3.1 TSD and IPWV
The study shows that the TSD and IPWV estimated from PRN2-PRN7 are different (results not shown). This is because each satellite subtends different angles of elevation at a location (Jaiswal et al. 2020). So, for an accurate estimation of TSD and IPWV, we considered the average values estimated from all the satellites.
A study (Jaiswal et al. 2021) shows that as the angle of elevation decreases, the IPWV increases. This is because a lesser elevation implies a larger path length, which means more moisture and hence, a larger delay. Thus, for accurate position estimation of a target, it is advisable to launch a satellite at a higher elevation angle, preferably at 90o.
The monthly variations of TSD and IPWV averaged at 00 and 12 hr, over all the locations show that the crests (troughs) of one exactly fall on the crests (troughs) of the other. Figures 1a-e respectively show the results over Bhubaneswar, Kolkata, Gadanki, Goa, and Kanakapura in 2018. The daily variations of the two quantities also show the same result (results not shown).
3.2 IPWV and zenith wet delay (ZWD)
The daily and monthly variations of IPWV and ZWD show very good correlations. The crests (troughs) of one fall on the crests (troughs) of the other. This is obvious as IPWV causes the delay. Figure 2 shows the daily variations of IPWV and ZWD over Kolkata in June 2018, at 00 hr. The same results are seen over other locations in all months (results not shown). The right panel shows the monthly variations of the two over Goa, at 00 hr. The same results are seen over all locations (results not shown). It is noteworthy that IPWV, TSD, TZD, and ZWD show strong correlations (results not shown).
3.3 Progress of IPWV with months
The investigation on IPWV shows that it shows a particular pattern throughout months, viz. if it shows the peak value at the beginning of the month, then the minimum occurs at the end. On the contrary, if the minimum occurs at the beginning of the month, then the maximum occurs at the end. For example, over Bhubaneswar, at 00 hr, during February-April, the maximum IPWV occurs in the beginning, while the minimum occurs at the end of the month. During May-June, the order reverses, i.e. the minimum occurs at the beginning of the month, while the maximum occurs at the end. During July-September, and October-December, again there is a reversal in order. Over other locations also, the IPWV shows a similar kind of behavior (results not shown).
3.4 Progress of IPWV with the onset of monsoon in India
Table 2 shows the monthly average IPWV values, averaged over 00 and 12 hr. It shows that from April through June, the IPWV gradually increases over all locations. Over Kolkata and Gadanki, the rise in IPWV continues till July. Then, the southwest monsoon appears. During July through September, IPWV gradually decreases over all locations (the fall continues till October over Gadanki, Bhubaneswar, and Kanakapura).
Table 2
Monthly average of IPWV over the stations in 2018 (average of 00 and 12 hr)
Month | IPWV (mm) |
Bhubaneswar | Kanakapura | Goa | Kolkata | Gadanki |
Jan | 976.08 | - | - | - | - |
Feb | 804.35 | - | - | - | - |
Mar | 597.86 | - | 441.57 | - | - |
Apr | 589.91 | 93.38 | 433.78 | 612.23 | 271.28 |
May | 701.38 | 104.45 | 510.29 | 707.92 | 306.57 |
June | 829.19 | 125.02 | 573.77 | 841.05 | 351.79 |
July | 816.81 | 107.34 | 573.46 | 864.71 | 351.89 |
Aug | 711.80 | 105.40 | 458.11 | 810.09 | 306.56 |
Sep | 598.68 | 95.19 | 439.04 | 662.96 | 269.83 |
Oct | 587.24 | 94.54 | 450.32 | 708.10 | 269.36 |
Nov | 654.44 | 102.60 | - | 778.55 | 316.80 |
Dec | 812.59 | 122.27 | 659.65 | 950.47 | 364.43 |
During the northeast monsoon (October-December), IPWV gradually increases over Gadanki, Kanakapura, and Bhubaneswar, and September-December over Kolkata and Goa. These observations can be explained as follows: at first, the IPWV peaks up in June-July. Then, the southwest monsoon arrives. As the southwest monsoon progresses, the moisture rains out. So, IPWV shows a fall from June/July-September/October. It again peaks up during the northeast monsoon. As the northeast monsoon progresses, IPWV does not decrease as it rains out. It may be because the northeast monsoon brings a continuous supply of moisture from the Bay of Bengal. A study by Huang et al. (2021) at Guilin, China showed that before a heavy rain event, the IPWV value showed a peak.
