2 gps-iwv jumps: a nowcasting application 8...
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GPS-IWV Jumps: A nowcasting application 2
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Luiz F. Sapucci1, Luiz A. T. Machado1, Eniuce Menezes de Souza2, Thamiris B. Campos3. 6
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Affiliation: 1. Centro de Previsão de Tempo e Estudos Climáticos, Instituto Nacional de 10
Pesquisas Espaciais, Cachoeira Paulista, São Paulo, Brazil. 11
2. Departamento de Estatística - Universidade Estadual de Maringá. Maringá, Paraná, 12
Brazil; 13
3. Programa de Pós Graduação em Meteorologia, Instituto Nacional de Pesquisas 14
Espaciais, Cachoeira Paulista, São Paulo, Brazil. 15
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Submitted to the Journal of Geophysical Research - Atmosphere 21
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Corresponding author address: Instituto Nacional de Pesquisas Espaciais, CPTEC, Rodovia 27
Presidente Dutra, km 40. Cep: 12630. Cachoeira Paulista, São Paulo, Brazil. 28
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ABSTRACT 30
Atmospheric water vapor plays a critical and determining role in weather severity in special 31
regions where both radiation and evaporation drive cumulus convection and atmospheric 32
circulation. The oscillations of the integrated water vapor time series from a Global Positioning 33
System (GPS-IWV) signal with very high temporal resolution (one minute) is evaluated here 34
during intense rainfall events. Several precipitation events of different intensity and spatial 35
dimension observed by X band radar, during the CHUVA Vale field campaign, have been 36
explored. A sharp increase in the GPS-IWV values before the occurrence of more intense 37
rainfalls has been found and termed as GPS-IWV jumps. The correlation and lags between GPS-38
IWV jumps and intense rainfall events are evaluated, and then the possible potential for a 39
nowcasting application is investigated. Wavelet cross-correlation analysis shows that there are 40
important oscillations that precede intense rainfall events in the time scale from 32 to 64 minutes. 41
The GPS-IWV jumps are generated by pulse succession associated with the conversion of water 42
vapor in liquid water, and consequently, a maximal derivative is not enough to anticipate the 43
precipitation severity. The GPS-IWV time-derivative histogram, for the period of 60 minutes 44
before the rainfall event, shows different distributions for higher intensity events. This feature can 45
be used for nowcasting intense rainfall events. 46
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Key points: 48
• GPS-IWV jumps are observed in the time scale from 32-64 minutes before intense precipitations. 49
• GPS-IWV derivatives before precipitations show different distributions for higher intensity cases. 50
• Integrated Water Vapor estimates from GPS observation can be used as nowcasting tool; 51
Keywords: 52
GPS-IWV; IWV time series; Nowcasting application; IWV Jump; GPS for nowcasting. 53
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1. Introduction 54
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The application of the Global Positioning System (GPS) signal delay due to neutral 56
atmosphere (i.e., the atmospheric layers that are not ionized) to estimate the Integrated Water 57
Vapor (hereafter, GPS-IWV) is a good example of an unconventional solution for quantifying 58
atmospheric humidity. The magnitude of this delay is associated with temperature, pressure and 59
water vapor [Bevis et al., 1992]. The wet component of this delay can be estimated and converted 60
in IWV values [Bevis et al., 1994] with an error of approximately 5% under all-weather 61
conditions [Wolfe and Gutman, 2000]. The most important application of the GPS-IWV estimate 62
is its assimilation into the Numerical Weather Prediction (NWP) process, which presents a 63
positive impact on short-range forecasts of humidity fields and consequently better forecast of the 64
precipitation during heavy rainfall events [Cucurull et al., 2004; Bennitt and Jupp, 2012]. 65
Although the humidity vertical structure is not characterized in the GPS-IWV estimates, the great 66
advantage of these values is that a very high temporal resolution can be achieved with reasonable 67
accuracy [Sapucci et al., 2007] in real time [Rocken et al., 1994]. When this characteristic is 68
associated with the dense GPS network over a continental region, other promising applications 69
become viable. GPS-IWV has been useful for tracking water vapor advection [Adams et al., 70
2011, 2015] and for nowcasting the activities of thunderstorms, as glimpsed by Jerrett and Nash 71
[2001]. 72
The first results regarding GPS-IWV application for nowcasting were reported by Haan 73
et al. [2004], who showed that GPS-IWV presented a clear signal at the passing time of a cold 74
front and make evident that these data contain information of the probability of the occurrence of 75
thunderstorms and heavy precipitation. Iwabuchi et al. [2006], in a preliminary study, presented 76
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one case study that showed rapid increase of the zenithal tropospheric delay (ZTD) prior to the 77
occurrence of the torrential rainfall that happened in Tokyo city. Haan [2006] developed a 78
method for detecting the stability of the atmosphere based on a nonisotropic GPS path-delay 79
signal (slant direction). 80
IWV data from a microwave radiometer (MWR) have been used in similar studies 81
dedicated to describing the observed relationship between IWV and precipitation in the tropics to 82
explain the precipitation-humidity relationship over a broader range of water vapor values 83
[Muller et al., 2009]. Chan [2009] evaluated the performance of ground-based MWR in intense 84
