Primary production (PP) is fundamental to ocean biogeochemistry, but challengingly variable. Satellite models are unique tools for investigating PP, but are difficult to compare and validate because of the scale separation between in situ and remote measurements, which also are rarely coincident. Here, I argue that satellite estimates should be log-skew-normally distributed, because of this scale separation and because PP measurements are log-normally distributed. Whether they conform to this distributional shape is therefore a powerful variability-based constraint on such models. Satellite models that do follow a log-skew-normal may then also be concisely characterized by three parameters (log-mean, log-standard deviation, and log-skewness). I show that the output from a recent satellite model (CAFE) over 2019 agrees excellently with the log-skew-normal, globally and for most spatiotemporal subsets investigated here. The exception is the Northern Hemisphere winter, which may suggest future model improvements. PP by plankton is essential to ocean ecology and biogeochemistry, so satellite models that estimate PP from remote sensing data are indispensable in numerous scientific applications. However, because the corresponding in situ data are rarely measured when a satellite passes overhead, are measured on a much smaller spatial scale, and are highly variable, it is very difficult to compare different satellite models, evaluate how accurate they are, or to constrain their parameters. Here, a different approach to evaluating, comparing, and constraining these models is described, which accounts for or avoids all of these issues with the standard approach. This approach finds excellent agreement overall with a recent satellite model, while also identifying room for improvement.

中文翻译：

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基于变量的海洋初级生产模型约束

初级生产 (PP) 是海洋生物地球化学的基础，但具有挑战性。卫星模型是研究 PP 的独特工具，但由于原位测量和远程测量之间的尺度分离而难以比较和验证，这也很少重合。在这里，我认为卫星估计应该是对数偏正态分布的，因为这种尺度分离并且因为 PP 测量是对数正态分布的。因此，它们是否符合这种分布形状是对此类模型的强大的基于可变性的约束。遵循对数偏斜正态的卫星模型也可以用三个参数（对数均值、对数标准差和对数偏斜度）简明地表征。我表明，2019 年最近的卫星模型 (CAFE) 的输出与对数偏斜正态、全局和此处调查的大多数时空子集非常吻合。北半球冬季是个例外，这可能表明未来的模型改进。浮游生物的 PP 对海洋生态学和生物地球化学至关重要，因此从遥感数据估计 PP 的卫星模型在众多科学应用中必不可少。然而，由于相应的原位数据很少在卫星经过头顶时测量，测量的空间尺度要小得多，并且变化很大，因此很难比较不同的卫星模型，评估它们的准确性，或限制他们的参数。这里描述了一种评估、比较和约束这些模型的不同方法，这说明或避免了标准方法的所有这些问题。这种方法总体上与最近的卫星模型非常吻合，同时也确定了改进的空间。