Nicole PapayRain Gauge LabDue: April 16, 2010

Abstract:

No matter where you are in the world, rainfall matters. People need to drink, bathe, and cool themselves, and each place in this world depends on the rainfall it receives. The amount of precipitation that falls is a way to understand droughts, floods, and can even aid in safety of the lives of people to know the amount of rain to fall. It is one of the easier meteorological quantities to measure, so one can even build his/her own rain gauge. This experiment was designed to determine whether or not a homemade rain gauge can be more precise and accurate than one made and used professionally by meteorologists, and also to determine the heterogeneity of a precipitation event within ~5km (in this experiment). We constructed a rain gauge out of household materials and calibrated the height of the rain container in centimeters. Precipitation was collected for 12 days. We were given a commercial gauge to collect precipitation in as well during this time period, to compare and contrast the differences in collected precipitation depending on the construction of the gauge. The two gauges are relatively accurate, but not very precise. Also, the heterogeneity of the precipitation field is small. The observed accuracy and precision of daily precipitation measurements using a homemade rain gauge is lower than or similar to the level of accuracy and precision suggested by error propagation calculations. Spatial heterogeneity of rainfall causes systematic and random differences in daily precipitation measurements that can be detected despite the observed instrumental systematic and random errors. Being that our results showed some large error between measurements, it is obvious that errors occurred during this experiment. One error that could have come from measurements taken of water that evaporated. Also, being that the measurements were taken from the roof of the Walker Building, the surroundings were not representative of the area of State College and the Airport.

Introduction:

The amount of precipitation that falls daily is an important quantity for meteorologists to measure, and for the general public to be informed about. Measuring precipitation can be done in many ways. The most simple way, however, is a simple design created many years ago, and is still used as one of the most common ways to measure precipitation: a rain gauge. A rain gauge uses a wide funnel

to collect precipitation into a smaller cylinder to measure the amount that fell.

Although the sound of a rain gauge is simple, the building and design of one can determine if that particular rain gauge will be as accurate and precise as the ones used professionally throughout the world. Some rain gauges prove to be more precise when it has a wider funnel and a smaller cylinder to collect rain. In addition to the design, the accuracy of the rain gauge can be limited by the location from which the gauge is collecting rain. Typically in the United States, there is a gauge collecting rain approximately every 10km. But what happens if there is a sudden small-area downpour right in between the location of two rain gauges, and they don’t measure any precipitation? The result of that is a loss in accuracy of those rain gauges.

In this experiment, the precision and accuracy of a homemade rain gauge will be tested. It is predicted that the homemade rain gauge will be more accurate and precise than the plastic commercial rain gauge collecting precipitation in the same location, due to the wider funnel and corresponding smaller collection container than the commercial gauge. In addition to the accuracy, the heterogeneous precipitation of State College, PA will be observed. Since the homemade rain gauge is within 5km of the professional rain gauge from the University Park Airport in this experiment, it is expected that a high heterogeneity in precipitation will be found.

Methods:

At the start of this experiment, we were instructed to create a homemade rain gauge.

Image 1: Picture of actual commercial rain gauge (left), and homemade rain gauge, Measure Mate (right).

The Measure Mate was made from simple household items: a Rubbermaid container, a plastic bucket, and a funnel. The Rubbermaid container was glued to the bottom of the bucket for stability, and the bucket was weighed down with several small rocks inside it, surrounding the bottom of the Rubbermaid container. The funnel itself was taped with duct tape during the experiment, to avoid any shifting or movement due to weather conditions. Rain was collected by the Measure Mate on the roof of the Walker Building on Penn State University’s campus in State College, PA, with the commercial rain gauge taped standing straight less than 10 feet away from the homemade gauge.

Figure 1: Locations in State College, Pennsylvania of homemade rain gauge (1) and commercial rain gauge (2).

Figure 2: Locations in State College, Pennsylvania of homemade rain gauge and commercial rain gauge.

