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Electronic Theses, Treatises and Dissertations The Graduate School
2003 Hurricane Surface Wind Model for Risk Management Lizabeth Marie Axe
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THE FLORIDA STATE UNIVERSITY
COLLEGE OF ARTS AND SCIENCES
HURRICANE SURFACE WIND MODEL FOR RISK MANAGEMENT
By
LIZABETH MARIE AXE
A Thesis submitted to the Department of Meteorology in partial fulfillment of the requirements for the degree of Masters of Science
Degree Awarded: Fall Semester, 2003
The members of the committee approve the thesis of Lizabeth Marie Axe defended on September 23, 2003.
______T. N. Krishnamurti Professor Directing Thesis
______Paul H. Ruscher Committee Member
______Philip Cunningham Committee Member
______Steven Cocke Committee Member
The Office of Graduate Studies has verified and approved the above named committee members.
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To my parents whose enduring and insurmountable love, encouragement, and support made this study and my entire academic career possible.
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ACKNOWLEDGEMENTS
First and foremost, I would like to thank God, for I am nothing without him. I give many thanks and appreciation to my major professor, Dr. T. N. Krishnamurti, for all of his support and encouragement. I would also like to thank my committee members, Dr. Paul H. Ruscher and Dr. Philip Cuningham, for their comments and suggestions. Thank you to everyone in the Dr. Krishnamurti’s lab for their assistance and advice, especially Dr. Steve Cocke for patience and the know-how, Brian Mackey for his never-ending help and advice, and Andy Schwartz for keeping the experience real. Finally, I give many thanks to my family and friends for their never-ending encouragement during my entire academic career.
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TABLE OF CONTENTS
LIST OF TABLES ...... vii
LIST OF FIGURES ...... viii
ABSTRACT...... xi
1 INTRODUCTION...... 1 1.1 Overview...... 1 1.2 Objectives and Organization of Thesis ...... 3
2 WIND COMPONENT...... 5 2.1 Synthetic Vortex Profile...... 5 2.1.1 Rankine Vortex Equations ...... 5 2.1.2 Model Parameters ...... 8 2.1.3 Model Example...... 8 2.2 Reduction of Flight Level Winds to the Surface Layer ...... 10 2.2.1 GPS Dropwindsonde Measurements ...... 10 2.2.2 Adjustment Function to the 300 m Level ...... 13 2.3 Wind Reduction From the Top of the Surface Layer to 10 m...... 14
3 ROUGHNESS COMPONENT...... 16 3.1 Introduction to Surface Roughness...... 16 3.2 Roughness Data Set ...... 16 3.2.1 Estimation of Surface Roughness by HAZUS ...... 17 3.2.2 Land-Use/Land-Cover Sources...... 18 3.2.3 Conversion From LULC Classes to Roughness Length...... 18 3.3 Effective Roughness ...... 19 3.4 The Source Area Model...... 23 3.5 Radial Weight Function...... 28 3.5.1 Derivation...... 29 3.5.2 Sensitivity to the Parameters...... 30 3.6 Azimuthal Dependence...... 32 3.7 Examples...... 33
4 RESULTS ...... 40 4.1 Comparison of Local vs. Effective Roughness...... 40
v 4.2 Sensitivity to Model Parameters ...... 44 4.3 Real World Examples ...... 49 4.3.1 Hurricane Andrew Case Study...... 49 4.3.2 Hurricane Erin Case Study...... 52 4.3.3 Hurricane Kate Case Study...... 54 4.3.4 Hurricane Donna Case Study...... 56 4.4 Historical Hurricane Scenarios ...... 58 4.4.1 Estimations of Unknown Parameters...... 59 4.4.2 1852 Hurricane Case Study...... 60
5 CONCLUSIONS ...... 62 5.1 Discussion and Summary...... 62 5.2 Future Work ...... 64
REFERENCES...... 65
BIOGRAPHICAL SKETCH...... 68
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LIST OF TABLES
1 Roughness lengths of homogeneous surface types (Wieringa 1993) ...... 17
2 FLUCCS Level 1 Classifications ...... 18
3 Example of the FLUCCS Level 2 Classification Using the Urban and Built-Up and Agricultural...... 19
4 Normalized Set of Isopleth Dimensions Relative to the 0.5 Isopleth using the Statistical Source Area Model (Schmid 1990) ...... 27
vii
LIST OF FIGURES
1 The wind model rankine-like vortex. The thick line represents the upper-level winds, and the thin line represents the 10 m winds...... 7
2 Model output of flight level winds for hurricane Andrew at the time landfall...... 9
3 Mean hurricane wind speed profiles for the eyewall and outer-vortex regions. Wind speeds are averaged and expressed as a fraction of the profile wind speed profile at 700 mb. The minimum number of profiles used to construct the averages is indicated (Franklin 2003)...... 11
4 Mean wind speed profiles for eyewall sondes released within 5.6 km (3 n mi.) of the flight level Rmax (RMW), for eyewall sondes released at least 7.4 km (4 n mi.) radially outward of the Rmax, and for eyewall sondes released at least 7.4 km radially inward of the Rmax. All winds are averaged and express as a percentage of the profile 700 mb wind speed (Franklin 2003)...... 12
5 Same as in Figure 3, but with the height plotted on a logarithmic scale (Franklin 2003)....13
6 HAZUS Roughness Lengths for the State of Florida in meters...... 20
7 The source area in one-dimensional patchiness determined by the distances at which an IMIF and EIF reach the sensor height (zs) (Schmid 1990)...... 23
8 Schematic cross-section of a P source area (Schmid 1990) ...... 24
9 The total effect of the source area at the sensor location (Schmid 1990)...... 25
10 Example diagram of the source area model results given in Schmid and Oke (1990)...... 26
11 Plot of P versus e with the corresponding fitted function...... 30
12 Plot of W(x) for zz = 10 and z0 = 0.1 ...... 31
13 Plot of W(x) for z0 = 0.1 and L = -1200 ...... 31
14 Plot of W(x) for zs = 10 m and L = -1200...... 32
15 A schematic of the box used in the roughness model to calculate the effective roughness values based on 8 storm tracks ...... 33
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16 Local Roughness Values for the Miami Area...... 35
17a Effective Roughness Values for Sectors 1 through 4 in the Miami Area...... 36
17b Effective Roughness Values for Sectors 5 through 8 in the Miami Area...... 37
18 Difference of Effective Roughness Values Between Sector 1 and 5...... 38
19 Difference of Effective Roughness Values Between Sector 3 and 7...... 39
20 Wind field of hurricane Andrew at the time of landfall using the local roughness coefficient...... 41
21 Same as in Figure 20, but using the calculated effective roughness coefficient...... 42
22 Difference between the 10 m winds using local roughness and effective roughness...... 43
23 Graph of the radial weight function (Equation 26) by varying the s parameter. The solid line indicates the function using the given value of s. The short dashed line is the function with s = s0/4. And the dashed line is with s = s0/10...... 44
24 The wind field of hurricane Andrew using the weight function with s = s0/4...... 46
25 Same as in Figure 24, but with s = s0/10...... 47
26 The difference of the model winds using the weight function with s = -0.85370 and the function using (a) s = s0/4 and (b) s = s0/10...... 48
27 10 m modeled winds for Hurricane Andrew at landfall 24 August 1992...... 50
28 H*Wind maximum 1-minute sustained winds at 10 m for hurricane Andrew at the time of landfall ...... 51
29 10 m modeled winds for Hurricane Erin at landfall 2 August 1995...... 53
30 H*Wind maximum 1-minute sustained winds at 10 m for hurricane Erin at the time of landfall ...... 54
31 10 m modeled winds for Hurricane Kate at landfall 21 November 1985...... 55
32 10 m modeled winds for Hurricane Donna on 10 September 1960...... 57
33 H*Wind maximum 1-minute sustained winds at 10 m for hurricane Donna at the time of landfall ...... 58
ix 34 10 m modeled winds for an 1852 hurricane on October 10...... 60
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ABSTRACT
The landfalls of extreme hurricane events in recent years reveal the need for more accurate predictions of winds during landfalling tropical cyclone events to help reduce property damage. The goal of this study is to develop a high-resolution surface wind exposure model that incorporates an effective roughness model. In this study, the wind model calculates flight-level winds of a rankine-like vortex in a simple synthetic large-scale environment at a 1 km resolution. The flight-level winds are then reduced to 10 m using a reduction scheme based on GPS dropwindsonde profiles. The roughness component calculates the effective roughness length using a radial weight function based on the source area model developed by Schmid and Oke, with an upwind fetch of 5 km. The weight function is dependent on the distance from sensor, sensor height, surface roughness (approximately 100 m resolution), and the Monin-Obukov length. The weighted average of roughness values is taken over 8 possible wind directions to give a more sophisticated effective roughness length for all land points. The high-resolution wind exposure model provides realistic analyses for hurricane Andrew (1992), Erin (1995), Kate (1985), and Donna (1960) at the time of their Florida landfalls. It is also useful for recreating historical hurricane case studies. There is a potential for further development into a real-time analysis and forecasting tool during tropical cyclone landfall events.
