California is an area of diverse topography and has what many scientists call a Mediterranean climate. Various precipitation patterns exist due to El Niño Southern Oscillation (ENSO) which can cause abnormal precipitation or droughts. As temperature increases mainly due to the increase of CO2 in the atmosphere, it is rapidly changing the climate of not only California but the world. An increase in temperature is leading to droughts in certain areas as other areas are experiencing heavy rainfall/flooding. Droughts in return are providing a foundation for fires harming the ecosystem and nearby population. Various natural hazards can be induced due to the coupling effects from inconsistent precipitation patterns and vice versa. Using wavelets, we were able to identify anomalies of high precipitation and droughts within California\u27s 7 climate divisions using NOAA\u27s hourly precipitation data from rain gauges and compared the results with modeled data, SOI, and PDO. The identification of anomalies can be used to compare and correct remote sensing measurements of precipitation and droughts. Promising results show a possible connection with increasing tropical moisture activity

Allali, Mohamed

el-Askary, Hesham

Rakovski, Cyril S

Rodriguez, Luciano

English

Chapman University Digital Commons

Chapman University
Chapman University Digital Commons
Student Research Day Abstracts and Posters Office of Undergraduate Research and CreativeActivity
12-10-2014
Long Term Ground Based Precipitation Data
Analysis: Spatial and Temporal Variability
Luciano Rodriguez
Chapman University, rodri178@mail.chapman.edu
Cyril S. Rakovski
Chapman University, rakovski@chapman.edu
Hesham el-Askary
Chapman University, elaskary@chapman.edu
Mohamed Allali
Chapman University, allali@chapman.edu
Follow this and additional works at: http://digitalcommons.chapman.edu/cusrd_abstracts
Part of the Atmospheric Sciences Commons, Climate Commons, Meteorology Commons, and
the Other Oceanography and Atmospheric Sciences and Meteorology Commons
This Poster is brought to you for free and open access by the Office of Undergraduate Research and Creative Activity at Chapman University Digital
Commons. It has been accepted for inclusion in Student Research Day Abstracts and Posters by an authorized administrator of Chapman University
Digital Commons. For more information, please contact laughtin@chapman.edu.
Recommended Citation
Rodriguez, Luciano; Rakovski, Cyril S.; el-Askary, Hesham; and Allali, Mohamed, "Long Term Ground Based Precipitation Data
Analysis: Spatial and Temporal Variability" (2014). Student Research Day Abstracts and Posters. Paper 48.
http://digitalcommons.chapman.edu/cusrd_abstracts/48
Long Term Ground Based Precipitation Data Analysis: 
Spatial and Temporal Variability
Rodriguez, L., Rakovski, C., El-Askary, H., Allali, M.
Schmid College Of Science and Technology Chapman University, 
Orange, CA
Abstract
California is an area of diverse topography and has what
many scientists call a Mediterranean climate. Various
precipitation patterns exist due to El Niño Southern Oscillation
(ENSO) which can cause abnormal precipitation or droughts. As
temperature increases mainly due to the increase of CO2 in the
atmosphere, it is rapidly changing the climate of not only
California but the world. An increase in temperature is leading to
droughts in certain areas as other areas are experiencing heavy
rainfall/flooding. Droughts in return are providing a foundation for
fires harming the ecosystem and nearby population. Various
natural hazards can be induced due to the coupling effects from
inconsistent precipitation patterns and vice versa. Using
wavelets, we were able to identify anomalies of high precipitation
and droughts within California's 7 climate divisions using NOAA's
hourly precipitation data from rain gauges and compared the
results with modeled data, SOI, and PDO. The identification of
anomalies can be used to compare and correct remote sensing
measurements of precipitation and droughts. Promising results
show a possible connection with increasing tropical moisture
activity.
Data and Study Area
Hourly precipitation data was used for the analysis from
National Climatic Data Center (NCDC) and NOAA's Forecast
Systems Laboratory (FSL) CD-ROM where there are more than
2500 active stations and 7000 total stations. The majority of the
data ranges from 1948 through 1995, however, there are some
stations that begin as early as 1900. The data extracted
concentrates on all the stations in California. The data obtained
needed a lot of corrections since there were many hours and
days missing, accumulated and deleted data. Secondly, to apply
the ARMA model, the data needs to be continuous in time.
