title: Enhancement of the Hooghoudt Drain-Spacing Equation

authors: Shokri, Ali

subjects: Science & Technology

abstract: The Hooghoudt equation is widely used as a simple means of specifying drain spacing when designing networks of parallel drains in drainage systems, based on estimating the maximum water table height between two drains. It is shown via comparison with a numerical model that the Hooghoudt equation can overestimate water table height and therefore yield drain spacings that may be too wide. This is because the Hooghoudt drain-spacing equation in fact has a concealed dependency on Van Genuchten soil-water retention curve parameters, which can bias the water table estimates unless adjustments are made explicitly. A modification of the Hooghoudt equation is presented that incorporates two new dimensionless coefficients to make allowance for this dependency. The modified expression yields improved accuracy as measured against the numerical reference model.

text: Enhancement of the Hooghoudt Drain-Spacing Equation The Hooghoudt equation is widely used as a simple means of specifying drain spacing when designing networks of parallel drains in drainage systems, based on estimating the maximum water table height between two drains. It is shown via comparison with a numerical model that the Hooghoudt equation can overestimate water table height and therefore yield drain spacings that may be too wide. This is because the Hooghoudt drain-spacing equation in fact has a concealed dependency on Van Genuchten soil-water retention curve parameters, which can bias the water table estimates unless adjustments are made explicitly. A modification of the Hooghoudt equation is presented that incorporates two new dimensionless coefficients to make allowance for this dependency. The modified expression yields improved accuracy as measured against the numerical reference model.

year: 2015-06-01

title: Scaling of anisotropy in hydromagnetic turbulence

authors: Matthaeus, William H.

subjects: turbulence

abstract: We present evidence that anisotropy of low frequency plasma turbulence scales linearly with the ratio of fluctuating to total magnetic field strength for a useful range of parameters, for incompressible, weakly compressible, and driven magnetohydrodynamic turbulence.

text: Scaling of anisotropy in hydromagnetic turbulence We present evidence that anisotropy of low frequency plasma turbulence scales linearly with the ratio of fluctuating to total magnetic field strength for a useful range of parameters, for incompressible, weakly compressible, and driven magnetohydrodynamic turbulence.

year: 1998

title: Phytoplankton nutrient limitation in Lake Rotorua

authors: Tempero, Grant Wayne

abstract: Lake Rotorua is one of 12 lakes jointly managed by the Rotorua Lakes Council, Te Arawa Lakes Trust and the Bay of Plenty Regional Council under the Rotorua Te Arawa Lakes Programme. The lake is currently classified as eutrophic and a Trophic Lake Index (TLI) value of 4.2 has been set as an integrated target for lake water quality. A number of catchment and lake management strategies have been implemented to achieve the targeted TLI including land use changes, wetland enhancement, lake weed harvesting, sediment detainment bunds, sewage reticulation and alum dosing. Alum (aluminium sulphate) is commonly applied to freshwater and wastewater systems to remove phosphorus, reducing its availability for phytoplankton growth. The initiation of alum dosing to the Utuhina Stream in 2006 and the Puarenga Stream in 2010 was associated with a significant decline in water column dissolved reactive phosphorus (DRP) and improvements in water quality of Lake Rotorua. 
The use of alum to control external and internal phosphorus loading has been identified as key component in the restoration of Lake Rotorua and recently observed improvements in water quality suggest that the lake could be transitioning to a more phosphorus limited state. Determination of phytoplankton nutrient limitation in Lake Rotorua was identified as a priority through the 2017 Plan Change 10 Science Review. An initial seasonal nutrient limitation study was carried out in 2019 with nutrient limitation assays conducted at 3-monthly intervals over the course of the year. Nitrogen limitation was indicated for the March assay and nutrient co-limitation for the December period, but results for the winter and spring periods were inconclusive. There has also been increasing recognition that nutrient availability in limnetic systems may vary in response to seasonal changes in external and external loading and even to isolated storm events. 
The University of Waikato was contracted to investigate potential changes in nutrient limitation within Lake Rotorua at sub-monthly time-scales, and to determine if alum dose rates could be optimised to take advantage of periods of phosphorus limitation. Phytoplankton nutrient limitation growth assays were conducted on a fortnightly basis from mid-October 2020 to May 2021. In addition to determination of lake surface nutrient and chlorophyll a concentrations, triplicate 1 L phytoplankton samples were spiked with either phosphorus (0.1 mg-P L⁻¹), nitrogen (1 mg-N L⁻¹) or phosphorus (0.1 mg-P L⁻¹) and nitrogen (1 mg-N L⁻¹) and incubated for 5-days under a single light intensity of 100 μmol m⁻²s⁻¹ PAR at lake surface temperature and photoperiod. Phytoplankton growth responses were measured as comparative chlorophyll a, comparative biomass and net biomass growth. Summarised results from the 16 assays along with the predicted nutrient state from the stoichiometric mass ratio of TN:TP are presented in the table below. 
Under the test conditions nitrogen limitation was indicated for most of the summer months (December–March) and nutrient co-limitation during the spring and late autumn. Only short (~2 weeks) periods of P-limitation were observed, one of which was associated with an intensive storm event at the end of March. These seasonal fluctuations in nitrogen and phosphorus supply are similar to those observed in other temperate limnetic systems. In the spring, external nitrogen and phosphorus loading is high, then decline in the summer as rainfall and associated inflows wane. During the summer, internal loading becomes more important in polymictic lakes due to repeated internal nutrient cycling from stratification and mixing events. This results in phosphorus limitation in the spring, transitioning to nitrogen limitation or colimitation (primarily nitrogen) in the summer, and then returning to phosphorus/colimitation during the winter due to increased nitrogen-loading from the catchment from increased catchment discharge. 
Due to the modest periods of phosphorus limitation indicated by the assays, there appears to be little potential for optimisation of alum dose rates in order capitalise on natural periods of phosphorus limitation. Further, changes in phytoplankton community composition and abundance appear to be more strongly driven by physical environmental factors such as temperature, light and wind speed, than nutrient availability. Although alum dosing is effective in removing DRP from the Utuhina and Puarenga inflows, its assumed effectiveness in reducing internal phosphorus loading in Lake Rotorua requires further evaluation.

