Statistical Analysis of Spatial and Temporal Variability of Maximum Precipitation Events on the Rio Grande do Sul

A statistical analysis of precipitation at Rio Grande do Sul State was presented in this article. The aim of this wor was to identify spatial and temporal patterns of maximum precipitation, which was achieved y ttin a theoretical vario ram in maximum annual rainfalls and its times of occurrence. n the literature, it was found that this pattern occurs accordin to phenomena typical from middle latitude, such as low and hi h level et, and interactions etween them. Some years a o, the relationship etween maximum annual rainfalls and synoptic predominant con urations was found. Therefore, this wor sou ht on understandin the climatic characteristics that are important in Aerospace and Aeronautics, as extreme weather can cause numerous consequences in these activities. The use and validation of this proposed method would ma e possi le its application in other re ions of interest in the ra ilian Aerospace. nderstandin these climatolo ical features of the atmospheric circulation dynamics, and analy in maximum annual rainfall would allow a more ef cient and appropriate climate trend forecast and its application in aerospace activities.


INTRODUCTION
In Rio Grande do Sul State, the formation of mesoscale convective systems (MCS) may be associated with different spatial and temporal scales, both in the planetary boundary layer (PBL) and mesoscale, with a wide range of mechanisms responsible for its formation.Helfand and Schubert (1995) argue that low-level jets (LLJ) are the key processes in the transportation balance of moisture entering the mainland United States overnight.Higgins et al. (1997) featured a daily cycle of precipitation using hourly observations from 1963 to 1993, revealing spring and in summer.
During the summer, there was 25% more precipitation during the night than during the day.The impact of LLJ on the balance sheet total precipitation shows an increase of more than 45% in average at night.In summer, this increase is considerably enhanced by the transport of water vapor States of America (Whiteman et al tion of radiosonde data in cases with and without jet has a transport performed of the LLJ overnight associated with et al. (1991) studied cyclones in the lee of the mountains (shortwave) in East Asia, in the Eastern Tibetan Plateau, especially in the summer rainy season over Southeast China and Taiwan area, from May to June.
This period is characterized by severe rainfall and is analyzing data of precipitation during the rainy season on China day.These severe rainfalls are closely associated with LLJ.
intensities of the order of 12.5 ms -1 , which occurred at the rainfall events.When LLJ were present on the island of Taiwan, a probability estimate had a likelihood of 91% between precipitation events and the LLJ.
sity of LLJ.This potential link between the bands of front precipitation and adiabatic redistribution of potential vorticity in the horizontal structure of the winds that accompany and Doswell III (1992) showed that the PBL may produce heat by convection and by condensation, and heat advection in the lower troposphere.
This process is associated with the circulations of the type latent heat in the lower atmosphere, dominating the differential vorticity advection in the middle troposphere, forcing upward vertically, resulting in the organization of convective events and generating MCS.Uccellini and Johnson (1979) show that the high level jet (HLJ) and LLJ can often be coupled by the adjustments of the vertical mass, which occurs with the spread of HLJ.
This transport in the lower troposphere helps creating a favorable environment for the development of severe thunderstorms, especially when the interaction of the jets occurs within the region's output of HLJ.
In South America, the work of Abdoulaev et al. (1996) portion of precipitation that occurs in Southern Brazil, occurring in at least 13 events per year, with intense rainfall and may be associated with LLJ intense.
Abdoulaev et al with mesoscale severe convection, observed the occurabout 6 o'clock in the morning, with a seasonal variability between the beginning and end of the convective cells.In summer, on average, the precipitations have a cycle of 6 hours.This led Abdoulaev et al the cycle of night and early morning storms are amplified and modulated by the convergence of water vapor, which is mainly characterized by the LLJ.
sonde data held in Porto Alegre and Uruguaiana the dynamic Flows in the vertical wind profile can be defined as streams that have varying speeds of the order of 5 ms -1 -1 ), and they do not also present the vertical structure of the jet.The flows are significant because they may be associated with the convergence of mass and energy even with lower magnitude speeds than a LLJ acting on synoptic scales typical of mesoalpha ( ) and mesobeta ( ), corresponding to spatial scales between in the troposphere have different spatial and temporal scales, featuring a wealth of combinations of structures in PBL and the lower atmosphere, connecting with meso to continental scale.This dynamic structure at low atmosphere levels results in a layered structure, in which there over Rio Grande do Sul.An important effect of LLJ is the daily cycle of moisture as water vapor, and the convergence of transport within the PBL implies a kind of moisture storage over large areas and basins.These can generate meteorological phenomena, such as restricted visibility by haze and fog and cloud layers and type as low stratus and stratucumulus.In cases where there is a positive balance, this moisture storage becomes a source of water vapor for future convection occurrence.Therefore, this structure balance of a watershed in middle latitudes.high rainfall, and the majority of studies on this topic are case ones with reanalysis data of global models, which according due to low resolution of the data.systems associated with the occurrence of precipitation in at characterizing the systems associated with precipitation criteria to identify the weather systems of large, meso and local scale precipitation associated with the CLA, the results This paper attempts to test the methodology of Geostaand using it in future researches to the region of Alcântara, in Maranhão.The use of data observed in this study, by is an attempt to identify spatial and temporal patterns in Corrêa, C.S.

