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Precipitation as the Input

Some Huge Rainfalls

~Amount (inches) Duration Location Year

1.7 3 minutesHaughton Grove,

Jamaica 1925

2.5 5 minutesPorto Bello,

Panama 19115 8 minutes Fussen, Bavaria 192012 40 minutes Holt, MO 194720 3 hours D'Hanis, TX 193530 6 hours Smethport, PA 194280 1 day Cherrapunji, India 1876

160 4 days Cherrapunji, India 1841950 1 year Cherrapunji, India 1886

Precipitation As Input

• Precipitation is generally “pre-processed”

• Uniform in space and time – never!

• Gages - Recording & non-recording

• Radar

• Satellite Derived

• QPF

The Basic Process….

Excess Precip. Model

Excess Precip.

Excess Precip.

Runoff Hydrograph

Runoff Hydrograph

Stream and/or Reservoir “Routing”

Downstream Hydrograph

Basin “Routing” UHG Methods

Necessary for a single basin

Focus on Precipitation

From A Basin View

Excess Precip. Model

Excess Precip.

Basin “Routing”

Unit Hydrograph

Runoff HydrographStream

“Routing”

Excess precip. is uniformly distributed!

PrecipitationPrecipitation• ... primary "input" for the hydrologic

cycle (or hydrologic budget). • … The patterns of the precipitation are

affected by large scale global patterns, mesoscale patterns, "regional" patterns, and micro-climates.

• … In addition to the quantity of precipitation, the spatial and temporal distributions of the precipitation have considerable effects on the hydrologic response.

PrecipitationPrecipitation

• … In lumped models, the precipitation is input in the form of average values over the basin. These average values are often referred to as mean aerial precipitation (MAP) values.

• … MAP's are estimated either from 1) precipitation gage data or 2) NEXRAD precipitation fields (MAPX).

Precipitation (cont.)Precipitation (cont.)• … If precipitation gage data is used,

then the MAP's are usually calculated by a weighting scheme.

• … a gage (or set of gages) has influence over an area and the amount of rain having been recorded at a particular gage (or set of gages) is assigned to an area.

• … Thiessen, isohyetal, and the inverse-distance squared are some of the more popular methods.

Precipitation Issues for the Hydrologist

• Characteristics of precipitation in or on my basin(s)!

• Quantity – How much are we getting?

• Space – Where will it fall?

• Time – When will it fall (and where)?

• Integrity of the Data – Is this data valid?

Characteristics

Convective, Frontal, Orographic, etc…

Convectional Storms....

• Thunderstorms are the classic example.

• Warm moist air is rapidly lifted - making it unstable.

• As the air lifts it cools and precipitation forms.

• As the precipitation falls - it cools the air

• This is why you may feel very cool bursts of air during those hot summer days when a thunderstorm kicks up.

Urban Areas & Thunderstorms...

• It has been reported that urban areas may contribute to the development of thunderstorms due to the presence of a heat source and the typically darker areas.

Orographic Effects.....

• Terrain can also cause lifting - which is a major component in the precipitation mechanism.

• The mountains provide a lifting mechanism for the warm advecting moist air.

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Orographic effects

Local Effects – e.g. the Great Lakes...

Do lake effect events alter the volume of Lake Superior?

Ice....

• Hail, Rime, Sleet, and Graupel

• Very difficult to measure

• Antifreeze or heated gages

Snow, A Few Brief Points .....

• Snow or snowfall reaches the ground to form the snowpack. Snowpack is generally reported as snow depth.

• We must also consider the snow water equivalent or SWE - WHY?

NOAA Photo Library

SWE....

• SWE is reported as a ratio - i.e. 10:1

• Meaning 10 inches of snow equal 1 inch of water - when melted.

• We also report this as density.

• 10:1 would be a density of 10% or 0.1.

• When is the snowfall most dense and least dense.

• When is the pack most or least dense?

NOAA Photo Library

Measuring Snow and SWE...

• Snow gages

• Snow tubes

• Radar - VERY difficult!! - WHY?????

Quantity

Measuring the Precipitation

Rainfall.....

• Rainfall varies in both space and time

• This is referred to as spatial and temporal variability.

• Rainfall amounts vary considerably

Measuring Precipitation....

