Division of Environmental and Water Resources Engineering, School of Civil and Environmental Engineering, Nanyang Technological University,Singapore
Corresponding author: E. Y.-M. Lo, Division of Environmental and Water Resources Engineering, School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Ave., Singapore 639798. (email@example.com)
Corresponding author: E. Y.-M. Lo, Division of Environmental and Water Resources Engineering, School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Ave., Singapore 639798. (firstname.lastname@example.org)
 This study is one of the few attempts to close water and heat budgets in tropical lakes and reservoirs on both daily and monthly time scales. A water budget of Kranji Reservoir is constructed for the year of 2007 using data for water level, reservoir gate operation records, and inflow predicted by a catchment rainfall-runoff model. A heat budget of Kranji Reservoir is also constructed for a field deployment period in 2007 using data for surface radiation fluxes measured by a meteorological station, heat fluxes associated with inflows and outflows, and heat content of the water column measured by thermistors. All the components of the water and heat budgets are accounted for on the basis of a complete data set obtained from field measurements and reliable model predictions, including those that were often neglected in the earlier studies, e.g., advective heat. The water budget of Kranji Reservoir is dominated by the discharge and catchment inflow, which are very sensitive to the variations in precipitation. Analysis of the gate operation records in 2007 shows an appreciable amount of the outflow of Kranji Reservoir was released, especially during storm events. The heat budget reveals that net heat flux of this shallow tropical reservoir is dominated by the net surface radiation fluxes and is also highly responsive to variations in stormflow conditions. It is noted that two critical components in the heat budget are latent heat and inflow advective heat, which equal 83% and 71% of net radiation, respectively.
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 Constructing and closing a water budget is a useful method to describe the hydrology of lakes and reservoirs [Assouline, 1993] and has been widely applied as such. Water residence time, for example, can be derived from the water budget and used to explain the variability of thermal stratification and primary production in lakes and reservoirs [Monsen et al., 2002; Rueda and Cowen, 2005]. Similarly, a heat budget is important in studying the variability in the thermal structure and mixing dynamics in a lake or reservoir during both shorter and longer time scales. Determining how surface heating and cooling and the advective heat transferred by inflows and outflows change the lake heat content are essential for understanding the vertical and horizontal thermal stratification and mixing in a lake or reservoir [Lewis, 1983a; Talling and Lemoalle, 1998].
 In a similar way, although the change in heat storage in a lake or reservoir has historically been considered important [e.g., Hutchinson, 1957] when describing the response of lakes to seasonal meteorological variations, its calculation has often been oversimplified or neglected. In some studies of lake heat budgets, the heat storage has been assumed to be equal to the residual of the heat balance equation [e.g., Rouse et al., 2003; Binyamin et al., 2006]. In studies where lake heat storage change is accounted for via water temperature changes and lake geometry, it is typically calculated using the equilibrium water temperature which is the surface temperature at which the net heat flux is zero [Livingstone and Imboden, 1989] or a depth-averaged water temperature [Keijman, 1974; Eggers and Tetzlaff, 1978; Spence et al., 2003; Oswald and Rouse, 2004; Rouse et al., 2008]. Even the more rigorous method of calculating lake heat content by integrating vertically the heat content of individual water layers can be an oversimplification since it assumes that the lake has a one-dimensional thermal structure, i.e., horizontal homogeneity [Livingstone and Imboden, 1989; Moreno-Ostos et al., 2008]. This method works well on lakes with small horizontal temperature differences while inherent errors may exist for lakes where there are significant horizontal temperature gradients.
 Tropical lakes are generally characterized by higher levels of and weaker seasonal variations in solar radiation than are experienced by temperate lakes throughout the year except for periods with high cloud cover [Gunkel and Casallas, 2002; Lewis, 1987; Talling and Lemoalle, 1998]. Compared to temperate deep lakes which have seasonal background stratification, shallow tropical lakes with average depths smaller than 5 m may achieve complete mixing of the whole water column multiple times every year, possibly even mixing diurnally [Lewis, 2000; Talling, 2001]. Examples include Pilkington Bay of Lake Victoria in tropical Africa [MacIntyre et al., 2002] and Lake Calado of the Amazon floodplain [MacIntyre and Melack, 1984]. However, comprehensive studies of water and heat budgets and the effects of different components on the water and heat balance equations of tropical lakes and reservoirs have been very limited. Of the few existing studies, many focus on the seasonal or annual variations in water and heat budgets [e.g., Lewis, 1983b; Yin and Nicholson, 1998; Verburg and Antenucci, 2010] or observed correlations of mixed layer depths with solar isolation and penetrative convection on a daily scale [MacIntyre and Melack, 1988]. Instantaneous flux measurements offer an approach to determine water and heat budgets on a daily basis and such budgets are needed in understanding the short time scale stratification and mixing in shallow tropical lakes [Talling and Lemoalle, 1998]. This study establishes the water and heat budgets of Kranji Reservoir accounting for advective heat via inflows and outflows, and change in heat storage. The observations we report here highlight the importance of the advective term in both the water and heat budgets. The originality of this current study is that it is one of the few attempts made at closing water and heat budgets in a tropical lake or reservoir on the daily time scale incorporating all key components.
