Natural and Anthropogenic Influences on the Mount Hope Bay Ecosystem 2006 Northeastern Naturalist 13(Special Issue 4):47–70 On the Heat Budget for Mount Hope Bay Yalin Fan1,2,* and Wendell S. Brown1 Abstract - A simple heat budget has been constructed for Mount Hope Bay (MHB) for two one-month periods: winter 1999 (February–March) and summer 1997 (August– September). The box model considered here includes the heat contributions to MHB from the Brayton Point Power Station (BPPS), the exchange across the air– water interface, the Taunton River, and the tidal exchange between MHB and both Narragansett Bay and the Sakonnet River (NB/SR). Comprehensive measurements of MHB temperature fields by Applied Science Associates, Inc., and meteorological data from T.F. Green Airport (Warwick, RI) were used to estimate the different heat flux component contributions. The box model results for winter show that the BPPS heating is balanced (within the uncertainty of the estimates) by air–water cooling alone. The simple winter balance does not hold during the summer, when heat losses due to tidal exchanges between MHB and NB/SR are important. The summer heat budget of MHB—including BPPS heating, air–water cooling and tidal exchange cooling—can be balanced (within the uncertainty of the estimates) by assuming that 3% of the colder NB/SR tidal input water is exchanged with the warmer MHB water during each tidal cycle. The air–water cooling accounts for 84.4% of the total cooling, and the tidal exchange accounts for 15.6% of the total cooling. Taunton River contributions to the heat budget were negligible in both seasons. Analyses show that the model temperature is most sensitive to uncertainty in the measurements used to estimate the air–water heat fluxes—the relative humidity in particular. Thus, local MHB measurements are important for accurate monitoring of the MHB heat budget in the future. Introduction Mount Hope Bay (“the Bay” or “MHB”) is situated in the northeast corner of Narragansett Bay (Fig. 1), lying within both Rhode Island to the south and west and Massachusetts to the north and east. In recent years, questions have been raised concerning the effect on the MHB ecosystem of the 1600-megawatt, fossil fuel-fired electrical generating facility at Brayton Point, MA. Recent studies of the Mount Hope/Narragansett Bay region have focused on the effects of the thermal discharge from Brayton Point Power Station (BPPS) on the thermal environment. One such study by Mustard et al. (1999) derived the seasonal variability of surface temperatures in the region from a composite of 14 infrared satellite images (Landsat TM Band 6) from a 12-year period from 1984 to 1995. The late summer average surface temperature of MHB was found to be 0.8 °C warmer than a “comparable” 1School for Marine Science and Technology, University of Massachusetts– Dartmouth, 706 South Rodney French Boulevard, New Bedford, MA 02744-1221. 2Current address - Graduate School of Oceanography, Unviersity of Rhode Island, Narragansett, RI. *Corresponding author - yfan@gso.uri.edu. 48 Northeastern Naturalist Vol. 13, Special Issue 4 upper Narragansett Bay subregion. This result has been often quoted in considering the power plant’s impact on the physical and biological environment in the Bay. In this paper, we report on the use of a simple box model to explore the heat budget for MHB during winter (February–March) 1999 and summer (August– September) 1997. The box model employed includes the heat flux contributions from: the BPPS, the heat exchange across the air–water interface, the heating/cooling due to the Taunton River, and the tidal exchange between MHB and both Narragansett Bay and the Sakonnet River. The meteorology at T.F. Green Airport (TFG) in Warwick, RI, and comprehensive measurements made by Applied Science Associates, Inc. (ASA), of the MHB temperature fields are used to estimate the contributions of the different components. The MHB Model Heat Budget In general, the heat exchange between MHB and its surrounding area can be described in terms of the simple heat budget model depicted in Figure 2. Figure 1. A location map region of the ASA, Inc. thermistor chain moorings (black dots) in MHB during summer 1997 and winter 1999. The dashed and solid circled station data were used to estimate lateral heat transport into MHB. The open square locates the BPPS. The inset shows the location of TFG. Figure 2. A box model of the Mt. Hope Bay heat inputs (see text). 