Simultaneous solution for water, heat and salt balances in a Mediterranean coastal lagoon (Mar Menor, Spain)

Estuarine, Coastal and Shelf Science 91 (2011) 250e261

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Simultaneous solution for water, heat and salt balances in a Mediterranean coastal lagoon (Mar Menor, Spain) V. Martínez-Alvarez*, B. Gallego-Elvira, J.F. Maestre-Valero, M. Tanguy Technical University of Cartagena, Paseo Alfonso XIII, 48, 30203 Cartagena (Murcia), Spain

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 April 2010 Accepted 29 October 2010 Available online 6 November 2010

A modelling approach is proposed to evaluate the environmental dynamics of coastal lagoons. The water, heat and salt balances are addressed simultaneously, providing a better estimation of evaporation and water exchanges. Compared to traditional approaches, the model presented accounts for the effects of water salinity, heat storage and net energy advected in the water body. The model was applied daily to the Mar Menor coastal lagoon (SE Spain) from 2003 through 2006. Water exchanges with the Mediterranean Sea were estimated based on the monthly trend of the lagoon salinity and were correlated with monthly averages of wind speed. The mean daily water exchange with the sea was 1.77 hm3 d
1. This exchange accounted for only 1% of the heat losses in the lagoon heat balance, and it is the most important flow in the water balance. The mean annual evaporation flux amounted to 101.3 W m
2 (3.55 mm d
1), while the sensible heat flux amounted to 19.7 W m
2, leading to an annual Bowen ratio on the order of 0.19. To validate the model, daily water temperatures were predicted based on the daily heat balance of the water body and were compared with remote sensing data from water surface standard products. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: evaporation heat storage remote sensing surface temperature water exchange

1. Introduction Coastal lagoons are confined systems partially or totally isolated from the open sea by coastal barriers. Mar Menor is a large shallow hypersaline coastal lagoon located in Southeast (SE) Spain with a few connecting channels. In hypersaline coastal lagoons evaporation exceeds rainfall plus freshwater inflow, as is the case with Mar Menor. This causes the negative water balance to be compensated for by marine and/or groundwater exchange. Over the last 40 years, many Southern European lagoons have experienced severe water budget and quality problems as a result of increasing anthropogenic pressures, such as mass tourism urbanization and industrial and intensive agricultural pressures on their shores and catchment areas (Viaroli et al., 2005). Eutrophication or changes in the lagoon water temperature and salinity are common consequences of anthropogenic impacts or even global climatic change trends (Eisenreich, 2005). Mar Menor is a clear example, as it has undergone variations in the quantity and quality of the lagoon freshwater inputs and a manmade improvement of sea connections in recent decades. Most recently, the decline in Mar Menor’s water quality has been related to the increased of nutrient

* Corresponding author. E-mail address: [email protected] (V. Martínez-Alvarez). 0272-7714/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ecss.2010.10.030

influx into the lagoon from agricultural sources (Pérez-Ruzafa et al., 2005; García-Pintado et al., 2007). Water temperature is a major water quality parameter of paramount ecological importance for lagoon ecosystems (Harley et al., 2006). It is the result of the heat balance, which is linked to the water balance through several fluxes, including evaporation, rainfall, streams and groundwater exchanges. Evaporation is one of the main components in both heat and water balances. Additionally, estimates of evaporation rates of saltwater bodies, such as coastal lagoons, are needed to properly assess the salt balance (Mudge et al., 2008). Evaporation depends on the vapour pressure deficit between the evaporating surface and the overlying air, which in turn depends on meteorological factors such as air temperature, relative humidity and wind speed (Penman, 1948; Brutsaert, 1982; Valiantzas, 2006). Water body characteristics such as size, shape and depth also affect the evaporation rate (Martínez-Alvarez et al., 2007). For saltwater bodies in particular, it is important to consider that the evaporation rate decreases with the increase of water salinity as a consequence of the reduction in water vapour pressure at the water surface (Oroud,1999; Kokya and Kokya, 2008). Another important consideration when studying evaporation in large lakes and lagoons is the water body’s seasonal variation of heat storage (De Bruin, 1982; Finch, 2001). Therefore, in saltwater bodies, it is not possible to accurately predict the evaporation unless the water, heat and salt balances can

V. Martínez-Alvarez et al. / Estuarine, Coastal and Shelf Science 91 (2011) 250e261

be addressed simultaneously. An approach for the simultaneous solution for the three balances was first proposed by Assouline (1993) for estimating the evaporation and saline spring components in the solute and water balance of Lake Kinneret (Israel). Later, other methodologies were presented by Rimmer and Gal (2003) and Lensky et al. (2005) for similar purposes. However, there are very few studies that provide a detailed insight to the dynamics of heat, water and salt balances of coastal lagoons (Kjerfve et al., 1996; Rodríguez-Rodríguez and Moreno-Ostos, 2006) and, to our knowledge, no detailed studies addressing the simultaneous solution of these balances have been published to date. The above mentioned considerations highlight the importance of more thoroughly investigating water, heat and salt balances in coastal lagoons because accurate models are essential for understanding (1) the system behaviour and (2) its reaction to possible changes in environmental conditions due to human activities or climate change. The Mar Menor lagoon has been extensively studied, with most studies focused on biological and ecological topics. Studies of the Mar Menor watershed, however, are scarce. Nevertheless, aspects relative to its geography, hydrography, geology, climate and vegetation have been studied. For further information on these topics the reader is referred to Mas (1996); Rosique (2000); Martínez et al. (2004) and FIEA (2009). Groundwater systems have also been recently studied and modelled in the area (Rodriguez-Estrella, 2004; FIEA, 2009). Previous work modelling the Mar Menor lagoon mainly focused on the estimation of runoff discharges and nutrient loads into the lagoon (Martinez et al., 2005; García-Pintado et al., 2007, 2009). Regarding water and salt balance modelling, the only notable prior study is the work of Carreño et al. (2005), which integrated flow component data from different sources into a static balance model of the lagoon in 2003. However, this study lacks reliable estimations of evaporation, runoff and groundwater flows, and it estimates exchanges with the Mediterranean Sea as a residual flow. The main aim of this study is to propose an original modelling approach that can be applied universally in order to assess the water, heat and salt balances simultaneously in coastal lagoons. This model predicts the water temperature based on the daily heat balance of the water body. Furthermore, the simultaneous solution for the water and salt balances enables the researcher to take into account the effect of water salinity on the evaporation rate, to

