7KH3UHGLFWLRQ0HWKRGRI:DWHU 7HPSHUDWXUHLQ'LVWULEXWLRQ3LSHV

Transcription

1 7KH3UHGLFWLRQHWKRGRI:DWHU 7HPSHUDWXUHLQ'LVWULEXWLRQ3LSHV 'U.6DNDXH'U.DPDWD'U6,ZDPRWR'U +1LPL\D (1) 6DNDXH#LVFPHLMLDFMS Dept. of Architecture, School of Science and Technology, Meiji University, Japan. () Dept. of Architecture, Graduate School of Engineering, University of Tokyo, Japan. (3) Dept. of Architecture, Fac. of Engineering, Kanagawa University, Japan. (4) Dept. of Environmental Design, Fac. of Design, Nagaoka Institute of Design, Japan. $EVWUDFW Hot water supply system accounts for more than 3% of all energy consumption in buildings such as hotel, residential houses and hospitals. In considering energy conservation in buildings, therefore, reduction of energy consumption in hot water supply system poses an important issue. The first step to grapple with this problem is to predict water supply temperatures. In this report we measured water temperatures at purification facilities in 9 major cities in Japan, conducted correlation analysis in relation to air temperature, and established regressive equations to predict water temperature from air temperature. A prediction method of water temperature is indicated based on the calculation models for two separate water passages: one from the source of rivers to purification facilities, the other from purification facilities to distribution pipes..h\zrugv Hot water supply system, Water distribution pipes, Water temperature, Prediction method,qwurgxfwlrq The percentages of energy consumption accounted for by hot water supply system in various types of buildings in Japan are: approximately 3% in office buildings, over 4% in hospitals, roughly 35% in residential houses and about 3% in hotels (Figure 1). In considering energy conservation in buildings, reduction of energy consumption in hot B4 1/15

2 water supply system plays an important role. To measure efficiency of energy conservation, we used coefficient of energy consumption for hot water supply (CEC/HW). In this method Japan is divided into 9 climatic regions and hot water supply loads are estimated for each region based on monthly water supply temperatures. Energy control of water supply system, therefore, necessitates prediction of water temperatures. In Japan approximately 3% of water used for water works is derived from underground and 7% from rivers (Figure ). The temperatures of river water when passing through purification facilities and distribution pipes are affected by weather conditions, particularly by air temperatures, and they can be estimated by calculation. In this present study we measured water temperatures at purification facilities in 9 cities on the basis of climatic regions in Japan (Figure 3), analyzed their relationship to air temperature and proposed regression equations to predict water temperature from air temperature data. Furthermore, methods for predicting water temperature were developed for two separate water passages; one from the source of rivers to purification facilities, the other from purification facilities to distribution pipes. &RUUHODWLRQEHWZHHQ :DWHUDQG$LU7HPSHUDWXUHV XWOLQHRI6XUYH\DQG$QDO\VLV Water temperatures at 9 major purification facilities (Sapporo, Sendai, Niigata, Nagoya, Tokyo, Osaka, Fukuoka, Kagoshima, and Kochi) over the period of were measured. The climatic data of AMeDAS (Automated Meteorological Data Acquisition System) were used for air temperatures. In order to find annual and seasonal changes in the relationship between water and air temperatures at the purification facilities in Tokyo, we conducted correlation analysis both annually (from January through December) and seasonally (spring: April and May, summer: June to September, fall: October and November, winter: December to March). Since it is highly likely that previous air temperatures have any effect on the water temperature at purification facilities, we checked air temperatures of 3 days prior to the measurement of water temperatures and moving average temperatures of up to 1 days prior against water temperatures for correlation. In the following text, tables, and figures, the day air temperature was measured is designated as DAY-, 1 day before DAY-1, days before DAY-, and 3 days before DAY-3 on the basis of the day measured water temperature, respectively. 5HVXOWV As the first step we will outline correlation analyses conducted for 4 days (on DAY-, DAY-1, DAY-, DAY-3) and moving average temperatures for up to 1 days before DAY- taking purification facilities in Tokyo for example. Next, the result of correlation analysis based on annual data of 9 cities and effect of low air temperatures are discussed. 5HVXOWRIDQDO\VLVLQ7RN\R Figure 4 shows the fluctuations of air and water temperatures in Tokyo. Water and air temperatures changed concomitantly, but air temperatures were typically higher than water temperatures in summer and the tendency was reversed in winter. B4 /15

