North Temperate Lakes LTER: Primary Production - Trout Lake Area 1986 - 2007

Crystal, Sparkling and Trout lakes are sampled approximately fortnightly throughout the ice free period and water is returned to the lab for 3 hour in vivo incubations at ambient temperature. On an annual rotation, one of the lakes is sampled to the bottom of the photic zone (ie. 0.5% of surface light) while only the epilimnion of the other 2 lakes is sampled. All samples are integrated by thermal layer and 14C uptake is deternimed at 10 light levels using a metal-halide lamp. All samples are acidified and bubbled before liquid scintillation counting and uptake is dark bottle corrected. DIC and chlorophyll are also measured. Each P-I (photosynthetic uptake vs irradiance ) set is further reduced to 3 parameters (alpha, beta, and Pmax) based on the work of Platt 1980. In addition, thermal information and lake light transparency profiles (collected approximately fortnightly on these three LTER lakes) along with daily incident PAR at 30 minute intervals (measured at Noble F. Lee Municipal Airport, Woodruff, WI) provide input to a mechanistic model of lake primary productivity. Primary productivity for a lake is calculated from productivity parameters derived from the laboratory uptake experiments, coupled with the lakes' thermal and light regimes. 1. PI parameters: Productivity (P), as a function of irradiance (I), is described by a hyperbolic tangent curve with three parameters (Platt 1980). The three parameters describe the initial slope of the curve, the I at which maximum P occurs, and the decay rate of P, following maximum P. All three parameters are fit simultaneously to laboratory observations, using minimization of a least squares objective function (Matlab v. 6, Mathworks, Inc.). The parameters allow for the calculation of P, as a function of I, for a given thermal stratum of a given lake on a given day. 2. LEC: Light extinction coefficients (LEC) for each lake are calculated as the slope of the best fit line through the natural logs of observations of light at depth. The light at depth data were obtained from the LTER core data set (light profiles are sampled approximately fortnightly throughout the ice-free period on LTER lakes 3. Thermal layers: The thermal layers for the lake are obtained from the LTER core data set (temperature profiles are sampled approximately fortnightly throughout the ice-free period on LTER lakes). 4. Lake productivity: Productivity for a given lake on a given day is calculated from the derived data in steps 1-3. Light versus depth is discretized for 0.5 m depth intervals to match the lake hypsometric data. Light for each 0.5 m disc is calculated for every 30 minutes from observed irradiance and LEC, using numerical integration through the depth of the disc. Productivity for every 30 minutes is calculated for a disc, using the light data applied to the parameters and equation described in #1. Productivity for every 30 minutes in the thermal layer is the sum of the disc productivities for that layer. Productivity for every 30 minutes in the lake is the sum of the productivity of the thermal layers. Productivity for the day is the sum of all 30 minute productivities for a given calendar day. Hypsometrically weighted productivity is calculated by weighting each of the discretized productivities by the hypsometric weight of that disc. 5. Interpolation: Rarely do all observations required to calculate productivity occur on the same day. PI parameters, LECs, and thermal layers were linearly interpolated to daily values. For any given day's productivity calculation, all data, other than observed irradiance, were considered constant Sampling Frequency: water samples are taken fortnightly; PAR measured every 30 minutes Number of sites: 3

在整个无冰期内，对水晶湖（Crystal Lake）、斯帕克林湖（Sparkling Lake）与特劳特湖（Trout Lake）约每两周开展一次采样，将采集的水样带回实验室，在环境温度下进行3小时的活体培养实验。
采用年度轮换采样方案：每年对其中一座湖泊采集至真光层（photic zone，即表面光照强度的0.5%处）的底部，另外两座湖泊仅采集湖上层（epilimnion）的水样。
所有样品均按热分层进行整合，使用金属卤化物灯设置10个光照梯度，测定14C摄取量。所有样品在进行液体闪烁计数前均经过酸化与鼓气处理，且摄取量已通过暗瓶校正。同时还会测定溶解无机碳（Dissolved Inorganic Carbon, DIC）与叶绿素含量。基于Platt（1980）的研究方法，每一组P-I（光合摄取量-光照强度）曲线数据均可简化为3个参数：α、β与Pmax。
此外，热分层信息、湖泊光照透明度剖面（在这三座长期生态研究（Long-Term Ecological Research, LTER）湖泊上约每两周采集一次），以及以30分钟为间隔的每日入射光合有效辐射（Photosynthetically Active Radiation, PAR，在威斯康星州伍德拉夫市的诺布尔·F·李市政机场测得），均可作为湖泊初级生产力机理模型的输入数据。湖泊的初级生产力可通过实验室摄取实验得到的生产力参数，结合湖泊的热分层与光照状况计算得到。
1. P-I参数：光合速率（P）作为光照强度（I）的函数，可通过含3个参数的双曲正切曲线进行描述（Platt, 1980）。这三个参数分别对应曲线的初始斜率、达到最大光合速率时的光照强度，以及最大光合速率出现后光合速率的衰减速率。采用最小二乘目标函数最小化方法（Matlab 6版，马思温公司Mathworks, Inc.），将三个参数同时拟合至实验室观测数据。通过这些参数，可计算特定日期内特定湖泊某一热分层的光照强度对应的光合速率。
2. 光消光系数（Light Extinction Coefficients, LEC）：各湖泊的光消光系数可通过深度光照观测值的自然对数拟合最优直线的斜率计算得到。深度光照数据取自LTER核心数据集（LTER湖泊在整个无冰期内约每两周采集一次光照剖面数据）。
3. 热分层信息：湖泊的热分层数据取自LTER核心数据集（LTER湖泊在整个无冰期内约每两周采集一次温度剖面数据）。
4. 湖泊生产力：特定日期内特定湖泊的生产力可通过步骤1至3得到的衍生数据计算得到。将水深按0.5米间隔进行离散化处理，以匹配湖泊的水深面积分布数据。利用数值积分法，基于观测到的光照强度与光消光系数，每30分钟计算一次每个0.5米水深区间的光照量。将步骤1中的参数与公式应用于该光照数据，可计算出每个0.5米水深区间的30分钟光合生产力。热分层的30分钟光合生产力为该分层内所有水深区间生产力的总和。湖泊整体的30分钟光合生产力为所有热分层生产力的总和。单日光合生产力为该日历日内所有30分钟时段生产力的总和。水深面积加权光合生产力通过将每个离散化水深区间的生产力乘以该区间的面积权重计算得到。
5. 插值处理：计算生产力所需的全部观测数据极少在同一天完成。因此，我们将P-I参数、光消光系数与热分层数据通过线性插值转换为日度值。在任意单日的生产力计算中，除观测到的光照强度外，其余数据均视为恒定值。
采样频率：水样每两周采集一次；光合有效辐射以每30分钟为间隔进行监测
采样点位数量：3个