 This paper is organized as follows. A description of Kranji Reservoir and field measurements from 2007 are presented in section 2. Section 3 describes the water balance and heat budget models. The data collected during 2007 is presented in section 4, along with the measured dam and pumping outflows. Section 5 discusses the results of water budget for Kranji Reservoir during the field deployment and for the whole year of 2007. Section 6 presents the results of heat budget for Kranji Reservoir during a field deployment in 2007 and discusses the effects of advective heat fluxes, as well as the stream temperature responses to precipitation and storm events. Some of the remaining challenges in further refining the heat budget are enumerated in section 7, and a summary of findings of this study is also discussed in this section.
2. Study Site and Methods
2.1. Study Site
 Kranji Reservoir (1°25′N, 103°43′E) is located at the northwest corner of Singapore. It is a former river, which was dammed at its mouth in 1972 to form a freshwater storage reservoir. It is one of the reservoirs for water supply in Singapore. The total area of the Kranji catchment is about 5.6 103 ha, where the surface area of Kranji Reservoir has been estimated to be about 3.0 106 m2 and maximum volume of 1.6 107 m3. The length of main channel of Kranji Reservoir is about 4 km with maximum depth of about 20 m and average depth of about 5 m. There are four major tributaries flowing into Kranji Reservoir, which are Sungei Kangkar, Sungei Tengah, Sungei Peng Siang and Sungei Pang Sua. Sungei Pang Sua was diverted into Kranji Reservoir at the end of 2005. Kranji Reservoir is almost entirely fed by dry weather flow and storm runoff from the four tributaries and direct precipitation on the reservoir. A map of Kranji Reservoir and its catchment is shown in Figure 1a.
2.2. Field Measurements
 An extensive array of hydrodynamic moorings was deployed in Kranji Reservoir from 10 April (year day 100) to 14 June (year day 165) in 2007. The moored instrumentation included Seabird SBE39 temperature loggers (one SBE39 each at M1, M2 and M3 and thermistor chains of multiple SBE39s at other locations), two 1200 KHz and one 600 KHz RDI/Teledyne acoustic Doppler current profilers (ADCP). Table 1 summarizes the deployed instruments and their setup in each mooring station. The locations of the eight mooring stations and the instruments deployed are shown in the contour map of Kranji Reservoir (see Figure 1b). The bathymetry of Kranji Reservoir was digitized from a survey map of Kranji Reservoir.
Table 1. Instruments Used at Each Mooring Site During Field Deployment in 2007a
The time interval and estimated accuracy of the thermistors are 30 s and 0.002°C respectively. The time interval of acoustic Doppler current profilers (ADCPs) is 4 min, and estimated accuracies are 0.64 cm s−1 at M4 and M5 and 0.46 cm s−1 at M6. In the details column, mab denotes meters above the reservoir bottom.
1, 2, 3, 4, 5 mab;
1200 KHz RDI ADCP
0.72–5.32 mab, 0.2 m bins
1, 2, 3, 4, 5, 6, 7 mab;
1200 KHz RDI ADCP
0.72–6.52 mab, 0.2 m bins
2, 4, 6, 7, 8, 9, 10, 11, 12 mab;
600 KHz RDI ADCP
1.61–11.11 mab, 0.5-m bins
1, 3, 5, 6 mab
0.5, 1.5, 2.3 mab
 A meteorological station was located on the water and close to M5 in the Kranji Reservoir during the field deployment period in 2007 (hereafter, Met station 1). The sensors of Met station 1 were installed at 1.5 m above water surface, recording air temperature, relative humidity, wind speed and direction, shortwave radiation, net radiation, as well as rainfall rate at 15 min intervals. Unfortunately, there was a short gap of about 10 days in the data recorded at the station from 6 May (year day 126) to 15 May 2007 (year day 135) because of an equipment malfunction. The meteorological data with the exception of the rainfall data was filtered with a fourth-order low-pass Butterworth filter with a cutoff time scale of 2 h.
2.3. Inflow and Outflow
 We have measured the inflow in the main channel of Kranji Reservoir during the 2007 field deployment period using the ADCP at M5 as M5 was located in the middle of the main channel and included inflow from all the four tributaries. In contrast the flow at M4 did not include tributary inflow from Sungei Pangsua and M6 was located near the shore of the main channel (see Figure 1b). The ADCP measured at 4 min interval and recorded velocities in 0.2 m bins. The inflow is also modeled by an established hydrological and hydraulic model which will be discussed later in section 3.1. The outflow of Kranji Reservoir has two components, i.e., daily discharge through the Kranji Gate at the Kranji Dam and transfer to Choa Chu Kang (CCK) Water Work by pumping. The Kranji Gate is a roller gate, which opens up when the water level rises during rainfall events.
2.4. Water Level
 The water level of Kranji Reservoir was measured at the Kranji Gate before and after each gate operation. It was also measured at M5 and M6 using the internal pressure sensors of ADCP during the field deployment period in 2007. The depths measured by ADCPs were further corrected by the barometric pressure measured by a Seabird 26plus located about 8 km away at Nanyang Technological University.
