Modelling Hydrodynamics for Water Quality of the Dwarka Region (Gujarat)

Rohit Goyal Environmental Science and Engineering Department, Indian School of Mines

Dhanbad, India. rohitgoyal1690@ismu.ac.in

Abstract-Hydrodynamic (HD) modelling is a prerequisite to environmental/ecological modelling; as it influences the biological and chemical processes .The flow determines the expected variations in water quality. Water quality can be impacted by the magnitude of flow, which dilutes loadings; the travel time, which affects the amount of material that can be produced or degraded; and the degree of mixing, which affects chemical gradients. Thus, the flow, the velocity, and the degree of mixing affect the assimilative capacity of streams and rivers. The present study aims at modelling the flow patterns prevailed off Dwarka during the period 05/12/2007 -05/01/2008. Measurements available for the above seasons have been used for the validation of model results. Based on the simulation results, circulation pattern off Dwarka is observed. Spatial and temporal variations of Dissolved Oxygen (DO) and Biochemical Oxygen Demand (BOD) in Rupen Bandar, Dwarka, India are assessed based on data collected since 1976.

Keywords: Hydrodynamic Modelling, Water Quality (Eutrophication), Mike 21

I. INTRODUCTION Coastal zone, the interface of land, ocean, and

atmosphere, is clearly of major economic and social importance. It is defined as the region from the 200m water depths at the sea to the 200m elevations on the land. The vulnerability of the coastlines and coastal resources due to adverse impact from natural hazard events, pollution due to industrial discharges, etc. remind us to have a wise and sustainable management of coast and coastal resources.

The coastal waters around Indian subcontinent are affected by the seasonally reversing winds which are very unique. During winter monsoon, currents along the WCI flow against the winds blowing from northeast. The surface currents were found to be pole ward in direction during the north east (NE) monsoon which is in contrast to the equator ward currents in the summer monsoon. The presence of this pole ward current was confirmed by the existence of fresher, warmer and lighter waters of the southern origin in the northern Arabian Sea along the WCI. During the winter season, the surface water became cooler, saltier and hence, denser towards north due to which that the warm, low saline water is spreading towards north. [1]

During the summer monsoon, there is an eastward current flow from the western Arabian Sea to the Bay of Bengal named Summer Monsoon Current (SMC) and during the winter monsoon the flow is westward, from the eastern boundary of the Bay to the western Arabian Sea, Winter Monsoon Current (WMC). The transfer of water mass in

Indian Ocean takes place because of these current. The mean tidal range along the west coast is 0.9 m in the south to 1.8 m in north. The change in sea level due to tides is much greater than that due to weather conditions along the WCI.

Spatial and temporal changes in water surface topography in coastal region is a response to the balance of pressure gradient forces (PGF) with combined effects of irregular bathymetry (e.g. sandbars, channels), varying bed resistance (dependent on depth, grain size, bed-forms), wave effects (run-up and set-up) and freshwater discharge. of hydrodynamics of coastal areas is that, it is the flow direction and speed that determines primarily the advection-dispersion of materials, sediment transport, transport of sewages, spreading of oil spill, fish larval transport, etc[2] .

The model used for the simulation of flow is the hydrodynamic module of MIKE21. The HD module can be used for studying the transport of pollutants and thermal plumes in rivers, estuaries and coastal regions. The model can incorporate flooding and drying conditions of land, and thus the areas that are prone to continuous flooding and drying can be treated more realistically.

HD modelling uses the concepts of scales of motion, dimensionality of flow, physical processes and forcing mechanisms [3]. In the coastal region where the bathymetry gradient is high, models and observations demonstrate that near-shore circulation is complex, even on beaches with relatively simple bathymetry. Modelling also uses coupling between near-shore waves, currents, and the changing bathymetry which shows variations in the near-shore bathymetry result from feedback between the driving forces and morphologic change [4]. In addition to predominant circulation due to currents, turbulent shear flows and eddies, instabilities, and both wave and wind forcing are also included.

Taking into account all these factors, the objectives of the study are framed as follows:

• To simulate tide-driven currents along the central WCI.

• To simulate water level and flow off Dwarka Region

• To quantify the flow velocity and analyze the circulation pattern and its seasonal variations.