3 D$QDO\VLVEDVHGRQDLUWHPSHUDWXUHV Correlation coefficient between water and air temperatures on each measurement day (DAY-, DAY-1, DAY-, DAY-3) based on annual data is shown in Figure 5, and that based on seasonal data is shown in Figure 6. Correlation coefficient tended higher for both annual and seasonal data on DAY-1 and DAY-. The highest correlation coefficient was.89 in spring and fall followed by.8 in summer and.7 in winter. E$QDO\VLVEDVHGRQPRYLQJDYHUDJHWHPSHUDWXUHV Correlation coefficient between water temperatures and moving average air temperatures based on annual data is shown in Figure 7, and that based on seasonal data in 1993 is shown in Figure 8. Correlation was the highest with 6 days moving average temperatures in annual analysis while seasonally correlation was high with 4 days moving average temperatures in spring and fall, with 6 days in summer, and 7 days in winter. In all seasons correlation with one day average was the lowest. Seasonally the highest correlation coefficient was.9 in spring and fall, and.81 in summer, then.76 in winter. This agrees with the result of analysis based on air temperatures measured on each measurement day. 5HVXOWVRIDQDO\VLVLQFLWLHV D$QDO\VLVEDVHGRQDLUWHPSHUDWXUHV Table 1 shows the days on which air temperatures were measured, highest and lowest values of correlation coefficient based on annual data for 8 cities in Here the analysis is based on purified water. However, the temperatures of river water were used for the cities where no data was obtained on purified water. Kagoshima is not included in the analysis since water temperature was measured only once a month in the city. Correlation coefficient was highest on DAY-3 in Sendai and Nagoya, DAY- in Osaka and DAY-1 in the other cities. The lowest correlation coefficient was seen on DAY-3 or DAY- except for Nagoya. In Sapporo and Sendai correlation coefficient was lower than the other cities. It is probable that low temperatures in these cities in winter lowered the correlative values between water temperatures and air temperatures. E5HODWLRQVKLSEHWZHHQZDWHUWHPSHUDWXUHDQGORZDLUWHPSHUDWXUH As mentioned above correlation coefficient in Sapporo and Sendai was lower than the other cities. It is assumed that in winter the water temperature does not change concomitantly with the air temperature in these cold regions because of a large number of days with average air temperatures below freezing point. Therefore we then analyzed the relationship between low air temperature and temperature of purified water taking Sapporo as an example. Figure 9 shows the changes in water temperatures and air temperatures from April 1991 through March It can be clearly seen that the temperature of purified water leveled off when air temperature is below 5 ºC, and the overall correlation is extremely low. In view of this fact two separate regression equations were created; one for the air temperatures where the correlation coefficient with water temperatures begin to increase and the other for the air temperatures below that point. The point where this shift in correlation occurred is called the shifting temperature point. As a result the air temperature at the shifting point was found to be 4 degrees centigrade, and the regression model is shown in Figure 1. B4 3/15

4 &DOFXODWLRQRI7DS:DWHU7HPSHUDWXUHLQHDFKUHJLRQ Based on the analyses described above, the highest correlation coefficient can be obtained when moving average temperatures of several days prior to DAY- are used. This procedure, however, requires complex calculation. On the other hand correlation coefficient derived from actual air temperatures is only a little lower than that obtained from moving average temperatures. When correlation coefficients on each air temperature measurement days are compared, the differences are insignificant, but coefficient is lowest on DAY-. Taking this fact into consideration, we adopted regression equations, which are based on air temperatures on DAY-. Table shows highest and lowest values of both water and air temperatures, regression coefficient and regression constant. The temperatures obtained from these regression equations are water temperature at purification facilities, and not necessarily identical to the temperature of tap water. Here, however, the two are considered as the same for the sake of convenience. 3UHGLFWLRQRI7DS:DWHU7HPSHUDWXUH Temperatures at two different water passages; one from rivers to purification facilities and the other from purification facilities to water taps were measured, and a prediction method was postulated. To test the accuracy of the method, temperatures were measured at Kanamachi purification facilities in Tokyo for both river water and purified water, and data were also collected from 13 thermometers installed throughout the distribution pipes. The climatic data of AMeDAS were used for air temperatures and solar radiation. 3UHGLFWLRQRI,QOHW:DWHU7HPSHUDWXUH The temperature of river water rises or drops as a result of heat exchange with atmosphere or riverbed as the river travels along. The temperatures predicted by Kondo s equations 3) were checked against the actual temperatures of inlet water (water temperatures at the inlets of purification facilities), and examined if the equations can be used as a prediction model. The actual inlet water temperatures were taken from 1993 data. In Kanamachi purification facilities, temperature at the water intake was considered identical to inlet water temperature since the water intake is only 1m away from the purification facilities. XWOLQHRIFDOFXODWLRQPRGHODQGPHWKRGV The temperature of river water is affected by atmospheric conditions (solar radiation, air temperature) and other factors such as water temperature at the source, water depth, flow speed, and thermal capacity and thermal conductivity at the riverbed. To begin with temperature at the river source (7 ) was calculated, and then temperature at the water intake (7 : ) was figured out from 7 R and equilibrium temperature (7). The equations are shown in Tables 3~5. Temperature at the river source was considered the same as that of raindrops when there is precipitation, and as an average of the soil temperatures at the depth of = (1.5m) and = (.1m) when there is no precipitation. River conditions were analyzed by changing water depth (G Z ) and the time (τ) that takes water to move from the river source to the purification facilities (O [ ). B4 4/15

