Plum rains are the unique weather and climate phenomenon that take place annually from May to June in eastern Asia, including the Taiwan region and coastal China. In addition to typhoons, plum rains can cause a lot of damage in Taiwan every year as they produce a large amount of rainfall over a very short period of time. From spring to summer, the northeastern monsoon and the southwestern monsoon bring cold and warm air currents, respectively. When the air currents merge, they become a frontal surface, as shown in Figure 1.

Because the strengths of the air currents are similar, they often form a stationary front. This front moves slowly from south to north, bringing plentiful rainfall. The rainfall in the southwest of Taiwan is usually much higher than that in the northeast of Taiwan due to the southwestern air current. As the frontal surface gradually moves north, the rainfall in the northern part of this region stops and the rainfall in the southern part remains. Figure 2 shows the average accumulated rainfall from 1992 to 2006 during the plum rain season (May and June).

Typhoons are the most severe weather system in Taiwan. Four or five typhoons affect Taiwan every year, bringing destructive winds and plentiful rainfall. They pose a danger to agriculture, industry, and human life. For example, the economic losses due to typhoons can be up to 20 billion NT dollars and that due to plum rains can be up to 1.7 billion NT dollars [1].

Despite their devastating effect, typhoons and plum rains together account for more than 50% of the annual accumulated rainfall, as shown in Figure 3. They are thus an important water resources which fill reservoirs around the island. Consequently, studies that develop effective monitoring approaches or tools to monitor these events are important because they can be used to prevent the loss of human life and economic activity.

There are many meteorological sensors available for studying the patterns and characteristics of meteorological events. Recently, many studies have used GPS as an alternative meteorological sensor. Distributed GPS stations around the earth can serve as a near real-time meteorological sensor network that can be used to detect potential threats. Continuous and well-distributed measurements of water vapor are of great interest for numerical weather forecasts, climate research, and atmospheric studies.

GPS signals going through the atmosphere get delayed by ionosphere and troposphere refractions. The refraction due to the ionosphere (the ionosphere is a dispersive medium) can be easily removed by linear combinations of dual frequency measurements because the ionospheric delay depends on the signal frequency [2].

When processing single frequency observations, the observations have to be corrected for ionospheric effects. Available empirical models include the broadcast Klobuchar ionospheric model, the post fit Klobuchar ionospheric model estimated by the Center for Orbit Determination in Europe (CODE), and the Global Ionospheric Maps available from International GNSS Service (IGS), respectively. The positional accuracy is generally not better than sub-meter when processing observations from single frequency receivers because of ionospheric effects.

The tropospheric delay cannot be removed using dual frequency measurements because in the GPS signal frequency band the troposphere is non-dispersive. The tropospheric delay is composed of two parts: a hydrostatic delay term that depends on atmospheric pressure and temperature, and a wet delay term that depends on the partial pressure of water vapor and temperature. While the hydrostatic delay can be accurately modeled using surface pressure measurements, the wet component is difficult to model because of its large spatial and temporal variability. Because meteorological values are insufficient to account for the wet path delay, wet tropospheric delays are usually estimated as an unknown parameter.

Reference [3] presented the idea of using GPS for measuring water vapor. This discussion shows a technical challenge using GPS to measure atmospheric water vapor. The total delay of the radio signals between a GPS satellite and a ground GPS receiver is essentially dependent on the total atmospheric mass, i.e., the pressure at the surface, and the columnar atmospheric moisture content.

Consequently, the primary meteorological measurements produced by GPS are tropospheric path delays at the zenith. The ZTD is estimated from the line of sight tropospheric delays corresponding to the GPS satellites in view. Each of these tropospheric delays is mapped to the zenith using an elevation dependent mapping function. The zenith tropospheric path delay of GPS signals can provide essential information on the long-term climate change of a given area of study.

Current carrier phase based GPS kinematic positioning systems are primarily based on a double differencing data processing approach which can provide centimeter to decimeter positional accuracy in real-time. Since the reduction of common errors depends on the inter-station baseline lengths, the base and rover station separation must be short, typically about 20 kilometers. The need for a base station increases the cost of equipment and labor and introduces inconsistency [4].

The availability of precise GPS satellite orbit and clock products provided by IGS has enabled the development of a novel positioning methodology known as PPP [5]. Based on the processing of pseudorange and carrier phase observations from a single GPS receiver, this approach effectively eliminates the inter-limitation introduced by differential GPS (DGPS) processing as no base station is necessary. Therefore, PPP offers an alternative to DGPS that is simpler than and almost as accurate as DGPS [6].

Users can directly use IGS products to obtain highly accurate frames of International Terrestrial Reference Frame (ITRF) using the PPP technique. This decreases costs because PPP needs only one receiver to perform high positioning accuracy, therefore, it is widely used in studies of the atmosphere, meteorology, and tides [7].

The present study investigates the applicability of using GPS network processed in PPP mode as meteorological sensors to monitor the characteristics of plum rains and typhoons in the Taiwan region.

As mentioned in the previous section, the zenith tropospheric delay is often composed of two parts: a hydrostatic delay term and a wet delay term. About 85-90% of the tropospheric delay comes from the dry component which can be accurately modeled with a precision approaching 1% when the pressure is known (to mm accuracy) using most available troposphere modeling methods. The wet component, however, is more difficult to model because of its large spatial and temporal variability; an error of 15-20% is common.