• To quantify the Water Quality Models (BOD and DO) of the Dwarka region.

Study Region

Dwarka is a coastal district of Gujarat having hot and

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3) Water Level

Tidal levels with appropriate phase lag and no cross flow conditions are used at the boundaries to simulate prevailing flow conditions. Tidal level at two locations, one at the northern boundary of the domain, Mithapur (22°29’ N, 70° E), and another at the southern boundary, Miyani (21°30’ N, 70° E), are generated using the MIKE21. Our study area is a meso-tidal region (tidal range = 2-4 m). Since the tidal effect is dominant in shallow waters, the impact of tidal currents on total current along the WCI decreases towards offshore. The period of the tidal forcing used is 12.42 hrs.

Fig.3. Simulated water level at Mithapur (Dec 2007-January 2008)

Fig.4. Simulated water level at Miyani (Dec 2007-January 2008)

4) Wind

When wind blows over the surface of the ocean, the momentum from the wind is transferred to the water via the wind stress. During the month of December and January, the prevailing surface wind is from north that drives the ocean surface water southwards. The wind stress force of wind gives the ocean an initial velocity in the direction of the wind, but the Coriolis Effect due to the earth's rotation exerts an acceleration proportional to velocity and at right angles to the direction of motion [7] .

In MIKE21, the driving force due to wind blows over the model area is calculated from the quadratic law as

Where Cw is the wind friction coefficient, ρ is the density and W is the wind velocity (in m/s) which is 10 m above the sea surface. Wind friction coefficient for strong and moderate wind is usually 0.0026, whereas smaller coefficient 0.0013 can be used for weak winds

Fig: 5. Blended wind Direction (Dec 07-Jan 08) at Dwarka

Fig: 6. Blended wind speed (Dec 2007-Jan 2008) at Dwarka

The recorded wind speed and direction of Autonomous Weather Station (AWS) at Dwarka were available for every ten minutes and the measured wind data is compared with blended wind data.

5) Current

Current data is obtained from the Recording Current meter (RCM) deployed at two depths, 30 m and 15 m located at 22°05’ N, 69°04’ E and 22°04’ N, 69°05’ E, respectively off Dwarka [8] .The data was available for the period 5/12/2007 to 5/01/2008. The current meter records speed and direction (θ) of currents at the mooring location, from which the u and v-components are calculated for validation of the simulated currents.

Fwind = Cw(ρair / ρwater)

Dwarka

Fig 2. Bathymetry of Dwarka Region

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U = east-west current (east is taken as positive and west is taken as negative).

V= north-south current (north is taken as positive and south is taken as negative). 6) Other Parameters Used

TABLE 1. SHOWS BASIC AND HYDRODYNAMIC PARAMETERS USED

Parameters Selection and values

Module selection Hydrodynamics only

Bathymetry Central west coast of India

Simulation period 05-12-2007 (05:30 h)– 05-01-2008 (05:30 h)

Open Boundaries West, North, and South

Flooding and drying Flooding :0.3 m, drying: 0.2 m (depth)

Eddy viscosity 0.5 (Smagorinsky constant)

Wind friction 0.0026

Bed resistance File with varying bed resistance

7) Modelling of BOD and DO

a) Input parameters for Ecological Modelling

Parameters

Module Selection

Model Mike 21/3 WQ Simple

Integration Euler Method

Frequency 4 Time Steps

Initial BOD 2.7 mg/l

Initial DO 6.45 mg/l

Temperature 25 degrees

Salinity 36psu b) Mathematical Formulations [4]

The MIKE 21/3 Ecolab solves the system of differential equations describing the physical, chemical and biological interactions involved in the survival of bacteria, degradation of organic matter, resulting oxygen conditions and excess levels of nutrients in coastal areas. Several combinations of the listed variables are implemented as “model levels” securing maximum flexibility. In this project only BOD and DO are modelled. Dissolved Oxygen (a) Oxygen processes

Reaeration=K3*(Cs−DO)

Pmax*F1 (H)*cos2Π (τ/a)* �1^ (T-20), if τ � (tup, tdown)

Photosynthesis=

0, otherwise

Respiration=R1*F1 (H)*F (N, P)* �1^ (T-20) +R2* �2^ (T-20) (level 4)

