Environmental factors and aquatic macrophyte response in regulated lakes - a statistical approach

Aquatic Botany, 19 (1984) 199--220 Elsevier Science Publishers B.V., Amsterdam --Printed in The Netherlands

199

E N V I R O N M E N T A L F A C T O R S AND A Q U A TIC M A C R O P H Y T E R E S P O N S E IN R E G U L A T E D L A K E S - A S T A T I S T I C A L A P P R O A C H

BJQRN

RORSLETT

Norwegian Institute for Water Research, P.O.B. 333, Blindern, N-Oslo 3 (Norway) (Accepted for publication 23 February 1984)

ABSTRACT

R~rslett, B., 1984. Environmental factors and aquatic macrophyte response in regulated lakes -- a statistical approach. Aquat. Bot., 19: 199--220. In regulated lakes, it is necessary to distinguish between depth and relative elevation. Depth is the height of water overlaying the plants at any time, thus the instantaneous value m a y be nil. The optimal "depth" and elevation datum is shown to be the median water level. However, depth in its time-averaged sense is not equivalent to relative elevation w h e n the water level fluctuates throughout time. The magnitude of the discrepancy is generally large in shallow waters. Environmental stress factors, e.g. ice-scour, influence aquatics over a m u c h larger part of the "depth" gradient with a variable water level. Factors operating through threshold statistics,e.g. subsurface irradiance, are most adversely influenced by a time-varying water level. In general, regulation impact results in a compressed vertical niche. Simultaneously, the potential niche is shifted into deeper waters. Vegetation data from nine oligotrophic, regulated Norwegian lakes show significant correlation to the reduced vertical niche defined by ice-scour and threshold irradiance. Water-level schedules determine the actual vegetational response; thus the total probability distribution of water levels should replace the regulation height or mean annual range of water level variation in an analysis of response features.

INTRODUCTION E n v ir o n men tal factors pot ent i al l y influencing aquatic m a c r o p h y t e s are often functionally related to the water d e p t h (Sculthorpe, 1967; Hutchinson, 1975). Pertinent examples are: subsurface irradiance, h y d r o static pressure, t e m p e r a t u r e , t u r b u l e n c e , and sediment particle size. Neglecting successional effects, potential plant sites in a lake are spatially fixed and stationary in time (cf. Stanley et al., 1976). In m ost lakes, however, t h e water level itself is fluctuating t h r o u g h o u t time. Scandinavian lakes situated in larger watersheds have natural wide fluctuations, with annual water-level variations of 2--5 m. Lakes regulated for hydro-electric pow er p r o d u c t i o n o f t e n have regulation heights exceeding 5 m. Nearly one-half of the Norwegian reservoirs is regulated at 10 m or m o r e (Statistisk Sentralbyr~i, 1983, p. 27). 0304-3770/84/$03.00

© 1984 Elsevier Science Publishers B.V.

200

The vertical distribution of submerged m a c r o p h y t e communities in regulated lakes is clearly influenced by the annual water level amplitude (Quennerstedt, 1958; Wass~n, 1966; Nilsson, 1981; R~brslett, 1983, 1984). The response details, however, differ significantly between lakes (R~brslett, 1984). Communities of isoetids, generally the main benthic producers in the oligotrophic lakes of Norway, are thriving in some lakes with water-level variations exceeding 6 m, b u t m a y be largely lacking in closely similar lakes with smaller annual fluctuations. The cause of such p h e n o m e n a has a major bearing on the planning of regulation schemes, in order to minimize the ecological impact o f the scheme. The depth c o n c e p t relates to the vertical extent, or dimension, of a water layer, as seen d o w n w a r d s from the current water surface. Equivalently, this equals the height of the water layer above the b o t t o m . The vertical extent of water overlaying a submerged plant population in regulated lakes is obviously a time-dependent variable. Consequently, the impact of depth-related environmental factors also changes t h r o u g h o u t time. This paper focuses on a statistical description of " d e p t h " , and environmental factors related to " d e p t h " , when the water level fluctuates in time. The approach selected is to describe the fluctuations in a time-fixed coordinate system, using the probability density of instantaneous deviations of water level from the coordinate d a t u m levels. Any environmental factor may then be functionally related to the time-fixed vertical levels. The general validity of this approach is demonstrated, based u p o n environmental and vegetational data from regulated lakes in Norway. In particular, the close relationship b e t w e e n the statistically described environmental factors and vegetational response is outlined. Vegetation distribution patterns are broadly described, aiming at the salient response features considered characteristic for low-to-intermediate altitude, oligotrophic, regulated lakes in Norway. The regulation impact is deliberately exemplified b y physical factors, because the invoked stress on the aquatic ecosystem is b o u n d to be of a mainly physical nature. MATERIAL AND METHODS S t u d y area and field data The statistical approach is discussed with vegetation and water-level data from nine selected Norwegian lakes. The location of the lakes is indicated on Fig. 1, and some pertinent data on the water-level variations are given in Table I. The evaluation of a lake's trophic state is based on extensive biological and hydrochemical investigations carried o u t by the Norwegian Institute for Water Research (NIVA) from the 1970's onwards. All lakes are more or less oligotrophic, with nominal regulation height ranging from 1.5 up to 7.0 m. Regulations for hydro-electric p o w e r purposes date back to the 1950's, or in

201 some cases even earlier. Thus, any post-regulation transient p h e n o m e n a can be ruled out. One lake (Vangsvatn) is unregulated, b u t has a naturally wide annual f l u c t u a t i o n in water level. Submerged vegetation was sampled by means o f under-w at er stereo-

1: 2: 3: 4: 5: 6: 7: 8: 9:

