The effect of irradiance, vertical mixing and temperature on spring phytoplankton dynamics under climate change: long-term observations and model analysis

Abstract

Spring algal development in deep temperate lakes is thought to be strongly influenced by surface irradiance, vertical mixing and temperature, all of which are expected to be altered by climate change. Based on long-term data from Lake Constance, we investigated the individual and combined effects of these variables on algal dynamics using descriptive statistics, multiple regression models and a process-oriented dynamic simulation model. The latter considered edible and less-edible algae and was forced by observed or anticipated irradiance, temperature and vertical mixing intensity. Unexpectedly, irradiance often dominated algal net growth rather than vertical mixing for the following reason: algal dynamics depended on algal net losses from the euphotic layer to larger depth due to vertical mixing. These losses strongly depended on the vertical algal gradient which, in turn, was determined by the mixing intensity during the previous days, thereby introducing a memory effect. This observation implied that during intense mixing that had already reduced the vertical algal gradient, net losses due to mixing were small. Consequently, even in deep Lake Constance, the reduction in primary production due to low light was often more influential than the net losses due to mixing. In the regression model, the dynamics of small, fast-growing algae was best explained by vertical mixing intensity and global irradiance, whereas those of larger algae were best explained by their biomass 1 week earlier. The simulation model additionally revealed that even in late winter grazing may represent an important loss factor during calm periods when losses due to mixing are small. The importance of losses by mixing and grazing changed rapidly as it depended on the variable mixing intensity. Higher temperature, lower global irradiance and enhanced mixing generated lower algal biomass and primary production in the dynamic simulation model. This suggests that potential consequences of climate change may partly counteract each other.

Appendix: model equations

Parameters are indicated by $\widetilde{},\;\hbox{e.g}.,\;\widetilde{r}.$ Their values are provided in Table 2. Variables taken from the time-series are indicated by (t) and are the following: water temperature (°C), T(t); global irradiance (W m⁻²), Globirad(t); vertical mixing intensity (day⁻¹) in the upper 20 m, mix(t)_0–20; deep vertical mixing intensity (day⁻¹), mix(t)_0–100 and mix(t)_8–100; chlorophyll a concentration (μg Chla  l⁻¹) in the euphotic layer, chla(t)_0–20, and in the aphotic layer, chla(t)_20–100.

The functional response of primary production to light and temperature is written as being dependent on regulating factors. As a general rule, the regulating factors are non-dimensional and are 1 under optimum conditions and tend toward 0 when phytoplankton is in a limiting situation. The following indices were used:

i::

we, le, tot referring to edible (we), less-edible (le) and total phytoplankton (tot), respectively;

j::

20, 100 referring to the euphotic layer (0–20 m) and the aphotic layer (20–100 m), respectively;

k::

A, H referring to autotrophic processes (A) and heterotrophic processes (H), respectively.

Equations referring to method section “Analysis of the impact of deep vertical mixing and global irradiance on algal growth”

Production rate (day⁻¹):

$$\hbox{prod} = \widetilde{r} \times \hbox{eI}$$

(1)

with light regulation factor (eI) (see below).

Net algal losses (day⁻¹):

$$\hbox{loss} = \hbox{mix}_{{{\text{deep}}}} \times {\left( {1 - \frac{1}{{\hbox{vag}_{{{\text{meas}}}}}}} \right)}.$$

(2)

Deep vertical mixing intensity (day⁻¹):

$$\hbox{mix}_{{{\text{deep}}}} = \hbox{mix}(t)_{{0 - 100}} \times \frac{8} {{20}} + \hbox{mix}(t)_{{8 - 100}} \times \frac{{12}}{{20}}.$$

(3)

Vertical algal gradient (measured):

$$\hbox{vag}_{{{\text{meas}}}} = \hbox{chla}{\left( t \right)}_{{0 - 20}} :\hbox{chla}{\left( t \right)}_{{20 - 100}} .$$

(4)

Equations of the primary production module providing eI, the light regulation factor [adopted from Baretta et al. (1995) and Kotzur (2003)]

Primary production of algal group i per day (prod _i ), averaged over the water column, is calculated as:

$$\hbox{prod}_{i} = \frac{1}{{\widetilde{d}}}{\int\limits_0^{\widetilde{d}} {p_{i} {\left( {I{\left( z \right)}} \right)}\hbox{d}z}}$$

(5)

with

p _i (I(z))::

production at depth z of algal group i;

I(z)::

photosynthetic active irradiance at depth z;

I(z)  =  I(0)  × e^{− κ  ×  z}:

κ: vertical extinction coefficient (m⁻¹).

Substitution results in

$$\hbox{prod}_{i} = \frac{1}{{\kappa \times \widetilde{d}}}{\int\limits_{I{\left( {\widetilde{d}} \right)}}^{I{\left( 0 \right)}} {\frac{{p_{i} {\left( I \right)}}}{I}\hbox{d}I}}.$$

(6)

For p _i (I) the formulation of Steele (1962) was chosen:

$$p_{i} {\left( I \right)} = \widetilde{r}_{i} \times \frac{I}{{I\_{\text{opt}}}} \times e^{{{\left( {1 - \frac{I}{{I\_{\text{opt}}}}} \right)}}} .$$

(7)

The resulting function of the primary production is:

$$\hbox{prod}_{i} = \frac{1}{\kappa\times\widetilde{d}}\int\limits_{I({d\widetilde{}})}^{I(0)}\frac{1}{I} \widetilde{r}_{i}\times \frac{I}{I\_{\text{opt}}} \times e^{\left({1} -\frac{I}{I\_{\text{opt}}}\right)} dI.$$

(8)