Therefore, we average the precipitation measurements of all the
stations pertaining to a climate region (Figure 1) to get an
adequate estimate of the climate per regions of California. Then
fill in the missing data by imputing timely averages.
The second set of data is monthly modeled data provided
by NOAA. The gauge data set will be used to compare the
modeled data set to see how well the model is performing.
Methodology (continued)
where __, __, and ____ are the parameters of the ARMA model. The error to 
this model is given by the following properties:  _____________, 
____________ , and __________.      . This model can be rewritten to establish 
a maximum likelihood error:
where ________________, _____________, and __________,
which is the lag operator. Using the maximum likelihood estimator one can 
calculate the residuals __ . Approaches to fitting the ARMA models to the 
residual is based on Akaike Information Criterion (AIC) minimization. The AIC 
model is given by:
The AIC model is optimal when the forecast mean square error (FMSE) 
measure is no more than a certain threshold.
Once the autocorrelation is calculated, a derivation of 95% confidence 
band is used to detect extreme values:
where corresponds to the residual output from the ARMA model and MSE is 
the mean square error. This equation reflects the confidence intervals of 
anomalies beyond the common observations in the residual decomposition
of the data. Thus the extreme observations ___ are given by:
Where __ are time dependent observations and __are time dependent residual 
values from the maximum likelihood. This methodology was perform in El-
Askary et al. article and was used in this project to model precipitation patterns 
and extract ENSO anomalies in California.
To compare the two time series data set (modeled and gauge), we 
subtract the two time series: , where     , is the modeled time series 
and    , is the gauge time series.  We then performed a test for trend using 
Mann-Kendall Test:
If a trend is detected, one can test the subtracted time series for stationarity
using the Augmented Dickey-Fuller Unit-Root Test:
The null hypothesis          against the alternative hypothesis          contains the 
unit root test: If the time series is stationary, then one can perform 
a hypothesis testing based on the z-scores: 
This notes whether the model is correctly measuring the true data (gauge).
Figure 1-2. 7 climate divisions of California: 1 - North Coast Drainage, 2 -
Sacramento Drainage, 3 - Northeast Interior Basins, 4 - Central Coast Drainage, 5 -
San Joaquin Drainage, 6 - South Coast Drainage, 7 - Southeast Desert Basin
Results (continued)
The model and gauge data have a similar pattern in the
residuals for all divisions. The months found to have excessive
precipitation are overlapping between the two sets of data. One of
the difference noted between the plots is that the model frequency
is, at times, lower than the gauge signifying that the model is not
capturing all precipitation fluctuations. The technique of taking the
difference between the two datasets (model and gauge) is useful to
find the differences between the two. Theoretically if both the
model and gauge time series are the same it should equal zero or it
would have a zero mean at worst case scenario. The histogram
shows that the majority of the time the model underestimates the
amount of precipitation. On another note, the difference of the two
time series should diminish any traces for seasonality and trend.
One can check if there is a trend present for all climate divisions
using the Mann-Kendall Test. The results show that climate
division 5 still has a trend present. This is the second time we
noted that the model is not a good estimator of precipitation.
Furthermore, if the differenced time series is stationary, which it is
by the Augmented Dickey-Fuller Unit-Root Test, one can check if
the time series has a mean of zero. We can check this using z-
scores. The results show that for all climate divisions the time
series is not zero mean. Overall, the model must be recalibrated.
Conclusions
Forecasting atmospheric hazards using historical
precipitation data is what scientist/researchers are attempting to do
well enough to be able to avoid catastrophic events. However, the
usage is different from researcher and location. Therefore, this
study focuses on historical hourly precipitation data to model
extreme precipitation (mainly related to ENSO) to have a proper
input for other models (climate, hydrological, crop, etcetera) to
ensure the public with food, water, and shelter. The data consisted
of 47 years of hourly observation at various regions in California.
The data provided insight to the tropical storm patterns traveling
west to east during the summer. Our results show that high