Vangsvatn Tyrifjord Randsfjord Maridalsvatn Kilefjord Byglandsfjord Araksfjord Hartevatn Breidvatn

Fig. 1. Location of the nine investigated lakes (South Norway). p h o t o g r a p h y (RCrslett et al., 1978), with quadrat size 0.25 m 2. Coverage o f species was d e t e r m i n e d by a nested grid m e t h o d (R~rslett, 1983), with statistical relative accuracy within + 20% for cover exceeding 0.1%, and within + 30% for very low cover in the 0.001--0.1% range. A t ot al o f some 3800 p h o t o g r a p h i c samples was obt ai ned f r o m 36 sites during t he years 1976--81. Preliminary analysis revealed a close relationship b e t w e e n comm u n i t y d e p t h distribution and site exposure, thus o n l y dat a f r o m t he m ost strongly ex p o s ed sites are considered here for between-lake comparisons.

202 TABLE I List o f t h e lakes s t u d i e d

Lake

Altitude Area

Regulation

( m a.s.1.)

height 1

(km 2 )

(m)

Water level a m p l i t u d e (m) Annual

Total

range =

Vangsvatn

Tyrifjord Randsfjord Maridalsvatn

Kilefjord Byglandsfjord

,~raksfjord Hartevatn Breidvatn

46 63 134 148 167 202 203 757 897

8.0 121.9 136.9 3.9 5.5 30.7 11.2 6.0 3.1

Mean

Max.

1.0 3.0 2.0 1.5 5.0 5.0 7.0

4.5 2.0 2.9 1.1 2.0 3.6 3.5 6.4

6.3 2.9 3.9 1.3 2.9 4.9 4.9 7.3

6.6 3.5 4.1 1.6 3.2 5.9 5.0 7.8

2.5

3.0

3.5

3.5

--

i Nominal regulated height (m) as licensed by Norwegian authorities. 2 Maximal annual range (m) during the years 1945--1978.

F u r t h e r details on vegetation and c o n v o l u t i o n s m o o t h i n g o f d e p t h distribution curves are f o u n d in R~rslett (1983, 1984). Subsurface p h o t o s y n t h e t i c available radiation (PAR, 3 5 0 - - 7 0 0 nm) was measured with a Li-Cor LI-185 Q u a n t u m m e t e r and sensor LI-192S ( L a m b d a Instruments, Inc.) i n t e r m i t t e n t l y during t he m o n t h s May--O ct ober. Estimation o f vertical a t t e n u a t i o n coefficients was p e r f o r m e d by a proprietary c o m p u t e r program, using a non-linear least squares fitting m e t h o d . Water-level data f r o m t he lakes were o b t a i n e d f r o m official gauges monitored b y th e Norwegian Water Resources and Electricity Board (NVE, Oslo). Daffy measurements of water levels were used whenever available. Statistics for water levels were c o m p u t e d f or t he years 1945 to 1978--81.

Statistical description of water-level fluctuations The major environmental gradient in any lake correlates with d e p t h (Hutchinson, 1975). Plants are distributed across this vertical gradient according to niche preferences. Neglecting within-lake gradients, t h e spatial niche projects on to segments of t he vertical gradient. Thus, t he niche description simplifies to the spatial coor di na t e s of t he vertical dimension, and the associated point-time pr oba bi l i t y distribution o f envi ronm ent al factors. Regulation impact should be assessed f r o m a " p l a n t ' s p o i n t o f view", i.e. with stationary spatial coor di na t e s for individuals, and time-varying e x t e n t o f water overlaying the plants. The c o o r d i n a t e system a d o p t e d is shown in Fig. 2, and the corresponding relations b e t w e e n the water level and vertical scales are given in Table II. C o o rd in ate axes are oriented positively upwards, e x c e p t for instantaneous

203

deviations o f water level, which are positive downwards in order to c o n f o r m with c o m m o n usage of " d e p t h " . Representing the time series of water levels as a continuous random variable W = w ( t ) , the cumulative probability distribution function (cdf) is P w ( w ) = Prob ( w ( t ) < w ) +z

W Watergauge

Z

w(t)

i.

o

Zo

....... T .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

]

v (z,tl

~. -

dw

~

-- I

.

N ~'~

Z

Time It)

Fig. 2. C o o r d i n a t e s y s t e m used t o d e s c r i b e t h e t i m e s t a t i s t i c s o f a c h a n g i n g w a t e r level, r e l a t e d t o spatially f i x e d p l a n t sites. R e f e r t o T a b l e II f o r a d e f i n i t i o n o f s y m b o l s . T A B L E II R e l a t i o n s b e t w e e n z-, Z- a n d W-scales. Base scale is z-scale, cf. Fig. 2 I t e m (cf. Fig. 2)

Relationship

Translocations Water level scale i n t o Z - c o o r d i n a t e ( e l e v a t i o n ) Z - c o o r d i n a t e i n t o local z-scale

Z=W+dWZ z=Z-Z o = W+dWz

I n s t a n t a n e o u s variables W a t e r level D e v i a t i o n o f w a t e r level re: t i m e - f i x e d zero p o i n t D e v i a t i o n o f w a t e r level re: z-scale D e p t h re: z-scale

w(t) = dw(t) + d WZ dz(t) = w(t) - Z o ffi d w ( t ) - d W z v(z, t) = dz( t ) - z /

d(z,t) = I

I

u(z,t)

