The Data Warehouse Lifecycle Toolkit Ebook Pdf Read more. Samsung Webcam Driver Download Read more. Ms Visio 2007 Portable Free Download Read more. Atmosfera Tiempo Y Clima Barry Chorley Pdf Viewer Read more. It is well known that some variables derived from topography and geography have some influence on precipitation (Barry and Chorley, 1984). 2.2)We consider the subgroup of variables of G1 defined by the Y variable, its square and cross products with other variables (subgroup G1Y), with the exception.

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Table I. Statistics for the annual and seasonal precipitation means for the 224 raingauges Statistics SPRI SUMM AUTU WINT ANNU Average 128.26 66.59 172.77 123.94 491.56 Stnd. Deviation 32.83 26.70 51.83 46.16 134.41 Minimum 60.78 17.71 83.40 54.70 233.30 Maximum 223.14 144.07 305.44 273.81 847.66 Range 162.36 126.35 222.04 219.11 614.36 Skewness 2.05 3.28 2.63 6.30 1.55 Kurtosis 0.07 − 0.43 − 0.99 2.63 − 0.40 For more than a decade, to the data measured by meteorological observatories, complementary information coming from other instruments (e.g., remote sensing from satellite, radar maps and information from lighting detection systems) can be added (see for example, New et al.,; Islam et al.,; Su et al., ). We have considered the possibility to fill the temporary series by means of the TRMM-based precipitation estimates, which are available for the research community at the following web site:. The global rainfall algorithm (3B43.v6) combines the estimates generated by combined instrument rain calibration and global gridded raingauge data.

The output is rainfall for 0.25 × 0.25 degree grid boxes for each month in the intervals of latitude 50°S - 50°N and longitude 180°W - 180°E. The starting date is 1998-01-01.

TRMM 3B43.v6 precipitation estimates provide a total of 72 data for our study area. In Figure (a), distribution is observed as compared to the situation of the 224 meteorological raingauges with useful information. It can be seen that—except for three sectors identified by the letters A, B, C—there is information from one or more raingauges at each sector. • • Comparison of TRMM 3B43.v6 data and raingauges data, where: (a) Raingauges superimposed to TRMM 3B43.v6 data. (b) Differences between rainfall data and TRMM 3B43.v6 precipitation estimates for spring 1998. This figure is available in colour online at To compare the records measured in observatories and estimates from the TRMM 3B43.v6 data, all raingauges located within each sector have been located, and average rainfall has been obtained. The difference between this value and the corresponding data on the TRMM 3B43.v6 spring 1998 is shown in Figure (b).

This figure also shows the amount of rainfall recorded at each raingauge. It can be observed that the greatest differences occur at the edges of the study area where there are fewer raingauges. This follows the findings reported in Su et al. (), which ensures that TRMM 3B43.v6 data tend to provide slightly larger estimates than that provided by the raingauge data; this difference is interpreted as mostly reflecting the climatological undercatch correction applied to TRMM data (Huffman et al., ).

Figure shows the scattergram of precipitation from averaged raingauges data and TRMM 3B43.v6 estimates for spring 1998. The best fit—with a determination coefficient of r 2 = 0.72—has been achieved through an equation of the second degree. This shows that the differences are exaggerated in the highest and lowest TRMM values. (1) where the a 0,, a are the regression coefficients and y 1( u),, y ( u) are the values of the different independent variables at location u. The MR procedure was carried out by using the STATGRAPHICS software. Considering all the secondary variables described in Table and their square and cross products, the total number of variables (350) was greater than the amount of rainfall data (179).

To reduce the number of variables the following steps were taken: • 1)First Step: After a visual inspection of all derived statistics (scatterplots, histograms, correlation coefficient), only those variables that are significantly correlated (in general at the 95% confidence level) with precipitation were considered. With this procedure, the number of selected variables was: 189 for SPRI, 194 for SUMM, 215 for AUTU, and 159 for WINT.