convective weather and reported useful indications of the accumulation of water vapor and the 85
increasing degree of instability of the troposphere before the occurrence of heavy rain. 86
Madhulatha et al. [2013] developed a nowcasting technique using IWV values from MWR 87
observations and 7 other thermodynamic indices, and an evaluation was performed using 26 88
thunderstorm cases. The results showed that there is a sharp increase in the IWV values 89
approximately 2–4 h before the occurrence of thunderstorms. 90
To understand the physical processes that occur inside clouds, several intensive 91
campaigns in tropical and subtropical regions were carried out during the CHUVA project 92
[Machado et al., 2014]. The GPS receiver network has been used in these experiments to provide 93
IWV data with good quality and high temporal resolution, which are used to monitor the 94
horizontal variations in the integrated water vapor before, during and after heavy precipitation 95
events. Adams et al. [2015] described the evolution of tropical and sea breeze regimes based on 96
the dense GPS network dataset collected during the CHUVA Belém field campaign. The GPS-97
IWV dataset, collected during the CHUVA Vale campaign in the southeast of Brazil, where a 98
large number of thunderstorms were recorded, is evaluated in this study. A sharp increase in the 99
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GPS-IWV values before the occurrence of more intense rainfalls has been found and termed as 100
GPS-IWV jumps. 101
The objective of this work is to quantify the GPS-IWV jumps and evaluate the GPS-102
IWV variability, correlation and lags with rainfall events for nowcasting application. Section 2 103
describes the data processing of GPS observations to obtain IWV values and Band X radar data 104
to quantify spatial-temporally the precipitation events. Section 3 presents the wavelet analysis for 105
IWV and precipitation time series. In section 4, GPS-IWV jumps are characterized in a study 106
case and time lag-correlation analysis is explored. A nowcasting methodology is proposed in 107
section 5, which is based on derivative analysis in the period preceding the precipitation events, 108
and section 6 presents the conclusions. 109
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2. Data collection design and processing method 111
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2.1. Data collect during CHUVA Vale experiment 113
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The CHUVA Vale experiment was one of the eight campaigns carried out by the 115
CHUVA Project [Machado et al., 2014], which was localized around São José dos Campos City 116
(23º 12’ 30” S and 45º 57’ 08” W), São Paulo State in Brazil and had an intensive operation 117
period from November 3rd to December 28th of 2011. The instruments used in this work are a 118
dual-frequency GPS receiver for scientific applications, a disdrometer and a mobile X-band dual 119
polarization radar (XPol). The GPS receiver is Trimble brand, NetR8 model, and was installed 11 120
km from the XPol radar, in the site denominated IEAV. Any sky obstruction around the GPS 121
receiver was avoided to minimize the multi-path effect in the GPS signal propagation. Fig. 1 122
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shows the geographic localization of the CHUVA Vale campaign and emphasizes the sites where 123
the instruments were employed in the study. 124
The GPS data were collected with a one-second interval using choke ring antenna. A 125
surface meteorological station (Vaisala brand), measuring pressure (with a precision of 0.2 hPa), 126
temperature and humidity every minute, was installed at a GPS antenna and coupled with the 127
GPS receiver. The Joss Waldvogel brand acoustic impact disdrometer [Joss and Waldvogel, 128
1967], model RD 80, was installed a few meters from the GPS receiver. The XPol radar scan 129
strategy data collected one volume scan every 6 minutes at 13 elevations, from 1o to 25o, with 1o 130
and 150 m of angular and radial resolution, respectively. The radar data were pre-processed using 131
the attenuation correction of the reflectivity employing the ZPHI algorithm proposed by Testud et 132
al. [2000]. For a detailed description of the radar and disdrometer pre-processing, see Calheiros 133
and Machado [2014]. 134
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2.2. GPS-IWV time series with high temporal resolution 136
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The ZTD were obtained by processing the GPS data using GOA-II software [Gregorius, 138
1996] by applying the precise point positioning method in post-processed mode, with precise 139
ephemerids of the GPS constellation provided by Jet Propulsion Laboratory (JPL). Global 140
Mapping Function [Boehm et al., 2006] with a cut-off elevation angle of 10° was used in this 141
processing. To ensure the good quality of the IWV time series with high temporal resolution 142
required in this study, the best processing strategy was adopted, with possible noise sources taken 143
into consideration. The latest version of the GOA-II software (version 6.3) was used. The ocean 144
tide model FES 2004 recommended by the International Global Navigation Satellite System 145
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Service has been applied in this processing [Lyard et al., 2006], and absolute calibration was 146
configured in the GOA-II for correct phase center variation (PCV), as reported by Görres [2006]. 147
The zenithal wet delay (ZWD) was obtained from ZTD after removing the zenithal hydrostatic 148
delay using an appropriated model and pressure measurements [Davis et al., 1985]. The ZWD 149
were converted into IWV using the relationship suggested by Bevis et al. [1992]. The mean 150