0

u ;* 0

v
Assuming a " s m o o t h " , i.e. differentiable, cdf, the corresponding probability density function (pdf) is dP(w) PW(W) =

thus

dw

204 W

pwtw)-

f pw(u)du

Assume the z-scale d a t u m , i.e. Z0, to be known. As shown in Table II, the z- and W-scales differ only by a translocation constant d Wz. Thus, the p d f Pv(Z) of instantaneous deviations of water level in the z-scale is p v ( z ) = p w ( z + d Wz)

and the cdf's axe related as Pv(z) = P w ( z + d Wz)

The cdf is preferably estimated from daily water-level data, spanning at least 10--15 years of measurement. The cdf P w ( w ) m a y be recognized as the " w a t e r level d u r a t i o n " curve of h y d r o l o g y , with a rotation of axes and labelling the cumulative probability as percentage of time. Translocation into the z-scale depends on the d a t u m level Z0. Noting the fundamental ecological difference between the aquatic and the terrestrial environment (Hutchinson, 1975), the d a t u m should optimalize the delineation between these contrasting environments t h r o u g h o u t time. This is equivalent to a 2-state classification (Aquatic:Terrestrial) of the total Z-scale gradient. The 2-state classification of the Z-scale is based on m u t u a l l y exclusive events, and is easily f o u n d by application of probability theory. The event E1 = " Z < Z 0 " implies (Z ~ Aquatic) and E2 = " Z i> Z 0 " implies (Z E Terrestrial) The associated probabilities are obviously p(E~ ) = Prob (w( t )> Zo ) = 1 - P w ( Z o ) p ( E 2 ) = Prob (w(t)<<.Zo) = P w ( Z o ) p(E1 ) + p ( E 2 ) = 1

with a m i n i m u m classification error in the case of p(E1 ) = p ( E 2 )

or P w ( Z o ) = 1/2 Thus, the optimal d a t u m Z0 is the median water level. This d a t u m can also be shown to maximize classification information (entropy) by i n f o r m a t i o n t h e o r y (R~brslett, 1983). Based on the d a t u m Z0, the vertical distribution of macrophytes along the Z-scale is easily described in the time-fixed z-coordinate system (cf. Fig. 2). This ensures, for example, t h a t limits of depth extension for any species in a lake axe (approximately) stationary in time, regardless of the actual water level at sampling time.

205

A generalized z-level function L e t H(z,t) be a n y f u n c t i o n o f e n v i r o n m e n t a l f a c t o r s in t h e vertical gradient, possibly d i s c o n t i n u o u s across t h e w a t e r surface (v(z, t) = 0). T h e n

l

f(v)

ifv~> 0

g(v)

if v < 0

H(z, t) = h(v) =

(1)

and v = d z ( t ) - z (Fig. 2) Assuming a w e a k l y s t a t i o n a r y process, t h e statistics o f H(z, t) are o b t a i n e d b y time-averaging. T h e t i m e - a v e r a g e d m e a n , or e x p e c t a t i o n o f H(z) is d i r e c t l y o b t a i n e d as

f

E(H(z)) =

f

--~

H(z-u,t)pv(u,t)dt du

--00

f

H(u)pv(z-u)du

f

h(z-u)pv(u)du

(2)

i.e. as t h e t i m e - d o m a i n c o n v o l u t i o n b y t h e p d f o f t h e i n s t a n t a n e o u s deviat i o n s f r o m t h e r e f e r e n c e d a t u m . T h e p r o o f o f eqn. (2) f o l l o w s d i r e c t l y f r o m t h e d e f i n i t i o n o f t h e e x p e c t a t i o n o f a r a n d o m variable, n o t i n g t h a t v = u - z. E q u a t i o n (2) is valid even with a t i m e - s t a t i o n a r y w a t e r level, in this case t h e pdfpv(z) d e g e n e r a t e s i n t o a Dirac spike c e n t e r e d at z = 0. T h e variance o f H(z) is f r o m (2) Var(H(z))

= E(H 2(z)) - E(H(z)) =

f

(H(u) - E(H(z)))2pv(z-u)du

(3)

f H(u)2pv (z-u)du - E(H(z)) 2 In general, v a r ( H ( z ) ) ¢ v a r ( H ( - z ) ) . T h e e x c e p t i o n is w i t h a n y linear a n d c o n t i n u o u s f u n c t i o n , as e v i d e n t f r o m eqn. (1).

Special functions Based u p o n eqn. (1), t h e vertical d i s t r i b u t i o n o f e n v i r o n m e n t a l f a c t o r s is given b y s u b s t i t u t i o n o f t h e f- and g - f u n c t i o n s i n t o e q n . (2).

206 A special case of eqn. from Table II is given by

D(z) = E(d(z)) =

f

(2) is the

actual mean depth D(z), which

max(u - z,O)pv(u)du

(4)

The mean depth D(z) re z-scale is always different from Izl (except in the rare case o f a constant water level}, and the magnitude of this difference depends on the pdf pv(z). Furthermore, D(z) is always greater t h a n zero for all levels n o t exceeding the maximal water level observed. The implication is t h a t depth in its time-averaged sense is n o t equivalent to relative elevation, even with elevation d a t u m located at the median water level. From D(z), the mean hydrostatic pressure at any z-level P(z) is

P(z) = K(Zo) + aD(z)

(5)

K -- pressure at Z0, approx. 1 Atm. a = pressure coefficient, approx. 0.1 Atm. m -1 water Thus, hydrostatic pressure equals the mean depth D(z) in its ecological information value. Ice-scour stress at draw-down IS(z) m a y be estimated from the p d f Pv ;winter(z } by a time-domain convolution as +oo

