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Basin morphometry can strongly affect lake-internal processes relevant for productivity, such as turbulent mixing, photosynthetic energy acquisition, sedimentation, and nutrient recycling. Yet, in both empirical and theoretical studies of whole-lake primary production, lake morphometry is often simplified to a single 1-dimensional measure – lake mean depth. Using the conceptual, process-based model 'Lake2D', we addressed the question: To what extent can pelagic and benthic producer dynamics, integrated over a lake basin, be captured by approaches that use mean depth as the only morphometrical variable? We created two models of algal biomass dynamics in a radially symmetric, cone-shaped lake – one preserving the lake’s vertical and radial dimensions, and one preserving only the lake’s mean depth – and compared model predictions of algal biomass dynamics across a wide range of lake sizes, mixing conditions, water transparency, and nutrient content. Our analyses reveal that model predictions differ substantially but predictably in much of the investigated parameter space, and identifies the light environment set by lake depth, water clarity and pelagic nutrients, but also lake area, as main drivers of the differences. Most commonly, the model based on mean depth underestimates benthic algal biomass and overestimates pelagic algal biomass, the net effect on total biomass being a 5-50\% underestimate in shallow lakes and a 5-20\% overestimate in many deeper lakes. Since gross primary production (GPP) in our model scales with algal biomass, we believe that global estimates of lake GPP should be corrected for the systematic errors inflicted by the prevailing 1-dimensional approaches.

Size, depth, and basin shape are important factors controlling the physics, chemistry, and ultimately, the productivity of lakes. To our knowledge, a comprehensive theoretical investigation of the physical determinants of lake primary production from a conceptual, process-based perspective has not been performed. To address this knowledge gap, we developed and analyzed ‘Lake2D’, a process-based, reaction-advection-diffusion model that adopts a 2-dimensional modeling approach by reducing lake bathymetry to its hypsographic depth distribution under the simplifying assumption of radial symmetry of the lake basin. In simpler terms, the model assumes that the lake basin is perfectly circular and uses a cross-section to represent its depth and shape. We used Lake2D to explore and analyze the dynamics of pelagic and benthic algae on a whole-lake scale in response to six environmental drivers (lake area and depth, horizontal and vertical turbulent mixing, water transparency, and nutrient status), which we varied over ranges that are representative of the vast majority of the world’s lakes. Numerical analyses reveal three distinct patterns across environmental parameter space. (1) Benthic algae dominate total biomass in shallow, clear lakes with low nutrient content. In these lakes, low horizontal and vertical mixing is beneficial to benthic but detrimental to pelagic algae, which experience high sinking losses, thus liberating nutrients and minimizing shading of benthic algae. (2) Increasing mean lake depth, abiotic turbidity and/or nutrient content strongly benefits pelagic algae, which increasingly shade out benthic algae and dominate total biomass. In these lakes, increased mixing affects both algal types positively due to increased nutrient transport to shallow, well-lit areas. (3) Finally, at high lake mean depth and/or abiotic turbidity, a large fraction of the lake volume is aphotic. In such lakes, high horizontal and vertical mixing is detrimental to pelagic algae but beneficial to benthic algae, because pelagic algae are mixed to aphotic depths, liberating nutrients and minimizing shading. Moving from shallow, clear lakes via deeper and/or nutrient-rich lakes to very deep and/or turbid lakes, benthic and pelagic algae therefore show opposite gradual biomass shifts in response to vertical and horizontal mixing. Specifically, benthic biomass is highest at low and lowest at high overall mixing in shallow, nutrient-poor lakes, but shows the opposite trend in all other lakes. Conversely, pelagic biomass is highest at low and lowest at high overall mixing in very deep and/or turbid lakes, but shows the opposite trend in all other lakes.

This study investigates the influence of mixed layer depth and lake size on the dynamics of pelagic and benthic algae in stratified lakes using a two-dimensional, spatially explicit modeling approach. To this end, we modified the process-based, two-dimensional model 'Lake2D' to account for stratification in lakes by simulating a shallow layer with fast turbulent mixing, and a deep layer with slow turbulent mixing, separated by a sharp boundary. Using this modified version of Lake2D we comprehensively explored pelagic and benthic algal dynamics across a wide range of ecological conditions by varying lake mean depth, total nutrient content, lake size, and mixing depth in a full-factorial manner. Our results reveal distinct regimes of whole-lake algal dynamics: In shallow, nutrient-poor lakes, pelagic algae are nutrient-limited and sparse, while benthic algae thrive and constitute the majority of the total biomass, with no notable influence of mixed layer depth on algal dynamics. As lakes become deeper or more nutrient-rich, pelagic biomass increases and can become the dominant constituent of total biomass. For deep lakes, the model shows a characteristic L-shaped pattern in algal biomass for varying lake size and mixing depth. Pelagic algae exhibit low biomass in small lakes with a deep mixed layer, and high biomass otherwise. Benthic algae show the opposite pattern, exhibiting high biomass in small, deep lakes with a deep mixed layer, and significantly lower biomass otherwise. The study also uncovers a novel phenomenon, a benthic deep chlorophyll maximum, where the benthic algal biomass peaks at an intermediate depth along the lake bottom. This phenomenon arises in lakes of moderate depth and nutrient content, where a shallow mixed layer enables opposing vertical gradients of light and nutrients. These findings highlight the role of mixed layer depth and horizontal transport in structuring the spatial distribution and overall composition of algal biomass in lakes, underscoring the importance of vertical mixing and lake size for understanding lake primary production.