73
Sea Level Variations at Jeddah, Eastern Coast of the Red Sea
Khalid M. Zubier
Marine Physics Department, Faculty of Marine Sciences, King Abdulaziz University
P.O. Box 80207 , Jeddah 21589, Saudi Arabia E-mail: [email protected]
Abstract. The sea level variations at Jeddah during the year 2000 were investigated. Tidal analysis showed that tide is responsible for 16.7%
of the variance. The daily-averaged residual (de-tided) sea level was statistically compared with daily means of atmospheric parameters that could contribute to sea level variations. Evaporation contribution was relatively significant during the late fall, while during early summer its contribution was smaller by about 50%. Atmospheric pressure has almost no contribution during the early summer but it showed significant contribution during both early winter and late fall.
For the overall record, the along-shore wind stress component showed relatively significant contribution in comparison with the cross-shore component, however, both wind stress components showed significant contribution during the early summer.
Introduction
Variations in sea level are caused by a combined effect of astronomical, oceanographic and atmospheric forcing. Tide is an astronomical force due to which short-term periodic sea level rise and fall occur in a magnitude that depends mainly on the location and the shape of the water body. Oceanographic forces include the steric effect that causes long- term sea level variations due to the seawater expansion and contraction with the seasonal increase and decrease of seawater temperature
respectively. Water exchange is another oceanographic factor that can cause significant sea level variations in semi-enclosed water bodies.
Evaporation is among the atmospheric factors that contribute to the variations in the sea level. Sea level also varies with atmospheric pressure that forces the sea level to decrease as it increases and vice versa. Wind stress is another atmospheric force with which the sea level changes due to the seawater convergence and divergence effects that it causes.
Red Sea is considered one of the marginal seas of the Indian Ocean (Fig. 1). Being a semi-enclosed water body, it is characterized by a tide of standing wave type with the highest tidal ranges occurring in the north and the south and the lowest tidal range occurs at the central part (Edwards, 1987). In terms of atmospheric conditions the Red Sea is influenced by the monsoonal system with a distinctive weather patterns.
As a result of this monsoonal system the wind over the northern part of the Red Sea blows from NNW all year long while in the southern part the direction from which it blows switches from NNW in the summer to SSE in the winter. The seasonal reversal of the monsoon associated wind patterns create different circulation patterns in the southern Red Sea that are responsible for the seasonality in the seawater exchange pattern that occurs with Gulf of Aden through Bab Al-Mandab Strait. This, in turn, contributes to the seasonal variations of the sea level in the Red Sea.
Located in an arid region, the Red Sea is exposed to an extremely hot weather during summer, and being a semi-enclosed sea, it has a quick response to the heating process which leads to loss of seawater due to evaporation that contributes to the variations in the sea level.
Changes in the sea level at Jeddah have been investigated by Ahmad and Sultan (1993), Sultan et al., (1995 a,b), Sultan and Ahmad (2000), Maghrabi (2003), Sultan and Elghribi (2003). In most of these studies, neither the evaporation rate nor the atmospheric pressure have shown significant correlation with the observed sea level changes at Jeddah, indicating minimal contribution of these atmospheric parameters.
According to these studies the variations in the sea level were attributed to the tide, the seawater exchange with Gulf of Aden and the along-shore component of the wind stress. In these studies, with the exception of the studies by Sultan et al., (1995-a) and Sultan and Elghribi (2003), the investigations of the relationship between the observed sea level and the different atmospheric parameter have been carried out using monthly
averaged records. The advantage of this approach is to roll-out all the small scale variability, however, it does not allow for investigating the correlations on segments of the data due to the limited number of data points that will lower the statistical significance of the results. Some of the above mentioned studies suggested that steric effect does not seem to have a direct influence on the observed sea level changes; however, the lack of seawater temperature records did not allow a further investigation of the steric effect. The studies conducted by Abdallah and Eid (1989) and Eid and Kamel (2004) have shown that the contribution of the steric effect to the sea level variations is minimal at the central part of the Red Sea, on which Jeddah is located.
Fig. 1. Jeddah location shown on a map of the Red Sea and surrounding areas.
