EXTENDED PRECIPITATION TIME-SERIES
FOR CONTINUOUS HYDROLOGICAL MODELING
IN WESTERN WASHINGTON
Hyetograph - SeaTac Airport
Hourly Precipitation (in)
0.40
0.35
Storm of February 5-9, 1996
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
12
24
36
48
60
72
84
Time (Hours)
Washington State
Department of Transportation
April 2002
MGS Engineering Consultants, Inc.
96
108
120
132
144
EXTENDED PRECIPITATION TIME-SERIES
FOR CONTINUOUS HYDROLOGICAL MODELING
IN WESTERN WASHINGTON
Prepared for:
Washington State
Department of Transportation
By
MGS Engineering Consultants, Inc.
MG Schaefer Ph.D. P.E.
BL Barker P.E.
April 2002
MGS Engineering Consultants, Inc.
EXTENDED PRECIPITATION TIME-SERIES
FOR CONTINUOUS HYDROLOGICAL MODELING
IN WESTERN WASHINGTON
April 2002
EXECUTIVE SUMMARY
Extended length precipitation time-series records have been developed for application in western
Washington based on combining of hourly records from high-quality precipitation measurement
stations. Hourly precipitation time-series records from Seattle Washington, Vancouver British
Columbia, and Salem Oregon were combined and rescaled to replicate the storm characteristics
representative of the Puget Sound lowlands. This approach yielded time-series with record lengths
of 158-years. Hourly precipitation time-series records from Seattle Washington and Portland
Oregon were combined and rescaled to replicate the storm characteristics representative of the
Vancouver-Castle Rock area. This yielded time-series with record lengths of 121-years.
Time-series records can be combined because the climatology and storm characteristics are very
similar for sites in the western interior lowlands of the Pacific Northwest. This is an
intermountain valley area generally extending from near Vancouver British Columbia on the
north to near Eugene Oregon to the south. For stations that are sufficiently distant from oneanother, a large storm that affects one station does not represent a significant storm at the other
station. Thus, the collection of large storms recorded at a given station have different magnitude
and temporal patterns than the collection of large storms recorded at the distant station. This
independence of storm events allows the construction of an extended precipitation time-series by
combining of time-series records.
The extended time-series were created by rescaling the original time-series at each station in a
manner that yields the desired storm statistics at a wide range of durations. This was accomplished
by utilizing eight durations for matching of the target site statistics, where the precipitation
statistics were based on regional analyses of 64 hourly and daily gages in western Washington.
The eight durations are the 2-hour, 6-hour, 24-hour, 72-hour, 10-day, 30-day, 90-day, and annual
(365-day) durations. The rescaling process may be viewed as preserving the shape and temporal
pattern of the original time-series, and rescaling the amplitudes of the hourly precipitation values.
Twenty-two extended time-series were created with applicability to sites with mean annual
precipitation ranging from 32-inches to 60-inches. A separate time-series was created for each
4-inch increment of mean annual precipitation. The extended 121-year and 158-year records
contain four to five-times the number of significant storm events and diversity of temporal storm
patterns and multi-day sequences of storms than would commonly be available from the short
record at a single station. This allows a very thorough analysis of watershed and stormwater
facility responses to various combinations of storm magnitudes, temporal patterns and sequences
of storms. The extended records also allow interpolation for estimation of extreme floods as
opposed to extrapolation that is required when using the short records that are typically available.
MGS Engineering Consultants, Inc.
i
MGS Engineering Consultants, Inc.
ii
EXTENDED PRECIPITATION TIME-SERIES
FOR CONTINUOUS HYDROLOGICAL MODELING
IN WESTERN WASHINGTON
TABLE OF CONTENTS
EXECUTIVE SUMMARY
i
INTRODUCTION
1
Project Goals and Products
2
APPROACH FOR CREATING AN EXTENDED PRECIPITATION TIME-SERIES
4
Transposition of Precipitation Time-Series
4
Selected Approach for Western Washington
4
BASIC CONCEPTS FOR CREATING AN EXTENDED PRECIPITATION TIME-SERIES
Criteria for Selection of Stations for Combining of Time-Series Records
PROCEDURES FOR CREATING AN EXTENDED PRECIPITATION TIME-SERIES
Scaling of Precipitation Time-Series
5
5
12
12
CHARACTERISTICS OF COMPLETED EXTENDED PRECIPITATION TIME-SERIES
15
Seasonality Characteristics of Extended Precipitation Time-Series
15
Magnitude-Frequency Curves for Extended Precipitation Time-Series
17
CREATION OF AN EVAPORATION TIME-SERIES
20
Stochastic Generation of Evaporation Time-Series
20
Simulation Procedure for Stochastic Generation of Daily Evaporation
22
APPLICATION OF TIME-SERIES
24
Recommended Limits of Application Consistent with Methods for Developing Time-Series
24
Length of Time-Step
24
Areal Distribution of Storms
25
Variation of Mean Annual Precipitation over Large Watersheds
25
Differences with Pierce County Time-Series
26
Application of Pierce County Time-Series in Southern King County
26
TIME-SERIES DELIVERABLES
26
SUMMARY
27
REFERENCES
28
MGS Engineering Consultants, Inc.
iii
TABLE OF CONTENTS
APPENDIX A
SIMILARITY OF SEASONALITIES OF STORM OCCURRENCES
Supporting Analyses for Combining of Time-Series Records
A-1
APPENDIX B
SIMILARITY OF STORM CHARACTERISTICS
Supporting Analyses for Combining of Time-Series Records
B-1
APPENDIX C
SIMILARITY OF PRECIPITATION-FREQUENCY CHARACTERISTICS
Supporting Analyses for Combining of Time-Series Records
C-1
APPENDIX D
CORRELATION ANALYSES CONFIRMATION OF INDEPENDENCE
Supporting Analyses for Combining of Time-Series Records
D-1
APPENDIX E
DESCRIPTIONS OF CLIMATIC REGIONS FOR APPLICABILITY OF TIME-SERIES E-1
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EXTENDED PRECIPITATION TIME-SERIES
FOR CONTINUOUS HYDROLOGICAL MODELING
IN WESTERN WASHINGTON
April 2002
INTRODUCTION
Continuous hydrologic modeling has recently been adopted as the standard for urban stormwater
modeling in western Washington4. Continuous flow modeling has distinct advantages in the
analysis of stormwater facilities over single event methods. These advantages stem from the
nature of storms in the Pacific Northwest. Flood events in undeveloped watersheds in the
northwest are commonly produced by long-duration winter storms, and sequences of storms, that
have relatively low precipitation intensities at the recurrence intervals of interest for urban
stormwater management. These long-duration winter storms result in long-duration flood events
with moderate flood peak discharges and large runoff volumes. As urbanization occurs, the
percentage of impervious area increases and results in greater amounts of surface runoff during
storm events. These land-use changes can dramatically alter the magnitude of flood peak
discharges and flow duration characteristics from the pre-developed conditions. In addition, shortduration high-intensity storms that produced little streamflow response in the undeveloped case
can often produce flashy flood peaks in urbanized watersheds.
Continuous hydrologic modeling allows an analysis of the full range of the magnitude and duration
of streamflow, in addition to the traditional analysis of individual flood events. Examination of
flow duration characteristics provides practical insights into the current and future hydrologic
regimes for flood peaks, runoff volumes, and flow duration. Information obtained from this
modeling approach provides the greatest opportunity for designing facilities and developing
strategies to mitigate the impacts from urbanization and to protect stream habitat and wetlands.
Successful application of continuous hydrologic modeling is dependent upon having a high quality,
long-term, precipitation time-series that is representative of the site under study. A precipitation
time-series with a long record length is needed for several reasons. The long record provides a rich
diversity of the storm temporal patterns, multi-day sequences of storms, and seasonality of
occurrence of storm events that are possible in western Washington24. This provides for a robust
examination of the performance of detention and water-quality facilities over a wide range of flow
conditions. Estimation of rare flood events is always of interest in hydrologic modeling. Use of the
long record lengths allows for interpolation rather than extrapolation in estimating the
characteristics of 50-year and 100-year floods. This is a particularly difficult problem when only
short records are available. The requirement that the precipitation time-series be representative of a
given site is important because storm characteristics vary from west to east across western
Washington for a given magnitude of mean annual precipitation for storm durations ranging from
several hours, to daily and weekly time frames. Thus, separate extended time-series are needed for
areas west and east of central Puget Sound.
In February 2001, MGS Engineering Consultants developed a suite of fifteen extended
precipitation time-series for application in Pierce County28 and adjacent areas. These time-series
have a record length of 158-years and are applicable to sites in Pierce County with mean annual
precipitation ranging from 38-inches to 52-inches. Separate time-series were developed for each
2-inch increment of mean annual precipitation in the range from 38-inches to 52-inches for sites
both west and east of central Puget Sound.
MGS Engineering Consultants, Inc.
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Project Goal and Products
The goal for this project was to develop a collection of long precipitation time-series based on
combining of hourly records from high-quality precipitation measurement stations that are
applicable to sites in the lowlands of western Washington. These time-series will supplement the
suite of time-series previously developed for Pierce County28.
The deliverables for this project include precipitation time-series for sites with mean annual
precipitation ranging from 32-inches to 60-inches in the lowland and foothill areas of Puget
Sound. Deliverables also include a suite of precipitation time-series for lowlands in the
Vancouver to Castle Rock corridor in southwestern Washington for sites with mean annual
precipitation ranging from 40-inches to 60-inches. These new time-series (Table 1), in
combination with those previously developed for Pierce County (Table 2), provide coverage for
lowland and foothill sites in western Washington with mean annual precipitation ranging from
32-inches to 60-inches (Figure 1). This represents coverage for nearly all of the more densely
populated areas in western Washington. The red-line boundaries in Figure 1 are drawn at the
32-inch and 60-inch isopluvials of mean annual precipitation. The blue-lines in Figure 1 delineate
sub-regions for applicability of the various time-series. Extended time-series (Tables 1,2) are
available for all sites within these boundaries.
This report presents the technical issues that were considered and the procedures that were
employed in creating a suite of extended precipitation time-series for sites in western
Washington.
Table 1 – Extended Precipitation Time-Series Developed for this Project
MEAN ANNUAL PRECIPITATION OF
EXTENDED PRECIPITATION TIME-SERIES
32, 36, 40, 44, 48, 52, 56, 60-inch
32, 36, 40, 44, 48, 52, 56, 60-inch
40, 44, 48, 52, 56, 60-inch
RECORD
LENGTH
158-years
158-years
121-years
TIME STEP
APPLICABILITY
hourly
hourly
hourly
Lowlands, West of Central Puget Sound
Lowlands, East of Central Puget Sound
Lowlands, Vancouver–Castle Rock Corridor
Table 2 – Extended Precipitation Time-Series Developed as Part of Pierce County Project28
MEAN ANNUAL PRECIPITATION OF
EXTENDED PRECIPITATION TIME-SERIES
40, 42, 44, 46, 48, 50, 52-inch
38-inch
40, 42, 44, 46, 48, 50, 52-inch
MGS Engineering Consultants, Inc.
RECORD
LENGTH
158-years
158-years
158-years
2
TIME STEP
15-min
15-min
15-min
APPLICABILITY
Lowlands, West of Central Puget Sound
Lowlands, Central Puget Sound
Lowlands, East of Central Puget Sound
West Puget Sound
East Puget Sound
Vancouver
Castle Rock
Corridor
Figure 1 – Mean Annual Precipitation Map of Western Washington and Delineation of Regions
for Application of Extended Precipitation Time-Series
(Map from Oregon Climate Service PRISM2,21 Model)
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3
APPROACH FOR CREATING AN EXTENDED PRECIPITATION TIME-SERIES
Transposition of Precipitation Time-Series
There are a limited number of hourly precipitation recording stations in western Washington.
Thus, hourly precipitation data are rarely available at the site of interest for hydrologic modeling.
To address this problem, it is necessary to transpose the hourly record from the station where it
was collected to the site of interest.
Past practice for providing a precipitation time-series for a given site is to take the hourly timeseries from a nearby station and rescale it in attempting to match the storm characteristics for the
site of interest. Several criteria need to be met to successfully make this transposition. First, the
climatic and storm characteristics for the chosen station must be similar to that of the site of
interest. This has usually been interpreted to mean that the chosen station has similar mean annual
precipitation to the target site and is located in a similar topographic setting. Next, a scaling
procedure must be adopted to rescale the storm characteristics from the chosen station to that of the
target site. In the past, very simplified scaling procedures have been employed that use a single
fixed scaling factor. Common choices have been to use a scaling factor computed as the ratio of the
mean annual precipitation from the two sites, or to use a ratio computed from the estimated 25-year,
24-hour precipitation for the two sites.
