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# ANALYSIS OF THE MISSOURI - page 17 / 25

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measurements suggests a correlation to some degree between air temperature and water temperature. Further, as expected, the presence of ice including floating ice typically corresponded to a water temperature of 0o C. Intuitively, it would seem that water temperature would be in part a function of air temperature and because water temperature does not change rapidly as compared to air temperature, it would seem that water temperature would be a function of the mean air temperature during some previous period. Further because the water at the time of measurement was previously upstream; the mean temperature of concern would be the air temperature at some upstream location. Accordingly, an effort was made to find mean air temperature measurements at an upstream location. A search for temperature records indicated that generally daily maximum and minimum temperature were available for Tyndall, South Dakota, during the period of interest (1929-1955). For the dates when the Tyndall record was incomplete, data for Yankton, South Dakota, were available. In general, the average of the maximum and minimum daily temperatures is a good approximation of the daily mean temperature. Using the data available, empirical equations were tested to find an equation that could predict water temperature at Sioux City with confidence. One such equation that yielded good results was

Calc.Water Temp= (0.2 x Tt)+(0.3 x Tt-1)+(0.3 x Tt-2)+(0.2 x Tt-3).

Where T is the mean temperature for the day of concern, and the subscript ‘t’ is the present day. The relation between calculated and observed water temperatures is shown in figure 10. The degree of codependence if any among air temperatures is unknown.

CALCULATED VERSUS MEASURED WATER TEMPERATURES FOR THE MISSOURI RIVER AT SIOUX CITY

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# Calculated Temperature (deg. C

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20

15

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y = 0.9872x R2 = 0.8885

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# 0.0

5.0

10.0

15.0 Measured Temperature (deg. C)

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25.0

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Figure 10. Calculated versus measured water temperatures for the Missouri River at Sioux City. Data from USGS and NOAA.

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