3. Model Description
3.1. Water Balance Model
 In order to calculate the water balance and assess the importance of each of the components in the water budget, a simple water balance equation is used:
where ΔV/Δt is the storage change of Kranji Reservoir calculated by the water level change over a certain time period, Qin is the total tributary inflows into the main channel, Qout is the total outflow from the reservoir including the discharge through the Kranji Gate and pumping transfer to CCK Water Work. P is the precipitation on the lake surface and E is the evaporation over the lake. Table 2 summarizes the variables used in the water balance model and methods to obtain them. We have not explicitly included possible water leakage through the bottom of the gate, the dam bed and seepage into the sediments in the water balance. Rather, these small effects are implicitly lumped into the much larger outflow component since the dam outflow is computed directly by the observed daily water level change in the reservoir. To balance the model, we calculated the total input and output terms and then the corresponding water imbalance percentages over different time scales.
Table 2. Variables Used in the Water Balance Model and Methods to Obtain Them
An average of the two pressure measurements by ADCPs at M5 and M6 was used for better accuracy and to account for spatial variability in method 1.
Storage change calculated by water level change
Method 1, water level change measured by internal pressure sensors of ADCP; method 2, water level change measured by Kranji Gate operationsa
Measured by rain gauge at Met Station 1
Total tributary inflows
Method 1, simulated by XP-SWMM; method 2, calculated from the velocities measured by ADCP
Measured by Kranji Gate and pumping operations
Used monthly average evaporation data for 12 years of MacRitchie Reservoir, another reservoir in Singapore as available from the Public Utilities Board
3.1.1. Inflow Model: Approach 1
 The XP Storm water & Wastewater Management Model [XP Software Inc., 2005] was established and calibrated to predict the direct runoff from the four main catchments in the Kranji Catchment [Lo et al., 2008]. The simulated total runoff hydrographs (time interval of 15 min) were compared with the measured hydrographs at several gauging stations in the Kranji catchment and the approach works well. The model was calibrated over both single and continuous stormflow events [Tan et al., 2008]. We configured XP-SWMM and ran it for the whole year of 2007.
3.1.2. Inflow Model: Approach 2
 For the field deployment period in 2007, the total tributary inflow can also be calculated from the ADCP measurements of depth-averaged velocities at M5. A mean velocity correction was used to transform the depth-averaged flow velocity to the mean flow velocity. We transformed the depth averaged flow velocity to mean velocity following Wilkerson and McGahan  and assuming a straight trapezoidal channel:
Here V0 is the mean velocity, Vz is the depth-averaged velocity at the centerline of the channel, Z is the cotangent of bank slope, is the lateral distance from the toe of slope to the point of interest (for centerline it is , where B is the bottom width of the channel) and Y is the flow depth over the channel bed. Thus the inflow is calculated as where Ac is the cross sectional area.
 This approach using ADCP is applicable to periods of storm events when the flow is dominated by inflows from tributaries. The flow is driven by weak winds with flow velocities unresolved by the ADCP on daily time scales during dry periods. The inflow for these periods is generated using XP-SWMM.
3.1.3. Outflow Model
 The tributary inflows during storm periods of the 2007 field deployment are estimated from the two approaches above. The calculated outflow from both approaches is compared to the measured outflow in order to evaluate the two inflow approaches. The following water balance equation is used:
where it is assumed that the rainfall and evaporation can be neglected in the calculation of outflow and the reservoir surface changes are in phase. Qout is the calculated outflow, Qin is the tributary inflows calculated from the two approaches, h is the average water level measured by ADCP at mooring stations M5 and M6, and As1 is the area of reservoir surface from M5 to the Kranji Gate.
3.1.4. Uncertainties in the Water Balance Model
 The uncertainty for each of the terms in the water budget can be estimated. The outflow measured by Kranji Gate uses a simple method of multiplying the surface area by the observed water level decrease after the release of water from each large rainfall event. The uncertainties come from three sources: (1) this method assumes that the water level decrease measured at the gate represents the whole reservoir, (2) it assumes the surface area is constant, and (3) there is error in the water level measurements. As the water level changes have little spatial variations in Kranji Reservoir (measured by ADCPs at M5 and M6, data not shown) and the reservoir surface area has small variations, the uncertainties from sources 1 and 2 are negligible. The water level measured manually at Kranji Gate is compared to measurements of the more accurate ADCPs and the maximum difference obtained is 0.1 m, about 2% of the average water depth of Kranji Reservoir. Thus we assumed, very conservatively that the uncertainty of the discharge through gate to be 10 times larger at 20% which is sufficient to account for the three sources of error listed above. The pumping to CCK Water Work is more accurate as it is measured at the CCK Water Work except for the last three months in 2007 when there was no available data. The uncertainty level of the first nine months is estimated to be the standard deviation of daily pumping data (computed to be 10%) while the uncertainty level of the last three months is assumed to be very conservatively 100% which is more than sufficient to account for any variations in pumping volume. The accuracy of the rain gauge is 1% and since the precipitation is much smaller than the outflow and tributary inflows, the uncertainty of precipitation can be neglected. The uncertainty of total tributary inflows simulated by XP-SWMM is assumed to be 20%, which is taken as the mean runoff volume error of earlier verification results of XP-SWMM [Lo et al., 2008]. Lastly the uncertainty of evaporation is assumed to be 30%, which is sufficient to account for errors associated with using the monthly average evaporation data for 12 years of MacRitchie Reservoir, a reservoir within 20 km of Kranji.