precipitation, which may be caused by various components (i.e. El
Niño, La Niña, etc. ), may cause increase in precipitation as well as
an increase in droughts and heat waves. The usage of 95%
confidence interval bands were used to isolate the times that
extreme precipitation and droughts were present. This method was
consistent in portraying high precipitation from thunderstorms and
heat waves related to the ENSO effects. This method allows a
good detection to forecast high precipitation that may be a possible
catalyst to tropical storms, which will allow authorities and civilians
to properly prepare for safety and evacuation if needed in terms of
flooding.
Future Research
The next step is to continue to map the ENSO patterns with
the usage of weekly, daily and hourly dataset. Also see what and
how one can improve the modeled data from NOAA .
Acknowledgements
The author would like to acknowledge the help received from
Dr. El-Askary for providing the idea and data for the project, Dr.
Cyril Rakovski for the time series lectures, and David Stack for the
Python code suggestions.
References
1. El-Askary, H., Allali, M., Rakovski, C., Prasad, A., Kafatos, M., and Struppa, D. Computational 
methods for climate data. WIREs: Computational Statistics 4, 4 (Aug. 2012), 359.
2. EL-Askary, H., Sarkar, S., Chiu, L., Kafatos, M., and El-Ghazawi, T. Rain gauge derived 
precipitation variability over virginia and its relation with the el nino southern oscillation. 
Advances in Space Research 33, 3 (2004), 338-342.
3. Foundation, P. S. Python Programming Language. http://www.python.org/, 2012.
4. Prasad, A., and Singh, R. Extreme rainfall event of july 2527, 2005 over mumbai, west coast, 
india. Journal of the Indian Society of Remote Sensing 33 (2005), 365{370. 
10.1007/BF02990007.
5. RDC, T. R: A language and environment for statistical computing. R Foundation for Statistical 
Computing, 2008.
Results
Methodology
The monthly precipitation was calculated over a period of 
47 years (1948 - 1995) and was implemented in a time series 
decomposition to remove seasonal and trend components. This 
work used local linear regression (loess) to remove such trends 
into a composition of seasonal, trend, and residual components 
(STL decomposition). It is given by: 
which decomposes the time series (   ) into three distinct 
components. The seasonal and trend components are of no 
interest to this study, but the residual (   ) is due to its fluctuation 
of anomalies. Moreover, an implementation for analysis of the 
stationary time series autoregressive-moving average (ARMA) 
model was used to analyze the residual component. 
Autoregressive-moving average model is defined as:
Monthly Gauge Augmented Excessive Rain in North Coast Drainage, 
California (1) 
Date CI Remainder_Value Date CI
Remainder_Val
ue
Oct-50 4.067634 5.757119 Oct-81 4.067634 4.23382
Dec-52 4.067634 4.980898 Dec-82 4.067634 4.239821
Dec-55 4.067634 10.5226 Feb-83 4.067634 5.356321
Feb-58 4.067634 6.942903 Mar-83 4.067634 4.307159
Feb-60 4.067634 4.348038 Nov-83 4.067634 6.528172
Oct-62 4.067634 6.927224 Dec-83 4.067634 5.318291
Dec-64 4.067634 6.721753 Nov-84 4.067634 10.87232
Jan-66 4.067634 4.258372 Feb-86 4.067634 12.10319
Jan-67 4.067634 6.189922 Dec-87 4.067634 4.125445
Jan-70 4.067634 7.924156 Mar-89 4.067634 5.649046
Nov-70 4.067634 5.542048 May-90 4.067634 5.816245
Nov-73 4.067634 10.79694 Mar-91 4.067634 4.845202
Mar-74 4.067634 4.11226 Dec-92 4.067634 4.491649
Mar-75 4.067634 6.896264 Jan-95 4.067634 8.969987
Oct-75 4.067634 5.288991 Mar-95 4.067634 7.866046
Nov-77 4.067634 7.849707 Dec-95 4.067634 10.39994
Monthly Modeled Excessive Rain in North Coast Drainage, California (1)
Date CI Remainder_Value Date CI
Remainder_Val
ue
Jan-50 4.024495 4.196245 Nov-73 4.024495 9.755491
Oct-50 4.024495 6.839264 Feb-75 4.024495 5.138798
Dec-51 4.024495 4.298942 Mar-75 4.024495 6.180109
Dec-52 4.024495 7.498336 Oct-75 4.024495 4.623324
Jan-53 4.024495 4.323402 Nov-81 4.024495 4.491962
Jan-54 4.024495 4.9192 Dec-81 4.024495 4.150797
Dec-55 4.024495 10.17264 Feb-83 4.024495 4.414713
Jan-56 4.024495 4.561349 Mar-83 4.024495 6.765538
Feb-58 4.024495 9.390391 Nov-83 4.024495 6.929051
Feb-60 4.024495 4.080439 Dec-83 4.024495 6.838359
Feb-62 4.024495 4.074846 Nov-84 4.024495 9.648742
Oct-62 4.024495 6.713863 Feb-86 4.024495 10.59648
Apr-63 4.024495 5.073475 Dec-87 4.024495 4.839672
Nov-63 4.024495 4.577761 Nov-88 4.024495 4.458243
Dec-64 4.024495 10.21712 Mar-89 4.024495 5.825754
Dec-68 4.024495 4.045503 May-90 4.024495 5.401517
Jan-69 4.024495 5.576568 Mar-91 4.024495 7.189508
Dec-69 4.024495 5.388231 Jan-95 4.024495 11.24316
Jan-70 4.024495 9.401017 Mar-95 4.024495 7.048231
Nov-70 4.024495 6.329715 Dec-95 4.024495 6.952523