Table 2 shows that over Goa, Gadanki, and Kolkata, the maximum monthly average IPWV occurs in December; over Bhubaneswar, and Kanakapura it occurs respectively in January and June. High values of IPWV are noted during the southwest monsoon months over all locations. Gadanki, Kanakapura, and Bhubaneswar record high IPWV in some of the northeast monsoon months also.
3.5 IPWV at 00 hr and 12 hr
We attempted to find if the IPWV is higher at 00 hr or 12 hr. The investigation shows that over the continental locations and Bhubaneswar, it is higher at 12 hr in comparison to that at 00 hr from May-September, while it is higher at 00 hr from October-December. Over Kolkata, from May to November, IPWV is higher at 00 hr. Thus, it is seen that the occurrence of higher IPWV at the 00 or 12 hr depends on the season and location. Choy et al. (2015) opine that PW depends on the season, topography, and other regional climatic conditions. Over Goa, no IPWV data are available at 12 hr.
3.6 Order of occurrence of the maxima/minima of SP, ST, RH, and IPWV
We observed the daily maxima and minima of SP, ST, RH, and IPWV over a location, to find out if the maxima or minima of SP, ST, and RH cause IPWV max/min, or if the latter controls the former three parameters. We observed the sequence of occurrence of the maxima and minima of these parameters in a month. If the max/min of a parameter follows that of a second one, then we assume that the second parameter controls the first one. The following sections describe the results.
We attempted to find if the maxima of IPWV are associated with the max/min of a parameter, or if the max/min of one follows those of the other. If the dates of the max (min) of one are the same as the max (min) of the other or are close to each other, then we assume that both are likely to maintain a direct relation. However, if the dates of occurrence of the maxima of one parameter superpose on the date of minima of the other, or are close, then an inverse relation is assumed.
3.6.1 IPWV and ST
The investigation reveals that over all locations, in some months, the STmax (min) follows the IPWVmax (min). In some months, the reverse is true. Thus, it appears that sometimes the IPWV governs ST. At times, ST controls IPWV. However, in November and December, ST controls IPWV. In some months, the ST max (min) and the IPWV max (min) occur on the same date, implying a direct relationship between the two. Sometimes, an inverse relation is seen. The relation between ST and IPWV varies from one location to another. Nayak and Takemi (2019) found that the relationship between extreme precipitable water events and ST varies from one region to another. He also found a higher occurrence of extreme precipitable water events in the tropics and at the mid-latitudes of the southern hemisphere in comparison to the northern hemisphere. This appears to be obvious as the southern hemisphere is mostly covered by oceans ensuring a higher level of moisture. Based on radiosonde data, Maghrabi and Dajani (2013) established a functional relationship between PW, pressure, and air temperature that yields a PW close to measurement. Stephens (1990) stated that the monthly mean PW data over the oceans can be obtained from the sea surface temperature. Thus, it appears that the IPWV and the ST are correlated.
3.6.2 IPWV and SP
The investigation shows that mostly the IPWV max/min follows the SP max/min, implying that SP controls IPWV. However, in a few months, the SP max/min follows the former. In December, over all locations, IPWV controls SP, except Kanakapura.
The investigation further reveals that the East Coast locations, viz. Kolkata and Bhubaneswar, show an inverse relation between SP and IPWV. Goa, lying along the West Coast, mostly shows a direct relationship. Continental locations, like Gadanki and Kanakapura, sometimes show a direct relation, while at times, an inverse relation is seen.
3.6.3 IPWV and RH
The IPWV always appears to control RH over Kolkata and Bhubaneswar. The max (min) of one is mostly associated with the max (min) of the other, implying a direct relationship between them. Over Goa and Kanakapura, RH mostly controls IPWV. Sometimes the two bear a direct relation, while at times, an inverse relation is seen between the two over Gadanki, Goa, and Kanakapura. Over Gadanki, sometimes IPWV controls RH.