3.2. Heat Budget Model
 A simple heat budget equation can be expressed as
where ΔH is the heat content change of Kranji Reservoir and Hsurf is the total net surface heat flux, Hin is the heat flux arising from tributary inflows into the main channel and Hout is the heat flux of the total outflow from the reservoir. Last, Hrain is the effective sensible heat flux of rainfall, a small contribution of which a positive value indicates loss of heat from water surface to the atmosphere [Gosnell et al., 1995]. Hrain is calculated as
where Cw is the specific heat of water, R is the rainfall rate, and Ts and Tr are the water surface and mean rain temperature, respectively [Gosnell et al., 1995]. We used the measured air temperature Ta to represent Tr because of lack of rain temperature measurements. This method underestimates Hrain compared to using wet bulb temperature for Tr. However, as the mean relative humidity at Kranji Reservoir is 84% (see section 4) this error can be neglected because the Web bulb temperature is close to the dry bulb temperature. Table 3 summarizes the variables used in the heat budget model, methods to obtain them and their mean values and uncertainties.
Table 3. Variables Used in the Heat Budget Model, Methods to Obtain Them, and Their Mean Values and Uncertainties
Mean Values and Uncertainties
Basis for Uncertainties Estimate
Measured by R. M. Young's 03,001-L5 wind sentry set at Met Station 1
1.27 ± 0.05 m s−1
Use ± with instrument accuracy of ±0.5 m s−1 and sample size of 96 daily
Measured by Vaisala Inc. HMP45C-L5 at Met Station 1
27.42°C ± 0.026°C
Instrument accuracy of ±0.25°C and sample size of 96 daily
Measured by Vaisala Inc. HMP45C-L5 at Met Station 1
84% ± 0.3%
Instrument accuracy of ±3% and sample size of 96 daily
Water surface temperature
Measured by Seabird SBE39 thermistor loggers deployed at the mooring stations
29.96°C ± 0.00004°C
Instrument accuracy of ±0.002°C and sample size of 2880 daily
Measured by Kipp and Zonen NR-LITE-L5 at Met Station 1
91.06 ± 0.28 W m−2
Instrument accuracy of ±3% and sample size of 96 daily
 The net radiation of Kranji Reservoir, defined as the sum of incoming shortwave radiation and net longwave radiation, was measured by Met station 1 near M5.
184.108.40.206. Sensible Heat Flux
 Sensible heat flux is due to convection and takes place at the surface of Kranji Reservoir. It is calculated using the standard bulk formula [Hicks, 1972]:
where ρA is the density of air, Cp is the specific heat of air (1012 J kg−1 °C−1), Cs is the bulk transfer coefficient for sensible heat, U10 is the wind speed at 10 m above the water surface, Ts is the measured water surface temperature and Ta is the measured air temperature at 10 m above the water surface. The air density is calculated as , where p is the air pressure, Rd, the gas constant for dry air is 287.05 J kg−1 K−1, and Tv = T (1 + 0.61q) is the virtual temperature with q being the specific humidity [Garratt, 1992]. The measured water surface temperature at M5 is used to specify Ts. For neutrally stable boundary layers it is recommended [Hicks, 1972]. However, as the atmospheric boundary layer over tropical lakes is often found to be unstable [e.g., MacIntyre et al., 2002; Verburg and Antenucci, 2010] and the fact that the daily average air temperature is always lower than the water surface temperature in Kranji Reservoir (see discussion in section 6 and Figure 7b), the atmospheric boundary layer over Kranji Reservoir is mostly unstable. We corrected for atmospheric stability following the procedure by Fairall et al.  and its implementation using the Matlab Air-Sea Toolbox Version 2 from Pawlowicz et al. . In the correction, the air shear velocity is calculated as = (CD)1/2 = κUz/[ln(z/z0)], and the surface roughness length z0 is defined through a Charnock constant α by z0 = α/g [Guan and Xie, 2004]. Here CD is the drag coefficient, Uz is the wind speed measured at height z and κ is the von Kármán constant which equals to 0.4. The Charnock constant has a range of reported values from 0.010 to 0.035 [Garratt, 1992] and it is larger at shorter fetch and shallower water depth. Considering the short fetch of Kranji Reservoir (∼4 km for winds aligned with the channel main axis) and comparing with studies of lakes with similar fetch and water depth [e.g., Vickers and Mahrt, 1997], a reasonable range of 0.018 (for fetch-limited coastal regions) to 0.035 (large lake) from Garratt  is adopted for the present calculations.