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CHAPTER 1
INTRODUCTION
1.1 Overview Tropical cyclones are among the world’s most serious threats to lives and property. As a result of landfalling topical cyclones, millions of dollars are lost each year in the United States and around the world. Economic losses in the U.S. caused by hurricanes have been drastically rising during the last 30 years. Most of the storm damages are due to storm surge, strong winds, and torrential rainfall. Population growth along coastal areas of the country is adding to the number of buildings and other structures that are in danger of being exposed to the natural power of the hurricane. Therefore, the risk of human injury and death has increased with migration to coastal regions. Extreme hurricane events in recent years, i.e. Hugo, 1988; Andrew, 1992; Opal, 1995; Georges, 1998; Mitch, 1998; and Floyd, 1999, have reinforced the proposition that the nation must move beyond weather prediction and evacuation to achieve significant damage reduction. The increasing population and urban development in the coastal areas not only highlight the dynamic nature of our vulnerability to hurricanes, but also the urgency of the problem. According to the 2000 U.S. census, the population in the most hurricane vulnerable states has increased by 20% in the last ten years and this trend is predicted to continue. The State of Florida is the most vulnerable to hurricanes, having suffered the most impacts and the most costly hurricane, i.e. hurricane Andrew in 1992. The landfalls of hurricanes in the last few decades and growing populations have illustrated the need for more accurate assessment of tropical cyclone wind fields and their associated effects inland. Meteorologists rely on the effective use of observed atmospheric measurements from aircraft, surface (both land and sea), and space to guide them in determining
1 storm’s strength and structure. Similarly, there are many models available that will generate tropical cyclone wind fields and help determine future intensity and movement, but it remains a challenge to accurately determine the extent of damaging winds along the coast and inland. Insurance companies around the world are trying to model property damages and predict lost costs that occur during the landfall of hurricanes of all strengths. Currently, the state of Florida is developing a public model for cooperative statewide hurricane risk assessment and mitigation research, with an emphasis on actual applications that could evolve into a nationwide effort. The Florida International University/International Hurricane Research Center (FIU/IHRC) Public Hurricane Risk and Loss Model Project hopes to achieve effective hurricane mitigation by identifying, developing, and implementing more cost effective measures to reduce the potential for direct, indirect, and consequential damage caused by the impact of hurricanes. In this research effort, a large stochastic storm database will be generated for the purpose of probabilistic assessment of risk to insured residential property associated with wind damage. The project is divided into four components: Meteorological, Engineering, Computational, and Actuarial. Florida State University (FSU) and the Hurricane Research Division (HRD) are combining their efforts for the Meteorological aspect of this project. With hurricane landfalls over the past few decades, the modeling community has been actively trying to predict the tropical cyclone wind field, both over water and land. In 1995, Kaplan and DeMaria developed a simple empirical model for predicting tropical cyclone winds after landfall known as the Inland Wind Decay Model. They directly predict the decreasing wind speeds as it moves over land, instead of calculating the pressure increase, then the wind speed, using wind-pressure relationships. They assume that the decay rate of a tropical cyclone is proportional to its landfall intensity. The model does not predict the spatial distribution of wind and does not account for land surface characteristics during landfall. Vickery and Twisdale (1995b) combine a wind field model and filling model to predict near surface wind fields. They use simplified equations of motion for a hurricane based on Shapiro (1985). Winds are reduced to 10 m using an empirical formula that includes distance from shoreline. Here the boundary layer depth is assumed to be a constant depth of 1 km. However, this depth has been suggested to be 500 m in the eyewall (Franklin 2003). The filling rate model uses an exponential decay using central pressure rather than maximum winds as with Kaplan and DeMaria (1995). The Hurricane Research Division has developed a wind analysis system called H*Wind other the past
2 decade (Powell 1998 and Burpee 1994). The analysis is based on all available observations from aircraft, buoys, C-MAN platforms, and surface airways that are processed to a common 10 m height. The resulting objective analysis is representative of the mean state of the storm at a given time period. It is designed to give the location and strength of the maximum wind and the extent of hurricane force winds. At landfall, land exposure analyses are constructed based on observations converted to open terrain (z0 = 0.03) values. The models above all do not provide estimates of 10 m winds due to varying land surfaces. Determining property damage from tropical cyclone winds requires that the wind fields over land incorporate all land surface characteristics. The focus of this research is to include this type of surface effect that can be used in wind models to help provide a more realistic wind field. In addition to modeling research, a surface wind model that accurately evaluates the land exposure has the potential to be used on a real-time analysis and forecasting basis. It can aid in the location of the maximum wind as well as the extent of hurricane force winds or gale force winds, which will help determine areas at higher risk of damage. Currently, HRD provides the National Hurricane Center with real-time hurricane analyses. According to Powell (1998), the real-time H*Wind analyses represent winds using a constant land exposure. Therefore, analyses can be improved by the addition of the appropriate land exposure values. 1.2 Objectives and Organization of Thesis FSU is developing a roughness model that will be used in conjunction with a surface wind exposure model to calculate tropical cyclone wind fields over land. This study focuses on the effect of the land surface on 10 m winds. The study will cover only the geographic extent of the state of Florida, but can easily be applied to any landmass where roughness values are known. The goal of this study is to develop a high-resolution surface wind exposure model that incorporates an effective roughness model. The objectives of this study are to • Develop a hurricane wind analysis model (to be incorporated into the FIU/IHRC Public Hurricane Risk and Loss Model Project). • Incorporate a new roughness model to account for the upwind land surface elements. • Examine the sensitivity of the improved wind model vs. the traditional model approach of using open terrain or local roughness values. • Provide historical and potential real-time hurricane analysis.
3 An overview of the wind model used in this study will be given in Chapter 2. The roughness data set from HAZUS project will be described and the background information on the construction of the data set will also be briefly explained in this chapter. Chapter 3 will give a detailed description of the local roughness length and effective roughness lengths, which also includes the improved effective roughness length detailing the formulation of the weighting function and roughness model. Chapter 4 will examine the sensitivity of the roughness model to boundary layer parameters and compare the resulting wind fields to recent Florida landfalling hurricanes: Andrew (1992), Erin (1995), Kate (1985) and Donna (1960). Finally, Chapter 5 contains the conclusions and future work.
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CHAPTER 2
WIND COMPONENT
2.1 Synthetic Vortex Profile Models have been developed over the years to try to represent surface wind fields, especially those in hurricanes. Both dynamical and empirical models are used today to accomplish this task. For the FIU/IHRC Public Hurricane Risk and Loss Model Project, thousands of stochastic storms are to be generated and for each time period in the storm life cycle the wind field is needed. Because of the need to produce many storm scenarios, at high resolution, dynamical numerical weather prediction models are not feasible. Furthermore, these numerical models require initialization of basic meteorological fields, data that is not available. Additionally, the computational expense would be too great. So a simple, efficient empirical model is needed to create the storm database. We have developed a wind model, based on Trinh and Krishnamurti (1992), which will calculate the flight level winds. Trinh and Krishnamurti developed a method to insert a bogus hurricane vortex in a large-scale environment. In the present study, we will use the bogus scheme, with a simple synthetic (no wind) large-scale environment, to place a hurricane in our domain. This model will eventually be replaced by another empirical model being developed by the Hurricane Research Division (HRD). The HRD model also calculates the flight level winds. 2.1.1 Rankine Vortex Equations Assuming the initial position, the central sea surface pressure, the maximum tangential wind speed cm, and the radius at which the maximum tangential wind speed occurs Rmax, the tangential wind of a hurricane can be calculated. Milne-Thompson (1968) described these winds as a function of the radial distance r by: r c = cm r ≤ Rmax (1) Rmax
5 −α r c c r R . (2) = m > max Rmax The decay parameter, α, is arbitrary, but we will define it as: Rmax α = log 2 log , (3) Rmax 2 where Rmax2 is the radius of half the wind maximum. From equations (1) and (2) we can compute the zonal and meridional components of the vortex tangential wind. The geopotential height, z, is assumed to be related to the wind field by the gradient wind relationship:
∂z c 2 = fc+ (4) ∂r r Now after replacing c from Eqs. (1) and (2) into (4) and integrating, we have:
c r rz )( m fR c c r R (5) = ()max + m + 1 ≤ max 2 Rmax
1−α −2α fR c r c2 r rz )( max m m c r R (6) = − + 2 > max 1−α Rmax 2α Rmax
Assuming the continuity of geopotential height at the radius of maximum of wind, c1 and c2 can be eliminated from both of the above equations. This will lead to: 1−α 2 fRmax cm R r rz )( = z(R) − 2 − (1+α) − (1−α) 2(1−α) R R max max
2 −2α 2 cm R r − − (1+α) +α r ≤ Rmax (7) 2α R R max max
1−α 1−α fRmax cm R r z(r) = z(R) - − 2(1−α) R R max max
2 −2α −2α cm R r − − r > Rmax (8) 2α R R max max
6 These equations now allow for z(r) to be computed within and outside of the radius of maximum wind Rmax given all the input parameters cm, Rmax, R, and z(R). The resultant wind field is a Rankine-like vortex or idealized symmetric vortex (Figure 1).
Figure 1: The wind model rankine-like vortex. The thick line represents the upper-level winds, and the thin line represents the 10 m winds.
The profile inside Rmax is linear, and outside Rmax it is logarithmic for both upper-level and 10 m winds. The flight level winds will be calculated by the equations above (7 & 8) and reduced to the 10 m level using observational and GPS dropwindsonde profile data and boundary layer theory (described later). The translational motion of the storm is also taken into consideration in the wind model. Past 6- hourly positions, the position at time zero, and the position 6 hours ahead are used to calculate the translational speed of the hurricane by fitting a polynomial of second order and are shown by
2 x = a1t + a2t + a3 (9)
2 y = b1t + b2t + b3 (10) where x and y are the latitude and longitude components of the storm track and t represents time. The initial storm movement at time zero (t = 0) is calculated by differentiation of equations (9) and (10) with respect to t. These translational wind components are then added to the tangential wind component.
