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Comparison of Normal Ratio Method and Distance Power Method for Estimating Missing Rainfall Data with Three Neighboring Stations

This study compared the performances of Normal Ratio Method and Distance Power Method as a tool for estimating missing rainfall data. The data utilized are the rainfall data of the three neighboring station of Catarman, Northern Samar, Philippines. These stations are Catbalogan Station (Samar Province), Legazpi (Bicol Province) and Masbate (Masbate Province). The observed daily rainfall data for the Catarman (Northern Samar), Catbalogan, Legazpi, and Masbate were obtained from the Philippine Atmospheric Geographical Astronomical Services Administration. The monthly rainfall were computed for the three (3) neighboring stations (Catbalogan, Legazpi, Masbate). The evaluation used the T-test for correlated samples and the Pearson’s Correlation Coefficient for the monthly rainfall data computed of the three neighboring Station of Catarman, Northern Samar with the three neighboring stations. Based from the results, Normal Ratio Method performs better than Distance Power Method as applied to three neighboring stations.


INTRODUCTION
For a reliable rainfall data input for whatever water resources management planning, a continuous data, say for 10 years or 30 years is immense. But the reality, some rainfall data for a particular station have gaps which may be due toloss of records, fire accidents, wars, typhoons, floods, etc. and occasional interruption abnormal function of the instruments used [1]. According to Pajuelas [2] estimation of missing data is the first stage of most climatological, environmental and hydrological studies.
In the Philippines, there are synoptic stations having gaps on their rainfall data. Hasan, et al. [3] said spatial interpolation techniques are widely used methods for filling the gaps in daily rainfall series through estimating the unknown rainfall amount for a point from the known data of adjacent stations. Normal-ratio and 3-stationaverage was explored to fill the missing values in monthly rainfall data by Paulhus and Kohler [4] and The Inverse Distance Weighting (IDW) methods estimate the rainfall amount of a location was considered by Teegavarapu and Chandramouli (2005). Ahrens [5] stated that correlation coefficients between data series can also be explored to estimate the weights. And so are regression based methods are also used for estimating missing precipitation values according Lo Presti et al. [6] considering the climate data, elevation, topography, proximity to coastal area etc. as explanatory.
A number of tools to estimate missing rainfall data for a location were developed. And this study attempted to compare the performances of Normal Ratio Method and Distance Power Method for estimating missing rainfall data [7,8].

METHODOLOGY
This study employed the quantitative correlational study, a descriptive research design. The correlation of the rainfall data of Catarman to the three identified neighboring stations, the Catbalogan, Legazpi and Masbate synoptic stations was determined to know whether the rainfall data of the latter be used to estimate the missing monthly rainfall of the former employing Normal Ratio Method or Distance Power Method. Based on the data requirements and level of accuracy, the Normal Ratio Method can be used only if the available daily rainfall data for each of the stations involved in the study runs for thirty-years, from January 1, 1986 to December 31, 2015 and for the Distance Power Method the available rainfall data should be at least for ten (10) continuous years. However, for comparison, in both methods, the rainfall data analyzed was from January 1986 to December 2015.
This study utilized the daily rainfall from the Philippine Atmospheric Geophysical and Astronomical Services Administration (PAGASA) of Catarman and the three neighboring synoptic rain gage stations, namely, Catbalogan, Legazpi and Masbate. The daily rainfall obtained from the Catarman, Catbalogan, Legazpi and Masbate Synoptic Stations were summed up to find the monthly rainfall.
A Double Mass Analysis was performed to test the homogeneity of the rainfall data set of Catarman Station and the rainfall data sets of the identified three neighboring stations. To adjust the data, the formula below was used.
= where: Pa = adjusted precipitation Po = observed precipitation ba = slope of graph to which records are adjusted bo = slope of graph at time Po was observed As shown in Fig. 1, the observed rainfall of the three neighboring stations, namely, Catbalogan, Legazpi and Masbate and that of the test station (Catarman) possess homogeneity and consistency.
Since the rainfall data for Catarman station and the three neighboring stations are homogeneous and consistent, the researcher started the computation of the estimated monthly rainfall for Catarman station using the monthly rainfall data from the three neighboring stations by the following formulas: where: x, y, z = are the coordinates of the Catarman Station; and xi, yi, zi = are the coordinates of any of the neighboring stations.
The statistical procedures employed in this study were the following : 1. "T" test for Correlated Samples (to determine if there is significant difference between the estimated missing monthly rainfall (at Catarman station) using the three methods and the observed monthly rainfall at Catarman station): ( − 1) where: D = main difference between observed monthly rainfall at Catarman station and the estimated missing monthly rainfall by any of the three methods employed n = sample size 2. Pearson's Correlation Coefficient (to determine the degree of correlation between the observed and estimated monthly rainfall for Catarman station) where: R = Pearson's Correlation Coefficient; X = monthly rainfall in any neighboring station included in the study; Y = the observed monthly rainfall data at Catarman station; and n = population size.

RESULTS
The normal monthly rainfall for Catarman, Catbalogan, Legazpi and Masbate stations were computed and presented in Table 1.
Using these normal rainfall values, the monthly rainfall in Catarman, N. Samar was estimated by the Normal Ratio Method as shown in Tables 2a  and 2b Tables 3a and 3b. Table 4 shows the results of the "T" test for Correlated Samples (to determine if there is significant difference between the estimated monthly rainfall at Catarman station) using the ttwo methods and the observed monthly rainfall at Catarman station) and the results of the Pearson's Correlation Coefficient computation (to determine the degree of correlation between the estimated monthly rainfall by the three methods and the observed monthly rainfall for Catarman station.

DISCUSSION AND CONCLUSION
The resulton Double Mass Analysis shows that rainfall data are homogeneous and also implied that the three neighboring stations have similar rainfall pattern with Catarman, hence the selection of these stations are justified. The normal annual rainfall, based on a 30 years rainfall data (1986 -2015) for Catarman (Northern Samar) ranged from 154.9 mm (May) to 645.1 mm (December). For the same period, the normal annual rainfall in Catbalogan ranged 127.2 mm (April) to 339.9 mm (December); in Legazpi, it ranged from 176.6 mm (April) to 583.5 mm (December); and in Masbate, it ranged from 53.7 mm (April) to 267.7 mm (December).
The coefficients of correlation between the monthly observed rainfall at Catarman station and any of the three identified neighboring stations without using any estimating tool were also determined. For Catarman and Catbalogan, the correlation coefficient was 0.737; for Catarman and Legazpi, 0.622; and for Catarman and Masbate, 0.698. However, these correlation coefficients were very low.
The monthly rainfall in Catarman for 30 years was estimated by using the two methods. The estimated monthly rainfall using each of the two methods was compared with the observed monthly rainfall in Catarman. The estimated monthly rainfall by the Normal Ratio Method has the lower "t" value of -0.3 compared that of Distance Power Method is -10.0 which means that the former method gave the nearest to the observed monthly rainfall.
The estimated monthly rainfall using the Normal Ratio Methods had correlation coefficients of 0.84 while for the Distance Power Method had a correlation coefficient of 0.76 only. With these findings, the Normal Ratio Method performed better than Distance Power Method. The researcher believes that distance has some bearing on the rainfall pattern.

RECOMMENDATIONS
Based from the results, it is recommended that similar study be conducted comparing other missing rainfall data estimating tools which may either be classical methods or machine learning techniques and with more than three stations.