Either of these choices results in reasonable scaling for the selected duration but can significantly
over-scale or under-scale at other durations. For urban stormwater modeling, the storm durations
of interest span the range from single storm events with durations from several hours through
several days, to sequences of storm events over a period of several days through perhaps two
weeks. Thus, both of these simplified procedures are flawed because storm characteristics vary by
duration24,26 and associated storm type, and by location within western Washington. Thus, a series
of scaling functions, rather than a single scaling factor, are needed to properly scale the time series
for the various durations.
In addition, there are several practical problems to overcome in transposition of records. There
are a limited number of hourly recording stations in western Washington that have high-quality
records. Prolonged periods and intermittent periods of missing data are common at many
stations. Many of the hourly recording stations have short records with fewer than 30-years of
data. Nearly all of the stations have tipping-bucket gages that record at 0.10-inch intervals,
which give poor temporal resolution for the low to moderate-intensity winter storms common in
western Washington. Tipping bucket gages with 0.10-inch buckets are also susceptible to
evaporation loses from partially full buckets between storm events. This can lead to significant
underestimation of monthly and annual precipitation totals.
Selected Approach for Western Washington
Each of the problems listed above was addressed in the development of the extended precipitation
time-series. First, only stations with very high-quality records were employed. Second, only
stations with long record lengths were selected. Lastly, only stations with high-resolution gages
were selected, gages measuring/recording at 0.01-inch increments or less.
Regional statistical analyses were conducted for precipitation data from 64 daily and hourly gages
within western Washington25,26 to derive the statistics needed for scaling of the various durations
within the time-series. Lastly, scaling procedures were employed to preserve storm statistics at the
2-hour, 6-hour, 24-hour, 72-hour, 10-day, 30-day, 90-day, and annual (365-day) durations.
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BASIC CONCEPTS FOR CREATING AN EXTENDED PRECIPITATION TIME-SERIES
An hourly precipitation time-series is considered representative of a particular site if the annual
maxima series data for the full spectrum of durations from hourly, through daily, multiple days,
weekly, monthly and annual, each conforms to the regional precipitation magnitude-frequency
relationship applicable to the site. Further, storm characteristics contained within the time-series
must conform to the storm characteristics representative of the site. Storm characteristics of interest
would include measures such as: seasonalities of storm occurrences for various durations and storm
types; interarrival time between storms; and total duration of precipitation (Appendices A,B).
Based on these considerations, an extended hourly precipitation time-series can be created by
combining hourly time-series records from stations in climatologically similar settings that are
sufficiently distant from each other that their records are independent at the durations of primary
interest. For urban stormwater applications, durations ranging from hourly through 10-days are
of primary interest for hydrologic modeling. Prior to combining records, the time-series record
at each station must be scaled to have the statistical characteristics exhibited in regional
precipitation analyses that are representative of the site of interest. This process may be viewed
as preserving the shape and temporal pattern of the time-series, and rescaling the amplitudes of
the hourly precipitation values.
The cornerstone of this approach is that the climatology and storm characteristics are very similar
for sites in the western interior lowlands of the Pacific Northwest. This is an intermountain valley
area generally extending from near Vancouver British Columbia on the north to near Eugene
Oregon to the south. The similarity in behavior of storm characteristics can be confirmed by the
similarity of the seasonality of storms at various durations, and by the similarity of the shape of
precipitation magnitude-frequency curves for stations in these areas.
For stations that are sufficiently distant from one-another, a large storm that affects one station
does not produce a concurrent precipitation amount at the other station that represents a significant
storm. Thus, the collection of large storms recorded at a given station has different magnitude and
temporal patterns than the collection of large storms recorded at the distant station. Therefore, in a
given n-year period of time, the two stations represent a collection of independent storms
equivalent to 2n-years of observation. This independence of storm events allows the construction
of an extended precipitation time-series by combining of time-series records. This provides the
desired diversity of storm temporal patterns exhibited in the long time-series record.
Criteria for Selection of Stations for Combining of Time-Series Records
Information from the previous considerations and concepts can be used to establish criteria that allows
combining of precipitation time-series records. These criteria include:
1.
2.
3.
4.
5.
Similar climatology and storm characteristics;
Similar seasonalities of occurrence for selected durations representative of various storm types;
Similarity in the shape of the precipitation magnitude-frequency curves for selected durations;
Similarity in observed seasonal storm durations and seasonal storm interarrival times;
Sufficient distance between candidate stations that the time-series records are essentially
independent at the storm durations of primary interest for hydrologic modeling. This
corresponds to durations ranging from hourly through about 2-weeks;
6. Selection of stations with long high-quality records with high resolution measurements
recorded at 0.01-inch increments or less.
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These criteria resulted in the selection of stations in the western interior lowlands of the Pacific
Northwest having long, high-quality records with gages that measured precipitation at either
0.01-inch or 0.1-mm increments. Stations at Seattle Washington, Salem Oregon, and Vancouver
British Columbia were selected for development of time-series in the Puget Sound area (Figure 1,
Table 3a). Combination of the records from these stations result in an hourly precipitation timeseries with a total length equivalent to 158-years of record.
Stations at Seattle Washington, and Portland Oregon were selected for development of timeseries for sites in the lowlands of southwestern Washington along the Vancouver-Castle Rock
corridor (Figure 1,Table 3b). Combination of the records from these stations result in an hourly
precipitation time-series with a total length equivalent to 121-years of record.
Table 3a – Stations Used for Creation of Extended Precipitation Time-Series
Applicable to Puget Sound Lowland Areas
Station ID
1108447
45-7488
45-7473
35-7500
Station Name
Vancouver Airport BC
Seattle City WSO
SeaTac Airport
Salem Oregon
Latitude
Longitude
Elevation
(feet)
Period of
Record
49.1833
47.6000
47.4500
44.9000
123.1667
122.3333
123.3000
122.9833
361 feet
10 feet
400 feet
196 feet
1960-1997
1940-1964
1965-1999
1940-1999
Mean Annual
Precipitation
(in)
43.5 in
35.8 in
35.8 in
40.3 in
Table 3b – Stations Used for Creation of Extended Precipitation Time-Series
Applicable to Lowlands Areas Along Vancouver-Castle Rock Corridor
Station ID
45-7488
45-7473
35-6751
Station Name
Seattle City WSO
SeaTac Airport
Portland Airport
Latitude
Longitude
Elevation
(feet)
Period of
Record
47.6000
47.4500
45.5833
122.3333
123.3000
122.6000
10 feet
400 feet
19 feet
1940-1964
1965-1999
1940-2000
Mean Annual
Precipitation
(in)
35.8 in
35.8 in
36.9 in
Confirmation that the records from these stations meet the selection criteria was accomplished by
comparison of various measures of storm characteristics. Extensive comparisons were made
between the Seattle, Salem, and Vancouver BC stations in the analyses previously conducted for the
Pierce County study. Some of those comparisons will be repeated in this report. However, the
reader is referred to the Pierce County study28 for a detailed description of precipitation
characteristics at the three stations identified in Table 3a.
The following sections contain several comparisons for the Seattle WA, Salem OR, and
Vancouver BC stations that were used for developing time-series in the Puget Sound area and for
the Seattle WA and Portland OR stations, which were used in developing the time-series for the
Vancouver–Castle Rock area in southwestern Washington. Additional comparisons are
contained in Appendices A, B, C, and D.
The monthly distribution of annual precipitation is one expression of climatology. Figures 2a,b
depict the monthly distribution of annual precipitation at the four stations. Similarity of the
monthly distributions at the four stations/locations is evident. Precipitation annual maxima are
precipitation amounts for a specified duration that are the largest during a specified annual period.
The annual period used in this study was the water year beginning October 1st and running through
September 30th. For example, a dataset of 60 annual maxima will be obtained from 60-years of
record. Figures 3a,b depict the seasonality of 24-hour precipitation annual maxima. Here again,
similarity between stations is seen with the majority of storms occurring in the late-fall and winter
period for the 24-hour duration.
6
MGS Engineering Consultants, Inc.
PERCENT OF ANNUAL
MONTHLY PRECIPITATION
20
18
16
14
12
10
8
6
4
2
0
Vancouver BC
Seattle
Salem
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure 2a - Monthly Distribution of Annual Precipitation for Vancouver British Columbia,
Seattle Washington, and Salem Oregon
PERCENT OF ANNUAL
MONTHLY PRECIPITATION
20
18
16
14
12
10
8
6
4
2
0
Seattle
Portland
OCT NOV DEC
JAN
FEB MAR APR MAY
JUN
JUL
AUG SEP
MONTH
Figure 2b - Monthly Distribution of Annual Precipitation for Stations Located at
Seattle Washington and Portland Oregon
Seasonality of 24-Hour Precipitation
0.32
24-Hour Annual Maxima
0.28
Vancouver BC
FREQUENCY
0.24
Seattle
0.20
Salem
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL AUG SEP
MONTH
Figure 3a – Seasonality of Occurrence of 24-Hour Precipitation Annual Maxima
for Vancouver British Columbia, Seattle Washington, and Salem Oregon
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7
Seasonality of 24-Hour Precipitation
0.32
24-Hour Annual Maxima
0.28
FREQUENCY
0.24
Seattle
0.20
Portland
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL AUG SEP
MONTH
Figure 3b – Seasonality of Occurrence of 24-Hour Precipitation Annual Maxima
for Stations Located at Seattle Washington and Portland Oregon
24-HOUR PRECIPITATION (in)
Figures 4a,b,c,d depict probability-plots for the four stations for 24-hour precipitation annual
maxima as compared to the regional magnitude-frequency curve25,26,27. The similarity of the
observed precipitation annual maxima for the four stations relative to the regional magnitudefrequency curves is apparent.
6.0
5.5
5.0
4.5
4.0
3.5
Extreme Value Type 1 Plotting Paper
Regional Curve
Seattle
3.0
2.5
2.0
1.5
1.0
0.5
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure 4a – Magnitude-Frequency Relationship for 24-Hour Precipitation Annual Maxima
for Seattle Washington for 1940-1999 Period
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8
24-HOUR PRECIPITATION (in)
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
Extreme Value Type 1 Plotting Paper
Vancouver BC
Regional Curve
1.5
1.0
0.5
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
24-HOUR PRECIPITATION
Figure 4b – Magnitude-Frequency Relationship for 24-Hour Precipitation Annual Maxima
for Vancouver British Columbia for 1960-1997 Period
6.0
5.5
5.0
4.5
Extreme Value Type 1 Plotting Paper
Portland
4.0
3.5
3.0
2.5
2.0
Regional Solution
1.5
1.0
0.5
0.0
1.01
2
1.25
5
3.3
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
24-HOUR PRECIPITATION (in)
Figure 4c – Magnitude-Frequency Relationship for 24-Hour Precipitation Annual Maxima
for Portland Oregon for 1940-2000 Period
6.0
5.5
5.0
4.5
4.0
3.5
Extreme Value Type 1 Plotting Paper
Regional Curve
Salem
3.0
2.5
2.0
1.5
1.0
0.5
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure 4d – Magnitude-Frequency Relationship for 24-Hour Precipitation Annual Maxima
for Salem Oregon for 1940-1999 Period
9
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Independence of storm events is one of the important criteria that allow the combining of the timeseries records. Figure 5 depicts the relationship between 24-hour precipitation annual maxima at
Portland Oregon with concurrent 24-hour precipitation at Seattle Washington. Independence of
the data is indicated by the lack of correlation between precipitation amounts1,7. Independence is
further confirmed by examination of the storm dates for the annual maxima at the stations, where it
was found that there are separate dates of occurrence for the 24-hour annual maxima at the
stations. Similar lack of correlation was found for all station combinations for durations less than
10-days. This represents the primary durations of interest for hydrologic modeling. Additional
information on independence of annual maxima data is contained in Appendix D.
While tests for independence are commonly conducted on concurrent precipitation amounts,
precipitation amounts are surrogates for independence of the temporal patterns, which are of
primary interest. As discussed previously, independence of storm dates is a clear indication of
independence of storm temporal patterns. Table 4 lists the dates of occurrence of the ten largest
24-hour annual maxima precipitation amounts at the Vancouver BC, Seattle WA and Salem
Oregon Stations. A review of Table 4 shows only one storm date in common out of the 30 events.
