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UNIVERSITY OF HAWAI'I LIBRARY

GPS METEOROLOGY AND THE PHENOMENOLOGY OF

PRECIPITABLE WATER

A DISSERTATION SUBMITIED TO THE GRADUATE DIVISION OF THE

UNIVERSITY OF HAWAI'IIN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSPOHY

IN

GEOLOGY AND GEOPHYSICS

DECEMBER 2002

By

James H. Foster

Dissertation Committee:

Michael Bevis, Chairman

Patricia Cooper

Gerard Fryer

Frederick Duennebier

Steven Businger

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Abstract

Three studies of precipitable water using the Global Positioning System are

presented. The first study finds that precipitable water in Hawai'i is best described by a

lognormal distribution. The long-term average value of precipitable water declines

exponentially with height, but the dispersion of precipitable water declines more linearly. The

change in skewness of the distributions is also linear, although in this case it increases with

elevation. The second and third studies use GPS meteorology to investigate a climatological

and a meteorological event respectively. First, the effect of the 1997-1998 EI Nino on

precipitable water in the westem tropical Pacific is studied and found to be consistent with a

model relating the formation of an anomalous high-pressure ridge to the EI Nino episode.

Finally, the details of the precipitable water field for the Ka'Q Storm, November 2000 are

examined. The results highlight the role of topography in controlling the location of

convection, The observed correlation between the precipitable water and rainfall is used to

generate estimates of rainfall based on GPS data, Comparing the GPS precipitable water

estimates with those from a weather model indicates that the underestimates of rainfall

produced by the weather model are probably due to correlated underestimates of precipitable

water.

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Table of Contents

Abstract... iii

Table of Contents iv

Table of Figures

vi

Chapter 1: Introduction1

Chapter 2: Lognormal Distribution of Precipitabie Water in Hawai'i

.4

Abstract..

4

Introduction

4

Data and Analysis

5

The Lognormal Distribution

7

Results

9

Discussion and Conclusions

14

Acknowledgments

17

Chapter 3: EI Nino, water vapor, and the Global Positioning System

18

Abstract

18

Introduction

19

Results

20

Conciusions 25

Acknowledgments

26

Chapter 4: The Ka'O Storm (Nov 2000): Imaging precipitable water using GPS

27

Abstract

27

Introduction

29

Network and Data Methodology

31

Results

35

Temporal Structure of the Precipitable Water

35

Spatial Structure of the Precipitable Water

37

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Precipitable Water and Rainfall44

GPS and the Mesoscale Spectral ModeL 54

Conclusions58

Acknowledgements

61

References 62

v

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Table of Figures

Figure 2.1. Location of GPS sites on the Big Island of Hawai'i. Sites with colocated

meteorological instruments are the solid black circles6

Figure 2.2. Histograms of precipitable water for MKEA, PGF2, and PGF4 with lognormal PDF

curves superimposed. The p a r a m e t e r s ~ , m, and s for each PDF curve are: -1, 2.19,

0.581; 0, 20.45, 0.301; 0, 28.14, 0.256 respectively8

Figure 2.3. Histograms of the three zenith delays for PGF2 with lognormal PDF curves

superimposed. The p a r a m e t e r s ~ , m, and s for each PDF curve are: 2147.5, 2268.1,

0.313; 2000, 2139.5, 0.030; 0, 127.28, 0.304 respectively 10

Figure 2.4. Plots showing the elevation dependence of the PW population averages and

dispersions. a) Mean (triangles) and median (circles) values. Sites with colocated

meteorological instruments are shown as solid black. Best fit exponential functions given

by a exp(-b elev) where a =32.15, b =.0005911 and a =31.62, b =.0006613

respectively. The PW scale heights implied are -1700 and -1500. b) Arithmetic

(triangles) and geometric (circles) standard deviations. The arithmetic standard deviation

(ASD) has units of mm of PW while the GSD is dimensionless. The GSD has been

multiplied by 10 to plot on the same range. The best-fit linear functions are given by a + b

elev where a =7.62, b =-0.00137 and a =0.222, and b=0.000111 respectively. c)

Median PW plotted on a log elevation scale. Intersection is at -544 m

ll

Figure 2.5. Histograms and lognormal PDF curves for various elevation levels for the RAOBS

at Lihue, Kauai. Histograms were generated by interpolating the cumulative PW profiles

for launches from 1998 to 2002 to a common set of elevations. Histograms are arbitrarily

shifted vertically for clarity. The scale bar indicates the frequency of PW falling within any

given 1 mm interval (bar is 1 mm wide). Shown as insets are the distribution medians

and geometric standard deViations (GSD) with respect to height.15

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Figure 3.1. Locations of existing IGS CGPS sites in the western tropicai Pacific with sea-level

pressure and surface winds for (a) November 1997, just prior to the onset of atmospheric

drying and (b) January 1998 when the drying episode was fUlly developed. Sites

discussed here have white boxes under their names. (GPS data from the Hawaiian sites

