Abstract
In this paper, determination of refractivity gradient and modified refractivity gradient for Cross River state was carried out. The year 2013 Radiosonde meteorological data from Nigerian Meteorological Agency (NIMET) was used. Refractivity, modified refractivity, refractivity gradient and modified refractivity gradient were computed. The results showed that in the year 2013, Cross River state had maximum modified refractivity gradient (dM/dz) of 114.9 (M -units/Km) and it occurred in December whereas the minimum modified refractivity gradient (dM/dz) on 81.9 (M–units/Km) and it occurred in October . Also, in the year 2013, the maximum refractivity gradient (dN/dz) was -42.1 (N-units/Km) and it occurred in December whereas the minimum refractivity gradient (dN/dz) was -75.1 (N-units/Km) and it occurred in October. The standard refractivity gradient of -39 N-units and standard modified refractivity gradient of 118 M-units occurred in December at altitude of 103 meters. In all the months the atmospheric condition was in the normal state except in the month of October where superrefraction occurred.
Keywords: Refractivity, Refractivity gradient, Radioclimatic factor, Modified refractivity gradient.
Received: 10 October 2018 / Revised: 13 November 2018 / Accepted: 18 December 2018/ Published: 8 January 2019
Contribution/ Originality
This study is one of very few studies which have investigated the modified refractivity gradient for Cross River state. Available related studies on Cross River State were mainly on refractivity gradient.
1. INTRODUCTION
Studies on atmospheric parameters are very essential in the wireless industry as the parameters have great impact on radio waves as they propagate through the atmosphere. Especially, radio refractivity which is a function of temperature pressure and relative humidity determines the extent to which radio signal path can be bent as it propagates through the atmosphere (Gao et al., 2008; Grabner et al., 2012; Hurter and Maier, 2013; Akinwumi et al., 2015; Series, 2015; Wang et al., 2017). The value of radio refractivity varies with altitude and hence, the gradient of the radio refractivity in the atmosphere is also required in wireless network design.
Importantly, the refractivity gradient is used to determine the nature and degree of curvature of the radio signal path in the atmosphere. Under normal atmospheric conditions radio waves tend to bend downwards towards the earth whereas for subrefraction condition radio waves bend upwards away from the earth (Sim, 2002; Usman et al., 2015; Bruin, 2016). In the case of superrefraction radio waves tend to bend downwards to the earth more than normal. Trapping occurs when the propagation path is bent downwards to such extent that it exceeds the curvature of the earth (Sim, 2002; Branson, 2008; Bhattacharjea, 2014; Bruin, 2016; Manjula et al., 2016). The visual representation of the different refractive conditions is given in Figure while the values of refractivity gradient and modified refractivity gradient for each of the different atmospheric conditions are listed in Table 1.
Figure-1. Visual representation of the different refractive conditions
Source: Bruin (2016) and Merrill (2008).
Table-1. Refractivity gradients and modified refractivity gradient under different conditions
Condition |
N-gradient (N/Km) |
M-gradient (M/Km) |
Subrefraction |
0<dN/dz |
157<dM/dz |
Normal |
-79<dN/dz<0 |
79<dM/dz≤157 |
Standard |
dN/dz = -79 |
dM/dz =118 |
Superrefraction |
-157<dN/dz<-79 |
0<dM/dz≤79 |
Trapping |
dN/dz <-157 |
dM/dz<0 |
Source: Bruin (2016) and Merrill (2008).
In this paper, the refractivity gradient and modified refractivity gradient for Cross River state in Nigeria are studied and the atmospheric conditions are identified based on the refractivity values for the various months in the year 2013. The study is based on the Radiosonde meteorological data from Nigerian Meteorological Agency (NIMET).
2. METHODOLOGY
Where
N is radio refractivity (dimensionless quantity in N-units).
M is Modified refractivity (dimensionless quantity in M-units).
z is Geometric height or the altitude (m)
Re is Radius of the earth (m).
3. RESULTS AND DISCUSSION
The vertical profile of the meteorological data for the month of January 2013 along with the computed refractivity, modified refractivity, refractivity gradient and modified refractivity gradient are given in Table 1. Similar tables for the months of October and December are given in Table 2 and Table 3 respectively.