251

consider the seasonal variation of water body heat storage and to calibrate the water exchange with the sea. The modelling approach reported here was applied to the Mar Menor coastal lagoon over a 4-year period in order to assess the daily values of the heat and water balance fluxes. Special attention was devoted to improving knowledge of the evaporation and the exchange of water with the Mediterranean Sea. The model validation was carried out by comparing the predicted daily water temperatures with those derived from MODIS remotely sensed thermal imagery, applying the methodology previously proposed by other researchers (Reinart and Reinhold, 2008; Nehorai et al., 2009). 2. Materials and methods 2.1. Study site Mar Menor is a sheltered hypersaline lagoon located in SE Spain (Fig. 1). It is one of the largest coastal lagoons in the Mediterranean region as well as in Europe. The lagoon has a maximum depth of 7.0 m and a mean depth of 4.5 m. The surface area is 135.5 km2, the perimeter is 74 km and the total volume of water in the lagoon is 610 hm3. ‘La Manga’, a sandbar 23 km in length with a maximum width of 900 m, acts as a barrier between the lagoon and the Mediterranean Sea. Five shallow channels in the sandbar connect the lagoon with the open sea. The coastline is low-lying, with sandy or rocky beaches. The climate in the area is semiarid Mediterranean, with mean annual temperatures ranging from 15 to 17  C. The mean annual rainfall is approximately 300 mm with most precipitation occurring in short-episodic storm events in the autumn and the winter. The mean reference evapotranspiration, estimated by means of the PenmaneMonteith method (Allen et al., 1998), is approximately 1350 mm y
1. Thus, the net hydrologic balance of the lagoon reaches annual deficits close to 1000 mm y
1, which are compensated for by freshwater inflows and by saltwater from the sea. The Spanish Mediterranean coast has semidiurnal tides with small amplitude. The lunar tide in the study area, predicted by the CEFMO model (Legos) is approximately 0.1 m. However, daily pressure fluctuations and wind stress drive barotropic tides resulting in total daily tide amplitudes ranging from 0.2 to 0.4 m. There are also seasonal pressure fluctuations that produce small

Fig. 1. Map and bathymetry of the Mar Menor coastal lagoon, including location of the meteorological station E1 (San Javier) and the marine buoys B1 (Mar Menor) and B2 (Mediterranean Sea).

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seasonal variations in the mean level of the Mediterranean Sea but there is not a clear seasonal variability pattern. Water exchanges are regulated by differences in the sea level between the lagoon, which has no appreciable water level variations, and the open sea, which is subjected to tidal dynamics. The average lagoon water renewal time is approximately 1.2 years (FIEA, 2009) and its circulation is mainly conducted by wind (PérezRuzafa et al., 2005). The Mar Menor watershed constitutes a wide (1200 km2) sedimentary plain with sediments of Neogene and Quaternary that are slightly inclined to the Mar Menor. The main materials constituting this basin are conglomerates, marls, sandstones, slimes and clays, resulting in high soil diversity due to the heterogeneity of geologic conditions (Martínez et al., 2004). The lagoon is influenced by the watershed through surface and groundwater flows. The relative isolation of Mar Menor from the Mediterranean Sea implies that the seasonal fluctuations of the environmental factors are much more marked in the lagoon than on the marine coast. This is evident in Rosique’s (2000) review of Mar Menor data availability, which shows that while the lagoon water temperature presents a regular seasonal cycle between 10 and 11  C in January and 29 and 30  C in August, the Mediterranean Sea temperature only varies between 13 and 27  C. Furthermore, these minimum and maximum values are delayed by a month from those of Mar Menor. Salinity also presents heterogeneous temporal behaviour, with a minimum of 43 Practical Salinity Units (PSU) and a maximum of 46 in late winter and summer, respectively. The Mediterranean Sea salinity, for comparison, remains quasi-constant at 37.5 throughout the year. Salinity is presented using PSU along the paper. 2.2. Data acquisition 2.2.1. Meteorological data The meteorological data required to run the model were daily air temperature (Ta) and relative humidity (RH), precipitation (P), wind speed (U) and solar global radiation (Rs) for the period from 2003 to 2006. Data were obtained at the meteorological station of the San Javier airport (37470 12”N 0 480 08”W, height: 2 m above sea level), located at the lagoon’s northewest coast (Fig. 1). All data were measured at a height of 2 m above ground with the exception of wind, which was measured at 10 m and corrected to derive the values at 2 m following the equation proposed by Allen et al. (1998). 2.2.2. Hydrologic data The water balance inflows are precipitation, runoff and groundwater discharges, as well as incoming water from the sea. The outflows are evaporation and the outgoing water to the sea. Daily water exchanges with the sea and evaporation in the lagoon were estimated by using the modelling approach and are discussed below. Runoff and groundwater discharges were evaluated as follows. The watershed is drained by more than twenty riverbeds that are constituted by ephemeral channels. The main collector in the drainage basin (El Albujón watercourse) maintains a regular flux fed by exfiltrated groundwater, which is only continuous in the last 5e8 km, depending on the season. The baseflow in the mouth of the basin is generally around 0.02 m3 s
1 (0.63 hm3 y
1). However, during a typical storm event (return period of 5 years) the flow rapidly increased up to 10.5 m3 s
1 and returned close to its baseflow level within less than 24 h (García-Pintado et al., 2007). The total runoff discharge in the lagoon was recently estimated between 5 and 8 hm3 y
1 (MIMAM, 2007), but there are no daily records to support these data. Considering the lack of reliable records of daily runoff discharge, as well as the irregularity and