Integration results in:

$$\hbox{prod}_{i} = \widetilde{r}_{i} \times {\underbrace {\frac{1}{{\kappa \times \widetilde{d}}} \times {\left( {e^{{{\left( {1 - \frac{{I( \widetilde{d})}}{{I\_{\text{opt}}}}} \right)}}} - e^{{{\left( {1 - \frac{{I{\left( 0 \right)}}}{{I\_{\text{opt}}}}} \right)}}}} \right)}}_{{\text{eI}}}}.$$

(9)

Photosynthetic active radiation at the surface (W m⁻²):

$$I{\left( 0 \right)} = \widetilde{q}_{\rm PAR} \times \hbox{Globirad}{\left( t \right)}.$$

(10)

Extinction coefficient (m⁻¹):

$$\kappa = \widetilde{\hbox{turb}}+ \widetilde{\hbox{selfsh}} \times A_{{\text{tot}},20}.$$

(11)

Radiation integrated over the water column (W m⁻²):

$$I\_m = I(0) \times \frac{{(1 - e^{{( - \kappa \times \widetilde{d})}})}}{{\kappa \times \widetilde{d}}}.$$

(12)

Optimum irradiance (W m⁻²):

$$I\_{\hbox{opt}} = \max {\left( {I\_m, I\_{\widetilde{\hbox{opt}}}\_{\text{min}}}\right)}.$$

(13)

Equations to describe algal dynamics

Algae in the euphotic layer: A _i,20 (mg C m⁻³):

$$\begin{aligned} \frac{{\hbox{d}A_{{i,20}}}}{{\hbox{d}t}} &= {\left( {\hbox{prod}_{{i,\,20}} - \hbox{resa}_{{i,\,20}} - \hbox{exud}_{{i,\,20}} - \hbox{resb}_{{i,\,20}}} \right)} \times A_{{i,\,20}}\\ &\quad- \hbox{mix}_{{{\text{deep}}}} \times{\left( {A_{{i,\,20}} - A_{{i,\,100}}} \right)} - M_{{i,\,20}} \times eT_{{20,\,H}} \times A_{{i,\,20}} - \hbox{sed}_{i} \times A_{{i,\,20}} . \end{aligned}$$

(14)

Algae in the aphotic layer: A _i,100 (mg C m⁻³):

$$\begin{aligned} \frac{{\hbox{d}A_{{i,100}}}}{{\hbox{d}t}}& = {\left( {- \hbox{resb}_{{i,\,100}}} \right)} \times A_{{i,\,100}} + \hbox{mix}_{{{\text{deep}}}} \times \widetilde{c} \times {\left( {A_{{i,\,20}} - A_{{i,\,100}}} \right)}\\ &\quad- M_{{i,\,100}} \times eT_{{100,\,H}} \times A_{{i,\,100}} + \hbox{sed}_{i} \times \widetilde{c} \times A_{{i,\,20}} - \hbox{sed}_{i} \times \widetilde{c} \times A_{{i,\,100}} . \end{aligned}$$

(15)

Production rate (day⁻¹):

$$\hbox{prod}_{{i,\,20}} = \widetilde{r}_{i} \times \min {\left( {eT_{{20,\,A}}, \hbox{eI}} \right)}.$$

(16)

Activity dependent respiration rate (day⁻¹):

$$ \hbox{resa}_{{i,\,20}} = \widetilde{\hbox{pura}}\times{\left( {\hbox{prod}_{{i,\,20}} - \hbox{exud}_{{i,\,20}}} \right)}.$$

(17)

Activity dependent exudation rate (day⁻¹):

$$\hbox{exud}_{{i,\,20}} = \widetilde{\hbox{puea}}\times \hbox{prod}_{{i,\,20}} .$$

(18)

Basal respiration rate (d⁻¹):

$$\hbox{resb}_{{i,\,j}} = \widetilde{\hbox{srs}}_{i} \times eT_{{j,\,H}} .$$

(19)

Dynamic mortality rate (day⁻¹):

$$\frac{{\hbox{d}M_{{i,\,j}}}}{{\hbox{d}t}} = \frac{1}{{\widetilde{\tau}_{i}}} \times {\left( {\widetilde{m}_{i} \times A^{{\widetilde{a}}}_{{i,\,j}} - M_{{i,\,j}}} \right)}.$$

(20)

Mimicking grazers with algal dependent growth and first order mortality.

Sedimentation rate (day⁻¹):

$$\hbox{sed}_{i} = \left\{ \begin{array}{*{20}c} \frac{\widetilde{\hbox{ssed}}_{i}} {\left(\hbox{mix}(t)_{0 - 20} + 0.1 \right)}, & \hbox{if mix}(t)_{0 - 100}\leqslant 0.1\\ {0}, &\hbox{if mix} (t)_{0 - 100}> 0.1 \\ \end{array} \right. .$$

(21)

It is assumed that sedimentation depends on the mixing intensity (turbulence) within the euphotic layer if the deep vertical mixing intensity is small. Otherwise sedimentation plays no role, as mix(t)_0–100 > 0.1 implies high values of mix(t)_0–20. During the winter and spring, 50% of the values of mix(t)_0–20 fell into the range of 0.05 and 0.43, resulting in a sedimentation rate between 13 and 4% if mix(t)_0–100 ≤ 0.1. This is consistent with the sedimentation rates reported by Güde and Gries (1998) and Tilzer (1984) (maximum values 10 and 15%, respectively).

Temperature regulation factor:

$$eT_{{j,\,k}} = \widetilde{Q}_{{10,\,k}} \frac{{{\left( {T_{j} {\left( t \right) - 10}} \right)}}}{{10}}.$$

(22)

Vertical algal gradient (modeled):

$$\hbox{vag}_{{{\text{mod}}}} = A_{{{\text{tot}},\,20}} :A_{{{\text{tot}},\,100}} .$$

(23)