Even in the cases where storm dates at distant stations coincide, the temporal patterns at distant
stations are often dissimilar. For example, Figures 6a,b depict the temporal patterns of hourly
precipitation for the February 1996 storm event, which was an extreme storm event at the 72-hour
duration for many sites in Washington and Oregon. It is seen there are major differences in the
temporal patterns recorded at Seattle and Portland for the February 1996 storm. This further
demonstrates independence of storm temporal patterns at distant stations, which is a critical
criterion that allows combining of records.
24-Hour Duration
Portland OR
4.0
Precipitation (in)
3.5
R 2 = 0.0125
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
Precipitation (in)
3.0
3.5
4.0
Seattle WA
Figure 5 – Relationship of 24-Hour Precipitation Annual Maxima at Portland Oregon
with Concurrent 24-Hour Precipitation at Seattle Washington
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Table 4- Listing of Largest 24-Hour Annual Maxima Precipitation Amounts at Selected Stations
RANK
VANCOUVER BC
st
1 Largest
2
3
4
5
6
7
8
9
10th Largest
SEATTLE WA
Dec 25, 1972
Dec 16, 1979
Oct 16, 1975
Jan 18, 1968
Nov 2, 1989
Oct 30, 1981
Jul 11, 1972
Jan 17, 1986
Nov 20, 1980
Aug 29, 1991
PORTLAND OR
Oct 5 1981
Nov 23, 1990
Nov 23, 1986
Feb 8, 1996
Jan 17, 1986
Nov 25 1998
Jan 8, 1990
Mar 4, 1972
Feb 6, 1945
Nov 19, 1959
Oct 26, 1994
Nov 18, 1996
Nov 10, 1995
Feb 9, 1945
Nov 15, 1973
Dec 12, 1977
Nov 1, 1984
Jan 6, 1948
Dec 26, 1942
Jan 3, 1956
Hyetograph - Seattle SeaTac AP
Hourly Precipitation (in)
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
12
24
36
48
60
72
84
96
108
120
132
144
Time (Hours)
Figure 6a – Temporal Pattern of Hourly Precipitation at SeaTac Airport
for February 5-9, 1996 Storm Event
Hyetograph - Portland AP
Hourly Precipitation (in)
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
12
24
36
48
60
72
84
96
108
120
132
144
Time (Hours)
Figure 6b – Temporal Pattern of Hourly Precipitation at Portland Airport
for February 5-9, 1996 Storm Event
MGS Engineering Consultants, Inc.
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PROCEDURES FOR CREATING AN EXTENDED PRECIPITATION TIME-SERIES
The extended precipitation time-series for an hourly time-step for a site of interest is created in two
steps. First, the original time-series at each station is rescaled to match the expected storm
characteristics for the site of interest. Second, the time-series for the two stations are linked
together in series to produce the total record. This resulted in a 158-year hourly record for the
three stations listed in Table 3a and 121-year hourly record for the two stations listed in Table 3b.
Scaling of Precipitation Time-Series
For the remaining discussions, the terms original station or original time-series, will be used in
referring to the station of measurement, and the terms target site or target time-series will be used
for the site of interest. As discussed previously, it is critical that the original time-series be
rescaled in a manner that yields the expected storm statistics for the target site at a wide range of
durations. This was accomplished by utilizing eight durations for matching of target site statistics.
The eight durations are the 2-hour, 6-hour, 24-hour, 72-hour, 10-day, 30-day, 90-day, and annual
(365-day) durations.
Specifically, the hourly time-series were scanned and each hourly precipitation amount was assigned
to one of the durations listed above. The assignment was made whenever a sequence of hourly
amounts exceeded a specified threshold. Thresholds were generally set at a magnitude corresponding
to events that occur several times per year. If an hourly amount was not part of a sequence that
exceeded one of the specified thresholds, it was assigned to the annual (365-day) duration.
Scaling of each hourly precipitation amount in the time-series was accomplished using a
standardized variates approach to preserve the mean and variance of the annual maxima series
for each duration at the target site. The standardized variates format1,23 has the form:
(Pt − μ t )
σt
=
(Po − xo )
(1)
so
where for each duration:
Pt is the precipitation total within the target hourly time-series for a particular storm event;
μt is the mean value of the annual maxima series for the target site;
σt is the standard deviation of the annual maxima series for the target site;
Po is the precipitation total within the original hourly time-series for a particular storm event;
- is the sample mean value of the annual maxima for the original time-series;
xo
so is the sample standard deviation of the annual maxima for the original time-series.
Specifically, each hourly precipitation amount in the original time-series is scaled by a scaling
factor (Ks) where the scaling factor is derived from the standardized variates format for a
specified duration (Equation 1). The scaling functions can be expressed as:
ht = Ks (ho)
Ks =
μt
Po
+
(2)
(Po −
xo ) σ t
P o so
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where:
ht is the hourly precipitation amount at the target site for a particular hour and date in the
target time-series;
ho is the corresponding hourly precipitation at the original station for a particular hour
and date in the original time-series;
This approach results in eight separate functional relationships (eight versions of Equation 3) to
preserve the mean and variance at each of the eight durations of interest in the target time-series.
This level of complexity is required to preserve the storm statistics over the wide range of
durations of interest. Although the scaling procedure may appear complex, the process may be
viewed simply as preserving the temporal pattern of the time-series and rescaling the amplitudes
of the hourly precipitation values.
Values of the mean (μt) and standard deviation (σt) for a given target site were obtained from
regional analyses of station statistics in western Washington. At-site mean values for target sites
were obtained from a regression relationship with mean annual precipitation. This analysis
identified behavior of at-site mean values that was different for sites in western Puget Sound relative
to that for eastern Puget Sound. This finding required that separate time-series be developed for
sites west and east of central Puget Sound. An example of the regression relationship for 72-hour atsite mean values is shown in Figure 7.
It is seen in Figure 7 that different relationships exist for sites west and east of central Puget Sound
that are immediately adjacent to the Puget Sound lowlands. Areas west of central Puget Sound and
leeward of the Olympic Mountains may generally be described as leeward areas with decreasing
values of mean annual precipitation in progressing from west to east towards Central Puget Sound21
(Figure 1). Conversely, areas east of central Puget Sound and near the Cascade foothills may
generally be described as windward areas with increasing values of mean annual precipitation in
progressing from west to east away from central Puget Sound and towards the Cascade Mountains.
Sites within the Vancouver-Castle Rock corridor are located in a more topographically confined
lowland area with a relatively rapid transition from leeward (west) to windward (east) storm
characteristics. Stations in this region have storm characteristics most similar to that of central
Puget Sound as depicted in Figure 7. Relationships such as Figure 7 were used for determining atsite mean values for target sites for all durations from 2-hours through 90-days, for sites west and
east of central Puget Sound and for sites in the Vancouver-Castle Rock corridor. These regions of
applicability are delineated in Figure 1.
The findings and procedures described above are consistent with the methods that were used for
developing maps of at-site mean values in the recently completed study of precipitation-frequency
for 24-hour and 2-hour durations in western Washington29. Figure 8 depicts the climatic regions
that were developed for that study, where regions 32 and 31 represent western and eastern Puget
Sound, respectively. Appendix E contains more detailed descriptions of the various climatic
regions developed for the precipitation-frequency study.
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Puget Sound and Adjacent Areas
72-Hour Annual Maxima
At-Site Mean (inches)
9.0
8.0
West of Central Puget Sound
Leeward of Olympics
7.0
6.0
5.0
4.0
East of Central Puget Sound
Cascade Foothills
3.0
2.0
Central Puget Sound
1.0
10
20
30
40
50
60
70
80
90
100
110
MEAN ANNUAL PRECIPITATION (inches)
Figure 7 – Relationship Between 72- Hour At-Site Mean Values
and Mean Annual Precipitation for Intermountain Locations Within and Near Puget Sound
Figure 8 – Climatic Regions Used in Precipitation-Frequency Studies for Western Washington29
MGS Engineering Consultants, Inc.
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Values of the standard deviation for target sites were obtained from regional analyses that were
previously conducted for Washington State25,26. Figures 9a,b depict the regional relationship25,26 of
the coefficient of variation (Cv) with mean annual precipitation. The standard deviation for the
target site can be computed from the coefficient of variation for each duration as:
σt
=
μt Cv
(4)
Regional Coefficient of Variation
0.36
Cv
0.32
2-Hour
0.28
6-Hour
0.24
0.20
0.16
24
28
32
36
40
44
48
52
56
60
64
68
MEAN ANNUAL PRECIPITATION (in)
Figures 9a – Relationships Between Regional Values of the Coefficient of Variation
and Mean Annual Precipitation for Lowland Areas in Western Washington
Regional Coefficient of Variation
0.36
Cv
0.32
24-Hour
0.28
72-Hour
10-Day
30-Day
90-Day
0.24
0.20
Annual
0.16
24
28
32
36
40
44
48
52
56
60
64
68
MEAN ANNUAL PRECIPITATION (in)
Figures 9b – Relationships Between Regional Values of the Coefficient of Variation
and Mean Annual Precipitation for Lowland Areas in Western Washington
CHARACTERISTICS OF COMPLETED EXTENDED PRECIPITATION TIME-SERIES
The following sections depict examples of the seasonalities and magnitude-frequency
characteristics of the hourly extended precipitation time-series that were developed.
Seasonality Characteristics of Extended Precipitation Time-Series
Examples of the seasonality of annual maxima for the 158-year Puget Sound time-series are shown
in Figures 10a,b,c,d for several durations. It is seen that the 2-hour annual maxima reflect a
combination of summer, fall, and winter events. Although the majority of 2-hour annual maxima
occur in the fall and winter seasons, the largest 2-hour annual maxima in lowland areas are
associated with summer thunderstorm events24,26. It is also seen that the seasonality of storms shift
into the late-fall and winter period as the duration increases. Similar behavior was exhibited for the
121-year time series applicable to the Vancouver-Castle Rock corridor. Additional seasonality
comparisons are contained in Appendix A.
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Seasonality of 2-Hour Precipitation
0.32
2-Hour Annual Maxima
0.28
158-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure 10a – Seasonality of Occurrence of 2-Hour Precipitation Annual Maxima
for Combined 158-Year Time-Series Record for Puget Sound Areas
Seasonality of 6-Hour Precipitation
0.32
6-Hour Annual Maxima
0.28
158-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure 10b – Seasonality of Occurrence of 24-Hour Precipitation Annual Maxima
for Combined 158-Year Time-Series Record for Puget Sound Areas
Seasonality of 24-Hour Precipitation
0.32
24-Hour Annual Maxima
0.28
158-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure 10c – Seasonality of Occurrence of 24-Hour Precipitation Annual Maxima
for Combined 158-Year Time-Series Record for Puget Sound Areas
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Seasonality of 10-Day Precipitation
0.32
10-Day Annual Maxima
0.28
158-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure 10d – Seasonality of Occurrence of 10-Day Precipitation Annual Maxima
for Combined 158-Year Time-Series Record for Puget Sound Areas
Magnitude-Frequency Curves for Extended Precipitation Time-Series
Examples of precipitation magnitude-frequency curves for annual maxima for several durations
for the 158-year time-series are shown in Figures 11a,b,c,d. Here it is seen that the probabilityplots of precipitation annual maxima for the rescaled time-series are consistent with the shape of
the regional magnitude-frequency curves for the Puget Sound Lowlands25,26,27,29. Likewise,
Figures 12a,b,c,d depict magnitude-frequency curves for several durations for a zone of 48inches mean annual precipitation in the Vancouver-Castle Rock corridor. Additional examples
of precipitation-frequency relationships are contained in Appendix C.