DATA AND METHODOLOGY
LLJ direction and they have variable frequency, are associated with weather systems, and may be responsible for generating part of the convection and, hence, rainfall.These precipita-mum precipitation, precipitation data at 52 rainfall stations of the Agência Nacional de Águas (ANA) in the state of Rio Grande do Sul were analyzed.We attempted to use only observation stations with complete series.
It was calculated, using the statistical software GENSTAT © determined, followed by a procedure similar to that used for the This statistical analysis used a model implemented in GENSTAT © that has the method of the semi-variogram, allowing a quantitative representation within the range of a localized where, Z(x) is the value of the random variable, is the mean of the variable Z(x), and the term (x) is a self-correlated random function with and h is the distance between the point x and x h.It is assumed that, on average, Z is constant in space such as Eq.3: The degree of dependence between points x and x h is represented by the variogram (h between the values given by Eq. 4: The variance depends not only on the distance h and the position x.The amount is semi-variance, which in turn is a function of m that is used to estimate the variogram.It is assumed the hypothesis "Matheron" and also that the process is second order stationary, in which the average random process 2), ence between Z(x) and Z(x h), represented by Eq. 5 and 6: (5) and The covariance is correlated by the semi-variogram by Eq. 7: To calculate the variogram, the "FVARIOGRAM" funcof variable values Z(x) distributed into one or two dimensions, where: Z(xi) and Z(xi h) are the values of the position xi h.The term m(h) is the number of pairs for comparison, which contributes to the estimate.As the data show scattering irregular spatial precipitation, h is discretized in such a way that its value is constant, the variation in the distance increase and the same change of direction are considered to be isotropic.

semi-variogram. With the estimated semi-variogram already variogram obtained.
In this analysis, we used a semi-linear variogram, by using the "MVARIOGRAM" in GENSTAT © .Table 1 shows considered when calculating the semi-variogram, homogeneity in all directions.Where N is the number of observations, h is the length and V is the estimated variance of the semivariogram (Table 1).This analysis uses a statistical hypothesis that performs the calculation of the ratio of the variance, showing how relationship, which can be interpreted as absence of spatial or temporal consistency of precipitation.low-linear relationship, which could be interpreted as the absence of spatially and temporal uniform precipitation.As the theoretical model has a linear adjustment, it is observed in the calculation of linear regression model that the best adjust- The method was used to perform a linear adjustment of nonlinear models as model "boundedlinear" and Gaussian could be used.However, it was used the linear model, which although simple has good results.This analysis also tried to consider the spatial homogeneity of variance, however this could not be considered, which would bring the calculation of the semi-variogram with estimates of predominant directions.obtained on the website www.cpc.ncep.noaa.gov,with the aim of correlating changes in scale with the spatial and temporal Figure 2 shows the spatial distribution of jobs and Table 2 shows the 52 rain gauge stations of the National Water Agency (ANA) on the state of Rio Grande do Sul.and minima patterns of behavior.They, when associated with tation, are connected to a particular group of weather systems (atmospheric waves, and locking systems MCS), which are part of a cascade structure comprising the variable climate in this respect, when this occurs, these structures can generate possible in-homogeneities, both spatial and temporal precipitations.
Table 4 shows that El Niño had two predominant situations, La Niña years, there were three situations, namely: three years with temporal coherence, three years without spatial coherence, and temporal and spatial coherence in four years.
temporal coherence and they are also from El Niño, La Niña, and ENSO unsigned.
The spatial coherence years were divided into years with El Niño and La Niña, but the El Niño years have been characterized by two predominant situations, with a spatial coherence and the other without spatial and temporal coherences.The weather systems of these periods had a dynamic, in which scales generating spatial coherence.
intensity and persistence than in other phases of ENSO, and, consequently, a greater intensity of LLJ in these periods.The passage of frontal systems, such as short-waves, mesoscale convective and other weather systems with organized conveccoherence, but these weather systems were not the same as the standard for consistency over time, which can be seen in