Long Term Ground Based Precipitation Data Analysis: Spatial and Temporal Variability

Chapman UniversityChapman University Digital CommonsStudent Research Day Abstracts and Posters Office of Undergraduate Research and CreativeActivity12-10-2014Long Term Ground Based Precipitation DataAnalysis: Spatial and Temporal VariabilityLuciano RodriguezChapman University, rodri178@mail.chapman.eduCyril S. RakovskiChapman University, rakovski@chapman.eduHesham el-AskaryChapman University, elaskary@chapman.eduMohamed AllaliChapman University, allali@chapman.eduFollow this and additional works at: http://digitalcommons.chapman.edu/cusrd_abstractsPart of the Atmospheric Sciences Commons, Climate Commons, Meteorology Commons, andthe Other Oceanography and Atmospheric Sciences and Meteorology CommonsThis Poster is brought to you for free and open access by the Office of Undergraduate Research and Creative Activity at Chapman University DigitalCommons. It has been accepted for inclusion in Student Research Day Abstracts and Posters by an authorized administrator of Chapman UniversityDigital Commons. For more information, please contact laughtin@chapman.edu.Recommended CitationRodriguez, Luciano; Rakovski, Cyril S.; el-Askary, Hesham; and Allali, Mohamed, "Long Term Ground Based Precipitation DataAnalysis: Spatial and Temporal Variability" (2014). Student Research Day Abstracts and Posters. Paper 48.http://digitalcommons.chapman.edu/cusrd_abstracts/48Long Term Ground Based Precipitation Data Analysis: Spatial and Temporal VariabilityRodriguez, L., Rakovski, C., El-Askary, H., Allali, M.Schmid College Of Science and Technology Chapman University, Orange, CAAbstractCalifornia is an area of diverse topography and has whatmany scientists call a Mediterranean climate. Variousprecipitation patterns exist due to El Niño Southern Oscillation(ENSO) which can cause abnormal precipitation or droughts. Astemperature increases mainly due to the increase of CO2 in theatmosphere, it is rapidly changing the climate of not onlyCalifornia but the world. An increase in temperature is leading todroughts in certain areas as other areas are experiencing heavyrainfall/flooding. Droughts in return are providing a foundation forfires harming the ecosystem and nearby population. Variousnatural hazards can be induced due to the coupling effects frominconsistent precipitation patterns and vice versa. Usingwavelets, we were able to identify anomalies of high precipitationand droughts within California's 7 climate divisions using NOAA'shourly precipitation data from rain gauges and compared theresults with modeled data, SOI, and PDO. The identification ofanomalies can be used to compare and correct remote sensingmeasurements of precipitation and droughts. Promising resultsshow a possible connection with increasing tropical moistureactivity.Data and Study AreaHourly precipitation data was used for the analysis fromNational Climatic Data Center (NCDC) and NOAA's ForecastSystems Laboratory (FSL) CD-ROM where there are more than2500 active stations and 7000 total stations. The majority of thedata ranges from 1948 through 1995, however, there are somestations that begin as early as 1900. The data extractedconcentrates on all the stations in California. The data obtainedneeded a lot of corrections since there were many hours anddays missing, accumulated and deleted data. Secondly, to applythe ARMA model, the data needs to be continuous in time.Therefore, we average the precipitation measurements of all thestations pertaining to a climate region (Figure 1) to get anadequate estimate of the climate per regions of California. Thenfill in the missing data by imputing timely averages.The second set of data is monthly modeled data providedby NOAA. The gauge data set will be used to compare themodeled data set to see how well the model is performing.Methodology (continued)where __, __, and ____ are the parameters of the ARMA model. The error to this model is given by the following properties:  _____________, ____________ , and __________.      . This model can be rewritten to establish a maximum likelihood error:where ________________, _____________, and __________,which is the lag operator. Using the maximum likelihood estimator one can calculate the residuals __ . Approaches to fitting the ARMA models to the residual is based on Akaike Information Criterion (AIC) minimization. The AIC model is given by:The AIC model is optimal when the forecast mean square error (FMSE) measure is no more than a certain threshold.Once the autocorrelation is calculated, a derivation of 95% confidence band is used to detect extreme values:where corresponds to the residual output from the ARMA model and MSE is the mean square error. This equation reflects the confidence intervals of anomalies beyond the common observations in the residual decompositionof the data. Thus the extreme observations ___ are given by:Where __ are time dependent observations and __are time dependent residual values from the maximum likelihood. This methodology was perform in El-Askary et al. article and was used in this project to model precipitation patterns and extract ENSO anomalies in California.To compare the two time series data set (modeled and gauge), we subtract the two time series: , where     , is the modeled time series and    , is the gauge time series.  We then performed a test for trend using Mann-Kendall Test:If a trend is detected, one can test the subtracted time series for stationarityusing the Augmented Dickey-Fuller Unit-Root Test:The null hypothesis          against the alternative hypothesis          contains the unit root test: If the time series is stationary, then one can perform a hypothesis testing based on the z-scores: This notes whether the model is correctly measuring the true data (gauge).Figure 1-2. 7 climate divisions of California: 1 - North Coast Drainage, 2 -Sacramento Drainage, 3 - Northeast Interior Basins, 4 - Central Coast Drainage, 5 -San Joaquin Drainage, 6 - South Coast Drainage, 7 - Southeast Desert BasinResults (continued)The model and gauge data have a similar pattern in theresiduals for all divisions. The months found to have excessiveprecipitation are overlapping between the two sets of data. One ofthe difference noted between the plots is that the model frequencyis, at times, lower than the gauge signifying that the model is notcapturing all precipitation fluctuations. The technique of taking thedifference between the two datasets (model and gauge) is useful tofind the differences between the two. Theoretically if both themodel and gauge time series are the same it should equal zero or itwould have a zero mean at worst case scenario. The histogramshows that the majority of the time the model underestimates theamount of precipitation. On another note, the difference of the twotime series should diminish any traces for seasonality and trend.One can check if there is a trend present for all climate divisionsusing the Mann-Kendall Test. The results show that climatedivision 5 still has a trend present. This is the second time wenoted that the model is not a good estimator of precipitation.Furthermore, if the differenced time series is stationary, which it isby the Augmented Dickey-Fuller Unit-Root Test, one can check ifthe time series has a mean of zero. We can check this using z-scores. The results show that for all climate divisions the timeseries is not zero mean. Overall, the model must be recalibrated.ConclusionsForecasting atmospheric hazards using historicalprecipitation data is what scientist/researchers are attempting to dowell enough to be able to avoid catastrophic events. However, theusage is different from researcher and location. Therefore, thisstudy focuses on historical hourly precipitation data to modelextreme precipitation (mainly related to ENSO) to have a properinput for other models (climate, hydrological, crop, etcetera) toensure the public with food, water, and shelter. The data consistedof 47 years of hourly observation at various regions in California.The data provided insight to the tropical storm patterns travelingwest to east during the summer. Our results show that highprecipitation, which may be caused by various components (i.e. ElNiño, La Niña, etc. ), may cause increase in precipitation as well asan increase in droughts and heat waves. The usage of 95%confidence interval bands were used to isolate the times thatextreme precipitation and droughts were present. This method wasconsistent in portraying high precipitation from thunderstorms andheat waves related to the ENSO effects. This method allows agood detection to forecast high precipitation that may be