INDIVIDUAL REPORT
UPRM - HYDRO CLIMATE /RAMIREZ/HARMSEN
(Performance period: March 1, 2008 to August 31, 2008)
RESEARCH COMPONENT
Thrust: Precipitation and Water Resources
Thrust 1a: Hydro Climate
Project 2: Validate Existing Precipitation Retrieval Algorithms
 Relevance to NOAA’s mission and the strategic plan
This study will provide information related to the strengths and weaknesses of the NOAA’s
operational Hydro-Estimator rainfall algorithm, and will help to guide the development of the
GOES-R era algorithm. This project will contribute directly to NOAA’s goals of supporting
activities directed toward helping to sustain healthy coastal areas, improving weather forecasting
and warnings, provide improved environmental forecasts/analyses, and to prepare for future
NOAA operational environmental satellite missions. This project will contribute to improving the
reliability, lead-time, and understanding of weather and water information and services that predict
changes in environmental conditions; expand and enhance advanced technology monitoring and
observing systems to provide accurate, up-to-date information.

Relevance to NOAA Line Office (i.e., National Weather Service, National Ocean
Service) strategic plan.
The project is producing results relevant to the NWS in Puerto Rico. This project supports the
following goals of NOAA and its Line Office by: expanding sources of reliable observational
data, continued integration of environmental sciences, providing data to satisfy the increased
demand for NWS warnings and response, will produce advances in science and technology, will
expand climate information, and will provide more explicit and more useful measures of forecast
certainty.
 Supervising PI or Co-Is (only faculty member(s) at your institution)
Dr. Eric Harmsen, Nazario Ramírez, Ramón Vásquez

Publications (during performance period):
-Total Journal Publications 3
-Journal Publications with Students 5
Harmsen, E. W., S. E. Gomez Mesa, E. Cabassa, N. D. Ramírez-Beltran, S. Cruz Pol, R. J.
Kuligowski And R. Vasquez, 2008. Satellite sub-pixel rainfall variability. International
Journal of Systems Engineering, Applications and Development, World Scientific and
Engineering Academy and Society. (accepted)
Ramirez-Beltran, N., R. J. Kuligowski, E. W. Harmsen, J. M. Castro, S. Cruz-Pol, and M. J.
Cardona, 2008. Rainfall Estimation from Convective Storms Using the Hydro-Estimator
and NEXRAD. Satellite sub-pixel rainfall variability. International Journal of Systems
Engineering, Applications and Development, World Scientific and Engineering Academy
and Society. (accepted)
Ramírez Beltran, N. D., J. M. Castro, E. W. Harmsen and R. Vásquez Espinoza, 2008. Stochastic
transfer function model and neural networks to estimate soil moisture. J. of the American
Water Resources Association, Vol. 44, No. 4:847-865.
-Total Refereed Proceedings 3
-Refereed Proceedings with Students 3
Harmsen, E. W., S. E. Gomez Mesa, N. D. Ramírez-Beltran, R. J. Kuligowski, and R. Vasquez,
2008. Remote sensing QPE uncertainties associated with sub-pixel rainfall variation.
Proceedings of the 12th WSEAS International Conference on SYSTEMS, Heraklion,
Greece, July 22-24, 2008. Pages 789-798. Pages 799-806.
Ramirez-Beltran, N. D., R. J. Kuligowski, E. W. Harmsen, J. M. Castro, S. Cruz-Pol, and M. J.
Cardona-Soto, 2008. Validation and Strategies to Improve the Hydro-Estimator and
NEXRAD over Puerto Rico. Proceedings of the 12th WSEAS International Conference on
SYSTEMS, Heraklion, Greece, July 22-24, 2008. Pages 789-798.
Ramirez Builes, V. H., E. W. Harmsen, and T.G. Porch, 2008. Estimation of actual
evapotranspiration using measured and calculated values of bulk surface resistance.
Proceedings of the ASCE World Environmental and Water Resources Congress 2008. May
13-16, 2008, Honolulu, Hawaii.

-Books
Dollar amount of funds leveraged with CREST funds (report for the performance period
ONLY)
$20,000 from NASA – GSFC. Project title: Rapid Detection of Soils and Drinking Water Sources Impacted
by Salt Water Flooding. Eric Harmsen, PI, UPRM and Leonid Roytman, Co-PI, CUNY. This project grew
out of a relationship developed on the NOAA-CREST Project. We hope to take advantage of the
Cooperative Agreement between CUNY and UPR to enlist students research assistants on this project. See
Appendix 1.
 Ongoing, New or Revised?
This is an ongoing project

Staff

Students MS
o Melvin Cordona, Department of Electrical and Computer Engineering
2

Undergraduate Students:
o Edvier Cabassa, Department of Electrical and Computer Engineering
o Orlando Santiago from the Department of Electrical and Computer Engineering
o Pablo Mejias from the Department of Civil Engineering

NOAA Collaborators (with Affiliations)
o Dr. Robert J. Kuligowski, at NOAA/NESDIS Center for Satellite Applications and
Research (STAR)
o Israel Matos from the National Weather Service, San Juan, Puerto Rico

Other Collaborators (with Affiliations)
o Dr. Daniel Lindsey from Cooperative the Institute for Research in the Atmosphere
(CIRA) at Colorado State University
o Dr. Sandra Cruz-Pol, Department of Computer and Electrical Engineering, University
of Puerto Rico.
o Dr. Mark Jury, Department of Physics, University of Puerto Rico – Mayaguez Campus.
 Operational Impact (Has Research been /or planned to be transitioned to operation)
N/A
• Other Activities
Presentation:
1. Remote sensing QPE uncertainties associated with sub-pixel rainfall variation. Proceedings
of the 12th WSEAS International Conference on SYSTEMS, Heraklion, Greece, July 22-24.
Presenter: Eric Harmsen
2. Estimation of actual evapotranspiration using measured and calculated values of bulk
surface resistance. Proceedings of the ASCE World Environmental and Water Resources
Congress 2008. May 13-16, 2008, Honolulu, Hawaii. Presenter: Eric Harmsen
3. Validation and Strategies to Improve the Hydro-Estimator and NEXRAD over Puerto Rico.
Proceedings of the 12th WSEAS International Conference on SYSTEMS, Heraklion, Greece,
July 22-24. Presenter: Nazario Ramirez
3
 Status of the project with respect to the goals/objectives and benchmarks previously
identified
Tasks (For year II as per the Milestone Chart) (provide a brief narrative on each task with
reasons if any for the delay)
Task (3) Validate NESDIS HE & GMSRA Rainfall Algorithms for Puerto Rico.
Owing to technical issues, our contact at NESDIS, Dr. Robert Kuligowski, has recommended
that we not pursue validation of GMSRA at this time.
The accuracy of the HE and the NEXRAD rainfall estimates were measured by decomposing the
rainfall process in sequences of discrete (rain / no rain) and continuous (rainfall rate) random
variables. Validation results were based on seven heavy storms that seriously impacted human life
and the economy of PR during the period 2003 to 2007. Additional details are presented in
Appendix 2.
In our previous reports we described validation efforts related to the HE at the GOES pixel scale (4
km x 4 km). The HE performed poorly when compared with the pixel-scale rain gauge network.
Therefore efforts are underway to improve the HE. Until the new algorithm is ready, pixel scale
validation efforts will be suspended. During the reporting period efforts were focused on the
quantification of sub-pixel scale rainfall variability. The results were published in a peer-review
proceedings of the WSEAS and an extended paper will be published in the WSEAS Journal of
Systems. For more detail please refer to Appendix 3.
Task (4) Develop a Validation Algorithm
A validation algorithm has been developed to measure the accuracy of the rainfall retrieval
algorithms. Validation of the rainfall retrieval algorithm consists of comparing the rainfall
estimates with corresponding observations (rain gauges in this study). The accuracy of rainfall
estimates can be measured by decomposing the rainfall process as sequences of discrete and
continuous random variables; i.e., the presence or absence of rainfall events (discrete variable) and
the amount of rainfall (continuous variable). The occurrence of rainfall events in a given area and
at a particular time follows a Bernoulli process and consequently the estimation accuracy of
rainfall events can be conducted by analyzing a contingency table, which is the bivariate
probability distribution of rainfall events. See Appendix 2 for more details.
Task (5) Improve NESDIS Rainfall Algorithm
It is known that precipitation processes in clouds with warm tops are very sensitive to the
microphysical structure of their tops. Specifically, precipitation processes are more efficient when
water droplets or/and ice particles grow to larger sizes. It has been shown that the uses of the
reflected portion of the near-IR during the daytime indicates the presence large cloud-top particles
and suggest rain in warm-top clouds. Preliminary work was conducted to explore improving the
HE warm rainy-cloud detection using the GOES band 2 (3.9 µm) reflectance during the daytime.
4
This will be used as a proxy for cloud-top particle size to identify any correlation with the presence
or absence of rain from warm-topped clouds over PR. In this work we presente the estimation of
daytime reflectance of band 2. See Appendix 2 for additional details.
Task (6) Validate NESDIS-SCaMPR Model over the US and Puerto Rico
The NESDIS-SCaMPR model was not validated for Puerto Rico since this algorithm is limited to
perform rainfall estimation above latitude 20oN or above. The second reason was because our
NESDIS advisor suggested we invest time on validating and improving the HE since this is a
NOAA/NESDIS operational algorithm, and since the HE estimates of rainfall are very poor in the
Caribbean region.
5
Project 3: Flood Forecasting using Satellite-based Rainfall Estimates
 Relevance to NOAA’s mission and the strategic plan
This project will contribute directly to NOAA’s goals of supporting activities directed toward
helping to sustain healthy coastal areas, improving flood forecasting and warnings. This project
will contribute to improving the reliability, lead-time, and understanding of flooding and services
that predict changes in environmental conditions; expand and enhance advanced technology
monitoring and observing systems to provide accurate, up-to-date information.

Relevance to NOAA Line Office (i.e., National Weather Service, National Ocean
Service) strategic plan.
The project is producing results relevant to the NWS in Puerto Rico. This project supports the
following goals of NOAA and its Line Office by: expanding sources of reliable observational
data, continued integration of environmental sciences, providing data to satisfy the increased
demand for NWS warnings and response, will produce advances in science and technology, will
expand climate information, and will provide more explicit and more useful measures of forecast
certainty.
 Supervising PI or Co-Is (only faculty member(s) at your institution)
Dr. Eric Harmsen
 Publications (during performance period):
-Total Journal Publications
-Journal Publications with Students
-Total Refereed Proceedings
-Refereed Proceedings with Students
-Books
 Dollar amount of funds leveraged with CREST funds (report for the performance period
ONLY)
$6,000 from NSF-CASA Project. Includes $3000 for Ph.D. student (Alejandra Rojas) developing
hydrologic model and $3000 MS student (Santa Elizabeth Gomez) evaluating rain gauge network data
(i.e.,performing literature review, statistical model for describing sub-pixel variation, and reclassification of
storm types). See Appendix 1.