BOD decay=K3*BOD*�3^ (T-20)* (DO/DO+HS_BOD) (One fraction of BOD)

Where,

IN = sum of inorganic nitrogen (mg N/l) S = salinity (pot) T = temperature (°C) Wv= wind speed (m/s) H = water depth (m) V = depth averaged flow velocity (m/s) NH3 = concentration of ammonia (mg/l) K4 = nitrification rate at 20°C (1/day) θ4= temperature coefficient for nitrification Y1 = yield factor for oxygen Photo = actual production (g O2/m2/day) Pmax= maximum production at noon (g O2/m2/day) τ = actual time of the day related to noon α = actual relative day length tup, down = time for sunrise and sunset Respiration = actual respiration rate of plants, bacteria and

(g O2/m2/day), R1= photosynthetic (autotrophic) respiration rate

at 20°C (g O2/m2/day) θ1= temperature coefficient for photosynthetic

respiration/production R2= respiration rate of animals and bacteria matter

(mg O2/l)

(b)Biological oxygen demand processes

BOD decay=-K3*BOD* �3^ (T-20)* (DO/DO+HS_BOD)

BODd decay=-Kd3*BODd* � d3^ (T-20)* (DO/DO+HS_BOD)

BODs decay=-Ks3*BODs* � s3^ (T-20)*(DO/DO+HS_BOD)

BODb decay=-Kb3*BODb* �b3^ (T-20)(DO/DO+HS_BOD)

Where,

T = temperature (°C) K3= degradation constant for organic matter at 20°C

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(l/day) θ3= Arrhenius temperature coefficient DO = Actual oxygen concentration (mg O2/l) HS_BOD = Half-saturation oxygen concentration for BOD (mg O2/l) BOD = actual concentration of organic matter (mg O2/l) BODd = actual concentration of suspended organic

matter (mg O2/l) BODs = actual concentration of suspended organic

matter (mg O2/l) BODb = actual amount of sedimentated organic matter

at the bottom (mg O2/l) Kd3 = degradation constant for dissolved organic

matter at 20°C (l/day). Normally suspended BODs will have a slower degradation rate than dissolved BODd.

θd3= Arrhenius temperature coefficient (dissolved BOD) Ks3= degradation constant for suspended organic

matter at 20°C (1/day). Normally suspended BODs will have a slower degradation rate than dissolved BODd.

θs3= Arrhenius temperature coefficient (suspended BOD)

Kb3 = degradation constant for sedimentated organic matter (l/day)

θb3= Arrhenius temperature coefficient (sedimentated BOD)

S1= resuspension rate for BODb (m/day)

B. Observed Meteorological Conditions at Dwarka[2] Time-series of surface meteorological parameters

from Dwarka has been measured at 10-minutes interval from the terrace of Hotel Guruprerna (Lat: 22° 14.508’ N; Long: 68°57.975' E) for a period of 30 days, from 5th December 2007 to 5th January 2008. Wind was vector-averaged. Gust (maximum wind speed within every 10-minute sampling) was also recorded. Thus, the 'gust' value recorded is the largest wind speed amongst an ensemble of 60 samples that have been detected during the 10-minute sampling span.

1) Wind

The maximum 10-minutes vector-averaged wind observed during the 30 days measurement was = 3 m/s

Fig: 7. [a]Ten minute vector averaged wind,[b]gust, and [c]Gust-wind

ratio in Dwarka during 05/12/2007-05/01/2008.

Fig 8. Scatter 10 min plot vector averaged wind over Dwarka during 30

days from 5th Dec 2009 to 5th Jan 2010.

2) Barometric Pressure

As expected from astronomical considerations, the barometric pressure is semidiurnal. Ten-minute averaged barometric pressure at Dwarka during 04 days from 5th December 2007 to 5th January 2008 (Fig.9) indicates that the semi-diurnal oscillations are modulated by weekly oscillations. A sharp dip in pressure around Julian day 345 (11th December 2007) is in association with a meteorological disturbance as is clearly seen by the corresponding fluctuations in speed and direction around this day.

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Fig 9. [a] Ten-minute averaged barometric pressure at Dwarka during

30 days from 5th Dec 07 to 5t h Jan 08; [b] daily-mean pressure.