KOKB and MKEA show anomalies similar to GUAM. NTUS was installed in 1998 and

TAIW has data only until 1997)

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Figure 3.2. a) GPS-derived precipitable water (PW) series for KWJ1. Green dots are PW

estimates, the thick black line is the running 30-day median PW value and the gray

shading represents the area encompassing 95% of the estimates. Also plotted is

outgoing long-wave radiation (OLR), sea-surface temperature (SST) and rainfall time

series for the same period. Red arrows show the onset of EI Nino conditions indicated by

(b). Black arrows indicate the sudden onset of drying. Blue arrows mark the beginning of

La Nina. OLR is used as a measure of convection. Deep, strong convection carries

clouds higher, cooling the tops and lowering their thermal emittance, thus low OLR

values reflect a moist, deeply convecting atmosphere while high values indicate a dry,

cloudless and non-convecting atmosphere. (OLR data are linearly interpolated to each

site from the 2.5

0grid of daily-averaged data measured by AVHRR on NOAA 14).

Reduction of ZND to PW used predicted meteorological data from a 3-D global weather

model23

Figure 4.1. Location map showing the GPS sites and rain gauges used in this study. Rain

gauges are marked by triangles, GPS sites by circles. The MSM-modeled surface wind

field for OOOOZ 3rd November (day 308) is overlain in dark gray arrows to illustrate the

regional wind field for the storm event. 28

Figure 4.2. a). Five GPS-derived precipitable water time series representing a vertical profile

from sea-level at PGF6 to MLSP at 4050 m on the summit of Mauna Loa. Also shown as

the lines marked a-d are the four times for which map-views are presented in Figure 3. b)

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Rainfall from Kapapala Ranch, to the west of the GPS transect and site of the highest

measured rainfall for this event. 36

Figure 4.3. Map views of precipitable water estimates for the epochs (a-d) marked in Figure

2. a) 04:00 (HST) 1$' Nov, during the precursory drying event. b) 08:00 (HST) 1$' Nov, all

sites show a rapid rise in PW. c) 01 :00 (HST) 2ndNov, as the Hilo and high-level PW

peaks, and d) 09:00 (HST) 2ndNov, as the low level PW on the south slopes of KTlauea

peaks and Kapapala Ranch records its maximum rain rates. (Note that the Mauna Kea

station went offline sometime after the peak of the storm.)

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Figure 4.4. Maps showing the normalized variability of PW (NPW) for the same epochs as

Figure 4.3. NPW =(PW - Mpw)/GSDpw. Mpw is the long-term median PW value at a site

and GSDpw is the long-term geometric standard deviation.42

Figure 4.5. Four GPS and rain-gauge site-pairs showing the relationship between the

precipitable water and rainfall time-series. (MLSP was used instead of MOKP, which is

closer to the rain gauge, because MOKP was not active until after the main storm event

had passed.) In addition to the absolute PW, the long-term median PW values and the

+1, +2 and +3 standard deviation values are shown. The vertical range for the 4 panels

has been chosen to provide the same vertical scaling for the PW

.45

Figure 4.6. Plot of total rainfall for this event against elevation of the gauges. The four gauges

chosen in Figure 4.5 for their proximity to GPS sites fall within well·defined group shown

with the larger filled circles. This group is chosen to represent the regional relationship

with the function: RAIN =826 - 0.1952 x ELEV .49

Figure 4.7. Scatter plot showing rain rates vs. precipitable water for the four site-pairs in Figure 4.5:

MLSP/MOK (diamonds), UWEVlUWEV (circles) WAOP/POC (triangles) and HILO/HILO (squares).

The 4 data sets have been displaced vertically for clarity and the vertical (rain rate) scale is shown.

The empirically determined bounds to the data are shown as dotted and solid lines. The lower

bound (dotted line) is described by the equation50

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Figure 4.8. Map views of the GPS-derived predictions of rainfall. The equation used to map

PW into rainfall is given in Figure 4.7 52

Figure 4.9. Bar graphs of accumulated 3-hr rainfall for UTe day 307 for the MSM and GPS

estimated rainfall and the measured rainfall. Gauges 1-9. MSM predicted rainfall shown

as black bars, GPS-derived estimates in gray and observed values in white 55

Figure 4.10. See Figure 4.9. Gauges 10-16 56

Figure 4.11. MSM predicted precipitable water and GPS observed precipitable water,

indicating pervasive MSM underestimate for higher values57

Figure 4.12. Misfit between MSM predicted rainfall and observed rainfall plotted against the

misfit between MSM predicted precipitable water and GPS estimated precipitable water.

