Recent Advances in the Estimation ofExtreme Precipitation and Extreme Floods –A Physics-based Perspective
M. L. Kavvas and Y. Iseri
Hydrologic Research Laboratory
Department of Civil & Environmental Engineering
University of California, Davis, CA 95616, USA

Approaches
to theestimationof extreme
floods:I. Purely statistical approach to the estimation of theextreme flood;
II. Estimation of extreme flood as a result of a rainfallrunoff analysis with input from statistical analysis ofextreme precipitation;
III. Conventional Probable Maximum
Precipitation/Probable Maximum Flood Estimation;
IV. Estimation of Maximum Flood based on Numerical
Modeling of the Critical Atmospheric-Hydrologic
Processes

I. Purely statistical approach to the estimation of the extreme flood
based on available historical hydrologic data:
A. Methodology based on considering the flood peak discharge as a random variable:

The standard procedure is to construct an empirical frequency histograma) for the peak discharge of an annual maximum flood event (Gumbel 1941, Dalrympl
1960, Stedinger 1983, Smith J. 1987, WMO 1989, Madsen et al. 1997, Katz et al. 2003,
Robson and Reed, 2008, and others), orb) of the peak discharge over a specified threshold (WMO 1989, Smith RL 1989, Katz et al.
2003, Robson and Reed 2008, and others) from the available hydrologic data.
▪ Extrapolate this histogram to long return periods based on the fit of the empiricalfrequency histogram by a theoretical probability distribution, such as Log Pearson Type III
distribution, Generalized Extreme Value Distribution, Gumbel’s distribution, etc.
▪ Then estimate the extreme flood discharge for a specified return period from thetheoretical probability distribution tail.

I. Purely statistical approach to the estimation of the extreme flood
based on available historical hydrologic data:
B. Methodology that considers flood peaks as a stochastic process:▪ This approach is mainly based on Peaks over a Threshold (POT) framework.
▪ After specifying a threshold, the flood peak discharge occurrences abovethat threshold are modeled as a point stochastic process, either as:▪ a Poisson process (Todorovic and Zelenhasic, 1970; RL Smith, 1989 andothers) that assumes flood peak occurrences are mutually independent, or▪ a Poisson Cluster process (Cervantes et al. 1983).

II. Estimation of the extreme flood based on a rainfall-runoff simulation with
input from extreme precipitation that is estimated by statistical approachesi.

Development of frequency curves for extreme precipitation (probable maximum precipitation),
considered as a random variable, based on historical data for specified durations;This approach, popularized by Herschfield (1961, 1965), develops estimates of maximum precipitation
depths as function of geographical location and precipitation duration. It is based on the frequency factor
formulation of Ven-Te-Chow (1951). Recent improvements to this estimation procedure were provided byvarious authors (Koutsoyiannis 1999, Papalexiou and Koutsoyiannis 2013, Nerantzaki and Papalexiou 2021).

ii. Development of a Stochastic Weather Generator (WG) for the time series of precipitation and otheratmospheric variables correlated with precipitation;
A WG produces synthetic time series of weather data for a location based on the statistical characteristics
of observed weather at that location (Hutchinson 1987, Richardson 1991). The first step in the developmentof a WG is to model daily precipitation in terms of a Markov Chain or an alternating Renewal Process. The
second step is to model the remaining weather variables of interest (temperature, solar radiation, humidity
and windspeed, etc.) conditional on precipitation occurrence.

II. Estimation of the extreme flood based on a rainfall-runoff simulation with
input from extreme precipitation that is estimated by statistical approachesiii. Modeling of precipitation by stochastic models;In this approach precipitation is modeled in terms of the occurrence times of precipitation events above a prespecified
threshold as a stochastic point process which are then marked by precipitation depths (Todorovic 1979, Cervantes et al.
1983, Waymire et al. 1984, Smith 1989, Rodrigues-Iturbe et al. 1988, Kavvas et al. 1988, Cowpertwait 1998 and others).

iv. Modeling precipitation random fields by fractals;
In this approach the precipitation fields are analyzed and modeled as fractal or multifractal fields to accommodate theirtime-space scaling (Schertzer and Lovejoy 1987, Gupta and Waymire 1993, Lovejoy and de Lima 2015, and others).

v. Modeling extreme precipitation by statistical storm transposition;
In this approach the historical precipitation field spatial shape is approximated by a certain geometric shape (circular or
elliptical) and the centroid of the approximate field is transposed according to a probability distribution (Gupta 1972,
Foufoula-Georgiou 1989). Then by means of the probability distribution of the storm centroid an ensemble ofprecipitation fields are generated, from which one can obtain basin precipitation depths corresponding to specified return
periods. However, this method of historical storm transposition does not conserve the mass, momentum or energy of thehistorical storm system. Also, the uncertainty in the storm centroid location is different then the chronological uncertainty.

After the precipitation fields are simulated by one of the above approaches, they can then be input to a rainfallrunoff model to produce a corresponding streamflow event that will correspond to the precipitation field of a
specified return period.