5 5HVXOWV The predicted temperatures matched most closely with actual temperatures when 11 hours elapsed, on condition of water depth : G ZÃ =.5m, elapsed time: τ= 1~ hours with an increment of 1 hour (Figure 11). Table 6 shows mean deviation between predicted and actual temperatures of inlet water when water depth (G Z ) was changed from.m to 1.m with an increment of.1m. As a result inlet water temperatures are found to be predicted with an accuracy of ±1.5~. ºC 3UHGLFWLRQRI7DS:DWHU7HPSHUDWXUH The temperature of water carried from purification facilities to water taps changes as a result of heat exchange with the soil around distribution pipes. Taking heat balance into consideration, we created equations to obtain tap water temperature from the length of distribution pipes, compared predicted water temperatures with actual water temperatures. XWOLQHRI&DOFXODWLRQRGHODQG&DOFXODWLRQHWKRG A simplified model of a distribution pipe is shown in Figure 1, an actual model including diameter and length in Figure 13, and a schematic representation of cross section of a pipe in Figure 14. Tables 7~9 show equations to obtain underground soil temperatures, over-all heat transfer coefficient, and temperatures at water tap. Mean deviations (Σ y - y /n) between predicted temperatures (y ) and actual temperatures (y) were obtained with depth of pipes and over-all heat transfer coefficient below as parameters, and the validity of the prediction equations was analyzed. Pipe diameters shown in Table 7 are those of the main pipes. ➀ depth of pipes (=): constant at 1.m and variable between.5m and 1.5m with an increment of.1m ➁ over-all heat transfer coefficient (. / ): variable in the range of ~419 kj/(m. h. ºC) with an increment of 9.5. &DOFXODWLRQUHVXOWV Mean deviations were calculated under the conditions shown in Table 7 with the depth of pipes as constant at 1.m. As a result water tap A showed the largest mean deviation and water tap M the smallest. Figure 1 and 13 show the changes of predicted temperatures and actual temperatures over time between the two water taps. When the depth of pipes were varied, mean deviation was the smallest at the depth of.7~.9m, but the difference from the result at the depth of 1.m was small (.5). The calculation results with variable over-all heat transfer coefficient showed small mean deviations when over-all heat transfer coefficient values are lower than those shown in Table 7. This was due to the fact that over-all heat transfer coefficients in Table 7 were calculated with a constant pipe diameter (diameter of main pipes). Mean deviations of over-all heat transfer coefficients and temperatures derived from a simplified model (with constant pipe diameter) and actual model (with variable diameters) on water tap A and water tap M are shown in Table 11. Over-all heat transfer coefficients are smaller in an actual model than in a simplified model. Mean deviations of tap water temperatures calculated with an actual model were approximately 1.9 (water tap A) and.5 (water tap M). Therefore we can conclude that the equations achieved a high degree of prediction accuracy. B4 5/15