• 2)Second Step: Considering the group of variables selected in the first step (named G1), we introduce these variables in the regression model by means of the following forward process: • 2.1)We consider the subgroup of variables of G1 defined by the X variable, its square and cross products with other variables (subgroup G1X). We introduce this subgroup in the regression model and then apply a backward selection method in order to reduce the number of variables, thus simplifying the regression equation.

In the obtained model we also eliminate the variables which may give the same information; for example, we choose one variable between X Z 5 and X Z 10. We also analyse the contribution of each variable to the R 2 coefficient of the regression model; thus we eliminate the variables that do not entail an improvement in the R 2 coefficient. • 2.2)We consider the subgroup of variables of G1 defined by the Y variable, its square and cross products with other variables (subgroup G1Y), with the exception of X Y (considered in the previous step 2.1). We add this subgroup to the regression model obtained in the step 2.1 and then apply a backward selection method in order to reduce the number of variables. Again we choose one variable from the subgroup which may give the same information to the model and eliminate the variables that do not significantly improve the R 2 coefficient.

• 2.3)We use the same procedure of steps 2.1) and 2.2) for the other 23 variables described in Table. • 3)Third Step: We analyse the residuals in the regression model in order to detect a possible autocorrelation.

For example, we observe the variation of the Durbin-Watson statistic when we introduce a new subgroup of variables in the model. Moreover, we want to obtain a regression model whose R 2 coefficient is higher than 0.75 needing the lesser number of variables.

As a result of steps 2) and 3), the number of variables (and R 2) was: 9 (0.80) for SPRI, 4 (0.88) for SUMM, 12 (0.86) for AUTU, and 18 (0.83) for WINT. 4.2. The OK method The kriging interpolation is based on the assumption that the parameter being interpolated can be treated as a regionalized variable (Goovaerts, ).

In the weighting function, the semivariogram is used as a measure of dissimilarity between observations. The experimental semivariogram is computed as half the average squared difference between the components of data pairs. (2) where is the number of pairs of data separated by a vector within a certain tolerance angle. In this paper the experimental semivariograms were computed by using the Geostatistical Analyst module of ArcMap (Johnston et al., ), and the obtained results were corroborated within the program VARIOWIN 2.2 (Pannatier,; Mardikis et al., ). We have used a lag size equal to 10000 m.

And a number of lags equal to 18. Then, the theoretical semivariogram models were defined taking into account the experimental behaviour near the origin and farther away. In some cases anisotropies were considered. Once the semivariogram models are defined, the kriging interpolation can be performed. All kriging estimators are variants of the basic linear regression estimator z*( u), which is defined as (Goovaerts, ).

(3) where n( u) is the number of neighbouring observations and λ ( u) is the weight assigned to z( u ) interpreted as a realization of the random variable Z( u ). The values m( u) and m( u ) are the expected values of the random variables Z( u) and Z( u ). Several kriging variants can be distinguished according to the model considered for the trend m( u) (Deutsch and Journel,; Goovaerts, ). In this paper we have used the Ordinary Kriging (OK). In order to choose the best-fit variogram model we also have used the cross-validation method, evaluating the error of the OK method by means of the five error statistics that offer the Geostatistical Analyst module of ArcMap: the mean prediction error, the root mean square prediction error, the average kriging standard error, the square standardized prediction error, and the root mean square statndardized prediction error.

More details of these statistics can be found in Evrendilek and Ertekin (). 4.3. MR with residual kriging (MRK) The regression residuals were kriged in order to correct for any local overestimation or underestimation (Prudhomme and Reed,; Agnew and Palutikof,; Ninyerola et al., ). OK was used in this case and exponential or spherical semivariograms were used. This methodology may be described by the following steps: • 1)We compute the residuals of the MR model described in section 2.1. (4) where λ ( u) is the weight assigned to the primary datum z 1( u ) and λ ( u), i >1, is the weight assigned to the additional data z i( u ). The quantities m 1( u) and m i( u ) are the expected values of the random variables Z 1( u) and Z i( u ).