Since the wet zenith troposphere delay residual is still significant for cm level positioning after a tropospheric correction model is used, it should be estimated as an unknown parameter along with other parameters such as the coordinates, the receiver clock offset, and the ambiguity. Figure 4 shows the data processing strategy of PPP. The details mathematical model of PPP can be found at [7]. To obtain an accurate zenith tropospheric wet delay estimate, the total tropospheric delay can be modeled as [8]: (1) d trop = m h ( e ) ⋅ D h z + m w ( e ) ⋅ D w z + m g ( e ) ⋅ [ G N ⋅ cos ( a ) + G E ⋅ sin ( a ) ]where:

D_hz the zenith hydrostatic delay

The estimation of tropospheric gradients is included to take into account the horizontal atmospheric variations. Neill Mapping Functions (NMFs) are applied for the hydrostatic and wet delays in this study. The following function was applied for gradient mapping [9]: (2) m g ( e ) = 1 sin ( e ) ⋅ tan ( e ) + 0.0032

The current DGPS based wet zenith troposphere delay estimate approach can only provide relative values between two reference stations and it requires a Water Vapor Radiometer (WVR) to be set up at one of those stations to provide proper calibration to obtain absolute zenith troposphere delay at the other site. In practice, the WVR is too expensive and fragile to operate during the visitation of typhoons as well as thunderstorms. Thus, the applicability of a conventional DGPS/WVR based approach to monitor the extreme weather events is rather limited. On the other hand, PPP can provide the direct estimate of absolute wet zenith troposphere delay by using a dual frequency GPS receiver with meteorological sensors that can provide pressure, temperature and humidity. It does not require a WVR to perform calibration and its data processing scheme is straight forward comparing to DGPS data processing. Therefore, when processing massive amount of measurements provided by a GPS network, PPP based approach is a cost effective option. In addition, [10] indicated the difference between the wet zenith troposphere delay the provided PPP and WVR was in the scope of several millimeters that can be considered acceptable for meteorological study.

The electronic-global satellite real-time kinematic positioning system (e-GPS) is managed by the National Land Survey and Mapping Center (NLSC), Ministry of the Interior, Executive Yuan of ROC (Taiwan). The e-GPS network uses continuous satellite observations and processes them continually. Users need to receive more than four GPS satellite signals to obtain high accuracy positioning coordinates in a short period of time. Figure 5 shows the distribution of the entire e-GPS network, which consists of approximately eighty operational stations located around the main island and on most of the offshore islands.

Most on-site GPS receivers of the e-GPS network operate 24 hours a day, even under severe weather conditions, such as typhoons and plum rains. Therefore, this well distributed e-GPS network processed in PPP mode can be considered as a supplemental meteorological sensor to study the patterns of typhoons and plum rains.

As mentioned previously, plum rains often occur from the middle of May to the middle of June. Therefore, the data set used to investigate the characteristics of plum rains was collected from June 1st 2008 to June 7th 2008. This time frame is right in the middle of plum rain season in Taiwan. Figure 6 shows the average accumulated rainfalls during plum rain season for major cities on the island (see Figure 2).

Figure 7 shows the path of typhoon Sinlaku that made landfall from the western Pacific. A sea warning for the typhoon was issued at 8:30 AM, on September 11th, 2008, and the land warning was issued at 2:30 PM, on September 16th, 2008. The data set used to study the characteristics of Typhoon Sinlaku was collected from September 11th to September 17th.

Figure 8 shows the data processing scheme used in this study. The measurements collected at most of the operable e-GPS observation stations were processed with the PPP technique to obtain tropospheric delay corrections and the site coordinates. The spatial and temporal variations of ZTD values estimated from the e-GPS network were analyzed with the movement of typhoon Sinlaku and plum rains.

The velocity of Typhoon Sinlaku was about 50 meters per second; the radius of the typhoon was approximately 250 kilometers. The typhoon made landfall in the northeast coast near Yilan at 1:40 AM, on September 14th, 2008. It left the island near Taipei at 8:00 AM, on September 15th, 2008. The ZTD values estimated by PPP and accumulated rainfall collected by the observation posts of CWB were normalized. The normalized algorithm of ZTD (or accumulated rainfall) is interpreted as Equation (3): (3) N L i = X i - X min X max - X minwhere NL_i denotes the normalized value of ZTD (or accumulated rainfall); X_i is the realistic ZTD value estimated by PPP (or the realistic accumulated rainfall at the collected time); X_min and X_max represent the minimum and maximum value of the realistic ZTD value (or the realistic accumulated rainfall) during the collected period, namely, Jun-01-2008 to Jun-07-2008, respectively. More than fifty e-GPS sites were used in this study; the number of CWB posts was twenty five. The density of the e-GPS network based monitoring approach is twice that of conventional meteorological sensors.

This study proposed using ZTD values estimated from the well-distributed e-GPS network of NLSC and PPP technique to implement supplemental meteorological sensors to investigate the characteristics of typhoons and plum rains. The preliminary results show strong correlations between the variations of ZTD values estimated using PPP and rainfall recorded at meteorological posts around the island during plum rain season and the passage of typhoon Sinlaku.

Several characteristics of typhoons, including the terrestrial rainfall in northwestern and central Taiwan during the passage of typhoon Sinlaku, are identified using the spatial and temporal analyses of ZTD values estimated from PPP. The well-distributed e-GPS network combined with PPP can be considered as alternative meteorological sensors for monitoring the patterns of typhoons and plum rains.