Ongoing, New or Revised? If this is a revised project, please describe revisions and the
impact
This project is ongoing
 Staff
 Students PhD
o Alejandra Rojas, Ph.D., Department of Civil Engineering, UPRM. (not funded by
NOAA-CREST)
 Students MS
o Santa Elizabeth Gomez, Department of Mathematics, UPRM. (not funded by
NOAA-CREST)
 Students Undergraduate
 NOAA Collaborators (with Affiliations) Dr. Baxter Vieux, University of Oklahoma,
Department of Civil Engineering
6
 Other Collaborators (with Affiliations) Dr. Pedro Restrepo, The Office of Hydrologic
Development, NOAA/NWS.
 Operational Impact (Has Research been /or planned to be transitioned to operation):
N/A
 Other Activities
 Presentation:
Assessment Predictability Limits in Small Watersheds to Enhance the Flash Flood Prediction
in Western Puerto Rico. ASCE World Environmental and Water Resources Congress 2008.
May 13-16, 2008, Honolulu, Hawaii. Presenter: Eric Harmsen

Status of the project with respect to the goals/objectives and benchmarks previously
identified
Tasks (For year II as per the Milestone Chart) (provide a brief narrative on each task with
reasons if any for the delay)
The work on this project is progressing but since there are no NOAA-CREST funds to cover
this project, progress is slower than originally anticipated.
Task (1) Modify a Hydrological Model by coupling with a Satellite-based Rainfall Retrieval
Algorithm
The coupling of the hydrologic model with satellite-based rainfall retrieval algorithm has not been
initiated yet. This sub-task has not been initiated because although the Hydro Estimator Nowcaster
is currently available, the Hydro Estimator is not capable of providing reliable rainfall estimates
within the study area. Therefore, efforts are being focused on improving the rainfall algorithm.
Task (2) Develop hydrologic model (Vflo) for the Mayagüez Bay drainage basin
A hydrologic model has been configured for the Mayaguez Bay drainage basin and could
theoretically be used with Hydro Estimator Nowcast data. However, the Mayaguez Bay drainage
basin model is not yet calibrated. Before the regional scale model is calibrated, a smaller testbed
subwatershed (TBSW) model will be developed. The TBSW is located within the GOES-12 study
pixel. After the high resolution (10 m grid spacing) TBSW model has been calibrated, an
upscaling process will be applied to determine the maximum grid spacing that can be used which
will provide accurate results. This optimal grid spacing will then be used in the regional scale
model and a calibration performed using stream flow data from the Añasco and Guanajibo. The
research described is part of a Ph.D. research project through the Department of Civil Engineering
(Funded by NSF, not NOAA-CREST).
Task (3) Develop algorithms for hydrologic model to assimilate the real-time satellite QPE
This task is actually the same as Task (1), therefore, please refer to sub-task 1. In future reports this
sub-task should be dropped.
7
Future Tasks (From the Milestones) (provide a brief narrative and reason for earlier start)
Project 2
Task 3 Validate NESDIS HE & GMSRA Rainfall Algorithms for Puerto Rico
Validation of the current version of HE has been completed.
Task 4 Develop a Validation Algorithm
The validation algorithm has been completed and was used to validate the current version of the
HE. The algorithm will continue to be improved in the future as necessary.
Task 5 Improve NESDIS Rainfall Algorithm
This task is well underway. This task was started early because the problem with the current
version of the HE was identified within the first year and a half of the NOAA CREST research.
Task 6 Validate NESDIS-SCaMPR Model over the US and Puerto Rico
The NESDIS-SCaMPR model will not be validated for Puerto Rico since this algorithm is limited
to perform rainfall estimation above latitude 20oN or above. The second reason was because our
NESDIS advisor suggested we invest more time validating and improving the HE since this is a
NOAA/NESDIS operational algorithm, and since the HE estimates of rainfall are very poor in the
Caribbean region.
Project 3
Task 1 Modify a Hydrological Model by coupling with a Satellite-based Rainfall Retrieval
Algorithm
During the next reporting period we will begin investigating the Nowcaster software and the
requirements for coupling the hydrologic model Vflo.
Task 2 Develop hydrologic model (Vflo) for the Mayagüez Bay drainage basin
A preliminary calibration of the Mayaguez Drainage Basin model is almost complete. However,
the more complex up-scaling calibration approach will probably take until next June.
Task 3 Develop algorithms for hydrologic model to assimilate the real-time satellite QPE
This task is actually the same as Task (1), therefore, please refer to that task. In future reports this
task should be dropped.
Task 4 Validate results of Hydrologic Model for Real Time
Although this task is scheduled to start during the next reporting period. It will not be possible to
validate the results of the real-time hydrologic model since it does not yet exist.
The principal cause for the delay in these tasks is that no NOAA CREST funds have been provided
to do the work.
New Tasks (NOT in the milestones) (provide a brief narrative and justify the deviation)
We plan to exploit information from the GOES product to estimate evapotranspiration (ET) over
Puerto Rico. Rainfall is only one aspect of “Hydro-Climate” and, therefore, we wish to broaden its
definition with regard to the NOAA CREST research. The ability to estimate ET will be a
8
valuable step towards estimating the complete island water budget at a high temporal and spatial
scale. A short proposal for this work is presented in Appendix 4.
9
Appendix 1
Leverage Funds (During the Reporting Period – March 1, 2008-August 31, 2008)
Project Title
Sponsoring
Agency
PI/Recipient/Group
NASAGSFC
Eric Harmsen/UPRRioPiedras
Dollarsi
Total
amount
(amount
Start
Date
End Date
$20,000
Sep 1,
2008
Feb 29,
2009
$6,000
Oct 1,
2007
Sep 30,
2008
this period)
Rapid Detection of
Soils and Drinking
Water Sources
Impacted by Salt Water
Flooding.
Collaberative Adaptive
Sensing of the
Atmosphere Puerto
Rico Student Testbed
L. Roytman, CUNY
NSF
Sandra Cruz
Pol/UPRM/NSF
CASA Project
10
11
Appendix 2
Rainfall Estimation from Convective Storms Using the HydroEstimator and NEXRAD
Nazario D. Ramirez-Beltran1, Robert J. Kuligowski2, Eric W. Harmsen3, Joan M. Castro4, Sandra Cruz-Pol4, and Melvin J. Cardona4
1
Department of Industrial Engineering, University of Puerto Rico, P.O. Box 9030, Mayagüez, PR 00681, U.S.A,
nazario@ece.uprm.edu
2
NOAA/NESDIS Center for Satellite Applications and Research (STAR), Camp Springs, MD 20746, U.S.A.
Bob.Kuligowski@noaa.gov
3
Department of Agricultural and Biosystems Engineering, University of Puerto Rico, P.O. Box 9030, Mayagüez, PR 00681, U.S.A.,
eharmsen@uprm.edu
4
Department of Computer and Electrical Engineering, University of Puerto Rico, P.O. Box 9040, Mayagüez, PR 00681, U.S.A,
joanmanuelcastro@yahoo.com, SandraCruzPol@ieee.org, cardonam@gmail.com
Abstract - Validation of the Hydro-Estimator (HE) and the Next Generation Radar (NEXRAD) during heavy storms over
Puerto Rico (PR) is reported. The HE is a high resolution rainfall retrieval algorithm based on satellite and numerical
whether prediction model data. The accuracy of the HE and the NEXRAD rainfall estimates can be measured by
decomposing the rainfall process into sequences of discrete (rain / no rain) and continuous (rainfall rate) random variables.
Validation results are based on five heavy storms that seriously impacted human life and the economy of PR during the
period 2003 to 2005. The average discrete validation results indicate acceptable hit rate values for both the HE and
NEXRAD (0.76 vs. 0.87) and reasonable discrete bias ratios (1.04 vs. 0.73) but a very low of probability of detection of
rain for both the HE and NEXRAD (0.36 vs. 0.52). The HE shows an overestimation on average whereas the NEXRAD
exhibits underestimation in the continuous validation results (continuous bias ratio of 1.14 vs 0.70 for NEXRAD), which
contributes to moderate overall errors for the HE and NEXRAD in terms of root mean squared error (2.14 mm vs. 1.66
mm) and mean absolute error (0.96 mm vs. 0.77 mm).
The HE algorithm was designed to operate over US continental areas and satisfactory results have been reported
in those regions. However, over tropical regions it was determined that warm clouds can generate substantial rainfall
amounts that are not detected by the HE algorithm. Infrared band differencing techniques are being used to explore the
possibility of improving the detection of warm-cloud rain events over PR. We are also classifying clouds based on
Geostationary Operational Environmental Satellite (GOES) Imager data in a manner that will lead to improved
relationships between infrared brightness temperatures and rainfall rates.
Key-words - validation, NEXRAD, Hydro-Estimator, retrieval algorithm, rain rate, GOES, brightness temperature.
11
1. Introduction
Estimation of rainfall amounts is critical for
protecting human lives and infrastructure,
particularly in the case of heavy rainfall that
triggers flash floods or landslides. In Puerto
Rico (PR) during 2003 to 2005, five severe
storms seriously impacted human lives and the
economy. PR has extremely diverse terrain,
and during the rainy season severe rainstorms
can develop due to complex orographic
attributes. Easterly winds come from the
eastern Atlantic almost all year and play an
important role in bringing humidity into the
island and stimulating orographic rainfall over
the mountains of PR. Cold fronts dominate
the weather pattern during wintertime.
Tropical waves occur during the rainy season
and frequently generate large amounts of
rainfall in the Caribbean basin. These tropical
waves are typically the precursor of tropical
storms and hurricanes from June to November.
For these types of events, estimates of
rainfall from instruments on geostationary
platforms such as the Geostationary
Operational Environmental Satellite (GOES)
are preferred over microwave-based estimates
of rainfall from Low-Earth-Orbiting (LEO)
platforms because of the rapid refresh (every
15 minutes) over the Continental United States
(CONUS) and nearby regions and very short
data latency times of GOES data relative to
low-Earth orbit data. Numerous algorithms
have been developed to estimate precipitation
from GOES-based satellite data. The current
generation of algorithms produced at the
National
Oceanic
and
Atmospheric
Administration
(NOAA)
National
Environmental Satellite, Data and Information
Service (NESDIS) are the Hydro-Estimator
(HE, [1]), GOES Multi-Spectral Rainfall
Algorithm (GMSRA, [2]), and the SelfCalibrating
Multivariate
Precipitation
Retrieval (SCaMPR, [3]). The HE relies on
GOES data from the infrared (IR) window
channel (10.7 µm) with a fixed relationship to
rainfall rates; similarly, Palmeira et al. [4]
presented a self-consistent algorithm for
rainfall estimation based on GOES data plus
lightning data in Brazil. The GMSRA uses
additional data from three other GOES
channels and updates its calibration in real
time based on matches with radar rain rates.
SCaMPR calibrates GOES IR parameters
against passive microwave rain rates, which is
an approach similar to Kidd et al. [5] and the
Precipitation Estimation from Remotely
Sensed Information using Artificial Neural
Network (PERSIANN, [6]) algorithm.