ISSUES WITH THE ABOVE STATISTICAL APPROACHES
1. None of the above statistical methods for estimating precipitation or floods are physically-based inthat they do not conserve neither the mass, nor the momentum nor the energy in the historicalstorm systems.
2. All of the above methods, except those studies that address the precipitation-flood events asclusters, consider the extreme flood event as a single event with a single extreme peak discharge,
although some early studies (WMO 1989) did stress the importance of treating floods as asequence of events. However, clustering of the flood events as a sequence of inflows to a dam
create the most critical conditions for the failure of the dam.
3. Those stochastic Poisson cluster models that address precipitation as a clustered process, do notaddress the modeling of the floods resulting from these precipitation field clusters.
4. None of the above statistical approaches differentiate and model explicitly the floods with respect
to different storm mechanisms (such as floods from atmospheric rivers, floods from extratropical
cyclonic systems, floods from mesoscale convective systems, floods from tropical
cyclones/hurricanes/typhoons, etc.). However, flood events may behave very differently under
different severe storm mechanisms.
5. None of the statistical methods produces realistic spatial configurations of the extreme precipitation
fields which vary drastically with different storm mechanisms.

Conventional Method for Estimating Probable Maximum Precipitation (PMP) and Probable
Maximum Flood (Paulhus and Gilman 1953, Hansen et al. 1977, Schreiner et al. 1978, WMO
1989, 2009, and various Hydrometeorological Reports of US NWS):

Definition of PMP and PMF (World Meteorological Organization (WMO), 2009)▪ Probable Maximum Precipitation (PMP) is defined as the theoreticalmaximum precipitation for a given duration under possible meteorologicalconditions.
▪ Probable Maximum Flood (PMF) is the theoretical maximum flood due to a
PMP at a specified river basin or geographical location (such as the inflow
location of a dam, or the location of a bridge, etc.).
Conventional PMP estimation procedure (WMO, 2009):
i. Select the historical representative severe storm event;ii. Compute the Depth-Area-Duration curves for the selected storm;iii. Separate the convergence part of the storm from its orographic component;
iv. Maximize the moisture in the convergence component of the storm with respect to precipitable water,
v. Transpose this maximized storm component virtually in order to maximize the precipitation over the target watershed;
vi. Adjust the estimate for the orographic component (elevation and barrier adjustment); adjust the estimate with respect
to duration and area.

Approximations of the Conventional Method for Estimating PMP:
1. The Conventional PMP estimation method artificially separates a storm into
non-orographic (convergence) and orographic components while in reality astorm system is a whole that cannot be separated into such components;
2. Precipitation is taken proportional to precipitable water, ignoring thecontribution of the moisture flux;
3. The storm transposition is performed virtually, not actually, by adjustingcertain storm characteristics;
4. The conservation of mass, momentum and energy of a storm system are notensured in the storm maximization operations of the Conventional PMP.

JANUARY 1 – FEBRUARY 28, 2017 SEVERE STORM AND FLOOD OVERCALIFORNIA

General weather pattern across the Eastern Pacific Ocean and West Coast for each storm period during
January and February 2017 (CNRFC, 2017).

Atmospheric River
In the west coast of US, severe storms are mainly caused by ahigh-moisture atmospheric flow coming from a tropical zoneof the Pacific Ocean, and referred to as “atmospheric river(AR)”.

[From NWS California-Nevada RFC]

Precipitable Water Fields over the Pacific Ocean near the coast of California on January-February, 2017 California FloodCalifornia River Network System and River Basins

Inflow hydrograph to Shasta Lake during January 1 – February 28, 2017 Flood at Shasta
Lake Watershed in California

Inflow to Folsom Lake at American River Watershed, California during the January 1 –February 28, 2017 Flood

In considering maximum precipitation in the Western Coastal regionof the US,
It is critical to consider how to maximize precipitation caused by the
Atmospheric River (AR).

Development of physically-based method
to maximize precipitation caused by ARs.

Precipitation Maximization by a Numerical Atmospheric
Model for Atmospheric River (AR) Storm Systems
I.

Select the historical severe storm events from the reconstructed
historical precipitation record at a target watershed✓ Identify the ARs that hit the specified watershed during each of
the selected historical severe storm events.

II. Perturbation of the atmospheric fields for the selected historicalsevere storm events.
II-1. Atmospheric Boundary
Condition Shifting

II-2. Relative humidity
optimization

III. Probable Maximum Precipitation (PMP) over a target watershed

I.

Select the historical severe storm events from the reconstructed
historical precipitation record at a target watershed;

Limitations in using observed precipitation data;• The number of observation stations in a target study area andtheir recording periods are insufficient.
• The PRISM daily data set (Daly et al. 2008, 2013) covers thecontinental US for the period 1981 to present at 4 km grid
resolution (PRISM Climate Group, 2016).
• Many of the recorded historical floods over a target watershed
may have happened prior to 1981.

Meanwhile, there are various historical atmospheric reanalysis
data sets some of whom date as far back as to 1851.