6 &RQFOXVLRQ In this report we have examined the method to predict tap water temperatures based on air temperatures. The results can be summarized as follows: (1) Comparison of water temperatures with air temperatures on DAY-, DAY-1, DAY-, and DAY-3 at purification facilities in 9 major cities showed the highest correlation coefficient on DAY-1 in 7 cities. () When compared with moving average air temperatures, correlation coefficient was highest with 6 days moving average. (3) Seasonally correlation coefficient was highest in spring and fall followed by summer and winter. (4) Correlation between air and water temperatures was extremely low when air temperature was below 4ºC. (5) We proposed regression equations (regression coefficient, regression constant) for each of the nine cities based on annual data with air temperatures as a variable. (6) We predicted inlet water temperatures using prediction equations, and found the equations have an accuracy of ±1~ºC. (7) We created prediction equations for water temperatures in distribution pipes and predicted the temperatures at 13 water taps. Comparison with actual data showed that the equations are accurate within a tolerance of ºC. As a next step we intend to develop a method to predict water temperatures in water and hot water supply systems in buildings, and establish an overall water temperature prediction system which covers the whole process of water supply from rivers to buildings. Note: Though we did not mention in the text, we measured the temperatures of inlet and outlet water at the purification facilities and found that the temperature of outlet water is approximately.5~1.5ºc higher than that of inlet water. 5HIHUHQFHV 1) Institute for Building Energy Conservation: Manual of the method of calculation and the standard of energy conservation in buildings, (1998). ) National Land Agency: White book on water sources, (1998). 3) S. Kondo: Meteorology of water environment, Asakura-shoten, (1994). 4) K. Sakaue: What is energy conservation, Journal of Healthcare Engineering Association of Japan, Vol. 41, No. 6, pp.11-1, (1999). 5) T. Ide, K. Sakaue et al: Studies on back ground prepared and examined for design for hot water supply system (Part 8), Investigation on water temperature (Part 5), Collective Reports of Academic Research Symposium, SHASE, pp.81-84, (1997). 6) N. Shoda, K. Sakaue et al: Studies on back ground prepared and examined for design for hot water supply system (Part 9), Investigation on water temperature (Part 6), Collective Reports of Academic Research Symposium, SHASE, pp.45-48, (1999). B4 6/15

7 Others Hot water supply Electric power Air conditioning House* Office Hospital Hotel Dep. store )LJXUH5DWLRRIHQHUJ\FRQVXPSWLRQIRUYDULRXVXVHVLQYDULRXVW\SHV RIEXLOGLQJV Others 3% * It s electric power includes others Ground water 8% River water 69% )LJXUH5DWLRRIYDULRXVW\SHVRIZDWHUVRXUFHVIRUZDWHUZRUNV 1. Sapporo. Sendai 3. Niigata 4. Tokyo 5. Nagoya 6. Osaka 7. Fukuoka 8. Kochi 9. Kagoshima Latitude 3 )LJXUHFLWLHVRQWKHEDVLVRIFOLPDWLFUHJLRQVLQ-DSDQ B4 7/15

8 3 Temperature [ºC] Air temperature Water temperature at purification facilities 5 4/1 5/1 6/1 7/1 8/1 9/1 1/1 11/1 1/1 1/1 /1 3/1 Month (month/first) )LJXUH&KDQJHVLQUHODWLRQVKLSEHWZHHQZDWHUWHPSHUDWXUHDWSXULILFDWLRQ IDFLOLWLHVDQGDLUWHPSHUDWXUH7RN\R 1..9 Correlation coefficient DAY- DAY-1 DAY- DAY Year )LJXUH&RUUHODWLRQFRHIILFLHQWEHWZHHQZDWHUDQGDLUWHPSHUDWXUH RQHDFK PHDVXUHPHQWGD\VEDVHGRQDQQXDOGDWD 1. Correlation coefficient DAY- DAY-1 DAY- DAY-3.4 Spring Summer Fall Winter )LJXUH&RUUHODWLRQFRHIILFLHQWEHWZHHQZDWHUDQGDLUWHPSHUDWXUHRQHDFK PHDVXUHPHQWGD\VEDVHGRQVHDVRQDOGDWDLQ B4 8/15