A study by Viswanadham (1981) reveals that mean monthly surface dew point temperature is a good indicator of mean monthly IPWV at all latitudes in winter, but, in the summer, the correlation between RH and IPWV is not strong between 0o-20o. Kelsey et al. (2021) demonstrated that RH and surface elevation are important in determining the functional relationship between the brightness temperature and PW. Guangxiong et al. (2006) established a functional relation between specific humidity and PW that yields RH if ST is known. Liu (1986) demonstrated that PW can predict surface-level humidity, but not surface temperature over the oceans.
The dissimilarities in the mutual relationships between the surface meteorological elements between the East and the West Coast occur due to the different geography, Earth’s crust, and climate in the two regions. However, the exact mechanism of geography and climate affecting the mutual relationships of surface meteorological elements is yet to understand in depth.
3.7 Controlling factors of IPWV
We attempted to find the factors that control the IPWV. As the incoming solar radiation (insolation) governs the weather and climate on the earth, we attempted to find the influence of the TSI on IPWV. As the insolation varies with the latitude, we attempted to find if IPWV depends on the latitude. Besides, we investigated the correlation of IPWV with a few more surface elements, e.g., ST, SP, and RH.
3.7.1 IPWV and latitude
The investigation shows that as latitude decreases, the IPWV decreases. To find the correlation between the two, we fitted the monthly average values of IPWV and the latitudes of the locations to various models, viz. linear, cubic, quadratic, log normal, power, exponential, logarithmic, logistic, sigmoid, inverse, and growth. The validity of the relation is judged by the F test at a 5% level of significance. It shows that at 00 hr, during April- December, a quadratic relation is suitable every month. At 12 hr, a cubic relation is seen during April-August. During September-December, at 12 hr, none of the relations are suitable. It may be because at 12 hr, no data are available over Goa. The monthly average IPWV (average of 00 hr and 12 hr) and the corresponding latitudes show a very strong quadratic relation. Figure 3 respectively shows the results of the investigation at 00 and 12 hr in April. The same results are seen in other months (results not shown).
3.7.2 IPWV versus SP, ST, RH, and TSI
To find the parameters that control the IPWV, we investigated SP, ST, RH, and TSI. To establish the functional relationship between the IPWV and a particular meteorological parameter, we fitted the two to different models as described above. We performed the investigation with the daily data for a particular month, and with monthly average data in four steps-at first, the correlation of IPWV as a function of a single parameter was carried out. Next, as a function of a combination of two parameters; then, as a combination of three parameters, and at last, all four parameters, i.e. SP, ST, RH, and TSI entered into the linear regression. We performed the investigation at 00 hr and 12 hr separately, and also with average values of the parameters at 00 hr and 12 hr. The investigation reveals that IPWV cannot be explained based on SP, ST, or RH separately. However, the inclusion of TSI as an independent variable in the regression indicates a stronger correlation marked by a high R2 value. Thus, the IPWV is the best explained based on SP, ST, RH, and TSI. As the number of independent variables entered into the regression increases, the R2 values also increase, indicating a stronger correlation between IPWV and the independent variables (results not shown).
Besides, we have established the functional relationships between these elements by including the daily data for the whole of 2018. We found strong correlations in most of the cases (results not shown). The correlations at 12 hr are more significant than those at 00 hr in some months, while in some other months the opposite happens (results not shown).
3.7.3 TSI and IPWV
To understand whether the Sun controls IPWV, we investigated the daily TSI and IPWV values over a location. The study shows that over all locations, from October-December, the IPWV max (min) is always associated with TSI max (min) except over Bhubaneswar in November, and December. Over Kolkata, in June and July; Over Bhubaneswar in February; over Gadanki in July, and over Goa in March, and September, the same result is seen. Besides, the peaks of IPWV occur immediately after the occurrence of the TSI peaks from the end of July to the beginning of August, over Bhubaneswar, and Kanakapura; and from the end of August to the beginning of September, over Kolkata, and Kanakapura. The investigation also shows that the IPWV max (min) is associated with TSI min (max) over all locations except October-December and above months.
To find out a functional relationship between the two, if any, we fitted the daily TSI and IPWV values over a location, to different models as described above. The investigation shows that from October-December, over all locations, and at both 00 and 12 hr, the two show a direct relationship, implying that as TSI increases, the IPWV increases. Only at 12 hr over Kolkata in October and Bhubaneswar in December, an inverse relation is seen between the two. In other months at both 00 and 12 hr, an inverse relation is seen except at 00 hr over Kolkata in April and September; over Goa in March; and over Bhubaneswar from February-May.