7 A more detailed description of the bogusing scheme can be found in Trinh and Krishnamurti (1992) and Zhan (1997). 2.1.2 Model Parameters The vortex model experiments preformed in this study require information on each storm being simulated. Parameter data may be obtained from historical record or synthetically generated in the case of the FIU/IHRC Public Hurricane Risk and Loss Model Project. In the Loss Model these parameters will be sampled from probability density functions based on the historical data. The historical data for all storms from 1851 to the present can be found in the National Hurricane Center's North Atlantic hurricane database known as HURDAT (Jarvinen et al 1984). The database contains six-hourly positions and intensities for all tropical systems during this time. The radius of maximum winds can be found in a database being created by HRD. Other information can be found in the National Hurricane Center's Preliminary Reports, by using satellite imagery, or experimental calculations. The model input parameters include the: • Maximum sustained flight level (700 mb) winds, • Storm position at the time of landfall and its earlier position, • Central pressure,
• Radius of maximum winds, Rmax, and,
• Radius of winds at half their maximum outside the Radius of maximum winds, Rmax2. The synthetic vortex profile above calculates winds at flight level, which commonly is 700 mb. To reduce the winds down to the 10 m level, there are two schemes that will be employed. 2.1.3 Model Example An example of the model output based on parameters estimated for Hurricane Andrew is shown in Figure (2). The figure represents flight-level (700 mb) winds of Andrew near the time of landfall using the model parameters: • 80.3 W and 25.5 N at landfall and 79.3 W and 25.4 N at the earlier position, • Central pressure of 922 mb, • Maximum sustained flight level winds of 83.3 m/s,
• Rmax of 20.4 km, and
8
Figure 2: Model output of flight level winds for hurricane Andrew at the time landfall.
9 • Rmax2 of 75 km. As we can see, the wind field at this level is highly symmetric and is suitable for our purposes. The reduced 10 m surface winds will be shown later. 2.2 Reduction of Flight Level Winds to the Surface Layer Over the past 50 years, research and reconnaissance aircraft in situ measurements have been primary tools for tropical cyclone studies. But in recent years, a new level of sophistication and accuracy in hurricane observations have enhanced what is already known about the storm environment. The increased accuracy has come from improved observations using global positioning system (GPS) dropwindsondes. They have allowed the wind and thermodynamic structure of the hurricane eyewall to be documented with accuracy and high resolution. Franklin (2003) recently used GPS wind profiles to help aid forecasters by defining wind reduction factors that can estimate the tropical cyclone surface winds based on reconnaissance observations. We will develop reduction factors based on the GPS dropwindsonde profiles of Franklin (2003) to aid in the 10 m wind reduction scheme. Above the surface layer (discussed later), it is assumed that the profiles are valid over land surfaces since GPS dropwindsondes are only used over water and storm observations during landfall are sparse. In the surface layer, we take terrain into account. 2.2.1 GPS Dropwindsonde Measurements Franklin (2003) found that the GPS dropwindsonde measurements made within the hurricane environment can lead to appropriate wind adjustments to the surface. In their study, 630 hurricane dropsonde profiles from the 1997-99 seasons were used to obtain mean wind profiles within the eyewall (429 sondes) and outside the eyewall (201 sondes). The individual profiles (soundings) were normalized by the wind speed at common reconnaissance flight levels (i.e. 700, 850, and 925 mb and 1000 ft) prior to averaging. Each sounding was assigned to either eyewall or outer vortex categories based on flight level radial wind profiles near the time of launch. Mean wind profiles were constructed using the normalized soundings in each category. For more information concerning GPS dropwindsondes, the reader is directed to Franklin (2003). Figure (3) shows the mean wind speed profile for the hurricane eyewall and outer vortex, in which the wind at each level was normalized by the wind speed at 700 mb. The normalized wind speed of the mean eyewall 700 mb height is 1. The strongest winds in the eyewall are
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Figure 3: Mean hurricane wind speed profiles for the eyewall and outer-vortex regions. Wind speeds are averaged and expressed as a fraction of the profile wind speed profile at 700 mb. The minimum number of profiles used to construct the averages is indicated (Franklin 2003). found near 500 m, which presumably represents the top of the boundary layer. The profile also shows that the peak winds near 500 m are about 20% higher than the 700 mb wind. In the outer vortex region (within 300 km of the cyclone center) the strongest winds are found just below 1 km, which is a little higher than the eyewall maximum.
Figure (4) shows three mean wind profiles for different distances from the Rmax. The peak winds nearest to the Rmax (solid line) are about 17% higher than the 700 mb wind. It is seen that for profiles in the outer portion of the eyewall (long dashed line) there is significantly less
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Figure 4: Mean wind speed profiles for eyewall sondes released within 5.6 km (3 n mi.) of the flight level Rmax (RMW), for eyewall sondes released at least 7.4 km (4 n mi.) radially outward of the Rmax, and for eyewall sondes released at least 7.4 km radially inward of the Rmax. All winds are averaged and express as a percentage of the profile 700 mb wind speed (Franklin 2003). speed shear than in the inner portion of the eye (short dashed line). The strongest winds within the eyewall are about 28% higher than 700 mb winds. Franklin determined surface-to-flight level wind ratios to be 0.9, 0.8, and 0.75 for 700 mb, 850 mb, and 925 mb, respectively. Under the assumption that the profiles are valid over land, it is necessary that the land surface characteristics be taken into account. Thus the flight
12 level winds will be reduced to a level above which frictional effects are seen. Therefore reduction factors to this level will be defined. 2.2.2 Adjustment Function to the 300 m Level In Figures (3) and (4), the mean wind profiles show that the wind increases with height linearly above the low-level wind maximum that is just above the boundary layer. It can be seen in these figures that the linearity remains true down to about 500 m, the top of the boundary layer. Below 300 m, the profiles become nearly logarithmic (Figure 5). Assuming that all frictional effects due to the surface occur in the layer between the surface and 300 m (called the surface layer) (Garratt 1992), we can derive the 300 m wind adjustment factors from these profiles.
Figure 5: Same as in Figure 3, but with the height plotted on a logarithmic scale (Franklin 2003). 13 The reduction varies based on the location within the storm environment. These factors will then be used to develop an adjustment function that is dependent on distance. From Figures (3) and (4), the 300 m reduction factors are: • In the eye ≈ 1.25 • In the eyewall ≈ 1.15 • Just Outside the eyewall ≈ 1.05 • Outer Vortex ≈ 1.00. We want to extend the above reduction factors to continuous distances from the center.
Therefore, we developed an adjustment function, Adj, dependent on the distance from Rmax. For distances, r, less than the Rmax, Adj(r) = 1.25. (11) This will take into account all areas within the eye, not including the eyewall. For distances within 7.4 km of the eyewall, a linear interpolation was used to find the function, .2 Adj r)( = 1.25− (r − (R − 7.4km)) . (12) 14.8km max
For distances outside 7.4 km of Rmax, but less than 30 km, the function again is linearly interpolated to get .05 Adj r)( = 1.05− (r − (R + 7.4km) . (13) 30km max Finally, for distances greater than 30 km, it is Adj(r) = 1.0. (14) The adjustment function is then used to reduce the flight-level winds to the top of the surface layer. Further reduction to the 10 m level will be evaluated in the following section. 2.3 Wind Reduction From the Top of the Surface Layer to 10 m Below the low-level wind maximum (or within the boundary layer), the profiles are nearly logarithmic below 300 m, which is easily seen in Figure (5) (Franklin 2003). In the frictional boundary layer, or surface layer, there is a sharp decrease in wind speed where the atmosphere is under neutral stability. This layer is characterized by constant stress and little change in wind direction (Powell 1996). The vertical distribution of momentum is controlled by the surface stress and roughness. The flow in this level is well represented by the Monin-Obukhov
14 similarity theory. Thus the log wind profile can be used to reduce 300 m winds down to 10 m by the equation log300 z0 U10 =U 300 , (15) log Z z0 where U10 is the wind speed at 10 m, U300 is the wind speed at 300 m, z0 is the surface roughness (described later), and Z is the height (Garratt 1992). Examples of the reduced wind field at 10 m for Hurricane Andrew using the model parameters from Section 2.1.3 will be shown in Chapter 4.
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CHAPTER 3
ROUGHNESS COMPONENT
3.1 Introduction to Surface Roughness In the previous chapter, the logarithmic wind profile was used to adjust the upper level winds, 300 m, to a common height of 10 m above the earth’s surface. In Equation 16, a variable was introduced that represents the land surface characteristics. It is known as the roughness length z0. z0 is defined as the height where the wind speed becomes zero using this logarithmic wind profile (Garratt 1992). It is a local value that depends on the land use/land cover at that local point. This value is well defined only for homogenous terrain and has been calculated experimentally by Grimmond (1998) and Lettau (1969), as well as many others. For heterogeneous terrain, we will define an effective roughness length. In this chapter, we will discuss the development of the roughness component of this study. First we examine the roughness data and how it was derived. Then the effective roughness length will be extensively reviewed using the notion of fetch. The development of the radial weight function is shown. Finally, examples of the data and the calculated effective roughness length will be evaluated. 3.2 Roughness Data Set The Federal Emergency Management Agency (FEMA) provided the roughness dataset used in this project. FEMA has developed a program that aims to mitigate hazards and prevent losses resulting from disasters called HAZUS (http://www.fema.gov/hazus/hz_index.shtm). HAZUS is a natural hazards loss methodology with modules for estimating potential losses from earthquakes, winds and floods. A critical component of the wind field modeling is the ground roughness. Generally, as the ground surface becomes rougher, the wind speed near the ground decreases due to increased friction. Surface roughness is a function of the height and spacing of obstructions on the ground surface. There is no direct database describing the distribution of the
16 surface roughness over land regions within the US. Consequently, it can be estimated indirectly from the land use and land cover (LULC) characteristics by associating roughness values with land use classes. 3.2.1 Estimation of the Surface Roughness by HAZUS There have been many experiments attempting to categorize the surface roughness parameter based upon ground exposure. The ground surface roughness parameter describes the frictional effect of the underlying surface geometry. It is also described as the surface momentum sink for the atmospheric flow (Wieringa 1993). It is well defined only locally for homogeneous terrain and neutral stratospheric conditions. Table (1) shows the best estimations of roughness as depicted by Wieringa (1993) and is a reasonable basis for determining appropriate roughness lengths for mainland areas.