The cokriging accounts for the spatial correlation between variables as captured by the cross-semivariogram or cross-covariance. The Geostatistical Analyst module of ArcMap uses the cross-covariance for geostatistical multivariate models that for two variables ( z 1, z 2) can be written as. As in the kriging approach, several cokriging variants can be distinguished according to the trend model m i( u) (Goovaerts,; Deutsch and Journel, ). In this paper the OCK estimator is considered. Only one secondary variable—which, in fact, took into consideration more secondary variables—was introduced. This new variable is made up of the predicted values of the MR method with residual kriging (MRK) calculated in the previous subsection. Using this variable, the interpolation procedure was simplified and the resulting cokriging models were enriched.

5. Results In this section it is presented, in first place, the correlations between the geographical/topographic variables and the registered values of mean rainfall on every station. Taking these results as a base, DRMs have been obtained by applying different interpolation methods. Finally, results of the statistical evaluation on each of the proposed models are shown.

5.1. Relationship between precipitation and secondary variables Results in Table show that the correlation between most of the secondary variables and the precipitation is only statistically significant for some of the seasons, not for all of them. In general, the secondary variables that have the highest correlations with precipitation are X, Y, S 5, S 10, C_ N 1, and C_ E. Other variables are more significant at the scalar products, as is the case of the variables derived form the synoptic flows ( VS_N1, VS_E, VA_N1, VA_E). Manual Ronco Calculator Wheels Up. None of the variables related with the orographic rainfall shadows ( SUPDIF, SUPDISTF, SUPDISDIS, ALTDIF, ALTDISTF, and ALTDIFDIS) shows a significant correlation with precipitation, even when they are used as scalar products within other variables.

Table IV. Multiple regression equations for the precipitation variables Rainfall variable Regression model • In these equations, for example, the cross product between the variables X and Y are denoted by X × Y (units are in tenths of mm). Table V. Computed semivariogram models for the kriging method Variable Semivariogram • The equations are: effect + (partial sill) 1 × Model 1. (major range 1, minor range 1, azimuth 1) + (partial sill) 2× Model 2. (major range 2, minor range 2, azimuth 2). Precipitation units are in mm. SPRI 101.49× Nugget + 1212.1× Spherical(171290, 124800, 294.5) SUMM 3.512× Nugget + 405.88× Spherical(179030)+ 276,64× Gaussian(179030) AUTU 255.89× Nugget + 3135.90× Gaussian(121940, 99840, 115.7) WINT 9.7155× Nugget + 2903.80× Spherical(123770) The computed semivariogram models for the MRK interpolation are shown in Table. To obtain these parameters we have computed an experimental semivariogram considering a lag spacing equal to 10000 m and the number of lags equals 18.

Geometric anisotropy is considered for the SPRI and WINT variables, which have a range higher than that of the SUMM and AUTU variables. Table VI. Computed semivariogram models for the residual kriging Variable Semivariogram • The equations are: ( h) = nugget effect + (partial sill)× Model (major range, minor range, azimuth). Precipitation units are in mm. SPRI 200.11× Nugget + 45.017× Exponential(171330, 109360, 56.3) SUMM 31.638× Nugget+ 50.438× Spherical (24260) AUTU 244.63× Nugget + 146.28× Exponential(24661) WINT 275.07× Nugget + 140.86× Exponential(171320, 93886, 24.1) Semivariogram and cross-covariance models for cokriging approaches are described in Table using the MRK model as secondary variable. For the SPRI, AUTU, and WINT variables geometric anisotropies were considered. The SUMM variable was deemed to be isotropic. As in the OK method we have chosen a spherical model for the SPRI and WINT variables.