Table-1. January 2013: The vertical profile of the meteorological data with the computed refractivity, modified refractivity, refractivity gradient and modified refractivity gradient
Altitude, z [m] |
T [C] |
U [%] |
P [hPa] |
N (N -Units) |
M (M-Units) |
dN/dz |
dM/dz |
0 |
30.6 |
64.87 |
1012.86 |
374.03 |
374.03 |
0 |
0 |
38.4 |
30.15 |
65.6 |
1008.65 |
372.01 |
378.03 |
-52.68 |
104.28 |
65 |
29.84 |
66.1 |
1005.73 |
370.6 |
380.8 |
-52.77 |
104.19 |
76.7 |
29.7 |
66.33 |
1004.44 |
369.98 |
382.02 |
-52.81 |
104.16 |
100 |
29.43 |
66.77 |
1001.89 |
368.74 |
384.44 |
-52.88 |
104.08 |
115.1 |
29.25 |
67.05 |
1000.23 |
367.88 |
385.95 |
-53.4 |
103.56 |
153.4 |
28.8 |
67.78 |
996.03 |
365.84 |
389.92 |
-53.39 |
103.58 |
191.8 |
28.35 |
68.51 |
991.81 |
363.78 |
393.89 |
-53.41 |
103.55 |
200 |
28.26 |
68.67 |
990.91 |
363.34 |
394.74 |
-53.42 |
103.54 |
230.1 |
27.91 |
69.24 |
987.61 |
361.73 |
397.84 |
-53.46 |
103.5 |
268.8 |
27.45 |
69.97 |
983.36 |
359.64 |
401.83 |
-53.52 |
103.44 |
300 |
27.09 |
70.57 |
979.94 |
357.96 |
405.05 |
-53.56 |
103.4 |
315.3 |
26.91 |
70.86 |
978.26 |
357.13 |
406.62 |
-53.59 |
103.37 |
371 |
26.26 |
71.92 |
972.15 |
354.12 |
412.35 |
-53.67 |
103.29 |
400 |
25.92 |
72.47 |
968.96 |
352.55 |
415.33 |
-53.71 |
103.25 |
422.3 |
25.66 |
72.89 |
966.52 |
351.34 |
417.62 |
-53.74 |
103.22 |
468.1 |
25.12 |
73.76 |
961.49 |
348.85 |
422.32 |
-53.79 |
103.17 |
500 |
24.75 |
74.37 |
957.99 |
347.11 |
425.6 |
-53.83 |
103.13 |
504.4 |
24.7 |
74.45 |
957.51 |
346.88 |
426.05 |
-53.83 |
103.13 |
541.8 |
24.26 |
75.16 |
953.4 |
344.84 |
429.88 |
-53.87 |
103.09 |
580.1 |
23.81 |
75.89 |
949.2 |
342.76 |
433.81 |
-53.9 |
103.06 |
620.8 |
23.34 |
76.66 |
944.73 |
340.55 |
437.99 |
-53.93 |
103.03 |
663.4 |
22.84 |
77.47 |
940.06 |
338.23 |
442.36 |
-53.96 |
103 |
Source: for T, U and P: NiMET (2013)
The graph of atmospheric temperature, pressure and relative humidity versus altitude for the month of January 2013 is given in Figure 1. Graph of refractivity and modified refractivity versus altitude for the month of January 2013 is given in Figure 2. Also, the graph of refractivity gradient and modified refractivity gradient versus altitude for the month of January 2013 are given in Figure 3. Table 1 and Figure 1 show that in January 2013 air temperature and pressure decrease with altitude whereas the relative humidity increases with altitude. This is in line with the generally observed pattern that air temperature and pressure decrease with altitude. However, , relative humidity does not generally decrease with altitude but varies depending on other atmospheric phenomena.
Figure-1. Graph of atmospheric Temperature, pressure and relative humidity versus altitude for the month of January 2013
Source: Generated by the authors using Mathlab program
Figure 2 shows that refractivity decreases with altitude as such in Figure 3 the refractivity gradient is negative. On the other hand, Figure 2 shows that modified refractivity increases with altitude and in Figure three, the modified refractivity gradient is positive.