Thus, it appears that IPWV can be very well explained in terms of TSI. The correlations of IPWV and TSI are significant with an R2 value of 0.8–0.99 in most of the cases (Fig. 4a-e). Figures 4(a-c) respectively show the correlations between the two over Gadanki in August, over Goa in May, and over Bhubaneswar in May, at 00 hr. Figures 4(d-e) respectively show the relationship between the two at 12 hr, over Kanakapura in September, and over Kolkata in October. Figures 4 (a-e) exhibits an inverse relation between IPWV and TSI. Results for other months are not shown.
3.8 Validation of IRNSS-retrieved IPWV with radiosonde-retrieved precipitable water
The validation of IPWV retrieved from the IRNSS with that retrieved from radiosonde shows that the two do not match well over any locations, except over Kanakapura, on a few days. Figure 5 respectively shows the validation between the two over Kanakapura at 00 hr and 12 hr in September. It is noteworthy that due to the higher elevation at Kanakapura, the estimated IPWV is lesser in comparison to other locations. Over other locations, the latitude being higher, the retrieved IPWV overestimates that obtained from the radiosonde. It is noteworthy that due to the non-availability of radiosonde data over Kanakapura, those were taken over Bangalore, 11.5 km away from there.
As the IRNSS-retrieved IPWV estimated by using the mapping function does not match well with the radiosonde-retrieved PW, we attempted to investigate the reason for such disagreement. We found that the IPWV estimated by the alternate approach described above, shows a good match with the latter over each location, both at 00 hr and 12 hr. Table 3 describes the root mean square error (RMSE) of the estimated IPWV validated against the radiosonde-retrieved PW. Table 3 shows that over Kanakapura, the two show the best match with an RMSE of 9.784 and 9.598 at 00 and 12 hr, respectively. Over Goa, the error is the maximum.
Table 3
Root mean square error (RMSE): IRNSS-retrieved IPWV vs. radiosonde-retrieved PW
Location | 00 hr | 12 hr |
Gadanki | 12.315 | 12.509 |
Goa | 25.076 | - |
Kolkata | 21.528 | 21.442 |
Kanakapura | 9.784 | 9.598 |
Bhubaneswar | 19.660 | 19.652 |
By observing the good agreement of radiosonde-retrieved PW with that estimated by the alternative approach along the vertical direction; and the poor agreement with that retrieved using the mapping function, it appears that the vertical component of the IRNSS-retrieved TSD may be approximated to the TZD, which may be used to estimate the columnar precipitable water over a location. The IPWV estimated by Khaleel (2015) without including its horizontal gradients shows good agreement with the radiosonde-retrieved PW.
Figures 6(a-e) respectively show the standard deviation of monthly IPWV retrieved from the IRNSS and radiosonde over Gadanki, Kanakapura, Kolkata, Bhubaneswar, and Goa at 00 hr. Figures 6(a-e) show that the difference in standard deviations at 00 hr ranges between 2.36–8.89 mm over Gadanki; 5.6-29.26 mm over Goa; 1.48–8.03 mm over Kanakapura; 0.14–7.77 mm over Kolkata and 0.318–13.23 mm over Bhubaneswar. The differential standard deviations of the two at 12 hr range between 4.698–7.35 mm; 0.709–9.405 mm; 0.568–9.389 mm; and 0.812–12.29 mm over Gadanki, Kanakapura, Kolkata, and Bhubaneswar, respectively (results not shown). Smith et al. (2006) reported a 2.0 mm standard deviation difference between the GPS-retrieved and the radiosonde-retrieved PW. It is noteworthy that using the alternate method we found a standard deviation of monthly average IPWV that varies between 0.38–8.56 mm at 00 hr, and 0.26–7.81 mm at 12 hr. The standard deviation of monthly average PW retrieved from the radiosonde varies between 2.58–30.40 mm at 00 hr, and 2.37–15.10 mm at 12 hr. Lu et al. (2015) demonstrated the necessity for estimating IPWV using multiple satellites.
Studies found good agreement between the radiosonde-retrieved and GNSS-retrieved PW (Huang et al. 2021), and GPS-retrieved PW (Choy et al. 2015). Jaiswal et al. (2021) found a very good agreement between the GPS-based IPWV and that retrieved from the radiosonde over Bangalore.