Table 2. Threshold and filter parameters for the extended Kalman filter for the Platte River at
North Bend, Nebraska.
Estimated
Parameter
standard
symbol
Parameter description
Estimate
Sensitivity
error
t_hi
High temperature at which ice breakup begins (in degrees
Celsius).
4.50
0.331
--
t_lo
Low temperature at which sudden increases in apparent
streamflow indicates ice accumulation (in degrees Celsius).
2.25
0.141
--
t_ou
High temperature at which ice breakup is complete (in
degrees Celsius).
10.0
0.206
--
t_wt
Exponential weighting factor for daily temperatures.
0.95
0.430
--
q_dl
Threshold at which changes in apparent daily streamflows
are considered large.
0.30
10.5
--
x2
Offset streamflow ratio.
0.0681
--
0.0132
x3
Autoregressive parameter for streamflow ratio.
0.990
--
0.000186
x4
Parameter relating air temperature to changes in streamflow
ratios (in degrees Celsius1).
0.000939
--
0.00000372
x5
Offset temperature (in degrees Celsius).
9.37
--
0.169
Results from Platte River data also point out that mode 1 dynamics are highly autoregressive, as
indicated by the parameter x3=0.990. Streamflow ratios increase at a rate x4 = 0.000939C1 about a
temperature offset x5 = 9.37C, a lower temperature than that estimated for the St. John River.
Unfortunately, the estimated streamflow ratio offset of x2 = 0.068 is not physically realizable. Anal-
ysis of the state error covariance matrix shows a maximum positive correlation of 0.81 between x3
correlations are not thought to be sufficient to significantly degrade parameter estimates. However,
eliminate (set to zero) the streamflow ratio offset from the difference equation for mode 1 dynamics.
Such an elimination would reduce the dimension of the state space, which would also likely reduce
parameter ambiguity caused by high correlations in the state error covariance matrix. Values for the
threshold parameters that are less than optimal also possibly explain the discrepancy between the
estimated value of x2 and the conceptualized value.
Sensitivities for threshold parameters (Table 2) were estimated as the change in the sum of
squared errors in the streamflow ratio estimate divided by the change in the corresponding param-
eter near the selected values. The results of simulations indicate that projections are most sensitive
to changes in the q_dl parameter and least sensitive to the t_lo parameter. Again, formal optimiza-
tion of the threshold parameters could lead to further improvement in filter performance.
The temporal updates of streamflow on days of direct measurements compare closely with pub-
lished daily mean values (Fig. 10). Results show that the correlation between log-transformed val-
ues of z1-) (k ′) and z(k ′) , based on 87 days of ice-affected measurements, is 0.864 and is 0.997 based
(
on 345 days of open-water measurements. Measurements at the Platte River used in this analysis
averaged 3.2 weeks apart.
The relationship between published and projected streamflow values at the Platte River during
periods of ice effects is linear and unbiased in the logarithms of streamflow (Fig. 11). The distribu-
tion of discrepancies between published and projected values (Fig. 12) during periods of ice effects
were analyzed by use of eq 18; the absolute value of elements in the e sequence are less than 8%,
90.7% of the time, and are less than 15%, 97.7% of the time.
Projected streamflows are shown with other flow and climatological data for the selected peri-
ods in Appendix A. Upper and lower projections were computed by adjusting the variance of Q to
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