IS(z) =

f

b(u - z)Pv;winter(u)du

(6)

with the " b o x " function b(u) defined by 1 if -0.1dice t> u 1> 0.9die e

b(u) 0 otherwise By normalizing IS(z) to u n i t y , IS(z) estimates the probability of ice scour at any z-level. Ice thickness dice is preferably a m e a n for the ice-covered period. The regulation impact on the actual subsurface light regime is complex. The following presentation aims at the salient features, and uses a much simplified statistical model. Subsurface irradiance in general follows an exponential law, which as a time-function of z-levels is conveniently described by

I(z, t) = Io (t)H(z, t)

(7a)

i(z, t) = I(z, t)/Io it)

(7b)

with

207

exp (-Kv(z,t))

v(z,t) ~ O

1

otherwise

H(z,t) = I0 K

= Irradiance immediately below the water surface = R a n d o m variable, distributed Normal (k,s 2) k = mean vertical coefficient o f attenuation (In-units m -~ ) s = standard deviation of K

The available subsurface irradiation at any depth correlates to the photosynthesis activity of submerged macrophytes. There is some evidence that underwater light controls the lower vertical range o f m a c r o p h y t e s through the probability of critical threshold levels (RCrslett, 1983, 1984). The threshold probabilities are easily related .to fluctuating water level by eqns. (2) and (7a, b). As a first approximation, the regulation impact on relative threshold intensities, r, is outlined. Seeking the probability (i(z)<.r), eqn. (7b) is simplified to In i(z, t) = - g d ( z , t)

(8)

which demonstrates t h a t the random variable In i(z,t) + kd(z,t)

sd(z,t) is distributed normal (0,1). Noting t h a t In i(z,t) = 0 for d(z,t) = 0, the threshold probability is obtained as 0

f (.klul+lnr) Prob (i(z) <. r) = G Pv (z-u)du _~ slul

(9)

where G() is the Gaussian integral t

G(t) = (2u) - I n

f

exp (-u2/2)du

--OO

The convolution integral in eqn. (8) is easily evaluated by computer, using a polynomial approximation to G (Davies, 1971). The lower limit o f integration is then the m a x i m u m depth magnitude.

Bias in depth references Assume a sinusoidal fluctuation of water level, with fixed amplitude A. In this case, the mean and median water levels coincide. Time-averaged depth D(z) now equals the magnitude of z for z ~ - A , and is true zero for z i> A. However, in the intermediate range IzJ ( A, the solution o f eqn. (2) with an appropriate p d f p s ( z ) (Bendat and Piersol, 1966, p. 62)

208

t l/Ir(A2-z2)-l12 ps(Z) =

/

IzI
0

otherwise

yields the time-averaged d e p t h in this region as

D(z) = II~(A 2 - z2) za - z(1 - Ps(z))

(10)

where Ps(z) = l / ~ ( n / 2 + Arcsin z / A ) Thus, appreciable bias in m a g n i t u d e exists when elevation is used in lieu o f t h e time-averaged d e p t h D(z), as evident f r o m Fig. 3. F r o m eqn. (10), t h e m a x i m u m deviation is A/Tr at z = 0. 1.5

E N 1.0 ~ O rEL "13 C 0.5 O Z

. . . . . . Stationary w. level

V

0"-01.5

- 1. 0

-0.5

O.O

0.5

1. O

Z, m Fig. 3, Bias in depth vs. relative elevation. Sinusoidal water level variation with amplitude Aflm. By definition, d = D(z) is a m o n o t o n e decreasing f u n c t i o n with d o m a i n z<~Zmax and range 0--Dmax; h e n c e there exists an inverse D -1 (d) = z. Thus, b o t h time-averaged d e p t h and z-scale (within the d o m a i n of D) t heoret i cal l y have th e same i n f o r m a t i o n c o n t e n t as vegetation distribution parameters. However, d e p t h D(z) is a measure of central t e n d e n c y (mean), n o t o f time and duration, on which t he z-scale is based. Towards th e lower limit o f D(z), a substantial part o f t h e z-domain maps into a restricted range o f D(z). This implies t h a t t h e inverse D -1 ( d ) m a y be difficult to c o m p u t e a c c ur at el y in this range.

209 RESULTS

AND DISCUSSION

Regulation impact on environmental factors The impact of regulations are now considered for the investigated lakes. The vertical distribution of environmental factors in the z-scale is estimated from eqn. (2) and the actual p d f p v ( z ). Regulation impact is then assessed by recalculating eqn. (2) with a Dirac-spike p d f centered at z = 0. In the following, the statistical t r e a t m e n t applies to no year in particular, but reflects the long-time properties of each lake.

Water-level statistics The cumulative probability of water levels are shown in Fig. 4 in dimensionless f o r m by scaling the abscissa as (z - Zmin)l(zma x - Zmin); thus allowing for easy comparison between lakes. 1.0

/ "" " " " - - " -

0.8

.

>- O. B ,

. 0.2 - ," .,,,; O* i~.'O

4/

1"'"/

,,' ,,,, t

3/

.

III iSlil

,'"~

-

II

/

I

a..~, l_l

II I ~

..-st

S~/

/

.~/j/// i ~/&t ~ /

. I"/

///if

0.2

0.4

0.6

0.8

1.O

(z-zmin) / (zmox-zmin) Fig. 4. Water level cumulative probability distribution for selected lakes. Abscissa scaled according to maximum range of water level variation. 1, Vangsvatn; 2, Kilefjord; 3, Tyrifjord; 4, Randsfjord; 5, Hartevatn.

Most regulated lakes in Norway are storage reservoirs, with water level draw-down at winter time. This results in a concave upwards calf, as exemplified by Lakes Randsfjord and Hartevatn in Fig. 4, due to the u n i f o r m l y distributed low water levels. The unregulated Lake Vangsvatn shows a strongly upwards convex cdf, indicating t h a t no particular level is prominent. The short-time regulated Kflefjord, and the large Tyrifjord with strong hydraulic damping, show intermediate cdf's, indicating the prominence of water levels close to the median.