tropospheric temperatures (Tm) were obtained from temperature and pressure measured at the 151
GPS antenna by applying the regional model suggested by Sapucci [2014], which is most suitable 152
for this region. The sampling rate of GPS-IWV values was 1 minute. The GPS-IWV time series 153
presented some short failures due to several reasons, such as: interruption in the data collection, 154
problem in the satellite ephemerides, unavailable pressure measurements and other unknown 155
causes. These time series interruptions occurred in 3183 epochs (3.1% of the total period) and 156
were corrected by applying an interpolation method by cubic spline. These failures were 157
concentrated in two specific days [Day of Year (hereafter called DoY) 331 and 348], which were 158
taken into consideration during the data analysis. 159
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2.3. Precipitation time series from disdrometer and XPol radar data 161
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The reason for choosing one disdrometer to quantify the precipitation is that this 163
instrument is able to provide an instantaneous and good quality measurement of rainfall intensity 164
(mm h-1) in the same GPS-IWV sampling rate, although this information is only representative of 165
a very small space scale. However, the XPol radar data are able to generate information with 166
different and more representative spatial resolution around the GPS receiver. 167
The precipitation rates from the Joss disdrometer data were obtained by applying the 168
methodology suggested by Kinnell [1976], in which the precipitation intensity of each minute is 169
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inferred from the size and concentration of the rain drops observed during this time period. The 170
precipitation data from XPol radar observation was obtained by applying the Dual Polarization 171
Surface Rainfall Intensity algorithm, which calculates the rainfall rate (R) from the reflectivity 172
(Z) and specific differential phase ( ) data obtained in multiple-elevation polar volumes. In 173
this method, polarimetric measurements are used to calculate R by applying the following 174
combined Z- -R relation [Gematronik, 2007]: 175
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= 19.63| | . for Z > 35 dBZ and > 0.3 deg km-1; (1) 177
= otherwise. (2) 178
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The a and b values used were 200 and 1.6, respectively. The final product of this 180
process is a gridded map (100 km around XPol) with a horizontal resolution of 200 m, in which 181
each of the grid point values of rainfall intensity (mm h-1) in a sampling rate of 6 minutes is 182
available. Time series of precipitation fraction from the radar were calculated by determining the 183
position of the GPS antenna in the gridded map and taking into consideration the area formed by 184
points in the longitudinal direction per same number of points in the latitudinal direction, where 185
the nearest point of the GPS antenna is located in the center of these areas. The dimension of the 186
precipitation area that influences GPS-IWV is a key factor in the development of this study 187
because its choice is associated with the leading time to indicate strong precipitation using the 188
GPS-IWV information. A reduced area is not enough to represent the precipitation associated 189
with significant variation of the GPS-IWV time series. On the other hand, larger areas permit that 190
distant precipitations, which are not directly associated with GPS-IWV oscillation, be taken into 191
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account. Different areas were tested, and the area of 22x22 (longitudinal per latitudinal direction) 192
points was more representative of the observed area by GPS and better for exploring the 193
correlation between precipitation occurrence and GPS-IWV information. The resultant area is of 194
4.4 km per 4.4 km (~20 km2) around the GPS antenna. Fig. 1 shows the disposition of the XPol 195
radar, GPS antenna and disdrometer in the CHUVA Vale experiment and highlights the area of 196
4.4 km per 4.4 km around the GPS antenna. The precipitation field observed by XPol on 197
December 14th (DoY 348) is presented in Fig. 1 to illustrate the points from the XPol gridded 198
map used to compose the precipitation area around the GPS antenna taken into account in this 199
study. As the focus here is to study the GPS-IWV behavior during intense rainfall, the statistical 200
measurements calculated from the radar data were the 95th percentile of the intensity of 201
precipitation observed in the area of 4.4 km per 4.4 km around the GPS antenna. Additionally, to 202
evaluate the rainfall events of different intensities, the rain fraction was computed as the fraction 203
of the studied area (4.4 km per 4.4 km) with precipitation rates above some chosen thresholds. 204
The first emphasizes the more intense localized precipitation events, and the second quantifies 205
simultaneously the intensity and extension of each event. These chosen thresholds were 206
computed to create time series of the following rainfall events intensities: moderate to heavy (20 207
mm h-1), heavy to intense (35 mm h-1) and intense to torrential (50 mm h-1). The disdrometer was 208
used in this study only for a reference and comparison with the radar rainfall estimations. Fig. 2 209
presents time series of GPS-IWV (Fig. 2a) and of the precipitation from the disdrometer data 210
(Fig. 2b) and from the XPol radar: 95th percentile of the precipitation intensity (Fig. 2c) and rain 211
fractions for different thresholds (Fig. 2d). The period studied here is from November 9th (DoY 212
313) to December 28th (DoY 362) of 2011, during which the GPS receiver, XPol radar and 213