220.127.116.11. Latent Heat Flux
 Latent heat flux due to evaporation at the surface of Kranji Reservoir is calculated using [Hicks, 1972]
where ρA is the density of air, LE is the latent heat of evaporation, CL is the bulk transfer coefficient for latent heat, U10 is the wind speed at 10 m above the water surface, qs is the saturation specific humidity (kg H2O kg−1 air) at the measured water surface temperature Ta and qa is the specific humidity of atmosphere at 10 m above the water surface. We corrected for the effects of atmospheric stability on the mass transfer coefficients, similar to the correction for sensible heat flux.
3.2.2. Advective Heat Fluxes
 The advective heat flux resulting from the summed tributary inflows is calculated by
where Qi and Ti are the flow rate and water temperature for each of the four tributaries of Kranji Reservoir. Qi was predicted by the XP-SWMM model (see section 3.1) and Ti was measured by thermistors located in each of the four tributaries (at M1, M2, M3 and M8, see Table 1 for details). The outflow heat flux is calculated as
where Qout and Tout is the flow rate and water temperature of the outflow. Qout was predicted by the XP-SWMM model and Tout was measured by thermistor at M7.
3.2.3. Lake Heat Content
 The lake heat content is calculated as
where Vi and Ti are the volume and water temperature of eight different blocks of water in the reservoir with temperature measured by the eight moorings M1 to M8. The boundaries between every adjacent block are defined on the basis of the lake bathymetry with the water temperature profile of each mooring representing the nearby waters with similar water depths (see Figure 1b for the defined boundaries of the eight blocks of water in Kranji Reservoir).
 The meteorological measurements during the field deployment period in 2007 are presented in Figure 2. Diurnal cycles of wind speed, solar radiation, air temperature and relative humidity are readily apparent. The wind speed had an average value of 1.27 m s−1 and the maximum value of 6.64 m s−1. The wind speed was generally higher in the afternoon when it blows from northeast and lower in the nighttime hours. For most of the days, incoming solar radiation peaked between 500 W m−2 and 1000 W m−2. The air temperature underwent a cooling period from year day 116 to 120 and increased again afterward. The relative humidity varied from about 50% (minimum observed was 48%) to nearly 100% daily and had a mean value of 84%. The deployment was during the intermonsoonal period of Singapore's climate which had occasional intense thunderstorm events, with larger events occurring between year day 110 to 120.
 The inflow was measured by the ADCP at M5 in the main channel of Kranji Reservoir during the field deployment period in 2007. The water temperature measured by thermistors, and the water depth and velocity aligned with the axis of the main channel as measured by the ADCP at M5 are shown in Figure 3. A large inflow event from year day 113 to 120 of 2007 was observed when water temperature dropped by around 2.5° and water depth rose by 0.3 m (see Figures 3b and 3c). The mean velocity along the main channel at M5 during the field deployment period in 2007 was only 0.001 m s−1 while the magnitude of peak velocity during the inflow event was around 0.05 m s−1 (see Figure 3a). The resulting flow was as large as 100 m3 s−1 during inflow event. Mean flows in the main channel of Kranji Reservoir were observed to be positive, which indicates that the flow was transported from tributaries to the dam. The large fluctuations of water depth (see Figure 3c) were due to the catchment inflow draining into the reservoir and the dam release.
 The pumping and gate opening data of Kranji Reservoir in 2007 were obtained from Public Utilities Board (PUB), Singapore and processed for the field deployment period in 2007. Analysis of gate opening data showed that there were 34 gate opening events during the 59 day mooring deployment with release events ranging from 1 h to 6 h and averaging 3 h and 15 min. The total discharge through the Kranji gate opening was 1.6 107 m3 from year day 103 to 162 of 2007. The total rainfall was 490 mm during the same period. During each gate opening event, the water level is reduced to a constant level. The average flow rate during the gate openings was 40 m3 s−1; the maximum flow rate was 4.0 102 m3 s−1 on year day 116. Analysis of pumping to CCK Water Work shows that there was no pumping to CCK Water Work from year day 103 to 106, while there was daily pumping from year day 107 to 162. The total of outflow through pumping to CCK Water Work was 3.0 106 m3 during this period. The average flow rate was 0.60 m3 s−1, while the maximum flow rate was 5.8 m3 s−1 on year day 108. The pumping outflow was roughly uniform after year day 108.
 A comparison of the water level measurements at the Kranji Gate and measured by ADCP during the field deployment period in 2007 is plotted in Figure 4. The general trend of the water level variations is fairly consistent between the two measurements.