PERSIANN uses
a combination of
geostationary IR and Tropical Rainfall
Measuring Mission (TRMM) microwave
information to estimate rainfall rate in an
hourly basis at spatial resolution of 0.25o.
Another algorithm called the CPC Morphing
Algorithm (CMORPH, [7]) also combines IR
data and microwave rain rates, but uses the IR
data as the basis for interpolating the
microwave rain rates in time between lowEarth orbit satellite overpasses.
The HE, which will be the focus of
this paper, also uses information from
numerical whether prediction models to
estimate rain rate [1]. Rainfall rates are
adjusted upward or downward for moist or dry
environments as indicated by National Centers
for Environmental Prediction (NCEP) North
American Model (NAM) or Global Forecast
System (GFS) total column precipitable water
and mean-layer relative humidity for the
lowest third of the model vertical domain.
Another adjustment enhances rainfall rates in
regions where the convective equilibrium level
temperature is relatively high; i.e., regions
where very cold cloud tops are not
thermodynamically possible but where strong
updrafts and heavy rainfall can still occur.
Finally, low-level winds and digital
topography are combined to produce
enhancements of rainfall rates in upslope
regions and reductions in downslope regions,
using a technique described in Vicente et al.
[8].
The HE has been the operational
satellite rainfall algorithm of the National
Environmental Satellite, Data, and Information
Service (NESDIS) since 2002 and produces
rainfall estimates at the full spatial and
temporal resolution of GOES over the CONUS
and surrounding regions, including PR; realtime estimates are also produced on an
experimental basis for the rest of the globe.
However, validation of the Hydro-Estimator
has generally focused on the CONUS (e.g., [1]
and [9]) and has not been performed over
Puerto Rico, and given the differences in
13
topography and climate of Puerto Rico relative
to the CONUS, previous validation efforts
may not necessarily be relevant to users in PR.
Furthermore, validation of the HE over PR
may illuminate opportunities to enhance the
algorithm for application over PR.
match these data with HE and NEXRAD data
at 15-minute resolution for validation. The
data set used for validation includes five heavy
storms that have been impacted PR: Three can
be characterized as a cold front and two as
tropical storms.
Validation of the rainfall retrieval
algorithm consists of comparing the rainfall
estimates with corresponding observations
(rain gauges in this study). The accuracy of
rainfall estimates can be measured by
decomposing the rainfall process into
sequences of discrete and continuous random
variables; i.e., the presence or absence of
rainfall events (discrete variable) and the
amount of rainfall (continuous variable). The
occurrence of rainfall events in a given area
and at a particular time follows a Bernoulli
process and consequently the estimation
accuracy of rainfall events can be conducted
by analyzing a contingency table. The typical
scores that measure the accuracy of categorical
forecasts are: hit rate (H), probability of
detection (POD), false-alarm rate (FAR), and
discrete bias (DB). The continuous validation
strategy focuses on the amount of rainfall that
occurred at specific area in a particular time
and the continuous measurements of accuracy
are mean absolute error (MAE), root mean
squared error (RMSE), and continuous bias
(CB).
NEXRAD data over Puerto Rico come
from a WSR-88D unit located in Cayey
(18.12°N, 66.08°W, 886.63 m elevation). The
radar frequency is 2.7 GHz and the maximum
horizontal range is 462.5 km, and the radar
scans the entire island every 6 minutes. The
NOAA National Severe Storms Laboratory
(NSSL) conducted a significant effort to make
possible an affordable nationwide operational
capture, distribution, and archive of Level II
NEXRAD data [10]. Unfortunately, for Puerto
Rico the Level II data are available only until
2003 with a significant amount of missing data
in that last year [11]. The NWS did resume
archiving level II data for PR during the
summer of 2007. On the other hand, Level III
data for PR are available continuously since
2000 [12], so the Level III data were selected
to perform validation since the most recent and
catastrophic floods over PR occurred after
2002. The scanning angle for reflectivity data
was selected as 0.5 degrees for this research in
order to avoid beam overshoot over western
PR. Fig. 1 shows the location of the radar and
the spatial distribution of the rain gauges.
The second section of this paper
describes the data collection process and
sources of information. The third section
describes
the
conventional
statistical
techniques used to perform validation. The
fourth section presents validation results
during heavy storms over PR, and includes a
comparison for rain gauges versus HE and rain
gauges versus NEXRAD. The fifth section
outlines some strategies for algorithm
improvements. The sixth section presents
some conclusions.
As mentioned in the Introduction, the
HE uses satellite IR window (10.7-µm) data
and numerical whether prediction data to
estimate rainfall over the CONUS and PR
every 15 minutes at 4 km spatial resolution,
and they are available for the entire period of
interest. In order to ensure consistency among
these data sets during the comparison, both the
NEXRAD and HE rain rates were aggregated
in time over the corresponding 15-minute
accumulation period of the gauges.
2. Data collection
Puerto Rico has a rain gauge network that
collects rainfall measurements every 5, 10, 15,
30 or 45 minutes and includes 125 rain gauges
with data available since January 2000. Since
the majority of gauges collect rainfall every 15
minutes a computer program was designed to
FIG. 1. Location of rain gauges (red stars) and
13
14
NEXRAD (black dot) in PR.
POD 
a
ac
(2)
FAR 
b
ab
(3)
DB 
ab
ac
(4)
3. Validation techniques
Validation of the rainfall retrieval algorithm
consists of comparing the rainfall estimates
with observations over the same time and
space. The accuracy of rainfall estimates can
be measured by decomposing the rainfall
process into sequences of discrete and
continuous random variables; i.e., the presence
or absence of rainfall events and the amounts
of rainfall. The occurrence of rainfall events
in a given area and at a particular time follows
a Bernoulli process and consequently the
estimation accuracy of rainfall events can be
conducted by analyzing contingency tables
and the bivariate probability distribution of
rainfall events [13]. Table 1 shows the
classical two-way contingency table.
It is assumed that the values provided
by the rain gauges are the “ground truth” while
the HE and the NEXRAD provide estimated
rainfall values.
The variable a in the
contingency table is the number of times that
the rain gauge identifies a rainfall event and
the estimator also correctly identifies a rainfall
event at the same time and location. The
variable d represents the number of times the
rain gauge does not observe a rainfall event
and the estimator correctly determines that
there is no rainfall event. The variable b
indicates the number of times the rain gauge
does not observe a rainfall event but the
estimator incorrectly indicates that there is a
rainfall event. The variable c shows the
number of times that the rain gauge detects a
rainfall event but the estimator incorrectly
does not detect the rainfall event.
where H is the hit rate, POD is the probability
of detection, FAR is the false-alarm rate, and
DB is the discrete bias. Hit rate is the fraction
of the no estimating occasions when the
categorical estimation correctly determines the
occurrence of rainfall event or nonevent.
Probability of detection is the likelihood that
the event would be estimated, given that it
occurred.
The false-alarm rate is the
proportion of estimated rainfall events that fail
to materialize. Bias is the ratio of the number
of estimated rainfall events to the number of
observed events [13].
The continuous validation strategy
consists of comparing the amount of rainfall
that occurred with the estimated amount of
rainfall at specific area in a particular time and
the continuous accuracy scores used here are:
eij  yij  yˆ ij i  1,, n and j  1,  , m (5)
MAE 
H
ad
, where no  a  b  c  d (1)
no
1 n m 2
 ei
n m i 1 j 1
RMSE 
TABLE 1. Sample contingency table.
Observed rainfall
(Rain gauge)
Yes
No
Estimated rainfall
Yes
a
b
(HE or NEXRAD)
No
c
d
The typical scores that measure the
accuracy of categorical estimation are:
1 n m
 eij
n m i 1 j 1
n
CB 
(6)
(7)
m
  yˆ ij
i 1 j 1
n m
  yij
(8)
i 1 j 1
where y and ŷ are the observed and estimated
amount of rainfall. The i and j subscripts
represent time and space, respectively. The
constant n is the total number of time intervals
for a given storm, and m is the number of rain
gauges that are collecting rain during a storm.
14
15
The error e is the deviation between the
observed and estimated amount of rainfall at a
particular time and space and is computed only
when at least one of y or ŷ is greater than zero.
MAE is the mean absolute error, RMSE the
root mean squared error, and CB is the
continuous bias.
4.2 Continuous validation
The accumulated rainfall across the island was
computed to compare the observed and the
estimated rainfall:
(9)
4. Validation results
4.1 Discrete validation
A contingency table was computed for each
rain gauge during a given storm and the scores
of those tables were summarized to create
contingency tables for each storm for the HE
and NEXRAD. These are shown in Tables 2a)
and 2b) while the associated scores are given
in Tables 3a) and 3b). The HE significantly
underestimates the number of raining pixels in
the three April-May events (DB of 0.49 to
0.52) but strongly overestimates the
November-December events (DB of 1.54 and
2.15). The physical reasons behind this
apparent strong seasonal variation in DB are
not known at this time. Meanwhile, the
NEXRAD had a consistent dry bias (0.620.68) for the last four events but virtually no
bias (1.02) for the first; again, it is not clear at
this time what led to such a significant
difference. The hit rates of the HE range from
0.62 to 0.91 with an average of 0.76 and
NEXRAD has a range from 0.82 to 0.95 with
average of 0.87. Although, both HE and
NEXRAD exhibit relatively high hit rate, the
HE has a lower percentage of correct rain / no
rain estimates than does the NEXRAD. The
probability of detection of the HE ranges from
0.14 to 0.57 with an average value of 0.36,
whereas, the NEXRAD shows a range from
0.4 to 0.74 with an average of 0.52. Thus, the
HE correctly detected a smaller percentage of
the observed rainfall events (36%) than did
NEXRAD (52%) for these events. The false
alarm rate for the HE varies between 0.39 to
0.73 with an average value of 0.61, meanwhile
the NEXRAD varies from 0.25 to 0.35 with an
average of 0.29. Thus, the false alarm rate was
actually higher for the HE (61%) than for
NEXRAD (29%).
Overall, the discrete
validation shows that the NEXRAD
outperforms the HE in terms of correct rain /
no rain estimates.
where Yi is the total rainfall recorded by all
125 rain gauges across the island or the closest
HE or radar pixels at the i th time.
TABLE 2a. Contingency tables for the HydroEstimator.
17 April 2003
Hydro-Estimator
Yes
No
Rain Gauge
Yes
No
1105
699
2603
6708
Yes
No
Rain Gauge
Yes
No
331
875
2000
30022
19-21 May, 2003
Hydro-Estimator
11-18 November, 2003
Hydro-Estimator
Yes
No
Rain Gauge
Yes
No
10430 18719
8465
47913
Yes
No
Rain Gauge
Yes
No
4882
13224
3538
23167
5 December 2003
Hydro-Estimator
20 April 2005
Hydro-Estimator
Yes
No
Rain Gauge
Yes
No
310
395
1039
8522
TABLE 2b. Contingency tables for NEXRAD.