210

The actual mean depth of water overlaying the submerged vegetation, D(z), m a y be computed from eqns. (2).and (4). Since the water levels in the investigated lakes show significant variations throughout time, the D(z)-

values are computed separately for the growth season (ice-freeperiod) and the winter (ice-covered period). 1O ~...

.-. . . . S t o t i o n o r y ~ . . ~

B xx

w. level

Summer

~"~'"',

_ _ . WintQr

E

.C N r-~

v

.(Z 4J Ct. (~

6

%%%%

''' q

I

I

% 4

I

", %%%

"" " ' . %.

c" (~

°-lO

-8

".,

-6

-4

-2

o Z,

2 m

°,,

...... Stationary

\ e

,,'-.. ~ x\-..~

E

s~ 'V

~

6

Summer

....

Winter

%.

"'.

f't

~" ""

~ ~....

4

f-

~

o

OJ ~-

w. level

• ,

~J • "o

....

",

~ 2

"'" x,,

"'.

(

°-to

-e

-6

-4

-2

0 Z,,

2 m

Fig. 5. Time-averaged mean depth D(z) vs. z-level, summer and winter situation in Lakes

Hartevatn (a) and Vangsvatn (b).

211 Figure 5a shows the pronounced difference of summer vs. winter D(z)values for the strongly regulated Lake Hartevatn. In this lake, s u m m e r D(z)values closely follow the vertical levels up to the - 3 m level. At higher elevations, D(z) exceeds the magnitude of z. The winter D(z)-values are far lower, approaching the magnitude of z at higher z-levels. The unregulated Lake Vangsvatn has a maximal water-level amplitude almost equal to Hartevatn (Table I). Summer D(z)-values in Vangsvatn exceed the magnitude of z at all levels (Fig. 5b), whereas the winter situation is reversed. D(z) is nearly linear below the - 1 m z-level, b u t is strongly nonlinear in z at higher levels. Vertical level thus is a heavily biased estimate of d e p t h in its time-averaged sense in these lakes, at least in the intermittently inundated zone. This could be expected from eqn. (10). Below the datum, i.e. the median water level, the bias magnitude is <~0.5 m for lakes with annual water-level variation less than 2 m.

Impact on the extent of ice-scour The normalized ice-scour stress IS(z) was c o m p u t e d from eqn. (6) with ice thickness data from field measurements. Examples o f IS(z) are shown in Fig. 6. In general, ice-scour extent positively correlated to the mean annual range of water level variation. However, the vertical scour distribution clearly differs in detail b e t w e e n lakes with similar ranges o f water fluctuations (cf. Fig. 6). Storage lakes with regular draw-down patterns, e.g. Hartevatn (and Breidvatn), display a pronounced 2-peaked distribution of IS(z), corresponding to the high water level at freeze-up time, and the prevailing low winter-time water level. At intermediate z-levels, ice-scour might be less intense (Fig. 6a). A large lake, Byglandsfjord, features an irregular winter draw-down, which is clearly reflected by the scour pattern (Fig. 6b). Lake Kilefjord is dominated by short-time regulation (R~brslett, 1983), and ice-scour in this lake is strongly concentrated at the 0, - 0 . 5 m z-range. Tyrifjord has a closely similar scour pattern. The estimated scour activity, however, extends to s o m e w h a t lower z-levels in this lake ( - 1 , - 1 . 6 m).

Light intensity and threshold distribution Based u p o n eqn. (7b), the relative light intensity in each lake was estimated for the ice-free growth season. Water level fluctuations influenced the estimate significantly in shallow waters, resulting in up to 40% deviation either way compared to a stationary water level. This effect ceased rapidly below the - 2 m z-level in all lakes except Hartevatn, in which an increase in average intensity could still be demonstrated at the - 4 m level. Regulation impact is severe, however, when the probability distribution o f threshold intensities is considered. Contrary to the direct intensity distribution, impact in this case is most adverse towards deeper waters. Based u p o n eqn. (9}, the regulation impact on threshold probability distribution is

212 I00

lOO

B y g l ondo¢ j~-d

Hor-tevatn

90 80

7O

70

t °° 6O

60

5O

40

]

30

]

30

-I

2O

]

lo

(a)

]0 "-8

-7

-6

-5

-4

-3

-2

.

-z

I

2

,

I

,

3

,o

(b) .

0 8

J

4

K

•

-7

i

,

-8

a

~

-5

-4

-3

-2

-1

z, m.

Kllef,.jor'd

gO

Rc~dJF j o r d

90 eO

80 70

70

60

60

50

5O

40

40

30

30

20

20

I0 •

i

-7

.

i

-6

,

i

-5

,

i

-4

•

i

-3

.

i

-2

,

i/'

-1

ii•-•._• ,

O z.m.

1

i

I0

(c) ,

i

2

(d)

,

s

3

i

-2 " -I

i

.

2

" z, m.

3

100

tO0

go

Voncjevotn

Tyr'lFjc~d

80

80 N

0 z. m.

100

I00

g(3

i.l,ll ] 2 3

?0

70

80

60 50

40

40

30

30 20.

(e)

10 •

i

S

lo •

0

(f) 8

.

J

7 z, L

.

,

-6

.

,

5

.

L

4

.

,

3

.

,

2

,

.

1

!

2

i

3

z.m.