2006 Y. Fan and W.S. Brown 49 Here we assume that a homogeneous (i.e., well-mixed) MHB can receive heat (a) through the air–water interface, and from (b) Narragansett Bay (NB), (c) the Sakonnet “River” (SR), (d) the Taunton River, and (e) the Brayton Point Power Station (BPPS). The time rate change of the total heat of MHB (Ht) can be expressed in terms of the time rate change of the volume-averaged temperature ( TMHB) and the incoming heat fluxes according to: 􀂴􀂦 􀂥 􀂲􀂤 􀂣 = = + + + dt dH dt dH dt dH Q A dt dT C V dt dH NBSR river BPPS air MHB MHB p MHB t 􀁬 (1) where r is the water density, Cp is the specific heat for water, Qair is the net heat flux to MHB through the MHB air–water interface with a surface area of AMHB, dHNBSR / dt is the combined NB/SR heat-flux rate to MHB, dHriver / dt is the Taunton River heat-flux rate, and dHBPPS / dt is the BPPS heat-flux rate to MHB. The lateral heat transport contributions from an arbitrary source (i.e., the ith source; e.g., Taunton River) to the MHB heating rate can be estimated from the following relationship: dHi / dt = 􀁬 Cp ui Ai 􀁢Ti = 􀁬 Cp Ui 􀁢Ti (2) where Ai is the cross-sectional area of the relevant passage, ui the sectionaveraged along-stream current, Ui the transport, and 􀁢Ti the difference between the section-averaged temperature at an upstream transect and the MHB temperature. The net heat flux across the air–water interface Qair into MHB can be decomposed into four component heat fluxes, namely: Qair = Qi + Qb + Qh + Qe (3) where Qi is the net incoming shortwave radiation, Qb is the effective longwave radiation, Qh is the sensible heat flux, and Qe is the latent heat flux (usually negative). The latent and sensible heat flux were estimated using the bulk formulae of Beardsley et al. (1998): Qh = SH =􀁬aCpaCHW(Ts - Ta) (4a) Qe = LH = 􀁬aLCEW[q(Ts) - qd] (4b) in which Ts is the water surface temperature, Ta is the surface air temperature at a reference elevation zr (usually 10 m), W is the wind speed at zr, L is the latent heat of vaporization of water, 􀁬a is the air density, Cpa is the specific heat capacity of dry air, CE and CH are the bulk transfer coefficients of moisture and heat, respectively, q is the saturation specific humidity at Ts, and qd is the saturation specific humidity at the dew point temperature Td at zR. Winter Heat Budget The heat-budget box model (Equation 1) was applied to MHB during a winter period between 17 February and 22 March 1999. The following details the measurements that were used to estimate the heat-flux components in Equation 3 and, thereby, the net air–water heat flux. 50 Northeastern Naturalist Vol. 13, Special Issue 4 Net air–water heat flux Qair, the time series of hourly MHB net air-to-sea heat flux (Fig. 3h) that was estimated according to Equation 2, shows the expected diurnal heating/ Figure 3. Hourly MHB winter 1999 heat-flux estimates: (a) wind stresses based on measurements at TFG, (b) air temperature at TFG (solid) and spatially averaged surface temperature for MHB (dashed), (c) relative humidity, (d) solar insolation, (e) longwave back radiation, (f) net sensible heat flux, (g) latent heat flux, and (h) net air–water heat flux Qair. 2006 Y. Fan and W.S. Brown 51 cooling cycle. The average heat flux from the atmosphere to the surface of MHB between 17 February and 22 March 1999 was negative, implying a loss of heat to the atmosphere. Qi, the hourly values of incident shortwave solar radiation, shows a clear diurnal cycle (Fig. 3d). Cloudiness attenuates the net clear-sky incoming solar radiative heat flux for about half of the days during this time. The measurements were made by R. Payne with an Eppley PSP pyranometer mounted on the roof of the Clark Building at the Quissett Campus of the Woods Hole Oceanographic Institution located at 70º42'W, 41º33'N. Since the air temperatures at the measurement site may differ considerably from temperatures at MHB, the incident shortwave solar radiation could be different at MHB. Howsever, since MHB is geographically close, we think the Woods Hole Qi is a good approximation. Qb, measurements of net longwave radiation to space, were not available. Using Mupparapu and Brown (2003) as a guide, Qb was set to be a constant value of -60 watts/m2 (Fig. 3e). Qb is proportional to the fourth power of the absolute surface temperature and thus is relatively insensitive to daily-toseasonal fluctuations of the surface temperature of the ocean. Therefore, our assumption of a constant Qb is reasonable. Qh, the net sensible heat flux in Equation 4a, is proportional to (1) the wind speed (W) at 10 m elevation and (2) the difference between air temperature (Ta) at 10 m elevation and sea surface temperature (Tw). The only air-temperature measurements available to us during the study periods were made at TFG, about 20 km due west across Narragansett Bay (located in Fig. 