In this paper, the observed variations in the sea level at Jeddah (Fig. 1) during the year 2000 were investigated. Tidal analysis allowed for de-tiding the observed hourly sea level record which was daily averaged afterward. Correlation investigations were then carried out between the daily-averaged de-tided sea level record and the daily- averaged atmospheric parameters for the whole records as well as for segments of the records that correspond to certain periods. The large number of data points allowed for carrying out the correlation investigation on segments of the data without extensively lowering the statistical significance of the results.
Data and Methods of Analysis
Sea level data are collected at an hourly interval near Jeddah by Aramco Tide Station (39° 09’ 17” W, 21° 25’ 52” N). Recorded sea level data for the year 2000 were analyzed using the t_tide (Pawlowicz et al., 2002) tidal harmonic analysis toolbox in Matlab® software package. The astronomical tide resulting from the tidal analysis was subtracted from the original sea level record to obtain the residual (de-tided) sea level record. Daily mean residual sea level record was obtained by averaging the hourly residual sea level.
Atmospheric data are collected by the Presidency of Meteorology and Environment (PME) at Jeddah King Abdulaziz Airport (39° 11’ 00”
W, 21° 42’ 00” N) Weather Station (WMO ID: 41024). The daily- averaged atmospheric data for the year 2000 were utilized in the estimation and calculation of the atmospheric parameters that could affect the sea level. Daily evaporation rates were estimated using the Bulk-Aerodynamic Method (Herting et al., 2004) based on the collected atmospheric data. Pressure at the sea surface was directly provided as a daily record. Daily wind stress was calculated, based on Smith (1988), using Woods Hole Oceanographic Institution (WHOI) air-sea toolbox (Beardlsley and Pawlowicz 1999) in Matlab® software package. Cross- shore and along-shore wind stress components were obtained using the calculated daily wind stress values and the wind direction record.
Correlation coefficient is a statistical parameter that is used to quantify the level of dependence between two variables (assuming one is dependant and the other is independent). In order to determine the dependence of sea level on the variations of the different atmospheric
parameters, correlation coefficients were calculated between the residual sea level and evaporation rate, sea surface pressure and wind stress (cross-shore and along-shore components).
Results and Discussion
Tidal harmonic analysis of the hourly sea level record showed that the astronomical tide is responsible for 16.7 % of the total variance. The amplitudes and phases of the major tidal constituents are given in Table 1. Plot of tidal constituent frequency and amplitude is also shown in Fig. 2. It can be seen from both Table 1 and Fig. 2 that the semi- diurnal (M2) tidal constituent dominates. The calculation of the ratio F = (K1 + O1) / (M2 + S2) gave a value of F=0.5745 indicating that the tide at Jeddah is of mixed type with the semidiurnal tide dominating. Figure 3 shows plots of the sea level record, astronomical tide and residual sea level obtained by subtracting the astronomical tide from the original sea level record. The figure shows that the residual seal level record varies with time from 39.67 cm to −27.15 cm with a difference of 66.82 cm.
The figure also shows that the de-tided sea level is considerably depressed during the summer months in comparison with the rest of the record, in consistent with the studies by Ahmad and Sultan (1993), Sultan et al., (1995 a,b), and Maghrabi (2003).
Table 1. Amplitudes and phases of some principal tidal constituents at Jeddah, based on tidal analysis for the year 2000.
Tidal Constituent
Frequency (cph)
Period (days)
Amplitude (cm)
Phase (deg)
SSA 0.0002282 182.59 5.41 121.97
MSM 0.0013098 31.81 2.82 85.28
MM 0.0015122 27.55 2.14 66.44
MSF 0.0028219 14.77 2.88 352.89
MF 0.0030501 13.66 2.58 84.91
O1 0.0387307 1.08 1.76 206.24
P1 0.0415526 1.00 0.86 210.37
K1 0.0417807 1.00 3.25 207.42
N2 0.0789992 0.53 2.42 164.63
M2 0.0805114 0.52 7.19 202.58
S2 0.0833333 0.50 1.53 244.18
Fig. 2. Amplitudes versus Frequencies of some principal tidal constituents at Jeddah for the year 2000.
Fig. 3. Astronomic and Residual Sea Level at Jeddah, based on the tidal analysis for the observed year 2000 record.