• Generally use rain gages

• Measure depth

• What are the problems with rain gages?– Point coverage...– Interference - wind, trees, etc...– How many others can you name?

• Radar

Standard Gage(non-recording)

Fisher & Porter Tipping Bucket

Universal

Precipitation Gage NetworksPrecipitation Gage Networks

• A system of gages

• Design Issues:– density– location– quality (of data)– collection & transmission– processing, filing, managing

Factors Affecting DensityFactors Affecting Density

• Purpose of Network – Desired Quality/Precision/Accuracy

• Finances – Installation and UPKEEP!

• Nature of Precipitation – rain, rain + snow, orographic, convective, etc..

• Accessibility

• to name a few.....

Network Densities

• Many studies• Brakensiek et al., 1979 – Brakensiek, D. L., H. B. Osborn, and W. J. Rawls,

cooridnators. 1979. Field Manual for research in Agricultural Hydrology. USDA, Agricultural Handbook, 224, 550 pp, illustrated.

Size of Watershed Number of Gage Sites40 acres 2

100 acres 3600 acres 4

5 square miles 1010 square miles 15

100 square miles 50300 square miles 100

Spatial Characteristics

Where will it fall and

how will I use it?

Precipitation in ModelsPrecipitation in Models

• … In lumped models, the precipitation is input in the form of average values over the basin. These average values are often referred to as mean aerial precipitation (MAP) values.

• … MAP's are estimated either from:– 1) precipitation gage data or

– 2) NEXRAD precipitation fields (MAPX).

Precipitation (cont.)Precipitation (cont.)• … The MAP's are usually calculated

by a weighting scheme.

• … a gage (or set of gages) has influence over an area and the amount of rain having been recorded at a particular gage (or set of gages) is assigned to an area.

• … Thiessen, isohyetal, and the inverse-distance squared are some of the more popular methods.

Calculating Areal Averages....

• Arithmetic

• Isohyetal

• Theissen

• Inverse Distance

Arithmetic....

ThiessenThiessen

•Thiessen methodThiessen method is a method for areally weighting rainfall through graphical means.

IsohyetalIsohyetal

•Isohyetal methodIsohyetal method is a method for areally weighting rainfall using contours of equal rainfall (isohyets).

Inverse-Distance SquaredInverse-Distance Squared

Used to compute average precipitation at any point based on nearby gages. The weight of the nearby gages is dependant on the distance from the point to each of the nearby gages.

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Gage A Gage B

Gage C

dA

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dB

Radar Precip. as Input

• Radar gives a good picture of where it is raining - may indicate how to adjust the Unit Hydrograph for moving and partial area storms!

• May also give good estimate of how much, BUT• Will differ from gages in total basin average.• Historical records are based on gages!• This makes calibration rather difficult.

WSR-88D

• Weather Surveillance Radars - 1988 Doppler

• 1st WSR-88D sites installed in 1991• At the present time, there are more than 160

radars in place.• Should optimally provide coverage for a large

percentage of the United States.• Optimally used because under many

circumstances, the useful range of the radars varies considerably.

Locations

NEXRADNEXRAD

•NexradNexrad is a method of areally weighting rainfall using satellite imaging of

the intensity of the rain during a storm.

Temporal

When will fall and where?

Temporal DistributionsTemporal Distributions

• Gages record data at intervals - 10 min., 15 min., 1 hour, 24 hour, etc....

• Models use the data at 1-hour, 6-hour, etc...• Must either aggregate or disaggregate

precipitation amounts....• i.e. Combine 1 hour values into a 6-hour value...

Not a problem!• Or... Break a 24-hour value into 6 hour values...

Much more difficult!

Temporal DisaggregationTemporal Disaggregation

24-hour gage3.6 inches total

1 hour gage with 2.2 total inches and the following distribution:

Distribute the 3.6 inches using the breakdown of the hourly gage

Intensity, Duration, & Frequency

• Intensity, duration, & frequency

• Duration - the length of time over which the rain falls.

• Intensity - the rate at which the rain falls or the amount / duration.

• Frequency - the frequency of occurrence - i.e. How rare is this storm? - We’ll get back to this.....