relative low impact on the water budget, this inflow was disregarded in the study (see Discussion Section). In relation to sub-surface hydrology, Mar Menor also receives subterranean flow contributions from the west, but only those belonging to the upper Quaternary aquifer, because the deeper aquifers (Triassic, upper Miocene, and Pliocene) are hydrogeologically disconnected due to the action of coastal faults (Rodriguez-Estrella, 2004). There is a coastal groundwater discharge along the contact front (30 km length, z 5 m depth) between the Quaternary aquifer and the lagoon as well as direct agricultural drainage channel discharges (Rodriguez-Estrella, 1995). The magnitude of these flows was recently estimated to be 7.6 and 18.3 hm3 y
1 respectively (FIEA, 2009). The average salinity of the Quaternary aquifer is approximately 4.5 (CHS, 1998). The piezometric network in the Mar Menor watershed (CHS, 1998) consists of 14 controlled wells with data from 1975 to the present. Their piezometric height remained stable during the last decade, resulting in a soft and constant hydraulic gradient (4.5$10
3 mm
1) that indicates that the groundwater discharge can be considered uniformly distributed throughout the year. Therefore, the groundwater discharge considered in this study was a daily constant value of (7.6 þ 18.3)/365 ¼ 71$10
3 hm3 d
1. It is assumed that this amount includes the watercourse’s baseflow (0.63 hm3 y
1) because it comes from exfiltrated groundwater. Data of water exchange with the Mediterranean Sea are available only for the major connection channel (El Estacio). Arévalo (1988) indicated that the exchange through El Estacio presented a highly fluctuant regime of currents with a frequent inversion of the direction of flows, which was regulated by the Mediterranean tidal dynamics. He further reported that the total water exchange reached a value of approximately 1.6 hm3 d
1 and was considerably higher than throughout the remainder of the channels. 2.2.3. Remotely sensed imagery data The Sea Surface Temperature (SST) data of Mar Menor and the nearby zone of the Mediterranean Sea for the period from 2003 to 2006 were obtained from the imagery provided by MODIS sensor, onboard of AQUA spatial platform. The software SeaDas 5.1 was used to process the images. Each pixel of the images has surface temperature, quality level and time of capture information. The quality level ranges from 0 for the best quality to 4 for the worst quality. For this study, only pixels with quality levels between 0 and 2 were selected. The MODIS-AQUA daily daytime images were taken in the study area between 12:30 and 14:00 GMT. The observed surface varied depending on the date and hence affected the availability of representative pixels of Mar Menor and its vicinity. Eighteen different types of images, corresponding to different satellite overpass times, were found for the study period. The number of days with available data and the mean number of pixels with information for each type of image are shown in Table 1. For each type of image, a macro was programmed to automatically filter the data and to calculate the mean temperature of the Mar Menor surface (Tw) and the selected vicinity of the Mediterranean Sea (Tw, Med). To evaluate whether the satellite temperatures between 12:30 and 14:00 GMT were representative of the mean daily temperature of Mar Menor and the Mediterranean Sea, two temperature data sets from marine buoys were used (Fig. 1). The first buoy was installed in Mar Menor and discontinuously operated during several periods from December 2001 to February 2003. The second one was installed in the Mediterranean Sea, in the vicinity of Mar Menor, and operated from July 2006 to January 2007. Fig. 2a and b depict the linear regression between the average daily temperature and the temperature at 13:00 GTM

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253

Table 1 Number of days and average number of pixels with information for each type of image during the 4 years of the study period. Image GMT Time

2003

2004

Days Mar menor

123000 123500 124000 124500 125000 125500 130000 130500 131000 131500 132000 132500 133000 133500 134000 134500 135000 135500

Total/Mean Mediterranean sea

123000 123500 124000 124500 125000 125500 130000 130500 131000 131500 132000 132500 133000 133500 134000 134500 135000 135500

Total/Mean

Pixels

2006

Days

Pixels

Days

Pixels

4.38 5.11 9.30 12.00 24.00 20.00 28.80 32.00 30.60 23.20 43.00 19.10 14.30 11.20 2.80 5.00 4.20 e

3 5 5 4 4 5 12 10 8 1 10 15 5 7 4 5 5 6

8.33 6.20 6.40 17.50 16.50 14.80 21.92 32.50 35.38 31.00 26.80 18.40 16.60 9.86 2.50 5.20 4.40 1.17

3 9 7 7 2 2 13 10 10 11 1 12 10 14 11 6 3 3

4.00 6.22 16.71 19.00 25.50 20.00 35.15 36.20 32.90 28.45 36.00 19.75 15.40 10.86 5.82 17.17 5.00 5.67

5 6 2 5 9 9 12 3 9 8 13 10 8 3 6 7 7 2

7.20 9.83 13.50 15.20 26.78 27.67 22.33 35.33 31.00 32.63 27.46 18.10 15.25 4.00 4.83 7.71 4.71 2.00

138

17.07

114

15.30

134

18.88

124

16.97

9 11 9 10 2 5 12 10 11 10 1 12 14 13 9 1 6 8

71.00 92.64 141.33 89.50 120.00 112.40 164.58 96.00 153.18 116.60 126.00 88.50 107.07 89.31 100.67 88.00 113.33 61.50

4 5 7 4 4 5 12 10 8 1 10 16 5 7 4 6 5 11

69.75 109.40 115.29 135.50 109.75 100.80 141.25 82.50 153.88 170.00 94.00 97.44 115.20 111.43 106.75 105.50 92.00 75.64

4 9 7 8 2 2 13 12 12 11 1 15 11 15 11 6 4 10

61.25 113.00 144.71 109.75 112.00 135.50 170.31 95.25 130.25 140.18 115.00 89.60 97.18 100.67 98.45 61.33 66.50 71.00

5 6 3 7 9 11 12 3 9 8 14 10 9 4 6 7 9 5

64.20 118.50 80.33 121.57 105.67 113.09 119.42 73.33 153.67 150.63 90.36 94.80 109.22 71.75 77.17 98.86 106.44 46.20

153

107.31

124

110.34

153

106.22

137

99.73

22

As is usually the case in shallow lagoons (Spaulding, 1994) Mar Menor has a well-mixed water column due to the stirring effect of wind. Previously published data indicated that there is no seasonal thermocline or halocline in the water body throughout the year (Mas, 1996; Rosique, 2000). There is, however, a small and sporadic thermal gradient during the daytime, especially in the summer, but it is

b

30 28

20

Tw at 13:00 GTM (ºC)

Tw at 13:00 GTM (ºC)

Pixels

8 9 9 8 2 5 12 10 11 9 1 13 13 13 9 1 5 e

(representative time of MODIS-SST images) in Mar Menor and the Mediterranean Sea buoys respectively. In both cases, the strong correlation (R2 ¼ 0.99) indicates that the temperature at 13:00 GTM is an excellent indicator of the mean daily temperature: the slope is practically 1 and the intersection is lower than 0.1  C.

a

2005

Days

18 16 14 12 y = 1.0028x + 0.1008 2 R = 0.992

10

26 24 22 20 18

y = 0.9994x + 0.0444 R2 = 0.999

16 14

8 8

10

12

14

16

18

Average daily Tw (ºC)

20

22

14

16

18

20

22

24

26

28

30

Average daily Tw (ºC)

Fig. 2. Linear regression between the average daily temperature and the temperature at 13:00 GTM (representative time of MODIS-SST images) in a) the Mar Menor and b) the Mediterranean Sea buoys.