The AUTU semivariogram is modelled by means of a Gaussian model and the SUMM variable uses a combination of the spherical and Gaussian models. Table VII. Computed semivariogram and cross-covariance models for the cokriging method Variable Computed models • The equations are: effect + (partial sill) 1× Model 1. (major range 1, minor range 1, azimuth 1) + (partial sill) 2× Model 2. (major range 2, minor range 2, azimuth 2). Precipitation units are in mm. Where z i is the ith-observed value, is the ith-predicted value, and n is the total number of test observations. The determination coefficient R 2 is a quantity that gives the quality of a least squares fitting to the original data, and therefore can be included as a first calculation of the reliability of the model.

Nevertheless, the relationship between R 2 and model performance is not well defined, and the magnitudes of R 2 are not consistently related to the accuracy of prediction. Therefore, the RMSE and MAE were also calculated, being considered as the best overall measures of model performance, as they summarize the mean difference in the units of the observed and predicted data. The difference between them is that RMSE places a lot of weight on high errors while MAE is less sensitive to extreme values (Vicente-Serrano et al., ). MRE is used to compare results obtained in different precipitation variables. We have reserved part of the initial data, (20% of the total) to check the validity of the models.

Therefore, models are achieved with 80% of the available data and the rest is used exclusively for model validity. In Table the obtained values are shown. Table VIII. Statistics of the different interpolation methods for each climate station Method R 2 RMSE MAE MRE (%) • The best results are highlighted.

For each raingauge that have been used in the tests for each season (Figures ). In spring, the MAE is smaller if MRK model is used; meanwhile the MRE is a slightly smaller if the OCK is used. The two locations where more significant errors do appear are in Ademuz and in the Betic range. From the analysis of Figure it is deduced that with the OCK there is a location (close to Ademuz) with a BIAS error greater than in the MRK model.

Furthermore, in the OCK model at the Betic ranges location, there appear four over valuated raingauges with more than ± 15% error, while in the MRK model there is only one raingauge with an error greater than ± 15%, although this one is greater than its corresponding one in the OCK model. In summer, for both cases errors are in general quite small (Figure ). In fact, for the MRK model—which is the model that works better—it is corroborated that the 89% of the considered raingauges do have a BIAS error smaller than ± 10%.

On the other hand, it is observed that in this model, only two raingauges do reach deviations from the estimated value by ± 15%. In the OCK model, there are six raingauges with these conditions. In autumn (Figure ) it is observed that the OCK model works better, as there is only one rainguge with errors reaching ± 23%, while in the MRK model there are four raingauges with these characteristics. Finally, the winter (Figure ) is the season worst modelled.

In the MRK model, a location close to Ademuz has a BIAS error close to ± 75%; these errors decrease to ± 58% in the OCK model. At the Betic area, the errors in the MRK do exceed ± 40%.

In fact, only a 53.2% of raingauges do have errors smaller than ± 10% in the MRK model; in the OCK, they represent 62.2% of the raingauges. • • BIAS errors for the WINT variable with the MRK and OCK methods. This figure is available in colour online at After the analysis of the generated maps, it is interesting to observe that, in most of cases—except for summer—the raingauges within greater BIAS errors are located at similar areas. It is an especially outstanding fact that the raingauge located close to Ademuz—overvaluated in all models except in both for the summer—has an error that can be related to a local effect. This raingauge is located at the bottom of a valley that has a N-S direction, being affected by an orographic shadow with respect to the wind fluxes coming from the sea. In summer, it is not affected because precipitations are not associated to sea winds, but they have a convective storms character.

Figure shows for the spring (Figure (a)) and autumn (Figure (b)), how the distribution of rainfall has been modelled and contrasted with the records measured in the raingauges. It is appreciated that in the case shown—a valley that presents a NS direction (in the area of Ademuz)—neither the MRK nor the OCK model is capable of recording the decrease in rainfall records that occurs in the bottom valley. The local orographic effects could also explain the systematic errors that are registered at the locations close to the Betic ranges. On the other hand, it is interesting to emphasize that, in general and more clearly in the MRK model, the greater errors are related to the raingauges located at the more exterior regions of the study area; models do work relatively better at the central regions.