9 Correlation coefficient Year With 1 day With days With 3 days With 4 days With 5 days With 6 days With 7 days With 8 days With 9 days With 1 days )LJXUH&RUUHODWLRQFRHIILFLHQWEHWZHHQZDWHUWHPSHUDWXUHDQGPRYLQJDYHUDJH DLUWHPSHUDWXUHZLWKHDFKaGD\VEDVHGRQDQQXDOGDWD Correlation coefficient Spring Summer Fall Winter With 1 day With days With 3 days With 4 days With 5 days With 6 days With 7 days With 8 days With 9 days With 1 days )LJXUH&RUUHODWLRQFRHIILFLHQWEHWZHHQZDWHUDQGPRYLQJDYHUDJHDLU WHPSHUDWXUHZLWKHDFKaGD\VEDVHGRQVHDVRQDOGDWDLQ 7DEOHD[DQGPLQRIFRUUHODWLRQFRHIILFLHQWEHWZHHQZDWHUDQGDLU WHPSHUDWXUHRQHDFKPHDVXUHPHQWGD\EDVHGDQQXDOGDWDLQFLWLHV Max. Min. City Correlation coefficient Measurement day of air temperature Correlation coefficient Measurement day of air temperature Sapporo.91 DAY-1.9 DAY-3 Sendai.93 DAY-3.9 DAY- Niigata.98 DAY-1.96 DAY-3 Nagoya.95 DAY-3.94 DAY- Tokyo.95 DAY-1.9 DAY- Osaka.99 DAY-.98 DAY- Fukuoka.95 DAY-1.9 DAY- Kochi.96 DAY-1.95 DAY-3 B4 9/15

10 15 Water temperature [ºC] Air temperature [ºC] )LJXUH5HODWLRQVKLSEHWZHHQZDWHUDQGDLUWHPSHUDWXUH'$< $SULOaDUFKLQ6DSSRUR Water temperature>ºc] Y Y=,74x~,61 Y=4 (4.,.4) X Temperature [ºC] )LJXUH5HJUHVVLRQPRGHOXVLQJVKLIWLQJWHPSHUDWXUHSRLQWž& 7DEOHD[DQGPLQRIZDWHUDQGDLUWHPSHUDWXUHDQGUHJUHVVLRQFRHIILFLHQW DQGFRQVWDQWLQFLWLHV City Air temperature [ºC] Water temperature[ºc] Regression coefficient Regression constant Max. Min. Max. Min. Sapporo Sendai Niigata Nagoya Tokyo Osaka Fukuoka Kagoshima Kochi DEOH(TXDWLRQVIRUWHPSHUDWXUHRIULYHUVRXUFH B4 1/15

11 7 7 = (] ) + 7 (] ) 1 1 (] ) = ) cos ( Qω W φ ) () Q < <1 <Q 7 ε Q = = I cos φ V ) Q = Q = 1 I Q Q ( Qω W ) (3) ω < exp ] D < 1 <1 1 ω<, ε = ] <Q (4) D 7 Ã Temperature of river source [ºC], Τ(]): Underground soil temperature [ºC], 7 6 Ã Ground surface temperature [ºC], ω : Frequency in a day(π/864[s -1 ]), φ: Phase difference, : Emissivity of water long wave, DTemperature diffusion coefficient (.7ò1 6 [m S -1 ]) [Affix] M: Average value in a day, Y: Seasonal variation, W: Water volume (1) 7DEOH(TXDWLRQVIRUHTXLOLEULXPWHPSHUDWXUH (UUR9tQFXORQmRYiOLGR (5) ( UHI ) = ε/ : χ = ιρ & 8 [ T ( 7 ) T ] + 6$7 3 µ = εσ7 + F ρ& 8 + ιρ& & 8 & (6) (7) 4 (8).8. ( ) ( ; ) = =, ( ) 1 ( 5.47 ) ( ) =.4615 / 1 ( ).6 S ( S.378H ) 6$7 & +8 =. (9) 8 = Τ Ã Equilibrium temperature [ºC], Τ Ã : Air temperature (=3[ºC]), 5 : Input solar radiation, ;Transport volume of latent heat [Wm- ], µcoefficient on infrared radiant, sensible heat and latent heat for condition of saturation humidity 7 : 7DEOH(TXDWLRQVIRUSUHGLFWHGZDWHUWHPSHUDWXUH = + * τ 7 ( ) exp τ (1) τ = F : ρ G : : µ (11) 7 Ã : Temperature of river source [ºC], τ: Elapsed time from river source to water intake [s], τ : Response time for water temperature [s] B4 11/15