2-HOUR PRECIPITATION (in)
2.00
Extreme Value Type 1 Plotting Paper
1.80
1.60
Puget Sound East
Mean Annual Precipitation 56-inches
1.40
1.20
Regional Solution
1.00
0.80
0.60
0.40
0.20
0.00
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure 11a – Magnitude-Frequency Relationship for 2-Hour Precipitation Annual Maxima
for 158-Year Time-Series for Puget Sound East, 52-Inches Mean Annual Precipitation
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24-HOUR PRECIPITATION (in)
7.0
Extreme Value Type 1 Plotting Paper
6.0
Puget Sound East
Mean Annual Precipitation 56-inches
5.0
Regional Solution
4.0
3.0
2.0
1.0
0.0
1.01
1.25
2
3.3
5
10
50
20
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure 11b – Magnitude-Frequency Relationship for 24-Hour Precipitation Annual Maxima
for 158-Year Time-Series for Puget Sound East, 52-Inches Mean Annual Precipitation
10-DAY PRECIPITATION (in)
16.0
Extreme Value Type 1 Plotting Paper
14.0
12.0
Puget Sound East
Mean Annual Precipitation 56-inches
10.0
Regional Solution
8.0
6.0
4.0
2.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure 11c – Magnitude-Frequency Relationship for 10-Day Precipitation Annual Maxima
for 158-Year Time-Series for Puget Sound East, 52-Inches Mean Annual Precipitation
365-DAY PRECIPITATION (in)
100.0
90.0
80.0
Extreme Value Type 1 Plotting Paper
Puget Sound East
Mean Annual Precipitation 56-inches
70.0
Regional Solution
60.0
50.0
40.0
30.0
20.0
10.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure 11d – Magnitude-Frequency Relationship for Annual Precipitation
for 158-Year Time-Series for Puget Sound East, 52-Inches Mean Annual Precipitation
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2-HOUR PRECIPITATION (in)
2.00
Extreme Value Type 1 Plotting Paper
1.80
Vancouver-Castle Rock Corridor
Mean Annual Precipitation 48-inches
1.60
1.40
1.20
Regional Solution
1.00
0.80
0.60
0.40
0.20
0.00
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure 12a – Magnitude-Frequency Relationship for 2-Hour Precipitation
for 121-Year Time-Series for Zone of 48-Inches Mean Annual Precipitation
24-HOUR PRECIPITATION (in)
7.0
Extreme Value Type 1 Plotting Paper
6.0
5.0
Vancouver-Castle Rock Corridor
Mean Annual Precipitation 48-inches
4.0
Regional Solution
3.0
2.0
1.0
0.0
1.01
1.25
2
3.3 5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure 12b – Magnitude-Frequency Relationship for 24-Hour Precipitation
for 121-Year Time-Series for Zone of 48-Inches Mean Annual Precipitation
10-DAY PRECIPITATION (in)
16.0
Extreme Value Type 1 Plotting Paper
14.0
12.0
Vancouver-Castle Rock Corridor
Mean Annual Precipitation 48-inches
10.0
Regional Solution
8.0
6.0
4.0
2.0
0.0
1.01
1.25
2
3.3 5
10
20
50
100 200
500 1000
RECURRENCE INTERVAL (Years)
Figure 12c – Magnitude-Frequency Relationship for 10-Day Precipitation
for 121-Year Time-Series for Zone of 48-Inches Mean Annual Precipitation
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365-DAY PRECIPITATION (in)
90.0
80.0
70.0
Extreme Value Type 1 Plotting Paper
Vancouver-Castle Rock Corridor
Mean Annual Precipitation 48-inches
Regional Solution
60.0
50.0
40.0
30.0
20.0
10.0
0.0
1.01
1.25
2
3.3
10
5
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure 12d – Magnitude-Frequency Relationship for Annual Precipitation
for 121-Year Time-Series for Zone of 48-Inches Mean Annual Precipitation
CREATION OF EVAPORATION TIME-SERIES
Evaporation time-series are needed in addition to the precipitation time-series for soil moisture
accounting in continuous hydrologic modeling. The evaporation time-series are related to the
precipitation time-series in that heavy cloud cover on rainy days reduces the solar radiation that is
effective in the evaporation process. Thus, for any given time-of-year, evaporation is lowest on days
with large precipitation totals, and highest on days without precipitation. Accordingly, the
evaporation time-series must be developed in a manner consistent with the precipitation time-series.
Past practice in estimating evapotranspiration for continuous flow modeling has relied upon
utilizing pan evaporation data. These datasets commonly have periods of missing evaporation data.
In these situations, missing periods of record are filled in using an evaporation estimation equation.
Evaporation estimation equations commonly used for this purpose were developed by JensenHaise14, Penman22, and Hamon6. These equations compute pan or potential evapotranspiration
using climatic inputs such as temperature, solar radiation, and wind movement.
This approach is not practical for computing extended evaporation time-series because extended
climatic time-series for solar radiation and wind would also have to be estimated for the inputs to
the evaporation estimation equations. Alternatively, a stochastic approach for generating daily
evaporation was utilized that preserved the statistical behavior of evaporation both seasonally and
as affected by cloud cover on rainy days.
Stochastic Generation of Evaporation Time-Series
The basic concept for simulating daily evaporation is that evaporation varies on a monthly basis
throughout the year and also varies with the magnitude of daily precipitation. Rainy days are
characterized by heavier cloud cover and higher relative humidity by comparison with clear days.
For any given month, lower evaporation rates occur on rainy days, with the lowest rates occurring
on days with larger precipitation amounts due to more prolonged periods of precipitation and cloud
cover. Accordingly, evaporation data were first analyzed by determining the statistical
characteristics of evaporation on a monthly basis for rain-free days. Separate analyses were then
conducted for various ranges of daily precipitation to establish the reduction in evaporation as the
magnitude of daily precipitation increases.
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The four-parameter Beta distribution1,15 was chosen for describing daily evaporation because it
has a lower and upper bound representing the minimum and maximum evaporation that could
occur on a given day. The Beta distribution parameters include lower and upper bounds δ1 and
δ2 , and shape parameters α1 and α2. Distribution parameters were computed using the method of
moments1. Separate parameter sets were computed for each month of the year and for ranges of
daily precipitation within each month. This approach recognizes that the rate of evaporation
varies seasonally, and with the amount of precipitation that falls in a given day.
Evaporation data are available from four gage sites in western Washington (Table 5). Data from
the Puyallup 2 West Experimental Station (Station 45-6803) was used to compute the Beta
distribution parameters. This gage was chosen over the other sites because it is located in the
Puget Sound area, and has one of the longest and most complete records in western Washington.
Daily precipitation is also collected at the site so that relationships between pan evaporation and
precipitation could be determined.
Table 5 – Evaporation Gage Sites in Western Washington
STATION ID
45-0564
45-0587
45-6803
45-7463
STATION NAME
Bellingham 2 N
Bellingham 3 SSW
Puyallup 2 W Exp Station
Seattle Maple Leaf Reservoir
COUNTY
Whatcom
Whatcom
Pierce
King
MEAN ANNUAL
PRECIPITATION ( IN)
35
35
40
38
PERIOD OF
RECORD
1967-1984
1985-1999
1961-1995
1948-1960
PERCENT
COMPLETE
42%
47%
60%
72%
Figure 13 depicts the monthly distribution of mean evaporation corresponding to ranges of daily
precipitation. In the summer, the difference between the amounts of evaporation occurring on
rainy versus non-rainy days is the most significant. In the months of November, December, and
January, the difference was negligible and no differentiation between evaporation for rainy
versus non-rainy days was made.
M e a n Da ily Eva pora tion (in)
0.25
0.20
0.15
0.10
0.05
0.00
JA N
FE B
M AR
A PR
M AY
JUN
Precipitation=0
JUL
A UG
S EP
OCT
NOV
DE C
Precipitation>0.20 in
Figure 13 – Monthly Variation of Mean Daily Evaporation
As a Function of Daily Precipitation
Figure 14 shows the monthly distribution of the standard deviation of daily evaporation. The
standard deviation of daily evaporation was found to not vary significantly with the daily
precipitation and no differentiation between the standard deviation for rainy versus non-rainy
days was required.
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0.10
S ta nda rd De via tion of
D a ily Eva pora tion (in)
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
JA N
FE B
MA R
AP R
M AY
JU N
JUL
A UG
S EP
OCT
NOV
DE C
Figure 14 – Monthly Variation of the Standard Deviation of Daily Evaporation
The mean and standard deviation values shown in Figures 13 and 14 were used to compute the
distribution parameters for each range of precipitation for each month.
Simulation Procedure for Stochastic Generation of Daily Evaporation
The procedure for stochastic generation13,23 of daily evaporation is accomplished in three steps.
For each day, the daily precipitation is determined from the extended precipitation time-series.
Next, the Beta distribution parameters are selected depending on the month and the amount of
precipitation that fell during the selected day. Finally, the amount of evaporation is simulated by
randomly sampling13,23 from the Beta distribution based on the selected distribution parameters.
To verify that the stochastic routines were correctly replicating the evaporation characteristics, an
extended evaporation time-series was computed using the extended precipitation time-series
corresponding to the Puyallup 2 West Experimental Station (40-inches mean annual precipitation,
East Pierce County). The stochastically generated monthly mean pan evaporation values are seen
to compare favorably with the recorded values from the Puyallup station (Figure 15).
Figure 16 compares daily recorded and stochastically generated pan evaporation values for a
two-year period. This figure shows that the daily and monthly variability of the simulated timeseries are consistent with the recorded time-series. It should be pointed out that there should not
be a one to one relationship between the two time-series because the stochastically generated
time-series is developed using random sampling procedures. Rather, the stochastically generated
time-series is intended to preserve the monthly evaporation statistical characteristics for rain-free
periods and for rainy days.
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Monthly Pan Evaporation (in)
6.0
5.0
4.0
3.0
2.0
1.0
0.0
JAN FEB MAR APR MAY JUN
Recorded
JUL
AUG SEP OCT NOV DEC
Stochastically Simulated
Daily Evaporation (in)
Figure 15 – Comparison of Mean Monthly Pan Evaporation
from the Puyallup 2 West Experimental Station (30-Years of Record) and
158-Year Stochastically Generated Evaporation Time-Series
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Jan Mar May
Jul
Sep Nov Jan
1962
Mar May
Jul
Sep Nov
1963
Stochastically Computed
Recorded
Figure 16 – Comparison Between Daily Recorded and Stochastically Generated
Pan Evaporation for a Two-Year Period
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APPLICATION OF PRECIPITATION TIME-SERIES
Twenty-two extended precipitation time-series have been developed for the Puget Sound lowlands
and Vancouver-Castle Rock corridor for zones of mean annual precipitation ranging from 32-inches
to 60-inches (Figure 1, Table 1). The hourly time-series for the Puget Sound area have a record
length of 158-years and the time-series developed for the Vancouver-Castle Rock area have a record
length of 121-years. Twenty-two evaporation time-series have been developed to accompany the
precipitation time-series. Each of the evaporation time-series has a record length to match that of the
precipitation time-series and has a daily time-step.
Recommended Limits of Application, Consistent with Methods for Developing Time-Series
It is anticipated that these time-series will be used predominately in continuous hydrologic modeling
for small developments in urban settings using computer model MGSFlood17 . However, the timeseries can also be used for hydrological modeling of larger watersheds using a watershed-scale
model such as HSPF32. Questions will arise regarding limitations on applicability of the extended
precipitation time-series. These modeling limitations exist because of hydrological/meteorological
considerations for modeling of very small versus larger urban watersheds. Factors to be considered
include: the length of the time-step; the areal distribution of individual storms over large
watersheds; the areal distribution of summer thunderstorms; and the variation of mean annual
precipitation over large watersheds such as in foothill areas. Each of these situations is discussed in
the following sections.
Length of Time-Step – Accurate computation of flood peak discharge is dependent upon many
factors. The length of the time-step for describing the temporal distribution of precipitation can be
a limiting factor in determining the smallest watershed for which the time-series can be expected to
yield accurate flood estimates for flood peak discharge. In particular, small-urbanized watersheds
can be sensitive to short-duration, high-intensity bursts of precipitation. Therefore, the length of
the time-step must be sufficiently short relative to the time of concentration of the watershed to
provide for reasonable description of the magnitude and temporal resolution of the high-intensity
segment(s) of storms.
Use of an hourly time-step is generally adequate for development of flow-duration characteristics
on undeveloped sites of a few acres in the lowlands of western Washington. In these instances, the
runoff response is primarily interflow with limited surface response. However, the hourly timestep is much too long for proper computation of peak discharges for sites of a few acres where
impervious surfaces are present. Therefore, the hourly time-series should not be used for
computing peak discharge for sizing conveyance facilities on small sites where the time of
concentration is markedly less than an hour. Use of a time-series with a 15-minute time-step, such
as that developed for Pierce County28, would significantly improve the estimation of peak
discharge and increase applicability to sites as small as perhaps 10-acres.