17 April 2003
NEXRAD
Yes
No
Rain Gauge
Yes
No
2713
951
1023
6311
Yes
No
Rain Gauge
Yes
No
1177
1149
399
30386
19-21 May, 2003
NEXRAD
15
16
Yes
No
Rain Gauge
Yes
No
8922
9967
3620
62901
apparent seasonal pattern like the HE. As a
result, both the mean absolute error and root
mean squared error of the HE are also higher
than that of NEXRAD.
Yes
No
Rain Gauge
Yes
No
3392
5026
1814
34462
TABLE 4a. Continuous validation scores for
the Hydro-Estimator.
17 19-21 11-18 5
20
Apr. May Nov. Dec. Apr.
2003 2003 2003 2003 2005
CB
0.26 0.23 1.68 2.42 0.16
MAE (mm) 1.33 0.74 1.10 0.86 0.79
RMSE (mm) 2.73 2.10 2.24 1.93 1.71
11-18 November 2003
NEXRAD
5 December 2003
NEXRAD
20 April 2005
Rain Gauge
Yes
No
NEXRAD
Yes
655
670
No
240
8583
TABLE 3a. Discrete validation scores for the
Hydro-Estimator.
17
Apr.
2003
DB
HR
POD
FAR
0.49
0.70
0.30
0.39
19115
20
21
18
Dec. Apr. Avg.
May Nov.
2003 2005
2003 2003
0.52 1.54 2.15 0.52 1.04
0.91 0.68 0.62 0.86 0.76
0.14 0.55 0.57 0.23 0.36
0.72 0.64 0.73 0.56 0.61
TABLE 3b. Discrete validation scores for the
NEXRAD.
17
Apr.
2003
DB
HR
POD
FAR
1.02
0.82
0.74
0.27
19115
20
21
18
Dec. Apr. Avg.
May Nov.
2003 2005
2003 2003
0.68 0.66 0.62 0.67 0.73
0.95 0.84 0.85 0.91 0.87
0.51 0.47 0.40 0.49 0.52
0.25 0.29 0.35 0.27 0.29
Tables 4a) and 4b) show the
continuous validation scores for HE and
NEXRAD, respectively. The continuous bias
of the HE is even more seasonally variable
than the DB, with values ranging from 0.160.26 for the April-May storms and 1.68-2.42
for the November-December events. The
lower CB relative to the DB for the April-May
storms suggests that the HE is underestimating
the conditional rainfall rates in addition to the
spatial extent of the rainfall, while the opposite
is happening for the November-December
events.
The NEXRAD has nearly no
continuous bias for two storms and a strong
dry bias for three (0.41-0.68), albeit with no
Avg.
0.95
0.96
2.14
TABLE 4b. Continuous validation scores for
NEXRAD.
17
Apr.
2003
CB
1.02
MAE (mm) 1.02
RMSE (mm) 1.91
19-21
May,
2003
0.68
0.66
1.79
11-18
Nov.
2003
0.41
0.85
1.78
5
Dec.
2003
0.42
0.53
1.15
20
Apr.
2005
1.01
0.80
1.68
5. NEXRAD bias
Radar measurements over the western part of
PR are frequently inaccurate. This is because
reflectivity measurements are conducted at
about 2000m above the surface as a result of
the elevated location of the radar and a
relatively high scan angle which was selected
to minimize beam block by nearby mountains.
In order to estimate the NEXRAD bias, the
following validation exercise was conducted.
PR was divided in three zones. The first zone
includes the rain gauges that are located in a
radius of equal or less that 35km, the second
region includes stations that are in the radii
that is larger than 35km but equal and smaller
than 90km, and the third region consists of
stations at a range larger than 90km from the
location of the NEXRAD. Figure 2 shows the
study zones, which were designed to provide
an appropriate sample size to derive reliable
statistics.
FIG. 2. Location of rain gauges (stars) and
16
Avg.
0.71
0.77
1.66
17
NEXRAD (black dot on Region I) in PR.
Black dots in Region III are small and high
resolution radar that will be used to derive the
bias correction factor for NEXRAD. The radii
of the circles are 35 km and 90 km.
Probability
of
detection
False
alarm rate
An unnamed tropical storm, which
becomes stationary over the PR area during
November 11-18, 2003, was studied to
determine the NEXRAD bias over the
designed zones. The continuous red lines in
Figures 3a, 3b and 3c show the cumulative
rainfall recorded every 15 minutes by all
gauges of PR rain-gauge network.
The
horizontal axis shows the Julian day and the
vertical
axis
shows the
15-minutes
accumulated rainfall in mm. The blue line
represents the 15-minutes accumulative
rainfall recorded by the radar pixel that is the
closest to each rain gauge. The difference
between the red and blue lines represents the
estimation error of the accumulative rainfall.
Figures 3a and 3b show reasonable rainfall
estimation by the radar. However, Figure 3c
shows that the NEXRAD exhibits a significant
underestimation in Region III.
The
corresponding scatter plots in Figures 4a, 4b,
and 4c show the actual rainfall amount
recorded by the individual gauges versus the
estimates from the radar pixels. These figures
also confirm that although Region III generally
experiences lighter rainfall events than in the
other two regions, the NEXRAD bias is largest
in this region.
TABLE 5b. Comparison of NEXRAD
performance
Region I
Region II
Region III
(0-35 km
(35-90 km
(>90km from
from
from
NEXRAD)
NEXRAD)
NEXRAD)
MAE
0.92mm
1.07mm
1.06mm
RMSE
1.76mm
2.07mm
2.18mm
CB
0.45
0.35
0.37
0.50
0.46
0.37
0.32
0.27
0.29
RG and N1P Cumulated Rainfall
140
Rain Gauges
N1P
120
100
mm
80
60
40
20
0
315.0417
316.0417
317.0417
318.0417
319.0417
time (julian days)
320.0417
321.0417
322.0417
FIG. 3a. Cumulative rainfall during November
11-18, 2003, over Region I.
RG and N1P Cumulated Rainfall
200
Rain Gauges
N1P
180
160
140
120
mm
Table 5 shows that the probability of
detection increases with distance from the
NEXRAD. Figures 3a, 3b and 3c show that
the NEXRAD exhibits underestimation in the
three regions; however, the underestimation is
larger in Region III. Table 5 shows that the
bias ratio become smaller, which indicates that
the estimation error becomes worse for larger
distances between the station and radar.
100
80
60
40
TABLE 5a. Discrete comparison of NEXRAD
performance for each region.
20
0
315.0417
Discrete
bias
Hit rate
Region I
Region II
Region III
(0-35 km
(35-90 km
(>90km
from
from
from
NEXRAD) NEXRAD) NEXRAD)
0.74
0.64
0.46
0.83
0.83
316.0417
317.0417
318.0417
319.0417
time (julian days)
320.0417
321.0417
322.0417
FIG. 3b. Cumulative rainfall during November
11-18, 2003 for Region II.
0.80
17
18
RG and N1P Cumulated Rainfall
60
Rain Gauges
N1P
FIG. 4b. Scatter diagram for rain gauges and
NEXRAD pixels during November 11-18,
2003 for Region II.
50
mm
40
30
20
10
0
315.0417
316.0417
317.0417
318.0417
319.0417
time (julian days)
320.0417
321.0417
322.0417
FIG. 3c. Cumulative rainfall during November
11-18, 2003 for Region III.
FIG. 4c. Scatter diagram for rain gauges and
NEXRAD pixels during November 11-18,
2003 for Region III.
6. Improvement Algorithms
6.1 Rainfall detection
FIG. 4a. Scatter diagram for rain gauges and
NEXRAD pixels during November 11-18,
2003 for Region I.
As stated previously, the HE uses GOES
brightness temperatures (Tb) from channel 4
(10.7 µm) to discriminate raining from nonraining events [1]. During the validation
exercise we noted that there are some warmtop convective events that are not detected by
the HE. The HE generally produces little or
no rainfall for brightness temperatures
exceeding 235K; however, there are numerous
events in PR where rainfall was in fact
observed at these temperatures. For instance,
Fig. 5 shows the observed accumulated rainfall
for all gauges located in PR (red line) and the
accumulated rainfall by the corresponding HE
pixels (blue line) on November 14, 2006. The
horizontal axes shows the time every 15
minutes and the vertical axis exhibits the
accumulated rainfall in mm. Fig. 6 shows the
distribution of brightness temperatures over
the GOES pixels corresponding to gauge
locations during this storm and there are few
pixels below 235 K; a comparison with Fig. 5
indicates that the poor detection by the HE was
at least in part because it was not calibrated to
produce rainfall from relatively warm clouds.
In order to improve the detection skill of the
HE, we plan to examine the differences in
brightness temperature between 10.7 µm and
18
19
the water vapor band (6.5 µm in GOES).
Positive values of the WV-infrared window
temperature difference have been shown to
correspond with convective cloud tops that are
above the tropopause (i.e. overshooting tops),
([14 and [15]).
Convective clouds with
positive differences indicate the possibility of
warm-top convection.
90
80
particles grow to larger sizes. It has been
shown that the uses of the reflected portion of
the near-IR during the daytime indicates the
presence large cloud-top particles and suggest
rain in warm-top clouds. [16] Rosenfeld and
Gutman (1994) and [17] Lensky and
Rosenfeld (1997) used the effective radius of
clouds particles derived from the AVHRR
3.75-µm window channel to detect warm
raining clouds. This concept was also applied
RG and HE Cumulated Rainfall
to rainfall estimation from GOES data in the
Rain Gauges
GMSRA [2].
Hydroestimator
Preliminary work was conducted to
explore improving the HE warm rainy-cloud
detection using the GOES band 2 (3.9 µm)
reflectance during the daytime. This will be
used as a proxy for cloud-top particle size to
identify any correlation with the presence or
absence of rain from warm-topped clouds over
PR. In this work we presente the estimation of
daytime reflectance of band 2.
70
60
mm
50
40
30
20
10
0
318.0104
318.2604
318.5104
time (hours UTC)
318.7604
FIG. 5. Comparison between observed and
estimated accumulated rainfall (Nov. 14,
2006).
It is assumed that during the daytimes
the total radiance measured by GOES band 2
(3.9 µm) is composed by the sum of emitted
radiances and the reflected radiances.
,
(10)
where T3.9,d is the total radiance during the
day, E3.9,d is the emitted radiance, and R3.9,d is
the reflected radiance of band 2 during the
day. However during the night since the sun is
not present the total radiance is equal to the
emitted radiances, as shown as follows:
,
FIG. 6. GOES-12 brightness temperature from
channel 4 (Nov. 14, 2006).
It is known that precipitation
processes in clouds with warm tops are very
sensitive to the microphysical structure of their
tops. Specifically, precipitation processes are
more efficient when water droplets or/and ice
(11)
An empirical equation can be developed to
estimate the emittance measured by band 2.
The emittance during the night it is assumed to
be a function of the radiance measured by
bands 3 (6.9 µm) and band 4 (10.7 µm ). The
general relationship may be expressed as
follows:
,
(12)
where E3.9 is the emittance of band 2, T6.9 is the
total radiance of band 3, and T10.7 is the total
radiance of band 4. A linear relationship was
assumed first and the performance of the
19
20
model will indicate whether or not a linear
model is appropriate. Thus, the postulated
model is as follows:
,
(13)
where Ê3.9,n is the estimated emittance of band
2 during the night, T6.9,n is the total radiance of
band 3, and T10.7,n is the total radiance of band
4 during the night, and the â’s are the
parameters of the linear equation.