Figure-2. Graph of refractivity and modified refractivity versus altitude for the month of January 2013
Source: Generated by the authors using Mathlab program
Figure-3. Graph of refractivity gradient and modified refractivity gradient versus altitude for the month of January 2013
Source: Generated by the authors using Mathlab program
Table-2. October 2013: The vertical profile meteorological data with the computed refractivity, modified refractivity, refractivity gradient and modified refractivity gradient
Altitude[m] |
T[C] |
U[%] |
P[hPa] |
N (N -Units) |
M |
dN/dz |
dM/dz |
0 |
26.81 |
78.18 |
1015.96 |
377.19 |
377.19 |
0 |
0 |
14.8 |
26.57 |
78.49 |
1014.28 |
376.01 |
378.34 |
-79.41 |
77.56 |
29.6 |
26.34 |
78.81 |
1012.61 |
374.84 |
379.49 |
-79.3 |
77.66 |
44.5 |
26.1 |
79.13 |
1010.93 |
373.67 |
380.65 |
-79.2 |
77.76 |
59.3 |
25.86 |
79.45 |
1009.25 |
372.5 |
381.81 |
-79.09 |
77.87 |
65 |
25.77 |
79.58 |
1008.61 |
372 |
382.2 |
-79.81 |
77.15 |
74.1 |
25.62 |
79.77 |
1007.58 |
371.29 |
382.92 |
-79.64 |
77.32 |
88.9 |
25.38 |
80.09 |
1005.91 |
370.13 |
384.08 |
-79.42 |
77.54 |
100 |
25.2 |
80.33 |
1004.65 |
369.26 |
384.96 |
-79.27 |
77.69 |
103.7 |
25.14 |
80.41 |
1004.23 |
368.97 |
385.25 |
-79.23 |
77.74 |
118.6 |
24.9 |
80.73 |
1002.55 |
367.81 |
386.43 |
-79.05 |
77.91 |
133.4 |
24.67 |
81.05 |
1000.88 |
366.67 |
387.6 |
-78.89 |
78.07 |
148.2 |
24.43 |
81.37 |
999.2 |
365.52 |
388.78 |
-78.74 |
78.22 |
163 |
24.19 |
81.69 |
997.53 |
364.38 |
389.96 |
-78.6 |
78.36 |
177.8 |
23.95 |
82.01 |
995.86 |
363.24 |
391.15 |
-78.46 |
78.5 |
200 |
23.6 |
82.49 |
993.35 |
361.54 |
392.93 |
-78.25 |
78.71 |
226.8 |
23.17 |
83.06 |
990.32 |
359.5 |
395.1 |
-78.01 |
78.95 |
300 |
21.99 |
84.64 |
982.04 |
353.98 |
401.07 |
-77.37 |
79.59 |
337 |
21.39 |
85.44 |
977.86 |
351.23 |
404.12 |
-77.04 |
79.92 |
400 |
20.38 |
86.8 |
970.74 |
346.6 |
409.38 |
-76.48 |
80.48 |
447.1 |
19.62 |
87.81 |
965.41 |
343.18 |
413.36 |
-76.06 |
80.9 |
500 |
18.77 |
88.95 |
959.43 |
339.4 |
417.88 |
-75.58 |
81.38 |
557.3 |
17.85 |
90.19 |
952.95 |
335.36 |
422.83 |
-75.06 |
81.9 |
Source: Generated by the authors using Mathlab program
Table-3. December 2013: The vertical profile meteorological data with the computed refractivity, modified refractivity, refractivity gradient and modified refractivity gradient
Altitude[m] |
T[C] |
U[%] |
P[hPa] |
N (N -Units) |
M |
dN/dz |
dM/dz |
0 |
31.07 |
66.24 |
1012.81 |
378.87 |
378.87 |
0 |
0 |
54.1 |
30.56 |
67.42 |
1006.94 |
376.86 |
385.35 |
-37.29 |
119.68 |
65 |
30.46 |
67.66 |
1005.76 |
376.45 |
386.65 |
-37.37 |
119.59 |
100 |
30.13 |
68.42 |
1001.96 |
375.11 |
390.81 |
-37.64 |
119.32 |
108.2 |
30.05 |
68.6 |
1001.08 |
374.8 |
391.78 |
-37.7 |
119.26 |
162.3 |
29.55 |
69.78 |
995.21 |
372.63 |
398.11 |
-38.46 |
118.51 |
200 |
29.19 |
70.6 |