Global Reanalysis data

NOAA/CIRES 20th Century
Reanalysis (20CR) Version 2c- 1851 – 2014
- Horizontal resolution of 2
degree (T62), 24 vertical levels

ECMWF Twentieth Century
Reanalysis (ERA-20C)- 1900 – 2010
- Horizontal resolution of 125 km(T159), 37 vertical levels

NCEP Climate Forecast System
Reanalysis (CFSR)- 1979 – 2016
- Horizontal resolution of 0.5
degree (T382), 64 vertical levels• Reconstruction of the historical atmospheric conditions over any target watershed over theworld can be performed by means of reanalysis global data sets that are available fromvarious atmospheric organizations around the world, such as US NCAR, ECMWF, etc.
• Hence, it is necessary to reconstruct the historical atmospheric conditions at hourly or
finer intervals by a numerical atmospheric model after the model is calibrated andvalidated by the available PRISM daily data.

Weather Research & Forecasting model (WRF)
Globalgriddeddata

Dynamically downscaled
into target region/domain

WRF and WRF pre-processing system
WPS (WRF Preprocessing
System):• Data format
conversion• Interpolation• Static data processing

WRF:
Dynamical downscaling ofa global reanalysis intohigh resolution regional
atmospheric data

I.

Select the historical severe storm events from the reconstructed
historical precipitation record at a target watershed

Use a numerical atmospheric model (WRF) toreconstruct atmospheric fields;
Choose the most severe historical storms based on the
moisture conditions in these storms (such as precipitation
depth or maximum IVT exceeding a specified threshold
during the storm duration);

Shift the atmospheric fields so that the atmosphericriver strikes the target watershed at the optimal
location and in the optimal direction to produce themaximum precipitation over the watershed.

II. Perturbation of the atmospheric fields for the selected historical severe storm events.
II-1. Atmospheric Boundary Condition Shifting Method
1.
2.

Shift the atmospheric BCs with respect to only latitude (Shift1D) and then also with longitude (Shift2D)(Ohara et al. 2011, Ishida et al. 2015);
Shift the atmospheric BCs along an identified AR until the basin-average precipitation reaches a maximum
and then starts to decrease.

Differences from traditional PMP Approach▪ Uses a physically-based numerical atmospheric model▪Produces all relevant atmospheric variables’ information for a given severe storm (besides the precipitation,
also the wind field, humidity field, temperature field, radiation field, etc. for the specified storm

II. Perturbation of the atmospheric fields for the selected historical severe storm events.

II-2. Relative humidity optimization
The Relative Humidity (RH) perturbation method (RHP-IVT method; Toride et al., 2019)
increases RH proportionally at those boundary sections where high IVT values are observedin order to maximize the storm event with physically realistic atmospheric fields.
1 300
ഥ𝐼𝑉𝑇 = න 𝑞ത 𝑈𝑑𝑝
𝑔 1000g: gravitational acceleration (m s-2), 𝑞ത is the mean layer specific humidity (kg kg-1),
ഥ mean layer horizontal wind speed (m s-1) , 𝑝: the pressure (hPa)
𝑈:

Left:
Example of moisture perturbation along the path of
an atmospheric river: a)Integrated water vapor
transport (IVT) in [kg/m-sec] at 0600 UTC 6 Feb 1996.
The black box shows the outer modeling domain.
Toride etal. 2019

II. Perturbation of the atmospheric fields for the selected historical severe storm events.

II-2. Relative humidity optimization
𝑅𝐻 = ቊ

min 𝛽RH0 , 97 ,RH0 ,𝑖𝑓 RH0 < 97%
𝑖𝑓 RH0 ≥ 97%

where RH0 is the original relative humidity (%) and 𝛽 is a multiplication factor
to determine the increment of RH.
The above equation sets the upper threshold of RH to 97% in order to avoid
quick saturation near the modeling boundary (Zhao et al., 1997).

• Relative humidity (over areas where the IVT > 250 kg/m/s) is gradually increased, alongwith BC shifting until a maximum basin-average precipitation depth is reached.
• 100s of regional atmospheric numerical simulations are performed in order to reach theatmospheric conditions that maximize the basin-average precipitation depth.

II. Perturbation of the atmospheric fields for the selected
historical severe storm events
The reconstructed atmospheric fields for theselected historical severe storm events
II-1. Atmospheric boundary
condition shifting

II-2. Relative humidity optimization&

III. Probable Maximum Precipitation (PMP) over a target watershedExample of physically-based PMP/PMF
estimation for
Seven Southern California watersheds

Locations and elevation map of the target watersheds, consisting of theCosumnes (CRW), Mokelumne (MRW), Stanislaus (SRW), Tuolumne (TRW),
Merced (MERW), Upper San Joaquin (SJRW), and Upper Kings (KRW).

Nested domains for the WRF simulation used with (a) CFSR reanalysis
and ERA-20C data sets; and (b) 20CRv2c reanalysis data set.

Atmospheric River (AR) position based on IVT:(a) before shifting; and (b) after atmospheric boundary condition
shifting.