1). However, for winter (and summer) 2001, we were able to compare the TFG air temperatures with those at the National Oceanic and Atmospheric Administration’s (NOAA) Physical Oceanography Real Time System (PORTS) in Fall River (Fig. 4). The variability of the two airtemperature records is very similar, with the temperature at TFG being about 1.1 ºC lower on average than the Fall River PORTS temperature for both seasons (Table 1). We added 1.1 °C to the winter 1999 TFG air-temperature time record, Ta (Fig. 3b), for our heat-flux calculation for MHB. Tw was estimated from the ASA thermistor chain (T-chain) temperatures (see Fig. 1 array map) measured between 17 February and 22 March 1999. The 5-minute ASA temperatures at 5 or 6 depths in the water column were linearly interpolated to hourly samples, and corrected for gaps and other Table 1. Statistics of air temperature measurements at TFG and Fall River during “winter” and “summer” 2001. Winter 2001 Summer 2001 TFG Fall River TFG Fall River Average (°C) 1.18 2.28 21.77 22.82 Standard deviation (°C) 4.53 4.08 4.19 3.45 Maximum (°C) 12.8 13.1 37.2 35.5 Minimum (°C) -11.1 -8.4 10.6 12.7 52 Northeastern Naturalist Vol. 13, Special Issue 4 Figure 4. Upper panel: comparison between the winter 2001 hourly air temperatures at Fall River (solid line) and TFG (solid line with circles). Lower panel: the summer 2001 hourly air temperatures at Fall River (solid line) and TFG (solid line with circles). 2006 Y. Fan and W.S. Brown 53 spurious data in some of these time series. The spatially weighted average surface (0.25 m) temperature (Tw) is shown in Figure 3b. Given the reasonably simple structure of the winter MHB surface temperature field (Fig. 5), the spatially averaged temperature should be a reasonable estimate (see Fan and Brown 2003 for more detailed data). W is the hourly winds from TFG. Since friction over land is generally greater than that over water, the wind speed at TFG could be an underestimate of wind speed at MHB. However, because TFG is geographically close to MHB, we assume W is a reasonable approximation, and it was used to estimate the wind stress shown in Figure 3a. The calculated sensible heat flux is shown in Figure 3f. Hr, the time series of hourly relative humidity from TFG, is shown in Figure 3c. Because there’s usually more water vapor in the air above a large water body than there is above land, the relative humidity over MHB may be larger than that at TFG. But, since Hr is already high during the study period, the hourly relative humidity record in MHB was assumed to be very similar to the relative humidity record at TFG. Qe, the latent heat flux (Fig. 3g) was estimated from measurements of Ta, Tw, W, and relative humidity Hr according to Equation 4b. Power plant heat input The BPPS heating rate of MHB (dHBPPS/dt; Fig. 6) has a diurnal variation ranging in amplitude between a midnight (local time) minima of about 1.6 x 106 kW and a mid-day (local time) maxima of about 2 x 106 kW. To assess the importance of Taunton River inflow and MHB/NB tidal heat exchange to the MHB heat budget, we compared the depth-averaged ASA temperature at the Mount Hope Bridge and Taunton River (Fig. 1) with the volume-averaged MHB temperature (Fig. 7). The results show that the temperatures at the Mount Hope Bridge and Taunton River measurement sites are very similar to the average MHB temperature. The nominal 0.5 °C temperature differences are so small that heating (River) and cooling (NB/ SR) contributions to the MHB heat budget are negligible compared to the BPPS heating and net air–water cooling. MHB temperature: Air–water and BPPS cooling/heating only Thus, we consider the box model based on just the net air–water cooling and BPPS heating processes. Assuming a totally mixed MHB and negligible heat inputs from the rivers and Narragansett Bay, Equation 1 reduces to: 􀂴􀂦 􀂥 􀂲􀂤 􀂣 = = + dt dH Q A dt dT C V dt dH BPPS air MHB MHB p MHB t 􀁬 (5) The effects of the heat exchange processes on the volume-averaged temperature of MHB can be estimated by integrating Equation 5. The finite difference form of the resulting integral of Equation 5 yields the time-dependent, volume- averaged temperature of MHB (TMHB) at discrete times tn according to: 54 Northeastern Naturalist Vol. 13, Special Issue 4 ( ) ( ( )) ( ) ( ) ( ) 0 0 0 1 t A Q t H t H t T t c V T t BPPS n BPPS MHB n i MHB air i p MHB MHB n + 􀂵 􀂘 􀂗 􀂳 􀂖 􀂕 􀀼 + 􀀶 = 􀀭= 􀁬 (6) where t0 is the referenced time 0 (0000 GMT 17 February 1999 for the winter calculation); ti = i􀀶t is the ith hourly time step; VMHB is the mean low-water volume (2.02 x 108 m3; Chinman and Nixon 1985); 􀁬 is 1027 kg/m3; and cp = 4.186 x 103 watt-sec/kg-°C. Figure 5. The late ebb-tide surface-temperature structure in MHB on 21 February 1999. The relevant values of Fall River sea level and BPPS heating rate are indicated (red dots) in the middle and bottom panels, respectively. 