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washed away due to nocturnal cooling at night. The Mediterranean Sea area close to the coast does not show water stratification either because it is characterized by low depths. Therefore the surface temperature, Ts, is assumed to represent the bulk temperature of Mar Menor and the Mediterranean Sea area close to the coast (see Discussion section). The daily remote sensed surface temperatures can thus be considered representative of the daily mean temperature in Mar Menor, Tw, and the Mediterranean Sea, Tw, Med. Tw was used for the model validation and Tw, Med was further used as input data in the modelling approach. 2.3. Mathematical modelling Free-surface evaporation is mainly driven by the vapour pressure gradient between the water surface (at temperature Ts) and the nearby surrounding air (at temperature Ta). This implies that the knowledge of Ts is a prerequisite for the calculation of the evaporation rate. The first step was to include in the modelling approach the dynamic daily heat balance assuming steady state conditions during the 1-day period. This model predicts Ts using daily averaged climate data and the geometric characteristics of the water body (surface and depth) as input data. In the case of hypersaline coastal lagoons, the effects on the heat balance of water salinity and water exchanges with the sea must be taken into account in order to accurately predict the evaporation. Thus, the second step was to set and solve the salt and water balances simultaneously with the heat balance in order to obtain Ts at a daily scale. All outputs of the model are daily averaged values. The modelling approach was solved by means of an iterative numerical scheme, programmed in Visual Basic(TM) and implemented in Microsoft Excel. The equations are given below. 2.3.1. Heat balance The heat balance model was based on the fundamental laws of physics for heat and mass exchange, following the approach used by Losordo and Piedrahita (1991), Jacobs et al. (1997) and MartínezAlvarez et al. (2007). Initial and boundary conditions were adapted to the special case of a coastal lagoon. In particular, it was assumed that thermal stratification was negligible (i.e. Ts ¼ Tw) and that the following fluxes can be disregarded due to their minor importance in the heat balance (Henderson-Sellers, 1986): 1) Heat losses by convection and conduction through the lagoon’s bed, 2) Advective heat fluxes due to precipitation and runoff or groundwater discharges (see Discussion section), and 3) Heat fluxes resulting from biological and chemical reactions. With these assumptions, the heat balance at a daily time step was expressed as:

Rn þ Hs þ lE þ QMed ¼ DQw

(1)
2


1

where all fluxes are in MJ m d . Rn is the net radiation of the water surface, Hs is the sensible heat exchanged between the air and the water surface, QMed is the heat exchanged with the Mediterranean Sea, DQw is the variation of heat in the water body occurring during the time interval, lE is the evaporation flux density from the surface, with E in kg m
2 d
1 (¼ mm d
1) and l is the latent heat of vaporization (¼ 2.45 MJ kg
1). All the fluxes have positive values when they represent heat inputs to the lagoon, and negative values when heat is lost. DQw is negative when heat is released and hence available for evaporation and positive when stored within the water column. Rn at the water surface was expressed as:

Rn ¼ ð1
aÞRs þ ð1
bÞRa
Rb

(2)

where a and b (¼ 0.030) are the short-wave and long-wave albedo of the water respectively, and Ra and Rb are the downward and upward

long-wave radiation respectively. a was taken following the cyclic monthly pattern proposed by Gallego-Elvira et al. (2010) in a 5 mdeep water body for the studied area. Ra was calculated from meteorological data with the equation proposed by the FAO (Allen et al., 1998) and Rb was calculated with the StefaneBoltzmann law. The daily evaporation rate, E (mm d
1) was derived from the knowledge of Ts by applying a mass transfer equation (Singh and Xu, 1997):

  E ¼ hv e*s
ea

(3)

where e*s (kPa) is the saturated water vapour pressure for saltwater at the temperature Tw, ea (kPa) is the actual vapour pressure of the air at 2 m, and hv refers to the daily-average convective coefficient for water vapour transfer in mm d
1 kPa
1 hv was considered to be proportional to the wind speed at 2 m, U (m s
1), and dependent on the area of the water body, A (m2), through an empirical function f (A), i.e. hv ¼ U f(A). Different formulations of f(A) can be found in the literature; we applied the function proposed by Martínez-Alvarez et al. (2007) for the study area:

f ðAÞ ¼ 0:037,log210 A
0:578,log10 A þ 3:583

(4)

The influence of water salinity in the saturated vapour pressure for saltwater, e*s , was calculated by introducing the relationship between water molar fraction, XH2 O , and water salinity, S, proposed for seawater (NaCl salt solutions) by Kokya and Kokya (2008):

XH2 O ¼ 1
5:71  10
4 S

(5)

where S is in PSU. Then XH2 O was applied to the saturated vapour pressure above pure liquid water, es (Richards, 1971):

e*s ¼ XH2 O $es

(6)

Hs was calculated as follows:

Hs ¼ hc ðTa
Tw Þ

(7)

where hc is the daily-average coefficient of convective heat exchange (MJ m
2 K
1 d
1). Assuming an analogy between mass and energy transfer, the value of hc was considered equal to hc ¼ g$hv , where g is the psychometric constant (kPa K
1). To determine QMed the following equation was applied:

QMed ¼

cw $Vin;Med $ Tw
Tw; Med A


(8)

where cw (MJ m
3 K
1) is the volumetric heat capacity of water at the temperature Tw, Vin,Med (m3 d
1) is the incoming water from the Mediterranean Sea, and Tw,Med stands for the mean daily temperature of the Mediterranean Sea (remote sensing data). The heat stored (or lost) by the lagoon, DQw, was computed through the following equation:

DT DQw ¼ cw D w Dt

(9)

where D (m) stands for the mean depth of the water body and DTw =Dt is the variation of water temperature occurring during the daily time step. 2.3.2. Water and salt balances In coastal lagoons, assuming constant water level, the daily water balance may be described using the following equations:

DV ¼ Vin
Vout ¼ 0 Dt

(10)

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Vin ¼ VP þ VR þ Vin;Med

(11)

Vout ¼ VE þ Vout;Med

(12)

where V is the volume of the lagoon (m ), Dt is the period of time over which the balance is calculated (1 day) and Vin and Vout are the inflow and outflow discharges respectively (m3 d
1). The inflow discharges are precipitation, VP, runoff and groundwater discharges, VR, and incoming water from the sea during the high tides, Vin,Med. The outflow discharges are evaporation, VE, and the outgoing water to the sea during the low tide, Vout,Med. As indicated in section 2.2.2 direct runoff inflow was disregarded in the study. Similar to the water balance, the solute balance of the lagoon can be written as: 3