Atmospheric parameters that could significantly affect the sea level record are evaporation, atmospheric pressure and wind stress. To quantify the significance of each of these atmospheric parameters on the
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Frequency (cph)
Amplitude (m)
0 50 100 150 200 250 300 350 400
-0.5 0 0.5 1 1.5 2
Days in Year 2000
Sea Level (m)
Observed Astronomic Residual
de-tided sea level record for the year 2000, correlation between every single parameter and the daily-averaged residual sea level record was made (Table 2). Daily evaporation rate is plotted along with the daily- averaged residual sea level record in Fig. 4. In general, the figure shows that the residual sea level decreases at the periods during which the evaporation increases and vice-versa. The correlation coefficient calculated between the daily evaporation rate and the daily-averaged residual sea level (−0.2661) indicates the reasonable significance of the evaporation rate. This quantification of the evaporation effect on sea level was not made in the study by Sultan et al., (1995-b). Sultan et al., (1995-a) have suggested that the evaporation effect on sea level during the winter is probably overshadowed by the wind effect while during summer the lowering of the monthly-averaged sea level is due to the combined effect of evaporation and wind. To further investigate this issue, the correlation coefficients were calculated for 50 days segments of the two records corresponding to early winter, early summer and late fall periods (Table 2), and the calculated correlation coefficients were equal to (−0.0103), (−0.1287) and (−0.2517) respectively.
Table 2. Correlation coefficients calculated between the daily-averaged residual (de-tided) seal level record and evaporation, atmospheric pressure, cross-shore wind stress (X) and along-shore wind stress (Y).
Atmospheric Parameter
Total Record
First 50 Days
Middle 50 Days
Last 50 Days
Evaporation −0.2661 −0.0103 −0.1287 −0.2517
Pressure (atm.) 0.3075 −0.6473 −0.0097 −0.6293
Wind Stress (X) −0.0232 0.0644 0.5367 0.2304
Wind Stress (Y) 0.2821 0.0375 0.501 0.0266
Both daily atmospheric pressure (at sea level height) and daily- averaged residual sea level records are shown in Fig. 5. The figure shows that during some periods (mainly the first and last 2 months) the daily residual sea level decreases with the increasing of the atmospheric pressure. However, the calculated correlation coefficient (Table 2) between the two records (+0.30) does not indicate an inverse correlation.
Therefore, correlation coefficients were calculated for 50 days segments of the two records, representing early winter, early summer and late fall (Table 2). The calculations gave correlation coefficients of (−0.6473) and (−0.6293) for early winter and late fall respectively, while for the early summer almost no correlation (−0.0097) was found between the two records. This indicated that the atmospheric pressure plays a significant
role on the sea level variations during the late fall and the early winter but not during the early summer. Sultan et al., (1995-a) have indicated somewhat similar results.
Fig. 4. Evaporation Rate and Residual Sea Level at Jeddah for the year 2000.
Fig. 5. Atmospheric Pressure and Residual Sea Level at Jeddah for the year 2000.
0 50 100 150 200 250 300 350 400
-0.5 0 0.5
SeaLevel (m)
Days in Year 2000
0 50 100 150 200 250 300 350 4000
20 40
Evaporation (mm/day)
0 50 100 150 200 250 300 350 400
-0.5 0 0.5
SeaLevel (m)
Days in Year 2000
0 50 100 150 200 250 300 350 400980
1000 1020
Pressure (hPa)
Figures (6 and 7) show plots of calculated cross-shore and along- shore wind stress records, respectively, along with the daily-averaged residual sea level record. It can be seen from both figures that the sea level somewhat responds to the variations in both cross-shore and along- shore wind stresses. The calculated correlation coefficient (Table 2) between the daily-averaged residual sea level and cross-shore wind stress was (−0.0232), while the calculated correlation coefficient between the daily-averaged residual sea level and Along-shore wind stress was (+
0.2821). These values indicate that in comparison with the cross-shore component , the along-shore component of wind stress plays a significant role on the sea level variations. Such a result was also indicated by Ahmad and Sultan (1993), Sultan et al., (1995 a,b) and Maghrabi (2003).
The correlation coefficients were also calculated between the daily- averaged residual sea level record and each wind stress component for 50 days segments corresponding to early winter, early summer and late fall (Table 2). The calculations showed that during the early summer the residual sea level was significantly correlated with both along-shore and cross-shore components of wind stress with coefficients (+0.5367) and (+0.5010). This indicates a significant contribution of both components of wind stress to the variation in the sea level during the early summer.