2006 Y. Fan and W.S. Brown 55 Figure 6. Hourly values of the Brayton Point Power Plant heating rate of MHB for winter 1999 (BPPS data). Figure 7. Measured depth-averaged temperature time series at the Mount Hope Bridge (black with open circles) and Taunton River (white) sites (see Fig. 1) compared with the MHB volume-averaged temperature (black). 56 Northeastern Naturalist Vol. 13, Special Issue 4 Table 2. Mean values of the heating rate of each air–water heating component, the BPPS heating rate, and the ratio of the mean solar heating rate to the mean BPPS heating rate. In this table, positive values stand for heating. Air–water heat flux (million kW) Heating ratio Qi Qb Qh Qe BPPS heating (million kW) BPPS/Qi 4.837 -2.112 -0.931 -2.778 1.643 0.34 The model temperature tracks the measured volume-averaged MHB temperature (Fig. 8) reasonably well relative to uncertainty limits that are based on model sensitivity testing described in Appendix A. On the other hand, the uncertainties in estimating the air–water heat fluxes are significant and need to be reduced for future work. The relative contributions of solar heating and BPPS heating of MHB for this study period are computed and documented in Table 2. We can see that the BPPS heating accounts for 25% of the total heating during this winter study period. Figure 8. Winter 1999 model MHB temperature (Equation 6; solid line with open squares)—a combination of BPPS (solid line with open circles) and air-sea (solid line with filled circles) heating/cooling processes. The MHB volume-averaged temperature (based on measurements; solid line with solid squares) is provided for reference. The grey band depicts the model MHB temperature range corresponding to a ± 20% difference in back-radiation estimate. 2006 Y. Fan and W.S. Brown 57 The Summer Heat Budget The heat budget box model Equation 1 was also applied to MHB during a summer period between 9 August and 11 September 1997. The following sections detail the measurements that were used to estimate these heat flux components in Equation 3 and thereby the net air–water heat flux. Net air–water heat flux (Qair ) The time series of hourly MHB net air-to-water heat flux (Fig. 9g), which was estimated according to Equation 2, shows the expected diurnal heating/ Figure 9. Hourly MHB summer 1997 heat-flux estimates: (a) wind stresses based on measurements at TFG; (b) air temperature at TFG (solid) and spatially averaged surface temperature for MHB (dashed); (c) solar insolation; (d) longwave back radiation; (e) net sensible heat flux; (f) latent heat flux; and (g) net air–water heat flux Qair. 58 Northeastern Naturalist Vol. 13, Special Issue 4 cooling cycle. The time-averaged heat-flux value for the study period is negative, indicating average heat loss from the surface of MHB waters during the 9 August to 11 September 1997 study period. Qi , the hourly values of incident shortwave solar radiation (obtained from R. Payne/WHOI), shows the expectedly clear diurnal cycle (Fig. 9c). Qb, measurements of net longwave radiation to space, were not available and Qb was set to a constant value of -100 watts/m2 (Fig. 9d). Qh , the net sensible heat flux (Fig. 9e), is proportional to the wind speed (W) at 10 m elevation and the difference between air temperature (Ta ) at 10 m elevation and water surface temperature (Tw), where: Tw, the surface water temperature, was derived from the 30 thermistor chain records that ASA deployed in Mount Hope Bay between 9 August and 10 September 1997 at the locations shown in Figure 1. Like the winter 1999 measurements, the temperatures were measured every 5 minutes at 5 or 6 depths from the surface to the bottom at these stations. The T-chain data, which was processed like the winter ASA data as described above, was spatially averaged to produce the Tw (Fig. 9b) that is dominated by diurnal fluctuations. Because the MHB surface temperature pattern in summer (e.g., Fig. 10; also see Fan and Brown 2003) is more complex than that in the winter (Fig. 4), the area-weighted space averaging that was used might lead to greater uncertainty in the heat-flux estimates. Ta: The air temperature from T.F. Green Airport from 9 August to 10 September 1997 are shown in Figure 9b. As we discussed above, 1.1 ºC was added to the record so that it would be more similar to the Fall River air temperature. W: The hourly winds from TFG were used to estimate the wind stress shown in Figure 