Dashed line indicates median fit to the data with the one extreme outlier removed........59

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Chapter 1: Introduction

The importance of the roles that atmospheric water vapor plays in climate and

weather systems can hardly be overstated [Anthes, 1983; Starr and Melfi, 1991]. Knowing its

distribution in space and time is crucial to better understanding of climate and climate change

and weather modeling and forecasting. The vertically integrated water vapor content of the

atmosphere, or precipitable water (PW) is also a quantity of great interest to space

geodesists. Water vapor induces a delay in radio signals propagating through the

atmosphere that is highly variable in space and time. In order to achieve the desired sub-

centimeter accuracy using space-based geodetic systems such as the Global Positioning

System (GPS), Very Long Baseline Interferometry (VLBI) and Interferometric Synthetic

Aperture Radar (InSAR) the PW delay must be accounted for [Hogg et aI., 1981; Lichten and

Border, 1987; Truehaft and Lanyi, 1987; Tralli et al., 1988].

GPS Meteorology inverts this problem and uses networks of continuously operating

GPS stations to estimate the PW history above each station in the network [Bevis et aI.,

1992; Duan et aI., 1996]. The propagation delay of the GPS signal as it travels through the

neutral atmosphere has wet and hydrostatic (or 'dry') components. The hydrostatic delay is

proportional to the total mass of atmosphere along the radio path, and hence to surface

pressure, while the wet delay is nearly proportional to the total amount of water vapor along

the radio path. Both delays increase in a predictable fashion as the path's elevation angle

decreases, thereby increasing the length of the path within the atmosphere. Geodesists

usually parameterize delays in terms of zenith (vertical) path deiays. GPS measures the total

neutral delay. Given surface pressure at a GPS station, we can compute the zenith

hydrostatic delay and subtract this from the zenith neutral delay (ZND), and thus isolate the

zenilh wet delay which, in turn, can be transformed into an estimate of PW [Bevis et al.,

1994].

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The technical aspects of GPS Meteorology are now reasonably well understood and

refined, however, the details of the processes that control the distribution of water vapor and

statistics that best describe them are not so well resolved. The processing of space geodetic

data and the retrieval of precipitable water estimates from the data could be improved by

incorporating the best possible statistical description of water vapor. The first study in this

dissertation addresses the weakness in our understanding of the statistics by using 4-year

time series of precipitable water from a GPS network in Hawai'i to examine the long-term

statistical properties of water vapor. It is found that the lognormal distribution is the best

description for precipitable water in Hawai'i which accords well with many previous

observations of the lognormal distribution for other meteorological parameters and is also

supported by a theoretical derivation for the distribution of relative humidity. The long-term

average value of precipitable water declines exponentially with height, but the dispersion of

precipitable water declines more linearly. The change in skewness of the distributions is aiso

linear, atthough in this case it increases with elevation.

Although GPS meteorology is now well established as a reliabie tool capable of

generating estimates of PW that are sufficiently accurate for both weather and climate

studies, the implementation of GPS as an operationai meteorological instrument is ongoing.

In chapters 3 and 4 GPS Meteorology is used for two case studies. In chapter 3, GPS

stations in the western tropical Pacific are used to investigate the effect of the 1997-1998 EI

Nino on PW. The pattern of sudden drying observed at both stations is found to be consistent

with the formation of an anomalous high-pressure ridge connected to the EI Nino episode.

In Chapter 4, the Ka'O Storm, an extreme rain event that impacted the southern and

eastern portions of the Big Island of Hawai'i during the 16' and 2ndof November, 2000, is

investigated, The temporal and spatial distribution of PW is examined using a network of

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GPS receivers and rain gauges and the connection between rainfall and PW is explored. A

heuristic algorithm is presented as a potential tool for mapping PW to rainfail. The

performance of a local weather model is also examined and its rainfall prediction is found to

be limited by its ability to model PW.

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Chapter 2: Lognormal Distribution of Precipitable

Water in Hawai'i

Abstract

We use four-year time series of precipitable water derived from a GPS network to

show that precipitable water in Hawai'i closely approximates a lognormal distribution. The

long-term average value of precipitable water declines exponentially with height, but the

dispersion of precipitable water declines more linearly. The change in skewness of the

distributions is also linear, although in this case it increases with elevation.