Fig. 6. Cross-shore wind stress and Residual Sea Level at Jeddah for the year 2000.
0 50 100 150 200 250 300 350 400
-0.5 0 0.5
SeaLevel (m)
Days in Year 2000
0 50 100 150 200 250 300 350 400-0.2
0 0.2
Cross-Shore Wind Stress (Nm-2 )
Fig. 7. Along-shore wind stress and Residual Sea Level at Jeddah for the year 2000.
Correlation coefficients were also calculated between the residual sea level record and the atmospheric parameters for the periods corresponding to the late-winter to late-spring and the late-summer to early-fall (calculations not shown in Table 2). For the late-winter to late- spring period , the correlation coefficients between the residual sea level and evaporation rate, atmospheric pressure, cross-shore wind stress and along-shore wind stress were (−0.0880), (+0.2710), (+0.2910) and (+0.3837) respectively. For the late-summer to early-fall period, the correlation coefficients between the residual sea level and evaporation rate, atmospheric pressure, cross-shore wind stress and along-shore wind stress were (−0.1872), (+0.2141), (−0.1478) and (+0.3678) respectively.
Based on these calculations, the along-shore wind stress component seems to have the strongest influence on the sea level variations among the atmospheric parameters during both periods. The contribution of cross-shore wind stress to the sea level variations is more significant during the late-winter to late-spring period than during the late-summer to early-fall period. The positive correlation coefficients between the residual sea level and the atmospheric pressure for the two periods do not indicate the typical inverse relationship. Evaporation rate seems to have stronger influence on the sea level variation during the late-winter to late- spring period than during the late-summer to early-fall period.
0 50 100 150 200 250 300 350 400
-0.4 -0.2 0 0.2 0.4
SeaLevel (m)
Days in Year 2000
0 50 100 150 200 250 300 350 400-0.2
-0.1 0 0.1 0.2
Along-Shore Wind Stress (Nm-2 )
Attempts were also made, in this study, to fit the full (year 200) data sets as well as the 50 days data segments into Multiple Linear Regression Models using the following equation:
ܻ=ܤ+ܤଵ ܺଵ+ܤଶ ܺଶ+ܤଷ ܺଷ+ܤସ ܺସ
Where B0, B1, B2, B3 and B4 are coefficients of the multiple linear regression model; Y, X1, X2, X3, and X4 are Daily values of seal level residual, evaporation rate, atmospheric pressure, cross-shore wind stress and along-shore wind stress, respectively.
In Fig. 8 and Fig. 9, comparisons are shown, as an example, between the residual sea level and sea level obtained through the multiple linear regression model for the first 50 days segment corresponding to the early winter. Table 3 shows the obtained coefficients of the linear regression models for the different data sets, as well as the corresponding statistical parameters. For the first, middle and last 50 days, the coefficients for evaporation terms were significantly small in value (range = −0.004
−0.006). For the first and last 50 days, the larger negative values of the coefficients for the pressure terms indicate the typical inverse relationship. The coefficient values for the wind stress terms were significantly larger for the middle 50 days. These results are in agreement with results of the correlation analysis (Table 2), which indicated that during the early winter and the late fall, pressure plays the most significant role in influencing the sea level variations; while during the early summer the wind stress components are the only factors significantly contributing to the sea level variations.
Fig. 8. Residual Sea Level and the Sea Level Obtained Through Multiple Linear Regression Model for the Early Winter of the Year 2000 at Jeddah.
0 5 10 15 20 25 30 35 40 45 50
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Days in Year (2000)
Sea Level (m)
Early Winter
Residual Modeled
Fig. 9. Comparison between Residual and Multiple Linear Regression Fitted Sea Level for the Early Winter of the Year 2000 at Jeddah.
Table 3. Coefficients and statistical parameters obtained using multiple linear regression analysis for the different data sets.
Data Set Coefficients Statistics
B0 B1 B2 B3 B4 R2 F-Stats P-Value
Full Data −10.1900 0.00009 0.010155 −0.13591 1.1428 0.2095 23.9171 0.00000 First 50 Days 44.1778 0.00539 −0.04357 −0.17651 −0.56701 0.4693 10.1676 0.00001 Mid. 50 Days −4.25990 0.00601 0.004142 1.1338 0.89876 0.3897 7.34360 0.00012 Last 50 Days 46.1223 −0.0045 −0.04540 0.27712 −0.15119 0.5272 12.8246 0.00000
Conclusions
Tides account for a small percentage (16.7%) of the total variations of the sea level at Jeddah near-shore area. This is due to the fact that Jeddah is located relatively close to the Red Sea amphedormic point of the M2 tidal constituent which is the most dominant tidal constituent.