• General relationships:– the greater the duration, the greater the amount

– the greater the duration, the lower the intensity

– the more frequent the storm, the the shorter the duration, and;

– the more frequent the storm, the less the intensity

Let’s Look at at an Example

First…

Let’s compute the Rainfall/Runoff ratios for the Little J at Spruce Creek.

The Situation….

1996 Totals

Some Issues

• How to handle the missing data

• Which basin averaging technique to use.– Gage Average– Thiessen– Isohyetal– Inverse Distance Weighting

Missing Data

• Filling in missing data is a major issue.

• In this case, we are filling it in space – not time.

• There are many ways to fill in this data:

• Averaging nearby stations

• Weighting (averaging is a special case)

• Isohyetal

The Missing Data

• Averaging = 57.06 inches• Weighting would depend on local

knowledge and would require creation of historical relationships between all of the local gages.

• Isohyetal would imply that the value is closer to 62 to 63 inches – see next slide

• For this exercise we will use 60 inches.

Isohyetal

Now Lets’ Find Basin Average

• Arithmetic Averaging

• Thiessen

• Isohyetal

• IDW

Gage Average

59.358.1157.1253.71

60288.24 SUM57.648 Average

I used Excel to average the gages. The small worksheet is shown at the right ->

Thiessen Polygons

Thiessen Wts. (%)

Combine % w/ TotalsReplace w/ 60.0

Thiessen - Final Computations

Precip pct Contribution59.3 0 0

58.11 0.6557 38.1027357.12 0.2459 14.0458153.71 0.0656 3.523376

60 0.0326 1.9560.9998 57.62791 TOTAL

Isohyetal Approach

Isohyetal Areas

Combine % and Precip. Values

Isohy Pct Precip ValuePrecip0 60 0

0.2623 59.5 15.606850.3279 58.5 19.182150.2295 57.5 13.196250.1475 56.5 8.333750.0164 55.7 0.913480.9836 57.23248 TOTAL

Inverse Distance Weighting

• Need coordinates of each gage

• Need coordinates of basin centroid or point of interest.

• Then Calculate gage weights:

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Measure 4 Distances

The Computations

Precip Distance (miles) dist squaredinv dist squared Weight Precip wtd Precip.59.3 24.7 610.09 0.001639102 0.018147325 59.3 1.076136

58.11 3.7 13.69 0.073046019 0.808729127 58.11 46.9952557.12 13.9 193.21 0.005175716 0.057302944 57.12 3.27314453.71 12.6 158.76 0.006298816 0.06973735 53.71 3.745593

60 15.5 240.25 0.004162331 0.046083254 60 2.764995SUMS 0.090321984 1 57.85512

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In SummaryR/R Ratio

Arithmetic 57.65 1.444862Thiessen 57.63 1.444361Isohyetal 57.23 1.434336IDW 57.85 1.449875TYRONE 58.1 1.45614

Runoff (calculated) 39.9

What if this had been a 6-hour storm instead of yearly totals?

What would we do?

Use Thiessen Weights

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Just average each incremental contribution using the pre-calculated Thiessen weights!

Area-Depth (amount) Relationship....

Indeed we should get less basin average precipitation than for a single gage……

Use this Chart

A gage in the middle of a 200 square mile basin records 5 inches of rain in 3 hours. Estimate the basin average rainfall:

For 200 square miles, the basin average is ~ 80% of the gage total or 0.8 * 5 = 4 inches!

Temporal Distributions

Understanding Temporal Distributions is very important,as this

greatly affects runoff timing and volumes.

Temporal DistributionsTemporal Distributions

• Precipitation is a continuous process.• Intensities vary depending on amount and duration• Gages record data at intervals - 10 min., 15 min., 1

hour, 24 hour, etc....• Models may use the data at 1-hour, 6-hour, etc...• Must either aggregate or disaggregate precipitation

amounts....• i.e. Combine 1 hour values into a 6-hour value...

Not a problem! Or... Break a 24-hour value into 6 hour values... Much more difficult!