The parameters were estimated using a
severe rainfall event that occurred on October
27-30, 2007. The data set was divided in two
parts: the first part (October 27-28) was used
to estimate the parameters and the second part
(October 29-30) for validation. The parameter
estimation results are summarized in Table 6.
Table 6. Parameter estimation
Parameter
Figure 7 Observed emittance of band 2 for a
nighttime image.
Estimate
-0.69348
0.083468
0.024352
The second part of the data was used to
perform validation. The mean absolute error
(MAE) and the coefficient of multiple
determination (R2) were computed to measure
the accuracy of equation (13) and were found
to be MAE=0.0389 mW/(m2–sr-cm-1) and
R2=0.92. A quadratic model was also fitted to
measure if a significant improvement can be
obtained.
However, the quadratic model
provides R2=0.93, and consequently, these
results show that the selected linear model
sufficiently
represents
the
estimated
reflectance.
Figures 7 and 8 show a
comparison between the observed and
estimated reflectance during the daytime.
Figure 8. Estimated emittance of band 2 for
the same image as in Figure 7.
Assuming that equation (13) also
holds during the daytime, the emittance of
band 2 can be estimated as follow:
(14)
where the subscript d refers to variables
observed during the daytimes and the
20
21
regression coefficients are obtained from
equation (13). Figure 9 shows the estimated
emittance which will be subtracted from the
observed radiance during daytime of band 2
and compared to corresponding rain / no rain
areas to determine its usefulness in
discriminating raining areas in relatively warm
clouds.
Figure 10 shows the observed
reflectivity (converted to rainfall rates) for the
same rainfall event.
Figure 10. Estimated rainfall from NEXRAD.
6.2 Improving rain rate estimates
Figure 9 Estimated emittance of band 2 during
the day
The rainfall retrieval procedure of the HE is
also mainly based on the relationship between
the brightness temperature (10.7 µm) and
observed rain rate. Estimation of the amount
of rainfall may be improved by classifying the
brightness temperature patterns (BTP) with the
corresponding rain formation processes. The
following channels will be used to classify the
BTP with the corresponding rain process.
Channel 1 (0.65 µm) will be used to classify
the events according to the cloud optical
thickness. The reflected portion of channel 2
(3.9 µm) during the daytime will be used as an
indirect measurement of the cloud drop size
distribution, thermodynamic phase, and
particle shape [16]. Channel 4 (10.7 µm) will
be used to classify the rainfall events
according to temperature.
Brightness
temperature differences will also be used to
develop the classification algorithm: The
difference between the 10.7-µm and 3.9-µm
brightness temperatures will be useful to
determine whether a cloud top is composed of
21
22
liquid water or ice. As stated previously, the
IR-WV difference (6.5–10.7 µm) is usually
negative; however, convective clouds with
positive differences have likely already begun
to precipitate, especially in tropical
atmospheres that support warm top
convection. The 13.3–10.7 µm differencing
technique is used to characterize and delineate
cumulus clouds. This research will focus on
convective clouds, and consequently, the
factors to be consider for the classification of
BTP and rain types are: area, depth, duration,
and updraft velocity.
events and the amounts of rainfall, whereas
NEXRAD is nearly unbiased in these respects.
The HE algorithm does exhibit a satisfactory
hit rate, but a very low probability of detection
and a large false alarm rate that is surprisingly
higher than that of NEXRAD despite the dry
bias of the HE. A research effort is undergone
to improve the performance of the HE for PR;
specifically, the algorithm proposed by
Ramirez-Beltran et al. [17] will be
implemented to improve the HE rainfall
detection and the equation that relates
brightness temperatures with rain rates.
A variable selection algorithm will be
used to identify the variables that best explain
rainfall variability. Thehe selected variables
will be used to develop training patterns for a
self-organized artificial neural network [17]
which will be used to identify a set of
homogenous groups that reveal similarities
within the member of a class, but different
among the classes. The Kohonen learning rule
will be used to determine the optimal weights
of the artificial neural network ([18], [19], and
[20]). A successful application was reported
[21] to identify the spatial variability of soil to
select the appropriate model to estimate soil
moisture.
8
Acknowledgements.
This research has been supported by NOAACREST grant number NA17AE1625, the NSFERC-CASA with a grant Number 0313747,
NOAA-NWS
grant
number
NA06NWS468001, and also by the University
of Puerto Rico at Mayagüez. The authors
appreciate and recognize the funding support
from these institutions. Pedro L. Diaz director
of PR-US Geological Survey provided the
rainfall data from the PR rain-gauge network;
we want to appreciate his invaluable
contribution.
References
7 Summary and conclusions
The HE is a high resolution satellite rainfall
retrieval algorithm run operationally by
NOAA/NESDIS that provides estimates of
rainfall every 15 minutes at 4-km resolution
over the CONUS and nearby areas including
PR. (Global estimates are also produced in
real time on an experimental basis.) The rain
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using parameters derived from a numerical
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events were located in the central and eastern
parts of the island where the radar data will be
most reliable.
Specifically, the HE
underestimates both the number of rainfall
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[20] Ramirez-Beltran, N.D., and A. Veneros
2004: Upper air information and
neural networks to estimate hurricane
intensity. Preprints, 26th Conference
on
Hurricanes
and
Tropical
Meteorology. Miami FL.
[21] Ramírez Beltran, N.D, J. M. Castro., E.
Harmsen, and R. Vasquez. 2008:
Stochastic transfer function models
and neural networks to estimate soil
moisture. J. of the Amer. Water
Resources Assoc. in press.
23
24
APPENDIX 2
Satellite Sub-Pixel Rainfall Variability
ERIC W. HARMSEN1
SANTA ELIZABETH GOMEZ MESA2
EDVIER CABASSA3
NAZARIO D. RAMÍREZ-BELTRAN4
SANDRA CRUZ POL5
ROBERT J. KULIGOWSKI6
RAMÓN VASQUEZ7
1
Department of Agricultural and Biosystems Engineering, University of Puerto Rico
P.O. Box 9030, Mayagüez, PR 00681,
U.S.A.
eharmsen@uprm.edu
2
Department of Mathematics, University of Puerto Rico,
P.O. Box 9030, Mayagüez, PR 00681,
U.S.A.
santagm3@gmail.com
3
Department of Computer and Electrical Engineering, University of Puerto Rico
P.O. Box 9040, Mayagüez, PR 00681,
U.S.A
ecabassa@gmail.com
4
Department of Industrial Engineering, University of Puerto Rico
P.O. Box 9030, Mayagüez, PR 00681,
U.S.A
nazario@ece.uprm.edu
5
Department of Computer and Electrical Engineering, University of Puerto Rico,
P.O. Box 9040, Mayagüez, PR 00681,
U.S.A
SandraCruzPol@ieee.org
6
NOAA/NESDIS Center for Satellite Applications and Research (STAR)
5200 Auth Rd., Camp Springs, MD 20746-4304
U.S.A.
Bob.Kuligowski@noaa.gov
7
Department of Computer and Electrical Engineering, University of Puerto Rico
P.O. Box 9040, Mayagüez, PR 00681,
U.S.A
reve@ece.uprm.edu
24
25
Abstract: - Rain gauge networks are used to calibrate and validate quantitative precipitation estimation (QPE) methods
based on remote sensing, which may be used as data sources for hydrologic models. The typical approach is to adjust
(calibrate) or compare (validate) the rainfall in the QPE pixel with the rain gauge located within the pixel. The QPE
result represents a mean rainfall over the pixel area, whereas the rainfall from the gauge represents a point, although it
is normally assumed to represent some area. In most cases the QPE pixel area is millions of square meter in size. We
hypothesize that some rain gauge networks in environments similar to this study (i.e., tropical coastal), which provide
only one rain gauge per remote sensing pixel, may lead to error when used to calibrate/validate QPE methods, and that
consequently these errors may be propagated throughout hydrologic models. The objective of this paper is to describe
a ground-truth rain gauge network located in western Puerto Rico which will be available to test our hypothesis. In
this paper we discuss observations from the rain gauge network, but do not present any QPE validation results. In
addition to being valuable for validating satellite and radar QPE data, the rain gauge network is being used to test and
calibrate atmospheric simulation models and to gain a better understanding of the sea breeze effect and its influence on
rainfall.
In this study, a large number of storms (> 60) were evaluated between August 2006 and August 2008. The
area covered by the rain gauge network was limited to a single GOES-12 pixel (4 km x 4 km). Five-minute and total
storm rainfall amounts were spatially variable at the sub-pixel scale. The average storm rainfall from 20% of the 120
possible rain gauge-pairs was found to be significantly different at the 5% of significance level, indicating significant
rainfall variation at the sub-pixel scale. The average coefficient of determination (r2), describing the goodness of fit of
a linear model relating rain gauge pairs, was 0.365, further suggesting a significant degree of variability at the satellite
sub-pixel scale. Although there were several different storm types identified (localized, upper westerly trough, tropical
easterly wave, tropical westerly trough, cold front and localized with cold front), there did not appear to be any
relationship between storm type and the correlation patterns among the gauges.
Key-Words: - satellite pixel, rainfall variability, QPE, rain gauge, radar, validation, hydrologic modeling
1 Introduction
Is it is commonly assumed that a single rain
gauge located within a QPE pixel represents the average
rainfall for the pixel area (e.g., [1] and [2]). The
National Oceanic and Atmospheric Administration’s
(NOAA) Hydro Estimator (HE) algorithm [3], which
utilizes data from the GOES geostationary satellite to
estimate rainfall, for example, has an approximate pixel
size of 4 km x 4 km (16,000,000 m2), compared to a
cross-sectional area of roughly 0.032 m2 for the standard
National Weather Service tipping bucket gauge. The
National Weather Service’s (NWS) Next Generation
Radar (NEXRAD) estimates rainfall within a radial
coordinate system (base resolution 2 to 4 km), in which
the pixel size increases with distance from the radar
antenna [4]. NEXRAD accuracy also decreases with
distance from the antenna owing to the curvature of the
earth and in some cases the presence of obstructions
(e.g., mountains); additional details can be found in [5].
The differences in temporal and spatial scales make the
comparison of QPE methods with ground-based rain
gauges difficult [6]. Other potential sources of error
include rain gauge inaccuracy, assumptions made in the
development of the QPE algorithm that may be violated
under local (e.g., tropical) rainfall conditions, and
navigation errors in the satellite pixel coordinates. For
example, the navigation errors of the GOES-12 pixels at
nadir are on the order of 4-6 km [7].