991.12 |
371.14 |
402.54 |
-38.65 |
118.31 |
216.4 |
29.04 |
70.96 |
989.34 |
370.49 |
404.46 |
-38.75 |
118.22 |
270.2 |
28.54 |
72.14 |
983.51 |
368.32 |
410.73 |
-39.06 |
117.9 |
300 |
28.26 |
72.79 |
980.28 |
367.1 |
414.19 |
-39.23 |
117.73 |
323.1 |
28.04 |
73.29 |
977.77 |
366.15 |
416.87 |
-39.37 |
117.59 |
375.2 |
27.55 |
74.43 |
972.12 |
363.99 |
422.88 |
-39.68 |
117.28 |
400 |
27.32 |
74.97 |
969.44 |
362.95 |
425.73 |
-39.82 |
117.14 |
427.9 |
27.06 |
75.58 |
966.41 |
361.77 |
428.93 |
-39.98 |
116.98 |
480.4 |
26.57 |
76.73 |
960.72 |
359.52 |
434.93 |
-40.28 |
116.68 |
500 |
26.39 |
77.16 |
958.59 |
358.68 |
437.16 |
-40.39 |
116.57 |
532 |
26.09 |
77.86 |
955.12 |
357.3 |
440.8 |
-40.56 |
116.4 |
582.4 |
25.61 |
78.96 |
949.66 |
355.1 |
446.51 |
-40.83 |
116.13 |
631.8 |
25.15 |
80.04 |
944.3 |
352.92 |
452.09 |
-41.08 |
115.88 |
682 |
24.68 |
81.13 |
938.86 |
350.68 |
457.73 |
-41.33 |
115.63 |
732.9 |
24.21 |
82.24 |
933.34 |
348.4 |
463.44 |
-41.58 |
115.38 |
785.3 |
23.71 |
83.39 |
927.66 |
346.03 |
469.29 |
-41.82 |
115.14 |
836.8 |
23.23 |
84.51 |
922.07 |
343.68 |
475.03 |
-42.05 |
114.91 |
Source: Generated by the authors using Mathlab program
The computed vertical profile of refractivity for the twelve months in 2013 are given in Table 4 and Figure 4. Similar table and figure for the modified refractivity are given in Table 5 and Figure 5. About 23 data points were used in the analysis for each of the months where the first data point 1 is the surface level data and the data point 23 is for the highest altitude. The altitudes for the different months are not the same, that is why data point serial number is used.
Table-4. The computed vertical profile of refractivity for the twelve months in 2013
S/N |
N (N-Units) Jan |
N (N-Units) Feb |
N (N-Units) March |
N (N-Units) Apr |
N (N-Units) May |
N (N-Units) Jun |
N (N-Units) Jul |
N (N-Units) Aug |
N (N-Units) Sep |
N (N-Units) Oct |
N (N-Units) Nov |
N (N-Units) Dec |
1 |
374 |
370.8 |
384 |
384.6 |
362.9 |
376.9 |
387.1 |
378.5 |
380 |
377.2 |
382.6 |
378.9 |
2 |
372 |
367.5 |
381.7 |
381.2 |
360.2 |
374.3 |
383.8 |
375.6 |
376.6 |
376 |
379.9 |
376.9 |
3 |
370.6 |
366.2 |
380.9 |
380.7 |
359.2 |
373.5 |
383.2 |
374.8 |
375.4 |
374.8 |
379.3 |
376.4 |
4 |
370 |
363.8 |
379.4 |
378.6 |
357.5 |
371.7 |
381.1 |
373 |
372.9 |
373.7 |
377.5 |
375.1 |
5 |
368.7 |
363.3 |
379.2 |
377.9 |
357.2 |
371.6 |
380.4 |
372.8 |
373.1 |
372.5 |
377.1 |
374.8 |
6 |
367.9 |
359 |
377 |
374.6 |
354.8 |
369 |
377.2 |
370.2 |
369.7 |
372 |
374.3 |
372.6 |
7 |
365.8 |
357 |
374.7 |
372.7 |
352.2 |
366.5 |
375 |
367.5 |
366.4 |
371.3 |
372.4 |
371.1 |
8 |
363.8 |
354.8 |
374.4 |
371.2 |
351.6 |
366.3 |
374.1 |
367.2 |
365.8 |
370.1 |
371.5 |
370.5 |
9 |
363.3 |
351.1 |
372.4 |
368 |
349.6 |
364 |
371.1 |
365.1 |