disdrometer were simultaneously collecting data. The disdrometer time series is well correlated to 214
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the 95th percentile time series, and differences are expected because the 95th percentile time series 215
represents a much larger area than the one recorded by the disdrometer. 216
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3. Wavelet analysis 218
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To perform a detailed intra-relation analysis of the GPS-IWV time series, as well as its 220
interrelation with the precipitation time series, wavelet analysis was explored. This methodology 221
allows for decomposing the IWV time series as a function of time and frequency simultaneously 222
[Daubechies, 1992]. Consequently, access to the information about signal amplitude/frequency 223
and its variation as a function of time becomes possible. This tool has been used intensively in 224
the last decades in digital signal processing to explore geophysics signals [Norman, 1953; many 225
others]. In this research, both continuous and discrete wavelets are investigated to achieve intra- 226
and interrelation analysis, respectively. 227
The continuous wavelet transform (CWT) ( )sWn of a discrete time series Xt (t = 1,…, n) 228
is obtained from the convolution of Xt with a wavelet mother ( 0ψ ) in several scales s and 229
translations in the time period. The mother wavelet ( 0ψ ) used in the continuous case was the 230
Morlet [Torrence and Compo, 1998], and because 0ψ is complex, ( )sWn is also complex but can 231
be separated into real (amplitude ( )sW n ) and imaginary parts. The square of this amplitude 232
term, well -known as the wavelet power spectrum, provides a detailed intra-relation evaluation of 233
how spectral characteristics change over scales (s) and time (t), but with highly redundant 234
information. 235
Continuous analysis is often easier to interpret because its redundancy tends to reinforce 236
the traits and makes all information more visible. However, for some specific choices of values 237
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for time and frequency, it is possible to have a discrete wavelet transform, which does not lose 238
important information and has the advantages of implementation and computational effort. This 239
is the case of the non-decimated discrete wavelet transform (NDWT), also called Maximal 240
Overlap Discrete Wavelet Transform, which can be seen as a compromise between the discrete 241
wavelet transform (DWT) and CWT because of its redundancy, but not as redundant as CWT. 242
The NDWT can be computed similarly to the ordinary DWT but without subsampling 243
(decimation), ensuring the translational invariance, which is ideal for analyzing time series, 244
especially interrelations between different time series. A time-variant transform disrupts the lag-245
resolution in a cross-correlation analysis. Furthermore, estimators calculated using the NDWT are 246
considered more preferable because they are asymptotically more efficient than the estimator 247
based on the DWT [Percival and Walden, 2000]. As the bivariate relationship between two time 248
series is essential for this research, a wavelet cross-correlation (WCC) constructed from NDTW 249
[Whitcher et al., 2000] is ideal for analyzing different scale structures and the interrelations of the 250
dynamic behavior of two time series, as the lead-lag relationships. Some lead-lag relations that 251
could not be distinguished in the usual cross-correlation can be investigated in the WCC, which 252
decomposes the cross-correlation on a scale-by-scale basis. 253
In practice, the NDWT is easily calculated by using the pyramidal algorithm, but it 254
requires a time series of dyadic length n=2J, where J represents the largest scale. Thus, the 255
number of points of the GPS-IWV time series applied in the wavelet analysis was restricted to 216 256
(65,536 points that correspond to 45 days, 12 hours and 16 minutes) because we preferred to 257
exclude some data to use border strategies to reach the following power of two length. One day at 258
the beginning and another at the end of the GPS-IWV series were excluded, beginning on 314 259
DoY (00 h UTC at November 10th) and finishing on 359 DoY (12:16 UTC at December 27th). 260
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The same time series length was used for both intra- and interrelations, even though this 261
restriction is not needed for continuous analyses. 262
As each scale j corresponds to a frequency band from 2j to 2j+1, whose inversion 263
produces the period of time, with the WCC of GPS-IWV and precipitation time series, an 264
interrelation analysis can be performed to evaluate the correlation in different lags in time, scale 265
by scale. This allows for identifying the most important time scale of the IWV oscillation during 266
precipitation events. 267
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3.1. Wavelet power spectrum analysis 269
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For an intra-relation analysis, the wavelet power spectrum of the GPS-IWV, the GPS-271
IWV and 95th percentile of the precipitation intensity time series are presented in Fig. 3. To 272
emphasize the highest frequency oscillations, the power spectrum in Fig. 3 shows the scales that 273
represent the period below 512 minutes (~8.5 h). The IWV diurnal cycle presents strong power 274
along all time series; consequently, it was not taken into consideration in this analysis. 275
The IWV series with a 1-minute temporal resolution presents oscillations of high 276
frequency, but, on the other hand, the frequency of occurrence of rainfall events is very low. For 277
this reason, to evaluate the high-frequency IWV oscillations, it is necessary to take into 278