Trinh et al. (2021)

Top 20 maximized 72-h precipitation (mm) depth events (identified by their dates) for
historical reconstruction (blue), 1D maximized 72-h precipitation depth (red), and 2D
maximized 72-h precipitation depth (green): (a) Cosumnes (CRW) watershed; (b) Tuolumne(TRW) watershed; and (c) Upper Kings (KRW) watershedWatershed

Event

Historicalprecipitation
depth
(mm)

Cosumnes

1997A
1963B
1965A
1886A
1888B

183.74250.22294.17150.82
138.24317.05328.51340.55
196.66
269.62366.53359.38353.47332.30302.54

−5
2
−2
5
−5

1
1
−1
1
1

1965A
1997A
1963B
1963A
1986A

299.59240.38339.35160.77312.30428.88377.01396.00391.32343.43428.88415.46397.43391.32361.24

−4
−5
2
−1
−1

0
1
1
0
−1

1965A
1997A
1963B
1963A
1943A

270.07241.08366.97180.49190.41433.08410.27402.76394.64337.81439.01434.75403.31394.64368.72

−5
−5
2
−1
−5

−1
1
1
0
−1

Watershed

Event

Historicalprecipitation
depth
(mm)

1D shifting
precipitation
depth
(mm)

2D shifting
precipitation
depth
(mm)

Shift to north(°)

Shift to east(°)

Tuolumne

1965A
1963B
1997A
1980A
1943A

253.80406.24226.64298.72211.80450.16428.05394.00327.38380.75460.00440.14433.32426.68409.58

−5
1
−5
−5
−5

1965A
1963B
1943A
1980A
1986A

214.81
402.18191.70254.42205.71478.16411.91378.77291.40387.86490.13411.91
407.93403.95402.89

1943A
1997A
1965A
1963B
1995A

224.51190.05
253.50442.29381.82521.43494.14475.13434.20407.61

1943A
1963B
1997A
1965A
1876A

225.72551.20209.51300.17
197.02678.20568.44608.97544.08490.49

Mokelumne

Stanislaus

MercedUpper San Joaquin

Upper Kings

1D shifting
precipitation
depth
(mm)

2D shifting
precipitation
depth
(mm)

Shift to north(°)

Shift to east(°)

Watershed

Event

Historicalprecipitation
depth
(mm)

Cosumnes

1965A
1997A
1886A
1963B
1986A

294.17183.74150.82250.22278.06340.55317.05
196.66328.51293.50353.47366.53332.30359.38300.85424.27416.60409.28387.87354.48

−1
−5
5
2
1

−1
−1
1
1
1

14
18
20
12
12

Mokelumne

1886A
1997A
1965A
1963B
1885A

210.24240.38299.59339.35172.79270.31377.01428.88396.00316.61306.79415.46425.99397.43323.73533.44500.77479.52452.76365.57

5
−5
−3
2
−2

1
0
0
1
0

20
20
20
12
14

Stanislaus

1997A
1886A
1965A
1963B
1986A

241.08227.42270.07366.97312.58410.27284.55433.08402.76339.70434.75303.74439.01
403.31
347.60517.49513.10491.86436.79397.97

−5
5
−5
2
1

0
1
−1
1
1

20
20
20
12
20

Tuolumne

1
1
1
1
−1

1886A
1997A
1965A
1963B
1980A

241.13226.64253.80406.24298.72293.71394.00450.16428.05327.38330.37433.32460.00440.14426.68556.09524.71491.51477.85427.03

5
−5
−5
2
−5

1
0
1
1
1

20
20
20
12
20

Merced

−5
1
−5
−5
−2

−1
0
−1
1
−1

1886A
1965A
1997A
1963B
1986A

226.21214.81
162.44402.18205.71252.89478.16398.35411.91387.86300.34490.13394.88410.93402.89559.41546.11491.78470.92441.69

5
−5
−5
2
1

1
−1
0
1
0

20
20
20
12
16

Upper San Joaquin

560.79494.14475.13465.32429.89

−4
−5
−5
1
1

−1
0
0
1
1

1886A
1997A
1943A
1965A
1963B

293.53190.05224.51
253.50442.29323.83494.14521.43475.13434.20376.18488.82560.79472.78465.32654.31607.81560.91527.72494.33

5
−5
−5
−5
−2

1
1
−1
−1
0

20
20
10
20
20

Upper Kings

745.59585.70608.97560.46525.53

−5
0
−5
−5
−5

−1
1
0
1
−1

1943A
1997A
1886A
1963B
1965A

225.72209.51335.88551.20300.17678.20608.97371.94568.44544.08745.59567.79430.53585.70560.46794.26723.37719.60640.23626.04

−5
−5
5
−2
−5

−1
−1
1
0
1

20
20
20
20
20

Top five events after precipitation
maximization using ABCS (Atmospheric BC
Shifting)

1D shifting
precipitation
depth
(mm)

2D shifting
precipitation
depth
(mm)

RHP-IVT
precipitation
depth
(mm)

Shift to north(°)

Shift to east(°)

Increase in
RHP-IVT(%)

Top five events after precipitation maximization
using RHP-IVT for each watershed