On each day of the experiment, we would measure the collected precipitation. We would measure the commercial gauges precipitation (as the commercial gauge is already calibrated in inches) and then convert the inches to centimeters. We would then pour the Measure Mate’s precipitation into the commercial gauge and measured in inches and converted to centimeters. The Measure Mate needed an equation to be calibrated properly. Using equation (1) below, we were able to determine that the radius of our funnel and the radius of the collecting Rubbermaid were equal:

piHM

=h1=r22

r12h2 .

(1)

Each day our rainwater was collected and measured at 1:15pm eastern standard time and recorded for each of the 12 days, starting on March 20, 2010. Results of the rain amounts can be seen in Table 1. For each of the 12 days we also took professional data from the University Park Airport. The Walker Building rooftop measurements were provided for us, but we chose to use the airport data instead because it allowed us to understand how the spatial errors are truly caused by larger distances. Also, the University Park Airport gave a better hourly analysis of the accumulated precipitation and we were able to closer calculate rain measurements for our times, approximately 1pm-1pm daily, rather than having to extrapolate the data from Walker Building roof as it was recorded at different times than our measurements.

After completing the collection of rain, we began the error analysis. First we calculated the percent error of the Measure Mate compared to the actual readings of the commercialized rain gauge, and then the Measure Mate compared to the University Park Airport measurements using the equation below. Results are displayed in Table 3.

(2)

Next we calculated theoretical instrumental errors. The following equations were used in these calculations, results can be found in Table 4.

δpr , iT

=δf=(∑j=1M

( ∂ f∂ x j )

2δx j2)12

(3)Equation (3): Theoretical estimate of instrumental random error.

δPrT

= 1N∑i=1

N δpr , iT

piCOM

⋅100 (4)

Equation (4): Average random error.

δps, iT

=piHM

(max )−piHM

(best ) (5)Equation (5): Theoretical estimate of instrumental systematic error.

δPsT

= 1N∑i=1

N δps , iT

piCOM

⋅100 (6)

Equation (6): Average systematic bias estimate.

After calculating the theoretical instrumental errors we calculated the observed instrumental errors, these results can be found in Table 5.

δPsO

= 1N∑i=1

N ( piHM−piCOM )

piCOM

⋅100 (7)

Equation (7): Observed instrumental systematic error in daily precipitation depth.

δPrO

=( 1N−1∑i=1

N [ (p iHM−piCOM )

piCOM

⋅100−δPsO]

2

)12

(8)Equation (8): Observed instrumental random error in daily precipitation depth.

ΔP= 1N∑i=1

N (p iCOM− piWS )

piWS

⋅100 (9)

Equation (9): Observed spatial systematic difference in daily precipitation depth.

σ P=( 1N−1∑i=1

N [ ( piCOM− piWS)

piWS

⋅100−ΔP ]2

)12

(10)Equation (10): Observed spatial random difference in daily precipitation depth.

At the end of this report, a page of sample calculations using the 10 equations above can be found.

Results and Discussion:

Experimental MeasurementsDate Type of

PrecipitationHomemade

Gauge Precipitation

(cm)

Commercial Gauge

Precipitation(cm)

University Park Airport Precipitation

(cm)

Meteorological Conditions

3/20/10 -- 0 0 0 Clear

3/21/10 -- 0 0 0 Clear3/22/10 Rain 0.3 0.03 0 Fog/Mist

3/23/10 Rain 0.9 0.3 0.64 Cloudy

3/24/10 Rain 0.2 0 0 Mostly Cloudy

3/25/10 Rain 0.03 0 0 Mostly Cloudy

3/26/10 Rain 1.7 2.5 1.88 Cloudy

3/27/10 -- 0 0 0 Clear

3/28/10 -- 0 0 0 Clear

3/29/10 Rain 2.6 2.3 1.98 Cloudy

3/30/10 Rain 0.03 0 0.03 Partly Cloudy3/31/10 -- 0 0 0 Clear

Table 1: Homemade and Commercial Gauge measurements were taken at 1:15 PM EST, daily.

Estimated ErrorRandom 0.05 cmSystematic 0.05 cm

Table 2: Estimated random and systematic error in the homemade precipitation measurements.