Table 1: Roughness lengths of homogeneous surface types (Wieringa 1993)
Surface Type Roughness Length (m) Sea, loose sand, and snow 0.0002 Concrete, flat desert, tidal flat 0.0002-0.0005 Flat snow field 0.0001-0.0007 Rough ice field 0.001-0.012 Fallow ground 0.001-0.004 Short grass and moss 0.008-0.03
Long grass and heather 0.02-0.06 Low mature agricultural crops 0.04-0.09 High mature crops ('grain') 0.12-0.18 Continuous bushland 0.35-0.45 Mature pine forest 0.8-1.6 Tropical forest 1.7-2.3 Dense low buildings ('suburb') 0.4-0.7 Regularly-built large town 0.7-1.5
Surface roughness can also be determined empirically. Lettau (1969) formulated z0 from a field experiment as
z0 = 0.5 HS / A (16) where H is the average height of obstacles within the area, S is the total projected frontal area of the obstacles, and A is the surface area. The 0.5-factor corresponds to the average drag coefficient of the area based upon the primary obstacle’s projected frontal area. For a relatively large variety of S values, the equation produces z0 that are within 25% of measured values from wind profiles. As the density of obstacles or elements increases, the surface drag increases, and
17 then so does z0 (Garratt 1992). This equation allows for some degree of upwind land characteristics to be taken into consideration. 3.2.2 Land-Use/Land-Cover Data Sources There are two sources of LULC data that are used in the HAZUS project: the National Land Cover Data (NLCD) for the conterminous US and a high resolution LULC system for the State of Florida. The NLCD covers the conterminous US and is at a coarse resolution (http://edc.usgs.gov/geodata/). The LULC dataset for the State of Florida is based on the databases of the five water management districts in the state. These databases are considered more recent, updated every five years, and the land-use classification system is more refined compared to that of the NLCD data. Each water management district independently prepared the LULC databases based upon the Florida Land Use and Land Cover Classification System (FLULCCS) developed by the Florida Department of Transportation with a scale of 1:24,000. Tables (2) and (3) show examples of this classification system. All of the water management districts of Florida use at least level 1 and level 2 classifications, but in some cases level 3 and 4 classifications have been used. According to HAZUS the Water Management District classifications are 85% to 95% accurate. For more information on the FLULCCS, refer to the FLULCCS manual (State of Florida 1999) or the HAZUS project.
Table 2: FLUCCS Level 1 Classifications.
Level 1 Classification 1000 Urban and Built-Up 2000 Agricultural 3000 Rangeland 4000 Upland Forests 5000 Water 6000 Wetlands 7000 Barren Land 8000 Transportation, Communications, and Utilities 9000 Special Classifications
3.2.3 Conversion from LULC Classes to Roughness Length HAZUS uses Lettau’s formulation of the surface roughness, aerial photographs, and engineering judgment to assign values for LULC classes, instead of theoretically based descriptions that do not take into the land cover directly. From Table (1), it is evident that roughness values vary
18
Table 3: Example of the FLUCCS Level 2 Classification Using the Urban and Built-Up and Agricultural
Level 2 Classification 1000 URBAN AND BUILT-UP 1100 Residential Low Density 1200 Residential Medium Density 1300 Residential High Density 1400 Commerical and Services 1500 Industrial 1600 Extractive 1700 Institutional 1800 Recreational 1900 Open Land 2000 AGRICULTURAL 2100 Cropland and Pastureland 2200 Tree Crops 2300 Feeding Operations 2400 Nurseries and Vineyards 2500 Specialty Farms 2600 Other Open Lands (Rural)
over similar terrain types; therefore HAZUS uses engineering judgment to determine the mid-
point value for each z0 range in the classes. Then once a roughness value is assigned to a given land use, a surface roughness map can be developed directly from a LULC map. This information can be used in wind models for calculating the 10 m surface winds within the storm environment. For a more detailed description of the roughness value assignment process or any aspect of the project, contact the HAZUS project (http://www.fema.gov/hazus/hz_index.shtm). The surface roughness data set is given in Figure (6). It has a resolution of nearly 111 m (.001° latitiude), which is superior for boundary layer calculations than the typical LULC data that is at about a 1 km resolution. The high resolution of the data set will hopefully lead to a more accurate determination of the effective surface roughness. 3.3 Effective Roughness In our case, it is essential to take into account land surfaces which have non-uniform distributions of objects, such as trees, houses, water, etc., to accurately determine 10 m winds. Obstacles and patches of high roughness are momentum sinks producing an extent of higher stress in the downwind direction. An integrated result of turbulent drag caused by these obstacles occurs when the earth’s boundary interacts with the atmospheric flow (Wieringa 1993).
19
re 6: HAZUS Roughness Lengths for the State of Florida in meters. Figu
20 Knowledge of the upwind terrain is essential to being able to calculate surface wind speed at any point. The region or area upwind of a wind observation, termed here as fetch, depends on the atmospheric conditions and its stability at the time of measurement. Some studies suggest that only a short distance is sufficient (Mason 1988, and Pasquill 1972), but others, Powell (1996) and Sempreviva (1990), suggest that a fetch of over 20 km influence wind observations. Mason (1988) found that the surface stress approaches equilibrium value about 20 km downstream of a roughness change in neutrally stable flow. He further
suggests that an observation made at 10 m will have an area average over horizontal scales of about 2 km. Wieringa (1993) suggests that roughness values derived from gustiness observed at 10 m generally have an upwind fetch of several kilometers. Theoretical estimates of fetch that reflect the influence of the surface elements on observations vary widely. An attempt to account for the fetch and upwind land characteristics is to define an
eff effective roughness lengthz0 . The effective roughness length is defined as the value of the roughness length, which in homogenous terrain, gives a value of stress equal to the area- averaged stress occurring in the heterogeneous terrain (Garratt 1992). Here we will discuss a
eff few of the main approaches of calculating z0 . Taylor (1987) describes the effective roughness length as the area-weighted logarithmic average of the roughness lengths and is given by
eff u∗ ln z0 ln z0 = ≈ ln z0 . (17) u∗
This method was found to be valid if z0 does not vary much over the area. Fiedler and Panofsky
eff (1972) define z0 as a length which homogeneous terrain would have in order to produce the same surface stress (τ) and is given by
1 2 2 u∗ z u = ln 1 (18) 1 eff κ z0
2 where u1 the wind speed at the lowest level z1, κ is the von Kármàn constant, and u∗ is calculated from a known z0 distribution by similarity theory. For neutral conditions this is similar to averaging the drag coefficients based on blending height (Mason 1988). To simplify
eff the equation above, Wieringa (1986) suggested that z0 could be calculated from the grid-square
21 average of the local drag coefficients CD. However, this assumes that wind speeds at the lowest level are constant over all surfaces. He made the assumption in his 10 m calculations that the
eff z0 errors were small and found the relation
−2 −2 ln z1 ln z1 eff = z , (19) z0 0 where the calculation level is z1 (normally on the order 10 m). Schmid (1995) interprets the effective roughness as a momentum sink of the entire (inhomogeneous) surface inside a model grid cell. In neutral static stability,
1 τ 2 z u = ln L (20) L eff k z0
eff is used by Schmid to calculate z0 , where zL is lowest model level, τ is kinematic momentum flux, and k is the von Karmen constant. The problem with Schmid’s equation over
eff inhomogeneous terrain is that z0 is not simply related to local roughness lengths. τ is the total momentum flux within the model grid cell, and since local wind profiles are not logarithmic over varying surfaces, the local fluxes cannot be related to local wind speeds and roughness lengths (Schmid 1995). Other methods, such as area-averaging and area-weighted averages, have been extensively researched. A simple area-average of the roughness values based on a given fetch does not accurately represent the roughness values within that area. Larger roughness values tend to be emphasized. Mason (1988) also found that large z0 values within a small area have a
eff bigger impact on calculated z0 than z0 smaller values. Other researchers, Wood and Mason (1991), have shown the same effect in their research, where the effects of high roughness areas depend on the distance away from the measuring point. Smith and Carson (1977) use weighted
eff averages to calculate z0 , where the terrain is divided into LULC types and the roughness length is calculated for each category using similarity theory. Then the weights are determined by wind observations. However, these types of averaging do not include sophisticated boundary layer theory to properly weigh the individual roughness lengths.
eff Some attempts to define z0 have used plume-diffusion models to define the horizontal area downwind of a point source that is affected by the source’s concentrations (Pasquill 1972).
