50

distribution. The *v*1 and *v*2 results and the differ-

ence between these values nondimensionalized

40

by the corresponding mean velocity are given in

Figure 9. Except for a few points, the absolute

30

value of this dimensionless difference was less

20

than 0.04 in both records, corresponding to an

absolute value of the difference between *v *and

Raw Data

10

either *v*1 or *v*2 of less than 0.02 *v*. The delineation

Peak Data

of the limits of each radar trace and calculation of

0

a mean θ has reduced the large potential beam-

0

4

8

12

16

20

24

28

Time (min)

width error to the same order as the other minor

ment. The peak data are smooth relative to the

raw data, but they are shifted systematically to

lower velocities, following the downward shift

of the far edge of the trace. The resulting mean

velocity of the peak radar record is 1.35 m/s, and

close to the near edge of the footprint, consistent

that of the raw radar record is 1.61 m/s.

with the inverse relationship between backscat-

The velocity data from the video record are

tered power and range to the fourth power given

shown with the selected polynomial fit and the

in eq 1.

corresponding normalized error in Figure 10.

Using eq 11 we calculated θa for both the raw

The mean and median of the normalized error

and peak detector data records; we present the

were very close to zero, with a standard devia-

respective results in Figure 8 as a function of

tion of 0.026. The maximum normalized error of

time. For the raw data record the mean, median,

about 0.06 *v *is within the measurement error

and mode of θa are approximately equal, with a

bound for this method (Ferrick et al. 1992). Com-

mean of 44.6, a standard deviation of 2.2, and a

parison of the radar and video velocities reveals

range of 10.0. The mean, median, and mode of

that the video results are consistently low. For

θa for the peak data record are also approximate-

ease of comparison we assume that this system-

ly equal, with a mean of 26.0, a standard devia-

atic difference is due entirely to video grid dis-

tion of 2.1, and a range of 9.4. The peak-finding

tortion. We obtain *C *in eq 14 from the ratio of the

algorithm significantly reduced the apparent

raw radar to video polynomial mean velocity

beam width of the radar without altering the θa

values as 1.067.

2.5

0.04

2.0

0.02

1.5

0

1.0

0.02

v1

0.5

0.04

v2

Raw Radar

Raw Radar

0

0.06

2.5

0.04

Peak Radar

Peak Radar

2.0

0.02

1.5

0

1.0

v1

0.02

0.5

v2

0

0.04

0

4

8

12

16

20

24

28

0

4

8

12

16

20

24

28

Time (min)

Time (min)

8