Error AnalysisDate Percent Error of

Homemade against Commercial

(%)

Percent Error of Homemade against University Park Airport Measurement

(%)3/20/10 0 03/21/10 0 03/22/10 900 --3/23/10 200 40.63/24/10 -- --3/25/10 -- --

3/26/10 32 9.573/27/10 0 03/28/10 0 03/29/10 13.04 31.33/30/10 -- 03/31/10 0 0

Table 3: Percent Error calculations.

3/22/10 3/23/10 3/26/10 3/29/10Random 41.7 4.17 0.50 0.54Systematic 0.25 0.85 1.65 2.55Average Systematic Bias

1.33

Table 4: Theoretical instrumental errors.

3/22/10 3/23/10 3/26/10 3/29/10 3/30/10Instrumental Systematic

225 50 -8 3.26 --

Instrumental Random 525 116.7 18.7 7.61 --Spatial Systematic -- -13.3 8.24 4.04 -25Spatial Random -- 31.0 19.2 9.43 58.3Table 5: Observed instrumental errors.

Our homemade rain gauge did not display much accuracy against the commercial gauge. When comparing measurements of the two gauges day by day, we observed that on days where a small amount of precipitation was measured using our homemade gauge no precipitation at all was recorded from the commercial gauge. This caused the percent error to be very large during those observation days. Within this experiment there are many sources of error. Obviously, on a day where heavy precipitation was present, the rain did not stop while we were measuring the accumulated rain. Therefore, during those measurement times, we could have missed a few hundredths of a centimeter and alter our results. There could also be errors in the accuracy of our measuring the precipitation amount with the naked eye. The design of our rain gauge became very important in determining how much trouble we would have making measurements.

Throughout the entire period of the experiment, our rain gauge collected and stored rain properly. We could have, however, had a much easier time with the measurements if we had placed our funnel into a graduated cylinder instead of a Rubbermaid container. Having the funnel go directly into a graduated cylinder would have made the calibration process much smoother.

The lab instructed us to use the official measurements of precipitation off the Walker Rooftop, but instead we used precipitation recordings made at the University Park Airport. The airport is located close to 5km from the Walker Building. The distance between the locations lead us to believe that the major source of error in this experiment was due to the spatial variability in the intensity and amount of rain that fell during a certain period of time. At times, rain was observed at our homemade and commercial setups on the Walker roof while the airport saw nothing in the way of precipitation. The placement of our rain gauges could have shown variability in our results. However, the locations of all three rain gauges were in open areas with a clear view of the sky. There was nothing in the way of the precipitation getting to the gauges. The ideal location for a rain gauge is in a location representative of the surrounding area with a non-obstructed view of the sky.

Our first hypothesis in this experiment states that the observed accuracy and precision of daily precipitation measurements using a homemade rain gauge is lower than or similar to the level of accuracy and precision suggested by error propagation calculations. After performing this experiment, we believe it is proven true. The error propogation equations used in this lab allow for an estimate of

variation to be made. We chose to use 0.05cm. as our estimate. This estimate may or may not have been constant from readings day to day, but we made the assumption that our rain gauge would have greater errors in accuracy and precision if we were to try and account for each specific days variation in readings.

The second hypothesis in this experiment states that spatial heterogeneity of rainfall causes systematic and random differences in daily precipitation measurements that can be detected despite the observed instrumental systematic and random errors. After performing this experiment, we believe this hypothesis to be true as well. We see the error analysis showing differences in the measurements made by the homemade rain gauge and the University Park Airport measurements, and through these differences we see evidence of there being random and systematic errors from spatial heterogeneity.

ConclusionBased on the results of our experiment, it is easy to see that the

two most crucial details of a rain gauge come with recording the measurements. Without a properly calibrated gauge, it would be easy to misread the information produced.

Based on our data, the spatial error for a point measurement is large for a small difference in location (~5km). It is not reasonable to characterize precipitation for an entire city or region based on a single point measurement. The heterogeneity of a precipitation field varies from place to place, and between storms. Having multiple rain gauges within a city or designated area will be able to more easily cover any differences in precipitation depending on region. The gauges should be places even closer together than the ~5km used in this experiment. These rain gauges should be made professionally, using plans from a gauge that has been proven accurate and precise. If the city were covered in home-made rain gauges, the data would be almost useless because no one would be able to know how precise each gauge was.