Hydrologic models used to estimate storm
hydrographs and flood levels and extent may be
sensitive to rainfall distribution at the QPE sub-pixel
scale [8]. Bevan and Hornberger [9] have stated that
“… an accurate portrayal of spatial variation in rainfall
is a prerequisite for accurate simulation of stream
flows”. Spatial rainfall variability greatly affects runoff
processes in watersheds [10]. Goodrich [11] has stated
that rainfall runoff accuracy will increase with an
increasing number of rain gauges in the watershed,
which will improve the representation of the spatial
characteristics of rainfall. Rainfall estimates at a point
differ from catchment averages because rainfall varies
spatially and its spatial distribution over the catchment
determines the amount of rainfall that is integrated in
time and space [12]. Moreiraa et al. [10] evaluated
rainfall spatial variability effects on catchment runoff.
The study area was a 2.1 km2 catchment in northeastern
Brazil. The catchment response of the relatively small
catchment area was quite sensitive to the occurrence of
rainfall with high spatial variability. Bell and Moore
[13] evaluated the sensitivity of simulated runoff using
rainfall data from gauges and radar. The rain gauge
system consisted of 49 gauges over the 135 km2 Brue
catchment in southwestern England. They evaluated
convective and stratiform rainfall events.
Runoff
variability was strongest during convective storm events
and weakest during stratiform events. Surprisingly, the
authors obtained the best performance using lower-
25
26
resolution rainfall data and a lower-resolution
hydrologic model. This result was attributed to the fact
that the original model was calibrated with lower
resolution data. Hydrologic models need to be
recalibrated when rainfall of a different resolution is
used.
Numerous small-scale rainfall variation studies
have been conducted (e.g., [10], [14], [15]). For
instance, Bidin and Chappell [14] evaluated rainfall
variation for differing wind fields with 46 rain gauges
within a 4 km2 rainforest in Northeastern Borneo. They
observed a very high degree of spatial variability.
Seasonal totals were correlated with gauge separation
distance, aspect and topographic relief. Changes in
rainfall patterns over the 4 km2 catchment were related
to complex local topographic effects in the regional
wind field. Goodrich et al. [15] studied small scale
rainfall variability within a 4.4 ha area in the semiarid
USDA Walnut Gulch Experimental (WGE) Watershed
in Arizona, USA. The average observed rainfall
gradient was 1.2 mm/100 m. They concluded that the
assumption of rainfall uniformity in convective
environments similar to the WGE Watershed is invalid.
Krajewski et al. [16]) compared rain gauges in Guam at
three time scales (5, 15, and 60 min) and three spatial
scales (1, 600, and 1100 m). The largest variations
occurred for the smallest time scale and the largest
spatial scale. The smallest variations occurred for the
largest time scale and the smallest spatial scale.
We hypothesize that many rain gauge networks
in environments similar to this study (i.e., tropical
coastal), which provide only one rain gauge per remote
sensing pixel, may be inadequate to calibrate/validate
QPE methods, and that consequently QPE data may be
inadequate to use with hydrologic models.
The
objective of this paper is to present results from a rain
gauge network that will be used to validate several QPE
methods (e.g., GOES Hydro-Estimator [3], SCaMPR
[17], NEXRAD and the University of Puerto Rico
Collaborative Adaptive Sensing of the Atmosphere radar
network).
Implications of the results on
calibration/validation of QPE methods are discussed.
equipped with a data logger capable of storing rainfall
depth every 5 minutes over a 24-day period. The study
area was located near to the University of Puerto Rico’s
Mayagüez Campus (UPRM) in western Puerto Rico
(Fig. 1). The pixel area of 4 km x 4 km (16 km2) was
divided into sixteen evenly spaced squares of 1 km2
each. To locate the rain gauges the following steps
were used:
1. The center points of the GOES pixels were
obtained from NESDIS.
2. An appropriate GOES pixel was selected, which
included a relatively large range of topographic
relief east of the Mayagüez Bay in western
Puerto Rico.
3. Using ArcGIS, sixteen points were located
(evenly spaced) within the GOES pixel.
4. With the assistance of a ground positioning
system (GPS), properties (mainly residential)
were located which were as close as possible to
the center point locations identified in step no. 3.
In each case it was necessary to obtain
permission from the property owner before
installing the rain gauges.
5. The actual coordinates of the installed rain
gauges were recorded and entered into ArcGIS
(Fig. 2).
Study
Area
Mayagüez
Bay
Figure 1. Study area in western Puerto
Rico corresponding to a GOES pixel (4
km x 4 km). Colors represent variations
in topography.
2 Methodology
During July 2006, sixteen tipping bucket rain gauges
(Spectrum Technology, Inc.1) were installed within the
area covered by one GOES pixel, with the objective of
comparing to the operational National Environmental
Satellite, Data, and Information Service (NESDIS)
Hydro-Estimator algorithm [18]. Each rain gauge is
1
Reference to a commercial product in no way
constitutes an endorsement of the product by the
authors.
26
27
Figure 2. Twenty-eight tipping bucket rain
gauges used in the study. The 12 rain gauges
installed in June of 2007 were distributed within a
subwatershed of the Añasco River.
Some of the rain gauges could not be located
close to the center points of the squares because of a
lack of access—generally to undeveloped valleys.
Consequently the final locations of rain gauges were not
evenly spaced; however, this resulted in producing a
random (possibly beneficial) aspect to the locations of
rain gauges within each sub-area.
The data logger clocks were synchronized and
programmed to record cumulative rainfall depth every 5
minutes. All rain gauges were placed in areas free from
obstructions. It was necessary to locate a few of the
gauges on roof tops (approximately 5 meters above the
ground) owing to inappropriate conditions on the
ground. An effort was made to level each of the rain
gauges to assure proper functioning.
In June of 2007, another 12 tipping bucket rain
gauges were added to the network. These rain gauges
were distributed within a subwatershed of the Añasco
River for future hydrologic evaluation. Figure 2 shows
the location of the 12 rain gauges within the
subwatershed and the location of a stream gauge (Solinst
Levelogger) installed at the outlet of the subwatershed.
It should be noted that to maintain consistency in this
study, only the original 16 rain gauges were used in the
statistical analysis.
Storm data were collected for 62 storms
between August 2006 and August 2007. The storm data
collected included: start and end times, storm duration,
number of operational rain gauges (n), average total
storm rainfall, standard deviation, and maximum and
minimum rain gauge amounts. Storms were classified
according to whether they were locally formed by sea
breezes and heating, or generated by large weather
systems of either easterly or westerly origin. For this it
was necessary to gather supplementary information on
the synoptic weather conditions, and the local pattern
and timing of convection near Mayagüez, Puerto Rico.
Supplementary information included large scale maps of
upper winds and precipitable water, visible or IR
satellite and radar images, and radiosonde profiles at San
Juan. The types of weather systems observed were:
•
Localized = isolated over western Puerto Rico
with trade wind convergence
•
Tropical westerly trough = southwesterly moist
flow and SW-NE cloud bands
•
Tropical easterly wave = deep easterly flow
with widespread cloudiness
•
Upper westerly trough = westerly flow in midlevels coming down from north
•
Cold front = frontal cloud band penetrating from
Florida
The Kolmogorov-Smirnov (K-S) test [19] was
used to evaluate normality of the non-tranformed and
log-transformed storm totals for each of the rain gauges
for 90 storms between August 2006 and August 2008.
In the case of the non-transformed data, not one of the
16 data sets was determined to be normal. In the case of
the log-transformed data, eleven of the sixteen data sets
were determined to be normally distribution. Therefore,
two non-parametric comparison tests were used which
do not require that the data come from a normal
distributions. The two tests used were the MannWhitney [20] and Wilcoxon [21] signed-rank tests. The
purpose of these two tests is to assess whether two
samples of observations come from the same
distribution.
If the analysis results in a small
probabilities (e.g., ≤ 0.05) then the null hypothesis must
be rejected, that is to say that the two samples are
significantly different. A Pearson correlation table was
also generated for the sixteen data sets. All statistical
analyses were performed using the computer software
StatMost32 [22].
The reason for conducting the significant
difference tests was based on the following rationale.
QPE methods based on remote sensing usually compare
(or adjust) the remotely sensed rainfall estimate based on
a single rain gauge located within the remotely sensed
pixel. The rain gauge, in virtually all cases, will be
randomly located within the pixel (as opposed to, for
example, being located at the pixel center). This is
because the entity that manages the satellite or radar is
typically different than the entity that installed the rain
gauges. If there is a large amount of sub-pixel rainfall
variation then the QPE will be compared with a rain
gauge that does not represent other locations within the
pixel. On the other hand, if there is no significant
difference between randomly located pairs of rain
gauges, then this would suggest that the sub-pixel
27
28
variability is low and the QPE can be compared (or
adjusted) to rain gauges located at any location within
the pixel.
3 Results
As an example of the measured rainfall data,
Fig. 3 shows the depth of rainfall measured every 5
minutes by sixteen rain gauges on 6 August 2006. Figure
4a shows the spatial distribution of total rainfall for the
same storm. It is clear that the rainfall can vary
significantly within the satellite pixel area. The average
and standard deviation for the rainfall were 30.8 mm and
13.6 mm, respectively, while the maximum and
minimum recorded rainfall were 55.6 mm and 9.2 mm,
respectively. In addition to 6 August 2006 (4a), Fig. 4
shows the rainfall variation for storms occurring on 16
August (4b), 18 August (4c) and 22 October (4d), 2006.
For these storms, the maximum rainfall gradients were
20.4, 56.9, 55, and 65 mm/km, respectively. Spatial
variation in rainfall distribution as shown in Fig. 4 is
commonly observed during the “wet” season (August
through November) in western Puerto Rico.
1
12
2
Rainfall (mm)
3
10
4
5
8
6
7
6
8
9
4
10
11
2
0
12:43
12
13
13:12
13:40
14:09
14:38
Time (hour)
15:07
15:36
16:04
14
15
16
Figure 3. Rainfall measured from rain gauges
on August 6th, 2006. Numbers 1-16 in the legend
represent the rain gauge number.
Table 1 lists the statistics associated with 62
storms which occurred between August 2006 and
August 2007. The table includes storm type, number for
of storms, average storm start and end times, average
storm durations, average number of operational rain
gauges (n), average total storm rainfall, average standard
deviation, average maximum and average minimum rain
gauge amounts. The overall average for each of the
parameters is presented at the bottom of Table 1. On
average, the rain storms started at 15:02 and ended at
17:22, with an average duration of 2.33 hours. The
average, maximum, and minimum rainfall depths were
15.94 mm, 30.14 mm and 4.53 mm, respectively.
The distribution of the storm classifications
were as follows (Table 1): localized = 22 cases, upper
westerly trough = 16 cases, tropical easterly wave = 11
cases, cold front = 6 cases, tropical westerly trough = 6
cases, and localized with cold front = 1. These results
indicate the importance of the localized sea-breeze
induced storm to the local hydrology. The average
rainfalls produced from each type of storm were 15.4
mm, 14.4 mm, 17.2 mm, 9 mm, 27.03 mm and 13.64 for
localized, upper westerly trough, tropical easterly wave,
cold front, storms tropical westerly trough, and localized
with cold front, respectively.