22 This can also be termed effective fetch. Schmid and Oke (1990) suggest that a reverse plume model may be used to estimate the source areas of turbulent exchange (sinks of momentum) and
eff will be described in the following section. This is the approach we will use to determine z0 . 3.4 The Source Area Model The source area model, developed by Schmid and Oke (1990), is based on the diffusion characteristics of a ground-level point source with a short-range plume model at its core. Figure (7) shows that for a one-dimensional discontinuity of roughness, the source area for a point at height zs is described in terms of an initial modification interface (IMIF) and an equilibrium boundary layer interface (EIF). In this case, the source area is defined by a region with an upwind leading edge –xe and a downstream boundary is –xi.
Figure 7: The source area in one-dimensional patchiness determined by the distances at which an IMIF and EIF reach the sensor height (zs) (Schmid 1990).
Due to increased complexity when considering a two-dimensional region, the area downwind from a surface element is treated as a plume. The one-dimensional approach, shown above, is too difficult to extend to more dimensions because the source area is controlled by the mean wind speed, vertical diffusion, and also lateral diffusion. The first attempt to calculate the two-dimensional source area was completed by Pasquill (1972), who tabulates the dimensions of this region relative to the source location for a set height, roughness, and stability (Pasquill’s Table 2). The reverse plume model of Schmid and Oke is used to estimate the source area.
23
Figure 8: Schematic cross-section of a P source area (Schmid 1990).
Consider the diffusion of a tracer in the horizontally homogeneous flow field and a sensor
at a height zs (Figure 8). If the source is shifted in any direction, the concentration of the tracer will shift in a complimentary fashion. The sensor will experience higher or lower concentrations depending on the location of the source. The location that causes the maximum concentration at the sensor is called the maximum source location. Then the total effect that the sensor experiences is determined by the weighted contributions of all the sources upstream Ω(x,y). If the source is moved away from the maximum source location in any direction, the sensed effect-
level will eventually decline to a minimum effect-level, χP. The geometric location of all point
sources, whose effect-level as the sensor location equals χP, forms a closed curve, which is the
boundary of the P-source area. This curve is in essentially outlining the χP isopleth at level zs derived from the maximum source location. A simple geometric translation of this isopleth may be used to find the source area dimensions. Similarly, the source weight distribution function ω = Ω(x,y) is a geometric
translation of the concentration or effect-level distribution function at level zs. Ω(x,y) can be found by reversing the wind direction, placing a virtual source at the ground underneath the sensor (assuming that it has the same effect pattern), and projecting the virtual effect-level
distribution at zs down onto the ground (Figure 8).
24
Figure 9: The total effect of the source area at the sensor location (Schmid 1990).
Now consider an arbitrary criterion ‘P’, which is needed to define the sensed concentration or the effect-level isopleth as the minimum sensed effect-level for a source to belong to the P-source area. Schmid suggests that ‘P’ is the fraction of the total effect of the source area at the sensor location and is given by
+∞+∞ E (x, y) dxdy (21) t = ∫ ∫Ω −∞ 0 where Et is the total effect at the sensor location so that it is the volume under the Ω(x,y) function
(Figure 4). The horizontal area bounded by each ω = ωP (where ωP corresponds to χP before the translation) represents that fraction ‘P’ of total effect at the sensor contained underneath the
Ω(x,y) surface portion bounded by the ωP isopleth (Figure 9):
+∞+∞ P = ∫∫ Ω(x, y)dxdy ∫ ∫Ω(x, y)dxdy (22) =ωω P −∞ 0 ‘P’ is the portion of the total integrated effect which is contributed by the P-criterion source area, bounded by the weight distribution function isopleth ω = ωP. This shows how a reverse plume model may be used to estimate the weighted source area of a sensor at any sensor height zs. A typical solution of the source area model (SAM) is shown in Figure (10) and the numerical solution for this figure is shown in Table (4). SAM provides a simple solution for source area estimates in a small perturbation approach. The procedure and input conditions (friction velocity, Monin-Obukhov length, roughness length, and wind direction) to produce this figure can be found in Schmid and Oke (1990). The source area is defined by the set of
25 characteristic dimensions of its bounding isopleth, i.e. a, b, c, d (Figure 10). In addition, the distance to the maximum source location in relation to the sensor, xm, to the area bounded by the isopleth is given by a + b + c = e, which is the maximum fetch and a is the minimum fetch. These form the principal results for a given run of the source area program. A statistical version of SAM was also developed to make concise and easy approximations to the full-scale model. The entire set of decile isopleths is approximated over a wide range of input values based upon sensitivity tests conducted by the authors. Table 4 lists the standardized set of isopleth dimensions relative to the 0.5 isopleth together with the expected standard errors. The 0.5 level isopleth is used as a reference because it contains half of the total effect of all the sources. In the Table (4), A ≡ ArP / Ar0.5 , etc.
Figure 10: Example diagram of the source area model results given in Schmid and Oke (1990).
26 Table 4: Normalized Set of Isopleth Dimensions Relative to the 0.5 Isopleth using the Statistical Source Area Model (Schmid 1990). Multiplication Factor for Dimensions
Level (%) WP /W0.1 A ±% a ±% e ±% d ±% ±% 10 0.081 4.0 1.65 6.8 0.33 4.5 0.31 5.1 1.000 0.0 20 0.21 2.8 1.36 4.5 0.48 3.5 0.48 3.4 0.648 2.3 30 0.39 1.9 1.19 2.8 0.63 2.5 0.64 2.2 0.443 3.6 40 0.65 0.9 1.08 1.3 0.81 1.3 0.81 1.2 0.316 4.7 50 1.00 0.0 1.00 0.0 1.00 0.0 1.00 0.0 0.229 5.4 60 1.50 0.7 0.93 1.2 1.23 1.3 1.21 1.2 0.162 5.7 70 2.31 2.2 0.87 2.4 1.53 3.0 1.48 2.3 0.101 8.4 80 3.88 5.0 0.80 4.0 2.00 5.9 1.91 3.6 0.052 13.2 90 8.43 11.4 0.72 6.2 2.97 12.0 2.78 5.2 0.019 25.9
Another result of the author’s tests is that the downwind distance a can be approximated in terms of the maximum source location xm. The shape of the isopleth is close to elliptic. It is also felt that the b and c dimensions do not have to be resolved separately. Therefore, a + b + c is compounded into a new dimension e. So therefore the statistical version of the model is reduced to finding approximation functions for xm and e in terms of zs, z0, and L and a in terms of xm and Ar. The appropriate forms of the functions for the P = 0.5 isopleth are:
0.96 1/ 2 e0.5 ≅ 7.7zs {ln( 0.23z s / z0 ) −ϕ(z s / L,30)}{ln( −L)} (23)
1/2 4/5 d 0.5 ≅ 0.24zs {6 + ln( zs / z0 )} {ln( −L)} συ /u∗ (24)
a0.5 ≅ .0 335xm (25)
Ar0.5 ≅47.0 π (e − a)d (26) and together with the auxiliary equations,
1/ 4 ϕ(z x / L, p) = (1− pzs / L) −1, (27)
1.03 −1/ 2 xm ≅ 1.7zs {ln( z / z0 ) −ϕ(z s / L,76 }() 1− z s / L) (28)
eff where zs is the sensor height, z0 may be taken as the average (or effective) roughness z0 , and L is Monin-Obukhov length. The valid ranges of the input parameters are
2.0 m ≤ zs ≤ 64 m (29)
0.005 m ≤ z0 ≤ 0.8 m (30)
27 5.0 m ≤ - L ≤ 5000 m (31)
1.0 ≤ συ/u∗ ≤ 6.0. (32) With equations (22) through (28) and Table (4) one can determine the characteristic dimensions of the isopleths. The source weight per area W can be written in terms of the source weight function
Ω(x,y) and normalized by the total effect Et as
+∆xx +∆yy W ( , yx )dxdy ( x y E ) (33) = ∫ ∫Ω ∆ ⋅∆ ⋅ t x y
The average source weight per unit area between isopleths P and (P – 0.1), WP, is
WP = 1.0 (ArP − ArP−0.1) (34) so that WP may be normalized with the average source weight per unit area for the smallest isopleth, W0.1, as
ArP WP W0.1 = . (35) (ArP − ArP−0.1)
Arp is the area bounded by the P-isopleth. The ratio above is a measure of the importance of an inhomogeneous unit area depending on its position relative to the sensor. Equation (35) is essentially a weighting function that can be easily calculated by determining Arp. The weighting function of the decile isopleths can be found by using Table (4). This weighting function defined by Schmid & Oke will form the basis of our weighting function described in the next section. 3.5 Radial Weight Function Using Schmid and Oke’s reverse plume model approach we want to extend the definition of the weight function. The plume model describes the concentration of a substance/pollutant per area downwind of its source. This is a valuable way to describe how the concentration is dispersed by the wind (also called total effect). It was also shown that the plume model could be reversed to define the area that affects a downwind sensor (referred to as the source area). We want to extend the definition of the average source weight per unit area (Equation 35) to continuous values of P. In so doing, we also want to derive an expression for P in terms of the radial distance from the source to the sensor.
28 3.5.1 Derivation Schmid and Oke define the source area isopleths by elliptically shaped regions with characteristic dimensions e, d, a, A. The dimensions for the P = 0.5 isopleth are given by equations (22) through (28). The dimensions of other isopleths are given as ratios of the P = 0.5 isopleth and are listed in Table (4). If a fraction of the total effect, dP, lies between P and P+dP isopleth, then the source area weight defined by dA = AP+dP – AP may be given as W ≡ dP dA . (36) by taking the continuous limit of Equation (35). Before in Equation (35), dP = 0.1. We shall
assume that crosswind fluctuations are very small, i.e. σ υ ≈ 0, so that the cross dimension d is very small, or at least smaller that the dimension of the roughness element tile, about 100m. In this approximation, the weighting function does not depend on the azimuthal angle, only on the
distance x from the sensor zs (azimuthal dependence will be brought in later). We then can rewrite the weighting function as W ≈ CdP/dx (37) where C is a constant taking into account the integrated angular component. We will neglect this constant for the time being, as normalizing W will find it later. Table (4) shows the values of the isopleth dimensions for discrete values of P. We wish to have a continuous range of values; so a smooth function is needed for continual isopleth dimensions. First it is necessary to find P as a function of x and then take the derivative to obtain
the weighting function W. Note that x = e pe0.5 is the distance of the P isopleth from the sensor (we are neglecting the minimum distance a for the time being).
