall data must be used very carefully.

19 International Journal of Climatology - For peer review only Page of Figure shows, for three stations, the plot of normalized number of dry days for whole period apportioned by day of week (left), along with the plot of two NACZP series (right) corresponding to days of week with the largest and lowest proportion of zero precipitation. The p-value for the proportion test, as presented in the legend, considers only days with the largest and the lowest proportions, and the null hypothesis is that the proportions of zero for these days are the same. For the three cases, we can note that the difference in the proportions is highly significant. The results for all stations are shown in Table. d) Break in q0 series The choice of median as testing variable in the homogeneity analysis offers some advantage over other quantities such as the total annual or the annual average due to its resistance to outliers (e.g. Wilks, ). For a given station, a break in a series of q 0 may have been caused by station relocation, change in instruments, etc. as already mentioned, but not necessarily due to the same factor that caused break in homogeneity of NACZP series. For example, a break in q 0 series may be caused only by change in the instrument and this does not necessarily cause a break in NACZP series. The opposite may also occur, i.e., a break in NACZP series not necessarily implies on breaks in median series. For example, the daily amount may have been collected in such irregular way, without respecting any rules, that only NACZP would reveal presence of breaks, as for this quantity the rainfall amount (>0) does not matter. The result of change-point analysis of the q 0 series is presented in Table. Regarding all * b N stations, the number ( N ) of stations exhibiting discontinuity in the q0 series is larger than that for time series of NACZP, % for the former against % for the latter, probably due to larger magnitude

20 Page of International Journal of Climatology - For peer review only of shift in q0 series than that in NACZP series. For instance, the number of q0 series rejected by supf test at the 0.0 significance level, N * b (0.0), is, against for NACZP series. Furthermore, we noted that.% of stations presenting break-point(s) in NACZP also reveal break-points(s) in q 0, while in.% of q 0 with break(s) present also break(s) in NACZP series. Interestingly, Mato Grosso, São Paulo and Rio Grande do Sul show larger number of series with break(s) in NACZP than for q 0. Figure shows examples of inhomogeneous q 0 series, for different regions of Brazil. The null hypothesis of no structural change for these series is rejected at the 0.0 significance level. e) Change in distribution of daily amount related to change-points in q0 series The presence of a break in q0 series already indicates change in the distribution of daily amount from one sub-period to another sub-period, but we can give a support to it or confirm the result of change-point analysis, in a more statistically meaningful way, by means of KS and AD tests as done earlier in Section b. Thus the m ( m+ ) / null hypotheses that the samples of daily amounts for m different segments of each q 0 series come from the same population were tested, isolating among these tests the most significant outcomes. The result for all * b N series indicated that of them (.%) are rejected at the 0.0 significance level, and all of them at the 0.0 significance level, giving an important support to the change-point analysis (see Table for more detail). f) Accumulation problem We showed earlier that for many stations the number of zero precipitation varies significantly with the day of week. We attempted to verify the presence of similar behaviour in the daily amounts that would be probably detected whether, for example, a gauge was often unread in some specific day

21 International Journal of Climatology - For peer review only Page 0 of of week and accumulating rainfall over more than one day. For the cases in which the gauge was not read at the weekends, Monday readings might be on errors or biased. Figure a shows one example in which 0% quantile for Sunday and Monday is larger than that for other days of week, mainly when compared to that for Tuesday. The station is C-00, whose behavior of the NACZP series was shown in Figures c-d. The large 0% quantile for Sunday may have been caused by the observer who reported only when it rains significantly or zero, neglecting small rainfall amount. It is consistent with the lowest number of wet days for this day (Figure b). For Monday which also has large 0% quantile, a possible reason is the accumulation over weekend, since it exhibits the largest frequency of wet days (Figure b). Figure c compares q0 0 series for Sunday and Tuesday. Note that the difference is relatively small only between mid-s and mid-0s coinciding with the period in which had more reliable observation according to station history (section ). For some years, for example, the discrepancy is so large that leads us to suspect that the observer either reported only extreme cases or guessed values. We addressed this question of improper accumulation testing for difference in the distribution of daily amount among days of week using AD test. The null hypothesis in this case is that the distributions of daily amounts are equal for every day of week, except by sampling fluctuations. The result is shown in Table. In this analysis we consider that the improper rainfall accumulations not necessarily are related to the weekend, and among all possible comparison only the most significant result was considered. g) Non climatic trend and overall evaluation of the tests Before testing a possible presence of nonclimatic trend, an evaluation of all tests considered so far is made in this section. The trend test is applied only to those series classified as homogeneous,

22 Page of International Journal of Climatology - For peer review only according to the previous tests. Thus, for isolating such series, we reject any series if it presents one of following conditions: (i) NACZP series exhibit at least one break at the significance level α of supf test (Section a), (ii) NAZCP series exhibit at least one break (Section a), and AD test (or KS test) indicates that the difference in the distribution of daily amount between different segments of NACZP series is statistically significant at the level α (Section b), (iii) the proportion test indicates the difference in the number of dry days among different days of week significant at the level α (Section c), (iv) at least one break is detected in the q0 series at the significance level α of supf (Section d), (v) at least one break is detected in the q0 series and AD test (or KS test) indicates that the difference in the distribution of the daily amounts among different segments of the q 0 is significant at the level α (Section e), (vi) the AD test indicates that the distribution of daily amounts for one day of week is different from that for any other day at the level α (Section f). In the conditions (ii) and (v) the significance level for supf is not taking into account, but only for AD test. Table presents a summary of this joint assessment of homogeneity, where N ac ( α ) is the number of stations which did not present none of the above conditions with respect to the significance levelα. A difficulty in statistic-based homogeneity assessment is the choice of significance level to decide which series should be rejected or not. It is especially true when metadata are not available to help identify potential non-homogeneity or for confirming the results of statistical analysis. As aforementioned, the metadata with the stations history available for the present work is only for a very restricted area collected through an interview, and far from completeness and precision such that its