5. Water Budget of Kranji Reservoir
 The daily tributary inflows calculated by XP-SWMM exhibits a strong linear relationship with the daily rainfall averaged over the five rain gauges in the Kranji Catchment (R2 = 0.93, plot not shown). The outflow calculated by the two approaches for tributary inflow (i.e., XP-SWMM predictions and ADCP velocity measurements, as described in the inflow model of section 3.1) compare well between each other not only on year day 116, the day with the largest inflow event (see Figure 5a), but also for a longer period of ten days (year day 110 to 120) with several storm events (see Figure 5b, with R2 = 0.66). The peaks of the hydrographs predicted by the two approaches and the time to peaks both match well while the peaks of dam outflow measured by Kranji Gate are generally less than the predictions of the two approaches except on year day 110. This is expected: the dam outflow data measured by Kranji Gate only has the start and end time of gate opening and the water depth change during this period. The dam outflow is estimated as dividing the total volume of outgoing water (calculated by the water depth change multiplied by reservoir surface area) by the time of gate opening. The resulting dam outflow has lower peaks but close to total volume compared to the outflow predicted by the two methods because of the lack of detailed information between the gate opening and closing. The outflows calculated by the two approaches are within 20% of difference between each other and with the discharge measured at the Kranji Gate. The possible causes of differences between the two methods are the uncertainties in converting ADCP velocity measurements at one specific location to the mean velocity at the M5 cross section and that the flow rate predicted by the XP-SWMM method represents an average across the channel width which may further have some time lag in transporting the storm flows to the outlet.
 The water budget for the whole year of 2007 was next analyzed. The XP-SWMM model was configured and run for the 2007 calendar year and model results were used as the total tributary inflows. The resulting monthly water budget of Kranji Reservoir in 2007 is plotted in Figure 6a. The inputs of the tributary inflows and the precipitation on the water surface are plotted as positive values, while the outputs comprising discharge through the Kranji Gate, pumping to CCK Water Work and evaporation are plotted as negative values. As the Kranji Gate opens up during rainfall events thus keeping the water level almost constant over the longer term, the monthly reservoir volume change, or ΔV is estimated to be zero. The uncertainty in the total water budget is calculated to be 22% by adopting the method of error propagation [Emery and Thomson, 2004] and on the basis of the uncertainty estimates of individual water budget components as described in section 3.1.
 On the basis of the 2007 monthly water budget of Kranji Reservoir in Figure 6a, the total input including tributary inflow and precipitation over the whole of 2007 is 7.6 × 107 m3 while the total output including dam outflow, pumping outflow and evaporation is 7.0 × 107 m3. The percentage of water imbalance between the total inputs and outputs in the annual water budget is 8.2%, well within the uncertainty level of 22%. The water budget is dominated by discharge (67% of the annual total output), and catchment inflow (83% of the annual total input), which are sensitive to variations in precipitation.
 The daily water imbalance calculated from the total water input and output on a daily basis is plotted in Figure 6c for the field deployment period from year day 103 to 162 in 2007. Over the field deployment period, the total input including tributary inflow and precipitation is 1.1 × 107 m3 while the total output including dam outflow, pumping outflow and evaporation is 1.0 × 107 m3. The much smaller daily water imbalance (max of 3.6 × 105 m3) indicates that the total input and total output match well on the daily time scale. The total input exceeds the total output by about 7.9% over the deployment period. For the storm period from year day 110 to 120, total input including tributary inflow and precipitation is 3.2 × 106 m3 while the total output including dam outflow, pumping outflow and evaporation is 3.8 × 106 m3. The total input is 14% less than the total output. Thus the water budget model overestimates the total input in the period without intensive storm events and underestimates the total input during the storm period. However, these differences are well within the 22% uncertainty level of the overall water budget and thus the daily water balance closes within the uncertainty limits.
6. Heat Budget of Kranji Reservoir
 The various surface heat fluxes that make up the surface heat budget of Kranji Reservoir during the field deployment period in 2007 are shown in Figure 7a. The uncertainties of each surface heat flux was small as calculated by the method of standard error propagation [Emery and Thomson, 2004] with estimated values shown in Table 3. Of the surface heat fluxes, the net radiation and latent heat flux are the dominant components. Large variations of all the three surface heat fluxes are observed for the two month record. The daily average water surface temperature measured by thermistors and air temperature measured by Met station 1 is shown in Figure 7b. The daily average water surface temperature is always warmer than the air temperature by 1°–4° during the field deployment period. Thus the lake transferred energy to the air and the calculated sensible heat flux was negative (heat loss to the atmosphere).
 In several earlier studies [e.g., Myrup et al., 1979], the lake heat content was calculated by using an average vertical temperature profile for the whole lake. In Kranji Reservoir, however, horizontal temperature differences along the main channel are substantial and comparable to vertical variations. For example, Figure 8 shows the vertical temperature profiles at the four mooring stations in the main channel of Kranji Reservoir on year day 116. The reservoir was well mixed in the early morning at all the locations. Cold inflows from the tributaries plunged into deeper parts of the junction (M4) from 13:00 LT and formed much larger vertical temperature differences in M4 and M5 than in M6 and M7. The Kranji Reservoir system is sometimes multidimensional in behavior where significant variations in temperature in the along and cross-reservoir directions are driven by cold inflow events, differential heating and potential reservoir releases (as above). As discussed in section 3.2.3, the lake heat content of Kranji Reservoir is hence calculated by integrating the heat content of eight different blocks of water in the reservoir represented by moorings M1 to M8, instead of using a uniform vertical temperature profile. The heat content change of Kranji Reservoir during the field deployment period in 2007 since year day 103 calculated by using the vertical temperature profiles at M4, M5, and M6 is plotted in Figure 9. Notable differences exist in the heat content change calculated by vertical temperature profiles at different stations. The reservoir underwent cooling periods from cold tributaries inflows during year day 113 to 123 and was then warmed again toward the end of the field deployment.