These considerations of the length of the time-step are most important for sizing of conveyance
structures on small, highly urbanized watersheds. The 15-minute time-step should not pose a
limitation in analysis of stormwater detention facilities whose design and operation is governed
by a combination of runoff volume and flood peak discharge. For these cases, long-duration
storms of low to moderate intensities in the late-fall through winter period are typically the
governing storm types.
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For larger watersheds, there may be little difference between the flood peak discharges computed
from use of a 15-minute time-step and that for a 1-hour time-step. This occurs because the flashier
flood hydrographs produced by the higher intensity bursts in the 15-minute time-step will be
attenuated by the effect of channel storage and channel routing as the flood progresses downstream
through the stream network. The differences between flood peak discharges computed using the
15-minute time-step relative to that for the 1-hour time-step will be dependent upon watershed
specific characteristics.
Areal Distribution of Storms – The precipitation time-series were developed from records at
hourly precipitation gages. The general rule-of-thumb in the meteorological community18,20 is
that gage measurements are representative of a nominal area of 1-square mile for localized shortduration convective storms (thunderstorms) such as those that occur in the summer season. Gage
measurements are representative of a nominal area of 10-square miles for long-duration storms
with widespread areal coverage such as those that occur in the winter season.
For storm areas and watersheds sizes greater than these limits, attenuation of the storm results in a
reduction in basin-wide precipitation amounts. Tables 6a,b presents areal reduction factors18,20,26
that could be applied to hourly precipitation values within the extended time-series to account for
the areal distribution of precipitation over larger watersheds. A review of Tables 6a,b indicates
that the magnitudes of the areal reduction factors are not sufficiently large to be significant factors
for most applications on small urban watersheds. If a decision is made not to use the areal
reduction factors for a larger watershed, the usual outcome is that flood peaks and runoff volumes
are overestimated. The amount of the overestimation is dependent upon the magnitude of the
difference between the applicable areal reduction factor and unity, and the sensitivity of the
watershed to short-duration high-intensity storms.
Application of areal reduction factors is beyond the scope of this study. They are mentioned here
to alert the reader of limitations of the time-series in applications on larger watersheds.
Table 6a – Areal Reduction Factors for Long-Duration Storms with Widespread Areal Coverage
STORM AREA SIZE (mi2)
AREAL REDUCTION FACTOR
1-mi2
1.00
2-mi2
1.00
5-mi2
1.00
10-mi2
1.00
20-mi2
0.98
50-mi2
0.95
Table 6b – Areal Reduction Factors for Short-Duration High-Intensity Summer Storms
STORM AREA SIZE (mi2)
AREAL REDUCTION FACTOR
1-mi2
1.00
2-mi2
0.96
5-mi2
0.87
10-mi2
0.78
20-mi2
0.69
50-mi2
0.52
Variation of Mean Annual Precipitation over Large Watersheds – Mean annual precipitation varies
from west to east across the lowlands of western Washington (Figure 1). It is possible for a large
watershed to span several ranges of mean annual precipitation and the question arises as to the
choice of the appropriate precipitation time-series to use for hydrologic modeling. One approach is
to use the time-series applicable to the basin-average value of mean annual precipitation. An
alternative is to use two precipitation time-series to act as separate “stations” that would be
applicable to selected sub-basins. This latter approach would be useful where it was important to
replicate the variation of mean annual precipitation across the watershed. In either case, methods
must be employed to incorporate the effects of storm areal reduction as discussed previously.
MGS Engineering Consultants, Inc.
25
Differences With Pierce County Time-Series
The extended precipitation time-series discussed here were developed using the same procedures
as those utilized for the Pierce County time-series28. These new time-series for the Puget Sound
area differ from those in Pierce County in the manner the transition is made from western Puget
Sound to eastern Puget Sound. The new time-series for the Puget Sound lowlands (Table 1) are
based on separate storm statistics specific to western and eastern Puget Sound (Figure 7). The
time-series for Pierce County provide a transition from western Pierce County to eastern Pierce
County (Table 2) at the zone of 38-inches Mean Annual Precipitation (MAP). Thus, the two
time-series for 40-inches MAP west and east of central Puget Sound in Pierce County have
greater similarity than the 40-inch time-series for west and east Puget Sound in this new study.
The new time-series for west and east Puget Sound are essentially the same as those for Pierce
County for zones of mean annual precipitation greater than about 44-inches.
Application of Pierce County Time-Series in Southern King County
The extended precipitation time-series developed for Pierce County for the 38-inch to 42-inch
range of mean annual precipitation may also be used in southern King County. As was the case
for Pierce County, there is a transition from the western to eastern Puget Sound lowlands in
southern King County at the 38-inch zone of mean annual precipitation (Table 2). For example,
the 38-inch zone of mean annual precipitation for central Puget Sound (Table 2) is the zone most
representative of SeaTac Airport.
TIME-SERIES DELIVERABLES
As part of this report, a Compact Disc (CD) is included that contains all of the hourly precipitation
time-series and daily evaporation time-series for the zones of mean annual precipitation listed in
Table 1. The precipitation and evaporation time-series are output in ASCII text column format in
the PLTGEN format32 utilized by HSPF.
MGS Engineering Consultants, Inc.
26
SUMMARY
Extended length precipitation time-series records have been developed for application in western
Washington based on combining of hourly records from high-quality precipitation measurement
stations. Hourly precipitation time-series records from Seattle Washington, Vancouver British
Columbia, and Salem Oregon were combined and rescaled to replicate the storm characteristics
representative of the Puget Sound lowlands. This approach yielded time-series with record lengths
of 158-years. Hourly precipitation time-series records from Seattle Washington and Portland
Oregon were combined and rescaled to replicate the storm characteristics representative of the
Vancouver-Castle Rock area. This yielded time-series with record lengths of 121-years.
Time-series records can be combined because the climatology and storm characteristics are very
similar for sites in the western interior lowlands of the Pacific Northwest. This is an intermountain
valley area generally extending from near Vancouver British Columbia on the north to near Eugene
Oregon to the south. For stations that are sufficiently distant from one-another, a large storm that
affects one station does not represent a significant storm at the other station. Thus, the collection of
large storms recorded at a given station have different magnitude and temporal patterns than the
collection of large storms recorded at the distant station. This independence of storm events allows
the construction of an extended precipitation time-series by combining of time-series records.
The extended time-series were created by rescaling the original time-series at each station in a
manner that yields the desired storm statistics at a wide range of durations. This was accomplished
by utilizing eight durations for matching of the target site statistics, where the precipitation
statistics were based on regional analyses of 64 hourly and daily gages in western Washington.
The eight durations are the 2-hour, 6-hour, 24-hour, 72-hour, 10-day, 30-day, 90-day, and annual
(365-day) durations. The rescaling process may be viewed as preserving the shape and temporal
pattern of the original time-series, and rescaling the amplitudes of the hourly precipitation values.
Twenty-two extended time-series were created with applicability to sites with mean annual
precipitation ranging from 32-inches to 60-inches. A separate time-series was created for each
4-inch increment of mean annual precipitation. The extended 121-year and 158-year records
contain four to five-times the number of significant storm events and diversity of temporal storm
patterns and multi-day sequences of storms than would commonly be available from the short
record at a single station. This allows a very thorough analysis of watershed and detention facility
responses to various combinations of storm magnitudes, temporal patterns and sequences of
storms. The extended records also allow interpolation for estimation of extreme floods as opposed
to extrapolation that is required when using the short records that are typically available.
MGS Engineering Consultants, Inc.
27
REFERENCES
1. Benjamin JR and Cornell CA, Probability, Statistics and Decision for Civil Engineers,
McGraw-Hill, 1970.
2. Daly C, Neilson RP, and Phillips DL, PRISM, A Statistical-Topographic Model for Mapping
Climatological Precipitation over Mountainous Terrain, Journal of Applied Meteorology,
Vol 33, pp140-158, 1994.
3. Dinicola RS, Characterization and Simulation of Rainfall Runoff Relations in Western King
and Snohomish Counties, Washington, U.S. Geological Survey, Water-Resources
Investigations Report 89-4052.
4. Ecology, Stormwater Management Manual for Western Washington, Washington State
Department of Ecology, Water Quality Program, Publication 99-13, August 2001.
5. Federal Highway Administration, SYNOP, Synoptic Rainfall Data Analysis Program,
US Department of Transportation, McLean, VA, 1989.
6. Hamon WR, Estimating Potential Evapotranspiration, Proceedings of the American Society
of Civil Engineers, Journal of the Hydraulic Division, Vol. 87, No. HY3, p 107-120, 1961.
7. Helsel DR and Hirsch RM, Statistical Methods in Water Resources, Elsevier Studies in
Environmental Science 49, NY, 1992.
8. Holtan HN, Stitner G J, Henson WH and Lopez NC, USDAHL-74 Revised Model of
Watershed Hydrology, Technical Bulletin No 1518, Agricultural Research Service, US
Department of Agriculture, 1975.
9. Hosking JRM, and Wallis JR, Regional Frequency Analysis - An Approach Based on
L-Moments, Cambridge Press, 1997.
10. Hosking JRM, The 4-Parameter Kappa Distribution, Mathematical Sciences Dept., IBM
Research Division
11. HydroSphere, Climate Data, HydroSphere Data Products, Boulder CO.
12. Interagency Advisory Committee on Water Data, Guidelines for Determining Flood flow
Frequency, Bulletin #17B, September, 1981.
13. Jain R, The Art of Computer Systems Performance Analysis, John Wiley and Sons, 1991.
14. Jensen ME and Haise HR, Estimating Evapotranspiration from Solar Radiation, Proceedings
of the American Society of Civil Engineers, Journal of Irrigation and Drainage, Vol. 89,
No. IR4, p 15-41.
15. Johnson NL and Kotz S, Distributions in Statistics - Three Volume Set, John Wiley and
Sons, 1970.
16. King County, Surface Water Design Manual, King County Department of Natural Resources,
September, 1998.
17. MGSFlood, A Continuous Hydrological Simulation Model for Stormwater Facility Analysis,
Users Manual, MGS Software LLC, April 2002.
18. Miller JF, Frederick RH, and Tracey RJ, NOAA Atlas 2, Precipitation Frequency Atlas of the
Western United States, US Dept. of Commerce, NOAA, National Weather Service, 1973.
MGS Engineering Consultants, Inc.
28
19. National Research Council (NRC), Estimating Probabilities of Extreme Floods, Methods and
Recommended Research, National Academy Press, Washington DC, 1988.
20. National Weather Service, Probable Maximum Precipitation for the Pacific Northwest
States - Columbia, Snake River, and Pacific Coastal Drainages, Hydrometeorological
Report No. 57, US Department of Commerce, NOAA, Silver Spring, MD, October 1994.
21. Oregon Climate Service, Mean Annual Precipitation Maps for Western United States, PRISM
Model, Corvallis Oregon, 1997.
22. Penman HL, Natural Evaporation from Open Water, Bare Soil, and Grass, Proceedings of the
Royal Society of London, Ser. A, Vol 193, No. 1032, April 1948, p. 120-145.
23. Salas JD, Delleur JW, Yevdjevich Y, and Lane WL, Applied Modeling of Hydrologic Time
Series, Water Resources Publications LLC, 1980.
24. Schaefer MG, Characteristics of Extreme Precipitation Events in Washington State,
Washington State Department of Ecology, Water Resources Program, 89-51, October 1989.
25. Schaefer MG, Regional Analyses of Precipitation Annual Maxima in Washington State,
Water Resources Research, Vol. 26, No. 1, pp. 119-132, January 1990.
26. Schaefer MG, Technical Note 3: Design Storm Construction, Washington State Department
of Ecology, Water Resources Program, Dam Safety Guidelines, 92-55G, April 1993.
27. Schaefer MG, Magnitude Frequency Characteristics of Precipitation Annual Maxima in
Southern British Columbia, MGS Engineering Consultants Inc., December 1997.
28. Schaefer MG, Barker BL, Wallis JR and Nelson RD, Creation of Extended Precipitation
Time-Series for Continuous Hydrological Modeling in Pierce County Washington, for Pierce
County Public Works Department, MGS Engineering Consultants, Inc, Entranco, and Dr. JR
Wallis, February 2001.
29. Schaefer MG, Barker BL, Taylor GH and Wallis JR, Regional Precipitation-Frequency
Analysis and Spatial Mapping of Precipitation for 24-Hour and 2-Hour Durations in Western
Washington, for Washington State Department of Transportation, MGS Engineering
Consultants, Inc, March 2002.