9a. The distinct diurnal cycle is due to the very strong summer sea breeze in the Narragansett Bay region (see Fan and Brown 2003). The sensible heat flux is shown in Figure 9e. Qe: The latent heat flux (Fig. 9f) was estimated according to Equation 4b from measured atmospheric temperature (Ta), water surface temperature (Tw), wind speed (W), and dew point temperature (TD), which is used to estimate relative humidity (Hr) as follows. Hr: The relative humidity of air parcels at 10 m elevation was estimated according to the following relation (Tetens 1930): Hr (%) = 100(ea / es) (7) where the air at the water surface is assumed to be saturated, and thus, es— the saturation vapor pressure—is: es = 0.6108 exp(17.27Ta / (Ta + 237.3)) (8) and where ea—the atmospheric vapor pressure—is: ea = 0.6108 exp(17.27TD / (TD + 237.3)) (9) in which TD is the dew point temperature of the air at elevation. 2006 Y. Fan and W.S. Brown 59 Figure 10. The late ebb-tide surface-temperature structure in MHB on 9 August 1997. Power plant heat input The diurnal variability of the Brayton Point Power Station heating rate of Mount Hope Bay (dHBPPS/dt; Fig. 11) ranges from mid-day maxima of about 1.5 x 106 kW to midnight minima of about 0.9 x 106 kW. MHB temperature: Air–water heat flux and BPPS heating only The model temperature record based on just the net air–water cooling and BPPS heating processes (see Equation 6) and referenced to the observed 60 Northeastern Naturalist Vol. 13, Special Issue 4 Figure 11. The hourly summer 1997 Brayton Point Power Plant heating rate of MHB (dHBPPS/dt) (BPPS data). 9 August 1997 temperature (0000 GMT 9 August 1997 is used as the referenced time 0) is much warmer than the measured volume-averaged MHB temperature (Fig. 12). The differences could be due solely to the potentially significant uncertainties of our estimate of air–water cooling (e.g., Qb); it could also be the result of unaccounted for cooling due to the NB/SR/MHB exchange. We address the latter issue next. Lateral heat inputs to MHB The depth-averaged temperature records for the summer (Fig. 13) clearly show that: (1) the Taunton River inflow heats MHB, and (2) the net tidal exchange between MHB and Narragansett Bay (and presumably the Sakonnet River) cools MHB. Clearly, we must consider the NB/SR tidal cooling of MHB. But first we estimate the heating rate of the Taunton River. Taunton River heat input. The application of Equation 2 to the Taunton River heating yields the following: dHriver / dt = 􀁬 cp Uriver 􀁢Triver (10) Where 􀁢Trive is the difference in temperature in the river and MHB. The transport rate (Uriver) is estimated from the daily Taunton River volume discharge rate time series (Fig. 14), which was obtained from the US Geological Survey Taunton River gauge near Bridgewater (41º56'02"N, 70º57'25"W). The average discharge of the Taunton River during the study period was about 2 x 105 m3/day (􀂧 2 m3/s). Assuming a Taunton River crosssection area Ai = Ariver = 1000 m x 5 m, the section-average velocity (Uriver) is about 40 m/day (􀂧 5 x 10-4 m/s). Appropriate substitutions into Equation 10 2006 Y. Fan and W.S. Brown 61 Figure 12. Model MHB temperature (i.e., Equation 7; solid line with solid squares) based on the combined BPPS (solid line with open circles) and air–sea (solid line with filled circles) heating/cooling processes. The measured MHB volume-averaged temperature (solid line with open squares) is shown for reference. The grey band depicts the model MHB temperature range corresponding to a ± 20% difference in back-radiation estimate. yields a Taunton River heat input to MHB of about 0.02 x 106 kW. Since this estimated Taunton River heating rate is only about 2% of the BPPS heating rate, it can be neglected here. Narrganasett Bay (Sakonnet River) heat input. During flood tide, cooler NB/SR water (􀁢Ti = 8 ºC) enters/exits MHB under the Mount Hope and Sakonnet River Bridges at an estimated average rate of about 6 x 106 m3/hr (􀂧 2 x 103 m3/s; see Rountree et al. 2003). (For simplicity, we have assumed that Sakonnet River water is the same temperature as Narragansett Bay water.) Turbulent mixing on the edges of the inflowing/outflowing NB/SR water effectively exchanges colder parcels with the warmer MHB parcels, leading to the cooling/warming of MHB and NB/SR waters, respectively. During ebb tidal phase, much of that water (now warmer through mixing with the MHB water) leaves MHB. The question is: how efficiently do the two water masses mix? The net amount of MHB cooling during each tidal cycle depends on: (1) the proportion (􀁟) of the entering cooler NB/SR water that mixes completely (i.e., exchanges parcels) with the