Historical and the maximized
atmospheric fields
Atmospheric data for historicalconditions(Spatial resolution: 3-km grids)

WEHY (hydrologic model
including snow process)

PMF estimation

WEHY MODEL(Watershed Environmental
Hydrology Model)
Land Surface process
Snow Model (WEHY-S)

Atmospheric data for
maximized conditions(Spatial resolution: 3-km grids)

Flow process Hillslope
and stream network
routing (WEHY-H)

Possibleextremerunoff eventson the target
watersheds

Schematic description of the proposed methodology
to simulate maximum flood events

(a) WEHY-S conceptualization of temperature profile, water content profile, andenergy balances within and around snowpack; (b) structural description of WEHY-H(Kavvas et al., 2013)

Validation comparisons of the daily mean discharge by WEHY simulations and the corresponding observations at eachwatershed during 10 years (1997–2006): (a) Cosumnes River watershed; (b) Upper Kings River watershed; (c) Mokelumne
River watershed; (d) Stanislaus River watershed; (e) Tuolumne River watershed; (f) San Joaquin River watershed; (g) MercedRiver watershedRanked events over KRW (top 10)
a. Ranked PMP events over KRW (tpp 10)
Kings River Watershed (KRW)Maximized 72-h
Event ID
precipitation (mm)
Rank
1943A0500s0100wivt250_20
794.26
1
1943A0500s0100wivt250_10
745.83
2
1997A0500s0100wivt250_20
723.37
3
1886A0500n0100eivt250_20
719.594
1963B0200s0000eivt250_20
640.22
5
1965A0500s0100eivt250_20
626.03
6
1965A0500s0100wivt250_20
588.67
7
1963B0100n0100e
570.948
1963B0200n0100eivt250_12
542.8991885A0200s0100eivt250_20
516.06
10

Historical 72-h
precipitation (mm)225.72225.72209.51335.88551.2
300.17335.88551.2
551.2
121.35b. Ranked stream flow events with input from PMP events over KRW (top 10)
Kings River Watershed (KRW)
Flow volumne
Event flow
Historical flow peak
Event IDrank
peak (cm)(cm)
1886A0500n0100eivt250_20
17035.72005.1
1943A0500s0100wivt250_20
24515.52058.2
1963B0200n0100eivt250_12
33176.82767.4
1943A0500s0100wivt250_100
43356.32058.2
1965A0500s0100eivt250_20
52836.81135.8
1963B0100n0100e
63038.62767.4
1963B0200s0000eivt250_20
72955.22767.4
1885A0200s0100eivt250_20
82505.5583.43
1965A0500s0100wivt250_20
92461.91135.8
1995A0000n0100e
102256.21378.3

Event volumne(m^3 x 10^8)
12.02
4.96
4.44
4.4
4.25
4.21
4.16
3.8
3.7
2.83

Ranked PMP and PMF events (top 10) at Upper Kings River Watershed (KRW)Comparison of KRW basin-averaged temperature under historical andmaximized precipitation conditions for the 1943 and 1886 events

Comparison of KRW basin-averaged fractional snow cover for the historicaland maximized precipitation conditions for the 1943 and 1886 events

Comparison of snow cover between the historical conditions and threedifferent precipitation-temperature conditions during the 1886 event(ATMvar1886AcP, ATMvar1886AcPT, ATMvar1886AcT)The maximization of extreme flood over the seven Southern California
watersheds showed:
1) The flood event due to the maximum precipitation event does notnecessarily result in the maximum flood;2) The optimum combination of precipitation and temperature leads tothe maximum flood event in snow-covered watersheds.

Physics-based numerical atmospheric-hydrologic modeling of the precipitation
fields and floods as clusters of events has been addressed only recently (Hiraga
et al. 2021, 2022; Kavvas et al. 2021, 2023). This topic still needs substantial
new research.

Tropical Cyclones/Typhoons
Tropical Cyclones (TCs) are intense atmospheric vortices that form over the warm tropical oceans”(Chan and Kepert (2010)).
Approximately 80 TCs form worldwide every year (De et al., 2004).
Their life duration is very variable as TCs can last from 1 day to several weeks.
Even if TCs have usually horizontal extents of several hundreds of kilometers, the strongest winds,
precipitation, and deep convection are located in a region of about 100 km in radius. As aconsequence, TCs can be considered as mesoscale systems (Holton and Hakim, 2013).
More precisely, a calm eye with a diameter between 20 and 100 km and pressure deficit up to 10%of the ambient atmosphere is surrounded by a slantwise ring of deep convective clouds that extends
through the whole troposphere. This ring is called the “eyewall”.
The primary circulation of a TC consists of the cyclonic flow around the storm center while theweaker secondary circulation consists of “inflow concentrated in the boundary layer, upflow in theeyewall and spiral rainbands, and outflow in a thin layer beneath the tropopause” (Chan and Kepert,
2010; Holton and Hakim, 2013). The secondary circulation is the energy source of the TC, and its
working may be idealized as a Carnot machine (Cram et al., 2007; Emanuel, 1991) as illustrated in
the following figure.

