9780521861724htl 1..2

Table 8.3Summary of parameters obtained by multifractal analysis of body- and particle-size
distributions in the streams Seebach (SB), Llwch (LL) and Mynach (MY).a(1),a(0) anda(1) are
the Lipschitz-Ho ̈lder exponents with1SEforq¼1,q¼0andq¼1 respectively.r^2 are the
coefficients of variation of the linear regression of log partition function on log size for eacha(q).

Stream Body-size distribution

(1) r^2 (0) r^2 (1) r^2

SB 1.0390.078 0.998 1.0120.027 0.997 0.8820.002 0.998
LL 1.1310.024 0.999 1.0440.003 0.999 0.9490.001 0.999
MY 1.0750.011 0.999 1.0300.001 0.999 0.9680.001 0.999

Stream Particle-size distribution

(1) r^2 (0) r^2 (1) r^2

SB 1.3890.096 0.995 1.1380.004 0.999 0.7920.003 0.996
LL 1.2440.047 0.996 1.0870.002 0.999 0.8420.003 0.996
MY 1.2890.033 0.999 1.0980.002 0.999 0.7670.002 0.997

LL

–20

–10

0

10

20

30

40

SB

Log partition function, log

μq

(λ

)–20

–10

0

10

20

30

40

MY

–20

–10

0

10

20

30

40

q = –10

q = 10

Log body-size, λ (mm)

–1.0–0.8–0.6–0.4–0.20.00.20.40.60.8

Figure 8.5Log partition function, logq(l), as

a function of log body-size (l)forq-moments in

the range between10 and 10 at 0.5 lag

increments for the streams SB, LL and MY.

Linear regressions are superimposed for each

q-moment (for allr^2 0.95;P<0.001).

Significant linear relationships are similar for

particle-size distributions not shown here.

BODY SIZE AND SCALE INVARIANCE 157