In mid-June 2007, 12 additional rain gauges
were added within a small subwatershed located within
the 4 km x 4 km pixel as shown in Fig. 2. Fig. 5 shows
the variation in 5 minute rainfall at four different times
(14:27, 14:37, 15:32 and 16:22) on 27 June 2007. Large
variations can be observed between the individual 5
minute intervals.
Table 2 shows the results of the statistical
comparison of all possible pairs of the sixteen rain gauge
data sets (green circles in Figure 2) derived from 90
storms between August 2006 and August 2008; however
data from all the rain gauges were not available for all
90 storms. For example, there were 77 rainfall totals
available for rain gauge no. 7. Rain gauge no. 8 had the
smallest data set with only 23 rainfall totals. The main
reason that data were not available for all storms was the
lack of measurement of rainfall by a rain gauge (i.e.,
rainfall measured was zero). Because we could not be
certain that this was real or if the rain gauge became
plugged with debris, for example, all zero rainfall values
were discarded. It should be noted that the decision to
discard this data will result in data sets that may
underestimate the variability of rainfall. Therefore, in
the statistical analysis presented below it should be kept
in mind that our assessment of variability is
conservatively low, because without a doubt, some of
the discarded zero rain gauge values were in fact correct.
For the Mann-Whitney and the Wilcoxon
analyses (log-transformed and non-transformed data), 17
to 25% (20.9% mean) of average rainfall totals for all
rain gauge pairs were significantly different (Table 2).
A Pearson Correlation Table (Dataxiom Software, Inc.,
2001) was generated for the sixteen data sets (not
shown) and the overall average correlation coefficient
(r) was 0.60. Pearson correlation indicates the strength
of a linear relationship between two variables. The
coefficient of determination (r2) can be estimated by
taking the square of r, which in this case yielded r2 =
0.37. Therefore, on average a linear model can explain
36.5% of the variance between two randomly selected
rain gauge data sets. This is quite a low coefficient of
determination, and is another indication of rainfall
variability at the satellite sub-pixel scale. Figures 6 and 7
show the frequency and cumulative frequency of r and
r2, respectively, for the 16 rain gauge pairs. Of the 120
r2 values, 90% were less than 0.7, 67% were less than
0.5, and 30% were less than 0.2.
28
29
Figure 8 shows the upper 95% confidence
interval (CIU) minus the lower 95% confidence interval
(CIL) for the mean gauge rainfall for the 90 storms. CIU
- CIU provides another indication of how variable the
data is with respect to the mean rain gauge data. The
average CIU - CIU was 15.6 mm (0.6 inches), while the
maximum CIU - CIU was 87.7 mm (3.5 inches).
Ironically, with such a large range between the upper
and lower 95% confidence limits, it may be relatively
easy to obtain a QPE which falls within this range.
What these results indicate is that we do not know what
the mean rainfall is with a high degree of certainty.
4 Discussion
Typically QPE methods are compared with
existing rain gauge networks. For example, Cruz
Gonzalez [1] compared the HE algorithm with an
existing U.S. Geological Survey rain gauge network in
Puerto Rico (125 rain gauges).
If we were to
superimpose the QPE pixels over the area of the island,
for example the HE method having a pixel resolution of
4 km x 4 km, the individual rain gauge would fall at
some random location within an HE pixel. As Figs. 4
and 5 illustrate, a large difference could be obtained
depending upon where the rain gauges were located
within the pixels. Statistically speaking, one out of
every five rain gauges would not be representative of the
rainfall occurring at other locations within the pixel.
This problem is reduced when averaging estimates over
time, but is most acute for short-term estimates within a
single storm [15]—the type of data needed for real-time
hydrologic flood forecasting [23, 24].
5 Summary and Conclusion
Figure 4. Spatial distribution of rainfall for
storms on 6 August (a), 16 August (b), 18 August
(c) and 22 October (d), 2006.
The purpose of this study was to evaluate the
spatial rainfall variability within a QPE pixel (4 km x 4
km HE pixel) in a tropical watershed located in western
PR. Graphical data were presented for four storms (total
storm rainfall), several 5-minute intervals within a single
storm on 27 June 2007, and tabular data were presented
for 62 storms. Rainfall was observed to be variable
within the 4 km x 4 km study area. Average storm
rainfall from more than one fifth (20.9%) of the 120 rain
gauge-pairs evaluated for 90 storms, based on nonparametric statistics, were significantly different at the
5% of significance level, indicating significant rainfall
variation at the sub-pixel scale. The overall coefficient
of determination was 0.37. Of the 120 r2 values, 90%
were less than 0.7, 67% were less than 0.5, and 30%
were less than 0.2. The average CIU - CIU was 15.6 mm
(0.6 inches), while the maximum CIU - CIU was 87.7
mm.
29
30
Results from this study clearly illustrate that for
existing rain gauge networks (e.g., USGS) used in
environments similar to this study (i.e., coastal tropical),
significant sub-pixel variation can be expected. In these
cases, where a single rain gauge exists within the QPE
pixels and is used to either calibrate or validate a
remotely sensed QPE method, error may be introduced
into the QPE, and may be propagated through any
hydrologic model used. The practical consequences of
this error propagation are that the hydrologic parameters
derived as part of the hydrologic model calibration will
be incorrect.
P3
P1
18.235
C1
C2
C4
C5
18.23
C3
P7
P5
C10
C6
18.225
C8
C7
C9
C11
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C12
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P10
18.215
14:27
18.21
P13
P14
-67.125
P16
P15
-67.12
-67.115
-67.11
-67.105
-67.1
P3
6 Acknowledgement
Financial support was received from NOAA-CREST,
NSF-CASA, NASA-IDEAS, USDA HATCH (H-402)
and USDA-TSTAR (100). Thanks to Dr. Mark Jury of
the University of Puerto Rico-Mayagüez for assistance
with determing storm classifications, and to Dr. Raúl
Macchiavelli for his advice on the statistical approach
used in this study. Thanks also to the students that
helped install rain gauges and collect rainfall data: Jerak
Cintrón, Ian García, Mariana León Pérez, Melvin
Cardona, Ramón Rodríguez, Marcel Giovanni Prieto,
Víctor Hugo Ramírez, Yaritza Pérez, Romara Santiago,
Alejandra Roja, Jorge Canals, Julian Harmsen and Lua
Harmsen.
P1
18.235
C1
C2
C4
C5
18.23
C3
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P5
C10
C6
18.225
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C7
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18.21
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P14
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-67.12
P16
P15
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-67.11
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-67.1
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P1
18.235
C1
C2
C4
C5
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C3
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P5
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C6
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C8
C7
C9
C11
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C12
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P10
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15:32
18.21
P13
P14
-67.125
-67.12
P16
P15
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-67.11
-67.105
-67.1
mm
P3
9
8.5
P1
8
18.235
7.5
7
C1
C2
C4
6.5
C5
18.23
C3
6
P7
P5
5.5
C10
C6
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C7
5
C8
C9
4.5
C11
4
18.22
C12
3.5
P11
P10
3
2.5
16:22
18.215
2
1.5
1
18.21
P13
-67.125
P14
-67.12
P16
P15
-67.115
-67.11
-67.105
-67.1
0.5
0
Figure 5. Spatial distribution of 5-minute rainfall
values (mm) at 14:27, 14:37, 15:32 and 16:22 hours,
for a storm occurring on 27 June, 2007.
30
31
Histogram of r values for 16 rain gauge
pairs
30
120%
Frequency
25
100%
Frequency
Cumulative %
20
80%
15
60%
10
40%
5
20%
0
0%
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 More
Bin
Figure 6. Frequency and cumulative frequency of
correlation coefficients (r) for 16 rain gauge pairs.
Frequency
Histogram of r2 values for 16 rain
gauge pairs
25
120%
20
100%
80%
15
Frequency
Cumulative %
60%
10
40%
5
20%
0
0%
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 More
Bin
Figure 7. Frequency and cumulative frequency of
coefficient of determination (r2) for 16 rain gauge
pairs.
Upper 95% C.I. minus the Lower 95% C.I.
100
90
80
CIU - CIL (mm)
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100
Storm Number
Figure 8. Upper 95% confidence interval (CIU) minus
the lower 95% confidence interval (CIL) for 90
storms.
References:
[1] Cruz Gonzalez, B., 2006: Validacion del Algoritmo
Hidro-Estimador en la Region de Puerto Rico
(Validation of the Hydro-Estimator Algorithm in the
Puerto Rico Region). Tesis Departamento de ININ,
Universidad de Puerto Rico Mayagüez.
[2] Vila D. and I. Velasco, 2002. Some experiences on
satellite rainfall estimation over South America.
Proceedings, 1st International Precipitation Working
Group (IPWG) Workshop Madrid, Spain.
[3] Scofield, R.A. and R.J. Kuligowski, 2003: Status
and outlook of operational satellite precipitation
algorithms for extreme-precipitation events. Wea,
Forecasting, 18, 1037-1051.
[4] Beringer D.B. and J.D. Ball, 2004: The Effects of
NexRad Graphical Data Resolution and Direct
Weather Viewing on Pilots’ Judgments of Weather
Severity and Their Willingness to Continue a Flight.
DOT/FAA/AM-04/5. [Available from the Office of
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257-266.
32
Table 1. Average Rainfall statistics by storm type for 62 storms between August 2006 and August 2007.
Number Storm
Type of Storm
of Storms start
Localized
22
15:18
Upper Westerly trough
16
15:22
Tropical Easterly Wave
11
14:41
Cold Front
6
14:59
Tropical Westerly trough
6
13:31
Localized with cold front
1
15:51
Overall Average
62
15:01
Storm
end
18:16
17:59
16:10
16:50
17:39
17:40
17:37
Storm
Duration
(hr)
2.97
2.63
1.47
1.85
4.14
1.82
2.60
n
14
12
17
12
17
13
14
Total
Average
Storm
Rainfall
(mm)
15.37
14.41
17.23
9.04
27.03
13.64
15.98
Standard
Deviation Maximum Minimum
(mm)
(mm)
(mm)
12.09
29.11
4.57
13.23
29.18
4.63
10.77
31.62
5.54
6.09
21.57
0.70
9.66
41.90
6.53
NA
32.60
1.80
10.37
30.23
4.48
n stands for sample size or the number of operational rain gauges.
Table 2. Results of statistical comparisons between storms totals for all combinations of 16 rain gauges.
Statistical Analysis
Mann-Whitney
Mann-Whitney
Wilcoxon
Wilcoxon
Average
Data
Transformation
None
Log
None
Log
Percent of rain gauge pairs showing
significant difference (%)
25.0
21.6
17.0
20.0
20.9
Appendix 4
PROPOSAL
Estimation of evapotranspiration using remote sensing techniques under tropical
coastal conditions
Prof. Eric Harmsen, Department of Agriculture and Biosystems Engineering, University of Puerto Rico, Mayaguez,
PR 00681
eharmsen@uprm.edu
Determination of evapotranspiration is important for evaluation of hydrologic resources
of a region, and evaluating irrigation requirements. Because of the inter-relation between
components of the hydrologic cycle, evapotranspiration is important in the evaluation soil water
content, surface runoff, and aquifer recharge. Evapotranspiration (ET) is defined as the
combination of evaporation from soil and plant surfaces, and transpiration from plant leaves.