30. Stedinger JR, Vogel RM, and Foufoula-Georgiou E, Frequency Analysis of Extreme Events,
Chapter 18, Handbook of Hydrology, McGraw Hill, 1992.
31. Thornthwaite CW and Mather JR, The Water Balance, Publications in Climatology, No. 8,
Centerton, New Jersey: Laboratory of Climatology, 1955.
32. US Environmental Protection Agency (USEPA), Hydrological Simulation Program-Fortran
(HSPF), Release 10, EPA/600/R-93/174, September 1993.
MGS Engineering Consultants, Inc.
29
APPENDIX A
SIMILARITY OF SEASONALITIES OF STORM OCCURRENCES
SUPPORTING ANALYSES
FOR
COMBINING OF TIME-SERIES RECORDS
MGS Engineering Consultants, Inc.
A-1
MGS Engineering Consultants, Inc.
A-2
SEASONALITIES OF ANNUAL MAXIMA AT VARIOUS DURATIONS
One of the criteria that must be met for combining of time-series records is that precipitation
annual maxima for the candidate stations have similar seasonality for a wide range of durations.
Figures A1a-A6d, depict the seasonality of occurrence for precipitation annual maxima for
durations of 2-hours, 6-hours, 24-hours, 72-hours, 10-days, and 30-days. Composite frequency
histograms of the seasonalities for the combination of annual maxima from the contributing
stations are also shown. For all durations, the seasonality characteristics are similar. It is also seen
that frequency histograms representative of the combination of seasonality data from the stations
provides a smoother and more representative seasonality histogram for each duration.
To summarize, the seasonality of precipitation annual maxima migrate further into the winter
storm season as the duration increases. Precipitation annual maxima at the 2-hour duration occur
more frequently in the fall and winter season, but also occur throughout the year. Separate
analyses shows that extreme precipitation events at the 2-hour duration in the lowlands of western
Washington are predominately thunderstorm events that occur in the warm season from late-spring
to early-fall24,26.
Precipitation annual maxima at the 6-hour duration occur more frequently in the early and late-fall
period. At the 24-hour duration, the seasonality of precipitation annual maxima has further
migrated to where the majority of annual maxima are late-fall and early-winter events. For
durations of 72-hour, 10-days, and 30-days, the annual maxima are predominately winter season
events.
MGS Engineering Consultants, Inc.
A-3
Seasonality of 2-Hour Precipitation
0.32
2-Hour Annual Maxima
0.28
Vancouver BC
FREQUENCY
0.24
Seattle
0.20
Salem
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL AUG SEP
MONTH
Figure A1a – Seasonality of 2-Hour Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
Seasonality of 2-Hour Precipitation
0.32
2-Hour Annual Maxima
0.28
158-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A1b – Seasonality of Combined 2-Hour Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
MGS Engineering Consultants, Inc.
A-4
Seasonality of 2-Hour Precipitation
0.32
2-Hour Annual Maxima
0.28
FREQUENCY
0.24
Seattle
0.20
Portland
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL AUG SEP
MONTH
Figure A1c – Seasonality of 2-Hour Annual Maxima
for Seattle WA and Portland OR
Seasonality of 2-Hour Precipitation
0.32
2-Hour Annual Maxima
0.28
121-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A1d – Seasonality of Combined 2-Hour Annual Maxima
for Seattle WA and Portland OR
MGS Engineering Consultants, Inc.
A-5
Seasonality of 6-Hour Precipitation
0.32
6-Hour Annual Maxima
0.28
Vancouver BC
FREQUENCY
0.24
Seattle
0.20
Salem
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A2a – Seasonality of 6-Hour Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
Seasonality of 6-Hour Precipitation
0.32
6-Hour Annual Maxima
0.28
158-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A2b – Seasonality of Combined 6-Hour Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
MGS Engineering Consultants, Inc.
A-6
Seasonality of 6-Hour Precipitation
0.32
6-Hour Annual Maxima
0.28
FREQUENCY
0.24
Seattle
0.20
Portland
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A2c – Seasonality of 6-Hour Annual Maxima
for Seattle WA and Portland OR
Seasonality of 6-Hour Precipitation
0.32
6-Hour Annual Maxima
0.28
121-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A2d – Seasonality of Combined 6-Hour Annual Maxima
for Seattle WA and Portland OR
MGS Engineering Consultants, Inc.
A-7
Seasonality of 24-Hour Precipitation
0.32
24-Hour Annual Maxima
0.28
Vancouver BC
FREQUENCY
0.24
Seattle
0.20
Salem
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL AUG SEP
MONTH
Figure A3a – Seasonality of 24-Hour Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
Seasonality of 24-Hour Precipitation
0.32
24-Hour Annual Maxima
0.28
158-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A3b – Seasonality of Combined 24-Hour Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
MGS Engineering Consultants, Inc.
A-8
Seasonality of 24-Hour Precipitation
0.32
24-Hour Annual Maxima
0.28
FREQUENCY
0.24
Seattle
0.20
Portland
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL AUG SEP
MONTH
Figure A3c – Seasonality of 24-Hour Annual Maxima
for Seattle WA and Portland OR
Seasonality of 24-Hour Precipitation
0.32
24-Hour Annual Maxima
0.28
121-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A3d – Seasonality of Combined 24-Hour Annual Maxima
for Seattle WA and Portland OR
MGS Engineering Consultants, Inc.
A-9
Seasonality of 72-Hour Precipitation
0.32
72-Hour Annual Maxima
0.28
Vancouver BC
FREQUENCY
0.24
Seattle
0.20
Salem
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL AUG SEP
MONTH
Figure A4a – Seasonality of 72-Hour Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
Seasonality of 72-Hour Precipitation
0.32
72-Hour Annual Maxima
0.28
158-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A4b – Seasonality of Combined 72-Hour Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
MGS Engineering Consultants, Inc.
A - 10
Seasonality of 72-Hour Precipitation
0.32
72-Hour Annual Maxima
0.28
FREQUENCY
0.24
Seattle
0.20
Portland
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A4c – Seasonality of 72-Hour Annual Maxima
for Seattle WA and Portland OR
Seasonality of 72-Hour Precipitation
0.32
72-Hour Annual Maxima
0.28
121-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A4d – Seasonality of Combined 72-Hour Annual Maxima
for Seattle WA and Portland OR
MGS Engineering Consultants, Inc.
A - 11
FREQUENCY
Seasonality of 10-Day Precipitation
0.44
0.40
0.36
0.32
0.28
10-Day Annual Maxima
Vancouver BC
Seattle
Salem
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A5a – Seasonality of 10-Day Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
Seasonality of 10-Day Precipitation
0.32
10-Day Annual Maxima
0.28
158-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A5b – Seasonality of Combined 10-Day Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
MGS Engineering Consultants, Inc.
A - 12
Seasonality of 10-Day Precipitation
0.32
10-Day Annual Maxima
0.28
FREQUENCY
0.24
Seattle
0.20
Portland
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP
MONTH
Figure A5c – Seasonality of 10-Day Annual Maxima
for Seattle WA and Portland OR
Seasonality of 10-Day Precipitation
0.32
10-Day Annual Maxima
0.28
121-Year Time-Series
FREQUENCY
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A5d – Seasonality of Combined 10-Day Annual Maxima
for Seattle WA and Portland OR
MGS Engineering Consultants, Inc.
A - 13
Seasonality of 30-Day Precipitation
0.36
30-Day Annual Maxima
0.32
Vancouver BC
FREQUENCY
0.28
Seattle
0.24
Salem
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL AUG SEP
MONTH
Figure A6a – Seasonality of 30-Day Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
Seasonality of 30-Day Precipitation
0.36
30-Day Annual Maxima
0.32
158-Year Time-Series
FREQUENCY
0.28
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A6b – Seasonality of Combined 30-Day Annual Maxima
for Vancouver BC, Seattle WA, and Salem OR
MGS Engineering Consultants, Inc.
A - 14
Seasonality of 30-Day Precipitation
0.36
30-Day Annual Maxima
0.32
FREQUENCY
0.28
Seattle
0.24
Portland
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A6c – Seasonality of 30-Day Annual Maxima
for Seattle WA and Portland OR
Seasonality of 30-Day Precipitation
0.36
30-Day Annual Maxima
0.32
121-Year Time-Series
FREQUENCY
0.28
0.24
0.20
0.16
0.12
0.08
0.04
0.00
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure A6d – Seasonality of Combined 30-Day Annual Maxima
for Seattle WA and Portland OR
MGS Engineering Consultants, Inc.
A - 15
APPENDIX B
SIMILARITY OF STORM CHARACTERISTICS
SUPPORTING ANALYSES
FOR
COMBINING OF TIME-SERIES RECORDS
MGS Engineering Consultants, Inc.
B-1
MEASURES OF TOTAL DURATION AND INTER-ARRIVAL TIME OF STORMS
A second criterion that must be met for combining of time-series records is that candidate stations
experience similar storm characteristics. Two measures of storm characteristics are storm total
duration and inter-arrival time between storms. To compute such measures, a definition of storm
must first be selected. The US Environmental Protection Agency has adopted a definition for
storm that is used in water quality analyses for stormwater. They define a storm as a period that
begins and ends with measurable precipitation and where no intermittent dry period during the
storm event exceeds n-hours. A value of 6-hours is commonly used for the maximum intermittent
dry period. Using this definition, precipitation time-series can be scanned and statistics computed
for measures such as average storm total duration, average storm volume, and average inter-arrival
time between storms. Statistics are computed for storms that exceed some specified threshold. For
these analyses, the threshold was set at 0.30 inches for the minimum storm to be considered, to
eliminate very small events that would not likely be hydrologically significant. Similar results are
obtained when other thresholds are used. The SYNOP computer program4 was used to scan the
time-series and compute storm statistics on a monthly basis.
Puget Sound Lowlands
The seasonal distribution of average storm duration, average storm volume, and inter-arrival time
between storms fore the Vancouver BC, Seattle WA, and Salem OR stations are shown in
Figures B1a, B2a, and B3a, respectively. The similarity in magnitude and seasonal behavior
between the three stations is apparent. In particular, differences in average storm volume
between stations (Figure B3b) are removed in the rescaling process.
One area of divergence appears in the inter-arrival time of storms in the summer season
(Figure B3a). This is primarily attributable to the generally lower summer precipitation in Salem
Oregon, and the slightly higher late-summer precipitation in Vancouver British Columbia
(Figure B3b). The magnitude of summer precipitation is small at all three stations and these
differences in warm season inter-arrival times have minimal hydrologic effect. In addition, the
combination of Vancouver BC and Salem OR values yields an average near that of the Seattle
WA station, in central Puget Sound.
Vancouver-Castle Rock Corridor
The seasonal distribution of average storm duration, average storm volume, and inter-arrival time
between storms for the Seattle WA and Portland OR stations are shown in Figures B1b, B2b, and
B4a, respectively. As was the case for the three station group above, similar behavior is seen in
the magnitude and seasonal behavior of storm characteristics for the Seattle and Portland stations.
MGS Engineering Consultants, Inc.
B-2
TIME (Hours)
Average Storm Total Duration
40
36
32
28
24
20
16
12
8
4
0
Storms exceeding 0.30 inches
Salem OR
SeaTac WA
Vancouver BC
OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT
MONTH
Figure B1a – Monthly Distribution of Average Storm Duration using US EPA Definition
of Storms for Vancouver BC, Seattle WA, and Salem OR
TIME (Hours)
Average Storm Total Duration
40
36
32
28
24
20
16
12
8
4
0
Storms exceeding 0.30 inches
Portland OR
SeaTac WA
OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT
MONTH
Figure B1b – Monthly Distribution of Average Storm Duration using US EPA Definition
of Storms for Seattle WA and Portland OR
MGS Engineering Consultants, Inc.
B-3
Average Storm Total Volume
PRECIPITATION (in)
1.40
Storms exceeding 0.30 inches
1.20
Salem OR
1.00
SeaTac WA
0.80
0.60
Vancouver BC
0.40
0.20
0.00
OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT
MONTH
Figure B2a – Monthly Distribution of Average Storm Volume using US EPA Definition
of Storms for Vancouver BC, Seattle WA, and Salem OR
Average Storm Total Volume
PRECIPITATION (in)
1.40
1.20
Storms exceeding 0.30 inches
Portland OR
1.00
SeaTac WA
0.80
0.60
0.40
0.20
0.00
OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT
MONTH
Figure B2b – Monthly Distribution of Average Storm Volume using US EPA Definition
of Storms for Seattle WA and Portland OR
MGS Engineering Consultants, Inc.