THREE POWERFUL HURRICANES, HURRICANE FRANCES,
HURRICANE IVAN AND HURRICANE JEANNE HIT EASTERN USA
WITHIN A SPAN 3.5 WEEKS DURING SEPTEMBER 2004

Best track positions for the eye of Hurricane Ivan for September 3–24, 2004 (reproduced from Stewart,2005). (Tropical Dep., Tropical Depression; Subtr. Storm, Subtropical Storm; Subtr. Dep., Subtropicaldepression; UTC, Universal Coordinated Time; mb, millibars).

Storm total rainfall depth map (inches) of Hurricane JeanneFrom “Hydrologic Effects of the 2004 Hurricane Season in NW Florida”, by R.J. Verdi, USGS Open-File Rept. 2005-1277

Hurricane Ivan
Hurricane Ivan developed over the tropical Atlantic Ocean, and on September 16. Ivan center cameashore as a category 3 hurricane just west of Gulf Shores, Alabama. Portions of the Interstate 10 bridge
system across Pensacola, Florida were severely damaged due to the severe wave action on top of the
10-15 foot storm surge. Storm surge occurred all the way to Tampa Bay, Florida about 500 miles from
Ivan’s point of landfall.

On September 16, 2004, Hurricane Ivan made landfall on the Gulf Coast at the Alabama–Florida border as a category 3 hurricane.
It then moved northeast into Alabama. As Hurricane Ivan moved northeast on the evening of September 16, winds decreased
and it was classified as a tropical storm over central Alabama.
As winds continued to decrease in the early morning of September 17, Ivan was classified as a tropical depression over northeast
Alabama.

Ivan continued to move northeast across Tennessee and Virginia before it became extratropical over the Delmarva Peninsula on
the afternoon of September 18.
Floods with recurrence intervals of 500 years or greater occurred at seven USGS stream gages throughout eastern Ohio during
the Period of Hurricanes Frances and Ivan during August 28–September 27.
Fortunately, Hurricane Jeanne that followed Hurricane Frances and Hurricane Ivan, did not develop into a severe storm over mostof Eastern USA, sparing the considerable destruction it could produce.

Nested domains used for the simulations of Hurricane Ivan. The small red area in western
North Carolina is the target watershedTarget area used for the precipitation maximization by TC shifting. (a) The target area is shown in red within
the model’s inner domain. (b) The target area corresponds to the drainage basin of the city of Asheville, N.C.

Numerical Simulation of Hurricane Ivan:
Two-way nesting was used for the simulations, meaning that the different domains (outer, intermediate and inner) are run simultaneously and communicate

with each other. The top of the model was taken at 50 mbar, with a total of 38 vertical layers, and a time step of 3 minutes was used.
A simple 1-dimensional ocean mixed layer model was used following Pollard et al. (1972). The parameterization schemes used for the simulations of Hurricane
Ivan are given in the below table. This combination of the parameterization schemes comes from the configuration of the WRF model for the reconstruction of
Hurricane Ivan. Cumulus parameterization was used only in the outer and intermediate domains. The simulation start date is 09/06/2004 00:00 UTC. At thattime, Hurricane Ivan was located off the coast of French Guyana and Suriname.

Parameterization schemes used for the simulations of Hurricane Ivan
Microphysics

WRF Double Moment 6-class (WDM6)

Cumulus Parameterization (domains 1 and 2 only)

New Simplified Arakawa-Schubert (SAS)Planetary Boundary Layer

Mellor-Yamada-Janvic (MYJ)

Longwave Radiation

Rapid Radiative Transfer Model (RRTM)

Shortwave Radiation

DudhiaLand Surface

Unified Noah Land Surface Model

Surface Layer

Eta Similarity Scheme

(a) Hurricane Ivan observed accumulated precipitation field in the inner-domain (from 09/14 00:00 UTC to 09/19 00:00
UTC). (b) Inner-domain WRF-simulated accumulated precipitation field (from 09/14 00:00 UTC to 09/19 00:00 UTC). (c)Arrow field: time-averaged (from 09/14 00:00 UTC to 09/19 00:00 UTC) integrated vapor transport (kg m-1 s-1). Colorplot: divergence of the time-averaged integrated vapor transport field (mm).

Description of the Tropical Cyclone/Hurricane/Typhoon Storm Transposition (Shifting) method

Initial and boundary conditions used for dynamical downscaling with a Regional Atmospheric Model (RAM) are usuallyobtained from the outputs of a general circulation model (GCM) or Reanalysis Data. This section presents a method to shift
the location of a TC in the initial conditions. The objective of this transposition is to modify the track of the storm so that its
precipitation field moves over a specified target area.
The transposition of the TC in the initial conditions is performed by executing the following procedure:
1. Identify the location (xc,yc) of the center of low pressure;
2. Identify the radius R of the cyclone;
3. Remove the TC from the background atmospheric fields by cutting off the inside of the circle of center (xc,yc) and of radius
R from the original atmospheric fields;
4. Interpolate the background fields to the inside of the circle;
5. Compute the perturbation fields by subtracting the background fields obtained in step 4 from the original fields. The
perturbation fields are zero everywhere except inside the circle;
6. Shift the perturbation fields;
7. Add the shifted perturbation fields to the corresponding background fields obtained in step 4.