Fig. 6. E s t i m a t e d vertical d i s t r i b u t i o n o f ice-scour stress IS(z). Stress f u n c t i o n scaled relative t o m a x i m u m value for e a c h lake.

illustrated for Lake Tyrifjord (Fig. 7). The vertical threshold probability distribution is shifted into shallower waters (i.e. higher z-levels) when due attention is paid to the varying extent of water overlaying each z-level. The threshold distributions for thresholds between 1 and 50% relative light intensity in the heavily regulated Lake Hartevatn are s h o w n in Fig. 8. The inflection point of each threshold probability distribution coincides with the time-averaged mean relative light intensity curve, as w o u l d be expected from eqn. (9), since the vertical attenuation coefficient K o f eqn. (8) is statistically independent of the water level probability distribution.

.

213 0

i

i

= ~

1

=

i

i

i

100

!

50 gO

-5

"0

I0

-lO

5

II

-15 N

1

-20

0.5 -25

>"

"-'

s

0 JD O L

0.1

-30

,

o.o5

U

-35 -40

g

,

-'0

I -8

I

I -6

I

I

i

-4

I

i

J

,

-2 ~'p

~0. O1

O M°

Fig. 7. Estimated vertical cumulative probability distribution for relative subsurface irradiation less than a threshold. A, stationary water level; B, actual pdf pv(z). Lake Tyrifjord, ice-free period, threshold r ffi 6%. 0

!

l

i

I

i

i

!

l

,

i

, E [i(z)]

G~

1O0 - SO

-5

"t)

10

-lO :5

-15 1

-20

!0.5 -25

>"

.,.,=

"-' 0 0 L

-30

E

o. os -35

-40

r = 1%

-lo

'

-8

2%

'

5%

-'8

10%

25%

'

-'2 Z,

i0%

'

;

0.01

m°

Fig. 8. Estimated vertical cumulative probability distribution for relative light thresholds 1--50%. Dashed line indicates expected relative light intensity E(i(z)) (use scale at right, as percentage o f intensity). L a k e Hartevatn, ice-free period.

214

Regulation impact on submerged macrophyte communities The macrophyte communities in the investigated lakes are mostly dominated by isoetids (mainly Isoetes lacustris L.). In the less extremely oligotrophic lakes (Tyrifjord, Randsfjord), some elodeids (e.g. Myriophyllum alterniflorum DC., Elodea canadensis Michx) are abundant. Deep-water communities with stoneworts (Nitella spp.), bryophytes (Sphagnum spp.) and freshwater sponges (Spongilla cf. lacustris (L.)) are characteristic of all lakes. Helophytes have negligible abundance in these lakes. The distribution patterns of macrophytes in the investigated lakes could not be statistically correlated to water chemistry, lake altitude, temperature or location of the thermocline (R~brslett, 1983, 1984). Site exposure affected significantly the lower depth limits reached by some species, e.g. Isoetes lacustris (RCrslett, 1983). However, community statistics such as upper vertical limits or mean (biomass-weighted) depth were not significantly correlated to site exposure within the extensively investigated Lake Tyrifjord (Rc,brslett, 1983).

Qualitative vegetation response to regulation The submerged macrophyte communities, in general, respond to increasing extent of regulation, i.e. larger annual water-level variation, along two response pathways: (1) A reduction in community diversity and organization pattern. The rstrategy species (e.g. NiteUa) gain in relative importance, compared to the K-strategy species (e.g. Isoetes). The mean number of aquatics reduces from typically 10--25 in lakes with regulation heights less than 3 m (Kilefjord, Breidvatn, Tyrifjord, Randsfjord), to 1--3 species in the more heavily regulated lakes (e.g. Hartevatn). Vegetation patchiness increases concurrently. (2) The peak community performance is shifted into deeper waters. These responses are illustrated in Fig. 9, based upon the available vegetation data from the lakes investigated. The vertical location of the prevailing submerged community is indicated by the characteristic (biomass-weighted mean) depth Dc (R~rslett, 1983). Time-averaged depth is applied in order to facilitate between-lake comparisons. The characteristic depth increases significantly with the mean annual range of water level variation (log Dc ffi 0.28 + 0.12 Range; P ~ 0.01). The gradual break-down of community structure reflects the increasing environmental stress and instability brought about by the regulation schemes. The mainly Isoetes lacustris-dominated communities survive to at least 5 m annual range of water-level variation. However, in some lakes with less annual fluctuation of water level, e.g. Randsfjord, Isoetes is conspicuously absent from many potential sites. This furnishes an " e m p t y " niche which, in the case of Randsfjord, was recently invaded by Elodea eanadensis. Perennial submerged macrophytes in general are confined to z-levels below

215 12 g Z

4~ (3-

12

. .."X ...'"

I0

8

I0

..."

8

@ ...'x

@ 0

"O (3

4

@

Oominont s D e c i e s

•

Isoetes

]ocustris

®

Isoetes/Nitello

x

Sphagnum/Nitella

0

Elodea canadensis

.'"

.@" ..-"

4

, , .-'""

2 o 0 L 0 r[.J

2

l~

...'"'0

'

21

,

41

,

61

,

~l

Neon woter l e v e l ronge, m. Fig. 9. Characteristic (biomass-weighted mean) depth D c of the prevailing submerged c o m m u n i t y in each lake, against the mean annual range of water level fluctuations. Each lake is represented by its most exposed site. Note that depth is applied in its time-averaged sense, in order to compare lakes with widely differing water level schedules.