V$DS ¼ VP SP þ VR SR þ Vin;Med SMed
Vout;Med S
VE SE Dt

(13)

where S is the daily salinity of the lagoon, SR ¼ 4.5 is the salinity of the Quaternary aquifer and SMed ¼ 37.5 refers to the salinity of the Mediterranean Sea. SP and SE are the salinity of rainfall and evaporation respectively, both considered equal to 0. 3. Results 3.1. Water exchanges with the Mediterranean Sea The incoming, Vin,Med, and outgoing, Vout,Med, water from the Mediterranean Sea are involved in the heat, water and salt balances. However, only coarse estimations of these discharges, not daily data, are available (Arévalo, 1988; FIEA, 2009). Therefore, the model was first run to estimate Vin,Med, and Vout,Med. Vin,Med, and Vout,Med are regulated by the Mediterranean Sea level variations, which are caused by the tides’ cycle and are strongly influenced by daily pressure fluctuations and wind stress (Candela and Lozano, 1994). The first water exchange estimation was conducted under the simplified hypothesis that Vout,Med depends only on a regular tide cycle and thus its daily value could be considered constant. The amount of water exchanged with the Mediterranean Sea markedly affects the salinity of Mar Menor. Fig. 3 depicts the salinity evolution in Mar Menor for the period from 2003 to 2006,

255

considering values of Vout,Med of 1.20, 1.70 and 2.20 hm3 d
1 and setting the salinity on the 1 January 2003 at S ¼ 44.3. A high sensitivity of the salinity evolution to Vout,Med was observed. When Vout,Med ¼ 1.70 hm3 d
1, the salinity values agreed in magnitude and timing with the reported maximum value of 46 in September and the minimum reported value of 43 in April. When the variations were 0.50 hm3, notable and progressive deviations in the salinity maximum and minimum were observed (Fig. 3). Therefore a constant Vout,Med value of 1.70 hm3 d
1 seemed to be quite robust. To analyse the wind stress influence on water exchanges, a second approach was considered. The daily Vout,Med values that make the predicted salinity fits the measured mean monthly salinity of Mar Menor were retrieved. The daily trend of salinity throughout the year was interpolated from the extant monthly data (Rosique, 2000; Pérez-Ruzafa et al., 2005). Although a daily relationship between wind intensity and Vout,Med was not found, the monthly values showed an increasing value of Vout,Med with increasing wind speed (Fig. 4). The correlation coefficient was R2 ¼ 0.24 and the value of Vout,Med corresponding to the mean annual value of U was 1.77 hm3 d
1, which is very close to the value of 1.70 hm3 d
1 obtained in the first approach. Considering these results, the next relationship was used in the model in order to estimate daily Vout,Med (m3 s
1) as a function of mean monthly wind speed (m s
1):

Vout;Med ¼ ð0:335,U þ 0:736Þ  106

(14)

The daily value of Vin,Med was calculated by solving the daily water balance (Eqs. 10e12).

3.2. Water temperature in Mar Menor The outputs provided by the model are the lagoon evaporation and water temperature and water exchanged with the Mediterranean Sea. The model validation was carried out by comparing the simulated daily Tw values with those derived from MODIS-SST images. This validation approach was considered due to the lack of direct measurements of evaporation in Mar Menor, such as water height data (water level variations as a result of water inputs and outputs are minimal) or eddy correlation technique data. Fig. 5

Fig. 3. Salinity evolution in the Mar Menor lagoon for the period 2003 to 2006, considering constant daily values of water exchanged with Mediterranean Sea of Vout,Med ¼ 1.20, 1.70 and 2.20 hm3 d
1.

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2.6

35

2.4

30

Tw satellite (ºC)

Vout,Med (m3·106)

2.2 2 1.8 1.6

25 20 15

1.4

y = 0.940x + 0.835

10

y = 0.335x + 0.736 R2 = 0.237

1.2

R2 = 0.988

5

1 2

2.5

3

3.5

4

5

4.5

10

15 20 25 Tw model (ºC)

U (ms ) -1

Fig. 4. Linear regression between monthly values of water exchanged with Mediterranean Sea (Vout,Med) and monthly wind speed 2 m aboveground (U).

shows the agreement between the predicted and the remotely sensed Tw for 2003, 2004 and 2005. During the late spring and summer, a slight overestimation of the predicted Tw was detected, which varies between þ0.5 and þ1.5  C with respect to the remotely sensed values, and this overestimation disappears in subsequent autumn days. During the rest of the year, the differences between the predicted and the remotely sensed Tw ranged between
1 and þ1  C, without any clear trend. Fig. 6 shows the regression analysis of the predicted and the remotely sensed daily values of Tw for the study period.

a

35

Fig. 6. Regression analysis between the predicted and the remote sensed water temperature (Tw) for the period 2003e2006.

A very high correlation can be observed (R2 ¼ 0.988), although the slope is a little lower than 1 (0.940) and the intersection with the ordinate axis is close to 1  C (0.835  C). If the intersection is forced to zero, the slope increases to 0.974. These results again indicate that the model slightly overestimates Tw with respect to remotely sensed Tw under high temperature water conditions, whereas the model marginally underestimates under low temperature conditions. Several error estimators were calculated to describe the differences between the daily modelled and measured Tw. The root mean square error (RMSE ¼ 0.933  C) measures both

32

2003

28

Tw (ºC)

30

Tw model Tw satellite

24 20 16 12

32 24

Tw model

20

Tw satellite

360

330

300

270

240

210

180

150

120

90

60

30

b Tw ( º C )

0

8

2004

28

16 12 210

240

270

300

330

360

210

240

270

300

330

360

150

150

180

120

120

180

90

60

32 28

Tw (ºC)

90

c

30

0

8

2005

24

Tw model

20

Tw satellite

16 12

60

30

0

8

DOY Fig. 5. Comparison of the predicted water temperature (Tw model) and the obtained using remote sensing (Tw satellite) in the Mar Menor during the years a) 2003, b) 2004 and c) 2005.

V. Martínez-Alvarez et al. / Estuarine, Coastal and Shelf Science 91 (2011) 250e261

257

systematic and random errors whereas the mean bias error (MBE ¼ 0.551  C) measures systematic errors. The low RMSE indicates a fairly good performance of the model, whereas the positive value of MBE makes clear the model’s tendency to overestimate Tw as explained above.