warmer MHB water during the 12.4 h semidiurnal flood–ebb tidal cycle, and (2) the effective transport rate of that mixed water. For purposes of this analysis, the NB/MHB tidal exchange process is conceptually modeled (Fig. 15) in terms of a steady stream of NB water 62 Northeastern Naturalist Vol. 13, Special Issue 4 Figure 13. Depth-averaged temperature time series at ASA sites (see Fig. 1) in the Taunton River (black line with filled circles) and the East Passage of Narragansett Bay (black line). Note that the Mount Hope Bridge temperature (white line) is only slightly warmer than the Narragansett Bay temperature. The MHB volume-averaged temperature (black line with open circles) is shown for reference. Figure 14. Taunton River daily discharge time series (from the USGS website). 2006 Y. Fan and W.S. Brown 63 Figure 15. A conceptual model of the tidal cooling of MHB during the summer. Steady streams of cooler water enter MHB through two semi-permeable pipes from Narragansett Bay and the Sakonnet River, respectively. The cooler waters are warmed through exchanges with MHB before they exit as shown. (UNB) that (a) flows into MHB through a permeable pipe on the south side of the entrance under the Mount Hope Bridge, (b) loops through and exchanges water with MHB at a rate 􀁟, and then (c) exits on the north side of the MHB entrance. (A similar conceptual loop model with transport (USR) can be constructed to deal with the Sakonnet River/MHB exchange). Here we combine the two processes into a single process with a steady composite NB/ SR transport rate (UNB/SR) that, to be consistent with the overall MHB tidal prism inflow/outflow, must be half the average tidal inflow/outflow rate, or about 103 m3/s. Thus, the heating rate relation for composite NB/SR tidal exchange cooling is: dHNBSR / dt = 􀁟 􀁬 cp UNB/SR 􀁢TNBSR, (11) where the temperature difference (􀁢TNBS) between Narragansett Bay/ Sakonnet River and MHB is assumed to be the same for both loops. How important is the tidal exchange cooling mechanism? Assume for example 64 Northeastern Naturalist Vol. 13, Special Issue 4 that, if 5% (􀁟 = 0.05) of the entering NB/SR tidal prism water mixes with the MHB waters, then UNB/SR = 50 m3/s of the cooler NB/SR water enters MHB and effectively replaces the warmer MHB water which exits at the same rate. Then Equation 11 yields a NB/SR heat input to MHB of about -1 x 106 kW— i.e., a cooling rate that is of the same order of magnitude as the BPPS heating rate and needs to be considered. MHB temperature: Air–water and NB/SR cooling with BPPS heating Assuming a totally mixed MHB and heat input from the power plant and exchanges with the Narragansett Bay/Sakonnet River, Equation 1 reduces in this situation to: 􀂴􀂦 􀂥 􀂲􀂤 􀂣 = = + + dt dH dt dH Q A dt dT C V dt dH NBSR BPPS air MHB MHB p MHB t 􀁬 (12) The corresponding temperature equation is: ( ) ( ( )) ( ) ( ) ( ) ( ) ( ) 0 0 0 0 1 T t t A Q t H t H t H t H t c V T t MHB BPPS n BPPS NBSR n NBSR n i MHB air i p MHB MHB n + 􀂵 􀂘 􀂗 􀂳 􀂖 􀂕 􀀼 + 􀀼 + 􀀶 = 􀀭= 􀁬 (13) where 0000 GMT 9 August 1997 is used as the referenced time 0, and the assumed values of the other constants are the same as in Equation 6. The temperature measurements at the East Passage station are used to estimate the MHB–Narragansett Bay temperature difference in Equation 2, since there was only a partial Mount Hope Bridge temperature (see Fig. 13). Nevertheless, the East Passage and the Mount Hope Bridge station temperature are nearly the same. Three estimates of model temperature in the Bay Equation 13 were made for the Narragansett Bay/Sakonnet River/MHB mixing, assuming the mixing coefficient 􀁟 to be 0.02 (2%), 0.03 (3%), and 0.04 (4%), respectively (Fig. 16). While the comparisons are not perfect, a mixing coefficient of 0.03 produces Bay average temperature records that match the observations reasonably well for the research period. The departures from a perfect match seem to be related to the effects of spring/neap tidal variability, which is not included in this analysis. The relative contributions of solar heating and BPPS heating of MHB, and the relative contributions of the atmospheric cooling and tidal cooling of MHB for this study period, are computed and documented in Table 3. We can see that the BPPS heating accounts for 15% of the total heating, while solar heating account for 85% of the total heating during this summer study period. As for the cooling process in MHB, the air–water cooling accounts for 84.4% of the total cooling, while the tidal exchange between NB/SR and MHB accounts for the other 15.6% of the total cooling. Discussion In these applications of the heat budget model, we assumed a