the ice-scour region, whereas some annuals (e.g. Eleocharis acicularis (L.) R.&S., Subularia aquatica L . ) m a n a g e to survive at the intermediate scour region f o u n d at e.g. Lakes Hartevatn and Breidvatn. The generally increased e x t e n t of ice-scour, however, means t h a t a large part o f the vertical z-domain remains hostile to submerged aquatics in the strongly regulated lakes. The vertical displacement towards deeper water reflects the truncation of the upper potential niche. Concurrently, typical shallow-water species such as Lobelia dortmann L., Littorella uniflora (L.) Aschers., and m a n y elodeids, are eliminated. The paucity of data on submerged communities in regulated Scandinavian lakes does n o t permit a generalization of the trend indicated in Fig. 9. Nilsson (1981) reports a sparse submerged c o m m u n i t y (Nitella, Callitriche and Ranunculus peltatus Schrank) from the North Swedish lake Ovra BjSrkvattnet, which has a 5.9 m nominal regulation height. No d e p t h data were given, but the c o m m u n i t y apparently occurred at more than 6 m below the m a x i m u m water level. Nilsson's observations could fit well into the trend shown by Fig. 9. Whether strongly regulated lakes with regulation heights in excess of 10 m are devoid of submerged vegetation or not, remains an open question.

Regulation impact on the e x t e n t o f the vertical niche The general pattern shown in Fig. 9 focusses on the e x t e n t and possible displacement of the vertical niche due to regulation impact. The vertical niche could be defined in probabilistic terms by the joint cumulative probability distribution of the ambient factors which c o n s t i t u t e

216

0

I

I

I

A

1

I

I

I

I

I

~g

100

-

-5

C

7O

so

-10

I0

:5

-15 -20

I

Tyrifjord

",'4

0.5

3

-25

.8° 0

c,

-30

o.

0. I

: 0.05

-35 -40

(-I,

(a) I

-10

I

-8

-6

-4

Z,

0

I

i

!

!

i

L

-2

i

!

0

'

20. O1

m.

!

i

i

i

! 1oo 50

oo - 5 "1o

I0

-10

!5 -15 -20

,P o.-s

"O. 5 -25

o

.o

0.!

-30

: 0.05 -35 -40

"' 3

(b)

-10

m -8

l

i

L -6

i

I -4

i

I

-2

i

i

0

a

" u

20.01

Fig. 10. Vertical c u m u l a t i v e p r o b a b i l i t y d i s t r i b u t i o n o f t h r e s h o l d l i g h t o c c u r r e n c e (A, r = 6%) a n d ice-scour stress I S ( z ) (B). Isoetes lacustris c o v e r a g e is p l o t t e d as c u r v e C, u s i n g dB-scale w i t h 0 d B ffi 1 0 0 % cover. Lake T y r i f j o r d , a b u n d a n t Isoete8 lacustris. Lake H a r t e v a t n , Isoetes lacustris a b s e n t .

217

the niche hyperspace, when these factors are functionally related to the vertical gradient. With statistically uncorrelated factors, the niche probability space is given by the set of individual cdf's. Derived cdf's might be c o m p u t e d for factors operating through cumulative or threshold effects. Deep-water p e n e t r a t i o n of isoetids correlates with light-induced thresholds (R@rslett, 1983). The actual vertical distribution o f subsurface thresholds was c o m p u t e d f r o m eqn. (9), with r = 6%. This value correlates significantly with the lower limit of depth extension for Isoetes lacustris in Lake Tyrifjord (R@rslett, 1983). Compared to the case of a stationary water level, regulation tends to shift the threshold distribution into shallower waters (cf. Fig. 8), thus the spatial e x t e n t of potential niches is reduced. The c o m p u t e d distributions clearly differ between lakes, depending both on the actual pdf pv(z) and the probability distribution parameters of the random variable K in eqn. (7b). The z-domain cumulative distribution of threshold light and ice-scour probability is given in Fig. 10 for two contrasting lakes (Tyrifjord, a b u n d a n t Isoetes lacustris, and Hartevatn, Isoetes lacustris completely lacking). Hartevatn is situated downstream of the less regulated Lake Breidvatn, in which Isoetes is abundant. The actual depth distribution of Isoetes lacustris is clearly b o u n d e d within the niche space defined by ice-scour and threshold underwater light climate (Fig. 10a, b). By transforming the niche axes spanned by these two factors into the equivalent probability space, the realized vertical niche of Isoetes lacustris in all the investigated lakes is represented in Fig. 11 in a m u c h condensed form. 1 O0

......

--

........

:

................

] O0

lsoetes >

,o -,~ ,-q

]ocustris

Coveroge

......... i ............. i .............. ! -

........ ,o

•

O'p .,.4

-5 dB -lO dB

0

"0

X

-20 dB

0 L

0 t-

O

-3o de

z~

-40

--

Missln 9

d~

o... •

%\_ i

,

...... i O. l

Oi

dB

0.]

:

. . . . . .'..i V I

Cum. p r o b o b i l i t y

lO

I00

g IS

Fig. 11. N i c h e p r o b a b i l i t y s p a c e f o r Isoetes lacustris, d e f i n e d b y t h r e s h o l d l i g h t o c c u r r e n c e (r = 6 % ) a n d i c e - s c o u r s t r e s s . D a t a f r o m all lakes.

218

Ice-scour is clearly an "all or n o n e " factor, thus Isoetes performance declines abruptly when ice-scour cumulative probability exceeds some 20% (cf. Fig. 11). Threshold light probability acts more gradually, as shown in Fig. 11. The synergistic effect of combined threshold light and ice-scour probability is evident, leading to t h e complete absence of Isoetes lacustris in central areas o f the probability space. The probability space representation suggests a 10% threshold light occurrence probability and a b o u t 20% ice-scour probability as niche limits, if Isoetes performance should exceed 1% ( - 2 0 dB) cover. With these limits, the vertical niche extents for all investigated lakes are given in Fig. 12. 12

:.

Z ~

2,

.:.-

ti"

10

12

Occu.nc.