3.3. Mar Menor’s water balance and evaporation Table 2 displays the monthly and annual average and standard deviation of the water balance flows (Eqs. 10e12) obtained from the modelled daily values for the study period. VP, VR, and Vin,Med accounted for 5.2%, 1.0% and 93.8% of the annual inflows respectively, and VE and Vout,Med accounted for 21.6% and 78.45% of the annual outflows in the lagoon respectively. In regards to the water balance, water exchange with the sea accounted for the bulk of the water flow. Daily E of Mar Menor during the study period (data not shown) showed minimum values during the winter, with values close to 0 mm d
1 and even negative rates in some cases (i.e. condensation), and maximum values in summer, when E surpassed 10 mm d
1 in several occasions. A high temporal variability of the evaporation was observed, mainly associated with the great variability of the wind regimes in the area due to the sea exposure. Monthly averages of daily E (Table 2) indicate that the minimum E was observed in February (1.42 mm d
1) while the maximum E was observed in August (6.25 mm d
1). A time lag of two months with regard to the maximum and minimum values of Rs was observed due to the high thermal inertia of the water body. The annual E ranged between 1290 and 1340 mm y
1, with the mean value of the studied period being 1310 mm y
1.

Fig. 7. Average monthly value of the net radiation components during the study period, Rs: solar radiation, Ra: long-wave radiation, Rb: outgoing long-wave radiation, aRs: reflected solar radiation, bRa: reflected long-wave radiation. All the fluxes are in W m
2.

Table 3 displays the monthly and annual average and standard deviation of the heat balance components (Eq. (1)) for the study period, calculated from the modelled daily values. Fig. 8 presents the predicted daily values of the heat balance components for Mar Menor during the year 2003. Similar to its components, net radiation (Rn) presented the largest values in July and the lowest in December. The monthly Rn value was positive during the whole year, but the daily Rn presented some negative values during the wintertime (Fig. 8) on days with very cloudy conditions. Furthermore, the ratio r ¼ Rn/Rs was 0.58 on an annual basis, with strong differences between July (r z 0.70) and December (r z 0.20). Sensible heat (Hs) was relatively small compared to the other components. The annual average Hs was
19.7 W m
2, accounting for 16.1% of the annual heat losses. Daily Hs values (Fig. 8) showed that during the spring, summer and autumn the lagoon usually loses sensible heat because the lagoon’s temperature is higher than the air temperature. Conversely, during wintertime, positive values of Hs are frequent and the lagoon takes heat from the atmosphere. Monthly latent heat (lE) flux was the most important heat loss, accounting for 82.9% of the annual losses. Monthly lE flux increased rapidly from February to July, reaching its highest values in August, followed by a rapid decline in autumn and reaching low steady rates (z40 W m
2) in winter. lE displayed a few positive daily values in late winter and early spring (Fig. 8) when air temperature increases more rapidly than the lagoon surface temperature due to the large heat capacity of the lagoon. During these days, condensation predominated over evaporation and lE flux could be considered as a freshwater input.

3.4. Heat balance components Fig. 7 depicts the average values of the different monthly fluxes that resulted in the net radiation component. Incoming ((1eb)Ra) and outgoing (Rb) long-wave radiation were the main components of the heat balance, with mean annual rates of 349.0 and
410.9 W m
2 respectively, doubling the influx from solar radiation (Rs ¼ 208.2 W m
2). However, the long-wave components, because of their opposite signs, compensate for each other and result in a net heat loss of
61.9 W m
2. Therefore, the main source of heat was the net short-wave radiation ((1ea)Rs) with a mean rate of 194.9 W m
2. Short-wave radiation (Rs) exhibited a characteristic seasonal variation with the highest rates in July and the lowest in December.

Table 2 Monthly and annual average and standard deviation of the water balance flows during the period 2003 to 2006. The inflows are precipitation, (VP), groundwater discharge (VR), and incoming water from the sea (Vin,Med). The outflows are evaporation (VE) and the outgoing water to the sea (Vout,Med). VP (hm3) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual

SD (hm3)

VR (hm3)

SD (hm3)

Vin,Med (hm3)

SD (hm3)

VE (hm3)

SD (hm3)

Vout,Med (hm3)

SD (hm3)

5.23 4.13 4.31 2.63 2.97 0.56 0.02 2.00 3.05 2.06 7.27 7.82

5.51 2.90 3.86 1.63 2.00 0.69 0.03 3.72 2.96 3.46 4.52 6.27

2.20 1.99 2.20 2.13 2.20 2.13 2.20 2.20 2.13 2.20 2.13 2.20

0 0 0 0 0 0 0 0 0 0 0 0

50.66 49.15 60.82 65.95 73.69 74.12 77.49 76.04 65.75 61.39 48.79 51.04

8.39 6.20 12.02 16.36 21.40 9.73 8.08 11.25 5.67 10.62 12.20 4.54

5.40 5.38 9.07 14.92 19.77 22.62 26.21 26.24 19.31 13.74 8.66 6.43

1.22 0.84 1.57 2.16 3.03 1.56 1.19 1.88 1.11 1.70 1.89 0.67

52.70 50.08 58.25 55.79 59.09 54.18 53.49 53.99 51.63 51.91 49.53 54.64

5.13 4.94 5.64 1.40 5.60 4.75 1.69 2.60 1.75 3.38 2.70 3.36

42.03

7.39

25.90

0

754.89

23.62

177.70

2.82

645.27

14.45

SD: Standard Deviation.

258

V. Martínez-Alvarez et al. / Estuarine, Coastal and Shelf Science 91 (2011) 250e261

The heat exchange with the Mediterranean Sea (QMed) was very small compared to the rest of the heat balance components, amounting to only 1% of the annual losses. Only a slight heat loss was observed from March to October, when TMed < Tw, and a small heat gain was observed during the rest of the year, when TMed > Tw. Lastly, the heat storage (DQw) showed a high daily variability (Fig. 8) that is balanced between positive and negative values on an annual basis. The evolution of monthly DQw was characterized by an annual cycle with a 6-month period of heat storage (from February until July) followed by another 6-month period of heat release (from August to January).

3.5. Sensitivity analysis An important aspect of water bodies balances is the effect of uncertainty related to evaluated components involved (Winter, 1981). This uncertainty arises from a variety of sources, such as measurements’ accuracy, parameters’ calibration or other input data uncertainty (Benke et al., 2008). In order to quantify the uncertainty of the computed values of evaporation (VE) and the outgoing water to the sea (Vout,Med) a deterministic sensitivity analysis was performed. Each input data was varied within a certain range while holding the remaining parameters constant to assess the magnitude and sensitivity of the model output to small changes in the value of a certain input parameter/variable. The variables and parameters considered in the sensitivity analysis were the meteorological measurements (Ta, RH, P, U and Rs), the lagoon parameters (A, D, a and b) and the estimated groundwater discharge (VR). Their reasonable associated uncertainties intervals were: 10% in the daily values of the meteorological measurements, 10% in the values of the lagoon parameters, and 25% in the daily VR. The results of this procedure are presented in Table 4 as percent error in mean daily values of estimated VE and Vout,Med for the 4-year period considered in this study. The VE rates were most sensitive to the lagoon area estimation (A), followed by the air relative humidity (RH) and the solar radiation (Rs). The air temperature (Ta) and wind speed (U) presented intermediate sensitivity values and the rest of the parameters affected the results to a minor extent. Vout,Med exchange was overall more sensible to model input variations than VE, especially to RH, Rs and A. Besides, the uncertainty of inputs affecting directly the water balance (P and VR), to which VE was barely sensitive, produced significant errors in Vout,Med. Note that the error variation for both model outputs was quasi-linear for the considered range of uncertainties values.