A plot of P versus e is given in Figure (11) using the values obtained for e p from Table 4,
where P represents the isopleths and e p is the normalized distance with respect to the P=0.5 isopleth. The plot appears to be exponential. Therefore, we fit the discrete values with the following function P =1− e +ba e . (38) Taking the log of both sides, we obtain ln(1− P) = r + se . (39)
29 A polynomial (degree 1) least squares fit gives r = 0.16014 and s = -0.85270. A plot of the fitted function is also given in Figure (11) and it can be seen that the function is a rather good fit. Written in terms of x, the function becomes
Figure 11: Plot of P versus e with the corresponding fitted function.
P =1− er+sx e0 .5 . (40) Taking the derivative, the weighting function becomes dP s W = = − e r+sx e0.5 . (41) dx e0.5
The weighting function depends on x and e0.5, which, according to Equation (22), is a
eff function of zs, z0, and L. Note that the weighting function, used to determine z0 , depends on
eff eff z0 . We will use an iterative approach to solve for z0 . 3.5.2 Sensitivity to the Parameters
We will now examine the sensitivity of the weight function on its parameters x, zs, z0, and L.
Figure (12) shows a plot of the un-normalized weighting function for the values of z0 =
0.1, zs = 10 m, and various values on L. It can be seen that the weighting function is not strongly
30 dependent on L for large negative values. For hurricane conditions, Moss (1975) calculated L to be about –1200 m using data from hurricanes Daisy (1958) and Inez (1966). Therefore we will assume L = -1200 in future calculations.
Figure 12: Plot of W(x) for zs = 10 and z0 = 0.1.
Figure 13: Plot of W(x) for z0 = 0.1 and L = -1200.
31 In Figure (13), a plot of the weighting function for various sensor heights zs with z0 = 0.1 and L = -1200. It shows that for increasing sensor height, the fetch increases, which is expected. Generally, a 10 m reference height is used to specify surface winds. Figure (14) shows a plot of the weighting function with various roughness length values.
Again, L = -1200 and zs = 10 m. From the plot we can see that for smoother values of terrain, i.e. 0.1 – 0.3 m, the fetch again becomes larger, and vice versa for rougher terrain values. This is again to be expected since smoother terrain does not create as much of a momentum sink. In our
eff algorithm of the weight function we will use z0 for z0.
Figure 14: Plot of W(x) for z = 10 m and L = -1200. s
3.6 Azimuthal Dependence We will now examine the azimuthal dependence of roughness values on the weighting function. The radial weight function is defined as a function of distance, sensor height, roughness, and the Monin-Obukov length. A box centered on each point of the model grid is constructed (Figure 15) to take into account the various azimuthal angles.
32 The size of the box was determined by the sensitivity tests of the variables zs, z0, and L from the previous section. It was found that the radial weight function (Equation 41) becomes negligible beyond 5 km. Therefore, an upwind distance or fetch of 5 km will be used in our calculations. Then the dimensions of the box are approximately 10 km by 10 km. To calculate the effective roughness coefficient for different wind directions, the box is, then, divided into octants (or 8 sectors) to represent 8 possible wind directions, with a sector size of 45° (Figure 15). 8 sectors were chosen for computational efficiency, but the model is not limited to these wind directions.
Figure 15: A schematic of the box used in the roughness model to calculate the effective roughness values based on 8 storm tracks.
The weights are calculated for each point in the box using the Equation (41). An additional 1/x factor is included to take into account the increasing arc length with radial distance. Then the weighted average of the roughness values is taken over each of the 8 sectors of the box. The resulting value is the effective roughness for each sector. This method is repeatedly followed for all points in the model grid. The resulting roughness values then can be used in the wind model to reduce the flight level winds to the 10 m level using the logarithmic wind profile (Equation 15). 3.7 Examples We will now show examples of the local surface roughness and effective roughness for the Miami area at approximately 100 m resolution.
33 Figure (16) shows the local roughness lengths in the Miami area. Warmer colors indicate higher roughness values. For example, along the eastern coast of the barrier islands where there are commercial services and high-density residential areas, such as apartments, condominiums, and hotels, higher roughness values are seen. Some of the highest values are found just to the west of downtown Miami. These are areas of urban build up and industry. On the other hand, cooler colors indicate lower roughness. Some of the smoother areas can be classified as agricultural areas and lower-density urban areas and can be found northeast of downtown. Figures (17a) and (17b) show the effective roughness values each of the 8 azimuthal sectors. It is interesting to note the values over water regions, such as Biscayne Bay and the Atlantic Ocean. When there is onshore flow, sectors 1, 2, 7, and 8, the higher roughness values of the barrier islands cause an increase in surface roughness over Biscayne Bay. This is due to the increase in upwind friction of the higher land roughness values. Likewise during offshore flow, sectors 3, 4, 5, and 6, the effects of the mainland are also seen in the bay and ocean. Figures (18) and (19) show the differences in effective roughness between onshore and offshore flow. Figure (18) shows the difference between an easterly onshore flow (sector 1) and a westerly offshore flow (sector 5). Figure (19) shows the difference between a northerly offshore flow (sector 3) and a southerly onshore flow (sector 7). The impact of the effective roughness coefficient on the 10 m wind field will be discussed in the next chapter.
34 Figure 16: Local Roughness Values for the Miami Area.
35
Figure 17a: Effective Roughness Values for Sectors 1 through 4 in the Miami Area.
36
Figure 17b: Effective Roughness Values for Sectors 5 through 8 in the Miami Area.
37
Figure 18: Difference of Effective Roughness Values Between Sectors 1 and 5.
38
Figure 19: Difference of Effective Roughness Values Between Sectors 3 and 7.
39
CHAPTER 4
RESULTS
4.1 Comparison of Local vs. Effective Roughness We will now compare the effects of the hurricane model wind fields using the local roughness length and the calculated effective roughness length. Figure (20) represents the wind field using the local roughness length, and Figure (21) represents the wind field using the effective roughness length. Both diagrams use hurricane Andrew as an example and are at approximately a 100 m resolution. The Input parameters can be found in Section 2.1.3. It is difficult to see the differences of the magnitude of the winds between both figures, but the averaging effect of using the effective roughness is quite apparent on the large scale. The wind field in Figure (20) is not as smooth and continuous as in Figure (21) where the averaging via the weighting function has been used. By examining the wind field along the coast, we see that the local roughness length uses a point-by-point method that does not consider surrounding areas. But the effective roughness length reduces the winds by looking at land surfaces upstream. For onshore flows, using effective roughness results in stronger winds that reach further inland due to the effective fetch of the ocean. This also applies to offshore winds where friction of the land is felt in the winds offshore until they become in equilibrium with the underlying water surface. Figure (22) is a graph of the difference in winds using the local roughness and the effective roughness at a smaller scale, which allows us to evaluate the local effects of the two roughness parameters. The biggest difference lies along the coast where the difference in the winds is ± 15 kt. These areas are especially vulnerable due to the higher property value on the coast and barrier islands where damage estimates are critical. A large error in wind speed can drastically change the amount of property damage and loss of life.
40
Figure 20: Wind field of hurricane Andrew at the time landfall using local roughness coefficient.
41
Figure 21: Same as in 20, but using the calculated effective roughness coefficient.
42
Figure 22: Difference between the 10 m winds using local roughness and effective roughness.
43 In this example, the effective roughness results in wind differences on the order of 10 – 15%. Since frictional effects are approximately proportional to the square of the velocity, this can result in force differences on the order of 20 - 25%. Therefore, the effective roughness length gives a reasonable approximation of the wind field due to its ability to take into account obstacles and land surfaces upstream, which has been shown by Mason (1988), Pasquill (1972), Powell (1996) and Sempreviva (1990) as well as many others. 4.2 Sensitivity to Model Parameters Model sensitivity is important to the overall understanding of how the model behaves. This section will be focused on evaluating the wind model and its reaction to changes in its parameters. In section 3.5, the weight function yields a fetch of approximately 5 km. However, some observations suggest the fetch may be much larger (Powell 1996 and Sempreviva 1990). Hence it would be useful to consider parameter changes that would lead to a larger fetch.
Unnormalized W
Distance (meters)
Figure 23: Graph of the radial weight function (Equation 26) by varying the s parameter. The solid line indicates the function using the given value of s. The short dashed line is the function with s = s0/4. And the dashed line is with s = s0/10.
44 Recalling Equation (41), the radial weight function can be rewritten as,
W = −csesx, (42) r where x is the radial distance, c is a constant e , and s is redefined to include e0.5. Therefore the sensitivity of the weight function can be seen in varying s. Essentially, changing s changes the effective fetch. That is, decreasing s results in a larger fetch. Figure (23) is a graph of the radial weight function with assorted values of s. The
function is shown with s as the original s0 value (solid line), s0/4 (short dashed line), and s0/10 (dashed line). Hurricane Andrew will again be used in the following figures to show the sensitivity of the wind field.
