 size and the final subwindow size were set at 64 × 64 pixels (equivalent to 128 × 128 km2) and 32 × 32 pixels (64 × 64 km2), respectively. With 50% overlap, the final vector resolution is 16 × 16 pixels (32 × 32 km2). The PIV image processing also includes postprocessing to remove spurious vectors using a median filter, and fill the usually small number of missing vectors using the Kriging interpolation method. See Mori and Chang (2003) for details.
Each AMV determined by PIV is a measure of tracer motion (i.e., cloud in the present study) on a horizontal plane at a certain elevation within that particular interrogation window. Since cloud may exist over a vast range of elevations and the atmospheric motion is known to be a function of elevation, it is necessary to assign a height for each AMV. The height assignment is also necessary when performing AMV validation. Following Nieman et al. (1993) and Deb et al. (2014), the present study adopts the infrared-window method for opaque cloud and the H2O-intercept method for semitransparent cloud.
The infrared-window method utilizes a threshold value as a proxy to represent the temperature of the top cloud. Based on Nieman et al. (1993), the threshold value is generally assigned as the 25% coldest brightness temperature in the target image from an infrared-window channel. As a result, the height of the AMVs at the top cloud can be determined by referencing the collocated temperature profile calculated by NWP model analysis–forecast (Nieman et al. 1993).
in which R is the received radiance, T is the brightness temperature, E is the effective emissivity, and TN is the cloud temperature. In addition, TF and TG are the brightness temperatures of the incoming upward radiation at the cloud-base level in the water vapor channel and the infrared-window channel, respectively. The subscripts 1 and 2 denote the water vapor channel and the infrared-window channel, respectively.
The values of a and b can be obtained by fitting the observed R1 and R2 from a semitransparent cirrus cloud with the disparate emissivity over several areas. Equation (5) is valid for the emissivity ranging from 0 to 1. Once a and b are determined, the cloud temperature for the target cirrus cloud under the blackbody conditions can be obtained using Eq. (5) with emissivity equal to 1. The cloud temperature corresponding to the blackbody conditions is essential information for obtaining the cloud height in the H2O-intercept method. Szejwach (1982) presented a comparison between the measured data curve and the ideal curve that considers the radiation emitted by blackbodies in both channels. In the graph exhibited by Szejwach, the overlapped curves or clearly indicate that the blackbody emission temperature represents the temperature of semitransparent cirrus cloud.
in which the subscript m indicates an individual wind measurement that contains V (velocity), T (temperature), P (pressure), dd (direction), and S (speed). The subscripts i, j, and k represent the axes in the coordinate system employed in the NWP regional model. With different subscripts, F denotes the weight of each cost item. The present study follows the suggested values reported by Nieman et al. (1997) and Holmlund et al. (2001). It should be noted that the wind measurement is excluded if the minimum value of the cost function within ±100 hPa with respect to the initial height is unable to be obtained.
Performing quality control on derived AMVs is a crucial step in its practical use. In the present study, the automatic quality control (AQC) method proposed by Holmlund (1998) was adopted. In this method, five consistency check tests are conducted, including direction consistency, speed consistency, vector consistency, spatial consistency, and forecast consistency, while each test yields a quality indicator (QI). Among the consistency check tests, direction, speed, and vector check tests compare the AMVs derived from two consecutive pairs of images (i.e., image triplet). These tests are equivalent to the temporal filtering and smoothing procedure for the PIV technique at an early stage of development. As the development evolved and more sophisticated and robust schemes were introduced, this postprocessing process applying the temporal consistency check has become unnecessary for the modern PIV technique, provided that the (traditional) postprocessing applying spatial filtering has been performed. Note that both the temporal filtering and spatial filtering are not expected to increase the accuracy of the computed displacement vectors but to remove/replace the stray vectors after the cross-correlation computation. As a result, direction, speed, and vector consistency check tests are not performed.
For a single consistency check test, QI is equal to Eq. (10), or ⁠. As suggested by Holmlund (1998), was used for a forecast consistency check, and was set as a threshold in the AQC performance on all the derived AMVs.