well-mixed MHB and used spatially-averaged surface temperatures in estimating the air– 2006 Y. Fan and W.S. Brown 65 Figure 16. MHB temperature (Equation 13) due to the combined influence of air–sea, NB/SR, and BPPS heating/cooling processes. The three temperature records are due to different mixing coefficients. The measured MHB volume-averaged temperature is presented for reference. Table 3. Mean values of the heating rate of each air–water heating component, the BPPS heating rate, the tidal cooling rate, the ratio of the mean solar heating rate to the mean BPPS heating rate, and the ratio of the mean solar cooling rate to the mean tidal cooling rate. In this table, positive values stand for heating. Air–water heating (million kW) BPPS heating Tidal cooling Heating ratio Cooling ratio Qi Qb Qh Qe (million kW) (million kW) BPPS/Qi (Qb+Qh+Qe)/tides 7.133 -3.52 -0.353 -3.768 1.258 -1.429 0.175 5.4179 water heat fluxes. During the winter, when the warm plume from the power plant had a relatively simple structure (Fig. 5), this may have been acceptable. In the summer, however, the BPPS plume expression was larger and more complex (Fig. 10), and its highest temperature portions may not have been resolved properly by the thermistor chains. To test this idea, the MHB surface area (AMHB) is first partitioned into two sections: a smaller portion (0.2 AMHB) representing the plume with an average surface temperature Tplume , and a larger portion (0.8 AMHB) representing MHB proper with an averaged surface temperature TBay. The percentage of the plume area was chosen based on the ASA thermistor measurements (see Fan and Brown 2003 for details). Assuming previous underestimates of surface 66 Northeastern Naturalist Vol. 13, Special Issue 4 Table 4. Vertical heat flux in the plume area. Tplume - TBay (oC) VHFplume (102 kW) E (%) 1 -2.186 16.6 2 -3.632 34.3 3 -5.160 52.9 4 -6.771 72.5 5 -8.466 93.2 6 -10.247 114.9 7 -12.118 137.7 8 -14.080 161.6 9 -16.138 186.7 10 -18.294 212.9 temperature in the plume region, Tplume is varied between TBay + 1 ºC and TBay + 10 ºC, where TBay = Tw from above. For this range of Tplume temperatures, the time-averaged vertical heating rate (heat flux • area) of the plume— VHFplume—is computed (see Table 4). This is compared with the T-chainbased time-averaged vertical heating rate for MHB or VHFBay = -8.2 x 102 kW in estimating the potential error. The normalized error (E) in the MHB heating rate for a particular Tplume is estimated by differencing VHFplume with the portion of VHFBay in the plume area according to: E = {(VHFplume - 0.2 VHFBay) / VHFBay}. (14) The results in Table 4 show how much error there would be in the overall MHB cooling rate for a particular downward bias of the T-chain “surface” temperature relative to the true temperature in a plume patch covering 20% of MHB. This result suggests that the spatial structure of air–water heat loss is very important for the heat budget estimation in MHB, especially during summer, when the temperature structures in the Bay are very complicated. It also suggests that due to this uncertainty in heat budget estimation, the proportion (􀁟) of the entering cooler NB/SR water that mixes completely with the warmer MHB water can have considerably large variations too. Summary and Conclusions Using a box model, heat budgets have been constructed for two onemonth periods during winter 1999 and summer 1997, respectively, in MHB. In this box model, we assume a homogenous MHB which receives heat (a) through the air–water interface, (b) from Narragansett Bay (NB), (c) from the Sakonnet “River” (SR), (d) from the Taunton River, and (e) from the Brayton Point Power Station. Comprehensive ASA measurements of MHB temperature fields and meteorological data from T.F. Green Airport were used to estimate the different heat flux component contributions. We also incorporated the Brayton Point Power Station heat-input measurements in our heat-budget estimation. River contributions to the heat budget were negligible in both seasons. 