text: Phytoplankton nutrient limitation in Lake Rotorua Lake Rotorua is one of 12 lakes jointly managed by the Rotorua Lakes Council, Te Arawa Lakes Trust and the Bay of Plenty Regional Council under the Rotorua Te Arawa Lakes Programme. The lake is currently classified as eutrophic and a Trophic Lake Index (TLI) value of 4.2 has been set as an integrated target for lake water quality. A number of catchment and lake management strategies have been implemented to achieve the targeted TLI including land use changes, wetland enhancement, lake weed harvesting, sediment detainment bunds, sewage reticulation and alum dosing. Alum (aluminium sulphate) is commonly applied to freshwater and wastewater systems to remove phosphorus, reducing its availability for phytoplankton growth. The initiation of alum dosing to the Utuhina Stream in 2006 and the Puarenga Stream in 2010 was associated with a significant decline in water column dissolved reactive phosphorus (DRP) and improvements in water quality of Lake Rotorua. 
The use of alum to control external and internal phosphorus loading has been identified as key component in the restoration of Lake Rotorua and recently observed improvements in water quality suggest that the lake could be transitioning to a more phosphorus limited state. Determination of phytoplankton nutrient limitation in Lake Rotorua was identified as a priority through the 2017 Plan Change 10 Science Review. An initial seasonal nutrient limitation study was carried out in 2019 with nutrient limitation assays conducted at 3-monthly intervals over the course of the year. Nitrogen limitation was indicated for the March assay and nutrient co-limitation for the December period, but results for the winter and spring periods were inconclusive. There has also been increasing recognition that nutrient availability in limnetic systems may vary in response to seasonal changes in external and external loading and even to isolated storm events. 
The University of Waikato was contracted to investigate potential changes in nutrient limitation within Lake Rotorua at sub-monthly time-scales, and to determine if alum dose rates could be optimised to take advantage of periods of phosphorus limitation. Phytoplankton nutrient limitation growth assays were conducted on a fortnightly basis from mid-October 2020 to May 2021. In addition to determination of lake surface nutrient and chlorophyll a concentrations, triplicate 1 L phytoplankton samples were spiked with either phosphorus (0.1 mg-P L⁻¹), nitrogen (1 mg-N L⁻¹) or phosphorus (0.1 mg-P L⁻¹) and nitrogen (1 mg-N L⁻¹) and incubated for 5-days under a single light intensity of 100 μmol m⁻²s⁻¹ PAR at lake surface temperature and photoperiod. Phytoplankton growth responses were measured as comparative chlorophyll a, comparative biomass and net biomass growth. Summarised results from the 16 assays along with the predicted nutrient state from the stoichiometric mass ratio of TN:TP are presented in the table below. 
Under the test conditions nitrogen limitation was indicated for most of the summer months (December–March) and nutrient co-limitation during the spring and late autumn. Only short (~2 weeks) periods of P-limitation were observed, one of which was associated with an intensive storm event at the end of March. These seasonal fluctuations in nitrogen and phosphorus supply are similar to those observed in other temperate limnetic systems. In the spring, external nitrogen and phosphorus loading is high, then decline in the summer as rainfall and associated inflows wane. During the summer, internal loading becomes more important in polymictic lakes due to repeated internal nutrient cycling from stratification and mixing events. This results in phosphorus limitation in the spring, transitioning to nitrogen limitation or colimitation (primarily nitrogen) in the summer, and then returning to phosphorus/colimitation during the winter due to increased nitrogen-loading from the catchment from increased catchment discharge. 
Due to the modest periods of phosphorus limitation indicated by the assays, there appears to be little potential for optimisation of alum dose rates in order capitalise on natural periods of phosphorus limitation. Further, changes in phytoplankton community composition and abundance appear to be more strongly driven by physical environmental factors such as temperature, light and wind speed, than nutrient availability. Although alum dosing is effective in removing DRP from the Utuhina and Puarenga inflows, its assumed effectiveness in reducing internal phosphorus loading in Lake Rotorua requires further evaluation.

year: 2022