363.2 |
369.3 |
368.8 |
368.3 |
10 |
361.7 |
350.4 |
370.2 |
366.8 |
346.1 |
361.3 |
369.2 |
362.5 |
360.2 |
369 |
367.3 |
367.1 |
11 |
359.6 |
347.4 |
369.6 |
364.9 |
344.4 |
361.1 |
368 |
361.6 |
359 |
367.8 |
366.1 |
366.2 |
12 |
358 |
343.9 |
368.1 |
361.7 |
341.8 |
358.7 |
364.9 |
359.8 |
357.2 |
366.7 |
363.5 |
364 |
13 |
357.1 |
343.8 |
364.9 |
361 |
340.6 |
356 |
363.3 |
357 |
354.2 |
365.5 |
362.2 |
362.9 |
14 |
354.1 |
340 |
366 |
358.2 |
339.3 |
355.9 |
361.4 |
356.1 |
352.4 |
364.4 |
360.8 |
361.8 |
15 |
352.5 |
337.6 |
363.9 |
355.2 |
336.7 |
353.2 |
357.8 |
354.3 |
351 |
363.2 |
358.1 |
359.5 |
16 |
351.3 |
336.2 |
361.7 |
354.5 |
335.2 |
350.7 |
357.6 |
351.6 |
345.9 |
361.5 |
357.2 |
358.7 |
17 |
348.8 |
332.5 |
360.2 |
351 |
334.5 |
350.3 |
354.1 |
350.6 |
348 |
359.5 |
355.5 |
357.3 |
18 |
347.1 |
329 |
359.4 |
347.7 |
332.1 |
347.7 |
350.1 |
348.7 |
345 |
354 |
353 |
355.1 |
19 |
346.9 |
325.6 |
357.2 |
344.2 |
327.5 |
345 |
346 |
345.6 |
342.1 |
351.2 |
350.5 |
352.9 |
20 |
344.8 |
322.3 |
355 |
341.3 |
325.3 |
342.5 |
341.6 |
342.6 |
339.3 |
346.6 |
348 |
350.7 |
21 |
342.8 |
318.9 |
352.6 |
338.5 |
323.2 |
339.8 |
337.3 |
339.4 |
336.5 |
343.2 |
345.4 |
348.4 |
22 |
340.5 |
315.6 |
350.2 |
335.9 |
320.9 |
337.2 |
333 |
336.1 |
333.7 |
339.4 |
342.8 |
346 |
23 |
338.2 |
312.5 |
347.7 |
333.2 |
318.6 |
334.5 |
329 |
333 |
331 |
335.4 |
340.3 |
343.7 |
Source: Generated by the authors using Mathlab program
Figure-4. The computed vertical profile of refractivity for the twelve months in 2013
Source: Generated by the authors using Mathlab program
From Table 4 and Figure 4 , the month of May has the lowest refractivity of 362.9(N-units). whereas April has the highest surface level refractivity value of 384.6 (N-units). Similar modified refractivity values are obtained from Table 5 and Figure 5.
Table-5. The computed vertical profile of modified refractivity for the twelve months in 2013
M (M-Units) Jan |
M (M-Units) Feb |
M (M-Units) March |
M (M-Units)Apr |
M (M-Units)May |
M (M-Units) Jun |
M (M-Units) Jul |
M (M-Units) Aug |
M (M-Units) Sep |
M (M-Units)Oct |
M (M-Units)Nov |
M (M-Units)Dec |
374 |
370.8 |
384 |
384.6 |
362.9 |
376.9 |
387.1 |
378.5 |
380 |
377.2 |
382.6 |
378.9 |
378 |
374.9 |
389.3 |
390.2 |
367.6 |
382.1 |
392.4 |
383.5 |
384.1 |
378.3 |
388.3 |
385.3 |
380.8 |
376.5 |
391.1 |
390.9 |
369.4 |
383.7 |
393.4 |
385 |
385.6 |
379.5 |
389.5 |
386.6 |
382 |
379.5 |
394.5 |
394.3 |
372.3 |
387.2 |
396.8 |
388.3 |
388.6 |
380.7 |
393.2 |
390.8 |
384.4 |
380.3 |
394.9 |
395.5 |
372.9 |
387.3 |
397.8 |
388.5 |
388.3 |
381.8 |
394.1 |
391.8 |
385.9 |
385.7 |
399.8 |
400.8 |
377.1 |
392.3 |
402.9 |
393.1 |
392.4 |
382.2 |
399.8 |
398.1 |
389.9 |
388.4 |
405 |
404 |
381.8 |
397.4 |
406.4 |
398 |
396.6 |
382.9 |
403.8 |
402.5 |
393.9 |
391.3 |
405.8 |