...""

10

."

"

lli'

."

!..."

locustris

•

Abundant

~

Scattered

X

Rare

-

Missln 9

4

..

2

Isoetes

2

r(-9

2 Mean w a t e r

I 4 level

,

'

1

~l

6 range,

m.

Fig. 12. Niche limits for Isoetes lacustris, superimposed on the characteristic depth D c for the prevailing submerged c o m m u n i t y in each investigated lake.

The vertical niche extent declines in the more strongly regulated lakes, mostly due to the unfavourable underwater light regime towards the deeper waters. The absence of Isoetes lacustris from the heavily regulated Lake Hartevatn could be explained by the fact t h a t the niche e x t e n t is nil in this lake. Marginal Isoetes lakes, such as Randsfjord and Bygiandsfjord, have a much reduced vertical niche e x t e n t compared to the Isoetes lacustrisd o m i n a t e d Lakes Kilefjord and Tyrifjord. The extension o f the vertical niche into shallower waters are fairly well correlated to the mean annual range of water-level variations (Fig. 12). However, the very different probability distributions of water levels in these lakes result in large deviations from the general trend. Lake Vangsvatn, with a wide natural fluctuation o f water level, is an evident example. Thus, it is necessary to consider the total probability distribution of water level fluctuations, and n o t just the mean depths and fluctuation ranges.

219 CONCLUSIONS Clearly, the concepts of depth and relative elevation need to be carefully distinguished. This is essential when a regulated lake with appreciable fluctuation of water level is considered. Even b y relating the vertical position of a plant site to the median water level as datum, site depth in its time-averaged sense is n o t equivalent to the relative elevation of this point. Furthermore, the magnitude discrepancies, in general, are large in shallow waters where many species attain their peak performance. Recasting the vertical distribution of submerged m a c r o p h y t e s in terms of the time-averaged depth D(z) resolves ambiguity. Between-lake comparisons of depth distributions are then facilitated. However, much of the information value residing in the p d f Pv(Z) is lost. Ambient factors are easily evaluated as functions of the z-scale, i.e. relative elevation. This approach caters for the time-probability associated with a fluctuating water level, and by definition includes instantaneous depths. Thus, the probability distributions of the ambient factors at any elevation are available, in addition to the expected (time-averaged) values. Betweenlake comparisons, however, are no more easy to perform with z-domain representation than with time-averaged depth, unless the data are transformed into the equivalent probability space. The prevailing winter-time draw-down of Norwegian regulated lakes results in extensive ice-scour along the vertical gradient. The extent of icescour governs the upper limits of perennial submerged species. Annual species might occur within the scour region; their quantitative performance, however, are reduced. The vertical niche of the dominant species in the lakes studied, Isoetes lacustris, is in general displaced towards lower z-levels, i.e. deeper waters, due to the regulation impact. In general, the vertical extent of the niche is reduced concurrently with an increased regulation height. Niche limits derived from the niche probability space representation fit the observed data well. Communities dominated by Isoetes lacustris survive to an annual water-level range in excess o f 5 m. However, the light conditions combined with the water level schedule determine the probability of Isoetes survival. ACKNOWLEDGEMENTS SCUBA diving assistance by Norman W. Green and Knut Kvalv~tgnaes provided the vegetation data on which this paper is based. Their efforts are much appreciated. Marit Mjelde assisted in the lengthy analysis of stereophotographic data. Funds were granted b y the Norwegian Institute for Water Research (NIVA, Oslo) through Research Project OF-81620.

220 REFERENCES Bendat, J.S. and Piersol, A.G., 1966. Measurement and Analysis o f R a n d o m Data. Wiley, New York, 390 pp. Davies, R.G., 1971. Computer Programming in Quantitative Biology. Academic Press, London, 492 pp. Hutchinson, G.E., 1975. A Treatise On Limnology. Vol. 3. Limnological Botany. Wiley, New York, 1075 pp. Nilsson, C., 1981. Dynamics of the shore vegetation of a North Swedish hydro-electric reservoir during a 5-year period. Acta Phytogeogr. Suec., 69: 1--94. Quennerstedt, N., 1958. Effects of water level fluctuation on lake vegetation. Verh. Int. Verein. Limnol., 13: 901--906. R~rslett, B., 1983. Tyrifjord og Steinsfjord. Unders~kelse av vannvegetasjon 1977--82. (Lakes Tyrifjord and Steinsfjord. Investigations on the aquatic vegetation 1977--82. In Norwegian). Norwegian Institute for Water Research, Report 0-7800604, 300 pp. P~rslett, B., 1984. Regulation impact on the submerged macrophytes in the oligotrophic lakes of Setesdal (S. Norway). Verh. Int. Verein. Limnol., 22: in press. R~rslett, B., Green, N.W. and Kvalv~gnves, K., 1978. S t e r e o p h o t o g r a p h y as a tool in aquatic biology. Aquat. Bot., 4: 73--81. Sculthorpe, C.D., 1967. The Biology of Aquatic Vascular Plants. Arnold, London, 610 pp. Stanley, R.A., Shackelford, E., Wade, D. and Warren, C., 1976. Effects of season and water depth on Eurasian watermilfoil. J. Aquat. Plant Manage., 14: 32--36. Statistisk Sentralbyr~l, 1983. Naturressurser 1982. (Norwegian nature resources 1982. In Norwegian). Central Bureau of Statistics of Norway, Report 83/1: 1--62. Wass~n, G., 1966. Gardiken. Vegetation und Flora eines lappl~indischen Seeufers. K. Sven. Vetenskapsakad. Skr. Naturskydds~'renden, 22, 142 pp.