For the case of s0/4, the weights are only notable within 12 km of the center. Figure (24)
shows a plot of the wind field using s0/4. The wind field is somewhat more smooth and continuous than that of Figure 21 due to the increased fetch. In the case of s0/10, the weights become almost negligible after 20 km, which causes the wind field to be more smooth and continuous (Figure 25) than the original 5 km version (Figure 21). In both figures, it is difficult, again, to see the major differences in the magnitude of the wind on such a large scale. Figure (26) is plot of the differences between the wind fields using s0 and the wind fields using (a) s0/4 and (b) s0/10 on a smaller scale. The differences range from – 10 kt to 4 kt, again, with the largest difference seen on the coast and barrier islands. In (a) and (b), we can see that the increased fetch is the dominant feature of the wind fields. A longer fetch allows for further penetration of stronger winds inland. In (a), the fetch is approximately 12 km as seen in Figure (23). Here the biggest difference occurs on the southeast mainland coastline a longer marine fetch is seen with an increase of winds in this case of 8 to 10 kt. In (b), the fetch is about 20 km. And on the same coastline the stronger winds penetrate much further inland and are about 10 kt stronger than the wind field using just s0. Comparing (a) and (b), the winds inland are about 1 kt stronger and on the coast they are approximately 5 kt stronger. In summary, our sensitivity tests show the magnitude of wind changes due to different fetch amounts are roughly the same order magnitude as in the previous section where we used a fetch of 5 km. Further studies are needed to properly determine the upwind fetch distance. These numbers may help provide estimates of the error due to the uncertainty of the size of fetch.
45
on
/4. 0 Figure 24: The wind field of hurricane Andrew using the weight functi with s =
46
/10. 0 Figure 25: Same as in 24, but with s =
47
-
/10. 0 /4 and (b) s = 0 Figure 26: The difference of the model winds using weight function with s = 0.85370 and the function using (a) s =
48 4.3 Real World Examples This section will be focused on specific case studies of Florida land falling hurricanes. A brief synoptic history and model simulations of specific storms will be reviewed. Hurricane Andrew (1992), hurricane Erin (1995), hurricane Kate (1985), and hurricane Donna (1960) will be used. Our model resolution for these simulations is approximately 1 km. We will also compare our computed wind field to those produced by HRD. It is not our plan to do a direct comparison of the two types of wind field models, but to see if our simple model calculates realistic winds. HRD has developed a wind analysis system called H*Wind. The analysis is based on all available observations from aircraft, buoys, C-MAN platforms, and surface airways that are processed to a common 10 m height. The domain consists of 3 nested meshes at controllable scales. The resulting objective analysis is representative of the mean state of the storm at a given time period. The product is a streamline and isotach contour plot for a given mesh. It is designed to give the location and strength of the maximum wind and the extent of hurricane force winds. At landfall, land exposure analyses are constructed based on observations converted to open terrain (z0 = 0.03). The analyses have been experimental since 1993. For further information on H*Wind, the reader is directed to Powell (1998) and Burpee (1994). All of the following H*Wind diagrams are available online at http://www.aoml.noaa.gov/hrd/data_sub/wind.html. 4.3.1 Hurricane Andrew Case Study Hurricane Andrew formed from a tropical wave that crossed the west coast of Africa on 14 August 1992. As it moved swiftly westward across the Atlantic, it transformed from a depression into a tropical storm rather quickly as vertical shear diminished. However, sporadic deep convection coupled with an unfavorable environment caused the storm to collapse to a low- level circulation by 20 August with surface winds of 21 m s-1 and an astonishing pressure of 1015 mb. The heading started to shift more west-northwest. Then a breakdown and split of a low east-southeast of Bermuda occurred. The northern half moved out and the southern half moved southwest of Andrew, which caused an increase of the upper-level storm outflow. Further the breakdown of an intense high-pressure center near the southeast coast of the U.S. allowed for a quick intensification. Andrew reached hurricane strength in the morning of 22 August. About 36 hours later, it was nearly a category 5 hurricane. The high-pressure steered the storm into the Bahamas 23 August and then to a landfall near Elliot Key in southeast Florida
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Figure 27: 10 m modeled winds for Hurricane Andrew at landfall 24 August 1992.
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Figure 28: H*Wind maximum 1-minute sustained winds at 10 m for hurricane Andrew at the time of landfall.
51 0840 UTC 24 August with 145 kt winds and a 922 mb central pressure. It continued into the Gulf of Mexico with little weakening over the Florida peninsula. A second landfall occurred in south-central Louisiana as category 2 hurricane at 0830 UTC 26 August with 100 kt winds and a 956 mb central pressure. During the weakening phase, it moved northward and then northeastward. On 28 August, the remnants merged with a front over the Mid-Atlantic States. For further information on Andrew the reader is directed to Mayfield (1992) and McAdie (2002). Figure (27) is a diagram of the modeled 10 m winds for Hurricane Andrew at 0905 UTC 24 August. The model input parameters are the same as previously discussed in Section 2.1.3, but here Rmax2 is estimated to be 50 km based on satellite imagery. In comparison, Figure (28) is the H*Wind analysis at the same time period. As we can see, the storm structure is similar. Over land areas, our model provides reasonable wind estimates due to the effective roughness component, where over the ocean the winds are in broad agreement with the HRD analysis. Overall, our simple model provides a realistic scenario of hurricane Andrew at landfall. 4.3.2 Hurricane Erin Case Study Hurricane Erin formed from a tropical wave the exited the coast of Africa on 22 July 1995. The wave had 2 low-level circulation centers and a large area of disturbed weather that moved towards the west-northwest over the next 5 days. By 27 July both centers were generating deep convection to the northeast of the Leeward Islands. 30 July satellite imagery indicated a tropical storm, but Erin did not have a low-level closed circulation center due to southwesterly vertical shear. Reconnaissance declared Erin a tropical storm on 31 July over the Bahamas. An upper- level low near Florida permitted a shift toward the northwest and slow strengthening. Erin became a hurricane late on 31 July. Two days later, Erin made landfall near Vero Beach, Florida at 0600 UTC 2 August as a category 2 hurricane. The weakening storm headed toward the west- northwest emerging into the Gulf of Mexico where it then reintensified to a category 2 system. After turning to the northwest the final landfall occurred near Pensacola, Florida on 3 August. It gradually merged with a frontal system over West Virginia on 6 August. For further information on Erin the reader is directed to Lawrence (1998). Figure (29) is a diagram of the modeled 10 m winds for Hurricane Erin at 0615 UTC 2 August. Model input parameters are 27.7 N, 80.3 W, 984 mb, and 75 kt. In addition, estimates of Rmax and Rmax2 are 160 km and 210 km based on radar and satellite imagery. Figure (30) shows HRD’s analysis of Erin near the landfall time period, but here we must mention that Erin
52 is not hurricane strength in the analysis even though this diagram is 10 minutes before the official landfall. We speculate that not all the observations are included in this version considering HURDAT shows that it is a hurricane at this time. Our storm structure is similar to HRD’s, but only stronger. However, our model in this case may be more realistic given the maximum sustained winds.
Figure 29: 10 m modeled winds for Hurricane Erin at landfall 2 August 1995.
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Figure 30: H*Wind maximum 1-minute sustained winds at 10 m for hurricane Erin at the time of landfall.
4.3.3 Hurricane Kate Case Study Hurricane Kate formed just northeast of the Virgin Islands with the interaction of a weak tropical wave and a 200 mb trough on 13-14 November 1985. By 15 November reconnaissance found storm force winds. A cutoff cyclonic circulation developed in the trough at 200 mb, and it accelerated to the northwest ahead of Kate. A large high-pressure center near Florida enhanced the outflow, which intensified Kate to a hurricane 16 November. Kate moved westward through the Bahamas and developed a well-defined eye on the 19th as it passed the north-central coast of
54 Cuba. Only slight weakening occurred while half the eyewall was over land. Kate tracked along the ridge of high pressure and intensified. A frontal trough moving from the west caused the hurricane to weaken while in the Gulf of Mexico.
Figure 31: 10 m modeled winds for Hurricane Kate at landfall 21 November
1985.
55 Kate made landfall at Mexico Beach, Florida at 2230 UTC on 21 November with a central pressure of 967 mb (a category 2 storm). Continual weakening occurred through Georgia and other states, but the remnants emerged into the Atlantic off the Carolina coast. Further information may be found in Case (1986). Figure (31) is a diagram of the modeled 10 m winds for Hurricane Kate at 2230 UTC 21 November. The observed winds during its landfall in Tallahassee, FL were about 40 kt and in
Apalachicola, FL were near 54 kt (Case 1986). The observations helped determine the Rmax to be
35 km and Rmax2 to be 120 km. The other model input parameters are 30.2 N, 85.1 W, 967 mb, and 85 kt. The wind field is only valid over the state of Florida; all other areas use a roughness value of 0.01 (open water value). An H*Wind analysis is not available for Kate. However, we can still show a realistic storm environment from other observations in Case (1986). 4.3.4 Hurricane Donna Case Study Hurricane Donna formed from a tropical wave in the eastern Atlantic late in August 1960. The system is thought to have moved west-northwest at a fast rate. On the evening of 4 September, the eye passed through the northern Leeward Islands. The storm weakened slightly before approaching the Islands. Surface observations in the islands show that it had 110 kt winds and a central pressure of 952 mb. A short-wave trough passing to its north caused the storm to head more westward. On 9 September Donna hit the northeastern coast of Cuba and then moved west-northwest toward the Florida Keys. The center passed over the middle Keys just northeast of Marathon in the early morning hours of 10 September where winds were estimated at 120 kt with a central pressure of 930 mb making it a category 3 storm. A trough in the mid-west U.S. allowed the storm to recurve along the southwest coast of Florida. The eye passed over Naples and Fort Meyers and continued to the northeast. It reentered the Atlantic north of Daytona Beach on 11 September where rapid re-intensification occurred. It continued to affect the east coast of the U.S. until it finally went extratropical inside the Canadian border. A more detailed description of Donna’s lifecycle can be found in Dunn (1960). Figure (32) is a diagram of the modeled 10 m winds for Hurricane Donna at 1200 UTC 10 September. Model input parameters are 25.3 N, 81.3 W, 938 mb, and 115 kt. According to
Dunn (1960) Donna’s eye was 21 mi in diameter. We then calculated Rmax as 17 km and Rmax2 was estimated as 110 km. Figure (33) is HRD’s diagram for Donna when it had just passed over the middle Keys. As with Andrew, our simple model provides a realistic scenario.