406.4 |
383 |
397.7 |
407.9 |
398.6 |
397.2 |
384.1 |
405.5 |
404.5 |
394.7 |
396.5 |
410.3 |
411.8 |
386.6 |
402.3 |
413 |
402.4 |
400.7 |
385 |
411.2 |
410.7 |
397.8 |
397.4 |
415.4 |
413.9 |
393.1 |
407.6 |
416.2 |
407.1 |
404.6 |
385.3 |
414.4 |
414.2 |
401.8 |
401.6 |
416.7 |
417 |
396.2 |
408.2 |
418.2 |
408.7 |
406.1 |
386.4 |
416.8 |
416.9 |
405 |
406.7 |
420.2 |
422.4 |
401.1 |
413 |
423.5 |
412 |
408.5 |
387.6 |
422.4 |
422.9 |
406.6 |
406.8 |
427.7 |
423.7 |
403.4 |
418.4 |
426.1 |
417.2 |
412.6 |
388.8 |
425 |
425.7 |
412.4 |
412.4 |
425 |
428.5 |
405.9 |
418.6 |
429.5 |
418.9 |
415.2 |
390 |
428 |
428.9 |
415.3 |
416 |
429.9 |
433.6 |
410.8 |
424 |
435.8 |
422.3 |
417 |
391.1 |
433.6 |
434.9 |
417.6 |
418 |
435.1 |
434.8 |
413.7 |
429.1 |
436.1 |
427.4 |
424.3 |
392.9 |
435.6 |
437.2 |
422.3 |
423.8 |
438.6 |
440.8 |
415.1 |
429.8 |
442.4 |
429.1 |
421.3 |
395.1 |
439 |
440.8 |
425.6 |
429.4 |
440.3 |
446.7 |
419.7 |
435.2 |
449.5 |
432.9 |
425.7 |
401.1 |
444.4 |
446.5 |
426 |
434.8 |
445.5 |
452.8 |
428.8 |
440.6 |
457.1 |
438.7 |
429.8 |
404.1 |
449.7 |
452.1 |
429.9 |
440.3 |
450.8 |
458 |
433.1 |
445.9 |
465.1 |
444.5 |
434 |
409.4 |
455 |
457.7 |
433.8 |
445.9 |
456.3 |
463 |
437.3 |
451.4 |
473.2 |
450.7 |
438.2 |
413.4 |
460.5 |
463.4 |
438 |
451.6 |
462 |
467.7 |
441.9 |
456.9 |
481.4 |
457.2 |
442.5 |
417.9 |
466.1 |
469.3 |
442.4 |
457 |
468 |
472.6 |
446.7 |
462.4 |
489.3 |
463.4 |
446.8 |
422.8 |
471.6 |
475 |
Source: Generated by the authors using Mathlab program
Figure-5. The computed vertical profile of modified refractivity for the twelve months in 2013
Source: Generated by the authors using Mathlab program
The computed vertical profile of refractivity gradient for the twelve months in 2013 are given in Table 6 and Figure 6. Similar table and figure for the modified refractivity gradient are given in Table 7 and Figure 7. From the results in Table 6 and Figure 6, he maximum refractivity gradient (dN/dz) = -42.1and it occurred in December whereas the minimum refractivity gradient (dN/dz) = -75.1 and it occurred in October. Also, From the results in Table 7 and Figure 7, in the year 2013, the maximum modified refractivity gradient (dM/dz) = 114.9 and it occurred in December whereas the minimum modified refractivity gradient (dM/dz) = 81.9 and it occurred in October.
Table-6. The computed vertical profile of refractivity gradient for the twelve months in 2013
dM/dz Jan |
dM/dz Feb |
dM/dz March |
dM/dz Apr |
dM/dz May |
dM/dz Jun |
dM/dz Jul |
dM/dz Aug |
dM/dz Sep |
dM/dz Oct |
dM/dz Nov |
dM/dz Dec |
104.3 |
86.9 |
108.7 |
97.3 |
100.1 |
104 |
96.2 |
100.2 |
84.9 |
77.6 |
105.9 |
119.7 |
104.2 |
87 |
108.8 |
97.3 |
100.2 |
104 |
96.3 |
100.2 |
85.1 |
77.7 |
105.9 |
119.6 |
104.2 |
87.3 |
108.8 |
97.4 |
100.3 |
104 |
96.4 |
100.3 |
85.4 |