 The average individual components in the heat budget of Kranji Reservoir as calculated from methods discussed in section 3 and the associated uncertainties are summarized in Table 4 for the field deployment in 2007. The average net surface heat flux as the sum of net radiation, latent heat and sensible heat is within the range of [4.93, 8.83] W m−2, with the lower bound using Charnock constant of 0.035 and the upper bound using Charnock constant of 0.018 (see section 3.2.1). On average 83% of the energy goes from net radiation into latent heat of evaporation. The inflow advective heat flux also represents a large component, at 71% of the net radiation. The average net advective heat flux, obtained by dividing the net advective heat by the reservoir surface area, is −4.00 W m−2 and average rain heat flux is −2.67 W m−2. The predicted average lake heat content change of Kranji Reservoir calculated as the sum of the surface heat flux, rain heat flux and advective heat flux is within the range of [−1.74, 2.16] W m−2 for the two different Charnock constants used. The heat imbalance between this predicted lake heat content change and the measured lake heat content change which averages 1.28 W m−2 over the field deployment period is within the range of [−3.02, 0.88] W m−2. The percentage of heat imbalance is 2%, well within the uncertainties limits of the calculated component terms. Although the heat budget of Kranji Reservoir is dominated by the surface heat fluxes (Table 4), the net advective heat flux cannot be neglected, since it is similar in magnitude to the net surface heat flux.
Table 4. Components of Average Daily Heat Budget of Kranji Reservoir With Uncertainties Over the Field Deployment Period From Year Days 103–162 in 2007a
The lower and upper values of latent and sensible heat use a Charnock constant of 0.035 and 0.018. The imbalance percentage is computed using the imbalance divided by the total input heat flux.
Net radiation (W m−2)
91.06 ± 0.28
Latent heat (W m−2)
[−77.64, −74.05] ± 0.66
Sensible heat (W m−2)
[−8.49, −8.18] ± 0.06
Net surface heat flux (W m−2)
[4.93, 8.83] ± 0.72
Heat flux of inflow (W m−2)
64.35 ± 6.4
Heat flux of outflow (W m−2)
−68.35 ± 6.8
Net advective heat flux (W m−2)
−4.00 ± 9.3
Rain heat flux (W m−2)
Predicted lake heat content change (W m−2)
[−1.74, 2.16] ± 9.3
Measured lake heat content change (W m−2)
Imbalance between measured and predicted lake heat content change (W m−2)
[−3.02, 0.88] ± 9.3
Imbalance percentage (%)
2 ± 6
 A daily heat budget was computed for the first 23 days of the 2007 field deployment; this time period is focused upon since there was a gap in meteorological measurements from year day 126 onward. The measured lake heat content starting from year day 103 and the predicted lake heat content as computed by the sum of surface heat fluxes, advective heat fluxes and the lake heat content are plotted in Figure 10a. Figure 10 includes sensible and latent heat calculated using the range of Charnock constant of [0.018, 0.035]. The predicted lake heat content is higher than the measured lake heat content from year day 104 to year day 116 and lower than the measured for the final ten days. A large fraction of the daily heat imbalance is attributable to the water budget imbalance (see Figure 10b). The predicted daily lake heat content can be corrected by the daily heat imbalance due to water budget imbalance (Figure 10c). This correction was computed by taking the water imbalance and accounting for its heat content at 00:00 LT daily using the mean measured water temperature in four tributaries since the water budget imbalance mainly comes from the discrepancy between total inflow and outflow (see section 5 for discussion on the daily water budget). As indicated in Figure 10c, the measured lake heat content and the corrected lake heat content predictions generally match well, not only in the overall trend during the 23 days but also exhibiting similar the day-to-day variations. The comparison in the last 5 days is not as good as the first 18 days as also can be seen in Figure 10b where water budget imbalance does not compensate for the heat imbalance as well as the first 18 days. However even the largest daily heat imbalance (on year day 125) is 4% of the heat content, well within the accuracy of the water budget closure which is 10% over the field deployment period.
 The daily heat budget has a larger imbalance than the average heat budget over the field deployment period which has a low imbalance percentage of 2% (see Table 4). This is because the uncertainties of the daily average component terms are much larger than the uncertainties of the component terms averaged over the whole field deployment period. The heat imbalance becomes smaller and falls within the range of uncertainties when averaging with the two month's data.
7. Discussion and Summary
 We have compared the Bowen ratio, the ratio of sensible to latent heat flux for Kranji Reservoir with reported values from some other tropical lakes and reservoirs as well as lakes in temperate region. This comparison is summarized in Table 5. The Bowen ratio is usually used to compare the heat losses by convection and evaporation [Bowen, 1926] and also used in heat budget calculations if one of the components is missing [Assouline et al., 2008]. Kranji Reservoir has a small Bowen ratio, daily mean of 0.11, standard deviation 0.04. This value is comparable to other Mediterranean and tropical lakes and reservoirs, e.g., Eshkol Reservoir in Israel, which has a shallow depth of 3.5 m and is in the Mediterranean climate [Assouline et al., 2008], Lake Tanganyika [Verburg and Antenucci, 2010] and Lake Victoria [Yin and Nicholson, 1998] in tropical Africa. It is much smaller than lakes in the temperate region, e.g., Great Lakes in North America [Lofgren and Zhu, 2000]. The small value is consistent with heat budget analysis of Kranji Reservoir, which shows that on average 83% of the energy from net radiation is converted into latent heat of evaporation.