Correlations between the residual sea level record and some of the atmospheric parameters indicated that these parameters can account for major portion of the variations in the sea level record during certain times. Pressure seems to be the most significant atmospheric parameter that influences the sea level variations during early winter. During late
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 -0.5
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Modeled Sea Level (m)
Residual Sea Level (m)
Early Winter
fall, all investigated atmospheric parameters have significantly contributed to the sea level variations with the highest contribution by pressure and almost equal contribution by both evaporation and the cross-shore wind stress component. For the early summer, the contribution of evaporation is less by about 50% (compared with late fall), atmospheric pressure have no contribution and both wind stress components significantly contributing to the variations in the daily- averaged residual sea level. Somewhat similar results were also obtained through fitting the data segments into multiple linear regression models.
Acknowledgments
The author would like to express his thanks to Saudi Aramco for providing the sea level data, to PME for providing the atmospheric data and to Prof. Fazal Ahmad for reviewing the manuscript.
References
Abdallah, A.M. and Eid, F.M. (1989) On the Steric Sea Level in the Red Sea. Int. Hydrog. Rev., Monoco, 66: 115-124.
Ahmad, F. and Sultan, S.A.R. (1993) Tidal and Sea Level Changes at Jeddah, Red Sea. Pakistan Journal of Marine Sciences, 2(2): 77-84.
Beardlsley, B. and Pawlowicz, R. (1999) Air_Sea Toolbox for Matlab®.
http://woodshole.er.usgs.gov/operations/sea-mat/air_sea-html/index.html.
Edwards, F.J. (1987) Climate and Oceanography in Red Sea. Eds.: Edwards, F. J. and Head, S.
M. Pergamon Press, 45-68.
Eid, F.M. and Kamel, M.S. (2004) Contribution of Water Density to Sea Level Fluctuations in Red Sea. JKAU: Mar. Sci., 15: 113-138.
Herting, A., Farmer, T. and Evans, J. (2004) Mapping Evaporative Loss from Elephant Butte Using Remote Sensing and GIS Technology. New Mexico State University. 31 p.
Maghrabi, S.O. (2003) Variations of Mean Sea Level in the Red Sea. Master Thesis. King Abdulaziz University. 98 p.
Pawlowicz, R., Beardsley, B. and Lentz, S. (2002) Classical Tidal Harmonic Analysis Including Error Estimates in MATLAB Using T_TIDE. Computers and Geosciences, 28: 929-937.
Smith, S. (1988) Coefficients for Sea Surface Wind Stress, Heat Flux, and Wind Profiles as a Function of Wind Speed and Temperature, J. Geophys. Res., 93(C12): 15467-15472.
Sultan, S.A.R., Ahmad, F. and Elghribi, N.M. (1995-a) Sea Level Variability in the Red Sea.
Oceanologica Acta, 18(2): 607-615.
Sultan, S.A.R., Ahmad, F. and El-Hassan, A. (1995-b) Seasonal Variations of the Sea Level in the Central Part of the Red Sea. Estuarine, Coastal and Shelf Science, 40: 1-8.
Sultan, S.A.R. and Ahmad, F. (2000) Annual and Semi-annual Variations of Sea Level at Jeddah, Central Coastal Station of the Red Sea. Indian Journal of Marine Sciences, 29(3):
201-205.
Sultan, S.A.R. and Elghribi, N.M. (2003) Sea level Changes in the Central Part of the Red Sea.
Indian Journal of Marine Sciences, 32(2): 114-122.
. .
.
. ! "# $ % &'#
"(
, " ) .
*
* )
! + ,!
- ./01 (
% 2 "# "3
.
3 2 "#
. .
4 # 2 562 3 40 /# 7
8#
.* 2 9# + "3 9 : .
40 /#
;3 . .2 &'# +3 7 <= /# "
4 # .
% * > & 1 3 &'#
3 % ! > & 1 3 * . .2 . .2 > & 1 3 %3 &'# 7?*
40 /#
.