23 International Journal of Climatology - For peer review only Page of usefulness is quite limited. However, it is important to consider that some statistical feature, such larger number of dry days for some particular day of week, must be attributed only to bad observing practices, since no physical process can be associated with it. In this case, a metadata is totally dispensable, and certainly this type of information would not have been reported by observers. Another case that can discards the metadata information is that related with positive correlation between average number of dry days and the median of daily amounts within the segments determined by break points. This relation can not be attributed to any physical process either. Such problems suggest that the choice of a critical level, as for example 0.0, appears to be more appropriate than less stringent critical level 0.0, which is used for example in the homogeneity analysis of European daily temperature and precipitation series (Wijngaard et al., 00). Thus, a record would be regarded as useful if it exhibits no inhomogeneity at the 0.0 significance level, in the applied tests. In the trend assessment, as above mentioned, we considered only those stations which passed in all previous tests at the 0.0 level, and considering as testing variables, the total annual as well as the previously considered NACZP and q 0. With the respect to the total annual, the presence of break was examined before trend analysis. To calculate total annual, a daily amount trespassing the limit defined by (see e.g. González-Rouco et al., 00) = Q IQR was considered as an outlier. The Pout + Q stands for % quantile of daily amount (>0) computed for each day of year regarding all records and IQR is interquartilic range, defined as Q Q. A procedure to estimate p-quantile for each day of year is described in Sugahara et al. (00). The daily amounts over P out were substituted by this limit. It was found that among stations in Table that passed at the significance level 0.0, five stations exhibit at least one break in their total annual at the 0.0 significance level, reducing the number of homogeneous (or useful) stations to, which are listed in Table. Their geographical positions are shown in Figure. Of these stations, three stations exhibit trend significant at the 0.0 significance level, one of them in NACZP and two other in total annual. Before using these series in

24 Page of International Journal of Climatology - For peer review only climate studies, further analysis is necessary to verify the origin of these trends, whether they were caused for example by sheltering effect associated with buildings, trees, etc.. Concluding remarks Raw data of historical daily rainfall series for stations belonging to different climate regions of Brazil were assessed for homogeneity, statistically. In principle this dataset is useful for climate studies, regarding the series length and completeness. But, unfortunately, our result shows that most series are infected by some type of non-climatic variation, most of them due to the bad observing practices, as flaw handling of missing observations and multi-day accumulation, among others. These problems were identified all across country. If the 0.0 significance level was taken as critical level for all the applied tests, only series may be considered homogeneous, corresponding to.% of total number of stations. The poor spatial station coverage given by these stations (Figure ), certainly poses difficulties in various climate studies. For example, if ascertaining the statistical significance of the influence of ENSO phenomenon on rainfall over Brazil or any other in which spatial coherence is an important aspect of the problem. The gridded analysis of daily rainfall for Brazil such as provided by CDC (Liebmann and Allured, 00) and CPC (Silva et al., 00) as well as those for monthly precipitation provided by Chen et al. (00), would not be an alternative for overcoming the problem of insufficient data coverage, since both analyses rely on the rain-gauge data from the same sources considered in the present work. The result of the present work also call attention to the need for recalculation of each currently used - period standard climatic normal for precipitation, which relied on inhomogeneous

25 International Journal of Climatology - For peer review only Page of series. This is important for example to give credibility of climate monitoring. Obviously, for this purpose, as well as for climate studies in general, a scheme for continuous data quality monitoring also should be implemented by institutions elected for maintaining the network of observations. Needless to say that homogeneity-adjustment of inhomogeneous series is also crucial for verification and validation of climate models performance. With respect to the climate-trend and climate variability studies, since they are sensitive to both inhomogeneity and homogeneity-adjustment the inhomogeneous series should be discarded, if one intends reliable results. Especially for Brazilian rain-gauge based climate series, for which were encountered serious problems of homogeneity, the procedures regarded in the present work could be considered as the first stage of any climate study based on data, as for guaranty of a minimum credibility, regardless data sources and period of interest. Although a large number of stations were not accessed for homogeneity due to our selection procedure, we suspect, on grounds of the present results, that many of them would be likely infected by the similar inhomogeneities. Acknowledgments The authors would like to thank Dr. Sergio Cirne de Toledo for valuable historical information about DAEE stations, and to the ANA and DAEE for providing their rainfall dataset. The research of the first and third authors was partially supported by Brazilian Financial Support Agency (FINEP) under contracts # and # The first author thanks to Marcos Antonio Antunes de Oliveira for his assistance in the computational work.

26 Page of International Journal of Climatology - For peer review only APPENDIX List of stations considered in this study for inhomogeneity assessment