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Figure 32: 10 m modeled winds for Hurricane Donna on 10 September 1960.
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Figure 33: H*Wind maximum 1-minute sustained winds at 10 m for hurricane Donna at the time of landfall.
4.4 Historical Hurricane Scenarios The high-resolution surface wind model can also be useful in simulating historical tropical cyclones. Historical storms generally have very little data. Since our model requires few parameters, we can provide an estimation of the storm’s surface environment. Also, the
58 restoration of previous storms can provide graphical insight to their structure and the magnitude and direction of the inland winds. The majority of the parameters needed in the model are found in the HURDAT database, i.e. the 6-hourly positions and sustained winds. The other model parameters can be determined based on other known variables or statistically representative values. This will be detailed in the following section. 4.4.1 Estimations of Unknown Parameters The central pressure can be estimated using the pressure-wind relationship, given the sustained wind speed. HRD has developed a regionally based relationship for the Atlantic basin (Landsea). For the Gulf of Mexico region, the relationship is
U = .10 627*(1013 − p)0.5640 (42) where U is the wind speed in knots and p is the central pressure in mb. This equation above can be rearranged to solve for p,
1.7730 p U = 1013− ( 10.627) . (43) This relationship generally holds true for over-water conditions and for low to medium translational speeds. We will assume this relationship holds for near landfall conditions where the strongest winds are offshore. The radius of maximum winds can be estimated from Vickery et al. (1995b & 2000). Using updated climatological data for the Atlantic and Gulf coasts, the authors developed
statistical relationships between the Rmax and ∆p and Rmax and the latitude. The relationships
were obtained using a linear regression technique. The mean Rmax (km) can be expressed as a
function of both central pressure and latitude:
2 ln Rmax = 2.636 − 0.00005086(p0 − p) + 0.0394899* Latitude (44) 2 where p0 is a constant 1013 mb and p is the central pressure. The correlation coefficient, r is 0.2765. This relationship is valid for storms below 30°N and provides a first guess estimate for
Rmax based on past storms.
Once Rmax is found, Rmax2 can easily be calculated using Equation 3 (from Ch. 2) by
rearranging the terms to solve for Rmax2. However, remembering that α is arbitrary in our study, we use a typical value of 0.9 as used in Zhan (1997). Thus the equation reduces to:
1 0.9 Rmax 2 = 2 Rmax . (45)
59 This allows us to simply estimate Rmax2 by a factor of the calculated Rmax. 4.4.2 1852 Hurricane Case Study An example of a historical hurricane that made landfall near St. Teresa, FL in 1852 is shown in Figure (34). On 9 October 1852 this hurricane struck the Panhandle with 85 kt winds, making it a category 1 hurricane.
Figure 34: 10 m modeled winds for an 1852 hurricane on October 10.
60 The location of this storm was interpolated from the HURDAT database to be 29.85 N, 85.4 W, and 85 kt. From Equations (43) through (45), the central pressure, Rmax, and Rmax2 were calculated as 973 mb, 41.8 km, and 90.3 km. In addition to evaluating recent tropical events, it is possible to examine historical cases using our model. We must keep in mind, however, that over time land use and land cover changes so the simulated wind field should be considered only hypothetical. An historical LULC database could be used. However, that does not take away from the fact that we can get a reasonable estimation of the surface winds.
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CHAPTER 5
CONCLUSIONS
5.1 Discussion and Summary Through the development of a high-resolution wind exposure model coupled with an effective roughness model, this study provides the framework for tropical cyclone landfall modeling. In Chapter 2, an overview is given of the development of the wind exposure model. The model uses a vortex bogusing scheme (Trinh and Krishnamurti 1992) coupled with a wind reduction scheme. The vortex is prescribed as a Rankine-like vortex. The wind adjustment factors from flight-level winds to 300 m are based on mean GPS dropwindsonde profiles of Franklin (2003). Furthermore, reduction factors vary according to location within the hurricane. These are then used to define an adjustment function dependent on radial distance from the storm center. Below 300 m, the wind is further reduced to the surface, 10 m, using the log wind profile. Chapter 3 details the development of an effective roughness model based on the Source Area Model (SAM) described in Schmidt and Oke (1990). SAM takes into account turbulence created by patchy terrain and determines relative importance of the turbulence source area to a downstream wind sensor. A weight function described in terms of radial distance is found and becomes negligible beyond a fetch of 5 km. The effective roughness coefficient is calculated using the weighted average of roughness lengths within 5 km of each model point and for 8 possible wind directions. The values are then used in the wind model to reduce winds from 300 m to 10 m in the log wind profile. This approach is particularly useful for coastal locations since onshore winds can be significantly stronger than winds over a land surface that used a constant or local roughness value. We also show improvement over current models that treat surface roughness lengths constant for all wind directions. The local roughness lengths for the state of Florida were provided by FEMA’s HAZUS project.
62 The results, in Chapter 4, show the effects of using the local roughness coefficient compared to using the azimuthally dependent effective roughness coefficient. The averaging effect is apparent on all scales by more smooth and continuous isotachs. The model is sensitive to changes in the weighting function spatial parameter s. We tried different values of s, which cause the effective fetch to vary from 5 km, 12 km, and 20 km. The differences in fetch cause the magnitude of the surface winds to range from –10 kt to 4 kt, with the largest difference along coastal areas. The larger the fetch, the farther inland stronger winds will penetrate. The standard SAM model simulations use a 5 km fetch. The surface wind fields of hurricanes Andrew (1992), Erin (1995), and Donna (1960) were simulated. The model produces a realistic storm structure for each storm, but is highly idealized. Compared to the H*Wind analyses which converts winds to an open exposure value (or a constant surface roughness value), our simplistic model may produce a more realistic wind estimate over land for landfalling systems. The model is also capable of reproducing diagrams of historical landfalling storms given the basic storm information found in the HURDAT database. The additional parameters needed that are not provided in the database are calculated using theoretical equations based on observed relationships. A pressure-wind relationship is used to determine the central pressure of any tropical system that is not known. Additionally, the radius of maximum wind can be found using a relationship based on the change of central pressure over time and latitude. Yet, it is necessary to understand that we are using roughness lengths based on recent LULC classifications. Over time land characteristics change and evolve, so our historical wind fields should be considered hypothetical. This model is the first to empirically model hurricane surface winds that incorporates wind direction and upstream surface characteristics into one parameter. The treatment of surface roughness at such a high resolution provides us with a more realistic value for the effective roughness coefficient. We have created a model that requires few parameters needed to initialize. This is particularly useful due to the large amount of simulations needed to create the storm database for the FIU/IHRC Public Hurricane Risk and Loss Model Project. This will help in their effort to probabilistically assess the risk to residential property from tropical cyclone wind damage.
63 Hopefully, we can help in the effort to save and protect people from the awesome but destructing power of the hurricane through effective mitigation. 5.2 Future Work This study develops an effective roughness model integrated into a hurricane wind exposure model. Since tropical cyclone research is continuing to evolve and improve with more observations and analyses, further research is needed. This includes • Investigating more sophisticated empirical surface wind models that can give a more realistic hurricane wind field, rather than using an idealized vortex or a full dynamical model. • Continuing to improve the effective roughness coefficient with detailed research of hurricane boundary layer and observations. Currently, there are a limited number of studies and observations regarding the hurricane boundary layer, but with technological advances in observational platforms, more information will further our understanding of this environment. • Generating real-time analyses and forecasts to aid the NHC in providing a more accurate estimation of winds and landfall position. It can increase the confidence of forecasts, warnings and advisories to the public so that evacuations and damages can be reduced.
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BIOGRAPHICAL SKETCH
Lizabeth Marie Axe was born on January 27, 1978 in Mt. Pleasant, Pennsylvania. She has resided in Scottdale, PA, Dunbar, PA, Solomons, MD, and Owings, MD. In 1996, Liza graduated from Calvert High School in Prince Frederick, MD. Later that year, she enrolled in Salisbury State University (now known as Salisbury University), where she received her B.S. in Geography and Geosciences in the spring of 2000. During her undergraduate studies, Liza was an active member of the Salisbury Sailing Team. Upon graduation, Liza was admitted to Florida State University to continue her academic career in the M.S. program in meteorology. For three semesters, she was a teaching assistant for Dr. Paul Ruscher and then for Dr. Philip Cunningham. Moreover, Liza worked under the direction of Dr. T. N. Krishnamurti as a research assistant. During the hurricane season of 2001, Liza represented the lab, along with Andrew Schwartz, in the NASA CAMEX-IV field program. She was fortunate to fly into Hurricanes Erin and Humberto. In 2003, she was admitted to Chi Epsilon Pi, the meteorology honor society.
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