consideration a long time period (with several precipitation events) and a short time step. 279
Consequently, in a general analysis of the IWV wavelet power spectrum, it is hard to discern 280
clearly which power is associated with each time step. However, in a more specific analysis of 281
the wavelet power spectrum during precipitation events indicates that there are expressive 282
changes in the power between different time scales in these cases, in which an increase of the 283
power of the oscillation from low to high frequency is observed. This result indicates that IWV 284
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oscillations smaller than 128 minutes present larger importance during precipitation events than 285
in periods without rain. Fig. 4 presents the same wavelet power spectrum presented in Fig. 3, but 286
with an amplification applied for precipitation events observed during the period from DoY 340 287
to DoY 343. The analysis of the power spectrum in these cases makes the result discussed in Fig. 288
3 more evident. A vertical line was put at the peak of the maximum precipitation in each event to 289
make the analysis easier. Fig. 4 shows that the power of the IWV oscillations between 128 and 32 290
minutes are more expressive during more intense precipitation events (for example, the events 291
that occurred on DoY 341 at 1836 UTC and DoY 342 at 1636 UTC) than during light events 292
(events observed during DoY 343) and periods without rain (DoY 340). The wavelet power 293
spectrum (Fig. 3) shows also the impact of the GPS fail data that occurred during DoY 331 and 294
348, which are unfortunately very close to the other intense precipitation events that occurred on 295
DoY 332 and in the beginning of DoY 348. For this reason, these cases are not emphasized in the 296
wavelet analysis. 297
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3.2. Wavelet cross-correlation analysis 299
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The most relevant difficulty found in this study is the comparison of two time series 301
(precipitation fraction and GPS-IWV) with very distinct or almost incomparable behaviors. The 302
precipitation time series presents discrete behavior with zero values during long periods that 303
change suddenly for expressive values. On the other hand, the GPS-IWV time series presents 304
high frequency values of oscillation in the range of 30 kg m-2 and never equal to zero. 305
Consequently, the correlation between these series is very low; however, the WCC permitted 306
identification of the correlation in each time-scale, indicating which GPS-IWV oscillations are 307
more important for predicting precipitation events. Fig. 5 shows the WCC between GPS-IWV 308
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and the 95th percentile of the precipitation intensity as a function of the wavelet scale. The mother 309
wavelet used in the NDWT to compute the WCC was a Symmlet wavelet with 10 vanishing 310
moments, which has good properties, such as quasi symmetry [Daubechies, 1992]. The results 311
show that wavelet correlation between IWV and precipitation intensity is low for high frequency 312
scale and increases for the time scale between 32 and 64 minutes. In this time scale, there is a 313
peak representing a statistically significant wavelet cross-correlation between GPS-IWV and 314
rainfall, which gives indication of the time scale where the most important GPS-IWV oscillation 315
associated with precipitation events occur. After this time scale, the correlation decreases, 316
followed by another increase due to the influence of the diurnal cycle. To evaluate the result 317
presented by Fig. 5 for different intensities of the precipitation, Fig. 6 shows the WCC between 318
GPS-IWV and precipitation fractions as a function of the wavelet scale for different rain fraction 319
intensities (>20 mm h-1, Fig. 6a, >35 mm h-1, Fig. 6b and >50 mm h-1, Fig. 6c). The results show 320
that the peak of the WCC observed in the time scale from 32 to 64 minutes is only significant for 321
rain fractions larger than 35 mm h-1. The plots of 6b and 6c make evident that this peak is more 322
expressive when only heavy to torrential precipitation events are taken into consideration 323
(hereafter called intense rain events). This result indicates that GPS-IWV carries some 324
information in the time scale from 32 to 64 minutes that signal the occurrence of more intense 325
precipitation events and emphasize its potential for nowcasting application. 326
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4. Behavior of IWV time series before precipitation events: the GPS-IWV jumps 328
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As described above, the high temporal resolution obtained with GPS-IWV allows for the 330
evaluation of the high frequency variability and its relationship with intense precipitation events. 331
This variability is probably associated with sudden changes of the water vapor horizontal 332
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advection and/or moisture convergence. The GPS-IWV series shows a pattern well defined 333
before the precipitation occurrence. There are strong oscillations, predominantly positive, 334
generating a significant increase in the total water vapor content until a maximum peak is 335
reached. Subsequently, a GPS-IWV strong reduction is observed, and after a few minutes, the 336
precipitation starts. Here, this pattern is called GPS-IWV jumps, which differs from lightning 337
jumps [Williams et al., 1999] because in this case, the pattern comprises not only one jump but a 338
succession of smaller jumps that complementary generate a preponderant crest in the IWV series 339
before the precipitation event. Fig. 7 shows a typical case to exemplify the IWV behavior before 340