Understanding Intensities

Time Depth (inches Intensity (inches/hr)1 min 1.23 73.8

15 min 7.8 31.22 hrs 10 min 19 8.8

15 hrs 34.5 2.324 hrs 46 1.948 hrs 65.8 1.47 days 131 0.81 year 1042 N/A

Intensities & Durations

• A 5-minute recording gage

• Recorded a storm for 40 minutes

• Calculate:– Total Rainfall– Cumulative Rainfall Curve– Max. 5,10, & 30 minute intensities– The average intensity

The Data

Time (min) Amount (mm)5 1.810 6.7215 15.620 6.9625 6.1230 11.6435 5.7640 1.56

Solutions

• Total rainfall – simply sum the precipitation values: 56.16 mm or 2.21 inches

• Cumulative data is shown and plotted below:

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10

20

30

40

50

60

5 10 15 20 25 30 35 40

Amount (mm)

Cumulative

Time (min) Amount (mm) Cumulative5 1.8 1.810 6.72 8.5215 15.6 24.1220 6.96 31.0825 6.12 37.230 11.64 48.8435 5.76 54.640 1.56 56.16

Solutions, cont….• The maximum 5 minute intensity was 15.6 mm between 10-15

minutes at 187.2 mm/hr or 7.3 inches/hr. This is illustrated in the

data below: Time (min) Amount (mm) Cumulative hourly intensities (mm/hr)

5 1.8 1.8 21.610 6.72 8.52 80.6415 15.6 24.12 187.220 6.96 31.08 83.5225 6.12 37.2 73.4430 11.64 48.84 139.6835 5.76 54.6 69.1240 1.56 56.16 18.72

56.16

Solutions, cont…• The maximum 10 minute intensity was found by aggregating

sequential 5-minute periods. The maximum 10-minute intensity is illustrated below, between 10-20 minutes with 22.56 mm or 135.36 mm/hr or 5.29 inches/hr.

Time (min) Amount (mm) 10-minute blocks Intensities (mm/hr)inches/hr5 1.8 0 0 010 6.72 8.52 51.12 1.99687515 15.6 22.32 133.92 5.2312520 6.96 22.56 135.36 5.287525 6.12 13.08 78.48 3.06562530 11.64 17.76 106.56 4.162535 5.76 17.4 104.4 4.07812540 1.56 7.32 43.92 1.715625

56.16

Solutions, cont…• The maximum 30 minute intensity was found by aggregating

sequential 5-minute periods. The maximum 30-minute intensity is illustrated below, between 5-35 minutes with 52.8 mm or 105.6 mm/hr or 4.125 inches/hr.

Time (min) Amount (mm) 30-minute blocks Intensities (mm/hr) inches/hr5 1.8 0 0 010 6.72 0 0 015 15.6 0 0 020 6.96 0 0 025 6.12 0 0 030 11.64 48.84 97.68 3.81562535 5.76 52.8 105.6 4.12540 1.56 47.64 95.28 3.721875

56.16

Solutions, cont…

The total rainfall was 56.16 mm over a duration of 40 minutes for an average intensity of 84.24 mm/hr or 3.29 inches/hr. In summary:

Intensity-Duration

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50

100

150

200

0 10 20 30 40 50

Time (minutes)

Inte

nsi

ty (

mm

/hr)

Series1

Minutes mm/hr5 187.210 135.3615202530 105.63540 84.24

Temporal AggregationTemporal Aggregation

Simply aggregate values to desired periods.

The Previous 40-minute Storm

• Recombine into 10, 20, and 40 minute hyetographs.

• What are the issues here?

The Graphs

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Series1

0

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10 20 30 40

Series1

5 minute

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20 40

Series1

Temporal DisaggregationTemporal Disaggregation

Basin gage records66.2 mm total

5-minute gage with 56.16 mm total precip. and the following distribution:

Distribute the 66.2 mm using the breakdown of the 5 minute gage

5 minute

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5 minute

The SolutionTime (min) 5 minute 5-min pct 66.2 mm dist.

5 1.8 0.032051 2.12179487210 6.72 0.119658 7.92136752115 15.6 0.277778 18.3888888920 6.96 0.123932 8.20427350425 6.12 0.108974 7.21410256430 11.64 0.207265 13.7209401735 5.76 0.102564 6.7897435940 1.56 0.027778 1.838888889

TOTALS 56.16 1 66.2

66.2 mm dist.

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66.2 mm dist.

We made a very large assumption about the 66.2 mm total duration – what was it ?

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Precipitation as the Input