3) Air Temperature

As expected from day/night variability in solar radiation, the observed air temperature is diurnal. Ten-minute averaged air temperature at Dwarka during 30 days from 5th December 2007 to 5th January 2008(Fig.10) indicates that the diurnal oscillations are modulated by some lower frequency oscillations.

Fig:10. [a]. Ten-minutes averaged air temperature at Dwarka during 30 days from 5th December 2007 to 6th January 2008; [b] daily-

mean temperature.

4) Relative Humidity

The observed relative humidity is diurnal. Ten-minute averaged relative humidity at Dwarka during 30 days from 5th December 2007 to 5th January 2008 indicates that a sharp dip in pressure around Julian day 345 (11th December 2007) in the association with a meteorological disturbance around this day is manifested also in the relative humidity in the form of a peak high around this day.

Fig. 11. [a] Ten-minutes averaged relative humidity at Dwarka during 30 days from 5th December 2007 to 5th January 2008; [b] daily-

mean relative humidity

C. Model validation 1) Validation for water level

Water level measurements are available for the period 5th Dec 2007 to 5th Jan 2008 and for this period simulated values were validated.

Fig 12: Comparison between measured and simulated water levels off Dwarka

2) Validation for current

The current meter data at 15 m and 30 m off Dwarka region have been used for validating the simulated currents during the study period.

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Fig 13: Shows comparative analysis between modelled and measured u and v component at 15m and 30m depth.

D. Simulation of hydrodynamics The MIKE21 HD runs with fresh inputs (cold start).

Therefore, velocity field is initialised to zero as an initial condition for starting the simulation. The digitised, interpolated bathymetry file was uploaded as input. The projection zone of the study area in UTM-42 is also provided. Coriolis forcing was given by

The simulation covered a total number of 89280 time

step, each having an interval of 10 s so that one full month simulation could be obtained. The initial surface level is set to a constant value applied over the whole model area by which the simulation will start. Cold start with U=V=0 is taken as the initial condition. The boundaries are automatically detected from the bathymetry file. Line series of water levels are applied on the west, south and north open boundaries. Surface elevation was specified at each time step at the open boundaries as sinusoidal tidal forcing function with a period 12.42 h. Wind conditions are incorporated in the model by uploading wind file of the Dwarka station, and assuming that the wind prevails constant over space. Wind friction coefficient, which is a function of wind speed, used is 0.0026. When all the input files are ready, the program will automatically validate all the inputs after which the model can start simulation. The simulation time taken is ~1 h. Altogether there are 739 time steps, having a time step of 3600 s.

III. RESULTS AND DISCUSSIONS The model was run for two conditions : 1) with wind

2) and without wind,

for the months December 2007-January 2008.

A. Water Level During December-January, the maximum water level is

found to be nearly 2.5 m with an average spring tidal range of 1.9 m and neap tidal range of 1.2 m.The currents are varying with the water level variation. Higher the water level, stronger is the current speed[9] . The water level along Dwarka coast in wind conditions shows the maximum tidal range of ~2.3 m. The water level in ‘No Wind’ conditions has a maximum tidal range of ~2.6 m.

B. Currents The current speed during ebb tide is stronger than the

flood tide since the wind driven currents are also in the same direction. During ebb tide, the predominant flow is towards south and during the high tide flow is towards north [10]. Tidal currents in the longshore direction is oscillating with little cross-shore current. The onshore and offshore currents (u-component) were meagre compared to the alongshore currents (v-component), irrespective of the period of simulation. The current slows down just before current reversal takes place. There will be no contribution by the fresh water discharges during NE monsoon period, but some contribution is expected during SW monsoon period, but that will be very minimal. The net longshore current is found to be southward during December-January. The current meter deployed at 15.6 m as well as the simulated output shows that, the alongshore component of velocity goes on decreasing towards the coast. This is due to increase in bed friction.

Fig 14: Current flow during flood tide

f =2ΏsinΦ, Φ~17°

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Fig: 15: Bathymetry at Ebb Tide

The magnitude of southward flow is higher than that the northward flow. During January, the prevailing wind is southwards. The maximum current speed during this period is around 0.355 m/s with southeast direction. This is the reason why the upwelling phenomenon is absent during the NE monsoon. In the present study, even without including the density effects, the simulated current matches well with the measurements obtained from RCM deployed at 35 m (~ 5 km seawards from shoreline).