77.8 |
105.9 |
119.3 |
104.1 |
87.4 |
108.8 |
97.4 |
100.3 |
104 |
96.5 |
100.3 |
85.3 |
77.9 |
105.9 |
119.3 |
103.6 |
87.6 |
108.5 |
97.1 |
100.1 |
103.7 |
96.4 |
100.1 |
85.4 |
77.2 |
105.6 |
118.5 |
103.6 |
87.9 |
108.7 |
97.3 |
100.4 |
103.9 |
96.6 |
100.3 |
85.9 |
77.3 |
105.7 |
118.3 |
103.5 |
88.2 |
108.7 |
97.4 |
100.4 |
103.9 |
96.7 |
100.3 |
86 |
77.5 |
105.7 |
118.2 |
103.5 |
88.7 |
108.8 |
97.5 |
100.6 |
104 |
96.9 |
100.5 |
86.4 |
77.7 |
105.8 |
117.9 |
103.5 |
88.8 |
108.9 |
97.6 |
100.9 |
104.1 |
97.1 |
100.6 |
86.8 |
77.7 |
105.9 |
117.7 |
103.4 |
89.2 |
108.9 |
97.7 |
101 |
104.1 |
97.2 |
100.7 |
86.9 |
77.9 |
105.9 |
117.6 |
103.4 |
89.7 |
108.9 |
97.8 |
101.2 |
104.2 |
97.4 |
100.8 |
87.2 |
78.1 |
105.9 |
117.3 |
103.4 |
89.7 |
109 |
97.9 |
101.3 |
104.3 |
97.5 |
100.9 |
87.6 |
78.2 |
106 |
117.1 |
103.3 |
90.2 |
109 |
98 |
101.4 |
104.3 |
97.7 |
101 |
87.8 |
78.4 |
106 |
117 |
103.3 |
90.5 |
109.1 |
98.1 |
101.5 |
104.3 |
98 |
101.1 |
88 |
78.5 |
106 |
116.7 |
103.2 |
90.7 |
109.1 |
98.1 |
101.6 |
104.4 |
98 |
101.2 |
88.6 |
78.7 |
106 |
116.6 |
103.2 |
91.1 |
109.2 |
98.3 |
101.7 |
104.4 |
98.2 |
101.3 |
88.3 |
78.9 |
106.1 |
116.4 |
103.1 |
91.6 |
109.2 |
98.4 |
101.8 |
104.5 |
98.5 |
101.4 |
88.7 |
79.6 |
106.1 |
116.1 |
103.1 |
92 |
109.3 |
98.6 |
102.1 |
104.6 |
98.8 |
101.6 |
89.1 |
79.9 |
106.2 |
115.9 |
103.1 |
92.4 |
109.3 |
98.7 |
102.3 |
104.7 |
99.1 |
101.7 |
89.4 |
80.5 |
106.2 |
115.6 |
103.1 |
92.9 |
109.4 |
98.9 |
102.4 |
104.7 |
99.4 |
101.9 |
89.8 |
80.9 |
106.2 |
115.4 |
103 |
93.3 |
109.5 |
99 |
102.6 |
104.8 |
99.7 |
102.1 |
90.1 |
81.4 |
106.3 |
115.1 |
103 |
93.7 |
109.5 |
99.1 |
102.7 |
104.9 |
100 |
102.2 |
90.5 |
81.9 |
106.3 |
114.9 |
Source: Generated by the authors using Mathlab program
Figure-6. The computed vertical profile of refractivity gradient for the twelve months in 2013
Source: Generated by the authors using Mathlab program
Table-7. The computed vertical profile of modified refractivity gradient for the twelve months in 2013
dN/dz Jan |
dN/dz Feb |
dN/dz March |
dN/dz Apr |
dN/dz May |
dN/dz Jun |
dN/dz Jul |
dN/dz Aug |
dN/dz Sep |
dN/dz Oct |
dN/dz Nov |
dN/dz Dec |
-52.7 |
-70.1 |
-48.2 |
-59.7 |
-56.8 |
-53 |
-60.7 |
-56.8 |
-72 |
-79.4 |
-51 |
-37.3 |
-52.8 |
-69.9 |
-48.2 |
-59.6 |
-56.8 |
-53 |
-60.7 |
-56.8 |
-71.9 |
-79.3 |
-51 |
-37.4 |
-52.8 |
-69.7 |
-48.2 |
-59.6 |
-56.7 |
-52.9 |
-60.6 |
-56.7 |
-71.6 |
-79.2 |
-51 |
-37.6 |
-52.9 |
-69.6 |
-48.2 |
-59.6 |
-56.6 |
-52.9 |
-60.5 |
-56.7 |
-71.6 |
-79.1 |
-51 |
-37.7 |
-53.4 |
-69.3 |
-48.5 |
-59.8 |
-56.8 |
-53.2 |
-60.6 |
-56.9 |
-71.5 |
-79.8 |
-51.3 |
-38.5 |
-53.4 |
-69 |
-48.3 |
-59.7 |
-56.6 |
-53.1 |
-60.4 |
-56.7 |
-71 |
-79.6 |
-51.2 |
-38.7 |
-53.4 |
-68.7 |
-48.3 |
-59.6 |
-56.5 |
-53.1 |
-60.3 |
-56.6 |
-71 |
-79.4 |
-51.2 |
-38.7 |