B-4
TIME (Hours)
Average InterArrival Time Between Storms
1000
900
800
700
600
500
400
300
200
100
0
Storms exceeding 0.30 inches
Salem OR
SeaTac WA
Vancouver BC
OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT
MONTH
Figure B3a – Monthly Distribution of Average Storm Volume using US EPA Definition
of Storms for Vancouver BC, Seattle WA, and Salem OR
PERCENT OF ANNUAL
MONTHLY PRECIPITATION
20
18
16
14
12
10
8
6
4
2
0
Vancouver BC
Seattle
Salem
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure B3b – Monthly Distribution of Annual Precipitation
for Vancouver BC, Seattle WA, and Salem OR
MGS Engineering Consultants, Inc.
B-5
TIME (Hours)
Average InterArrival Time Between Storms
1000
900
800
700
600
500
400
300
200
100
0
Storms exceeding 0.30 inches
Portland OR
SeaTac WA
OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP OCT
MONTH
Figure B4a – Monthly Distribution of Average Storm Volume using US EPA Definition
of Storms for Seattle WA and Portland OR
PERCENT OF ANNUAL
MONTHLY PRECIPITATION
20
18
16
14
12
10
8
6
4
2
0
Seattle
Portland
OCT NOV DEC
JAN
FEB MAR APR MAY JUN
JUL
AUG SEP
MONTH
Figure B4b – Monthly Distribution of Annual Precipitation
for Seattle WA and Portland OR
MGS Engineering Consultants, Inc.
B-6
APPENDIX C
SIMILARITY OF
PRECIPITATION-FREQUENCY CHARACTERISTICS
SUPPORTING ANALYSES
FOR
COMBINING OF TIME-SERIES RECORDS
MGS Engineering Consultants, Inc.
C-1
PRECIPITATION MAGNITUDE-FREQUENCY RELATIONSHIPS
A third criterion that must be met for combining of time-series records is the similarity of
precipitation magnitude-frequency relationships at the candidate stations for selected durations.
This comparison was made by constructing probability-plots of precipitation annual maxima for
the 2-hour, 6-hour, 24-hour, 72-hour, 10-day, 30-day, 90-day, and annual durations at each of the
stations. The probability plots were compared against regional growth curves for precipitation
magnitude-frequency that have been developed based on regional analyses of all precipitation
gages in western Washington24,25. These plots allow comparisons to be made of the slope and
shape of the precipitation annual maxima relative to the regional curves.
The probability-plots for the four stations and eight durations are depicted in Figures C1a-C8d.
It is seen that the precipitation annual maxima at the four stations compare well with the regional
frequency curves for all durations and all stations. This similarity allows straightforward
application of the scaling routines described in Equations 1-4 in the main body of the report.
MGS Engineering Consultants, Inc.
C-2
2-HOUR PRECIPITATION (in)
2.00
Extreme Value Type 1 Plotting Paper
1.80
1.60
Vancouver BC
1.40
Regional Curve
1.20
1.00
0.80
0.60
0.40
0.20
0.00
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C1a – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 2-Hour Duration for Vancouver BC for 1960-1997
2-HOUR PRECIPITATION (in)
2.00
Extreme Value Type 1 Plotting Paper
1.80
1.60
1.40
Salem OR
1.20
Regional Curve
1.00
0.80
0.60
0.40
0.20
0.00
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C1b – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 2-Hour Duration for Salem OR for 1940-1999
MGS Engineering Consultants, Inc.
C-3
2-HOUR PRECIPITATION (in)
2.00
Extreme Value Type 1 Plotting Paper
1.80
1.60
Regional Curve
Seattle WA
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
1.01
2
1.25
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C1c – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 2-Hour Duration for Seattle WA for 1940-1999
2-HOUR PRECIPITATION (in)
2.00
Extreme Value Type 1 Plotting Paper
1.80
1.60
Regional Solution
Portland OR
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C1d – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 2-Hour Duration for Portland OR for 1940-2000
MGS Engineering Consultants, Inc.
C-4
6-HOUR PRECIPITATION (in)
3.00
Extreme Value Type 1 Plotting Paper
2.80
2.60
2.40 Vancouver BC
2.20
2.00
1.80
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
20
2
1.01
1.25
3.3 5
10
Regional Curve
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
6-HOUR PRECIPITATION (in)
Figure C2a – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 6-Hour Duration for Vancouver BC for 1960-1997
3.00
Extreme Value Type 1 Plotting Paper
2.80
2.60
Salem OR
2.40
Regional Curve
2.20
2.00
1.80
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
20
50
2
1.01
1.25
3.3 5
10
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C2b – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 6-Hour Duration for Salem OR for 1940-1999
MGS Engineering Consultants, Inc.
C-5
6-HOUR PRECIPITATION (in)
2.60
Extreme Value Type 1 Plotting Paper
2.40
2.20
2.00
Seattle WA
1.80
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
20
2
1.01
1.25
3.3 5
10
Regional Curve
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
6-HOUR PRECIPITATION (in)
Figure C2c – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 6-Hour Duration for Seattle WA for 1940-1999
2.80
2.60
2.40
2.20
2.00
1.80
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
Extreme Value Type 1 Plotting Paper
Portland OR
Regional Solution
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C2d – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 6-Hour Duration for Portland OR for 1940-2000
MGS Engineering Consultants, Inc.
C-6
24-HOUR PRECIPITATION (in)
6.0
5.5
Extreme Value Type 1 Plotting Paper
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
Vancouver BC
0.5
0.0
1.01
1.25
2
Regional Curve
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
24-HOUR PRECIPITATION (in)
Figure C3a – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 24-Hour Duration for Vancouver BC for 1960-1997
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
Extreme Value Type 1 Plotting Paper
Regional Curve
Salem OR
0.5
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C3b – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 24-Hour Duration for Salem OR for 1940-1999
MGS Engineering Consultants, Inc.
C-7
24-HOUR PRECIPITATION (in)
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
Extreme Value Type 1 Plotting Paper
Regional Curve
Seattle WA
0.5
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
24-HOUR PRECIPITATION
Figure C3c – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 24-Hour Duration for Seattle WA for 1940-1999
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
Extreme Value Type 1 Plotting Paper
Portland OR
Regional Solution
1.5
1.0
0.5
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C3d – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 24-Hour Duration for Portland OR for 1940-2000
MGS Engineering Consultants, Inc.
C-8
72-HOUR PRECIPITATION (in)
9.0
Extreme Value Type 1 Plotting Paper
8.0
7.0
Vancouver BC
Regional Curve
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C4a – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 72-Hour Duration for Vancouver BC for 1960-1997
72-HOUR PRECIPITATION (in)
9.0
Extreme Value Type 1 Plotting Paper
8.0
7.0
Salem OR
Regional Curve
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C4b – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 72-Hour Duration for Salem OR for 1940-1999
MGS Engineering Consultants, Inc.
C-9
72-HOUR PRECIPITATION (in)
8.0
Extreme Value Type 1 Plotting Paper
7.0
6.0
Regional Curve
Seattle WA
5.0
4.0
3.0
2.0
1.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C4c – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 72-Hour Duration for Seattle WA for 1940-1999
72-HOUR PRECIPITATION (in)
8.00
Extreme Value Type 1 Plotting Paper
7.00
Portland OR
6.00
5.00
Regional Solution
4.00
3.00
2.00
1.00
0.00
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C4d – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 72-Hour Duration for Portland OR for 1940-2000
MGS Engineering Consultants, Inc.
C - 10
10-DAY PRECIPITATION (in)
14.0
Extreme Value Type 1 Plotting Paper
12.0
Vancouver BC
Regional Curve
10.0
8.0
6.0
4.0
2.0
0.0
1.01
1.25
2
3.3
5
20
10
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C5a – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 10-Day Duration for Vancouver BC for 1960-1997
10-DAY PRECIPITATION (in)
14.0
Extreme Value Type 1 Plotting Paper
12.0
Regional Curve
Salem OR
10.0
8.0
6.0
4.0
2.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C5b – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 10-Day Duration for Salem OR for 1940-1999
MGS Engineering Consultants, Inc.
C - 11
10-DAY PRECIPITATION (in)
12.0
11.0
Extreme Value Type 1 Plotting Paper
10.0
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
Seattle WA
Regional Curve
1.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C5c – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 10-Day Duration for Seattle WA for 1949-1999
10-DAY PRECIPITATION (in)
12.0
Extreme Value Type 1 Plotting Paper
10.0
Portland OR
8.0
Regional Solution
6.0
4.0
2.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C5d – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 10-Day Duration for Portland OR for 1949-2000
MGS Engineering Consultants, Inc.
C - 12
30-DAY PRECIPITATION (in)
22.0
Extreme Value Type 1 Plotting Paper
20.0
Regional Curve
18.0
16.0
Vancouver BC
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C6a – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 30-Day Duration for Vancouver BC for 1960-1997
30-DAY PRECIPITATION (in)
22.0
Extreme Value Type 1 Plotting Paper
20.0
18.0
16.0
Salem OR
Regional Curve
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C6b – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 30-Day Duration for Salem OR for 1940-1999
MGS Engineering Consultants, Inc.
C - 13
30-DAY PRECIPITATION (in)
18.0
Extreme Value Type 1 Plotting Paper
16.0
Regional Curve
Seattle WA
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C6c – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 30-Day Duration for Seattle WA for 1940-1999
30-DAY PRECIPITATION (in)
20.0
Extreme Value Type 1 Plotting Paper
18.0
16.0
Portland OR
14.0
12.0
Regional Solution
10.0
8.0
6.0
4.0
2.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C6d – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 30-Day Duration for Portland OR for 1940-2000
MGS Engineering Consultants, Inc.
C - 14
90-DAY PRECIPITATION (in)
40.0
Extreme Value Type 1 Plotting Paper
36.0
Vancouver BC
32.0
Regional Curve
28.0
24.0
20.0
16.0
12.0
8.0
4.0
0.0
1.01
2
1.25
5
3.3
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C7a – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 90-Day Duration for Vancouver BC for 1960-1997
90-DAY PRECIPITATION (in)
40.0
Extreme Value Type 1 Plotting Paper
36.0
32.0
28.0
Salem OR
Regional Curve
24.0
20.0
16.0
12.0
8.0
4.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C7b – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 90-Day Duration for Salem OR for 1940-1999
MGS Engineering Consultants, Inc.
C - 15
90-DAY PRECIPITATION (in)
36.0
Extreme Value Type 1 Plotting Paper
32.0
28.0
Seattle WA
Regional Curve
24.0
20.0
16.0
12.0
8.0
4.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C7c – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 90-Day Duration for Seattle WA for 1940-1999
90-DAY PRECIPITATION (in)
36.0
Extreme Value Type 1 Plotting Paper
32.0
28.0
Portland OR
Regional Solution
24.0
20.0
16.0
12.0
8.0
4.0
0.0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C7d – Comparison of Regional Magnitude-Frequency Curve with
Precipitation Annual Maxima at 90-Day Duration for Portland OR for 1940-2000
MGS Engineering Consultants, Inc.
C - 16
ANNUAL PRECIPITATION (in)
75
Extreme Value Type 1 Plotting Paper
70
65
Vancouver BC
60
55
50
45
40
35
30
25
20
15
10
5
0
20
2
10
1.01
1.25
3.3 5
Regional Curve
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
ANNUAL PRECIPITATION (in)
Figure C8a – Comparison of Regional Magnitude-Frequency Curve with
Annual Precipitation for Vancouver BC for 1960-1997
70
Extreme Value Type 1 Plotting Paper
65
60
Salem OR
55
50
45
40
35
30
25
20
15
10
5
0
20
2
10
1.01
1.25
3.3 5
Regional Solution
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C8b – Comparison of Regional Magnitude-Frequency Curve with
Annual Precipitation for Salem OR for 1940-1999
MGS Engineering Consultants, Inc.