precipitation occurred on 341 DoY; this was one of the strongest events registered during the 341
CHUVA Vale experiment. Before the precipitation starts, the GPS-IWV follows several pulses, 342
increasing the value and forming the IWV jump, until it reaches a peak of maximum value. After 343
the GPS-IWV peak, a decrease period is observed some minutes before precipitation starts. Fig. 7 344
clearly shows this configuration of a crest in the GPS-IWV time series before precipitation, 345
composed of several pulses, and its subsequent decrease just before the beginning of 346
precipitation. The wavelet analysis indicates that oscillations in the time scale from 32 to 64 347
minutes are associated with the more intense rainfall occurrence, which suggests that the GPS-348
IWV jumps are concentrated in this time-scale. This GPS-IWV behavior before precipitation 349
does not occur only for more intense events but also for lower rain rates, as shown in Fig. 4 350
before the event occurred on 343 DoY at 23:30 UTC. However, the intensity of these oscillations 351
(jumps) is greater before more intense precipitations, which corroborates with the results 352
presented by the WCC analysis discussed in the previous section. 353
A possible mechanism to explain the GPS-IWV jump before precipitation events could 354
be associated to the moisture convergence produced by wave patterns generated by gravity waves 355
forced by the released latent heating in the strong convective process [Lindzen and Tung, 1976]. 356
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This process could be responsible for the GPS-IWV jump, increasing significantly its value until 357
reaching the maximum peak; at that time, the atmosphere reaches saturation and the conversion 358
process from water vapor to liquid water is initiated. The conversion of the water vapor to liquid 359
water changes the dielectric medium, where the refractivity is induced by the displacement of 360
charge [Solheim et al., 1999]. While the refractivity from water vapor is due to the polar nature of 361
the water molecule, the GPS phase delay induced by liquid water (hydrometeor) is proportional 362
to the electric permittivity of the formed dielectric medium and, consequently, much lower than 363
the delay generated by water vapor. Sometimes, a GPS-IWV increase is observed after the 364
maximum precipitation, which is probably due to rainfall evaporation processes that could 365
increase the precipitable water. Obviously, this is a general pattern of the IWV time series 366
variations before a rainfall event, but some differences in this behavior are expected due to the 367
numerous boundary conditions of the atmosphere; however, the GPS-IWV jumps are strongly 368
remarkable. 369
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4.1. Time Lag-correlation analysis 371
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Although the relationship between rainfall intensity (or rain fraction) and the GPS-IWV 373
is different for each event, depending on the precipitation intensity and the dominant conversion 374
process from water vapor to liquid water, the GPS-IWV peak is a well-delineated pattern. The 375
time interval between the time of the IWV crest and the maximal precipitation can vary among 376
the cases. Although WCC has showed in which temporal scale (lags) the correlation between the 377
GPS-IWV and precipitation time series is more evident, the evaluation of the lag correlation of 378
positive and negative correlations is also important for the further development of nowcasting 379
tools. Fig. 8 shows the histogram of the lag correlations (the time lag for the maximum and 380
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minimum correlation) between the GPS-IWV and rain fraction for all events in which the rain 381
rate observed around the GPS antenna was above 20 mm h-1. A total of 18 events were evaluated, 382
in which different rain fractions were observed by XPol radar. Table 1 presents these 383
precipitation events and respective precipitation values observed by the radar. The histogram was 384
built based on the correlation time lag found for the positive correlation (maximum) and negative 385
correlation (minimum). The search time lag interval for positive (negative) correlation was 386
restricted for a period before (after) the precipitation because there are some subsequent rain 387
events very near that could contaminate the results. 388
The type of correlation used in this study was Spearman's rho [Best and Roberts, 1975] 389
because the GPS-IWV does not have a normal distribution. Additionally, the statistical 390
significance of each correlation was evaluated by rejecting the hypothesis of null correlation 391
when the p-value was smaller than a 5% significance level. 392
The histograms presented in Fig. 8 are evidences that GPS-IWV crests are more frequent 393
in the time-interval between 15 and 30 minutes before precipitation occurs (39% of the cases 394
evaluated), and 85% of the positive correlations occurred between 15 and 60 minutes. After the 395
rainfall events, when GPS-IWV decreased, the time lag observed was between 15 and 60 396
minutes. In 50% of the cases, the minimum GPS-IWV occurred between 45 and 60 minutes. The 397
process of water vapor conversion to liquid water is complex because it includes several different 398
processes, such as the rainfall evaporation, at different heights, entrainment and condensation. 399
This result corroborates the pattern observed in Fig. 7 showing the GPS-IWV maximum before 400
the precipitation event and its minimum after the maximum precipitation, which illustrates the 401
conceptual model that allows for the use of this information in nowcasting. 402
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5. GPS-IWV derivative analysis as tool for nowcasting 405