Fig. 8. Daily heat balance (Eq.(1)) in the Mar Menor for the year 2003. See legend in Table 3.

This sensitivity analysis provides valuable insight into the accuracy of the final result and helps guide others to where more research is required. 4. Discussion The daily water exchanges with the Mediterranean Sea (Vin,Med and Vout,Med) were estimated based on the water balance and by forcing the model to fit the mean daily trend of the lagoon salinity throughout the year. As the salinity evolution was observed to be highly sensitive to water exchange (Fig. 3), it was interesting to analyse the sensitivity of the estimated values of Vin,Med and Vout,Med to other water balance components consideration or disregarding. The surface runoff discharge (5e8 hm3 y
1) was not considered in the water balance due to lack of data. If one assumes a uniformly distributed surface runoff inflow of 6.5 hm3 y
1, the mean daily value of Vout,Med would only decrease to 1.67 hm3 d
1 (
5.8%). However,

Table 3 Monthly and annual average and standard deviation of the heat balance components during the period 2003 to 2006. The components are net radiation (Rn), sensible heat (HS), heat exchange with the Mediterranean Sea (QMed), evaporation flux (lE) and variation of heat in the lagoon (DQw). Rn (W m
2)

SD (W m
2)

Hs (W m
2)

SD (W m
2)

QMed (W m
2)

SD (W m
2)

lE (W m
2)

SD (W m
2)

DQw

(W m
2)

SD (W m
2)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

34.2 61.3 113.5 161.5 190.9 220.7 221.0 191.7 136.2 77.8 30.4 20.3

5.5 3.5 11.3 10.5 15.4 7.3 2.6 6.6 6.3 6.5 3.9 2.6


5.8
9.1
11.9
28.4
34.4
28.9
30.2
25.5
22.3
19.3
15.2
5.3

5.6 4.3 8.9 0.8 5.3 5.7 2.8 2.6 3.3 2.2 2.3 5.9

2.09 1.33
0.56
2.71
4.15
4.51
4.40
3.20
1.76
0.45 1.32 2.39

0.34 0.58 0.50 0.91 0.73 1.04 0.67 0.32 0.49 0.40 0.36 0.26


36.7
40.7
61.6
104.3
133.2
157.0
175.6
175.8
134.0
92.6
60.6
43.8

8.3 6.4 10.6 15.0 20.3 10.9 7.9 12.5 7.8 11.5 13.2 4.6


6.2 12.8 39.4 26.0 19.1 35.2 10.1
12.8
21.9
34.5
44.1
26.4

11.6 11.1 20.0 8.0 12.9 9.6 9.5 9.3 5.6 14.2 18.8 12.6

Annual

122.0

2.0


19.7

1.2


1.22

0.21


101.3

1.6


0.3

0.8

V. Martínez-Alvarez et al. / Estuarine, Coastal and Shelf Science 91 (2011) 250e261

259

Table 4 Sensitivity analysis results. Error in evaporation (VE) and the outgoing water to the sea (Vout,Med) for different levels of uncertainty of meteorological variables (Ta, RH, P, U and Rs), lagoon parameters (A, D, a and b) and estimated water flows (VR). Variable or parameter

Uncertainty interval

Level of uncertainty
10%


5%

Level of uncertainty þ5%

þ10%

a b


5%

þ5%

þ10%

Error (%) in VE

Error (%) in Vout.Med Meteorological variables Ta RH P U Rs Lagoon parameters A D