Evaporation is the process whereby liquid water is converted to water vapor and removed from
the evaporating surface (Allen et al., 1998). Transpiration is the vaporization of liquid water
contained in plant tissues and its subsequent removal to the atmosphere. Crops predominately
loss water through small openings in their leaves called stomata. Evapotranspiration can be
expressed in units of mm/day (or in/day), or as an energy flux in units of MJ m-2 day-1 (Allen et
al., 1998). Evapotranspiration is important because it is often the largest component of the
hydrologic cycle after rainfall. Under arid conditions, potential evapotranspiration can easily
exceed rainfall.
Remote sensing methods for estimating evapotranspiration are needed for tropical coastal
conditions. Various techniques have been developed based on radiation methods (e.g. Sumner et
al., 2008) and surface energy budgets (e.g., Gowda et al., 2007 and Allen et al., 2008). In this
study we will estimate the evapotranspiration flux using the Penman-Monteith method (Allen et
al., 1998) and Priestly-Taylor (Priestly and Taylor, 1972) in combination with the solar radiation
and surface temperature products of the GOES-12 satellite. Solar radiation will be derived using
the radiative transfer model of Diak et al. (1996). Input required for the Penman-Monteith will
be based on procedures developed for Puerto Rico by Harmsen et al. (2002). The advantage of
using a geostationary satellite platform is that sensor readings are available every 15 minutes,
and therefore ET can be estimated on a sub-hourly basis. Although, accurate surface solar
radiation estimates are limited to cloudless conditions, the frequent measurement from this
platform means that evapotranspiration can be estimated through much of the day when clear
skies are present.
Objective
 Evaluate estimates of evapotranspiration using the Penman-Monteith and Priestly-Taylor
methods in combination with GOES-derived solar radiation and surface temperature, and
other parameter estimations procedures developed for Puerto Rico. Remotely sensed ET
will be compared with several ground based methods including meteorological, Bowen
ratio, scintillation methods.
34
Methods
Reference evapotranspiration (ETo) will be estimated with the Penman-Monteith method
(Allen et al., 1989):
 900  u  e  e
 2  s a
 T  273 
0.408   Rn  G   
ETo 
    1  0.34 u2
.
(1)
where is slope of the vapor pressure curve, Rn is net radiation at the surface [Wm-2], G is soil
heat flux density [Wm-2],  is psychrometric constant, T is mean daily air temperature at 2-m
height, u2 is wind speed at 2-m height, es is the saturated vapor pressure and ea is the actual vapor
pressure [Kpa]. Equation 1 applies specifically to a hypothetical reference crop with an assumed
crop height of 0.12 m, a fixed surface resistance of 70 sec.m-1 and an albedo of 0.23.
In 1990 a committee of the United Nations Food and Agriculture Organization (FAO, 1990)
recommended the Penman-Monteith method (equ. 1) as the single approach to be used for
calculating reference ETo. This recommendation was based on comprehensive studies, which
compared twenty ET calculation methods with weighing lysimeter data (Jensen et al., 1990).
These studies found the Penman-Monteith method to produce superior results relative to all other
methods.
Vapor pressure will calculated using the following equation:
17.27  T 

 T  237.3 
e ( T)  0.6108  exp 
.
(2)
where e(T) is vapor pressure [Kpa] evaluated at temperature T [K]. Saturated and actual vapor
pressures will be estimated using equation 2 with the mean daily air temperature (Tmean) [Co] and
mean daily dew point temperature (Tdew) [Co], respectively. Air temperatures will be derived
from GOES surface temperatures using the method of Narasimhan et al. (2003). The FAO
(Allen et al., 1998) has reported that Tdew can be estimated based on the use of the daily
minimum air temperature (Tmin) and this approach will be used in this study. A correction factor
is recommended by Allen et al. (1998, equation 6-6) based on local conditions: Tdew = Tmin + Ko,
where Ko is a temperature correction factor. Harmsen et al. (2002) derived values of Ko for the
six NOAA Climate Divisions in Puerto Rico (Figure 1). In this study T dew will be estimated
using the GOES-derived daily minimum air temperature plus the appropriate correction factor.
The FAO recommends that wind speed be estimated from nearby weather stations, or as a
preliminary first approximation, the worldwide average of 2 m/sec can be used. In this study we
will use the wind speed values presented by Harmsen et al. (2002), which were based on average
station data within the Climatic Divisions established by the NOAA, and are presented in Table
3. The data in Table 3 were derived from wind speed sensors located at airports and university
35
experiment stations. Average wind speeds were based on San Juan and Aguadilla for Div. 1;
Ponce, Aguirre, Fortuna and Lajas, for Div. 2; Isabela and Rio Piedras for Div. 3; Mayagüez,
Roosevelt Rd. and Yabucoa for Div. 4; Gurabo for Div. 5; and Corozal and Adjuntas for Div. 6..
The sensor heights were 10 m and 0.58 m above the ground for the airports and experiment
stations, respectively. Measured wind speeds were adjusted to the wind speed at 2 m above the
ground using the following equation (Allen et al., 2005): u2 = (4.87 uz) / [ln (67.8 z -5.42)],
where uz is the wind speed at height z above the ground. Note also that the wind speeds in Table
3 are the average daytime wind speeds.
M
A
L
Figure 1. Map of Puerto Rico showing the locations of Adjuntas (A), Mayagüez (M) and
Lajas (L) . Numbers indicate National Oceanic and Atmospheric Administration (NOAA)
Climatic Divisions. 1, North Coastal; 2 South coastal; 3, Northern Slopes; 4, Southern
Slopes; 5, Eastern Interior; and 6; Western Interior.
Table 3. Average daily wind speeds 2 meters above the ground by month and NOAA
Climatic Division* within Puerto Rico. (From Harmsen et al., 2002)
Average Daily Wind Speeds (m/s)**
NOAA
Climatic
Division*
1
2
3
4
5
6
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
2.7
1.8
2.2
1.8
1.1
1.3
2.8
2.0
2.4
2.0
1.3
1.5
3.0
2.2
2.6
2.1
1.4
1.5
2.9
2.1
2.4
2.1
1.5
1.5
2.6
2.2
2.2
2.0
1.6
1.6
2.6
2.4
2.4
2.0
1.7
1.8
2.9
2.4
2.7
2.0
1.6
1.8
2.7
2.1
2.5
1.8
1.3
1.5
2.1
1.7
2.0
1.6
1.1
1.2
1.9
1.5
1.8
1.6
0.9
1.1
2.2
1.4
2.0
1.6
0.9
1.0
2.6
1.5
2.3
1.6
0.9
1.0
* See Figure 1 for NOAA Climate Divisions
** Averages are based on San Juan and Aguadilla for Div. 1; Ponce, Aguirre, Fortuna and Lajas, for Div. 2; Isabela and Rio Piedras for Div. 3;
Mayagüez, Roosevelt Rd. and Yabucoa for Div. 4; Gurabo for Div. 5; and Corozal and Adjuntas for Div. 6.
Solar radiation (Rs) will be estimated with the radiative transfer model of Diak et al.
(1996) using data from the visible-channel of the GOES satellite. The methods presented in
Allen et al. (2005) to calculate extraterrestrial radiation (Ra), Rnet and G will be utilized in this
study. In addition to using the Penman-Monteith method (equ. 1), the method of Taylor and
36
Priestly (1972) will also be used:
ETo 
PTc     Rn  G
   
.
where PTc [unitless] is the Priestly-Taylor location parameter, and all other variables/parameters
have been previously defined. An obvious advantage of this approach is that it does not depend
on as many parameters as does the Penman-Monteith method.
Actual evapotranspiration will be obtained from the following formula: ET = Kc ETo,
where Kc is the crop factor, which accounts for not climatic factors such as vegetation color,
stage of growth, leaf area, etc. The spatially variable crop factor will be derived using remotely
sensed estimates of leaf area index from the MODIS-derived natural difference vegetation index
(NDVI). The remotely sensed ET will be compared with several ground-based ET methods
including: meteorological, Bowen ratio, Eddy Covariance and Scintillation methods.
References
Allen, R. G., I. A. Walter, R. Elliott, R. Howell, D. Itenfisu and M. Jensen, R. L. Snyder, 2005.
The ASCE Standardized Reference Evapotranspiration Equation. Environmental and
Water Resources Institute of the American Society of Civil Engineers. 57 pages.
Allen, R. G., L. S. Pereira, Dirk Raes and M. Smith, 1998. Crop Evapotranspiration Guidelines for Computing Crop
Water Requirements. FAO Irrigation and Drainage Paper 56, Food and Agriculture Organization of the
United Nations, Rome.
Allen, R. G., M. Tasumi, R. Trezza, C. W. Robison, M. Garcia, D. Toll, K. Arsenault, J.M.H.
Hendrickx, and J. Kjaersgaard, 2008. Comparison of Evapotranspiration Images Derived
from MODIS and Landsat along the Middle Rio Grande. Proceedings of the ASCE
World Environmental and Water Resources Congress 2008 Ahupua'a.
Diak, G. R., W. L. Bland, and J. R. Mecikalski, 1996. A note on first estimates of surface
insolation from GOES-8 visible satellite data, Agric. For. Meteor., 82, 219–226.
FAO, United Nations, 1990, Expert consultation Italy, on revision of FAO methodologies, 28-31
May for crop water requirements, Annex V. Rome.
Gowda, P. H., J. L. Chávez, P. D. Colaizzi, S. R. Evett, T. A. Howell, and J. A. Tolk, 2007.
Remote sensing based energy balance algorithms for mapping ET: Current status and
future challenges. Transactions of the American Society of Agricultural and Biological
Engineers. Vol. 50(5): 1639-1644.
Harmsen, E. W., M. R. Goyal, and S. Torres Justiniano, 2002. Estimating Evapotranspiration in
Puerto Rico. J. Agric. Univ. P.R. 86(1-2):35-54.
Jensen, M. E., R. D. Burman, and R. G. Allen. 1990. Evapotranspiration and irrigation water
requirements. ASCE Manuals and Reports on Engineering Practice No. 70. 332 pp.
B. Narasimhan, R. Srinivasan, A. D. Whittaker, 2003. Estimation of potential evapotranspiration
from NOAA–AVHRR satellite. ASABE, Applied Engineering in Agriculture, Vol.
19(3): 309–318.
Priestly, C.H.B. and R.J. Taylor. 1972. On the assessment of surface heat flux and evaporation
using large scale parameters. Mon.Weath. Rev. 100:81-92.
Sumner, D. M, C. S. Pathak, J. R. Mecikalski, S. J. Paech, Q. Wu, and T. Sangoyomi, 2008.
37
Calibration of GOES-derived Solar Radiation Data Using Network of Surface
Measurements in Florida, USA. Proceedings of the ASCE World Environmental and
Water Resources Congress 2008 Ahupua'a.
Projects
Task (with each Projects
CREST Researchers
NOAA Collaborators
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Other Co
39