2006 Y. Fan and W.S. Brown 67 The winter (February–March) 1999 results show that the BPPS heating is balanced (within the uncertainty of the estimates) by air–water cooling alone. By contrast, the summer (August–September) 1997 results show that the BPPS heating of MHB is approximately balanced by air–water cooling, which accounts for 84.4% of the total cooling, and cooling due to tidal exchange between MHB and NB/SK, which accounts for 15.6% of the total cooling. The summer heat balance between the BPPS heating and cooling is achieved by assuming that 3% of the colder NB/SK tidal input water is exchanged with the warmer MHB during each tidal cycle. Studies of model sensitivity to the air–water heat exchange show model MHB temperature is sensitive to inaccuracies in the environmental heat-flux estimates. In particular, the model MHB temperature is most sensitive to percentage errors in relative humidity. Air–water heat loss estimates are sensitive to the actual structure of the surface temperature field, especially during summertime, when the temperature structures in the Bay are very complicated. More work is necessary to improve the heat budgets in MHB, e.g., obtaining more accurate local meteorological measurements in MHB, exploring spatial structure of air–water heat loss, and better defining the Narragansett Bay/Sakonnet River tidal cooling process. Acknowledgments The research described herein has benefited from the work of a great many individuals, including Richard E. Payne, who made the shortwave radiation data available to us, as well as our colleagues Lou Goodman, Dan MacDonald, and Zhitao Yu, with whom we have had great discussions on this topic; Meredith Simas at Brayton Point Power Station, who provided us with the power station heat-input measurements; and Applied Science Associates, Inc, who provided us with the themistor chain measurements. Support for Y. Fan was provided by the Brayton Point Power Station. This paper is #03-0801 in the SMAST Contribution Series, School for Marine Science and Technology, University of Massachussetts Dartmouth. Literature Cited Beardsley, R.C., E.P. Dever, S.J. Lentz, and J.P. Dean. 1998. Surface heat-flux variability over the northern California shelf. Journal of Geophysical Research 103:21553–21586. Chinman, R.A., and S.W. Nixon, 1985. Depth-area-volume relationships in Narragansett Bay. NOAA/Sea Grant marine Technical Report 87. University of Rhode Island, Narragansett, RI. 64 pp. Fan, Y., and W.S. Brown 2003. The heat budget for Mount Hope Bay. Technical Report, SMAST-03-0801, School for Marine Science and Technology, University of Massachusetts, Dartmouth, MA. Mupparapu, P., and W.S. Brown 2003. Role of convection in winter mixed-layer formation in the Gulf of Maine, February 1987. Journal of Geophysical Research, 107(C12):3229 68 Northeastern Naturalist Vol. 13, Special Issue 4 Mustard, J.F, M.A. Carney, and A. Sen, 1999. The use of satellite data to quantify thermal-effluent impacts. Estuarine, Coastal, and Shelf Science 49:509–524. Rountree R., D. Borkman, W.S. Brown, Y. Fan, L. Goodman, B. Howes, B. Rothschild, M. Sundermeyer, and J. Tunner 2003. Framework for formulating the Mount Hope Bay Natural Laboratory: A synthesis and summary. Technical Report. SMAST-03-0501, School for Marine Science and Technology, University of Massachusetts, Dartmouth, MA. Tetens, O. 1930. Uber einige meteorolgische Begriffe. Zeitschrift fur Geophysik 6:297–309. 2006 Y. Fan and W.S. Brown 69 Appendix. Sensitivity test. The accuracy of TMHB is subject to the significant uncertainties in the quantities that were used to estimate the Bay cooling. Therefore, we tested the sensitivity of MHB temperature TMHB (Eq. 13) to a range of values for relative humidity, wind speed, and longwave radiation through their effects on vertical heat flux. For these tests, we assumed a constant longwave radiation Qb = -100 watt/m2 and 3% tidal mixing. Sensitivity to relative humidity uncertainty Figure A1 shows that relative humidity uncertainties of ± 20% produce Bay temperature uncertainties of ± 6.5 °C. Sensitivity to wind speed uncertainty Figure A2 shows that wind speed uncertainties of ± 20% produce Bay temperature uncertainties of ± 2.7 °C. Sensitivity to long-wave radiation (Qb) uncertainty Figure A3 shows that longwave radiation uncertainties of ± 20% produce Bay temperature uncertainties of ± 2.0 °C. Figure A1. Model MHB temperatures (Eq. 12) due to relative humidity values that are ± 20% relative to the reference case relative humidity. The volume average measured MHB temperature (grey line with solid squares) and model MHB temperature (black line with triangles) are given for reference. 70 Northeastern Naturalist Vol. 13, Special Issue 4 Figure A2. Model MHB temperatures (Eq .12) due to wind speed values that are ± 20% relative to the reference case wind speeds. The volume average measured MHB temperature (grey line with solid squares) and model MHB temperature (black line with triangles) are given for reference. Figure A3. Model MHB temperatures (Eq. 12) due to longwave radiation values that are ± 20% relative to the reference case longwave radiation. The volume average measured MHB temperature (grey line with solid squares) and model MHB temperature (black line with triangles) are given for reference.