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Although the GPS-IWV pattern before precipitation described in the previous section is 407
well defined, its use as an index for the occurrence of severe storms is not simple. Several studies 408
have been made taking into account the intensity of rainfall events. The use of only a maximum 409
threshold from a GPS-IWV derivative (as suggested by Iwabuchi et al. [2006]) is not enough to 410
predict intense rainfall because in nature, the processes responsible for the maintenance of 411
precipitable water suspended in the atmosphere are very complex and highly nonlinear. These 412
processes generate, in the IWV time series, a pulse succession associated with conversion 413
processes from water vapor to liquid water of clouds fed by moisture advection from other 414
regions during a humidity convergence. The intensity of the precipitation has strong correlation 415
with the intensity and frequency of these pulses; consequently, the occurrence of more intense 416
rain is not signaled by only the maximum derivative but also the frequency distribution of 417
positive and negative derivatives before the occurrence of precipitation. 418
To evaluate the GPS-IWV derivative before precipitations of different intensities, taking 419
into consideration the extension of the events, the area fraction with precipitation observed were 420
used. Fig. 9 shows the distribution of the GPS-IWV time derivative for the period of 60 minutes 421
before the maximum peak of precipitation for the 18 evaluated events for different terciles of rain 422
fraction (>35 mm h-1). This threshold was employed in this analysis because it has been shown to 423
be the lowest threshold of rainfall intensity evaluated that presents a significant WCC between 424
GPS-IWV in this time window. Table 1 shows the list of the rainfall events in the terciles and the 425
precipitation fraction observed by XPol radar during the maximum precipitation peak for each 426
event. In Fig. 2d, each event can be visualized by observing the respective DoY. The same 427
calculation was conducted for all other rainfall events with intensities smaller than 20 mm h-1 and 428
19
periods without observed precipitation, which is denominated in Fig. 9 as “other cases”. The time 429
derivations were calculated every minute by using a Δt of 6 minutes. This interval time was 430
selected because it is the sampling rate of the precipitation observed by XPol radar. Statistical 431
metrics of the derivative for different terciles of the precipitation intensity, such as average, 432
standard deviation, median, modal, maximum and minimum values, are shown in Table 2. 433
Fig. 9 clearly shows an expressive change in the pattern of the derivative distribution as 434
a function of the different precipitation intensity terciles. In the period without significant rain, 435
the derivative frequency polygon is similar to Gaussian distribution with an average of zero and a 436
standard deviation of 2.5 kg m-2 h-1. However, the average of the derivative increases when the 437
precipitation fraction increases and the maximum peak changes to positive values for higher 438
terciles. It is notable that this effect is evident for middle and upper terciles and almost not 439
detected for lower terciles. The lower terciles represent the events with observed precipitation in 440
a reduced area, and the derivative histogram shows that in these cases, the differences for rain 441
events smaller than 20 mm h-1 and periods without observed precipitation are not expressive. 442
This pattern impacts the average value of the derivative, which for upper tercile is +0.13 kg m-2 h-443
1 (±5.57 kg m-2 h-1), middle tercile is -0.38 kg m-2 h-1 (±4.76 kg m-2 h-1) and is -0.18 kg m-2 h-1 444
(±3.18 kg m-2 h-1) for lower tercile. 445
The negative derivatives, the majority of which occur after the peak of maximum GPS-446
IWV, less than -9.5 kg m-2 h-1 are more frequent for events with a larger precipitation fraction, 447
such as the upper and middle terciles (5.47% and 4.68%, respectively), than for the events 448
contained in the lower tercile, in which these derivative values are not observed. This increase of 449
the stronger negative derivatives frequency before more intense events (upper and middle 450
terciles) is associated with the conversion process from water vapor to water liquid, which is also 451
more intense in these cases. The positive derivative frequencies, the majority of which occur 452
20
before the peak of maximum GPS-IWV, above +9.5 kg m-2 h-1 increase more substantially before 453
events in the upper tercile (7.81%) than events contained in the middle (0.78%) and lower 454
terciles, which are not observed. In other words, these derivatives are important in the frequency 455
distribution when the tercile increases and are significant before the most precipitation intense 456
events. This result suggests that for the development of an algorithm for severe precipitation 457
forecasting using GPS-IWV values, the following considerations should be recommended: (a) 458
increase of GPS-IWV positives variation in comparison with negative ones, in which the median 459
values of the variation in the last 60 minutes reaches positive values, and (b) simultaneously an 460
increase of the population of the GPS-IWV derivatives above +9.5 kg m-2 h-1. 461
The GPS-IWV values evaluated in this study are post-processed, and additional study is 462
required to evaluate if these estimates in real time are able to capture the jumps before the 463
precipitation reported in this study. True real-time processing for IWV estimates in dense and 464
regional GPS networks have been explored in other studies related to nowcasting applications 465