C. Circulation The circulation of waters on the shelf region is

characterized by complex pattern of currents [11]. The circulation in the WCI is dominated by the WICC. The WICC moves against weak alongshore wind component during the NE monsoon. Since the study domain is a coastal region, the density driven currents have least significance. The main parameters that frame out the flow in the present study are winds and tides.

Model results are in good agreement with the measurements which indicate that the flow is primarily by winds and tides. The prominent circulation pattern off Dwarka is southward, irrespective of seasons [12]. But, the intensity of flow is relatively higher during the SW monsoon period. The u-component of current (zonal) is too feeble to have a considerable impact on the circulation pattern.

The flow pattern also shows that apart from wind and tide, the bathymetry also plays a crucial role in driving the water since bathymetry shows an upward slope to the north

[13]. The WICC is having a poleward component during the NE monsoon which is contributed mainly by the equatorially trapped Rossby and Kelvin waves as well as coastally trapped Kelvin waves [14]. But the poleward flowing WICC becomes weaker with the increase in latitude. This might also favour the southward flow during NE monsoon as evident by the measured currents.

D. BOD and DO The values of BOD (Biological Oxygen Demand) and

DO(Dissolved Oxygen) obtained at the observation site were compared on the basis of the water quality criteria set by Central Pollution Control Board (CPCB) of India [It was constituted under section 3 of the ‘Water prevention and control of pollution Act’, 1974.]

Results were obtained by considering two cases

Case 1: when BOD is taken 2.7 mg/l

Fig 16: DO and BOD analysis of Dwarka at 15m and 30m depth for a

period 5/12/2009-5/12/2010.

After Simulation of the model the computed values were as follows

DO: Concentration 2.0-6.3 mg / l which was according to CPCB criteria was a drinking water source after conventional purification methods are applied. It was consistently increasing after a drop with a few uphill’s and downhill’s which was due to variations in temperature and pressure as shown in Fig 17.

Fig 17: DO variations for 15m and 30m depth for a period 5/12/2009-

5/12/2010.

BOD: Concentration was <2.8 mg/l which also confirmed it as drinking water after conventional treatment. It consistently decreased to Zero as shown in Fig 18.

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Fig 18: BOD variations for 15m and 30m depth for a period 5/12/2009-5/12/2010.

Case 2: when BOD is taken 5.4 mg/l

Fig 19: DO and BOD analysis of Dwarka at 15m and 30m depth for a

period 5/12/2009-5/12/2010 for case 2.

After Simulation of the model the computed values were as follows:

DO: Concentration 2-6.3 mg / l which was according to CPCB criteria was a drinking water source after conventional purification methods are applied. It was consistently increasing after the drop.

BOD: Concentration was <5.4 mg/l which according to CPCB can neither be designated it as drinking water after conventional treatment nor for irrigation and industrial cooling. From the Fig 19 it was clear that with decrease in BOD, DO was increasing. As compared to Case 1. The decrease in BOD in case 2. was much gentle.

IV.CONCLUSIONS The study examines the hydrodynamics of Dwarka

coastal region using MIKE21 HD model. Results obtained from model simulation matched very well with the measurements. Hence, the model was further used for the simulation of hydrodynamics for other months also. The simulated hydrodynamics reasonably agreed with most of the earlier studies. The tidal flows were modelled accurately on coarse grids since they were large-scale processes. The water level showed very marginal seasonal variation. But, it was the current that have marked seasonal pattern of flow. The model has provided a general understanding of the surface flows off the Dwarka region. The reason for variability of currents from the actual measurements may be due to the usage of lower resolution bathymetry and limitations of the model to generate precise HD of the region. The Hydrodynamic results can be further used to study a wide range of phenomena related to hydrodynamics, such as water quality, heat and salt transport and sediment transport processes.

The Model also provided specifications of the water quality off the Dwarka region. Seasonal variations were

observed which may be due to variations in temperature and pressure. A good understanding of circulation of currents was required as it changes DO and BOD values and also salinity etc. Result showed that water quality of the region is good.

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