Figure 3 shows comparisons between AMVs derived from Himawari-8 imagery using the PIV method and the corresponding analysis wind vectors obtained by NWP at 0000 UTC 18 June 2017. Note that in the present study the Weather Research and Forecasting (WRF) Model was employed as the NWP model. For a detailed description of the WRF Model, the reader is referred to Skamarock et al. (2005) while its applications in typhoon predictions can be found in Hsiao et al. (2015).
AMVs derived from satellite imagery and calculated using NWP. Red, yellow, and cyan vectors represent derived AMVs in ranges from 50 to 250 hPa, 251 to 350 hPa, and 351 to 1050 hPa, respectively. The green vectors represent the analyzed wind vectors at 300 hPa from the NWP regional model. Note that the x and y axes represent the longitude and latitude, respectively.
In Fig. 3, the AMVs in three different vertical regions—50–250 hPa, 251–350 hPa, and below 351 hPa—are presented and colored as red, yellow, and cyan, respectively. The background green vectors are the analysis wind vectors at 300 hPa from a NWP regional model. In the comparisons, both the PIV-derived AMVs and the NWP wind field are very similar. Moreover, with some special signatures in the cloud patterns, one can see that the atmospheric circulation is clearly captured by the AMVs. The cloud patterns show two westerly jets: one is along the north of South Korea (from 110° to 130° longitude and from 40° to 45° latitude) and the other is along the south of Japan (from 110° to 140° longitude and from 20° to 35° latitude) with a trough shape, forming a weak cyclone circulating around the Tsushima basin. Furthermore, a weak anticyclone circulation pattern is noticeable around the junction of the Indochina peninsula and China (from 90° to 110° longitude and from 20° to 30° latitude).
Figure 4 presents a comparison between the PIV-derived AMVs and NWP analysis wind field by matching the grids between AMVs and the NWP winds (which have much higher spatial resolution). Good agreement in both magnitude and direction can be found at most grids. Accordingly, Fig. 4 indicates that AMVs obtained using the PIV method are capable of quantitatively depicting the atmospheric circulation. Figure 5 further shows detailed comparisons among the AMVs, NWP analysis vectors, and radiosonde observations at six stations around Taiwan. Overall, the PIV-derived AMVs match the radiosonde wind vectors well.
AMVs derived from satellite imagery and calculated using NWP. Red vectors indicate the derived AMVs between 200 and 300 hPa. Green vectors show the analysis wind vectors at 250 hPa from the NWP regional model. Note that the x and y axes represent the longitude and latitude, respectively.
Comparison of wind vectors among the radiosonde data (black vectors), NWP analysis winds (blue vectors), and derived AMVs (red vectors). Note that the x and y axes represent the longitude and latitude, respectively.
To evaluate the uncertainty of PIV-derived AMVs, errors in both AMVs and NWP analysis winds were estimated by comparing to the radiosonde observations. The errors feature the mean vector difference (MVD), the root-mean-square error (RMSE), the standard deviation (SD), and the wind speed bias (BIAS). The mathematical expressions for evaluating these errors can be found in Nieman et al. (1997). To match the radiosonde observations, the NWP data were interpolated to the location of the radiosonde observation stations. For the PIV AMVs, the average value of the data closest to the radiosonde observation station within a horizontal distance of 150 km and a vertical range of 20 hPa was used. The calculated results are listed in Table 1 along with the mean wind speed (SPEED) and the sample number (NUM) for 13 cases, including 12 separated moments (denoted as date and time) and all of the moments combined (denoted as case All).
The MVD, RMSE, and standard deviation of the PIV-derived AMVs are 3.70, 4.29, and 2.17 m s−1, respectively, which are slightly larger than those of the NWP data (3.35, 3.88, and 1.97 m s−1). The wind speed bias of the PIV-derived AMVs is −1.05 m s−1, and the slow speed bias is found in each case. Figure 6 further shows a scatterplot of AMVs versus radiosonde data. Many studies (Nieman et al. 1997; Genkova et al. 2008; Bresky et al. 2012) indicate that the slow speed bias is mainly caused by the