12 3 5 Predicted è water temperature Actual Œ temperature 11h Temperature[ºC] )LJXUH&RPSDULVRQRISUHGLFWHGZDWHUWHPSHUDWXUHZLWKDFWXDOZDWHU WHPSHUDWXUHDWLQOHWRISXULILFDWLRQIDFLOLWLHV Days 7DEOHHDQGHYLDWLRQEHWZHHQSUHGLFWHGDQGDFWXDOWHPSHUDWXUHRI LQOHWZDWHUFKDQJLQJHODSVHGWLPHDQGZDWHUGHSWKGZ Elapsed time (τ) ) Water depth (GZ ) [m] [h] B4 1/15

13 G.L Underground soil temperature (Surface temperature in distribution pipes)θ s Depth of pipes Z Water temperature at outlet of purification facilities θ in Water temperature at water tap θ out Length of piping distribution piping L )LJXUH6LPSOLILHGPRGHORIGLVWULEXWLRQSLSLQJ L L Ã / L L.. / L L. 1 / 1 +. / + + L = = / /. L / L )LJXUH$FWXDOPRGHORIGLVWULEXWLRQSLSLQJ Asphalt λ 1 =1.17[kJ/(m. h.ºc)] Carbon steel λ =193[kJ/(m. h.ºc)] D D : Inside diameter D 1 : Outside diameter of first layer D : Outside diameter of second layer D 3 : Outside diameter D 1 D D 3 )LJXUH&URVVVHFWLRQRIGLVWULEXWLRQSLSLQJ B4 13/15

14 7DEOH&RQGLWLRQVRIGLVWULEXWLRQSLSLQJZLWKZDWHUWDSV Water Nominal Outside diameter Internal diameter Length of Over-all heat transfer Distribution line tap diameter [mm] [mm] [mm] piping [m] coefficient [kj/(m. h. ºC)] A Touzai line B Yotugi line C Terashima line D Touzai line E Terashima line F Mizue line G Terashima line H Senjyu line I Senjyu line J Kahama line K Kahama line L Kahama line M Kahama line DEOH(TXDWLRQIRUHDUWKWHPSHUDWXUH {.1714( Q = )}. = 7 = H cos 556 (1) *5= *5 *56 7 *5= : Underground soil temperature [ºC], 7 : Average temperature of a year [ºC], *5 =: Depth of pipes [m], 7 : Difference of ground surface temperature in a year [ºC], n: Days *56 1 7DEOH(TXDWLRQIRURYHUDOOKHDWWUDQVIHUFRHIILFLHQW ' = L log (13) π α' L= λ ' L α ' / 1. / : Over-all heat transfer coefficient [kj/(m.h. ºC)], ' : Inside diameter [m], ' 1 : Outside diameter [m], ', : Outside diameter of L layer [m], λ, : Thermal conduction rate of L layer [kj/( m.h. ºC )], α α Ã1 : Heat transfer rate of inside surface and outside surface [kj/(m.h. ºC)], θ θ RXW RXW 7DEOH(TXDWLRQIRUSUHGLFWHGZDWHUWHPSHUDWXUH../ = θ + ( θ θ ) H[S V LQ V F.* Z : Water temperature at outlet of piping (tap water temperature) [ºC], θ : Water temperature at inlet of piping (water temperature at outlet of purification facilities) [ºC], LQ θ : Underground soil temperature [ºC],.Over-all heat transfer coefficient [kj/(m. h. ºC)], 6 =: Depth of pipes [m], /Length of piping [m], & Z : Specific heat of water (=4.19[kJ/(kg. ºC)]), *: Flow rate [kg/h] (14) B4 14/15

15 7DEOHHDQGHYLDWLRQRISUHGLFWHGZDWHUWHPSHUDWXUHDWZDWHUWDSE\DFWXDO PRGHODQGVLPSOLILHGPRGHO Water tap Model of distribution piping Over-all heat transfer coefficient [kj/(m. h. ºC)] Mean deviation of tap water temperature ºC A M Actual model (Z=1.m) Simplified model (Z=1. m) Actual model (Z=1.m) Simplified model (Z=1. m) Temperature ºC Predicted water temperature Actual water temperature Days )LJXUH&RPSDULVRQRISUHGLFWHGZDWHUWHPSHUDWXUHZLWKDFWXDOZDWHU WHPSHUDWXUHDWZDWHUWDS$ Temperature Predicted water temperature Actual water temperature Days )LJXUH&RPSDULVRQRISUHGLFWHGZDWHUWHPSHUDWXUHZLWKDFWXDOZDWHU WHPSHUDWXUHDWZDWHUWDS B4 15/15