-53.4 |
-68.2 |
-48.2 |
-59.4 |
-56.4 |
-53 |
-60 |
-56.5 |
-70.6 |
-79.3 |
-51.1 |
-39.1 |
-53.5 |
-68.1 |
-48.1 |
-59.4 |
-56.1 |
-52.9 |
-59.9 |
-56.3 |
-70.2 |
-79.2 |
-51.1 |
-39.2 |
-53.5 |
-67.7 |
-48.1 |
-59.3 |
-56 |
-52.9 |
-59.8 |
-56.3 |
-70 |
-79.1 |
-51.1 |
-39.4 |
-53.6 |
-67.3 |
-48 |
-59.1 |
-55.8 |
-52.8 |
-59.5 |
-56.2 |
-69.8 |
-78.9 |
-51 |
-39.7 |
-53.6 |
-67.3 |
-47.9 |
-59.1 |
-55.7 |
-52.7 |
-59.4 |
-56 |
-69.4 |
-78.7 |
-51 |
-39.8 |
-53.7 |
-66.8 |
-48 |
-59 |
-55.6 |
-52.7 |
-59.3 |
-56 |
-69.2 |
-78.6 |
-51 |
-40 |
-53.7 |
-66.5 |
-47.9 |
-58.9 |
-55.4 |
-52.6 |
-59 |
-55.9 |
-69 |
-78.5 |
-50.9 |
-40.3 |
-53.7 |
-66.3 |
-47.8 |
-58.8 |
-55.3 |
-52.5 |
-59 |
-55.7 |
-68.3 |
-78.3 |
-50.9 |
-40.4 |
-53.8 |
-65.8 |
-47.8 |
-58.7 |
-55.3 |
-52.5 |
-58.7 |
-55.7 |
-68.6 |
-78 |
-50.9 |
-40.6 |
-53.8 |
-65.4 |
-47.7 |
-58.5 |
-55.1 |
-52.5 |
-58.4 |
-55.6 |
-68.2 |
-77.4 |
-50.8 |
-40.8 |
-53.8 |
-65 |
-47.7 |
-58.4 |
-54.8 |
-52.4 |
-58.1 |
-55.4 |
-67.9 |
-77 |
-50.8 |
-41.1 |
-53.9 |
-64.5 |
-47.6 |
-58.2 |
-54.7 |
-52.3 |
-57.8 |
-55.3 |
-67.5 |
-76.5 |
-50.8 |
-41.3 |
-53.9 |
-64.1 |
-47.6 |
-58.1 |
-54.6 |
-52.2 |
-57.5 |
-55.1 |
-67.2 |
-76.1 |
-50.7 |
-41.6 |
-53.9 |
-63.7 |
-47.5 |
-58 |
-54.4 |
-52.1 |
-57.2 |
-54.9 |
-66.8 |
-75.6 |
-50.7 |
-41.8 |
-54 |
-63.3 |
-47.4 |
-57.8 |
-54.3 |
-52.1 |
-56.9 |
-54.7 |
-66.5 |
-75.1 |
-50.6 |
-42.1 |
Source: Generated by the authors using Mathlab program
Figure-7. The computed vertical profile of modified refractivity gradient for the twelve months in 2013
Source: Generated by the authors using Mathlab program
In all, from the results in Table 6 and Table 7, the standard refractivity gradient of -39 and standard modified refractivity gradient of 118 occurred in December at an altitude of 103 meters. In all the months the atmospheric condition was in the normal state except in the month of October where superrefraction occurred.
4. CONCLUSION
A study of the refractivity gradient and modified refractivity gradient for Cross River state was presented. Radiosonde meteorological data from Nigerian Meteorological Agency (NIMET) for the year 2013 was used. The vertical profile of each of the following four parameters was computed for the twelve months; refractivity, modified refractivity, refractivity gradient and modified refractivity gradient. The result showed that Cross River state is generally in the normal atmospheric condition except for the month of October where superrefraction was observed.
| Funding: This study received no specific financial support. |
| Competing Interests: The authors declare that they have no competing interests. |
| Contributors/Acknowledgement: All authors contributed equally to the conception and design of the study. |
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