Application of the transposition (shifting) procedure to the initial
surface zonal wind velocity (m.s-1) in Hurricane Ivan.

Hurricane Ivan was transposed in a direction orthogonal to its direction of propagation at the simulation start date (below
figure). The transposition exercise was first performed for 29 amounts of shift (including zero shift), from 1.67 degree west
and 7.18 degree south to 1.67 degree east and 7.18 degree north, which corresponds to the black dots in below figure. The
WRF model was run for each of these amounts of shift, and the maximum 72-hour (3-day) accumulated precipitation over
the target watershed, which corresponds to the 72-h time window that contains the largest basin average precipitation,
was calculated for every simulation. Results for this first step are presented in the second figure below. Note that theshifting results are represented by plotting them only against the West-East component of the shift that occurs along theline of black dots shown in the below figure.

The color plot shows the mean sea level pressure field (mbar) on 09/06/2014 00:00 UTC (from CFSR) for zero shift. The
green point gives the location of the center of low pressure in the original TC (zero shift). The black points give the locationof the center of low pressure after shifting. The black arrow indicates the directon of propagation of Hurricane Ivan.

72-h basin average precipitation as a function of the West-East component of the shift. (a) Results for the 29 shifts in degrees first considered (above figure).
(b) Results after the first refinement. (c) Results after the second refinement. The green square gives the 72-h basin average precipitation in the case of no shift.
The yellow diamonds show the refinement performed around the local maxima. The red diamond in (c) indicates the maximum 72-h basin average precipitation.

Above figure shows that Hurricane Ivan responds nonlinearly to the transposition of its initial conditions. Indeed the location of the
precipitation field does not change homogeneously as the amount of shift is increased from 1.67 degrees west and 7.18 degrees south to 1.67
degrees east and 7.18 degrees north. For example, the 72-h accumulated precipitation field corresponding to an amount of shift of 1.07
degrees west and 4.61 degrees south (third plot on Row 2 in above figure) is located east of the 72-h accumulated percipitation fieldcorresponding to an amount of shift of 1.01 degrees west and 4.36 degrees south (fourth plot on Row 2 in above figure). This behavior
explains the presence of multiple peaks in the graphs of the 72-h basin average precipitation as a function of the zonal component of the shiftpresented in the figure before the above figure.
Given 1) the strong nonlinearity involved in the dynamics of a TC, 2) the fact that we used no nudging and data assimilation, and 3) the early
simulation start date (about ten days before the time of landfall), it is not expected that the numerical model manages to reproduce
accurately the track of the TC, including the time and location of landfall. In order to place the simulated precipitation field in the rightlocation, it is necessary to use a later simulation start date, as was done for the configuration of the WRF model for which the simulation startdate was only two days before the time of landfall.

72-h accumulated precipitation field as a function of the amount of shift. The first plot (top-left) corresponds to the mostwesterly and southerly shift (1.67 degrees west and 7.18 degrees south) while the last plot (bottom-right) corresponds to themost easterly and northerly shift (1.67 degrees east and 7.18 degrees north). The maximum 72-h basin average precipitation is
obtained for the 8th plot (fourth plot on Row 2).

(a) 72-h accumulated precipitation (mm) field (from 09/16 08:00 UTC until 09/19 08:00 UTC) for the simulation which maximized the 72-h basin
average precipitation. (b) 7-day accumulated precipitation field (from 09/14 00:00 UTC until 09/21 00:00 UTC) for the simulation which
maximized the 72-h basin average precipitation. (c) Observed 7-day accumulated precipitation field (from 09/14 00:00 UTC until 09/21 00:00
UTC).
It is observed that the maximized precipitation field is overall significantly more intense than the observed field, which shows that the physically
based transposition method does not result in a simple transposition of the storm’s precipitation field, as it is often assumed in the traditional
PMP approaches. While the maximized 7-day precipitation over the Asheville watershed is around 200 mm, the observed 7-day precipitation due
to Hurricane Ivan is in the 80 – 190 mm range. In about half of the watershed area the observed 7-day precipitation is less than 130 mm.

PRECIPITATION MAXIMIZATION OF HURRICANE FRANCES OVER EASTERN USA

(a) 72-h (from 09/06/2004 23:00 UTC until 09/09/2004 23:00 UTC) accumulated precipitation (mm) field in Hurricane Frances for thesimulation which maximized the 72-h basin average precipitation. (b) 7-day (from 09/04/2004 00:00 UTC until 09/11/2004 00:00 UTC)
accumulated precipitation field in Hurricane Frances for the simulation which maximized the 72-h basin average precipitation. (c) Observed
7-day (from 09/04/2004 00:00 UTC until 09/11/2004 00:00 UTC) accumulated precipitation field in Hurricane Frances.
While the maximized 7-day precipitation over Asheville watershed is around 260 mm, the observed 7-day precipitation over Ashevillewatershed due to Hurricane Frances is in the 74-192 mm range. Half of the watershed area during the observed Hurricane Frances receives lessthan 118 mm 7-day precipitation.