10%

10% 10% 10% 10% 10%


8.0 þ11.6 þ3.9
5.2
11.8


4.0 þ5.8 þ1.9
2.6
5.9

þ4.1
5.7
2.0 þ2.6 þ6.0

þ8.4
11.4
3.9 þ5.0 þ11.9


5.2 þ7.0
0.02
3.2
7.4


2.6 þ3.5
0.01
1.6
3.7

þ2.7
3.5 þ0.01 þ1.5 þ3.7

þ5.4
7.0 þ0.02 þ3.0 þ7.4

10% 10% 10% 10%


12.2 þ0.20 þ1.2 þ0.62


6.1 þ0.10 þ0.62 þ0.30

þ6.1
0.10
0.59
0.29

þ12.2
0.21
1.2
0.57


10.0 þ0.01 þ0.74 þ0.42


5.0 þ0.01 þ0.37 þ0.21

þ5.0
0.01
0.37
0.20

þ10.0
0.01
0.74
0.41


25%
0.03


10%
0.01

þ10% þ0.01

þ25% þ0.03

Estimated water flows VR

25%


25% þ5.3


10% þ2.2

not considering precipitation (VP) and groundwater inflows (VR) in the water balance would make a significant difference as Vout,Med would increase up to 2.89 hm3 d
1 (þ63.3%). These results highlight the sensitivity of the predicted values of Vin,Med and Vout,Med to the inaccuracy or underestimation of other lagoon water balance components. Disregarding surface runoff discharge seems acceptable because it is the less important water balance component and the calculated mean daily values of incoming and outgoing water (Vin,Med ¼ 2.06 hm3 d
1 and Vout,Med ¼ 1.77 hm3 d
1) are consistent with the exchange value of 1.6 hm3 d
1 reported by Arévalo (1988) for the major connection channel (El Estacio). The resulting lagoon water renewal time is 1.06 years, also in close agreement with the previously reported value of 1.2 years (FIEA, 2009). It is important to highlight that the calculated water exchanges refer to effective exchange and do not correspond to the hydraulic flows in the connection channels. The frequent inversion of the flow direction due to the Mediterranean tidal dynamics prevents incoming water during the high tides from merging completely with the lagoon water body. Part of this flow then returns to the sea during the next low tide. Therefore, the actual incoming and outgoing hydraulic flow would be higher than Vin,Med and Vout,Med. The heat balance was set assuming that the advective heat fluxes due to precipitation, runoff and groundwater discharges could be disregarded. It was also interesting to analyse the sensitivity of the lagoon water temperature, and therefore the evaporation, to this assumption. The knowledge of precipitation, runoff or groundwater water temperature is needed to properly consider them in the heat balance. This information is generally unavailable, as in the case with Mar Menor. Furthermore, these advective fluxes are generally very small compared to the others. As a result they are usually neglected in heat balance studies, particularly in studies of large water bodies (Henderson-Sellers, 1986; Sturrock et al., 1992; Stanhill, 1994; dos Reis and Dias, 1998; Winter et al., 2003; Rodríguez-Rodríguez and Moreno-Ostos, 2006; Gianniou and Antonopoulos, 2007; Momii and Ito, 2008). For instance, a 30mm rainfall event with a temperature difference of þ/
4  C with respect to Mar Menor is equivalent to a heat flux of þ/
5.8 W m
2, very small compared to the mean values of incoming and outgoing long-wave radiation (349.0 and
410.9 W m
2 respectively), solar radiation (208.2 W m
2) or evaporation (101.3 W m
2). Note also that mean annual rainfall in the area is only 300 mm. Runoff or groundwater heat fluxes are still lower than precipitation (Table 2).

þ10%
2.2

þ25%
5.3

Taking into account the minor importance of precipitation, runoff and groundwater discharges heat fluxes, the model was expected to provide satisfactory estimations of water temperature (Tw) in Mar Menor, even though the mentioned advective fluxes were neglected. In fact, a reasonably good agreement between the predicted and the remotely sensed Tw was observed (Figs. 5 and 6). The differences between them were normally lower than 1  C. This difference could be ascribed to the lack of precision of the values of Tw retrieved from remote sensing, whose accuracy was around 0.4  C (Reinart and Reinhold, 2008), and to the model’s performance. However, the characteristic overestimation of Tw during the late spring and summer (þ0.5 and þ1.5  C) does not seem to be related to model inaccuracy. A possible explanation for this could be that the cooling of Mar Menor’s surface during midday affects the values of Tw derived from MODIS-SST images (captured from 12:30 to 14:00 GMT). In agreement with this suggestion, several studies (Mas, 1996; Rosique, 2000) have pointed out a slight and sporadic vertical thermal gradient (2e3  C) during summer daytime. The model also provided a good estimation of the evaporation rate (E) of the lagoon. The mean annual E of the studied period was 1310 mm y
1. For the same period, the annual Class-A pan evaporation rate in the Mar Menor area varied from 1700 to 1800 mm y
1 (Martínez-Alvarez et al., 2008). For these values, the pan coefficient (ratio between the water body and Class-A pan evaporation rates) ranges from 0.696 to 0.736, values similar to the ones recommended in the literature for large water bodies (Linacre, 1994). The annual reference evapotranspiration estimated using the PenmaneMonteith method is also considered by many authors to be a valid reference to estimate the annual E in water bodies. Its mean annual value for the studied period at the meteorological station of the San Javier airport is 1344 mm y
1, very close to the value estimated by the model. All these values corroborate the validity of evaporation estimations provided by the model. Regarding the heat balance, the heat storage flux, DQw exhibited a clear annual cycle with a 6-month period of heat storage followed by another 6-month period of heat release. This fact explains the two-months lag phase between the time of occurrence of the maximum and minimum fluxes of Rn and lE. In the warm season, the downwelling solar radiation is absorbed throughout the water column, rather than at the surface, as is the case with other land surfaces. This heat is afterwards released during the fall, enhancing the evaporation and decoupling this term from net radiation.

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The monthly trend of the Bowen ratio, B ¼ Hs/lE, was calculated using the estimates of lE and Hs (Table 3). Monthly B was rather conservative throughout the year, varying within the range of 0.10e0.30. Daily B showed a very small variability during the warm season, while a large variability was observed for the winter months. This was due to the occurrence of negative values of B corresponding to very cloudy conditions and low available energy. The magnitude of the annual value of B (¼ 0.194) was similar to previously published estimations for large water bodies under different climate conditions, for example, 0.23 for Sparkling Lake in USA (0.64 km2, mean depth 10.9 m, Lenters et al., 2005), 0.21 for Lake Titicaca in South America (8560 km2, mean depth 105 m, Delclaux et al., 2007) and 0.19 for Lake Ikeda in Japan (10.62 km2, mean depth 125 m, Momii and Ito, 2008).

5. Conclusions The hydrologic balance of a saltwater body is linked to its salt and heat balances. Therefore an accurate prediction of the water, heat and salt balance components is only possible if these balances are addressed simultaneously. A modelling approach, based on meteorological data and water body geometry, was proposed for the simultaneous solution of these three balances in coastal lagoons. The model incorporates the effect of water salinity and heat storage in the evaporation rate, as well as the water exchange with the adjacent sea. The proposed model was used to analyse the daily environmental behaviour of the Mar Menor coastal lagoon during a 4-year period. First, the model was run to estimate the water exchanges with the sea. Mar Menor salinity is highly sensitive to the daily amount of water outgoing to the Mediterranean Sea, which ranged in the runs from 1.2 to 2.2 hm3 d
1. When the predicted salinity fit the mean salinity values observed in Mar Menor, a direct relationship with wind intensity was found at a monthly scale, confirming the influence of wind in the lagoon water circulation and water renewal time. Once water exchanges were calibrated, the model’s performance was assessed by comparing the predicted daily water temperatures with those from remotely sensed thermal imagery (MODIS-SST product). A reasonable agreement was obtained between the predicted and the remotely sensed water temperature, which suggests a satisfying simultaneous solution for heat, water and salt balances. The model presented a systematic slight overestimation of water temperature under high temperature conditions, which could be attributed to a slight cooling at the surface with respect to the mean water body temperature of Mar Menor at midday, when the satellite obtains the temperature measurement. Therefore, the hypothesis of an isothermal behaviour of Mar Menor was adequate for modelling purposes, but it produced a minor error when validating the model with remotely sensed data. Overall, the proposed approach provided a sound basis for describing and explaining the physical mechanisms underlying the water, salt and heat balances of coastal lagoons. The implementation of the techniques used in this study is straightforward and relatively cost effective to test assumptions about water salinity and water exchanges in shallow coastal systems. Furthermore, the data needed for applying the proposed methodology are standard and readily available.

Acknowledgements The authors acknowledge the Fundación Instituto Euromediterráneo del Agua (Murcia, Spain) for the financial support that made possible this study.

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