[Iwabuchi et al., 2006]. Haan and Holleman [2009] reported the construction and validation of a 466
real-time IWV map from a GPS network combined with data from the weather radar, a lightning 467
detection network, and surface wind observations. They tested a nowcasting algorithm for three 468
thunderstorm cases studies and concluded that GPS-IWV in real time can be helpful for the 469
nowcasting of severe thunderstorms. 470
471
6. Conclusions 472
473
This work evaluates the correlation between GPS-IWV values with high temporal 474
resolution (one minute) and the occurrence of intense rainfall events and investigates the potential 475
use of a GPS receiver for nowcasting application. Wavelet analysis for GPS-IWV time series was 476
21
explored and clearly shows that during precipitation events, there are significant changes in the 477
power spectrum between different time scales, in which an increase of the power of the 478
oscillations from low to high frequency is observed. Additionally, the application of wavelet 479
cross-correlation between IWV and precipitation showed that important oscillations exist 480
between these variables in the time scale from 32 to 64 minutes, which is more expressive for 481
events of large intensity. 482
A detailed analysis of the GPS-IWV time series was carried out, and strong and sudden 483
oscillations, predominantly positive, before the precipitation events were identified and called 484
GPS-IWV jumps. In this process, a crest in the IWV series is remarkable before the precipitation 485
events. Although this pattern can be observed in any precipitation event, it is preponderant before 486
more intense precipitation events. A time lag-correlation histogram shows that in 85% of the 487
studied events the crest in the IWV time series occurs between 15 and 60 min before the 488
maximum precipitation. 489
These GPS-IWV jumps are a consequence of the nonlinear process generated by the 490
pulses succession associated to the moisture convergence. For this reason, the methodology 491
suggested by nowcasting takes into consideration not only a derivative value but also the 492
monitoring of the derivative histogram, which shows the distribution change for different 493
precipitation intensities terciles. The average values of the GPS-IWV derivatives present an 494
increase in positive values as a function of the increase in rainfall intensity terciles. The results 495
suggest that the derivative average values in the interval of 60 minutes before precipitation 496
changes for positive values and an increase in the frequency of the derivative above +9.5 kg m-2 497
h-1 can indicate the occurrence of severe precipitation, but additional studies will be necessary to 498
define an appropriate algorithm and characterize the skill of this tool. 499
500
22
501
Acknowledgments 502
The authors thank the CHUVA team who were involved directly or indirectly in the data 503
collection by XPol radar and disdrometer and GPS receiver during the CHUVA- VALE 504
experiment in São José dos Campos-S.P. Special thanks is given to Thiago Souza Biscaro. This 505
research was supported by the Fundação de Amparo a Pesquisa do Estado de São Paulo 506
(FAPESP), which directly supported this experiment [Grant Process 2009/15235-8 (CHUVA 507
project)], and the Contractual Instrument of the Thematic Network of Geotectonic Studies CT-508
PETRO (PETROBRAS) and INPE (Grant number: 600289299), which provided the GPS 509
receiver used in this experiment. 510
511
23
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26
Tables 635
Table 1. The precipitation events observed by radar during CHUVA vale 636
experiment in different intensity terciles as a function of the precipitation 637
fractions above 35 mm h-1. 638
Event
DoY
Maximal radar precipitation
UTC Time (hh:mm)
Precipitation fraction observed by XPol Radar (%)
Terciles Above
50 mm h-1
Above
35 mm h-1
Above
20 mm h-1
1 348 02:42 73 85 95
2 354 21:12 28 45 63
3 341 18:36 36 41 45 Upper
4 315 17:12 26 41 49 tercile
5 335 19:24 30 38 42
6 352 20:00 2 33 84
7 342 16:36 24 27 28
8 326 21:18 8 26 45
9 343 01:06 4 9 15 Middle
10 338 20:18 0 8 19 tercile
11 332 19:18 5 5 5
12 333 19:42 0 2 8
13 314 21:06 2 2 7
14 327 00:36 0 1 25
15 358 23:00 0 1 10 Lower
16 317 21:48 0 1 2 tercile
17 318 08:48 0 0 19
18 331 17:12 0 0 2
639
640
27
Table 2. Statistic measurements of the GPS-IWV derivative for different 641
intensity terciles of the precipitation events. 642
Statistic Measurements Other
cases
Terciles
Lower Middle Upper
Average values (kg m-2 h-1) +0.04 -0.18 -0.38 0.13
Standard Deviation (kg m-2 h-1) ±2.52 ±3.18 ±4.76 ±5.57
Median (kg m-2 h-1) 0.00 0.00 +0.29 +0.65
Modal (kg m-2 h-1) 0.00 0.00 +1.00 +1.00
Maximal value (kg m-2 h-1) +21.13 +8.42 +11.00 +13.25
Minimal Value (kg m-2 h-1) -19.07 -6.99 -17.30 -14.15
% > +9.5 kg m2 h-1 0.21% 0.00% 0.78% 7.81%
% < -9.5 kg m2 h-1 0.38% 0.00% 4.68% 5.47%
643
644
34
677
Fig. 6. Wavelet cross-correlation values between GPS-IWV and precipitation time series in 678
different wavelet scales for (a) percentage of point above 20 mm h-1 observed by Radar around 679
GPS antenna; (b) the same above 35 mm h-1 (c) and the same but above 50 mm h-1. 680
681
682
683
684
685
Fig. 7. G
DoY (18
GPS-IWV jum
:36 UTC at 7
mps observe
7th Decembe
ed in the 2 h
er of 2011).
35
hours period before heavve storm occcurred during
g 341
36
686 Fig. 8. Spearman correlation histogram of positive (a) and negative (b) correlations as function of 687
the lag of occurrence for GPS-IWV values and precipitation events. All 18 precipitation events 688
listed in Table 1 were taken into account in this analysis. 689
690
37
691
Fig. 9. Frequency polygons of the GPS-IWV derivatives calculated over the period of 60 minutes 692
before precipitation events for different terciles of the precipitation fraction above 35 mm h-1 693
observed by XPol radar. 694
695
696
697