C - 17
ANNUAL PRECIPITATION (in)
65
Extreme Value Type 1 Plotting Paper
60
55
Seattle WA
50
45
40
35
30
25
20
15
10
5
0
20
2
10
1.01
1.25
3.3 5
Regional Curve
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C8c – Comparison of Regional Magnitude-Frequency Curve with
Annual Precipitation for Seattle WA for 1940-1999
365-DAY PRECIPITATION (in)
70
60
Extreme Value Type 1 Plotting Paper
Portland OR
50
40
Regional Solution
30
20
10
0
1.01
1.25
2
3.3
5
10
20
50
100
200
500 1000
RECURRENCE INTERVAL (Years)
Figure C8d – Comparison of Regional Magnitude-Frequency Curve with
Annual Precipitation for Portland OR for 1940-2000
MGS Engineering Consultants, Inc.
C - 18
APPENDIX D
CORRELATION ANALYSES
CONFIRMATION OF INDEPENDENCE
SUPPORTING ANALYSES
FOR
COMBINING OF TIME-SERIES RECORDS
MGS Engineering Consultants, Inc.
D-1
MEASURE OF INDEPENDENCE OF PRECIPITATION ANNUAL MAXIMA
The critical criterion that allows combining of time-series records is the independence of storm
events at candidate stations. Tests for independence were made by conducting correlation
analyses7 of concurrent precipitation events for each of the eight durations for all combinations
of station pairs. Specifically, the paired datasets for the station pairs were comprised of the
precipitation annual maxima at the first station and concurrent precipitation at the second station
for the date of the annual maxima at the first station. To allow differences due to the timing of
storm passage, the concurrent precipitation amount was determined as the maximum
precipitation for the duration of interest in the time-window spanning one-day either side of the
date of the annual maxima at the first station.
The results of the correlation analyses for the 2-hour, 6-hour, 24-hour, and 72-hour durations are
depicted in Figures D1a –D4b. A review of the scatterplots for these durations shows little or no
relationship between concurrent precipitation events. All correlation coefficients were found not
to be significantly different from zero at the 95% level and the hypothesis of independence could
not be rejected. In short, the stations are sufficiently distant that significant storms at one site are
not associated with concurrent significant precipitation at the distant station.
2-Hour Duration
Vancouver BC
Precipitation (in)
0.8
y = -0.0659x + 0.2869
R 2 = 0.0054
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
Precipitation (in)
1.0
1.2
Seattle WA
Figure D1a – Correlation Relationship of 2-Hour Precipitation
for Vancouver BC and Seattle WA
2-Hour Duration
Portland OR
Precipitation (in)
1.2
y = -0.0179x + 0.2451
R 2 = 0.0003
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
Precipitation (in)
1.0
1.2
Seattle WA
Figure D1b – Correlation Relationship of 2-Hour Precipitation
for Portland Oregon and Seattle WA
MGS Engineering Consultants, Inc.
D-2
6-Hour Duration
Seattle WA
Precipitation (in)
1.6
y = 0.1509x + 0.3098
R 2 = 0.0165
1.2
0.8
0.4
0.0
0.0
0.4
0.8
1.2
Precipitation (in)
1.6
2.0
Vancouver BC
Figure D2a – Correlation Relationship of 6-Hour Precipitation
for Seattle WA and Vancouver BC
6-Hour Duration
Seattle WA
Precipitation (in)
2.0
y = -0.0833x + 0.6123
R 2 = 0.0049
1.6
1.2
0.8
0.4
0.0
0.0
0.4
0.8
1.2
Precipitation (in)
1.6
2.0
Portland OR
Figure D2b – Correlation Relationship of 6-Hour Precipitation
for Seattle WA and Portland Oregon
MGS Engineering Consultants, Inc.
D-3
24-Hour Duration
Seattle WA
Precipitation (in)
3.0
y = 0.2402x + 0.6369
R 2 = 0.0379
2.5
2.0
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Vancouver BC
Precipitation (in)
Figure D3a – Correlation Relationship of 24-Hour Precipitation
for Seattle WA and Vancouver BC
24-Hour Duration
Seattle WA
4.0
y = 0.1915x + 0.679
R 2 = 0.0368
Precipitation (in)
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Precipitation (in)
3.5
4.0
4.5
5.0
Portland OR
Figure D3b – Correlation Relationship of 24-Hour Precipitation
for Seattle WA and Portland Oregon
MGS Engineering Consultants, Inc.
D-4
72-Hour Duration
Precipitation (in)
Vancouver BC
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
y = 0.2107x + 1.3013
R 2 = 0.0424
0.0
1.0
2.0
3.0
4.0
Precipitation (in)
5.0
6.0
Seattle WA
Figure D4a – Correlation Relationship of 72-Hour Precipitation
for Vancouver BC and Seattle WA
72-Hour Duration
Portland OR
7.0
y = 0.3277x + 1.1542
R 2 = 0.0626
Precipitation (in)
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0.0
1.0
2.0
3.0
4.0
Precipitation (in)
5.0
6.0
Seattle WA
Figure D4b – Correlation Relationship of 72-Hour Precipitation
for Portland Oregon and Seattle WA
MGS Engineering Consultants, Inc.
D-5
The results of the correlation analyses for the 10-day duration are depicted in Figures D5ab.
Minor levels of correlation are present and correlation coefficients are near the threshold for
rejection of the hypothesis of independence at the 95% level of significance. It is concluded that
a very minor amount of correlation exists between precipitation totals on concurrent dates for the
10-day duration. The durations of primary interest for hydrologic modeling are in the range from
less than an hour through about 10-days. This represents durations associated with short,
intermediate and long duration storms as well as sequences of storms. Independence has been
demonstrated for these durations.
10-Day Duration
Precipitation (in)
Vancouver BC
12
11
10
9
8
7
6
5
4
3
2
1
0
y = 0.6404x + 0.9724
R 2 = 0.1663
0
1
2
3
4
5
6
7
8
9
10
Seattle WA
Precipitation (in)
Figure D5a – Correlation Relationship of 10-Day Precipitation
for Vancouver BC and Seattle WA
10-Day Duration
Precipitation (in)
Portland OR
10
9
8
7
6
5
4
3
2
1
0
y = 0.4766x + 1.9051
R 2 = 0.1017
0
1
2
3
4
5
6
Precipitation (in)
7
8
9
10
Seattle WA
Figure D5b – Correlation Relationship of 10-Day Precipitation
for Portland Oregon and Seattle WA
MGS Engineering Consultants, Inc.
D-6
The results of the correlation analyses for the 30-day, 90-day, and annual (365-day) durations are
depicted in Figures D6a–D8b. Correlation coefficients are seen to incrementally increase
progressing from minor to moderate levels of correlation as the duration increases. This is a
natural consequence of unusually wet years being associated with long-term regional weather
patterns that affect very broad areas. Likewise, protracted dry conditions are associated with
regional weather patterns that affect very broad areas. El-Nino and La-Nina years are two
examples of these types of regional multi-month or multi-year types of weather phenomenon.
These conditions have the effect of reducing the effective record length of the extended time-series
for these durations. This can be interpreted to mean that the effective number of independent years
of record is something less than the 158-years or 121-years of the time-series. A review of the
precipitation magnitude-frequency relationships in Appendix C (Figures C6a-C8d) shows high
variability for monthly through annual precipitation, which includes extremely wet and extremely
dry periods. Given this high variability, the minor to moderate levels of correlation in the 30-day,
90-day, and annual durations are not judged to significantly degrade the effective record length of
the extended time-series for these long durations.
30-Day Duration
Vancouver BC
16
y = 0.5425x + 3.5399
R 2 = 0.1473
Precipitation (in)
14
12
10
8
6
4
2
0
0
2
4
6
8
10
12
14
16
Seattle WA
Precipitation (in)
Figure D6a – Correlation Relationship of 30-Day Precipitation
for Vancouver BC and Seattle WA
30-Day Duration
Precipitation (in)
Portland OR
20
18
y = 0.5926x + 2.9793
16
R 2 = 0.1943
14
12
10
8
6
4
2
0
0
2
4
6
8
10
Precipitation (in)
12
14
16
Seattle WA
Figure D6b – Correlation Relationship of 30-Day Precipitation
for Portland Oregon and Seattle WA
MGS Engineering Consultants, Inc.
D-7
90-Day Duration
Seattle WA
36
y = 0.5871x + 5.3124
R 2 = 0.4532
Precipitation (in)
32
28
24
20
16
12
8
4
0
0
4
8
12
16
20
24
28
32
Vancouver BC
Precipitation (in)
Figure D7a – Correlation Relationship of 90-Day Precipitation
for Seattle WA and Vancouver BC
90-Day Duration
Seattle WA
32
y = 0.5956x + 5.8995
Precipitation (in)
28
2
R = 0.5503
24
20
16
12
8
4
0
0
4
8
12
16
20
24
Precipitation (in)
28
32
36
40
Portland OR
Figure D7b – Correlation Relationship of 90-Day Precipitation
for Seattle WA and Portland Oregon
MGS Engineering Consultants, Inc.
D-8
Annual Precipitation
Vancouver BC
Precipitation (in)
60
y = 0.7765x + 14.933
R 2 = 0.3609
50
40
30
20
10
0
0
10
20
30
40
50
60
Seattle WA
Precipitation (in)
Figure D8a – Correlation Relationship of Annual Precipitation
for Vancouver BC and Seattle WA
Annual Precipitation
Seattle WA
70
y = 0.7782x + 9.0871
R 2 = 0.5578
Precipitation (in)
60
50
40
30
20
10
0
0
10
20
30
40
Precipitation (in)
50
60
70
Portland OR
Figure D8b – Correlation Relationship of Annual Precipitation
for Seattle WA and Portland Oregon
MGS Engineering Consultants, Inc.
D-9
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D - 10
APPENDIX E
DESCRIPTIONS OF CLIMATIC REGIONS
FOR APPLICABILITY OF TIME-SERIES
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E-1
DESCRIPTION OF CLIMATIC/GEOGRAPHIC REGIONS
Climatic regions were previously identified as part of the regional precipitation-frequency analysis
conducted for western Washington29. In that context, climatic regions are areas having similar
climatological and topographical characteristics. The magnitude and gradient of mean annual
precipitation were the primary measures used to define the boundaries between the regions. Those
regions include:
Coastal Lowlands (Region 5) – The lowlands along the west coast of Washington, Oregon and
Vancouver Island that are open to the Pacific Ocean. The eastern boundary is either a generalized
contour line of 1,000 feet elevation, or the ridgeline of mean annual precipitation that separates the
coastal lowlands from the interior lowlands, such as within the Aberdeen-Montesano gap.
Coastal Mountains West (Region 151) – The windward faces of the Olympic Mountains,
Willapa Hills, Black Hills, Coastal Mountains in Oregon, and Vancouver Island Mountains in
British Columbia above a generalized contour line of 1,000 feet elevation. These areas are
bounded to the west by the 1,000 feet contour line, and bounded to the east by the ridgeline of
mean annual precipitation near the crestline of the mountain barrier.
Coastal Mountains East (Region 142) – The leeward faces of the Olympic Mountains, Willapa
Hills, Black Hills, Coastal Mountains in Oregon, and Vancouver Island Mountains in British
Columbia above a generalized contour line of 1,000 feet elevation. These areas are bounded to
the west by the ridgeline of mean annual precipitation near the crestline of the mountain barrier,
and bounded to the east by the 1,000 feet contour line.
Interior Lowlands West (Region 32) – The interior lowlands below a generalized contour line
of 1,000 feet elevation bounded to the east by the trough-line of mean annual precipitation
through the Strait of Juan De Fuca, Puget Sound Lowlands and Willamette Valley. This is a
zone of low orography where mean annual precipitation generally decreases from west to east.
Interior Lowlands East (Region 31) – The interior lowlands below a generalized contour line of
1,000 feet elevation bounded to the west by the trough-line of mean annual precipitation through
the Strait of Juan De Fuca, Puget Sound Lowlands and Willamette Valley. This is a zone of low
orography where mean annual precipitation generally increases from west to east.
Cascade Mountains West (Region 15) – The windward face of the Cascade Mountains in
Washington, Oregon, and British Columbia above a generalized contour line of 1,000 feet elevation.
This region is bounded to the east by the ridgeline of mean annual precipitation near the Cascade crest.
Cascade Mountains East (Region 14) – The leeward face of the Cascade Mountains in
Washington, Oregon, and British Columbia above the 20-inch isopluvial of mean annual
precipitation. This region is bounded to the west by the ridgeline of mean annual precipitation
near the Cascade crest.
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E-2
Figure E1 – Delineation of Climatic Regions for Western Washington Study Area
MGS Engineering Consultants, Inc.
E-3