High temperature at which ice breakup begins (in degrees

Celsius).

4.50

0.331

--

Low temperature at which sudden increases in apparent

streamflow indicates ice accumulation (in degrees Celsius).

2.25

0.141

--

High temperature at which ice breakup is complete (in

degrees Celsius).

10.0

0.206

--

Exponential weighting factor for daily temperatures.

0.95

0.430

--

Threshold at which changes in apparent daily streamflows

are considered large.

0.30

10.5

--

Offset streamflow ratio.

0.0681

--

0.0132

Autoregressive parameter for streamflow ratio.

0.990

--

0.000186

Parameter relating air temperature to changes in streamflow

ratios (in degrees Celsius1).

0.000939

--

0.00000372

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 *x*3=0.990. Streamflow ratios increase at a rate *x*4 = 0.000939C1 about a

temperature offset *x*5 = 9.37C, a lower temperature than that estimated for the St. John River.

Unfortunately, the estimated streamflow ratio offset of *x*2 = 0.068 is not physically realizable. Anal-

ysis of the state error covariance matrix shows a maximum positive correlation of 0.81 between *x*3

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 *x*2 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 *z*1-) (*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

13