Introduction

The importance of the roles that atmospheric water vapor plays in the climate and

weather systems can hardly be overstated [Starr and Melfi, 1991; Anthes, 1983]. The

vertically integrated water vapor content of the atmosphere, or precipitable water (PW), is

also of great interest to space geodesists. Atmospheric water vapor induces a propagation

delay in the radio signals from the satellites of the Global Positioning System (GPS) that is

highly variable both in space and in time. The statistical properties of PW and the associated

'wet delay' are relevant to geodesists designing algorithms to estimate atmospheric

propagation delays from the data collected by networks of geodetic GPS receivers and by

related space-geodetic systems such as Very Long Baseline Interferometry [Hogg et aI.,

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1981; Truehaft and Lanyi, 1987; Lichten and Border, 1987]. With the advent of 'GPS

meteorology' where networks of continuously operating GPS stations are used to estimate

the PW history above each station in the network [Bevis et al., 1992; Duan et aI., 1996;

Gutman and Benjamin, 2001] long time series of PW measurements are now becoming

available, and this is contributing to a resurgence of interest in the statistics of PW. Most of

this research has focused on the autocorrelation structure and power spectra of PW time

series acquired at a given point in space, or on the spatial correlation or cross power spectra

of PW time series collected at different locations [e.g. Williams et aI., 1998; Davis, 2001]. In

this paper we take a different approach, and investigate the statistical distribution of PW

measurements accumulated over time periods of several years. This initial study is focused

on Hawaii because the availability of GPS stations over a wide range of elevations provides

us with an unusual opportunity to examine how the statistical distribution of PW varies with

height.

Data and Analysis

The GPS network on the Big Island of Hawari (Figure 2.1) consists of 24 sites spanning a

height range from sea level to the summits of the two main voicanoes, Mauna Kea and

Mauna Loa, at -4000 m. Of these sites only 9 have colocated meteorological instruments to

provide direct measurements of pressure and temperature. For these sites the PW is

estimated to be accurate to -1.5 mm [Tregoning et aI., 1998]. In order to be able to

incorporate the other sites into our study we extrapolated the pressure and temperature fields

to each location, constraining the process by incorporating data interpolated from the NCEP

Global Reanalyses. The predicted pressures and temperatures have rms errors of -0.25

mbar and -1.5 °C respectively. This is sufficiently accurate to permit us to include in our

analysis PW solutions from all the sites, wnh the accuracy for those sites using the

extrapolated meteorological data estimated as better than 2 mm.

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20.25

20

19.75

19.5

19.25

19

156155.75155.5 155.25155

Figure 2.1. Location of GPS sites on the Big Island of

Hawai'i. Sites with colocated meteorological

instruments are the solid black circles

All GPS data available from 1997 through 2000 were processed using GAMIT [King

and Bock. 2000]. with 24 atmospheric delay parameters estimated in each 24-hour batch

solution (following Duan et al. [1996]). giving hourly estimates of zenith neutral delay (ZND)

for the entire 4-year period. Surface pressure was converted to zenith hydrostatic delay

(ZHD) [Saastamoinen. 1972] and the mapping parametern was calculated from surface

temperature using the seasonal climatology determined by Ross and Rosenfeld [1997]. The

final transformation into PW is simply given by PW =n (ZND - ZHD).

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The Lognormal Distribution

The two most common probability distributions for atmospheric variables are the normal (N)

and lognormal (A) distributions. Largely through historical chance N became "normal" while

the closely related A was considered derivative. Stated simply, a variable is considered to be

lognormally distributed if its logarithm is normally distributed. For detailed discussion of A see

Aitchison and Brown [1957]; here we will simply summarize some of the key details.

Whereas the probability distribution function (PDF) for variate X (-co < X < 00) is defined by the

mean ( ~ ) and the arithmetic standard deviation (0) if it is distributed according to N, if X is

distributed as A the PDF is defined in terms of the geometric standard deviation s and the

geometric mean or median M, or in terms of sand m = log M with a< x < 00. The PDF for X is

then given by:

1

~

r.-(1ogx-m)2}

l

2s

exp~

2

,O<x<oo

xs.,,2Il

The population mean is M exp(s2/2) and the population variance is

M 2 exp(s2)(exp(s2) -1). Note thatthe mean is a function of s indicating that a change in

the variance of the distribution will also induce a change in the mean. This is an important

property with consequences for the interpretation of trends in mean water vapor.

A slightly more general version of A is called the 3-parameter distribution. Here an extra term

~ is included as a "threshold" parameter. The threshold parameter allows the distribution to

7