Liebmann et al et al
The physical processes that are involved in the generation of precipitations as in MCS have different spatial dimensions, and their formation is associated with different meteorological mechanisms, instabilities forming isolating or forming groups, as in cells Cumulunimbus (Cb) (a few miles) to clusters Cb in a vary from a few to hundreds of kilometers.This is an important feature of the precipitation, since the generation mechanisms of MCS not always repeat in time, variability in the state of Rio Grande do Sul implies that rainfall varies in the four seasons, both in intensity and duration in the spring in Rio Grande do Sul and the ENSO signal during the same season or earlier, with the possibility of predicting seasonal rainfall.showed no spatial coherence, but showed consistency over time.This fact is interesting because it was La Niña years situation characterizes periods of drought, causing a tendency to decrease frequency and intensity of weather phenomena with different scales on Rio Grande do Sul.
Another important point illustrated in Table 3 shows the situation in which the lack of spatial and temporal coherence, namely, 1993, 1994, 1996, is distributed in all stages of ENOS signal.These periods have not showed characteristics of spatial and temporal coherences, which can result in characterizing the physiscales of different types of weather structures in space and time.
The different types of weather systems had relations in space, and time variations can occur only at mesoscale, or act in concert with other scales (meso to meso, meso and macro, macro to macro scale), resulting in changes in the characteristics of weather systems, and may intensify them or diminish them in intensity.
The combinations of these structures show a trend of stability and uniformity in growth, development, and persistence of weather systems, hence, an increase of spatial coherence, but these same relationships may or may not have temporal divergent instabilities associated with HLJ, they may have irregularities on a spatial region of the order of mesoscale.deepened, generating a wave structure in the atmosphere (tropical cyclones) with a higher spatial and temporal scales, the level of continental scale leads to a dynamic structure and a possibly HLJ are more intense and persistent and they are associated with The physical mechanisms of weather systems are strongly baroclinic (turbulent), however, through their relationships between the different meteorological scales involved, their physical properties in space and time change, both intensify and weaken these systems.There is, within this dynamic system, a range of interaction between different synoptic structures, which is very important in the maintenance and generation of baroclinic within this turbulent structure is to be a link between the different are associated.Therefore, in heavy rainfall periods, they are associated with large-scale meteorological vertical development in the atmosphere, whether as locks, associated with the the atmosphere and the years of ENSO (El Niño), with strong LLJ.This structure of continental scale and meso, with strong bution in space and time, the size of the spatial and temporal scale involved, as the year of 1997.
In other situations, the LLJ may be weaker and predominant in the order and mesoscale, which can generate and maintain structures and baroclinic instabilities that can cause irregular or regular precipitations in space and time.In this LLJ always occurs, independent of whether there is spatial homogeneity or temporal variability of rainfall.
Therefore, the same weather scale may act differently in structure that comprises a set of dynamic weather systems,

CONCLUSIONS
In this study, it was observed that in La Niña years, there is no predominant feature that characterizes an ENSO those years.However, during the El Niño, there was wellcharacterized evidence for the spatial coherence tendency.Therefore, the use of Geostatistical analysis calculating the tion of the spatial and temporal coherences of rainfall on the state of Rio Grande do Sul.These results could obtain charand their application to forecast climate trends.Consequently, it enabled its use in planning activities in aviation airports in Southern Brazil, and the estimation of the most likely year for the Aerospace activities.

Figure 1 .
Figure 1.Adjustment of the linear model to the semi-variogram.

Figure 2 .
Figure 2. Spatial distribution map of rainfall and weather stations in Rio Grande do Sul.

Table 1 .
Estimations of computing the semi-variogram.

Table 2 .
Rainfall stations of ANA in Rio Grande do Sul.
the adjustment of the linear model with the ENSO signal,