a possiblecatalyst to tropical storms, which will allow authorities and civiliansto properly prepare for safety and evacuation if needed in terms offlooding.Future ResearchThe next step is to continue to map the ENSO patterns withthe usage of weekly, daily and hourly dataset. Also see what andhow one can improve the modeled data from NOAA .AcknowledgementsThe author would like to acknowledge the help received fromDr. El-Askary for providing the idea and data for the project, Dr.Cyril Rakovski for the time series lectures, and David Stack for thePython code suggestions.References1. El-Askary, H., Allali, M., Rakovski, C., Prasad, A., Kafatos, M., and Struppa, D. Computational methods for climate data. WIREs: Computational Statistics 4, 4 (Aug. 2012), 359.2. EL-Askary, H., Sarkar, S., Chiu, L., Kafatos, M., and El-Ghazawi, T. Rain gauge derived precipitation variability over virginia and its relation with the el nino southern oscillation. Advances in Space Research 33, 3 (2004), 338-342.3. Foundation, P. S. Python Programming Language. http://www.python.org/, 2012.4. Prasad, A., and Singh, R. Extreme rainfall event of july 2527, 2005 over mumbai, west coast, india. Journal of the Indian Society of Remote Sensing 33 (2005), 365{370. 10.1007/BF02990007.5. RDC, T. R: A language and environment for statistical computing. R Foundation for Statistical Computing, 2008.ResultsMethodologyThe monthly precipitation was calculated over a period of 47 years (1948 - 1995) and was implemented in a time series decomposition to remove seasonal and trend components. This work used local linear regression (loess) to remove such trends into a composition of seasonal, trend, and residual components (STL decomposition). It is given by: which decomposes the time series (   ) into three distinct components. The seasonal and trend components are of no interest to this study, but the residual (   ) is due to its fluctuation of anomalies. Moreover, an implementation for analysis of the stationary time series autoregressive-moving average (ARMA) model was used to analyze the residual component. Autoregressive-moving average model is defined as:Monthly Gauge Augmented Excessive Rain in North Coast Drainage, California (1) Date CI Remainder_Value Date CIRemainder_ValueOct-50 4.067634 5.757119 Oct-81 4.067634 4.23382Dec-52 4.067634 4.980898 Dec-82 4.067634 4.239821Dec-55 4.067634 10.5226 Feb-83 4.067634 5.356321Feb-58 4.067634 6.942903 Mar-83 4.067634 4.307159Feb-60 4.067634 4.348038 Nov-83 4.067634 6.528172Oct-62 4.067634 6.927224 Dec-83 4.067634 5.318291Dec-64 4.067634 6.721753 Nov-84 4.067634 10.87232Jan-66 4.067634 4.258372 Feb-86 4.067634 12.10319Jan-67 4.067634 6.189922 Dec-87 4.067634 4.125445Jan-70 4.067634 7.924156 Mar-89 4.067634 5.649046Nov-70 4.067634 5.542048 May-90 4.067634 5.816245Nov-73 4.067634 10.79694 Mar-91 4.067634 4.845202Mar-74 4.067634 4.11226 Dec-92 4.067634 4.491649Mar-75 4.067634 6.896264 Jan-95 4.067634 8.969987Oct-75 4.067634 5.288991 Mar-95 4.067634 7.866046Nov-77 4.067634 7.849707 Dec-95 4.067634 10.39994Monthly Modeled Excessive Rain in North Coast Drainage, California (1)Date CI Remainder_Value Date CIRemainder_ValueJan-50 4.024495 4.196245 Nov-73 4.024495 9.755491Oct-50 4.024495 6.839264 Feb-75 4.024495 5.138798Dec-51 4.024495 4.298942 Mar-75 4.024495 6.180109Dec-52 4.024495 7.498336 Oct-75 4.024495 4.623324Jan-53 4.024495 4.323402 Nov-81 4.024495 4.491962Jan-54 4.024495 4.9192 Dec-81 4.024495 4.150797Dec-55 4.024495 10.17264 Feb-83 4.024495 4.414713Jan-56 4.024495 4.561349 Mar-83 4.024495 6.765538Feb-58 4.024495 9.390391 Nov-83 4.024495 6.929051Feb-60 4.024495 4.080439 Dec-83 4.024495 6.838359Feb-62 4.024495 4.074846 Nov-84 4.024495 9.648742Oct-62 4.024495 6.713863 Feb-86 4.024495 10.59648Apr-63 4.024495 5.073475 Dec-87 4.024495 4.839672Nov-63 4.024495 4.577761 Nov-88 4.024495 4.458243Dec-64 4.024495 10.21712 Mar-89 4.024495 5.825754Dec-68 4.024495 4.045503 May-90 4.024495 5.401517Jan-69 4.024495 5.576568 Mar-91 4.024495 7.189508Dec-69 4.024495 5.388231 Jan-95 4.024495 11.24316Jan-70 4.024495 9.401017 Mar-95 4.024495 7.048231Nov-70 4.024495 6.329715 Dec-95 4.024495 6.952523

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Long Term Ground Based Precipitation Data Analysis: Spatial and Temporal Variability

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