Table 5. Comparison of Bowen Ratio in Lakes and Reservoirs
 Our measurements also show that, the advective heat flux is an important component of the overall heat budget and thus cannot be neglected. Even though the tributary inflows of the whole year of 2007 can be predicted by XP-SWMM, we cannot construct an accurate heat budget for 2007 because of the limited period of tributary surface temperature measurements. As a side note, measurements of the stream temperature in Pangsua Channel suggest challenges in further refining the heat budget during storm events. The stream temperature had negative correlations with precipitation magnitude, event inflow volume, as well as mean and peak inflow rates (not shown) while it had positive correlations with air temperature and solar radiation (not shown). However, all the relationships are not significant with small R2 and the data show large deviations from the derived linear fits. From this limited data, it would thus be difficult to predict stream temperature from rainfall, inflow and/or meteorological measurements as any derived linear regression model is likely to be inadequate for explaining a large fraction of the variations.
 This study has not considered the spatial differences in meteorological data such as rainfall, wind speed and direction, and air temperature as only measurements in Met station 1 were used in formulating the water and heat budgets for the 2007 field deployment period. Spatial variability of rainfall over distance as short as 1 km has been noted in prior studies [Singh, 1997; Chaubey et al., 1999] as an important factor contributing to the uncertainties of runoff generations. Analysis of precipitation data measured by the five rain gauges located in the Kranji Catchment further indicates that the correlation between two rain gauges has an inverse relationship to the distance between them (not shown). Future studies on water and heat budgets need to take into account the variability of meteorological conditions of the reservoir since it can be a large source of uncertainty.
 In summary, the water budget of Kranji Reservoir is dominated by the discharge and catchment inflow, which are very sensitive to the variations in precipitation. Outflow calculated by the two approaches of using XP-SWMM calculations and ACDP measurements for the inflows compare favorably with the outflow measured by Kranji Gate during periods of storm events. XP-SWMM is demonstrated to be useful in predictions of water budgets for reservoirs with flow driven by rainfall. The deduced water budget for the entire year 2007 is closed to within 10%. The heat budget of Kranji Reservoir is dominated by the surface heat flux but the advective heat flux can also be very important. Both the water and heat budgets close to within the uncertainty associated with the different terms in the balance equations on both daily and longer time scales. The water budget closes to within 10% and the heat budget within 2% during the two months of detailed field measurements. All the components in the water and heat budgets are accounted for on the basis of a complete data set obtained from field measurements and reliable model predictions, including those that have often been neglected in the earlier studies, e.g., advective heat. For lakes or reservoirs with frequent and large storm events like Kranji Reservoir, similar approaches of using gauged stream temperature and measured or predicted stream runoff to compute advective heat can be adopted. The lake heat content of Kranji Reservoir is calculated by integrating the heat content of different blocks of water in the reservoir represented by deployed moorings instead of the widely adopted methods of using a uniform vertical temperature profile or an equilibrium water temperature. In the same way, for lakes with significant horizontal temperature gradients, this offers a significant advantage in closing the heat and water budgets.
storage change calculated by water level change.
total tributary inflows.
flow rate for each of the four tributaries of Kranji Reservoir.
volume of eight different blocks of water in Kranji reservoir.
water temperature of the outflow.
mean velocity along the channel.
depth-averaged velocity at the centerline of the channel.
cotangent of bank slope.
bottom width of the channel.
flow depth over the channel bed.
cross sectional area.
surface area from M5 to the Kranji Gate of Kranji Reservoir.
average water level measured by ADCP at mooring stations M5 and M6.
air temperature at 10 m above water surface.
mean rain temperature.
water surface temperature.
wind speed at 10 m above water surface.
specific heat of air.
specific heat of water.
bulk transfer coefficient for sensible heat and
bulk transfer coefficient for latent heat.
gas constant for dry air.
air shear velocity.
wind speed measured at height z.
Von Kármán constant.
surface roughness length.
latent heat of evaporation.
saturation specific humidity at the measured water surface temperature.
specific humidity of atmosphere at 10 m above water surface.
heat content change.
heat flux brought in by the tributary inflows into the main channel.
heat flux brought away by the total outflow from the reservoir.
net surface heat flux.
heat flux of rainfall.
 The authors are grateful to the Public Utilities Board (PUB) of Singapore for providing access to the reservoir as well as logistic support during equipment deployment and retrieval. The authors would also like to thank Liv Walter and Jonah Steinbuck from Stanford University and the laboratory technicians at the Hydraulics Laboratory of the School of Civil and Environmental Engineering, Nanyang Technological University, for their help during the deployment and recovery of the field instruments. This research was sponsored by the Singapore Stanford Partnership program.