Hurricanes Frances (9/4 – 9/11/2004), Ivan (9/13 – 9/28/2004) and Jeanne (9/25 –9/30/2004) were clustered in time within a 3-weeks period, following each othersequentially.
Such a historical occurrence of three hurricanes in a sequence within a time window of 3
weeks is not addressed in any of the conventional extreme precipitation estimation
approaches, nor in the conventional extreme flood estimation approaches.
As may be seen from their maximized precipitation states over the Asheville watershed, if
these hurricanes would hit the watershed in their maximized forms, they would produce
tremendous flooding and resulting disaster.
The reported study was confined only to the maximization of precipitation fields. As such,the resulting Probable Maximum Flood could not be estimated.

Estimation of the Return Periods of Extreme Floods under Changing Climate
One approach to the estimation of extreme flood return periods under the evolving hydro-climate of the 21st
century, is by means of the integrated atmospheric-hydrologic numerical model simulations of the extreme
floods, based on an ensemble of GCM hydro-climate projections that will cover a range of possible emission
scenarios (Kavvas et al. 2017; Trinh et al. 2016)

Trinh et al. (2016)

Trinh et al. (2016)

Comparison of the flood frequency curve at Yolo station
using observed flows (1903-2012),
with the curve estimated by the WEHY model-simulated flows based on thedownscaled GCM historical control run simulations

1,600

Obs

Control_run

Discharge [m3/s]

1,400

1,200
1,000
800
600
400

200
0

0
Trinh et al. (2016)

20

40
60
80
Return period (years)

100

120

Annual maximum model-simulated streamflows
during 21st century at Yolo gauging station
3000

2500

A1B

A1B1

A1B2

A1B3

A2

A2-1

A2-3

B1

B1-1

B1-2

B1-3

A1FI

A2-2

2000

1500

1000

500

0
2010

Trinh et al. (2016)

2020

2030

2040

2050

2060

2070

2080

2090

Relative frequency histograms of annual maximum flows
separated into 45-year increments for all flow projections
during 21st century at Yolo gauging station
2010-2054

2055-2099

0.14
0.12

Density

0.1
0.08
0.06
0.04
0.02
0
50

Trinh et al. (2016)

300

550

800
1050
1300
1550
annual maximum flow [m3/s]

1800

2050

2300

Evolution of the annual maximum flow as function of return periods throughout
the 21st century for all flow projections at Yolo gauging station

3000

2010-2054

2055-2099

Flow magnitude (cms)

2500

2000

1500

1000

500

0
0

Trinh et al. (2016)

20

40

60

80

100
120
Return Period (years)

140

160

180

200

Evolution of the annual maximum flow as function of return periods throughout
the 21st century for all flow projections at Yolo gauging station
195yearyear flood
200
flood

2000.00

2010-2054
97.5 year flood

3000

100 year flood

2000.00

2500

Flow magnitude (cms)2055-2099

1500.00
1000.00

1500.00

500.001000.00

0.00

500.00
0.00

2000

1500
195yearyear flood
flood
200

1000

1500.00

97.5
yearflood
flood
100
year

2000.00
1500.00

500

1000.00

1000.00

500.00500.000.00
17-Feb-30 18-Feb-30 20-Feb-30 22-Feb-30 24-Feb-30

0.00

0
0

Kavvas et al. (2017)

20

40

60

80

100
120
Return Period (years)

140

160

180

200

Comparison between Fitted LP3 and GEV distributions that were calibrated by historical observations, against hydroclimate
simulations-based distributions
during two periods of future projection
3000

2010-2054
Obs_LP3_prediction
OBS_prediction

annual maximum
flow [m3/s]

2500

2055-2099
Obs_predic_5%

Obs_prediction_95%

2000
1500
1000

500
0
0

20

40

60

80

100

120

140

160

180

200

160

180

200

Return Period (years)
3000
2010-2054
Obs_GEV_prediction
5% GEVannual maximum
flow [m3/s]

2500

2055-2099
95% GEV

2000
1500
1000
500
0

Kavvas et al. (2017)

0

20

40

60

80

100

120

Return Period (years)

140

Annual maximum flow as function of return period throughout the 21st century for all flow projections at
Yolo gauging station

3000

2010-2100

2500

2000

1170_year flood

2500.00

585 year flood

2000.00
2000.00
1500.00

1500

1500.00

1000.00

1000.00

500.00390 year flood
500.001000

0.00
21-Feb-61

0.00
26-Dec-90 28-Dec-90 31-Dec-90 2-Jan-91

1600.00

23-Feb-61

24-Feb-61

26-Feb-61

5-Jan-91

800.00500
0.00
8-Jan-34

10-Jan-34 13-Jan-34 16-Jan-34 19-Jan-34

00Kavvas et al. (2017)

200

400

600

800

1000

1200

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